Adding upstream version 1.64.0+dfsg1.upstream/1.64.0+dfsg1

Signed-off-by: Daniel Baumann <daniel.baumann@progress-linux.org>

41 files changed, 17677 insertions, 0 deletions

diff --git a/library/core/src/num/bignum.rs b/library/core/src/num/bignum.rs
new file mode 100644
index 000000000..de85fdd6e
--- /dev/null
+++ b/library/core/src/num/bignum.rs
@@ -0,0 +1,434 @@
+//! Custom arbitrary-precision number (bignum) implementation.
+//!
+//! This is designed to avoid the heap allocation at expense of stack memory.
+//! The most used bignum type, `Big32x40`, is limited by 32 × 40 = 1,280 bits
+//! and will take at most 160 bytes of stack memory. This is more than enough
+//! for round-tripping all possible finite `f64` values.
+//!
+//! In principle it is possible to have multiple bignum types for different
+//! inputs, but we don't do so to avoid the code bloat. Each bignum is still
+//! tracked for the actual usages, so it normally doesn't matter.
+
+// This module is only for dec2flt and flt2dec, and only public because of coretests.
+// It is not intended to ever be stabilized.
+#![doc(hidden)]
+#![unstable(
+    feature = "core_private_bignum",
+    reason = "internal routines only exposed for testing",
+    issue = "none"
+)]
+#![macro_use]
+
+/// Arithmetic operations required by bignums.
+pub trait FullOps: Sized {
+    /// Returns `(carry', v')` such that `carry' * 2^W + v' = self * other + other2 + carry`,
+    /// where `W` is the number of bits in `Self`.
+    fn full_mul_add(self, other: Self, other2: Self, carry: Self) -> (Self /* carry */, Self);
+
+    /// Returns `(quo, rem)` such that `borrow * 2^W + self = quo * other + rem`
+    /// and `0 <= rem < other`, where `W` is the number of bits in `Self`.
+    fn full_div_rem(self, other: Self, borrow: Self)
+    -> (Self /* quotient */, Self /* remainder */);
+}
+
+macro_rules! impl_full_ops {
+    ($($ty:ty: add($addfn:path), mul/div($bigty:ident);)*) => (
+        $(
+            impl FullOps for $ty {
+                fn full_mul_add(self, other: $ty, other2: $ty, carry: $ty) -> ($ty, $ty) {
+                    // This cannot overflow;
+                    // the output is between `0` and `2^nbits * (2^nbits - 1)`.
+                    let v = (self as $bigty) * (other as $bigty) + (other2 as $bigty) +
+                            (carry as $bigty);
+                    ((v >> <$ty>::BITS) as $ty, v as $ty)
+                }
+
+                fn full_div_rem(self, other: $ty, borrow: $ty) -> ($ty, $ty) {
+                    debug_assert!(borrow < other);
+                    // This cannot overflow; the output is between `0` and `other * (2^nbits - 1)`.
+                    let lhs = ((borrow as $bigty) << <$ty>::BITS) | (self as $bigty);
+                    let rhs = other as $bigty;
+                    ((lhs / rhs) as $ty, (lhs % rhs) as $ty)
+                }
+            }
+        )*
+    )
+}
+
+impl_full_ops! {
+    u8:  add(intrinsics::u8_add_with_overflow),  mul/div(u16);
+    u16: add(intrinsics::u16_add_with_overflow), mul/div(u32);
+    u32: add(intrinsics::u32_add_with_overflow), mul/div(u64);
+    // See RFC #521 for enabling this.
+    // u64: add(intrinsics::u64_add_with_overflow), mul/div(u128);
+}
+
+/// Table of powers of 5 representable in digits. Specifically, the largest {u8, u16, u32} value
+/// that's a power of five, plus the corresponding exponent. Used in `mul_pow5`.
+const SMALL_POW5: [(u64, usize); 3] = [(125, 3), (15625, 6), (1_220_703_125, 13)];
+
+macro_rules! define_bignum {
+    ($name:ident: type=$ty:ty, n=$n:expr) => {
+        /// Stack-allocated arbitrary-precision (up to certain limit) integer.
+        ///
+        /// This is backed by a fixed-size array of given type ("digit").
+        /// While the array is not very large (normally some hundred bytes),
+        /// copying it recklessly may result in the performance hit.
+        /// Thus this is intentionally not `Copy`.
+        ///
+        /// All operations available to bignums panic in the case of overflows.
+        /// The caller is responsible to use large enough bignum types.
+        pub struct $name {
+            /// One plus the offset to the maximum "digit" in use.
+            /// This does not decrease, so be aware of the computation order.
+            /// `base[size..]` should be zero.
+            size: usize,
+            /// Digits. `[a, b, c, ...]` represents `a + b*2^W + c*2^(2W) + ...`
+            /// where `W` is the number of bits in the digit type.
+            base: [$ty; $n],
+        }
+
+        impl $name {
+            /// Makes a bignum from one digit.
+            pub fn from_small(v: $ty) -> $name {
+                let mut base = [0; $n];
+                base[0] = v;
+                $name { size: 1, base }
+            }
+
+            /// Makes a bignum from `u64` value.
+            pub fn from_u64(mut v: u64) -> $name {
+                let mut base = [0; $n];
+                let mut sz = 0;
+                while v > 0 {
+                    base[sz] = v as $ty;
+                    v >>= <$ty>::BITS;
+                    sz += 1;
+                }
+                $name { size: sz, base }
+            }
+
+            /// Returns the internal digits as a slice `[a, b, c, ...]` such that the numeric
+            /// value is `a + b * 2^W + c * 2^(2W) + ...` where `W` is the number of bits in
+            /// the digit type.
+            pub fn digits(&self) -> &[$ty] {
+                &self.base[..self.size]
+            }
+
+            /// Returns the `i`-th bit where bit 0 is the least significant one.
+            /// In other words, the bit with weight `2^i`.
+            pub fn get_bit(&self, i: usize) -> u8 {
+                let digitbits = <$ty>::BITS as usize;
+                let d = i / digitbits;
+                let b = i % digitbits;
+                ((self.base[d] >> b) & 1) as u8
+            }
+
+            /// Returns `true` if the bignum is zero.
+            pub fn is_zero(&self) -> bool {
+                self.digits().iter().all(|&v| v == 0)
+            }
+
+            /// Returns the number of bits necessary to represent this value. Note that zero
+            /// is considered to need 0 bits.
+            pub fn bit_length(&self) -> usize {
+                let digitbits = <$ty>::BITS as usize;
+                let digits = self.digits();
+                // Find the most significant non-zero digit.
+                let msd = digits.iter().rposition(|&x| x != 0);
+                match msd {
+                    Some(msd) => msd * digitbits + digits[msd].log2() as usize + 1,
+                    // There are no non-zero digits, i.e., the number is zero.
+                    _ => 0,
+                }
+            }
+
+            /// Adds `other` to itself and returns its own mutable reference.
+            pub fn add<'a>(&'a mut self, other: &$name) -> &'a mut $name {
+                use crate::cmp;
+                use crate::iter;
+
+                let mut sz = cmp::max(self.size, other.size);
+                let mut carry = false;
+                for (a, b) in iter::zip(&mut self.base[..sz], &other.base[..sz]) {
+                    let (v, c) = (*a).carrying_add(*b, carry);
+                    *a = v;
+                    carry = c;
+                }
+                if carry {
+                    self.base[sz] = 1;
+                    sz += 1;
+                }
+                self.size = sz;
+                self
+            }
+
+            pub fn add_small(&mut self, other: $ty) -> &mut $name {
+                let (v, mut carry) = self.base[0].carrying_add(other, false);
+                self.base[0] = v;
+                let mut i = 1;
+                while carry {
+                    let (v, c) = self.base[i].carrying_add(0, carry);
+                    self.base[i] = v;
+                    carry = c;
+                    i += 1;
+                }
+                if i > self.size {
+                    self.size = i;
+                }
+                self
+            }
+
+            /// Subtracts `other` from itself and returns its own mutable reference.
+            pub fn sub<'a>(&'a mut self, other: &$name) -> &'a mut $name {
+                use crate::cmp;
+                use crate::iter;
+
+                let sz = cmp::max(self.size, other.size);
+                let mut noborrow = true;
+                for (a, b) in iter::zip(&mut self.base[..sz], &other.base[..sz]) {
+                    let (v, c) = (*a).carrying_add(!*b, noborrow);
+                    *a = v;
+                    noborrow = c;
+                }
+                assert!(noborrow);
+                self.size = sz;
+                self
+            }
+
+            /// Multiplies itself by a digit-sized `other` and returns its own
+            /// mutable reference.
+            pub fn mul_small(&mut self, other: $ty) -> &mut $name {
+                let mut sz = self.size;
+                let mut carry = 0;
+                for a in &mut self.base[..sz] {
+                    let (v, c) = (*a).carrying_mul(other, carry);
+                    *a = v;
+                    carry = c;
+                }
+                if carry > 0 {
+                    self.base[sz] = carry;
+                    sz += 1;
+                }
+                self.size = sz;
+                self
+            }
+
+            /// Multiplies itself by `2^bits` and returns its own mutable reference.
+            pub fn mul_pow2(&mut self, bits: usize) -> &mut $name {
+                let digitbits = <$ty>::BITS as usize;
+                let digits = bits / digitbits;
+                let bits = bits % digitbits;
+
+                assert!(digits < $n);
+                debug_assert!(self.base[$n - digits..].iter().all(|&v| v == 0));
+                debug_assert!(bits == 0 || (self.base[$n - digits - 1] >> (digitbits - bits)) == 0);
+
+                // shift by `digits * digitbits` bits
+                for i in (0..self.size).rev() {
+                    self.base[i + digits] = self.base[i];
+                }
+                for i in 0..digits {
+                    self.base[i] = 0;
+                }
+
+                // shift by `bits` bits
+                let mut sz = self.size + digits;
+                if bits > 0 {
+                    let last = sz;
+                    let overflow = self.base[last - 1] >> (digitbits - bits);
+                    if overflow > 0 {
+                        self.base[last] = overflow;
+                        sz += 1;
+                    }
+                    for i in (digits + 1..last).rev() {
+                        self.base[i] =
+                            (self.base[i] << bits) | (self.base[i - 1] >> (digitbits - bits));
+                    }
+                    self.base[digits] <<= bits;
+                    // self.base[..digits] is zero, no need to shift
+                }
+
+                self.size = sz;
+                self
+            }
+
+            /// Multiplies itself by `5^e` and returns its own mutable reference.
+            pub fn mul_pow5(&mut self, mut e: usize) -> &mut $name {
+                use crate::mem;
+                use crate::num::bignum::SMALL_POW5;
+
+                // There are exactly n trailing zeros on 2^n, and the only relevant digit sizes
+                // are consecutive powers of two, so this is well suited index for the table.
+                let table_index = mem::size_of::<$ty>().trailing_zeros() as usize;
+                let (small_power, small_e) = SMALL_POW5[table_index];
+                let small_power = small_power as $ty;
+
+                // Multiply with the largest single-digit power as long as possible ...
+                while e >= small_e {
+                    self.mul_small(small_power);
+                    e -= small_e;
+                }
+
+                // ... then finish off the remainder.
+                let mut rest_power = 1;
+                for _ in 0..e {
+                    rest_power *= 5;
+                }
+                self.mul_small(rest_power);
+
+                self
+            }
+
+            /// Multiplies itself by a number described by `other[0] + other[1] * 2^W +
+            /// other[2] * 2^(2W) + ...` (where `W` is the number of bits in the digit type)
+            /// and returns its own mutable reference.
+            pub fn mul_digits<'a>(&'a mut self, other: &[$ty]) -> &'a mut $name {
+                // the internal routine. works best when aa.len() <= bb.len().
+                fn mul_inner(ret: &mut [$ty; $n], aa: &[$ty], bb: &[$ty]) -> usize {
+                    use crate::num::bignum::FullOps;
+
+                    let mut retsz = 0;
+                    for (i, &a) in aa.iter().enumerate() {
+                        if a == 0 {
+                            continue;
+                        }
+                        let mut sz = bb.len();
+                        let mut carry = 0;
+                        for (j, &b) in bb.iter().enumerate() {
+                            let (c, v) = a.full_mul_add(b, ret[i + j], carry);
+                            ret[i + j] = v;
+                            carry = c;
+                        }
+                        if carry > 0 {
+                            ret[i + sz] = carry;
+                            sz += 1;
+                        }
+                        if retsz < i + sz {
+                            retsz = i + sz;
+                        }
+                    }
+                    retsz
+                }
+
+                let mut ret = [0; $n];
+                let retsz = if self.size < other.len() {
+                    mul_inner(&mut ret, &self.digits(), other)
+                } else {
+                    mul_inner(&mut ret, other, &self.digits())
+                };
+                self.base = ret;
+                self.size = retsz;
+                self
+            }
+
+            /// Divides itself by a digit-sized `other` and returns its own
+            /// mutable reference *and* the remainder.
+            pub fn div_rem_small(&mut self, other: $ty) -> (&mut $name, $ty) {
+                use crate::num::bignum::FullOps;
+
+                assert!(other > 0);
+
+                let sz = self.size;
+                let mut borrow = 0;
+                for a in self.base[..sz].iter_mut().rev() {
+                    let (q, r) = (*a).full_div_rem(other, borrow);
+                    *a = q;
+                    borrow = r;
+                }
+                (self, borrow)
+            }
+
+            /// Divide self by another bignum, overwriting `q` with the quotient and `r` with the
+            /// remainder.
+            pub fn div_rem(&self, d: &$name, q: &mut $name, r: &mut $name) {
+                // Stupid slow base-2 long division taken from
+                // https://en.wikipedia.org/wiki/Division_algorithm
+                // FIXME use a greater base ($ty) for the long division.
+                assert!(!d.is_zero());
+                let digitbits = <$ty>::BITS as usize;
+                for digit in &mut q.base[..] {
+                    *digit = 0;
+                }
+                for digit in &mut r.base[..] {
+                    *digit = 0;
+                }
+                r.size = d.size;
+                q.size = 1;
+                let mut q_is_zero = true;
+                let end = self.bit_length();
+                for i in (0..end).rev() {
+                    r.mul_pow2(1);
+                    r.base[0] |= self.get_bit(i) as $ty;
+                    if &*r >= d {
+                        r.sub(d);
+                        // Set bit `i` of q to 1.
+                        let digit_idx = i / digitbits;
+                        let bit_idx = i % digitbits;
+                        if q_is_zero {
+                            q.size = digit_idx + 1;
+                            q_is_zero = false;
+                        }
+                        q.base[digit_idx] |= 1 << bit_idx;
+                    }
+                }
+                debug_assert!(q.base[q.size..].iter().all(|&d| d == 0));
+                debug_assert!(r.base[r.size..].iter().all(|&d| d == 0));
+            }
+        }
+
+        impl crate::cmp::PartialEq for $name {
+            fn eq(&self, other: &$name) -> bool {
+                self.base[..] == other.base[..]
+            }
+        }
+
+        impl crate::cmp::Eq for $name {}
+
+        impl crate::cmp::PartialOrd for $name {
+            fn partial_cmp(&self, other: &$name) -> crate::option::Option<crate::cmp::Ordering> {
+                crate::option::Option::Some(self.cmp(other))
+            }
+        }
+
+        impl crate::cmp::Ord for $name {
+            fn cmp(&self, other: &$name) -> crate::cmp::Ordering {
+                use crate::cmp::max;
+                let sz = max(self.size, other.size);
+                let lhs = self.base[..sz].iter().cloned().rev();
+                let rhs = other.base[..sz].iter().cloned().rev();
+                lhs.cmp(rhs)
+            }
+        }
+
+        impl crate::clone::Clone for $name {
+            fn clone(&self) -> Self {
+                Self { size: self.size, base: self.base }
+            }
+        }
+
+        impl crate::fmt::Debug for $name {
+            fn fmt(&self, f: &mut crate::fmt::Formatter<'_>) -> crate::fmt::Result {
+                let sz = if self.size < 1 { 1 } else { self.size };
+                let digitlen = <$ty>::BITS as usize / 4;
+
+                write!(f, "{:#x}", self.base[sz - 1])?;
+                for &v in self.base[..sz - 1].iter().rev() {
+                    write!(f, "_{:01$x}", v, digitlen)?;
+                }
+                crate::result::Result::Ok(())
+            }
+        }
+    };
+}
+
+/// The digit type for `Big32x40`.
+pub type Digit32 = u32;
+
+define_bignum!(Big32x40: type=Digit32, n=40);
+
+// this one is used for testing only.
+#[doc(hidden)]
+pub mod tests {
+    define_bignum!(Big8x3: type=u8, n=3);
+}
diff --git a/library/core/src/num/dec2flt/common.rs b/library/core/src/num/dec2flt/common.rs
new file mode 100644
index 000000000..17957d7e7
--- /dev/null
+++ b/library/core/src/num/dec2flt/common.rs
@@ -0,0 +1,198 @@
+//! Common utilities, for internal use only.
+
+use crate::ptr;
+
+/// Helper methods to process immutable bytes.
+pub(crate) trait ByteSlice: AsRef<[u8]> {
+    unsafe fn first_unchecked(&self) -> u8 {
+        debug_assert!(!self.is_empty());
+        // SAFETY: safe as long as self is not empty
+        unsafe { *self.as_ref().get_unchecked(0) }
+    }
+
+    /// Get if the slice contains no elements.
+    fn is_empty(&self) -> bool {
+        self.as_ref().is_empty()
+    }
+
+    /// Check if the slice at least `n` length.
+    fn check_len(&self, n: usize) -> bool {
+        n <= self.as_ref().len()
+    }
+
+    /// Check if the first character in the slice is equal to c.
+    fn first_is(&self, c: u8) -> bool {
+        self.as_ref().first() == Some(&c)
+    }
+
+    /// Check if the first character in the slice is equal to c1 or c2.
+    fn first_is2(&self, c1: u8, c2: u8) -> bool {
+        if let Some(&c) = self.as_ref().first() { c == c1 || c == c2 } else { false }
+    }
+
+    /// Bounds-checked test if the first character in the slice is a digit.
+    fn first_isdigit(&self) -> bool {
+        if let Some(&c) = self.as_ref().first() { c.is_ascii_digit() } else { false }
+    }
+
+    /// Check if self starts with u with a case-insensitive comparison.
+    fn starts_with_ignore_case(&self, u: &[u8]) -> bool {
+        debug_assert!(self.as_ref().len() >= u.len());
+        let iter = self.as_ref().iter().zip(u.iter());
+        let d = iter.fold(0, |i, (&x, &y)| i | (x ^ y));
+        d == 0 || d == 32
+    }
+
+    /// Get the remaining slice after the first N elements.
+    fn advance(&self, n: usize) -> &[u8] {
+        &self.as_ref()[n..]
+    }
+
+    /// Get the slice after skipping all leading characters equal c.
+    fn skip_chars(&self, c: u8) -> &[u8] {
+        let mut s = self.as_ref();
+        while s.first_is(c) {
+            s = s.advance(1);
+        }
+        s
+    }
+
+    /// Get the slice after skipping all leading characters equal c1 or c2.
+    fn skip_chars2(&self, c1: u8, c2: u8) -> &[u8] {
+        let mut s = self.as_ref();
+        while s.first_is2(c1, c2) {
+            s = s.advance(1);
+        }
+        s
+    }
+
+    /// Read 8 bytes as a 64-bit integer in little-endian order.
+    unsafe fn read_u64_unchecked(&self) -> u64 {
+        debug_assert!(self.check_len(8));
+        let src = self.as_ref().as_ptr() as *const u64;
+        // SAFETY: safe as long as self is at least 8 bytes
+        u64::from_le(unsafe { ptr::read_unaligned(src) })
+    }
+
+    /// Try to read the next 8 bytes from the slice.
+    fn read_u64(&self) -> Option<u64> {
+        if self.check_len(8) {
+            // SAFETY: self must be at least 8 bytes.
+            Some(unsafe { self.read_u64_unchecked() })
+        } else {
+            None
+        }
+    }
+
+    /// Calculate the offset of slice from another.
+    fn offset_from(&self, other: &Self) -> isize {
+        other.as_ref().len() as isize - self.as_ref().len() as isize
+    }
+}
+
+impl ByteSlice for [u8] {}
+
+/// Helper methods to process mutable bytes.
+pub(crate) trait ByteSliceMut: AsMut<[u8]> {
+    /// Write a 64-bit integer as 8 bytes in little-endian order.
+    unsafe fn write_u64_unchecked(&mut self, value: u64) {
+        debug_assert!(self.as_mut().len() >= 8);
+        let dst = self.as_mut().as_mut_ptr() as *mut u64;
+        // NOTE: we must use `write_unaligned`, since dst is not
+        // guaranteed to be properly aligned. Miri will warn us
+        // if we use `write` instead of `write_unaligned`, as expected.
+        // SAFETY: safe as long as self is at least 8 bytes
+        unsafe {
+            ptr::write_unaligned(dst, u64::to_le(value));
+        }
+    }
+}
+
+impl ByteSliceMut for [u8] {}
+
+/// Bytes wrapper with specialized methods for ASCII characters.
+#[derive(Debug, Clone, Copy, PartialEq, Eq)]
+pub(crate) struct AsciiStr<'a> {
+    slc: &'a [u8],
+}
+
+impl<'a> AsciiStr<'a> {
+    pub fn new(slc: &'a [u8]) -> Self {
+        Self { slc }
+    }
+
+    /// Advance the view by n, advancing it in-place to (n..).
+    pub unsafe fn step_by(&mut self, n: usize) -> &mut Self {
+        // SAFETY: safe as long n is less than the buffer length
+        self.slc = unsafe { self.slc.get_unchecked(n..) };
+        self
+    }
+
+    /// Advance the view by n, advancing it in-place to (1..).
+    pub unsafe fn step(&mut self) -> &mut Self {
+        // SAFETY: safe as long as self is not empty
+        unsafe { self.step_by(1) }
+    }
+
+    /// Iteratively parse and consume digits from bytes.
+    pub fn parse_digits(&mut self, mut func: impl FnMut(u8)) {
+        while let Some(&c) = self.as_ref().first() {
+            let c = c.wrapping_sub(b'0');
+            if c < 10 {
+                func(c);
+                // SAFETY: self cannot be empty
+                unsafe {
+                    self.step();
+                }
+            } else {
+                break;
+            }
+        }
+    }
+}
+
+impl<'a> AsRef<[u8]> for AsciiStr<'a> {
+    #[inline]
+    fn as_ref(&self) -> &[u8] {
+        self.slc
+    }
+}
+
+impl<'a> ByteSlice for AsciiStr<'a> {}
+
+/// Determine if 8 bytes are all decimal digits.
+/// This does not care about the order in which the bytes were loaded.
+pub(crate) fn is_8digits(v: u64) -> bool {
+    let a = v.wrapping_add(0x4646_4646_4646_4646);
+    let b = v.wrapping_sub(0x3030_3030_3030_3030);
+    (a | b) & 0x8080_8080_8080_8080 == 0
+}
+
+/// Iteratively parse and consume digits from bytes.
+pub(crate) fn parse_digits(s: &mut &[u8], mut f: impl FnMut(u8)) {
+    while let Some(&c) = s.get(0) {
+        let c = c.wrapping_sub(b'0');
+        if c < 10 {
+            f(c);
+            *s = s.advance(1);
+        } else {
+            break;
+        }
+    }
+}
+
+/// A custom 64-bit floating point type, representing `f * 2^e`.
+/// e is biased, so it be directly shifted into the exponent bits.
+#[derive(Debug, Copy, Clone, PartialEq, Eq, Default)]
+pub struct BiasedFp {
+    /// The significant digits.
+    pub f: u64,
+    /// The biased, binary exponent.
+    pub e: i32,
+}
+
+impl BiasedFp {
+    pub const fn zero_pow2(e: i32) -> Self {
+        Self { f: 0, e }
+    }
+}
diff --git a/library/core/src/num/dec2flt/decimal.rs b/library/core/src/num/dec2flt/decimal.rs
new file mode 100644
index 000000000..f8edc3625
--- /dev/null
+++ b/library/core/src/num/dec2flt/decimal.rs
@@ -0,0 +1,351 @@
+//! Arbitrary-precision decimal class for fallback algorithms.
+//!
+//! This is only used if the fast-path (native floats) and
+//! the Eisel-Lemire algorithm are unable to unambiguously
+//! determine the float.
+//!
+//! The technique used is "Simple Decimal Conversion", developed
+//! by Nigel Tao and Ken Thompson. A detailed description of the
+//! algorithm can be found in "ParseNumberF64 by Simple Decimal Conversion",
+//! available online: <https://nigeltao.github.io/blog/2020/parse-number-f64-simple.html>.
+
+use crate::num::dec2flt::common::{is_8digits, parse_digits, ByteSlice, ByteSliceMut};
+
+#[derive(Clone)]
+pub struct Decimal {
+    /// The number of significant digits in the decimal.
+    pub num_digits: usize,
+    /// The offset of the decimal point in the significant digits.
+    pub decimal_point: i32,
+    /// If the number of significant digits stored in the decimal is truncated.
+    pub truncated: bool,
+    /// Buffer of the raw digits, in the range [0, 9].
+    pub digits: [u8; Self::MAX_DIGITS],
+}
+
+impl Default for Decimal {
+    fn default() -> Self {
+        Self { num_digits: 0, decimal_point: 0, truncated: false, digits: [0; Self::MAX_DIGITS] }
+    }
+}
+
+impl Decimal {
+    /// The maximum number of digits required to unambiguously round a float.
+    ///
+    /// For a double-precision IEEE-754 float, this required 767 digits,
+    /// so we store the max digits + 1.
+    ///
+    /// We can exactly represent a float in radix `b` from radix 2 if
+    /// `b` is divisible by 2. This function calculates the exact number of
+    /// digits required to exactly represent that float.
+    ///
+    /// According to the "Handbook of Floating Point Arithmetic",
+    /// for IEEE754, with emin being the min exponent, p2 being the
+    /// precision, and b being the radix, the number of digits follows as:
+    ///
+    /// `−emin + p2 + ⌊(emin + 1) log(2, b) − log(1 − 2^(−p2), b)⌋`
+    ///
+    /// For f32, this follows as:
+    ///     emin = -126
+    ///     p2 = 24
+    ///
+    /// For f64, this follows as:
+    ///     emin = -1022
+    ///     p2 = 53
+    ///
+    /// In Python:
+    ///     `-emin + p2 + math.floor((emin+ 1)*math.log(2, b)-math.log(1-2**(-p2), b))`
+    pub const MAX_DIGITS: usize = 768;
+    /// The max digits that can be exactly represented in a 64-bit integer.
+    pub const MAX_DIGITS_WITHOUT_OVERFLOW: usize = 19;
+    pub const DECIMAL_POINT_RANGE: i32 = 2047;
+
+    /// Append a digit to the buffer.
+    pub fn try_add_digit(&mut self, digit: u8) {
+        if self.num_digits < Self::MAX_DIGITS {
+            self.digits[self.num_digits] = digit;
+        }
+        self.num_digits += 1;
+    }
+
+    /// Trim trailing zeros from the buffer.
+    pub fn trim(&mut self) {
+        // All of the following calls to `Decimal::trim` can't panic because:
+        //
+        //  1. `parse_decimal` sets `num_digits` to a max of `Decimal::MAX_DIGITS`.
+        //  2. `right_shift` sets `num_digits` to `write_index`, which is bounded by `num_digits`.
+        //  3. `left_shift` `num_digits` to a max of `Decimal::MAX_DIGITS`.
+        //
+        // Trim is only called in `right_shift` and `left_shift`.
+        debug_assert!(self.num_digits <= Self::MAX_DIGITS);
+        while self.num_digits != 0 && self.digits[self.num_digits - 1] == 0 {
+            self.num_digits -= 1;
+        }
+    }
+
+    pub fn round(&self) -> u64 {
+        if self.num_digits == 0 || self.decimal_point < 0 {
+            return 0;
+        } else if self.decimal_point > 18 {
+            return 0xFFFF_FFFF_FFFF_FFFF_u64;
+        }
+        let dp = self.decimal_point as usize;
+        let mut n = 0_u64;
+        for i in 0..dp {
+            n *= 10;
+            if i < self.num_digits {
+                n += self.digits[i] as u64;
+            }
+        }
+        let mut round_up = false;
+        if dp < self.num_digits {
+            round_up = self.digits[dp] >= 5;
+            if self.digits[dp] == 5 && dp + 1 == self.num_digits {
+                round_up = self.truncated || ((dp != 0) && (1 & self.digits[dp - 1] != 0))
+            }
+        }
+        if round_up {
+            n += 1;
+        }
+        n
+    }
+
+    /// Computes decimal * 2^shift.
+    pub fn left_shift(&mut self, shift: usize) {
+        if self.num_digits == 0 {
+            return;
+        }
+        let num_new_digits = number_of_digits_decimal_left_shift(self, shift);
+        let mut read_index = self.num_digits;
+        let mut write_index = self.num_digits + num_new_digits;
+        let mut n = 0_u64;
+        while read_index != 0 {
+            read_index -= 1;
+            write_index -= 1;
+            n += (self.digits[read_index] as u64) << shift;
+            let quotient = n / 10;
+            let remainder = n - (10 * quotient);
+            if write_index < Self::MAX_DIGITS {
+                self.digits[write_index] = remainder as u8;
+            } else if remainder > 0 {
+                self.truncated = true;
+            }
+            n = quotient;
+        }
+        while n > 0 {
+            write_index -= 1;
+            let quotient = n / 10;
+            let remainder = n - (10 * quotient);
+            if write_index < Self::MAX_DIGITS {
+                self.digits[write_index] = remainder as u8;
+            } else if remainder > 0 {
+                self.truncated = true;
+            }
+            n = quotient;
+        }
+        self.num_digits += num_new_digits;
+        if self.num_digits > Self::MAX_DIGITS {
+            self.num_digits = Self::MAX_DIGITS;
+        }
+        self.decimal_point += num_new_digits as i32;
+        self.trim();
+    }
+
+    /// Computes decimal * 2^-shift.
+    pub fn right_shift(&mut self, shift: usize) {
+        let mut read_index = 0;
+        let mut write_index = 0;
+        let mut n = 0_u64;
+        while (n >> shift) == 0 {
+            if read_index < self.num_digits {
+                n = (10 * n) + self.digits[read_index] as u64;
+                read_index += 1;
+            } else if n == 0 {
+                return;
+            } else {
+                while (n >> shift) == 0 {
+                    n *= 10;
+                    read_index += 1;
+                }
+                break;
+            }
+        }
+        self.decimal_point -= read_index as i32 - 1;
+        if self.decimal_point < -Self::DECIMAL_POINT_RANGE {
+            // `self = Self::Default()`, but without the overhead of clearing `digits`.
+            self.num_digits = 0;
+            self.decimal_point = 0;
+            self.truncated = false;
+            return;
+        }
+        let mask = (1_u64 << shift) - 1;
+        while read_index < self.num_digits {
+            let new_digit = (n >> shift) as u8;
+            n = (10 * (n & mask)) + self.digits[read_index] as u64;
+            read_index += 1;
+            self.digits[write_index] = new_digit;
+            write_index += 1;
+        }
+        while n > 0 {
+            let new_digit = (n >> shift) as u8;
+            n = 10 * (n & mask);
+            if write_index < Self::MAX_DIGITS {
+                self.digits[write_index] = new_digit;
+                write_index += 1;
+            } else if new_digit > 0 {
+                self.truncated = true;
+            }
+        }
+        self.num_digits = write_index;
+        self.trim();
+    }
+}
+
+/// Parse a big integer representation of the float as a decimal.
+pub fn parse_decimal(mut s: &[u8]) -> Decimal {
+    let mut d = Decimal::default();
+    let start = s;
+    s = s.skip_chars(b'0');
+    parse_digits(&mut s, |digit| d.try_add_digit(digit));
+    if s.first_is(b'.') {
+        s = s.advance(1);
+        let first = s;
+        // Skip leading zeros.
+        if d.num_digits == 0 {
+            s = s.skip_chars(b'0');
+        }
+        while s.len() >= 8 && d.num_digits + 8 < Decimal::MAX_DIGITS {
+            // SAFETY: s is at least 8 bytes.
+            let v = unsafe { s.read_u64_unchecked() };
+            if !is_8digits(v) {
+                break;
+            }
+            // SAFETY: d.num_digits + 8 is less than d.digits.len()
+            unsafe {
+                d.digits[d.num_digits..].write_u64_unchecked(v - 0x3030_3030_3030_3030);
+            }
+            d.num_digits += 8;
+            s = s.advance(8);
+        }
+        parse_digits(&mut s, |digit| d.try_add_digit(digit));
+        d.decimal_point = s.len() as i32 - first.len() as i32;
+    }
+    if d.num_digits != 0 {
+        // Ignore the trailing zeros if there are any
+        let mut n_trailing_zeros = 0;
+        for &c in start[..(start.len() - s.len())].iter().rev() {
+            if c == b'0' {
+                n_trailing_zeros += 1;
+            } else if c != b'.' {
+                break;
+            }
+        }
+        d.decimal_point += n_trailing_zeros as i32;
+        d.num_digits -= n_trailing_zeros;
+        d.decimal_point += d.num_digits as i32;
+        if d.num_digits > Decimal::MAX_DIGITS {
+            d.truncated = true;
+            d.num_digits = Decimal::MAX_DIGITS;
+        }
+    }
+    if s.first_is2(b'e', b'E') {
+        s = s.advance(1);
+        let mut neg_exp = false;
+        if s.first_is(b'-') {
+            neg_exp = true;
+            s = s.advance(1);
+        } else if s.first_is(b'+') {
+            s = s.advance(1);
+        }
+        let mut exp_num = 0_i32;
+        parse_digits(&mut s, |digit| {
+            if exp_num < 0x10000 {
+                exp_num = 10 * exp_num + digit as i32;
+            }
+        });
+        d.decimal_point += if neg_exp { -exp_num } else { exp_num };
+    }
+    for i in d.num_digits..Decimal::MAX_DIGITS_WITHOUT_OVERFLOW {
+        d.digits[i] = 0;
+    }
+    d
+}
+
+fn number_of_digits_decimal_left_shift(d: &Decimal, mut shift: usize) -> usize {
+    #[rustfmt::skip]
+    const TABLE: [u16; 65] = [
+        0x0000, 0x0800, 0x0801, 0x0803, 0x1006, 0x1009, 0x100D, 0x1812, 0x1817, 0x181D, 0x2024,
+        0x202B, 0x2033, 0x203C, 0x2846, 0x2850, 0x285B, 0x3067, 0x3073, 0x3080, 0x388E, 0x389C,
+        0x38AB, 0x38BB, 0x40CC, 0x40DD, 0x40EF, 0x4902, 0x4915, 0x4929, 0x513E, 0x5153, 0x5169,
+        0x5180, 0x5998, 0x59B0, 0x59C9, 0x61E3, 0x61FD, 0x6218, 0x6A34, 0x6A50, 0x6A6D, 0x6A8B,
+        0x72AA, 0x72C9, 0x72E9, 0x7B0A, 0x7B2B, 0x7B4D, 0x8370, 0x8393, 0x83B7, 0x83DC, 0x8C02,
+        0x8C28, 0x8C4F, 0x9477, 0x949F, 0x94C8, 0x9CF2, 0x051C, 0x051C, 0x051C, 0x051C,
+    ];
+    #[rustfmt::skip]
+    const TABLE_POW5: [u8; 0x051C] = [
+        5, 2, 5, 1, 2, 5, 6, 2, 5, 3, 1, 2, 5, 1, 5, 6, 2, 5, 7, 8, 1, 2, 5, 3, 9, 0, 6, 2, 5, 1,
+        9, 5, 3, 1, 2, 5, 9, 7, 6, 5, 6, 2, 5, 4, 8, 8, 2, 8, 1, 2, 5, 2, 4, 4, 1, 4, 0, 6, 2, 5,
+        1, 2, 2, 0, 7, 0, 3, 1, 2, 5, 6, 1, 0, 3, 5, 1, 5, 6, 2, 5, 3, 0, 5, 1, 7, 5, 7, 8, 1, 2,
+        5, 1, 5, 2, 5, 8, 7, 8, 9, 0, 6, 2, 5, 7, 6, 2, 9, 3, 9, 4, 5, 3, 1, 2, 5, 3, 8, 1, 4, 6,
+        9, 7, 2, 6, 5, 6, 2, 5, 1, 9, 0, 7, 3, 4, 8, 6, 3, 2, 8, 1, 2, 5, 9, 5, 3, 6, 7, 4, 3, 1,
+        6, 4, 0, 6, 2, 5, 4, 7, 6, 8, 3, 7, 1, 5, 8, 2, 0, 3, 1, 2, 5, 2, 3, 8, 4, 1, 8, 5, 7, 9,
+        1, 0, 1, 5, 6, 2, 5, 1, 1, 9, 2, 0, 9, 2, 8, 9, 5, 5, 0, 7, 8, 1, 2, 5, 5, 9, 6, 0, 4, 6,
+        4, 4, 7, 7, 5, 3, 9, 0, 6, 2, 5, 2, 9, 8, 0, 2, 3, 2, 2, 3, 8, 7, 6, 9, 5, 3, 1, 2, 5, 1,
+        4, 9, 0, 1, 1, 6, 1, 1, 9, 3, 8, 4, 7, 6, 5, 6, 2, 5, 7, 4, 5, 0, 5, 8, 0, 5, 9, 6, 9, 2,
+        3, 8, 2, 8, 1, 2, 5, 3, 7, 2, 5, 2, 9, 0, 2, 9, 8, 4, 6, 1, 9, 1, 4, 0, 6, 2, 5, 1, 8, 6,
+        2, 6, 4, 5, 1, 4, 9, 2, 3, 0, 9, 5, 7, 0, 3, 1, 2, 5, 9, 3, 1, 3, 2, 2, 5, 7, 4, 6, 1, 5,
+        4, 7, 8, 5, 1, 5, 6, 2, 5, 4, 6, 5, 6, 6, 1, 2, 8, 7, 3, 0, 7, 7, 3, 9, 2, 5, 7, 8, 1, 2,
+        5, 2, 3, 2, 8, 3, 0, 6, 4, 3, 6, 5, 3, 8, 6, 9, 6, 2, 8, 9, 0, 6, 2, 5, 1, 1, 6, 4, 1, 5,
+        3, 2, 1, 8, 2, 6, 9, 3, 4, 8, 1, 4, 4, 5, 3, 1, 2, 5, 5, 8, 2, 0, 7, 6, 6, 0, 9, 1, 3, 4,
+        6, 7, 4, 0, 7, 2, 2, 6, 5, 6, 2, 5, 2, 9, 1, 0, 3, 8, 3, 0, 4, 5, 6, 7, 3, 3, 7, 0, 3, 6,
+        1, 3, 2, 8, 1, 2, 5, 1, 4, 5, 5, 1, 9, 1, 5, 2, 2, 8, 3, 6, 6, 8, 5, 1, 8, 0, 6, 6, 4, 0,
+        6, 2, 5, 7, 2, 7, 5, 9, 5, 7, 6, 1, 4, 1, 8, 3, 4, 2, 5, 9, 0, 3, 3, 2, 0, 3, 1, 2, 5, 3,
+        6, 3, 7, 9, 7, 8, 8, 0, 7, 0, 9, 1, 7, 1, 2, 9, 5, 1, 6, 6, 0, 1, 5, 6, 2, 5, 1, 8, 1, 8,
+        9, 8, 9, 4, 0, 3, 5, 4, 5, 8, 5, 6, 4, 7, 5, 8, 3, 0, 0, 7, 8, 1, 2, 5, 9, 0, 9, 4, 9, 4,
+        7, 0, 1, 7, 7, 2, 9, 2, 8, 2, 3, 7, 9, 1, 5, 0, 3, 9, 0, 6, 2, 5, 4, 5, 4, 7, 4, 7, 3, 5,
+        0, 8, 8, 6, 4, 6, 4, 1, 1, 8, 9, 5, 7, 5, 1, 9, 5, 3, 1, 2, 5, 2, 2, 7, 3, 7, 3, 6, 7, 5,
+        4, 4, 3, 2, 3, 2, 0, 5, 9, 4, 7, 8, 7, 5, 9, 7, 6, 5, 6, 2, 5, 1, 1, 3, 6, 8, 6, 8, 3, 7,
+        7, 2, 1, 6, 1, 6, 0, 2, 9, 7, 3, 9, 3, 7, 9, 8, 8, 2, 8, 1, 2, 5, 5, 6, 8, 4, 3, 4, 1, 8,
+        8, 6, 0, 8, 0, 8, 0, 1, 4, 8, 6, 9, 6, 8, 9, 9, 4, 1, 4, 0, 6, 2, 5, 2, 8, 4, 2, 1, 7, 0,
+        9, 4, 3, 0, 4, 0, 4, 0, 0, 7, 4, 3, 4, 8, 4, 4, 9, 7, 0, 7, 0, 3, 1, 2, 5, 1, 4, 2, 1, 0,
+        8, 5, 4, 7, 1, 5, 2, 0, 2, 0, 0, 3, 7, 1, 7, 4, 2, 2, 4, 8, 5, 3, 5, 1, 5, 6, 2, 5, 7, 1,
+        0, 5, 4, 2, 7, 3, 5, 7, 6, 0, 1, 0, 0, 1, 8, 5, 8, 7, 1, 1, 2, 4, 2, 6, 7, 5, 7, 8, 1, 2,
+        5, 3, 5, 5, 2, 7, 1, 3, 6, 7, 8, 8, 0, 0, 5, 0, 0, 9, 2, 9, 3, 5, 5, 6, 2, 1, 3, 3, 7, 8,
+        9, 0, 6, 2, 5, 1, 7, 7, 6, 3, 5, 6, 8, 3, 9, 4, 0, 0, 2, 5, 0, 4, 6, 4, 6, 7, 7, 8, 1, 0,
+        6, 6, 8, 9, 4, 5, 3, 1, 2, 5, 8, 8, 8, 1, 7, 8, 4, 1, 9, 7, 0, 0, 1, 2, 5, 2, 3, 2, 3, 3,
+        8, 9, 0, 5, 3, 3, 4, 4, 7, 2, 6, 5, 6, 2, 5, 4, 4, 4, 0, 8, 9, 2, 0, 9, 8, 5, 0, 0, 6, 2,
+        6, 1, 6, 1, 6, 9, 4, 5, 2, 6, 6, 7, 2, 3, 6, 3, 2, 8, 1, 2, 5, 2, 2, 2, 0, 4, 4, 6, 0, 4,
+        9, 2, 5, 0, 3, 1, 3, 0, 8, 0, 8, 4, 7, 2, 6, 3, 3, 3, 6, 1, 8, 1, 6, 4, 0, 6, 2, 5, 1, 1,
+        1, 0, 2, 2, 3, 0, 2, 4, 6, 2, 5, 1, 5, 6, 5, 4, 0, 4, 2, 3, 6, 3, 1, 6, 6, 8, 0, 9, 0, 8,
+        2, 0, 3, 1, 2, 5, 5, 5, 5, 1, 1, 1, 5, 1, 2, 3, 1, 2, 5, 7, 8, 2, 7, 0, 2, 1, 1, 8, 1, 5,
+        8, 3, 4, 0, 4, 5, 4, 1, 0, 1, 5, 6, 2, 5, 2, 7, 7, 5, 5, 5, 7, 5, 6, 1, 5, 6, 2, 8, 9, 1,
+        3, 5, 1, 0, 5, 9, 0, 7, 9, 1, 7, 0, 2, 2, 7, 0, 5, 0, 7, 8, 1, 2, 5, 1, 3, 8, 7, 7, 7, 8,
+        7, 8, 0, 7, 8, 1, 4, 4, 5, 6, 7, 5, 5, 2, 9, 5, 3, 9, 5, 8, 5, 1, 1, 3, 5, 2, 5, 3, 9, 0,
+        6, 2, 5, 6, 9, 3, 8, 8, 9, 3, 9, 0, 3, 9, 0, 7, 2, 2, 8, 3, 7, 7, 6, 4, 7, 6, 9, 7, 9, 2,
+        5, 5, 6, 7, 6, 2, 6, 9, 5, 3, 1, 2, 5, 3, 4, 6, 9, 4, 4, 6, 9, 5, 1, 9, 5, 3, 6, 1, 4, 1,
+        8, 8, 8, 2, 3, 8, 4, 8, 9, 6, 2, 7, 8, 3, 8, 1, 3, 4, 7, 6, 5, 6, 2, 5, 1, 7, 3, 4, 7, 2,
+        3, 4, 7, 5, 9, 7, 6, 8, 0, 7, 0, 9, 4, 4, 1, 1, 9, 2, 4, 4, 8, 1, 3, 9, 1, 9, 0, 6, 7, 3,
+        8, 2, 8, 1, 2, 5, 8, 6, 7, 3, 6, 1, 7, 3, 7, 9, 8, 8, 4, 0, 3, 5, 4, 7, 2, 0, 5, 9, 6, 2,
+        2, 4, 0, 6, 9, 5, 9, 5, 3, 3, 6, 9, 1, 4, 0, 6, 2, 5,
+    ];
+
+    shift &= 63;
+    let x_a = TABLE[shift];
+    let x_b = TABLE[shift + 1];
+    let num_new_digits = (x_a >> 11) as _;
+    let pow5_a = (0x7FF & x_a) as usize;
+    let pow5_b = (0x7FF & x_b) as usize;
+    let pow5 = &TABLE_POW5[pow5_a..];
+    for (i, &p5) in pow5.iter().enumerate().take(pow5_b - pow5_a) {
+        if i >= d.num_digits {
+            return num_new_digits - 1;
+        } else if d.digits[i] == p5 {
+            continue;
+        } else if d.digits[i] < p5 {
+            return num_new_digits - 1;
+        } else {
+            return num_new_digits;
+        }
+    }
+    num_new_digits
+}
diff --git a/library/core/src/num/dec2flt/float.rs b/library/core/src/num/dec2flt/float.rs
new file mode 100644
index 000000000..5921c5ed4
--- /dev/null
+++ b/library/core/src/num/dec2flt/float.rs
@@ -0,0 +1,207 @@
+//! Helper trait for generic float types.
+
+use crate::fmt::{Debug, LowerExp};
+use crate::num::FpCategory;
+use crate::ops::{Add, Div, Mul, Neg};
+
+/// A helper trait to avoid duplicating basically all the conversion code for `f32` and `f64`.
+///
+/// See the parent module's doc comment for why this is necessary.
+///
+/// Should **never ever** be implemented for other types or be used outside the dec2flt module.
+#[doc(hidden)]
+pub trait RawFloat:
+    Sized
+    + Div<Output = Self>
+    + Neg<Output = Self>
+    + Mul<Output = Self>
+    + Add<Output = Self>
+    + LowerExp
+    + PartialEq
+    + PartialOrd
+    + Default
+    + Clone
+    + Copy
+    + Debug
+{
+    const INFINITY: Self;
+    const NEG_INFINITY: Self;
+    const NAN: Self;
+    const NEG_NAN: Self;
+
+    /// The number of bits in the significand, *excluding* the hidden bit.
+    const MANTISSA_EXPLICIT_BITS: usize;
+
+    // Round-to-even only happens for negative values of q
+    // when q ≥ −4 in the 64-bit case and when q ≥ −17 in
+    // the 32-bitcase.
+    //
+    // When q ≥ 0,we have that 5^q ≤ 2m+1. In the 64-bit case,we
+    // have 5^q ≤ 2m+1 ≤ 2^54 or q ≤ 23. In the 32-bit case,we have
+    // 5^q ≤ 2m+1 ≤ 2^25 or q ≤ 10.
+    //
+    // When q < 0, we have w ≥ (2m+1)×5^−q. We must have that w < 2^64
+    // so (2m+1)×5^−q < 2^64. We have that 2m+1 > 2^53 (64-bit case)
+    // or 2m+1 > 2^24 (32-bit case). Hence,we must have 2^53×5^−q < 2^64
+    // (64-bit) and 2^24×5^−q < 2^64 (32-bit). Hence we have 5^−q < 2^11
+    // or q ≥ −4 (64-bit case) and 5^−q < 2^40 or q ≥ −17 (32-bitcase).
+    //
+    // Thus we have that we only need to round ties to even when
+    // we have that q ∈ [−4,23](in the 64-bit case) or q∈[−17,10]
+    // (in the 32-bit case). In both cases,the power of five(5^|q|)
+    // fits in a 64-bit word.
+    const MIN_EXPONENT_ROUND_TO_EVEN: i32;
+    const MAX_EXPONENT_ROUND_TO_EVEN: i32;
+
+    // Minimum exponent that for a fast path case, or `-⌊(MANTISSA_EXPLICIT_BITS+1)/log2(5)⌋`
+    const MIN_EXPONENT_FAST_PATH: i64;
+
+    // Maximum exponent that for a fast path case, or `⌊(MANTISSA_EXPLICIT_BITS+1)/log2(5)⌋`
+    const MAX_EXPONENT_FAST_PATH: i64;
+
+    // Maximum exponent that can be represented for a disguised-fast path case.
+    // This is `MAX_EXPONENT_FAST_PATH + ⌊(MANTISSA_EXPLICIT_BITS+1)/log2(10)⌋`
+    const MAX_EXPONENT_DISGUISED_FAST_PATH: i64;
+
+    // Minimum exponent value `-(1 << (EXP_BITS - 1)) + 1`.
+    const MINIMUM_EXPONENT: i32;
+
+    // Largest exponent value `(1 << EXP_BITS) - 1`.
+    const INFINITE_POWER: i32;
+
+    // Index (in bits) of the sign.
+    const SIGN_INDEX: usize;
+
+    // Smallest decimal exponent for a non-zero value.
+    const SMALLEST_POWER_OF_TEN: i32;
+
+    // Largest decimal exponent for a non-infinite value.
+    const LARGEST_POWER_OF_TEN: i32;
+
+    // Maximum mantissa for the fast-path (`1 << 53` for f64).
+    const MAX_MANTISSA_FAST_PATH: u64 = 2_u64 << Self::MANTISSA_EXPLICIT_BITS;
+
+    /// Convert integer into float through an as cast.
+    /// This is only called in the fast-path algorithm, and therefore
+    /// will not lose precision, since the value will always have
+    /// only if the value is <= Self::MAX_MANTISSA_FAST_PATH.
+    fn from_u64(v: u64) -> Self;
+
+    /// Performs a raw transmutation from an integer.
+    fn from_u64_bits(v: u64) -> Self;
+
+    /// Get a small power-of-ten for fast-path multiplication.
+    fn pow10_fast_path(exponent: usize) -> Self;
+
+    /// Returns the category that this number falls into.
+    fn classify(self) -> FpCategory;
+
+    /// Returns the mantissa, exponent and sign as integers.
+    fn integer_decode(self) -> (u64, i16, i8);
+}
+
+impl RawFloat for f32 {
+    const INFINITY: Self = f32::INFINITY;
+    const NEG_INFINITY: Self = f32::NEG_INFINITY;
+    const NAN: Self = f32::NAN;
+    const NEG_NAN: Self = -f32::NAN;
+
+    const MANTISSA_EXPLICIT_BITS: usize = 23;
+    const MIN_EXPONENT_ROUND_TO_EVEN: i32 = -17;
+    const MAX_EXPONENT_ROUND_TO_EVEN: i32 = 10;
+    const MIN_EXPONENT_FAST_PATH: i64 = -10; // assuming FLT_EVAL_METHOD = 0
+    const MAX_EXPONENT_FAST_PATH: i64 = 10;
+    const MAX_EXPONENT_DISGUISED_FAST_PATH: i64 = 17;
+    const MINIMUM_EXPONENT: i32 = -127;
+    const INFINITE_POWER: i32 = 0xFF;
+    const SIGN_INDEX: usize = 31;
+    const SMALLEST_POWER_OF_TEN: i32 = -65;
+    const LARGEST_POWER_OF_TEN: i32 = 38;
+
+    fn from_u64(v: u64) -> Self {
+        debug_assert!(v <= Self::MAX_MANTISSA_FAST_PATH);
+        v as _
+    }
+
+    fn from_u64_bits(v: u64) -> Self {
+        f32::from_bits((v & 0xFFFFFFFF) as u32)
+    }
+
+    fn pow10_fast_path(exponent: usize) -> Self {
+        #[allow(clippy::use_self)]
+        const TABLE: [f32; 16] =
+            [1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9, 1e10, 0., 0., 0., 0., 0.];
+        TABLE[exponent & 15]
+    }
+
+    /// Returns the mantissa, exponent and sign as integers.
+    fn integer_decode(self) -> (u64, i16, i8) {
+        let bits = self.to_bits();
+        let sign: i8 = if bits >> 31 == 0 { 1 } else { -1 };
+        let mut exponent: i16 = ((bits >> 23) & 0xff) as i16;
+        let mantissa =
+            if exponent == 0 { (bits & 0x7fffff) << 1 } else { (bits & 0x7fffff) | 0x800000 };
+        // Exponent bias + mantissa shift
+        exponent -= 127 + 23;
+        (mantissa as u64, exponent, sign)
+    }
+
+    fn classify(self) -> FpCategory {
+        self.classify()
+    }
+}
+
+impl RawFloat for f64 {
+    const INFINITY: Self = f64::INFINITY;
+    const NEG_INFINITY: Self = f64::NEG_INFINITY;
+    const NAN: Self = f64::NAN;
+    const NEG_NAN: Self = -f64::NAN;
+
+    const MANTISSA_EXPLICIT_BITS: usize = 52;
+    const MIN_EXPONENT_ROUND_TO_EVEN: i32 = -4;
+    const MAX_EXPONENT_ROUND_TO_EVEN: i32 = 23;
+    const MIN_EXPONENT_FAST_PATH: i64 = -22; // assuming FLT_EVAL_METHOD = 0
+    const MAX_EXPONENT_FAST_PATH: i64 = 22;
+    const MAX_EXPONENT_DISGUISED_FAST_PATH: i64 = 37;
+    const MINIMUM_EXPONENT: i32 = -1023;
+    const INFINITE_POWER: i32 = 0x7FF;
+    const SIGN_INDEX: usize = 63;
+    const SMALLEST_POWER_OF_TEN: i32 = -342;
+    const LARGEST_POWER_OF_TEN: i32 = 308;
+
+    fn from_u64(v: u64) -> Self {
+        debug_assert!(v <= Self::MAX_MANTISSA_FAST_PATH);
+        v as _
+    }
+
+    fn from_u64_bits(v: u64) -> Self {
+        f64::from_bits(v)
+    }
+
+    fn pow10_fast_path(exponent: usize) -> Self {
+        const TABLE: [f64; 32] = [
+            1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9, 1e10, 1e11, 1e12, 1e13, 1e14, 1e15,
+            1e16, 1e17, 1e18, 1e19, 1e20, 1e21, 1e22, 0., 0., 0., 0., 0., 0., 0., 0., 0.,
+        ];
+        TABLE[exponent & 31]
+    }
+
+    /// Returns the mantissa, exponent and sign as integers.
+    fn integer_decode(self) -> (u64, i16, i8) {
+        let bits = self.to_bits();
+        let sign: i8 = if bits >> 63 == 0 { 1 } else { -1 };
+        let mut exponent: i16 = ((bits >> 52) & 0x7ff) as i16;
+        let mantissa = if exponent == 0 {
+            (bits & 0xfffffffffffff) << 1
+        } else {
+            (bits & 0xfffffffffffff) | 0x10000000000000
+        };
+        // Exponent bias + mantissa shift
+        exponent -= 1023 + 52;
+        (mantissa, exponent, sign)
+    }
+
+    fn classify(self) -> FpCategory {
+        self.classify()
+    }
+}
diff --git a/library/core/src/num/dec2flt/fpu.rs b/library/core/src/num/dec2flt/fpu.rs
new file mode 100644
index 000000000..ec5fa45fd
--- /dev/null
+++ b/library/core/src/num/dec2flt/fpu.rs
@@ -0,0 +1,90 @@
+//! Platform-specific, assembly instructions to avoid
+//! intermediate rounding on architectures with FPUs.
+
+pub use fpu_precision::set_precision;
+
+// On x86, the x87 FPU is used for float operations if the SSE/SSE2 extensions are not available.
+// The x87 FPU operates with 80 bits of precision by default, which means that operations will
+// round to 80 bits causing double rounding to happen when values are eventually represented as
+// 32/64 bit float values. To overcome this, the FPU control word can be set so that the
+// computations are performed in the desired precision.
+#[cfg(all(target_arch = "x86", not(target_feature = "sse2")))]
+mod fpu_precision {
+    use core::arch::asm;
+    use core::mem::size_of;
+
+    /// A structure used to preserve the original value of the FPU control word, so that it can be
+    /// restored when the structure is dropped.
+    ///
+    /// The x87 FPU is a 16-bits register whose fields are as follows:
+    ///
+    /// | 12-15 | 10-11 | 8-9 | 6-7 |  5 |  4 |  3 |  2 |  1 |  0 |
+    /// |------:|------:|----:|----:|---:|---:|---:|---:|---:|---:|
+    /// |       | RC    | PC  |     | PM | UM | OM | ZM | DM | IM |
+    ///
+    /// The documentation for all of the fields is available in the IA-32 Architectures Software
+    /// Developer's Manual (Volume 1).
+    ///
+    /// The only field which is relevant for the following code is PC, Precision Control. This
+    /// field determines the precision of the operations performed by the  FPU. It can be set to:
+    ///  - 0b00, single precision i.e., 32-bits
+    ///  - 0b10, double precision i.e., 64-bits
+    ///  - 0b11, double extended precision i.e., 80-bits (default state)
+    /// The 0b01 value is reserved and should not be used.
+    pub struct FPUControlWord(u16);
+
+    fn set_cw(cw: u16) {
+        // SAFETY: the `fldcw` instruction has been audited to be able to work correctly with
+        // any `u16`
+        unsafe {
+            asm!(
+                "fldcw word ptr [{}]",
+                in(reg) &cw,
+                options(nostack),
+            )
+        }
+    }
+
+    /// Sets the precision field of the FPU to `T` and returns a `FPUControlWord`.
+    pub fn set_precision<T>() -> FPUControlWord {
+        let mut cw = 0_u16;
+
+        // Compute the value for the Precision Control field that is appropriate for `T`.
+        let cw_precision = match size_of::<T>() {
+            4 => 0x0000, // 32 bits
+            8 => 0x0200, // 64 bits
+            _ => 0x0300, // default, 80 bits
+        };
+
+        // Get the original value of the control word to restore it later, when the
+        // `FPUControlWord` structure is dropped
+        // SAFETY: the `fnstcw` instruction has been audited to be able to work correctly with
+        // any `u16`
+        unsafe {
+            asm!(
+                "fnstcw word ptr [{}]",
+                in(reg) &mut cw,
+                options(nostack),
+            )
+        }
+
+        // Set the control word to the desired precision. This is achieved by masking away the old
+        // precision (bits 8 and 9, 0x300) and replacing it with the precision flag computed above.
+        set_cw((cw & 0xFCFF) | cw_precision);
+
+        FPUControlWord(cw)
+    }
+
+    impl Drop for FPUControlWord {
+        fn drop(&mut self) {
+            set_cw(self.0)
+        }
+    }
+}
+
+// In most architectures, floating point operations have an explicit bit size, therefore the
+// precision of the computation is determined on a per-operation basis.
+#[cfg(any(not(target_arch = "x86"), target_feature = "sse2"))]
+mod fpu_precision {
+    pub fn set_precision<T>() {}
+}
diff --git a/library/core/src/num/dec2flt/lemire.rs b/library/core/src/num/dec2flt/lemire.rs
new file mode 100644
index 000000000..75405f471
--- /dev/null
+++ b/library/core/src/num/dec2flt/lemire.rs
@@ -0,0 +1,166 @@
+//! Implementation of the Eisel-Lemire algorithm.
+
+use crate::num::dec2flt::common::BiasedFp;
+use crate::num::dec2flt::float::RawFloat;
+use crate::num::dec2flt::table::{
+    LARGEST_POWER_OF_FIVE, POWER_OF_FIVE_128, SMALLEST_POWER_OF_FIVE,
+};
+
+/// Compute a float using an extended-precision representation.
+///
+/// Fast conversion of a the significant digits and decimal exponent
+/// a float to an extended representation with a binary float. This
+/// algorithm will accurately parse the vast majority of cases,
+/// and uses a 128-bit representation (with a fallback 192-bit
+/// representation).
+///
+/// This algorithm scales the exponent by the decimal exponent
+/// using pre-computed powers-of-5, and calculates if the
+/// representation can be unambiguously rounded to the nearest
+/// machine float. Near-halfway cases are not handled here,
+/// and are represented by a negative, biased binary exponent.
+///
+/// The algorithm is described in detail in "Daniel Lemire, Number Parsing
+/// at a Gigabyte per Second" in section 5, "Fast Algorithm", and
+/// section 6, "Exact Numbers And Ties", available online:
+/// <https://arxiv.org/abs/2101.11408.pdf>.
+pub fn compute_float<F: RawFloat>(q: i64, mut w: u64) -> BiasedFp {
+    let fp_zero = BiasedFp::zero_pow2(0);
+    let fp_inf = BiasedFp::zero_pow2(F::INFINITE_POWER);
+    let fp_error = BiasedFp::zero_pow2(-1);
+
+    // Short-circuit if the value can only be a literal 0 or infinity.
+    if w == 0 || q < F::SMALLEST_POWER_OF_TEN as i64 {
+        return fp_zero;
+    } else if q > F::LARGEST_POWER_OF_TEN as i64 {
+        return fp_inf;
+    }
+    // Normalize our significant digits, so the most-significant bit is set.
+    let lz = w.leading_zeros();
+    w <<= lz;
+    let (lo, hi) = compute_product_approx(q, w, F::MANTISSA_EXPLICIT_BITS + 3);
+    if lo == 0xFFFF_FFFF_FFFF_FFFF {
+        // If we have failed to approximate w x 5^-q with our 128-bit value.
+        // Since the addition of 1 could lead to an overflow which could then
+        // round up over the half-way point, this can lead to improper rounding
+        // of a float.
+        //
+        // However, this can only occur if q ∈ [-27, 55]. The upper bound of q
+        // is 55 because 5^55 < 2^128, however, this can only happen if 5^q > 2^64,
+        // since otherwise the product can be represented in 64-bits, producing
+        // an exact result. For negative exponents, rounding-to-even can
+        // only occur if 5^-q < 2^64.
+        //
+        // For detailed explanations of rounding for negative exponents, see
+        // <https://arxiv.org/pdf/2101.11408.pdf#section.9.1>. For detailed
+        // explanations of rounding for positive exponents, see
+        // <https://arxiv.org/pdf/2101.11408.pdf#section.8>.
+        let inside_safe_exponent = (q >= -27) && (q <= 55);
+        if !inside_safe_exponent {
+            return fp_error;
+        }
+    }
+    let upperbit = (hi >> 63) as i32;
+    let mut mantissa = hi >> (upperbit + 64 - F::MANTISSA_EXPLICIT_BITS as i32 - 3);
+    let mut power2 = power(q as i32) + upperbit - lz as i32 - F::MINIMUM_EXPONENT;
+    if power2 <= 0 {
+        if -power2 + 1 >= 64 {
+            // Have more than 64 bits below the minimum exponent, must be 0.
+            return fp_zero;
+        }
+        // Have a subnormal value.
+        mantissa >>= -power2 + 1;
+        mantissa += mantissa & 1;
+        mantissa >>= 1;
+        power2 = (mantissa >= (1_u64 << F::MANTISSA_EXPLICIT_BITS)) as i32;
+        return BiasedFp { f: mantissa, e: power2 };
+    }
+    // Need to handle rounding ties. Normally, we need to round up,
+    // but if we fall right in between and and we have an even basis, we
+    // need to round down.
+    //
+    // This will only occur if:
+    //  1. The lower 64 bits of the 128-bit representation is 0.
+    //      IE, 5^q fits in single 64-bit word.
+    //  2. The least-significant bit prior to truncated mantissa is odd.
+    //  3. All the bits truncated when shifting to mantissa bits + 1 are 0.
+    //
+    // Or, we may fall between two floats: we are exactly halfway.
+    if lo <= 1
+        && q >= F::MIN_EXPONENT_ROUND_TO_EVEN as i64
+        && q <= F::MAX_EXPONENT_ROUND_TO_EVEN as i64
+        && mantissa & 3 == 1
+        && (mantissa << (upperbit + 64 - F::MANTISSA_EXPLICIT_BITS as i32 - 3)) == hi
+    {
+        // Zero the lowest bit, so we don't round up.
+        mantissa &= !1_u64;
+    }
+    // Round-to-even, then shift the significant digits into place.
+    mantissa += mantissa & 1;
+    mantissa >>= 1;
+    if mantissa >= (2_u64 << F::MANTISSA_EXPLICIT_BITS) {
+        // Rounding up overflowed, so the carry bit is set. Set the
+        // mantissa to 1 (only the implicit, hidden bit is set) and
+        // increase the exponent.
+        mantissa = 1_u64 << F::MANTISSA_EXPLICIT_BITS;
+        power2 += 1;
+    }
+    // Zero out the hidden bit.
+    mantissa &= !(1_u64 << F::MANTISSA_EXPLICIT_BITS);
+    if power2 >= F::INFINITE_POWER {
+        // Exponent is above largest normal value, must be infinite.
+        return fp_inf;
+    }
+    BiasedFp { f: mantissa, e: power2 }
+}
+
+/// Calculate a base 2 exponent from a decimal exponent.
+/// This uses a pre-computed integer approximation for
+/// log2(10), where 217706 / 2^16 is accurate for the
+/// entire range of non-finite decimal exponents.
+fn power(q: i32) -> i32 {
+    (q.wrapping_mul(152_170 + 65536) >> 16) + 63
+}
+
+fn full_multiplication(a: u64, b: u64) -> (u64, u64) {
+    let r = (a as u128) * (b as u128);
+    (r as u64, (r >> 64) as u64)
+}
+
+// This will compute or rather approximate w * 5**q and return a pair of 64-bit words
+// approximating the result, with the "high" part corresponding to the most significant
+// bits and the low part corresponding to the least significant bits.
+fn compute_product_approx(q: i64, w: u64, precision: usize) -> (u64, u64) {
+    debug_assert!(q >= SMALLEST_POWER_OF_FIVE as i64);
+    debug_assert!(q <= LARGEST_POWER_OF_FIVE as i64);
+    debug_assert!(precision <= 64);
+
+    let mask = if precision < 64 {
+        0xFFFF_FFFF_FFFF_FFFF_u64 >> precision
+    } else {
+        0xFFFF_FFFF_FFFF_FFFF_u64
+    };
+
+    // 5^q < 2^64, then the multiplication always provides an exact value.
+    // That means whenever we need to round ties to even, we always have
+    // an exact value.
+    let index = (q - SMALLEST_POWER_OF_FIVE as i64) as usize;
+    let (lo5, hi5) = POWER_OF_FIVE_128[index];
+    // Only need one multiplication as long as there is 1 zero but
+    // in the explicit mantissa bits, +1 for the hidden bit, +1 to
+    // determine the rounding direction, +1 for if the computed
+    // product has a leading zero.
+    let (mut first_lo, mut first_hi) = full_multiplication(w, lo5);
+    if first_hi & mask == mask {
+        // Need to do a second multiplication to get better precision
+        // for the lower product. This will always be exact
+        // where q is < 55, since 5^55 < 2^128. If this wraps,
+        // then we need to need to round up the hi product.
+        let (_, second_hi) = full_multiplication(w, hi5);
+        first_lo = first_lo.wrapping_add(second_hi);
+        if second_hi > first_lo {
+            first_hi += 1;
+        }
+    }
+    (first_lo, first_hi)
+}
diff --git a/library/core/src/num/dec2flt/mod.rs b/library/core/src/num/dec2flt/mod.rs
new file mode 100644
index 000000000..a888ced49
--- /dev/null
+++ b/library/core/src/num/dec2flt/mod.rs
@@ -0,0 +1,269 @@
+//! Converting decimal strings into IEEE 754 binary floating point numbers.
+//!
+//! # Problem statement
+//!
+//! We are given a decimal string such as `12.34e56`. This string consists of integral (`12`),
+//! fractional (`34`), and exponent (`56`) parts. All parts are optional and interpreted as zero
+//! when missing.
+//!
+//! We seek the IEEE 754 floating point number that is closest to the exact value of the decimal
+//! string. It is well-known that many decimal strings do not have terminating representations in
+//! base two, so we round to 0.5 units in the last place (in other words, as well as possible).
+//! Ties, decimal values exactly half-way between two consecutive floats, are resolved with the
+//! half-to-even strategy, also known as banker's rounding.
+//!
+//! Needless to say, this is quite hard, both in terms of implementation complexity and in terms
+//! of CPU cycles taken.
+//!
+//! # Implementation
+//!
+//! First, we ignore signs. Or rather, we remove it at the very beginning of the conversion
+//! process and re-apply it at the very end. This is correct in all edge cases since IEEE
+//! floats are symmetric around zero, negating one simply flips the first bit.
+//!
+//! Then we remove the decimal point by adjusting the exponent: Conceptually, `12.34e56` turns
+//! into `1234e54`, which we describe with a positive integer `f = 1234` and an integer `e = 54`.
+//! The `(f, e)` representation is used by almost all code past the parsing stage.
+//!
+//! We then try a long chain of progressively more general and expensive special cases using
+//! machine-sized integers and small, fixed-sized floating point numbers (first `f32`/`f64`, then
+//! a type with 64 bit significand). The extended-precision algorithm
+//! uses the Eisel-Lemire algorithm, which uses a 128-bit (or 192-bit)
+//! representation that can accurately and quickly compute the vast majority
+//! of floats. When all these fail, we bite the bullet and resort to using
+//! a large-decimal representation, shifting the digits into range, calculating
+//! the upper significant bits and exactly round to the nearest representation.
+//!
+//! Another aspect that needs attention is the ``RawFloat`` trait by which almost all functions
+//! are parametrized. One might think that it's enough to parse to `f64` and cast the result to
+//! `f32`. Unfortunately this is not the world we live in, and this has nothing to do with using
+//! base two or half-to-even rounding.
+//!
+//! Consider for example two types `d2` and `d4` representing a decimal type with two decimal
+//! digits and four decimal digits each and take "0.01499" as input. Let's use half-up rounding.
+//! Going directly to two decimal digits gives `0.01`, but if we round to four digits first,
+//! we get `0.0150`, which is then rounded up to `0.02`. The same principle applies to other
+//! operations as well, if you want 0.5 ULP accuracy you need to do *everything* in full precision
+//! and round *exactly once, at the end*, by considering all truncated bits at once.
+//!
+//! Primarily, this module and its children implement the algorithms described in:
+//! "Number Parsing at a Gigabyte per Second", available online:
+//! <https://arxiv.org/abs/2101.11408>.
+//!
+//! # Other
+//!
+//! The conversion should *never* panic. There are assertions and explicit panics in the code,
+//! but they should never be triggered and only serve as internal sanity checks. Any panics should
+//! be considered a bug.
+//!
+//! There are unit tests but they are woefully inadequate at ensuring correctness, they only cover
+//! a small percentage of possible errors. Far more extensive tests are located in the directory
+//! `src/etc/test-float-parse` as a Python script.
+//!
+//! A note on integer overflow: Many parts of this file perform arithmetic with the decimal
+//! exponent `e`. Primarily, we shift the decimal point around: Before the first decimal digit,
+//! after the last decimal digit, and so on. This could overflow if done carelessly. We rely on
+//! the parsing submodule to only hand out sufficiently small exponents, where "sufficient" means
+//! "such that the exponent +/- the number of decimal digits fits into a 64 bit integer".
+//! Larger exponents are accepted, but we don't do arithmetic with them, they are immediately
+//! turned into {positive,negative} {zero,infinity}.
+
+#![doc(hidden)]
+#![unstable(
+    feature = "dec2flt",
+    reason = "internal routines only exposed for testing",
+    issue = "none"
+)]
+
+use crate::fmt;
+use crate::str::FromStr;
+
+use self::common::{BiasedFp, ByteSlice};
+use self::float::RawFloat;
+use self::lemire::compute_float;
+use self::parse::{parse_inf_nan, parse_number};
+use self::slow::parse_long_mantissa;
+
+mod common;
+mod decimal;
+mod fpu;
+mod slow;
+mod table;
+// float is used in flt2dec, and all are used in unit tests.
+pub mod float;
+pub mod lemire;
+pub mod number;
+pub mod parse;
+
+macro_rules! from_str_float_impl {
+    ($t:ty) => {
+        #[stable(feature = "rust1", since = "1.0.0")]
+        impl FromStr for $t {
+            type Err = ParseFloatError;
+
+            /// Converts a string in base 10 to a float.
+            /// Accepts an optional decimal exponent.
+            ///
+            /// This function accepts strings such as
+            ///
+            /// * '3.14'
+            /// * '-3.14'
+            /// * '2.5E10', or equivalently, '2.5e10'
+            /// * '2.5E-10'
+            /// * '5.'
+            /// * '.5', or, equivalently, '0.5'
+            /// * 'inf', '-inf', '+infinity', 'NaN'
+            ///
+            /// Note that alphabetical characters are not case-sensitive.
+            ///
+            /// Leading and trailing whitespace represent an error.
+            ///
+            /// # Grammar
+            ///
+            /// All strings that adhere to the following [EBNF] grammar when
+            /// lowercased will result in an [`Ok`] being returned:
+            ///
+            /// ```txt
+            /// Float  ::= Sign? ( 'inf' | 'infinity' | 'nan' | Number )
+            /// Number ::= ( Digit+ |
+            ///              Digit+ '.' Digit* |
+            ///              Digit* '.' Digit+ ) Exp?
+            /// Exp    ::= 'e' Sign? Digit+
+            /// Sign   ::= [+-]
+            /// Digit  ::= [0-9]
+            /// ```
+            ///
+            /// [EBNF]: https://www.w3.org/TR/REC-xml/#sec-notation
+            ///
+            /// # Arguments
+            ///
+            /// * src - A string
+            ///
+            /// # Return value
+            ///
+            /// `Err(ParseFloatError)` if the string did not represent a valid
+            /// number. Otherwise, `Ok(n)` where `n` is the closest
+            /// representable floating-point number to the number represented
+            /// by `src` (following the same rules for rounding as for the
+            /// results of primitive operations).
+            #[inline]
+            fn from_str(src: &str) -> Result<Self, ParseFloatError> {
+                dec2flt(src)
+            }
+        }
+    };
+}
+from_str_float_impl!(f32);
+from_str_float_impl!(f64);
+
+/// An error which can be returned when parsing a float.
+///
+/// This error is used as the error type for the [`FromStr`] implementation
+/// for [`f32`] and [`f64`].
+///
+/// # Example
+///
+/// ```
+/// use std::str::FromStr;
+///
+/// if let Err(e) = f64::from_str("a.12") {
+///     println!("Failed conversion to f64: {e}");
+/// }
+/// ```
+#[derive(Debug, Clone, PartialEq, Eq)]
+#[stable(feature = "rust1", since = "1.0.0")]
+pub struct ParseFloatError {
+    kind: FloatErrorKind,
+}
+
+#[derive(Debug, Clone, PartialEq, Eq)]
+enum FloatErrorKind {
+    Empty,
+    Invalid,
+}
+
+impl ParseFloatError {
+    #[unstable(
+        feature = "int_error_internals",
+        reason = "available through Error trait and this method should \
+                  not be exposed publicly",
+        issue = "none"
+    )]
+    #[doc(hidden)]
+    pub fn __description(&self) -> &str {
+        match self.kind {
+            FloatErrorKind::Empty => "cannot parse float from empty string",
+            FloatErrorKind::Invalid => "invalid float literal",
+        }
+    }
+}
+
+#[stable(feature = "rust1", since = "1.0.0")]
+impl fmt::Display for ParseFloatError {
+    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
+        self.__description().fmt(f)
+    }
+}
+
+pub(super) fn pfe_empty() -> ParseFloatError {
+    ParseFloatError { kind: FloatErrorKind::Empty }
+}
+
+// Used in unit tests, keep public.
+// This is much better than making FloatErrorKind and ParseFloatError::kind public.
+pub fn pfe_invalid() -> ParseFloatError {
+    ParseFloatError { kind: FloatErrorKind::Invalid }
+}
+
+/// Converts a `BiasedFp` to the closest machine float type.
+fn biased_fp_to_float<T: RawFloat>(x: BiasedFp) -> T {
+    let mut word = x.f;
+    word |= (x.e as u64) << T::MANTISSA_EXPLICIT_BITS;
+    T::from_u64_bits(word)
+}
+
+/// Converts a decimal string into a floating point number.
+pub fn dec2flt<F: RawFloat>(s: &str) -> Result<F, ParseFloatError> {
+    let mut s = s.as_bytes();
+    let c = if let Some(&c) = s.first() {
+        c
+    } else {
+        return Err(pfe_empty());
+    };
+    let negative = c == b'-';
+    if c == b'-' || c == b'+' {
+        s = s.advance(1);
+    }
+    if s.is_empty() {
+        return Err(pfe_invalid());
+    }
+
+    let num = match parse_number(s, negative) {
+        Some(r) => r,
+        None if let Some(value) = parse_inf_nan(s, negative) => return Ok(value),
+        None => return Err(pfe_invalid()),
+    };
+    if let Some(value) = num.try_fast_path::<F>() {
+        return Ok(value);
+    }
+
+    // If significant digits were truncated, then we can have rounding error
+    // only if `mantissa + 1` produces a different result. We also avoid
+    // redundantly using the Eisel-Lemire algorithm if it was unable to
+    // correctly round on the first pass.
+    let mut fp = compute_float::<F>(num.exponent, num.mantissa);
+    if num.many_digits && fp.e >= 0 && fp != compute_float::<F>(num.exponent, num.mantissa + 1) {
+        fp.e = -1;
+    }
+    // Unable to correctly round the float using the Eisel-Lemire algorithm.
+    // Fallback to a slower, but always correct algorithm.
+    if fp.e < 0 {
+        fp = parse_long_mantissa::<F>(s);
+    }
+
+    let mut float = biased_fp_to_float::<F>(fp);
+    if num.negative {
+        float = -float;
+    }
+    Ok(float)
+}
diff --git a/library/core/src/num/dec2flt/number.rs b/library/core/src/num/dec2flt/number.rs
new file mode 100644
index 000000000..405f7e7b6
--- /dev/null
+++ b/library/core/src/num/dec2flt/number.rs
@@ -0,0 +1,86 @@
+//! Representation of a float as the significant digits and exponent.
+
+use crate::num::dec2flt::float::RawFloat;
+use crate::num::dec2flt::fpu::set_precision;
+
+#[rustfmt::skip]
+const INT_POW10: [u64; 16] = [
+    1,
+    10,
+    100,
+    1000,
+    10000,
+    100000,
+    1000000,
+    10000000,
+    100000000,
+    1000000000,
+    10000000000,
+    100000000000,
+    1000000000000,
+    10000000000000,
+    100000000000000,
+    1000000000000000,
+];
+
+#[derive(Clone, Copy, Debug, Default, PartialEq, Eq)]
+pub struct Number {
+    pub exponent: i64,
+    pub mantissa: u64,
+    pub negative: bool,
+    pub many_digits: bool,
+}
+
+impl Number {
+    /// Detect if the float can be accurately reconstructed from native floats.
+    fn is_fast_path<F: RawFloat>(&self) -> bool {
+        F::MIN_EXPONENT_FAST_PATH <= self.exponent
+            && self.exponent <= F::MAX_EXPONENT_DISGUISED_FAST_PATH
+            && self.mantissa <= F::MAX_MANTISSA_FAST_PATH
+            && !self.many_digits
+    }
+
+    /// The fast path algorithm using machine-sized integers and floats.
+    ///
+    /// This is extracted into a separate function so that it can be attempted before constructing
+    /// a Decimal. This only works if both the mantissa and the exponent
+    /// can be exactly represented as a machine float, since IEE-754 guarantees
+    /// no rounding will occur.
+    ///
+    /// There is an exception: disguised fast-path cases, where we can shift
+    /// powers-of-10 from the exponent to the significant digits.
+    pub fn try_fast_path<F: RawFloat>(&self) -> Option<F> {
+        // The fast path crucially depends on arithmetic being rounded to the correct number of bits
+        // without any intermediate rounding. On x86 (without SSE or SSE2) this requires the precision
+        // of the x87 FPU stack to be changed so that it directly rounds to 64/32 bit.
+        // The `set_precision` function takes care of setting the precision on architectures which
+        // require setting it by changing the global state (like the control word of the x87 FPU).
+        let _cw = set_precision::<F>();
+
+        if self.is_fast_path::<F>() {
+            let mut value = if self.exponent <= F::MAX_EXPONENT_FAST_PATH {
+                // normal fast path
+                let value = F::from_u64(self.mantissa);
+                if self.exponent < 0 {
+                    value / F::pow10_fast_path((-self.exponent) as _)
+                } else {
+                    value * F::pow10_fast_path(self.exponent as _)
+                }
+            } else {
+                // disguised fast path
+                let shift = self.exponent - F::MAX_EXPONENT_FAST_PATH;
+                let mantissa = self.mantissa.checked_mul(INT_POW10[shift as usize])?;
+                if mantissa > F::MAX_MANTISSA_FAST_PATH {
+                    return None;
+                }
+                F::from_u64(mantissa) * F::pow10_fast_path(F::MAX_EXPONENT_FAST_PATH as _)
+            };
+            if self.negative {
+                value = -value;
+            }
+            Some(value)
+        } else {
+            None
+        }
+    }
+}
diff --git a/library/core/src/num/dec2flt/parse.rs b/library/core/src/num/dec2flt/parse.rs
new file mode 100644
index 000000000..1a90e0d20
--- /dev/null
+++ b/library/core/src/num/dec2flt/parse.rs
@@ -0,0 +1,233 @@
+//! Functions to parse floating-point numbers.
+
+use crate::num::dec2flt::common::{is_8digits, AsciiStr, ByteSlice};
+use crate::num::dec2flt::float::RawFloat;
+use crate::num::dec2flt::number::Number;
+
+const MIN_19DIGIT_INT: u64 = 100_0000_0000_0000_0000;
+
+/// Parse 8 digits, loaded as bytes in little-endian order.
+///
+/// This uses the trick where every digit is in [0x030, 0x39],
+/// and therefore can be parsed in 3 multiplications, much
+/// faster than the normal 8.
+///
+/// This is based off the algorithm described in "Fast numeric string to
+/// int", available here: <https://johnnylee-sde.github.io/Fast-numeric-string-to-int/>.
+fn parse_8digits(mut v: u64) -> u64 {
+    const MASK: u64 = 0x0000_00FF_0000_00FF;
+    const MUL1: u64 = 0x000F_4240_0000_0064;
+    const MUL2: u64 = 0x0000_2710_0000_0001;
+    v -= 0x3030_3030_3030_3030;
+    v = (v * 10) + (v >> 8); // will not overflow, fits in 63 bits
+    let v1 = (v & MASK).wrapping_mul(MUL1);
+    let v2 = ((v >> 16) & MASK).wrapping_mul(MUL2);
+    ((v1.wrapping_add(v2) >> 32) as u32) as u64
+}
+
+/// Parse digits until a non-digit character is found.
+fn try_parse_digits(s: &mut AsciiStr<'_>, x: &mut u64) {
+    // may cause overflows, to be handled later
+    s.parse_digits(|digit| {
+        *x = x.wrapping_mul(10).wrapping_add(digit as _);
+    });
+}
+
+/// Parse up to 19 digits (the max that can be stored in a 64-bit integer).
+fn try_parse_19digits(s: &mut AsciiStr<'_>, x: &mut u64) {
+    while *x < MIN_19DIGIT_INT {
+        if let Some(&c) = s.as_ref().first() {
+            let digit = c.wrapping_sub(b'0');
+            if digit < 10 {
+                *x = (*x * 10) + digit as u64; // no overflows here
+                // SAFETY: cannot be empty
+                unsafe {
+                    s.step();
+                }
+            } else {
+                break;
+            }
+        } else {
+            break;
+        }
+    }
+}
+
+/// Try to parse 8 digits at a time, using an optimized algorithm.
+fn try_parse_8digits(s: &mut AsciiStr<'_>, x: &mut u64) {
+    // may cause overflows, to be handled later
+    if let Some(v) = s.read_u64() {
+        if is_8digits(v) {
+            *x = x.wrapping_mul(1_0000_0000).wrapping_add(parse_8digits(v));
+            // SAFETY: already ensured the buffer was >= 8 bytes in read_u64.
+            unsafe {
+                s.step_by(8);
+            }
+            if let Some(v) = s.read_u64() {
+                if is_8digits(v) {
+                    *x = x.wrapping_mul(1_0000_0000).wrapping_add(parse_8digits(v));
+                    // SAFETY: already ensured the buffer was >= 8 bytes in try_read_u64.
+                    unsafe {
+                        s.step_by(8);
+                    }
+                }
+            }
+        }
+    }
+}
+
+/// Parse the scientific notation component of a float.
+fn parse_scientific(s: &mut AsciiStr<'_>) -> Option<i64> {
+    let mut exponent = 0_i64;
+    let mut negative = false;
+    if let Some(&c) = s.as_ref().get(0) {
+        negative = c == b'-';
+        if c == b'-' || c == b'+' {
+            // SAFETY: s cannot be empty
+            unsafe {
+                s.step();
+            }
+        }
+    }
+    if s.first_isdigit() {
+        s.parse_digits(|digit| {
+            // no overflows here, saturate well before overflow
+            if exponent < 0x10000 {
+                exponent = 10 * exponent + digit as i64;
+            }
+        });
+        if negative { Some(-exponent) } else { Some(exponent) }
+    } else {
+        None
+    }
+}
+
+/// Parse a partial, non-special floating point number.
+///
+/// This creates a representation of the float as the
+/// significant digits and the decimal exponent.
+fn parse_partial_number(s: &[u8], negative: bool) -> Option<(Number, usize)> {
+    let mut s = AsciiStr::new(s);
+    let start = s;
+    debug_assert!(!s.is_empty());
+
+    // parse initial digits before dot
+    let mut mantissa = 0_u64;
+    let digits_start = s;
+    try_parse_digits(&mut s, &mut mantissa);
+    let mut n_digits = s.offset_from(&digits_start);
+
+    // handle dot with the following digits
+    let mut n_after_dot = 0;
+    let mut exponent = 0_i64;
+    let int_end = s;
+    if s.first_is(b'.') {
+        // SAFETY: s cannot be empty due to first_is
+        unsafe { s.step() };
+        let before = s;
+        try_parse_8digits(&mut s, &mut mantissa);
+        try_parse_digits(&mut s, &mut mantissa);
+        n_after_dot = s.offset_from(&before);
+        exponent = -n_after_dot as i64;
+    }
+
+    n_digits += n_after_dot;
+    if n_digits == 0 {
+        return None;
+    }
+
+    // handle scientific format
+    let mut exp_number = 0_i64;
+    if s.first_is2(b'e', b'E') {
+        // SAFETY: s cannot be empty
+        unsafe {
+            s.step();
+        }
+        // If None, we have no trailing digits after exponent, or an invalid float.
+        exp_number = parse_scientific(&mut s)?;
+        exponent += exp_number;
+    }
+
+    let len = s.offset_from(&start) as _;
+
+    // handle uncommon case with many digits
+    if n_digits <= 19 {
+        return Some((Number { exponent, mantissa, negative, many_digits: false }, len));
+    }
+
+    n_digits -= 19;
+    let mut many_digits = false;
+    let mut p = digits_start;
+    while p.first_is2(b'0', b'.') {
+        // SAFETY: p cannot be empty due to first_is2
+        unsafe {
+            // '0' = b'.' + 2
+            n_digits -= p.first_unchecked().saturating_sub(b'0' - 1) as isize;
+            p.step();
+        }
+    }
+    if n_digits > 0 {
+        // at this point we have more than 19 significant digits, let's try again
+        many_digits = true;
+        mantissa = 0;
+        let mut s = digits_start;
+        try_parse_19digits(&mut s, &mut mantissa);
+        exponent = if mantissa >= MIN_19DIGIT_INT {
+            // big int
+            int_end.offset_from(&s)
+        } else {
+            // SAFETY: the next byte must be present and be '.'
+            // We know this is true because we had more than 19
+            // digits previously, so we overflowed a 64-bit integer,
+            // but parsing only the integral digits produced less
+            // than 19 digits. That means we must have a decimal
+            // point, and at least 1 fractional digit.
+            unsafe { s.step() };
+            let before = s;
+            try_parse_19digits(&mut s, &mut mantissa);
+            -s.offset_from(&before)
+        } as i64;
+        // add back the explicit part
+        exponent += exp_number;
+    }
+
+    Some((Number { exponent, mantissa, negative, many_digits }, len))
+}
+
+/// Try to parse a non-special floating point number.
+pub fn parse_number(s: &[u8], negative: bool) -> Option<Number> {
+    if let Some((float, rest)) = parse_partial_number(s, negative) {
+        if rest == s.len() {
+            return Some(float);
+        }
+    }
+    None
+}
+
+/// Parse a partial representation of a special, non-finite float.
+fn parse_partial_inf_nan<F: RawFloat>(s: &[u8]) -> Option<(F, usize)> {
+    fn parse_inf_rest(s: &[u8]) -> usize {
+        if s.len() >= 8 && s[3..].as_ref().starts_with_ignore_case(b"inity") { 8 } else { 3 }
+    }
+    if s.len() >= 3 {
+        if s.starts_with_ignore_case(b"nan") {
+            return Some((F::NAN, 3));
+        } else if s.starts_with_ignore_case(b"inf") {
+            return Some((F::INFINITY, parse_inf_rest(s)));
+        }
+    }
+    None
+}
+
+/// Try to parse a special, non-finite float.
+pub fn parse_inf_nan<F: RawFloat>(s: &[u8], negative: bool) -> Option<F> {
+    if let Some((mut float, rest)) = parse_partial_inf_nan::<F>(s) {
+        if rest == s.len() {
+            if negative {
+                float = -float;
+            }
+            return Some(float);
+        }
+    }
+    None
+}
diff --git a/library/core/src/num/dec2flt/slow.rs b/library/core/src/num/dec2flt/slow.rs
new file mode 100644
index 000000000..bf1044033
--- /dev/null
+++ b/library/core/src/num/dec2flt/slow.rs
@@ -0,0 +1,109 @@
+//! Slow, fallback algorithm for cases the Eisel-Lemire algorithm cannot round.
+
+use crate::num::dec2flt::common::BiasedFp;
+use crate::num::dec2flt::decimal::{parse_decimal, Decimal};
+use crate::num::dec2flt::float::RawFloat;
+
+/// Parse the significant digits and biased, binary exponent of a float.
+///
+/// This is a fallback algorithm that uses a big-integer representation
+/// of the float, and therefore is considerably slower than faster
+/// approximations. However, it will always determine how to round
+/// the significant digits to the nearest machine float, allowing
+/// use to handle near half-way cases.
+///
+/// Near half-way cases are halfway between two consecutive machine floats.
+/// For example, the float `16777217.0` has a bitwise representation of
+/// `100000000000000000000000 1`. Rounding to a single-precision float,
+/// the trailing `1` is truncated. Using round-nearest, tie-even, any
+/// value above `16777217.0` must be rounded up to `16777218.0`, while
+/// any value before or equal to `16777217.0` must be rounded down
+/// to `16777216.0`. These near-halfway conversions therefore may require
+/// a large number of digits to unambiguously determine how to round.
+///
+/// The algorithms described here are based on "Processing Long Numbers Quickly",
+/// available here: <https://arxiv.org/pdf/2101.11408.pdf#section.11>.
+pub(crate) fn parse_long_mantissa<F: RawFloat>(s: &[u8]) -> BiasedFp {
+    const MAX_SHIFT: usize = 60;
+    const NUM_POWERS: usize = 19;
+    const POWERS: [u8; 19] =
+        [0, 3, 6, 9, 13, 16, 19, 23, 26, 29, 33, 36, 39, 43, 46, 49, 53, 56, 59];
+
+    let get_shift = |n| {
+        if n < NUM_POWERS { POWERS[n] as usize } else { MAX_SHIFT }
+    };
+
+    let fp_zero = BiasedFp::zero_pow2(0);
+    let fp_inf = BiasedFp::zero_pow2(F::INFINITE_POWER);
+
+    let mut d = parse_decimal(s);
+
+    // Short-circuit if the value can only be a literal 0 or infinity.
+    if d.num_digits == 0 || d.decimal_point < -324 {
+        return fp_zero;
+    } else if d.decimal_point >= 310 {
+        return fp_inf;
+    }
+    let mut exp2 = 0_i32;
+    // Shift right toward (1/2 ... 1].
+    while d.decimal_point > 0 {
+        let n = d.decimal_point as usize;
+        let shift = get_shift(n);
+        d.right_shift(shift);
+        if d.decimal_point < -Decimal::DECIMAL_POINT_RANGE {
+            return fp_zero;
+        }
+        exp2 += shift as i32;
+    }
+    // Shift left toward (1/2 ... 1].
+    while d.decimal_point <= 0 {
+        let shift = if d.decimal_point == 0 {
+            match d.digits[0] {
+                digit if digit >= 5 => break,
+                0 | 1 => 2,
+                _ => 1,
+            }
+        } else {
+            get_shift((-d.decimal_point) as _)
+        };
+        d.left_shift(shift);
+        if d.decimal_point > Decimal::DECIMAL_POINT_RANGE {
+            return fp_inf;
+        }
+        exp2 -= shift as i32;
+    }
+    // We are now in the range [1/2 ... 1] but the binary format uses [1 ... 2].
+    exp2 -= 1;
+    while (F::MINIMUM_EXPONENT + 1) > exp2 {
+        let mut n = ((F::MINIMUM_EXPONENT + 1) - exp2) as usize;
+        if n > MAX_SHIFT {
+            n = MAX_SHIFT;
+        }
+        d.right_shift(n);
+        exp2 += n as i32;
+    }
+    if (exp2 - F::MINIMUM_EXPONENT) >= F::INFINITE_POWER {
+        return fp_inf;
+    }
+    // Shift the decimal to the hidden bit, and then round the value
+    // to get the high mantissa+1 bits.
+    d.left_shift(F::MANTISSA_EXPLICIT_BITS + 1);
+    let mut mantissa = d.round();
+    if mantissa >= (1_u64 << (F::MANTISSA_EXPLICIT_BITS + 1)) {
+        // Rounding up overflowed to the carry bit, need to
+        // shift back to the hidden bit.
+        d.right_shift(1);
+        exp2 += 1;
+        mantissa = d.round();
+        if (exp2 - F::MINIMUM_EXPONENT) >= F::INFINITE_POWER {
+            return fp_inf;
+        }
+    }
+    let mut power2 = exp2 - F::MINIMUM_EXPONENT;
+    if mantissa < (1_u64 << F::MANTISSA_EXPLICIT_BITS) {
+        power2 -= 1;
+    }
+    // Zero out all the bits above the explicit mantissa bits.
+    mantissa &= (1_u64 << F::MANTISSA_EXPLICIT_BITS) - 1;
+    BiasedFp { f: mantissa, e: power2 }
+}
diff --git a/library/core/src/num/dec2flt/table.rs b/library/core/src/num/dec2flt/table.rs
new file mode 100644
index 000000000..4856074a6
--- /dev/null
+++ b/library/core/src/num/dec2flt/table.rs
@@ -0,0 +1,670 @@
+//! Pre-computed tables powers-of-5 for extended-precision representations.
+//!
+//! These tables enable fast scaling of the significant digits
+//! of a float to the decimal exponent, with minimal rounding
+//! errors, in a 128 or 192-bit representation.
+//!
+//! DO NOT MODIFY: Generated by `src/etc/dec2flt_table.py`
+
+pub const SMALLEST_POWER_OF_FIVE: i32 = -342;
+pub const LARGEST_POWER_OF_FIVE: i32 = 308;
+pub const N_POWERS_OF_FIVE: usize = (LARGEST_POWER_OF_FIVE - SMALLEST_POWER_OF_FIVE + 1) as usize;
+
+// Use static to avoid long compile times: Rust compiler errors
+// can have the entire table compiled multiple times, and then
+// emit code multiple times, even if it's stripped out in
+// the final binary.
+#[rustfmt::skip]
+pub static POWER_OF_FIVE_128: [(u64, u64); N_POWERS_OF_FIVE] = [
+    (0xeef453d6923bd65a, 0x113faa2906a13b3f), // 5^-342
+    (0x9558b4661b6565f8, 0x4ac7ca59a424c507), // 5^-341
+    (0xbaaee17fa23ebf76, 0x5d79bcf00d2df649), // 5^-340
+    (0xe95a99df8ace6f53, 0xf4d82c2c107973dc), // 5^-339
+    (0x91d8a02bb6c10594, 0x79071b9b8a4be869), // 5^-338
+    (0xb64ec836a47146f9, 0x9748e2826cdee284), // 5^-337
+    (0xe3e27a444d8d98b7, 0xfd1b1b2308169b25), // 5^-336
+    (0x8e6d8c6ab0787f72, 0xfe30f0f5e50e20f7), // 5^-335
+    (0xb208ef855c969f4f, 0xbdbd2d335e51a935), // 5^-334
+    (0xde8b2b66b3bc4723, 0xad2c788035e61382), // 5^-333
+    (0x8b16fb203055ac76, 0x4c3bcb5021afcc31), // 5^-332
+    (0xaddcb9e83c6b1793, 0xdf4abe242a1bbf3d), // 5^-331
+    (0xd953e8624b85dd78, 0xd71d6dad34a2af0d), // 5^-330
+    (0x87d4713d6f33aa6b, 0x8672648c40e5ad68), // 5^-329
+    (0xa9c98d8ccb009506, 0x680efdaf511f18c2), // 5^-328
+    (0xd43bf0effdc0ba48, 0x212bd1b2566def2),  // 5^-327
+    (0x84a57695fe98746d, 0x14bb630f7604b57),  // 5^-326
+    (0xa5ced43b7e3e9188, 0x419ea3bd35385e2d), // 5^-325
+    (0xcf42894a5dce35ea, 0x52064cac828675b9), // 5^-324
+    (0x818995ce7aa0e1b2, 0x7343efebd1940993), // 5^-323
+    (0xa1ebfb4219491a1f, 0x1014ebe6c5f90bf8), // 5^-322
+    (0xca66fa129f9b60a6, 0xd41a26e077774ef6), // 5^-321
+    (0xfd00b897478238d0, 0x8920b098955522b4), // 5^-320
+    (0x9e20735e8cb16382, 0x55b46e5f5d5535b0), // 5^-319
+    (0xc5a890362fddbc62, 0xeb2189f734aa831d), // 5^-318
+    (0xf712b443bbd52b7b, 0xa5e9ec7501d523e4), // 5^-317
+    (0x9a6bb0aa55653b2d, 0x47b233c92125366e), // 5^-316
+    (0xc1069cd4eabe89f8, 0x999ec0bb696e840a), // 5^-315
+    (0xf148440a256e2c76, 0xc00670ea43ca250d), // 5^-314
+    (0x96cd2a865764dbca, 0x380406926a5e5728), // 5^-313
+    (0xbc807527ed3e12bc, 0xc605083704f5ecf2), // 5^-312
+    (0xeba09271e88d976b, 0xf7864a44c633682e), // 5^-311
+    (0x93445b8731587ea3, 0x7ab3ee6afbe0211d), // 5^-310
+    (0xb8157268fdae9e4c, 0x5960ea05bad82964), // 5^-309
+    (0xe61acf033d1a45df, 0x6fb92487298e33bd), // 5^-308
+    (0x8fd0c16206306bab, 0xa5d3b6d479f8e056), // 5^-307
+    (0xb3c4f1ba87bc8696, 0x8f48a4899877186c), // 5^-306
+    (0xe0b62e2929aba83c, 0x331acdabfe94de87), // 5^-305
+    (0x8c71dcd9ba0b4925, 0x9ff0c08b7f1d0b14), // 5^-304
+    (0xaf8e5410288e1b6f, 0x7ecf0ae5ee44dd9),  // 5^-303
+    (0xdb71e91432b1a24a, 0xc9e82cd9f69d6150), // 5^-302
+    (0x892731ac9faf056e, 0xbe311c083a225cd2), // 5^-301
+    (0xab70fe17c79ac6ca, 0x6dbd630a48aaf406), // 5^-300
+    (0xd64d3d9db981787d, 0x92cbbccdad5b108),  // 5^-299
+    (0x85f0468293f0eb4e, 0x25bbf56008c58ea5), // 5^-298
+    (0xa76c582338ed2621, 0xaf2af2b80af6f24e), // 5^-297
+    (0xd1476e2c07286faa, 0x1af5af660db4aee1), // 5^-296
+    (0x82cca4db847945ca, 0x50d98d9fc890ed4d), // 5^-295
+    (0xa37fce126597973c, 0xe50ff107bab528a0), // 5^-294
+    (0xcc5fc196fefd7d0c, 0x1e53ed49a96272c8), // 5^-293
+    (0xff77b1fcbebcdc4f, 0x25e8e89c13bb0f7a), // 5^-292
+    (0x9faacf3df73609b1, 0x77b191618c54e9ac), // 5^-291
+    (0xc795830d75038c1d, 0xd59df5b9ef6a2417), // 5^-290
+    (0xf97ae3d0d2446f25, 0x4b0573286b44ad1d), // 5^-289
+    (0x9becce62836ac577, 0x4ee367f9430aec32), // 5^-288
+    (0xc2e801fb244576d5, 0x229c41f793cda73f), // 5^-287
+    (0xf3a20279ed56d48a, 0x6b43527578c1110f), // 5^-286
+    (0x9845418c345644d6, 0x830a13896b78aaa9), // 5^-285
+    (0xbe5691ef416bd60c, 0x23cc986bc656d553), // 5^-284
+    (0xedec366b11c6cb8f, 0x2cbfbe86b7ec8aa8), // 5^-283
+    (0x94b3a202eb1c3f39, 0x7bf7d71432f3d6a9), // 5^-282
+    (0xb9e08a83a5e34f07, 0xdaf5ccd93fb0cc53), // 5^-281
+    (0xe858ad248f5c22c9, 0xd1b3400f8f9cff68), // 5^-280
+    (0x91376c36d99995be, 0x23100809b9c21fa1), // 5^-279
+    (0xb58547448ffffb2d, 0xabd40a0c2832a78a), // 5^-278
+    (0xe2e69915b3fff9f9, 0x16c90c8f323f516c), // 5^-277
+    (0x8dd01fad907ffc3b, 0xae3da7d97f6792e3), // 5^-276
+    (0xb1442798f49ffb4a, 0x99cd11cfdf41779c), // 5^-275
+    (0xdd95317f31c7fa1d, 0x40405643d711d583), // 5^-274
+    (0x8a7d3eef7f1cfc52, 0x482835ea666b2572), // 5^-273
+    (0xad1c8eab5ee43b66, 0xda3243650005eecf), // 5^-272
+    (0xd863b256369d4a40, 0x90bed43e40076a82), // 5^-271
+    (0x873e4f75e2224e68, 0x5a7744a6e804a291), // 5^-270
+    (0xa90de3535aaae202, 0x711515d0a205cb36), // 5^-269
+    (0xd3515c2831559a83, 0xd5a5b44ca873e03),  // 5^-268
+    (0x8412d9991ed58091, 0xe858790afe9486c2), // 5^-267
+    (0xa5178fff668ae0b6, 0x626e974dbe39a872), // 5^-266
+    (0xce5d73ff402d98e3, 0xfb0a3d212dc8128f), // 5^-265
+    (0x80fa687f881c7f8e, 0x7ce66634bc9d0b99), // 5^-264
+    (0xa139029f6a239f72, 0x1c1fffc1ebc44e80), // 5^-263
+    (0xc987434744ac874e, 0xa327ffb266b56220), // 5^-262
+    (0xfbe9141915d7a922, 0x4bf1ff9f0062baa8), // 5^-261
+    (0x9d71ac8fada6c9b5, 0x6f773fc3603db4a9), // 5^-260
+    (0xc4ce17b399107c22, 0xcb550fb4384d21d3), // 5^-259
+    (0xf6019da07f549b2b, 0x7e2a53a146606a48), // 5^-258
+    (0x99c102844f94e0fb, 0x2eda7444cbfc426d), // 5^-257
+    (0xc0314325637a1939, 0xfa911155fefb5308), // 5^-256
+    (0xf03d93eebc589f88, 0x793555ab7eba27ca), // 5^-255
+    (0x96267c7535b763b5, 0x4bc1558b2f3458de), // 5^-254
+    (0xbbb01b9283253ca2, 0x9eb1aaedfb016f16), // 5^-253
+    (0xea9c227723ee8bcb, 0x465e15a979c1cadc), // 5^-252
+    (0x92a1958a7675175f, 0xbfacd89ec191ec9),  // 5^-251
+    (0xb749faed14125d36, 0xcef980ec671f667b), // 5^-250
+    (0xe51c79a85916f484, 0x82b7e12780e7401a), // 5^-249
+    (0x8f31cc0937ae58d2, 0xd1b2ecb8b0908810), // 5^-248
+    (0xb2fe3f0b8599ef07, 0x861fa7e6dcb4aa15), // 5^-247
+    (0xdfbdcece67006ac9, 0x67a791e093e1d49a), // 5^-246
+    (0x8bd6a141006042bd, 0xe0c8bb2c5c6d24e0), // 5^-245
+    (0xaecc49914078536d, 0x58fae9f773886e18), // 5^-244
+    (0xda7f5bf590966848, 0xaf39a475506a899e), // 5^-243
+    (0x888f99797a5e012d, 0x6d8406c952429603), // 5^-242
+    (0xaab37fd7d8f58178, 0xc8e5087ba6d33b83), // 5^-241
+    (0xd5605fcdcf32e1d6, 0xfb1e4a9a90880a64), // 5^-240
+    (0x855c3be0a17fcd26, 0x5cf2eea09a55067f), // 5^-239
+    (0xa6b34ad8c9dfc06f, 0xf42faa48c0ea481e), // 5^-238
+    (0xd0601d8efc57b08b, 0xf13b94daf124da26), // 5^-237
+    (0x823c12795db6ce57, 0x76c53d08d6b70858), // 5^-236
+    (0xa2cb1717b52481ed, 0x54768c4b0c64ca6e), // 5^-235
+    (0xcb7ddcdda26da268, 0xa9942f5dcf7dfd09), // 5^-234
+    (0xfe5d54150b090b02, 0xd3f93b35435d7c4c), // 5^-233
+    (0x9efa548d26e5a6e1, 0xc47bc5014a1a6daf), // 5^-232
+    (0xc6b8e9b0709f109a, 0x359ab6419ca1091b), // 5^-231
+    (0xf867241c8cc6d4c0, 0xc30163d203c94b62), // 5^-230
+    (0x9b407691d7fc44f8, 0x79e0de63425dcf1d), // 5^-229
+    (0xc21094364dfb5636, 0x985915fc12f542e4), // 5^-228
+    (0xf294b943e17a2bc4, 0x3e6f5b7b17b2939d), // 5^-227
+    (0x979cf3ca6cec5b5a, 0xa705992ceecf9c42), // 5^-226
+    (0xbd8430bd08277231, 0x50c6ff782a838353), // 5^-225
+    (0xece53cec4a314ebd, 0xa4f8bf5635246428), // 5^-224
+    (0x940f4613ae5ed136, 0x871b7795e136be99), // 5^-223
+    (0xb913179899f68584, 0x28e2557b59846e3f), // 5^-222
+    (0xe757dd7ec07426e5, 0x331aeada2fe589cf), // 5^-221
+    (0x9096ea6f3848984f, 0x3ff0d2c85def7621), // 5^-220
+    (0xb4bca50b065abe63, 0xfed077a756b53a9),  // 5^-219
+    (0xe1ebce4dc7f16dfb, 0xd3e8495912c62894), // 5^-218
+    (0x8d3360f09cf6e4bd, 0x64712dd7abbbd95c), // 5^-217
+    (0xb080392cc4349dec, 0xbd8d794d96aacfb3), // 5^-216
+    (0xdca04777f541c567, 0xecf0d7a0fc5583a0), // 5^-215
+    (0x89e42caaf9491b60, 0xf41686c49db57244), // 5^-214
+    (0xac5d37d5b79b6239, 0x311c2875c522ced5), // 5^-213
+    (0xd77485cb25823ac7, 0x7d633293366b828b), // 5^-212
+    (0x86a8d39ef77164bc, 0xae5dff9c02033197), // 5^-211
+    (0xa8530886b54dbdeb, 0xd9f57f830283fdfc), // 5^-210
+    (0xd267caa862a12d66, 0xd072df63c324fd7b), // 5^-209
+    (0x8380dea93da4bc60, 0x4247cb9e59f71e6d), // 5^-208
+    (0xa46116538d0deb78, 0x52d9be85f074e608), // 5^-207
+    (0xcd795be870516656, 0x67902e276c921f8b), // 5^-206
+    (0x806bd9714632dff6, 0xba1cd8a3db53b6),   // 5^-205
+    (0xa086cfcd97bf97f3, 0x80e8a40eccd228a4), // 5^-204
+    (0xc8a883c0fdaf7df0, 0x6122cd128006b2cd), // 5^-203
+    (0xfad2a4b13d1b5d6c, 0x796b805720085f81), // 5^-202
+    (0x9cc3a6eec6311a63, 0xcbe3303674053bb0), // 5^-201
+    (0xc3f490aa77bd60fc, 0xbedbfc4411068a9c), // 5^-200
+    (0xf4f1b4d515acb93b, 0xee92fb5515482d44), // 5^-199
+    (0x991711052d8bf3c5, 0x751bdd152d4d1c4a), // 5^-198
+    (0xbf5cd54678eef0b6, 0xd262d45a78a0635d), // 5^-197
+    (0xef340a98172aace4, 0x86fb897116c87c34), // 5^-196
+    (0x9580869f0e7aac0e, 0xd45d35e6ae3d4da0), // 5^-195
+    (0xbae0a846d2195712, 0x8974836059cca109), // 5^-194
+    (0xe998d258869facd7, 0x2bd1a438703fc94b), // 5^-193
+    (0x91ff83775423cc06, 0x7b6306a34627ddcf), // 5^-192
+    (0xb67f6455292cbf08, 0x1a3bc84c17b1d542), // 5^-191
+    (0xe41f3d6a7377eeca, 0x20caba5f1d9e4a93), // 5^-190
+    (0x8e938662882af53e, 0x547eb47b7282ee9c), // 5^-189
+    (0xb23867fb2a35b28d, 0xe99e619a4f23aa43), // 5^-188
+    (0xdec681f9f4c31f31, 0x6405fa00e2ec94d4), // 5^-187
+    (0x8b3c113c38f9f37e, 0xde83bc408dd3dd04), // 5^-186
+    (0xae0b158b4738705e, 0x9624ab50b148d445), // 5^-185
+    (0xd98ddaee19068c76, 0x3badd624dd9b0957), // 5^-184
+    (0x87f8a8d4cfa417c9, 0xe54ca5d70a80e5d6), // 5^-183
+    (0xa9f6d30a038d1dbc, 0x5e9fcf4ccd211f4c), // 5^-182
+    (0xd47487cc8470652b, 0x7647c3200069671f), // 5^-181
+    (0x84c8d4dfd2c63f3b, 0x29ecd9f40041e073), // 5^-180
+    (0xa5fb0a17c777cf09, 0xf468107100525890), // 5^-179
+    (0xcf79cc9db955c2cc, 0x7182148d4066eeb4), // 5^-178
+    (0x81ac1fe293d599bf, 0xc6f14cd848405530), // 5^-177
+    (0xa21727db38cb002f, 0xb8ada00e5a506a7c), // 5^-176
+    (0xca9cf1d206fdc03b, 0xa6d90811f0e4851c), // 5^-175
+    (0xfd442e4688bd304a, 0x908f4a166d1da663), // 5^-174
+    (0x9e4a9cec15763e2e, 0x9a598e4e043287fe), // 5^-173
+    (0xc5dd44271ad3cdba, 0x40eff1e1853f29fd), // 5^-172
+    (0xf7549530e188c128, 0xd12bee59e68ef47c), // 5^-171
+    (0x9a94dd3e8cf578b9, 0x82bb74f8301958ce), // 5^-170
+    (0xc13a148e3032d6e7, 0xe36a52363c1faf01), // 5^-169
+    (0xf18899b1bc3f8ca1, 0xdc44e6c3cb279ac1), // 5^-168
+    (0x96f5600f15a7b7e5, 0x29ab103a5ef8c0b9), // 5^-167
+    (0xbcb2b812db11a5de, 0x7415d448f6b6f0e7), // 5^-166
+    (0xebdf661791d60f56, 0x111b495b3464ad21), // 5^-165
+    (0x936b9fcebb25c995, 0xcab10dd900beec34), // 5^-164
+    (0xb84687c269ef3bfb, 0x3d5d514f40eea742), // 5^-163
+    (0xe65829b3046b0afa, 0xcb4a5a3112a5112),  // 5^-162
+    (0x8ff71a0fe2c2e6dc, 0x47f0e785eaba72ab), // 5^-161
+    (0xb3f4e093db73a093, 0x59ed216765690f56), // 5^-160
+    (0xe0f218b8d25088b8, 0x306869c13ec3532c), // 5^-159
+    (0x8c974f7383725573, 0x1e414218c73a13fb), // 5^-158
+    (0xafbd2350644eeacf, 0xe5d1929ef90898fa), // 5^-157
+    (0xdbac6c247d62a583, 0xdf45f746b74abf39), // 5^-156
+    (0x894bc396ce5da772, 0x6b8bba8c328eb783), // 5^-155
+    (0xab9eb47c81f5114f, 0x66ea92f3f326564),  // 5^-154
+    (0xd686619ba27255a2, 0xc80a537b0efefebd), // 5^-153
+    (0x8613fd0145877585, 0xbd06742ce95f5f36), // 5^-152
+    (0xa798fc4196e952e7, 0x2c48113823b73704), // 5^-151
+    (0xd17f3b51fca3a7a0, 0xf75a15862ca504c5), // 5^-150
+    (0x82ef85133de648c4, 0x9a984d73dbe722fb), // 5^-149
+    (0xa3ab66580d5fdaf5, 0xc13e60d0d2e0ebba), // 5^-148
+    (0xcc963fee10b7d1b3, 0x318df905079926a8), // 5^-147
+    (0xffbbcfe994e5c61f, 0xfdf17746497f7052), // 5^-146
+    (0x9fd561f1fd0f9bd3, 0xfeb6ea8bedefa633), // 5^-145
+    (0xc7caba6e7c5382c8, 0xfe64a52ee96b8fc0), // 5^-144
+    (0xf9bd690a1b68637b, 0x3dfdce7aa3c673b0), // 5^-143
+    (0x9c1661a651213e2d, 0x6bea10ca65c084e),  // 5^-142
+    (0xc31bfa0fe5698db8, 0x486e494fcff30a62), // 5^-141
+    (0xf3e2f893dec3f126, 0x5a89dba3c3efccfa), // 5^-140
+    (0x986ddb5c6b3a76b7, 0xf89629465a75e01c), // 5^-139
+    (0xbe89523386091465, 0xf6bbb397f1135823), // 5^-138
+    (0xee2ba6c0678b597f, 0x746aa07ded582e2c), // 5^-137
+    (0x94db483840b717ef, 0xa8c2a44eb4571cdc), // 5^-136
+    (0xba121a4650e4ddeb, 0x92f34d62616ce413), // 5^-135
+    (0xe896a0d7e51e1566, 0x77b020baf9c81d17), // 5^-134
+    (0x915e2486ef32cd60, 0xace1474dc1d122e),  // 5^-133
+    (0xb5b5ada8aaff80b8, 0xd819992132456ba),  // 5^-132
+    (0xe3231912d5bf60e6, 0x10e1fff697ed6c69), // 5^-131
+    (0x8df5efabc5979c8f, 0xca8d3ffa1ef463c1), // 5^-130
+    (0xb1736b96b6fd83b3, 0xbd308ff8a6b17cb2), // 5^-129
+    (0xddd0467c64bce4a0, 0xac7cb3f6d05ddbde), // 5^-128
+    (0x8aa22c0dbef60ee4, 0x6bcdf07a423aa96b), // 5^-127
+    (0xad4ab7112eb3929d, 0x86c16c98d2c953c6), // 5^-126
+    (0xd89d64d57a607744, 0xe871c7bf077ba8b7), // 5^-125
+    (0x87625f056c7c4a8b, 0x11471cd764ad4972), // 5^-124
+    (0xa93af6c6c79b5d2d, 0xd598e40d3dd89bcf), // 5^-123
+    (0xd389b47879823479, 0x4aff1d108d4ec2c3), // 5^-122
+    (0x843610cb4bf160cb, 0xcedf722a585139ba), // 5^-121
+    (0xa54394fe1eedb8fe, 0xc2974eb4ee658828), // 5^-120
+    (0xce947a3da6a9273e, 0x733d226229feea32), // 5^-119
+    (0x811ccc668829b887, 0x806357d5a3f525f),  // 5^-118
+    (0xa163ff802a3426a8, 0xca07c2dcb0cf26f7), // 5^-117
+    (0xc9bcff6034c13052, 0xfc89b393dd02f0b5), // 5^-116
+    (0xfc2c3f3841f17c67, 0xbbac2078d443ace2), // 5^-115
+    (0x9d9ba7832936edc0, 0xd54b944b84aa4c0d), // 5^-114
+    (0xc5029163f384a931, 0xa9e795e65d4df11),  // 5^-113
+    (0xf64335bcf065d37d, 0x4d4617b5ff4a16d5), // 5^-112
+    (0x99ea0196163fa42e, 0x504bced1bf8e4e45), // 5^-111
+    (0xc06481fb9bcf8d39, 0xe45ec2862f71e1d6), // 5^-110
+    (0xf07da27a82c37088, 0x5d767327bb4e5a4c), // 5^-109
+    (0x964e858c91ba2655, 0x3a6a07f8d510f86f), // 5^-108
+    (0xbbe226efb628afea, 0x890489f70a55368b), // 5^-107
+    (0xeadab0aba3b2dbe5, 0x2b45ac74ccea842e), // 5^-106
+    (0x92c8ae6b464fc96f, 0x3b0b8bc90012929d), // 5^-105
+    (0xb77ada0617e3bbcb, 0x9ce6ebb40173744),  // 5^-104
+    (0xe55990879ddcaabd, 0xcc420a6a101d0515), // 5^-103
+    (0x8f57fa54c2a9eab6, 0x9fa946824a12232d), // 5^-102
+    (0xb32df8e9f3546564, 0x47939822dc96abf9), // 5^-101
+    (0xdff9772470297ebd, 0x59787e2b93bc56f7), // 5^-100
+    (0x8bfbea76c619ef36, 0x57eb4edb3c55b65a), // 5^-99
+    (0xaefae51477a06b03, 0xede622920b6b23f1), // 5^-98
+    (0xdab99e59958885c4, 0xe95fab368e45eced), // 5^-97
+    (0x88b402f7fd75539b, 0x11dbcb0218ebb414), // 5^-96
+    (0xaae103b5fcd2a881, 0xd652bdc29f26a119), // 5^-95
+    (0xd59944a37c0752a2, 0x4be76d3346f0495f), // 5^-94
+    (0x857fcae62d8493a5, 0x6f70a4400c562ddb), // 5^-93
+    (0xa6dfbd9fb8e5b88e, 0xcb4ccd500f6bb952), // 5^-92
+    (0xd097ad07a71f26b2, 0x7e2000a41346a7a7), // 5^-91
+    (0x825ecc24c873782f, 0x8ed400668c0c28c8), // 5^-90
+    (0xa2f67f2dfa90563b, 0x728900802f0f32fa), // 5^-89
+    (0xcbb41ef979346bca, 0x4f2b40a03ad2ffb9), // 5^-88
+    (0xfea126b7d78186bc, 0xe2f610c84987bfa8), // 5^-87
+    (0x9f24b832e6b0f436, 0xdd9ca7d2df4d7c9),  // 5^-86
+    (0xc6ede63fa05d3143, 0x91503d1c79720dbb), // 5^-85
+    (0xf8a95fcf88747d94, 0x75a44c6397ce912a), // 5^-84
+    (0x9b69dbe1b548ce7c, 0xc986afbe3ee11aba), // 5^-83
+    (0xc24452da229b021b, 0xfbe85badce996168), // 5^-82
+    (0xf2d56790ab41c2a2, 0xfae27299423fb9c3), // 5^-81
+    (0x97c560ba6b0919a5, 0xdccd879fc967d41a), // 5^-80
+    (0xbdb6b8e905cb600f, 0x5400e987bbc1c920), // 5^-79
+    (0xed246723473e3813, 0x290123e9aab23b68), // 5^-78
+    (0x9436c0760c86e30b, 0xf9a0b6720aaf6521), // 5^-77
+    (0xb94470938fa89bce, 0xf808e40e8d5b3e69), // 5^-76
+    (0xe7958cb87392c2c2, 0xb60b1d1230b20e04), // 5^-75
+    (0x90bd77f3483bb9b9, 0xb1c6f22b5e6f48c2), // 5^-74
+    (0xb4ecd5f01a4aa828, 0x1e38aeb6360b1af3), // 5^-73
+    (0xe2280b6c20dd5232, 0x25c6da63c38de1b0), // 5^-72
+    (0x8d590723948a535f, 0x579c487e5a38ad0e), // 5^-71
+    (0xb0af48ec79ace837, 0x2d835a9df0c6d851), // 5^-70
+    (0xdcdb1b2798182244, 0xf8e431456cf88e65), // 5^-69
+    (0x8a08f0f8bf0f156b, 0x1b8e9ecb641b58ff), // 5^-68
+    (0xac8b2d36eed2dac5, 0xe272467e3d222f3f), // 5^-67
+    (0xd7adf884aa879177, 0x5b0ed81dcc6abb0f), // 5^-66
+    (0x86ccbb52ea94baea, 0x98e947129fc2b4e9), // 5^-65
+    (0xa87fea27a539e9a5, 0x3f2398d747b36224), // 5^-64
+    (0xd29fe4b18e88640e, 0x8eec7f0d19a03aad), // 5^-63
+    (0x83a3eeeef9153e89, 0x1953cf68300424ac), // 5^-62
+    (0xa48ceaaab75a8e2b, 0x5fa8c3423c052dd7), // 5^-61
+    (0xcdb02555653131b6, 0x3792f412cb06794d), // 5^-60
+    (0x808e17555f3ebf11, 0xe2bbd88bbee40bd0), // 5^-59
+    (0xa0b19d2ab70e6ed6, 0x5b6aceaeae9d0ec4), // 5^-58
+    (0xc8de047564d20a8b, 0xf245825a5a445275), // 5^-57
+    (0xfb158592be068d2e, 0xeed6e2f0f0d56712), // 5^-56
+    (0x9ced737bb6c4183d, 0x55464dd69685606b), // 5^-55
+    (0xc428d05aa4751e4c, 0xaa97e14c3c26b886), // 5^-54
+    (0xf53304714d9265df, 0xd53dd99f4b3066a8), // 5^-53
+    (0x993fe2c6d07b7fab, 0xe546a8038efe4029), // 5^-52
+    (0xbf8fdb78849a5f96, 0xde98520472bdd033), // 5^-51
+    (0xef73d256a5c0f77c, 0x963e66858f6d4440), // 5^-50
+    (0x95a8637627989aad, 0xdde7001379a44aa8), // 5^-49
+    (0xbb127c53b17ec159, 0x5560c018580d5d52), // 5^-48
+    (0xe9d71b689dde71af, 0xaab8f01e6e10b4a6), // 5^-47
+    (0x9226712162ab070d, 0xcab3961304ca70e8), // 5^-46
+    (0xb6b00d69bb55c8d1, 0x3d607b97c5fd0d22), // 5^-45
+    (0xe45c10c42a2b3b05, 0x8cb89a7db77c506a), // 5^-44
+    (0x8eb98a7a9a5b04e3, 0x77f3608e92adb242), // 5^-43
+    (0xb267ed1940f1c61c, 0x55f038b237591ed3), // 5^-42
+    (0xdf01e85f912e37a3, 0x6b6c46dec52f6688), // 5^-41
+    (0x8b61313bbabce2c6, 0x2323ac4b3b3da015), // 5^-40
+    (0xae397d8aa96c1b77, 0xabec975e0a0d081a), // 5^-39
+    (0xd9c7dced53c72255, 0x96e7bd358c904a21), // 5^-38
+    (0x881cea14545c7575, 0x7e50d64177da2e54), // 5^-37
+    (0xaa242499697392d2, 0xdde50bd1d5d0b9e9), // 5^-36
+    (0xd4ad2dbfc3d07787, 0x955e4ec64b44e864), // 5^-35
+    (0x84ec3c97da624ab4, 0xbd5af13bef0b113e), // 5^-34
+    (0xa6274bbdd0fadd61, 0xecb1ad8aeacdd58e), // 5^-33
+    (0xcfb11ead453994ba, 0x67de18eda5814af2), // 5^-32
+    (0x81ceb32c4b43fcf4, 0x80eacf948770ced7), // 5^-31
+    (0xa2425ff75e14fc31, 0xa1258379a94d028d), // 5^-30
+    (0xcad2f7f5359a3b3e, 0x96ee45813a04330),  // 5^-29
+    (0xfd87b5f28300ca0d, 0x8bca9d6e188853fc), // 5^-28
+    (0x9e74d1b791e07e48, 0x775ea264cf55347e), // 5^-27
+    (0xc612062576589dda, 0x95364afe032a819e), // 5^-26
+    (0xf79687aed3eec551, 0x3a83ddbd83f52205), // 5^-25
+    (0x9abe14cd44753b52, 0xc4926a9672793543), // 5^-24
+    (0xc16d9a0095928a27, 0x75b7053c0f178294), // 5^-23
+    (0xf1c90080baf72cb1, 0x5324c68b12dd6339), // 5^-22
+    (0x971da05074da7bee, 0xd3f6fc16ebca5e04), // 5^-21
+    (0xbce5086492111aea, 0x88f4bb1ca6bcf585), // 5^-20
+    (0xec1e4a7db69561a5, 0x2b31e9e3d06c32e6), // 5^-19
+    (0x9392ee8e921d5d07, 0x3aff322e62439fd0), // 5^-18
+    (0xb877aa3236a4b449, 0x9befeb9fad487c3),  // 5^-17
+    (0xe69594bec44de15b, 0x4c2ebe687989a9b4), // 5^-16
+    (0x901d7cf73ab0acd9, 0xf9d37014bf60a11),  // 5^-15
+    (0xb424dc35095cd80f, 0x538484c19ef38c95), // 5^-14
+    (0xe12e13424bb40e13, 0x2865a5f206b06fba), // 5^-13
+    (0x8cbccc096f5088cb, 0xf93f87b7442e45d4), // 5^-12
+    (0xafebff0bcb24aafe, 0xf78f69a51539d749), // 5^-11
+    (0xdbe6fecebdedd5be, 0xb573440e5a884d1c), // 5^-10
+    (0x89705f4136b4a597, 0x31680a88f8953031), // 5^-9
+    (0xabcc77118461cefc, 0xfdc20d2b36ba7c3e), // 5^-8
+    (0xd6bf94d5e57a42bc, 0x3d32907604691b4d), // 5^-7
+    (0x8637bd05af6c69b5, 0xa63f9a49c2c1b110), // 5^-6
+    (0xa7c5ac471b478423, 0xfcf80dc33721d54),  // 5^-5
+    (0xd1b71758e219652b, 0xd3c36113404ea4a9), // 5^-4
+    (0x83126e978d4fdf3b, 0x645a1cac083126ea), // 5^-3
+    (0xa3d70a3d70a3d70a, 0x3d70a3d70a3d70a4), // 5^-2
+    (0xcccccccccccccccc, 0xcccccccccccccccd), // 5^-1
+    (0x8000000000000000, 0x0),                // 5^0
+    (0xa000000000000000, 0x0),                // 5^1
+    (0xc800000000000000, 0x0),                // 5^2
+    (0xfa00000000000000, 0x0),                // 5^3
+    (0x9c40000000000000, 0x0),                // 5^4
+    (0xc350000000000000, 0x0),                // 5^5
+    (0xf424000000000000, 0x0),                // 5^6
+    (0x9896800000000000, 0x0),                // 5^7
+    (0xbebc200000000000, 0x0),                // 5^8
+    (0xee6b280000000000, 0x0),                // 5^9
+    (0x9502f90000000000, 0x0),                // 5^10
+    (0xba43b74000000000, 0x0),                // 5^11
+    (0xe8d4a51000000000, 0x0),                // 5^12
+    (0x9184e72a00000000, 0x0),                // 5^13
+    (0xb5e620f480000000, 0x0),                // 5^14
+    (0xe35fa931a0000000, 0x0),                // 5^15
+    (0x8e1bc9bf04000000, 0x0),                // 5^16
+    (0xb1a2bc2ec5000000, 0x0),                // 5^17
+    (0xde0b6b3a76400000, 0x0),                // 5^18
+    (0x8ac7230489e80000, 0x0),                // 5^19
+    (0xad78ebc5ac620000, 0x0),                // 5^20
+    (0xd8d726b7177a8000, 0x0),                // 5^21
+    (0x878678326eac9000, 0x0),                // 5^22
+    (0xa968163f0a57b400, 0x0),                // 5^23
+    (0xd3c21bcecceda100, 0x0),                // 5^24
+    (0x84595161401484a0, 0x0),                // 5^25
+    (0xa56fa5b99019a5c8, 0x0),                // 5^26
+    (0xcecb8f27f4200f3a, 0x0),                // 5^27
+    (0x813f3978f8940984, 0x4000000000000000), // 5^28
+    (0xa18f07d736b90be5, 0x5000000000000000), // 5^29
+    (0xc9f2c9cd04674ede, 0xa400000000000000), // 5^30
+    (0xfc6f7c4045812296, 0x4d00000000000000), // 5^31
+    (0x9dc5ada82b70b59d, 0xf020000000000000), // 5^32
+    (0xc5371912364ce305, 0x6c28000000000000), // 5^33
+    (0xf684df56c3e01bc6, 0xc732000000000000), // 5^34
+    (0x9a130b963a6c115c, 0x3c7f400000000000), // 5^35
+    (0xc097ce7bc90715b3, 0x4b9f100000000000), // 5^36
+    (0xf0bdc21abb48db20, 0x1e86d40000000000), // 5^37
+    (0x96769950b50d88f4, 0x1314448000000000), // 5^38
+    (0xbc143fa4e250eb31, 0x17d955a000000000), // 5^39
+    (0xeb194f8e1ae525fd, 0x5dcfab0800000000), // 5^40
+    (0x92efd1b8d0cf37be, 0x5aa1cae500000000), // 5^41
+    (0xb7abc627050305ad, 0xf14a3d9e40000000), // 5^42
+    (0xe596b7b0c643c719, 0x6d9ccd05d0000000), // 5^43
+    (0x8f7e32ce7bea5c6f, 0xe4820023a2000000), // 5^44
+    (0xb35dbf821ae4f38b, 0xdda2802c8a800000), // 5^45
+    (0xe0352f62a19e306e, 0xd50b2037ad200000), // 5^46
+    (0x8c213d9da502de45, 0x4526f422cc340000), // 5^47
+    (0xaf298d050e4395d6, 0x9670b12b7f410000), // 5^48
+    (0xdaf3f04651d47b4c, 0x3c0cdd765f114000), // 5^49
+    (0x88d8762bf324cd0f, 0xa5880a69fb6ac800), // 5^50
+    (0xab0e93b6efee0053, 0x8eea0d047a457a00), // 5^51
+    (0xd5d238a4abe98068, 0x72a4904598d6d880), // 5^52
+    (0x85a36366eb71f041, 0x47a6da2b7f864750), // 5^53
+    (0xa70c3c40a64e6c51, 0x999090b65f67d924), // 5^54
+    (0xd0cf4b50cfe20765, 0xfff4b4e3f741cf6d), // 5^55
+    (0x82818f1281ed449f, 0xbff8f10e7a8921a4), // 5^56
+    (0xa321f2d7226895c7, 0xaff72d52192b6a0d), // 5^57
+    (0xcbea6f8ceb02bb39, 0x9bf4f8a69f764490), // 5^58
+    (0xfee50b7025c36a08, 0x2f236d04753d5b4),  // 5^59
+    (0x9f4f2726179a2245, 0x1d762422c946590),  // 5^60
+    (0xc722f0ef9d80aad6, 0x424d3ad2b7b97ef5), // 5^61
+    (0xf8ebad2b84e0d58b, 0xd2e0898765a7deb2), // 5^62
+    (0x9b934c3b330c8577, 0x63cc55f49f88eb2f), // 5^63
+    (0xc2781f49ffcfa6d5, 0x3cbf6b71c76b25fb), // 5^64
+    (0xf316271c7fc3908a, 0x8bef464e3945ef7a), // 5^65
+    (0x97edd871cfda3a56, 0x97758bf0e3cbb5ac), // 5^66
+    (0xbde94e8e43d0c8ec, 0x3d52eeed1cbea317), // 5^67
+    (0xed63a231d4c4fb27, 0x4ca7aaa863ee4bdd), // 5^68
+    (0x945e455f24fb1cf8, 0x8fe8caa93e74ef6a), // 5^69
+    (0xb975d6b6ee39e436, 0xb3e2fd538e122b44), // 5^70
+    (0xe7d34c64a9c85d44, 0x60dbbca87196b616), // 5^71
+    (0x90e40fbeea1d3a4a, 0xbc8955e946fe31cd), // 5^72
+    (0xb51d13aea4a488dd, 0x6babab6398bdbe41), // 5^73
+    (0xe264589a4dcdab14, 0xc696963c7eed2dd1), // 5^74
+    (0x8d7eb76070a08aec, 0xfc1e1de5cf543ca2), // 5^75
+    (0xb0de65388cc8ada8, 0x3b25a55f43294bcb), // 5^76
+    (0xdd15fe86affad912, 0x49ef0eb713f39ebe), // 5^77
+    (0x8a2dbf142dfcc7ab, 0x6e3569326c784337), // 5^78
+    (0xacb92ed9397bf996, 0x49c2c37f07965404), // 5^79
+    (0xd7e77a8f87daf7fb, 0xdc33745ec97be906), // 5^80
+    (0x86f0ac99b4e8dafd, 0x69a028bb3ded71a3), // 5^81
+    (0xa8acd7c0222311bc, 0xc40832ea0d68ce0c), // 5^82
+    (0xd2d80db02aabd62b, 0xf50a3fa490c30190), // 5^83
+    (0x83c7088e1aab65db, 0x792667c6da79e0fa), // 5^84
+    (0xa4b8cab1a1563f52, 0x577001b891185938), // 5^85
+    (0xcde6fd5e09abcf26, 0xed4c0226b55e6f86), // 5^86
+    (0x80b05e5ac60b6178, 0x544f8158315b05b4), // 5^87
+    (0xa0dc75f1778e39d6, 0x696361ae3db1c721), // 5^88
+    (0xc913936dd571c84c, 0x3bc3a19cd1e38e9),  // 5^89
+    (0xfb5878494ace3a5f, 0x4ab48a04065c723),  // 5^90
+    (0x9d174b2dcec0e47b, 0x62eb0d64283f9c76), // 5^91
+    (0xc45d1df942711d9a, 0x3ba5d0bd324f8394), // 5^92
+    (0xf5746577930d6500, 0xca8f44ec7ee36479), // 5^93
+    (0x9968bf6abbe85f20, 0x7e998b13cf4e1ecb), // 5^94
+    (0xbfc2ef456ae276e8, 0x9e3fedd8c321a67e), // 5^95
+    (0xefb3ab16c59b14a2, 0xc5cfe94ef3ea101e), // 5^96
+    (0x95d04aee3b80ece5, 0xbba1f1d158724a12), // 5^97
+    (0xbb445da9ca61281f, 0x2a8a6e45ae8edc97), // 5^98
+    (0xea1575143cf97226, 0xf52d09d71a3293bd), // 5^99
+    (0x924d692ca61be758, 0x593c2626705f9c56), // 5^100
+    (0xb6e0c377cfa2e12e, 0x6f8b2fb00c77836c), // 5^101
+    (0xe498f455c38b997a, 0xb6dfb9c0f956447),  // 5^102
+    (0x8edf98b59a373fec, 0x4724bd4189bd5eac), // 5^103
+    (0xb2977ee300c50fe7, 0x58edec91ec2cb657), // 5^104
+    (0xdf3d5e9bc0f653e1, 0x2f2967b66737e3ed), // 5^105
+    (0x8b865b215899f46c, 0xbd79e0d20082ee74), // 5^106
+    (0xae67f1e9aec07187, 0xecd8590680a3aa11), // 5^107
+    (0xda01ee641a708de9, 0xe80e6f4820cc9495), // 5^108
+    (0x884134fe908658b2, 0x3109058d147fdcdd), // 5^109
+    (0xaa51823e34a7eede, 0xbd4b46f0599fd415), // 5^110
+    (0xd4e5e2cdc1d1ea96, 0x6c9e18ac7007c91a), // 5^111
+    (0x850fadc09923329e, 0x3e2cf6bc604ddb0),  // 5^112
+    (0xa6539930bf6bff45, 0x84db8346b786151c), // 5^113
+    (0xcfe87f7cef46ff16, 0xe612641865679a63), // 5^114
+    (0x81f14fae158c5f6e, 0x4fcb7e8f3f60c07e), // 5^115
+    (0xa26da3999aef7749, 0xe3be5e330f38f09d), // 5^116
+    (0xcb090c8001ab551c, 0x5cadf5bfd3072cc5), // 5^117
+    (0xfdcb4fa002162a63, 0x73d9732fc7c8f7f6), // 5^118
+    (0x9e9f11c4014dda7e, 0x2867e7fddcdd9afa), // 5^119
+    (0xc646d63501a1511d, 0xb281e1fd541501b8), // 5^120
+    (0xf7d88bc24209a565, 0x1f225a7ca91a4226), // 5^121
+    (0x9ae757596946075f, 0x3375788de9b06958), // 5^122
+    (0xc1a12d2fc3978937, 0x52d6b1641c83ae),   // 5^123
+    (0xf209787bb47d6b84, 0xc0678c5dbd23a49a), // 5^124
+    (0x9745eb4d50ce6332, 0xf840b7ba963646e0), // 5^125
+    (0xbd176620a501fbff, 0xb650e5a93bc3d898), // 5^126
+    (0xec5d3fa8ce427aff, 0xa3e51f138ab4cebe), // 5^127
+    (0x93ba47c980e98cdf, 0xc66f336c36b10137), // 5^128
+    (0xb8a8d9bbe123f017, 0xb80b0047445d4184), // 5^129
+    (0xe6d3102ad96cec1d, 0xa60dc059157491e5), // 5^130
+    (0x9043ea1ac7e41392, 0x87c89837ad68db2f), // 5^131
+    (0xb454e4a179dd1877, 0x29babe4598c311fb), // 5^132
+    (0xe16a1dc9d8545e94, 0xf4296dd6fef3d67a), // 5^133
+    (0x8ce2529e2734bb1d, 0x1899e4a65f58660c), // 5^134
+    (0xb01ae745b101e9e4, 0x5ec05dcff72e7f8f), // 5^135
+    (0xdc21a1171d42645d, 0x76707543f4fa1f73), // 5^136
+    (0x899504ae72497eba, 0x6a06494a791c53a8), // 5^137
+    (0xabfa45da0edbde69, 0x487db9d17636892),  // 5^138
+    (0xd6f8d7509292d603, 0x45a9d2845d3c42b6), // 5^139
+    (0x865b86925b9bc5c2, 0xb8a2392ba45a9b2),  // 5^140
+    (0xa7f26836f282b732, 0x8e6cac7768d7141e), // 5^141
+    (0xd1ef0244af2364ff, 0x3207d795430cd926), // 5^142
+    (0x8335616aed761f1f, 0x7f44e6bd49e807b8), // 5^143
+    (0xa402b9c5a8d3a6e7, 0x5f16206c9c6209a6), // 5^144
+    (0xcd036837130890a1, 0x36dba887c37a8c0f), // 5^145
+    (0x802221226be55a64, 0xc2494954da2c9789), // 5^146
+    (0xa02aa96b06deb0fd, 0xf2db9baa10b7bd6c), // 5^147
+    (0xc83553c5c8965d3d, 0x6f92829494e5acc7), // 5^148
+    (0xfa42a8b73abbf48c, 0xcb772339ba1f17f9), // 5^149
+    (0x9c69a97284b578d7, 0xff2a760414536efb), // 5^150
+    (0xc38413cf25e2d70d, 0xfef5138519684aba), // 5^151
+    (0xf46518c2ef5b8cd1, 0x7eb258665fc25d69), // 5^152
+    (0x98bf2f79d5993802, 0xef2f773ffbd97a61), // 5^153
+    (0xbeeefb584aff8603, 0xaafb550ffacfd8fa), // 5^154
+    (0xeeaaba2e5dbf6784, 0x95ba2a53f983cf38), // 5^155
+    (0x952ab45cfa97a0b2, 0xdd945a747bf26183), // 5^156
+    (0xba756174393d88df, 0x94f971119aeef9e4), // 5^157
+    (0xe912b9d1478ceb17, 0x7a37cd5601aab85d), // 5^158
+    (0x91abb422ccb812ee, 0xac62e055c10ab33a), // 5^159
+    (0xb616a12b7fe617aa, 0x577b986b314d6009), // 5^160
+    (0xe39c49765fdf9d94, 0xed5a7e85fda0b80b), // 5^161
+    (0x8e41ade9fbebc27d, 0x14588f13be847307), // 5^162
+    (0xb1d219647ae6b31c, 0x596eb2d8ae258fc8), // 5^163
+    (0xde469fbd99a05fe3, 0x6fca5f8ed9aef3bb), // 5^164
+    (0x8aec23d680043bee, 0x25de7bb9480d5854), // 5^165
+    (0xada72ccc20054ae9, 0xaf561aa79a10ae6a), // 5^166
+    (0xd910f7ff28069da4, 0x1b2ba1518094da04), // 5^167
+    (0x87aa9aff79042286, 0x90fb44d2f05d0842), // 5^168
+    (0xa99541bf57452b28, 0x353a1607ac744a53), // 5^169
+    (0xd3fa922f2d1675f2, 0x42889b8997915ce8), // 5^170
+    (0x847c9b5d7c2e09b7, 0x69956135febada11), // 5^171
+    (0xa59bc234db398c25, 0x43fab9837e699095), // 5^172
+    (0xcf02b2c21207ef2e, 0x94f967e45e03f4bb), // 5^173
+    (0x8161afb94b44f57d, 0x1d1be0eebac278f5), // 5^174
+    (0xa1ba1ba79e1632dc, 0x6462d92a69731732), // 5^175
+    (0xca28a291859bbf93, 0x7d7b8f7503cfdcfe), // 5^176
+    (0xfcb2cb35e702af78, 0x5cda735244c3d43e), // 5^177
+    (0x9defbf01b061adab, 0x3a0888136afa64a7), // 5^178
+    (0xc56baec21c7a1916, 0x88aaa1845b8fdd0),  // 5^179
+    (0xf6c69a72a3989f5b, 0x8aad549e57273d45), // 5^180
+    (0x9a3c2087a63f6399, 0x36ac54e2f678864b), // 5^181
+    (0xc0cb28a98fcf3c7f, 0x84576a1bb416a7dd), // 5^182
+    (0xf0fdf2d3f3c30b9f, 0x656d44a2a11c51d5), // 5^183
+    (0x969eb7c47859e743, 0x9f644ae5a4b1b325), // 5^184
+    (0xbc4665b596706114, 0x873d5d9f0dde1fee), // 5^185
+    (0xeb57ff22fc0c7959, 0xa90cb506d155a7ea), // 5^186
+    (0x9316ff75dd87cbd8, 0x9a7f12442d588f2),  // 5^187
+    (0xb7dcbf5354e9bece, 0xc11ed6d538aeb2f),  // 5^188
+    (0xe5d3ef282a242e81, 0x8f1668c8a86da5fa), // 5^189
+    (0x8fa475791a569d10, 0xf96e017d694487bc), // 5^190
+    (0xb38d92d760ec4455, 0x37c981dcc395a9ac), // 5^191
+    (0xe070f78d3927556a, 0x85bbe253f47b1417), // 5^192
+    (0x8c469ab843b89562, 0x93956d7478ccec8e), // 5^193
+    (0xaf58416654a6babb, 0x387ac8d1970027b2), // 5^194
+    (0xdb2e51bfe9d0696a, 0x6997b05fcc0319e),  // 5^195
+    (0x88fcf317f22241e2, 0x441fece3bdf81f03), // 5^196
+    (0xab3c2fddeeaad25a, 0xd527e81cad7626c3), // 5^197
+    (0xd60b3bd56a5586f1, 0x8a71e223d8d3b074), // 5^198
+    (0x85c7056562757456, 0xf6872d5667844e49), // 5^199
+    (0xa738c6bebb12d16c, 0xb428f8ac016561db), // 5^200
+    (0xd106f86e69d785c7, 0xe13336d701beba52), // 5^201
+    (0x82a45b450226b39c, 0xecc0024661173473), // 5^202
+    (0xa34d721642b06084, 0x27f002d7f95d0190), // 5^203
+    (0xcc20ce9bd35c78a5, 0x31ec038df7b441f4), // 5^204
+    (0xff290242c83396ce, 0x7e67047175a15271), // 5^205
+    (0x9f79a169bd203e41, 0xf0062c6e984d386),  // 5^206
+    (0xc75809c42c684dd1, 0x52c07b78a3e60868), // 5^207
+    (0xf92e0c3537826145, 0xa7709a56ccdf8a82), // 5^208
+    (0x9bbcc7a142b17ccb, 0x88a66076400bb691), // 5^209
+    (0xc2abf989935ddbfe, 0x6acff893d00ea435), // 5^210
+    (0xf356f7ebf83552fe, 0x583f6b8c4124d43),  // 5^211
+    (0x98165af37b2153de, 0xc3727a337a8b704a), // 5^212
+    (0xbe1bf1b059e9a8d6, 0x744f18c0592e4c5c), // 5^213
+    (0xeda2ee1c7064130c, 0x1162def06f79df73), // 5^214
+    (0x9485d4d1c63e8be7, 0x8addcb5645ac2ba8), // 5^215
+    (0xb9a74a0637ce2ee1, 0x6d953e2bd7173692), // 5^216
+    (0xe8111c87c5c1ba99, 0xc8fa8db6ccdd0437), // 5^217
+    (0x910ab1d4db9914a0, 0x1d9c9892400a22a2), // 5^218
+    (0xb54d5e4a127f59c8, 0x2503beb6d00cab4b), // 5^219
+    (0xe2a0b5dc971f303a, 0x2e44ae64840fd61d), // 5^220
+    (0x8da471a9de737e24, 0x5ceaecfed289e5d2), // 5^221
+    (0xb10d8e1456105dad, 0x7425a83e872c5f47), // 5^222
+    (0xdd50f1996b947518, 0xd12f124e28f77719), // 5^223
+    (0x8a5296ffe33cc92f, 0x82bd6b70d99aaa6f), // 5^224
+    (0xace73cbfdc0bfb7b, 0x636cc64d1001550b), // 5^225
+    (0xd8210befd30efa5a, 0x3c47f7e05401aa4e), // 5^226
+    (0x8714a775e3e95c78, 0x65acfaec34810a71), // 5^227
+    (0xa8d9d1535ce3b396, 0x7f1839a741a14d0d), // 5^228
+    (0xd31045a8341ca07c, 0x1ede48111209a050), // 5^229
+    (0x83ea2b892091e44d, 0x934aed0aab460432), // 5^230
+    (0xa4e4b66b68b65d60, 0xf81da84d5617853f), // 5^231
+    (0xce1de40642e3f4b9, 0x36251260ab9d668e), // 5^232
+    (0x80d2ae83e9ce78f3, 0xc1d72b7c6b426019), // 5^233
+    (0xa1075a24e4421730, 0xb24cf65b8612f81f), // 5^234
+    (0xc94930ae1d529cfc, 0xdee033f26797b627), // 5^235
+    (0xfb9b7cd9a4a7443c, 0x169840ef017da3b1), // 5^236
+    (0x9d412e0806e88aa5, 0x8e1f289560ee864e), // 5^237
+    (0xc491798a08a2ad4e, 0xf1a6f2bab92a27e2), // 5^238
+    (0xf5b5d7ec8acb58a2, 0xae10af696774b1db), // 5^239
+    (0x9991a6f3d6bf1765, 0xacca6da1e0a8ef29), // 5^240
+    (0xbff610b0cc6edd3f, 0x17fd090a58d32af3), // 5^241
+    (0xeff394dcff8a948e, 0xddfc4b4cef07f5b0), // 5^242
+    (0x95f83d0a1fb69cd9, 0x4abdaf101564f98e), // 5^243
+    (0xbb764c4ca7a4440f, 0x9d6d1ad41abe37f1), // 5^244
+    (0xea53df5fd18d5513, 0x84c86189216dc5ed), // 5^245
+    (0x92746b9be2f8552c, 0x32fd3cf5b4e49bb4), // 5^246
+    (0xb7118682dbb66a77, 0x3fbc8c33221dc2a1), // 5^247
+    (0xe4d5e82392a40515, 0xfabaf3feaa5334a),  // 5^248
+    (0x8f05b1163ba6832d, 0x29cb4d87f2a7400e), // 5^249
+    (0xb2c71d5bca9023f8, 0x743e20e9ef511012), // 5^250
+    (0xdf78e4b2bd342cf6, 0x914da9246b255416), // 5^251
+    (0x8bab8eefb6409c1a, 0x1ad089b6c2f7548e), // 5^252
+    (0xae9672aba3d0c320, 0xa184ac2473b529b1), // 5^253
+    (0xda3c0f568cc4f3e8, 0xc9e5d72d90a2741e), // 5^254
+    (0x8865899617fb1871, 0x7e2fa67c7a658892), // 5^255
+    (0xaa7eebfb9df9de8d, 0xddbb901b98feeab7), // 5^256
+    (0xd51ea6fa85785631, 0x552a74227f3ea565), // 5^257
+    (0x8533285c936b35de, 0xd53a88958f87275f), // 5^258
+    (0xa67ff273b8460356, 0x8a892abaf368f137), // 5^259
+    (0xd01fef10a657842c, 0x2d2b7569b0432d85), // 5^260
+    (0x8213f56a67f6b29b, 0x9c3b29620e29fc73), // 5^261
+    (0xa298f2c501f45f42, 0x8349f3ba91b47b8f), // 5^262
+    (0xcb3f2f7642717713, 0x241c70a936219a73), // 5^263
+    (0xfe0efb53d30dd4d7, 0xed238cd383aa0110), // 5^264
+    (0x9ec95d1463e8a506, 0xf4363804324a40aa), // 5^265
+    (0xc67bb4597ce2ce48, 0xb143c6053edcd0d5), // 5^266
+    (0xf81aa16fdc1b81da, 0xdd94b7868e94050a), // 5^267
+    (0x9b10a4e5e9913128, 0xca7cf2b4191c8326), // 5^268
+    (0xc1d4ce1f63f57d72, 0xfd1c2f611f63a3f0), // 5^269
+    (0xf24a01a73cf2dccf, 0xbc633b39673c8cec), // 5^270
+    (0x976e41088617ca01, 0xd5be0503e085d813), // 5^271
+    (0xbd49d14aa79dbc82, 0x4b2d8644d8a74e18), // 5^272
+    (0xec9c459d51852ba2, 0xddf8e7d60ed1219e), // 5^273
+    (0x93e1ab8252f33b45, 0xcabb90e5c942b503), // 5^274
+    (0xb8da1662e7b00a17, 0x3d6a751f3b936243), // 5^275
+    (0xe7109bfba19c0c9d, 0xcc512670a783ad4),  // 5^276
+    (0x906a617d450187e2, 0x27fb2b80668b24c5), // 5^277
+    (0xb484f9dc9641e9da, 0xb1f9f660802dedf6), // 5^278
+    (0xe1a63853bbd26451, 0x5e7873f8a0396973), // 5^279
+    (0x8d07e33455637eb2, 0xdb0b487b6423e1e8), // 5^280
+    (0xb049dc016abc5e5f, 0x91ce1a9a3d2cda62), // 5^281
+    (0xdc5c5301c56b75f7, 0x7641a140cc7810fb), // 5^282
+    (0x89b9b3e11b6329ba, 0xa9e904c87fcb0a9d), // 5^283
+    (0xac2820d9623bf429, 0x546345fa9fbdcd44), // 5^284
+    (0xd732290fbacaf133, 0xa97c177947ad4095), // 5^285
+    (0x867f59a9d4bed6c0, 0x49ed8eabcccc485d), // 5^286
+    (0xa81f301449ee8c70, 0x5c68f256bfff5a74), // 5^287
+    (0xd226fc195c6a2f8c, 0x73832eec6fff3111), // 5^288
+    (0x83585d8fd9c25db7, 0xc831fd53c5ff7eab), // 5^289
+    (0xa42e74f3d032f525, 0xba3e7ca8b77f5e55), // 5^290
+    (0xcd3a1230c43fb26f, 0x28ce1bd2e55f35eb), // 5^291
+    (0x80444b5e7aa7cf85, 0x7980d163cf5b81b3), // 5^292
+    (0xa0555e361951c366, 0xd7e105bcc332621f), // 5^293
+    (0xc86ab5c39fa63440, 0x8dd9472bf3fefaa7), // 5^294
+    (0xfa856334878fc150, 0xb14f98f6f0feb951), // 5^295
+    (0x9c935e00d4b9d8d2, 0x6ed1bf9a569f33d3), // 5^296
+    (0xc3b8358109e84f07, 0xa862f80ec4700c8),  // 5^297
+    (0xf4a642e14c6262c8, 0xcd27bb612758c0fa), // 5^298
+    (0x98e7e9cccfbd7dbd, 0x8038d51cb897789c), // 5^299
+    (0xbf21e44003acdd2c, 0xe0470a63e6bd56c3), // 5^300
+    (0xeeea5d5004981478, 0x1858ccfce06cac74), // 5^301
+    (0x95527a5202df0ccb, 0xf37801e0c43ebc8),  // 5^302
+    (0xbaa718e68396cffd, 0xd30560258f54e6ba), // 5^303
+    (0xe950df20247c83fd, 0x47c6b82ef32a2069), // 5^304
+    (0x91d28b7416cdd27e, 0x4cdc331d57fa5441), // 5^305
+    (0xb6472e511c81471d, 0xe0133fe4adf8e952), // 5^306
+    (0xe3d8f9e563a198e5, 0x58180fddd97723a6), // 5^307
+    (0x8e679c2f5e44ff8f, 0x570f09eaa7ea7648), // 5^308
+];
diff --git a/library/core/src/num/diy_float.rs b/library/core/src/num/diy_float.rs
new file mode 100644
index 000000000..ce7f6475d
--- /dev/null
+++ b/library/core/src/num/diy_float.rs
@@ -0,0 +1,81 @@
+//! Extended precision "soft float", for internal use only.
+
+// This module is only for dec2flt and flt2dec, and only public because of coretests.
+// It is not intended to ever be stabilized.
+#![doc(hidden)]
+#![unstable(
+    feature = "core_private_diy_float",
+    reason = "internal routines only exposed for testing",
+    issue = "none"
+)]
+
+/// A custom 64-bit floating point type, representing `f * 2^e`.
+#[derive(Copy, Clone, Debug)]
+#[doc(hidden)]
+pub struct Fp {
+    /// The integer mantissa.
+    pub f: u64,
+    /// The exponent in base 2.
+    pub e: i16,
+}
+
+impl Fp {
+    /// Returns a correctly rounded product of itself and `other`.
+    pub fn mul(&self, other: &Fp) -> Fp {
+        const MASK: u64 = 0xffffffff;
+        let a = self.f >> 32;
+        let b = self.f & MASK;
+        let c = other.f >> 32;
+        let d = other.f & MASK;
+        let ac = a * c;
+        let bc = b * c;
+        let ad = a * d;
+        let bd = b * d;
+        let tmp = (bd >> 32) + (ad & MASK) + (bc & MASK) + (1 << 31) /* round */;
+        let f = ac + (ad >> 32) + (bc >> 32) + (tmp >> 32);
+        let e = self.e + other.e + 64;
+        Fp { f, e }
+    }
+
+    /// Normalizes itself so that the resulting mantissa is at least `2^63`.
+    pub fn normalize(&self) -> Fp {
+        let mut f = self.f;
+        let mut e = self.e;
+        if f >> (64 - 32) == 0 {
+            f <<= 32;
+            e -= 32;
+        }
+        if f >> (64 - 16) == 0 {
+            f <<= 16;
+            e -= 16;
+        }
+        if f >> (64 - 8) == 0 {
+            f <<= 8;
+            e -= 8;
+        }
+        if f >> (64 - 4) == 0 {
+            f <<= 4;
+            e -= 4;
+        }
+        if f >> (64 - 2) == 0 {
+            f <<= 2;
+            e -= 2;
+        }
+        if f >> (64 - 1) == 0 {
+            f <<= 1;
+            e -= 1;
+        }
+        debug_assert!(f >= (1 << 63));
+        Fp { f, e }
+    }
+
+    /// Normalizes itself to have the shared exponent.
+    /// It can only decrease the exponent (and thus increase the mantissa).
+    pub fn normalize_to(&self, e: i16) -> Fp {
+        let edelta = self.e - e;
+        assert!(edelta >= 0);
+        let edelta = edelta as usize;
+        assert_eq!(self.f << edelta >> edelta, self.f);
+        Fp { f: self.f << edelta, e }
+    }
+}
diff --git a/library/core/src/num/error.rs b/library/core/src/num/error.rs
new file mode 100644
index 000000000..1a223016d
--- /dev/null
+++ b/library/core/src/num/error.rs
@@ -0,0 +1,146 @@
+//! Error types for conversion to integral types.
+
+use crate::convert::Infallible;
+use crate::fmt;
+
+/// The error type returned when a checked integral type conversion fails.
+#[stable(feature = "try_from", since = "1.34.0")]
+#[derive(Debug, Copy, Clone, PartialEq, Eq)]
+pub struct TryFromIntError(pub(crate) ());
+
+impl TryFromIntError {
+    #[unstable(
+        feature = "int_error_internals",
+        reason = "available through Error trait and this method should \
+                  not be exposed publicly",
+        issue = "none"
+    )]
+    #[doc(hidden)]
+    pub fn __description(&self) -> &str {
+        "out of range integral type conversion attempted"
+    }
+}
+
+#[stable(feature = "try_from", since = "1.34.0")]
+impl fmt::Display for TryFromIntError {
+    fn fmt(&self, fmt: &mut fmt::Formatter<'_>) -> fmt::Result {
+        self.__description().fmt(fmt)
+    }
+}
+
+#[stable(feature = "try_from", since = "1.34.0")]
+#[rustc_const_unstable(feature = "const_convert", issue = "88674")]
+impl const From<Infallible> for TryFromIntError {
+    fn from(x: Infallible) -> TryFromIntError {
+        match x {}
+    }
+}
+
+#[unstable(feature = "never_type", issue = "35121")]
+impl const From<!> for TryFromIntError {
+    fn from(never: !) -> TryFromIntError {
+        // Match rather than coerce to make sure that code like
+        // `From<Infallible> for TryFromIntError` above will keep working
+        // when `Infallible` becomes an alias to `!`.
+        match never {}
+    }
+}
+
+/// An error which can be returned when parsing an integer.
+///
+/// This error is used as the error type for the `from_str_radix()` functions
+/// on the primitive integer types, such as [`i8::from_str_radix`].
+///
+/// # Potential causes
+///
+/// Among other causes, `ParseIntError` can be thrown because of leading or trailing whitespace
+/// in the string e.g., when it is obtained from the standard input.
+/// Using the [`str::trim()`] method ensures that no whitespace remains before parsing.
+///
+/// # Example
+///
+/// ```
+/// if let Err(e) = i32::from_str_radix("a12", 10) {
+///     println!("Failed conversion to i32: {e}");
+/// }
+/// ```
+#[derive(Debug, Clone, PartialEq, Eq)]
+#[stable(feature = "rust1", since = "1.0.0")]
+pub struct ParseIntError {
+    pub(super) kind: IntErrorKind,
+}
+
+/// Enum to store the various types of errors that can cause parsing an integer to fail.
+///
+/// # Example
+///
+/// ```
+/// # fn main() {
+/// if let Err(e) = i32::from_str_radix("a12", 10) {
+///     println!("Failed conversion to i32: {:?}", e.kind());
+/// }
+/// # }
+/// ```
+#[stable(feature = "int_error_matching", since = "1.55.0")]
+#[derive(Debug, Clone, PartialEq, Eq)]
+#[non_exhaustive]
+pub enum IntErrorKind {
+    /// Value being parsed is empty.
+    ///
+    /// This variant will be constructed when parsing an empty string.
+    #[stable(feature = "int_error_matching", since = "1.55.0")]
+    Empty,
+    /// Contains an invalid digit in its context.
+    ///
+    /// Among other causes, this variant will be constructed when parsing a string that
+    /// contains a non-ASCII char.
+    ///
+    /// This variant is also constructed when a `+` or `-` is misplaced within a string
+    /// either on its own or in the middle of a number.
+    #[stable(feature = "int_error_matching", since = "1.55.0")]
+    InvalidDigit,
+    /// Integer is too large to store in target integer type.
+    #[stable(feature = "int_error_matching", since = "1.55.0")]
+    PosOverflow,
+    /// Integer is too small to store in target integer type.
+    #[stable(feature = "int_error_matching", since = "1.55.0")]
+    NegOverflow,
+    /// Value was Zero
+    ///
+    /// This variant will be emitted when the parsing string has a value of zero, which
+    /// would be illegal for non-zero types.
+    #[stable(feature = "int_error_matching", since = "1.55.0")]
+    Zero,
+}
+
+impl ParseIntError {
+    /// Outputs the detailed cause of parsing an integer failing.
+    #[must_use]
+    #[stable(feature = "int_error_matching", since = "1.55.0")]
+    pub fn kind(&self) -> &IntErrorKind {
+        &self.kind
+    }
+    #[unstable(
+        feature = "int_error_internals",
+        reason = "available through Error trait and this method should \
+                  not be exposed publicly",
+        issue = "none"
+    )]
+    #[doc(hidden)]
+    pub fn __description(&self) -> &str {
+        match self.kind {
+            IntErrorKind::Empty => "cannot parse integer from empty string",
+            IntErrorKind::InvalidDigit => "invalid digit found in string",
+            IntErrorKind::PosOverflow => "number too large to fit in target type",
+            IntErrorKind::NegOverflow => "number too small to fit in target type",
+            IntErrorKind::Zero => "number would be zero for non-zero type",
+        }
+    }
+}
+
+#[stable(feature = "rust1", since = "1.0.0")]
+impl fmt::Display for ParseIntError {
+    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
+        self.__description().fmt(f)
+    }
+}
diff --git a/library/core/src/num/f32.rs b/library/core/src/num/f32.rs
new file mode 100644
index 000000000..6548ad2e5
--- /dev/null
+++ b/library/core/src/num/f32.rs
@@ -0,0 +1,1296 @@
+//! Constants specific to the `f32` single-precision floating point type.
+//!
+//! *[See also the `f32` primitive type][f32].*
+//!
+//! Mathematically significant numbers are provided in the `consts` sub-module.
+//!
+//! For the constants defined directly in this module
+//! (as distinct from those defined in the `consts` sub-module),
+//! new code should instead use the associated constants
+//! defined directly on the `f32` type.
+
+#![stable(feature = "rust1", since = "1.0.0")]
+
+use crate::convert::FloatToInt;
+#[cfg(not(test))]
+use crate::intrinsics;
+use crate::mem;
+use crate::num::FpCategory;
+
+/// The radix or base of the internal representation of `f32`.
+/// Use [`f32::RADIX`] instead.
+///
+/// # Examples
+///
+/// ```rust
+/// // deprecated way
+/// # #[allow(deprecated, deprecated_in_future)]
+/// let r = std::f32::RADIX;
+///
+/// // intended way
+/// let r = f32::RADIX;
+/// ```
+#[stable(feature = "rust1", since = "1.0.0")]
+#[deprecated(since = "TBD", note = "replaced by the `RADIX` associated constant on `f32`")]
+pub const RADIX: u32 = f32::RADIX;
+
+/// Number of significant digits in base 2.
+/// Use [`f32::MANTISSA_DIGITS`] instead.
+///
+/// # Examples
+///
+/// ```rust
+/// // deprecated way
+/// # #[allow(deprecated, deprecated_in_future)]
+/// let d = std::f32::MANTISSA_DIGITS;
+///
+/// // intended way
+/// let d = f32::MANTISSA_DIGITS;
+/// ```
+#[stable(feature = "rust1", since = "1.0.0")]
+#[deprecated(
+    since = "TBD",
+    note = "replaced by the `MANTISSA_DIGITS` associated constant on `f32`"
+)]
+pub const MANTISSA_DIGITS: u32 = f32::MANTISSA_DIGITS;
+
+/// Approximate number of significant digits in base 10.
+/// Use [`f32::DIGITS`] instead.
+///
+/// # Examples
+///
+/// ```rust
+/// // deprecated way
+/// # #[allow(deprecated, deprecated_in_future)]
+/// let d = std::f32::DIGITS;
+///
+/// // intended way
+/// let d = f32::DIGITS;
+/// ```
+#[stable(feature = "rust1", since = "1.0.0")]
+#[deprecated(since = "TBD", note = "replaced by the `DIGITS` associated constant on `f32`")]
+pub const DIGITS: u32 = f32::DIGITS;
+
+/// [Machine epsilon] value for `f32`.
+/// Use [`f32::EPSILON`] instead.
+///
+/// This is the difference between `1.0` and the next larger representable number.
+///
+/// [Machine epsilon]: https://en.wikipedia.org/wiki/Machine_epsilon
+///
+/// # Examples
+///
+/// ```rust
+/// // deprecated way
+/// # #[allow(deprecated, deprecated_in_future)]
+/// let e = std::f32::EPSILON;
+///
+/// // intended way
+/// let e = f32::EPSILON;
+/// ```
+#[stable(feature = "rust1", since = "1.0.0")]
+#[deprecated(since = "TBD", note = "replaced by the `EPSILON` associated constant on `f32`")]
+pub const EPSILON: f32 = f32::EPSILON;
+
+/// Smallest finite `f32` value.
+/// Use [`f32::MIN`] instead.
+///
+/// # Examples
+///
+/// ```rust
+/// // deprecated way
+/// # #[allow(deprecated, deprecated_in_future)]
+/// let min = std::f32::MIN;
+///
+/// // intended way
+/// let min = f32::MIN;
+/// ```
+#[stable(feature = "rust1", since = "1.0.0")]
+#[deprecated(since = "TBD", note = "replaced by the `MIN` associated constant on `f32`")]
+pub const MIN: f32 = f32::MIN;
+
+/// Smallest positive normal `f32` value.
+/// Use [`f32::MIN_POSITIVE`] instead.
+///
+/// # Examples
+///
+/// ```rust
+/// // deprecated way
+/// # #[allow(deprecated, deprecated_in_future)]
+/// let min = std::f32::MIN_POSITIVE;
+///
+/// // intended way
+/// let min = f32::MIN_POSITIVE;
+/// ```
+#[stable(feature = "rust1", since = "1.0.0")]
+#[deprecated(since = "TBD", note = "replaced by the `MIN_POSITIVE` associated constant on `f32`")]
+pub const MIN_POSITIVE: f32 = f32::MIN_POSITIVE;
+
+/// Largest finite `f32` value.
+/// Use [`f32::MAX`] instead.
+///
+/// # Examples
+///
+/// ```rust
+/// // deprecated way
+/// # #[allow(deprecated, deprecated_in_future)]
+/// let max = std::f32::MAX;
+///
+/// // intended way
+/// let max = f32::MAX;
+/// ```
+#[stable(feature = "rust1", since = "1.0.0")]
+#[deprecated(since = "TBD", note = "replaced by the `MAX` associated constant on `f32`")]
+pub const MAX: f32 = f32::MAX;
+
+/// One greater than the minimum possible normal power of 2 exponent.
+/// Use [`f32::MIN_EXP`] instead.
+///
+/// # Examples
+///
+/// ```rust
+/// // deprecated way
+/// # #[allow(deprecated, deprecated_in_future)]
+/// let min = std::f32::MIN_EXP;
+///
+/// // intended way
+/// let min = f32::MIN_EXP;
+/// ```
+#[stable(feature = "rust1", since = "1.0.0")]
+#[deprecated(since = "TBD", note = "replaced by the `MIN_EXP` associated constant on `f32`")]
+pub const MIN_EXP: i32 = f32::MIN_EXP;
+
+/// Maximum possible power of 2 exponent.
+/// Use [`f32::MAX_EXP`] instead.
+///
+/// # Examples
+///
+/// ```rust
+/// // deprecated way
+/// # #[allow(deprecated, deprecated_in_future)]
+/// let max = std::f32::MAX_EXP;
+///
+/// // intended way
+/// let max = f32::MAX_EXP;
+/// ```
+#[stable(feature = "rust1", since = "1.0.0")]
+#[deprecated(since = "TBD", note = "replaced by the `MAX_EXP` associated constant on `f32`")]
+pub const MAX_EXP: i32 = f32::MAX_EXP;
+
+/// Minimum possible normal power of 10 exponent.
+/// Use [`f32::MIN_10_EXP`] instead.
+///
+/// # Examples
+///
+/// ```rust
+/// // deprecated way
+/// # #[allow(deprecated, deprecated_in_future)]
+/// let min = std::f32::MIN_10_EXP;
+///
+/// // intended way
+/// let min = f32::MIN_10_EXP;
+/// ```
+#[stable(feature = "rust1", since = "1.0.0")]
+#[deprecated(since = "TBD", note = "replaced by the `MIN_10_EXP` associated constant on `f32`")]
+pub const MIN_10_EXP: i32 = f32::MIN_10_EXP;
+
+/// Maximum possible power of 10 exponent.
+/// Use [`f32::MAX_10_EXP`] instead.
+///
+/// # Examples
+///
+/// ```rust
+/// // deprecated way
+/// # #[allow(deprecated, deprecated_in_future)]
+/// let max = std::f32::MAX_10_EXP;
+///
+/// // intended way
+/// let max = f32::MAX_10_EXP;
+/// ```
+#[stable(feature = "rust1", since = "1.0.0")]
+#[deprecated(since = "TBD", note = "replaced by the `MAX_10_EXP` associated constant on `f32`")]
+pub const MAX_10_EXP: i32 = f32::MAX_10_EXP;
+
+/// Not a Number (NaN).
+/// Use [`f32::NAN`] instead.
+///
+/// # Examples
+///
+/// ```rust
+/// // deprecated way
+/// # #[allow(deprecated, deprecated_in_future)]
+/// let nan = std::f32::NAN;
+///
+/// // intended way
+/// let nan = f32::NAN;
+/// ```
+#[stable(feature = "rust1", since = "1.0.0")]
+#[deprecated(since = "TBD", note = "replaced by the `NAN` associated constant on `f32`")]
+pub const NAN: f32 = f32::NAN;
+
+/// Infinity (∞).
+/// Use [`f32::INFINITY`] instead.
+///
+/// # Examples
+///
+/// ```rust
+/// // deprecated way
+/// # #[allow(deprecated, deprecated_in_future)]
+/// let inf = std::f32::INFINITY;
+///
+/// // intended way
+/// let inf = f32::INFINITY;
+/// ```
+#[stable(feature = "rust1", since = "1.0.0")]
+#[deprecated(since = "TBD", note = "replaced by the `INFINITY` associated constant on `f32`")]
+pub const INFINITY: f32 = f32::INFINITY;
+
+/// Negative infinity (−∞).
+/// Use [`f32::NEG_INFINITY`] instead.
+///
+/// # Examples
+///
+/// ```rust
+/// // deprecated way
+/// # #[allow(deprecated, deprecated_in_future)]
+/// let ninf = std::f32::NEG_INFINITY;
+///
+/// // intended way
+/// let ninf = f32::NEG_INFINITY;
+/// ```
+#[stable(feature = "rust1", since = "1.0.0")]
+#[deprecated(since = "TBD", note = "replaced by the `NEG_INFINITY` associated constant on `f32`")]
+pub const NEG_INFINITY: f32 = f32::NEG_INFINITY;
+
+/// Basic mathematical constants.
+#[stable(feature = "rust1", since = "1.0.0")]
+pub mod consts {
+    // FIXME: replace with mathematical constants from cmath.
+
+    /// Archimedes' constant (π)
+    #[stable(feature = "rust1", since = "1.0.0")]
+    pub const PI: f32 = 3.14159265358979323846264338327950288_f32;
+
+    /// The full circle constant (τ)
+    ///
+    /// Equal to 2π.
+    #[stable(feature = "tau_constant", since = "1.47.0")]
+    pub const TAU: f32 = 6.28318530717958647692528676655900577_f32;
+
+    /// π/2
+    #[stable(feature = "rust1", since = "1.0.0")]
+    pub const FRAC_PI_2: f32 = 1.57079632679489661923132169163975144_f32;
+
+    /// π/3
+    #[stable(feature = "rust1", since = "1.0.0")]
+    pub const FRAC_PI_3: f32 = 1.04719755119659774615421446109316763_f32;
+
+    /// π/4
+    #[stable(feature = "rust1", since = "1.0.0")]
+    pub const FRAC_PI_4: f32 = 0.785398163397448309615660845819875721_f32;
+
+    /// π/6
+    #[stable(feature = "rust1", since = "1.0.0")]
+    pub const FRAC_PI_6: f32 = 0.52359877559829887307710723054658381_f32;
+
+    /// π/8
+    #[stable(feature = "rust1", since = "1.0.0")]
+    pub const FRAC_PI_8: f32 = 0.39269908169872415480783042290993786_f32;
+
+    /// 1/π
+    #[stable(feature = "rust1", since = "1.0.0")]
+    pub const FRAC_1_PI: f32 = 0.318309886183790671537767526745028724_f32;
+
+    /// 2/π
+    #[stable(feature = "rust1", since = "1.0.0")]
+    pub const FRAC_2_PI: f32 = 0.636619772367581343075535053490057448_f32;
+
+    /// 2/sqrt(π)
+    #[stable(feature = "rust1", since = "1.0.0")]
+    pub const FRAC_2_SQRT_PI: f32 = 1.12837916709551257389615890312154517_f32;
+
+    /// sqrt(2)
+    #[stable(feature = "rust1", since = "1.0.0")]
+    pub const SQRT_2: f32 = 1.41421356237309504880168872420969808_f32;
+
+    /// 1/sqrt(2)
+    #[stable(feature = "rust1", since = "1.0.0")]
+    pub const FRAC_1_SQRT_2: f32 = 0.707106781186547524400844362104849039_f32;
+
+    /// Euler's number (e)
+    #[stable(feature = "rust1", since = "1.0.0")]
+    pub const E: f32 = 2.71828182845904523536028747135266250_f32;
+
+    /// log<sub>2</sub>(e)
+    #[stable(feature = "rust1", since = "1.0.0")]
+    pub const LOG2_E: f32 = 1.44269504088896340735992468100189214_f32;
+
+    /// log<sub>2</sub>(10)
+    #[stable(feature = "extra_log_consts", since = "1.43.0")]
+    pub const LOG2_10: f32 = 3.32192809488736234787031942948939018_f32;
+
+    /// log<sub>10</sub>(e)
+    #[stable(feature = "rust1", since = "1.0.0")]
+    pub const LOG10_E: f32 = 0.434294481903251827651128918916605082_f32;
+
+    /// log<sub>10</sub>(2)
+    #[stable(feature = "extra_log_consts", since = "1.43.0")]
+    pub const LOG10_2: f32 = 0.301029995663981195213738894724493027_f32;
+
+    /// ln(2)
+    #[stable(feature = "rust1", since = "1.0.0")]
+    pub const LN_2: f32 = 0.693147180559945309417232121458176568_f32;
+
+    /// ln(10)
+    #[stable(feature = "rust1", since = "1.0.0")]
+    pub const LN_10: f32 = 2.30258509299404568401799145468436421_f32;
+}
+
+#[cfg(not(test))]
+impl f32 {
+    /// The radix or base of the internal representation of `f32`.
+    #[stable(feature = "assoc_int_consts", since = "1.43.0")]
+    pub const RADIX: u32 = 2;
+
+    /// Number of significant digits in base 2.
+    #[stable(feature = "assoc_int_consts", since = "1.43.0")]
+    pub const MANTISSA_DIGITS: u32 = 24;
+
+    /// Approximate number of significant digits in base 10.
+    #[stable(feature = "assoc_int_consts", since = "1.43.0")]
+    pub const DIGITS: u32 = 6;
+
+    /// [Machine epsilon] value for `f32`.
+    ///
+    /// This is the difference between `1.0` and the next larger representable number.
+    ///
+    /// [Machine epsilon]: https://en.wikipedia.org/wiki/Machine_epsilon
+    #[stable(feature = "assoc_int_consts", since = "1.43.0")]
+    pub const EPSILON: f32 = 1.19209290e-07_f32;
+
+    /// Smallest finite `f32` value.
+    #[stable(feature = "assoc_int_consts", since = "1.43.0")]
+    pub const MIN: f32 = -3.40282347e+38_f32;
+    /// Smallest positive normal `f32` value.
+    #[stable(feature = "assoc_int_consts", since = "1.43.0")]
+    pub const MIN_POSITIVE: f32 = 1.17549435e-38_f32;
+    /// Largest finite `f32` value.
+    #[stable(feature = "assoc_int_consts", since = "1.43.0")]
+    pub const MAX: f32 = 3.40282347e+38_f32;
+
+    /// One greater than the minimum possible normal power of 2 exponent.
+    #[stable(feature = "assoc_int_consts", since = "1.43.0")]
+    pub const MIN_EXP: i32 = -125;
+    /// Maximum possible power of 2 exponent.
+    #[stable(feature = "assoc_int_consts", since = "1.43.0")]
+    pub const MAX_EXP: i32 = 128;
+
+    /// Minimum possible normal power of 10 exponent.
+    #[stable(feature = "assoc_int_consts", since = "1.43.0")]
+    pub const MIN_10_EXP: i32 = -37;
+    /// Maximum possible power of 10 exponent.
+    #[stable(feature = "assoc_int_consts", since = "1.43.0")]
+    pub const MAX_10_EXP: i32 = 38;
+
+    /// Not a Number (NaN).
+    ///
+    /// Note that IEEE-745 doesn't define just a single NaN value;
+    /// a plethora of bit patterns are considered to be NaN.
+    /// Furthermore, the standard makes a difference
+    /// between a "signaling" and a "quiet" NaN,
+    /// and allows inspecting its "payload" (the unspecified bits in the bit pattern).
+    /// This constant isn't guaranteed to equal to any specific NaN bitpattern,
+    /// and the stability of its representation over Rust versions
+    /// and target platforms isn't guaranteed.
+    #[stable(feature = "assoc_int_consts", since = "1.43.0")]
+    pub const NAN: f32 = 0.0_f32 / 0.0_f32;
+    /// Infinity (∞).
+    #[stable(feature = "assoc_int_consts", since = "1.43.0")]
+    pub const INFINITY: f32 = 1.0_f32 / 0.0_f32;
+    /// Negative infinity (−∞).
+    #[stable(feature = "assoc_int_consts", since = "1.43.0")]
+    pub const NEG_INFINITY: f32 = -1.0_f32 / 0.0_f32;
+
+    /// Returns `true` if this value is NaN.
+    ///
+    /// ```
+    /// let nan = f32::NAN;
+    /// let f = 7.0_f32;
+    ///
+    /// assert!(nan.is_nan());
+    /// assert!(!f.is_nan());
+    /// ```
+    #[must_use]
+    #[stable(feature = "rust1", since = "1.0.0")]
+    #[rustc_const_unstable(feature = "const_float_classify", issue = "72505")]
+    #[inline]
+    pub const fn is_nan(self) -> bool {
+        self != self
+    }
+
+    // FIXME(#50145): `abs` is publicly unavailable in libcore due to
+    // concerns about portability, so this implementation is for
+    // private use internally.
+    #[inline]
+    #[rustc_const_unstable(feature = "const_float_classify", issue = "72505")]
+    pub(crate) const fn abs_private(self) -> f32 {
+        // SAFETY: This transmutation is fine. Probably. For the reasons std is using it.
+        unsafe { mem::transmute::<u32, f32>(mem::transmute::<f32, u32>(self) & 0x7fff_ffff) }
+    }
+
+    /// Returns `true` if this value is positive infinity or negative infinity, and
+    /// `false` otherwise.
+    ///
+    /// ```
+    /// let f = 7.0f32;
+    /// let inf = f32::INFINITY;
+    /// let neg_inf = f32::NEG_INFINITY;
+    /// let nan = f32::NAN;
+    ///
+    /// assert!(!f.is_infinite());
+    /// assert!(!nan.is_infinite());
+    ///
+    /// assert!(inf.is_infinite());
+    /// assert!(neg_inf.is_infinite());
+    /// ```
+    #[must_use]
+    #[stable(feature = "rust1", since = "1.0.0")]
+    #[rustc_const_unstable(feature = "const_float_classify", issue = "72505")]
+    #[inline]
+    pub const fn is_infinite(self) -> bool {
+        // Getting clever with transmutation can result in incorrect answers on some FPUs
+        // FIXME: alter the Rust <-> Rust calling convention to prevent this problem.
+        // See https://github.com/rust-lang/rust/issues/72327
+        (self == f32::INFINITY) | (self == f32::NEG_INFINITY)
+    }
+
+    /// Returns `true` if this number is neither infinite nor NaN.
+    ///
+    /// ```
+    /// let f = 7.0f32;
+    /// let inf = f32::INFINITY;
+    /// let neg_inf = f32::NEG_INFINITY;
+    /// let nan = f32::NAN;
+    ///
+    /// assert!(f.is_finite());
+    ///
+    /// assert!(!nan.is_finite());
+    /// assert!(!inf.is_finite());
+    /// assert!(!neg_inf.is_finite());
+    /// ```
+    #[must_use]
+    #[stable(feature = "rust1", since = "1.0.0")]
+    #[rustc_const_unstable(feature = "const_float_classify", issue = "72505")]
+    #[inline]
+    pub const fn is_finite(self) -> bool {
+        // There's no need to handle NaN separately: if self is NaN,
+        // the comparison is not true, exactly as desired.
+        self.abs_private() < Self::INFINITY
+    }
+
+    /// Returns `true` if the number is [subnormal].
+    ///
+    /// ```
+    /// let min = f32::MIN_POSITIVE; // 1.17549435e-38f32
+    /// let max = f32::MAX;
+    /// let lower_than_min = 1.0e-40_f32;
+    /// let zero = 0.0_f32;
+    ///
+    /// assert!(!min.is_subnormal());
+    /// assert!(!max.is_subnormal());
+    ///
+    /// assert!(!zero.is_subnormal());
+    /// assert!(!f32::NAN.is_subnormal());
+    /// assert!(!f32::INFINITY.is_subnormal());
+    /// // Values between `0` and `min` are Subnormal.
+    /// assert!(lower_than_min.is_subnormal());
+    /// ```
+    /// [subnormal]: https://en.wikipedia.org/wiki/Denormal_number
+    #[must_use]
+    #[stable(feature = "is_subnormal", since = "1.53.0")]
+    #[rustc_const_unstable(feature = "const_float_classify", issue = "72505")]
+    #[inline]
+    pub const fn is_subnormal(self) -> bool {
+        matches!(self.classify(), FpCategory::Subnormal)
+    }
+
+    /// Returns `true` if the number is neither zero, infinite,
+    /// [subnormal], or NaN.
+    ///
+    /// ```
+    /// let min = f32::MIN_POSITIVE; // 1.17549435e-38f32
+    /// let max = f32::MAX;
+    /// let lower_than_min = 1.0e-40_f32;
+    /// let zero = 0.0_f32;
+    ///
+    /// assert!(min.is_normal());
+    /// assert!(max.is_normal());
+    ///
+    /// assert!(!zero.is_normal());
+    /// assert!(!f32::NAN.is_normal());
+    /// assert!(!f32::INFINITY.is_normal());
+    /// // Values between `0` and `min` are Subnormal.
+    /// assert!(!lower_than_min.is_normal());
+    /// ```
+    /// [subnormal]: https://en.wikipedia.org/wiki/Denormal_number
+    #[must_use]
+    #[stable(feature = "rust1", since = "1.0.0")]
+    #[rustc_const_unstable(feature = "const_float_classify", issue = "72505")]
+    #[inline]
+    pub const fn is_normal(self) -> bool {
+        matches!(self.classify(), FpCategory::Normal)
+    }
+
+    /// Returns the floating point category of the number. If only one property
+    /// is going to be tested, it is generally faster to use the specific
+    /// predicate instead.
+    ///
+    /// ```
+    /// use std::num::FpCategory;
+    ///
+    /// let num = 12.4_f32;
+    /// let inf = f32::INFINITY;
+    ///
+    /// assert_eq!(num.classify(), FpCategory::Normal);
+    /// assert_eq!(inf.classify(), FpCategory::Infinite);
+    /// ```
+    #[stable(feature = "rust1", since = "1.0.0")]
+    #[rustc_const_unstable(feature = "const_float_classify", issue = "72505")]
+    pub const fn classify(self) -> FpCategory {
+        // A previous implementation tried to only use bitmask-based checks,
+        // using f32::to_bits to transmute the float to its bit repr and match on that.
+        // Unfortunately, floating point numbers can be much worse than that.
+        // This also needs to not result in recursive evaluations of f64::to_bits.
+        //
+        // On some processors, in some cases, LLVM will "helpfully" lower floating point ops,
+        // in spite of a request for them using f32 and f64, to things like x87 operations.
+        // These have an f64's mantissa, but can have a larger than normal exponent.
+        // FIXME(jubilee): Using x87 operations is never necessary in order to function
+        // on x86 processors for Rust-to-Rust calls, so this issue should not happen.
+        // Code generation should be adjusted to use non-C calling conventions, avoiding this.
+        //
+        if self.is_infinite() {
+            // Thus, a value may compare unequal to infinity, despite having a "full" exponent mask.
+            FpCategory::Infinite
+        } else if self.is_nan() {
+            // And it may not be NaN, as it can simply be an "overextended" finite value.
+            FpCategory::Nan
+        } else {
+            // However, std can't simply compare to zero to check for zero, either,
+            // as correctness requires avoiding equality tests that may be Subnormal == -0.0
+            // because it may be wrong under "denormals are zero" and "flush to zero" modes.
+            // Most of std's targets don't use those, but they are used for thumbv7neon.
+            // So, this does use bitpattern matching for the rest.
+
+            // SAFETY: f32 to u32 is fine. Usually.
+            // If classify has gotten this far, the value is definitely in one of these categories.
+            unsafe { f32::partial_classify(self) }
+        }
+    }
+
+    // This doesn't actually return a right answer for NaN on purpose,
+    // seeing as how it cannot correctly discern between a floating point NaN,
+    // and some normal floating point numbers truncated from an x87 FPU.
+    // FIXME(jubilee): This probably could at least answer things correctly for Infinity,
+    // like the f64 version does, but I need to run more checks on how things go on x86.
+    // I fear losing mantissa data that would have answered that differently.
+    //
+    // # Safety
+    // This requires making sure you call this function for values it answers correctly on,
+    // otherwise it returns a wrong answer. This is not important for memory safety per se,
+    // but getting floats correct is important for not accidentally leaking const eval
+    // runtime-deviating logic which may or may not be acceptable.
+    #[rustc_const_unstable(feature = "const_float_classify", issue = "72505")]
+    const unsafe fn partial_classify(self) -> FpCategory {
+        const EXP_MASK: u32 = 0x7f800000;
+        const MAN_MASK: u32 = 0x007fffff;
+
+        // SAFETY: The caller is not asking questions for which this will tell lies.
+        let b = unsafe { mem::transmute::<f32, u32>(self) };
+        match (b & MAN_MASK, b & EXP_MASK) {
+            (0, 0) => FpCategory::Zero,
+            (_, 0) => FpCategory::Subnormal,
+            _ => FpCategory::Normal,
+        }
+    }
+
+    // This operates on bits, and only bits, so it can ignore concerns about weird FPUs.
+    // FIXME(jubilee): In a just world, this would be the entire impl for classify,
+    // plus a transmute. We do not live in a just world, but we can make it more so.
+    #[rustc_const_unstable(feature = "const_float_classify", issue = "72505")]
+    const fn classify_bits(b: u32) -> FpCategory {
+        const EXP_MASK: u32 = 0x7f800000;
+        const MAN_MASK: u32 = 0x007fffff;
+
+        match (b & MAN_MASK, b & EXP_MASK) {
+            (0, EXP_MASK) => FpCategory::Infinite,
+            (_, EXP_MASK) => FpCategory::Nan,
+            (0, 0) => FpCategory::Zero,
+            (_, 0) => FpCategory::Subnormal,
+            _ => FpCategory::Normal,
+        }
+    }
+
+    /// Returns `true` if `self` has a positive sign, including `+0.0`, NaNs with
+    /// positive sign bit and positive infinity. Note that IEEE-745 doesn't assign any
+    /// meaning to the sign bit in case of a NaN, and as Rust doesn't guarantee that
+    /// the bit pattern of NaNs are conserved over arithmetic operations, the result of
+    /// `is_sign_positive` on a NaN might produce an unexpected result in some cases.
+    /// See [explanation of NaN as a special value](f32) for more info.
+    ///
+    /// ```
+    /// let f = 7.0_f32;
+    /// let g = -7.0_f32;
+    ///
+    /// assert!(f.is_sign_positive());
+    /// assert!(!g.is_sign_positive());
+    /// ```
+    #[must_use]
+    #[stable(feature = "rust1", since = "1.0.0")]
+    #[rustc_const_unstable(feature = "const_float_classify", issue = "72505")]
+    #[inline]
+    pub const fn is_sign_positive(self) -> bool {
+        !self.is_sign_negative()
+    }
+
+    /// Returns `true` if `self` has a negative sign, including `-0.0`, NaNs with
+    /// negative sign bit and negative infinity. Note that IEEE-745 doesn't assign any
+    /// meaning to the sign bit in case of a NaN, and as Rust doesn't guarantee that
+    /// the bit pattern of NaNs are conserved over arithmetic operations, the result of
+    /// `is_sign_negative` on a NaN might produce an unexpected result in some cases.
+    /// See [explanation of NaN as a special value](f32) for more info.
+    ///
+    /// ```
+    /// let f = 7.0f32;
+    /// let g = -7.0f32;
+    ///
+    /// assert!(!f.is_sign_negative());
+    /// assert!(g.is_sign_negative());
+    /// ```
+    #[must_use]
+    #[stable(feature = "rust1", since = "1.0.0")]
+    #[rustc_const_unstable(feature = "const_float_classify", issue = "72505")]
+    #[inline]
+    pub const fn is_sign_negative(self) -> bool {
+        // IEEE754 says: isSignMinus(x) is true if and only if x has negative sign. isSignMinus
+        // applies to zeros and NaNs as well.
+        // SAFETY: This is just transmuting to get the sign bit, it's fine.
+        unsafe { mem::transmute::<f32, u32>(self) & 0x8000_0000 != 0 }
+    }
+
+    /// Takes the reciprocal (inverse) of a number, `1/x`.
+    ///
+    /// ```
+    /// let x = 2.0_f32;
+    /// let abs_difference = (x.recip() - (1.0 / x)).abs();
+    ///
+    /// assert!(abs_difference <= f32::EPSILON);
+    /// ```
+    #[must_use = "this returns the result of the operation, without modifying the original"]
+    #[stable(feature = "rust1", since = "1.0.0")]
+    #[inline]
+    pub fn recip(self) -> f32 {
+        1.0 / self
+    }
+
+    /// Converts radians to degrees.
+    ///
+    /// ```
+    /// let angle = std::f32::consts::PI;
+    ///
+    /// let abs_difference = (angle.to_degrees() - 180.0).abs();
+    ///
+    /// assert!(abs_difference <= f32::EPSILON);
+    /// ```
+    #[must_use = "this returns the result of the operation, \
+                  without modifying the original"]
+    #[stable(feature = "f32_deg_rad_conversions", since = "1.7.0")]
+    #[inline]
+    pub fn to_degrees(self) -> f32 {
+        // Use a constant for better precision.
+        const PIS_IN_180: f32 = 57.2957795130823208767981548141051703_f32;
+        self * PIS_IN_180
+    }
+
+    /// Converts degrees to radians.
+    ///
+    /// ```
+    /// let angle = 180.0f32;
+    ///
+    /// let abs_difference = (angle.to_radians() - std::f32::consts::PI).abs();
+    ///
+    /// assert!(abs_difference <= f32::EPSILON);
+    /// ```
+    #[must_use = "this returns the result of the operation, \
+                  without modifying the original"]
+    #[stable(feature = "f32_deg_rad_conversions", since = "1.7.0")]
+    #[inline]
+    pub fn to_radians(self) -> f32 {
+        let value: f32 = consts::PI;
+        self * (value / 180.0f32)
+    }
+
+    /// Returns the maximum of the two numbers, ignoring NaN.
+    ///
+    /// If one of the arguments is NaN, then the other argument is returned.
+    /// This follows the IEEE-754 2008 semantics for maxNum, except for handling of signaling NaNs;
+    /// this function handles all NaNs the same way and avoids maxNum's problems with associativity.
+    /// This also matches the behavior of libm’s fmax.
+    ///
+    /// ```
+    /// let x = 1.0f32;
+    /// let y = 2.0f32;
+    ///
+    /// assert_eq!(x.max(y), y);
+    /// ```
+    #[must_use = "this returns the result of the comparison, without modifying either input"]
+    #[stable(feature = "rust1", since = "1.0.0")]
+    #[inline]
+    pub fn max(self, other: f32) -> f32 {
+        intrinsics::maxnumf32(self, other)
+    }
+
+    /// Returns the minimum of the two numbers, ignoring NaN.
+    ///
+    /// If one of the arguments is NaN, then the other argument is returned.
+    /// This follows the IEEE-754 2008 semantics for minNum, except for handling of signaling NaNs;
+    /// this function handles all NaNs the same way and avoids minNum's problems with associativity.
+    /// This also matches the behavior of libm’s fmin.
+    ///
+    /// ```
+    /// let x = 1.0f32;
+    /// let y = 2.0f32;
+    ///
+    /// assert_eq!(x.min(y), x);
+    /// ```
+    #[must_use = "this returns the result of the comparison, without modifying either input"]
+    #[stable(feature = "rust1", since = "1.0.0")]
+    #[inline]
+    pub fn min(self, other: f32) -> f32 {
+        intrinsics::minnumf32(self, other)
+    }
+
+    /// Returns the maximum of the two numbers, propagating NaN.
+    ///
+    /// This returns NaN when *either* argument is NaN, as opposed to
+    /// [`f32::max`] which only returns NaN when *both* arguments are NaN.
+    ///
+    /// ```
+    /// #![feature(float_minimum_maximum)]
+    /// let x = 1.0f32;
+    /// let y = 2.0f32;
+    ///
+    /// assert_eq!(x.maximum(y), y);
+    /// assert!(x.maximum(f32::NAN).is_nan());
+    /// ```
+    ///
+    /// If one of the arguments is NaN, then NaN is returned. Otherwise this returns the greater
+    /// of the two numbers. For this operation, -0.0 is considered to be less than +0.0.
+    /// Note that this follows the semantics specified in IEEE 754-2019.
+    ///
+    /// Also note that "propagation" of NaNs here doesn't necessarily mean that the bitpattern of a NaN
+    /// operand is conserved; see [explanation of NaN as a special value](f32) for more info.
+    #[must_use = "this returns the result of the comparison, without modifying either input"]
+    #[unstable(feature = "float_minimum_maximum", issue = "91079")]
+    #[inline]
+    pub fn maximum(self, other: f32) -> f32 {
+        if self > other {
+            self
+        } else if other > self {
+            other
+        } else if self == other {
+            if self.is_sign_positive() && other.is_sign_negative() { self } else { other }
+        } else {
+            self + other
+        }
+    }
+
+    /// Returns the minimum of the two numbers, propagating NaN.
+    ///
+    /// This returns NaN when *either* argument is NaN, as opposed to
+    /// [`f32::min`] which only returns NaN when *both* arguments are NaN.
+    ///
+    /// ```
+    /// #![feature(float_minimum_maximum)]
+    /// let x = 1.0f32;
+    /// let y = 2.0f32;
+    ///
+    /// assert_eq!(x.minimum(y), x);
+    /// assert!(x.minimum(f32::NAN).is_nan());
+    /// ```
+    ///
+    /// If one of the arguments is NaN, then NaN is returned. Otherwise this returns the lesser
+    /// of the two numbers. For this operation, -0.0 is considered to be less than +0.0.
+    /// Note that this follows the semantics specified in IEEE 754-2019.
+    ///
+    /// Also note that "propagation" of NaNs here doesn't necessarily mean that the bitpattern of a NaN
+    /// operand is conserved; see [explanation of NaN as a special value](f32) for more info.
+    #[must_use = "this returns the result of the comparison, without modifying either input"]
+    #[unstable(feature = "float_minimum_maximum", issue = "91079")]
+    #[inline]
+    pub fn minimum(self, other: f32) -> f32 {
+        if self < other {
+            self
+        } else if other < self {
+            other
+        } else if self == other {
+            if self.is_sign_negative() && other.is_sign_positive() { self } else { other }
+        } else {
+            self + other
+        }
+    }
+
+    /// Rounds toward zero and converts to any primitive integer type,
+    /// assuming that the value is finite and fits in that type.
+    ///
+    /// ```
+    /// let value = 4.6_f32;
+    /// let rounded = unsafe { value.to_int_unchecked::<u16>() };
+    /// assert_eq!(rounded, 4);
+    ///
+    /// let value = -128.9_f32;
+    /// let rounded = unsafe { value.to_int_unchecked::<i8>() };
+    /// assert_eq!(rounded, i8::MIN);
+    /// ```
+    ///
+    /// # Safety
+    ///
+    /// The value must:
+    ///
+    /// * Not be `NaN`
+    /// * Not be infinite
+    /// * Be representable in the return type `Int`, after truncating off its fractional part
+    #[must_use = "this returns the result of the operation, \
+                  without modifying the original"]
+    #[stable(feature = "float_approx_unchecked_to", since = "1.44.0")]
+    #[inline]
+    pub unsafe fn to_int_unchecked<Int>(self) -> Int
+    where
+        Self: FloatToInt<Int>,
+    {
+        // SAFETY: the caller must uphold the safety contract for
+        // `FloatToInt::to_int_unchecked`.
+        unsafe { FloatToInt::<Int>::to_int_unchecked(self) }
+    }
+
+    /// Raw transmutation to `u32`.
+    ///
+    /// This is currently identical to `transmute::<f32, u32>(self)` on all platforms.
+    ///
+    /// See [`from_bits`](Self::from_bits) for some discussion of the
+    /// portability of this operation (there are almost no issues).
+    ///
+    /// Note that this function is distinct from `as` casting, which attempts to
+    /// preserve the *numeric* value, and not the bitwise value.
+    ///
+    /// # Examples
+    ///
+    /// ```
+    /// assert_ne!((1f32).to_bits(), 1f32 as u32); // to_bits() is not casting!
+    /// assert_eq!((12.5f32).to_bits(), 0x41480000);
+    ///
+    /// ```
+    #[must_use = "this returns the result of the operation, \
+                  without modifying the original"]
+    #[stable(feature = "float_bits_conv", since = "1.20.0")]
+    #[rustc_const_unstable(feature = "const_float_bits_conv", issue = "72447")]
+    #[inline]
+    pub const fn to_bits(self) -> u32 {
+        // SAFETY: `u32` is a plain old datatype so we can always transmute to it.
+        // ...sorta.
+        //
+        // It turns out that at runtime, it is possible for a floating point number
+        // to be subject to a floating point mode that alters nonzero subnormal numbers
+        // to zero on reads and writes, aka "denormals are zero" and "flush to zero".
+        // This is not a problem per se, but at least one tier2 platform for Rust
+        // actually exhibits this behavior by default.
+        //
+        // In addition, on x86 targets with SSE or SSE2 disabled and the x87 FPU enabled,
+        // i.e. not soft-float, the way Rust does parameter passing can actually alter
+        // a number that is "not infinity" to have the same exponent as infinity,
+        // in a slightly unpredictable manner.
+        //
+        // And, of course evaluating to a NaN value is fairly nondeterministic.
+        // More precisely: when NaN should be returned is knowable, but which NaN?
+        // So far that's defined by a combination of LLVM and the CPU, not Rust.
+        // This function, however, allows observing the bitstring of a NaN,
+        // thus introspection on CTFE.
+        //
+        // In order to preserve, at least for the moment, const-to-runtime equivalence,
+        // we reject any of these possible situations from happening.
+        #[rustc_const_unstable(feature = "const_float_bits_conv", issue = "72447")]
+        const fn ct_f32_to_u32(ct: f32) -> u32 {
+            match ct.classify() {
+                FpCategory::Nan => {
+                    panic!("const-eval error: cannot use f32::to_bits on a NaN")
+                }
+                FpCategory::Subnormal => {
+                    panic!("const-eval error: cannot use f32::to_bits on a subnormal number")
+                }
+                FpCategory::Infinite | FpCategory::Normal | FpCategory::Zero => {
+                    // SAFETY: We have a normal floating point number. Now we transmute, i.e. do a bitcopy.
+                    unsafe { mem::transmute::<f32, u32>(ct) }
+                }
+            }
+        }
+        // SAFETY: `u32` is a plain old datatype so we can always... uh...
+        // ...look, just pretend you forgot what you just read.
+        // Stability concerns.
+        let rt_f32_to_u32 = |rt| unsafe { mem::transmute::<f32, u32>(rt) };
+        // SAFETY: We use internal implementations that either always work or fail at compile time.
+        unsafe { intrinsics::const_eval_select((self,), ct_f32_to_u32, rt_f32_to_u32) }
+    }
+
+    /// Raw transmutation from `u32`.
+    ///
+    /// This is currently identical to `transmute::<u32, f32>(v)` on all platforms.
+    /// It turns out this is incredibly portable, for two reasons:
+    ///
+    /// * Floats and Ints have the same endianness on all supported platforms.
+    /// * IEEE-754 very precisely specifies the bit layout of floats.
+    ///
+    /// However there is one caveat: prior to the 2008 version of IEEE-754, how
+    /// to interpret the NaN signaling bit wasn't actually specified. Most platforms
+    /// (notably x86 and ARM) picked the interpretation that was ultimately
+    /// standardized in 2008, but some didn't (notably MIPS). As a result, all
+    /// signaling NaNs on MIPS are quiet NaNs on x86, and vice-versa.
+    ///
+    /// Rather than trying to preserve signaling-ness cross-platform, this
+    /// implementation favors preserving the exact bits. This means that
+    /// any payloads encoded in NaNs will be preserved even if the result of
+    /// this method is sent over the network from an x86 machine to a MIPS one.
+    ///
+    /// If the results of this method are only manipulated by the same
+    /// architecture that produced them, then there is no portability concern.
+    ///
+    /// If the input isn't NaN, then there is no portability concern.
+    ///
+    /// If you don't care about signalingness (very likely), then there is no
+    /// portability concern.
+    ///
+    /// Note that this function is distinct from `as` casting, which attempts to
+    /// preserve the *numeric* value, and not the bitwise value.
+    ///
+    /// # Examples
+    ///
+    /// ```
+    /// let v = f32::from_bits(0x41480000);
+    /// assert_eq!(v, 12.5);
+    /// ```
+    #[stable(feature = "float_bits_conv", since = "1.20.0")]
+    #[rustc_const_unstable(feature = "const_float_bits_conv", issue = "72447")]
+    #[must_use]
+    #[inline]
+    pub const fn from_bits(v: u32) -> Self {
+        // It turns out the safety issues with sNaN were overblown! Hooray!
+        // SAFETY: `u32` is a plain old datatype so we can always transmute from it
+        // ...sorta.
+        //
+        // It turns out that at runtime, it is possible for a floating point number
+        // to be subject to floating point modes that alter nonzero subnormal numbers
+        // to zero on reads and writes, aka "denormals are zero" and "flush to zero".
+        // This is not a problem usually, but at least one tier2 platform for Rust
+        // actually exhibits this behavior by default: thumbv7neon
+        // aka "the Neon FPU in AArch32 state"
+        //
+        // In addition, on x86 targets with SSE or SSE2 disabled and the x87 FPU enabled,
+        // i.e. not soft-float, the way Rust does parameter passing can actually alter
+        // a number that is "not infinity" to have the same exponent as infinity,
+        // in a slightly unpredictable manner.
+        //
+        // And, of course evaluating to a NaN value is fairly nondeterministic.
+        // More precisely: when NaN should be returned is knowable, but which NaN?
+        // So far that's defined by a combination of LLVM and the CPU, not Rust.
+        // This function, however, allows observing the bitstring of a NaN,
+        // thus introspection on CTFE.
+        //
+        // In order to preserve, at least for the moment, const-to-runtime equivalence,
+        // reject any of these possible situations from happening.
+        #[rustc_const_unstable(feature = "const_float_bits_conv", issue = "72447")]
+        const fn ct_u32_to_f32(ct: u32) -> f32 {
+            match f32::classify_bits(ct) {
+                FpCategory::Subnormal => {
+                    panic!("const-eval error: cannot use f32::from_bits on a subnormal number")
+                }
+                FpCategory::Nan => {
+                    panic!("const-eval error: cannot use f32::from_bits on NaN")
+                }
+                FpCategory::Infinite | FpCategory::Normal | FpCategory::Zero => {
+                    // SAFETY: It's not a frumious number
+                    unsafe { mem::transmute::<u32, f32>(ct) }
+                }
+            }
+        }
+        // SAFETY: `u32` is a plain old datatype so we can always... uh...
+        // ...look, just pretend you forgot what you just read.
+        // Stability concerns.
+        let rt_u32_to_f32 = |rt| unsafe { mem::transmute::<u32, f32>(rt) };
+        // SAFETY: We use internal implementations that either always work or fail at compile time.
+        unsafe { intrinsics::const_eval_select((v,), ct_u32_to_f32, rt_u32_to_f32) }
+    }
+
+    /// Return the memory representation of this floating point number as a byte array in
+    /// big-endian (network) byte order.
+    ///
+    /// See [`from_bits`](Self::from_bits) for some discussion of the
+    /// portability of this operation (there are almost no issues).
+    ///
+    /// # Examples
+    ///
+    /// ```
+    /// let bytes = 12.5f32.to_be_bytes();
+    /// assert_eq!(bytes, [0x41, 0x48, 0x00, 0x00]);
+    /// ```
+    #[must_use = "this returns the result of the operation, \
+                  without modifying the original"]
+    #[stable(feature = "float_to_from_bytes", since = "1.40.0")]
+    #[rustc_const_unstable(feature = "const_float_bits_conv", issue = "72447")]
+    #[inline]
+    pub const fn to_be_bytes(self) -> [u8; 4] {
+        self.to_bits().to_be_bytes()
+    }
+
+    /// Return the memory representation of this floating point number as a byte array in
+    /// little-endian byte order.
+    ///
+    /// See [`from_bits`](Self::from_bits) for some discussion of the
+    /// portability of this operation (there are almost no issues).
+    ///
+    /// # Examples
+    ///
+    /// ```
+    /// let bytes = 12.5f32.to_le_bytes();
+    /// assert_eq!(bytes, [0x00, 0x00, 0x48, 0x41]);
+    /// ```
+    #[must_use = "this returns the result of the operation, \
+                  without modifying the original"]
+    #[stable(feature = "float_to_from_bytes", since = "1.40.0")]
+    #[rustc_const_unstable(feature = "const_float_bits_conv", issue = "72447")]
+    #[inline]
+    pub const fn to_le_bytes(self) -> [u8; 4] {
+        self.to_bits().to_le_bytes()
+    }
+
+    /// Return the memory representation of this floating point number as a byte array in
+    /// native byte order.
+    ///
+    /// As the target platform's native endianness is used, portable code
+    /// should use [`to_be_bytes`] or [`to_le_bytes`], as appropriate, instead.
+    ///
+    /// [`to_be_bytes`]: f32::to_be_bytes
+    /// [`to_le_bytes`]: f32::to_le_bytes
+    ///
+    /// See [`from_bits`](Self::from_bits) for some discussion of the
+    /// portability of this operation (there are almost no issues).
+    ///
+    /// # Examples
+    ///
+    /// ```
+    /// let bytes = 12.5f32.to_ne_bytes();
+    /// assert_eq!(
+    ///     bytes,
+    ///     if cfg!(target_endian = "big") {
+    ///         [0x41, 0x48, 0x00, 0x00]
+    ///     } else {
+    ///         [0x00, 0x00, 0x48, 0x41]
+    ///     }
+    /// );
+    /// ```
+    #[must_use = "this returns the result of the operation, \
+                  without modifying the original"]
+    #[stable(feature = "float_to_from_bytes", since = "1.40.0")]
+    #[rustc_const_unstable(feature = "const_float_bits_conv", issue = "72447")]
+    #[inline]
+    pub const fn to_ne_bytes(self) -> [u8; 4] {
+        self.to_bits().to_ne_bytes()
+    }
+
+    /// Create a floating point value from its representation as a byte array in big endian.
+    ///
+    /// See [`from_bits`](Self::from_bits) for some discussion of the
+    /// portability of this operation (there are almost no issues).
+    ///
+    /// # Examples
+    ///
+    /// ```
+    /// let value = f32::from_be_bytes([0x41, 0x48, 0x00, 0x00]);
+    /// assert_eq!(value, 12.5);
+    /// ```
+    #[stable(feature = "float_to_from_bytes", since = "1.40.0")]
+    #[rustc_const_unstable(feature = "const_float_bits_conv", issue = "72447")]
+    #[must_use]
+    #[inline]
+    pub const fn from_be_bytes(bytes: [u8; 4]) -> Self {
+        Self::from_bits(u32::from_be_bytes(bytes))
+    }
+
+    /// Create a floating point value from its representation as a byte array in little endian.
+    ///
+    /// See [`from_bits`](Self::from_bits) for some discussion of the
+    /// portability of this operation (there are almost no issues).
+    ///
+    /// # Examples
+    ///
+    /// ```
+    /// let value = f32::from_le_bytes([0x00, 0x00, 0x48, 0x41]);
+    /// assert_eq!(value, 12.5);
+    /// ```
+    #[stable(feature = "float_to_from_bytes", since = "1.40.0")]
+    #[rustc_const_unstable(feature = "const_float_bits_conv", issue = "72447")]
+    #[must_use]
+    #[inline]
+    pub const fn from_le_bytes(bytes: [u8; 4]) -> Self {
+        Self::from_bits(u32::from_le_bytes(bytes))
+    }
+
+    /// Create a floating point value from its representation as a byte array in native endian.
+    ///
+    /// As the target platform's native endianness is used, portable code
+    /// likely wants to use [`from_be_bytes`] or [`from_le_bytes`], as
+    /// appropriate instead.
+    ///
+    /// [`from_be_bytes`]: f32::from_be_bytes
+    /// [`from_le_bytes`]: f32::from_le_bytes
+    ///
+    /// See [`from_bits`](Self::from_bits) for some discussion of the
+    /// portability of this operation (there are almost no issues).
+    ///
+    /// # Examples
+    ///
+    /// ```
+    /// let value = f32::from_ne_bytes(if cfg!(target_endian = "big") {
+    ///     [0x41, 0x48, 0x00, 0x00]
+    /// } else {
+    ///     [0x00, 0x00, 0x48, 0x41]
+    /// });
+    /// assert_eq!(value, 12.5);
+    /// ```
+    #[stable(feature = "float_to_from_bytes", since = "1.40.0")]
+    #[rustc_const_unstable(feature = "const_float_bits_conv", issue = "72447")]
+    #[must_use]
+    #[inline]
+    pub const fn from_ne_bytes(bytes: [u8; 4]) -> Self {
+        Self::from_bits(u32::from_ne_bytes(bytes))
+    }
+
+    /// Return the ordering between `self` and `other`.
+    ///
+    /// Unlike the standard partial comparison between floating point numbers,
+    /// this comparison always produces an ordering in accordance to
+    /// the `totalOrder` predicate as defined in the IEEE 754 (2008 revision)
+    /// floating point standard. The values are ordered in the following sequence:
+    ///
+    /// - negative quiet NaN
+    /// - negative signaling NaN
+    /// - negative infinity
+    /// - negative numbers
+    /// - negative subnormal numbers
+    /// - negative zero
+    /// - positive zero
+    /// - positive subnormal numbers
+    /// - positive numbers
+    /// - positive infinity
+    /// - positive signaling NaN
+    /// - positive quiet NaN.
+    ///
+    /// The ordering established by this function does not always agree with the
+    /// [`PartialOrd`] and [`PartialEq`] implementations of `f32`. For example,
+    /// they consider negative and positive zero equal, while `total_cmp`
+    /// doesn't.
+    ///
+    /// The interpretation of the signaling NaN bit follows the definition in
+    /// the IEEE 754 standard, which may not match the interpretation by some of
+    /// the older, non-conformant (e.g. MIPS) hardware implementations.
+    ///
+    /// # Example
+    ///
+    /// ```
+    /// struct GoodBoy {
+    ///     name: String,
+    ///     weight: f32,
+    /// }
+    ///
+    /// let mut bois = vec![
+    ///     GoodBoy { name: "Pucci".to_owned(), weight: 0.1 },
+    ///     GoodBoy { name: "Woofer".to_owned(), weight: 99.0 },
+    ///     GoodBoy { name: "Yapper".to_owned(), weight: 10.0 },
+    ///     GoodBoy { name: "Chonk".to_owned(), weight: f32::INFINITY },
+    ///     GoodBoy { name: "Abs. Unit".to_owned(), weight: f32::NAN },
+    ///     GoodBoy { name: "Floaty".to_owned(), weight: -5.0 },
+    /// ];
+    ///
+    /// bois.sort_by(|a, b| a.weight.total_cmp(&b.weight));
+    /// # assert!(bois.into_iter().map(|b| b.weight)
+    /// #     .zip([-5.0, 0.1, 10.0, 99.0, f32::INFINITY, f32::NAN].iter())
+    /// #     .all(|(a, b)| a.to_bits() == b.to_bits()))
+    /// ```
+    #[stable(feature = "total_cmp", since = "1.62.0")]
+    #[must_use]
+    #[inline]
+    pub fn total_cmp(&self, other: &Self) -> crate::cmp::Ordering {
+        let mut left = self.to_bits() as i32;
+        let mut right = other.to_bits() as i32;
+
+        // In case of negatives, flip all the bits except the sign
+        // to achieve a similar layout as two's complement integers
+        //
+        // Why does this work? IEEE 754 floats consist of three fields:
+        // Sign bit, exponent and mantissa. The set of exponent and mantissa
+        // fields as a whole have the property that their bitwise order is
+        // equal to the numeric magnitude where the magnitude is defined.
+        // The magnitude is not normally defined on NaN values, but
+        // IEEE 754 totalOrder defines the NaN values also to follow the
+        // bitwise order. This leads to order explained in the doc comment.
+        // However, the representation of magnitude is the same for negative
+        // and positive numbers – only the sign bit is different.
+        // To easily compare the floats as signed integers, we need to
+        // flip the exponent and mantissa bits in case of negative numbers.
+        // We effectively convert the numbers to "two's complement" form.
+        //
+        // To do the flipping, we construct a mask and XOR against it.
+        // We branchlessly calculate an "all-ones except for the sign bit"
+        // mask from negative-signed values: right shifting sign-extends
+        // the integer, so we "fill" the mask with sign bits, and then
+        // convert to unsigned to push one more zero bit.
+        // On positive values, the mask is all zeros, so it's a no-op.
+        left ^= (((left >> 31) as u32) >> 1) as i32;
+        right ^= (((right >> 31) as u32) >> 1) as i32;
+
+        left.cmp(&right)
+    }
+
+    /// Restrict a value to a certain interval unless it is NaN.
+    ///
+    /// Returns `max` if `self` is greater than `max`, and `min` if `self` is
+    /// less than `min`. Otherwise this returns `self`.
+    ///
+    /// Note that this function returns NaN if the initial value was NaN as
+    /// well.
+    ///
+    /// # Panics
+    ///
+    /// Panics if `min > max`, `min` is NaN, or `max` is NaN.
+    ///
+    /// # Examples
+    ///
+    /// ```
+    /// assert!((-3.0f32).clamp(-2.0, 1.0) == -2.0);
+    /// assert!((0.0f32).clamp(-2.0, 1.0) == 0.0);
+    /// assert!((2.0f32).clamp(-2.0, 1.0) == 1.0);
+    /// assert!((f32::NAN).clamp(-2.0, 1.0).is_nan());
+    /// ```
+    #[must_use = "method returns a new number and does not mutate the original value"]
+    #[stable(feature = "clamp", since = "1.50.0")]
+    #[inline]
+    pub fn clamp(self, min: f32, max: f32) -> f32 {
+        assert!(min <= max);
+        let mut x = self;
+        if x < min {
+            x = min;
+        }
+        if x > max {
+            x = max;
+        }
+        x
+    }
+}
diff --git a/library/core/src/num/f64.rs b/library/core/src/num/f64.rs
new file mode 100644
index 000000000..75c92c2f8
--- /dev/null
+++ b/library/core/src/num/f64.rs
@@ -0,0 +1,1294 @@
+//! Constants specific to the `f64` double-precision floating point type.
+//!
+//! *[See also the `f64` primitive type][f64].*
+//!
+//! Mathematically significant numbers are provided in the `consts` sub-module.
+//!
+//! For the constants defined directly in this module
+//! (as distinct from those defined in the `consts` sub-module),
+//! new code should instead use the associated constants
+//! defined directly on the `f64` type.
+
+#![stable(feature = "rust1", since = "1.0.0")]
+
+use crate::convert::FloatToInt;
+#[cfg(not(test))]
+use crate::intrinsics;
+use crate::mem;
+use crate::num::FpCategory;
+
+/// The radix or base of the internal representation of `f64`.
+/// Use [`f64::RADIX`] instead.
+///
+/// # Examples
+///
+/// ```rust
+/// // deprecated way
+/// # #[allow(deprecated, deprecated_in_future)]
+/// let r = std::f64::RADIX;
+///
+/// // intended way
+/// let r = f64::RADIX;
+/// ```
+#[stable(feature = "rust1", since = "1.0.0")]
+#[deprecated(since = "TBD", note = "replaced by the `RADIX` associated constant on `f64`")]
+pub const RADIX: u32 = f64::RADIX;
+
+/// Number of significant digits in base 2.
+/// Use [`f64::MANTISSA_DIGITS`] instead.
+///
+/// # Examples
+///
+/// ```rust
+/// // deprecated way
+/// # #[allow(deprecated, deprecated_in_future)]
+/// let d = std::f64::MANTISSA_DIGITS;
+///
+/// // intended way
+/// let d = f64::MANTISSA_DIGITS;
+/// ```
+#[stable(feature = "rust1", since = "1.0.0")]
+#[deprecated(
+    since = "TBD",
+    note = "replaced by the `MANTISSA_DIGITS` associated constant on `f64`"
+)]
+pub const MANTISSA_DIGITS: u32 = f64::MANTISSA_DIGITS;
+
+/// Approximate number of significant digits in base 10.
+/// Use [`f64::DIGITS`] instead.
+///
+/// # Examples
+///
+/// ```rust
+/// // deprecated way
+/// # #[allow(deprecated, deprecated_in_future)]
+/// let d = std::f64::DIGITS;
+///
+/// // intended way
+/// let d = f64::DIGITS;
+/// ```
+#[stable(feature = "rust1", since = "1.0.0")]
+#[deprecated(since = "TBD", note = "replaced by the `DIGITS` associated constant on `f64`")]
+pub const DIGITS: u32 = f64::DIGITS;
+
+/// [Machine epsilon] value for `f64`.
+/// Use [`f64::EPSILON`] instead.
+///
+/// This is the difference between `1.0` and the next larger representable number.
+///
+/// [Machine epsilon]: https://en.wikipedia.org/wiki/Machine_epsilon
+///
+/// # Examples
+///
+/// ```rust
+/// // deprecated way
+/// # #[allow(deprecated, deprecated_in_future)]
+/// let e = std::f64::EPSILON;
+///
+/// // intended way
+/// let e = f64::EPSILON;
+/// ```
+#[stable(feature = "rust1", since = "1.0.0")]
+#[deprecated(since = "TBD", note = "replaced by the `EPSILON` associated constant on `f64`")]
+pub const EPSILON: f64 = f64::EPSILON;
+
+/// Smallest finite `f64` value.
+/// Use [`f64::MIN`] instead.
+///
+/// # Examples
+///
+/// ```rust
+/// // deprecated way
+/// # #[allow(deprecated, deprecated_in_future)]
+/// let min = std::f64::MIN;
+///
+/// // intended way
+/// let min = f64::MIN;
+/// ```
+#[stable(feature = "rust1", since = "1.0.0")]
+#[deprecated(since = "TBD", note = "replaced by the `MIN` associated constant on `f64`")]
+pub const MIN: f64 = f64::MIN;
+
+/// Smallest positive normal `f64` value.
+/// Use [`f64::MIN_POSITIVE`] instead.
+///
+/// # Examples
+///
+/// ```rust
+/// // deprecated way
+/// # #[allow(deprecated, deprecated_in_future)]
+/// let min = std::f64::MIN_POSITIVE;
+///
+/// // intended way
+/// let min = f64::MIN_POSITIVE;
+/// ```
+#[stable(feature = "rust1", since = "1.0.0")]
+#[deprecated(since = "TBD", note = "replaced by the `MIN_POSITIVE` associated constant on `f64`")]
+pub const MIN_POSITIVE: f64 = f64::MIN_POSITIVE;
+
+/// Largest finite `f64` value.
+/// Use [`f64::MAX`] instead.
+///
+/// # Examples
+///
+/// ```rust
+/// // deprecated way
+/// # #[allow(deprecated, deprecated_in_future)]
+/// let max = std::f64::MAX;
+///
+/// // intended way
+/// let max = f64::MAX;
+/// ```
+#[stable(feature = "rust1", since = "1.0.0")]
+#[deprecated(since = "TBD", note = "replaced by the `MAX` associated constant on `f64`")]
+pub const MAX: f64 = f64::MAX;
+
+/// One greater than the minimum possible normal power of 2 exponent.
+/// Use [`f64::MIN_EXP`] instead.
+///
+/// # Examples
+///
+/// ```rust
+/// // deprecated way
+/// # #[allow(deprecated, deprecated_in_future)]
+/// let min = std::f64::MIN_EXP;
+///
+/// // intended way
+/// let min = f64::MIN_EXP;
+/// ```
+#[stable(feature = "rust1", since = "1.0.0")]
+#[deprecated(since = "TBD", note = "replaced by the `MIN_EXP` associated constant on `f64`")]
+pub const MIN_EXP: i32 = f64::MIN_EXP;
+
+/// Maximum possible power of 2 exponent.
+/// Use [`f64::MAX_EXP`] instead.
+///
+/// # Examples
+///
+/// ```rust
+/// // deprecated way
+/// # #[allow(deprecated, deprecated_in_future)]
+/// let max = std::f64::MAX_EXP;
+///
+/// // intended way
+/// let max = f64::MAX_EXP;
+/// ```
+#[stable(feature = "rust1", since = "1.0.0")]
+#[deprecated(since = "TBD", note = "replaced by the `MAX_EXP` associated constant on `f64`")]
+pub const MAX_EXP: i32 = f64::MAX_EXP;
+
+/// Minimum possible normal power of 10 exponent.
+/// Use [`f64::MIN_10_EXP`] instead.
+///
+/// # Examples
+///
+/// ```rust
+/// // deprecated way
+/// # #[allow(deprecated, deprecated_in_future)]
+/// let min = std::f64::MIN_10_EXP;
+///
+/// // intended way
+/// let min = f64::MIN_10_EXP;
+/// ```
+#[stable(feature = "rust1", since = "1.0.0")]
+#[deprecated(since = "TBD", note = "replaced by the `MIN_10_EXP` associated constant on `f64`")]
+pub const MIN_10_EXP: i32 = f64::MIN_10_EXP;
+
+/// Maximum possible power of 10 exponent.
+/// Use [`f64::MAX_10_EXP`] instead.
+///
+/// # Examples
+///
+/// ```rust
+/// // deprecated way
+/// # #[allow(deprecated, deprecated_in_future)]
+/// let max = std::f64::MAX_10_EXP;
+///
+/// // intended way
+/// let max = f64::MAX_10_EXP;
+/// ```
+#[stable(feature = "rust1", since = "1.0.0")]
+#[deprecated(since = "TBD", note = "replaced by the `MAX_10_EXP` associated constant on `f64`")]
+pub const MAX_10_EXP: i32 = f64::MAX_10_EXP;
+
+/// Not a Number (NaN).
+/// Use [`f64::NAN`] instead.
+///
+/// # Examples
+///
+/// ```rust
+/// // deprecated way
+/// # #[allow(deprecated, deprecated_in_future)]
+/// let nan = std::f64::NAN;
+///
+/// // intended way
+/// let nan = f64::NAN;
+/// ```
+#[stable(feature = "rust1", since = "1.0.0")]
+#[deprecated(since = "TBD", note = "replaced by the `NAN` associated constant on `f64`")]
+pub const NAN: f64 = f64::NAN;
+
+/// Infinity (∞).
+/// Use [`f64::INFINITY`] instead.
+///
+/// # Examples
+///
+/// ```rust
+/// // deprecated way
+/// # #[allow(deprecated, deprecated_in_future)]
+/// let inf = std::f64::INFINITY;
+///
+/// // intended way
+/// let inf = f64::INFINITY;
+/// ```
+#[stable(feature = "rust1", since = "1.0.0")]
+#[deprecated(since = "TBD", note = "replaced by the `INFINITY` associated constant on `f64`")]
+pub const INFINITY: f64 = f64::INFINITY;
+
+/// Negative infinity (−∞).
+/// Use [`f64::NEG_INFINITY`] instead.
+///
+/// # Examples
+///
+/// ```rust
+/// // deprecated way
+/// # #[allow(deprecated, deprecated_in_future)]
+/// let ninf = std::f64::NEG_INFINITY;
+///
+/// // intended way
+/// let ninf = f64::NEG_INFINITY;
+/// ```
+#[stable(feature = "rust1", since = "1.0.0")]
+#[deprecated(since = "TBD", note = "replaced by the `NEG_INFINITY` associated constant on `f64`")]
+pub const NEG_INFINITY: f64 = f64::NEG_INFINITY;
+
+/// Basic mathematical constants.
+#[stable(feature = "rust1", since = "1.0.0")]
+pub mod consts {
+    // FIXME: replace with mathematical constants from cmath.
+
+    /// Archimedes' constant (π)
+    #[stable(feature = "rust1", since = "1.0.0")]
+    pub const PI: f64 = 3.14159265358979323846264338327950288_f64;
+
+    /// The full circle constant (τ)
+    ///
+    /// Equal to 2π.
+    #[stable(feature = "tau_constant", since = "1.47.0")]
+    pub const TAU: f64 = 6.28318530717958647692528676655900577_f64;
+
+    /// π/2
+    #[stable(feature = "rust1", since = "1.0.0")]
+    pub const FRAC_PI_2: f64 = 1.57079632679489661923132169163975144_f64;
+
+    /// π/3
+    #[stable(feature = "rust1", since = "1.0.0")]
+    pub const FRAC_PI_3: f64 = 1.04719755119659774615421446109316763_f64;
+
+    /// π/4
+    #[stable(feature = "rust1", since = "1.0.0")]
+    pub const FRAC_PI_4: f64 = 0.785398163397448309615660845819875721_f64;
+
+    /// π/6
+    #[stable(feature = "rust1", since = "1.0.0")]
+    pub const FRAC_PI_6: f64 = 0.52359877559829887307710723054658381_f64;
+
+    /// π/8
+    #[stable(feature = "rust1", since = "1.0.0")]
+    pub const FRAC_PI_8: f64 = 0.39269908169872415480783042290993786_f64;
+
+    /// 1/π
+    #[stable(feature = "rust1", since = "1.0.0")]
+    pub const FRAC_1_PI: f64 = 0.318309886183790671537767526745028724_f64;
+
+    /// 2/π
+    #[stable(feature = "rust1", since = "1.0.0")]
+    pub const FRAC_2_PI: f64 = 0.636619772367581343075535053490057448_f64;
+
+    /// 2/sqrt(π)
+    #[stable(feature = "rust1", since = "1.0.0")]
+    pub const FRAC_2_SQRT_PI: f64 = 1.12837916709551257389615890312154517_f64;
+
+    /// sqrt(2)
+    #[stable(feature = "rust1", since = "1.0.0")]
+    pub const SQRT_2: f64 = 1.41421356237309504880168872420969808_f64;
+
+    /// 1/sqrt(2)
+    #[stable(feature = "rust1", since = "1.0.0")]
+    pub const FRAC_1_SQRT_2: f64 = 0.707106781186547524400844362104849039_f64;
+
+    /// Euler's number (e)
+    #[stable(feature = "rust1", since = "1.0.0")]
+    pub const E: f64 = 2.71828182845904523536028747135266250_f64;
+
+    /// log<sub>2</sub>(10)
+    #[stable(feature = "extra_log_consts", since = "1.43.0")]
+    pub const LOG2_10: f64 = 3.32192809488736234787031942948939018_f64;
+
+    /// log<sub>2</sub>(e)
+    #[stable(feature = "rust1", since = "1.0.0")]
+    pub const LOG2_E: f64 = 1.44269504088896340735992468100189214_f64;
+
+    /// log<sub>10</sub>(2)
+    #[stable(feature = "extra_log_consts", since = "1.43.0")]
+    pub const LOG10_2: f64 = 0.301029995663981195213738894724493027_f64;
+
+    /// log<sub>10</sub>(e)
+    #[stable(feature = "rust1", since = "1.0.0")]
+    pub const LOG10_E: f64 = 0.434294481903251827651128918916605082_f64;
+
+    /// ln(2)
+    #[stable(feature = "rust1", since = "1.0.0")]
+    pub const LN_2: f64 = 0.693147180559945309417232121458176568_f64;
+
+    /// ln(10)
+    #[stable(feature = "rust1", since = "1.0.0")]
+    pub const LN_10: f64 = 2.30258509299404568401799145468436421_f64;
+}
+
+#[cfg(not(test))]
+impl f64 {
+    /// The radix or base of the internal representation of `f64`.
+    #[stable(feature = "assoc_int_consts", since = "1.43.0")]
+    pub const RADIX: u32 = 2;
+
+    /// Number of significant digits in base 2.
+    #[stable(feature = "assoc_int_consts", since = "1.43.0")]
+    pub const MANTISSA_DIGITS: u32 = 53;
+    /// Approximate number of significant digits in base 10.
+    #[stable(feature = "assoc_int_consts", since = "1.43.0")]
+    pub const DIGITS: u32 = 15;
+
+    /// [Machine epsilon] value for `f64`.
+    ///
+    /// This is the difference between `1.0` and the next larger representable number.
+    ///
+    /// [Machine epsilon]: https://en.wikipedia.org/wiki/Machine_epsilon
+    #[stable(feature = "assoc_int_consts", since = "1.43.0")]
+    pub const EPSILON: f64 = 2.2204460492503131e-16_f64;
+
+    /// Smallest finite `f64` value.
+    #[stable(feature = "assoc_int_consts", since = "1.43.0")]
+    pub const MIN: f64 = -1.7976931348623157e+308_f64;
+    /// Smallest positive normal `f64` value.
+    #[stable(feature = "assoc_int_consts", since = "1.43.0")]
+    pub const MIN_POSITIVE: f64 = 2.2250738585072014e-308_f64;
+    /// Largest finite `f64` value.
+    #[stable(feature = "assoc_int_consts", since = "1.43.0")]
+    pub const MAX: f64 = 1.7976931348623157e+308_f64;
+
+    /// One greater than the minimum possible normal power of 2 exponent.
+    #[stable(feature = "assoc_int_consts", since = "1.43.0")]
+    pub const MIN_EXP: i32 = -1021;
+    /// Maximum possible power of 2 exponent.
+    #[stable(feature = "assoc_int_consts", since = "1.43.0")]
+    pub const MAX_EXP: i32 = 1024;
+
+    /// Minimum possible normal power of 10 exponent.
+    #[stable(feature = "assoc_int_consts", since = "1.43.0")]
+    pub const MIN_10_EXP: i32 = -307;
+    /// Maximum possible power of 10 exponent.
+    #[stable(feature = "assoc_int_consts", since = "1.43.0")]
+    pub const MAX_10_EXP: i32 = 308;
+
+    /// Not a Number (NaN).
+    ///
+    /// Note that IEEE-745 doesn't define just a single NaN value;
+    /// a plethora of bit patterns are considered to be NaN.
+    /// Furthermore, the standard makes a difference
+    /// between a "signaling" and a "quiet" NaN,
+    /// and allows inspecting its "payload" (the unspecified bits in the bit pattern).
+    /// This constant isn't guaranteed to equal to any specific NaN bitpattern,
+    /// and the stability of its representation over Rust versions
+    /// and target platforms isn't guaranteed.
+    #[stable(feature = "assoc_int_consts", since = "1.43.0")]
+    pub const NAN: f64 = 0.0_f64 / 0.0_f64;
+    /// Infinity (∞).
+    #[stable(feature = "assoc_int_consts", since = "1.43.0")]
+    pub const INFINITY: f64 = 1.0_f64 / 0.0_f64;
+    /// Negative infinity (−∞).
+    #[stable(feature = "assoc_int_consts", since = "1.43.0")]
+    pub const NEG_INFINITY: f64 = -1.0_f64 / 0.0_f64;
+
+    /// Returns `true` if this value is NaN.
+    ///
+    /// ```
+    /// let nan = f64::NAN;
+    /// let f = 7.0_f64;
+    ///
+    /// assert!(nan.is_nan());
+    /// assert!(!f.is_nan());
+    /// ```
+    #[must_use]
+    #[stable(feature = "rust1", since = "1.0.0")]
+    #[rustc_const_unstable(feature = "const_float_classify", issue = "72505")]
+    #[inline]
+    pub const fn is_nan(self) -> bool {
+        self != self
+    }
+
+    // FIXME(#50145): `abs` is publicly unavailable in libcore due to
+    // concerns about portability, so this implementation is for
+    // private use internally.
+    #[inline]
+    #[rustc_const_unstable(feature = "const_float_classify", issue = "72505")]
+    pub(crate) const fn abs_private(self) -> f64 {
+        // SAFETY: This transmutation is fine. Probably. For the reasons std is using it.
+        unsafe {
+            mem::transmute::<u64, f64>(mem::transmute::<f64, u64>(self) & 0x7fff_ffff_ffff_ffff)
+        }
+    }
+
+    /// Returns `true` if this value is positive infinity or negative infinity, and
+    /// `false` otherwise.
+    ///
+    /// ```
+    /// let f = 7.0f64;
+    /// let inf = f64::INFINITY;
+    /// let neg_inf = f64::NEG_INFINITY;
+    /// let nan = f64::NAN;
+    ///
+    /// assert!(!f.is_infinite());
+    /// assert!(!nan.is_infinite());
+    ///
+    /// assert!(inf.is_infinite());
+    /// assert!(neg_inf.is_infinite());
+    /// ```
+    #[must_use]
+    #[stable(feature = "rust1", since = "1.0.0")]
+    #[rustc_const_unstable(feature = "const_float_classify", issue = "72505")]
+    #[inline]
+    pub const fn is_infinite(self) -> bool {
+        // Getting clever with transmutation can result in incorrect answers on some FPUs
+        // FIXME: alter the Rust <-> Rust calling convention to prevent this problem.
+        // See https://github.com/rust-lang/rust/issues/72327
+        (self == f64::INFINITY) | (self == f64::NEG_INFINITY)
+    }
+
+    /// Returns `true` if this number is neither infinite nor NaN.
+    ///
+    /// ```
+    /// let f = 7.0f64;
+    /// let inf: f64 = f64::INFINITY;
+    /// let neg_inf: f64 = f64::NEG_INFINITY;
+    /// let nan: f64 = f64::NAN;
+    ///
+    /// assert!(f.is_finite());
+    ///
+    /// assert!(!nan.is_finite());
+    /// assert!(!inf.is_finite());
+    /// assert!(!neg_inf.is_finite());
+    /// ```
+    #[must_use]
+    #[stable(feature = "rust1", since = "1.0.0")]
+    #[rustc_const_unstable(feature = "const_float_classify", issue = "72505")]
+    #[inline]
+    pub const fn is_finite(self) -> bool {
+        // There's no need to handle NaN separately: if self is NaN,
+        // the comparison is not true, exactly as desired.
+        self.abs_private() < Self::INFINITY
+    }
+
+    /// Returns `true` if the number is [subnormal].
+    ///
+    /// ```
+    /// let min = f64::MIN_POSITIVE; // 2.2250738585072014e-308_f64
+    /// let max = f64::MAX;
+    /// let lower_than_min = 1.0e-308_f64;
+    /// let zero = 0.0_f64;
+    ///
+    /// assert!(!min.is_subnormal());
+    /// assert!(!max.is_subnormal());
+    ///
+    /// assert!(!zero.is_subnormal());
+    /// assert!(!f64::NAN.is_subnormal());
+    /// assert!(!f64::INFINITY.is_subnormal());
+    /// // Values between `0` and `min` are Subnormal.
+    /// assert!(lower_than_min.is_subnormal());
+    /// ```
+    /// [subnormal]: https://en.wikipedia.org/wiki/Denormal_number
+    #[must_use]
+    #[stable(feature = "is_subnormal", since = "1.53.0")]
+    #[rustc_const_unstable(feature = "const_float_classify", issue = "72505")]
+    #[inline]
+    pub const fn is_subnormal(self) -> bool {
+        matches!(self.classify(), FpCategory::Subnormal)
+    }
+
+    /// Returns `true` if the number is neither zero, infinite,
+    /// [subnormal], or NaN.
+    ///
+    /// ```
+    /// let min = f64::MIN_POSITIVE; // 2.2250738585072014e-308f64
+    /// let max = f64::MAX;
+    /// let lower_than_min = 1.0e-308_f64;
+    /// let zero = 0.0f64;
+    ///
+    /// assert!(min.is_normal());
+    /// assert!(max.is_normal());
+    ///
+    /// assert!(!zero.is_normal());
+    /// assert!(!f64::NAN.is_normal());
+    /// assert!(!f64::INFINITY.is_normal());
+    /// // Values between `0` and `min` are Subnormal.
+    /// assert!(!lower_than_min.is_normal());
+    /// ```
+    /// [subnormal]: https://en.wikipedia.org/wiki/Denormal_number
+    #[must_use]
+    #[stable(feature = "rust1", since = "1.0.0")]
+    #[rustc_const_unstable(feature = "const_float_classify", issue = "72505")]
+    #[inline]
+    pub const fn is_normal(self) -> bool {
+        matches!(self.classify(), FpCategory::Normal)
+    }
+
+    /// Returns the floating point category of the number. If only one property
+    /// is going to be tested, it is generally faster to use the specific
+    /// predicate instead.
+    ///
+    /// ```
+    /// use std::num::FpCategory;
+    ///
+    /// let num = 12.4_f64;
+    /// let inf = f64::INFINITY;
+    ///
+    /// assert_eq!(num.classify(), FpCategory::Normal);
+    /// assert_eq!(inf.classify(), FpCategory::Infinite);
+    /// ```
+    #[stable(feature = "rust1", since = "1.0.0")]
+    #[rustc_const_unstable(feature = "const_float_classify", issue = "72505")]
+    pub const fn classify(self) -> FpCategory {
+        // A previous implementation tried to only use bitmask-based checks,
+        // using f64::to_bits to transmute the float to its bit repr and match on that.
+        // Unfortunately, floating point numbers can be much worse than that.
+        // This also needs to not result in recursive evaluations of f64::to_bits.
+        //
+        // On some processors, in some cases, LLVM will "helpfully" lower floating point ops,
+        // in spite of a request for them using f32 and f64, to things like x87 operations.
+        // These have an f64's mantissa, but can have a larger than normal exponent.
+        // FIXME(jubilee): Using x87 operations is never necessary in order to function
+        // on x86 processors for Rust-to-Rust calls, so this issue should not happen.
+        // Code generation should be adjusted to use non-C calling conventions, avoiding this.
+        //
+        // Thus, a value may compare unequal to infinity, despite having a "full" exponent mask.
+        // And it may not be NaN, as it can simply be an "overextended" finite value.
+        if self.is_nan() {
+            FpCategory::Nan
+        } else {
+            // However, std can't simply compare to zero to check for zero, either,
+            // as correctness requires avoiding equality tests that may be Subnormal == -0.0
+            // because it may be wrong under "denormals are zero" and "flush to zero" modes.
+            // Most of std's targets don't use those, but they are used for thumbv7neon.
+            // So, this does use bitpattern matching for the rest.
+
+            // SAFETY: f64 to u64 is fine. Usually.
+            // If control flow has gotten this far, the value is definitely in one of the categories
+            // that f64::partial_classify can correctly analyze.
+            unsafe { f64::partial_classify(self) }
+        }
+    }
+
+    // This doesn't actually return a right answer for NaN on purpose,
+    // seeing as how it cannot correctly discern between a floating point NaN,
+    // and some normal floating point numbers truncated from an x87 FPU.
+    #[rustc_const_unstable(feature = "const_float_classify", issue = "72505")]
+    const unsafe fn partial_classify(self) -> FpCategory {
+        const EXP_MASK: u64 = 0x7ff0000000000000;
+        const MAN_MASK: u64 = 0x000fffffffffffff;
+
+        // SAFETY: The caller is not asking questions for which this will tell lies.
+        let b = unsafe { mem::transmute::<f64, u64>(self) };
+        match (b & MAN_MASK, b & EXP_MASK) {
+            (0, EXP_MASK) => FpCategory::Infinite,
+            (0, 0) => FpCategory::Zero,
+            (_, 0) => FpCategory::Subnormal,
+            _ => FpCategory::Normal,
+        }
+    }
+
+    // This operates on bits, and only bits, so it can ignore concerns about weird FPUs.
+    // FIXME(jubilee): In a just world, this would be the entire impl for classify,
+    // plus a transmute. We do not live in a just world, but we can make it more so.
+    #[rustc_const_unstable(feature = "const_float_classify", issue = "72505")]
+    const fn classify_bits(b: u64) -> FpCategory {
+        const EXP_MASK: u64 = 0x7ff0000000000000;
+        const MAN_MASK: u64 = 0x000fffffffffffff;
+
+        match (b & MAN_MASK, b & EXP_MASK) {
+            (0, EXP_MASK) => FpCategory::Infinite,
+            (_, EXP_MASK) => FpCategory::Nan,
+            (0, 0) => FpCategory::Zero,
+            (_, 0) => FpCategory::Subnormal,
+            _ => FpCategory::Normal,
+        }
+    }
+
+    /// Returns `true` if `self` has a positive sign, including `+0.0`, NaNs with
+    /// positive sign bit and positive infinity. Note that IEEE-745 doesn't assign any
+    /// meaning to the sign bit in case of a NaN, and as Rust doesn't guarantee that
+    /// the bit pattern of NaNs are conserved over arithmetic operations, the result of
+    /// `is_sign_positive` on a NaN might produce an unexpected result in some cases.
+    /// See [explanation of NaN as a special value](f32) for more info.
+    ///
+    /// ```
+    /// let f = 7.0_f64;
+    /// let g = -7.0_f64;
+    ///
+    /// assert!(f.is_sign_positive());
+    /// assert!(!g.is_sign_positive());
+    /// ```
+    #[must_use]
+    #[stable(feature = "rust1", since = "1.0.0")]
+    #[rustc_const_unstable(feature = "const_float_classify", issue = "72505")]
+    #[inline]
+    pub const fn is_sign_positive(self) -> bool {
+        !self.is_sign_negative()
+    }
+
+    #[must_use]
+    #[stable(feature = "rust1", since = "1.0.0")]
+    #[deprecated(since = "1.0.0", note = "renamed to is_sign_positive")]
+    #[inline]
+    #[doc(hidden)]
+    pub fn is_positive(self) -> bool {
+        self.is_sign_positive()
+    }
+
+    /// Returns `true` if `self` has a negative sign, including `-0.0`, NaNs with
+    /// negative sign bit and negative infinity. Note that IEEE-745 doesn't assign any
+    /// meaning to the sign bit in case of a NaN, and as Rust doesn't guarantee that
+    /// the bit pattern of NaNs are conserved over arithmetic operations, the result of
+    /// `is_sign_negative` on a NaN might produce an unexpected result in some cases.
+    /// See [explanation of NaN as a special value](f32) for more info.
+    ///
+    /// ```
+    /// let f = 7.0_f64;
+    /// let g = -7.0_f64;
+    ///
+    /// assert!(!f.is_sign_negative());
+    /// assert!(g.is_sign_negative());
+    /// ```
+    #[must_use]
+    #[stable(feature = "rust1", since = "1.0.0")]
+    #[rustc_const_unstable(feature = "const_float_classify", issue = "72505")]
+    #[inline]
+    pub const fn is_sign_negative(self) -> bool {
+        // IEEE754 says: isSignMinus(x) is true if and only if x has negative sign. isSignMinus
+        // applies to zeros and NaNs as well.
+        // SAFETY: This is just transmuting to get the sign bit, it's fine.
+        unsafe { mem::transmute::<f64, u64>(self) & 0x8000_0000_0000_0000 != 0 }
+    }
+
+    #[must_use]
+    #[stable(feature = "rust1", since = "1.0.0")]
+    #[deprecated(since = "1.0.0", note = "renamed to is_sign_negative")]
+    #[inline]
+    #[doc(hidden)]
+    pub fn is_negative(self) -> bool {
+        self.is_sign_negative()
+    }
+
+    /// Takes the reciprocal (inverse) of a number, `1/x`.
+    ///
+    /// ```
+    /// let x = 2.0_f64;
+    /// let abs_difference = (x.recip() - (1.0 / x)).abs();
+    ///
+    /// assert!(abs_difference < 1e-10);
+    /// ```
+    #[must_use = "this returns the result of the operation, without modifying the original"]
+    #[stable(feature = "rust1", since = "1.0.0")]
+    #[inline]
+    pub fn recip(self) -> f64 {
+        1.0 / self
+    }
+
+    /// Converts radians to degrees.
+    ///
+    /// ```
+    /// let angle = std::f64::consts::PI;
+    ///
+    /// let abs_difference = (angle.to_degrees() - 180.0).abs();
+    ///
+    /// assert!(abs_difference < 1e-10);
+    /// ```
+    #[must_use = "this returns the result of the operation, \
+                  without modifying the original"]
+    #[stable(feature = "rust1", since = "1.0.0")]
+    #[inline]
+    pub fn to_degrees(self) -> f64 {
+        // The division here is correctly rounded with respect to the true
+        // value of 180/π. (This differs from f32, where a constant must be
+        // used to ensure a correctly rounded result.)
+        self * (180.0f64 / consts::PI)
+    }
+
+    /// Converts degrees to radians.
+    ///
+    /// ```
+    /// let angle = 180.0_f64;
+    ///
+    /// let abs_difference = (angle.to_radians() - std::f64::consts::PI).abs();
+    ///
+    /// assert!(abs_difference < 1e-10);
+    /// ```
+    #[must_use = "this returns the result of the operation, \
+                  without modifying the original"]
+    #[stable(feature = "rust1", since = "1.0.0")]
+    #[inline]
+    pub fn to_radians(self) -> f64 {
+        let value: f64 = consts::PI;
+        self * (value / 180.0)
+    }
+
+    /// Returns the maximum of the two numbers, ignoring NaN.
+    ///
+    /// If one of the arguments is NaN, then the other argument is returned.
+    /// This follows the IEEE-754 2008 semantics for maxNum, except for handling of signaling NaNs;
+    /// this function handles all NaNs the same way and avoids maxNum's problems with associativity.
+    /// This also matches the behavior of libm’s fmax.
+    ///
+    /// ```
+    /// let x = 1.0_f64;
+    /// let y = 2.0_f64;
+    ///
+    /// assert_eq!(x.max(y), y);
+    /// ```
+    #[must_use = "this returns the result of the comparison, without modifying either input"]
+    #[stable(feature = "rust1", since = "1.0.0")]
+    #[inline]
+    pub fn max(self, other: f64) -> f64 {
+        intrinsics::maxnumf64(self, other)
+    }
+
+    /// Returns the minimum of the two numbers, ignoring NaN.
+    ///
+    /// If one of the arguments is NaN, then the other argument is returned.
+    /// This follows the IEEE-754 2008 semantics for minNum, except for handling of signaling NaNs;
+    /// this function handles all NaNs the same way and avoids minNum's problems with associativity.
+    /// This also matches the behavior of libm’s fmin.
+    ///
+    /// ```
+    /// let x = 1.0_f64;
+    /// let y = 2.0_f64;
+    ///
+    /// assert_eq!(x.min(y), x);
+    /// ```
+    #[must_use = "this returns the result of the comparison, without modifying either input"]
+    #[stable(feature = "rust1", since = "1.0.0")]
+    #[inline]
+    pub fn min(self, other: f64) -> f64 {
+        intrinsics::minnumf64(self, other)
+    }
+
+    /// Returns the maximum of the two numbers, propagating NaN.
+    ///
+    /// This returns NaN when *either* argument is NaN, as opposed to
+    /// [`f64::max`] which only returns NaN when *both* arguments are NaN.
+    ///
+    /// ```
+    /// #![feature(float_minimum_maximum)]
+    /// let x = 1.0_f64;
+    /// let y = 2.0_f64;
+    ///
+    /// assert_eq!(x.maximum(y), y);
+    /// assert!(x.maximum(f64::NAN).is_nan());
+    /// ```
+    ///
+    /// If one of the arguments is NaN, then NaN is returned. Otherwise this returns the greater
+    /// of the two numbers. For this operation, -0.0 is considered to be less than +0.0.
+    /// Note that this follows the semantics specified in IEEE 754-2019.
+    ///
+    /// Also note that "propagation" of NaNs here doesn't necessarily mean that the bitpattern of a NaN
+    /// operand is conserved; see [explanation of NaN as a special value](f32) for more info.
+    #[must_use = "this returns the result of the comparison, without modifying either input"]
+    #[unstable(feature = "float_minimum_maximum", issue = "91079")]
+    #[inline]
+    pub fn maximum(self, other: f64) -> f64 {
+        if self > other {
+            self
+        } else if other > self {
+            other
+        } else if self == other {
+            if self.is_sign_positive() && other.is_sign_negative() { self } else { other }
+        } else {
+            self + other
+        }
+    }
+
+    /// Returns the minimum of the two numbers, propagating NaN.
+    ///
+    /// This returns NaN when *either* argument is NaN, as opposed to
+    /// [`f64::min`] which only returns NaN when *both* arguments are NaN.
+    ///
+    /// ```
+    /// #![feature(float_minimum_maximum)]
+    /// let x = 1.0_f64;
+    /// let y = 2.0_f64;
+    ///
+    /// assert_eq!(x.minimum(y), x);
+    /// assert!(x.minimum(f64::NAN).is_nan());
+    /// ```
+    ///
+    /// If one of the arguments is NaN, then NaN is returned. Otherwise this returns the lesser
+    /// of the two numbers. For this operation, -0.0 is considered to be less than +0.0.
+    /// Note that this follows the semantics specified in IEEE 754-2019.
+    ///
+    /// Also note that "propagation" of NaNs here doesn't necessarily mean that the bitpattern of a NaN
+    /// operand is conserved; see [explanation of NaN as a special value](f32) for more info.
+    #[must_use = "this returns the result of the comparison, without modifying either input"]
+    #[unstable(feature = "float_minimum_maximum", issue = "91079")]
+    #[inline]
+    pub fn minimum(self, other: f64) -> f64 {
+        if self < other {
+            self
+        } else if other < self {
+            other
+        } else if self == other {
+            if self.is_sign_negative() && other.is_sign_positive() { self } else { other }
+        } else {
+            self + other
+        }
+    }
+
+    /// Rounds toward zero and converts to any primitive integer type,
+    /// assuming that the value is finite and fits in that type.
+    ///
+    /// ```
+    /// let value = 4.6_f64;
+    /// let rounded = unsafe { value.to_int_unchecked::<u16>() };
+    /// assert_eq!(rounded, 4);
+    ///
+    /// let value = -128.9_f64;
+    /// let rounded = unsafe { value.to_int_unchecked::<i8>() };
+    /// assert_eq!(rounded, i8::MIN);
+    /// ```
+    ///
+    /// # Safety
+    ///
+    /// The value must:
+    ///
+    /// * Not be `NaN`
+    /// * Not be infinite
+    /// * Be representable in the return type `Int`, after truncating off its fractional part
+    #[must_use = "this returns the result of the operation, \
+                  without modifying the original"]
+    #[stable(feature = "float_approx_unchecked_to", since = "1.44.0")]
+    #[inline]
+    pub unsafe fn to_int_unchecked<Int>(self) -> Int
+    where
+        Self: FloatToInt<Int>,
+    {
+        // SAFETY: the caller must uphold the safety contract for
+        // `FloatToInt::to_int_unchecked`.
+        unsafe { FloatToInt::<Int>::to_int_unchecked(self) }
+    }
+
+    /// Raw transmutation to `u64`.
+    ///
+    /// This is currently identical to `transmute::<f64, u64>(self)` on all platforms.
+    ///
+    /// See [`from_bits`](Self::from_bits) for some discussion of the
+    /// portability of this operation (there are almost no issues).
+    ///
+    /// Note that this function is distinct from `as` casting, which attempts to
+    /// preserve the *numeric* value, and not the bitwise value.
+    ///
+    /// # Examples
+    ///
+    /// ```
+    /// assert!((1f64).to_bits() != 1f64 as u64); // to_bits() is not casting!
+    /// assert_eq!((12.5f64).to_bits(), 0x4029000000000000);
+    ///
+    /// ```
+    #[must_use = "this returns the result of the operation, \
+                  without modifying the original"]
+    #[stable(feature = "float_bits_conv", since = "1.20.0")]
+    #[rustc_const_unstable(feature = "const_float_bits_conv", issue = "72447")]
+    #[inline]
+    pub const fn to_bits(self) -> u64 {
+        // SAFETY: `u64` is a plain old datatype so we can always transmute to it.
+        // ...sorta.
+        //
+        // See the SAFETY comment in f64::from_bits for more.
+        #[rustc_const_unstable(feature = "const_float_bits_conv", issue = "72447")]
+        const fn ct_f64_to_u64(ct: f64) -> u64 {
+            match ct.classify() {
+                FpCategory::Nan => {
+                    panic!("const-eval error: cannot use f64::to_bits on a NaN")
+                }
+                FpCategory::Subnormal => {
+                    panic!("const-eval error: cannot use f64::to_bits on a subnormal number")
+                }
+                FpCategory::Infinite | FpCategory::Normal | FpCategory::Zero => {
+                    // SAFETY: We have a normal floating point number. Now we transmute, i.e. do a bitcopy.
+                    unsafe { mem::transmute::<f64, u64>(ct) }
+                }
+            }
+        }
+        // SAFETY: `u64` is a plain old datatype so we can always... uh...
+        // ...look, just pretend you forgot what you just read.
+        // Stability concerns.
+        let rt_f64_to_u64 = |rt| unsafe { mem::transmute::<f64, u64>(rt) };
+        // SAFETY: We use internal implementations that either always work or fail at compile time.
+        unsafe { intrinsics::const_eval_select((self,), ct_f64_to_u64, rt_f64_to_u64) }
+    }
+
+    /// Raw transmutation from `u64`.
+    ///
+    /// This is currently identical to `transmute::<u64, f64>(v)` on all platforms.
+    /// It turns out this is incredibly portable, for two reasons:
+    ///
+    /// * Floats and Ints have the same endianness on all supported platforms.
+    /// * IEEE-754 very precisely specifies the bit layout of floats.
+    ///
+    /// However there is one caveat: prior to the 2008 version of IEEE-754, how
+    /// to interpret the NaN signaling bit wasn't actually specified. Most platforms
+    /// (notably x86 and ARM) picked the interpretation that was ultimately
+    /// standardized in 2008, but some didn't (notably MIPS). As a result, all
+    /// signaling NaNs on MIPS are quiet NaNs on x86, and vice-versa.
+    ///
+    /// Rather than trying to preserve signaling-ness cross-platform, this
+    /// implementation favors preserving the exact bits. This means that
+    /// any payloads encoded in NaNs will be preserved even if the result of
+    /// this method is sent over the network from an x86 machine to a MIPS one.
+    ///
+    /// If the results of this method are only manipulated by the same
+    /// architecture that produced them, then there is no portability concern.
+    ///
+    /// If the input isn't NaN, then there is no portability concern.
+    ///
+    /// If you don't care about signaling-ness (very likely), then there is no
+    /// portability concern.
+    ///
+    /// Note that this function is distinct from `as` casting, which attempts to
+    /// preserve the *numeric* value, and not the bitwise value.
+    ///
+    /// # Examples
+    ///
+    /// ```
+    /// let v = f64::from_bits(0x4029000000000000);
+    /// assert_eq!(v, 12.5);
+    /// ```
+    #[stable(feature = "float_bits_conv", since = "1.20.0")]
+    #[rustc_const_unstable(feature = "const_float_bits_conv", issue = "72447")]
+    #[must_use]
+    #[inline]
+    pub const fn from_bits(v: u64) -> Self {
+        // It turns out the safety issues with sNaN were overblown! Hooray!
+        // SAFETY: `u64` is a plain old datatype so we can always transmute from it
+        // ...sorta.
+        //
+        // It turns out that at runtime, it is possible for a floating point number
+        // to be subject to floating point modes that alter nonzero subnormal numbers
+        // to zero on reads and writes, aka "denormals are zero" and "flush to zero".
+        // This is not a problem usually, but at least one tier2 platform for Rust
+        // actually exhibits an FTZ behavior by default: thumbv7neon
+        // aka "the Neon FPU in AArch32 state"
+        //
+        // Even with this, not all instructions exhibit the FTZ behaviors on thumbv7neon,
+        // so this should load the same bits if LLVM emits the "correct" instructions,
+        // but LLVM sometimes makes interesting choices about float optimization,
+        // and other FPUs may do similar. Thus, it is wise to indulge luxuriously in caution.
+        //
+        // In addition, on x86 targets with SSE or SSE2 disabled and the x87 FPU enabled,
+        // i.e. not soft-float, the way Rust does parameter passing can actually alter
+        // a number that is "not infinity" to have the same exponent as infinity,
+        // in a slightly unpredictable manner.
+        //
+        // And, of course evaluating to a NaN value is fairly nondeterministic.
+        // More precisely: when NaN should be returned is knowable, but which NaN?
+        // So far that's defined by a combination of LLVM and the CPU, not Rust.
+        // This function, however, allows observing the bitstring of a NaN,
+        // thus introspection on CTFE.
+        //
+        // In order to preserve, at least for the moment, const-to-runtime equivalence,
+        // reject any of these possible situations from happening.
+        #[rustc_const_unstable(feature = "const_float_bits_conv", issue = "72447")]
+        const fn ct_u64_to_f64(ct: u64) -> f64 {
+            match f64::classify_bits(ct) {
+                FpCategory::Subnormal => {
+                    panic!("const-eval error: cannot use f64::from_bits on a subnormal number")
+                }
+                FpCategory::Nan => {
+                    panic!("const-eval error: cannot use f64::from_bits on NaN")
+                }
+                FpCategory::Infinite | FpCategory::Normal | FpCategory::Zero => {
+                    // SAFETY: It's not a frumious number
+                    unsafe { mem::transmute::<u64, f64>(ct) }
+                }
+            }
+        }
+        // SAFETY: `u64` is a plain old datatype so we can always... uh...
+        // ...look, just pretend you forgot what you just read.
+        // Stability concerns.
+        let rt_u64_to_f64 = |rt| unsafe { mem::transmute::<u64, f64>(rt) };
+        // SAFETY: We use internal implementations that either always work or fail at compile time.
+        unsafe { intrinsics::const_eval_select((v,), ct_u64_to_f64, rt_u64_to_f64) }
+    }
+
+    /// Return the memory representation of this floating point number as a byte array in
+    /// big-endian (network) byte order.
+    ///
+    /// See [`from_bits`](Self::from_bits) for some discussion of the
+    /// portability of this operation (there are almost no issues).
+    ///
+    /// # Examples
+    ///
+    /// ```
+    /// let bytes = 12.5f64.to_be_bytes();
+    /// assert_eq!(bytes, [0x40, 0x29, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00]);
+    /// ```
+    #[must_use = "this returns the result of the operation, \
+                  without modifying the original"]
+    #[stable(feature = "float_to_from_bytes", since = "1.40.0")]
+    #[rustc_const_unstable(feature = "const_float_bits_conv", issue = "72447")]
+    #[inline]
+    pub const fn to_be_bytes(self) -> [u8; 8] {
+        self.to_bits().to_be_bytes()
+    }
+
+    /// Return the memory representation of this floating point number as a byte array in
+    /// little-endian byte order.
+    ///
+    /// See [`from_bits`](Self::from_bits) for some discussion of the
+    /// portability of this operation (there are almost no issues).
+    ///
+    /// # Examples
+    ///
+    /// ```
+    /// let bytes = 12.5f64.to_le_bytes();
+    /// assert_eq!(bytes, [0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x29, 0x40]);
+    /// ```
+    #[must_use = "this returns the result of the operation, \
+                  without modifying the original"]
+    #[stable(feature = "float_to_from_bytes", since = "1.40.0")]
+    #[rustc_const_unstable(feature = "const_float_bits_conv", issue = "72447")]
+    #[inline]
+    pub const fn to_le_bytes(self) -> [u8; 8] {
+        self.to_bits().to_le_bytes()
+    }
+
+    /// Return the memory representation of this floating point number as a byte array in
+    /// native byte order.
+    ///
+    /// As the target platform's native endianness is used, portable code
+    /// should use [`to_be_bytes`] or [`to_le_bytes`], as appropriate, instead.
+    ///
+    /// [`to_be_bytes`]: f64::to_be_bytes
+    /// [`to_le_bytes`]: f64::to_le_bytes
+    ///
+    /// See [`from_bits`](Self::from_bits) for some discussion of the
+    /// portability of this operation (there are almost no issues).
+    ///
+    /// # Examples
+    ///
+    /// ```
+    /// let bytes = 12.5f64.to_ne_bytes();
+    /// assert_eq!(
+    ///     bytes,
+    ///     if cfg!(target_endian = "big") {
+    ///         [0x40, 0x29, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00]
+    ///     } else {
+    ///         [0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x29, 0x40]
+    ///     }
+    /// );
+    /// ```
+    #[must_use = "this returns the result of the operation, \
+                  without modifying the original"]
+    #[stable(feature = "float_to_from_bytes", since = "1.40.0")]
+    #[rustc_const_unstable(feature = "const_float_bits_conv", issue = "72447")]
+    #[inline]
+    pub const fn to_ne_bytes(self) -> [u8; 8] {
+        self.to_bits().to_ne_bytes()
+    }
+
+    /// Create a floating point value from its representation as a byte array in big endian.
+    ///
+    /// See [`from_bits`](Self::from_bits) for some discussion of the
+    /// portability of this operation (there are almost no issues).
+    ///
+    /// # Examples
+    ///
+    /// ```
+    /// let value = f64::from_be_bytes([0x40, 0x29, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00]);
+    /// assert_eq!(value, 12.5);
+    /// ```
+    #[stable(feature = "float_to_from_bytes", since = "1.40.0")]
+    #[rustc_const_unstable(feature = "const_float_bits_conv", issue = "72447")]
+    #[must_use]
+    #[inline]
+    pub const fn from_be_bytes(bytes: [u8; 8]) -> Self {
+        Self::from_bits(u64::from_be_bytes(bytes))
+    }
+
+    /// Create a floating point value from its representation as a byte array in little endian.
+    ///
+    /// See [`from_bits`](Self::from_bits) for some discussion of the
+    /// portability of this operation (there are almost no issues).
+    ///
+    /// # Examples
+    ///
+    /// ```
+    /// let value = f64::from_le_bytes([0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x29, 0x40]);
+    /// assert_eq!(value, 12.5);
+    /// ```
+    #[stable(feature = "float_to_from_bytes", since = "1.40.0")]
+    #[rustc_const_unstable(feature = "const_float_bits_conv", issue = "72447")]
+    #[must_use]
+    #[inline]
+    pub const fn from_le_bytes(bytes: [u8; 8]) -> Self {
+        Self::from_bits(u64::from_le_bytes(bytes))
+    }
+
+    /// Create a floating point value from its representation as a byte array in native endian.
+    ///
+    /// As the target platform's native endianness is used, portable code
+    /// likely wants to use [`from_be_bytes`] or [`from_le_bytes`], as
+    /// appropriate instead.
+    ///
+    /// [`from_be_bytes`]: f64::from_be_bytes
+    /// [`from_le_bytes`]: f64::from_le_bytes
+    ///
+    /// See [`from_bits`](Self::from_bits) for some discussion of the
+    /// portability of this operation (there are almost no issues).
+    ///
+    /// # Examples
+    ///
+    /// ```
+    /// let value = f64::from_ne_bytes(if cfg!(target_endian = "big") {
+    ///     [0x40, 0x29, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00]
+    /// } else {
+    ///     [0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x29, 0x40]
+    /// });
+    /// assert_eq!(value, 12.5);
+    /// ```
+    #[stable(feature = "float_to_from_bytes", since = "1.40.0")]
+    #[rustc_const_unstable(feature = "const_float_bits_conv", issue = "72447")]
+    #[must_use]
+    #[inline]
+    pub const fn from_ne_bytes(bytes: [u8; 8]) -> Self {
+        Self::from_bits(u64::from_ne_bytes(bytes))
+    }
+
+    /// Return the ordering between `self` and `other`.
+    ///
+    /// Unlike the standard partial comparison between floating point numbers,
+    /// this comparison always produces an ordering in accordance to
+    /// the `totalOrder` predicate as defined in the IEEE 754 (2008 revision)
+    /// floating point standard. The values are ordered in the following sequence:
+    ///
+    /// - negative quiet NaN
+    /// - negative signaling NaN
+    /// - negative infinity
+    /// - negative numbers
+    /// - negative subnormal numbers
+    /// - negative zero
+    /// - positive zero
+    /// - positive subnormal numbers
+    /// - positive numbers
+    /// - positive infinity
+    /// - positive signaling NaN
+    /// - positive quiet NaN.
+    ///
+    /// The ordering established by this function does not always agree with the
+    /// [`PartialOrd`] and [`PartialEq`] implementations of `f64`. For example,
+    /// they consider negative and positive zero equal, while `total_cmp`
+    /// doesn't.
+    ///
+    /// The interpretation of the signaling NaN bit follows the definition in
+    /// the IEEE 754 standard, which may not match the interpretation by some of
+    /// the older, non-conformant (e.g. MIPS) hardware implementations.
+    ///
+    /// # Example
+    ///
+    /// ```
+    /// struct GoodBoy {
+    ///     name: String,
+    ///     weight: f64,
+    /// }
+    ///
+    /// let mut bois = vec![
+    ///     GoodBoy { name: "Pucci".to_owned(), weight: 0.1 },
+    ///     GoodBoy { name: "Woofer".to_owned(), weight: 99.0 },
+    ///     GoodBoy { name: "Yapper".to_owned(), weight: 10.0 },
+    ///     GoodBoy { name: "Chonk".to_owned(), weight: f64::INFINITY },
+    ///     GoodBoy { name: "Abs. Unit".to_owned(), weight: f64::NAN },
+    ///     GoodBoy { name: "Floaty".to_owned(), weight: -5.0 },
+    /// ];
+    ///
+    /// bois.sort_by(|a, b| a.weight.total_cmp(&b.weight));
+    /// # assert!(bois.into_iter().map(|b| b.weight)
+    /// #     .zip([-5.0, 0.1, 10.0, 99.0, f64::INFINITY, f64::NAN].iter())
+    /// #     .all(|(a, b)| a.to_bits() == b.to_bits()))
+    /// ```
+    #[stable(feature = "total_cmp", since = "1.62.0")]
+    #[must_use]
+    #[inline]
+    pub fn total_cmp(&self, other: &Self) -> crate::cmp::Ordering {
+        let mut left = self.to_bits() as i64;
+        let mut right = other.to_bits() as i64;
+
+        // In case of negatives, flip all the bits except the sign
+        // to achieve a similar layout as two's complement integers
+        //
+        // Why does this work? IEEE 754 floats consist of three fields:
+        // Sign bit, exponent and mantissa. The set of exponent and mantissa
+        // fields as a whole have the property that their bitwise order is
+        // equal to the numeric magnitude where the magnitude is defined.
+        // The magnitude is not normally defined on NaN values, but
+        // IEEE 754 totalOrder defines the NaN values also to follow the
+        // bitwise order. This leads to order explained in the doc comment.
+        // However, the representation of magnitude is the same for negative
+        // and positive numbers – only the sign bit is different.
+        // To easily compare the floats as signed integers, we need to
+        // flip the exponent and mantissa bits in case of negative numbers.
+        // We effectively convert the numbers to "two's complement" form.
+        //
+        // To do the flipping, we construct a mask and XOR against it.
+        // We branchlessly calculate an "all-ones except for the sign bit"
+        // mask from negative-signed values: right shifting sign-extends
+        // the integer, so we "fill" the mask with sign bits, and then
+        // convert to unsigned to push one more zero bit.
+        // On positive values, the mask is all zeros, so it's a no-op.
+        left ^= (((left >> 63) as u64) >> 1) as i64;
+        right ^= (((right >> 63) as u64) >> 1) as i64;
+
+        left.cmp(&right)
+    }
+
+    /// Restrict a value to a certain interval unless it is NaN.
+    ///
+    /// Returns `max` if `self` is greater than `max`, and `min` if `self` is
+    /// less than `min`. Otherwise this returns `self`.
+    ///
+    /// Note that this function returns NaN if the initial value was NaN as
+    /// well.
+    ///
+    /// # Panics
+    ///
+    /// Panics if `min > max`, `min` is NaN, or `max` is NaN.
+    ///
+    /// # Examples
+    ///
+    /// ```
+    /// assert!((-3.0f64).clamp(-2.0, 1.0) == -2.0);
+    /// assert!((0.0f64).clamp(-2.0, 1.0) == 0.0);
+    /// assert!((2.0f64).clamp(-2.0, 1.0) == 1.0);
+    /// assert!((f64::NAN).clamp(-2.0, 1.0).is_nan());
+    /// ```
+    #[must_use = "method returns a new number and does not mutate the original value"]
+    #[stable(feature = "clamp", since = "1.50.0")]
+    #[inline]
+    pub fn clamp(self, min: f64, max: f64) -> f64 {
+        assert!(min <= max);
+        let mut x = self;
+        if x < min {
+            x = min;
+        }
+        if x > max {
+            x = max;
+        }
+        x
+    }
+}
diff --git a/library/core/src/num/flt2dec/decoder.rs b/library/core/src/num/flt2dec/decoder.rs
new file mode 100644
index 000000000..576386054
--- /dev/null
+++ b/library/core/src/num/flt2dec/decoder.rs
@@ -0,0 +1,100 @@
+//! Decodes a floating-point value into individual parts and error ranges.
+
+use crate::num::dec2flt::float::RawFloat;
+use crate::num::FpCategory;
+
+/// Decoded unsigned finite value, such that:
+///
+/// - The original value equals to `mant * 2^exp`.
+///
+/// - Any number from `(mant - minus) * 2^exp` to `(mant + plus) * 2^exp` will
+///   round to the original value. The range is inclusive only when
+///   `inclusive` is `true`.
+#[derive(Copy, Clone, Debug, PartialEq, Eq)]
+pub struct Decoded {
+    /// The scaled mantissa.
+    pub mant: u64,
+    /// The lower error range.
+    pub minus: u64,
+    /// The upper error range.
+    pub plus: u64,
+    /// The shared exponent in base 2.
+    pub exp: i16,
+    /// True when the error range is inclusive.
+    ///
+    /// In IEEE 754, this is true when the original mantissa was even.
+    pub inclusive: bool,
+}
+
+/// Decoded unsigned value.
+#[derive(Copy, Clone, Debug, PartialEq, Eq)]
+pub enum FullDecoded {
+    /// Not-a-number.
+    Nan,
+    /// Infinities, either positive or negative.
+    Infinite,
+    /// Zero, either positive or negative.
+    Zero,
+    /// Finite numbers with further decoded fields.
+    Finite(Decoded),
+}
+
+/// A floating point type which can be `decode`d.
+pub trait DecodableFloat: RawFloat + Copy {
+    /// The minimum positive normalized value.
+    fn min_pos_norm_value() -> Self;
+}
+
+impl DecodableFloat for f32 {
+    fn min_pos_norm_value() -> Self {
+        f32::MIN_POSITIVE
+    }
+}
+
+impl DecodableFloat for f64 {
+    fn min_pos_norm_value() -> Self {
+        f64::MIN_POSITIVE
+    }
+}
+
+/// Returns a sign (true when negative) and `FullDecoded` value
+/// from given floating point number.
+pub fn decode<T: DecodableFloat>(v: T) -> (/*negative?*/ bool, FullDecoded) {
+    let (mant, exp, sign) = v.integer_decode();
+    let even = (mant & 1) == 0;
+    let decoded = match v.classify() {
+        FpCategory::Nan => FullDecoded::Nan,
+        FpCategory::Infinite => FullDecoded::Infinite,
+        FpCategory::Zero => FullDecoded::Zero,
+        FpCategory::Subnormal => {
+            // neighbors: (mant - 2, exp) -- (mant, exp) -- (mant + 2, exp)
+            // Float::integer_decode always preserves the exponent,
+            // so the mantissa is scaled for subnormals.
+            FullDecoded::Finite(Decoded { mant, minus: 1, plus: 1, exp, inclusive: even })
+        }
+        FpCategory::Normal => {
+            let minnorm = <T as DecodableFloat>::min_pos_norm_value().integer_decode();
+            if mant == minnorm.0 {
+                // neighbors: (maxmant, exp - 1) -- (minnormmant, exp) -- (minnormmant + 1, exp)
+                // where maxmant = minnormmant * 2 - 1
+                FullDecoded::Finite(Decoded {
+                    mant: mant << 2,
+                    minus: 1,
+                    plus: 2,
+                    exp: exp - 2,
+                    inclusive: even,
+                })
+            } else {
+                // neighbors: (mant - 1, exp) -- (mant, exp) -- (mant + 1, exp)
+                FullDecoded::Finite(Decoded {
+                    mant: mant << 1,
+                    minus: 1,
+                    plus: 1,
+                    exp: exp - 1,
+                    inclusive: even,
+                })
+            }
+        }
+    };
+    (sign < 0, decoded)
+}
diff --git a/library/core/src/num/flt2dec/estimator.rs b/library/core/src/num/flt2dec/estimator.rs
new file mode 100644
index 000000000..50e2f7052
--- /dev/null
+++ b/library/core/src/num/flt2dec/estimator.rs
@@ -0,0 +1,14 @@
+//! The exponent estimator.
+
+/// Finds `k_0` such that `10^(k_0-1) < mant * 2^exp <= 10^(k_0+1)`.
+///
+/// This is used to approximate `k = ceil(log_10 (mant * 2^exp))`;
+/// the true `k` is either `k_0` or `k_0+1`.
+#[doc(hidden)]
+pub fn estimate_scaling_factor(mant: u64, exp: i16) -> i16 {
+    // 2^(nbits-1) < mant <= 2^nbits if mant > 0
+    let nbits = 64 - (mant - 1).leading_zeros() as i64;
+    // 1292913986 = floor(2^32 * log_10 2)
+    // therefore this always underestimates (or is exact), but not much.
+    (((nbits + exp as i64) * 1292913986) >> 32) as i16
+}
diff --git a/library/core/src/num/flt2dec/mod.rs b/library/core/src/num/flt2dec/mod.rs
new file mode 100644
index 000000000..1ff2e8c82
--- /dev/null
+++ b/library/core/src/num/flt2dec/mod.rs
@@ -0,0 +1,673 @@
+/*!
+
+Floating-point number to decimal conversion routines.
+
+# Problem statement
+
+We are given the floating-point number `v = f * 2^e` with an integer `f`,
+and its bounds `minus` and `plus` such that any number between `v - minus` and
+`v + plus` will be rounded to `v`. For the simplicity we assume that
+this range is exclusive. Then we would like to get the unique decimal
+representation `V = 0.d[0..n-1] * 10^k` such that:
+
+- `d[0]` is non-zero.
+
+- It's correctly rounded when parsed back: `v - minus < V < v + plus`.
+  Furthermore it is shortest such one, i.e., there is no representation
+  with less than `n` digits that is correctly rounded.
+
+- It's closest to the original value: `abs(V - v) <= 10^(k-n) / 2`. Note that
+  there might be two representations satisfying this uniqueness requirement,
+  in which case some tie-breaking mechanism is used.
+
+We will call this mode of operation as to the *shortest* mode. This mode is used
+when there is no additional constraint, and can be thought as a "natural" mode
+as it matches the ordinary intuition (it at least prints `0.1f32` as "0.1").
+
+We have two more modes of operation closely related to each other. In these modes
+we are given either the number of significant digits `n` or the last-digit
+limitation `limit` (which determines the actual `n`), and we would like to get
+the representation `V = 0.d[0..n-1] * 10^k` such that:
+
+- `d[0]` is non-zero, unless `n` was zero in which case only `k` is returned.
+
+- It's closest to the original value: `abs(V - v) <= 10^(k-n) / 2`. Again,
+  there might be some tie-breaking mechanism.
+
+When `limit` is given but not `n`, we set `n` such that `k - n = limit`
+so that the last digit `d[n-1]` is scaled by `10^(k-n) = 10^limit`.
+If such `n` is negative, we clip it to zero so that we will only get `k`.
+We are also limited by the supplied buffer. This limitation is used to print
+the number up to given number of fractional digits without knowing
+the correct `k` beforehand.
+
+We will call the mode of operation requiring `n` as to the *exact* mode,
+and one requiring `limit` as to the *fixed* mode. The exact mode is a subset of
+the fixed mode: the sufficiently large last-digit limitation will eventually fill
+the supplied buffer and let the algorithm to return.
+
+# Implementation overview
+
+It is easy to get the floating point printing correct but slow (Russ Cox has
+[demonstrated](https://research.swtch.com/ftoa) how it's easy), or incorrect but
+fast (naïve division and modulo). But it is surprisingly hard to print
+floating point numbers correctly *and* efficiently.
+
+There are two classes of algorithms widely known to be correct.
+
+- The "Dragon" family of algorithm is first described by Guy L. Steele Jr. and
+  Jon L. White. They rely on the fixed-size big integer for their correctness.
+  A slight improvement was found later, which is posthumously described by
+  Robert G. Burger and R. Kent Dybvig. David Gay's `dtoa.c` routine is
+  a popular implementation of this strategy.
+
+- The "Grisu" family of algorithm is first described by Florian Loitsch.
+  They use very cheap integer-only procedure to determine the close-to-correct
+  representation which is at least guaranteed to be shortest. The variant,
+  Grisu3, actively detects if the resulting representation is incorrect.
+
+We implement both algorithms with necessary tweaks to suit our requirements.
+In particular, published literatures are short of the actual implementation
+difficulties like how to avoid arithmetic overflows. Each implementation,
+available in `strategy::dragon` and `strategy::grisu` respectively,
+extensively describes all necessary justifications and many proofs for them.
+(It is still difficult to follow though. You have been warned.)
+
+Both implementations expose two public functions:
+
+- `format_shortest(decoded, buf)`, which always needs at least
+  `MAX_SIG_DIGITS` digits of buffer. Implements the shortest mode.
+
+- `format_exact(decoded, buf, limit)`, which accepts as small as
+  one digit of buffer. Implements exact and fixed modes.
+
+They try to fill the `u8` buffer with digits and returns the number of digits
+written and the exponent `k`. They are total for all finite `f32` and `f64`
+inputs (Grisu internally falls back to Dragon if necessary).
+
+The rendered digits are formatted into the actual string form with
+four functions:
+
+- `to_shortest_str` prints the shortest representation, which can be padded by
+  zeroes to make *at least* given number of fractional digits.
+
+- `to_shortest_exp_str` prints the shortest representation, which can be
+  padded by zeroes when its exponent is in the specified ranges,
+  or can be printed in the exponential form such as `1.23e45`.
+
+- `to_exact_exp_str` prints the exact representation with given number of
+  digits in the exponential form.
+
+- `to_exact_fixed_str` prints the fixed representation with *exactly*
+  given number of fractional digits.
+
+They all return a slice of preallocated `Part` array, which corresponds to
+the individual part of strings: a fixed string, a part of rendered digits,
+a number of zeroes or a small (`u16`) number. The caller is expected to
+provide a large enough buffer and `Part` array, and to assemble the final
+string from resulting `Part`s itself.
+
+All algorithms and formatting functions are accompanied by extensive tests
+in `coretests::num::flt2dec` module. It also shows how to use individual
+functions.
+
+*/
+
+// while this is extensively documented, this is in principle private which is
+// only made public for testing. do not expose us.
+#![doc(hidden)]
+#![unstable(
+    feature = "flt2dec",
+    reason = "internal routines only exposed for testing",
+    issue = "none"
+)]
+
+pub use self::decoder::{decode, DecodableFloat, Decoded, FullDecoded};
+
+use super::fmt::{Formatted, Part};
+use crate::mem::MaybeUninit;
+
+pub mod decoder;
+pub mod estimator;
+
+/// Digit-generation algorithms.
+pub mod strategy {
+    pub mod dragon;
+    pub mod grisu;
+}
+
+/// The minimum size of buffer necessary for the shortest mode.
+///
+/// It is a bit non-trivial to derive, but this is one plus the maximal number of
+/// significant decimal digits from formatting algorithms with the shortest result.
+/// The exact formula is `ceil(# bits in mantissa * log_10 2 + 1)`.
+pub const MAX_SIG_DIGITS: usize = 17;
+
+/// When `d` contains decimal digits, increase the last digit and propagate carry.
+/// Returns a next digit when it causes the length to change.
+#[doc(hidden)]
+pub fn round_up(d: &mut [u8]) -> Option<u8> {
+    match d.iter().rposition(|&c| c != b'9') {
+        Some(i) => {
+            // d[i+1..n] is all nines
+            d[i] += 1;
+            for j in i + 1..d.len() {
+                d[j] = b'0';
+            }
+            None
+        }
+        None if d.len() > 0 => {
+            // 999..999 rounds to 1000..000 with an increased exponent
+            d[0] = b'1';
+            for j in 1..d.len() {
+                d[j] = b'0';
+            }
+            Some(b'0')
+        }
+        None => {
+            // an empty buffer rounds up (a bit strange but reasonable)
+            Some(b'1')
+        }
+    }
+}
+
+/// Formats given decimal digits `0.<...buf...> * 10^exp` into the decimal form
+/// with at least given number of fractional digits. The result is stored to
+/// the supplied parts array and a slice of written parts is returned.
+///
+/// `frac_digits` can be less than the number of actual fractional digits in `buf`;
+/// it will be ignored and full digits will be printed. It is only used to print
+/// additional zeroes after rendered digits. Thus `frac_digits` of 0 means that
+/// it will only print given digits and nothing else.
+fn digits_to_dec_str<'a>(
+    buf: &'a [u8],
+    exp: i16,
+    frac_digits: usize,
+    parts: &'a mut [MaybeUninit<Part<'a>>],
+) -> &'a [Part<'a>] {
+    assert!(!buf.is_empty());
+    assert!(buf[0] > b'0');
+    assert!(parts.len() >= 4);
+
+    // if there is the restriction on the last digit position, `buf` is assumed to be
+    // left-padded with the virtual zeroes. the number of virtual zeroes, `nzeroes`,
+    // equals to `max(0, exp + frac_digits - buf.len())`, so that the position of
+    // the last digit `exp - buf.len() - nzeroes` is no more than `-frac_digits`:
+    //
+    //                       |<-virtual->|
+    //       |<---- buf ---->|  zeroes   |     exp
+    //    0. 1 2 3 4 5 6 7 8 9 _ _ _ _ _ _ x 10
+    //    |                  |           |
+    // 10^exp    10^(exp-buf.len())   10^(exp-buf.len()-nzeroes)
+    //
+    // `nzeroes` is individually calculated for each case in order to avoid overflow.
+
+    if exp <= 0 {
+        // the decimal point is before rendered digits: [0.][000...000][1234][____]
+        let minus_exp = -(exp as i32) as usize;
+        parts[0] = MaybeUninit::new(Part::Copy(b"0."));
+        parts[1] = MaybeUninit::new(Part::Zero(minus_exp));
+        parts[2] = MaybeUninit::new(Part::Copy(buf));
+        if frac_digits > buf.len() && frac_digits - buf.len() > minus_exp {
+            parts[3] = MaybeUninit::new(Part::Zero((frac_digits - buf.len()) - minus_exp));
+            // SAFETY: we just initialized the elements `..4`.
+            unsafe { MaybeUninit::slice_assume_init_ref(&parts[..4]) }
+        } else {
+            // SAFETY: we just initialized the elements `..3`.
+            unsafe { MaybeUninit::slice_assume_init_ref(&parts[..3]) }
+        }
+    } else {
+        let exp = exp as usize;
+        if exp < buf.len() {
+            // the decimal point is inside rendered digits: [12][.][34][____]
+            parts[0] = MaybeUninit::new(Part::Copy(&buf[..exp]));
+            parts[1] = MaybeUninit::new(Part::Copy(b"."));
+            parts[2] = MaybeUninit::new(Part::Copy(&buf[exp..]));
+            if frac_digits > buf.len() - exp {
+                parts[3] = MaybeUninit::new(Part::Zero(frac_digits - (buf.len() - exp)));
+                // SAFETY: we just initialized the elements `..4`.
+                unsafe { MaybeUninit::slice_assume_init_ref(&parts[..4]) }
+            } else {
+                // SAFETY: we just initialized the elements `..3`.
+                unsafe { MaybeUninit::slice_assume_init_ref(&parts[..3]) }
+            }
+        } else {
+            // the decimal point is after rendered digits: [1234][____0000] or [1234][__][.][__].
+            parts[0] = MaybeUninit::new(Part::Copy(buf));
+            parts[1] = MaybeUninit::new(Part::Zero(exp - buf.len()));
+            if frac_digits > 0 {
+                parts[2] = MaybeUninit::new(Part::Copy(b"."));
+                parts[3] = MaybeUninit::new(Part::Zero(frac_digits));
+                // SAFETY: we just initialized the elements `..4`.
+                unsafe { MaybeUninit::slice_assume_init_ref(&parts[..4]) }
+            } else {
+                // SAFETY: we just initialized the elements `..2`.
+                unsafe { MaybeUninit::slice_assume_init_ref(&parts[..2]) }
+            }
+        }
+    }
+}
+
+/// Formats the given decimal digits `0.<...buf...> * 10^exp` into the exponential
+/// form with at least the given number of significant digits. When `upper` is `true`,
+/// the exponent will be prefixed by `E`; otherwise that's `e`. The result is
+/// stored to the supplied parts array and a slice of written parts is returned.
+///
+/// `min_digits` can be less than the number of actual significant digits in `buf`;
+/// it will be ignored and full digits will be printed. It is only used to print
+/// additional zeroes after rendered digits. Thus, `min_digits == 0` means that
+/// it will only print the given digits and nothing else.
+fn digits_to_exp_str<'a>(
+    buf: &'a [u8],
+    exp: i16,
+    min_ndigits: usize,
+    upper: bool,
+    parts: &'a mut [MaybeUninit<Part<'a>>],
+) -> &'a [Part<'a>] {
+    assert!(!buf.is_empty());
+    assert!(buf[0] > b'0');
+    assert!(parts.len() >= 6);
+
+    let mut n = 0;
+
+    parts[n] = MaybeUninit::new(Part::Copy(&buf[..1]));
+    n += 1;
+
+    if buf.len() > 1 || min_ndigits > 1 {
+        parts[n] = MaybeUninit::new(Part::Copy(b"."));
+        parts[n + 1] = MaybeUninit::new(Part::Copy(&buf[1..]));
+        n += 2;
+        if min_ndigits > buf.len() {
+            parts[n] = MaybeUninit::new(Part::Zero(min_ndigits - buf.len()));
+            n += 1;
+        }
+    }
+
+    // 0.1234 x 10^exp = 1.234 x 10^(exp-1)
+    let exp = exp as i32 - 1; // avoid underflow when exp is i16::MIN
+    if exp < 0 {
+        parts[n] = MaybeUninit::new(Part::Copy(if upper { b"E-" } else { b"e-" }));
+        parts[n + 1] = MaybeUninit::new(Part::Num(-exp as u16));
+    } else {
+        parts[n] = MaybeUninit::new(Part::Copy(if upper { b"E" } else { b"e" }));
+        parts[n + 1] = MaybeUninit::new(Part::Num(exp as u16));
+    }
+    // SAFETY: we just initialized the elements `..n + 2`.
+    unsafe { MaybeUninit::slice_assume_init_ref(&parts[..n + 2]) }
+}
+
+/// Sign formatting options.
+#[derive(Copy, Clone, PartialEq, Eq, Debug)]
+pub enum Sign {
+    /// Prints `-` for any negative value.
+    Minus, // -inf -1 -0  0  1  inf nan
+    /// Prints `-` for any negative value, or `+` otherwise.
+    MinusPlus, // -inf -1 -0 +0 +1 +inf nan
+}
+
+/// Returns the static byte string corresponding to the sign to be formatted.
+/// It can be either `""`, `"+"` or `"-"`.
+fn determine_sign(sign: Sign, decoded: &FullDecoded, negative: bool) -> &'static str {
+    match (*decoded, sign) {
+        (FullDecoded::Nan, _) => "",
+        (_, Sign::Minus) => {
+            if negative {
+                "-"
+            } else {
+                ""
+            }
+        }
+        (_, Sign::MinusPlus) => {
+            if negative {
+                "-"
+            } else {
+                "+"
+            }
+        }
+    }
+}
+
+/// Formats the given floating point number into the decimal form with at least
+/// given number of fractional digits. The result is stored to the supplied parts
+/// array while utilizing given byte buffer as a scratch. `upper` is currently
+/// unused but left for the future decision to change the case of non-finite values,
+/// i.e., `inf` and `nan`. The first part to be rendered is always a `Part::Sign`
+/// (which can be an empty string if no sign is rendered).
+///
+/// `format_shortest` should be the underlying digit-generation function.
+/// It should return the part of the buffer that it initialized.
+/// You probably would want `strategy::grisu::format_shortest` for this.
+///
+/// `frac_digits` can be less than the number of actual fractional digits in `v`;
+/// it will be ignored and full digits will be printed. It is only used to print
+/// additional zeroes after rendered digits. Thus `frac_digits` of 0 means that
+/// it will only print given digits and nothing else.
+///
+/// The byte buffer should be at least `MAX_SIG_DIGITS` bytes long.
+/// There should be at least 4 parts available, due to the worst case like
+/// `[+][0.][0000][2][0000]` with `frac_digits = 10`.
+pub fn to_shortest_str<'a, T, F>(
+    mut format_shortest: F,
+    v: T,
+    sign: Sign,
+    frac_digits: usize,
+    buf: &'a mut [MaybeUninit<u8>],
+    parts: &'a mut [MaybeUninit<Part<'a>>],
+) -> Formatted<'a>
+where
+    T: DecodableFloat,
+    F: FnMut(&Decoded, &'a mut [MaybeUninit<u8>]) -> (&'a [u8], i16),
+{
+    assert!(parts.len() >= 4);
+    assert!(buf.len() >= MAX_SIG_DIGITS);
+
+    let (negative, full_decoded) = decode(v);
+    let sign = determine_sign(sign, &full_decoded, negative);
+    match full_decoded {
+        FullDecoded::Nan => {
+            parts[0] = MaybeUninit::new(Part::Copy(b"NaN"));
+            // SAFETY: we just initialized the elements `..1`.
+            Formatted { sign, parts: unsafe { MaybeUninit::slice_assume_init_ref(&parts[..1]) } }
+        }
+        FullDecoded::Infinite => {
+            parts[0] = MaybeUninit::new(Part::Copy(b"inf"));
+            // SAFETY: we just initialized the elements `..1`.
+            Formatted { sign, parts: unsafe { MaybeUninit::slice_assume_init_ref(&parts[..1]) } }
+        }
+        FullDecoded::Zero => {
+            if frac_digits > 0 {
+                // [0.][0000]
+                parts[0] = MaybeUninit::new(Part::Copy(b"0."));
+                parts[1] = MaybeUninit::new(Part::Zero(frac_digits));
+                Formatted {
+                    sign,
+                    // SAFETY: we just initialized the elements `..2`.
+                    parts: unsafe { MaybeUninit::slice_assume_init_ref(&parts[..2]) },
+                }
+            } else {
+                parts[0] = MaybeUninit::new(Part::Copy(b"0"));
+                Formatted {
+                    sign,
+                    // SAFETY: we just initialized the elements `..1`.
+                    parts: unsafe { MaybeUninit::slice_assume_init_ref(&parts[..1]) },
+                }
+            }
+        }
+        FullDecoded::Finite(ref decoded) => {
+            let (buf, exp) = format_shortest(decoded, buf);
+            Formatted { sign, parts: digits_to_dec_str(buf, exp, frac_digits, parts) }
+        }
+    }
+}
+
+/// Formats the given floating point number into the decimal form or
+/// the exponential form, depending on the resulting exponent. The result is
+/// stored to the supplied parts array while utilizing given byte buffer
+/// as a scratch. `upper` is used to determine the case of non-finite values
+/// (`inf` and `nan`) or the case of the exponent prefix (`e` or `E`).
+/// The first part to be rendered is always a `Part::Sign` (which can be
+/// an empty string if no sign is rendered).
+///
+/// `format_shortest` should be the underlying digit-generation function.
+/// It should return the part of the buffer that it initialized.
+/// You probably would want `strategy::grisu::format_shortest` for this.
+///
+/// The `dec_bounds` is a tuple `(lo, hi)` such that the number is formatted
+/// as decimal only when `10^lo <= V < 10^hi`. Note that this is the *apparent* `V`
+/// instead of the actual `v`! Thus any printed exponent in the exponential form
+/// cannot be in this range, avoiding any confusion.
+///
+/// The byte buffer should be at least `MAX_SIG_DIGITS` bytes long.
+/// There should be at least 6 parts available, due to the worst case like
+/// `[+][1][.][2345][e][-][6]`.
+pub fn to_shortest_exp_str<'a, T, F>(
+    mut format_shortest: F,
+    v: T,
+    sign: Sign,
+    dec_bounds: (i16, i16),
+    upper: bool,
+    buf: &'a mut [MaybeUninit<u8>],
+    parts: &'a mut [MaybeUninit<Part<'a>>],
+) -> Formatted<'a>
+where
+    T: DecodableFloat,
+    F: FnMut(&Decoded, &'a mut [MaybeUninit<u8>]) -> (&'a [u8], i16),
+{
+    assert!(parts.len() >= 6);
+    assert!(buf.len() >= MAX_SIG_DIGITS);
+    assert!(dec_bounds.0 <= dec_bounds.1);
+
+    let (negative, full_decoded) = decode(v);
+    let sign = determine_sign(sign, &full_decoded, negative);
+    match full_decoded {
+        FullDecoded::Nan => {
+            parts[0] = MaybeUninit::new(Part::Copy(b"NaN"));
+            // SAFETY: we just initialized the elements `..1`.
+            Formatted { sign, parts: unsafe { MaybeUninit::slice_assume_init_ref(&parts[..1]) } }
+        }
+        FullDecoded::Infinite => {
+            parts[0] = MaybeUninit::new(Part::Copy(b"inf"));
+            // SAFETY: we just initialized the elements `..1`.
+            Formatted { sign, parts: unsafe { MaybeUninit::slice_assume_init_ref(&parts[..1]) } }
+        }
+        FullDecoded::Zero => {
+            parts[0] = if dec_bounds.0 <= 0 && 0 < dec_bounds.1 {
+                MaybeUninit::new(Part::Copy(b"0"))
+            } else {
+                MaybeUninit::new(Part::Copy(if upper { b"0E0" } else { b"0e0" }))
+            };
+            // SAFETY: we just initialized the elements `..1`.
+            Formatted { sign, parts: unsafe { MaybeUninit::slice_assume_init_ref(&parts[..1]) } }
+        }
+        FullDecoded::Finite(ref decoded) => {
+            let (buf, exp) = format_shortest(decoded, buf);
+            let vis_exp = exp as i32 - 1;
+            let parts = if dec_bounds.0 as i32 <= vis_exp && vis_exp < dec_bounds.1 as i32 {
+                digits_to_dec_str(buf, exp, 0, parts)
+            } else {
+                digits_to_exp_str(buf, exp, 0, upper, parts)
+            };
+            Formatted { sign, parts }
+        }
+    }
+}
+
+/// Returns a rather crude approximation (upper bound) for the maximum buffer size
+/// calculated from the given decoded exponent.
+///
+/// The exact limit is:
+///
+/// - when `exp < 0`, the maximum length is `ceil(log_10 (5^-exp * (2^64 - 1)))`.
+/// - when `exp >= 0`, the maximum length is `ceil(log_10 (2^exp * (2^64 - 1)))`.
+///
+/// `ceil(log_10 (x^exp * (2^64 - 1)))` is less than `ceil(log_10 (2^64 - 1)) +
+/// ceil(exp * log_10 x)`, which is in turn less than `20 + (1 + exp * log_10 x)`.
+/// We use the facts that `log_10 2 < 5/16` and `log_10 5 < 12/16`, which is
+/// enough for our purposes.
+///
+/// Why do we need this? `format_exact` functions will fill the entire buffer
+/// unless limited by the last digit restriction, but it is possible that
+/// the number of digits requested is ridiculously large (say, 30,000 digits).
+/// The vast majority of buffer will be filled with zeroes, so we don't want to
+/// allocate all the buffer beforehand. Consequently, for any given arguments,
+/// 826 bytes of buffer should be sufficient for `f64`. Compare this with
+/// the actual number for the worst case: 770 bytes (when `exp = -1074`).
+fn estimate_max_buf_len(exp: i16) -> usize {
+    21 + ((if exp < 0 { -12 } else { 5 } * exp as i32) as usize >> 4)
+}
+
+/// Formats given floating point number into the exponential form with
+/// exactly given number of significant digits. The result is stored to
+/// the supplied parts array while utilizing given byte buffer as a scratch.
+/// `upper` is used to determine the case of the exponent prefix (`e` or `E`).
+/// The first part to be rendered is always a `Part::Sign` (which can be
+/// an empty string if no sign is rendered).
+///
+/// `format_exact` should be the underlying digit-generation function.
+/// It should return the part of the buffer that it initialized.
+/// You probably would want `strategy::grisu::format_exact` for this.
+///
+/// The byte buffer should be at least `ndigits` bytes long unless `ndigits` is
+/// so large that only the fixed number of digits will be ever written.
+/// (The tipping point for `f64` is about 800, so 1000 bytes should be enough.)
+/// There should be at least 6 parts available, due to the worst case like
+/// `[+][1][.][2345][e][-][6]`.
+pub fn to_exact_exp_str<'a, T, F>(
+    mut format_exact: F,
+    v: T,
+    sign: Sign,
+    ndigits: usize,
+    upper: bool,
+    buf: &'a mut [MaybeUninit<u8>],
+    parts: &'a mut [MaybeUninit<Part<'a>>],
+) -> Formatted<'a>
+where
+    T: DecodableFloat,
+    F: FnMut(&Decoded, &'a mut [MaybeUninit<u8>], i16) -> (&'a [u8], i16),
+{
+    assert!(parts.len() >= 6);
+    assert!(ndigits > 0);
+
+    let (negative, full_decoded) = decode(v);
+    let sign = determine_sign(sign, &full_decoded, negative);
+    match full_decoded {
+        FullDecoded::Nan => {
+            parts[0] = MaybeUninit::new(Part::Copy(b"NaN"));
+            // SAFETY: we just initialized the elements `..1`.
+            Formatted { sign, parts: unsafe { MaybeUninit::slice_assume_init_ref(&parts[..1]) } }
+        }
+        FullDecoded::Infinite => {
+            parts[0] = MaybeUninit::new(Part::Copy(b"inf"));
+            // SAFETY: we just initialized the elements `..1`.
+            Formatted { sign, parts: unsafe { MaybeUninit::slice_assume_init_ref(&parts[..1]) } }
+        }
+        FullDecoded::Zero => {
+            if ndigits > 1 {
+                // [0.][0000][e0]
+                parts[0] = MaybeUninit::new(Part::Copy(b"0."));
+                parts[1] = MaybeUninit::new(Part::Zero(ndigits - 1));
+                parts[2] = MaybeUninit::new(Part::Copy(if upper { b"E0" } else { b"e0" }));
+                Formatted {
+                    sign,
+                    // SAFETY: we just initialized the elements `..3`.
+                    parts: unsafe { MaybeUninit::slice_assume_init_ref(&parts[..3]) },
+                }
+            } else {
+                parts[0] = MaybeUninit::new(Part::Copy(if upper { b"0E0" } else { b"0e0" }));
+                Formatted {
+                    sign,
+                    // SAFETY: we just initialized the elements `..1`.
+                    parts: unsafe { MaybeUninit::slice_assume_init_ref(&parts[..1]) },
+                }
+            }
+        }
+        FullDecoded::Finite(ref decoded) => {
+            let maxlen = estimate_max_buf_len(decoded.exp);
+            assert!(buf.len() >= ndigits || buf.len() >= maxlen);
+
+            let trunc = if ndigits < maxlen { ndigits } else { maxlen };
+            let (buf, exp) = format_exact(decoded, &mut buf[..trunc], i16::MIN);
+            Formatted { sign, parts: digits_to_exp_str(buf, exp, ndigits, upper, parts) }
+        }
+    }
+}
+
+/// Formats given floating point number into the decimal form with exactly
+/// given number of fractional digits. The result is stored to the supplied parts
+/// array while utilizing given byte buffer as a scratch. `upper` is currently
+/// unused but left for the future decision to change the case of non-finite values,
+/// i.e., `inf` and `nan`. The first part to be rendered is always a `Part::Sign`
+/// (which can be an empty string if no sign is rendered).
+///
+/// `format_exact` should be the underlying digit-generation function.
+/// It should return the part of the buffer that it initialized.
+/// You probably would want `strategy::grisu::format_exact` for this.
+///
+/// The byte buffer should be enough for the output unless `frac_digits` is
+/// so large that only the fixed number of digits will be ever written.
+/// (The tipping point for `f64` is about 800, and 1000 bytes should be enough.)
+/// There should be at least 4 parts available, due to the worst case like
+/// `[+][0.][0000][2][0000]` with `frac_digits = 10`.
+pub fn to_exact_fixed_str<'a, T, F>(
+    mut format_exact: F,
+    v: T,
+    sign: Sign,
+    frac_digits: usize,
+    buf: &'a mut [MaybeUninit<u8>],
+    parts: &'a mut [MaybeUninit<Part<'a>>],
+) -> Formatted<'a>
+where
+    T: DecodableFloat,
+    F: FnMut(&Decoded, &'a mut [MaybeUninit<u8>], i16) -> (&'a [u8], i16),
+{
+    assert!(parts.len() >= 4);
+
+    let (negative, full_decoded) = decode(v);
+    let sign = determine_sign(sign, &full_decoded, negative);
+    match full_decoded {
+        FullDecoded::Nan => {
+            parts[0] = MaybeUninit::new(Part::Copy(b"NaN"));
+            // SAFETY: we just initialized the elements `..1`.
+            Formatted { sign, parts: unsafe { MaybeUninit::slice_assume_init_ref(&parts[..1]) } }
+        }
+        FullDecoded::Infinite => {
+            parts[0] = MaybeUninit::new(Part::Copy(b"inf"));
+            // SAFETY: we just initialized the elements `..1`.
+            Formatted { sign, parts: unsafe { MaybeUninit::slice_assume_init_ref(&parts[..1]) } }
+        }
+        FullDecoded::Zero => {
+            if frac_digits > 0 {
+                // [0.][0000]
+                parts[0] = MaybeUninit::new(Part::Copy(b"0."));
+                parts[1] = MaybeUninit::new(Part::Zero(frac_digits));
+                Formatted {
+                    sign,
+                    // SAFETY: we just initialized the elements `..2`.
+                    parts: unsafe { MaybeUninit::slice_assume_init_ref(&parts[..2]) },
+                }
+            } else {
+                parts[0] = MaybeUninit::new(Part::Copy(b"0"));
+                Formatted {
+                    sign,
+                    // SAFETY: we just initialized the elements `..1`.
+                    parts: unsafe { MaybeUninit::slice_assume_init_ref(&parts[..1]) },
+                }
+            }
+        }
+        FullDecoded::Finite(ref decoded) => {
+            let maxlen = estimate_max_buf_len(decoded.exp);
+            assert!(buf.len() >= maxlen);
+
+            // it *is* possible that `frac_digits` is ridiculously large.
+            // `format_exact` will end rendering digits much earlier in this case,
+            // because we are strictly limited by `maxlen`.
+            let limit = if frac_digits < 0x8000 { -(frac_digits as i16) } else { i16::MIN };
+            let (buf, exp) = format_exact(decoded, &mut buf[..maxlen], limit);
+            if exp <= limit {
+                // the restriction couldn't been met, so this should render like zero no matter
+                // `exp` was. this does not include the case that the restriction has been met
+                // only after the final rounding-up; it's a regular case with `exp = limit + 1`.
+                debug_assert_eq!(buf.len(), 0);
+                if frac_digits > 0 {
+                    // [0.][0000]
+                    parts[0] = MaybeUninit::new(Part::Copy(b"0."));
+                    parts[1] = MaybeUninit::new(Part::Zero(frac_digits));
+                    Formatted {
+                        sign,
+                        // SAFETY: we just initialized the elements `..2`.
+                        parts: unsafe { MaybeUninit::slice_assume_init_ref(&parts[..2]) },
+                    }
+                } else {
+                    parts[0] = MaybeUninit::new(Part::Copy(b"0"));
+                    Formatted {
+                        sign,
+                        // SAFETY: we just initialized the elements `..1`.
+                        parts: unsafe { MaybeUninit::slice_assume_init_ref(&parts[..1]) },
+                    }
+                }
+            } else {
+                Formatted { sign, parts: digits_to_dec_str(buf, exp, frac_digits, parts) }
+            }
+        }
+    }
+}
diff --git a/library/core/src/num/flt2dec/strategy/dragon.rs b/library/core/src/num/flt2dec/strategy/dragon.rs
new file mode 100644
index 000000000..8ced5971e
--- /dev/null
+++ b/library/core/src/num/flt2dec/strategy/dragon.rs
@@ -0,0 +1,388 @@
+//! Almost direct (but slightly optimized) Rust translation of Figure 3 of "Printing
+//! Floating-Point Numbers Quickly and Accurately"[^1].
+//!
+//! [^1]: Burger, R. G. and Dybvig, R. K. 1996. Printing floating-point numbers
+//!   quickly and accurately. SIGPLAN Not. 31, 5 (May. 1996), 108-116.
+
+use crate::cmp::Ordering;
+use crate::mem::MaybeUninit;
+
+use crate::num::bignum::Big32x40 as Big;
+use crate::num::bignum::Digit32 as Digit;
+use crate::num::flt2dec::estimator::estimate_scaling_factor;
+use crate::num::flt2dec::{round_up, Decoded, MAX_SIG_DIGITS};
+
+static POW10: [Digit; 10] =
+    [1, 10, 100, 1000, 10000, 100000, 1000000, 10000000, 100000000, 1000000000];
+static TWOPOW10: [Digit; 10] =
+    [2, 20, 200, 2000, 20000, 200000, 2000000, 20000000, 200000000, 2000000000];
+
+// precalculated arrays of `Digit`s for 10^(2^n)
+static POW10TO16: [Digit; 2] = [0x6fc10000, 0x2386f2];
+static POW10TO32: [Digit; 4] = [0, 0x85acef81, 0x2d6d415b, 0x4ee];
+static POW10TO64: [Digit; 7] = [0, 0, 0xbf6a1f01, 0x6e38ed64, 0xdaa797ed, 0xe93ff9f4, 0x184f03];
+static POW10TO128: [Digit; 14] = [
+    0, 0, 0, 0, 0x2e953e01, 0x3df9909, 0xf1538fd, 0x2374e42f, 0xd3cff5ec, 0xc404dc08, 0xbccdb0da,
+    0xa6337f19, 0xe91f2603, 0x24e,
+];
+static POW10TO256: [Digit; 27] = [
+    0, 0, 0, 0, 0, 0, 0, 0, 0x982e7c01, 0xbed3875b, 0xd8d99f72, 0x12152f87, 0x6bde50c6, 0xcf4a6e70,
+    0xd595d80f, 0x26b2716e, 0xadc666b0, 0x1d153624, 0x3c42d35a, 0x63ff540e, 0xcc5573c0, 0x65f9ef17,
+    0x55bc28f2, 0x80dcc7f7, 0xf46eeddc, 0x5fdcefce, 0x553f7,
+];
+
+#[doc(hidden)]
+pub fn mul_pow10(x: &mut Big, n: usize) -> &mut Big {
+    debug_assert!(n < 512);
+    if n & 7 != 0 {
+        x.mul_small(POW10[n & 7]);
+    }
+    if n & 8 != 0 {
+        x.mul_small(POW10[8]);
+    }
+    if n & 16 != 0 {
+        x.mul_digits(&POW10TO16);
+    }
+    if n & 32 != 0 {
+        x.mul_digits(&POW10TO32);
+    }
+    if n & 64 != 0 {
+        x.mul_digits(&POW10TO64);
+    }
+    if n & 128 != 0 {
+        x.mul_digits(&POW10TO128);
+    }
+    if n & 256 != 0 {
+        x.mul_digits(&POW10TO256);
+    }
+    x
+}
+
+fn div_2pow10(x: &mut Big, mut n: usize) -> &mut Big {
+    let largest = POW10.len() - 1;
+    while n > largest {
+        x.div_rem_small(POW10[largest]);
+        n -= largest;
+    }
+    x.div_rem_small(TWOPOW10[n]);
+    x
+}
+
+// only usable when `x < 16 * scale`; `scaleN` should be `scale.mul_small(N)`
+fn div_rem_upto_16<'a>(
+    x: &'a mut Big,
+    scale: &Big,
+    scale2: &Big,
+    scale4: &Big,
+    scale8: &Big,
+) -> (u8, &'a mut Big) {
+    let mut d = 0;
+    if *x >= *scale8 {
+        x.sub(scale8);
+        d += 8;
+    }
+    if *x >= *scale4 {
+        x.sub(scale4);
+        d += 4;
+    }
+    if *x >= *scale2 {
+        x.sub(scale2);
+        d += 2;
+    }
+    if *x >= *scale {
+        x.sub(scale);
+        d += 1;
+    }
+    debug_assert!(*x < *scale);
+    (d, x)
+}
+
+/// The shortest mode implementation for Dragon.
+pub fn format_shortest<'a>(
+    d: &Decoded,
+    buf: &'a mut [MaybeUninit<u8>],
+) -> (/*digits*/ &'a [u8], /*exp*/ i16) {
+    // the number `v` to format is known to be:
+    // - equal to `mant * 2^exp`;
+    // - preceded by `(mant - 2 * minus) * 2^exp` in the original type; and
+    // - followed by `(mant + 2 * plus) * 2^exp` in the original type.
+    //
+    // obviously, `minus` and `plus` cannot be zero. (for infinities, we use out-of-range values.)
+    // also we assume that at least one digit is generated, i.e., `mant` cannot be zero too.
+    //
+    // this also means that any number between `low = (mant - minus) * 2^exp` and
+    // `high = (mant + plus) * 2^exp` will map to this exact floating point number,
+    // with bounds included when the original mantissa was even (i.e., `!mant_was_odd`).
+
+    assert!(d.mant > 0);
+    assert!(d.minus > 0);
+    assert!(d.plus > 0);
+    assert!(d.mant.checked_add(d.plus).is_some());
+    assert!(d.mant.checked_sub(d.minus).is_some());
+    assert!(buf.len() >= MAX_SIG_DIGITS);
+
+    // `a.cmp(&b) < rounding` is `if d.inclusive {a <= b} else {a < b}`
+    let rounding = if d.inclusive { Ordering::Greater } else { Ordering::Equal };
+
+    // estimate `k_0` from original inputs satisfying `10^(k_0-1) < high <= 10^(k_0+1)`.
+    // the tight bound `k` satisfying `10^(k-1) < high <= 10^k` is calculated later.
+    let mut k = estimate_scaling_factor(d.mant + d.plus, d.exp);
+
+    // convert `{mant, plus, minus} * 2^exp` into the fractional form so that:
+    // - `v = mant / scale`
+    // - `low = (mant - minus) / scale`
+    // - `high = (mant + plus) / scale`
+    let mut mant = Big::from_u64(d.mant);
+    let mut minus = Big::from_u64(d.minus);
+    let mut plus = Big::from_u64(d.plus);
+    let mut scale = Big::from_small(1);
+    if d.exp < 0 {
+        scale.mul_pow2(-d.exp as usize);
+    } else {
+        mant.mul_pow2(d.exp as usize);
+        minus.mul_pow2(d.exp as usize);
+        plus.mul_pow2(d.exp as usize);
+    }
+
+    // divide `mant` by `10^k`. now `scale / 10 < mant + plus <= scale * 10`.
+    if k >= 0 {
+        mul_pow10(&mut scale, k as usize);
+    } else {
+        mul_pow10(&mut mant, -k as usize);
+        mul_pow10(&mut minus, -k as usize);
+        mul_pow10(&mut plus, -k as usize);
+    }
+
+    // fixup when `mant + plus > scale` (or `>=`).
+    // we are not actually modifying `scale`, since we can skip the initial multiplication instead.
+    // now `scale < mant + plus <= scale * 10` and we are ready to generate digits.
+    //
+    // note that `d[0]` *can* be zero, when `scale - plus < mant < scale`.
+    // in this case rounding-up condition (`up` below) will be triggered immediately.
+    if scale.cmp(mant.clone().add(&plus)) < rounding {
+        // equivalent to scaling `scale` by 10
+        k += 1;
+    } else {
+        mant.mul_small(10);
+        minus.mul_small(10);
+        plus.mul_small(10);
+    }
+
+    // cache `(2, 4, 8) * scale` for digit generation.
+    let mut scale2 = scale.clone();
+    scale2.mul_pow2(1);
+    let mut scale4 = scale.clone();
+    scale4.mul_pow2(2);
+    let mut scale8 = scale.clone();
+    scale8.mul_pow2(3);
+
+    let mut down;
+    let mut up;
+    let mut i = 0;
+    loop {
+        // invariants, where `d[0..n-1]` are digits generated so far:
+        // - `v = mant / scale * 10^(k-n-1) + d[0..n-1] * 10^(k-n)`
+        // - `v - low = minus / scale * 10^(k-n-1)`
+        // - `high - v = plus / scale * 10^(k-n-1)`
+        // - `(mant + plus) / scale <= 10` (thus `mant / scale < 10`)
+        // where `d[i..j]` is a shorthand for `d[i] * 10^(j-i) + ... + d[j-1] * 10 + d[j]`.
+
+        // generate one digit: `d[n] = floor(mant / scale) < 10`.
+        let (d, _) = div_rem_upto_16(&mut mant, &scale, &scale2, &scale4, &scale8);
+        debug_assert!(d < 10);
+        buf[i] = MaybeUninit::new(b'0' + d);
+        i += 1;
+
+        // this is a simplified description of the modified Dragon algorithm.
+        // many intermediate derivations and completeness arguments are omitted for convenience.
+        //
+        // start with modified invariants, as we've updated `n`:
+        // - `v = mant / scale * 10^(k-n) + d[0..n-1] * 10^(k-n)`
+        // - `v - low = minus / scale * 10^(k-n)`
+        // - `high - v = plus / scale * 10^(k-n)`
+        //
+        // assume that `d[0..n-1]` is the shortest representation between `low` and `high`,
+        // i.e., `d[0..n-1]` satisfies both of the following but `d[0..n-2]` doesn't:
+        // - `low < d[0..n-1] * 10^(k-n) < high` (bijectivity: digits round to `v`); and
+        // - `abs(v / 10^(k-n) - d[0..n-1]) <= 1/2` (the last digit is correct).
+        //
+        // the second condition simplifies to `2 * mant <= scale`.
+        // solving invariants in terms of `mant`, `low` and `high` yields
+        // a simpler version of the first condition: `-plus < mant < minus`.
+        // since `-plus < 0 <= mant`, we have the correct shortest representation
+        // when `mant < minus` and `2 * mant <= scale`.
+        // (the former becomes `mant <= minus` when the original mantissa is even.)
+        //
+        // when the second doesn't hold (`2 * mant > scale`), we need to increase the last digit.
+        // this is enough for restoring that condition: we already know that
+        // the digit generation guarantees `0 <= v / 10^(k-n) - d[0..n-1] < 1`.
+        // in this case, the first condition becomes `-plus < mant - scale < minus`.
+        // since `mant < scale` after the generation, we have `scale < mant + plus`.
+        // (again, this becomes `scale <= mant + plus` when the original mantissa is even.)
+        //
+        // in short:
+        // - stop and round `down` (keep digits as is) when `mant < minus` (or `<=`).
+        // - stop and round `up` (increase the last digit) when `scale < mant + plus` (or `<=`).
+        // - keep generating otherwise.
+        down = mant.cmp(&minus) < rounding;
+        up = scale.cmp(mant.clone().add(&plus)) < rounding;
+        if down || up {
+            break;
+        } // we have the shortest representation, proceed to the rounding
+
+        // restore the invariants.
+        // this makes the algorithm always terminating: `minus` and `plus` always increases,
+        // but `mant` is clipped modulo `scale` and `scale` is fixed.
+        mant.mul_small(10);
+        minus.mul_small(10);
+        plus.mul_small(10);
+    }
+
+    // rounding up happens when
+    // i) only the rounding-up condition was triggered, or
+    // ii) both conditions were triggered and tie breaking prefers rounding up.
+    if up && (!down || *mant.mul_pow2(1) >= scale) {
+        // if rounding up changes the length, the exponent should also change.
+        // it seems that this condition is very hard to satisfy (possibly impossible),
+        // but we are just being safe and consistent here.
+        // SAFETY: we initialized that memory above.
+        if let Some(c) = round_up(unsafe { MaybeUninit::slice_assume_init_mut(&mut buf[..i]) }) {
+            buf[i] = MaybeUninit::new(c);
+            i += 1;
+            k += 1;
+        }
+    }
+
+    // SAFETY: we initialized that memory above.
+    (unsafe { MaybeUninit::slice_assume_init_ref(&buf[..i]) }, k)
+}
+
+/// The exact and fixed mode implementation for Dragon.
+pub fn format_exact<'a>(
+    d: &Decoded,
+    buf: &'a mut [MaybeUninit<u8>],
+    limit: i16,
+) -> (/*digits*/ &'a [u8], /*exp*/ i16) {
+    assert!(d.mant > 0);
+    assert!(d.minus > 0);
+    assert!(d.plus > 0);
+    assert!(d.mant.checked_add(d.plus).is_some());
+    assert!(d.mant.checked_sub(d.minus).is_some());
+
+    // estimate `k_0` from original inputs satisfying `10^(k_0-1) < v <= 10^(k_0+1)`.
+    let mut k = estimate_scaling_factor(d.mant, d.exp);
+
+    // `v = mant / scale`.
+    let mut mant = Big::from_u64(d.mant);
+    let mut scale = Big::from_small(1);
+    if d.exp < 0 {
+        scale.mul_pow2(-d.exp as usize);
+    } else {
+        mant.mul_pow2(d.exp as usize);
+    }
+
+    // divide `mant` by `10^k`. now `scale / 10 < mant <= scale * 10`.
+    if k >= 0 {
+        mul_pow10(&mut scale, k as usize);
+    } else {
+        mul_pow10(&mut mant, -k as usize);
+    }
+
+    // fixup when `mant + plus >= scale`, where `plus / scale = 10^-buf.len() / 2`.
+    // in order to keep the fixed-size bignum, we actually use `mant + floor(plus) >= scale`.
+    // we are not actually modifying `scale`, since we can skip the initial multiplication instead.
+    // again with the shortest algorithm, `d[0]` can be zero but will be eventually rounded up.
+    if *div_2pow10(&mut scale.clone(), buf.len()).add(&mant) >= scale {
+        // equivalent to scaling `scale` by 10
+        k += 1;
+    } else {
+        mant.mul_small(10);
+    }
+
+    // if we are working with the last-digit limitation, we need to shorten the buffer
+    // before the actual rendering in order to avoid double rounding.
+    // note that we have to enlarge the buffer again when rounding up happens!
+    let mut len = if k < limit {
+        // oops, we cannot even produce *one* digit.
+        // this is possible when, say, we've got something like 9.5 and it's being rounded to 10.
+        // we return an empty buffer, with an exception of the later rounding-up case
+        // which occurs when `k == limit` and has to produce exactly one digit.
+        0
+    } else if ((k as i32 - limit as i32) as usize) < buf.len() {
+        (k - limit) as usize
+    } else {
+        buf.len()
+    };
+
+    if len > 0 {
+        // cache `(2, 4, 8) * scale` for digit generation.
+        // (this can be expensive, so do not calculate them when the buffer is empty.)
+        let mut scale2 = scale.clone();
+        scale2.mul_pow2(1);
+        let mut scale4 = scale.clone();
+        scale4.mul_pow2(2);
+        let mut scale8 = scale.clone();
+        scale8.mul_pow2(3);
+
+        for i in 0..len {
+            if mant.is_zero() {
+                // following digits are all zeroes, we stop here
+                // do *not* try to perform rounding! rather, fill remaining digits.
+                for c in &mut buf[i..len] {
+                    *c = MaybeUninit::new(b'0');
+                }
+                // SAFETY: we initialized that memory above.
+                return (unsafe { MaybeUninit::slice_assume_init_ref(&buf[..len]) }, k);
+            }
+
+            let mut d = 0;
+            if mant >= scale8 {
+                mant.sub(&scale8);
+                d += 8;
+            }
+            if mant >= scale4 {
+                mant.sub(&scale4);
+                d += 4;
+            }
+            if mant >= scale2 {
+                mant.sub(&scale2);
+                d += 2;
+            }
+            if mant >= scale {
+                mant.sub(&scale);
+                d += 1;
+            }
+            debug_assert!(mant < scale);
+            debug_assert!(d < 10);
+            buf[i] = MaybeUninit::new(b'0' + d);
+            mant.mul_small(10);
+        }
+    }
+
+    // rounding up if we stop in the middle of digits
+    // if the following digits are exactly 5000..., check the prior digit and try to
+    // round to even (i.e., avoid rounding up when the prior digit is even).
+    let order = mant.cmp(scale.mul_small(5));
+    if order == Ordering::Greater
+        || (order == Ordering::Equal
+            // SAFETY: `buf[len-1]` is initialized.
+            && (len == 0 || unsafe { buf[len - 1].assume_init() } & 1 == 1))
+    {
+        // if rounding up changes the length, the exponent should also change.
+        // but we've been requested a fixed number of digits, so do not alter the buffer...
+        // SAFETY: we initialized that memory above.
+        if let Some(c) = round_up(unsafe { MaybeUninit::slice_assume_init_mut(&mut buf[..len]) }) {
+            // ...unless we've been requested the fixed precision instead.
+            // we also need to check that, if the original buffer was empty,
+            // the additional digit can only be added when `k == limit` (edge case).
+            k += 1;
+            if k > limit && len < buf.len() {
+                buf[len] = MaybeUninit::new(c);
+                len += 1;
+            }
+        }
+    }
+
+    // SAFETY: we initialized that memory above.
+    (unsafe { MaybeUninit::slice_assume_init_ref(&buf[..len]) }, k)
+}
diff --git a/library/core/src/num/flt2dec/strategy/grisu.rs b/library/core/src/num/flt2dec/strategy/grisu.rs
new file mode 100644
index 000000000..a4cb51c62
--- /dev/null
+++ b/library/core/src/num/flt2dec/strategy/grisu.rs
@@ -0,0 +1,764 @@
+//! Rust adaptation of the Grisu3 algorithm described in "Printing Floating-Point Numbers Quickly
+//! and Accurately with Integers"[^1]. It uses about 1KB of precomputed table, and in turn, it's
+//! very quick for most inputs.
+//!
+//! [^1]: Florian Loitsch. 2010. Printing floating-point numbers quickly and
+//!   accurately with integers. SIGPLAN Not. 45, 6 (June 2010), 233-243.
+
+use crate::mem::MaybeUninit;
+use crate::num::diy_float::Fp;
+use crate::num::flt2dec::{round_up, Decoded, MAX_SIG_DIGITS};
+
+// see the comments in `format_shortest_opt` for the rationale.
+#[doc(hidden)]
+pub const ALPHA: i16 = -60;
+#[doc(hidden)]
+pub const GAMMA: i16 = -32;
+
+/*
+# the following Python code generates this table:
+for i in xrange(-308, 333, 8):
+    if i >= 0: f = 10**i; e = 0
+    else: f = 2**(80-4*i) // 10**-i; e = 4 * i - 80
+    l = f.bit_length()
+    f = ((f << 64 >> (l-1)) + 1) >> 1; e += l - 64
+    print '    (%#018x, %5d, %4d),' % (f, e, i)
+*/
+
+#[doc(hidden)]
+pub static CACHED_POW10: [(u64, i16, i16); 81] = [
+    // (f, e, k)
+    (0xe61acf033d1a45df, -1087, -308),
+    (0xab70fe17c79ac6ca, -1060, -300),
+    (0xff77b1fcbebcdc4f, -1034, -292),
+    (0xbe5691ef416bd60c, -1007, -284),
+    (0x8dd01fad907ffc3c, -980, -276),
+    (0xd3515c2831559a83, -954, -268),
+    (0x9d71ac8fada6c9b5, -927, -260),
+    (0xea9c227723ee8bcb, -901, -252),
+    (0xaecc49914078536d, -874, -244),
+    (0x823c12795db6ce57, -847, -236),
+    (0xc21094364dfb5637, -821, -228),
+    (0x9096ea6f3848984f, -794, -220),
+    (0xd77485cb25823ac7, -768, -212),
+    (0xa086cfcd97bf97f4, -741, -204),
+    (0xef340a98172aace5, -715, -196),
+    (0xb23867fb2a35b28e, -688, -188),
+    (0x84c8d4dfd2c63f3b, -661, -180),
+    (0xc5dd44271ad3cdba, -635, -172),
+    (0x936b9fcebb25c996, -608, -164),
+    (0xdbac6c247d62a584, -582, -156),
+    (0xa3ab66580d5fdaf6, -555, -148),
+    (0xf3e2f893dec3f126, -529, -140),
+    (0xb5b5ada8aaff80b8, -502, -132),
+    (0x87625f056c7c4a8b, -475, -124),
+    (0xc9bcff6034c13053, -449, -116),
+    (0x964e858c91ba2655, -422, -108),
+    (0xdff9772470297ebd, -396, -100),
+    (0xa6dfbd9fb8e5b88f, -369, -92),
+    (0xf8a95fcf88747d94, -343, -84),
+    (0xb94470938fa89bcf, -316, -76),
+    (0x8a08f0f8bf0f156b, -289, -68),
+    (0xcdb02555653131b6, -263, -60),
+    (0x993fe2c6d07b7fac, -236, -52),
+    (0xe45c10c42a2b3b06, -210, -44),
+    (0xaa242499697392d3, -183, -36),
+    (0xfd87b5f28300ca0e, -157, -28),
+    (0xbce5086492111aeb, -130, -20),
+    (0x8cbccc096f5088cc, -103, -12),
+    (0xd1b71758e219652c, -77, -4),
+    (0x9c40000000000000, -50, 4),
+    (0xe8d4a51000000000, -24, 12),
+    (0xad78ebc5ac620000, 3, 20),
+    (0x813f3978f8940984, 30, 28),
+    (0xc097ce7bc90715b3, 56, 36),
+    (0x8f7e32ce7bea5c70, 83, 44),
+    (0xd5d238a4abe98068, 109, 52),
+    (0x9f4f2726179a2245, 136, 60),
+    (0xed63a231d4c4fb27, 162, 68),
+    (0xb0de65388cc8ada8, 189, 76),
+    (0x83c7088e1aab65db, 216, 84),
+    (0xc45d1df942711d9a, 242, 92),
+    (0x924d692ca61be758, 269, 100),
+    (0xda01ee641a708dea, 295, 108),
+    (0xa26da3999aef774a, 322, 116),
+    (0xf209787bb47d6b85, 348, 124),
+    (0xb454e4a179dd1877, 375, 132),
+    (0x865b86925b9bc5c2, 402, 140),
+    (0xc83553c5c8965d3d, 428, 148),
+    (0x952ab45cfa97a0b3, 455, 156),
+    (0xde469fbd99a05fe3, 481, 164),
+    (0xa59bc234db398c25, 508, 172),
+    (0xf6c69a72a3989f5c, 534, 180),
+    (0xb7dcbf5354e9bece, 561, 188),
+    (0x88fcf317f22241e2, 588, 196),
+    (0xcc20ce9bd35c78a5, 614, 204),
+    (0x98165af37b2153df, 641, 212),
+    (0xe2a0b5dc971f303a, 667, 220),
+    (0xa8d9d1535ce3b396, 694, 228),
+    (0xfb9b7cd9a4a7443c, 720, 236),
+    (0xbb764c4ca7a44410, 747, 244),
+    (0x8bab8eefb6409c1a, 774, 252),
+    (0xd01fef10a657842c, 800, 260),
+    (0x9b10a4e5e9913129, 827, 268),
+    (0xe7109bfba19c0c9d, 853, 276),
+    (0xac2820d9623bf429, 880, 284),
+    (0x80444b5e7aa7cf85, 907, 292),
+    (0xbf21e44003acdd2d, 933, 300),
+    (0x8e679c2f5e44ff8f, 960, 308),
+    (0xd433179d9c8cb841, 986, 316),
+    (0x9e19db92b4e31ba9, 1013, 324),
+    (0xeb96bf6ebadf77d9, 1039, 332),
+];
+
+#[doc(hidden)]
+pub const CACHED_POW10_FIRST_E: i16 = -1087;
+#[doc(hidden)]
+pub const CACHED_POW10_LAST_E: i16 = 1039;
+
+#[doc(hidden)]
+pub fn cached_power(alpha: i16, gamma: i16) -> (i16, Fp) {
+    let offset = CACHED_POW10_FIRST_E as i32;
+    let range = (CACHED_POW10.len() as i32) - 1;
+    let domain = (CACHED_POW10_LAST_E - CACHED_POW10_FIRST_E) as i32;
+    let idx = ((gamma as i32) - offset) * range / domain;
+    let (f, e, k) = CACHED_POW10[idx as usize];
+    debug_assert!(alpha <= e && e <= gamma);
+    (k, Fp { f, e })
+}
+
+/// Given `x > 0`, returns `(k, 10^k)` such that `10^k <= x < 10^(k+1)`.
+#[doc(hidden)]
+pub fn max_pow10_no_more_than(x: u32) -> (u8, u32) {
+    debug_assert!(x > 0);
+
+    const X9: u32 = 10_0000_0000;
+    const X8: u32 = 1_0000_0000;
+    const X7: u32 = 1000_0000;
+    const X6: u32 = 100_0000;
+    const X5: u32 = 10_0000;
+    const X4: u32 = 1_0000;
+    const X3: u32 = 1000;
+    const X2: u32 = 100;
+    const X1: u32 = 10;
+
+    if x < X4 {
+        if x < X2 {
+            if x < X1 { (0, 1) } else { (1, X1) }
+        } else {
+            if x < X3 { (2, X2) } else { (3, X3) }
+        }
+    } else {
+        if x < X6 {
+            if x < X5 { (4, X4) } else { (5, X5) }
+        } else if x < X8 {
+            if x < X7 { (6, X6) } else { (7, X7) }
+        } else {
+            if x < X9 { (8, X8) } else { (9, X9) }
+        }
+    }
+}
+
+/// The shortest mode implementation for Grisu.
+///
+/// It returns `None` when it would return an inexact representation otherwise.
+pub fn format_shortest_opt<'a>(
+    d: &Decoded,
+    buf: &'a mut [MaybeUninit<u8>],
+) -> Option<(/*digits*/ &'a [u8], /*exp*/ i16)> {
+    assert!(d.mant > 0);
+    assert!(d.minus > 0);
+    assert!(d.plus > 0);
+    assert!(d.mant.checked_add(d.plus).is_some());
+    assert!(d.mant.checked_sub(d.minus).is_some());
+    assert!(buf.len() >= MAX_SIG_DIGITS);
+    assert!(d.mant + d.plus < (1 << 61)); // we need at least three bits of additional precision
+
+    // start with the normalized values with the shared exponent
+    let plus = Fp { f: d.mant + d.plus, e: d.exp }.normalize();
+    let minus = Fp { f: d.mant - d.minus, e: d.exp }.normalize_to(plus.e);
+    let v = Fp { f: d.mant, e: d.exp }.normalize_to(plus.e);
+
+    // find any `cached = 10^minusk` such that `ALPHA <= minusk + plus.e + 64 <= GAMMA`.
+    // since `plus` is normalized, this means `2^(62 + ALPHA) <= plus * cached < 2^(64 + GAMMA)`;
+    // given our choices of `ALPHA` and `GAMMA`, this puts `plus * cached` into `[4, 2^32)`.
+    //
+    // it is obviously desirable to maximize `GAMMA - ALPHA`,
+    // so that we don't need many cached powers of 10, but there are some considerations:
+    //
+    // 1. we want to keep `floor(plus * cached)` within `u32` since it needs a costly division.
+    //    (this is not really avoidable, remainder is required for accuracy estimation.)
+    // 2. the remainder of `floor(plus * cached)` repeatedly gets multiplied by 10,
+    //    and it should not overflow.
+    //
+    // the first gives `64 + GAMMA <= 32`, while the second gives `10 * 2^-ALPHA <= 2^64`;
+    // -60 and -32 is the maximal range with this constraint, and V8 also uses them.
+    let (minusk, cached) = cached_power(ALPHA - plus.e - 64, GAMMA - plus.e - 64);
+
+    // scale fps. this gives the maximal error of 1 ulp (proved from Theorem 5.1).
+    let plus = plus.mul(&cached);
+    let minus = minus.mul(&cached);
+    let v = v.mul(&cached);
+    debug_assert_eq!(plus.e, minus.e);
+    debug_assert_eq!(plus.e, v.e);
+
+    //         +- actual range of minus
+    //   | <---|---------------------- unsafe region --------------------------> |
+    //   |     |                                                                 |
+    //   |  |<--->|  | <--------------- safe region ---------------> |           |
+    //   |  |     |  |                                               |           |
+    //   |1 ulp|1 ulp|                 |1 ulp|1 ulp|                 |1 ulp|1 ulp|
+    //   |<--->|<--->|                 |<--->|<--->|                 |<--->|<--->|
+    //   |-----|-----|-------...-------|-----|-----|-------...-------|-----|-----|
+    //   |   minus   |                 |     v     |                 |   plus    |
+    // minus1     minus0           v - 1 ulp   v + 1 ulp           plus0       plus1
+    //
+    // above `minus`, `v` and `plus` are *quantized* approximations (error < 1 ulp).
+    // as we don't know the error is positive or negative, we use two approximations spaced equally
+    // and have the maximal error of 2 ulps.
+    //
+    // the "unsafe region" is a liberal interval which we initially generate.
+    // the "safe region" is a conservative interval which we only accept.
+    // we start with the correct repr within the unsafe region, and try to find the closest repr
+    // to `v` which is also within the safe region. if we can't, we give up.
+    let plus1 = plus.f + 1;
+    //  let plus0 = plus.f - 1; // only for explanation
+    //  let minus0 = minus.f + 1; // only for explanation
+    let minus1 = minus.f - 1;
+    let e = -plus.e as usize; // shared exponent
+
+    // divide `plus1` into integral and fractional parts.
+    // integral parts are guaranteed to fit in u32, since cached power guarantees `plus < 2^32`
+    // and normalized `plus.f` is always less than `2^64 - 2^4` due to the precision requirement.
+    let plus1int = (plus1 >> e) as u32;
+    let plus1frac = plus1 & ((1 << e) - 1);
+
+    // calculate the largest `10^max_kappa` no more than `plus1` (thus `plus1 < 10^(max_kappa+1)`).
+    // this is an upper bound of `kappa` below.
+    let (max_kappa, max_ten_kappa) = max_pow10_no_more_than(plus1int);
+
+    let mut i = 0;
+    let exp = max_kappa as i16 - minusk + 1;
+
+    // Theorem 6.2: if `k` is the greatest integer s.t. `0 <= y mod 10^k <= y - x`,
+    //              then `V = floor(y / 10^k) * 10^k` is in `[x, y]` and one of the shortest
+    //              representations (with the minimal number of significant digits) in that range.
+    //
+    // find the digit length `kappa` between `(minus1, plus1)` as per Theorem 6.2.
+    // Theorem 6.2 can be adopted to exclude `x` by requiring `y mod 10^k < y - x` instead.
+    // (e.g., `x` = 32000, `y` = 32777; `kappa` = 2 since `y mod 10^3 = 777 < y - x = 777`.)
+    // the algorithm relies on the later verification phase to exclude `y`.
+    let delta1 = plus1 - minus1;
+    //  let delta1int = (delta1 >> e) as usize; // only for explanation
+    let delta1frac = delta1 & ((1 << e) - 1);
+
+    // render integral parts, while checking for the accuracy at each step.
+    let mut kappa = max_kappa as i16;
+    let mut ten_kappa = max_ten_kappa; // 10^kappa
+    let mut remainder = plus1int; // digits yet to be rendered
+    loop {
+        // we always have at least one digit to render, as `plus1 >= 10^kappa`
+        // invariants:
+        // - `delta1int <= remainder < 10^(kappa+1)`
+        // - `plus1int = d[0..n-1] * 10^(kappa+1) + remainder`
+        //   (it follows that `remainder = plus1int % 10^(kappa+1)`)
+
+        // divide `remainder` by `10^kappa`. both are scaled by `2^-e`.
+        let q = remainder / ten_kappa;
+        let r = remainder % ten_kappa;
+        debug_assert!(q < 10);
+        buf[i] = MaybeUninit::new(b'0' + q as u8);
+        i += 1;
+
+        let plus1rem = ((r as u64) << e) + plus1frac; // == (plus1 % 10^kappa) * 2^e
+        if plus1rem < delta1 {
+            // `plus1 % 10^kappa < delta1 = plus1 - minus1`; we've found the correct `kappa`.
+            let ten_kappa = (ten_kappa as u64) << e; // scale 10^kappa back to the shared exponent
+            return round_and_weed(
+                // SAFETY: we initialized that memory above.
+                unsafe { MaybeUninit::slice_assume_init_mut(&mut buf[..i]) },
+                exp,
+                plus1rem,
+                delta1,
+                plus1 - v.f,
+                ten_kappa,
+                1,
+            );
+        }
+
+        // break the loop when we have rendered all integral digits.
+        // the exact number of digits is `max_kappa + 1` as `plus1 < 10^(max_kappa+1)`.
+        if i > max_kappa as usize {
+            debug_assert_eq!(ten_kappa, 1);
+            debug_assert_eq!(kappa, 0);
+            break;
+        }
+
+        // restore invariants
+        kappa -= 1;
+        ten_kappa /= 10;
+        remainder = r;
+    }
+
+    // render fractional parts, while checking for the accuracy at each step.
+    // this time we rely on repeated multiplications, as division will lose the precision.
+    let mut remainder = plus1frac;
+    let mut threshold = delta1frac;
+    let mut ulp = 1;
+    loop {
+        // the next digit should be significant as we've tested that before breaking out
+        // invariants, where `m = max_kappa + 1` (# of digits in the integral part):
+        // - `remainder < 2^e`
+        // - `plus1frac * 10^(n-m) = d[m..n-1] * 2^e + remainder`
+
+        remainder *= 10; // won't overflow, `2^e * 10 < 2^64`
+        threshold *= 10;
+        ulp *= 10;
+
+        // divide `remainder` by `10^kappa`.
+        // both are scaled by `2^e / 10^kappa`, so the latter is implicit here.
+        let q = remainder >> e;
+        let r = remainder & ((1 << e) - 1);
+        debug_assert!(q < 10);
+        buf[i] = MaybeUninit::new(b'0' + q as u8);
+        i += 1;
+
+        if r < threshold {
+            let ten_kappa = 1 << e; // implicit divisor
+            return round_and_weed(
+                // SAFETY: we initialized that memory above.
+                unsafe { MaybeUninit::slice_assume_init_mut(&mut buf[..i]) },
+                exp,
+                r,
+                threshold,
+                (plus1 - v.f) * ulp,
+                ten_kappa,
+                ulp,
+            );
+        }
+
+        // restore invariants
+        kappa -= 1;
+        remainder = r;
+    }
+
+    // we've generated all significant digits of `plus1`, but not sure if it's the optimal one.
+    // for example, if `minus1` is 3.14153... and `plus1` is 3.14158..., there are 5 different
+    // shortest representation from 3.14154 to 3.14158 but we only have the greatest one.
+    // we have to successively decrease the last digit and check if this is the optimal repr.
+    // there are at most 9 candidates (..1 to ..9), so this is fairly quick. ("rounding" phase)
+    //
+    // the function checks if this "optimal" repr is actually within the ulp ranges,
+    // and also, it is possible that the "second-to-optimal" repr can actually be optimal
+    // due to the rounding error. in either cases this returns `None`. ("weeding" phase)
+    //
+    // all arguments here are scaled by the common (but implicit) value `k`, so that:
+    // - `remainder = (plus1 % 10^kappa) * k`
+    // - `threshold = (plus1 - minus1) * k` (and also, `remainder < threshold`)
+    // - `plus1v = (plus1 - v) * k` (and also, `threshold > plus1v` from prior invariants)
+    // - `ten_kappa = 10^kappa * k`
+    // - `ulp = 2^-e * k`
+    fn round_and_weed(
+        buf: &mut [u8],
+        exp: i16,
+        remainder: u64,
+        threshold: u64,
+        plus1v: u64,
+        ten_kappa: u64,
+        ulp: u64,
+    ) -> Option<(&[u8], i16)> {
+        assert!(!buf.is_empty());
+
+        // produce two approximations to `v` (actually `plus1 - v`) within 1.5 ulps.
+        // the resulting representation should be the closest representation to both.
+        //
+        // here `plus1 - v` is used since calculations are done with respect to `plus1`
+        // in order to avoid overflow/underflow (hence the seemingly swapped names).
+        let plus1v_down = plus1v + ulp; // plus1 - (v - 1 ulp)
+        let plus1v_up = plus1v - ulp; // plus1 - (v + 1 ulp)
+
+        // decrease the last digit and stop at the closest representation to `v + 1 ulp`.
+        let mut plus1w = remainder; // plus1w(n) = plus1 - w(n)
+        {
+            let last = buf.last_mut().unwrap();
+
+            // we work with the approximated digits `w(n)`, which is initially equal to `plus1 -
+            // plus1 % 10^kappa`. after running the loop body `n` times, `w(n) = plus1 -
+            // plus1 % 10^kappa - n * 10^kappa`. we set `plus1w(n) = plus1 - w(n) =
+            // plus1 % 10^kappa + n * 10^kappa` (thus `remainder = plus1w(0)`) to simplify checks.
+            // note that `plus1w(n)` is always increasing.
+            //
+            // we have three conditions to terminate. any of them will make the loop unable to
+            // proceed, but we then have at least one valid representation known to be closest to
+            // `v + 1 ulp` anyway. we will denote them as TC1 through TC3 for brevity.
+            //
+            // TC1: `w(n) <= v + 1 ulp`, i.e., this is the last repr that can be the closest one.
+            // this is equivalent to `plus1 - w(n) = plus1w(n) >= plus1 - (v + 1 ulp) = plus1v_up`.
+            // combined with TC2 (which checks if `w(n+1)` is valid), this prevents the possible
+            // overflow on the calculation of `plus1w(n)`.
+            //
+            // TC2: `w(n+1) < minus1`, i.e., the next repr definitely does not round to `v`.
+            // this is equivalent to `plus1 - w(n) + 10^kappa = plus1w(n) + 10^kappa >
+            // plus1 - minus1 = threshold`. the left hand side can overflow, but we know
+            // `threshold > plus1v`, so if TC1 is false, `threshold - plus1w(n) >
+            // threshold - (plus1v - 1 ulp) > 1 ulp` and we can safely test if
+            // `threshold - plus1w(n) < 10^kappa` instead.
+            //
+            // TC3: `abs(w(n) - (v + 1 ulp)) <= abs(w(n+1) - (v + 1 ulp))`, i.e., the next repr is
+            // no closer to `v + 1 ulp` than the current repr. given `z(n) = plus1v_up - plus1w(n)`,
+            // this becomes `abs(z(n)) <= abs(z(n+1))`. again assuming that TC1 is false, we have
+            // `z(n) > 0`. we have two cases to consider:
+            //
+            // - when `z(n+1) >= 0`: TC3 becomes `z(n) <= z(n+1)`. as `plus1w(n)` is increasing,
+            //   `z(n)` should be decreasing and this is clearly false.
+            // - when `z(n+1) < 0`:
+            //   - TC3a: the precondition is `plus1v_up < plus1w(n) + 10^kappa`. assuming TC2 is
+            //     false, `threshold >= plus1w(n) + 10^kappa` so it cannot overflow.
+            //   - TC3b: TC3 becomes `z(n) <= -z(n+1)`, i.e., `plus1v_up - plus1w(n) >=
+            //     plus1w(n+1) - plus1v_up = plus1w(n) + 10^kappa - plus1v_up`. the negated TC1
+            //     gives `plus1v_up > plus1w(n)`, so it cannot overflow or underflow when
+            //     combined with TC3a.
+            //
+            // consequently, we should stop when `TC1 || TC2 || (TC3a && TC3b)`. the following is
+            // equal to its inverse, `!TC1 && !TC2 && (!TC3a || !TC3b)`.
+            while plus1w < plus1v_up
+                && threshold - plus1w >= ten_kappa
+                && (plus1w + ten_kappa < plus1v_up
+                    || plus1v_up - plus1w >= plus1w + ten_kappa - plus1v_up)
+            {
+                *last -= 1;
+                debug_assert!(*last > b'0'); // the shortest repr cannot end with `0`
+                plus1w += ten_kappa;
+            }
+        }
+
+        // check if this representation is also the closest representation to `v - 1 ulp`.
+        //
+        // this is simply same to the terminating conditions for `v + 1 ulp`, with all `plus1v_up`
+        // replaced by `plus1v_down` instead. overflow analysis equally holds.
+        if plus1w < plus1v_down
+            && threshold - plus1w >= ten_kappa
+            && (plus1w + ten_kappa < plus1v_down
+                || plus1v_down - plus1w >= plus1w + ten_kappa - plus1v_down)
+        {
+            return None;
+        }
+
+        // now we have the closest representation to `v` between `plus1` and `minus1`.
+        // this is too liberal, though, so we reject any `w(n)` not between `plus0` and `minus0`,
+        // i.e., `plus1 - plus1w(n) <= minus0` or `plus1 - plus1w(n) >= plus0`. we utilize the facts
+        // that `threshold = plus1 - minus1` and `plus1 - plus0 = minus0 - minus1 = 2 ulp`.
+        if 2 * ulp <= plus1w && plus1w <= threshold - 4 * ulp { Some((buf, exp)) } else { None }
+    }
+}
+
+/// The shortest mode implementation for Grisu with Dragon fallback.
+///
+/// This should be used for most cases.
+pub fn format_shortest<'a>(
+    d: &Decoded,
+    buf: &'a mut [MaybeUninit<u8>],
+) -> (/*digits*/ &'a [u8], /*exp*/ i16) {
+    use crate::num::flt2dec::strategy::dragon::format_shortest as fallback;
+    // SAFETY: The borrow checker is not smart enough to let us use `buf`
+    // in the second branch, so we launder the lifetime here. But we only re-use
+    // `buf` if `format_shortest_opt` returned `None` so this is okay.
+    match format_shortest_opt(d, unsafe { &mut *(buf as *mut _) }) {
+        Some(ret) => ret,
+        None => fallback(d, buf),
+    }
+}
+
+/// The exact and fixed mode implementation for Grisu.
+///
+/// It returns `None` when it would return an inexact representation otherwise.
+pub fn format_exact_opt<'a>(
+    d: &Decoded,
+    buf: &'a mut [MaybeUninit<u8>],
+    limit: i16,
+) -> Option<(/*digits*/ &'a [u8], /*exp*/ i16)> {
+    assert!(d.mant > 0);
+    assert!(d.mant < (1 << 61)); // we need at least three bits of additional precision
+    assert!(!buf.is_empty());
+
+    // normalize and scale `v`.
+    let v = Fp { f: d.mant, e: d.exp }.normalize();
+    let (minusk, cached) = cached_power(ALPHA - v.e - 64, GAMMA - v.e - 64);
+    let v = v.mul(&cached);
+
+    // divide `v` into integral and fractional parts.
+    let e = -v.e as usize;
+    let vint = (v.f >> e) as u32;
+    let vfrac = v.f & ((1 << e) - 1);
+
+    // both old `v` and new `v` (scaled by `10^-k`) has an error of < 1 ulp (Theorem 5.1).
+    // as we don't know the error is positive or negative, we use two approximations
+    // spaced equally and have the maximal error of 2 ulps (same to the shortest case).
+    //
+    // the goal is to find the exactly rounded series of digits that are common to
+    // both `v - 1 ulp` and `v + 1 ulp`, so that we are maximally confident.
+    // if this is not possible, we don't know which one is the correct output for `v`,
+    // so we give up and fall back.
+    //
+    // `err` is defined as `1 ulp * 2^e` here (same to the ulp in `vfrac`),
+    // and we will scale it whenever `v` gets scaled.
+    let mut err = 1;
+
+    // calculate the largest `10^max_kappa` no more than `v` (thus `v < 10^(max_kappa+1)`).
+    // this is an upper bound of `kappa` below.
+    let (max_kappa, max_ten_kappa) = max_pow10_no_more_than(vint);
+
+    let mut i = 0;
+    let exp = max_kappa as i16 - minusk + 1;
+
+    // if we are working with the last-digit limitation, we need to shorten the buffer
+    // before the actual rendering in order to avoid double rounding.
+    // note that we have to enlarge the buffer again when rounding up happens!
+    let len = if exp <= limit {
+        // oops, we cannot even produce *one* digit.
+        // this is possible when, say, we've got something like 9.5 and it's being rounded to 10.
+        //
+        // in principle we can immediately call `possibly_round` with an empty buffer,
+        // but scaling `max_ten_kappa << e` by 10 can result in overflow.
+        // thus we are being sloppy here and widen the error range by a factor of 10.
+        // this will increase the false negative rate, but only very, *very* slightly;
+        // it can only matter noticeably when the mantissa is bigger than 60 bits.
+        //
+        // SAFETY: `len=0`, so the obligation of having initialized this memory is trivial.
+        return unsafe {
+            possibly_round(buf, 0, exp, limit, v.f / 10, (max_ten_kappa as u64) << e, err << e)
+        };
+    } else if ((exp as i32 - limit as i32) as usize) < buf.len() {
+        (exp - limit) as usize
+    } else {
+        buf.len()
+    };
+    debug_assert!(len > 0);
+
+    // render integral parts.
+    // the error is entirely fractional, so we don't need to check it in this part.
+    let mut kappa = max_kappa as i16;
+    let mut ten_kappa = max_ten_kappa; // 10^kappa
+    let mut remainder = vint; // digits yet to be rendered
+    loop {
+        // we always have at least one digit to render
+        // invariants:
+        // - `remainder < 10^(kappa+1)`
+        // - `vint = d[0..n-1] * 10^(kappa+1) + remainder`
+        //   (it follows that `remainder = vint % 10^(kappa+1)`)
+
+        // divide `remainder` by `10^kappa`. both are scaled by `2^-e`.
+        let q = remainder / ten_kappa;
+        let r = remainder % ten_kappa;
+        debug_assert!(q < 10);
+        buf[i] = MaybeUninit::new(b'0' + q as u8);
+        i += 1;
+
+        // is the buffer full? run the rounding pass with the remainder.
+        if i == len {
+            let vrem = ((r as u64) << e) + vfrac; // == (v % 10^kappa) * 2^e
+            // SAFETY: we have initialized `len` many bytes.
+            return unsafe {
+                possibly_round(buf, len, exp, limit, vrem, (ten_kappa as u64) << e, err << e)
+            };
+        }
+
+        // break the loop when we have rendered all integral digits.
+        // the exact number of digits is `max_kappa + 1` as `plus1 < 10^(max_kappa+1)`.
+        if i > max_kappa as usize {
+            debug_assert_eq!(ten_kappa, 1);
+            debug_assert_eq!(kappa, 0);
+            break;
+        }
+
+        // restore invariants
+        kappa -= 1;
+        ten_kappa /= 10;
+        remainder = r;
+    }
+
+    // render fractional parts.
+    //
+    // in principle we can continue to the last available digit and check for the accuracy.
+    // unfortunately we are working with the finite-sized integers, so we need some criterion
+    // to detect the overflow. V8 uses `remainder > err`, which becomes false when
+    // the first `i` significant digits of `v - 1 ulp` and `v` differ. however this rejects
+    // too many otherwise valid input.
+    //
+    // since the later phase has a correct overflow detection, we instead use tighter criterion:
+    // we continue til `err` exceeds `10^kappa / 2`, so that the range between `v - 1 ulp` and
+    // `v + 1 ulp` definitely contains two or more rounded representations. this is same to
+    // the first two comparisons from `possibly_round`, for the reference.
+    let mut remainder = vfrac;
+    let maxerr = 1 << (e - 1);
+    while err < maxerr {
+        // invariants, where `m = max_kappa + 1` (# of digits in the integral part):
+        // - `remainder < 2^e`
+        // - `vfrac * 10^(n-m) = d[m..n-1] * 2^e + remainder`
+        // - `err = 10^(n-m)`
+
+        remainder *= 10; // won't overflow, `2^e * 10 < 2^64`
+        err *= 10; // won't overflow, `err * 10 < 2^e * 5 < 2^64`
+
+        // divide `remainder` by `10^kappa`.
+        // both are scaled by `2^e / 10^kappa`, so the latter is implicit here.
+        let q = remainder >> e;
+        let r = remainder & ((1 << e) - 1);
+        debug_assert!(q < 10);
+        buf[i] = MaybeUninit::new(b'0' + q as u8);
+        i += 1;
+
+        // is the buffer full? run the rounding pass with the remainder.
+        if i == len {
+            // SAFETY: we have initialized `len` many bytes.
+            return unsafe { possibly_round(buf, len, exp, limit, r, 1 << e, err) };
+        }
+
+        // restore invariants
+        remainder = r;
+    }
+
+    // further calculation is useless (`possibly_round` definitely fails), so we give up.
+    return None;
+
+    // we've generated all requested digits of `v`, which should be also same to corresponding
+    // digits of `v - 1 ulp`. now we check if there is a unique representation shared by
+    // both `v - 1 ulp` and `v + 1 ulp`; this can be either same to generated digits, or
+    // to the rounded-up version of those digits. if the range contains multiple representations
+    // of the same length, we cannot be sure and should return `None` instead.
+    //
+    // all arguments here are scaled by the common (but implicit) value `k`, so that:
+    // - `remainder = (v % 10^kappa) * k`
+    // - `ten_kappa = 10^kappa * k`
+    // - `ulp = 2^-e * k`
+    //
+    // SAFETY: the first `len` bytes of `buf` must be initialized.
+    unsafe fn possibly_round(
+        buf: &mut [MaybeUninit<u8>],
+        mut len: usize,
+        mut exp: i16,
+        limit: i16,
+        remainder: u64,
+        ten_kappa: u64,
+        ulp: u64,
+    ) -> Option<(&[u8], i16)> {
+        debug_assert!(remainder < ten_kappa);
+
+        //           10^kappa
+        //    :   :   :<->:   :
+        //    :   :   :   :   :
+        //    :|1 ulp|1 ulp|  :
+        //    :|<--->|<--->|  :
+        // ----|-----|-----|----
+        //     |     v     |
+        // v - 1 ulp   v + 1 ulp
+        //
+        // (for the reference, the dotted line indicates the exact value for
+        // possible representations in given number of digits.)
+        //
+        // error is too large that there are at least three possible representations
+        // between `v - 1 ulp` and `v + 1 ulp`. we cannot determine which one is correct.
+        if ulp >= ten_kappa {
+            return None;
+        }
+
+        //    10^kappa
+        //   :<------->:
+        //   :         :
+        //   : |1 ulp|1 ulp|
+        //   : |<--->|<--->|
+        // ----|-----|-----|----
+        //     |     v     |
+        // v - 1 ulp   v + 1 ulp
+        //
+        // in fact, 1/2 ulp is enough to introduce two possible representations.
+        // (remember that we need a unique representation for both `v - 1 ulp` and `v + 1 ulp`.)
+        // this won't overflow, as `ulp < ten_kappa` from the first check.
+        if ten_kappa - ulp <= ulp {
+            return None;
+        }
+
+        //     remainder
+        //       :<->|                           :
+        //       :   |                           :
+        //       :<--------- 10^kappa ---------->:
+        //     | :   |                           :
+        //     |1 ulp|1 ulp|                     :
+        //     |<--->|<--->|                     :
+        // ----|-----|-----|------------------------
+        //     |     v     |
+        // v - 1 ulp   v + 1 ulp
+        //
+        // if `v + 1 ulp` is closer to the rounded-down representation (which is already in `buf`),
+        // then we can safely return. note that `v - 1 ulp` *can* be less than the current
+        // representation, but as `1 ulp < 10^kappa / 2`, this condition is enough:
+        // the distance between `v - 1 ulp` and the current representation
+        // cannot exceed `10^kappa / 2`.
+        //
+        // the condition equals to `remainder + ulp < 10^kappa / 2`.
+        // since this can easily overflow, first check if `remainder < 10^kappa / 2`.
+        // we've already verified that `ulp < 10^kappa / 2`, so as long as
+        // `10^kappa` did not overflow after all, the second check is fine.
+        if ten_kappa - remainder > remainder && ten_kappa - 2 * remainder >= 2 * ulp {
+            // SAFETY: our caller initialized that memory.
+            return Some((unsafe { MaybeUninit::slice_assume_init_ref(&buf[..len]) }, exp));
+        }
+
+        //   :<------- remainder ------>|   :
+        //   :                          |   :
+        //   :<--------- 10^kappa --------->:
+        //   :                    |     |   : |
+        //   :                    |1 ulp|1 ulp|
+        //   :                    |<--->|<--->|
+        // -----------------------|-----|-----|-----
+        //                        |     v     |
+        //                    v - 1 ulp   v + 1 ulp
+        //
+        // on the other hands, if `v - 1 ulp` is closer to the rounded-up representation,
+        // we should round up and return. for the same reason we don't need to check `v + 1 ulp`.
+        //
+        // the condition equals to `remainder - ulp >= 10^kappa / 2`.
+        // again we first check if `remainder > ulp` (note that this is not `remainder >= ulp`,
+        // as `10^kappa` is never zero). also note that `remainder - ulp <= 10^kappa`,
+        // so the second check does not overflow.
+        if remainder > ulp && ten_kappa - (remainder - ulp) <= remainder - ulp {
+            if let Some(c) =
+                // SAFETY: our caller must have initialized that memory.
+                round_up(unsafe { MaybeUninit::slice_assume_init_mut(&mut buf[..len]) })
+            {
+                // only add an additional digit when we've been requested the fixed precision.
+                // we also need to check that, if the original buffer was empty,
+                // the additional digit can only be added when `exp == limit` (edge case).
+                exp += 1;
+                if exp > limit && len < buf.len() {
+                    buf[len] = MaybeUninit::new(c);
+                    len += 1;
+                }
+            }
+            // SAFETY: we and our caller initialized that memory.
+            return Some((unsafe { MaybeUninit::slice_assume_init_ref(&buf[..len]) }, exp));
+        }
+
+        // otherwise we are doomed (i.e., some values between `v - 1 ulp` and `v + 1 ulp` are
+        // rounding down and others are rounding up) and give up.
+        None
+    }
+}
+
+/// The exact and fixed mode implementation for Grisu with Dragon fallback.
+///
+/// This should be used for most cases.
+pub fn format_exact<'a>(
+    d: &Decoded,
+    buf: &'a mut [MaybeUninit<u8>],
+    limit: i16,
+) -> (/*digits*/ &'a [u8], /*exp*/ i16) {
+    use crate::num::flt2dec::strategy::dragon::format_exact as fallback;
+    // SAFETY: The borrow checker is not smart enough to let us use `buf`
+    // in the second branch, so we launder the lifetime here. But we only re-use
+    // `buf` if `format_exact_opt` returned `None` so this is okay.
+    match format_exact_opt(d, unsafe { &mut *(buf as *mut _) }, limit) {
+        Some(ret) => ret,
+        None => fallback(d, buf, limit),
+    }
+}
diff --git a/library/core/src/num/fmt.rs b/library/core/src/num/fmt.rs
new file mode 100644
index 000000000..ed6119715
--- /dev/null
+++ b/library/core/src/num/fmt.rs
@@ -0,0 +1,108 @@
+//! Shared utilities used by both float and integer formatting.
+#![doc(hidden)]
+#![unstable(
+    feature = "numfmt",
+    reason = "internal routines only exposed for testing",
+    issue = "none"
+)]
+
+/// Formatted parts.
+#[derive(Copy, Clone, PartialEq, Eq, Debug)]
+pub enum Part<'a> {
+    /// Given number of zero digits.
+    Zero(usize),
+    /// A literal number up to 5 digits.
+    Num(u16),
+    /// A verbatim copy of given bytes.
+    Copy(&'a [u8]),
+}
+
+impl<'a> Part<'a> {
+    /// Returns the exact byte length of given part.
+    pub fn len(&self) -> usize {
+        match *self {
+            Part::Zero(nzeroes) => nzeroes,
+            Part::Num(v) => {
+                if v < 1_000 {
+                    if v < 10 {
+                        1
+                    } else if v < 100 {
+                        2
+                    } else {
+                        3
+                    }
+                } else {
+                    if v < 10_000 { 4 } else { 5 }
+                }
+            }
+            Part::Copy(buf) => buf.len(),
+        }
+    }
+
+    /// Writes a part into the supplied buffer.
+    /// Returns the number of written bytes, or `None` if the buffer is not enough.
+    /// (It may still leave partially written bytes in the buffer; do not rely on that.)
+    pub fn write(&self, out: &mut [u8]) -> Option<usize> {
+        let len = self.len();
+        if out.len() >= len {
+            match *self {
+                Part::Zero(nzeroes) => {
+                    for c in &mut out[..nzeroes] {
+                        *c = b'0';
+                    }
+                }
+                Part::Num(mut v) => {
+                    for c in out[..len].iter_mut().rev() {
+                        *c = b'0' + (v % 10) as u8;
+                        v /= 10;
+                    }
+                }
+                Part::Copy(buf) => {
+                    out[..buf.len()].copy_from_slice(buf);
+                }
+            }
+            Some(len)
+        } else {
+            None
+        }
+    }
+}
+
+/// Formatted result containing one or more parts.
+/// This can be written to the byte buffer or converted to the allocated string.
+#[allow(missing_debug_implementations)]
+#[derive(Clone)]
+pub struct Formatted<'a> {
+    /// A byte slice representing a sign, either `""`, `"-"` or `"+"`.
+    pub sign: &'static str,
+    /// Formatted parts to be rendered after a sign and optional zero padding.
+    pub parts: &'a [Part<'a>],
+}
+
+impl<'a> Formatted<'a> {
+    /// Returns the exact byte length of combined formatted result.
+    pub fn len(&self) -> usize {
+        let mut len = self.sign.len();
+        for part in self.parts {
+            len += part.len();
+        }
+        len
+    }
+
+    /// Writes all formatted parts into the supplied buffer.
+    /// Returns the number of written bytes, or `None` if the buffer is not enough.
+    /// (It may still leave partially written bytes in the buffer; do not rely on that.)
+    pub fn write(&self, out: &mut [u8]) -> Option<usize> {
+        if out.len() < self.sign.len() {
+            return None;
+        }
+        out[..self.sign.len()].copy_from_slice(self.sign.as_bytes());
+
+        let mut written = self.sign.len();
+        for part in self.parts {
+            let len = part.write(&mut out[written..])?;
+            written += len;
+        }
+        Some(written)
+    }
+}
diff --git a/library/core/src/num/int_log10.rs b/library/core/src/num/int_log10.rs
new file mode 100644
index 000000000..cc26c04a5
--- /dev/null
+++ b/library/core/src/num/int_log10.rs
@@ -0,0 +1,140 @@
+/// These functions compute the integer logarithm of their type, assuming
+/// that someone has already checked that the the value is strictly positive.
+
+// 0 < val <= u8::MAX
+#[inline]
+pub const fn u8(val: u8) -> u32 {
+    let val = val as u32;
+
+    // For better performance, avoid branches by assembling the solution
+    // in the bits above the low 8 bits.
+
+    // Adding c1 to val gives 10 in the top bits for val < 10, 11 for val >= 10
+    const C1: u32 = 0b11_00000000 - 10; // 758
+    // Adding c2 to val gives 01 in the top bits for val < 100, 10 for val >= 100
+    const C2: u32 = 0b10_00000000 - 100; // 412
+
+    // Value of top bits:
+    //            +c1  +c2  1&2
+    //     0..=9   10   01   00 = 0
+    //   10..=99   11   01   01 = 1
+    // 100..=255   11   10   10 = 2
+    ((val + C1) & (val + C2)) >> 8
+}
+
+// 0 < val < 100_000
+#[inline]
+const fn less_than_5(val: u32) -> u32 {
+    // Similar to u8, when adding one of these constants to val,
+    // we get two possible bit patterns above the low 17 bits,
+    // depending on whether val is below or above the threshold.
+    const C1: u32 = 0b011_00000000000000000 - 10; // 393206
+    const C2: u32 = 0b100_00000000000000000 - 100; // 524188
+    const C3: u32 = 0b111_00000000000000000 - 1000; // 916504
+    const C4: u32 = 0b100_00000000000000000 - 10000; // 514288
+
+    // Value of top bits:
+    //                +c1  +c2  1&2  +c3  +c4  3&4   ^
+    //         0..=9  010  011  010  110  011  010  000 = 0
+    //       10..=99  011  011  011  110  011  010  001 = 1
+    //     100..=999  011  100  000  110  011  010  010 = 2
+    //   1000..=9999  011  100  000  111  011  011  011 = 3
+    // 10000..=99999  011  100  000  111  100  100  100 = 4
+    (((val + C1) & (val + C2)) ^ ((val + C3) & (val + C4))) >> 17
+}
+
+// 0 < val <= u16::MAX
+#[inline]
+pub const fn u16(val: u16) -> u32 {
+    less_than_5(val as u32)
+}
+
+// 0 < val <= u32::MAX
+#[inline]
+pub const fn u32(mut val: u32) -> u32 {
+    let mut log = 0;
+    if val >= 100_000 {
+        val /= 100_000;
+        log += 5;
+    }
+    log + less_than_5(val)
+}
+
+// 0 < val <= u64::MAX
+#[inline]
+pub const fn u64(mut val: u64) -> u32 {
+    let mut log = 0;
+    if val >= 10_000_000_000 {
+        val /= 10_000_000_000;
+        log += 10;
+    }
+    if val >= 100_000 {
+        val /= 100_000;
+        log += 5;
+    }
+    log + less_than_5(val as u32)
+}
+
+// 0 < val <= u128::MAX
+#[inline]
+pub const fn u128(mut val: u128) -> u32 {
+    let mut log = 0;
+    if val >= 100_000_000_000_000_000_000_000_000_000_000 {
+        val /= 100_000_000_000_000_000_000_000_000_000_000;
+        log += 32;
+        return log + u32(val as u32);
+    }
+    if val >= 10_000_000_000_000_000 {
+        val /= 10_000_000_000_000_000;
+        log += 16;
+    }
+    log + u64(val as u64)
+}
+
+#[cfg(target_pointer_width = "16")]
+#[inline]
+pub const fn usize(val: usize) -> u32 {
+    u16(val as _)
+}
+
+#[cfg(target_pointer_width = "32")]
+#[inline]
+pub const fn usize(val: usize) -> u32 {
+    u32(val as _)
+}
+
+#[cfg(target_pointer_width = "64")]
+#[inline]
+pub const fn usize(val: usize) -> u32 {
+    u64(val as _)
+}
+
+// 0 < val <= i8::MAX
+#[inline]
+pub const fn i8(val: i8) -> u32 {
+    u8(val as u8)
+}
+
+// 0 < val <= i16::MAX
+#[inline]
+pub const fn i16(val: i16) -> u32 {
+    u16(val as u16)
+}
+
+// 0 < val <= i32::MAX
+#[inline]
+pub const fn i32(val: i32) -> u32 {
+    u32(val as u32)
+}
+
+// 0 < val <= i64::MAX
+#[inline]
+pub const fn i64(val: i64) -> u32 {
+    u64(val as u64)
+}
+
+// 0 < val <= i128::MAX
+#[inline]
+pub const fn i128(val: i128) -> u32 {
+    u128(val as u128)
+}
diff --git a/library/core/src/num/int_macros.rs b/library/core/src/num/int_macros.rs
new file mode 100644
index 000000000..a66de19ba
--- /dev/null
+++ b/library/core/src/num/int_macros.rs
@@ -0,0 +1,2744 @@
+macro_rules! int_impl {
+    ($SelfT:ty, $ActualT:ident, $UnsignedT:ty, $BITS:expr, $BITS_MINUS_ONE:expr, $Min:expr, $Max:expr,
+     $rot:expr, $rot_op:expr, $rot_result:expr, $swap_op:expr, $swapped:expr,
+     $reversed:expr, $le_bytes:expr, $be_bytes:expr,
+     $to_xe_bytes_doc:expr, $from_xe_bytes_doc:expr,
+     $bound_condition:expr) => {
+        /// The smallest value that can be represented by this integer type
+        #[doc = concat!("(&minus;2<sup>", $BITS_MINUS_ONE, "</sup>", $bound_condition, ")")]
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        #[doc = concat!("assert_eq!(", stringify!($SelfT), "::MIN, ", stringify!($Min), ");")]
+        /// ```
+        #[stable(feature = "assoc_int_consts", since = "1.43.0")]
+        pub const MIN: Self = !0 ^ ((!0 as $UnsignedT) >> 1) as Self;
+
+        /// The largest value that can be represented by this integer type
+        #[doc = concat!("(2<sup>", $BITS_MINUS_ONE, "</sup> &minus; 1", $bound_condition, ")")]
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        #[doc = concat!("assert_eq!(", stringify!($SelfT), "::MAX, ", stringify!($Max), ");")]
+        /// ```
+        #[stable(feature = "assoc_int_consts", since = "1.43.0")]
+        pub const MAX: Self = !Self::MIN;
+
+        /// The size of this integer type in bits.
+        ///
+        /// # Examples
+        ///
+        /// ```
+        #[doc = concat!("assert_eq!(", stringify!($SelfT), "::BITS, ", stringify!($BITS), ");")]
+        /// ```
+        #[stable(feature = "int_bits_const", since = "1.53.0")]
+        pub const BITS: u32 = $BITS;
+
+        /// Converts a string slice in a given base to an integer.
+        ///
+        /// The string is expected to be an optional `+` or `-` sign followed by digits.
+        /// Leading and trailing whitespace represent an error. Digits are a subset of these characters,
+        /// depending on `radix`:
+        ///
+        ///  * `0-9`
+        ///  * `a-z`
+        ///  * `A-Z`
+        ///
+        /// # Panics
+        ///
+        /// This function panics if `radix` is not in the range from 2 to 36.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        #[doc = concat!("assert_eq!(", stringify!($SelfT), "::from_str_radix(\"A\", 16), Ok(10));")]
+        /// ```
+        #[stable(feature = "rust1", since = "1.0.0")]
+        pub fn from_str_radix(src: &str, radix: u32) -> Result<Self, ParseIntError> {
+            from_str_radix(src, radix)
+        }
+
+        /// Returns the number of ones in the binary representation of `self`.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        #[doc = concat!("let n = 0b100_0000", stringify!($SelfT), ";")]
+        ///
+        /// assert_eq!(n.count_ones(), 1);
+        /// ```
+        ///
+        #[stable(feature = "rust1", since = "1.0.0")]
+        #[rustc_const_stable(feature = "const_int_methods", since = "1.32.0")]
+        #[doc(alias = "popcount")]
+        #[doc(alias = "popcnt")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline(always)]
+        pub const fn count_ones(self) -> u32 { (self as $UnsignedT).count_ones() }
+
+        /// Returns the number of zeros in the binary representation of `self`.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        #[doc = concat!("assert_eq!(", stringify!($SelfT), "::MAX.count_zeros(), 1);")]
+        /// ```
+        #[stable(feature = "rust1", since = "1.0.0")]
+        #[rustc_const_stable(feature = "const_int_methods", since = "1.32.0")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline(always)]
+        pub const fn count_zeros(self) -> u32 {
+            (!self).count_ones()
+        }
+
+        /// Returns the number of leading zeros in the binary representation of `self`.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        #[doc = concat!("let n = -1", stringify!($SelfT), ";")]
+        ///
+        /// assert_eq!(n.leading_zeros(), 0);
+        /// ```
+        #[stable(feature = "rust1", since = "1.0.0")]
+        #[rustc_const_stable(feature = "const_int_methods", since = "1.32.0")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline(always)]
+        pub const fn leading_zeros(self) -> u32 {
+            (self as $UnsignedT).leading_zeros()
+        }
+
+        /// Returns the number of trailing zeros in the binary representation of `self`.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        #[doc = concat!("let n = -4", stringify!($SelfT), ";")]
+        ///
+        /// assert_eq!(n.trailing_zeros(), 2);
+        /// ```
+        #[stable(feature = "rust1", since = "1.0.0")]
+        #[rustc_const_stable(feature = "const_int_methods", since = "1.32.0")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline(always)]
+        pub const fn trailing_zeros(self) -> u32 {
+            (self as $UnsignedT).trailing_zeros()
+        }
+
+        /// Returns the number of leading ones in the binary representation of `self`.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        #[doc = concat!("let n = -1", stringify!($SelfT), ";")]
+        ///
+        #[doc = concat!("assert_eq!(n.leading_ones(), ", stringify!($BITS), ");")]
+        /// ```
+        #[stable(feature = "leading_trailing_ones", since = "1.46.0")]
+        #[rustc_const_stable(feature = "leading_trailing_ones", since = "1.46.0")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline(always)]
+        pub const fn leading_ones(self) -> u32 {
+            (self as $UnsignedT).leading_ones()
+        }
+
+        /// Returns the number of trailing ones in the binary representation of `self`.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        #[doc = concat!("let n = 3", stringify!($SelfT), ";")]
+        ///
+        /// assert_eq!(n.trailing_ones(), 2);
+        /// ```
+        #[stable(feature = "leading_trailing_ones", since = "1.46.0")]
+        #[rustc_const_stable(feature = "leading_trailing_ones", since = "1.46.0")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline(always)]
+        pub const fn trailing_ones(self) -> u32 {
+            (self as $UnsignedT).trailing_ones()
+        }
+
+        /// Shifts the bits to the left by a specified amount, `n`,
+        /// wrapping the truncated bits to the end of the resulting integer.
+        ///
+        /// Please note this isn't the same operation as the `<<` shifting operator!
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        #[doc = concat!("let n = ", $rot_op, stringify!($SelfT), ";")]
+        #[doc = concat!("let m = ", $rot_result, ";")]
+        ///
+        #[doc = concat!("assert_eq!(n.rotate_left(", $rot, "), m);")]
+        /// ```
+        #[stable(feature = "rust1", since = "1.0.0")]
+        #[rustc_const_stable(feature = "const_int_methods", since = "1.32.0")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline(always)]
+        pub const fn rotate_left(self, n: u32) -> Self {
+            (self as $UnsignedT).rotate_left(n) as Self
+        }
+
+        /// Shifts the bits to the right by a specified amount, `n`,
+        /// wrapping the truncated bits to the beginning of the resulting
+        /// integer.
+        ///
+        /// Please note this isn't the same operation as the `>>` shifting operator!
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        #[doc = concat!("let n = ", $rot_result, stringify!($SelfT), ";")]
+        #[doc = concat!("let m = ", $rot_op, ";")]
+        ///
+        #[doc = concat!("assert_eq!(n.rotate_right(", $rot, "), m);")]
+        /// ```
+        #[stable(feature = "rust1", since = "1.0.0")]
+        #[rustc_const_stable(feature = "const_int_methods", since = "1.32.0")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline(always)]
+        pub const fn rotate_right(self, n: u32) -> Self {
+            (self as $UnsignedT).rotate_right(n) as Self
+        }
+
+        /// Reverses the byte order of the integer.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        #[doc = concat!("let n = ", $swap_op, stringify!($SelfT), ";")]
+        ///
+        /// let m = n.swap_bytes();
+        ///
+        #[doc = concat!("assert_eq!(m, ", $swapped, ");")]
+        /// ```
+        #[stable(feature = "rust1", since = "1.0.0")]
+        #[rustc_const_stable(feature = "const_int_methods", since = "1.32.0")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline(always)]
+        pub const fn swap_bytes(self) -> Self {
+            (self as $UnsignedT).swap_bytes() as Self
+        }
+
+        /// Reverses the order of bits in the integer. The least significant bit becomes the most significant bit,
+        ///                 second least-significant bit becomes second most-significant bit, etc.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        #[doc = concat!("let n = ", $swap_op, stringify!($SelfT), ";")]
+        /// let m = n.reverse_bits();
+        ///
+        #[doc = concat!("assert_eq!(m, ", $reversed, ");")]
+        #[doc = concat!("assert_eq!(0, 0", stringify!($SelfT), ".reverse_bits());")]
+        /// ```
+        #[stable(feature = "reverse_bits", since = "1.37.0")]
+        #[rustc_const_stable(feature = "reverse_bits", since = "1.37.0")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline(always)]
+        pub const fn reverse_bits(self) -> Self {
+            (self as $UnsignedT).reverse_bits() as Self
+        }
+
+        /// Converts an integer from big endian to the target's endianness.
+        ///
+        /// On big endian this is a no-op. On little endian the bytes are swapped.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        #[doc = concat!("let n = 0x1A", stringify!($SelfT), ";")]
+        ///
+        /// if cfg!(target_endian = "big") {
+        #[doc = concat!("    assert_eq!(", stringify!($SelfT), "::from_be(n), n)")]
+        /// } else {
+        #[doc = concat!("    assert_eq!(", stringify!($SelfT), "::from_be(n), n.swap_bytes())")]
+        /// }
+        /// ```
+        #[stable(feature = "rust1", since = "1.0.0")]
+        #[rustc_const_stable(feature = "const_int_conversions", since = "1.32.0")]
+        #[must_use]
+        #[inline]
+        pub const fn from_be(x: Self) -> Self {
+            #[cfg(target_endian = "big")]
+            {
+                x
+            }
+            #[cfg(not(target_endian = "big"))]
+            {
+                x.swap_bytes()
+            }
+        }
+
+        /// Converts an integer from little endian to the target's endianness.
+        ///
+        /// On little endian this is a no-op. On big endian the bytes are swapped.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        #[doc = concat!("let n = 0x1A", stringify!($SelfT), ";")]
+        ///
+        /// if cfg!(target_endian = "little") {
+        #[doc = concat!("    assert_eq!(", stringify!($SelfT), "::from_le(n), n)")]
+        /// } else {
+        #[doc = concat!("    assert_eq!(", stringify!($SelfT), "::from_le(n), n.swap_bytes())")]
+        /// }
+        /// ```
+        #[stable(feature = "rust1", since = "1.0.0")]
+        #[rustc_const_stable(feature = "const_int_conversions", since = "1.32.0")]
+        #[must_use]
+        #[inline]
+        pub const fn from_le(x: Self) -> Self {
+            #[cfg(target_endian = "little")]
+            {
+                x
+            }
+            #[cfg(not(target_endian = "little"))]
+            {
+                x.swap_bytes()
+            }
+        }
+
+        /// Converts `self` to big endian from the target's endianness.
+        ///
+        /// On big endian this is a no-op. On little endian the bytes are swapped.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        #[doc = concat!("let n = 0x1A", stringify!($SelfT), ";")]
+        ///
+        /// if cfg!(target_endian = "big") {
+        ///     assert_eq!(n.to_be(), n)
+        /// } else {
+        ///     assert_eq!(n.to_be(), n.swap_bytes())
+        /// }
+        /// ```
+        #[stable(feature = "rust1", since = "1.0.0")]
+        #[rustc_const_stable(feature = "const_int_conversions", since = "1.32.0")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline]
+        pub const fn to_be(self) -> Self { // or not to be?
+            #[cfg(target_endian = "big")]
+            {
+                self
+            }
+            #[cfg(not(target_endian = "big"))]
+            {
+                self.swap_bytes()
+            }
+        }
+
+        /// Converts `self` to little endian from the target's endianness.
+        ///
+        /// On little endian this is a no-op. On big endian the bytes are swapped.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        #[doc = concat!("let n = 0x1A", stringify!($SelfT), ";")]
+        ///
+        /// if cfg!(target_endian = "little") {
+        ///     assert_eq!(n.to_le(), n)
+        /// } else {
+        ///     assert_eq!(n.to_le(), n.swap_bytes())
+        /// }
+        /// ```
+        #[stable(feature = "rust1", since = "1.0.0")]
+        #[rustc_const_stable(feature = "const_int_conversions", since = "1.32.0")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline]
+        pub const fn to_le(self) -> Self {
+            #[cfg(target_endian = "little")]
+            {
+                self
+            }
+            #[cfg(not(target_endian = "little"))]
+            {
+                self.swap_bytes()
+            }
+        }
+
+        /// Checked integer addition. Computes `self + rhs`, returning `None`
+        /// if overflow occurred.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        #[doc = concat!("assert_eq!((", stringify!($SelfT), "::MAX - 2).checked_add(1), Some(", stringify!($SelfT), "::MAX - 1));")]
+        #[doc = concat!("assert_eq!((", stringify!($SelfT), "::MAX - 2).checked_add(3), None);")]
+        /// ```
+        #[stable(feature = "rust1", since = "1.0.0")]
+        #[rustc_const_stable(feature = "const_checked_int_methods", since = "1.47.0")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline]
+        pub const fn checked_add(self, rhs: Self) -> Option<Self> {
+            let (a, b) = self.overflowing_add(rhs);
+            if unlikely!(b) {None} else {Some(a)}
+        }
+
+        /// Unchecked integer addition. Computes `self + rhs`, assuming overflow
+        /// cannot occur.
+        ///
+        /// # Safety
+        ///
+        /// This results in undefined behavior when
+        #[doc = concat!("`self + rhs > ", stringify!($SelfT), "::MAX` or `self + rhs < ", stringify!($SelfT), "::MIN`,")]
+        /// i.e. when [`checked_add`] would return `None`.
+        ///
+        #[doc = concat!("[`checked_add`]: ", stringify!($SelfT), "::checked_add")]
+        #[unstable(
+            feature = "unchecked_math",
+            reason = "niche optimization path",
+            issue = "85122",
+        )]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[rustc_const_unstable(feature = "const_inherent_unchecked_arith", issue = "85122")]
+        #[inline(always)]
+        #[cfg_attr(miri, track_caller)] // even without panics, this helps for Miri backtraces
+        pub const unsafe fn unchecked_add(self, rhs: Self) -> Self {
+            // SAFETY: the caller must uphold the safety contract for
+            // `unchecked_add`.
+            unsafe { intrinsics::unchecked_add(self, rhs) }
+        }
+
+        /// Checked addition with an unsigned integer. Computes `self + rhs`,
+        /// returning `None` if overflow occurred.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        /// # #![feature(mixed_integer_ops)]
+        #[doc = concat!("assert_eq!(1", stringify!($SelfT), ".checked_add_unsigned(2), Some(3));")]
+        #[doc = concat!("assert_eq!((", stringify!($SelfT), "::MAX - 2).checked_add_unsigned(3), None);")]
+        /// ```
+        #[unstable(feature = "mixed_integer_ops", issue = "87840")]
+        #[rustc_const_unstable(feature = "mixed_integer_ops", issue = "87840")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline]
+        pub const fn checked_add_unsigned(self, rhs: $UnsignedT) -> Option<Self> {
+            let (a, b) = self.overflowing_add_unsigned(rhs);
+            if unlikely!(b) {None} else {Some(a)}
+        }
+
+        /// Checked integer subtraction. Computes `self - rhs`, returning `None` if
+        /// overflow occurred.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        #[doc = concat!("assert_eq!((", stringify!($SelfT), "::MIN + 2).checked_sub(1), Some(", stringify!($SelfT), "::MIN + 1));")]
+        #[doc = concat!("assert_eq!((", stringify!($SelfT), "::MIN + 2).checked_sub(3), None);")]
+        /// ```
+        #[stable(feature = "rust1", since = "1.0.0")]
+        #[rustc_const_stable(feature = "const_checked_int_methods", since = "1.47.0")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline]
+        pub const fn checked_sub(self, rhs: Self) -> Option<Self> {
+            let (a, b) = self.overflowing_sub(rhs);
+            if unlikely!(b) {None} else {Some(a)}
+        }
+
+        /// Unchecked integer subtraction. Computes `self - rhs`, assuming overflow
+        /// cannot occur.
+        ///
+        /// # Safety
+        ///
+        /// This results in undefined behavior when
+        #[doc = concat!("`self - rhs > ", stringify!($SelfT), "::MAX` or `self - rhs < ", stringify!($SelfT), "::MIN`,")]
+        /// i.e. when [`checked_sub`] would return `None`.
+        ///
+        #[doc = concat!("[`checked_sub`]: ", stringify!($SelfT), "::checked_sub")]
+        #[unstable(
+            feature = "unchecked_math",
+            reason = "niche optimization path",
+            issue = "85122",
+        )]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[rustc_const_unstable(feature = "const_inherent_unchecked_arith", issue = "85122")]
+        #[inline(always)]
+        #[cfg_attr(miri, track_caller)] // even without panics, this helps for Miri backtraces
+        pub const unsafe fn unchecked_sub(self, rhs: Self) -> Self {
+            // SAFETY: the caller must uphold the safety contract for
+            // `unchecked_sub`.
+            unsafe { intrinsics::unchecked_sub(self, rhs) }
+        }
+
+        /// Checked subtraction with an unsigned integer. Computes `self - rhs`,
+        /// returning `None` if overflow occurred.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        /// # #![feature(mixed_integer_ops)]
+        #[doc = concat!("assert_eq!(1", stringify!($SelfT), ".checked_sub_unsigned(2), Some(-1));")]
+        #[doc = concat!("assert_eq!((", stringify!($SelfT), "::MIN + 2).checked_sub_unsigned(3), None);")]
+        /// ```
+        #[unstable(feature = "mixed_integer_ops", issue = "87840")]
+        #[rustc_const_unstable(feature = "mixed_integer_ops", issue = "87840")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline]
+        pub const fn checked_sub_unsigned(self, rhs: $UnsignedT) -> Option<Self> {
+            let (a, b) = self.overflowing_sub_unsigned(rhs);
+            if unlikely!(b) {None} else {Some(a)}
+        }
+
+        /// Checked integer multiplication. Computes `self * rhs`, returning `None` if
+        /// overflow occurred.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        #[doc = concat!("assert_eq!(", stringify!($SelfT), "::MAX.checked_mul(1), Some(", stringify!($SelfT), "::MAX));")]
+        #[doc = concat!("assert_eq!(", stringify!($SelfT), "::MAX.checked_mul(2), None);")]
+        /// ```
+        #[stable(feature = "rust1", since = "1.0.0")]
+        #[rustc_const_stable(feature = "const_checked_int_methods", since = "1.47.0")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline]
+        pub const fn checked_mul(self, rhs: Self) -> Option<Self> {
+            let (a, b) = self.overflowing_mul(rhs);
+            if unlikely!(b) {None} else {Some(a)}
+        }
+
+        /// Unchecked integer multiplication. Computes `self * rhs`, assuming overflow
+        /// cannot occur.
+        ///
+        /// # Safety
+        ///
+        /// This results in undefined behavior when
+        #[doc = concat!("`self * rhs > ", stringify!($SelfT), "::MAX` or `self * rhs < ", stringify!($SelfT), "::MIN`,")]
+        /// i.e. when [`checked_mul`] would return `None`.
+        ///
+        #[doc = concat!("[`checked_mul`]: ", stringify!($SelfT), "::checked_mul")]
+        #[unstable(
+            feature = "unchecked_math",
+            reason = "niche optimization path",
+            issue = "85122",
+        )]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[rustc_const_unstable(feature = "const_inherent_unchecked_arith", issue = "85122")]
+        #[inline(always)]
+        #[cfg_attr(miri, track_caller)] // even without panics, this helps for Miri backtraces
+        pub const unsafe fn unchecked_mul(self, rhs: Self) -> Self {
+            // SAFETY: the caller must uphold the safety contract for
+            // `unchecked_mul`.
+            unsafe { intrinsics::unchecked_mul(self, rhs) }
+        }
+
+        /// Checked integer division. Computes `self / rhs`, returning `None` if `rhs == 0`
+        /// or the division results in overflow.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        #[doc = concat!("assert_eq!((", stringify!($SelfT), "::MIN + 1).checked_div(-1), Some(", stringify!($Max), "));")]
+        #[doc = concat!("assert_eq!(", stringify!($SelfT), "::MIN.checked_div(-1), None);")]
+        #[doc = concat!("assert_eq!((1", stringify!($SelfT), ").checked_div(0), None);")]
+        /// ```
+        #[stable(feature = "rust1", since = "1.0.0")]
+        #[rustc_const_stable(feature = "const_checked_int_div", since = "1.52.0")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline]
+        pub const fn checked_div(self, rhs: Self) -> Option<Self> {
+            if unlikely!(rhs == 0 || ((self == Self::MIN) && (rhs == -1))) {
+                None
+            } else {
+                // SAFETY: div by zero and by INT_MIN have been checked above
+                Some(unsafe { intrinsics::unchecked_div(self, rhs) })
+            }
+        }
+
+        /// Checked Euclidean division. Computes `self.div_euclid(rhs)`,
+        /// returning `None` if `rhs == 0` or the division results in overflow.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        #[doc = concat!("assert_eq!((", stringify!($SelfT), "::MIN + 1).checked_div_euclid(-1), Some(", stringify!($Max), "));")]
+        #[doc = concat!("assert_eq!(", stringify!($SelfT), "::MIN.checked_div_euclid(-1), None);")]
+        #[doc = concat!("assert_eq!((1", stringify!($SelfT), ").checked_div_euclid(0), None);")]
+        /// ```
+        #[stable(feature = "euclidean_division", since = "1.38.0")]
+        #[rustc_const_stable(feature = "const_euclidean_int_methods", since = "1.52.0")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline]
+        pub const fn checked_div_euclid(self, rhs: Self) -> Option<Self> {
+            // Using `&` helps LLVM see that it is the same check made in division.
+            if unlikely!(rhs == 0 || ((self == Self::MIN) & (rhs == -1))) {
+                None
+            } else {
+                Some(self.div_euclid(rhs))
+            }
+        }
+
+        /// Checked integer remainder. Computes `self % rhs`, returning `None` if
+        /// `rhs == 0` or the division results in overflow.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        ///
+        #[doc = concat!("assert_eq!(5", stringify!($SelfT), ".checked_rem(2), Some(1));")]
+        #[doc = concat!("assert_eq!(5", stringify!($SelfT), ".checked_rem(0), None);")]
+        #[doc = concat!("assert_eq!(", stringify!($SelfT), "::MIN.checked_rem(-1), None);")]
+        /// ```
+        #[stable(feature = "wrapping", since = "1.7.0")]
+        #[rustc_const_stable(feature = "const_checked_int_div", since = "1.52.0")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline]
+        pub const fn checked_rem(self, rhs: Self) -> Option<Self> {
+            if unlikely!(rhs == 0 || ((self == Self::MIN) && (rhs == -1))) {
+                None
+            } else {
+                // SAFETY: div by zero and by INT_MIN have been checked above
+                Some(unsafe { intrinsics::unchecked_rem(self, rhs) })
+            }
+        }
+
+        /// Checked Euclidean remainder. Computes `self.rem_euclid(rhs)`, returning `None`
+        /// if `rhs == 0` or the division results in overflow.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        #[doc = concat!("assert_eq!(5", stringify!($SelfT), ".checked_rem_euclid(2), Some(1));")]
+        #[doc = concat!("assert_eq!(5", stringify!($SelfT), ".checked_rem_euclid(0), None);")]
+        #[doc = concat!("assert_eq!(", stringify!($SelfT), "::MIN.checked_rem_euclid(-1), None);")]
+        /// ```
+        #[stable(feature = "euclidean_division", since = "1.38.0")]
+        #[rustc_const_stable(feature = "const_euclidean_int_methods", since = "1.52.0")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline]
+        pub const fn checked_rem_euclid(self, rhs: Self) -> Option<Self> {
+            // Using `&` helps LLVM see that it is the same check made in division.
+            if unlikely!(rhs == 0 || ((self == Self::MIN) & (rhs == -1))) {
+                None
+            } else {
+                Some(self.rem_euclid(rhs))
+            }
+        }
+
+        /// Checked negation. Computes `-self`, returning `None` if `self == MIN`.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        ///
+        #[doc = concat!("assert_eq!(5", stringify!($SelfT), ".checked_neg(), Some(-5));")]
+        #[doc = concat!("assert_eq!(", stringify!($SelfT), "::MIN.checked_neg(), None);")]
+        /// ```
+        #[stable(feature = "wrapping", since = "1.7.0")]
+        #[rustc_const_stable(feature = "const_checked_int_methods", since = "1.47.0")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline]
+        pub const fn checked_neg(self) -> Option<Self> {
+            let (a, b) = self.overflowing_neg();
+            if unlikely!(b) {None} else {Some(a)}
+        }
+
+        /// Checked shift left. Computes `self << rhs`, returning `None` if `rhs` is larger
+        /// than or equal to the number of bits in `self`.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        #[doc = concat!("assert_eq!(0x1", stringify!($SelfT), ".checked_shl(4), Some(0x10));")]
+        #[doc = concat!("assert_eq!(0x1", stringify!($SelfT), ".checked_shl(129), None);")]
+        /// ```
+        #[stable(feature = "wrapping", since = "1.7.0")]
+        #[rustc_const_stable(feature = "const_checked_int_methods", since = "1.47.0")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline]
+        pub const fn checked_shl(self, rhs: u32) -> Option<Self> {
+            let (a, b) = self.overflowing_shl(rhs);
+            if unlikely!(b) {None} else {Some(a)}
+        }
+
+        /// Unchecked shift left. Computes `self << rhs`, assuming that
+        /// `rhs` is less than the number of bits in `self`.
+        ///
+        /// # Safety
+        ///
+        /// This results in undefined behavior if `rhs` is larger than
+        /// or equal to the number of bits in `self`,
+        /// i.e. when [`checked_shl`] would return `None`.
+        ///
+        #[doc = concat!("[`checked_shl`]: ", stringify!($SelfT), "::checked_shl")]
+        #[unstable(
+            feature = "unchecked_math",
+            reason = "niche optimization path",
+            issue = "85122",
+        )]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[rustc_const_unstable(feature = "const_inherent_unchecked_arith", issue = "85122")]
+        #[inline(always)]
+        #[cfg_attr(miri, track_caller)] // even without panics, this helps for Miri backtraces
+        pub const unsafe fn unchecked_shl(self, rhs: Self) -> Self {
+            // SAFETY: the caller must uphold the safety contract for
+            // `unchecked_shl`.
+            unsafe { intrinsics::unchecked_shl(self, rhs) }
+        }
+
+        /// Checked shift right. Computes `self >> rhs`, returning `None` if `rhs` is
+        /// larger than or equal to the number of bits in `self`.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        #[doc = concat!("assert_eq!(0x10", stringify!($SelfT), ".checked_shr(4), Some(0x1));")]
+        #[doc = concat!("assert_eq!(0x10", stringify!($SelfT), ".checked_shr(128), None);")]
+        /// ```
+        #[stable(feature = "wrapping", since = "1.7.0")]
+        #[rustc_const_stable(feature = "const_checked_int_methods", since = "1.47.0")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline]
+        pub const fn checked_shr(self, rhs: u32) -> Option<Self> {
+            let (a, b) = self.overflowing_shr(rhs);
+            if unlikely!(b) {None} else {Some(a)}
+        }
+
+        /// Unchecked shift right. Computes `self >> rhs`, assuming that
+        /// `rhs` is less than the number of bits in `self`.
+        ///
+        /// # Safety
+        ///
+        /// This results in undefined behavior if `rhs` is larger than
+        /// or equal to the number of bits in `self`,
+        /// i.e. when [`checked_shr`] would return `None`.
+        ///
+        #[doc = concat!("[`checked_shr`]: ", stringify!($SelfT), "::checked_shr")]
+        #[unstable(
+            feature = "unchecked_math",
+            reason = "niche optimization path",
+            issue = "85122",
+        )]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[rustc_const_unstable(feature = "const_inherent_unchecked_arith", issue = "85122")]
+        #[inline(always)]
+        #[cfg_attr(miri, track_caller)] // even without panics, this helps for Miri backtraces
+        pub const unsafe fn unchecked_shr(self, rhs: Self) -> Self {
+            // SAFETY: the caller must uphold the safety contract for
+            // `unchecked_shr`.
+            unsafe { intrinsics::unchecked_shr(self, rhs) }
+        }
+
+        /// Checked absolute value. Computes `self.abs()`, returning `None` if
+        /// `self == MIN`.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        ///
+        #[doc = concat!("assert_eq!((-5", stringify!($SelfT), ").checked_abs(), Some(5));")]
+        #[doc = concat!("assert_eq!(", stringify!($SelfT), "::MIN.checked_abs(), None);")]
+        /// ```
+        #[stable(feature = "no_panic_abs", since = "1.13.0")]
+        #[rustc_const_stable(feature = "const_checked_int_methods", since = "1.47.0")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline]
+        pub const fn checked_abs(self) -> Option<Self> {
+            if self.is_negative() {
+                self.checked_neg()
+            } else {
+                Some(self)
+            }
+        }
+
+        /// Checked exponentiation. Computes `self.pow(exp)`, returning `None` if
+        /// overflow occurred.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        #[doc = concat!("assert_eq!(8", stringify!($SelfT), ".checked_pow(2), Some(64));")]
+        #[doc = concat!("assert_eq!(", stringify!($SelfT), "::MAX.checked_pow(2), None);")]
+        /// ```
+
+        #[stable(feature = "no_panic_pow", since = "1.34.0")]
+        #[rustc_const_stable(feature = "const_int_pow", since = "1.50.0")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline]
+        pub const fn checked_pow(self, mut exp: u32) -> Option<Self> {
+            if exp == 0 {
+                return Some(1);
+            }
+            let mut base = self;
+            let mut acc: Self = 1;
+
+            while exp > 1 {
+                if (exp & 1) == 1 {
+                    acc = try_opt!(acc.checked_mul(base));
+                }
+                exp /= 2;
+                base = try_opt!(base.checked_mul(base));
+            }
+            // since exp!=0, finally the exp must be 1.
+            // Deal with the final bit of the exponent separately, since
+            // squaring the base afterwards is not necessary and may cause a
+            // needless overflow.
+            Some(try_opt!(acc.checked_mul(base)))
+        }
+
+        /// Saturating integer addition. Computes `self + rhs`, saturating at the numeric
+        /// bounds instead of overflowing.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        #[doc = concat!("assert_eq!(100", stringify!($SelfT), ".saturating_add(1), 101);")]
+        #[doc = concat!("assert_eq!(", stringify!($SelfT), "::MAX.saturating_add(100), ", stringify!($SelfT), "::MAX);")]
+        #[doc = concat!("assert_eq!(", stringify!($SelfT), "::MIN.saturating_add(-1), ", stringify!($SelfT), "::MIN);")]
+        /// ```
+
+        #[stable(feature = "rust1", since = "1.0.0")]
+        #[rustc_const_stable(feature = "const_saturating_int_methods", since = "1.47.0")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline(always)]
+        pub const fn saturating_add(self, rhs: Self) -> Self {
+            intrinsics::saturating_add(self, rhs)
+        }
+
+        /// Saturating addition with an unsigned integer. Computes `self + rhs`,
+        /// saturating at the numeric bounds instead of overflowing.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        /// # #![feature(mixed_integer_ops)]
+        #[doc = concat!("assert_eq!(1", stringify!($SelfT), ".saturating_add_unsigned(2), 3);")]
+        #[doc = concat!("assert_eq!(", stringify!($SelfT), "::MAX.saturating_add_unsigned(100), ", stringify!($SelfT), "::MAX);")]
+        /// ```
+        #[unstable(feature = "mixed_integer_ops", issue = "87840")]
+        #[rustc_const_unstable(feature = "mixed_integer_ops", issue = "87840")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline]
+        pub const fn saturating_add_unsigned(self, rhs: $UnsignedT) -> Self {
+            // Overflow can only happen at the upper bound
+            // We cannot use `unwrap_or` here because it is not `const`
+            match self.checked_add_unsigned(rhs) {
+                Some(x) => x,
+                None => Self::MAX,
+            }
+        }
+
+        /// Saturating integer subtraction. Computes `self - rhs`, saturating at the
+        /// numeric bounds instead of overflowing.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        #[doc = concat!("assert_eq!(100", stringify!($SelfT), ".saturating_sub(127), -27);")]
+        #[doc = concat!("assert_eq!(", stringify!($SelfT), "::MIN.saturating_sub(100), ", stringify!($SelfT), "::MIN);")]
+        #[doc = concat!("assert_eq!(", stringify!($SelfT), "::MAX.saturating_sub(-1), ", stringify!($SelfT), "::MAX);")]
+        /// ```
+        #[stable(feature = "rust1", since = "1.0.0")]
+        #[rustc_const_stable(feature = "const_saturating_int_methods", since = "1.47.0")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline(always)]
+        pub const fn saturating_sub(self, rhs: Self) -> Self {
+            intrinsics::saturating_sub(self, rhs)
+        }
+
+        /// Saturating subtraction with an unsigned integer. Computes `self - rhs`,
+        /// saturating at the numeric bounds instead of overflowing.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        /// # #![feature(mixed_integer_ops)]
+        #[doc = concat!("assert_eq!(100", stringify!($SelfT), ".saturating_sub_unsigned(127), -27);")]
+        #[doc = concat!("assert_eq!(", stringify!($SelfT), "::MIN.saturating_sub_unsigned(100), ", stringify!($SelfT), "::MIN);")]
+        /// ```
+        #[unstable(feature = "mixed_integer_ops", issue = "87840")]
+        #[rustc_const_unstable(feature = "mixed_integer_ops", issue = "87840")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline]
+        pub const fn saturating_sub_unsigned(self, rhs: $UnsignedT) -> Self {
+            // Overflow can only happen at the lower bound
+            // We cannot use `unwrap_or` here because it is not `const`
+            match self.checked_sub_unsigned(rhs) {
+                Some(x) => x,
+                None => Self::MIN,
+            }
+        }
+
+        /// Saturating integer negation. Computes `-self`, returning `MAX` if `self == MIN`
+        /// instead of overflowing.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        #[doc = concat!("assert_eq!(100", stringify!($SelfT), ".saturating_neg(), -100);")]
+        #[doc = concat!("assert_eq!((-100", stringify!($SelfT), ").saturating_neg(), 100);")]
+        #[doc = concat!("assert_eq!(", stringify!($SelfT), "::MIN.saturating_neg(), ", stringify!($SelfT), "::MAX);")]
+        #[doc = concat!("assert_eq!(", stringify!($SelfT), "::MAX.saturating_neg(), ", stringify!($SelfT), "::MIN + 1);")]
+        /// ```
+
+        #[stable(feature = "saturating_neg", since = "1.45.0")]
+        #[rustc_const_stable(feature = "const_saturating_int_methods", since = "1.47.0")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline(always)]
+        pub const fn saturating_neg(self) -> Self {
+            intrinsics::saturating_sub(0, self)
+        }
+
+        /// Saturating absolute value. Computes `self.abs()`, returning `MAX` if `self ==
+        /// MIN` instead of overflowing.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        #[doc = concat!("assert_eq!(100", stringify!($SelfT), ".saturating_abs(), 100);")]
+        #[doc = concat!("assert_eq!((-100", stringify!($SelfT), ").saturating_abs(), 100);")]
+        #[doc = concat!("assert_eq!(", stringify!($SelfT), "::MIN.saturating_abs(), ", stringify!($SelfT), "::MAX);")]
+        #[doc = concat!("assert_eq!((", stringify!($SelfT), "::MIN + 1).saturating_abs(), ", stringify!($SelfT), "::MAX);")]
+        /// ```
+
+        #[stable(feature = "saturating_neg", since = "1.45.0")]
+        #[rustc_const_stable(feature = "const_saturating_int_methods", since = "1.47.0")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline]
+        pub const fn saturating_abs(self) -> Self {
+            if self.is_negative() {
+                self.saturating_neg()
+            } else {
+                self
+            }
+        }
+
+        /// Saturating integer multiplication. Computes `self * rhs`, saturating at the
+        /// numeric bounds instead of overflowing.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        ///
+        #[doc = concat!("assert_eq!(10", stringify!($SelfT), ".saturating_mul(12), 120);")]
+        #[doc = concat!("assert_eq!(", stringify!($SelfT), "::MAX.saturating_mul(10), ", stringify!($SelfT), "::MAX);")]
+        #[doc = concat!("assert_eq!(", stringify!($SelfT), "::MIN.saturating_mul(10), ", stringify!($SelfT), "::MIN);")]
+        /// ```
+        #[stable(feature = "wrapping", since = "1.7.0")]
+        #[rustc_const_stable(feature = "const_saturating_int_methods", since = "1.47.0")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline]
+        pub const fn saturating_mul(self, rhs: Self) -> Self {
+            match self.checked_mul(rhs) {
+                Some(x) => x,
+                None => if (self < 0) == (rhs < 0) {
+                    Self::MAX
+                } else {
+                    Self::MIN
+                }
+            }
+        }
+
+        /// Saturating integer division. Computes `self / rhs`, saturating at the
+        /// numeric bounds instead of overflowing.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        #[doc = concat!("assert_eq!(5", stringify!($SelfT), ".saturating_div(2), 2);")]
+        #[doc = concat!("assert_eq!(", stringify!($SelfT), "::MAX.saturating_div(-1), ", stringify!($SelfT), "::MIN + 1);")]
+        #[doc = concat!("assert_eq!(", stringify!($SelfT), "::MIN.saturating_div(-1), ", stringify!($SelfT), "::MAX);")]
+        ///
+        /// ```
+        ///
+        /// ```should_panic
+        #[doc = concat!("let _ = 1", stringify!($SelfT), ".saturating_div(0);")]
+        ///
+        /// ```
+        #[stable(feature = "saturating_div", since = "1.58.0")]
+        #[rustc_const_stable(feature = "saturating_div", since = "1.58.0")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline]
+        pub const fn saturating_div(self, rhs: Self) -> Self {
+            match self.overflowing_div(rhs) {
+                (result, false) => result,
+                (_result, true) => Self::MAX, // MIN / -1 is the only possible saturating overflow
+            }
+        }
+
+        /// Saturating integer exponentiation. Computes `self.pow(exp)`,
+        /// saturating at the numeric bounds instead of overflowing.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        ///
+        #[doc = concat!("assert_eq!((-4", stringify!($SelfT), ").saturating_pow(3), -64);")]
+        #[doc = concat!("assert_eq!(", stringify!($SelfT), "::MIN.saturating_pow(2), ", stringify!($SelfT), "::MAX);")]
+        #[doc = concat!("assert_eq!(", stringify!($SelfT), "::MIN.saturating_pow(3), ", stringify!($SelfT), "::MIN);")]
+        /// ```
+        #[stable(feature = "no_panic_pow", since = "1.34.0")]
+        #[rustc_const_stable(feature = "const_int_pow", since = "1.50.0")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline]
+        pub const fn saturating_pow(self, exp: u32) -> Self {
+            match self.checked_pow(exp) {
+                Some(x) => x,
+                None if self < 0 && exp % 2 == 1 => Self::MIN,
+                None => Self::MAX,
+            }
+        }
+
+        /// Wrapping (modular) addition. Computes `self + rhs`, wrapping around at the
+        /// boundary of the type.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        #[doc = concat!("assert_eq!(100", stringify!($SelfT), ".wrapping_add(27), 127);")]
+        #[doc = concat!("assert_eq!(", stringify!($SelfT), "::MAX.wrapping_add(2), ", stringify!($SelfT), "::MIN + 1);")]
+        /// ```
+        #[stable(feature = "rust1", since = "1.0.0")]
+        #[rustc_const_stable(feature = "const_int_methods", since = "1.32.0")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline(always)]
+        pub const fn wrapping_add(self, rhs: Self) -> Self {
+            intrinsics::wrapping_add(self, rhs)
+        }
+
+        /// Wrapping (modular) addition with an unsigned integer. Computes
+        /// `self + rhs`, wrapping around at the boundary of the type.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        /// # #![feature(mixed_integer_ops)]
+        #[doc = concat!("assert_eq!(100", stringify!($SelfT), ".wrapping_add_unsigned(27), 127);")]
+        #[doc = concat!("assert_eq!(", stringify!($SelfT), "::MAX.wrapping_add_unsigned(2), ", stringify!($SelfT), "::MIN + 1);")]
+        /// ```
+        #[unstable(feature = "mixed_integer_ops", issue = "87840")]
+        #[rustc_const_unstable(feature = "mixed_integer_ops", issue = "87840")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline(always)]
+        pub const fn wrapping_add_unsigned(self, rhs: $UnsignedT) -> Self {
+            self.wrapping_add(rhs as Self)
+        }
+
+        /// Wrapping (modular) subtraction. Computes `self - rhs`, wrapping around at the
+        /// boundary of the type.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        #[doc = concat!("assert_eq!(0", stringify!($SelfT), ".wrapping_sub(127), -127);")]
+        #[doc = concat!("assert_eq!((-2", stringify!($SelfT), ").wrapping_sub(", stringify!($SelfT), "::MAX), ", stringify!($SelfT), "::MAX);")]
+        /// ```
+        #[stable(feature = "rust1", since = "1.0.0")]
+        #[rustc_const_stable(feature = "const_int_methods", since = "1.32.0")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline(always)]
+        pub const fn wrapping_sub(self, rhs: Self) -> Self {
+            intrinsics::wrapping_sub(self, rhs)
+        }
+
+        /// Wrapping (modular) subtraction with an unsigned integer. Computes
+        /// `self - rhs`, wrapping around at the boundary of the type.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        /// # #![feature(mixed_integer_ops)]
+        #[doc = concat!("assert_eq!(0", stringify!($SelfT), ".wrapping_sub_unsigned(127), -127);")]
+        #[doc = concat!("assert_eq!((-2", stringify!($SelfT), ").wrapping_sub_unsigned(", stringify!($UnsignedT), "::MAX), -1);")]
+        /// ```
+        #[unstable(feature = "mixed_integer_ops", issue = "87840")]
+        #[rustc_const_unstable(feature = "mixed_integer_ops", issue = "87840")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline(always)]
+        pub const fn wrapping_sub_unsigned(self, rhs: $UnsignedT) -> Self {
+            self.wrapping_sub(rhs as Self)
+        }
+
+        /// Wrapping (modular) multiplication. Computes `self * rhs`, wrapping around at
+        /// the boundary of the type.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        #[doc = concat!("assert_eq!(10", stringify!($SelfT), ".wrapping_mul(12), 120);")]
+        /// assert_eq!(11i8.wrapping_mul(12), -124);
+        /// ```
+        #[stable(feature = "rust1", since = "1.0.0")]
+        #[rustc_const_stable(feature = "const_int_methods", since = "1.32.0")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline(always)]
+        pub const fn wrapping_mul(self, rhs: Self) -> Self {
+            intrinsics::wrapping_mul(self, rhs)
+        }
+
+        /// Wrapping (modular) division. Computes `self / rhs`, wrapping around at the
+        /// boundary of the type.
+        ///
+        /// The only case where such wrapping can occur is when one divides `MIN / -1` on a signed type (where
+        /// `MIN` is the negative minimal value for the type); this is equivalent to `-MIN`, a positive value
+        /// that is too large to represent in the type. In such a case, this function returns `MIN` itself.
+        ///
+        /// # Panics
+        ///
+        /// This function will panic if `rhs` is 0.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        #[doc = concat!("assert_eq!(100", stringify!($SelfT), ".wrapping_div(10), 10);")]
+        /// assert_eq!((-128i8).wrapping_div(-1), -128);
+        /// ```
+        #[stable(feature = "num_wrapping", since = "1.2.0")]
+        #[rustc_const_stable(feature = "const_wrapping_int_methods", since = "1.52.0")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline]
+        pub const fn wrapping_div(self, rhs: Self) -> Self {
+            self.overflowing_div(rhs).0
+        }
+
+        /// Wrapping Euclidean division. Computes `self.div_euclid(rhs)`,
+        /// wrapping around at the boundary of the type.
+        ///
+        /// Wrapping will only occur in `MIN / -1` on a signed type (where `MIN` is the negative minimal value
+        /// for the type). This is equivalent to `-MIN`, a positive value that is too large to represent in the
+        /// type. In this case, this method returns `MIN` itself.
+        ///
+        /// # Panics
+        ///
+        /// This function will panic if `rhs` is 0.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        #[doc = concat!("assert_eq!(100", stringify!($SelfT), ".wrapping_div_euclid(10), 10);")]
+        /// assert_eq!((-128i8).wrapping_div_euclid(-1), -128);
+        /// ```
+        #[stable(feature = "euclidean_division", since = "1.38.0")]
+        #[rustc_const_stable(feature = "const_euclidean_int_methods", since = "1.52.0")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline]
+        pub const fn wrapping_div_euclid(self, rhs: Self) -> Self {
+            self.overflowing_div_euclid(rhs).0
+        }
+
+        /// Wrapping (modular) remainder. Computes `self % rhs`, wrapping around at the
+        /// boundary of the type.
+        ///
+        /// Such wrap-around never actually occurs mathematically; implementation artifacts make `x % y`
+        /// invalid for `MIN / -1` on a signed type (where `MIN` is the negative minimal value). In such a case,
+        /// this function returns `0`.
+        ///
+        /// # Panics
+        ///
+        /// This function will panic if `rhs` is 0.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        #[doc = concat!("assert_eq!(100", stringify!($SelfT), ".wrapping_rem(10), 0);")]
+        /// assert_eq!((-128i8).wrapping_rem(-1), 0);
+        /// ```
+        #[stable(feature = "num_wrapping", since = "1.2.0")]
+        #[rustc_const_stable(feature = "const_wrapping_int_methods", since = "1.52.0")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline]
+        pub const fn wrapping_rem(self, rhs: Self) -> Self {
+            self.overflowing_rem(rhs).0
+        }
+
+        /// Wrapping Euclidean remainder. Computes `self.rem_euclid(rhs)`, wrapping around
+        /// at the boundary of the type.
+        ///
+        /// Wrapping will only occur in `MIN % -1` on a signed type (where `MIN` is the negative minimal value
+        /// for the type). In this case, this method returns 0.
+        ///
+        /// # Panics
+        ///
+        /// This function will panic if `rhs` is 0.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        #[doc = concat!("assert_eq!(100", stringify!($SelfT), ".wrapping_rem_euclid(10), 0);")]
+        /// assert_eq!((-128i8).wrapping_rem_euclid(-1), 0);
+        /// ```
+        #[stable(feature = "euclidean_division", since = "1.38.0")]
+        #[rustc_const_stable(feature = "const_euclidean_int_methods", since = "1.52.0")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline]
+        pub const fn wrapping_rem_euclid(self, rhs: Self) -> Self {
+            self.overflowing_rem_euclid(rhs).0
+        }
+
+        /// Wrapping (modular) negation. Computes `-self`, wrapping around at the boundary
+        /// of the type.
+        ///
+        /// The only case where such wrapping can occur is when one negates `MIN` on a signed type (where `MIN`
+        /// is the negative minimal value for the type); this is a positive value that is too large to represent
+        /// in the type. In such a case, this function returns `MIN` itself.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        #[doc = concat!("assert_eq!(100", stringify!($SelfT), ".wrapping_neg(), -100);")]
+        #[doc = concat!("assert_eq!(", stringify!($SelfT), "::MIN.wrapping_neg(), ", stringify!($SelfT), "::MIN);")]
+        /// ```
+        #[stable(feature = "num_wrapping", since = "1.2.0")]
+        #[rustc_const_stable(feature = "const_int_methods", since = "1.32.0")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline(always)]
+        pub const fn wrapping_neg(self) -> Self {
+            (0 as $SelfT).wrapping_sub(self)
+        }
+
+        /// Panic-free bitwise shift-left; yields `self << mask(rhs)`, where `mask` removes
+        /// any high-order bits of `rhs` that would cause the shift to exceed the bitwidth of the type.
+        ///
+        /// Note that this is *not* the same as a rotate-left; the RHS of a wrapping shift-left is restricted to
+        /// the range of the type, rather than the bits shifted out of the LHS being returned to the other end.
+        /// The primitive integer types all implement a [`rotate_left`](Self::rotate_left) function,
+        /// which may be what you want instead.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        #[doc = concat!("assert_eq!((-1", stringify!($SelfT), ").wrapping_shl(7), -128);")]
+        #[doc = concat!("assert_eq!((-1", stringify!($SelfT), ").wrapping_shl(128), -1);")]
+        /// ```
+        #[stable(feature = "num_wrapping", since = "1.2.0")]
+        #[rustc_const_stable(feature = "const_int_methods", since = "1.32.0")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline(always)]
+        pub const fn wrapping_shl(self, rhs: u32) -> Self {
+            // SAFETY: the masking by the bitsize of the type ensures that we do not shift
+            // out of bounds
+            unsafe {
+                intrinsics::unchecked_shl(self, (rhs & ($BITS - 1)) as $SelfT)
+            }
+        }
+
+        /// Panic-free bitwise shift-right; yields `self >> mask(rhs)`, where `mask`
+        /// removes any high-order bits of `rhs` that would cause the shift to exceed the bitwidth of the type.
+        ///
+        /// Note that this is *not* the same as a rotate-right; the RHS of a wrapping shift-right is restricted
+        /// to the range of the type, rather than the bits shifted out of the LHS being returned to the other
+        /// end. The primitive integer types all implement a [`rotate_right`](Self::rotate_right) function,
+        /// which may be what you want instead.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        #[doc = concat!("assert_eq!((-128", stringify!($SelfT), ").wrapping_shr(7), -1);")]
+        /// assert_eq!((-128i16).wrapping_shr(64), -128);
+        /// ```
+        #[stable(feature = "num_wrapping", since = "1.2.0")]
+        #[rustc_const_stable(feature = "const_int_methods", since = "1.32.0")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline(always)]
+        pub const fn wrapping_shr(self, rhs: u32) -> Self {
+            // SAFETY: the masking by the bitsize of the type ensures that we do not shift
+            // out of bounds
+            unsafe {
+                intrinsics::unchecked_shr(self, (rhs & ($BITS - 1)) as $SelfT)
+            }
+        }
+
+        /// Wrapping (modular) absolute value. Computes `self.abs()`, wrapping around at
+        /// the boundary of the type.
+        ///
+        /// The only case where such wrapping can occur is when one takes the absolute value of the negative
+        /// minimal value for the type; this is a positive value that is too large to represent in the type. In
+        /// such a case, this function returns `MIN` itself.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        #[doc = concat!("assert_eq!(100", stringify!($SelfT), ".wrapping_abs(), 100);")]
+        #[doc = concat!("assert_eq!((-100", stringify!($SelfT), ").wrapping_abs(), 100);")]
+        #[doc = concat!("assert_eq!(", stringify!($SelfT), "::MIN.wrapping_abs(), ", stringify!($SelfT), "::MIN);")]
+        /// assert_eq!((-128i8).wrapping_abs() as u8, 128);
+        /// ```
+        #[stable(feature = "no_panic_abs", since = "1.13.0")]
+        #[rustc_const_stable(feature = "const_int_methods", since = "1.32.0")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[allow(unused_attributes)]
+        #[inline]
+        pub const fn wrapping_abs(self) -> Self {
+             if self.is_negative() {
+                 self.wrapping_neg()
+             } else {
+                 self
+             }
+        }
+
+        /// Computes the absolute value of `self` without any wrapping
+        /// or panicking.
+        ///
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        #[doc = concat!("assert_eq!(100", stringify!($SelfT), ".unsigned_abs(), 100", stringify!($UnsignedT), ");")]
+        #[doc = concat!("assert_eq!((-100", stringify!($SelfT), ").unsigned_abs(), 100", stringify!($UnsignedT), ");")]
+        /// assert_eq!((-128i8).unsigned_abs(), 128u8);
+        /// ```
+        #[stable(feature = "unsigned_abs", since = "1.51.0")]
+        #[rustc_const_stable(feature = "unsigned_abs", since = "1.51.0")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline]
+        pub const fn unsigned_abs(self) -> $UnsignedT {
+             self.wrapping_abs() as $UnsignedT
+        }
+
+        /// Wrapping (modular) exponentiation. Computes `self.pow(exp)`,
+        /// wrapping around at the boundary of the type.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        #[doc = concat!("assert_eq!(3", stringify!($SelfT), ".wrapping_pow(4), 81);")]
+        /// assert_eq!(3i8.wrapping_pow(5), -13);
+        /// assert_eq!(3i8.wrapping_pow(6), -39);
+        /// ```
+        #[stable(feature = "no_panic_pow", since = "1.34.0")]
+        #[rustc_const_stable(feature = "const_int_pow", since = "1.50.0")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline]
+        pub const fn wrapping_pow(self, mut exp: u32) -> Self {
+            if exp == 0 {
+                return 1;
+            }
+            let mut base = self;
+            let mut acc: Self = 1;
+
+            while exp > 1 {
+                if (exp & 1) == 1 {
+                    acc = acc.wrapping_mul(base);
+                }
+                exp /= 2;
+                base = base.wrapping_mul(base);
+            }
+
+            // since exp!=0, finally the exp must be 1.
+            // Deal with the final bit of the exponent separately, since
+            // squaring the base afterwards is not necessary and may cause a
+            // needless overflow.
+            acc.wrapping_mul(base)
+        }
+
+        /// Calculates `self` + `rhs`
+        ///
+        /// Returns a tuple of the addition along with a boolean indicating whether an arithmetic overflow would
+        /// occur. If an overflow would have occurred then the wrapped value is returned.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        ///
+        #[doc = concat!("assert_eq!(5", stringify!($SelfT), ".overflowing_add(2), (7, false));")]
+        #[doc = concat!("assert_eq!(", stringify!($SelfT), "::MAX.overflowing_add(1), (", stringify!($SelfT), "::MIN, true));")]
+        /// ```
+        #[stable(feature = "wrapping", since = "1.7.0")]
+        #[rustc_const_stable(feature = "const_int_methods", since = "1.32.0")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline(always)]
+        pub const fn overflowing_add(self, rhs: Self) -> (Self, bool) {
+            let (a, b) = intrinsics::add_with_overflow(self as $ActualT, rhs as $ActualT);
+            (a as Self, b)
+        }
+
+        /// Calculates `self` + `rhs` with an unsigned `rhs`
+        ///
+        /// Returns a tuple of the addition along with a boolean indicating
+        /// whether an arithmetic overflow would occur. If an overflow would
+        /// have occurred then the wrapped value is returned.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        /// # #![feature(mixed_integer_ops)]
+        #[doc = concat!("assert_eq!(1", stringify!($SelfT), ".overflowing_add_unsigned(2), (3, false));")]
+        #[doc = concat!("assert_eq!((", stringify!($SelfT), "::MIN).overflowing_add_unsigned(", stringify!($UnsignedT), "::MAX), (", stringify!($SelfT), "::MAX, false));")]
+        #[doc = concat!("assert_eq!((", stringify!($SelfT), "::MAX - 2).overflowing_add_unsigned(3), (", stringify!($SelfT), "::MIN, true));")]
+        /// ```
+        #[unstable(feature = "mixed_integer_ops", issue = "87840")]
+        #[rustc_const_unstable(feature = "mixed_integer_ops", issue = "87840")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline]
+        pub const fn overflowing_add_unsigned(self, rhs: $UnsignedT) -> (Self, bool) {
+            let rhs = rhs as Self;
+            let (res, overflowed) = self.overflowing_add(rhs);
+            (res, overflowed ^ (rhs < 0))
+        }
+
+        /// Calculates `self` - `rhs`
+        ///
+        /// Returns a tuple of the subtraction along with a boolean indicating whether an arithmetic overflow
+        /// would occur. If an overflow would have occurred then the wrapped value is returned.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        ///
+        #[doc = concat!("assert_eq!(5", stringify!($SelfT), ".overflowing_sub(2), (3, false));")]
+        #[doc = concat!("assert_eq!(", stringify!($SelfT), "::MIN.overflowing_sub(1), (", stringify!($SelfT), "::MAX, true));")]
+        /// ```
+        #[stable(feature = "wrapping", since = "1.7.0")]
+        #[rustc_const_stable(feature = "const_int_methods", since = "1.32.0")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline(always)]
+        pub const fn overflowing_sub(self, rhs: Self) -> (Self, bool) {
+            let (a, b) = intrinsics::sub_with_overflow(self as $ActualT, rhs as $ActualT);
+            (a as Self, b)
+        }
+
+        /// Calculates `self` - `rhs` with an unsigned `rhs`
+        ///
+        /// Returns a tuple of the subtraction along with a boolean indicating
+        /// whether an arithmetic overflow would occur. If an overflow would
+        /// have occurred then the wrapped value is returned.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        /// # #![feature(mixed_integer_ops)]
+        #[doc = concat!("assert_eq!(1", stringify!($SelfT), ".overflowing_sub_unsigned(2), (-1, false));")]
+        #[doc = concat!("assert_eq!((", stringify!($SelfT), "::MAX).overflowing_sub_unsigned(", stringify!($UnsignedT), "::MAX), (", stringify!($SelfT), "::MIN, false));")]
+        #[doc = concat!("assert_eq!((", stringify!($SelfT), "::MIN + 2).overflowing_sub_unsigned(3), (", stringify!($SelfT), "::MAX, true));")]
+        /// ```
+        #[unstable(feature = "mixed_integer_ops", issue = "87840")]
+        #[rustc_const_unstable(feature = "mixed_integer_ops", issue = "87840")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline]
+        pub const fn overflowing_sub_unsigned(self, rhs: $UnsignedT) -> (Self, bool) {
+            let rhs = rhs as Self;
+            let (res, overflowed) = self.overflowing_sub(rhs);
+            (res, overflowed ^ (rhs < 0))
+        }
+
+        /// Calculates the multiplication of `self` and `rhs`.
+        ///
+        /// Returns a tuple of the multiplication along with a boolean indicating whether an arithmetic overflow
+        /// would occur. If an overflow would have occurred then the wrapped value is returned.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        #[doc = concat!("assert_eq!(5", stringify!($SelfT), ".overflowing_mul(2), (10, false));")]
+        /// assert_eq!(1_000_000_000i32.overflowing_mul(10), (1410065408, true));
+        /// ```
+        #[stable(feature = "wrapping", since = "1.7.0")]
+        #[rustc_const_stable(feature = "const_int_methods", since = "1.32.0")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline(always)]
+        pub const fn overflowing_mul(self, rhs: Self) -> (Self, bool) {
+            let (a, b) = intrinsics::mul_with_overflow(self as $ActualT, rhs as $ActualT);
+            (a as Self, b)
+        }
+
+        /// Calculates the divisor when `self` is divided by `rhs`.
+        ///
+        /// Returns a tuple of the divisor along with a boolean indicating whether an arithmetic overflow would
+        /// occur. If an overflow would occur then self is returned.
+        ///
+        /// # Panics
+        ///
+        /// This function will panic if `rhs` is 0.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        ///
+        #[doc = concat!("assert_eq!(5", stringify!($SelfT), ".overflowing_div(2), (2, false));")]
+        #[doc = concat!("assert_eq!(", stringify!($SelfT), "::MIN.overflowing_div(-1), (", stringify!($SelfT), "::MIN, true));")]
+        /// ```
+        #[inline]
+        #[stable(feature = "wrapping", since = "1.7.0")]
+        #[rustc_const_stable(feature = "const_overflowing_int_methods", since = "1.52.0")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        pub const fn overflowing_div(self, rhs: Self) -> (Self, bool) {
+            // Using `&` helps LLVM see that it is the same check made in division.
+            if unlikely!((self == Self::MIN) & (rhs == -1)) {
+                (self, true)
+            } else {
+                (self / rhs, false)
+            }
+        }
+
+        /// Calculates the quotient of Euclidean division `self.div_euclid(rhs)`.
+        ///
+        /// Returns a tuple of the divisor along with a boolean indicating whether an arithmetic overflow would
+        /// occur. If an overflow would occur then `self` is returned.
+        ///
+        /// # Panics
+        ///
+        /// This function will panic if `rhs` is 0.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        #[doc = concat!("assert_eq!(5", stringify!($SelfT), ".overflowing_div_euclid(2), (2, false));")]
+        #[doc = concat!("assert_eq!(", stringify!($SelfT), "::MIN.overflowing_div_euclid(-1), (", stringify!($SelfT), "::MIN, true));")]
+        /// ```
+        #[inline]
+        #[stable(feature = "euclidean_division", since = "1.38.0")]
+        #[rustc_const_stable(feature = "const_euclidean_int_methods", since = "1.52.0")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        pub const fn overflowing_div_euclid(self, rhs: Self) -> (Self, bool) {
+            // Using `&` helps LLVM see that it is the same check made in division.
+            if unlikely!((self == Self::MIN) & (rhs == -1)) {
+                (self, true)
+            } else {
+                (self.div_euclid(rhs), false)
+            }
+        }
+
+        /// Calculates the remainder when `self` is divided by `rhs`.
+        ///
+        /// Returns a tuple of the remainder after dividing along with a boolean indicating whether an
+        /// arithmetic overflow would occur. If an overflow would occur then 0 is returned.
+        ///
+        /// # Panics
+        ///
+        /// This function will panic if `rhs` is 0.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        ///
+        #[doc = concat!("assert_eq!(5", stringify!($SelfT), ".overflowing_rem(2), (1, false));")]
+        #[doc = concat!("assert_eq!(", stringify!($SelfT), "::MIN.overflowing_rem(-1), (0, true));")]
+        /// ```
+        #[inline]
+        #[stable(feature = "wrapping", since = "1.7.0")]
+        #[rustc_const_stable(feature = "const_overflowing_int_methods", since = "1.52.0")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        pub const fn overflowing_rem(self, rhs: Self) -> (Self, bool) {
+            if unlikely!(rhs == -1) {
+                (0, self == Self::MIN)
+            } else {
+                (self % rhs, false)
+            }
+        }
+
+
+        /// Overflowing Euclidean remainder. Calculates `self.rem_euclid(rhs)`.
+        ///
+        /// Returns a tuple of the remainder after dividing along with a boolean indicating whether an
+        /// arithmetic overflow would occur. If an overflow would occur then 0 is returned.
+        ///
+        /// # Panics
+        ///
+        /// This function will panic if `rhs` is 0.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        #[doc = concat!("assert_eq!(5", stringify!($SelfT), ".overflowing_rem_euclid(2), (1, false));")]
+        #[doc = concat!("assert_eq!(", stringify!($SelfT), "::MIN.overflowing_rem_euclid(-1), (0, true));")]
+        /// ```
+        #[stable(feature = "euclidean_division", since = "1.38.0")]
+        #[rustc_const_stable(feature = "const_euclidean_int_methods", since = "1.52.0")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline]
+        pub const fn overflowing_rem_euclid(self, rhs: Self) -> (Self, bool) {
+            if unlikely!(rhs == -1) {
+                (0, self == Self::MIN)
+            } else {
+                (self.rem_euclid(rhs), false)
+            }
+        }
+
+
+        /// Negates self, overflowing if this is equal to the minimum value.
+        ///
+        /// Returns a tuple of the negated version of self along with a boolean indicating whether an overflow
+        /// happened. If `self` is the minimum value (e.g., `i32::MIN` for values of type `i32`), then the
+        /// minimum value will be returned again and `true` will be returned for an overflow happening.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        #[doc = concat!("assert_eq!(2", stringify!($SelfT), ".overflowing_neg(), (-2, false));")]
+        #[doc = concat!("assert_eq!(", stringify!($SelfT), "::MIN.overflowing_neg(), (", stringify!($SelfT), "::MIN, true));")]
+        /// ```
+        #[inline]
+        #[stable(feature = "wrapping", since = "1.7.0")]
+        #[rustc_const_stable(feature = "const_int_methods", since = "1.32.0")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[allow(unused_attributes)]
+        pub const fn overflowing_neg(self) -> (Self, bool) {
+            if unlikely!(self == Self::MIN) {
+                (Self::MIN, true)
+            } else {
+                (-self, false)
+            }
+        }
+
+        /// Shifts self left by `rhs` bits.
+        ///
+        /// Returns a tuple of the shifted version of self along with a boolean indicating whether the shift
+        /// value was larger than or equal to the number of bits. If the shift value is too large, then value is
+        /// masked (N-1) where N is the number of bits, and this value is then used to perform the shift.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        #[doc = concat!("assert_eq!(0x1", stringify!($SelfT),".overflowing_shl(4), (0x10, false));")]
+        /// assert_eq!(0x1i32.overflowing_shl(36), (0x10, true));
+        /// ```
+        #[stable(feature = "wrapping", since = "1.7.0")]
+        #[rustc_const_stable(feature = "const_int_methods", since = "1.32.0")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline]
+        pub const fn overflowing_shl(self, rhs: u32) -> (Self, bool) {
+            (self.wrapping_shl(rhs), (rhs > ($BITS - 1)))
+        }
+
+        /// Shifts self right by `rhs` bits.
+        ///
+        /// Returns a tuple of the shifted version of self along with a boolean indicating whether the shift
+        /// value was larger than or equal to the number of bits. If the shift value is too large, then value is
+        /// masked (N-1) where N is the number of bits, and this value is then used to perform the shift.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        #[doc = concat!("assert_eq!(0x10", stringify!($SelfT), ".overflowing_shr(4), (0x1, false));")]
+        /// assert_eq!(0x10i32.overflowing_shr(36), (0x1, true));
+        /// ```
+        #[stable(feature = "wrapping", since = "1.7.0")]
+        #[rustc_const_stable(feature = "const_int_methods", since = "1.32.0")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline]
+        pub const fn overflowing_shr(self, rhs: u32) -> (Self, bool) {
+            (self.wrapping_shr(rhs), (rhs > ($BITS - 1)))
+        }
+
+        /// Computes the absolute value of `self`.
+        ///
+        /// Returns a tuple of the absolute version of self along with a boolean indicating whether an overflow
+        /// happened. If self is the minimum value
+        #[doc = concat!("(e.g., ", stringify!($SelfT), "::MIN for values of type ", stringify!($SelfT), "),")]
+        /// then the minimum value will be returned again and true will be returned
+        /// for an overflow happening.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        #[doc = concat!("assert_eq!(10", stringify!($SelfT), ".overflowing_abs(), (10, false));")]
+        #[doc = concat!("assert_eq!((-10", stringify!($SelfT), ").overflowing_abs(), (10, false));")]
+        #[doc = concat!("assert_eq!((", stringify!($SelfT), "::MIN).overflowing_abs(), (", stringify!($SelfT), "::MIN, true));")]
+        /// ```
+        #[stable(feature = "no_panic_abs", since = "1.13.0")]
+        #[rustc_const_stable(feature = "const_int_methods", since = "1.32.0")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline]
+        pub const fn overflowing_abs(self) -> (Self, bool) {
+            (self.wrapping_abs(), self == Self::MIN)
+        }
+
+        /// Raises self to the power of `exp`, using exponentiation by squaring.
+        ///
+        /// Returns a tuple of the exponentiation along with a bool indicating
+        /// whether an overflow happened.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        #[doc = concat!("assert_eq!(3", stringify!($SelfT), ".overflowing_pow(4), (81, false));")]
+        /// assert_eq!(3i8.overflowing_pow(5), (-13, true));
+        /// ```
+        #[stable(feature = "no_panic_pow", since = "1.34.0")]
+        #[rustc_const_stable(feature = "const_int_pow", since = "1.50.0")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline]
+        pub const fn overflowing_pow(self, mut exp: u32) -> (Self, bool) {
+            if exp == 0 {
+                return (1,false);
+            }
+            let mut base = self;
+            let mut acc: Self = 1;
+            let mut overflown = false;
+            // Scratch space for storing results of overflowing_mul.
+            let mut r;
+
+            while exp > 1 {
+                if (exp & 1) == 1 {
+                    r = acc.overflowing_mul(base);
+                    acc = r.0;
+                    overflown |= r.1;
+                }
+                exp /= 2;
+                r = base.overflowing_mul(base);
+                base = r.0;
+                overflown |= r.1;
+            }
+
+            // since exp!=0, finally the exp must be 1.
+            // Deal with the final bit of the exponent separately, since
+            // squaring the base afterwards is not necessary and may cause a
+            // needless overflow.
+            r = acc.overflowing_mul(base);
+            r.1 |= overflown;
+            r
+        }
+
+        /// Raises self to the power of `exp`, using exponentiation by squaring.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        #[doc = concat!("let x: ", stringify!($SelfT), " = 2; // or any other integer type")]
+        ///
+        /// assert_eq!(x.pow(5), 32);
+        /// ```
+        #[stable(feature = "rust1", since = "1.0.0")]
+        #[rustc_const_stable(feature = "const_int_pow", since = "1.50.0")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline]
+        #[rustc_inherit_overflow_checks]
+        pub const fn pow(self, mut exp: u32) -> Self {
+            if exp == 0 {
+                return 1;
+            }
+            let mut base = self;
+            let mut acc = 1;
+
+            while exp > 1 {
+                if (exp & 1) == 1 {
+                    acc = acc * base;
+                }
+                exp /= 2;
+                base = base * base;
+            }
+
+            // since exp!=0, finally the exp must be 1.
+            // Deal with the final bit of the exponent separately, since
+            // squaring the base afterwards is not necessary and may cause a
+            // needless overflow.
+            acc * base
+        }
+
+        /// Calculates the quotient of Euclidean division of `self` by `rhs`.
+        ///
+        /// This computes the integer `q` such that `self = q * rhs + r`, with
+        /// `r = self.rem_euclid(rhs)` and `0 <= r < abs(rhs)`.
+        ///
+        /// In other words, the result is `self / rhs` rounded to the integer `q`
+        /// such that `self >= q * rhs`.
+        /// If `self > 0`, this is equal to round towards zero (the default in Rust);
+        /// if `self < 0`, this is equal to round towards +/- infinity.
+        ///
+        /// # Panics
+        ///
+        /// This function will panic if `rhs` is 0 or the division results in overflow.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        #[doc = concat!("let a: ", stringify!($SelfT), " = 7; // or any other integer type")]
+        /// let b = 4;
+        ///
+        /// assert_eq!(a.div_euclid(b), 1); // 7 >= 4 * 1
+        /// assert_eq!(a.div_euclid(-b), -1); // 7 >= -4 * -1
+        /// assert_eq!((-a).div_euclid(b), -2); // -7 >= 4 * -2
+        /// assert_eq!((-a).div_euclid(-b), 2); // -7 >= -4 * 2
+        /// ```
+        #[stable(feature = "euclidean_division", since = "1.38.0")]
+        #[rustc_const_stable(feature = "const_euclidean_int_methods", since = "1.52.0")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline]
+        #[rustc_inherit_overflow_checks]
+        pub const fn div_euclid(self, rhs: Self) -> Self {
+            let q = self / rhs;
+            if self % rhs < 0 {
+                return if rhs > 0 { q - 1 } else { q + 1 }
+            }
+            q
+        }
+
+
+        /// Calculates the least nonnegative remainder of `self (mod rhs)`.
+        ///
+        /// This is done as if by the Euclidean division algorithm -- given
+        /// `r = self.rem_euclid(rhs)`, `self = rhs * self.div_euclid(rhs) + r`, and
+        /// `0 <= r < abs(rhs)`.
+        ///
+        /// # Panics
+        ///
+        /// This function will panic if `rhs` is 0 or the division results in overflow.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        #[doc = concat!("let a: ", stringify!($SelfT), " = 7; // or any other integer type")]
+        /// let b = 4;
+        ///
+        /// assert_eq!(a.rem_euclid(b), 3);
+        /// assert_eq!((-a).rem_euclid(b), 1);
+        /// assert_eq!(a.rem_euclid(-b), 3);
+        /// assert_eq!((-a).rem_euclid(-b), 1);
+        /// ```
+        #[stable(feature = "euclidean_division", since = "1.38.0")]
+        #[rustc_const_stable(feature = "const_euclidean_int_methods", since = "1.52.0")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline]
+        #[rustc_inherit_overflow_checks]
+        pub const fn rem_euclid(self, rhs: Self) -> Self {
+            let r = self % rhs;
+            if r < 0 {
+                if rhs < 0 {
+                    r - rhs
+                } else {
+                    r + rhs
+                }
+            } else {
+                r
+            }
+        }
+
+        /// Calculates the quotient of `self` and `rhs`, rounding the result towards negative infinity.
+        ///
+        /// # Panics
+        ///
+        /// This function will panic if `rhs` is zero.
+        ///
+        /// ## Overflow behavior
+        ///
+        /// On overflow, this function will panic if overflow checks are enabled (default in debug
+        /// mode) and wrap if overflow checks are disabled (default in release mode).
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        /// #![feature(int_roundings)]
+        #[doc = concat!("let a: ", stringify!($SelfT)," = 8;")]
+        /// let b = 3;
+        ///
+        /// assert_eq!(a.div_floor(b), 2);
+        /// assert_eq!(a.div_floor(-b), -3);
+        /// assert_eq!((-a).div_floor(b), -3);
+        /// assert_eq!((-a).div_floor(-b), 2);
+        /// ```
+        #[unstable(feature = "int_roundings", issue = "88581")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline]
+        #[rustc_inherit_overflow_checks]
+        pub const fn div_floor(self, rhs: Self) -> Self {
+            let d = self / rhs;
+            let r = self % rhs;
+            if (r > 0 && rhs < 0) || (r < 0 && rhs > 0) {
+                d - 1
+            } else {
+                d
+            }
+        }
+
+        /// Calculates the quotient of `self` and `rhs`, rounding the result towards positive infinity.
+        ///
+        /// # Panics
+        ///
+        /// This function will panic if `rhs` is zero.
+        ///
+        /// ## Overflow behavior
+        ///
+        /// On overflow, this function will panic if overflow checks are enabled (default in debug
+        /// mode) and wrap if overflow checks are disabled (default in release mode).
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        /// #![feature(int_roundings)]
+        #[doc = concat!("let a: ", stringify!($SelfT)," = 8;")]
+        /// let b = 3;
+        ///
+        /// assert_eq!(a.div_ceil(b), 3);
+        /// assert_eq!(a.div_ceil(-b), -2);
+        /// assert_eq!((-a).div_ceil(b), -2);
+        /// assert_eq!((-a).div_ceil(-b), 3);
+        /// ```
+        #[unstable(feature = "int_roundings", issue = "88581")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline]
+        #[rustc_inherit_overflow_checks]
+        pub const fn div_ceil(self, rhs: Self) -> Self {
+            let d = self / rhs;
+            let r = self % rhs;
+            if (r > 0 && rhs > 0) || (r < 0 && rhs < 0) {
+                d + 1
+            } else {
+                d
+            }
+        }
+
+        /// If `rhs` is positive, calculates the smallest value greater than or
+        /// equal to `self` that is a multiple of `rhs`. If `rhs` is negative,
+        /// calculates the largest value less than or equal to `self` that is a
+        /// multiple of `rhs`.
+        ///
+        /// # Panics
+        ///
+        /// This function will panic if `rhs` is zero.
+        ///
+        /// ## Overflow behavior
+        ///
+        /// On overflow, this function will panic if overflow checks are enabled (default in debug
+        /// mode) and wrap if overflow checks are disabled (default in release mode).
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        /// #![feature(int_roundings)]
+        #[doc = concat!("assert_eq!(16_", stringify!($SelfT), ".next_multiple_of(8), 16);")]
+        #[doc = concat!("assert_eq!(23_", stringify!($SelfT), ".next_multiple_of(8), 24);")]
+        #[doc = concat!("assert_eq!(16_", stringify!($SelfT), ".next_multiple_of(-8), 16);")]
+        #[doc = concat!("assert_eq!(23_", stringify!($SelfT), ".next_multiple_of(-8), 16);")]
+        #[doc = concat!("assert_eq!((-16_", stringify!($SelfT), ").next_multiple_of(8), -16);")]
+        #[doc = concat!("assert_eq!((-23_", stringify!($SelfT), ").next_multiple_of(8), -16);")]
+        #[doc = concat!("assert_eq!((-16_", stringify!($SelfT), ").next_multiple_of(-8), -16);")]
+        #[doc = concat!("assert_eq!((-23_", stringify!($SelfT), ").next_multiple_of(-8), -24);")]
+        /// ```
+        #[unstable(feature = "int_roundings", issue = "88581")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline]
+        #[rustc_inherit_overflow_checks]
+        pub const fn next_multiple_of(self, rhs: Self) -> Self {
+            // This would otherwise fail when calculating `r` when self == T::MIN.
+            if rhs == -1 {
+                return self;
+            }
+
+            let r = self % rhs;
+            let m = if (r > 0 && rhs < 0) || (r < 0 && rhs > 0) {
+                r + rhs
+            } else {
+                r
+            };
+
+            if m == 0 {
+                self
+            } else {
+                self + (rhs - m)
+            }
+        }
+
+        /// If `rhs` is positive, calculates the smallest value greater than or
+        /// equal to `self` that is a multiple of `rhs`. If `rhs` is negative,
+        /// calculates the largest value less than or equal to `self` that is a
+        /// multiple of `rhs`. Returns `None` if `rhs` is zero or the operation
+        /// would result in overflow.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        /// #![feature(int_roundings)]
+        #[doc = concat!("assert_eq!(16_", stringify!($SelfT), ".checked_next_multiple_of(8), Some(16));")]
+        #[doc = concat!("assert_eq!(23_", stringify!($SelfT), ".checked_next_multiple_of(8), Some(24));")]
+        #[doc = concat!("assert_eq!(16_", stringify!($SelfT), ".checked_next_multiple_of(-8), Some(16));")]
+        #[doc = concat!("assert_eq!(23_", stringify!($SelfT), ".checked_next_multiple_of(-8), Some(16));")]
+        #[doc = concat!("assert_eq!((-16_", stringify!($SelfT), ").checked_next_multiple_of(8), Some(-16));")]
+        #[doc = concat!("assert_eq!((-23_", stringify!($SelfT), ").checked_next_multiple_of(8), Some(-16));")]
+        #[doc = concat!("assert_eq!((-16_", stringify!($SelfT), ").checked_next_multiple_of(-8), Some(-16));")]
+        #[doc = concat!("assert_eq!((-23_", stringify!($SelfT), ").checked_next_multiple_of(-8), Some(-24));")]
+        #[doc = concat!("assert_eq!(1_", stringify!($SelfT), ".checked_next_multiple_of(0), None);")]
+        #[doc = concat!("assert_eq!(", stringify!($SelfT), "::MAX.checked_next_multiple_of(2), None);")]
+        /// ```
+        #[unstable(feature = "int_roundings", issue = "88581")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline]
+        pub const fn checked_next_multiple_of(self, rhs: Self) -> Option<Self> {
+            // This would otherwise fail when calculating `r` when self == T::MIN.
+            if rhs == -1 {
+                return Some(self);
+            }
+
+            let r = try_opt!(self.checked_rem(rhs));
+            let m = if (r > 0 && rhs < 0) || (r < 0 && rhs > 0) {
+                // r + rhs cannot overflow because they have opposite signs
+                r + rhs
+            } else {
+                r
+            };
+
+            if m == 0 {
+                Some(self)
+            } else {
+                // rhs - m cannot overflow because m has the same sign as rhs
+                self.checked_add(rhs - m)
+            }
+        }
+
+        /// Returns the logarithm of the number with respect to an arbitrary base,
+        /// rounded down.
+        ///
+        /// This method might not be optimized owing to implementation details;
+        /// `log2` can produce results more efficiently for base 2, and `log10`
+        /// can produce results more efficiently for base 10.
+        ///
+        /// # Panics
+        ///
+        /// When the number is negative, zero, or if the base is not at least 2; it
+        /// panics in debug mode and the return value is 0 in release
+        /// mode.
+        ///
+        /// # Examples
+        ///
+        /// ```
+        /// #![feature(int_log)]
+        #[doc = concat!("assert_eq!(5", stringify!($SelfT), ".log(5), 1);")]
+        /// ```
+        #[unstable(feature = "int_log", issue = "70887")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline]
+        #[track_caller]
+        #[rustc_inherit_overflow_checks]
+        #[allow(arithmetic_overflow)]
+        pub const fn log(self, base: Self) -> u32 {
+            match self.checked_log(base) {
+                Some(n) => n,
+                None => {
+                    // In debug builds, trigger a panic on None.
+                    // This should optimize completely out in release builds.
+                    let _ = Self::MAX + 1;
+
+                    0
+                },
+            }
+        }
+
+        /// Returns the base 2 logarithm of the number, rounded down.
+        ///
+        /// # Panics
+        ///
+        /// When the number is negative or zero it panics in debug mode and the return value
+        /// is 0 in release mode.
+        ///
+        /// # Examples
+        ///
+        /// ```
+        /// #![feature(int_log)]
+        #[doc = concat!("assert_eq!(2", stringify!($SelfT), ".log2(), 1);")]
+        /// ```
+        #[unstable(feature = "int_log", issue = "70887")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline]
+        #[track_caller]
+        #[rustc_inherit_overflow_checks]
+        #[allow(arithmetic_overflow)]
+        pub const fn log2(self) -> u32 {
+            match self.checked_log2() {
+                Some(n) => n,
+                None => {
+                    // In debug builds, trigger a panic on None.
+                    // This should optimize completely out in release builds.
+                    let _ = Self::MAX + 1;
+
+                    0
+                },
+            }
+        }
+
+        /// Returns the base 10 logarithm of the number, rounded down.
+        ///
+        /// # Panics
+        ///
+        /// When the number is negative or zero it panics in debug mode and the return value
+        /// is 0 in release mode.
+        ///
+        /// # Example
+        ///
+        /// ```
+        /// #![feature(int_log)]
+        #[doc = concat!("assert_eq!(10", stringify!($SelfT), ".log10(), 1);")]
+        /// ```
+        #[unstable(feature = "int_log", issue = "70887")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline]
+        #[track_caller]
+        #[rustc_inherit_overflow_checks]
+        #[allow(arithmetic_overflow)]
+        pub const fn log10(self) -> u32 {
+            match self.checked_log10() {
+                Some(n) => n,
+                None => {
+                    // In debug builds, trigger a panic on None.
+                    // This should optimize completely out in release builds.
+                    let _ = Self::MAX + 1;
+
+                    0
+                },
+            }
+        }
+
+        /// Returns the logarithm of the number with respect to an arbitrary base,
+        /// rounded down.
+        ///
+        /// Returns `None` if the number is negative or zero, or if the base is not at least 2.
+        ///
+        /// This method might not be optimized owing to implementation details;
+        /// `checked_log2` can produce results more efficiently for base 2, and
+        /// `checked_log10` can produce results more efficiently for base 10.
+        ///
+        /// # Examples
+        ///
+        /// ```
+        /// #![feature(int_log)]
+        #[doc = concat!("assert_eq!(5", stringify!($SelfT), ".checked_log(5), Some(1));")]
+        /// ```
+        #[unstable(feature = "int_log", issue = "70887")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline]
+        pub const fn checked_log(self, base: Self) -> Option<u32> {
+            if self <= 0 || base <= 1 {
+                None
+            } else {
+                let mut n = 0;
+                let mut r = self;
+
+                // Optimization for 128 bit wide integers.
+                if Self::BITS == 128 {
+                    let b = Self::log2(self) / (Self::log2(base) + 1);
+                    n += b;
+                    r /= base.pow(b as u32);
+                }
+
+                while r >= base {
+                    r /= base;
+                    n += 1;
+                }
+                Some(n)
+            }
+        }
+
+        /// Returns the base 2 logarithm of the number, rounded down.
+        ///
+        /// Returns `None` if the number is negative or zero.
+        ///
+        /// # Examples
+        ///
+        /// ```
+        /// #![feature(int_log)]
+        #[doc = concat!("assert_eq!(2", stringify!($SelfT), ".checked_log2(), Some(1));")]
+        /// ```
+        #[unstable(feature = "int_log", issue = "70887")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline]
+        pub const fn checked_log2(self) -> Option<u32> {
+            if self <= 0 {
+                None
+            } else {
+                // SAFETY: We just checked that this number is positive
+                let log = (Self::BITS - 1) - unsafe { intrinsics::ctlz_nonzero(self) as u32 };
+                Some(log)
+            }
+        }
+
+        /// Returns the base 10 logarithm of the number, rounded down.
+        ///
+        /// Returns `None` if the number is negative or zero.
+        ///
+        /// # Example
+        ///
+        /// ```
+        /// #![feature(int_log)]
+        #[doc = concat!("assert_eq!(10", stringify!($SelfT), ".checked_log10(), Some(1));")]
+        /// ```
+        #[unstable(feature = "int_log", issue = "70887")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline]
+        pub const fn checked_log10(self) -> Option<u32> {
+            if self > 0 {
+                Some(int_log10::$ActualT(self as $ActualT))
+            } else {
+                None
+            }
+        }
+
+        /// Computes the absolute value of `self`.
+        ///
+        /// # Overflow behavior
+        ///
+        /// The absolute value of
+        #[doc = concat!("`", stringify!($SelfT), "::MIN`")]
+        /// cannot be represented as an
+        #[doc = concat!("`", stringify!($SelfT), "`,")]
+        /// and attempting to calculate it will cause an overflow. This means
+        /// that code in debug mode will trigger a panic on this case and
+        /// optimized code will return
+        #[doc = concat!("`", stringify!($SelfT), "::MIN`")]
+        /// without a panic.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        #[doc = concat!("assert_eq!(10", stringify!($SelfT), ".abs(), 10);")]
+        #[doc = concat!("assert_eq!((-10", stringify!($SelfT), ").abs(), 10);")]
+        /// ```
+        #[stable(feature = "rust1", since = "1.0.0")]
+        #[rustc_const_stable(feature = "const_int_methods", since = "1.32.0")]
+        #[allow(unused_attributes)]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline]
+        #[rustc_inherit_overflow_checks]
+        pub const fn abs(self) -> Self {
+            // Note that the #[rustc_inherit_overflow_checks] and #[inline]
+            // above mean that the overflow semantics of the subtraction
+            // depend on the crate we're being called from.
+            if self.is_negative() {
+                -self
+            } else {
+                self
+            }
+        }
+
+        /// Computes the absolute difference between `self` and `other`.
+        ///
+        /// This function always returns the correct answer without overflow or
+        /// panics by returning an unsigned integer.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        #[doc = concat!("assert_eq!(100", stringify!($SelfT), ".abs_diff(80), 20", stringify!($UnsignedT), ");")]
+        #[doc = concat!("assert_eq!(100", stringify!($SelfT), ".abs_diff(110), 10", stringify!($UnsignedT), ");")]
+        #[doc = concat!("assert_eq!((-100", stringify!($SelfT), ").abs_diff(80), 180", stringify!($UnsignedT), ");")]
+        #[doc = concat!("assert_eq!((-100", stringify!($SelfT), ").abs_diff(-120), 20", stringify!($UnsignedT), ");")]
+        #[doc = concat!("assert_eq!(", stringify!($SelfT), "::MIN.abs_diff(", stringify!($SelfT), "::MAX), ", stringify!($UnsignedT), "::MAX);")]
+        /// ```
+        #[stable(feature = "int_abs_diff", since = "1.60.0")]
+        #[rustc_const_stable(feature = "int_abs_diff", since = "1.60.0")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline]
+        pub const fn abs_diff(self, other: Self) -> $UnsignedT {
+            if self < other {
+                // Converting a non-negative x from signed to unsigned by using
+                // `x as U` is left unchanged, but a negative x is converted
+                // to value x + 2^N. Thus if `s` and `o` are binary variables
+                // respectively indicating whether `self` and `other` are
+                // negative, we are computing the mathematical value:
+                //
+                //    (other + o*2^N) - (self + s*2^N)    mod  2^N
+                //    other - self + (o-s)*2^N            mod  2^N
+                //    other - self                        mod  2^N
+                //
+                // Finally, taking the mod 2^N of the mathematical value of
+                // `other - self` does not change it as it already is
+                // in the range [0, 2^N).
+                (other as $UnsignedT).wrapping_sub(self as $UnsignedT)
+            } else {
+                (self as $UnsignedT).wrapping_sub(other as $UnsignedT)
+            }
+        }
+
+        /// Returns a number representing sign of `self`.
+        ///
+        ///  - `0` if the number is zero
+        ///  - `1` if the number is positive
+        ///  - `-1` if the number is negative
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        #[doc = concat!("assert_eq!(10", stringify!($SelfT), ".signum(), 1);")]
+        #[doc = concat!("assert_eq!(0", stringify!($SelfT), ".signum(), 0);")]
+        #[doc = concat!("assert_eq!((-10", stringify!($SelfT), ").signum(), -1);")]
+        /// ```
+        #[stable(feature = "rust1", since = "1.0.0")]
+        #[rustc_const_stable(feature = "const_int_sign", since = "1.47.0")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline(always)]
+        pub const fn signum(self) -> Self {
+            match self {
+                n if n > 0 =>  1,
+                0          =>  0,
+                _          => -1,
+            }
+        }
+
+        /// Returns `true` if `self` is positive and `false` if the number is zero or
+        /// negative.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        #[doc = concat!("assert!(10", stringify!($SelfT), ".is_positive());")]
+        #[doc = concat!("assert!(!(-10", stringify!($SelfT), ").is_positive());")]
+        /// ```
+        #[must_use]
+        #[stable(feature = "rust1", since = "1.0.0")]
+        #[rustc_const_stable(feature = "const_int_methods", since = "1.32.0")]
+        #[inline(always)]
+        pub const fn is_positive(self) -> bool { self > 0 }
+
+        /// Returns `true` if `self` is negative and `false` if the number is zero or
+        /// positive.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        #[doc = concat!("assert!((-10", stringify!($SelfT), ").is_negative());")]
+        #[doc = concat!("assert!(!10", stringify!($SelfT), ".is_negative());")]
+        /// ```
+        #[must_use]
+        #[stable(feature = "rust1", since = "1.0.0")]
+        #[rustc_const_stable(feature = "const_int_methods", since = "1.32.0")]
+        #[inline(always)]
+        pub const fn is_negative(self) -> bool { self < 0 }
+
+        /// Return the memory representation of this integer as a byte array in
+        /// big-endian (network) byte order.
+        ///
+        #[doc = $to_xe_bytes_doc]
+        ///
+        /// # Examples
+        ///
+        /// ```
+        #[doc = concat!("let bytes = ", $swap_op, stringify!($SelfT), ".to_be_bytes();")]
+        #[doc = concat!("assert_eq!(bytes, ", $be_bytes, ");")]
+        /// ```
+        #[stable(feature = "int_to_from_bytes", since = "1.32.0")]
+        #[rustc_const_stable(feature = "const_int_conversion", since = "1.44.0")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline]
+        pub const fn to_be_bytes(self) -> [u8; mem::size_of::<Self>()] {
+            self.to_be().to_ne_bytes()
+        }
+
+        /// Return the memory representation of this integer as a byte array in
+        /// little-endian byte order.
+        ///
+        #[doc = $to_xe_bytes_doc]
+        ///
+        /// # Examples
+        ///
+        /// ```
+        #[doc = concat!("let bytes = ", $swap_op, stringify!($SelfT), ".to_le_bytes();")]
+        #[doc = concat!("assert_eq!(bytes, ", $le_bytes, ");")]
+        /// ```
+        #[stable(feature = "int_to_from_bytes", since = "1.32.0")]
+        #[rustc_const_stable(feature = "const_int_conversion", since = "1.44.0")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline]
+        pub const fn to_le_bytes(self) -> [u8; mem::size_of::<Self>()] {
+            self.to_le().to_ne_bytes()
+        }
+
+        /// Return the memory representation of this integer as a byte array in
+        /// native byte order.
+        ///
+        /// As the target platform's native endianness is used, portable code
+        /// should use [`to_be_bytes`] or [`to_le_bytes`], as appropriate,
+        /// instead.
+        ///
+        #[doc = $to_xe_bytes_doc]
+        ///
+        /// [`to_be_bytes`]: Self::to_be_bytes
+        /// [`to_le_bytes`]: Self::to_le_bytes
+        ///
+        /// # Examples
+        ///
+        /// ```
+        #[doc = concat!("let bytes = ", $swap_op, stringify!($SelfT), ".to_ne_bytes();")]
+        /// assert_eq!(
+        ///     bytes,
+        ///     if cfg!(target_endian = "big") {
+        #[doc = concat!("        ", $be_bytes)]
+        ///     } else {
+        #[doc = concat!("        ", $le_bytes)]
+        ///     }
+        /// );
+        /// ```
+        #[stable(feature = "int_to_from_bytes", since = "1.32.0")]
+        #[rustc_const_stable(feature = "const_int_conversion", since = "1.44.0")]
+        // SAFETY: const sound because integers are plain old datatypes so we can always
+        // transmute them to arrays of bytes
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline]
+        pub const fn to_ne_bytes(self) -> [u8; mem::size_of::<Self>()] {
+            // SAFETY: integers are plain old datatypes so we can always transmute them to
+            // arrays of bytes
+            unsafe { mem::transmute(self) }
+        }
+
+        /// Create an integer value from its representation as a byte array in
+        /// big endian.
+        ///
+        #[doc = $from_xe_bytes_doc]
+        ///
+        /// # Examples
+        ///
+        /// ```
+        #[doc = concat!("let value = ", stringify!($SelfT), "::from_be_bytes(", $be_bytes, ");")]
+        #[doc = concat!("assert_eq!(value, ", $swap_op, ");")]
+        /// ```
+        ///
+        /// When starting from a slice rather than an array, fallible conversion APIs can be used:
+        ///
+        /// ```
+        #[doc = concat!("fn read_be_", stringify!($SelfT), "(input: &mut &[u8]) -> ", stringify!($SelfT), " {")]
+        #[doc = concat!("    let (int_bytes, rest) = input.split_at(std::mem::size_of::<", stringify!($SelfT), ">());")]
+        ///     *input = rest;
+        #[doc = concat!("    ", stringify!($SelfT), "::from_be_bytes(int_bytes.try_into().unwrap())")]
+        /// }
+        /// ```
+        #[stable(feature = "int_to_from_bytes", since = "1.32.0")]
+        #[rustc_const_stable(feature = "const_int_conversion", since = "1.44.0")]
+        #[must_use]
+        #[inline]
+        pub const fn from_be_bytes(bytes: [u8; mem::size_of::<Self>()]) -> Self {
+            Self::from_be(Self::from_ne_bytes(bytes))
+        }
+
+        /// Create an integer value from its representation as a byte array in
+        /// little endian.
+        ///
+        #[doc = $from_xe_bytes_doc]
+        ///
+        /// # Examples
+        ///
+        /// ```
+        #[doc = concat!("let value = ", stringify!($SelfT), "::from_le_bytes(", $le_bytes, ");")]
+        #[doc = concat!("assert_eq!(value, ", $swap_op, ");")]
+        /// ```
+        ///
+        /// When starting from a slice rather than an array, fallible conversion APIs can be used:
+        ///
+        /// ```
+        #[doc = concat!("fn read_le_", stringify!($SelfT), "(input: &mut &[u8]) -> ", stringify!($SelfT), " {")]
+        #[doc = concat!("    let (int_bytes, rest) = input.split_at(std::mem::size_of::<", stringify!($SelfT), ">());")]
+        ///     *input = rest;
+        #[doc = concat!("    ", stringify!($SelfT), "::from_le_bytes(int_bytes.try_into().unwrap())")]
+        /// }
+        /// ```
+        #[stable(feature = "int_to_from_bytes", since = "1.32.0")]
+        #[rustc_const_stable(feature = "const_int_conversion", since = "1.44.0")]
+        #[must_use]
+        #[inline]
+        pub const fn from_le_bytes(bytes: [u8; mem::size_of::<Self>()]) -> Self {
+            Self::from_le(Self::from_ne_bytes(bytes))
+        }
+
+        /// Create an integer value from its memory representation as a byte
+        /// array in native endianness.
+        ///
+        /// As the target platform's native endianness is used, portable code
+        /// likely wants to use [`from_be_bytes`] or [`from_le_bytes`], as
+        /// appropriate instead.
+        ///
+        /// [`from_be_bytes`]: Self::from_be_bytes
+        /// [`from_le_bytes`]: Self::from_le_bytes
+        ///
+        #[doc = $from_xe_bytes_doc]
+        ///
+        /// # Examples
+        ///
+        /// ```
+        #[doc = concat!("let value = ", stringify!($SelfT), "::from_ne_bytes(if cfg!(target_endian = \"big\") {")]
+        #[doc = concat!("    ", $be_bytes)]
+        /// } else {
+        #[doc = concat!("    ", $le_bytes)]
+        /// });
+        #[doc = concat!("assert_eq!(value, ", $swap_op, ");")]
+        /// ```
+        ///
+        /// When starting from a slice rather than an array, fallible conversion APIs can be used:
+        ///
+        /// ```
+        #[doc = concat!("fn read_ne_", stringify!($SelfT), "(input: &mut &[u8]) -> ", stringify!($SelfT), " {")]
+        #[doc = concat!("    let (int_bytes, rest) = input.split_at(std::mem::size_of::<", stringify!($SelfT), ">());")]
+        ///     *input = rest;
+        #[doc = concat!("    ", stringify!($SelfT), "::from_ne_bytes(int_bytes.try_into().unwrap())")]
+        /// }
+        /// ```
+        #[stable(feature = "int_to_from_bytes", since = "1.32.0")]
+        #[rustc_const_stable(feature = "const_int_conversion", since = "1.44.0")]
+        #[must_use]
+        // SAFETY: const sound because integers are plain old datatypes so we can always
+        // transmute to them
+        #[inline]
+        pub const fn from_ne_bytes(bytes: [u8; mem::size_of::<Self>()]) -> Self {
+            // SAFETY: integers are plain old datatypes so we can always transmute to them
+            unsafe { mem::transmute(bytes) }
+        }
+
+        /// New code should prefer to use
+        #[doc = concat!("[`", stringify!($SelfT), "::MIN", "`] instead.")]
+        ///
+        /// Returns the smallest value that can be represented by this integer type.
+        #[stable(feature = "rust1", since = "1.0.0")]
+        #[inline(always)]
+        #[rustc_promotable]
+        #[rustc_const_stable(feature = "const_min_value", since = "1.32.0")]
+        #[deprecated(since = "TBD", note = "replaced by the `MIN` associated constant on this type")]
+        pub const fn min_value() -> Self {
+            Self::MIN
+        }
+
+        /// New code should prefer to use
+        #[doc = concat!("[`", stringify!($SelfT), "::MAX", "`] instead.")]
+        ///
+        /// Returns the largest value that can be represented by this integer type.
+        #[stable(feature = "rust1", since = "1.0.0")]
+        #[inline(always)]
+        #[rustc_promotable]
+        #[rustc_const_stable(feature = "const_max_value", since = "1.32.0")]
+        #[deprecated(since = "TBD", note = "replaced by the `MAX` associated constant on this type")]
+        pub const fn max_value() -> Self {
+            Self::MAX
+        }
+    }
+}
diff --git a/library/core/src/num/mod.rs b/library/core/src/num/mod.rs
new file mode 100644
index 000000000..f481399fd
--- /dev/null
+++ b/library/core/src/num/mod.rs
@@ -0,0 +1,1124 @@
+//! Numeric traits and functions for the built-in numeric types.
+
+#![stable(feature = "rust1", since = "1.0.0")]
+
+use crate::ascii;
+use crate::intrinsics;
+use crate::mem;
+use crate::ops::{Add, Mul, Sub};
+use crate::str::FromStr;
+
+// Used because the `?` operator is not allowed in a const context.
+macro_rules! try_opt {
+    ($e:expr) => {
+        match $e {
+            Some(x) => x,
+            None => return None,
+        }
+    };
+}
+
+#[allow_internal_unstable(const_likely)]
+macro_rules! unlikely {
+    ($e: expr) => {
+        intrinsics::unlikely($e)
+    };
+}
+
+// All these modules are technically private and only exposed for coretests:
+#[cfg(not(no_fp_fmt_parse))]
+pub mod bignum;
+#[cfg(not(no_fp_fmt_parse))]
+pub mod dec2flt;
+#[cfg(not(no_fp_fmt_parse))]
+pub mod diy_float;
+#[cfg(not(no_fp_fmt_parse))]
+pub mod flt2dec;
+pub mod fmt;
+
+#[macro_use]
+mod int_macros; // import int_impl!
+#[macro_use]
+mod uint_macros; // import uint_impl!
+
+mod error;
+mod int_log10;
+mod nonzero;
+#[unstable(feature = "saturating_int_impl", issue = "87920")]
+mod saturating;
+mod wrapping;
+
+#[unstable(feature = "saturating_int_impl", issue = "87920")]
+pub use saturating::Saturating;
+#[stable(feature = "rust1", since = "1.0.0")]
+pub use wrapping::Wrapping;
+
+#[stable(feature = "rust1", since = "1.0.0")]
+#[cfg(not(no_fp_fmt_parse))]
+pub use dec2flt::ParseFloatError;
+
+#[stable(feature = "rust1", since = "1.0.0")]
+pub use error::ParseIntError;
+
+#[stable(feature = "nonzero", since = "1.28.0")]
+pub use nonzero::{NonZeroU128, NonZeroU16, NonZeroU32, NonZeroU64, NonZeroU8, NonZeroUsize};
+
+#[stable(feature = "signed_nonzero", since = "1.34.0")]
+pub use nonzero::{NonZeroI128, NonZeroI16, NonZeroI32, NonZeroI64, NonZeroI8, NonZeroIsize};
+
+#[stable(feature = "try_from", since = "1.34.0")]
+pub use error::TryFromIntError;
+
+#[stable(feature = "int_error_matching", since = "1.55.0")]
+pub use error::IntErrorKind;
+
+macro_rules! usize_isize_to_xe_bytes_doc {
+    () => {
+        "
+
+**Note**: This function returns an array of length 2, 4 or 8 bytes
+depending on the target pointer size.
+
+"
+    };
+}
+
+macro_rules! usize_isize_from_xe_bytes_doc {
+    () => {
+        "
+
+**Note**: This function takes an array of length 2, 4 or 8 bytes
+depending on the target pointer size.
+
+"
+    };
+}
+
+macro_rules! widening_impl {
+    ($SelfT:ty, $WideT:ty, $BITS:literal, unsigned) => {
+        /// Calculates the complete product `self * rhs` without the possibility to overflow.
+        ///
+        /// This returns the low-order (wrapping) bits and the high-order (overflow) bits
+        /// of the result as two separate values, in that order.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// Please note that this example is shared between integer types.
+        /// Which explains why `u32` is used here.
+        ///
+        /// ```
+        /// #![feature(bigint_helper_methods)]
+        /// assert_eq!(5u32.widening_mul(2), (10, 0));
+        /// assert_eq!(1_000_000_000u32.widening_mul(10), (1410065408, 2));
+        /// ```
+        #[unstable(feature = "bigint_helper_methods", issue = "85532")]
+        #[rustc_const_unstable(feature = "const_bigint_helper_methods", issue = "85532")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline]
+        pub const fn widening_mul(self, rhs: Self) -> (Self, Self) {
+            // note: longer-term this should be done via an intrinsic,
+            //   but for now we can deal without an impl for u128/i128
+            // SAFETY: overflow will be contained within the wider types
+            let wide = unsafe { (self as $WideT).unchecked_mul(rhs as $WideT) };
+            (wide as $SelfT, (wide >> $BITS) as $SelfT)
+        }
+
+        /// Calculates the "full multiplication" `self * rhs + carry`
+        /// without the possibility to overflow.
+        ///
+        /// This returns the low-order (wrapping) bits and the high-order (overflow) bits
+        /// of the result as two separate values, in that order.
+        ///
+        /// Performs "long multiplication" which takes in an extra amount to add, and may return an
+        /// additional amount of overflow. This allows for chaining together multiple
+        /// multiplications to create "big integers" which represent larger values.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// Please note that this example is shared between integer types.
+        /// Which explains why `u32` is used here.
+        ///
+        /// ```
+        /// #![feature(bigint_helper_methods)]
+        /// assert_eq!(5u32.carrying_mul(2, 0), (10, 0));
+        /// assert_eq!(5u32.carrying_mul(2, 10), (20, 0));
+        /// assert_eq!(1_000_000_000u32.carrying_mul(10, 0), (1410065408, 2));
+        /// assert_eq!(1_000_000_000u32.carrying_mul(10, 10), (1410065418, 2));
+        #[doc = concat!("assert_eq!(",
+            stringify!($SelfT), "::MAX.carrying_mul(", stringify!($SelfT), "::MAX, ", stringify!($SelfT), "::MAX), ",
+            "(0, ", stringify!($SelfT), "::MAX));"
+        )]
+        /// ```
+        ///
+        /// If `carry` is zero, this is similar to [`overflowing_mul`](Self::overflowing_mul),
+        /// except that it gives the value of the overflow instead of just whether one happened:
+        ///
+        /// ```
+        /// #![feature(bigint_helper_methods)]
+        /// let r = u8::carrying_mul(7, 13, 0);
+        /// assert_eq!((r.0, r.1 != 0), u8::overflowing_mul(7, 13));
+        /// let r = u8::carrying_mul(13, 42, 0);
+        /// assert_eq!((r.0, r.1 != 0), u8::overflowing_mul(13, 42));
+        /// ```
+        ///
+        /// The value of the first field in the returned tuple matches what you'd get
+        /// by combining the [`wrapping_mul`](Self::wrapping_mul) and
+        /// [`wrapping_add`](Self::wrapping_add) methods:
+        ///
+        /// ```
+        /// #![feature(bigint_helper_methods)]
+        /// assert_eq!(
+        ///     789_u16.carrying_mul(456, 123).0,
+        ///     789_u16.wrapping_mul(456).wrapping_add(123),
+        /// );
+        /// ```
+        #[unstable(feature = "bigint_helper_methods", issue = "85532")]
+        #[rustc_const_unstable(feature = "bigint_helper_methods", issue = "85532")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline]
+        pub const fn carrying_mul(self, rhs: Self, carry: Self) -> (Self, Self) {
+            // note: longer-term this should be done via an intrinsic,
+            //   but for now we can deal without an impl for u128/i128
+            // SAFETY: overflow will be contained within the wider types
+            let wide = unsafe {
+                (self as $WideT).unchecked_mul(rhs as $WideT).unchecked_add(carry as $WideT)
+            };
+            (wide as $SelfT, (wide >> $BITS) as $SelfT)
+        }
+    };
+}
+
+impl i8 {
+    int_impl! { i8, i8, u8, 8, 7, -128, 127, 2, "-0x7e", "0xa", "0x12", "0x12", "0x48",
+    "[0x12]", "[0x12]", "", "", "" }
+}
+
+impl i16 {
+    int_impl! { i16, i16, u16, 16, 15, -32768, 32767, 4, "-0x5ffd", "0x3a", "0x1234", "0x3412",
+    "0x2c48", "[0x34, 0x12]", "[0x12, 0x34]", "", "", "" }
+}
+
+impl i32 {
+    int_impl! { i32, i32, u32, 32, 31, -2147483648, 2147483647, 8, "0x10000b3", "0xb301",
+    "0x12345678", "0x78563412", "0x1e6a2c48", "[0x78, 0x56, 0x34, 0x12]",
+    "[0x12, 0x34, 0x56, 0x78]", "", "", "" }
+}
+
+impl i64 {
+    int_impl! { i64, i64, u64, 64, 63, -9223372036854775808, 9223372036854775807, 12,
+    "0xaa00000000006e1", "0x6e10aa", "0x1234567890123456", "0x5634129078563412",
+    "0x6a2c48091e6a2c48", "[0x56, 0x34, 0x12, 0x90, 0x78, 0x56, 0x34, 0x12]",
+    "[0x12, 0x34, 0x56, 0x78, 0x90, 0x12, 0x34, 0x56]", "", "", "" }
+}
+
+impl i128 {
+    int_impl! { i128, i128, u128, 128, 127, -170141183460469231731687303715884105728,
+    170141183460469231731687303715884105727, 16,
+    "0x13f40000000000000000000000004f76", "0x4f7613f4", "0x12345678901234567890123456789012",
+    "0x12907856341290785634129078563412", "0x48091e6a2c48091e6a2c48091e6a2c48",
+    "[0x12, 0x90, 0x78, 0x56, 0x34, 0x12, 0x90, 0x78, \
+      0x56, 0x34, 0x12, 0x90, 0x78, 0x56, 0x34, 0x12]",
+    "[0x12, 0x34, 0x56, 0x78, 0x90, 0x12, 0x34, 0x56, \
+      0x78, 0x90, 0x12, 0x34, 0x56, 0x78, 0x90, 0x12]", "", "", "" }
+}
+
+#[cfg(target_pointer_width = "16")]
+impl isize {
+    int_impl! { isize, i16, usize, 16, 15, -32768, 32767, 4, "-0x5ffd", "0x3a", "0x1234",
+    "0x3412", "0x2c48", "[0x34, 0x12]", "[0x12, 0x34]",
+    usize_isize_to_xe_bytes_doc!(), usize_isize_from_xe_bytes_doc!(),
+    " on 16-bit targets" }
+}
+
+#[cfg(target_pointer_width = "32")]
+impl isize {
+    int_impl! { isize, i32, usize, 32, 31, -2147483648, 2147483647, 8, "0x10000b3", "0xb301",
+    "0x12345678", "0x78563412", "0x1e6a2c48", "[0x78, 0x56, 0x34, 0x12]",
+    "[0x12, 0x34, 0x56, 0x78]",
+    usize_isize_to_xe_bytes_doc!(), usize_isize_from_xe_bytes_doc!(),
+    " on 32-bit targets" }
+}
+
+#[cfg(target_pointer_width = "64")]
+impl isize {
+    int_impl! { isize, i64, usize, 64, 63, -9223372036854775808, 9223372036854775807,
+    12, "0xaa00000000006e1", "0x6e10aa",  "0x1234567890123456", "0x5634129078563412",
+    "0x6a2c48091e6a2c48", "[0x56, 0x34, 0x12, 0x90, 0x78, 0x56, 0x34, 0x12]",
+    "[0x12, 0x34, 0x56, 0x78, 0x90, 0x12, 0x34, 0x56]",
+    usize_isize_to_xe_bytes_doc!(), usize_isize_from_xe_bytes_doc!(),
+    " on 64-bit targets" }
+}
+
+/// If 6th bit set ascii is upper case.
+const ASCII_CASE_MASK: u8 = 0b0010_0000;
+
+impl u8 {
+    uint_impl! { u8, u8, i8, NonZeroU8, 8, 255, 2, "0x82", "0xa", "0x12", "0x12", "0x48", "[0x12]",
+    "[0x12]", "", "", "" }
+    widening_impl! { u8, u16, 8, unsigned }
+
+    /// Checks if the value is within the ASCII range.
+    ///
+    /// # Examples
+    ///
+    /// ```
+    /// let ascii = 97u8;
+    /// let non_ascii = 150u8;
+    ///
+    /// assert!(ascii.is_ascii());
+    /// assert!(!non_ascii.is_ascii());
+    /// ```
+    #[must_use]
+    #[stable(feature = "ascii_methods_on_intrinsics", since = "1.23.0")]
+    #[rustc_const_stable(feature = "const_u8_is_ascii", since = "1.43.0")]
+    #[inline]
+    pub const fn is_ascii(&self) -> bool {
+        *self & 128 == 0
+    }
+
+    /// Makes a copy of the value in its ASCII upper case equivalent.
+    ///
+    /// ASCII letters 'a' to 'z' are mapped to 'A' to 'Z',
+    /// but non-ASCII letters are unchanged.
+    ///
+    /// To uppercase the value in-place, use [`make_ascii_uppercase`].
+    ///
+    /// # Examples
+    ///
+    /// ```
+    /// let lowercase_a = 97u8;
+    ///
+    /// assert_eq!(65, lowercase_a.to_ascii_uppercase());
+    /// ```
+    ///
+    /// [`make_ascii_uppercase`]: Self::make_ascii_uppercase
+    #[must_use = "to uppercase the value in-place, use `make_ascii_uppercase()`"]
+    #[stable(feature = "ascii_methods_on_intrinsics", since = "1.23.0")]
+    #[rustc_const_stable(feature = "const_ascii_methods_on_intrinsics", since = "1.52.0")]
+    #[inline]
+    pub const fn to_ascii_uppercase(&self) -> u8 {
+        // Toggle the fifth bit if this is a lowercase letter
+        *self ^ ((self.is_ascii_lowercase() as u8) * ASCII_CASE_MASK)
+    }
+
+    /// Makes a copy of the value in its ASCII lower case equivalent.
+    ///
+    /// ASCII letters 'A' to 'Z' are mapped to 'a' to 'z',
+    /// but non-ASCII letters are unchanged.
+    ///
+    /// To lowercase the value in-place, use [`make_ascii_lowercase`].
+    ///
+    /// # Examples
+    ///
+    /// ```
+    /// let uppercase_a = 65u8;
+    ///
+    /// assert_eq!(97, uppercase_a.to_ascii_lowercase());
+    /// ```
+    ///
+    /// [`make_ascii_lowercase`]: Self::make_ascii_lowercase
+    #[must_use = "to lowercase the value in-place, use `make_ascii_lowercase()`"]
+    #[stable(feature = "ascii_methods_on_intrinsics", since = "1.23.0")]
+    #[rustc_const_stable(feature = "const_ascii_methods_on_intrinsics", since = "1.52.0")]
+    #[inline]
+    pub const fn to_ascii_lowercase(&self) -> u8 {
+        // Set the fifth bit if this is an uppercase letter
+        *self | (self.is_ascii_uppercase() as u8 * ASCII_CASE_MASK)
+    }
+
+    /// Assumes self is ascii
+    #[inline]
+    pub(crate) const fn ascii_change_case_unchecked(&self) -> u8 {
+        *self ^ ASCII_CASE_MASK
+    }
+
+    /// Checks that two values are an ASCII case-insensitive match.
+    ///
+    /// This is equivalent to `to_ascii_lowercase(a) == to_ascii_lowercase(b)`.
+    ///
+    /// # Examples
+    ///
+    /// ```
+    /// let lowercase_a = 97u8;
+    /// let uppercase_a = 65u8;
+    ///
+    /// assert!(lowercase_a.eq_ignore_ascii_case(&uppercase_a));
+    /// ```
+    #[stable(feature = "ascii_methods_on_intrinsics", since = "1.23.0")]
+    #[rustc_const_stable(feature = "const_ascii_methods_on_intrinsics", since = "1.52.0")]
+    #[inline]
+    pub const fn eq_ignore_ascii_case(&self, other: &u8) -> bool {
+        self.to_ascii_lowercase() == other.to_ascii_lowercase()
+    }
+
+    /// Converts this value to its ASCII upper case equivalent in-place.
+    ///
+    /// ASCII letters 'a' to 'z' are mapped to 'A' to 'Z',
+    /// but non-ASCII letters are unchanged.
+    ///
+    /// To return a new uppercased value without modifying the existing one, use
+    /// [`to_ascii_uppercase`].
+    ///
+    /// # Examples
+    ///
+    /// ```
+    /// let mut byte = b'a';
+    ///
+    /// byte.make_ascii_uppercase();
+    ///
+    /// assert_eq!(b'A', byte);
+    /// ```
+    ///
+    /// [`to_ascii_uppercase`]: Self::to_ascii_uppercase
+    #[stable(feature = "ascii_methods_on_intrinsics", since = "1.23.0")]
+    #[inline]
+    pub fn make_ascii_uppercase(&mut self) {
+        *self = self.to_ascii_uppercase();
+    }
+
+    /// Converts this value to its ASCII lower case equivalent in-place.
+    ///
+    /// ASCII letters 'A' to 'Z' are mapped to 'a' to 'z',
+    /// but non-ASCII letters are unchanged.
+    ///
+    /// To return a new lowercased value without modifying the existing one, use
+    /// [`to_ascii_lowercase`].
+    ///
+    /// # Examples
+    ///
+    /// ```
+    /// let mut byte = b'A';
+    ///
+    /// byte.make_ascii_lowercase();
+    ///
+    /// assert_eq!(b'a', byte);
+    /// ```
+    ///
+    /// [`to_ascii_lowercase`]: Self::to_ascii_lowercase
+    #[stable(feature = "ascii_methods_on_intrinsics", since = "1.23.0")]
+    #[inline]
+    pub fn make_ascii_lowercase(&mut self) {
+        *self = self.to_ascii_lowercase();
+    }
+
+    /// Checks if the value is an ASCII alphabetic character:
+    ///
+    /// - U+0041 'A' ..= U+005A 'Z', or
+    /// - U+0061 'a' ..= U+007A 'z'.
+    ///
+    /// # Examples
+    ///
+    /// ```
+    /// let uppercase_a = b'A';
+    /// let uppercase_g = b'G';
+    /// let a = b'a';
+    /// let g = b'g';
+    /// let zero = b'0';
+    /// let percent = b'%';
+    /// let space = b' ';
+    /// let lf = b'\n';
+    /// let esc = b'\x1b';
+    ///
+    /// assert!(uppercase_a.is_ascii_alphabetic());
+    /// assert!(uppercase_g.is_ascii_alphabetic());
+    /// assert!(a.is_ascii_alphabetic());
+    /// assert!(g.is_ascii_alphabetic());
+    /// assert!(!zero.is_ascii_alphabetic());
+    /// assert!(!percent.is_ascii_alphabetic());
+    /// assert!(!space.is_ascii_alphabetic());
+    /// assert!(!lf.is_ascii_alphabetic());
+    /// assert!(!esc.is_ascii_alphabetic());
+    /// ```
+    #[must_use]
+    #[stable(feature = "ascii_ctype_on_intrinsics", since = "1.24.0")]
+    #[rustc_const_stable(feature = "const_ascii_ctype_on_intrinsics", since = "1.47.0")]
+    #[inline]
+    pub const fn is_ascii_alphabetic(&self) -> bool {
+        matches!(*self, b'A'..=b'Z' | b'a'..=b'z')
+    }
+
+    /// Checks if the value is an ASCII uppercase character:
+    /// U+0041 'A' ..= U+005A 'Z'.
+    ///
+    /// # Examples
+    ///
+    /// ```
+    /// let uppercase_a = b'A';
+    /// let uppercase_g = b'G';
+    /// let a = b'a';
+    /// let g = b'g';
+    /// let zero = b'0';
+    /// let percent = b'%';
+    /// let space = b' ';
+    /// let lf = b'\n';
+    /// let esc = b'\x1b';
+    ///
+    /// assert!(uppercase_a.is_ascii_uppercase());
+    /// assert!(uppercase_g.is_ascii_uppercase());
+    /// assert!(!a.is_ascii_uppercase());
+    /// assert!(!g.is_ascii_uppercase());
+    /// assert!(!zero.is_ascii_uppercase());
+    /// assert!(!percent.is_ascii_uppercase());
+    /// assert!(!space.is_ascii_uppercase());
+    /// assert!(!lf.is_ascii_uppercase());
+    /// assert!(!esc.is_ascii_uppercase());
+    /// ```
+    #[must_use]
+    #[stable(feature = "ascii_ctype_on_intrinsics", since = "1.24.0")]
+    #[rustc_const_stable(feature = "const_ascii_ctype_on_intrinsics", since = "1.47.0")]
+    #[inline]
+    pub const fn is_ascii_uppercase(&self) -> bool {
+        matches!(*self, b'A'..=b'Z')
+    }
+
+    /// Checks if the value is an ASCII lowercase character:
+    /// U+0061 'a' ..= U+007A 'z'.
+    ///
+    /// # Examples
+    ///
+    /// ```
+    /// let uppercase_a = b'A';
+    /// let uppercase_g = b'G';
+    /// let a = b'a';
+    /// let g = b'g';
+    /// let zero = b'0';
+    /// let percent = b'%';
+    /// let space = b' ';
+    /// let lf = b'\n';
+    /// let esc = b'\x1b';
+    ///
+    /// assert!(!uppercase_a.is_ascii_lowercase());
+    /// assert!(!uppercase_g.is_ascii_lowercase());
+    /// assert!(a.is_ascii_lowercase());
+    /// assert!(g.is_ascii_lowercase());
+    /// assert!(!zero.is_ascii_lowercase());
+    /// assert!(!percent.is_ascii_lowercase());
+    /// assert!(!space.is_ascii_lowercase());
+    /// assert!(!lf.is_ascii_lowercase());
+    /// assert!(!esc.is_ascii_lowercase());
+    /// ```
+    #[must_use]
+    #[stable(feature = "ascii_ctype_on_intrinsics", since = "1.24.0")]
+    #[rustc_const_stable(feature = "const_ascii_ctype_on_intrinsics", since = "1.47.0")]
+    #[inline]
+    pub const fn is_ascii_lowercase(&self) -> bool {
+        matches!(*self, b'a'..=b'z')
+    }
+
+    /// Checks if the value is an ASCII alphanumeric character:
+    ///
+    /// - U+0041 'A' ..= U+005A 'Z', or
+    /// - U+0061 'a' ..= U+007A 'z', or
+    /// - U+0030 '0' ..= U+0039 '9'.
+    ///
+    /// # Examples
+    ///
+    /// ```
+    /// let uppercase_a = b'A';
+    /// let uppercase_g = b'G';
+    /// let a = b'a';
+    /// let g = b'g';
+    /// let zero = b'0';
+    /// let percent = b'%';
+    /// let space = b' ';
+    /// let lf = b'\n';
+    /// let esc = b'\x1b';
+    ///
+    /// assert!(uppercase_a.is_ascii_alphanumeric());
+    /// assert!(uppercase_g.is_ascii_alphanumeric());
+    /// assert!(a.is_ascii_alphanumeric());
+    /// assert!(g.is_ascii_alphanumeric());
+    /// assert!(zero.is_ascii_alphanumeric());
+    /// assert!(!percent.is_ascii_alphanumeric());
+    /// assert!(!space.is_ascii_alphanumeric());
+    /// assert!(!lf.is_ascii_alphanumeric());
+    /// assert!(!esc.is_ascii_alphanumeric());
+    /// ```
+    #[must_use]
+    #[stable(feature = "ascii_ctype_on_intrinsics", since = "1.24.0")]
+    #[rustc_const_stable(feature = "const_ascii_ctype_on_intrinsics", since = "1.47.0")]
+    #[inline]
+    pub const fn is_ascii_alphanumeric(&self) -> bool {
+        matches!(*self, b'0'..=b'9' | b'A'..=b'Z' | b'a'..=b'z')
+    }
+
+    /// Checks if the value is an ASCII decimal digit:
+    /// U+0030 '0' ..= U+0039 '9'.
+    ///
+    /// # Examples
+    ///
+    /// ```
+    /// let uppercase_a = b'A';
+    /// let uppercase_g = b'G';
+    /// let a = b'a';
+    /// let g = b'g';
+    /// let zero = b'0';
+    /// let percent = b'%';
+    /// let space = b' ';
+    /// let lf = b'\n';
+    /// let esc = b'\x1b';
+    ///
+    /// assert!(!uppercase_a.is_ascii_digit());
+    /// assert!(!uppercase_g.is_ascii_digit());
+    /// assert!(!a.is_ascii_digit());
+    /// assert!(!g.is_ascii_digit());
+    /// assert!(zero.is_ascii_digit());
+    /// assert!(!percent.is_ascii_digit());
+    /// assert!(!space.is_ascii_digit());
+    /// assert!(!lf.is_ascii_digit());
+    /// assert!(!esc.is_ascii_digit());
+    /// ```
+    #[must_use]
+    #[stable(feature = "ascii_ctype_on_intrinsics", since = "1.24.0")]
+    #[rustc_const_stable(feature = "const_ascii_ctype_on_intrinsics", since = "1.47.0")]
+    #[inline]
+    pub const fn is_ascii_digit(&self) -> bool {
+        matches!(*self, b'0'..=b'9')
+    }
+
+    /// Checks if the value is an ASCII hexadecimal digit:
+    ///
+    /// - U+0030 '0' ..= U+0039 '9', or
+    /// - U+0041 'A' ..= U+0046 'F', or
+    /// - U+0061 'a' ..= U+0066 'f'.
+    ///
+    /// # Examples
+    ///
+    /// ```
+    /// let uppercase_a = b'A';
+    /// let uppercase_g = b'G';
+    /// let a = b'a';
+    /// let g = b'g';
+    /// let zero = b'0';
+    /// let percent = b'%';
+    /// let space = b' ';
+    /// let lf = b'\n';
+    /// let esc = b'\x1b';
+    ///
+    /// assert!(uppercase_a.is_ascii_hexdigit());
+    /// assert!(!uppercase_g.is_ascii_hexdigit());
+    /// assert!(a.is_ascii_hexdigit());
+    /// assert!(!g.is_ascii_hexdigit());
+    /// assert!(zero.is_ascii_hexdigit());
+    /// assert!(!percent.is_ascii_hexdigit());
+    /// assert!(!space.is_ascii_hexdigit());
+    /// assert!(!lf.is_ascii_hexdigit());
+    /// assert!(!esc.is_ascii_hexdigit());
+    /// ```
+    #[must_use]
+    #[stable(feature = "ascii_ctype_on_intrinsics", since = "1.24.0")]
+    #[rustc_const_stable(feature = "const_ascii_ctype_on_intrinsics", since = "1.47.0")]
+    #[inline]
+    pub const fn is_ascii_hexdigit(&self) -> bool {
+        matches!(*self, b'0'..=b'9' | b'A'..=b'F' | b'a'..=b'f')
+    }
+
+    /// Checks if the value is an ASCII punctuation character:
+    ///
+    /// - U+0021 ..= U+002F `! " # $ % & ' ( ) * + , - . /`, or
+    /// - U+003A ..= U+0040 `: ; < = > ? @`, or
+    /// - U+005B ..= U+0060 ``[ \ ] ^ _ ` ``, or
+    /// - U+007B ..= U+007E `{ | } ~`
+    ///
+    /// # Examples
+    ///
+    /// ```
+    /// let uppercase_a = b'A';
+    /// let uppercase_g = b'G';
+    /// let a = b'a';
+    /// let g = b'g';
+    /// let zero = b'0';
+    /// let percent = b'%';
+    /// let space = b' ';
+    /// let lf = b'\n';
+    /// let esc = b'\x1b';
+    ///
+    /// assert!(!uppercase_a.is_ascii_punctuation());
+    /// assert!(!uppercase_g.is_ascii_punctuation());
+    /// assert!(!a.is_ascii_punctuation());
+    /// assert!(!g.is_ascii_punctuation());
+    /// assert!(!zero.is_ascii_punctuation());
+    /// assert!(percent.is_ascii_punctuation());
+    /// assert!(!space.is_ascii_punctuation());
+    /// assert!(!lf.is_ascii_punctuation());
+    /// assert!(!esc.is_ascii_punctuation());
+    /// ```
+    #[must_use]
+    #[stable(feature = "ascii_ctype_on_intrinsics", since = "1.24.0")]
+    #[rustc_const_stable(feature = "const_ascii_ctype_on_intrinsics", since = "1.47.0")]
+    #[inline]
+    pub const fn is_ascii_punctuation(&self) -> bool {
+        matches!(*self, b'!'..=b'/' | b':'..=b'@' | b'['..=b'`' | b'{'..=b'~')
+    }
+
+    /// Checks if the value is an ASCII graphic character:
+    /// U+0021 '!' ..= U+007E '~'.
+    ///
+    /// # Examples
+    ///
+    /// ```
+    /// let uppercase_a = b'A';
+    /// let uppercase_g = b'G';
+    /// let a = b'a';
+    /// let g = b'g';
+    /// let zero = b'0';
+    /// let percent = b'%';
+    /// let space = b' ';
+    /// let lf = b'\n';
+    /// let esc = b'\x1b';
+    ///
+    /// assert!(uppercase_a.is_ascii_graphic());
+    /// assert!(uppercase_g.is_ascii_graphic());
+    /// assert!(a.is_ascii_graphic());
+    /// assert!(g.is_ascii_graphic());
+    /// assert!(zero.is_ascii_graphic());
+    /// assert!(percent.is_ascii_graphic());
+    /// assert!(!space.is_ascii_graphic());
+    /// assert!(!lf.is_ascii_graphic());
+    /// assert!(!esc.is_ascii_graphic());
+    /// ```
+    #[must_use]
+    #[stable(feature = "ascii_ctype_on_intrinsics", since = "1.24.0")]
+    #[rustc_const_stable(feature = "const_ascii_ctype_on_intrinsics", since = "1.47.0")]
+    #[inline]
+    pub const fn is_ascii_graphic(&self) -> bool {
+        matches!(*self, b'!'..=b'~')
+    }
+
+    /// Checks if the value is an ASCII whitespace character:
+    /// U+0020 SPACE, U+0009 HORIZONTAL TAB, U+000A LINE FEED,
+    /// U+000C FORM FEED, or U+000D CARRIAGE RETURN.
+    ///
+    /// Rust uses the WhatWG Infra Standard's [definition of ASCII
+    /// whitespace][infra-aw]. There are several other definitions in
+    /// wide use. For instance, [the POSIX locale][pct] includes
+    /// U+000B VERTICAL TAB as well as all the above characters,
+    /// but—from the very same specification—[the default rule for
+    /// "field splitting" in the Bourne shell][bfs] considers *only*
+    /// SPACE, HORIZONTAL TAB, and LINE FEED as whitespace.
+    ///
+    /// If you are writing a program that will process an existing
+    /// file format, check what that format's definition of whitespace is
+    /// before using this function.
+    ///
+    /// [infra-aw]: https://infra.spec.whatwg.org/#ascii-whitespace
+    /// [pct]: https://pubs.opengroup.org/onlinepubs/9699919799/basedefs/V1_chap07.html#tag_07_03_01
+    /// [bfs]: https://pubs.opengroup.org/onlinepubs/9699919799/utilities/V3_chap02.html#tag_18_06_05
+    ///
+    /// # Examples
+    ///
+    /// ```
+    /// let uppercase_a = b'A';
+    /// let uppercase_g = b'G';
+    /// let a = b'a';
+    /// let g = b'g';
+    /// let zero = b'0';
+    /// let percent = b'%';
+    /// let space = b' ';
+    /// let lf = b'\n';
+    /// let esc = b'\x1b';
+    ///
+    /// assert!(!uppercase_a.is_ascii_whitespace());
+    /// assert!(!uppercase_g.is_ascii_whitespace());
+    /// assert!(!a.is_ascii_whitespace());
+    /// assert!(!g.is_ascii_whitespace());
+    /// assert!(!zero.is_ascii_whitespace());
+    /// assert!(!percent.is_ascii_whitespace());
+    /// assert!(space.is_ascii_whitespace());
+    /// assert!(lf.is_ascii_whitespace());
+    /// assert!(!esc.is_ascii_whitespace());
+    /// ```
+    #[must_use]
+    #[stable(feature = "ascii_ctype_on_intrinsics", since = "1.24.0")]
+    #[rustc_const_stable(feature = "const_ascii_ctype_on_intrinsics", since = "1.47.0")]
+    #[inline]
+    pub const fn is_ascii_whitespace(&self) -> bool {
+        matches!(*self, b'\t' | b'\n' | b'\x0C' | b'\r' | b' ')
+    }
+
+    /// Checks if the value is an ASCII control character:
+    /// U+0000 NUL ..= U+001F UNIT SEPARATOR, or U+007F DELETE.
+    /// Note that most ASCII whitespace characters are control
+    /// characters, but SPACE is not.
+    ///
+    /// # Examples
+    ///
+    /// ```
+    /// let uppercase_a = b'A';
+    /// let uppercase_g = b'G';
+    /// let a = b'a';
+    /// let g = b'g';
+    /// let zero = b'0';
+    /// let percent = b'%';
+    /// let space = b' ';
+    /// let lf = b'\n';
+    /// let esc = b'\x1b';
+    ///
+    /// assert!(!uppercase_a.is_ascii_control());
+    /// assert!(!uppercase_g.is_ascii_control());
+    /// assert!(!a.is_ascii_control());
+    /// assert!(!g.is_ascii_control());
+    /// assert!(!zero.is_ascii_control());
+    /// assert!(!percent.is_ascii_control());
+    /// assert!(!space.is_ascii_control());
+    /// assert!(lf.is_ascii_control());
+    /// assert!(esc.is_ascii_control());
+    /// ```
+    #[must_use]
+    #[stable(feature = "ascii_ctype_on_intrinsics", since = "1.24.0")]
+    #[rustc_const_stable(feature = "const_ascii_ctype_on_intrinsics", since = "1.47.0")]
+    #[inline]
+    pub const fn is_ascii_control(&self) -> bool {
+        matches!(*self, b'\0'..=b'\x1F' | b'\x7F')
+    }
+
+    /// Returns an iterator that produces an escaped version of a `u8`,
+    /// treating it as an ASCII character.
+    ///
+    /// The behavior is identical to [`ascii::escape_default`].
+    ///
+    /// # Examples
+    ///
+    /// ```
+    ///
+    /// assert_eq!("0", b'0'.escape_ascii().to_string());
+    /// assert_eq!("\\t", b'\t'.escape_ascii().to_string());
+    /// assert_eq!("\\r", b'\r'.escape_ascii().to_string());
+    /// assert_eq!("\\n", b'\n'.escape_ascii().to_string());
+    /// assert_eq!("\\'", b'\''.escape_ascii().to_string());
+    /// assert_eq!("\\\"", b'"'.escape_ascii().to_string());
+    /// assert_eq!("\\\\", b'\\'.escape_ascii().to_string());
+    /// assert_eq!("\\x9d", b'\x9d'.escape_ascii().to_string());
+    /// ```
+    #[must_use = "this returns the escaped byte as an iterator, \
+                  without modifying the original"]
+    #[stable(feature = "inherent_ascii_escape", since = "1.60.0")]
+    #[inline]
+    pub fn escape_ascii(self) -> ascii::EscapeDefault {
+        ascii::escape_default(self)
+    }
+
+    #[inline]
+    pub(crate) const fn is_utf8_char_boundary(self) -> bool {
+        // This is bit magic equivalent to: b < 128 || b >= 192
+        (self as i8) >= -0x40
+    }
+}
+
+impl u16 {
+    uint_impl! { u16, u16, i16, NonZeroU16, 16, 65535, 4, "0xa003", "0x3a", "0x1234", "0x3412", "0x2c48",
+    "[0x34, 0x12]", "[0x12, 0x34]", "", "", "" }
+    widening_impl! { u16, u32, 16, unsigned }
+
+    /// Checks if the value is a Unicode surrogate code point, which are disallowed values for [`char`].
+    ///
+    /// # Examples
+    ///
+    /// ```
+    /// #![feature(utf16_extra)]
+    ///
+    /// let low_non_surrogate = 0xA000u16;
+    /// let low_surrogate = 0xD800u16;
+    /// let high_surrogate = 0xDC00u16;
+    /// let high_non_surrogate = 0xE000u16;
+    ///
+    /// assert!(!low_non_surrogate.is_utf16_surrogate());
+    /// assert!(low_surrogate.is_utf16_surrogate());
+    /// assert!(high_surrogate.is_utf16_surrogate());
+    /// assert!(!high_non_surrogate.is_utf16_surrogate());
+    /// ```
+    #[must_use]
+    #[unstable(feature = "utf16_extra", issue = "94919")]
+    #[rustc_const_unstable(feature = "utf16_extra_const", issue = "94919")]
+    #[inline]
+    pub const fn is_utf16_surrogate(self) -> bool {
+        matches!(self, 0xD800..=0xDFFF)
+    }
+}
+
+impl u32 {
+    uint_impl! { u32, u32, i32, NonZeroU32, 32, 4294967295, 8, "0x10000b3", "0xb301", "0x12345678",
+    "0x78563412", "0x1e6a2c48", "[0x78, 0x56, 0x34, 0x12]", "[0x12, 0x34, 0x56, 0x78]", "", "", "" }
+    widening_impl! { u32, u64, 32, unsigned }
+}
+
+impl u64 {
+    uint_impl! { u64, u64, i64, NonZeroU64, 64, 18446744073709551615, 12, "0xaa00000000006e1", "0x6e10aa",
+    "0x1234567890123456", "0x5634129078563412", "0x6a2c48091e6a2c48",
+    "[0x56, 0x34, 0x12, 0x90, 0x78, 0x56, 0x34, 0x12]",
+    "[0x12, 0x34, 0x56, 0x78, 0x90, 0x12, 0x34, 0x56]",
+    "", "", ""}
+    widening_impl! { u64, u128, 64, unsigned }
+}
+
+impl u128 {
+    uint_impl! { u128, u128, i128, NonZeroU128, 128, 340282366920938463463374607431768211455, 16,
+    "0x13f40000000000000000000000004f76", "0x4f7613f4", "0x12345678901234567890123456789012",
+    "0x12907856341290785634129078563412", "0x48091e6a2c48091e6a2c48091e6a2c48",
+    "[0x12, 0x90, 0x78, 0x56, 0x34, 0x12, 0x90, 0x78, \
+      0x56, 0x34, 0x12, 0x90, 0x78, 0x56, 0x34, 0x12]",
+    "[0x12, 0x34, 0x56, 0x78, 0x90, 0x12, 0x34, 0x56, \
+      0x78, 0x90, 0x12, 0x34, 0x56, 0x78, 0x90, 0x12]",
+     "", "", ""}
+}
+
+#[cfg(target_pointer_width = "16")]
+impl usize {
+    uint_impl! { usize, u16, isize, NonZeroUsize, 16, 65535, 4, "0xa003", "0x3a", "0x1234", "0x3412", "0x2c48",
+    "[0x34, 0x12]", "[0x12, 0x34]",
+    usize_isize_to_xe_bytes_doc!(), usize_isize_from_xe_bytes_doc!(),
+    " on 16-bit targets" }
+    widening_impl! { usize, u32, 16, unsigned }
+}
+#[cfg(target_pointer_width = "32")]
+impl usize {
+    uint_impl! { usize, u32, isize, NonZeroUsize, 32, 4294967295, 8, "0x10000b3", "0xb301", "0x12345678",
+    "0x78563412", "0x1e6a2c48", "[0x78, 0x56, 0x34, 0x12]", "[0x12, 0x34, 0x56, 0x78]",
+    usize_isize_to_xe_bytes_doc!(), usize_isize_from_xe_bytes_doc!(),
+    " on 32-bit targets" }
+    widening_impl! { usize, u64, 32, unsigned }
+}
+
+#[cfg(target_pointer_width = "64")]
+impl usize {
+    uint_impl! { usize, u64, isize, NonZeroUsize, 64, 18446744073709551615, 12, "0xaa00000000006e1", "0x6e10aa",
+    "0x1234567890123456", "0x5634129078563412", "0x6a2c48091e6a2c48",
+    "[0x56, 0x34, 0x12, 0x90, 0x78, 0x56, 0x34, 0x12]",
+    "[0x12, 0x34, 0x56, 0x78, 0x90, 0x12, 0x34, 0x56]",
+    usize_isize_to_xe_bytes_doc!(), usize_isize_from_xe_bytes_doc!(),
+    " on 64-bit targets" }
+    widening_impl! { usize, u128, 64, unsigned }
+}
+
+impl usize {
+    /// Returns an `usize` where every byte is equal to `x`.
+    #[inline]
+    pub(crate) const fn repeat_u8(x: u8) -> usize {
+        usize::from_ne_bytes([x; mem::size_of::<usize>()])
+    }
+
+    /// Returns an `usize` where every byte pair is equal to `x`.
+    #[inline]
+    pub(crate) const fn repeat_u16(x: u16) -> usize {
+        let mut r = 0usize;
+        let mut i = 0;
+        while i < mem::size_of::<usize>() {
+            // Use `wrapping_shl` to make it work on targets with 16-bit `usize`
+            r = r.wrapping_shl(16) | (x as usize);
+            i += 2;
+        }
+        r
+    }
+}
+
+/// A classification of floating point numbers.
+///
+/// This `enum` is used as the return type for [`f32::classify`] and [`f64::classify`]. See
+/// their documentation for more.
+///
+/// # Examples
+///
+/// ```
+/// use std::num::FpCategory;
+///
+/// let num = 12.4_f32;
+/// let inf = f32::INFINITY;
+/// let zero = 0f32;
+/// let sub: f32 = 1.1754942e-38;
+/// let nan = f32::NAN;
+///
+/// assert_eq!(num.classify(), FpCategory::Normal);
+/// assert_eq!(inf.classify(), FpCategory::Infinite);
+/// assert_eq!(zero.classify(), FpCategory::Zero);
+/// assert_eq!(nan.classify(), FpCategory::Nan);
+/// assert_eq!(sub.classify(), FpCategory::Subnormal);
+/// ```
+#[derive(Copy, Clone, PartialEq, Eq, Debug)]
+#[stable(feature = "rust1", since = "1.0.0")]
+pub enum FpCategory {
+    /// NaN (not a number): this value results from calculations like `(-1.0).sqrt()`.
+    ///
+    /// See [the documentation for `f32`](f32) for more information on the unusual properties
+    /// of NaN.
+    #[stable(feature = "rust1", since = "1.0.0")]
+    Nan,
+
+    /// Positive or negative infinity, which often results from dividing a nonzero number
+    /// by zero.
+    #[stable(feature = "rust1", since = "1.0.0")]
+    Infinite,
+
+    /// Positive or negative zero.
+    ///
+    /// See [the documentation for `f32`](f32) for more information on the signedness of zeroes.
+    #[stable(feature = "rust1", since = "1.0.0")]
+    Zero,
+
+    /// “Subnormal” or “denormal” floating point representation (less precise, relative to
+    /// their magnitude, than [`Normal`]).
+    ///
+    /// Subnormal numbers are larger in magnitude than [`Zero`] but smaller in magnitude than all
+    /// [`Normal`] numbers.
+    ///
+    /// [`Normal`]: Self::Normal
+    /// [`Zero`]: Self::Zero
+    #[stable(feature = "rust1", since = "1.0.0")]
+    Subnormal,
+
+    /// A regular floating point number, not any of the exceptional categories.
+    ///
+    /// The smallest positive normal numbers are [`f32::MIN_POSITIVE`] and [`f64::MIN_POSITIVE`],
+    /// and the largest positive normal numbers are [`f32::MAX`] and [`f64::MAX`]. (Unlike signed
+    /// integers, floating point numbers are symmetric in their range, so negating any of these
+    /// constants will produce their negative counterpart.)
+    #[stable(feature = "rust1", since = "1.0.0")]
+    Normal,
+}
+
+#[doc(hidden)]
+trait FromStrRadixHelper:
+    PartialOrd + Copy + Add<Output = Self> + Sub<Output = Self> + Mul<Output = Self>
+{
+    const MIN: Self;
+    fn from_u32(u: u32) -> Self;
+    fn checked_mul(&self, other: u32) -> Option<Self>;
+    fn checked_sub(&self, other: u32) -> Option<Self>;
+    fn checked_add(&self, other: u32) -> Option<Self>;
+}
+
+macro_rules! from_str_radix_int_impl {
+    ($($t:ty)*) => {$(
+        #[stable(feature = "rust1", since = "1.0.0")]
+        impl FromStr for $t {
+            type Err = ParseIntError;
+            fn from_str(src: &str) -> Result<Self, ParseIntError> {
+                from_str_radix(src, 10)
+            }
+        }
+    )*}
+}
+from_str_radix_int_impl! { isize i8 i16 i32 i64 i128 usize u8 u16 u32 u64 u128 }
+
+macro_rules! impl_helper_for {
+    ($($t:ty)*) => ($(impl FromStrRadixHelper for $t {
+        const MIN: Self = Self::MIN;
+        #[inline]
+        fn from_u32(u: u32) -> Self { u as Self }
+        #[inline]
+        fn checked_mul(&self, other: u32) -> Option<Self> {
+            Self::checked_mul(*self, other as Self)
+        }
+        #[inline]
+        fn checked_sub(&self, other: u32) -> Option<Self> {
+            Self::checked_sub(*self, other as Self)
+        }
+        #[inline]
+        fn checked_add(&self, other: u32) -> Option<Self> {
+            Self::checked_add(*self, other as Self)
+        }
+    })*)
+}
+impl_helper_for! { i8 i16 i32 i64 i128 isize u8 u16 u32 u64 u128 usize }
+
+/// Determines if a string of text of that length of that radix could be guaranteed to be
+/// stored in the given type T.
+/// Note that if the radix is known to the compiler, it is just the check of digits.len that
+/// is done at runtime.
+#[doc(hidden)]
+#[inline(always)]
+#[unstable(issue = "none", feature = "std_internals")]
+pub fn can_not_overflow<T>(radix: u32, is_signed_ty: bool, digits: &[u8]) -> bool {
+    radix <= 16 && digits.len() <= mem::size_of::<T>() * 2 - is_signed_ty as usize
+}
+
+fn from_str_radix<T: FromStrRadixHelper>(src: &str, radix: u32) -> Result<T, ParseIntError> {
+    use self::IntErrorKind::*;
+    use self::ParseIntError as PIE;
+
+    assert!(
+        (2..=36).contains(&radix),
+        "from_str_radix_int: must lie in the range `[2, 36]` - found {}",
+        radix
+    );
+
+    if src.is_empty() {
+        return Err(PIE { kind: Empty });
+    }
+
+    let is_signed_ty = T::from_u32(0) > T::MIN;
+
+    // all valid digits are ascii, so we will just iterate over the utf8 bytes
+    // and cast them to chars. .to_digit() will safely return None for anything
+    // other than a valid ascii digit for the given radix, including the first-byte
+    // of multi-byte sequences
+    let src = src.as_bytes();
+
+    let (is_positive, digits) = match src[0] {
+        b'+' | b'-' if src[1..].is_empty() => {
+            return Err(PIE { kind: InvalidDigit });
+        }
+        b'+' => (true, &src[1..]),
+        b'-' if is_signed_ty => (false, &src[1..]),
+        _ => (true, src),
+    };
+
+    let mut result = T::from_u32(0);
+
+    if can_not_overflow::<T>(radix, is_signed_ty, digits) {
+        // If the len of the str is short compared to the range of the type
+        // we are parsing into, then we can be certain that an overflow will not occur.
+        // This bound is when `radix.pow(digits.len()) - 1 <= T::MAX` but the condition
+        // above is a faster (conservative) approximation of this.
+        //
+        // Consider radix 16 as it has the highest information density per digit and will thus overflow the earliest:
+        // `u8::MAX` is `ff` - any str of len 2 is guaranteed to not overflow.
+        // `i8::MAX` is `7f` - only a str of len 1 is guaranteed to not overflow.
+        macro_rules! run_unchecked_loop {
+            ($unchecked_additive_op:expr) => {
+                for &c in digits {
+                    result = result * T::from_u32(radix);
+                    let x = (c as char).to_digit(radix).ok_or(PIE { kind: InvalidDigit })?;
+                    result = $unchecked_additive_op(result, T::from_u32(x));
+                }
+            };
+        }
+        if is_positive {
+            run_unchecked_loop!(<T as core::ops::Add>::add)
+        } else {
+            run_unchecked_loop!(<T as core::ops::Sub>::sub)
+        };
+    } else {
+        macro_rules! run_checked_loop {
+            ($checked_additive_op:ident, $overflow_err:expr) => {
+                for &c in digits {
+                    // When `radix` is passed in as a literal, rather than doing a slow `imul`
+                    // the compiler can use shifts if `radix` can be expressed as a
+                    // sum of powers of 2 (x*10 can be written as x*8 + x*2).
+                    // When the compiler can't use these optimisations,
+                    // the latency of the multiplication can be hidden by issuing it
+                    // before the result is needed to improve performance on
+                    // modern out-of-order CPU as multiplication here is slower
+                    // than the other instructions, we can get the end result faster
+                    // doing multiplication first and let the CPU spends other cycles
+                    // doing other computation and get multiplication result later.
+                    let mul = result.checked_mul(radix);
+                    let x = (c as char).to_digit(radix).ok_or(PIE { kind: InvalidDigit })?;
+                    result = mul.ok_or_else($overflow_err)?;
+                    result = T::$checked_additive_op(&result, x).ok_or_else($overflow_err)?;
+                }
+            };
+        }
+        if is_positive {
+            run_checked_loop!(checked_add, || PIE { kind: PosOverflow })
+        } else {
+            run_checked_loop!(checked_sub, || PIE { kind: NegOverflow })
+        };
+    }
+    Ok(result)
+}
diff --git a/library/core/src/num/nonzero.rs b/library/core/src/num/nonzero.rs
new file mode 100644
index 000000000..4de0a0cf5
--- /dev/null
+++ b/library/core/src/num/nonzero.rs
@@ -0,0 +1,1134 @@
+//! Definitions of integer that is known not to equal zero.
+
+use crate::fmt;
+use crate::ops::{BitOr, BitOrAssign, Div, Rem};
+use crate::str::FromStr;
+
+use super::from_str_radix;
+use super::{IntErrorKind, ParseIntError};
+use crate::intrinsics;
+
+macro_rules! impl_nonzero_fmt {
+    ( #[$stability: meta] ( $( $Trait: ident ),+ ) for $Ty: ident ) => {
+        $(
+            #[$stability]
+            impl fmt::$Trait for $Ty {
+                #[inline]
+                fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
+                    self.get().fmt(f)
+                }
+            }
+        )+
+    }
+}
+
+macro_rules! nonzero_integers {
+    ( $( #[$stability: meta] #[$const_new_unchecked_stability: meta] $Ty: ident($Int: ty); )+ ) => {
+        $(
+            /// An integer that is known not to equal zero.
+            ///
+            /// This enables some memory layout optimization.
+            #[doc = concat!("For example, `Option<", stringify!($Ty), ">` is the same size as `", stringify!($Int), "`:")]
+            ///
+            /// ```rust
+            /// use std::mem::size_of;
+            #[doc = concat!("assert_eq!(size_of::<Option<core::num::", stringify!($Ty), ">>(), size_of::<", stringify!($Int), ">());")]
+            /// ```
+            #[$stability]
+            #[derive(Copy, Clone, Eq, PartialEq, Ord, PartialOrd, Hash)]
+            #[repr(transparent)]
+            #[rustc_layout_scalar_valid_range_start(1)]
+            #[rustc_nonnull_optimization_guaranteed]
+            #[rustc_diagnostic_item = stringify!($Ty)]
+            pub struct $Ty($Int);
+
+            impl $Ty {
+                /// Creates a non-zero without checking whether the value is non-zero.
+                /// This results in undefined behaviour if the value is zero.
+                ///
+                /// # Safety
+                ///
+                /// The value must not be zero.
+                #[$stability]
+                #[$const_new_unchecked_stability]
+                #[must_use]
+                #[inline]
+                pub const unsafe fn new_unchecked(n: $Int) -> Self {
+                    // SAFETY: this is guaranteed to be safe by the caller.
+                    unsafe {
+                        core::intrinsics::assert_unsafe_precondition!(n != 0);
+                        Self(n)
+                    }
+                }
+
+                /// Creates a non-zero if the given value is not zero.
+                #[$stability]
+                #[rustc_const_stable(feature = "const_nonzero_int_methods", since = "1.47.0")]
+                #[must_use]
+                #[inline]
+                pub const fn new(n: $Int) -> Option<Self> {
+                    if n != 0 {
+                        // SAFETY: we just checked that there's no `0`
+                        Some(unsafe { Self(n) })
+                    } else {
+                        None
+                    }
+                }
+
+                /// Returns the value as a primitive type.
+                #[$stability]
+                #[inline]
+                #[rustc_const_stable(feature = "const_nonzero_get", since = "1.34.0")]
+                pub const fn get(self) -> $Int {
+                    self.0
+                }
+
+            }
+
+            #[stable(feature = "from_nonzero", since = "1.31.0")]
+            #[rustc_const_unstable(feature = "const_num_from_num", issue = "87852")]
+            impl const From<$Ty> for $Int {
+                #[doc = concat!("Converts a `", stringify!($Ty), "` into an `", stringify!($Int), "`")]
+                #[inline]
+                fn from(nonzero: $Ty) -> Self {
+                    nonzero.0
+                }
+            }
+
+            #[stable(feature = "nonzero_bitor", since = "1.45.0")]
+            #[rustc_const_unstable(feature = "const_ops", issue = "90080")]
+            impl const BitOr for $Ty {
+                type Output = Self;
+                #[inline]
+                fn bitor(self, rhs: Self) -> Self::Output {
+                    // SAFETY: since `self` and `rhs` are both nonzero, the
+                    // result of the bitwise-or will be nonzero.
+                    unsafe { $Ty::new_unchecked(self.get() | rhs.get()) }
+                }
+            }
+
+            #[stable(feature = "nonzero_bitor", since = "1.45.0")]
+            #[rustc_const_unstable(feature = "const_ops", issue = "90080")]
+            impl const BitOr<$Int> for $Ty {
+                type Output = Self;
+                #[inline]
+                fn bitor(self, rhs: $Int) -> Self::Output {
+                    // SAFETY: since `self` is nonzero, the result of the
+                    // bitwise-or will be nonzero regardless of the value of
+                    // `rhs`.
+                    unsafe { $Ty::new_unchecked(self.get() | rhs) }
+                }
+            }
+
+            #[stable(feature = "nonzero_bitor", since = "1.45.0")]
+            #[rustc_const_unstable(feature = "const_ops", issue = "90080")]
+            impl const BitOr<$Ty> for $Int {
+                type Output = $Ty;
+                #[inline]
+                fn bitor(self, rhs: $Ty) -> Self::Output {
+                    // SAFETY: since `rhs` is nonzero, the result of the
+                    // bitwise-or will be nonzero regardless of the value of
+                    // `self`.
+                    unsafe { $Ty::new_unchecked(self | rhs.get()) }
+                }
+            }
+
+            #[stable(feature = "nonzero_bitor", since = "1.45.0")]
+            #[rustc_const_unstable(feature = "const_ops", issue = "90080")]
+            impl const BitOrAssign for $Ty {
+                #[inline]
+                fn bitor_assign(&mut self, rhs: Self) {
+                    *self = *self | rhs;
+                }
+            }
+
+            #[stable(feature = "nonzero_bitor", since = "1.45.0")]
+            #[rustc_const_unstable(feature = "const_ops", issue = "90080")]
+            impl const BitOrAssign<$Int> for $Ty {
+                #[inline]
+                fn bitor_assign(&mut self, rhs: $Int) {
+                    *self = *self | rhs;
+                }
+            }
+
+            impl_nonzero_fmt! {
+                #[$stability] (Debug, Display, Binary, Octal, LowerHex, UpperHex) for $Ty
+            }
+        )+
+    }
+}
+
+nonzero_integers! {
+    #[stable(feature = "nonzero", since = "1.28.0")] #[rustc_const_stable(feature = "nonzero", since = "1.28.0")] NonZeroU8(u8);
+    #[stable(feature = "nonzero", since = "1.28.0")] #[rustc_const_stable(feature = "nonzero", since = "1.28.0")] NonZeroU16(u16);
+    #[stable(feature = "nonzero", since = "1.28.0")] #[rustc_const_stable(feature = "nonzero", since = "1.28.0")] NonZeroU32(u32);
+    #[stable(feature = "nonzero", since = "1.28.0")] #[rustc_const_stable(feature = "nonzero", since = "1.28.0")] NonZeroU64(u64);
+    #[stable(feature = "nonzero", since = "1.28.0")] #[rustc_const_stable(feature = "nonzero", since = "1.28.0")] NonZeroU128(u128);
+    #[stable(feature = "nonzero", since = "1.28.0")] #[rustc_const_stable(feature = "nonzero", since = "1.28.0")] NonZeroUsize(usize);
+    #[stable(feature = "signed_nonzero", since = "1.34.0")] #[rustc_const_stable(feature = "signed_nonzero", since = "1.34.0")] NonZeroI8(i8);
+    #[stable(feature = "signed_nonzero", since = "1.34.0")] #[rustc_const_stable(feature = "signed_nonzero", since = "1.34.0")] NonZeroI16(i16);
+    #[stable(feature = "signed_nonzero", since = "1.34.0")] #[rustc_const_stable(feature = "signed_nonzero", since = "1.34.0")] NonZeroI32(i32);
+    #[stable(feature = "signed_nonzero", since = "1.34.0")] #[rustc_const_stable(feature = "signed_nonzero", since = "1.34.0")] NonZeroI64(i64);
+    #[stable(feature = "signed_nonzero", since = "1.34.0")] #[rustc_const_stable(feature = "signed_nonzero", since = "1.34.0")] NonZeroI128(i128);
+    #[stable(feature = "signed_nonzero", since = "1.34.0")] #[rustc_const_stable(feature = "signed_nonzero", since = "1.34.0")] NonZeroIsize(isize);
+}
+
+macro_rules! from_str_radix_nzint_impl {
+    ($($t:ty)*) => {$(
+        #[stable(feature = "nonzero_parse", since = "1.35.0")]
+        impl FromStr for $t {
+            type Err = ParseIntError;
+            fn from_str(src: &str) -> Result<Self, Self::Err> {
+                Self::new(from_str_radix(src, 10)?)
+                    .ok_or(ParseIntError {
+                        kind: IntErrorKind::Zero
+                    })
+            }
+        }
+    )*}
+}
+
+from_str_radix_nzint_impl! { NonZeroU8 NonZeroU16 NonZeroU32 NonZeroU64 NonZeroU128 NonZeroUsize
+NonZeroI8 NonZeroI16 NonZeroI32 NonZeroI64 NonZeroI128 NonZeroIsize }
+
+macro_rules! nonzero_leading_trailing_zeros {
+    ( $( $Ty: ident($Uint: ty) , $LeadingTestExpr:expr ;)+ ) => {
+        $(
+            impl $Ty {
+                /// Returns the number of leading zeros in the binary representation of `self`.
+                ///
+                /// On many architectures, this function can perform better than `leading_zeros()` on the underlying integer type, as special handling of zero can be avoided.
+                ///
+                /// # Examples
+                ///
+                /// Basic usage:
+                ///
+                /// ```
+                #[doc = concat!("let n = std::num::", stringify!($Ty), "::new(", stringify!($LeadingTestExpr), ").unwrap();")]
+                ///
+                /// assert_eq!(n.leading_zeros(), 0);
+                /// ```
+                #[stable(feature = "nonzero_leading_trailing_zeros", since = "1.53.0")]
+                #[rustc_const_stable(feature = "nonzero_leading_trailing_zeros", since = "1.53.0")]
+                #[must_use = "this returns the result of the operation, \
+                              without modifying the original"]
+                #[inline]
+                pub const fn leading_zeros(self) -> u32 {
+                    // SAFETY: since `self` cannot be zero, it is safe to call `ctlz_nonzero`.
+                    unsafe { intrinsics::ctlz_nonzero(self.0 as $Uint) as u32 }
+                }
+
+                /// Returns the number of trailing zeros in the binary representation
+                /// of `self`.
+                ///
+                /// On many architectures, this function can perform better than `trailing_zeros()` on the underlying integer type, as special handling of zero can be avoided.
+                ///
+                /// # Examples
+                ///
+                /// Basic usage:
+                ///
+                /// ```
+                #[doc = concat!("let n = std::num::", stringify!($Ty), "::new(0b0101000).unwrap();")]
+                ///
+                /// assert_eq!(n.trailing_zeros(), 3);
+                /// ```
+                #[stable(feature = "nonzero_leading_trailing_zeros", since = "1.53.0")]
+                #[rustc_const_stable(feature = "nonzero_leading_trailing_zeros", since = "1.53.0")]
+                #[must_use = "this returns the result of the operation, \
+                              without modifying the original"]
+                #[inline]
+                pub const fn trailing_zeros(self) -> u32 {
+                    // SAFETY: since `self` cannot be zero, it is safe to call `cttz_nonzero`.
+                    unsafe { intrinsics::cttz_nonzero(self.0 as $Uint) as u32 }
+                }
+
+            }
+        )+
+    }
+}
+
+nonzero_leading_trailing_zeros! {
+    NonZeroU8(u8), u8::MAX;
+    NonZeroU16(u16), u16::MAX;
+    NonZeroU32(u32), u32::MAX;
+    NonZeroU64(u64), u64::MAX;
+    NonZeroU128(u128), u128::MAX;
+    NonZeroUsize(usize), usize::MAX;
+    NonZeroI8(u8), -1i8;
+    NonZeroI16(u16), -1i16;
+    NonZeroI32(u32), -1i32;
+    NonZeroI64(u64), -1i64;
+    NonZeroI128(u128), -1i128;
+    NonZeroIsize(usize), -1isize;
+}
+
+macro_rules! nonzero_integers_div {
+    ( $( $Ty: ident($Int: ty); )+ ) => {
+        $(
+            #[stable(feature = "nonzero_div", since = "1.51.0")]
+            #[rustc_const_unstable(feature = "const_ops", issue = "90080")]
+            impl const Div<$Ty> for $Int {
+                type Output = $Int;
+                /// This operation rounds towards zero,
+                /// truncating any fractional part of the exact result, and cannot panic.
+                #[inline]
+                fn div(self, other: $Ty) -> $Int {
+                    // SAFETY: div by zero is checked because `other` is a nonzero,
+                    // and MIN/-1 is checked because `self` is an unsigned int.
+                    unsafe { crate::intrinsics::unchecked_div(self, other.get()) }
+                }
+            }
+
+            #[stable(feature = "nonzero_div", since = "1.51.0")]
+            #[rustc_const_unstable(feature = "const_ops", issue = "90080")]
+            impl const Rem<$Ty> for $Int {
+                type Output = $Int;
+                /// This operation satisfies `n % d == n - (n / d) * d`, and cannot panic.
+                #[inline]
+                fn rem(self, other: $Ty) -> $Int {
+                    // SAFETY: rem by zero is checked because `other` is a nonzero,
+                    // and MIN/-1 is checked because `self` is an unsigned int.
+                    unsafe { crate::intrinsics::unchecked_rem(self, other.get()) }
+                }
+            }
+        )+
+    }
+}
+
+nonzero_integers_div! {
+    NonZeroU8(u8);
+    NonZeroU16(u16);
+    NonZeroU32(u32);
+    NonZeroU64(u64);
+    NonZeroU128(u128);
+    NonZeroUsize(usize);
+}
+
+// A bunch of methods for unsigned nonzero types only.
+macro_rules! nonzero_unsigned_operations {
+    ( $( $Ty: ident($Int: ident); )+ ) => {
+        $(
+            impl $Ty {
+                /// Add an unsigned integer to a non-zero value.
+                /// Check for overflow and return [`None`] on overflow
+                /// As a consequence, the result cannot wrap to zero.
+                ///
+                ///
+                /// # Examples
+                ///
+                /// ```
+                #[doc = concat!("# use std::num::", stringify!($Ty), ";")]
+                ///
+                /// # fn main() { test().unwrap(); }
+                /// # fn test() -> Option<()> {
+                #[doc = concat!("let one = ", stringify!($Ty), "::new(1)?;")]
+                #[doc = concat!("let two = ", stringify!($Ty), "::new(2)?;")]
+                #[doc = concat!("let max = ", stringify!($Ty), "::new(",
+                                stringify!($Int), "::MAX)?;")]
+                ///
+                /// assert_eq!(Some(two), one.checked_add(1));
+                /// assert_eq!(None, max.checked_add(1));
+                /// # Some(())
+                /// # }
+                /// ```
+                #[stable(feature = "nonzero_checked_ops", since = "1.64.0")]
+                #[rustc_const_stable(feature = "const_nonzero_checked_ops", since = "1.64.0")]
+                #[must_use = "this returns the result of the operation, \
+                              without modifying the original"]
+                #[inline]
+                pub const fn checked_add(self, other: $Int) -> Option<$Ty> {
+                    if let Some(result) = self.get().checked_add(other) {
+                        // SAFETY: $Int::checked_add returns None on overflow
+                        // so the result cannot be zero.
+                        Some(unsafe { $Ty::new_unchecked(result) })
+                    } else {
+                        None
+                    }
+                }
+
+                /// Add an unsigned integer to a non-zero value.
+                #[doc = concat!("Return [`", stringify!($Int), "::MAX`] on overflow.")]
+                ///
+                /// # Examples
+                ///
+                /// ```
+                #[doc = concat!("# use std::num::", stringify!($Ty), ";")]
+                ///
+                /// # fn main() { test().unwrap(); }
+                /// # fn test() -> Option<()> {
+                #[doc = concat!("let one = ", stringify!($Ty), "::new(1)?;")]
+                #[doc = concat!("let two = ", stringify!($Ty), "::new(2)?;")]
+                #[doc = concat!("let max = ", stringify!($Ty), "::new(",
+                                stringify!($Int), "::MAX)?;")]
+                ///
+                /// assert_eq!(two, one.saturating_add(1));
+                /// assert_eq!(max, max.saturating_add(1));
+                /// # Some(())
+                /// # }
+                /// ```
+                #[stable(feature = "nonzero_checked_ops", since = "1.64.0")]
+                #[rustc_const_stable(feature = "const_nonzero_checked_ops", since = "1.64.0")]
+                #[must_use = "this returns the result of the operation, \
+                              without modifying the original"]
+                #[inline]
+                pub const fn saturating_add(self, other: $Int) -> $Ty {
+                    // SAFETY: $Int::saturating_add returns $Int::MAX on overflow
+                    // so the result cannot be zero.
+                    unsafe { $Ty::new_unchecked(self.get().saturating_add(other)) }
+                }
+
+                /// Add an unsigned integer to a non-zero value,
+                /// assuming overflow cannot occur.
+                /// Overflow is unchecked, and it is undefined behaviour to overflow
+                /// *even if the result would wrap to a non-zero value*.
+                /// The behaviour is undefined as soon as
+                #[doc = concat!("`self + rhs > ", stringify!($Int), "::MAX`.")]
+                ///
+                /// # Examples
+                ///
+                /// ```
+                /// #![feature(nonzero_ops)]
+                #[doc = concat!("# use std::num::", stringify!($Ty), ";")]
+                ///
+                /// # fn main() { test().unwrap(); }
+                /// # fn test() -> Option<()> {
+                #[doc = concat!("let one = ", stringify!($Ty), "::new(1)?;")]
+                #[doc = concat!("let two = ", stringify!($Ty), "::new(2)?;")]
+                ///
+                /// assert_eq!(two, unsafe { one.unchecked_add(1) });
+                /// # Some(())
+                /// # }
+                /// ```
+                #[unstable(feature = "nonzero_ops", issue = "84186")]
+                #[must_use = "this returns the result of the operation, \
+                              without modifying the original"]
+                #[inline]
+                pub const unsafe fn unchecked_add(self, other: $Int) -> $Ty {
+                    // SAFETY: The caller ensures there is no overflow.
+                    unsafe { $Ty::new_unchecked(self.get().unchecked_add(other)) }
+                }
+
+                /// Returns the smallest power of two greater than or equal to n.
+                /// Check for overflow and return [`None`]
+                /// if the next power of two is greater than the type’s maximum value.
+                /// As a consequence, the result cannot wrap to zero.
+                ///
+                /// # Examples
+                ///
+                /// ```
+                #[doc = concat!("# use std::num::", stringify!($Ty), ";")]
+                ///
+                /// # fn main() { test().unwrap(); }
+                /// # fn test() -> Option<()> {
+                #[doc = concat!("let two = ", stringify!($Ty), "::new(2)?;")]
+                #[doc = concat!("let three = ", stringify!($Ty), "::new(3)?;")]
+                #[doc = concat!("let four = ", stringify!($Ty), "::new(4)?;")]
+                #[doc = concat!("let max = ", stringify!($Ty), "::new(",
+                                stringify!($Int), "::MAX)?;")]
+                ///
+                /// assert_eq!(Some(two), two.checked_next_power_of_two() );
+                /// assert_eq!(Some(four), three.checked_next_power_of_two() );
+                /// assert_eq!(None, max.checked_next_power_of_two() );
+                /// # Some(())
+                /// # }
+                /// ```
+                #[stable(feature = "nonzero_checked_ops", since = "1.64.0")]
+                #[rustc_const_stable(feature = "const_nonzero_checked_ops", since = "1.64.0")]
+                #[must_use = "this returns the result of the operation, \
+                              without modifying the original"]
+                #[inline]
+                pub const fn checked_next_power_of_two(self) -> Option<$Ty> {
+                    if let Some(nz) = self.get().checked_next_power_of_two() {
+                        // SAFETY: The next power of two is positive
+                        // and overflow is checked.
+                        Some(unsafe { $Ty::new_unchecked(nz) })
+                    } else {
+                        None
+                    }
+                }
+
+                /// Returns the base 2 logarithm of the number, rounded down.
+                ///
+                /// This is the same operation as
+                #[doc = concat!("[`", stringify!($Int), "::log2`],")]
+                /// except that it has no failure cases to worry about
+                /// since this value can never be zero.
+                ///
+                /// # Examples
+                ///
+                /// ```
+                /// #![feature(int_log)]
+                #[doc = concat!("# use std::num::", stringify!($Ty), ";")]
+                ///
+                #[doc = concat!("assert_eq!(", stringify!($Ty), "::new(7).unwrap().log2(), 2);")]
+                #[doc = concat!("assert_eq!(", stringify!($Ty), "::new(8).unwrap().log2(), 3);")]
+                #[doc = concat!("assert_eq!(", stringify!($Ty), "::new(9).unwrap().log2(), 3);")]
+                /// ```
+                #[unstable(feature = "int_log", issue = "70887")]
+                #[must_use = "this returns the result of the operation, \
+                              without modifying the original"]
+                #[inline]
+                pub const fn log2(self) -> u32 {
+                    Self::BITS - 1 - self.leading_zeros()
+                }
+
+                /// Returns the base 10 logarithm of the number, rounded down.
+                ///
+                /// This is the same operation as
+                #[doc = concat!("[`", stringify!($Int), "::log10`],")]
+                /// except that it has no failure cases to worry about
+                /// since this value can never be zero.
+                ///
+                /// # Examples
+                ///
+                /// ```
+                /// #![feature(int_log)]
+                #[doc = concat!("# use std::num::", stringify!($Ty), ";")]
+                ///
+                #[doc = concat!("assert_eq!(", stringify!($Ty), "::new(99).unwrap().log10(), 1);")]
+                #[doc = concat!("assert_eq!(", stringify!($Ty), "::new(100).unwrap().log10(), 2);")]
+                #[doc = concat!("assert_eq!(", stringify!($Ty), "::new(101).unwrap().log10(), 2);")]
+                /// ```
+                #[unstable(feature = "int_log", issue = "70887")]
+                #[must_use = "this returns the result of the operation, \
+                              without modifying the original"]
+                #[inline]
+                pub const fn log10(self) -> u32 {
+                    super::int_log10::$Int(self.0)
+                }
+            }
+        )+
+    }
+}
+
+nonzero_unsigned_operations! {
+    NonZeroU8(u8);
+    NonZeroU16(u16);
+    NonZeroU32(u32);
+    NonZeroU64(u64);
+    NonZeroU128(u128);
+    NonZeroUsize(usize);
+}
+
+// A bunch of methods for signed nonzero types only.
+macro_rules! nonzero_signed_operations {
+    ( $( $Ty: ident($Int: ty) -> $Uty: ident($Uint: ty); )+ ) => {
+        $(
+            impl $Ty {
+                /// Computes the absolute value of self.
+                #[doc = concat!("See [`", stringify!($Int), "::abs`]")]
+                /// for documentation on overflow behaviour.
+                ///
+                /// # Example
+                ///
+                /// ```
+                #[doc = concat!("# use std::num::", stringify!($Ty), ";")]
+                ///
+                /// # fn main() { test().unwrap(); }
+                /// # fn test() -> Option<()> {
+                #[doc = concat!("let pos = ", stringify!($Ty), "::new(1)?;")]
+                #[doc = concat!("let neg = ", stringify!($Ty), "::new(-1)?;")]
+                ///
+                /// assert_eq!(pos, pos.abs());
+                /// assert_eq!(pos, neg.abs());
+                /// # Some(())
+                /// # }
+                /// ```
+                #[stable(feature = "nonzero_checked_ops", since = "1.64.0")]
+                #[rustc_const_stable(feature = "const_nonzero_checked_ops", since = "1.64.0")]
+                #[must_use = "this returns the result of the operation, \
+                              without modifying the original"]
+                #[inline]
+                pub const fn abs(self) -> $Ty {
+                    // SAFETY: This cannot overflow to zero.
+                    unsafe { $Ty::new_unchecked(self.get().abs()) }
+                }
+
+                /// Checked absolute value.
+                /// Check for overflow and returns [`None`] if
+                #[doc = concat!("`self == ", stringify!($Int), "::MIN`.")]
+                /// The result cannot be zero.
+                ///
+                /// # Example
+                ///
+                /// ```
+                #[doc = concat!("# use std::num::", stringify!($Ty), ";")]
+                ///
+                /// # fn main() { test().unwrap(); }
+                /// # fn test() -> Option<()> {
+                #[doc = concat!("let pos = ", stringify!($Ty), "::new(1)?;")]
+                #[doc = concat!("let neg = ", stringify!($Ty), "::new(-1)?;")]
+                #[doc = concat!("let min = ", stringify!($Ty), "::new(",
+                                stringify!($Int), "::MIN)?;")]
+                ///
+                /// assert_eq!(Some(pos), neg.checked_abs());
+                /// assert_eq!(None, min.checked_abs());
+                /// # Some(())
+                /// # }
+                /// ```
+                #[stable(feature = "nonzero_checked_ops", since = "1.64.0")]
+                #[rustc_const_stable(feature = "const_nonzero_checked_ops", since = "1.64.0")]
+                #[must_use = "this returns the result of the operation, \
+                              without modifying the original"]
+                #[inline]
+                pub const fn checked_abs(self) -> Option<$Ty> {
+                    if let Some(nz) = self.get().checked_abs() {
+                        // SAFETY: absolute value of nonzero cannot yield zero values.
+                        Some(unsafe { $Ty::new_unchecked(nz) })
+                    } else {
+                        None
+                    }
+                }
+
+                /// Computes the absolute value of self,
+                /// with overflow information, see
+                #[doc = concat!("[`", stringify!($Int), "::overflowing_abs`].")]
+                ///
+                /// # Example
+                ///
+                /// ```
+                #[doc = concat!("# use std::num::", stringify!($Ty), ";")]
+                ///
+                /// # fn main() { test().unwrap(); }
+                /// # fn test() -> Option<()> {
+                #[doc = concat!("let pos = ", stringify!($Ty), "::new(1)?;")]
+                #[doc = concat!("let neg = ", stringify!($Ty), "::new(-1)?;")]
+                #[doc = concat!("let min = ", stringify!($Ty), "::new(",
+                                stringify!($Int), "::MIN)?;")]
+                ///
+                /// assert_eq!((pos, false), pos.overflowing_abs());
+                /// assert_eq!((pos, false), neg.overflowing_abs());
+                /// assert_eq!((min, true), min.overflowing_abs());
+                /// # Some(())
+                /// # }
+                /// ```
+                #[stable(feature = "nonzero_checked_ops", since = "1.64.0")]
+                #[rustc_const_stable(feature = "const_nonzero_checked_ops", since = "1.64.0")]
+                #[must_use = "this returns the result of the operation, \
+                              without modifying the original"]
+                #[inline]
+                pub const fn overflowing_abs(self) -> ($Ty, bool) {
+                    let (nz, flag) = self.get().overflowing_abs();
+                    (
+                        // SAFETY: absolute value of nonzero cannot yield zero values.
+                        unsafe { $Ty::new_unchecked(nz) },
+                        flag,
+                    )
+                }
+
+                /// Saturating absolute value, see
+                #[doc = concat!("[`", stringify!($Int), "::saturating_abs`].")]
+                ///
+                /// # Example
+                ///
+                /// ```
+                #[doc = concat!("# use std::num::", stringify!($Ty), ";")]
+                ///
+                /// # fn main() { test().unwrap(); }
+                /// # fn test() -> Option<()> {
+                #[doc = concat!("let pos = ", stringify!($Ty), "::new(1)?;")]
+                #[doc = concat!("let neg = ", stringify!($Ty), "::new(-1)?;")]
+                #[doc = concat!("let min = ", stringify!($Ty), "::new(",
+                                stringify!($Int), "::MIN)?;")]
+                #[doc = concat!("let min_plus = ", stringify!($Ty), "::new(",
+                                stringify!($Int), "::MIN + 1)?;")]
+                #[doc = concat!("let max = ", stringify!($Ty), "::new(",
+                                stringify!($Int), "::MAX)?;")]
+                ///
+                /// assert_eq!(pos, pos.saturating_abs());
+                /// assert_eq!(pos, neg.saturating_abs());
+                /// assert_eq!(max, min.saturating_abs());
+                /// assert_eq!(max, min_plus.saturating_abs());
+                /// # Some(())
+                /// # }
+                /// ```
+                #[stable(feature = "nonzero_checked_ops", since = "1.64.0")]
+                #[rustc_const_stable(feature = "const_nonzero_checked_ops", since = "1.64.0")]
+                #[must_use = "this returns the result of the operation, \
+                              without modifying the original"]
+                #[inline]
+                pub const fn saturating_abs(self) -> $Ty {
+                    // SAFETY: absolute value of nonzero cannot yield zero values.
+                    unsafe { $Ty::new_unchecked(self.get().saturating_abs()) }
+                }
+
+                /// Wrapping absolute value, see
+                #[doc = concat!("[`", stringify!($Int), "::wrapping_abs`].")]
+                ///
+                /// # Example
+                ///
+                /// ```
+                #[doc = concat!("# use std::num::", stringify!($Ty), ";")]
+                ///
+                /// # fn main() { test().unwrap(); }
+                /// # fn test() -> Option<()> {
+                #[doc = concat!("let pos = ", stringify!($Ty), "::new(1)?;")]
+                #[doc = concat!("let neg = ", stringify!($Ty), "::new(-1)?;")]
+                #[doc = concat!("let min = ", stringify!($Ty), "::new(",
+                                stringify!($Int), "::MIN)?;")]
+                #[doc = concat!("let max = ", stringify!($Ty), "::new(",
+                                stringify!($Int), "::MAX)?;")]
+                ///
+                /// assert_eq!(pos, pos.wrapping_abs());
+                /// assert_eq!(pos, neg.wrapping_abs());
+                /// assert_eq!(min, min.wrapping_abs());
+                /// # // FIXME: add once Neg is implemented?
+                /// # // assert_eq!(max, (-max).wrapping_abs());
+                /// # Some(())
+                /// # }
+                /// ```
+                #[stable(feature = "nonzero_checked_ops", since = "1.64.0")]
+                #[rustc_const_stable(feature = "const_nonzero_checked_ops", since = "1.64.0")]
+                #[must_use = "this returns the result of the operation, \
+                              without modifying the original"]
+                #[inline]
+                pub const fn wrapping_abs(self) -> $Ty {
+                    // SAFETY: absolute value of nonzero cannot yield zero values.
+                    unsafe { $Ty::new_unchecked(self.get().wrapping_abs()) }
+                }
+
+                /// Computes the absolute value of self
+                /// without any wrapping or panicking.
+                ///
+                /// # Example
+                ///
+                /// ```
+                #[doc = concat!("# use std::num::", stringify!($Ty), ";")]
+                #[doc = concat!("# use std::num::", stringify!($Uty), ";")]
+                ///
+                /// # fn main() { test().unwrap(); }
+                /// # fn test() -> Option<()> {
+                #[doc = concat!("let u_pos = ", stringify!($Uty), "::new(1)?;")]
+                #[doc = concat!("let i_pos = ", stringify!($Ty), "::new(1)?;")]
+                #[doc = concat!("let i_neg = ", stringify!($Ty), "::new(-1)?;")]
+                #[doc = concat!("let i_min = ", stringify!($Ty), "::new(",
+                                stringify!($Int), "::MIN)?;")]
+                #[doc = concat!("let u_max = ", stringify!($Uty), "::new(",
+                                stringify!($Uint), "::MAX / 2 + 1)?;")]
+                ///
+                /// assert_eq!(u_pos, i_pos.unsigned_abs());
+                /// assert_eq!(u_pos, i_neg.unsigned_abs());
+                /// assert_eq!(u_max, i_min.unsigned_abs());
+                /// # Some(())
+                /// # }
+                /// ```
+                #[stable(feature = "nonzero_checked_ops", since = "1.64.0")]
+                #[rustc_const_stable(feature = "const_nonzero_checked_ops", since = "1.64.0")]
+                #[must_use = "this returns the result of the operation, \
+                              without modifying the original"]
+                #[inline]
+                pub const fn unsigned_abs(self) -> $Uty {
+                    // SAFETY: absolute value of nonzero cannot yield zero values.
+                    unsafe { $Uty::new_unchecked(self.get().unsigned_abs()) }
+                }
+            }
+        )+
+    }
+}
+
+nonzero_signed_operations! {
+    NonZeroI8(i8) -> NonZeroU8(u8);
+    NonZeroI16(i16) -> NonZeroU16(u16);
+    NonZeroI32(i32) -> NonZeroU32(u32);
+    NonZeroI64(i64) -> NonZeroU64(u64);
+    NonZeroI128(i128) -> NonZeroU128(u128);
+    NonZeroIsize(isize) -> NonZeroUsize(usize);
+}
+
+// A bunch of methods for both signed and unsigned nonzero types.
+macro_rules! nonzero_unsigned_signed_operations {
+    ( $( $signedness:ident $Ty: ident($Int: ty); )+ ) => {
+        $(
+            impl $Ty {
+                /// Multiply two non-zero integers together.
+                /// Check for overflow and return [`None`] on overflow.
+                /// As a consequence, the result cannot wrap to zero.
+                ///
+                /// # Examples
+                ///
+                /// ```
+                #[doc = concat!("# use std::num::", stringify!($Ty), ";")]
+                ///
+                /// # fn main() { test().unwrap(); }
+                /// # fn test() -> Option<()> {
+                #[doc = concat!("let two = ", stringify!($Ty), "::new(2)?;")]
+                #[doc = concat!("let four = ", stringify!($Ty), "::new(4)?;")]
+                #[doc = concat!("let max = ", stringify!($Ty), "::new(",
+                                stringify!($Int), "::MAX)?;")]
+                ///
+                /// assert_eq!(Some(four), two.checked_mul(two));
+                /// assert_eq!(None, max.checked_mul(two));
+                /// # Some(())
+                /// # }
+                /// ```
+                #[stable(feature = "nonzero_checked_ops", since = "1.64.0")]
+                #[rustc_const_stable(feature = "const_nonzero_checked_ops", since = "1.64.0")]
+                #[must_use = "this returns the result of the operation, \
+                              without modifying the original"]
+                #[inline]
+                pub const fn checked_mul(self, other: $Ty) -> Option<$Ty> {
+                    if let Some(result) = self.get().checked_mul(other.get()) {
+                        // SAFETY: checked_mul returns None on overflow
+                        // and `other` is also non-null
+                        // so the result cannot be zero.
+                        Some(unsafe { $Ty::new_unchecked(result) })
+                    } else {
+                        None
+                    }
+                }
+
+                /// Multiply two non-zero integers together.
+                #[doc = concat!("Return [`", stringify!($Int), "::MAX`] on overflow.")]
+                ///
+                /// # Examples
+                ///
+                /// ```
+                #[doc = concat!("# use std::num::", stringify!($Ty), ";")]
+                ///
+                /// # fn main() { test().unwrap(); }
+                /// # fn test() -> Option<()> {
+                #[doc = concat!("let two = ", stringify!($Ty), "::new(2)?;")]
+                #[doc = concat!("let four = ", stringify!($Ty), "::new(4)?;")]
+                #[doc = concat!("let max = ", stringify!($Ty), "::new(",
+                                stringify!($Int), "::MAX)?;")]
+                ///
+                /// assert_eq!(four, two.saturating_mul(two));
+                /// assert_eq!(max, four.saturating_mul(max));
+                /// # Some(())
+                /// # }
+                /// ```
+                #[stable(feature = "nonzero_checked_ops", since = "1.64.0")]
+                #[rustc_const_stable(feature = "const_nonzero_checked_ops", since = "1.64.0")]
+                #[must_use = "this returns the result of the operation, \
+                              without modifying the original"]
+                #[inline]
+                pub const fn saturating_mul(self, other: $Ty) -> $Ty {
+                    // SAFETY: saturating_mul returns u*::MAX on overflow
+                    // and `other` is also non-null
+                    // so the result cannot be zero.
+                    unsafe { $Ty::new_unchecked(self.get().saturating_mul(other.get())) }
+                }
+
+                /// Multiply two non-zero integers together,
+                /// assuming overflow cannot occur.
+                /// Overflow is unchecked, and it is undefined behaviour to overflow
+                /// *even if the result would wrap to a non-zero value*.
+                /// The behaviour is undefined as soon as
+                #[doc = sign_dependent_expr!{
+                    $signedness ?
+                    if signed {
+                        concat!("`self * rhs > ", stringify!($Int), "::MAX`, ",
+                                "or `self * rhs < ", stringify!($Int), "::MIN`.")
+                    }
+                    if unsigned {
+                        concat!("`self * rhs > ", stringify!($Int), "::MAX`.")
+                    }
+                }]
+                ///
+                /// # Examples
+                ///
+                /// ```
+                /// #![feature(nonzero_ops)]
+                #[doc = concat!("# use std::num::", stringify!($Ty), ";")]
+                ///
+                /// # fn main() { test().unwrap(); }
+                /// # fn test() -> Option<()> {
+                #[doc = concat!("let two = ", stringify!($Ty), "::new(2)?;")]
+                #[doc = concat!("let four = ", stringify!($Ty), "::new(4)?;")]
+                ///
+                /// assert_eq!(four, unsafe { two.unchecked_mul(two) });
+                /// # Some(())
+                /// # }
+                /// ```
+                #[unstable(feature = "nonzero_ops", issue = "84186")]
+                #[must_use = "this returns the result of the operation, \
+                              without modifying the original"]
+                #[inline]
+                pub const unsafe fn unchecked_mul(self, other: $Ty) -> $Ty {
+                    // SAFETY: The caller ensures there is no overflow.
+                    unsafe { $Ty::new_unchecked(self.get().unchecked_mul(other.get())) }
+                }
+
+                /// Raise non-zero value to an integer power.
+                /// Check for overflow and return [`None`] on overflow.
+                /// As a consequence, the result cannot wrap to zero.
+                ///
+                /// # Examples
+                ///
+                /// ```
+                #[doc = concat!("# use std::num::", stringify!($Ty), ";")]
+                ///
+                /// # fn main() { test().unwrap(); }
+                /// # fn test() -> Option<()> {
+                #[doc = concat!("let three = ", stringify!($Ty), "::new(3)?;")]
+                #[doc = concat!("let twenty_seven = ", stringify!($Ty), "::new(27)?;")]
+                #[doc = concat!("let half_max = ", stringify!($Ty), "::new(",
+                                stringify!($Int), "::MAX / 2)?;")]
+                ///
+                /// assert_eq!(Some(twenty_seven), three.checked_pow(3));
+                /// assert_eq!(None, half_max.checked_pow(3));
+                /// # Some(())
+                /// # }
+                /// ```
+                #[stable(feature = "nonzero_checked_ops", since = "1.64.0")]
+                #[rustc_const_stable(feature = "const_nonzero_checked_ops", since = "1.64.0")]
+                #[must_use = "this returns the result of the operation, \
+                              without modifying the original"]
+                #[inline]
+                pub const fn checked_pow(self, other: u32) -> Option<$Ty> {
+                    if let Some(result) = self.get().checked_pow(other) {
+                        // SAFETY: checked_pow returns None on overflow
+                        // so the result cannot be zero.
+                        Some(unsafe { $Ty::new_unchecked(result) })
+                    } else {
+                        None
+                    }
+                }
+
+                /// Raise non-zero value to an integer power.
+                #[doc = sign_dependent_expr!{
+                    $signedness ?
+                    if signed {
+                        concat!("Return [`", stringify!($Int), "::MIN`] ",
+                                    "or [`", stringify!($Int), "::MAX`] on overflow.")
+                    }
+                    if unsigned {
+                        concat!("Return [`", stringify!($Int), "::MAX`] on overflow.")
+                    }
+                }]
+                ///
+                /// # Examples
+                ///
+                /// ```
+                #[doc = concat!("# use std::num::", stringify!($Ty), ";")]
+                ///
+                /// # fn main() { test().unwrap(); }
+                /// # fn test() -> Option<()> {
+                #[doc = concat!("let three = ", stringify!($Ty), "::new(3)?;")]
+                #[doc = concat!("let twenty_seven = ", stringify!($Ty), "::new(27)?;")]
+                #[doc = concat!("let max = ", stringify!($Ty), "::new(",
+                                stringify!($Int), "::MAX)?;")]
+                ///
+                /// assert_eq!(twenty_seven, three.saturating_pow(3));
+                /// assert_eq!(max, max.saturating_pow(3));
+                /// # Some(())
+                /// # }
+                /// ```
+                #[stable(feature = "nonzero_checked_ops", since = "1.64.0")]
+                #[rustc_const_stable(feature = "const_nonzero_checked_ops", since = "1.64.0")]
+                #[must_use = "this returns the result of the operation, \
+                              without modifying the original"]
+                #[inline]
+                pub const fn saturating_pow(self, other: u32) -> $Ty {
+                    // SAFETY: saturating_pow returns u*::MAX on overflow
+                    // so the result cannot be zero.
+                    unsafe { $Ty::new_unchecked(self.get().saturating_pow(other)) }
+                }
+            }
+        )+
+    }
+}
+
+// Use this when the generated code should differ between signed and unsigned types.
+macro_rules! sign_dependent_expr {
+    (signed ? if signed { $signed_case:expr } if unsigned { $unsigned_case:expr } ) => {
+        $signed_case
+    };
+    (unsigned ? if signed { $signed_case:expr } if unsigned { $unsigned_case:expr } ) => {
+        $unsigned_case
+    };
+}
+
+nonzero_unsigned_signed_operations! {
+    unsigned NonZeroU8(u8);
+    unsigned NonZeroU16(u16);
+    unsigned NonZeroU32(u32);
+    unsigned NonZeroU64(u64);
+    unsigned NonZeroU128(u128);
+    unsigned NonZeroUsize(usize);
+    signed NonZeroI8(i8);
+    signed NonZeroI16(i16);
+    signed NonZeroI32(i32);
+    signed NonZeroI64(i64);
+    signed NonZeroI128(i128);
+    signed NonZeroIsize(isize);
+}
+
+macro_rules! nonzero_unsigned_is_power_of_two {
+    ( $( $Ty: ident )+ ) => {
+        $(
+            impl $Ty {
+
+                /// Returns `true` if and only if `self == (1 << k)` for some `k`.
+                ///
+                /// On many architectures, this function can perform better than `is_power_of_two()`
+                /// on the underlying integer type, as special handling of zero can be avoided.
+                ///
+                /// # Examples
+                ///
+                /// Basic usage:
+                ///
+                /// ```
+                #[doc = concat!("let eight = std::num::", stringify!($Ty), "::new(8).unwrap();")]
+                /// assert!(eight.is_power_of_two());
+                #[doc = concat!("let ten = std::num::", stringify!($Ty), "::new(10).unwrap();")]
+                /// assert!(!ten.is_power_of_two());
+                /// ```
+                #[must_use]
+                #[stable(feature = "nonzero_is_power_of_two", since = "1.59.0")]
+                #[rustc_const_stable(feature = "nonzero_is_power_of_two", since = "1.59.0")]
+                #[inline]
+                pub const fn is_power_of_two(self) -> bool {
+                    // LLVM 11 normalizes `unchecked_sub(x, 1) & x == 0` to the implementation seen here.
+                    // On the basic x86-64 target, this saves 3 instructions for the zero check.
+                    // On x86_64 with BMI1, being nonzero lets it codegen to `BLSR`, which saves an instruction
+                    // compared to the `POPCNT` implementation on the underlying integer type.
+
+                    intrinsics::ctpop(self.get()) < 2
+                }
+
+            }
+        )+
+    }
+}
+
+nonzero_unsigned_is_power_of_two! { NonZeroU8 NonZeroU16 NonZeroU32 NonZeroU64 NonZeroU128 NonZeroUsize }
+
+macro_rules! nonzero_min_max_unsigned {
+    ( $( $Ty: ident($Int: ident); )+ ) => {
+        $(
+            impl $Ty {
+                /// The smallest value that can be represented by this non-zero
+                /// integer type, 1.
+                ///
+                /// # Examples
+                ///
+                /// ```
+                /// #![feature(nonzero_min_max)]
+                #[doc = concat!("# use std::num::", stringify!($Ty), ";")]
+                ///
+                #[doc = concat!("assert_eq!(", stringify!($Ty), "::MIN.get(), 1", stringify!($Int), ");")]
+                /// ```
+                #[unstable(feature = "nonzero_min_max", issue = "89065")]
+                pub const MIN: Self = Self::new(1).unwrap();
+
+                /// The largest value that can be represented by this non-zero
+                /// integer type,
+                #[doc = concat!("equal to [`", stringify!($Int), "::MAX`].")]
+                ///
+                /// # Examples
+                ///
+                /// ```
+                /// #![feature(nonzero_min_max)]
+                #[doc = concat!("# use std::num::", stringify!($Ty), ";")]
+                ///
+                #[doc = concat!("assert_eq!(", stringify!($Ty), "::MAX.get(), ", stringify!($Int), "::MAX);")]
+                /// ```
+                #[unstable(feature = "nonzero_min_max", issue = "89065")]
+                pub const MAX: Self = Self::new(<$Int>::MAX).unwrap();
+            }
+        )+
+    }
+}
+
+macro_rules! nonzero_min_max_signed {
+    ( $( $Ty: ident($Int: ident); )+ ) => {
+        $(
+            impl $Ty {
+                /// The smallest value that can be represented by this non-zero
+                /// integer type,
+                #[doc = concat!("equal to [`", stringify!($Int), "::MIN`].")]
+                ///
+                /// Note: While most integer types are defined for every whole
+                /// number between `MIN` and `MAX`, signed non-zero integers are
+                /// a special case. They have a "gap" at 0.
+                ///
+                /// # Examples
+                ///
+                /// ```
+                /// #![feature(nonzero_min_max)]
+                #[doc = concat!("# use std::num::", stringify!($Ty), ";")]
+                ///
+                #[doc = concat!("assert_eq!(", stringify!($Ty), "::MIN.get(), ", stringify!($Int), "::MIN);")]
+                /// ```
+                #[unstable(feature = "nonzero_min_max", issue = "89065")]
+                pub const MIN: Self = Self::new(<$Int>::MIN).unwrap();
+
+                /// The largest value that can be represented by this non-zero
+                /// integer type,
+                #[doc = concat!("equal to [`", stringify!($Int), "::MAX`].")]
+                ///
+                /// Note: While most integer types are defined for every whole
+                /// number between `MIN` and `MAX`, signed non-zero integers are
+                /// a special case. They have a "gap" at 0.
+                ///
+                /// # Examples
+                ///
+                /// ```
+                /// #![feature(nonzero_min_max)]
+                #[doc = concat!("# use std::num::", stringify!($Ty), ";")]
+                ///
+                #[doc = concat!("assert_eq!(", stringify!($Ty), "::MAX.get(), ", stringify!($Int), "::MAX);")]
+                /// ```
+                #[unstable(feature = "nonzero_min_max", issue = "89065")]
+                pub const MAX: Self = Self::new(<$Int>::MAX).unwrap();
+            }
+        )+
+    }
+}
+
+nonzero_min_max_unsigned! {
+    NonZeroU8(u8);
+    NonZeroU16(u16);
+    NonZeroU32(u32);
+    NonZeroU64(u64);
+    NonZeroU128(u128);
+    NonZeroUsize(usize);
+}
+
+nonzero_min_max_signed! {
+    NonZeroI8(i8);
+    NonZeroI16(i16);
+    NonZeroI32(i32);
+    NonZeroI64(i64);
+    NonZeroI128(i128);
+    NonZeroIsize(isize);
+}
+
+macro_rules! nonzero_bits {
+    ( $( $Ty: ident($Int: ty); )+ ) => {
+        $(
+            impl $Ty {
+                /// The size of this non-zero integer type in bits.
+                ///
+                #[doc = concat!("This value is equal to [`", stringify!($Int), "::BITS`].")]
+                ///
+                /// # Examples
+                ///
+                /// ```
+                /// #![feature(nonzero_bits)]
+                #[doc = concat!("# use std::num::", stringify!($Ty), ";")]
+                ///
+                #[doc = concat!("assert_eq!(", stringify!($Ty), "::BITS, ", stringify!($Int), "::BITS);")]
+                /// ```
+                #[unstable(feature = "nonzero_bits", issue = "94881")]
+                pub const BITS: u32 = <$Int>::BITS;
+            }
+        )+
+    }
+}
+
+nonzero_bits! {
+    NonZeroU8(u8);
+    NonZeroI8(i8);
+    NonZeroU16(u16);
+    NonZeroI16(i16);
+    NonZeroU32(u32);
+    NonZeroI32(i32);
+    NonZeroU64(u64);
+    NonZeroI64(i64);
+    NonZeroU128(u128);
+    NonZeroI128(i128);
+    NonZeroUsize(usize);
+    NonZeroIsize(isize);
+}
diff --git a/library/core/src/num/saturating.rs b/library/core/src/num/saturating.rs
new file mode 100644
index 000000000..8982473b2
--- /dev/null
+++ b/library/core/src/num/saturating.rs
@@ -0,0 +1,1081 @@
+//! Definitions of `Saturating<T>`.
+
+use crate::fmt;
+use crate::ops::{Add, AddAssign, BitAnd, BitAndAssign, BitOr, BitOrAssign};
+use crate::ops::{BitXor, BitXorAssign, Div, DivAssign};
+use crate::ops::{Mul, MulAssign, Neg, Not, Rem, RemAssign};
+use crate::ops::{Shl, ShlAssign, Shr, ShrAssign, Sub, SubAssign};
+
+/// Provides intentionally-saturating arithmetic on `T`.
+///
+/// Operations like `+` on `u32` values are intended to never overflow,
+/// and in some debug configurations overflow is detected and results
+/// in a panic. While most arithmetic falls into this category, some
+/// code explicitly expects and relies upon saturating arithmetic.
+///
+/// Saturating arithmetic can be achieved either through methods like
+/// `saturating_add`, or through the `Saturating<T>` type, which says that
+/// all standard arithmetic operations on the underlying value are
+/// intended to have saturating semantics.
+///
+/// The underlying value can be retrieved through the `.0` index of the
+/// `Saturating` tuple.
+///
+/// # Examples
+///
+/// ```
+/// #![feature(saturating_int_impl)]
+/// use std::num::Saturating;
+///
+/// let max = Saturating(u32::MAX);
+/// let one = Saturating(1u32);
+///
+/// assert_eq!(u32::MAX, (max + one).0);
+/// ```
+#[unstable(feature = "saturating_int_impl", issue = "87920")]
+#[derive(PartialEq, Eq, PartialOrd, Ord, Clone, Copy, Default, Hash)]
+#[repr(transparent)]
+pub struct Saturating<T>(#[unstable(feature = "saturating_int_impl", issue = "87920")] pub T);
+
+#[unstable(feature = "saturating_int_impl", issue = "87920")]
+impl<T: fmt::Debug> fmt::Debug for Saturating<T> {
+    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
+        self.0.fmt(f)
+    }
+}
+
+#[unstable(feature = "saturating_int_impl", issue = "87920")]
+impl<T: fmt::Display> fmt::Display for Saturating<T> {
+    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
+        self.0.fmt(f)
+    }
+}
+
+#[unstable(feature = "saturating_int_impl", issue = "87920")]
+impl<T: fmt::Binary> fmt::Binary for Saturating<T> {
+    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
+        self.0.fmt(f)
+    }
+}
+
+#[unstable(feature = "saturating_int_impl", issue = "87920")]
+impl<T: fmt::Octal> fmt::Octal for Saturating<T> {
+    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
+        self.0.fmt(f)
+    }
+}
+
+#[unstable(feature = "saturating_int_impl", issue = "87920")]
+impl<T: fmt::LowerHex> fmt::LowerHex for Saturating<T> {
+    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
+        self.0.fmt(f)
+    }
+}
+
+#[unstable(feature = "saturating_int_impl", issue = "87920")]
+impl<T: fmt::UpperHex> fmt::UpperHex for Saturating<T> {
+    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
+        self.0.fmt(f)
+    }
+}
+#[allow(unused_macros)]
+macro_rules! sh_impl_signed {
+    ($t:ident, $f:ident) => {
+        // FIXME what is the correct implementation here? see discussion https://github.com/rust-lang/rust/pull/87921#discussion_r695870065
+        //
+        // #[unstable(feature = "saturating_int_impl", issue = "87920")]
+        // impl Shl<$f> for Saturating<$t> {
+        //     type Output = Saturating<$t>;
+        //
+        //     #[inline]
+        //     fn shl(self, other: $f) -> Saturating<$t> {
+        //         if other < 0 {
+        //             Saturating(self.0.shr((-other & self::shift_max::$t as $f) as u32))
+        //         } else {
+        //             Saturating(self.0.shl((other & self::shift_max::$t as $f) as u32))
+        //         }
+        //     }
+        // }
+        // forward_ref_binop! { impl Shl, shl for Saturating<$t>, $f,
+        // #[unstable(feature = "saturating_int_impl", issue = "87920")] }
+        //
+        // #[unstable(feature = "saturating_int_impl", issue = "87920")]
+        // impl ShlAssign<$f> for Saturating<$t> {
+        //     #[inline]
+        //     fn shl_assign(&mut self, other: $f) {
+        //         *self = *self << other;
+        //     }
+        // }
+        // forward_ref_op_assign! { impl ShlAssign, shl_assign for Saturating<$t>, $f }
+
+        #[unstable(feature = "saturating_int_impl", issue = "87920")]
+        impl Shr<$f> for Saturating<$t> {
+            type Output = Saturating<$t>;
+
+            #[inline]
+            fn shr(self, other: $f) -> Saturating<$t> {
+                if other < 0 {
+                    Saturating(self.0.shl((-other & self::shift_max::$t as $f) as u32))
+                } else {
+                    Saturating(self.0.shr((other & self::shift_max::$t as $f) as u32))
+                }
+            }
+        }
+        forward_ref_binop! { impl Shr, shr for Saturating<$t>, $f,
+        #[unstable(feature = "saturating_int_impl", issue = "87920")] }
+
+        #[unstable(feature = "saturating_int_impl", issue = "87920")]
+        impl ShrAssign<$f> for Saturating<$t> {
+            #[inline]
+            fn shr_assign(&mut self, other: $f) {
+                *self = *self >> other;
+            }
+        }
+        forward_ref_op_assign! { impl ShrAssign, shr_assign for Saturating<$t>, $f }
+    };
+}
+
+macro_rules! sh_impl_unsigned {
+    ($t:ident, $f:ident) => {
+        #[unstable(feature = "saturating_int_impl", issue = "87920")]
+        impl Shl<$f> for Saturating<$t> {
+            type Output = Saturating<$t>;
+
+            #[inline]
+            fn shl(self, other: $f) -> Saturating<$t> {
+                Saturating(self.0.wrapping_shl(other as u32))
+            }
+        }
+        forward_ref_binop! { impl Shl, shl for Saturating<$t>, $f,
+        #[unstable(feature = "saturating_int_impl", issue = "87920")] }
+
+        #[unstable(feature = "saturating_int_impl", issue = "87920")]
+        impl ShlAssign<$f> for Saturating<$t> {
+            #[inline]
+            fn shl_assign(&mut self, other: $f) {
+                *self = *self << other;
+            }
+        }
+        forward_ref_op_assign! { impl ShlAssign, shl_assign for Saturating<$t>, $f }
+
+        #[unstable(feature = "saturating_int_impl", issue = "87920")]
+        impl Shr<$f> for Saturating<$t> {
+            type Output = Saturating<$t>;
+
+            #[inline]
+            fn shr(self, other: $f) -> Saturating<$t> {
+                Saturating(self.0.wrapping_shr(other as u32))
+            }
+        }
+        forward_ref_binop! { impl Shr, shr for Saturating<$t>, $f,
+        #[unstable(feature = "saturating_int_impl", issue = "87920")] }
+
+        #[unstable(feature = "saturating_int_impl", issue = "87920")]
+        impl ShrAssign<$f> for Saturating<$t> {
+            #[inline]
+            fn shr_assign(&mut self, other: $f) {
+                *self = *self >> other;
+            }
+        }
+        forward_ref_op_assign! { impl ShrAssign, shr_assign for Saturating<$t>, $f }
+    };
+}
+
+// FIXME (#23545): uncomment the remaining impls
+macro_rules! sh_impl_all {
+    ($($t:ident)*) => ($(
+        //sh_impl_unsigned! { $t, u8 }
+        //sh_impl_unsigned! { $t, u16 }
+        //sh_impl_unsigned! { $t, u32 }
+        //sh_impl_unsigned! { $t, u64 }
+        //sh_impl_unsigned! { $t, u128 }
+        sh_impl_unsigned! { $t, usize }
+
+        //sh_impl_signed! { $t, i8 }
+        //sh_impl_signed! { $t, i16 }
+        //sh_impl_signed! { $t, i32 }
+        //sh_impl_signed! { $t, i64 }
+        //sh_impl_signed! { $t, i128 }
+        //sh_impl_signed! { $t, isize }
+    )*)
+}
+
+sh_impl_all! { u8 u16 u32 u64 u128 usize i8 i16 i32 i64 i128 isize }
+
+// FIXME(30524): impl Op<T> for Saturating<T>, impl OpAssign<T> for Saturating<T>
+macro_rules! saturating_impl {
+    ($($t:ty)*) => ($(
+        #[unstable(feature = "saturating_int_impl", issue = "87920")]
+        impl Add for Saturating<$t> {
+            type Output = Saturating<$t>;
+
+            #[inline]
+            fn add(self, other: Saturating<$t>) -> Saturating<$t> {
+                Saturating(self.0.saturating_add(other.0))
+            }
+        }
+        forward_ref_binop! { impl Add, add for Saturating<$t>, Saturating<$t>,
+                #[unstable(feature = "saturating_int_impl", issue = "87920")] }
+
+        #[unstable(feature = "saturating_int_impl", issue = "87920")]
+        impl AddAssign for Saturating<$t> {
+            #[inline]
+            fn add_assign(&mut self, other: Saturating<$t>) {
+                *self = *self + other;
+            }
+        }
+        forward_ref_op_assign! { impl AddAssign, add_assign for Saturating<$t>, Saturating<$t> }
+
+        #[unstable(feature = "saturating_int_assign_impl", issue = "92354")]
+        impl AddAssign<$t> for Saturating<$t> {
+            #[inline]
+            fn add_assign(&mut self, other: $t) {
+                *self = *self + Saturating(other);
+            }
+        }
+        forward_ref_op_assign! { impl AddAssign, add_assign for Saturating<$t>, $t }
+
+        #[unstable(feature = "saturating_int_impl", issue = "87920")]
+        impl Sub for Saturating<$t> {
+            type Output = Saturating<$t>;
+
+            #[inline]
+            fn sub(self, other: Saturating<$t>) -> Saturating<$t> {
+                Saturating(self.0.saturating_sub(other.0))
+            }
+        }
+        forward_ref_binop! { impl Sub, sub for Saturating<$t>, Saturating<$t>,
+                #[unstable(feature = "saturating_int_impl", issue = "87920")] }
+
+        #[unstable(feature = "saturating_int_impl", issue = "87920")]
+        impl SubAssign for Saturating<$t> {
+            #[inline]
+            fn sub_assign(&mut self, other: Saturating<$t>) {
+                *self = *self - other;
+            }
+        }
+        forward_ref_op_assign! { impl SubAssign, sub_assign for Saturating<$t>, Saturating<$t> }
+
+        #[unstable(feature = "saturating_int_assign_impl", issue = "92354")]
+        impl SubAssign<$t> for Saturating<$t> {
+            #[inline]
+            fn sub_assign(&mut self, other: $t) {
+                *self = *self - Saturating(other);
+            }
+        }
+        forward_ref_op_assign! { impl SubAssign, sub_assign for Saturating<$t>, $t }
+
+        #[unstable(feature = "saturating_int_impl", issue = "87920")]
+        impl Mul for Saturating<$t> {
+            type Output = Saturating<$t>;
+
+            #[inline]
+            fn mul(self, other: Saturating<$t>) -> Saturating<$t> {
+                Saturating(self.0.saturating_mul(other.0))
+            }
+        }
+        forward_ref_binop! { impl Mul, mul for Saturating<$t>, Saturating<$t>,
+                #[unstable(feature = "saturating_int_impl", issue = "87920")] }
+
+        #[unstable(feature = "saturating_int_impl", issue = "87920")]
+        impl MulAssign for Saturating<$t> {
+            #[inline]
+            fn mul_assign(&mut self, other: Saturating<$t>) {
+                *self = *self * other;
+            }
+        }
+        forward_ref_op_assign! { impl MulAssign, mul_assign for Saturating<$t>, Saturating<$t> }
+
+        #[unstable(feature = "saturating_int_assign_impl", issue = "92354")]
+        impl MulAssign<$t> for Saturating<$t> {
+            #[inline]
+            fn mul_assign(&mut self, other: $t) {
+                *self = *self * Saturating(other);
+            }
+        }
+        forward_ref_op_assign! { impl MulAssign, mul_assign for Saturating<$t>, $t }
+
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        /// #![feature(saturating_int_impl)]
+        /// use std::num::Saturating;
+        ///
+        #[doc = concat!("assert_eq!(Saturating(2", stringify!($t), "), Saturating(5", stringify!($t), ") / Saturating(2));")]
+        #[doc = concat!("assert_eq!(Saturating(", stringify!($t), "::MAX), Saturating(", stringify!($t), "::MAX) / Saturating(1));")]
+        #[doc = concat!("assert_eq!(Saturating(", stringify!($t), "::MIN), Saturating(", stringify!($t), "::MIN) / Saturating(1));")]
+        /// ```
+        ///
+        /// ```should_panic
+        /// #![feature(saturating_int_impl)]
+        /// use std::num::Saturating;
+        ///
+        #[doc = concat!("let _ = Saturating(0", stringify!($t), ") / Saturating(0);")]
+        /// ```
+        #[unstable(feature = "saturating_int_impl", issue = "87920")]
+        impl Div for Saturating<$t> {
+            type Output = Saturating<$t>;
+
+            #[inline]
+            fn div(self, other: Saturating<$t>) -> Saturating<$t> {
+                Saturating(self.0.saturating_div(other.0))
+            }
+        }
+        forward_ref_binop! { impl Div, div for Saturating<$t>, Saturating<$t>,
+                #[unstable(feature = "saturating_int_impl", issue = "87920")] }
+
+
+        #[unstable(feature = "saturating_int_impl", issue = "87920")]
+        impl DivAssign for Saturating<$t> {
+            #[inline]
+            fn div_assign(&mut self, other: Saturating<$t>) {
+                *self = *self / other;
+            }
+        }
+        forward_ref_op_assign! { impl DivAssign, div_assign for Saturating<$t>, Saturating<$t> }
+
+        #[unstable(feature = "saturating_int_assign_impl", issue = "92354")]
+        impl DivAssign<$t> for Saturating<$t> {
+            #[inline]
+            fn div_assign(&mut self, other: $t) {
+                *self = *self / Saturating(other);
+            }
+        }
+        forward_ref_op_assign! { impl DivAssign, div_assign for Saturating<$t>, $t }
+
+        #[unstable(feature = "saturating_int_impl", issue = "87920")]
+        impl Rem for Saturating<$t> {
+            type Output = Saturating<$t>;
+
+            #[inline]
+            fn rem(self, other: Saturating<$t>) -> Saturating<$t> {
+                Saturating(self.0.rem(other.0))
+            }
+        }
+        forward_ref_binop! { impl Rem, rem for Saturating<$t>, Saturating<$t>,
+                #[unstable(feature = "saturating_int_impl", issue = "87920")] }
+
+        #[unstable(feature = "saturating_int_impl", issue = "87920")]
+        impl RemAssign for Saturating<$t> {
+            #[inline]
+            fn rem_assign(&mut self, other: Saturating<$t>) {
+                *self = *self % other;
+            }
+        }
+        forward_ref_op_assign! { impl RemAssign, rem_assign for Saturating<$t>, Saturating<$t> }
+
+        #[unstable(feature = "saturating_int_assign_impl", issue = "92354")]
+        impl RemAssign<$t> for Saturating<$t> {
+            #[inline]
+            fn rem_assign(&mut self, other: $t) {
+                *self = *self % Saturating(other);
+            }
+        }
+        forward_ref_op_assign! { impl RemAssign, rem_assign for Saturating<$t>, $t }
+
+        #[unstable(feature = "saturating_int_impl", issue = "87920")]
+        impl Not for Saturating<$t> {
+            type Output = Saturating<$t>;
+
+            #[inline]
+            fn not(self) -> Saturating<$t> {
+                Saturating(!self.0)
+            }
+        }
+        forward_ref_unop! { impl Not, not for Saturating<$t>,
+                #[unstable(feature = "saturating_int_impl", issue = "87920")] }
+
+        #[unstable(feature = "saturating_int_impl", issue = "87920")]
+        impl BitXor for Saturating<$t> {
+            type Output = Saturating<$t>;
+
+            #[inline]
+            fn bitxor(self, other: Saturating<$t>) -> Saturating<$t> {
+                Saturating(self.0 ^ other.0)
+            }
+        }
+        forward_ref_binop! { impl BitXor, bitxor for Saturating<$t>, Saturating<$t>,
+                #[unstable(feature = "saturating_int_impl", issue = "87920")] }
+
+        #[unstable(feature = "saturating_int_impl", issue = "87920")]
+        impl BitXorAssign for Saturating<$t> {
+            #[inline]
+            fn bitxor_assign(&mut self, other: Saturating<$t>) {
+                *self = *self ^ other;
+            }
+        }
+        forward_ref_op_assign! { impl BitXorAssign, bitxor_assign for Saturating<$t>, Saturating<$t> }
+
+        #[unstable(feature = "saturating_int_assign_impl", issue = "92354")]
+        impl BitXorAssign<$t> for Saturating<$t> {
+            #[inline]
+            fn bitxor_assign(&mut self, other: $t) {
+                *self = *self ^ Saturating(other);
+            }
+        }
+        forward_ref_op_assign! { impl BitXorAssign, bitxor_assign for Saturating<$t>, $t }
+
+        #[unstable(feature = "saturating_int_impl", issue = "87920")]
+        impl BitOr for Saturating<$t> {
+            type Output = Saturating<$t>;
+
+            #[inline]
+            fn bitor(self, other: Saturating<$t>) -> Saturating<$t> {
+                Saturating(self.0 | other.0)
+            }
+        }
+        forward_ref_binop! { impl BitOr, bitor for Saturating<$t>, Saturating<$t>,
+                #[unstable(feature = "saturating_int_impl", issue = "87920")] }
+
+        #[unstable(feature = "saturating_int_impl", issue = "87920")]
+        impl BitOrAssign for Saturating<$t> {
+            #[inline]
+            fn bitor_assign(&mut self, other: Saturating<$t>) {
+                *self = *self | other;
+            }
+        }
+        forward_ref_op_assign! { impl BitOrAssign, bitor_assign for Saturating<$t>, Saturating<$t> }
+
+        #[unstable(feature = "saturating_int_assign_impl", issue = "92354")]
+        impl BitOrAssign<$t> for Saturating<$t> {
+            #[inline]
+            fn bitor_assign(&mut self, other: $t) {
+                *self = *self | Saturating(other);
+            }
+        }
+        forward_ref_op_assign! { impl BitOrAssign, bitor_assign for Saturating<$t>, $t }
+
+        #[unstable(feature = "saturating_int_impl", issue = "87920")]
+        impl BitAnd for Saturating<$t> {
+            type Output = Saturating<$t>;
+
+            #[inline]
+            fn bitand(self, other: Saturating<$t>) -> Saturating<$t> {
+                Saturating(self.0 & other.0)
+            }
+        }
+        forward_ref_binop! { impl BitAnd, bitand for Saturating<$t>, Saturating<$t>,
+                #[unstable(feature = "saturating_int_impl", issue = "87920")] }
+
+        #[unstable(feature = "saturating_int_impl", issue = "87920")]
+        impl BitAndAssign for Saturating<$t> {
+            #[inline]
+            fn bitand_assign(&mut self, other: Saturating<$t>) {
+                *self = *self & other;
+            }
+        }
+        forward_ref_op_assign! { impl BitAndAssign, bitand_assign for Saturating<$t>, Saturating<$t> }
+
+        #[unstable(feature = "saturating_int_assign_impl", issue = "92354")]
+        impl BitAndAssign<$t> for Saturating<$t> {
+            #[inline]
+            fn bitand_assign(&mut self, other: $t) {
+                *self = *self & Saturating(other);
+            }
+        }
+        forward_ref_op_assign! { impl BitAndAssign, bitand_assign for Saturating<$t>, $t }
+
+    )*)
+}
+
+saturating_impl! { usize u8 u16 u32 u64 u128 isize i8 i16 i32 i64 i128 }
+
+macro_rules! saturating_int_impl {
+    ($($t:ty)*) => ($(
+        impl Saturating<$t> {
+            /// Returns the smallest value that can be represented by this integer type.
+            ///
+            /// # Examples
+            ///
+            /// Basic usage:
+            ///
+            /// ```
+            /// #![feature(saturating_int_impl)]
+            /// use std::num::Saturating;
+            ///
+            #[doc = concat!("assert_eq!(<Saturating<", stringify!($t), ">>::MIN, Saturating(", stringify!($t), "::MIN));")]
+            /// ```
+            #[unstable(feature = "saturating_int_impl", issue = "87920")]
+            pub const MIN: Self = Self(<$t>::MIN);
+
+            /// Returns the largest value that can be represented by this integer type.
+            ///
+            /// # Examples
+            ///
+            /// Basic usage:
+            ///
+            /// ```
+            /// #![feature(saturating_int_impl)]
+            /// use std::num::Saturating;
+            ///
+            #[doc = concat!("assert_eq!(<Saturating<", stringify!($t), ">>::MAX, Saturating(", stringify!($t), "::MAX));")]
+            /// ```
+            #[unstable(feature = "saturating_int_impl", issue = "87920")]
+            pub const MAX: Self = Self(<$t>::MAX);
+
+            /// Returns the size of this integer type in bits.
+            ///
+            /// # Examples
+            ///
+            /// Basic usage:
+            ///
+            /// ```
+            /// #![feature(saturating_int_impl)]
+            /// use std::num::Saturating;
+            ///
+            #[doc = concat!("assert_eq!(<Saturating<", stringify!($t), ">>::BITS, ", stringify!($t), "::BITS);")]
+            /// ```
+            #[unstable(feature = "saturating_int_impl", issue = "87920")]
+            pub const BITS: u32 = <$t>::BITS;
+
+            /// Returns the number of ones in the binary representation of `self`.
+            ///
+            /// # Examples
+            ///
+            /// Basic usage:
+            ///
+            /// ```
+            /// #![feature(saturating_int_impl)]
+            /// use std::num::Saturating;
+            ///
+            #[doc = concat!("let n = Saturating(0b01001100", stringify!($t), ");")]
+            ///
+            /// assert_eq!(n.count_ones(), 3);
+            /// ```
+            #[inline]
+            #[doc(alias = "popcount")]
+            #[doc(alias = "popcnt")]
+            #[must_use = "this returns the result of the operation, \
+                          without modifying the original"]
+            #[unstable(feature = "saturating_int_impl", issue = "87920")]
+            pub const fn count_ones(self) -> u32 {
+                self.0.count_ones()
+            }
+
+            /// Returns the number of zeros in the binary representation of `self`.
+            ///
+            /// # Examples
+            ///
+            /// Basic usage:
+            ///
+            /// ```
+            /// #![feature(saturating_int_impl)]
+            /// use std::num::Saturating;
+            ///
+            #[doc = concat!("assert_eq!(Saturating(!0", stringify!($t), ").count_zeros(), 0);")]
+            /// ```
+            #[inline]
+            #[must_use = "this returns the result of the operation, \
+                          without modifying the original"]
+            #[unstable(feature = "saturating_int_impl", issue = "87920")]
+            pub const fn count_zeros(self) -> u32 {
+                self.0.count_zeros()
+            }
+
+            /// Returns the number of trailing zeros in the binary representation of `self`.
+            ///
+            /// # Examples
+            ///
+            /// Basic usage:
+            ///
+            /// ```
+            /// #![feature(saturating_int_impl)]
+            /// use std::num::Saturating;
+            ///
+            #[doc = concat!("let n = Saturating(0b0101000", stringify!($t), ");")]
+            ///
+            /// assert_eq!(n.trailing_zeros(), 3);
+            /// ```
+            #[inline]
+            #[must_use = "this returns the result of the operation, \
+                          without modifying the original"]
+            #[unstable(feature = "saturating_int_impl", issue = "87920")]
+            pub const fn trailing_zeros(self) -> u32 {
+                self.0.trailing_zeros()
+            }
+
+            /// Shifts the bits to the left by a specified amount, `n`,
+            /// saturating the truncated bits to the end of the resulting
+            /// integer.
+            ///
+            /// Please note this isn't the same operation as the `<<` shifting
+            /// operator!
+            ///
+            /// # Examples
+            ///
+            /// Basic usage:
+            ///
+            /// ```
+            /// #![feature(saturating_int_impl)]
+            /// use std::num::Saturating;
+            ///
+            /// let n: Saturating<i64> = Saturating(0x0123456789ABCDEF);
+            /// let m: Saturating<i64> = Saturating(-0x76543210FEDCBA99);
+            ///
+            /// assert_eq!(n.rotate_left(32), m);
+            /// ```
+            #[inline]
+            #[must_use = "this returns the result of the operation, \
+                          without modifying the original"]
+            #[unstable(feature = "saturating_int_impl", issue = "87920")]
+            pub const fn rotate_left(self, n: u32) -> Self {
+                Saturating(self.0.rotate_left(n))
+            }
+
+            /// Shifts the bits to the right by a specified amount, `n`,
+            /// saturating the truncated bits to the beginning of the resulting
+            /// integer.
+            ///
+            /// Please note this isn't the same operation as the `>>` shifting
+            /// operator!
+            ///
+            /// # Examples
+            ///
+            /// Basic usage:
+            ///
+            /// ```
+            /// #![feature(saturating_int_impl)]
+            /// use std::num::Saturating;
+            ///
+            /// let n: Saturating<i64> = Saturating(0x0123456789ABCDEF);
+            /// let m: Saturating<i64> = Saturating(-0xFEDCBA987654322);
+            ///
+            /// assert_eq!(n.rotate_right(4), m);
+            /// ```
+            #[inline]
+            #[must_use = "this returns the result of the operation, \
+                          without modifying the original"]
+            #[unstable(feature = "saturating_int_impl", issue = "87920")]
+            pub const fn rotate_right(self, n: u32) -> Self {
+                Saturating(self.0.rotate_right(n))
+            }
+
+            /// Reverses the byte order of the integer.
+            ///
+            /// # Examples
+            ///
+            /// Basic usage:
+            ///
+            /// ```
+            /// #![feature(saturating_int_impl)]
+            /// use std::num::Saturating;
+            ///
+            /// let n: Saturating<i16> = Saturating(0b0000000_01010101);
+            /// assert_eq!(n, Saturating(85));
+            ///
+            /// let m = n.swap_bytes();
+            ///
+            /// assert_eq!(m, Saturating(0b01010101_00000000));
+            /// assert_eq!(m, Saturating(21760));
+            /// ```
+            #[inline]
+            #[must_use = "this returns the result of the operation, \
+                          without modifying the original"]
+            #[unstable(feature = "saturating_int_impl", issue = "87920")]
+            pub const fn swap_bytes(self) -> Self {
+                Saturating(self.0.swap_bytes())
+            }
+
+            /// Reverses the bit pattern of the integer.
+            ///
+            /// # Examples
+            ///
+            /// Please note that this example is shared between integer types.
+            /// Which explains why `i16` is used here.
+            ///
+            /// Basic usage:
+            ///
+            /// ```
+            /// #![feature(saturating_int_impl)]
+            /// use std::num::Saturating;
+            ///
+            /// let n = Saturating(0b0000000_01010101i16);
+            /// assert_eq!(n, Saturating(85));
+            ///
+            /// let m = n.reverse_bits();
+            ///
+            /// assert_eq!(m.0 as u16, 0b10101010_00000000);
+            /// assert_eq!(m, Saturating(-22016));
+            /// ```
+            #[inline]
+            #[unstable(feature = "saturating_int_impl", issue = "87920")]
+            #[rustc_const_unstable(feature = "saturating_int_impl", issue = "87920")]
+            #[must_use = "this returns the result of the operation, \
+                          without modifying the original"]
+            pub const fn reverse_bits(self) -> Self {
+                Saturating(self.0.reverse_bits())
+            }
+
+            /// Converts an integer from big endian to the target's endianness.
+            ///
+            /// On big endian this is a no-op. On little endian the bytes are
+            /// swapped.
+            ///
+            /// # Examples
+            ///
+            /// Basic usage:
+            ///
+            /// ```
+            /// #![feature(saturating_int_impl)]
+            /// use std::num::Saturating;
+            ///
+            #[doc = concat!("let n = Saturating(0x1A", stringify!($t), ");")]
+            ///
+            /// if cfg!(target_endian = "big") {
+            #[doc = concat!("    assert_eq!(<Saturating<", stringify!($t), ">>::from_be(n), n)")]
+            /// } else {
+            #[doc = concat!("    assert_eq!(<Saturating<", stringify!($t), ">>::from_be(n), n.swap_bytes())")]
+            /// }
+            /// ```
+            #[inline]
+            #[must_use]
+            #[unstable(feature = "saturating_int_impl", issue = "87920")]
+            pub const fn from_be(x: Self) -> Self {
+                Saturating(<$t>::from_be(x.0))
+            }
+
+            /// Converts an integer from little endian to the target's endianness.
+            ///
+            /// On little endian this is a no-op. On big endian the bytes are
+            /// swapped.
+            ///
+            /// # Examples
+            ///
+            /// Basic usage:
+            ///
+            /// ```
+            /// #![feature(saturating_int_impl)]
+            /// use std::num::Saturating;
+            ///
+            #[doc = concat!("let n = Saturating(0x1A", stringify!($t), ");")]
+            ///
+            /// if cfg!(target_endian = "little") {
+            #[doc = concat!("    assert_eq!(<Saturating<", stringify!($t), ">>::from_le(n), n)")]
+            /// } else {
+            #[doc = concat!("    assert_eq!(<Saturating<", stringify!($t), ">>::from_le(n), n.swap_bytes())")]
+            /// }
+            /// ```
+            #[inline]
+            #[must_use]
+            #[unstable(feature = "saturating_int_impl", issue = "87920")]
+            pub const fn from_le(x: Self) -> Self {
+                Saturating(<$t>::from_le(x.0))
+            }
+
+            /// Converts `self` to big endian from the target's endianness.
+            ///
+            /// On big endian this is a no-op. On little endian the bytes are
+            /// swapped.
+            ///
+            /// # Examples
+            ///
+            /// Basic usage:
+            ///
+            /// ```
+            /// #![feature(saturating_int_impl)]
+            /// use std::num::Saturating;
+            ///
+            #[doc = concat!("let n = Saturating(0x1A", stringify!($t), ");")]
+            ///
+            /// if cfg!(target_endian = "big") {
+            ///     assert_eq!(n.to_be(), n)
+            /// } else {
+            ///     assert_eq!(n.to_be(), n.swap_bytes())
+            /// }
+            /// ```
+            #[inline]
+            #[unstable(feature = "saturating_int_impl", issue = "87920")]
+            #[must_use = "this returns the result of the operation, \
+                          without modifying the original"]
+            pub const fn to_be(self) -> Self {
+                Saturating(self.0.to_be())
+            }
+
+            /// Converts `self` to little endian from the target's endianness.
+            ///
+            /// On little endian this is a no-op. On big endian the bytes are
+            /// swapped.
+            ///
+            /// # Examples
+            ///
+            /// Basic usage:
+            ///
+            /// ```
+            /// #![feature(saturating_int_impl)]
+            /// use std::num::Saturating;
+            ///
+            #[doc = concat!("let n = Saturating(0x1A", stringify!($t), ");")]
+            ///
+            /// if cfg!(target_endian = "little") {
+            ///     assert_eq!(n.to_le(), n)
+            /// } else {
+            ///     assert_eq!(n.to_le(), n.swap_bytes())
+            /// }
+            /// ```
+            #[inline]
+            #[unstable(feature = "saturating_int_impl", issue = "87920")]
+            #[must_use = "this returns the result of the operation, \
+                          without modifying the original"]
+            pub const fn to_le(self) -> Self {
+                Saturating(self.0.to_le())
+            }
+
+            /// Raises self to the power of `exp`, using exponentiation by squaring.
+            ///
+            /// # Examples
+            ///
+            /// Basic usage:
+            ///
+            /// ```
+            /// #![feature(saturating_int_impl)]
+            /// use std::num::Saturating;
+            ///
+            #[doc = concat!("assert_eq!(Saturating(3", stringify!($t), ").pow(4), Saturating(81));")]
+            /// ```
+            ///
+            /// Results that are too large are saturated:
+            ///
+            /// ```
+            /// #![feature(saturating_int_impl)]
+            /// use std::num::Saturating;
+            ///
+            /// assert_eq!(Saturating(3i8).pow(5), Saturating(127));
+            /// assert_eq!(Saturating(3i8).pow(6), Saturating(127));
+            /// ```
+            #[inline]
+            #[unstable(feature = "saturating_int_impl", issue = "87920")]
+            #[must_use = "this returns the result of the operation, \
+                          without modifying the original"]
+            pub fn pow(self, exp: u32) -> Self {
+                Saturating(self.0.saturating_pow(exp))
+            }
+        }
+    )*)
+}
+
+saturating_int_impl! { usize u8 u16 u32 u64 u128 isize i8 i16 i32 i64 i128 }
+
+macro_rules! saturating_int_impl_signed {
+    ($($t:ty)*) => ($(
+        impl Saturating<$t> {
+            /// Returns the number of leading zeros in the binary representation of `self`.
+            ///
+            /// # Examples
+            ///
+            /// Basic usage:
+            ///
+            /// ```
+            /// #![feature(saturating_int_impl)]
+            /// use std::num::Saturating;
+            ///
+            #[doc = concat!("let n = Saturating(", stringify!($t), "::MAX >> 2);")]
+            ///
+            /// assert_eq!(n.leading_zeros(), 3);
+            /// ```
+            #[inline]
+            #[unstable(feature = "saturating_int_impl", issue = "87920")]
+            #[must_use = "this returns the result of the operation, \
+                          without modifying the original"]
+            pub const fn leading_zeros(self) -> u32 {
+                self.0.leading_zeros()
+            }
+
+            /// Saturating absolute value. Computes `self.abs()`, returning `MAX` if `self == MIN`
+            /// instead of overflowing.
+            ///
+            /// # Examples
+            ///
+            /// Basic usage:
+            ///
+            /// ```
+            /// #![feature(saturating_int_impl)]
+            /// use std::num::Saturating;
+            ///
+            #[doc = concat!("assert_eq!(Saturating(100", stringify!($t), ").abs(), Saturating(100));")]
+            #[doc = concat!("assert_eq!(Saturating(-100", stringify!($t), ").abs(), Saturating(100));")]
+            #[doc = concat!("assert_eq!(Saturating(", stringify!($t), "::MIN).abs(), Saturating((", stringify!($t), "::MIN + 1).abs()));")]
+            #[doc = concat!("assert_eq!(Saturating(", stringify!($t), "::MIN).abs(), Saturating(", stringify!($t), "::MIN.saturating_abs()));")]
+            #[doc = concat!("assert_eq!(Saturating(", stringify!($t), "::MIN).abs(), Saturating(", stringify!($t), "::MAX));")]
+            /// ```
+            #[inline]
+            #[unstable(feature = "saturating_int_impl", issue = "87920")]
+            #[must_use = "this returns the result of the operation, \
+                          without modifying the original"]
+            pub fn abs(self) -> Saturating<$t> {
+                Saturating(self.0.saturating_abs())
+            }
+
+            /// Returns a number representing sign of `self`.
+            ///
+            ///  - `0` if the number is zero
+            ///  - `1` if the number is positive
+            ///  - `-1` if the number is negative
+            ///
+            /// # Examples
+            ///
+            /// Basic usage:
+            ///
+            /// ```
+            /// #![feature(saturating_int_impl)]
+            /// use std::num::Saturating;
+            ///
+            #[doc = concat!("assert_eq!(Saturating(10", stringify!($t), ").signum(), Saturating(1));")]
+            #[doc = concat!("assert_eq!(Saturating(0", stringify!($t), ").signum(), Saturating(0));")]
+            #[doc = concat!("assert_eq!(Saturating(-10", stringify!($t), ").signum(), Saturating(-1));")]
+            /// ```
+            #[inline]
+            #[unstable(feature = "saturating_int_impl", issue = "87920")]
+            #[must_use = "this returns the result of the operation, \
+                          without modifying the original"]
+            pub fn signum(self) -> Saturating<$t> {
+                Saturating(self.0.signum())
+            }
+
+            /// Returns `true` if `self` is positive and `false` if the number is zero or
+            /// negative.
+            ///
+            /// # Examples
+            ///
+            /// Basic usage:
+            ///
+            /// ```
+            /// #![feature(saturating_int_impl)]
+            /// use std::num::Saturating;
+            ///
+            #[doc = concat!("assert!(Saturating(10", stringify!($t), ").is_positive());")]
+            #[doc = concat!("assert!(!Saturating(-10", stringify!($t), ").is_positive());")]
+            /// ```
+            #[must_use]
+            #[inline]
+            #[unstable(feature = "saturating_int_impl", issue = "87920")]
+            pub const fn is_positive(self) -> bool {
+                self.0.is_positive()
+            }
+
+            /// Returns `true` if `self` is negative and `false` if the number is zero or
+            /// positive.
+            ///
+            /// # Examples
+            ///
+            /// Basic usage:
+            ///
+            /// ```
+            /// #![feature(saturating_int_impl)]
+            /// use std::num::Saturating;
+            ///
+            #[doc = concat!("assert!(Saturating(-10", stringify!($t), ").is_negative());")]
+            #[doc = concat!("assert!(!Saturating(10", stringify!($t), ").is_negative());")]
+            /// ```
+            #[must_use]
+            #[inline]
+            #[unstable(feature = "saturating_int_impl", issue = "87920")]
+            pub const fn is_negative(self) -> bool {
+                self.0.is_negative()
+            }
+        }
+
+        #[unstable(feature = "saturating_int_impl", issue = "87920")]
+        impl Neg for Saturating<$t> {
+            type Output = Self;
+            #[inline]
+            fn neg(self) -> Self {
+                Saturating(self.0.saturating_neg())
+            }
+        }
+        forward_ref_unop! { impl Neg, neg for Saturating<$t>,
+                #[unstable(feature = "saturating_int_impl", issue = "87920")] }
+    )*)
+}
+
+saturating_int_impl_signed! { isize i8 i16 i32 i64 i128 }
+
+macro_rules! saturating_int_impl_unsigned {
+    ($($t:ty)*) => ($(
+        impl Saturating<$t> {
+            /// Returns the number of leading zeros in the binary representation of `self`.
+            ///
+            /// # Examples
+            ///
+            /// Basic usage:
+            ///
+            /// ```
+            /// #![feature(saturating_int_impl)]
+            /// use std::num::Saturating;
+            ///
+            #[doc = concat!("let n = Saturating(", stringify!($t), "::MAX >> 2);")]
+            ///
+            /// assert_eq!(n.leading_zeros(), 2);
+            /// ```
+            #[inline]
+            #[unstable(feature = "saturating_int_impl", issue = "87920")]
+            #[must_use = "this returns the result of the operation, \
+                          without modifying the original"]
+            pub const fn leading_zeros(self) -> u32 {
+                self.0.leading_zeros()
+            }
+
+            /// Returns `true` if and only if `self == 2^k` for some `k`.
+            ///
+            /// # Examples
+            ///
+            /// Basic usage:
+            ///
+            /// ```
+            /// #![feature(saturating_int_impl)]
+            /// use std::num::Saturating;
+            ///
+            #[doc = concat!("assert!(Saturating(16", stringify!($t), ").is_power_of_two());")]
+            #[doc = concat!("assert!(!Saturating(10", stringify!($t), ").is_power_of_two());")]
+            /// ```
+            #[must_use]
+            #[inline]
+            #[unstable(feature = "saturating_int_impl", issue = "87920")]
+            pub fn is_power_of_two(self) -> bool {
+                self.0.is_power_of_two()
+            }
+
+        }
+    )*)
+}
+
+saturating_int_impl_unsigned! { usize u8 u16 u32 u64 u128 }
+
+// Related to potential Shl and ShlAssign implementation
+//
+// mod shift_max {
+//     #![allow(non_upper_case_globals)]
+//
+//     #[cfg(target_pointer_width = "16")]
+//     mod platform {
+//         pub const usize: u32 = super::u16;
+//         pub const isize: u32 = super::i16;
+//     }
+//
+//     #[cfg(target_pointer_width = "32")]
+//     mod platform {
+//         pub const usize: u32 = super::u32;
+//         pub const isize: u32 = super::i32;
+//     }
+//
+//     #[cfg(target_pointer_width = "64")]
+//     mod platform {
+//         pub const usize: u32 = super::u64;
+//         pub const isize: u32 = super::i64;
+//     }
+//
+//     pub const i8: u32 = (1 << 3) - 1;
+//     pub const i16: u32 = (1 << 4) - 1;
+//     pub const i32: u32 = (1 << 5) - 1;
+//     pub const i64: u32 = (1 << 6) - 1;
+//     pub const i128: u32 = (1 << 7) - 1;
+//     pub use self::platform::isize;
+//
+//     pub const u8: u32 = i8;
+//     pub const u16: u32 = i16;
+//     pub const u32: u32 = i32;
+//     pub const u64: u32 = i64;
+//     pub const u128: u32 = i128;
+//     pub use self::platform::usize;
+// }
diff --git a/library/core/src/num/shells/i128.rs b/library/core/src/num/shells/i128.rs
new file mode 100644
index 000000000..7b048dc52
--- /dev/null
+++ b/library/core/src/num/shells/i128.rs
@@ -0,0 +1,13 @@
+//! Constants for the 128-bit signed integer type.
+//!
+//! *[See also the `i128` primitive type][i128].*
+//!
+//! New code should use the associated constants directly on the primitive type.
+
+#![stable(feature = "i128", since = "1.26.0")]
+#![deprecated(
+    since = "TBD",
+    note = "all constants in this module replaced by associated constants on `i128`"
+)]
+
+int_module! { i128, #[stable(feature = "i128", since="1.26.0")] }
diff --git a/library/core/src/num/shells/i16.rs b/library/core/src/num/shells/i16.rs
new file mode 100644
index 000000000..5c5812d5c
--- /dev/null
+++ b/library/core/src/num/shells/i16.rs
@@ -0,0 +1,13 @@
+//! Constants for the 16-bit signed integer type.
+//!
+//! *[See also the `i16` primitive type][i16].*
+//!
+//! New code should use the associated constants directly on the primitive type.
+
+#![stable(feature = "rust1", since = "1.0.0")]
+#![deprecated(
+    since = "TBD",
+    note = "all constants in this module replaced by associated constants on `i16`"
+)]
+
+int_module! { i16 }
diff --git a/library/core/src/num/shells/i32.rs b/library/core/src/num/shells/i32.rs
new file mode 100644
index 000000000..b283ac644
--- /dev/null
+++ b/library/core/src/num/shells/i32.rs
@@ -0,0 +1,13 @@
+//! Constants for the 32-bit signed integer type.
+//!
+//! *[See also the `i32` primitive type][i32].*
+//!
+//! New code should use the associated constants directly on the primitive type.
+
+#![stable(feature = "rust1", since = "1.0.0")]
+#![deprecated(
+    since = "TBD",
+    note = "all constants in this module replaced by associated constants on `i32`"
+)]
+
+int_module! { i32 }
diff --git a/library/core/src/num/shells/i64.rs b/library/core/src/num/shells/i64.rs
new file mode 100644
index 000000000..a416fa7e9
--- /dev/null
+++ b/library/core/src/num/shells/i64.rs
@@ -0,0 +1,13 @@
+//! Constants for the 64-bit signed integer type.
+//!
+//! *[See also the `i64` primitive type][i64].*
+//!
+//! New code should use the associated constants directly on the primitive type.
+
+#![stable(feature = "rust1", since = "1.0.0")]
+#![deprecated(
+    since = "TBD",
+    note = "all constants in this module replaced by associated constants on `i64`"
+)]
+
+int_module! { i64 }
diff --git a/library/core/src/num/shells/i8.rs b/library/core/src/num/shells/i8.rs
new file mode 100644
index 000000000..02465013a
--- /dev/null
+++ b/library/core/src/num/shells/i8.rs
@@ -0,0 +1,13 @@
+//! Constants for the 8-bit signed integer type.
+//!
+//! *[See also the `i8` primitive type][i8].*
+//!
+//! New code should use the associated constants directly on the primitive type.
+
+#![stable(feature = "rust1", since = "1.0.0")]
+#![deprecated(
+    since = "TBD",
+    note = "all constants in this module replaced by associated constants on `i8`"
+)]
+
+int_module! { i8 }
diff --git a/library/core/src/num/shells/int_macros.rs b/library/core/src/num/shells/int_macros.rs
new file mode 100644
index 000000000..2b1133e11
--- /dev/null
+++ b/library/core/src/num/shells/int_macros.rs
@@ -0,0 +1,44 @@
+#![doc(hidden)]
+
+macro_rules! int_module {
+    ($T:ident) => (int_module!($T, #[stable(feature = "rust1", since = "1.0.0")]););
+    ($T:ident, #[$attr:meta]) => (
+        #[doc = concat!(
+            "The smallest value that can be represented by this integer type. Use ",
+            "[`", stringify!($T), "::MIN", "`] instead."
+        )]
+        ///
+        /// # Examples
+        ///
+        /// ```rust
+        /// // deprecated way
+        #[doc = concat!("let min = std::", stringify!($T), "::MIN;")]
+        ///
+        /// // intended way
+        #[doc = concat!("let min = ", stringify!($T), "::MIN;")]
+        /// ```
+        ///
+        #[$attr]
+        #[deprecated(since = "TBD", note = "replaced by the `MIN` associated constant on this type")]
+        pub const MIN: $T = $T::MIN;
+
+        #[doc = concat!(
+            "The largest value that can be represented by this integer type. Use ",
+            "[`", stringify!($T), "::MAX", "`] instead."
+        )]
+        ///
+        /// # Examples
+        ///
+        /// ```rust
+        /// // deprecated way
+        #[doc = concat!("let max = std::", stringify!($T), "::MAX;")]
+        ///
+        /// // intended way
+        #[doc = concat!("let max = ", stringify!($T), "::MAX;")]
+        /// ```
+        ///
+        #[$attr]
+        #[deprecated(since = "TBD", note = "replaced by the `MAX` associated constant on this type")]
+        pub const MAX: $T = $T::MAX;
+    )
+}
diff --git a/library/core/src/num/shells/isize.rs b/library/core/src/num/shells/isize.rs
new file mode 100644
index 000000000..1579fbab6
--- /dev/null
+++ b/library/core/src/num/shells/isize.rs
@@ -0,0 +1,13 @@
+//! Constants for the pointer-sized signed integer type.
+//!
+//! *[See also the `isize` primitive type][isize].*
+//!
+//! New code should use the associated constants directly on the primitive type.
+
+#![stable(feature = "rust1", since = "1.0.0")]
+#![deprecated(
+    since = "TBD",
+    note = "all constants in this module replaced by associated constants on `isize`"
+)]
+
+int_module! { isize }
diff --git a/library/core/src/num/shells/u128.rs b/library/core/src/num/shells/u128.rs
new file mode 100644
index 000000000..fe08cee58
--- /dev/null
+++ b/library/core/src/num/shells/u128.rs
@@ -0,0 +1,13 @@
+//! Constants for the 128-bit unsigned integer type.
+//!
+//! *[See also the `u128` primitive type][u128].*
+//!
+//! New code should use the associated constants directly on the primitive type.
+
+#![stable(feature = "i128", since = "1.26.0")]
+#![deprecated(
+    since = "TBD",
+    note = "all constants in this module replaced by associated constants on `u128`"
+)]
+
+int_module! { u128, #[stable(feature = "i128", since="1.26.0")] }
diff --git a/library/core/src/num/shells/u16.rs b/library/core/src/num/shells/u16.rs
new file mode 100644
index 000000000..36f8c6978
--- /dev/null
+++ b/library/core/src/num/shells/u16.rs
@@ -0,0 +1,13 @@
+//! Constants for the 16-bit unsigned integer type.
+//!
+//! *[See also the `u16` primitive type][u16].*
+//!
+//! New code should use the associated constants directly on the primitive type.
+
+#![stable(feature = "rust1", since = "1.0.0")]
+#![deprecated(
+    since = "TBD",
+    note = "all constants in this module replaced by associated constants on `u16`"
+)]
+
+int_module! { u16 }
diff --git a/library/core/src/num/shells/u32.rs b/library/core/src/num/shells/u32.rs
new file mode 100644
index 000000000..1c369097d
--- /dev/null
+++ b/library/core/src/num/shells/u32.rs
@@ -0,0 +1,13 @@
+//! Constants for the 32-bit unsigned integer type.
+//!
+//! *[See also the `u32` primitive type][u32].*
+//!
+//! New code should use the associated constants directly on the primitive type.
+
+#![stable(feature = "rust1", since = "1.0.0")]
+#![deprecated(
+    since = "TBD",
+    note = "all constants in this module replaced by associated constants on `u32`"
+)]
+
+int_module! { u32 }
diff --git a/library/core/src/num/shells/u64.rs b/library/core/src/num/shells/u64.rs
new file mode 100644
index 000000000..e8b691d15
--- /dev/null
+++ b/library/core/src/num/shells/u64.rs
@@ -0,0 +1,13 @@
+//! Constants for the 64-bit unsigned integer type.
+//!
+//! *[See also the `u64` primitive type][u64].*
+//!
+//! New code should use the associated constants directly on the primitive type.
+
+#![stable(feature = "rust1", since = "1.0.0")]
+#![deprecated(
+    since = "TBD",
+    note = "all constants in this module replaced by associated constants on `u64`"
+)]
+
+int_module! { u64 }
diff --git a/library/core/src/num/shells/u8.rs b/library/core/src/num/shells/u8.rs
new file mode 100644
index 000000000..817c6a18a
--- /dev/null
+++ b/library/core/src/num/shells/u8.rs
@@ -0,0 +1,13 @@
+//! Constants for the 8-bit unsigned integer type.
+//!
+//! *[See also the `u8` primitive type][u8].*
+//!
+//! New code should use the associated constants directly on the primitive type.
+
+#![stable(feature = "rust1", since = "1.0.0")]
+#![deprecated(
+    since = "TBD",
+    note = "all constants in this module replaced by associated constants on `u8`"
+)]
+
+int_module! { u8 }
diff --git a/library/core/src/num/shells/usize.rs b/library/core/src/num/shells/usize.rs
new file mode 100644
index 000000000..3e1bec5ec
--- /dev/null
+++ b/library/core/src/num/shells/usize.rs
@@ -0,0 +1,13 @@
+//! Constants for the pointer-sized unsigned integer type.
+//!
+//! *[See also the `usize` primitive type][usize].*
+//!
+//! New code should use the associated constants directly on the primitive type.
+
+#![stable(feature = "rust1", since = "1.0.0")]
+#![deprecated(
+    since = "TBD",
+    note = "all constants in this module replaced by associated constants on `usize`"
+)]
+
+int_module! { usize }
diff --git a/library/core/src/num/uint_macros.rs b/library/core/src/num/uint_macros.rs
new file mode 100644
index 000000000..733655442
--- /dev/null
+++ b/library/core/src/num/uint_macros.rs
@@ -0,0 +1,2454 @@
+macro_rules! uint_impl {
+    ($SelfT:ty, $ActualT:ident, $SignedT:ident, $NonZeroT:ident,
+        $BITS:expr, $MaxV:expr,
+        $rot:expr, $rot_op:expr, $rot_result:expr, $swap_op:expr, $swapped:expr,
+        $reversed:expr, $le_bytes:expr, $be_bytes:expr,
+        $to_xe_bytes_doc:expr, $from_xe_bytes_doc:expr,
+        $bound_condition:expr) => {
+        /// The smallest value that can be represented by this integer type.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        #[doc = concat!("assert_eq!(", stringify!($SelfT), "::MIN, 0);")]
+        /// ```
+        #[stable(feature = "assoc_int_consts", since = "1.43.0")]
+        pub const MIN: Self = 0;
+
+        /// The largest value that can be represented by this integer type
+        #[doc = concat!("(2<sup>", $BITS, "</sup> &minus; 1", $bound_condition, ")")]
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        #[doc = concat!("assert_eq!(", stringify!($SelfT), "::MAX, ", stringify!($MaxV), ");")]
+        /// ```
+        #[stable(feature = "assoc_int_consts", since = "1.43.0")]
+        pub const MAX: Self = !0;
+
+        /// The size of this integer type in bits.
+        ///
+        /// # Examples
+        ///
+        /// ```
+        #[doc = concat!("assert_eq!(", stringify!($SelfT), "::BITS, ", stringify!($BITS), ");")]
+        /// ```
+        #[stable(feature = "int_bits_const", since = "1.53.0")]
+        pub const BITS: u32 = $BITS;
+
+        /// Converts a string slice in a given base to an integer.
+        ///
+        /// The string is expected to be an optional `+` sign
+        /// followed by digits.
+        /// Leading and trailing whitespace represent an error.
+        /// Digits are a subset of these characters, depending on `radix`:
+        ///
+        /// * `0-9`
+        /// * `a-z`
+        /// * `A-Z`
+        ///
+        /// # Panics
+        ///
+        /// This function panics if `radix` is not in the range from 2 to 36.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        #[doc = concat!("assert_eq!(", stringify!($SelfT), "::from_str_radix(\"A\", 16), Ok(10));")]
+        /// ```
+        #[stable(feature = "rust1", since = "1.0.0")]
+        pub fn from_str_radix(src: &str, radix: u32) -> Result<Self, ParseIntError> {
+            from_str_radix(src, radix)
+        }
+
+        /// Returns the number of ones in the binary representation of `self`.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        #[doc = concat!("let n = 0b01001100", stringify!($SelfT), ";")]
+        ///
+        /// assert_eq!(n.count_ones(), 3);
+        /// ```
+        #[stable(feature = "rust1", since = "1.0.0")]
+        #[rustc_const_stable(feature = "const_math", since = "1.32.0")]
+        #[doc(alias = "popcount")]
+        #[doc(alias = "popcnt")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline(always)]
+        pub const fn count_ones(self) -> u32 {
+            intrinsics::ctpop(self as $ActualT) as u32
+        }
+
+        /// Returns the number of zeros in the binary representation of `self`.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        #[doc = concat!("assert_eq!(", stringify!($SelfT), "::MAX.count_zeros(), 0);")]
+        /// ```
+        #[stable(feature = "rust1", since = "1.0.0")]
+        #[rustc_const_stable(feature = "const_math", since = "1.32.0")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline(always)]
+        pub const fn count_zeros(self) -> u32 {
+            (!self).count_ones()
+        }
+
+        /// Returns the number of leading zeros in the binary representation of `self`.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        #[doc = concat!("let n = ", stringify!($SelfT), "::MAX >> 2;")]
+        ///
+        /// assert_eq!(n.leading_zeros(), 2);
+        /// ```
+        #[stable(feature = "rust1", since = "1.0.0")]
+        #[rustc_const_stable(feature = "const_math", since = "1.32.0")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline(always)]
+        pub const fn leading_zeros(self) -> u32 {
+            intrinsics::ctlz(self as $ActualT) as u32
+        }
+
+        /// Returns the number of trailing zeros in the binary representation
+        /// of `self`.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        #[doc = concat!("let n = 0b0101000", stringify!($SelfT), ";")]
+        ///
+        /// assert_eq!(n.trailing_zeros(), 3);
+        /// ```
+        #[stable(feature = "rust1", since = "1.0.0")]
+        #[rustc_const_stable(feature = "const_math", since = "1.32.0")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline(always)]
+        pub const fn trailing_zeros(self) -> u32 {
+            intrinsics::cttz(self) as u32
+        }
+
+        /// Returns the number of leading ones in the binary representation of `self`.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        #[doc = concat!("let n = !(", stringify!($SelfT), "::MAX >> 2);")]
+        ///
+        /// assert_eq!(n.leading_ones(), 2);
+        /// ```
+        #[stable(feature = "leading_trailing_ones", since = "1.46.0")]
+        #[rustc_const_stable(feature = "leading_trailing_ones", since = "1.46.0")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline(always)]
+        pub const fn leading_ones(self) -> u32 {
+            (!self).leading_zeros()
+        }
+
+        /// Returns the number of trailing ones in the binary representation
+        /// of `self`.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        #[doc = concat!("let n = 0b1010111", stringify!($SelfT), ";")]
+        ///
+        /// assert_eq!(n.trailing_ones(), 3);
+        /// ```
+        #[stable(feature = "leading_trailing_ones", since = "1.46.0")]
+        #[rustc_const_stable(feature = "leading_trailing_ones", since = "1.46.0")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline(always)]
+        pub const fn trailing_ones(self) -> u32 {
+            (!self).trailing_zeros()
+        }
+
+        /// Shifts the bits to the left by a specified amount, `n`,
+        /// wrapping the truncated bits to the end of the resulting integer.
+        ///
+        /// Please note this isn't the same operation as the `<<` shifting operator!
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        #[doc = concat!("let n = ", $rot_op, stringify!($SelfT), ";")]
+        #[doc = concat!("let m = ", $rot_result, ";")]
+        ///
+        #[doc = concat!("assert_eq!(n.rotate_left(", $rot, "), m);")]
+        /// ```
+        #[stable(feature = "rust1", since = "1.0.0")]
+        #[rustc_const_stable(feature = "const_math", since = "1.32.0")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline(always)]
+        pub const fn rotate_left(self, n: u32) -> Self {
+            intrinsics::rotate_left(self, n as $SelfT)
+        }
+
+        /// Shifts the bits to the right by a specified amount, `n`,
+        /// wrapping the truncated bits to the beginning of the resulting
+        /// integer.
+        ///
+        /// Please note this isn't the same operation as the `>>` shifting operator!
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        #[doc = concat!("let n = ", $rot_result, stringify!($SelfT), ";")]
+        #[doc = concat!("let m = ", $rot_op, ";")]
+        ///
+        #[doc = concat!("assert_eq!(n.rotate_right(", $rot, "), m);")]
+        /// ```
+        #[stable(feature = "rust1", since = "1.0.0")]
+        #[rustc_const_stable(feature = "const_math", since = "1.32.0")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline(always)]
+        pub const fn rotate_right(self, n: u32) -> Self {
+            intrinsics::rotate_right(self, n as $SelfT)
+        }
+
+        /// Reverses the byte order of the integer.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        #[doc = concat!("let n = ", $swap_op, stringify!($SelfT), ";")]
+        /// let m = n.swap_bytes();
+        ///
+        #[doc = concat!("assert_eq!(m, ", $swapped, ");")]
+        /// ```
+        #[stable(feature = "rust1", since = "1.0.0")]
+        #[rustc_const_stable(feature = "const_math", since = "1.32.0")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline(always)]
+        pub const fn swap_bytes(self) -> Self {
+            intrinsics::bswap(self as $ActualT) as Self
+        }
+
+        /// Reverses the order of bits in the integer. The least significant bit becomes the most significant bit,
+        ///                 second least-significant bit becomes second most-significant bit, etc.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        #[doc = concat!("let n = ", $swap_op, stringify!($SelfT), ";")]
+        /// let m = n.reverse_bits();
+        ///
+        #[doc = concat!("assert_eq!(m, ", $reversed, ");")]
+        #[doc = concat!("assert_eq!(0, 0", stringify!($SelfT), ".reverse_bits());")]
+        /// ```
+        #[stable(feature = "reverse_bits", since = "1.37.0")]
+        #[rustc_const_stable(feature = "reverse_bits", since = "1.37.0")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline(always)]
+        pub const fn reverse_bits(self) -> Self {
+            intrinsics::bitreverse(self as $ActualT) as Self
+        }
+
+        /// Converts an integer from big endian to the target's endianness.
+        ///
+        /// On big endian this is a no-op. On little endian the bytes are
+        /// swapped.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        #[doc = concat!("let n = 0x1A", stringify!($SelfT), ";")]
+        ///
+        /// if cfg!(target_endian = "big") {
+        #[doc = concat!("    assert_eq!(", stringify!($SelfT), "::from_be(n), n)")]
+        /// } else {
+        #[doc = concat!("    assert_eq!(", stringify!($SelfT), "::from_be(n), n.swap_bytes())")]
+        /// }
+        /// ```
+        #[stable(feature = "rust1", since = "1.0.0")]
+        #[rustc_const_stable(feature = "const_math", since = "1.32.0")]
+        #[must_use]
+        #[inline(always)]
+        pub const fn from_be(x: Self) -> Self {
+            #[cfg(target_endian = "big")]
+            {
+                x
+            }
+            #[cfg(not(target_endian = "big"))]
+            {
+                x.swap_bytes()
+            }
+        }
+
+        /// Converts an integer from little endian to the target's endianness.
+        ///
+        /// On little endian this is a no-op. On big endian the bytes are
+        /// swapped.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        #[doc = concat!("let n = 0x1A", stringify!($SelfT), ";")]
+        ///
+        /// if cfg!(target_endian = "little") {
+        #[doc = concat!("    assert_eq!(", stringify!($SelfT), "::from_le(n), n)")]
+        /// } else {
+        #[doc = concat!("    assert_eq!(", stringify!($SelfT), "::from_le(n), n.swap_bytes())")]
+        /// }
+        /// ```
+        #[stable(feature = "rust1", since = "1.0.0")]
+        #[rustc_const_stable(feature = "const_math", since = "1.32.0")]
+        #[must_use]
+        #[inline(always)]
+        pub const fn from_le(x: Self) -> Self {
+            #[cfg(target_endian = "little")]
+            {
+                x
+            }
+            #[cfg(not(target_endian = "little"))]
+            {
+                x.swap_bytes()
+            }
+        }
+
+        /// Converts `self` to big endian from the target's endianness.
+        ///
+        /// On big endian this is a no-op. On little endian the bytes are
+        /// swapped.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        #[doc = concat!("let n = 0x1A", stringify!($SelfT), ";")]
+        ///
+        /// if cfg!(target_endian = "big") {
+        ///     assert_eq!(n.to_be(), n)
+        /// } else {
+        ///     assert_eq!(n.to_be(), n.swap_bytes())
+        /// }
+        /// ```
+        #[stable(feature = "rust1", since = "1.0.0")]
+        #[rustc_const_stable(feature = "const_math", since = "1.32.0")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline(always)]
+        pub const fn to_be(self) -> Self { // or not to be?
+            #[cfg(target_endian = "big")]
+            {
+                self
+            }
+            #[cfg(not(target_endian = "big"))]
+            {
+                self.swap_bytes()
+            }
+        }
+
+        /// Converts `self` to little endian from the target's endianness.
+        ///
+        /// On little endian this is a no-op. On big endian the bytes are
+        /// swapped.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        #[doc = concat!("let n = 0x1A", stringify!($SelfT), ";")]
+        ///
+        /// if cfg!(target_endian = "little") {
+        ///     assert_eq!(n.to_le(), n)
+        /// } else {
+        ///     assert_eq!(n.to_le(), n.swap_bytes())
+        /// }
+        /// ```
+        #[stable(feature = "rust1", since = "1.0.0")]
+        #[rustc_const_stable(feature = "const_math", since = "1.32.0")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline(always)]
+        pub const fn to_le(self) -> Self {
+            #[cfg(target_endian = "little")]
+            {
+                self
+            }
+            #[cfg(not(target_endian = "little"))]
+            {
+                self.swap_bytes()
+            }
+        }
+
+        /// Checked integer addition. Computes `self + rhs`, returning `None`
+        /// if overflow occurred.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        #[doc = concat!(
+            "assert_eq!((", stringify!($SelfT), "::MAX - 2).checked_add(1), ",
+            "Some(", stringify!($SelfT), "::MAX - 1));"
+        )]
+        #[doc = concat!("assert_eq!((", stringify!($SelfT), "::MAX - 2).checked_add(3), None);")]
+        /// ```
+        #[stable(feature = "rust1", since = "1.0.0")]
+        #[rustc_const_stable(feature = "const_checked_int_methods", since = "1.47.0")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline]
+        pub const fn checked_add(self, rhs: Self) -> Option<Self> {
+            let (a, b) = self.overflowing_add(rhs);
+            if unlikely!(b) {None} else {Some(a)}
+        }
+
+        /// Unchecked integer addition. Computes `self + rhs`, assuming overflow
+        /// cannot occur.
+        ///
+        /// # Safety
+        ///
+        /// This results in undefined behavior when
+        #[doc = concat!("`self + rhs > ", stringify!($SelfT), "::MAX` or `self + rhs < ", stringify!($SelfT), "::MIN`,")]
+        /// i.e. when [`checked_add`] would return `None`.
+        ///
+        #[doc = concat!("[`checked_add`]: ", stringify!($SelfT), "::checked_add")]
+        #[unstable(
+            feature = "unchecked_math",
+            reason = "niche optimization path",
+            issue = "85122",
+        )]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[rustc_const_unstable(feature = "const_inherent_unchecked_arith", issue = "85122")]
+        #[inline(always)]
+        #[cfg_attr(miri, track_caller)] // even without panics, this helps for Miri backtraces
+        pub const unsafe fn unchecked_add(self, rhs: Self) -> Self {
+            // SAFETY: the caller must uphold the safety contract for
+            // `unchecked_add`.
+            unsafe { intrinsics::unchecked_add(self, rhs) }
+        }
+
+        /// Checked addition with a signed integer. Computes `self + rhs`,
+        /// returning `None` if overflow occurred.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        /// # #![feature(mixed_integer_ops)]
+        #[doc = concat!("assert_eq!(1", stringify!($SelfT), ".checked_add_signed(2), Some(3));")]
+        #[doc = concat!("assert_eq!(1", stringify!($SelfT), ".checked_add_signed(-2), None);")]
+        #[doc = concat!("assert_eq!((", stringify!($SelfT), "::MAX - 2).checked_add_signed(3), None);")]
+        /// ```
+        #[unstable(feature = "mixed_integer_ops", issue = "87840")]
+        #[rustc_const_unstable(feature = "mixed_integer_ops", issue = "87840")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline]
+        pub const fn checked_add_signed(self, rhs: $SignedT) -> Option<Self> {
+            let (a, b) = self.overflowing_add_signed(rhs);
+            if unlikely!(b) {None} else {Some(a)}
+        }
+
+        /// Checked integer subtraction. Computes `self - rhs`, returning
+        /// `None` if overflow occurred.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        #[doc = concat!("assert_eq!(1", stringify!($SelfT), ".checked_sub(1), Some(0));")]
+        #[doc = concat!("assert_eq!(0", stringify!($SelfT), ".checked_sub(1), None);")]
+        /// ```
+        #[stable(feature = "rust1", since = "1.0.0")]
+        #[rustc_const_stable(feature = "const_checked_int_methods", since = "1.47.0")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline]
+        pub const fn checked_sub(self, rhs: Self) -> Option<Self> {
+            let (a, b) = self.overflowing_sub(rhs);
+            if unlikely!(b) {None} else {Some(a)}
+        }
+
+        /// Unchecked integer subtraction. Computes `self - rhs`, assuming overflow
+        /// cannot occur.
+        ///
+        /// # Safety
+        ///
+        /// This results in undefined behavior when
+        #[doc = concat!("`self - rhs > ", stringify!($SelfT), "::MAX` or `self - rhs < ", stringify!($SelfT), "::MIN`,")]
+        /// i.e. when [`checked_sub`] would return `None`.
+        ///
+        #[doc = concat!("[`checked_sub`]: ", stringify!($SelfT), "::checked_sub")]
+        #[unstable(
+            feature = "unchecked_math",
+            reason = "niche optimization path",
+            issue = "85122",
+        )]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[rustc_const_unstable(feature = "const_inherent_unchecked_arith", issue = "85122")]
+        #[inline(always)]
+        #[cfg_attr(miri, track_caller)] // even without panics, this helps for Miri backtraces
+        pub const unsafe fn unchecked_sub(self, rhs: Self) -> Self {
+            // SAFETY: the caller must uphold the safety contract for
+            // `unchecked_sub`.
+            unsafe { intrinsics::unchecked_sub(self, rhs) }
+        }
+
+        /// Checked integer multiplication. Computes `self * rhs`, returning
+        /// `None` if overflow occurred.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        #[doc = concat!("assert_eq!(5", stringify!($SelfT), ".checked_mul(1), Some(5));")]
+        #[doc = concat!("assert_eq!(", stringify!($SelfT), "::MAX.checked_mul(2), None);")]
+        /// ```
+        #[stable(feature = "rust1", since = "1.0.0")]
+        #[rustc_const_stable(feature = "const_checked_int_methods", since = "1.47.0")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline]
+        pub const fn checked_mul(self, rhs: Self) -> Option<Self> {
+            let (a, b) = self.overflowing_mul(rhs);
+            if unlikely!(b) {None} else {Some(a)}
+        }
+
+        /// Unchecked integer multiplication. Computes `self * rhs`, assuming overflow
+        /// cannot occur.
+        ///
+        /// # Safety
+        ///
+        /// This results in undefined behavior when
+        #[doc = concat!("`self * rhs > ", stringify!($SelfT), "::MAX` or `self * rhs < ", stringify!($SelfT), "::MIN`,")]
+        /// i.e. when [`checked_mul`] would return `None`.
+        ///
+        #[doc = concat!("[`checked_mul`]: ", stringify!($SelfT), "::checked_mul")]
+        #[unstable(
+            feature = "unchecked_math",
+            reason = "niche optimization path",
+            issue = "85122",
+        )]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[rustc_const_unstable(feature = "const_inherent_unchecked_arith", issue = "85122")]
+        #[inline(always)]
+        #[cfg_attr(miri, track_caller)] // even without panics, this helps for Miri backtraces
+        pub const unsafe fn unchecked_mul(self, rhs: Self) -> Self {
+            // SAFETY: the caller must uphold the safety contract for
+            // `unchecked_mul`.
+            unsafe { intrinsics::unchecked_mul(self, rhs) }
+        }
+
+        /// Checked integer division. Computes `self / rhs`, returning `None`
+        /// if `rhs == 0`.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        #[doc = concat!("assert_eq!(128", stringify!($SelfT), ".checked_div(2), Some(64));")]
+        #[doc = concat!("assert_eq!(1", stringify!($SelfT), ".checked_div(0), None);")]
+        /// ```
+        #[stable(feature = "rust1", since = "1.0.0")]
+        #[rustc_const_stable(feature = "const_checked_int_div", since = "1.52.0")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline]
+        pub const fn checked_div(self, rhs: Self) -> Option<Self> {
+            if unlikely!(rhs == 0) {
+                None
+            } else {
+                // SAFETY: div by zero has been checked above and unsigned types have no other
+                // failure modes for division
+                Some(unsafe { intrinsics::unchecked_div(self, rhs) })
+            }
+        }
+
+        /// Checked Euclidean division. Computes `self.div_euclid(rhs)`, returning `None`
+        /// if `rhs == 0`.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        #[doc = concat!("assert_eq!(128", stringify!($SelfT), ".checked_div_euclid(2), Some(64));")]
+        #[doc = concat!("assert_eq!(1", stringify!($SelfT), ".checked_div_euclid(0), None);")]
+        /// ```
+        #[stable(feature = "euclidean_division", since = "1.38.0")]
+        #[rustc_const_stable(feature = "const_euclidean_int_methods", since = "1.52.0")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline]
+        pub const fn checked_div_euclid(self, rhs: Self) -> Option<Self> {
+            if unlikely!(rhs == 0) {
+                None
+            } else {
+                Some(self.div_euclid(rhs))
+            }
+        }
+
+
+        /// Checked integer remainder. Computes `self % rhs`, returning `None`
+        /// if `rhs == 0`.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        #[doc = concat!("assert_eq!(5", stringify!($SelfT), ".checked_rem(2), Some(1));")]
+        #[doc = concat!("assert_eq!(5", stringify!($SelfT), ".checked_rem(0), None);")]
+        /// ```
+        #[stable(feature = "wrapping", since = "1.7.0")]
+        #[rustc_const_stable(feature = "const_checked_int_div", since = "1.52.0")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline]
+        pub const fn checked_rem(self, rhs: Self) -> Option<Self> {
+            if unlikely!(rhs == 0) {
+                None
+            } else {
+                // SAFETY: div by zero has been checked above and unsigned types have no other
+                // failure modes for division
+                Some(unsafe { intrinsics::unchecked_rem(self, rhs) })
+            }
+        }
+
+        /// Checked Euclidean modulo. Computes `self.rem_euclid(rhs)`, returning `None`
+        /// if `rhs == 0`.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        #[doc = concat!("assert_eq!(5", stringify!($SelfT), ".checked_rem_euclid(2), Some(1));")]
+        #[doc = concat!("assert_eq!(5", stringify!($SelfT), ".checked_rem_euclid(0), None);")]
+        /// ```
+        #[stable(feature = "euclidean_division", since = "1.38.0")]
+        #[rustc_const_stable(feature = "const_euclidean_int_methods", since = "1.52.0")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline]
+        pub const fn checked_rem_euclid(self, rhs: Self) -> Option<Self> {
+            if unlikely!(rhs == 0) {
+                None
+            } else {
+                Some(self.rem_euclid(rhs))
+            }
+        }
+
+        /// Returns the logarithm of the number with respect to an arbitrary base,
+        /// rounded down.
+        ///
+        /// This method might not be optimized owing to implementation details;
+        /// `log2` can produce results more efficiently for base 2, and `log10`
+        /// can produce results more efficiently for base 10.
+        ///
+        /// # Panics
+        ///
+        /// When the number is zero, or if the base is not at least 2;
+        /// it panics in debug mode and the return value is 0 in release mode.
+        ///
+        /// # Examples
+        ///
+        /// ```
+        /// #![feature(int_log)]
+        #[doc = concat!("assert_eq!(5", stringify!($SelfT), ".log(5), 1);")]
+        /// ```
+        #[unstable(feature = "int_log", issue = "70887")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline]
+        #[track_caller]
+        #[rustc_inherit_overflow_checks]
+        #[allow(arithmetic_overflow)]
+        pub const fn log(self, base: Self) -> u32 {
+            match self.checked_log(base) {
+                Some(n) => n,
+                None => {
+                    // In debug builds, trigger a panic on None.
+                    // This should optimize completely out in release builds.
+                    let _ = Self::MAX + 1;
+
+                    0
+                },
+            }
+        }
+
+        /// Returns the base 2 logarithm of the number, rounded down.
+        ///
+        /// # Panics
+        ///
+        /// When the number is zero it panics in debug mode and
+        /// the return value is 0 in release mode.
+        ///
+        /// # Examples
+        ///
+        /// ```
+        /// #![feature(int_log)]
+        #[doc = concat!("assert_eq!(2", stringify!($SelfT), ".log2(), 1);")]
+        /// ```
+        #[unstable(feature = "int_log", issue = "70887")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline]
+        #[track_caller]
+        #[rustc_inherit_overflow_checks]
+        #[allow(arithmetic_overflow)]
+        pub const fn log2(self) -> u32 {
+            match self.checked_log2() {
+                Some(n) => n,
+                None => {
+                    // In debug builds, trigger a panic on None.
+                    // This should optimize completely out in release builds.
+                    let _ = Self::MAX + 1;
+
+                    0
+                },
+            }
+        }
+
+        /// Returns the base 10 logarithm of the number, rounded down.
+        ///
+        /// # Panics
+        ///
+        /// When the number is zero it panics in debug mode and the
+        /// return value is 0 in release mode.
+        ///
+        /// # Example
+        ///
+        /// ```
+        /// #![feature(int_log)]
+        #[doc = concat!("assert_eq!(10", stringify!($SelfT), ".log10(), 1);")]
+        /// ```
+        #[unstable(feature = "int_log", issue = "70887")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline]
+        #[track_caller]
+        #[rustc_inherit_overflow_checks]
+        #[allow(arithmetic_overflow)]
+        pub const fn log10(self) -> u32 {
+            match self.checked_log10() {
+                Some(n) => n,
+                None => {
+                    // In debug builds, trigger a panic on None.
+                    // This should optimize completely out in release builds.
+                    let _ = Self::MAX + 1;
+
+                    0
+                },
+            }
+        }
+
+        /// Returns the logarithm of the number with respect to an arbitrary base,
+        /// rounded down.
+        ///
+        /// Returns `None` if the number is zero, or if the base is not at least 2.
+        ///
+        /// This method might not be optimized owing to implementation details;
+        /// `checked_log2` can produce results more efficiently for base 2, and
+        /// `checked_log10` can produce results more efficiently for base 10.
+        ///
+        /// # Examples
+        ///
+        /// ```
+        /// #![feature(int_log)]
+        #[doc = concat!("assert_eq!(5", stringify!($SelfT), ".checked_log(5), Some(1));")]
+        /// ```
+        #[unstable(feature = "int_log", issue = "70887")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline]
+        pub const fn checked_log(self, base: Self) -> Option<u32> {
+            if self <= 0 || base <= 1 {
+                None
+            } else {
+                let mut n = 0;
+                let mut r = self;
+
+                // Optimization for 128 bit wide integers.
+                if Self::BITS == 128 {
+                    let b = Self::log2(self) / (Self::log2(base) + 1);
+                    n += b;
+                    r /= base.pow(b as u32);
+                }
+
+                while r >= base {
+                    r /= base;
+                    n += 1;
+                }
+                Some(n)
+            }
+        }
+
+        /// Returns the base 2 logarithm of the number, rounded down.
+        ///
+        /// Returns `None` if the number is zero.
+        ///
+        /// # Examples
+        ///
+        /// ```
+        /// #![feature(int_log)]
+        #[doc = concat!("assert_eq!(2", stringify!($SelfT), ".checked_log2(), Some(1));")]
+        /// ```
+        #[unstable(feature = "int_log", issue = "70887")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline]
+        pub const fn checked_log2(self) -> Option<u32> {
+            if let Some(x) = <$NonZeroT>::new(self) {
+                Some(x.log2())
+            } else {
+                None
+            }
+        }
+
+        /// Returns the base 10 logarithm of the number, rounded down.
+        ///
+        /// Returns `None` if the number is zero.
+        ///
+        /// # Examples
+        ///
+        /// ```
+        /// #![feature(int_log)]
+        #[doc = concat!("assert_eq!(10", stringify!($SelfT), ".checked_log10(), Some(1));")]
+        /// ```
+        #[unstable(feature = "int_log", issue = "70887")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline]
+        pub const fn checked_log10(self) -> Option<u32> {
+            if let Some(x) = <$NonZeroT>::new(self) {
+                Some(x.log10())
+            } else {
+                None
+            }
+        }
+
+        /// Checked negation. Computes `-self`, returning `None` unless `self ==
+        /// 0`.
+        ///
+        /// Note that negating any positive integer will overflow.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        #[doc = concat!("assert_eq!(0", stringify!($SelfT), ".checked_neg(), Some(0));")]
+        #[doc = concat!("assert_eq!(1", stringify!($SelfT), ".checked_neg(), None);")]
+        /// ```
+        #[stable(feature = "wrapping", since = "1.7.0")]
+        #[rustc_const_stable(feature = "const_checked_int_methods", since = "1.47.0")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline]
+        pub const fn checked_neg(self) -> Option<Self> {
+            let (a, b) = self.overflowing_neg();
+            if unlikely!(b) {None} else {Some(a)}
+        }
+
+        /// Checked shift left. Computes `self << rhs`, returning `None`
+        /// if `rhs` is larger than or equal to the number of bits in `self`.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        #[doc = concat!("assert_eq!(0x1", stringify!($SelfT), ".checked_shl(4), Some(0x10));")]
+        #[doc = concat!("assert_eq!(0x10", stringify!($SelfT), ".checked_shl(129), None);")]
+        /// ```
+        #[stable(feature = "wrapping", since = "1.7.0")]
+        #[rustc_const_stable(feature = "const_checked_int_methods", since = "1.47.0")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline]
+        pub const fn checked_shl(self, rhs: u32) -> Option<Self> {
+            let (a, b) = self.overflowing_shl(rhs);
+            if unlikely!(b) {None} else {Some(a)}
+        }
+
+        /// Unchecked shift left. Computes `self << rhs`, assuming that
+        /// `rhs` is less than the number of bits in `self`.
+        ///
+        /// # Safety
+        ///
+        /// This results in undefined behavior if `rhs` is larger than
+        /// or equal to the number of bits in `self`,
+        /// i.e. when [`checked_shl`] would return `None`.
+        ///
+        #[doc = concat!("[`checked_shl`]: ", stringify!($SelfT), "::checked_shl")]
+        #[unstable(
+            feature = "unchecked_math",
+            reason = "niche optimization path",
+            issue = "85122",
+        )]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[rustc_const_unstable(feature = "const_inherent_unchecked_arith", issue = "85122")]
+        #[inline(always)]
+        #[cfg_attr(miri, track_caller)] // even without panics, this helps for Miri backtraces
+        pub const unsafe fn unchecked_shl(self, rhs: Self) -> Self {
+            // SAFETY: the caller must uphold the safety contract for
+            // `unchecked_shl`.
+            unsafe { intrinsics::unchecked_shl(self, rhs) }
+        }
+
+        /// Checked shift right. Computes `self >> rhs`, returning `None`
+        /// if `rhs` is larger than or equal to the number of bits in `self`.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        #[doc = concat!("assert_eq!(0x10", stringify!($SelfT), ".checked_shr(4), Some(0x1));")]
+        #[doc = concat!("assert_eq!(0x10", stringify!($SelfT), ".checked_shr(129), None);")]
+        /// ```
+        #[stable(feature = "wrapping", since = "1.7.0")]
+        #[rustc_const_stable(feature = "const_checked_int_methods", since = "1.47.0")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline]
+        pub const fn checked_shr(self, rhs: u32) -> Option<Self> {
+            let (a, b) = self.overflowing_shr(rhs);
+            if unlikely!(b) {None} else {Some(a)}
+        }
+
+        /// Unchecked shift right. Computes `self >> rhs`, assuming that
+        /// `rhs` is less than the number of bits in `self`.
+        ///
+        /// # Safety
+        ///
+        /// This results in undefined behavior if `rhs` is larger than
+        /// or equal to the number of bits in `self`,
+        /// i.e. when [`checked_shr`] would return `None`.
+        ///
+        #[doc = concat!("[`checked_shr`]: ", stringify!($SelfT), "::checked_shr")]
+        #[unstable(
+            feature = "unchecked_math",
+            reason = "niche optimization path",
+            issue = "85122",
+        )]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[rustc_const_unstable(feature = "const_inherent_unchecked_arith", issue = "85122")]
+        #[inline(always)]
+        #[cfg_attr(miri, track_caller)] // even without panics, this helps for Miri backtraces
+        pub const unsafe fn unchecked_shr(self, rhs: Self) -> Self {
+            // SAFETY: the caller must uphold the safety contract for
+            // `unchecked_shr`.
+            unsafe { intrinsics::unchecked_shr(self, rhs) }
+        }
+
+        /// Checked exponentiation. Computes `self.pow(exp)`, returning `None` if
+        /// overflow occurred.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        #[doc = concat!("assert_eq!(2", stringify!($SelfT), ".checked_pow(5), Some(32));")]
+        #[doc = concat!("assert_eq!(", stringify!($SelfT), "::MAX.checked_pow(2), None);")]
+        /// ```
+        #[stable(feature = "no_panic_pow", since = "1.34.0")]
+        #[rustc_const_stable(feature = "const_int_pow", since = "1.50.0")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline]
+        pub const fn checked_pow(self, mut exp: u32) -> Option<Self> {
+            if exp == 0 {
+                return Some(1);
+            }
+            let mut base = self;
+            let mut acc: Self = 1;
+
+            while exp > 1 {
+                if (exp & 1) == 1 {
+                    acc = try_opt!(acc.checked_mul(base));
+                }
+                exp /= 2;
+                base = try_opt!(base.checked_mul(base));
+            }
+
+            // since exp!=0, finally the exp must be 1.
+            // Deal with the final bit of the exponent separately, since
+            // squaring the base afterwards is not necessary and may cause a
+            // needless overflow.
+
+            Some(try_opt!(acc.checked_mul(base)))
+        }
+
+        /// Saturating integer addition. Computes `self + rhs`, saturating at
+        /// the numeric bounds instead of overflowing.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        #[doc = concat!("assert_eq!(100", stringify!($SelfT), ".saturating_add(1), 101);")]
+        #[doc = concat!("assert_eq!(", stringify!($SelfT), "::MAX.saturating_add(127), ", stringify!($SelfT), "::MAX);")]
+        /// ```
+        #[stable(feature = "rust1", since = "1.0.0")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[rustc_const_stable(feature = "const_saturating_int_methods", since = "1.47.0")]
+        #[inline(always)]
+        pub const fn saturating_add(self, rhs: Self) -> Self {
+            intrinsics::saturating_add(self, rhs)
+        }
+
+        /// Saturating addition with a signed integer. Computes `self + rhs`,
+        /// saturating at the numeric bounds instead of overflowing.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        /// # #![feature(mixed_integer_ops)]
+        #[doc = concat!("assert_eq!(1", stringify!($SelfT), ".saturating_add_signed(2), 3);")]
+        #[doc = concat!("assert_eq!(1", stringify!($SelfT), ".saturating_add_signed(-2), 0);")]
+        #[doc = concat!("assert_eq!((", stringify!($SelfT), "::MAX - 2).saturating_add_signed(4), ", stringify!($SelfT), "::MAX);")]
+        /// ```
+        #[unstable(feature = "mixed_integer_ops", issue = "87840")]
+        #[rustc_const_unstable(feature = "mixed_integer_ops", issue = "87840")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline]
+        pub const fn saturating_add_signed(self, rhs: $SignedT) -> Self {
+            let (res, overflow) = self.overflowing_add(rhs as Self);
+            if overflow == (rhs < 0) {
+                res
+            } else if overflow {
+                Self::MAX
+            } else {
+                0
+            }
+        }
+
+        /// Saturating integer subtraction. Computes `self - rhs`, saturating
+        /// at the numeric bounds instead of overflowing.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        #[doc = concat!("assert_eq!(100", stringify!($SelfT), ".saturating_sub(27), 73);")]
+        #[doc = concat!("assert_eq!(13", stringify!($SelfT), ".saturating_sub(127), 0);")]
+        /// ```
+        #[stable(feature = "rust1", since = "1.0.0")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[rustc_const_stable(feature = "const_saturating_int_methods", since = "1.47.0")]
+        #[inline(always)]
+        pub const fn saturating_sub(self, rhs: Self) -> Self {
+            intrinsics::saturating_sub(self, rhs)
+        }
+
+        /// Saturating integer multiplication. Computes `self * rhs`,
+        /// saturating at the numeric bounds instead of overflowing.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        #[doc = concat!("assert_eq!(2", stringify!($SelfT), ".saturating_mul(10), 20);")]
+        #[doc = concat!("assert_eq!((", stringify!($SelfT), "::MAX).saturating_mul(10), ", stringify!($SelfT),"::MAX);")]
+        /// ```
+        #[stable(feature = "wrapping", since = "1.7.0")]
+        #[rustc_const_stable(feature = "const_saturating_int_methods", since = "1.47.0")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline]
+        pub const fn saturating_mul(self, rhs: Self) -> Self {
+            match self.checked_mul(rhs) {
+                Some(x) => x,
+                None => Self::MAX,
+            }
+        }
+
+        /// Saturating integer division. Computes `self / rhs`, saturating at the
+        /// numeric bounds instead of overflowing.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        #[doc = concat!("assert_eq!(5", stringify!($SelfT), ".saturating_div(2), 2);")]
+        ///
+        /// ```
+        ///
+        /// ```should_panic
+        #[doc = concat!("let _ = 1", stringify!($SelfT), ".saturating_div(0);")]
+        ///
+        /// ```
+        #[stable(feature = "saturating_div", since = "1.58.0")]
+        #[rustc_const_stable(feature = "saturating_div", since = "1.58.0")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline]
+        pub const fn saturating_div(self, rhs: Self) -> Self {
+            // on unsigned types, there is no overflow in integer division
+            self.wrapping_div(rhs)
+        }
+
+        /// Saturating integer exponentiation. Computes `self.pow(exp)`,
+        /// saturating at the numeric bounds instead of overflowing.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        #[doc = concat!("assert_eq!(4", stringify!($SelfT), ".saturating_pow(3), 64);")]
+        #[doc = concat!("assert_eq!(", stringify!($SelfT), "::MAX.saturating_pow(2), ", stringify!($SelfT), "::MAX);")]
+        /// ```
+        #[stable(feature = "no_panic_pow", since = "1.34.0")]
+        #[rustc_const_stable(feature = "const_int_pow", since = "1.50.0")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline]
+        pub const fn saturating_pow(self, exp: u32) -> Self {
+            match self.checked_pow(exp) {
+                Some(x) => x,
+                None => Self::MAX,
+            }
+        }
+
+        /// Wrapping (modular) addition. Computes `self + rhs`,
+        /// wrapping around at the boundary of the type.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        #[doc = concat!("assert_eq!(200", stringify!($SelfT), ".wrapping_add(55), 255);")]
+        #[doc = concat!("assert_eq!(200", stringify!($SelfT), ".wrapping_add(", stringify!($SelfT), "::MAX), 199);")]
+        /// ```
+        #[stable(feature = "rust1", since = "1.0.0")]
+        #[rustc_const_stable(feature = "const_wrapping_math", since = "1.32.0")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline(always)]
+        pub const fn wrapping_add(self, rhs: Self) -> Self {
+            intrinsics::wrapping_add(self, rhs)
+        }
+
+        /// Wrapping (modular) addition with a signed integer. Computes
+        /// `self + rhs`, wrapping around at the boundary of the type.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        /// # #![feature(mixed_integer_ops)]
+        #[doc = concat!("assert_eq!(1", stringify!($SelfT), ".wrapping_add_signed(2), 3);")]
+        #[doc = concat!("assert_eq!(1", stringify!($SelfT), ".wrapping_add_signed(-2), ", stringify!($SelfT), "::MAX);")]
+        #[doc = concat!("assert_eq!((", stringify!($SelfT), "::MAX - 2).wrapping_add_signed(4), 1);")]
+        /// ```
+        #[unstable(feature = "mixed_integer_ops", issue = "87840")]
+        #[rustc_const_unstable(feature = "mixed_integer_ops", issue = "87840")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline]
+        pub const fn wrapping_add_signed(self, rhs: $SignedT) -> Self {
+            self.wrapping_add(rhs as Self)
+        }
+
+        /// Wrapping (modular) subtraction. Computes `self - rhs`,
+        /// wrapping around at the boundary of the type.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        #[doc = concat!("assert_eq!(100", stringify!($SelfT), ".wrapping_sub(100), 0);")]
+        #[doc = concat!("assert_eq!(100", stringify!($SelfT), ".wrapping_sub(", stringify!($SelfT), "::MAX), 101);")]
+        /// ```
+        #[stable(feature = "rust1", since = "1.0.0")]
+        #[rustc_const_stable(feature = "const_wrapping_math", since = "1.32.0")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline(always)]
+        pub const fn wrapping_sub(self, rhs: Self) -> Self {
+            intrinsics::wrapping_sub(self, rhs)
+        }
+
+        /// Wrapping (modular) multiplication. Computes `self *
+        /// rhs`, wrapping around at the boundary of the type.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// Please note that this example is shared between integer types.
+        /// Which explains why `u8` is used here.
+        ///
+        /// ```
+        /// assert_eq!(10u8.wrapping_mul(12), 120);
+        /// assert_eq!(25u8.wrapping_mul(12), 44);
+        /// ```
+        #[stable(feature = "rust1", since = "1.0.0")]
+        #[rustc_const_stable(feature = "const_wrapping_math", since = "1.32.0")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline(always)]
+        pub const fn wrapping_mul(self, rhs: Self) -> Self {
+            intrinsics::wrapping_mul(self, rhs)
+        }
+
+        /// Wrapping (modular) division. Computes `self / rhs`.
+        /// Wrapped division on unsigned types is just normal division.
+        /// There's no way wrapping could ever happen.
+        /// This function exists, so that all operations
+        /// are accounted for in the wrapping operations.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        #[doc = concat!("assert_eq!(100", stringify!($SelfT), ".wrapping_div(10), 10);")]
+        /// ```
+        #[stable(feature = "num_wrapping", since = "1.2.0")]
+        #[rustc_const_stable(feature = "const_wrapping_int_methods", since = "1.52.0")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline(always)]
+        pub const fn wrapping_div(self, rhs: Self) -> Self {
+            self / rhs
+        }
+
+        /// Wrapping Euclidean division. Computes `self.div_euclid(rhs)`.
+        /// Wrapped division on unsigned types is just normal division.
+        /// There's no way wrapping could ever happen.
+        /// This function exists, so that all operations
+        /// are accounted for in the wrapping operations.
+        /// Since, for the positive integers, all common
+        /// definitions of division are equal, this
+        /// is exactly equal to `self.wrapping_div(rhs)`.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        #[doc = concat!("assert_eq!(100", stringify!($SelfT), ".wrapping_div_euclid(10), 10);")]
+        /// ```
+        #[stable(feature = "euclidean_division", since = "1.38.0")]
+        #[rustc_const_stable(feature = "const_euclidean_int_methods", since = "1.52.0")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline(always)]
+        pub const fn wrapping_div_euclid(self, rhs: Self) -> Self {
+            self / rhs
+        }
+
+        /// Wrapping (modular) remainder. Computes `self % rhs`.
+        /// Wrapped remainder calculation on unsigned types is
+        /// just the regular remainder calculation.
+        /// There's no way wrapping could ever happen.
+        /// This function exists, so that all operations
+        /// are accounted for in the wrapping operations.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        #[doc = concat!("assert_eq!(100", stringify!($SelfT), ".wrapping_rem(10), 0);")]
+        /// ```
+        #[stable(feature = "num_wrapping", since = "1.2.0")]
+        #[rustc_const_stable(feature = "const_wrapping_int_methods", since = "1.52.0")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline(always)]
+        pub const fn wrapping_rem(self, rhs: Self) -> Self {
+            self % rhs
+        }
+
+        /// Wrapping Euclidean modulo. Computes `self.rem_euclid(rhs)`.
+        /// Wrapped modulo calculation on unsigned types is
+        /// just the regular remainder calculation.
+        /// There's no way wrapping could ever happen.
+        /// This function exists, so that all operations
+        /// are accounted for in the wrapping operations.
+        /// Since, for the positive integers, all common
+        /// definitions of division are equal, this
+        /// is exactly equal to `self.wrapping_rem(rhs)`.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        #[doc = concat!("assert_eq!(100", stringify!($SelfT), ".wrapping_rem_euclid(10), 0);")]
+        /// ```
+        #[stable(feature = "euclidean_division", since = "1.38.0")]
+        #[rustc_const_stable(feature = "const_euclidean_int_methods", since = "1.52.0")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline(always)]
+        pub const fn wrapping_rem_euclid(self, rhs: Self) -> Self {
+            self % rhs
+        }
+
+        /// Wrapping (modular) negation. Computes `-self`,
+        /// wrapping around at the boundary of the type.
+        ///
+        /// Since unsigned types do not have negative equivalents
+        /// all applications of this function will wrap (except for `-0`).
+        /// For values smaller than the corresponding signed type's maximum
+        /// the result is the same as casting the corresponding signed value.
+        /// Any larger values are equivalent to `MAX + 1 - (val - MAX - 1)` where
+        /// `MAX` is the corresponding signed type's maximum.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// Please note that this example is shared between integer types.
+        /// Which explains why `i8` is used here.
+        ///
+        /// ```
+        /// assert_eq!(100i8.wrapping_neg(), -100);
+        /// assert_eq!((-128i8).wrapping_neg(), -128);
+        /// ```
+        #[stable(feature = "num_wrapping", since = "1.2.0")]
+        #[rustc_const_stable(feature = "const_wrapping_math", since = "1.32.0")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline(always)]
+        pub const fn wrapping_neg(self) -> Self {
+            (0 as $SelfT).wrapping_sub(self)
+        }
+
+        /// Panic-free bitwise shift-left; yields `self << mask(rhs)`,
+        /// where `mask` removes any high-order bits of `rhs` that
+        /// would cause the shift to exceed the bitwidth of the type.
+        ///
+        /// Note that this is *not* the same as a rotate-left; the
+        /// RHS of a wrapping shift-left is restricted to the range
+        /// of the type, rather than the bits shifted out of the LHS
+        /// being returned to the other end. The primitive integer
+        /// types all implement a [`rotate_left`](Self::rotate_left) function,
+        /// which may be what you want instead.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        #[doc = concat!("assert_eq!(1", stringify!($SelfT), ".wrapping_shl(7), 128);")]
+        #[doc = concat!("assert_eq!(1", stringify!($SelfT), ".wrapping_shl(128), 1);")]
+        /// ```
+        #[stable(feature = "num_wrapping", since = "1.2.0")]
+        #[rustc_const_stable(feature = "const_wrapping_math", since = "1.32.0")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline(always)]
+        pub const fn wrapping_shl(self, rhs: u32) -> Self {
+            // SAFETY: the masking by the bitsize of the type ensures that we do not shift
+            // out of bounds
+            unsafe {
+                intrinsics::unchecked_shl(self, (rhs & ($BITS - 1)) as $SelfT)
+            }
+        }
+
+        /// Panic-free bitwise shift-right; yields `self >> mask(rhs)`,
+        /// where `mask` removes any high-order bits of `rhs` that
+        /// would cause the shift to exceed the bitwidth of the type.
+        ///
+        /// Note that this is *not* the same as a rotate-right; the
+        /// RHS of a wrapping shift-right is restricted to the range
+        /// of the type, rather than the bits shifted out of the LHS
+        /// being returned to the other end. The primitive integer
+        /// types all implement a [`rotate_right`](Self::rotate_right) function,
+        /// which may be what you want instead.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        #[doc = concat!("assert_eq!(128", stringify!($SelfT), ".wrapping_shr(7), 1);")]
+        #[doc = concat!("assert_eq!(128", stringify!($SelfT), ".wrapping_shr(128), 128);")]
+        /// ```
+        #[stable(feature = "num_wrapping", since = "1.2.0")]
+        #[rustc_const_stable(feature = "const_wrapping_math", since = "1.32.0")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline(always)]
+        pub const fn wrapping_shr(self, rhs: u32) -> Self {
+            // SAFETY: the masking by the bitsize of the type ensures that we do not shift
+            // out of bounds
+            unsafe {
+                intrinsics::unchecked_shr(self, (rhs & ($BITS - 1)) as $SelfT)
+            }
+        }
+
+        /// Wrapping (modular) exponentiation. Computes `self.pow(exp)`,
+        /// wrapping around at the boundary of the type.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        #[doc = concat!("assert_eq!(3", stringify!($SelfT), ".wrapping_pow(5), 243);")]
+        /// assert_eq!(3u8.wrapping_pow(6), 217);
+        /// ```
+        #[stable(feature = "no_panic_pow", since = "1.34.0")]
+        #[rustc_const_stable(feature = "const_int_pow", since = "1.50.0")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline]
+        pub const fn wrapping_pow(self, mut exp: u32) -> Self {
+            if exp == 0 {
+                return 1;
+            }
+            let mut base = self;
+            let mut acc: Self = 1;
+
+            while exp > 1 {
+                if (exp & 1) == 1 {
+                    acc = acc.wrapping_mul(base);
+                }
+                exp /= 2;
+                base = base.wrapping_mul(base);
+            }
+
+            // since exp!=0, finally the exp must be 1.
+            // Deal with the final bit of the exponent separately, since
+            // squaring the base afterwards is not necessary and may cause a
+            // needless overflow.
+            acc.wrapping_mul(base)
+        }
+
+        /// Calculates `self` + `rhs`
+        ///
+        /// Returns a tuple of the addition along with a boolean indicating
+        /// whether an arithmetic overflow would occur. If an overflow would
+        /// have occurred then the wrapped value is returned.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage
+        ///
+        /// ```
+        ///
+        #[doc = concat!("assert_eq!(5", stringify!($SelfT), ".overflowing_add(2), (7, false));")]
+        #[doc = concat!("assert_eq!(", stringify!($SelfT), "::MAX.overflowing_add(1), (0, true));")]
+        /// ```
+        #[stable(feature = "wrapping", since = "1.7.0")]
+        #[rustc_const_stable(feature = "const_wrapping_math", since = "1.32.0")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline(always)]
+        pub const fn overflowing_add(self, rhs: Self) -> (Self, bool) {
+            let (a, b) = intrinsics::add_with_overflow(self as $ActualT, rhs as $ActualT);
+            (a as Self, b)
+        }
+
+        /// Calculates `self + rhs + carry` without the ability to overflow.
+        ///
+        /// Performs "ternary addition" which takes in an extra bit to add, and may return an
+        /// additional bit of overflow. This allows for chaining together multiple additions
+        /// to create "big integers" which represent larger values.
+        ///
+        #[doc = concat!("This can be thought of as a ", stringify!($BITS), "-bit \"full adder\", in the electronics sense.")]
+        ///
+        /// # Examples
+        ///
+        /// Basic usage
+        ///
+        /// ```
+        /// #![feature(bigint_helper_methods)]
+        #[doc = concat!("assert_eq!(5", stringify!($SelfT), ".carrying_add(2, false), (7, false));")]
+        #[doc = concat!("assert_eq!(5", stringify!($SelfT), ".carrying_add(2, true), (8, false));")]
+        #[doc = concat!("assert_eq!(", stringify!($SelfT), "::MAX.carrying_add(1, false), (0, true));")]
+        #[doc = concat!("assert_eq!(", stringify!($SelfT), "::MAX.carrying_add(0, true), (0, true));")]
+        #[doc = concat!("assert_eq!(", stringify!($SelfT), "::MAX.carrying_add(1, true), (1, true));")]
+        #[doc = concat!("assert_eq!(",
+            stringify!($SelfT), "::MAX.carrying_add(", stringify!($SelfT), "::MAX, true), ",
+            "(", stringify!($SelfT), "::MAX, true));"
+        )]
+        /// ```
+        ///
+        /// If `carry` is false, this method is equivalent to [`overflowing_add`](Self::overflowing_add):
+        ///
+        /// ```
+        /// #![feature(bigint_helper_methods)]
+        #[doc = concat!("assert_eq!(5_", stringify!($SelfT), ".carrying_add(2, false), 5_", stringify!($SelfT), ".overflowing_add(2));")]
+        #[doc = concat!("assert_eq!(", stringify!($SelfT), "::MAX.carrying_add(1, false), ", stringify!($SelfT), "::MAX.overflowing_add(1));")]
+        /// ```
+        #[unstable(feature = "bigint_helper_methods", issue = "85532")]
+        #[rustc_const_unstable(feature = "const_bigint_helper_methods", issue = "85532")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline]
+        pub const fn carrying_add(self, rhs: Self, carry: bool) -> (Self, bool) {
+            // note: longer-term this should be done via an intrinsic, but this has been shown
+            //   to generate optimal code for now, and LLVM doesn't have an equivalent intrinsic
+            let (a, b) = self.overflowing_add(rhs);
+            let (c, d) = a.overflowing_add(carry as $SelfT);
+            (c, b || d)
+        }
+
+        /// Calculates `self` + `rhs` with a signed `rhs`
+        ///
+        /// Returns a tuple of the addition along with a boolean indicating
+        /// whether an arithmetic overflow would occur. If an overflow would
+        /// have occurred then the wrapped value is returned.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        /// # #![feature(mixed_integer_ops)]
+        #[doc = concat!("assert_eq!(1", stringify!($SelfT), ".overflowing_add_signed(2), (3, false));")]
+        #[doc = concat!("assert_eq!(1", stringify!($SelfT), ".overflowing_add_signed(-2), (", stringify!($SelfT), "::MAX, true));")]
+        #[doc = concat!("assert_eq!((", stringify!($SelfT), "::MAX - 2).overflowing_add_signed(4), (1, true));")]
+        /// ```
+        #[unstable(feature = "mixed_integer_ops", issue = "87840")]
+        #[rustc_const_unstable(feature = "mixed_integer_ops", issue = "87840")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline]
+        pub const fn overflowing_add_signed(self, rhs: $SignedT) -> (Self, bool) {
+            let (res, overflowed) = self.overflowing_add(rhs as Self);
+            (res, overflowed ^ (rhs < 0))
+        }
+
+        /// Calculates `self` - `rhs`
+        ///
+        /// Returns a tuple of the subtraction along with a boolean indicating
+        /// whether an arithmetic overflow would occur. If an overflow would
+        /// have occurred then the wrapped value is returned.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage
+        ///
+        /// ```
+        ///
+        #[doc = concat!("assert_eq!(5", stringify!($SelfT), ".overflowing_sub(2), (3, false));")]
+        #[doc = concat!("assert_eq!(0", stringify!($SelfT), ".overflowing_sub(1), (", stringify!($SelfT), "::MAX, true));")]
+        /// ```
+        #[stable(feature = "wrapping", since = "1.7.0")]
+        #[rustc_const_stable(feature = "const_wrapping_math", since = "1.32.0")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline(always)]
+        pub const fn overflowing_sub(self, rhs: Self) -> (Self, bool) {
+            let (a, b) = intrinsics::sub_with_overflow(self as $ActualT, rhs as $ActualT);
+            (a as Self, b)
+        }
+
+        /// Calculates `self - rhs - borrow` without the ability to overflow.
+        ///
+        /// Performs "ternary subtraction" which takes in an extra bit to subtract, and may return
+        /// an additional bit of overflow. This allows for chaining together multiple subtractions
+        /// to create "big integers" which represent larger values.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage
+        ///
+        /// ```
+        /// #![feature(bigint_helper_methods)]
+        #[doc = concat!("assert_eq!(5", stringify!($SelfT), ".borrowing_sub(2, false), (3, false));")]
+        #[doc = concat!("assert_eq!(5", stringify!($SelfT), ".borrowing_sub(2, true), (2, false));")]
+        #[doc = concat!("assert_eq!(0", stringify!($SelfT), ".borrowing_sub(1, false), (", stringify!($SelfT), "::MAX, true));")]
+        #[doc = concat!("assert_eq!(0", stringify!($SelfT), ".borrowing_sub(1, true), (", stringify!($SelfT), "::MAX - 1, true));")]
+        /// ```
+        #[unstable(feature = "bigint_helper_methods", issue = "85532")]
+        #[rustc_const_unstable(feature = "const_bigint_helper_methods", issue = "85532")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline]
+        pub const fn borrowing_sub(self, rhs: Self, borrow: bool) -> (Self, bool) {
+            // note: longer-term this should be done via an intrinsic, but this has been shown
+            //   to generate optimal code for now, and LLVM doesn't have an equivalent intrinsic
+            let (a, b) = self.overflowing_sub(rhs);
+            let (c, d) = a.overflowing_sub(borrow as $SelfT);
+            (c, b || d)
+        }
+
+        /// Computes the absolute difference between `self` and `other`.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        #[doc = concat!("assert_eq!(100", stringify!($SelfT), ".abs_diff(80), 20", stringify!($SelfT), ");")]
+        #[doc = concat!("assert_eq!(100", stringify!($SelfT), ".abs_diff(110), 10", stringify!($SelfT), ");")]
+        /// ```
+        #[stable(feature = "int_abs_diff", since = "1.60.0")]
+        #[rustc_const_stable(feature = "int_abs_diff", since = "1.60.0")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline]
+        pub const fn abs_diff(self, other: Self) -> Self {
+            if mem::size_of::<Self>() == 1 {
+                // Trick LLVM into generating the psadbw instruction when SSE2
+                // is available and this function is autovectorized for u8's.
+                (self as i32).wrapping_sub(other as i32).abs() as Self
+            } else {
+                if self < other {
+                    other - self
+                } else {
+                    self - other
+                }
+            }
+        }
+
+        /// Calculates the multiplication of `self` and `rhs`.
+        ///
+        /// Returns a tuple of the multiplication along with a boolean
+        /// indicating whether an arithmetic overflow would occur. If an
+        /// overflow would have occurred then the wrapped value is returned.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// Please note that this example is shared between integer types.
+        /// Which explains why `u32` is used here.
+        ///
+        /// ```
+        /// assert_eq!(5u32.overflowing_mul(2), (10, false));
+        /// assert_eq!(1_000_000_000u32.overflowing_mul(10), (1410065408, true));
+        /// ```
+        #[stable(feature = "wrapping", since = "1.7.0")]
+        #[rustc_const_stable(feature = "const_wrapping_math", since = "1.32.0")]
+        #[must_use = "this returns the result of the operation, \
+                          without modifying the original"]
+        #[inline(always)]
+        pub const fn overflowing_mul(self, rhs: Self) -> (Self, bool) {
+            let (a, b) = intrinsics::mul_with_overflow(self as $ActualT, rhs as $ActualT);
+            (a as Self, b)
+        }
+
+        /// Calculates the divisor when `self` is divided by `rhs`.
+        ///
+        /// Returns a tuple of the divisor along with a boolean indicating
+        /// whether an arithmetic overflow would occur. Note that for unsigned
+        /// integers overflow never occurs, so the second value is always
+        /// `false`.
+        ///
+        /// # Panics
+        ///
+        /// This function will panic if `rhs` is 0.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage
+        ///
+        /// ```
+        #[doc = concat!("assert_eq!(5", stringify!($SelfT), ".overflowing_div(2), (2, false));")]
+        /// ```
+        #[inline(always)]
+        #[stable(feature = "wrapping", since = "1.7.0")]
+        #[rustc_const_stable(feature = "const_overflowing_int_methods", since = "1.52.0")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        pub const fn overflowing_div(self, rhs: Self) -> (Self, bool) {
+            (self / rhs, false)
+        }
+
+        /// Calculates the quotient of Euclidean division `self.div_euclid(rhs)`.
+        ///
+        /// Returns a tuple of the divisor along with a boolean indicating
+        /// whether an arithmetic overflow would occur. Note that for unsigned
+        /// integers overflow never occurs, so the second value is always
+        /// `false`.
+        /// Since, for the positive integers, all common
+        /// definitions of division are equal, this
+        /// is exactly equal to `self.overflowing_div(rhs)`.
+        ///
+        /// # Panics
+        ///
+        /// This function will panic if `rhs` is 0.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage
+        ///
+        /// ```
+        #[doc = concat!("assert_eq!(5", stringify!($SelfT), ".overflowing_div_euclid(2), (2, false));")]
+        /// ```
+        #[inline(always)]
+        #[stable(feature = "euclidean_division", since = "1.38.0")]
+        #[rustc_const_stable(feature = "const_euclidean_int_methods", since = "1.52.0")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        pub const fn overflowing_div_euclid(self, rhs: Self) -> (Self, bool) {
+            (self / rhs, false)
+        }
+
+        /// Calculates the remainder when `self` is divided by `rhs`.
+        ///
+        /// Returns a tuple of the remainder after dividing along with a boolean
+        /// indicating whether an arithmetic overflow would occur. Note that for
+        /// unsigned integers overflow never occurs, so the second value is
+        /// always `false`.
+        ///
+        /// # Panics
+        ///
+        /// This function will panic if `rhs` is 0.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage
+        ///
+        /// ```
+        #[doc = concat!("assert_eq!(5", stringify!($SelfT), ".overflowing_rem(2), (1, false));")]
+        /// ```
+        #[inline(always)]
+        #[stable(feature = "wrapping", since = "1.7.0")]
+        #[rustc_const_stable(feature = "const_overflowing_int_methods", since = "1.52.0")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        pub const fn overflowing_rem(self, rhs: Self) -> (Self, bool) {
+            (self % rhs, false)
+        }
+
+        /// Calculates the remainder `self.rem_euclid(rhs)` as if by Euclidean division.
+        ///
+        /// Returns a tuple of the modulo after dividing along with a boolean
+        /// indicating whether an arithmetic overflow would occur. Note that for
+        /// unsigned integers overflow never occurs, so the second value is
+        /// always `false`.
+        /// Since, for the positive integers, all common
+        /// definitions of division are equal, this operation
+        /// is exactly equal to `self.overflowing_rem(rhs)`.
+        ///
+        /// # Panics
+        ///
+        /// This function will panic if `rhs` is 0.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage
+        ///
+        /// ```
+        #[doc = concat!("assert_eq!(5", stringify!($SelfT), ".overflowing_rem_euclid(2), (1, false));")]
+        /// ```
+        #[inline(always)]
+        #[stable(feature = "euclidean_division", since = "1.38.0")]
+        #[rustc_const_stable(feature = "const_euclidean_int_methods", since = "1.52.0")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        pub const fn overflowing_rem_euclid(self, rhs: Self) -> (Self, bool) {
+            (self % rhs, false)
+        }
+
+        /// Negates self in an overflowing fashion.
+        ///
+        /// Returns `!self + 1` using wrapping operations to return the value
+        /// that represents the negation of this unsigned value. Note that for
+        /// positive unsigned values overflow always occurs, but negating 0 does
+        /// not overflow.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage
+        ///
+        /// ```
+        #[doc = concat!("assert_eq!(0", stringify!($SelfT), ".overflowing_neg(), (0, false));")]
+        #[doc = concat!("assert_eq!(2", stringify!($SelfT), ".overflowing_neg(), (-2i32 as ", stringify!($SelfT), ", true));")]
+        /// ```
+        #[inline(always)]
+        #[stable(feature = "wrapping", since = "1.7.0")]
+        #[rustc_const_stable(feature = "const_wrapping_math", since = "1.32.0")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        pub const fn overflowing_neg(self) -> (Self, bool) {
+            ((!self).wrapping_add(1), self != 0)
+        }
+
+        /// Shifts self left by `rhs` bits.
+        ///
+        /// Returns a tuple of the shifted version of self along with a boolean
+        /// indicating whether the shift value was larger than or equal to the
+        /// number of bits. If the shift value is too large, then value is
+        /// masked (N-1) where N is the number of bits, and this value is then
+        /// used to perform the shift.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage
+        ///
+        /// ```
+        #[doc = concat!("assert_eq!(0x1", stringify!($SelfT), ".overflowing_shl(4), (0x10, false));")]
+        #[doc = concat!("assert_eq!(0x1", stringify!($SelfT), ".overflowing_shl(132), (0x10, true));")]
+        /// ```
+        #[stable(feature = "wrapping", since = "1.7.0")]
+        #[rustc_const_stable(feature = "const_wrapping_math", since = "1.32.0")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline(always)]
+        pub const fn overflowing_shl(self, rhs: u32) -> (Self, bool) {
+            (self.wrapping_shl(rhs), (rhs > ($BITS - 1)))
+        }
+
+        /// Shifts self right by `rhs` bits.
+        ///
+        /// Returns a tuple of the shifted version of self along with a boolean
+        /// indicating whether the shift value was larger than or equal to the
+        /// number of bits. If the shift value is too large, then value is
+        /// masked (N-1) where N is the number of bits, and this value is then
+        /// used to perform the shift.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage
+        ///
+        /// ```
+        #[doc = concat!("assert_eq!(0x10", stringify!($SelfT), ".overflowing_shr(4), (0x1, false));")]
+        #[doc = concat!("assert_eq!(0x10", stringify!($SelfT), ".overflowing_shr(132), (0x1, true));")]
+        /// ```
+        #[stable(feature = "wrapping", since = "1.7.0")]
+        #[rustc_const_stable(feature = "const_wrapping_math", since = "1.32.0")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline(always)]
+        pub const fn overflowing_shr(self, rhs: u32) -> (Self, bool) {
+            (self.wrapping_shr(rhs), (rhs > ($BITS - 1)))
+        }
+
+        /// Raises self to the power of `exp`, using exponentiation by squaring.
+        ///
+        /// Returns a tuple of the exponentiation along with a bool indicating
+        /// whether an overflow happened.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        #[doc = concat!("assert_eq!(3", stringify!($SelfT), ".overflowing_pow(5), (243, false));")]
+        /// assert_eq!(3u8.overflowing_pow(6), (217, true));
+        /// ```
+        #[stable(feature = "no_panic_pow", since = "1.34.0")]
+        #[rustc_const_stable(feature = "const_int_pow", since = "1.50.0")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline]
+        pub const fn overflowing_pow(self, mut exp: u32) -> (Self, bool) {
+            if exp == 0{
+                return (1,false);
+            }
+            let mut base = self;
+            let mut acc: Self = 1;
+            let mut overflown = false;
+            // Scratch space for storing results of overflowing_mul.
+            let mut r;
+
+            while exp > 1 {
+                if (exp & 1) == 1 {
+                    r = acc.overflowing_mul(base);
+                    acc = r.0;
+                    overflown |= r.1;
+                }
+                exp /= 2;
+                r = base.overflowing_mul(base);
+                base = r.0;
+                overflown |= r.1;
+            }
+
+            // since exp!=0, finally the exp must be 1.
+            // Deal with the final bit of the exponent separately, since
+            // squaring the base afterwards is not necessary and may cause a
+            // needless overflow.
+            r = acc.overflowing_mul(base);
+            r.1 |= overflown;
+
+            r
+        }
+
+        /// Raises self to the power of `exp`, using exponentiation by squaring.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        #[doc = concat!("assert_eq!(2", stringify!($SelfT), ".pow(5), 32);")]
+        /// ```
+        #[stable(feature = "rust1", since = "1.0.0")]
+        #[rustc_const_stable(feature = "const_int_pow", since = "1.50.0")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline]
+        #[rustc_inherit_overflow_checks]
+        pub const fn pow(self, mut exp: u32) -> Self {
+            if exp == 0 {
+                return 1;
+            }
+            let mut base = self;
+            let mut acc = 1;
+
+            while exp > 1 {
+                if (exp & 1) == 1 {
+                    acc = acc * base;
+                }
+                exp /= 2;
+                base = base * base;
+            }
+
+            // since exp!=0, finally the exp must be 1.
+            // Deal with the final bit of the exponent separately, since
+            // squaring the base afterwards is not necessary and may cause a
+            // needless overflow.
+            acc * base
+        }
+
+        /// Performs Euclidean division.
+        ///
+        /// Since, for the positive integers, all common
+        /// definitions of division are equal, this
+        /// is exactly equal to `self / rhs`.
+        ///
+        /// # Panics
+        ///
+        /// This function will panic if `rhs` is 0.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        #[doc = concat!("assert_eq!(7", stringify!($SelfT), ".div_euclid(4), 1); // or any other integer type")]
+        /// ```
+        #[stable(feature = "euclidean_division", since = "1.38.0")]
+        #[rustc_const_stable(feature = "const_euclidean_int_methods", since = "1.52.0")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline(always)]
+        #[rustc_inherit_overflow_checks]
+        pub const fn div_euclid(self, rhs: Self) -> Self {
+            self / rhs
+        }
+
+
+        /// Calculates the least remainder of `self (mod rhs)`.
+        ///
+        /// Since, for the positive integers, all common
+        /// definitions of division are equal, this
+        /// is exactly equal to `self % rhs`.
+        ///
+        /// # Panics
+        ///
+        /// This function will panic if `rhs` is 0.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        #[doc = concat!("assert_eq!(7", stringify!($SelfT), ".rem_euclid(4), 3); // or any other integer type")]
+        /// ```
+        #[stable(feature = "euclidean_division", since = "1.38.0")]
+        #[rustc_const_stable(feature = "const_euclidean_int_methods", since = "1.52.0")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline(always)]
+        #[rustc_inherit_overflow_checks]
+        pub const fn rem_euclid(self, rhs: Self) -> Self {
+            self % rhs
+        }
+
+        /// Calculates the quotient of `self` and `rhs`, rounding the result towards negative infinity.
+        ///
+        /// This is the same as performing `self / rhs` for all unsigned integers.
+        ///
+        /// # Panics
+        ///
+        /// This function will panic if `rhs` is zero.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        /// #![feature(int_roundings)]
+        #[doc = concat!("assert_eq!(7_", stringify!($SelfT), ".div_floor(4), 1);")]
+        /// ```
+        #[unstable(feature = "int_roundings", issue = "88581")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline(always)]
+        pub const fn div_floor(self, rhs: Self) -> Self {
+            self / rhs
+        }
+
+        /// Calculates the quotient of `self` and `rhs`, rounding the result towards positive infinity.
+        ///
+        /// # Panics
+        ///
+        /// This function will panic if `rhs` is zero.
+        ///
+        /// ## Overflow behavior
+        ///
+        /// On overflow, this function will panic if overflow checks are enabled (default in debug
+        /// mode) and wrap if overflow checks are disabled (default in release mode).
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        /// #![feature(int_roundings)]
+        #[doc = concat!("assert_eq!(7_", stringify!($SelfT), ".div_ceil(4), 2);")]
+        /// ```
+        #[unstable(feature = "int_roundings", issue = "88581")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline]
+        #[rustc_inherit_overflow_checks]
+        pub const fn div_ceil(self, rhs: Self) -> Self {
+            let d = self / rhs;
+            let r = self % rhs;
+            if r > 0 && rhs > 0 {
+                d + 1
+            } else {
+                d
+            }
+        }
+
+        /// Calculates the smallest value greater than or equal to `self` that
+        /// is a multiple of `rhs`.
+        ///
+        /// # Panics
+        ///
+        /// This function will panic if `rhs` is zero.
+        ///
+        /// ## Overflow behavior
+        ///
+        /// On overflow, this function will panic if overflow checks are enabled (default in debug
+        /// mode) and wrap if overflow checks are disabled (default in release mode).
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        /// #![feature(int_roundings)]
+        #[doc = concat!("assert_eq!(16_", stringify!($SelfT), ".next_multiple_of(8), 16);")]
+        #[doc = concat!("assert_eq!(23_", stringify!($SelfT), ".next_multiple_of(8), 24);")]
+        /// ```
+        #[unstable(feature = "int_roundings", issue = "88581")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline]
+        #[rustc_inherit_overflow_checks]
+        pub const fn next_multiple_of(self, rhs: Self) -> Self {
+            match self % rhs {
+                0 => self,
+                r => self + (rhs - r)
+            }
+        }
+
+        /// Calculates the smallest value greater than or equal to `self` that
+        /// is a multiple of `rhs`. Returns `None` if `rhs` is zero or the
+        /// operation would result in overflow.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        /// #![feature(int_roundings)]
+        #[doc = concat!("assert_eq!(16_", stringify!($SelfT), ".checked_next_multiple_of(8), Some(16));")]
+        #[doc = concat!("assert_eq!(23_", stringify!($SelfT), ".checked_next_multiple_of(8), Some(24));")]
+        #[doc = concat!("assert_eq!(1_", stringify!($SelfT), ".checked_next_multiple_of(0), None);")]
+        #[doc = concat!("assert_eq!(", stringify!($SelfT), "::MAX.checked_next_multiple_of(2), None);")]
+        /// ```
+        #[unstable(feature = "int_roundings", issue = "88581")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline]
+        pub const fn checked_next_multiple_of(self, rhs: Self) -> Option<Self> {
+            match try_opt!(self.checked_rem(rhs)) {
+                0 => Some(self),
+                // rhs - r cannot overflow because r is smaller than rhs
+                r => self.checked_add(rhs - r)
+            }
+        }
+
+        /// Returns `true` if and only if `self == 2^k` for some `k`.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        #[doc = concat!("assert!(16", stringify!($SelfT), ".is_power_of_two());")]
+        #[doc = concat!("assert!(!10", stringify!($SelfT), ".is_power_of_two());")]
+        /// ```
+        #[must_use]
+        #[stable(feature = "rust1", since = "1.0.0")]
+        #[rustc_const_stable(feature = "const_is_power_of_two", since = "1.32.0")]
+        #[inline(always)]
+        pub const fn is_power_of_two(self) -> bool {
+            self.count_ones() == 1
+        }
+
+        // Returns one less than next power of two.
+        // (For 8u8 next power of two is 8u8 and for 6u8 it is 8u8)
+        //
+        // 8u8.one_less_than_next_power_of_two() == 7
+        // 6u8.one_less_than_next_power_of_two() == 7
+        //
+        // This method cannot overflow, as in the `next_power_of_two`
+        // overflow cases it instead ends up returning the maximum value
+        // of the type, and can return 0 for 0.
+        #[inline]
+        #[rustc_const_stable(feature = "const_int_pow", since = "1.50.0")]
+        const fn one_less_than_next_power_of_two(self) -> Self {
+            if self <= 1 { return 0; }
+
+            let p = self - 1;
+            // SAFETY: Because `p > 0`, it cannot consist entirely of leading zeros.
+            // That means the shift is always in-bounds, and some processors
+            // (such as intel pre-haswell) have more efficient ctlz
+            // intrinsics when the argument is non-zero.
+            let z = unsafe { intrinsics::ctlz_nonzero(p) };
+            <$SelfT>::MAX >> z
+        }
+
+        /// Returns the smallest power of two greater than or equal to `self`.
+        ///
+        /// When return value overflows (i.e., `self > (1 << (N-1))` for type
+        /// `uN`), it panics in debug mode and the return value is wrapped to 0 in
+        /// release mode (the only situation in which method can return 0).
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        #[doc = concat!("assert_eq!(2", stringify!($SelfT), ".next_power_of_two(), 2);")]
+        #[doc = concat!("assert_eq!(3", stringify!($SelfT), ".next_power_of_two(), 4);")]
+        /// ```
+        #[stable(feature = "rust1", since = "1.0.0")]
+        #[rustc_const_stable(feature = "const_int_pow", since = "1.50.0")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline]
+        #[rustc_inherit_overflow_checks]
+        pub const fn next_power_of_two(self) -> Self {
+            self.one_less_than_next_power_of_two() + 1
+        }
+
+        /// Returns the smallest power of two greater than or equal to `n`. If
+        /// the next power of two is greater than the type's maximum value,
+        /// `None` is returned, otherwise the power of two is wrapped in `Some`.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        #[doc = concat!("assert_eq!(2", stringify!($SelfT), ".checked_next_power_of_two(), Some(2));")]
+        #[doc = concat!("assert_eq!(3", stringify!($SelfT), ".checked_next_power_of_two(), Some(4));")]
+        #[doc = concat!("assert_eq!(", stringify!($SelfT), "::MAX.checked_next_power_of_two(), None);")]
+        /// ```
+        #[inline]
+        #[stable(feature = "rust1", since = "1.0.0")]
+        #[rustc_const_stable(feature = "const_int_pow", since = "1.50.0")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        pub const fn checked_next_power_of_two(self) -> Option<Self> {
+            self.one_less_than_next_power_of_two().checked_add(1)
+        }
+
+        /// Returns the smallest power of two greater than or equal to `n`. If
+        /// the next power of two is greater than the type's maximum value,
+        /// the return value is wrapped to `0`.
+        ///
+        /// # Examples
+        ///
+        /// Basic usage:
+        ///
+        /// ```
+        /// #![feature(wrapping_next_power_of_two)]
+        ///
+        #[doc = concat!("assert_eq!(2", stringify!($SelfT), ".wrapping_next_power_of_two(), 2);")]
+        #[doc = concat!("assert_eq!(3", stringify!($SelfT), ".wrapping_next_power_of_two(), 4);")]
+        #[doc = concat!("assert_eq!(", stringify!($SelfT), "::MAX.wrapping_next_power_of_two(), 0);")]
+        /// ```
+        #[inline]
+        #[unstable(feature = "wrapping_next_power_of_two", issue = "32463",
+                   reason = "needs decision on wrapping behaviour")]
+        #[rustc_const_unstable(feature = "wrapping_next_power_of_two", issue = "32463")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        pub const fn wrapping_next_power_of_two(self) -> Self {
+            self.one_less_than_next_power_of_two().wrapping_add(1)
+        }
+
+        /// Return the memory representation of this integer as a byte array in
+        /// big-endian (network) byte order.
+        ///
+        #[doc = $to_xe_bytes_doc]
+        ///
+        /// # Examples
+        ///
+        /// ```
+        #[doc = concat!("let bytes = ", $swap_op, stringify!($SelfT), ".to_be_bytes();")]
+        #[doc = concat!("assert_eq!(bytes, ", $be_bytes, ");")]
+        /// ```
+        #[stable(feature = "int_to_from_bytes", since = "1.32.0")]
+        #[rustc_const_stable(feature = "const_int_conversion", since = "1.44.0")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline]
+        pub const fn to_be_bytes(self) -> [u8; mem::size_of::<Self>()] {
+            self.to_be().to_ne_bytes()
+        }
+
+        /// Return the memory representation of this integer as a byte array in
+        /// little-endian byte order.
+        ///
+        #[doc = $to_xe_bytes_doc]
+        ///
+        /// # Examples
+        ///
+        /// ```
+        #[doc = concat!("let bytes = ", $swap_op, stringify!($SelfT), ".to_le_bytes();")]
+        #[doc = concat!("assert_eq!(bytes, ", $le_bytes, ");")]
+        /// ```
+        #[stable(feature = "int_to_from_bytes", since = "1.32.0")]
+        #[rustc_const_stable(feature = "const_int_conversion", since = "1.44.0")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        #[inline]
+        pub const fn to_le_bytes(self) -> [u8; mem::size_of::<Self>()] {
+            self.to_le().to_ne_bytes()
+        }
+
+        /// Return the memory representation of this integer as a byte array in
+        /// native byte order.
+        ///
+        /// As the target platform's native endianness is used, portable code
+        /// should use [`to_be_bytes`] or [`to_le_bytes`], as appropriate,
+        /// instead.
+        ///
+        #[doc = $to_xe_bytes_doc]
+        ///
+        /// [`to_be_bytes`]: Self::to_be_bytes
+        /// [`to_le_bytes`]: Self::to_le_bytes
+        ///
+        /// # Examples
+        ///
+        /// ```
+        #[doc = concat!("let bytes = ", $swap_op, stringify!($SelfT), ".to_ne_bytes();")]
+        /// assert_eq!(
+        ///     bytes,
+        ///     if cfg!(target_endian = "big") {
+        #[doc = concat!("        ", $be_bytes)]
+        ///     } else {
+        #[doc = concat!("        ", $le_bytes)]
+        ///     }
+        /// );
+        /// ```
+        #[stable(feature = "int_to_from_bytes", since = "1.32.0")]
+        #[rustc_const_stable(feature = "const_int_conversion", since = "1.44.0")]
+        #[must_use = "this returns the result of the operation, \
+                      without modifying the original"]
+        // SAFETY: const sound because integers are plain old datatypes so we can always
+        // transmute them to arrays of bytes
+        #[inline]
+        pub const fn to_ne_bytes(self) -> [u8; mem::size_of::<Self>()] {
+            // SAFETY: integers are plain old datatypes so we can always transmute them to
+            // arrays of bytes
+            unsafe { mem::transmute(self) }
+        }
+
+        /// Create a native endian integer value from its representation
+        /// as a byte array in big endian.
+        ///
+        #[doc = $from_xe_bytes_doc]
+        ///
+        /// # Examples
+        ///
+        /// ```
+        #[doc = concat!("let value = ", stringify!($SelfT), "::from_be_bytes(", $be_bytes, ");")]
+        #[doc = concat!("assert_eq!(value, ", $swap_op, ");")]
+        /// ```
+        ///
+        /// When starting from a slice rather than an array, fallible conversion APIs can be used:
+        ///
+        /// ```
+        #[doc = concat!("fn read_be_", stringify!($SelfT), "(input: &mut &[u8]) -> ", stringify!($SelfT), " {")]
+        #[doc = concat!("    let (int_bytes, rest) = input.split_at(std::mem::size_of::<", stringify!($SelfT), ">());")]
+        ///     *input = rest;
+        #[doc = concat!("    ", stringify!($SelfT), "::from_be_bytes(int_bytes.try_into().unwrap())")]
+        /// }
+        /// ```
+        #[stable(feature = "int_to_from_bytes", since = "1.32.0")]
+        #[rustc_const_stable(feature = "const_int_conversion", since = "1.44.0")]
+        #[must_use]
+        #[inline]
+        pub const fn from_be_bytes(bytes: [u8; mem::size_of::<Self>()]) -> Self {
+            Self::from_be(Self::from_ne_bytes(bytes))
+        }
+
+        /// Create a native endian integer value from its representation
+        /// as a byte array in little endian.
+        ///
+        #[doc = $from_xe_bytes_doc]
+        ///
+        /// # Examples
+        ///
+        /// ```
+        #[doc = concat!("let value = ", stringify!($SelfT), "::from_le_bytes(", $le_bytes, ");")]
+        #[doc = concat!("assert_eq!(value, ", $swap_op, ");")]
+        /// ```
+        ///
+        /// When starting from a slice rather than an array, fallible conversion APIs can be used:
+        ///
+        /// ```
+        #[doc = concat!("fn read_le_", stringify!($SelfT), "(input: &mut &[u8]) -> ", stringify!($SelfT), " {")]
+        #[doc = concat!("    let (int_bytes, rest) = input.split_at(std::mem::size_of::<", stringify!($SelfT), ">());")]
+        ///     *input = rest;
+        #[doc = concat!("    ", stringify!($SelfT), "::from_le_bytes(int_bytes.try_into().unwrap())")]
+        /// }
+        /// ```
+        #[stable(feature = "int_to_from_bytes", since = "1.32.0")]
+        #[rustc_const_stable(feature = "const_int_conversion", since = "1.44.0")]
+        #[must_use]
+        #[inline]
+        pub const fn from_le_bytes(bytes: [u8; mem::size_of::<Self>()]) -> Self {
+            Self::from_le(Self::from_ne_bytes(bytes))
+        }
+
+        /// Create a native endian integer value from its memory representation
+        /// as a byte array in native endianness.
+        ///
+        /// As the target platform's native endianness is used, portable code
+        /// likely wants to use [`from_be_bytes`] or [`from_le_bytes`], as
+        /// appropriate instead.
+        ///
+        /// [`from_be_bytes`]: Self::from_be_bytes
+        /// [`from_le_bytes`]: Self::from_le_bytes
+        ///
+        #[doc = $from_xe_bytes_doc]
+        ///
+        /// # Examples
+        ///
+        /// ```
+        #[doc = concat!("let value = ", stringify!($SelfT), "::from_ne_bytes(if cfg!(target_endian = \"big\") {")]
+        #[doc = concat!("    ", $be_bytes, "")]
+        /// } else {
+        #[doc = concat!("    ", $le_bytes, "")]
+        /// });
+        #[doc = concat!("assert_eq!(value, ", $swap_op, ");")]
+        /// ```
+        ///
+        /// When starting from a slice rather than an array, fallible conversion APIs can be used:
+        ///
+        /// ```
+        #[doc = concat!("fn read_ne_", stringify!($SelfT), "(input: &mut &[u8]) -> ", stringify!($SelfT), " {")]
+        #[doc = concat!("    let (int_bytes, rest) = input.split_at(std::mem::size_of::<", stringify!($SelfT), ">());")]
+        ///     *input = rest;
+        #[doc = concat!("    ", stringify!($SelfT), "::from_ne_bytes(int_bytes.try_into().unwrap())")]
+        /// }
+        /// ```
+        #[stable(feature = "int_to_from_bytes", since = "1.32.0")]
+        #[rustc_const_stable(feature = "const_int_conversion", since = "1.44.0")]
+        #[must_use]
+        // SAFETY: const sound because integers are plain old datatypes so we can always
+        // transmute to them
+        #[inline]
+        pub const fn from_ne_bytes(bytes: [u8; mem::size_of::<Self>()]) -> Self {
+            // SAFETY: integers are plain old datatypes so we can always transmute to them
+            unsafe { mem::transmute(bytes) }
+        }
+
+        /// New code should prefer to use
+        #[doc = concat!("[`", stringify!($SelfT), "::MIN", "`] instead.")]
+        ///
+        /// Returns the smallest value that can be represented by this integer type.
+        #[stable(feature = "rust1", since = "1.0.0")]
+        #[rustc_promotable]
+        #[inline(always)]
+        #[rustc_const_stable(feature = "const_max_value", since = "1.32.0")]
+        #[deprecated(since = "TBD", note = "replaced by the `MIN` associated constant on this type")]
+        pub const fn min_value() -> Self { Self::MIN }
+
+        /// New code should prefer to use
+        #[doc = concat!("[`", stringify!($SelfT), "::MAX", "`] instead.")]
+        ///
+        /// Returns the largest value that can be represented by this integer type.
+        #[stable(feature = "rust1", since = "1.0.0")]
+        #[rustc_promotable]
+        #[inline(always)]
+        #[rustc_const_stable(feature = "const_max_value", since = "1.32.0")]
+        #[deprecated(since = "TBD", note = "replaced by the `MAX` associated constant on this type")]
+        pub const fn max_value() -> Self { Self::MAX }
+    }
+}
diff --git a/library/core/src/num/wrapping.rs b/library/core/src/num/wrapping.rs
new file mode 100644
index 000000000..5353d900e
--- /dev/null
+++ b/library/core/src/num/wrapping.rs
@@ -0,0 +1,1123 @@
+//! Definitions of `Wrapping<T>`.
+
+use crate::fmt;
+use crate::ops::{Add, AddAssign, BitAnd, BitAndAssign, BitOr, BitOrAssign};
+use crate::ops::{BitXor, BitXorAssign, Div, DivAssign};
+use crate::ops::{Mul, MulAssign, Neg, Not, Rem, RemAssign};
+use crate::ops::{Shl, ShlAssign, Shr, ShrAssign, Sub, SubAssign};
+
+/// Provides intentionally-wrapped arithmetic on `T`.
+///
+/// Operations like `+` on `u32` values are intended to never overflow,
+/// and in some debug configurations overflow is detected and results
+/// in a panic. While most arithmetic falls into this category, some
+/// code explicitly expects and relies upon modular arithmetic (e.g.,
+/// hashing).
+///
+/// Wrapping arithmetic can be achieved either through methods like
+/// `wrapping_add`, or through the `Wrapping<T>` type, which says that
+/// all standard arithmetic operations on the underlying value are
+/// intended to have wrapping semantics.
+///
+/// The underlying value can be retrieved through the `.0` index of the
+/// `Wrapping` tuple.
+///
+/// # Examples
+///
+/// ```
+/// use std::num::Wrapping;
+///
+/// let zero = Wrapping(0u32);
+/// let one = Wrapping(1u32);
+///
+/// assert_eq!(u32::MAX, (zero - one).0);
+/// ```
+///
+/// # Layout
+///
+/// `Wrapping<T>` is guaranteed to have the same layout and ABI as `T`.
+#[stable(feature = "rust1", since = "1.0.0")]
+#[derive(PartialEq, Eq, PartialOrd, Ord, Clone, Copy, Default, Hash)]
+#[repr(transparent)]
+pub struct Wrapping<T>(#[stable(feature = "rust1", since = "1.0.0")] pub T);
+
+#[stable(feature = "rust1", since = "1.0.0")]
+impl<T: fmt::Debug> fmt::Debug for Wrapping<T> {
+    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
+        self.0.fmt(f)
+    }
+}
+
+#[stable(feature = "wrapping_display", since = "1.10.0")]
+impl<T: fmt::Display> fmt::Display for Wrapping<T> {
+    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
+        self.0.fmt(f)
+    }
+}
+
+#[stable(feature = "wrapping_fmt", since = "1.11.0")]
+impl<T: fmt::Binary> fmt::Binary for Wrapping<T> {
+    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
+        self.0.fmt(f)
+    }
+}
+
+#[stable(feature = "wrapping_fmt", since = "1.11.0")]
+impl<T: fmt::Octal> fmt::Octal for Wrapping<T> {
+    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
+        self.0.fmt(f)
+    }
+}
+
+#[stable(feature = "wrapping_fmt", since = "1.11.0")]
+impl<T: fmt::LowerHex> fmt::LowerHex for Wrapping<T> {
+    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
+        self.0.fmt(f)
+    }
+}
+
+#[stable(feature = "wrapping_fmt", since = "1.11.0")]
+impl<T: fmt::UpperHex> fmt::UpperHex for Wrapping<T> {
+    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
+        self.0.fmt(f)
+    }
+}
+
+#[allow(unused_macros)]
+macro_rules! sh_impl_signed {
+    ($t:ident, $f:ident) => {
+        #[stable(feature = "rust1", since = "1.0.0")]
+        #[rustc_const_unstable(feature = "const_ops", issue = "90080")]
+        impl const Shl<$f> for Wrapping<$t> {
+            type Output = Wrapping<$t>;
+
+            #[inline]
+            fn shl(self, other: $f) -> Wrapping<$t> {
+                if other < 0 {
+                    Wrapping(self.0.wrapping_shr((-other & self::shift_max::$t as $f) as u32))
+                } else {
+                    Wrapping(self.0.wrapping_shl((other & self::shift_max::$t as $f) as u32))
+                }
+            }
+        }
+        forward_ref_binop! { impl const Shl, shl for Wrapping<$t>, $f,
+        #[stable(feature = "wrapping_ref_ops", since = "1.39.0")] }
+
+        #[stable(feature = "op_assign_traits", since = "1.8.0")]
+        #[rustc_const_unstable(feature = "const_ops", issue = "90080")]
+        impl const ShlAssign<$f> for Wrapping<$t> {
+            #[inline]
+            fn shl_assign(&mut self, other: $f) {
+                *self = *self << other;
+            }
+        }
+        forward_ref_op_assign! { impl const ShlAssign, shl_assign for Wrapping<$t>, $f }
+
+        #[stable(feature = "rust1", since = "1.0.0")]
+        #[rustc_const_unstable(feature = "const_ops", issue = "90080")]
+        impl const Shr<$f> for Wrapping<$t> {
+            type Output = Wrapping<$t>;
+
+            #[inline]
+            fn shr(self, other: $f) -> Wrapping<$t> {
+                if other < 0 {
+                    Wrapping(self.0.wrapping_shl((-other & self::shift_max::$t as $f) as u32))
+                } else {
+                    Wrapping(self.0.wrapping_shr((other & self::shift_max::$t as $f) as u32))
+                }
+            }
+        }
+        forward_ref_binop! { impl const Shr, shr for Wrapping<$t>, $f,
+        #[stable(feature = "wrapping_ref_ops", since = "1.39.0")] }
+
+        #[stable(feature = "op_assign_traits", since = "1.8.0")]
+        #[rustc_const_unstable(feature = "const_ops", issue = "90080")]
+        impl const ShrAssign<$f> for Wrapping<$t> {
+            #[inline]
+            fn shr_assign(&mut self, other: $f) {
+                *self = *self >> other;
+            }
+        }
+        forward_ref_op_assign! { impl const ShrAssign, shr_assign for Wrapping<$t>, $f }
+    };
+}
+
+macro_rules! sh_impl_unsigned {
+    ($t:ident, $f:ident) => {
+        #[stable(feature = "rust1", since = "1.0.0")]
+        #[rustc_const_unstable(feature = "const_ops", issue = "90080")]
+        impl const Shl<$f> for Wrapping<$t> {
+            type Output = Wrapping<$t>;
+
+            #[inline]
+            fn shl(self, other: $f) -> Wrapping<$t> {
+                Wrapping(self.0.wrapping_shl((other & self::shift_max::$t as $f) as u32))
+            }
+        }
+        forward_ref_binop! { impl const Shl, shl for Wrapping<$t>, $f,
+        #[stable(feature = "wrapping_ref_ops", since = "1.39.0")] }
+
+        #[stable(feature = "op_assign_traits", since = "1.8.0")]
+        #[rustc_const_unstable(feature = "const_ops", issue = "90080")]
+        impl const ShlAssign<$f> for Wrapping<$t> {
+            #[inline]
+            fn shl_assign(&mut self, other: $f) {
+                *self = *self << other;
+            }
+        }
+        forward_ref_op_assign! { impl const ShlAssign, shl_assign for Wrapping<$t>, $f }
+
+        #[stable(feature = "rust1", since = "1.0.0")]
+        #[rustc_const_unstable(feature = "const_ops", issue = "90080")]
+        impl const Shr<$f> for Wrapping<$t> {
+            type Output = Wrapping<$t>;
+
+            #[inline]
+            fn shr(self, other: $f) -> Wrapping<$t> {
+                Wrapping(self.0.wrapping_shr((other & self::shift_max::$t as $f) as u32))
+            }
+        }
+        forward_ref_binop! { impl const Shr, shr for Wrapping<$t>, $f,
+        #[stable(feature = "wrapping_ref_ops", since = "1.39.0")] }
+
+        #[stable(feature = "op_assign_traits", since = "1.8.0")]
+        #[rustc_const_unstable(feature = "const_ops", issue = "90080")]
+        impl const ShrAssign<$f> for Wrapping<$t> {
+            #[inline]
+            fn shr_assign(&mut self, other: $f) {
+                *self = *self >> other;
+            }
+        }
+        forward_ref_op_assign! { impl const ShrAssign, shr_assign for Wrapping<$t>, $f }
+    };
+}
+
+// FIXME (#23545): uncomment the remaining impls
+macro_rules! sh_impl_all {
+    ($($t:ident)*) => ($(
+        //sh_impl_unsigned! { $t, u8 }
+        //sh_impl_unsigned! { $t, u16 }
+        //sh_impl_unsigned! { $t, u32 }
+        //sh_impl_unsigned! { $t, u64 }
+        //sh_impl_unsigned! { $t, u128 }
+        sh_impl_unsigned! { $t, usize }
+
+        //sh_impl_signed! { $t, i8 }
+        //sh_impl_signed! { $t, i16 }
+        //sh_impl_signed! { $t, i32 }
+        //sh_impl_signed! { $t, i64 }
+        //sh_impl_signed! { $t, i128 }
+        //sh_impl_signed! { $t, isize }
+    )*)
+}
+
+sh_impl_all! { u8 u16 u32 u64 u128 usize i8 i16 i32 i64 i128 isize }
+
+// FIXME(30524): impl Op<T> for Wrapping<T>, impl OpAssign<T> for Wrapping<T>
+macro_rules! wrapping_impl {
+    ($($t:ty)*) => ($(
+        #[stable(feature = "rust1", since = "1.0.0")]
+        #[rustc_const_unstable(feature = "const_ops", issue = "90080")]
+        impl const Add for Wrapping<$t> {
+            type Output = Wrapping<$t>;
+
+            #[inline]
+            fn add(self, other: Wrapping<$t>) -> Wrapping<$t> {
+                Wrapping(self.0.wrapping_add(other.0))
+            }
+        }
+        forward_ref_binop! { impl const Add, add for Wrapping<$t>, Wrapping<$t>,
+                #[stable(feature = "wrapping_ref", since = "1.14.0")] }
+
+        #[stable(feature = "op_assign_traits", since = "1.8.0")]
+        #[rustc_const_unstable(feature = "const_ops", issue = "90080")]
+        impl const AddAssign for Wrapping<$t> {
+            #[inline]
+            fn add_assign(&mut self, other: Wrapping<$t>) {
+                *self = *self + other;
+            }
+        }
+        forward_ref_op_assign! { impl const AddAssign, add_assign for Wrapping<$t>, Wrapping<$t> }
+
+        #[stable(feature = "wrapping_int_assign_impl", since = "1.60.0")]
+        #[rustc_const_unstable(feature = "const_ops", issue = "90080")]
+        impl const AddAssign<$t> for Wrapping<$t> {
+            #[inline]
+            fn add_assign(&mut self, other: $t) {
+                *self = *self + Wrapping(other);
+            }
+        }
+        forward_ref_op_assign! { impl const AddAssign, add_assign for Wrapping<$t>, $t }
+
+        #[stable(feature = "rust1", since = "1.0.0")]
+        #[rustc_const_unstable(feature = "const_ops", issue = "90080")]
+        impl const Sub for Wrapping<$t> {
+            type Output = Wrapping<$t>;
+
+            #[inline]
+            fn sub(self, other: Wrapping<$t>) -> Wrapping<$t> {
+                Wrapping(self.0.wrapping_sub(other.0))
+            }
+        }
+        forward_ref_binop! { impl const Sub, sub for Wrapping<$t>, Wrapping<$t>,
+                #[stable(feature = "wrapping_ref", since = "1.14.0")] }
+
+        #[stable(feature = "op_assign_traits", since = "1.8.0")]
+        #[rustc_const_unstable(feature = "const_ops", issue = "90080")]
+        impl const SubAssign for Wrapping<$t> {
+            #[inline]
+            fn sub_assign(&mut self, other: Wrapping<$t>) {
+                *self = *self - other;
+            }
+        }
+        forward_ref_op_assign! { impl const SubAssign, sub_assign for Wrapping<$t>, Wrapping<$t> }
+
+        #[stable(feature = "wrapping_int_assign_impl", since = "1.60.0")]
+        #[rustc_const_unstable(feature = "const_ops", issue = "90080")]
+        impl const SubAssign<$t> for Wrapping<$t> {
+            #[inline]
+            fn sub_assign(&mut self, other: $t) {
+                *self = *self - Wrapping(other);
+            }
+        }
+        forward_ref_op_assign! { impl const SubAssign, sub_assign for Wrapping<$t>, $t }
+
+        #[stable(feature = "rust1", since = "1.0.0")]
+        #[rustc_const_unstable(feature = "const_ops", issue = "90080")]
+        impl const Mul for Wrapping<$t> {
+            type Output = Wrapping<$t>;
+
+            #[inline]
+            fn mul(self, other: Wrapping<$t>) -> Wrapping<$t> {
+                Wrapping(self.0.wrapping_mul(other.0))
+            }
+        }
+        forward_ref_binop! { impl Mul, mul for Wrapping<$t>, Wrapping<$t>,
+                #[stable(feature = "wrapping_ref", since = "1.14.0")] }
+
+        #[stable(feature = "op_assign_traits", since = "1.8.0")]
+        #[rustc_const_unstable(feature = "const_ops", issue = "90080")]
+        impl const MulAssign for Wrapping<$t> {
+            #[inline]
+            fn mul_assign(&mut self, other: Wrapping<$t>) {
+                *self = *self * other;
+            }
+        }
+        forward_ref_op_assign! { impl const MulAssign, mul_assign for Wrapping<$t>, Wrapping<$t> }
+
+        #[stable(feature = "wrapping_int_assign_impl", since = "1.60.0")]
+        #[rustc_const_unstable(feature = "const_ops", issue = "90080")]
+        impl const MulAssign<$t> for Wrapping<$t> {
+            #[inline]
+            fn mul_assign(&mut self, other: $t) {
+                *self = *self * Wrapping(other);
+            }
+        }
+        forward_ref_op_assign! { impl const MulAssign, mul_assign for Wrapping<$t>, $t }
+
+        #[stable(feature = "wrapping_div", since = "1.3.0")]
+        #[rustc_const_unstable(feature = "const_ops", issue = "90080")]
+        impl const Div for Wrapping<$t> {
+            type Output = Wrapping<$t>;
+
+            #[inline]
+            fn div(self, other: Wrapping<$t>) -> Wrapping<$t> {
+                Wrapping(self.0.wrapping_div(other.0))
+            }
+        }
+        forward_ref_binop! { impl const Div, div for Wrapping<$t>, Wrapping<$t>,
+                #[stable(feature = "wrapping_ref", since = "1.14.0")] }
+
+        #[stable(feature = "op_assign_traits", since = "1.8.0")]
+        #[rustc_const_unstable(feature = "const_ops", issue = "90080")]
+        impl const DivAssign for Wrapping<$t> {
+            #[inline]
+            fn div_assign(&mut self, other: Wrapping<$t>) {
+                *self = *self / other;
+            }
+        }
+        forward_ref_op_assign! { impl const DivAssign, div_assign for Wrapping<$t>, Wrapping<$t> }
+
+        #[stable(feature = "wrapping_int_assign_impl", since = "1.60.0")]
+        #[rustc_const_unstable(feature = "const_ops", issue = "90080")]
+        impl const DivAssign<$t> for Wrapping<$t> {
+            #[inline]
+            fn div_assign(&mut self, other: $t) {
+                *self = *self / Wrapping(other);
+            }
+        }
+        forward_ref_op_assign! { impl const DivAssign, div_assign for Wrapping<$t>, $t }
+
+        #[stable(feature = "wrapping_impls", since = "1.7.0")]
+        #[rustc_const_unstable(feature = "const_ops", issue = "90080")]
+        impl const Rem for Wrapping<$t> {
+            type Output = Wrapping<$t>;
+
+            #[inline]
+            fn rem(self, other: Wrapping<$t>) -> Wrapping<$t> {
+                Wrapping(self.0.wrapping_rem(other.0))
+            }
+        }
+        forward_ref_binop! { impl const Rem, rem for Wrapping<$t>, Wrapping<$t>,
+                #[stable(feature = "wrapping_ref", since = "1.14.0")] }
+
+        #[stable(feature = "op_assign_traits", since = "1.8.0")]
+        #[rustc_const_unstable(feature = "const_ops", issue = "90080")]
+        impl const RemAssign for Wrapping<$t> {
+            #[inline]
+            fn rem_assign(&mut self, other: Wrapping<$t>) {
+                *self = *self % other;
+            }
+        }
+        forward_ref_op_assign! { impl const RemAssign, rem_assign for Wrapping<$t>, Wrapping<$t> }
+
+        #[stable(feature = "wrapping_int_assign_impl", since = "1.60.0")]
+        #[rustc_const_unstable(feature = "const_ops", issue = "90080")]
+        impl const RemAssign<$t> for Wrapping<$t> {
+            #[inline]
+            fn rem_assign(&mut self, other: $t) {
+                *self = *self % Wrapping(other);
+            }
+        }
+        forward_ref_op_assign! { impl const RemAssign, rem_assign for Wrapping<$t>, $t }
+
+        #[stable(feature = "rust1", since = "1.0.0")]
+        #[rustc_const_unstable(feature = "const_ops", issue = "90080")]
+        impl const Not for Wrapping<$t> {
+            type Output = Wrapping<$t>;
+
+            #[inline]
+            fn not(self) -> Wrapping<$t> {
+                Wrapping(!self.0)
+            }
+        }
+        forward_ref_unop! { impl const Not, not for Wrapping<$t>,
+                #[stable(feature = "wrapping_ref", since = "1.14.0")] }
+
+        #[stable(feature = "rust1", since = "1.0.0")]
+        #[rustc_const_unstable(feature = "const_ops", issue = "90080")]
+        impl const BitXor for Wrapping<$t> {
+            type Output = Wrapping<$t>;
+
+            #[inline]
+            fn bitxor(self, other: Wrapping<$t>) -> Wrapping<$t> {
+                Wrapping(self.0 ^ other.0)
+            }
+        }
+        forward_ref_binop! { impl const BitXor, bitxor for Wrapping<$t>, Wrapping<$t>,
+                #[stable(feature = "wrapping_ref", since = "1.14.0")] }
+
+        #[stable(feature = "op_assign_traits", since = "1.8.0")]
+        #[rustc_const_unstable(feature = "const_ops", issue = "90080")]
+        impl const BitXorAssign for Wrapping<$t> {
+            #[inline]
+            fn bitxor_assign(&mut self, other: Wrapping<$t>) {
+                *self = *self ^ other;
+            }
+        }
+        forward_ref_op_assign! { impl const BitXorAssign, bitxor_assign for Wrapping<$t>, Wrapping<$t> }
+
+        #[stable(feature = "wrapping_int_assign_impl", since = "1.60.0")]
+        #[rustc_const_unstable(feature = "const_ops", issue = "90080")]
+        impl const BitXorAssign<$t> for Wrapping<$t> {
+            #[inline]
+            fn bitxor_assign(&mut self, other: $t) {
+                *self = *self ^ Wrapping(other);
+            }
+        }
+        forward_ref_op_assign! { impl const BitXorAssign, bitxor_assign for Wrapping<$t>, $t }
+
+        #[stable(feature = "rust1", since = "1.0.0")]
+        #[rustc_const_unstable(feature = "const_ops", issue = "90080")]
+        impl const BitOr for Wrapping<$t> {
+            type Output = Wrapping<$t>;
+
+            #[inline]
+            fn bitor(self, other: Wrapping<$t>) -> Wrapping<$t> {
+                Wrapping(self.0 | other.0)
+            }
+        }
+        forward_ref_binop! { impl const BitOr, bitor for Wrapping<$t>, Wrapping<$t>,
+                #[stable(feature = "wrapping_ref", since = "1.14.0")] }
+
+        #[stable(feature = "op_assign_traits", since = "1.8.0")]
+        #[rustc_const_unstable(feature = "const_ops", issue = "90080")]
+        impl const BitOrAssign for Wrapping<$t> {
+            #[inline]
+            fn bitor_assign(&mut self, other: Wrapping<$t>) {
+                *self = *self | other;
+            }
+        }
+        forward_ref_op_assign! { impl const BitOrAssign, bitor_assign for Wrapping<$t>, Wrapping<$t> }
+
+        #[stable(feature = "wrapping_int_assign_impl", since = "1.60.0")]
+        #[rustc_const_unstable(feature = "const_ops", issue = "90080")]
+        impl const BitOrAssign<$t> for Wrapping<$t> {
+            #[inline]
+            fn bitor_assign(&mut self, other: $t) {
+                *self = *self | Wrapping(other);
+            }
+        }
+        forward_ref_op_assign! { impl const BitOrAssign, bitor_assign for Wrapping<$t>, $t }
+
+        #[stable(feature = "rust1", since = "1.0.0")]
+        #[rustc_const_unstable(feature = "const_ops", issue = "90080")]
+        impl const BitAnd for Wrapping<$t> {
+            type Output = Wrapping<$t>;
+
+            #[inline]
+            fn bitand(self, other: Wrapping<$t>) -> Wrapping<$t> {
+                Wrapping(self.0 & other.0)
+            }
+        }
+        forward_ref_binop! { impl const BitAnd, bitand for Wrapping<$t>, Wrapping<$t>,
+                #[stable(feature = "wrapping_ref", since = "1.14.0")] }
+
+        #[stable(feature = "op_assign_traits", since = "1.8.0")]
+        #[rustc_const_unstable(feature = "const_ops", issue = "90080")]
+        impl const BitAndAssign for Wrapping<$t> {
+            #[inline]
+            fn bitand_assign(&mut self, other: Wrapping<$t>) {
+                *self = *self & other;
+            }
+        }
+        forward_ref_op_assign! { impl const BitAndAssign, bitand_assign for Wrapping<$t>, Wrapping<$t> }
+
+        #[stable(feature = "wrapping_int_assign_impl", since = "1.60.0")]
+        #[rustc_const_unstable(feature = "const_ops", issue = "90080")]
+        impl const BitAndAssign<$t> for Wrapping<$t> {
+            #[inline]
+            fn bitand_assign(&mut self, other: $t) {
+                *self = *self & Wrapping(other);
+            }
+        }
+        forward_ref_op_assign! { impl const BitAndAssign, bitand_assign for Wrapping<$t>, $t }
+
+        #[stable(feature = "wrapping_neg", since = "1.10.0")]
+        #[rustc_const_unstable(feature = "const_ops", issue = "90080")]
+        impl const Neg for Wrapping<$t> {
+            type Output = Self;
+            #[inline]
+            fn neg(self) -> Self {
+                Wrapping(0) - self
+            }
+        }
+        forward_ref_unop! { impl const Neg, neg for Wrapping<$t>,
+                #[stable(feature = "wrapping_ref", since = "1.14.0")] }
+
+    )*)
+}
+
+wrapping_impl! { usize u8 u16 u32 u64 u128 isize i8 i16 i32 i64 i128 }
+
+macro_rules! wrapping_int_impl {
+    ($($t:ty)*) => ($(
+        impl Wrapping<$t> {
+            /// Returns the smallest value that can be represented by this integer type.
+            ///
+            /// # Examples
+            ///
+            /// Basic usage:
+            ///
+            /// ```
+            /// #![feature(wrapping_int_impl)]
+            /// use std::num::Wrapping;
+            ///
+            #[doc = concat!("assert_eq!(<Wrapping<", stringify!($t), ">>::MIN, Wrapping(", stringify!($t), "::MIN));")]
+            /// ```
+            #[unstable(feature = "wrapping_int_impl", issue = "32463")]
+            pub const MIN: Self = Self(<$t>::MIN);
+
+            /// Returns the largest value that can be represented by this integer type.
+            ///
+            /// # Examples
+            ///
+            /// Basic usage:
+            ///
+            /// ```
+            /// #![feature(wrapping_int_impl)]
+            /// use std::num::Wrapping;
+            ///
+            #[doc = concat!("assert_eq!(<Wrapping<", stringify!($t), ">>::MAX, Wrapping(", stringify!($t), "::MAX));")]
+            /// ```
+            #[unstable(feature = "wrapping_int_impl", issue = "32463")]
+            pub const MAX: Self = Self(<$t>::MAX);
+
+            /// Returns the size of this integer type in bits.
+            ///
+            /// # Examples
+            ///
+            /// Basic usage:
+            ///
+            /// ```
+            /// #![feature(wrapping_int_impl)]
+            /// use std::num::Wrapping;
+            ///
+            #[doc = concat!("assert_eq!(<Wrapping<", stringify!($t), ">>::BITS, ", stringify!($t), "::BITS);")]
+            /// ```
+            #[unstable(feature = "wrapping_int_impl", issue = "32463")]
+            pub const BITS: u32 = <$t>::BITS;
+
+            /// Returns the number of ones in the binary representation of `self`.
+            ///
+            /// # Examples
+            ///
+            /// Basic usage:
+            ///
+            /// ```
+            /// #![feature(wrapping_int_impl)]
+            /// use std::num::Wrapping;
+            ///
+            #[doc = concat!("let n = Wrapping(0b01001100", stringify!($t), ");")]
+            ///
+            /// assert_eq!(n.count_ones(), 3);
+            /// ```
+            #[inline]
+            #[doc(alias = "popcount")]
+            #[doc(alias = "popcnt")]
+            #[must_use = "this returns the result of the operation, \
+                          without modifying the original"]
+            #[unstable(feature = "wrapping_int_impl", issue = "32463")]
+            pub const fn count_ones(self) -> u32 {
+                self.0.count_ones()
+            }
+
+            /// Returns the number of zeros in the binary representation of `self`.
+            ///
+            /// # Examples
+            ///
+            /// Basic usage:
+            ///
+            /// ```
+            /// #![feature(wrapping_int_impl)]
+            /// use std::num::Wrapping;
+            ///
+            #[doc = concat!("assert_eq!(Wrapping(!0", stringify!($t), ").count_zeros(), 0);")]
+            /// ```
+            #[inline]
+            #[must_use = "this returns the result of the operation, \
+                          without modifying the original"]
+            #[unstable(feature = "wrapping_int_impl", issue = "32463")]
+            pub const fn count_zeros(self) -> u32 {
+                self.0.count_zeros()
+            }
+
+            /// Returns the number of trailing zeros in the binary representation of `self`.
+            ///
+            /// # Examples
+            ///
+            /// Basic usage:
+            ///
+            /// ```
+            /// #![feature(wrapping_int_impl)]
+            /// use std::num::Wrapping;
+            ///
+            #[doc = concat!("let n = Wrapping(0b0101000", stringify!($t), ");")]
+            ///
+            /// assert_eq!(n.trailing_zeros(), 3);
+            /// ```
+            #[inline]
+            #[must_use = "this returns the result of the operation, \
+                          without modifying the original"]
+            #[unstable(feature = "wrapping_int_impl", issue = "32463")]
+            pub const fn trailing_zeros(self) -> u32 {
+                self.0.trailing_zeros()
+            }
+
+            /// Shifts the bits to the left by a specified amount, `n`,
+            /// wrapping the truncated bits to the end of the resulting
+            /// integer.
+            ///
+            /// Please note this isn't the same operation as the `<<` shifting
+            /// operator!
+            ///
+            /// # Examples
+            ///
+            /// Basic usage:
+            ///
+            /// ```
+            /// #![feature(wrapping_int_impl)]
+            /// use std::num::Wrapping;
+            ///
+            /// let n: Wrapping<i64> = Wrapping(0x0123456789ABCDEF);
+            /// let m: Wrapping<i64> = Wrapping(-0x76543210FEDCBA99);
+            ///
+            /// assert_eq!(n.rotate_left(32), m);
+            /// ```
+            #[inline]
+            #[must_use = "this returns the result of the operation, \
+                          without modifying the original"]
+            #[unstable(feature = "wrapping_int_impl", issue = "32463")]
+            pub const fn rotate_left(self, n: u32) -> Self {
+                Wrapping(self.0.rotate_left(n))
+            }
+
+            /// Shifts the bits to the right by a specified amount, `n`,
+            /// wrapping the truncated bits to the beginning of the resulting
+            /// integer.
+            ///
+            /// Please note this isn't the same operation as the `>>` shifting
+            /// operator!
+            ///
+            /// # Examples
+            ///
+            /// Basic usage:
+            ///
+            /// ```
+            /// #![feature(wrapping_int_impl)]
+            /// use std::num::Wrapping;
+            ///
+            /// let n: Wrapping<i64> = Wrapping(0x0123456789ABCDEF);
+            /// let m: Wrapping<i64> = Wrapping(-0xFEDCBA987654322);
+            ///
+            /// assert_eq!(n.rotate_right(4), m);
+            /// ```
+            #[inline]
+            #[must_use = "this returns the result of the operation, \
+                          without modifying the original"]
+            #[unstable(feature = "wrapping_int_impl", issue = "32463")]
+            pub const fn rotate_right(self, n: u32) -> Self {
+                Wrapping(self.0.rotate_right(n))
+            }
+
+            /// Reverses the byte order of the integer.
+            ///
+            /// # Examples
+            ///
+            /// Basic usage:
+            ///
+            /// ```
+            /// #![feature(wrapping_int_impl)]
+            /// use std::num::Wrapping;
+            ///
+            /// let n: Wrapping<i16> = Wrapping(0b0000000_01010101);
+            /// assert_eq!(n, Wrapping(85));
+            ///
+            /// let m = n.swap_bytes();
+            ///
+            /// assert_eq!(m, Wrapping(0b01010101_00000000));
+            /// assert_eq!(m, Wrapping(21760));
+            /// ```
+            #[inline]
+            #[must_use = "this returns the result of the operation, \
+                          without modifying the original"]
+            #[unstable(feature = "wrapping_int_impl", issue = "32463")]
+            pub const fn swap_bytes(self) -> Self {
+                Wrapping(self.0.swap_bytes())
+            }
+
+            /// Reverses the bit pattern of the integer.
+            ///
+            /// # Examples
+            ///
+            /// Please note that this example is shared between integer types.
+            /// Which explains why `i16` is used here.
+            ///
+            /// Basic usage:
+            ///
+            /// ```
+            /// use std::num::Wrapping;
+            ///
+            /// let n = Wrapping(0b0000000_01010101i16);
+            /// assert_eq!(n, Wrapping(85));
+            ///
+            /// let m = n.reverse_bits();
+            ///
+            /// assert_eq!(m.0 as u16, 0b10101010_00000000);
+            /// assert_eq!(m, Wrapping(-22016));
+            /// ```
+            #[stable(feature = "reverse_bits", since = "1.37.0")]
+            #[rustc_const_stable(feature = "const_reverse_bits", since = "1.37.0")]
+            #[must_use = "this returns the result of the operation, \
+                          without modifying the original"]
+            #[inline]
+            pub const fn reverse_bits(self) -> Self {
+                Wrapping(self.0.reverse_bits())
+            }
+
+            /// Converts an integer from big endian to the target's endianness.
+            ///
+            /// On big endian this is a no-op. On little endian the bytes are
+            /// swapped.
+            ///
+            /// # Examples
+            ///
+            /// Basic usage:
+            ///
+            /// ```
+            /// #![feature(wrapping_int_impl)]
+            /// use std::num::Wrapping;
+            ///
+            #[doc = concat!("let n = Wrapping(0x1A", stringify!($t), ");")]
+            ///
+            /// if cfg!(target_endian = "big") {
+            #[doc = concat!("    assert_eq!(<Wrapping<", stringify!($t), ">>::from_be(n), n)")]
+            /// } else {
+            #[doc = concat!("    assert_eq!(<Wrapping<", stringify!($t), ">>::from_be(n), n.swap_bytes())")]
+            /// }
+            /// ```
+            #[inline]
+            #[must_use]
+            #[unstable(feature = "wrapping_int_impl", issue = "32463")]
+            pub const fn from_be(x: Self) -> Self {
+                Wrapping(<$t>::from_be(x.0))
+            }
+
+            /// Converts an integer from little endian to the target's endianness.
+            ///
+            /// On little endian this is a no-op. On big endian the bytes are
+            /// swapped.
+            ///
+            /// # Examples
+            ///
+            /// Basic usage:
+            ///
+            /// ```
+            /// #![feature(wrapping_int_impl)]
+            /// use std::num::Wrapping;
+            ///
+            #[doc = concat!("let n = Wrapping(0x1A", stringify!($t), ");")]
+            ///
+            /// if cfg!(target_endian = "little") {
+            #[doc = concat!("    assert_eq!(<Wrapping<", stringify!($t), ">>::from_le(n), n)")]
+            /// } else {
+            #[doc = concat!("    assert_eq!(<Wrapping<", stringify!($t), ">>::from_le(n), n.swap_bytes())")]
+            /// }
+            /// ```
+            #[inline]
+            #[must_use]
+            #[unstable(feature = "wrapping_int_impl", issue = "32463")]
+            pub const fn from_le(x: Self) -> Self {
+                Wrapping(<$t>::from_le(x.0))
+            }
+
+            /// Converts `self` to big endian from the target's endianness.
+            ///
+            /// On big endian this is a no-op. On little endian the bytes are
+            /// swapped.
+            ///
+            /// # Examples
+            ///
+            /// Basic usage:
+            ///
+            /// ```
+            /// #![feature(wrapping_int_impl)]
+            /// use std::num::Wrapping;
+            ///
+            #[doc = concat!("let n = Wrapping(0x1A", stringify!($t), ");")]
+            ///
+            /// if cfg!(target_endian = "big") {
+            ///     assert_eq!(n.to_be(), n)
+            /// } else {
+            ///     assert_eq!(n.to_be(), n.swap_bytes())
+            /// }
+            /// ```
+            #[inline]
+            #[must_use = "this returns the result of the operation, \
+                          without modifying the original"]
+            #[unstable(feature = "wrapping_int_impl", issue = "32463")]
+            pub const fn to_be(self) -> Self {
+                Wrapping(self.0.to_be())
+            }
+
+            /// Converts `self` to little endian from the target's endianness.
+            ///
+            /// On little endian this is a no-op. On big endian the bytes are
+            /// swapped.
+            ///
+            /// # Examples
+            ///
+            /// Basic usage:
+            ///
+            /// ```
+            /// #![feature(wrapping_int_impl)]
+            /// use std::num::Wrapping;
+            ///
+            #[doc = concat!("let n = Wrapping(0x1A", stringify!($t), ");")]
+            ///
+            /// if cfg!(target_endian = "little") {
+            ///     assert_eq!(n.to_le(), n)
+            /// } else {
+            ///     assert_eq!(n.to_le(), n.swap_bytes())
+            /// }
+            /// ```
+            #[inline]
+            #[must_use = "this returns the result of the operation, \
+                          without modifying the original"]
+            #[unstable(feature = "wrapping_int_impl", issue = "32463")]
+            pub const fn to_le(self) -> Self {
+                Wrapping(self.0.to_le())
+            }
+
+            /// Raises self to the power of `exp`, using exponentiation by squaring.
+            ///
+            /// # Examples
+            ///
+            /// Basic usage:
+            ///
+            /// ```
+            /// #![feature(wrapping_int_impl)]
+            /// use std::num::Wrapping;
+            ///
+            #[doc = concat!("assert_eq!(Wrapping(3", stringify!($t), ").pow(4), Wrapping(81));")]
+            /// ```
+            ///
+            /// Results that are too large are wrapped:
+            ///
+            /// ```
+            /// #![feature(wrapping_int_impl)]
+            /// use std::num::Wrapping;
+            ///
+            /// assert_eq!(Wrapping(3i8).pow(5), Wrapping(-13));
+            /// assert_eq!(Wrapping(3i8).pow(6), Wrapping(-39));
+            /// ```
+            #[inline]
+            #[must_use = "this returns the result of the operation, \
+                          without modifying the original"]
+            #[unstable(feature = "wrapping_int_impl", issue = "32463")]
+            pub fn pow(self, exp: u32) -> Self {
+                Wrapping(self.0.wrapping_pow(exp))
+            }
+        }
+    )*)
+}
+
+wrapping_int_impl! { usize u8 u16 u32 u64 u128 isize i8 i16 i32 i64 i128 }
+
+macro_rules! wrapping_int_impl_signed {
+    ($($t:ty)*) => ($(
+        impl Wrapping<$t> {
+            /// Returns the number of leading zeros in the binary representation of `self`.
+            ///
+            /// # Examples
+            ///
+            /// Basic usage:
+            ///
+            /// ```
+            /// #![feature(wrapping_int_impl)]
+            /// use std::num::Wrapping;
+            ///
+            #[doc = concat!("let n = Wrapping(", stringify!($t), "::MAX) >> 2;")]
+            ///
+            /// assert_eq!(n.leading_zeros(), 3);
+            /// ```
+            #[inline]
+            #[must_use = "this returns the result of the operation, \
+                          without modifying the original"]
+            #[unstable(feature = "wrapping_int_impl", issue = "32463")]
+            pub const fn leading_zeros(self) -> u32 {
+                self.0.leading_zeros()
+            }
+
+            /// Computes the absolute value of `self`, wrapping around at
+            /// the boundary of the type.
+            ///
+            /// The only case where such wrapping can occur is when one takes the absolute value of the negative
+            /// minimal value for the type this is a positive value that is too large to represent in the type. In
+            /// such a case, this function returns `MIN` itself.
+            ///
+            /// # Examples
+            ///
+            /// Basic usage:
+            ///
+            /// ```
+            /// #![feature(wrapping_int_impl)]
+            /// use std::num::Wrapping;
+            ///
+            #[doc = concat!("assert_eq!(Wrapping(100", stringify!($t), ").abs(), Wrapping(100));")]
+            #[doc = concat!("assert_eq!(Wrapping(-100", stringify!($t), ").abs(), Wrapping(100));")]
+            #[doc = concat!("assert_eq!(Wrapping(", stringify!($t), "::MIN).abs(), Wrapping(", stringify!($t), "::MIN));")]
+            /// assert_eq!(Wrapping(-128i8).abs().0 as u8, 128u8);
+            /// ```
+            #[inline]
+            #[must_use = "this returns the result of the operation, \
+                          without modifying the original"]
+            #[unstable(feature = "wrapping_int_impl", issue = "32463")]
+            pub fn abs(self) -> Wrapping<$t> {
+                Wrapping(self.0.wrapping_abs())
+            }
+
+            /// Returns a number representing sign of `self`.
+            ///
+            ///  - `0` if the number is zero
+            ///  - `1` if the number is positive
+            ///  - `-1` if the number is negative
+            ///
+            /// # Examples
+            ///
+            /// Basic usage:
+            ///
+            /// ```
+            /// #![feature(wrapping_int_impl)]
+            /// use std::num::Wrapping;
+            ///
+            #[doc = concat!("assert_eq!(Wrapping(10", stringify!($t), ").signum(), Wrapping(1));")]
+            #[doc = concat!("assert_eq!(Wrapping(0", stringify!($t), ").signum(), Wrapping(0));")]
+            #[doc = concat!("assert_eq!(Wrapping(-10", stringify!($t), ").signum(), Wrapping(-1));")]
+            /// ```
+            #[inline]
+            #[must_use = "this returns the result of the operation, \
+                          without modifying the original"]
+            #[unstable(feature = "wrapping_int_impl", issue = "32463")]
+            pub fn signum(self) -> Wrapping<$t> {
+                Wrapping(self.0.signum())
+            }
+
+            /// Returns `true` if `self` is positive and `false` if the number is zero or
+            /// negative.
+            ///
+            /// # Examples
+            ///
+            /// Basic usage:
+            ///
+            /// ```
+            /// #![feature(wrapping_int_impl)]
+            /// use std::num::Wrapping;
+            ///
+            #[doc = concat!("assert!(Wrapping(10", stringify!($t), ").is_positive());")]
+            #[doc = concat!("assert!(!Wrapping(-10", stringify!($t), ").is_positive());")]
+            /// ```
+            #[must_use]
+            #[inline]
+            #[unstable(feature = "wrapping_int_impl", issue = "32463")]
+            pub const fn is_positive(self) -> bool {
+                self.0.is_positive()
+            }
+
+            /// Returns `true` if `self` is negative and `false` if the number is zero or
+            /// positive.
+            ///
+            /// # Examples
+            ///
+            /// Basic usage:
+            ///
+            /// ```
+            /// #![feature(wrapping_int_impl)]
+            /// use std::num::Wrapping;
+            ///
+            #[doc = concat!("assert!(Wrapping(-10", stringify!($t), ").is_negative());")]
+            #[doc = concat!("assert!(!Wrapping(10", stringify!($t), ").is_negative());")]
+            /// ```
+            #[must_use]
+            #[inline]
+            #[unstable(feature = "wrapping_int_impl", issue = "32463")]
+            pub const fn is_negative(self) -> bool {
+                self.0.is_negative()
+            }
+        }
+    )*)
+}
+
+wrapping_int_impl_signed! { isize i8 i16 i32 i64 i128 }
+
+macro_rules! wrapping_int_impl_unsigned {
+    ($($t:ty)*) => ($(
+        impl Wrapping<$t> {
+            /// Returns the number of leading zeros in the binary representation of `self`.
+            ///
+            /// # Examples
+            ///
+            /// Basic usage:
+            ///
+            /// ```
+            /// #![feature(wrapping_int_impl)]
+            /// use std::num::Wrapping;
+            ///
+            #[doc = concat!("let n = Wrapping(", stringify!($t), "::MAX) >> 2;")]
+            ///
+            /// assert_eq!(n.leading_zeros(), 2);
+            /// ```
+            #[inline]
+            #[must_use = "this returns the result of the operation, \
+                          without modifying the original"]
+            #[unstable(feature = "wrapping_int_impl", issue = "32463")]
+            pub const fn leading_zeros(self) -> u32 {
+                self.0.leading_zeros()
+            }
+
+            /// Returns `true` if and only if `self == 2^k` for some `k`.
+            ///
+            /// # Examples
+            ///
+            /// Basic usage:
+            ///
+            /// ```
+            /// #![feature(wrapping_int_impl)]
+            /// use std::num::Wrapping;
+            ///
+            #[doc = concat!("assert!(Wrapping(16", stringify!($t), ").is_power_of_two());")]
+            #[doc = concat!("assert!(!Wrapping(10", stringify!($t), ").is_power_of_two());")]
+            /// ```
+            #[must_use]
+            #[inline]
+            #[unstable(feature = "wrapping_int_impl", issue = "32463")]
+            pub fn is_power_of_two(self) -> bool {
+                self.0.is_power_of_two()
+            }
+
+            /// Returns the smallest power of two greater than or equal to `self`.
+            ///
+            /// When return value overflows (i.e., `self > (1 << (N-1))` for type
+            /// `uN`), overflows to `2^N = 0`.
+            ///
+            /// # Examples
+            ///
+            /// Basic usage:
+            ///
+            /// ```
+            /// #![feature(wrapping_next_power_of_two)]
+            /// use std::num::Wrapping;
+            ///
+            #[doc = concat!("assert_eq!(Wrapping(2", stringify!($t), ").next_power_of_two(), Wrapping(2));")]
+            #[doc = concat!("assert_eq!(Wrapping(3", stringify!($t), ").next_power_of_two(), Wrapping(4));")]
+            #[doc = concat!("assert_eq!(Wrapping(200_u8).next_power_of_two(), Wrapping(0));")]
+            /// ```
+            #[inline]
+            #[must_use = "this returns the result of the operation, \
+                          without modifying the original"]
+            #[unstable(feature = "wrapping_next_power_of_two", issue = "32463",
+                       reason = "needs decision on wrapping behaviour")]
+            pub fn next_power_of_two(self) -> Self {
+                Wrapping(self.0.wrapping_next_power_of_two())
+            }
+        }
+    )*)
+}
+
+wrapping_int_impl_unsigned! { usize u8 u16 u32 u64 u128 }
+
+mod shift_max {
+    #![allow(non_upper_case_globals)]
+
+    #[cfg(target_pointer_width = "16")]
+    mod platform {
+        pub const usize: u32 = super::u16;
+        pub const isize: u32 = super::i16;
+    }
+
+    #[cfg(target_pointer_width = "32")]
+    mod platform {
+        pub const usize: u32 = super::u32;
+        pub const isize: u32 = super::i32;
+    }
+
+    #[cfg(target_pointer_width = "64")]
+    mod platform {
+        pub const usize: u32 = super::u64;
+        pub const isize: u32 = super::i64;
+    }
+
+    pub const i8: u32 = (1 << 3) - 1;
+    pub const i16: u32 = (1 << 4) - 1;
+    pub const i32: u32 = (1 << 5) - 1;
+    pub const i64: u32 = (1 << 6) - 1;
+    pub const i128: u32 = (1 << 7) - 1;
+    pub use self::platform::isize;
+
+    pub const u8: u32 = i8;
+    pub const u16: u32 = i16;
+    pub const u32: u32 = i32;
+    pub const u64: u32 = i64;
+    pub const u128: u32 = i128;
+    pub use self::platform::usize;
+}