10 files changed, 2379 insertions, 0 deletions

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
+];