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Diffstat (limited to 'library/core/src/num')
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!("(−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> − 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> − 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; +} |