build(ariadne): vendor serde crates

2026-09-05 20:21:54 -04:00
1 parent 90f46026f0
commit 64773e0948
@@ -0,0 +1,195 @@
+// Adapted from https://github.com/Alexhuszagh/rust-lexical.
+
+//! Algorithms to efficiently convert strings to floats.
+
+use super::bhcomp::*;
+use super::cached::*;
+use super::errors::*;
+use super::float::ExtendedFloat;
+use super::num::*;
+use super::small_powers::*;
+
+// FAST
+// ----
+
+/// Convert mantissa to exact value for a non-base2 power.
+///
+/// Returns the resulting float and if the value can be represented exactly.
+pub(crate) fn fast_path<F>(mantissa: u64, exponent: i32) -> Option<F>
+where
+    F: Float,
+{
+    // `mantissa >> (F::MANTISSA_SIZE+1) != 0` effectively checks if the
+    // value has a no bits above the hidden bit, which is what we want.
+    let (min_exp, max_exp) = F::exponent_limit();
+    let shift_exp = F::mantissa_limit();
+    let mantissa_size = F::MANTISSA_SIZE + 1;
+    if mantissa == 0 {
+        Some(F::ZERO)
+    } else if mantissa >> mantissa_size != 0 {
+        // Would require truncation of the mantissa.
+        None
+    } else if exponent == 0 {
+        // 0 exponent, same as value, exact representation.
+        let float = F::as_cast(mantissa);
+        Some(float)
+    } else if exponent >= min_exp && exponent <= max_exp {
+        // Value can be exactly represented, return the value.
+        // Do not use powi, since powi can incrementally introduce
+        // error.
+        let float = F::as_cast(mantissa);
+        Some(float.pow10(exponent))
+    } else if exponent >= 0 && exponent <= max_exp + shift_exp {
+        // Check to see if we have a disguised fast-path, where the
+        // number of digits in the mantissa is very small, but and
+        // so digits can be shifted from the exponent to the mantissa.
+        // https://www.exploringbinary.com/fast-path-decimal-to-floating-point-conversion/
+        let small_powers = POW10_64;
+        let shift = exponent - max_exp;
+        let power = small_powers[shift as usize];
+
+        // Compute the product of the power, if it overflows,
+        // prematurely return early, otherwise, if we didn't overshoot,
+        // we can get an exact value.
+        let Some(value) = mantissa.checked_mul(power) else {
+            return None;
+        };
+        if value >> mantissa_size != 0 {
+            None
+        } else {
+            // Use powi, since it's correct, and faster on
+            // the fast-path.
+            let float = F::as_cast(value);
+            Some(float.pow10(max_exp))
+        }
+    } else {
+        // Cannot be exactly represented, exponent too small or too big,
+        // would require truncation.
+        None
+    }
+}
+
+// MODERATE
+// --------
+
+/// Multiply the floating-point by the exponent.
+///
+/// Multiply by pre-calculated powers of the base, modify the extended-
+/// float, and return if new value and if the value can be represented
+/// accurately.
+fn multiply_exponent_extended<F>(fp: &mut ExtendedFloat, exponent: i32, truncated: bool) -> bool
+where
+    F: Float,
+{
+    let powers = ExtendedFloat::get_powers();
+    let exponent = exponent.saturating_add(powers.bias);
+    let small_index = exponent % powers.step;
+    let large_index = exponent / powers.step;
+    if exponent < 0 {
+        // Guaranteed underflow (assign 0).
+        fp.mant = 0;
+        true
+    } else if large_index as usize >= powers.large.len() {
+        // Overflow (assign infinity)
+        fp.mant = 1 << 63;
+        fp.exp = 0x7FF;
+        true
+    } else {
+        // Within the valid exponent range, multiply by the large and small
+        // exponents and return the resulting value.
+
+        // Track errors to as a factor of unit in last-precision.
+        let mut errors: u32 = 0;
+        if truncated {
+            errors += u64::error_halfscale();
+        }
+
+        // Multiply by the small power.
+        // Check if we can directly multiply by an integer, if not,
+        // use extended-precision multiplication.
+        match fp
+            .mant
+            .overflowing_mul(powers.get_small_int(small_index as usize))
+        {
+            // Overflow, multiplication unsuccessful, go slow path.
+            (_, true) => {
+                fp.normalize();
+                fp.imul(&powers.get_small(small_index as usize));
+                errors += u64::error_halfscale();
+            }
+            // No overflow, multiplication successful.
+            (mant, false) => {
+                fp.mant = mant;
+                fp.normalize();
+            }
+        }
+
+        // Multiply by the large power
+        fp.imul(&powers.get_large(large_index as usize));
+        if errors > 0 {
+            errors += 1;
+        }
+        errors += u64::error_halfscale();
+
+        // Normalize the floating point (and the errors).
+        let shift = fp.normalize();
+        errors <<= shift;
+
+        u64::error_is_accurate::<F>(errors, fp)
+    }
+}
+
+/// Create a precise native float using an intermediate extended-precision float.
+///
+/// Return the float approximation and if the value can be accurately
+/// represented with mantissa bits of precision.
+#[inline]
+pub(crate) fn moderate_path<F>(
+    mantissa: u64,
+    exponent: i32,
+    truncated: bool,
+) -> (ExtendedFloat, bool)
+where
+    F: Float,
+{
+    let mut fp = ExtendedFloat {
+        mant: mantissa,
+        exp: 0,
+    };
+    let valid = multiply_exponent_extended::<F>(&mut fp, exponent, truncated);
+    (fp, valid)
+}
+
+// FALLBACK
+// --------
+
+/// Fallback path when the fast path does not work.
+///
+/// Uses the moderate path, if applicable, otherwise, uses the slow path
+/// as required.
+pub(crate) fn fallback_path<F>(
+    integer: &[u8],
+    fraction: &[u8],
+    mantissa: u64,
+    exponent: i32,
+    mantissa_exponent: i32,
+    truncated: bool,
+) -> F
+where
+    F: Float,
+{
+    // Moderate path (use an extended 80-bit representation).
+    let (fp, valid) = moderate_path::<F>(mantissa, mantissa_exponent, truncated);
+    if valid {
+        return fp.into_float::<F>();
+    }
+
+    // Slow path, fast path didn't work.
+    let b = fp.into_downward_float::<F>();
+    if b.is_special() {
+        // We have a non-finite number, we get to leave early.
+        b
+    } else {
+        bhcomp(b, integer, fraction, exponent)
+    }
+}
@@ -0,0 +1,218 @@
+// Adapted from https://github.com/Alexhuszagh/rust-lexical.
+
+//! Compare the mantissa to the halfway representation of the float.
+//!
+//! Compares the actual significant digits of the mantissa to the
+//! theoretical digits from `b+h`, scaled into the proper range.
+
+use super::bignum::*;
+use super::digit::*;
+use super::exponent::*;
+use super::float::*;
+use super::math::*;
+use super::num::*;
+use super::rounding::*;
+use core::{cmp, mem};
+
+// MANTISSA
+
+/// Parse the full mantissa into a big integer.
+///
+/// Max digits is the maximum number of digits plus one.
+fn parse_mantissa<F>(integer: &[u8], fraction: &[u8]) -> Bigint
+where
+    F: Float,
+{
+    // Main loop
+    let small_powers = POW10_LIMB;
+    let step = small_powers.len() - 2;
+    let max_digits = F::MAX_DIGITS - 1;
+    let mut counter = 0;
+    let mut value: Limb = 0;
+    let mut i: usize = 0;
+    let mut result = Bigint::default();
+
+    // Iteratively process all the data in the mantissa.
+    for &digit in integer.iter().chain(fraction) {
+        // We've parsed the max digits using small values, add to bignum
+        if counter == step {
+            result.imul_small(small_powers[counter]);
+            result.iadd_small(value);
+            counter = 0;
+            value = 0;
+        }
+
+        value *= 10;
+        value += as_limb(to_digit(digit).unwrap());
+
+        i += 1;
+        counter += 1;
+        if i == max_digits {
+            break;
+        }
+    }
+
+    // We will always have a remainder, as long as we entered the loop
+    // once, or counter % step is 0.
+    if counter != 0 {
+        result.imul_small(small_powers[counter]);
+        result.iadd_small(value);
+    }
+
+    // If we have any remaining digits after the last value, we need
+    // to add a 1 after the rest of the array, it doesn't matter where,
+    // just move it up. This is good for the worst-possible float
+    // representation. We also need to return an index.
+    // Since we already trimmed trailing zeros, we know there has
+    // to be a non-zero digit if there are any left.
+    if i < integer.len() + fraction.len() {
+        result.imul_small(10);
+        result.iadd_small(1);
+    }
+
+    result
+}
+
+// FLOAT OPS
+
+/// Calculate `b` from a representation of `b` as a float.
+#[inline]
+pub(super) fn b_extended<F: Float>(f: F) -> ExtendedFloat {
+    ExtendedFloat::from_float(f)
+}
+
+/// Calculate `b+h` from a representation of `b` as a float.
+#[inline]
+pub(super) fn bh_extended<F: Float>(f: F) -> ExtendedFloat {
+    // None of these can overflow.
+    let b = b_extended(f);
+    ExtendedFloat {
+        mant: (b.mant << 1) + 1,
+        exp: b.exp - 1,
+    }
+}
+
+// ROUNDING
+
+/// Custom round-nearest, tie-event algorithm for bhcomp.
+#[inline]
+fn round_nearest_tie_even(fp: &mut ExtendedFloat, shift: i32, is_truncated: bool) {
+    let (mut is_above, mut is_halfway) = round_nearest(fp, shift);
+    if is_halfway && is_truncated {
+        is_above = true;
+        is_halfway = false;
+    }
+    tie_even(fp, is_above, is_halfway);
+}
+
+// BHCOMP
+
+/// Calculate the mantissa for a big integer with a positive exponent.
+fn large_atof<F>(mantissa: Bigint, exponent: i32) -> F
+where
+    F: Float,
+{
+    let bits = mem::size_of::<u64>() * 8;
+
+    // Simple, we just need to multiply by the power of the radix.
+    // Now, we can calculate the mantissa and the exponent from this.
+    // The binary exponent is the binary exponent for the mantissa
+    // shifted to the hidden bit.
+    let mut bigmant = mantissa;
+    bigmant.imul_pow10(exponent as u32);
+
+    // Get the exact representation of the float from the big integer.
+    let (mant, is_truncated) = bigmant.hi64();
+    let exp = bigmant.bit_length() as i32 - bits as i32;
+    let mut fp = ExtendedFloat { mant, exp };
+    fp.round_to_native::<F, _>(|fp, shift| round_nearest_tie_even(fp, shift, is_truncated));
+    into_float(fp)
+}
+
+/// Calculate the mantissa for a big integer with a negative exponent.
+///
+/// This invokes the comparison with `b+h`.
+fn small_atof<F>(mantissa: Bigint, exponent: i32, f: F) -> F
+where
+    F: Float,
+{
+    // Get the significant digits and radix exponent for the real digits.
+    let mut real_digits = mantissa;
+    let real_exp = exponent;
+    debug_assert!(real_exp < 0);
+
+    // Get the significant digits and the binary exponent for `b+h`.
+    let theor = bh_extended(f);
+    let mut theor_digits = Bigint::from_u64(theor.mant);
+    let theor_exp = theor.exp;
+
+    // We need to scale the real digits and `b+h` digits to be the same
+    // order. We currently have `real_exp`, in `radix`, that needs to be
+    // shifted to `theor_digits` (since it is negative), and `theor_exp`
+    // to either `theor_digits` or `real_digits` as a power of 2 (since it
+    // may be positive or negative). Try to remove as many powers of 2
+    // as possible. All values are relative to `theor_digits`, that is,
+    // reflect the power you need to multiply `theor_digits` by.
+
+    // Can remove a power-of-two, since the radix is 10.
+    // Both are on opposite-sides of equation, can factor out a
+    // power of two.
+    //
+    // Example: 10^-10, 2^-10   -> ( 0, 10, 0)
+    // Example: 10^-10, 2^-15   -> (-5, 10, 0)
+    // Example: 10^-10, 2^-5    -> ( 5, 10, 0)
+    // Example: 10^-10, 2^5 -> (15, 10, 0)
+    let binary_exp = theor_exp - real_exp;
+    let halfradix_exp = -real_exp;
+    let radix_exp = 0;
+
+    // Carry out our multiplication.
+    if halfradix_exp != 0 {
+        theor_digits.imul_pow5(halfradix_exp as u32);
+    }
+    if radix_exp != 0 {
+        theor_digits.imul_pow10(radix_exp as u32);
+    }
+    if binary_exp > 0 {
+        theor_digits.imul_pow2(binary_exp as u32);
+    } else if binary_exp < 0 {
+        real_digits.imul_pow2(-binary_exp as u32);
+    }
+
+    // Compare real digits to theoretical digits and round the float.
+    match real_digits.compare(&theor_digits) {
+        cmp::Ordering::Greater => f.next_positive(),
+        cmp::Ordering::Less => f,
+        cmp::Ordering::Equal => f.round_positive_even(),
+    }
+}
+
+/// Calculate the exact value of the float.
+///
+/// Note: fraction must not have trailing zeros.
+pub(crate) fn bhcomp<F>(b: F, integer: &[u8], mut fraction: &[u8], exponent: i32) -> F
+where
+    F: Float,
+{
+    // Calculate the number of integer digits and use that to determine
+    // where the significant digits start in the fraction.
+    let integer_digits = integer.len();
+    let fraction_digits = fraction.len();
+    let digits_start = if integer_digits == 0 {
+        let start = fraction.iter().take_while(|&x| *x == b'0').count();
+        fraction = &fraction[start..];
+        start
+    } else {
+        0
+    };
+    let sci_exp = scientific_exponent(exponent, integer_digits, digits_start);
+    let count = F::MAX_DIGITS.min(integer_digits + fraction_digits - digits_start);
+    let scaled_exponent = sci_exp + 1 - count as i32;
+
+    let mantissa = parse_mantissa::<F>(integer, fraction);
+    if scaled_exponent >= 0 {
+        large_atof(mantissa, scaled_exponent)
+    } else {
+        small_atof(mantissa, scaled_exponent, b)
+    }
+}
@@ -0,0 +1,34 @@
+// Adapted from https://github.com/Alexhuszagh/rust-lexical.
+
+//! Big integer type definition.
+
+use super::math::*;
+#[allow(unused_imports)]
+use alloc::vec::Vec;
+
+/// Storage for a big integer type.
+#[derive(Clone, PartialEq, Eq)]
+pub(crate) struct Bigint {
+    /// Internal storage for the Bigint, in little-endian order.
+    pub(crate) data: Vec<Limb>,
+}
+
+impl Default for Bigint {
+    fn default() -> Self {
+        Bigint {
+            data: Vec::with_capacity(20),
+        }
+    }
+}
+
+impl Math for Bigint {
+    #[inline]
+    fn data(&self) -> &Vec<Limb> {
+        &self.data
+    }
+
+    #[inline]
+    fn data_mut(&mut self) -> &mut Vec<Limb> {
+        &mut self.data
+    }
+}
@@ -0,0 +1,82 @@
+// Adapted from https://github.com/Alexhuszagh/rust-lexical.
+
+//! Cached powers trait for extended-precision floats.
+
+use super::cached_float80;
+use super::float::ExtendedFloat;
+
+// POWERS
+
+/// Precalculated powers that uses two-separate arrays for memory-efficiency.
+#[doc(hidden)]
+pub(crate) struct ExtendedFloatArray {
+    // Pre-calculated mantissa for the powers.
+    pub mant: &'static [u64],
+    // Pre-calculated binary exponents for the powers.
+    pub exp: &'static [i32],
+}
+
+/// Allow indexing of values without bounds checking
+impl ExtendedFloatArray {
+    #[inline]
+    pub fn get_extended_float(&self, index: usize) -> ExtendedFloat {
+        let mant = self.mant[index];
+        let exp = self.exp[index];
+        ExtendedFloat { mant, exp }
+    }
+
+    #[inline]
+    pub fn len(&self) -> usize {
+        self.mant.len()
+    }
+}
+
+// MODERATE PATH POWERS
+
+/// Precalculated powers of base N for the moderate path.
+#[doc(hidden)]
+pub(crate) struct ModeratePathPowers {
+    // Pre-calculated small powers.
+    pub small: ExtendedFloatArray,
+    // Pre-calculated large powers.
+    pub large: ExtendedFloatArray,
+    /// Pre-calculated small powers as 64-bit integers
+    pub small_int: &'static [u64],
+    // Step between large powers and number of small powers.
+    pub step: i32,
+    // Exponent bias for the large powers.
+    pub bias: i32,
+}
+
+/// Allow indexing of values without bounds checking
+impl ModeratePathPowers {
+    #[inline]
+    pub fn get_small(&self, index: usize) -> ExtendedFloat {
+        self.small.get_extended_float(index)
+    }
+
+    #[inline]
+    pub fn get_large(&self, index: usize) -> ExtendedFloat {
+        self.large.get_extended_float(index)
+    }
+
+    #[inline]
+    pub fn get_small_int(&self, index: usize) -> u64 {
+        self.small_int[index]
+    }
+}
+
+// CACHED EXTENDED POWERS
+
+/// Cached powers as a trait for a floating-point type.
+pub(crate) trait ModeratePathCache {
+    /// Get cached powers.
+    fn get_powers() -> &'static ModeratePathPowers;
+}
+
+impl ModeratePathCache for ExtendedFloat {
+    #[inline]
+    fn get_powers() -> &'static ModeratePathPowers {
+        cached_float80::get_powers()
+    }
+}
@@ -0,0 +1,206 @@
+// Adapted from https://github.com/Alexhuszagh/rust-lexical.
+
+//! Cached exponents for basen values with 80-bit extended floats.
+//!
+//! Exact versions of base**n as an extended-precision float, with both
+//! large and small powers. Use the large powers to minimize the amount
+//! of compounded error.
+//!
+//! These values were calculated using Python, using the arbitrary-precision
+//! integer to calculate exact extended-representation of each value.
+//! These values are all normalized.
+
+use super::cached::{ExtendedFloatArray, ModeratePathPowers};
+
+// LOW-LEVEL
+// ---------
+
+// BASE10
+
+const BASE10_SMALL_MANTISSA: [u64; 10] = [
+    9223372036854775808,  // 10^0
+    11529215046068469760, // 10^1
+    14411518807585587200, // 10^2
+    18014398509481984000, // 10^3
+    11258999068426240000, // 10^4
+    14073748835532800000, // 10^5
+    17592186044416000000, // 10^6
+    10995116277760000000, // 10^7
+    13743895347200000000, // 10^8
+    17179869184000000000, // 10^9
+];
+const BASE10_SMALL_EXPONENT: [i32; 10] = [
+    -63, // 10^0
+    -60, // 10^1
+    -57, // 10^2
+    -54, // 10^3
+    -50, // 10^4
+    -47, // 10^5
+    -44, // 10^6
+    -40, // 10^7
+    -37, // 10^8
+    -34, // 10^9
+];
+const BASE10_LARGE_MANTISSA: [u64; 66] = [
+    11555125961253852697, // 10^-350
+    13451937075301367670, // 10^-340
+    15660115838168849784, // 10^-330
+    18230774251475056848, // 10^-320
+    10611707258198326947, // 10^-310
+    12353653155963782858, // 10^-300
+    14381545078898527261, // 10^-290
+    16742321987285426889, // 10^-280
+    9745314011399999080,  // 10^-270
+    11345038669416679861, // 10^-260
+    13207363278391631158, // 10^-250
+    15375394465392026070, // 10^-240
+    17899314949046850752, // 10^-230
+    10418772551374772303, // 10^-220
+    12129047596099288555, // 10^-210
+    14120069793541087484, // 10^-200
+    16437924692338667210, // 10^-190
+    9568131466127621947,  // 10^-180
+    11138771039116687545, // 10^-170
+    12967236152753102995, // 10^-160
+    15095849699286165408, // 10^-150
+    17573882009934360870, // 10^-140
+    10229345649675443343, // 10^-130
+    11908525658859223294, // 10^-120
+    13863348470604074297, // 10^-110
+    16139061738043178685, // 10^-100
+    9394170331095332911,  // 10^-90
+    10936253623915059621, // 10^-80
+    12731474852090538039, // 10^-70
+    14821387422376473014, // 10^-60
+    17254365866976409468, // 10^-50
+    10043362776618689222, // 10^-40
+    11692013098647223345, // 10^-30
+    13611294676837538538, // 10^-20
+    15845632502852867518, // 10^-10
+    9223372036854775808,  // 10^0
+    10737418240000000000, // 10^10
+    12500000000000000000, // 10^20
+    14551915228366851806, // 10^30
+    16940658945086006781, // 10^40
+    9860761315262647567,  // 10^50
+    11479437019748901445, // 10^60
+    13363823550460978230, // 10^70
+    15557538194652854267, // 10^80
+    18111358157653424735, // 10^90
+    10542197943230523224, // 10^100
+    12272733663244316382, // 10^110
+    14287342391028437277, // 10^120
+    16632655625031838749, // 10^130
+    9681479787123295682,  // 10^140
+    11270725851789228247, // 10^150
+    13120851772591970218, // 10^160
+    15274681817498023410, // 10^170
+    17782069995880619867, // 10^180
+    10350527006597618960, // 10^190
+    12049599325514420588, // 10^200
+    14027579833653779454, // 10^210
+    16330252207878254650, // 10^220
+    9505457831475799117,  // 10^230
+    11065809325636130661, // 10^240
+    12882297539194266616, // 10^250
+    14996968138956309548, // 10^260
+    17458768723248864463, // 10^270
+    10162340898095201970, // 10^280
+    11830521861667747109, // 10^290
+    13772540099066387756, // 10^300
+];
+const BASE10_LARGE_EXPONENT: [i32; 66] = [
+    -1226, // 10^-350
+    -1193, // 10^-340
+    -1160, // 10^-330
+    -1127, // 10^-320
+    -1093, // 10^-310
+    -1060, // 10^-300
+    -1027, // 10^-290
+    -994,  // 10^-280
+    -960,  // 10^-270
+    -927,  // 10^-260
+    -894,  // 10^-250
+    -861,  // 10^-240
+    -828,  // 10^-230
+    -794,  // 10^-220
+    -761,  // 10^-210
+    -728,  // 10^-200
+    -695,  // 10^-190
+    -661,  // 10^-180
+    -628,  // 10^-170
+    -595,  // 10^-160
+    -562,  // 10^-150
+    -529,  // 10^-140
+    -495,  // 10^-130
+    -462,  // 10^-120
+    -429,  // 10^-110
+    -396,  // 10^-100
+    -362,  // 10^-90
+    -329,  // 10^-80
+    -296,  // 10^-70
+    -263,  // 10^-60
+    -230,  // 10^-50
+    -196,  // 10^-40
+    -163,  // 10^-30
+    -130,  // 10^-20
+    -97,   // 10^-10
+    -63,   // 10^0
+    -30,   // 10^10
+    3,     // 10^20
+    36,    // 10^30
+    69,    // 10^40
+    103,   // 10^50
+    136,   // 10^60
+    169,   // 10^70
+    202,   // 10^80
+    235,   // 10^90
+    269,   // 10^100
+    302,   // 10^110
+    335,   // 10^120
+    368,   // 10^130
+    402,   // 10^140
+    435,   // 10^150
+    468,   // 10^160
+    501,   // 10^170
+    534,   // 10^180
+    568,   // 10^190
+    601,   // 10^200
+    634,   // 10^210
+    667,   // 10^220
+    701,   // 10^230
+    734,   // 10^240
+    767,   // 10^250
+    800,   // 10^260
+    833,   // 10^270
+    867,   // 10^280
+    900,   // 10^290
+    933,   // 10^300
+];
+const BASE10_SMALL_INT_POWERS: [u64; 10] = [
+    1, 10, 100, 1000, 10000, 100000, 1000000, 10000000, 100000000, 1000000000,
+];
+const BASE10_STEP: i32 = 10;
+const BASE10_BIAS: i32 = 350;
+
+// HIGH LEVEL
+// ----------
+
+const BASE10_POWERS: ModeratePathPowers = ModeratePathPowers {
+    small: ExtendedFloatArray {
+        mant: &BASE10_SMALL_MANTISSA,
+        exp: &BASE10_SMALL_EXPONENT,
+    },
+    large: ExtendedFloatArray {
+        mant: &BASE10_LARGE_MANTISSA,
+        exp: &BASE10_LARGE_EXPONENT,
+    },
+    small_int: &BASE10_SMALL_INT_POWERS,
+    step: BASE10_STEP,
+    bias: BASE10_BIAS,
+};
+
+/// Get powers from base.
+pub(crate) fn get_powers() -> &'static ModeratePathPowers {
+    &BASE10_POWERS
+}
@@ -0,0 +1,18 @@
+// Adapted from https://github.com/Alexhuszagh/rust-lexical.
+
+//! Helpers to convert and add digits from characters.
+
+// Convert u8 to digit.
+#[inline]
+pub(crate) fn to_digit(c: u8) -> Option<u32> {
+    (c as char).to_digit(10)
+}
+
+// Add digit to mantissa.
+#[inline]
+pub(crate) fn add_digit(value: u64, digit: u32) -> Option<u64> {
+    match value.checked_mul(10) {
+        None => None,
+        Some(n) => n.checked_add(digit as u64),
+    }
+}
@@ -0,0 +1,132 @@
+// Adapted from https://github.com/Alexhuszagh/rust-lexical.
+
+//! Estimate the error in an 80-bit approximation of a float.
+//!
+//! This estimates the error in a floating-point representation.
+//!
+//! This implementation is loosely based off the Golang implementation,
+//! found here: <https://golang.org/src/strconv/atof.go>
+
+use super::float::*;
+use super::num::*;
+use super::rounding::*;
+
+pub(crate) trait FloatErrors {
+    /// Get the full error scale.
+    fn error_scale() -> u32;
+    /// Get the half error scale.
+    fn error_halfscale() -> u32;
+    /// Determine if the number of errors is tolerable for float precision.
+    fn error_is_accurate<F: Float>(count: u32, fp: &ExtendedFloat) -> bool;
+}
+
+/// Check if the error is accurate with a round-nearest rounding scheme.
+#[inline]
+fn nearest_error_is_accurate(errors: u64, fp: &ExtendedFloat, extrabits: u64) -> bool {
+    // Round-to-nearest, need to use the halfway point.
+    if extrabits == 65 {
+        // Underflow, we have a shift larger than the mantissa.
+        // Representation is valid **only** if the value is close enough
+        // overflow to the next bit within errors. If it overflows,
+        // the representation is **not** valid.
+        !fp.mant.overflowing_add(errors).1
+    } else {
+        let mask: u64 = lower_n_mask(extrabits);
+        let extra: u64 = fp.mant & mask;
+
+        // Round-to-nearest, need to check if we're close to halfway.
+        // IE, b10100 | 100000, where `|` signifies the truncation point.
+        let halfway: u64 = lower_n_halfway(extrabits);
+        let cmp1 = halfway.wrapping_sub(errors) < extra;
+        let cmp2 = extra < halfway.wrapping_add(errors);
+
+        // If both comparisons are true, we have significant rounding error,
+        // and the value cannot be exactly represented. Otherwise, the
+        // representation is valid.
+        !(cmp1 && cmp2)
+    }
+}
+
+impl FloatErrors for u64 {
+    #[inline]
+    fn error_scale() -> u32 {
+        8
+    }
+
+    #[inline]
+    fn error_halfscale() -> u32 {
+        u64::error_scale() / 2
+    }
+
+    #[inline]
+    fn error_is_accurate<F: Float>(count: u32, fp: &ExtendedFloat) -> bool {
+        // Determine if extended-precision float is a good approximation.
+        // If the error has affected too many units, the float will be
+        // inaccurate, or if the representation is too close to halfway
+        // that any operations could affect this halfway representation.
+        // See the documentation for dtoa for more information.
+        let bias = -(F::EXPONENT_BIAS - F::MANTISSA_SIZE);
+        let denormal_exp = bias - 63;
+        // This is always a valid u32, since (denormal_exp - fp.exp)
+        // will always be positive and the significand size is {23, 52}.
+        let extrabits = if fp.exp <= denormal_exp {
+            64 - F::MANTISSA_SIZE + denormal_exp - fp.exp
+        } else {
+            63 - F::MANTISSA_SIZE
+        };
+
+        // Our logic is as follows: we want to determine if the actual
+        // mantissa and the errors during calculation differ significantly
+        // from the rounding point. The rounding point for round-nearest
+        // is the halfway point, IE, this when the truncated bits start
+        // with b1000..., while the rounding point for the round-toward
+        // is when the truncated bits are equal to 0.
+        // To do so, we can check whether the rounding point +/- the error
+        // are >/< the actual lower n bits.
+        //
+        // For whether we need to use signed or unsigned types for this
+        // analysis, see this example, using u8 rather than u64 to simplify
+        // things.
+        //
+        // # Comparisons
+        //      cmp1 = (halfway - errors) < extra
+        //      cmp1 = extra < (halfway + errors)
+        //
+        // # Large Extrabits, Low Errors
+        //
+        //      extrabits = 8
+        //      halfway          =  0b10000000
+        //      extra            =  0b10000010
+        //      errors           =  0b00000100
+        //      halfway - errors =  0b01111100
+        //      halfway + errors =  0b10000100
+        //
+        //      Unsigned:
+        //          halfway - errors = 124
+        //          halfway + errors = 132
+        //          extra            = 130
+        //          cmp1             = true
+        //          cmp2             = true
+        //      Signed:
+        //          halfway - errors = 124
+        //          halfway + errors = -124
+        //          extra            = -126
+        //          cmp1             = false
+        //          cmp2             = true
+        //
+        // # Conclusion
+        //
+        // Since errors will always be small, and since we want to detect
+        // if the representation is accurate, we need to use an **unsigned**
+        // type for comparisons.
+
+        let extrabits = extrabits as u64;
+        let errors = count as u64;
+        if extrabits > 65 {
+            // Underflow, we have a literal 0.
+            return true;
+        }
+
+        nearest_error_is_accurate(errors, fp, extrabits)
+    }
+}
@@ -0,0 +1,50 @@
+// Adapted from https://github.com/Alexhuszagh/rust-lexical.
+
+//! Utilities to calculate exponents.
+
+/// Convert usize into i32 without overflow.
+///
+/// This is needed to ensure when adjusting the exponent relative to
+/// the mantissa we do not overflow for comically-long exponents.
+#[inline]
+fn into_i32(value: usize) -> i32 {
+    if value > i32::MAX as usize {
+        i32::MAX
+    } else {
+        value as i32
+    }
+}
+
+// EXPONENT CALCULATION
+
+// Calculate the scientific notation exponent without overflow.
+//
+// For example, 0.1 would be -1, and 10 would be 1 in base 10.
+#[inline]
+pub(crate) fn scientific_exponent(
+    exponent: i32,
+    integer_digits: usize,
+    fraction_start: usize,
+) -> i32 {
+    if integer_digits == 0 {
+        let fraction_start = into_i32(fraction_start);
+        exponent.saturating_sub(fraction_start).saturating_sub(1)
+    } else {
+        let integer_shift = into_i32(integer_digits - 1);
+        exponent.saturating_add(integer_shift)
+    }
+}
+
+// Calculate the mantissa exponent without overflow.
+//
+// Remove the number of digits that contributed to the mantissa past
+// the dot, and add the number of truncated digits from the mantissa,
+// to calculate the scaling factor for the mantissa from a raw exponent.
+#[inline]
+pub(crate) fn mantissa_exponent(exponent: i32, fraction_digits: usize, truncated: usize) -> i32 {
+    if fraction_digits > truncated {
+        exponent.saturating_sub(into_i32(fraction_digits - truncated))
+    } else {
+        exponent.saturating_add(into_i32(truncated - fraction_digits))
+    }
+}
@@ -0,0 +1,183 @@
+// Adapted from https://github.com/Alexhuszagh/rust-lexical.
+
+// FLOAT TYPE
+
+use super::num::*;
+use super::rounding::*;
+use super::shift::*;
+
+/// Extended precision floating-point type.
+///
+/// Private implementation, exposed only for testing purposes.
+#[doc(hidden)]
+#[derive(Clone, Copy, Debug, PartialEq, Eq)]
+pub(crate) struct ExtendedFloat {
+    /// Mantissa for the extended-precision float.
+    pub mant: u64,
+    /// Binary exponent for the extended-precision float.
+    pub exp: i32,
+}
+
+impl ExtendedFloat {
+    // PROPERTIES
+
+    // OPERATIONS
+
+    /// Multiply two normalized extended-precision floats, as if by `a*b`.
+    ///
+    /// The precision is maximal when the numbers are normalized, however,
+    /// decent precision will occur as long as both values have high bits
+    /// set. The result is not normalized.
+    ///
+    /// Algorithm:
+    ///     1. Non-signed multiplication of mantissas (requires 2x as many bits as input).
+    ///     2. Normalization of the result (not done here).
+    ///     3. Addition of exponents.
+    pub(crate) fn mul(&self, b: &ExtendedFloat) -> ExtendedFloat {
+        // Logic check, values must be decently normalized prior to multiplication.
+        debug_assert!((self.mant & u64::HIMASK != 0) && (b.mant & u64::HIMASK != 0));
+
+        // Extract high-and-low masks.
+        let ah = self.mant >> u64::HALF;
+        let al = self.mant & u64::LOMASK;
+        let bh = b.mant >> u64::HALF;
+        let bl = b.mant & u64::LOMASK;
+
+        // Get our products
+        let ah_bl = ah * bl;
+        let al_bh = al * bh;
+        let al_bl = al * bl;
+        let ah_bh = ah * bh;
+
+        let mut tmp = (ah_bl & u64::LOMASK) + (al_bh & u64::LOMASK) + (al_bl >> u64::HALF);
+        // round up
+        tmp += 1 << (u64::HALF - 1);
+
+        ExtendedFloat {
+            mant: ah_bh + (ah_bl >> u64::HALF) + (al_bh >> u64::HALF) + (tmp >> u64::HALF),
+            exp: self.exp + b.exp + u64::FULL,
+        }
+    }
+
+    /// Multiply in-place, as if by `a*b`.
+    ///
+    /// The result is not normalized.
+    #[inline]
+    pub(crate) fn imul(&mut self, b: &ExtendedFloat) {
+        *self = self.mul(b);
+    }
+
+    // NORMALIZE
+
+    /// Normalize float-point number.
+    ///
+    /// Shift the mantissa so the number of leading zeros is 0, or the value
+    /// itself is 0.
+    ///
+    /// Get the number of bytes shifted.
+    #[inline]
+    pub(crate) fn normalize(&mut self) -> u32 {
+        // Note:
+        // Using the cltz intrinsic via leading_zeros is way faster (~10x)
+        // than shifting 1-bit at a time, via while loop, and also way
+        // faster (~2x) than an unrolled loop that checks at 32, 16, 4,
+        // 2, and 1 bit.
+        //
+        // Using a modulus of pow2 (which will get optimized to a bitwise
+        // and with 0x3F or faster) is slightly slower than an if/then,
+        // however, removing the if/then will likely optimize more branched
+        // code as it removes conditional logic.
+
+        // Calculate the number of leading zeros, and then zero-out
+        // any overflowing bits, to avoid shl overflow when self.mant == 0.
+        let shift = if self.mant == 0 {
+            0
+        } else {
+            self.mant.leading_zeros()
+        };
+        shl(self, shift as i32);
+        shift
+    }
+
+    // ROUND
+
+    /// Lossy round float-point number to native mantissa boundaries.
+    #[inline]
+    pub(crate) fn round_to_native<F, Algorithm>(&mut self, algorithm: Algorithm)
+    where
+        F: Float,
+        Algorithm: FnOnce(&mut ExtendedFloat, i32),
+    {
+        round_to_native::<F, _>(self, algorithm);
+    }
+
+    // FROM
+
+    /// Create extended float from native float.
+    #[inline]
+    pub fn from_float<F: Float>(f: F) -> ExtendedFloat {
+        from_float(f)
+    }
+
+    // INTO
+
+    /// Convert into default-rounded, lower-precision native float.
+    #[inline]
+    pub(crate) fn into_float<F: Float>(mut self) -> F {
+        self.round_to_native::<F, _>(round_nearest_tie_even);
+        into_float(self)
+    }
+
+    /// Convert into downward-rounded, lower-precision native float.
+    #[inline]
+    pub(crate) fn into_downward_float<F: Float>(mut self) -> F {
+        self.round_to_native::<F, _>(round_downward);
+        into_float(self)
+    }
+}
+
+// FROM FLOAT
+
+// Import ExtendedFloat from native float.
+#[inline]
+pub(crate) fn from_float<F>(f: F) -> ExtendedFloat
+where
+    F: Float,
+{
+    ExtendedFloat {
+        mant: u64::as_cast(f.mantissa()),
+        exp: f.exponent(),
+    }
+}
+
+// INTO FLOAT
+
+// Export extended-precision float to native float.
+//
+// The extended-precision float must be in native float representation,
+// with overflow/underflow appropriately handled.
+#[inline]
+pub(crate) fn into_float<F>(fp: ExtendedFloat) -> F
+where
+    F: Float,
+{
+    // Export floating-point number.
+    if fp.mant == 0 || fp.exp < F::DENORMAL_EXPONENT {
+        // sub-denormal, underflow
+        F::ZERO
+    } else if fp.exp >= F::MAX_EXPONENT {
+        // overflow
+        F::from_bits(F::INFINITY_BITS)
+    } else {
+        // calculate the exp and fraction bits, and return a float from bits.
+        let exp: u64;
+        if (fp.exp == F::DENORMAL_EXPONENT) && (fp.mant & F::HIDDEN_BIT_MASK.as_u64()) == 0 {
+            exp = 0;
+        } else {
+            exp = (fp.exp + F::EXPONENT_BIAS) as u64;
+        }
+        let exp = exp << F::MANTISSA_SIZE;
+        let mant = fp.mant & F::MANTISSA_MASK.as_u64();
+        F::from_bits(F::Unsigned::as_cast(mant | exp))
+    }
+}
@@ -0,0 +1,9 @@
+// Adapted from https://github.com/Alexhuszagh/rust-lexical.
+
+//! Precalculated large powers for limbs.
+
+#[cfg(fast_arithmetic = "32")]
+pub(crate) use super::large_powers32::*;
+
+#[cfg(fast_arithmetic = "64")]
+pub(crate) use super::large_powers64::*;
@@ -0,0 +1,183 @@
+// Adapted from https://github.com/Alexhuszagh/rust-lexical.
+
+//! Precalculated large powers for 32-bit limbs.
+
+/// Large powers (`&[u32]`) for base5 operations.
+const POW5_1: [u32; 1] = [5];
+const POW5_2: [u32; 1] = [25];
+const POW5_3: [u32; 1] = [625];
+const POW5_4: [u32; 1] = [390625];
+const POW5_5: [u32; 2] = [2264035265, 35];
+const POW5_6: [u32; 3] = [2242703233, 762134875, 1262];
+const POW5_7: [u32; 5] = [3211403009, 1849224548, 3668416493, 3913284084, 1593091];
+const POW5_8: [u32; 10] = [
+    781532673, 64985353, 253049085, 594863151, 3553621484, 3288652808, 3167596762, 2788392729,
+    3911132675, 590,
+];
+const POW5_9: [u32; 19] = [
+    2553183233, 3201533787, 3638140786, 303378311, 1809731782, 3477761648, 3583367183, 649228654,
+    2915460784, 487929380, 1011012442, 1677677582, 3428152256, 1710878487, 1438394610, 2161952759,
+    4100910556, 1608314830, 349175,
+];
+const POW5_10: [u32; 38] = [
+    4234999809, 2012377703, 2408924892, 1570150255, 3090844311, 3273530073, 1187251475, 2498123591,
+    3364452033, 1148564857, 687371067, 2854068671, 1883165473, 505794538, 2988060450, 3159489326,
+    2531348317, 3215191468, 849106862, 3892080979, 3288073877, 2242451748, 4183778142, 2995818208,
+    2477501924, 325481258, 2487842652, 1774082830, 1933815724, 2962865281, 1168579910, 2724829000,
+    2360374019, 2315984659, 2360052375, 3251779801, 1664357844, 28,
+];
+const POW5_11: [u32; 75] = [
+    689565697, 4116392818, 1853628763, 516071302, 2568769159, 365238920, 336250165, 1283268122,
+    3425490969, 248595470, 2305176814, 2111925499, 507770399, 2681111421, 589114268, 591287751,
+    1708941527, 4098957707, 475844916, 3378731398, 2452339615, 2817037361, 2678008327, 1656645978,
+    2383430340, 73103988, 448667107, 2329420453, 3124020241, 3625235717, 3208634035, 2412059158,
+    2981664444, 4117622508, 838560765, 3069470027, 270153238, 1802868219, 3692709886, 2161737865,
+    2159912357, 2585798786, 837488486, 4237238160, 2540319504, 3798629246, 3748148874, 1021550776,
+    2386715342, 1973637538, 1823520457, 1146713475, 833971519, 3277251466, 905620390, 26278816,
+    2680483154, 2294040859, 373297482, 5996609, 4109575006, 512575049, 917036550, 1942311753,
+    2816916778, 3248920332, 1192784020, 3537586671, 2456567643, 2925660628, 759380297, 888447942,
+    3559939476, 3654687237, 805,
+];
+const POW5_12: [u32; 149] = [
+    322166785, 3809044581, 2994556223, 1239584207, 3962455841, 4001882964, 3053876612, 915114683,
+    2783289745, 785739093, 4253185907, 3931164994, 1370983858, 2553556126, 3360742076, 2255410929,
+    422849554, 2457422215, 3539495362, 1720790602, 1908931983, 1470596141, 592794347, 4219465164,
+    4085652704, 941661409, 2534650953, 885063988, 2355909854, 2812815516, 767256131, 3821757683,
+    2155151105, 3817418473, 281116564, 2834395026, 2821201622, 2524625843, 1511330880, 2572352493,
+    330571332, 2951088579, 2730271766, 4044456479, 4212286644, 2444937588, 3603420843, 2387148597,
+    1142537539, 3299235429, 1751012624, 861228086, 2873722519, 230498814, 1023297821, 2553128038,
+    3421129895, 2651917435, 2042981258, 1606787143, 2228751918, 447345732, 1930371132, 1784132011,
+    3612538790, 2275925090, 2487567871, 1080427616, 2009179183, 3383506781, 3899054063, 1950782960,
+    2168622213, 2717674390, 3616636027, 2079341593, 1530129217, 1461057425, 2406264415, 3674671357,
+    2972036238, 2019354295, 1455849819, 1866918619, 1324269294, 424891864, 2722422332, 2641594816,
+    1400249021, 3482963993, 3734946379, 225889849, 1891545473, 777383150, 3589824633, 4117601611,
+    4220028667, 334453379, 1083130821, 1060342180, 4208163139, 1489826908, 4163762246, 1096580926,
+    689301528, 2336054516, 1782865703, 4175148410, 3398369392, 2329412588, 3001580596, 59740741,
+    3202189932, 3351895776, 246185302, 718535188, 3772647488, 4151666556, 4055698133, 2461934110,
+    2281316281, 3466396836, 3536023465, 1064267812, 2955456354, 2423805422, 3627960790, 1325057500,
+    3876919979, 2009959531, 175455101, 184092852, 2358785571, 3842977831, 2485266289, 487121622,
+    4159252710, 4075707558, 459389244, 300652075, 2521346588, 3458976673, 888631636, 2076098096,
+    3844514585, 2363697580, 3729421522, 3051115477, 649395,
+];
+const POW5_13: [u32; 298] = [
+    711442433, 3564261005, 2399042279, 4170849936, 4010295575, 1423987028, 330414929, 1349249065,
+    4213813618, 3852031822, 4040843590, 2154565331, 3094013374, 1159028371, 3227065538, 2115927092,
+    2085102554, 488590542, 2609619432, 3602898805, 3812736528, 3269439096, 23816114, 253984538,
+    1035905997, 2942969204, 3400787671, 338562688, 1637191975, 740509713, 2264962817, 3410753922,
+    4162231428, 2282041228, 1759373012, 3155367777, 4278913285, 1420532801, 1981002276, 438054990,
+    1006507643, 1142697287, 1332538012, 2029019521, 3949305784, 818392641, 2491288846, 2716584663,
+    3648886102, 556814413, 444795339, 4071412999, 1066321706, 4253169466, 2510832316, 672091442,
+    4083256000, 2165985028, 1841538484, 3549854235, 364431512, 3707648143, 1162785440, 2268641545,
+    281340310, 735693841, 848809228, 1700785200, 2919703985, 4094234344, 58530286, 965505005,
+    1000010347, 3381961808, 3040089923, 1973852082, 2890971585, 1019960210, 4292895237, 2821887841,
+    3756675650, 3951282907, 3885870583, 1008791145, 503998487, 1881258362, 1949332730, 392996726,
+    2012973814, 3970014187, 2461725150, 2942547730, 3728066699, 2766901132, 3778532841, 1085564064,
+    2278673896, 1116879805, 3448726271, 774279411, 157211670, 1506320155, 531168605, 1362654525,
+    956967721, 2148871960, 769186085, 4186232894, 2055679604, 3248365487, 3981268013, 3975787984,
+    2489510517, 3309046495, 212771124, 933418041, 3371839114, 562115198, 1853601831, 757336096,
+    1354633440, 1486083256, 2872126393, 522920738, 1141587749, 3210903262, 1926940553, 3054024853,
+    2021162538, 2262742000, 1877899947, 3147002868, 669840763, 4158174590, 4238502559, 1023731922,
+    3386840011, 829588074, 3449720188, 2835142880, 2999162007, 813056473, 482949569, 638108879,
+    3067201471, 1026714238, 4004452838, 2383667807, 3999477803, 771648919, 630660440, 3827121348,
+    176185980, 2878191002, 2666149832, 3909811063, 2429163983, 2665690412, 907266128, 4269332098,
+    2022665808, 1527122180, 3072053668, 1072477492, 3006022924, 549664855, 2800340954, 37352654,
+    1212772743, 2711280533, 3029527946, 2511120040, 1305308377, 3474662224, 4226330922, 442988428,
+    954940108, 3274548099, 4212288177, 2688499880, 3982226758, 3922609956, 1279948029, 1939943640,
+    3650489901, 2733364929, 2494263275, 1864579964, 1225941120, 2390465139, 1267503249, 3533240729,
+    904410805, 2842550015, 2517736241, 1796069820, 3335274381, 673539835, 1924694759, 3598098235,
+    2792633405, 16535707, 3703535497, 3592841791, 2929082877, 1317622811, 294990855, 1396706563,
+    2383271770, 3853857605, 277813677, 277580220, 1101318484, 3761974115, 1132150143, 2544692622,
+    3419825776, 743770306, 1695464553, 1548693232, 2421159615, 2575672031, 2678971806, 1591267897,
+    626546738, 3823443129, 267710932, 1455435162, 2353985540, 3248523795, 335348168, 3872552561,
+    2814522612, 2634118860, 3503767026, 1301019273, 1414467789, 722985138, 3070909565, 4253482569,
+    3744939841, 558142907, 2229819389, 13833173, 77003966, 2763671364, 3905603970, 2931990126,
+    2280419384, 1879090457, 2934846267, 4284933164, 2331863845, 62191163, 3178861020, 1522063815,
+    785672270, 1215568492, 2936443917, 802972489, 2956820173, 3916732783, 2893572089, 1391232801,
+    3168640330, 2396859648, 894950918, 1103583736, 961991865, 2807302642, 305977505, 3054505899,
+    1048256994, 781017659, 2459278754, 3164823415, 537658277, 905753687, 464963300, 4149131560,
+    1029507924, 2278300961, 1231291503, 414073408, 3630740085, 2345841814, 475358196, 3258243317,
+    4167625072, 4178911231, 2927355042, 655438830, 3138378018, 623200562, 2785714112, 273403236,
+    807993669, 98,
+];
+const POW5_14: [u32; 595] = [
+    1691320321, 2671006246, 1682531301, 2072858707, 1240508969, 3108358191, 1125119096, 2470144952,
+    1610099978, 1690632660, 1941696884, 2663506355, 1006364675, 3909158537, 4147711374, 1072663936,
+    4078768933, 745751659, 4123687570, 471458681, 655028926, 4113407388, 3945524552, 985625313,
+    1254424514, 2127508744, 570530434, 945388122, 3194649404, 2589065070, 2731705399, 202030749,
+    2090780394, 3348662271, 1481754777, 1130635472, 4025144705, 1924486271, 2578567861, 125491448,
+    1558036315, 994248173, 3817216711, 763950077, 1030439870, 959586474, 3845661701, 483795093,
+    1637944470, 2275463649, 3398804829, 1758016486, 2665513698, 2004912571, 1094885097, 4223064276,
+    3307819021, 651121777, 1757003305, 3603542336, 129917786, 2215974994, 3042386306, 2205352757,
+    3944939700, 3710987569, 97967515, 1217242524, 930630949, 3660328512, 1787663098, 1784141600,
+    2500542892, 4034561586, 3444961378, 785043562, 3869499367, 885623728, 2625011087, 3053789617,
+    1965731793, 3900511934, 2648823592, 3851062028, 3321968688, 799195417, 1011847510, 1369129160,
+    1348009103, 2876796955, 2915408967, 3305284948, 263399535, 1715990604, 2645821294, 1587844552,
+    2624912049, 3035631499, 2306636348, 3499275462, 675152704, 854794152, 4004972748, 1739996642,
+    1333476491, 4012621867, 3658792931, 3297985728, 2864481726, 3066357406, 785287846, 1671499798,
+    433044045, 1919608025, 264833858, 3999983367, 1116778570, 1301982149, 4213901070, 4081649357,
+    536169226, 1389008649, 188923873, 373495152, 2551132278, 1800758715, 3951840330, 2632334454,
+    3118778225, 1034046547, 1862428410, 3037609062, 1994608505, 29051798, 2571685694, 264151332,
+    2260643090, 2717535964, 3508441116, 3283713017, 1903365635, 923575694, 1219598101, 2288281570,
+    3676533911, 1014136356, 555142354, 2389170030, 4185108175, 884862419, 836141292, 2957159173,
+    1997444768, 4233903127, 2876184692, 3089125070, 1480848293, 1097600237, 299700527, 2507669891,
+    2982628312, 2114881043, 2529576251, 2812279824, 2987750993, 4241938954, 2204775591, 1037094060,
+    829315638, 1231047149, 52608178, 3735136637, 3455232602, 962039123, 488286513, 50685385,
+    3516451821, 843975207, 1572355722, 675489076, 2428445672, 1555117248, 3708476086, 10375249,
+    4172112346, 2117510871, 2227658327, 3187664554, 3050656558, 328034318, 3179601324, 1247769761,
+    3439263953, 1431538938, 2962525068, 1213366289, 3813013550, 2651093719, 1860661503, 3933716208,
+    264320617, 789980519, 2257856172, 102000748, 977269860, 1113845122, 3008928583, 1461738106,
+    557786285, 2926560363, 1038106190, 3643478847, 828004507, 457818698, 1933056971, 373408056,
+    2076808229, 3160935130, 2781854874, 2519636100, 177606000, 4237103862, 3977834316, 1621936232,
+    2599050516, 319893558, 3343370366, 765044144, 976657331, 7026264, 294277429, 3829376742,
+    3029627280, 2705178718, 3614653880, 230519152, 3288033233, 293525479, 3805751881, 3227511198,
+    2520308544, 3648103003, 1111086184, 437622105, 2232033852, 3239146386, 584244184, 1450926016,
+    2462430443, 3226534010, 298582169, 4214576928, 1762099469, 964985185, 1585788148, 1641127666,
+    787006566, 2315956284, 3258232694, 2275058964, 2541003317, 1508235863, 2613339827, 4080647514,
+    1152057965, 3149266279, 731345410, 914737650, 65395712, 1884566942, 1379520432, 2611027720,
+    4163073378, 2619704967, 2746552541, 1388822415, 3005141199, 843440249, 4288674003, 3136174279,
+    4051522914, 4144149433, 3427566947, 3419023197, 3758479825, 3893877676, 96899594, 1657725776,
+    253618880, 434129337, 1499045748, 2996992534, 4036042074, 2110713869, 906222950, 928326225,
+    2541827893, 1604330202, 226792470, 4022228930, 815850898, 1466012310, 3377712199, 292769859,
+    2822055597, 3225701344, 3052947004, 385831222, 705324593, 4030158636, 3540280538, 2982120874,
+    2136414455, 255762046, 3852783591, 3262064164, 2358991588, 3756586117, 4143612643, 3326743817,
+    2897365738, 807711264, 3719310016, 3721264861, 3627337076, 944539331, 3640975513, 3712525681,
+    1162911839, 2008243316, 2179489649, 2867584109, 261861553, 3570253908, 2062868357, 2220328623,
+    3857004679, 3744109002, 4138041873, 1451860932, 2364975637, 2802161722, 2680106834, 753401584,
+    1223182946, 1245401957, 4163377735, 3565815922, 2216942838, 4036140094, 71979081, 3924559643,
+    400477238, 551750683, 1174153235, 859969898, 1185921017, 1711399735, 812991545, 4051735761,
+    3549118738, 1631653329, 3631835958, 3648867800, 1206500363, 2155893137, 361030362, 3454286017,
+    2505909489, 1083595169, 453595313, 1510564703, 1706163902, 1632924345, 1381875722, 1661526119,
+    1082778324, 3571910052, 1140625929, 851544870, 1145546234, 2938573139, 907528924, 1304752338,
+    1764668294, 1788942063, 1700368828, 104979467, 1413911959, 3327497828, 1956384744, 1272712474,
+    2815637534, 3307809377, 1320574940, 1111968962, 4073107827, 434096622, 169451929, 3201183459,
+    3331028877, 2852366972, 3369830128, 2924794558, 3106537952, 3739481231, 1612955817, 4138608722,
+    2721281595, 2755775390, 843505117, 982234295, 1157276611, 814674632, 4246504726, 3532006708,
+    992340967, 1647538031, 204696133, 193866982, 3899126129, 300851698, 1379496684, 1759463683,
+    1354782756, 1374637239, 3410883240, 1073406229, 3038431791, 1053909855, 3607043270, 173719711,
+    3733903830, 171820911, 1573050589, 932781534, 4183534770, 2158849555, 372245998, 3573073830,
+    841339264, 2759200520, 1610547277, 2603293319, 3890906486, 1557138278, 3964109906, 677238797,
+    537994297, 1124184993, 4287078344, 4207654540, 2943022776, 2977947524, 3255359985, 4098397558,
+    2274666217, 2915862060, 243524940, 2467726756, 2869020032, 507521339, 3403121914, 522051455,
+    1803903108, 3471254194, 473535371, 1948602036, 3352095732, 3116527002, 1795743673, 775867940,
+    2551469548, 3757442064, 3162525227, 3765412747, 3040105484, 1927625810, 48214767, 2997207130,
+    1342349989, 2536583992, 1501320191, 3592287317, 887432730, 967585477, 3334212779, 948663609,
+    1064513472, 15386372, 2465931737, 3230242590, 3036652803, 2063155087, 1927500726, 2821790499,
+    2187774383, 501520074, 3688568496, 3606711121, 2576459247, 3176542345, 378322447, 156541411,
+    1400607301, 1406179107, 677848877, 2253753529, 193196070, 4207435024, 4166396241, 509467541,
+    2906024136, 1221753746, 3375413222, 431327897, 2749265123, 2848827671, 3412997614, 2051920238,
+    1283516885, 1300498239, 1957256104, 2634010560, 3531900395, 360276850, 1461184973, 2012063967,
+    2873572430, 2914608609, 4289554777, 1539331673, 1859532928, 4213441063, 538215691, 3512720863,
+    4258743698, 3040408445, 982396546, 343095663, 4138069496, 1021581857, 214185242, 1968079460,
+    2864275059, 3347192726, 4096783459, 3259169450, 3707808869, 142485006, 399610869, 230556456,
+    2219467721, 4191227798, 2242548189, 3136366572, 179755707, 3464881829, 452317775, 3887426070,
+    3446430233, 1473370015, 1576807208, 3964523248, 419325089, 2373067114, 1596072055, 1928415752,
+    3635452689, 1005598891, 3335462724, 3290848636, 3669078247, 1178176812, 2110774376, 3068593619,
+    1253036518, 908857731, 3631223047, 4138506423, 2903592318, 3596915748, 3289036113, 3721512676,
+    2704409359, 3386016968, 3676268074, 2185259502, 1096257611, 3360076717, 3548676554, 170167319,
+    3360064287, 3899940843, 9640,
+];
+
+pub(crate) const POW5: [&'static [u32]; 14] = [
+    &POW5_1, &POW5_2, &POW5_3, &POW5_4, &POW5_5, &POW5_6, &POW5_7, &POW5_8, &POW5_9, &POW5_10,
+    &POW5_11, &POW5_12, &POW5_13, &POW5_14,
+];
@@ -0,0 +1,625 @@
+// Adapted from https://github.com/Alexhuszagh/rust-lexical.
+
+//! Precalculated large powers for 64-bit limbs.
+
+/// Large powers (`&[u64]`) for base5 operations.
+const POW5_1: [u64; 1] = [5];
+const POW5_2: [u64; 1] = [25];
+const POW5_3: [u64; 1] = [625];
+const POW5_4: [u64; 1] = [390625];
+const POW5_5: [u64; 1] = [152587890625];
+const POW5_6: [u64; 2] = [3273344365508751233, 1262];
+const POW5_7: [u64; 3] = [7942358959831785217, 16807427164405733357, 1593091];
+const POW5_8: [u64; 5] = [
+    279109966635548161,
+    2554917779393558781,
+    14124656261812188652,
+    11976055582626787546,
+    2537941837315,
+];
+const POW5_9: [u64; 10] = [
+    13750482914757213185,
+    1302999927698857842,
+    14936872543252795590,
+    2788415840139466767,
+    2095640732773017264,
+    7205570348933370714,
+    7348167152523113408,
+    9285516396840364274,
+    6907659600622710236,
+    349175,
+];
+const POW5_10: [u64; 19] = [
+    8643096425819600897,
+    6743743997439985372,
+    14059704609098336919,
+    10729359125898331411,
+    4933048501514368705,
+    12258131603170554683,
+    2172371001088594721,
+    13569903330219142946,
+    13809142207969578845,
+    16716360519037769646,
+    9631256923806107285,
+    12866941232305103710,
+    1397931361048440292,
+    7619627737732970332,
+    12725409486282665900,
+    11703051443360963910,
+    9947078370803086083,
+    13966287901448440471,
+    121923442132,
+];
+const POW5_11: [u64; 38] = [
+    17679772531488845825,
+    2216509366347768155,
+    1568689219195129479,
+    5511594616325588277,
+    1067709417009240089,
+    9070650952098657518,
+    11515285870634858015,
+    2539561553659505564,
+    17604889300961091799,
+    14511540856854204724,
+    12099083339557485471,
+    7115240299237943815,
+    313979240050606788,
+    10004784664717172195,
+    15570268847930131473,
+    10359715202835930803,
+    17685054012115162812,
+    13183273382855797757,
+    7743260039872919062,
+    9284593436392572926,
+    11105921222066415013,
+    18198799323400703846,
+    16314988383739458320,
+    4387527177871570570,
+    8476708682254672590,
+    4925096874831034057,
+    14075687868072027455,
+    112866656203221926,
+    9852830467773230418,
+    25755239915196746,
+    2201493076310172510,
+    8342165458688466438,
+    13954006576066379050,
+    15193819059903295636,
+    12565616718911389531,
+    3815854855847885129,
+    15696762163583540628,
+    805,
+];
+const POW5_12: [u64; 75] = [
+    16359721904723189761,
+    5323973632697650495,
+    17187956456762001185,
+    3930387638628283780,
+    3374723710406992273,
+    16884225088663222131,
+    10967440051041439154,
+    9686916182456720060,
+    10554548046311730194,
+    7390739362393647554,
+    6316162333127736719,
+    18122464886584070891,
+    4044404959645932768,
+    3801320885861987401,
+    12080950653257274590,
+    16414324262488991299,
+    16395687498836410113,
+    12173633940896186260,
+    10843185433142632150,
+    11048169832730399808,
+    12674828934734683716,
+    17370808310130582550,
+    10500926985433408692,
+    10252725158410704555,
+    14170108270502067523,
+    3698946465517688080,
+    989984870770509463,
+    10965601426733943069,
+    11389898658438335655,
+    6901098232861256586,
+    1921335291173932590,
+    7662788640922083388,
+    9775023833308395430,
+    4640401278902814207,
+    14532050972198413359,
+    8378549018693130223,
+    11672322628395371653,
+    8930704142764178555,
+    6275193859483102017,
+    15782593304269205087,
+    8673060659034172558,
+    8018354414354334043,
+    1824896661540749038,
+    11345563346725559868,
+    14959216444480821949,
+    970189517688324683,
+    3338835207603007873,
+    17684964260791738489,
+    1436466329061721851,
+    4554134986752476101,
+    6398757850768963907,
+    4709779218751158342,
+    10033277748582410264,
+    17932125878679265063,
+    10004750887749091440,
+    256584531835386932,
+    14396282740722731628,
+    3086085133731396950,
+    17831272085689600064,
+    10573926491412564693,
+    14888061047859191737,
+    4570995450261499817,
+    10410165022312935266,
+    5691078631447480790,
+    8632710455805418155,
+    790672778942823293,
+    16505464105756800547,
+    2092171438149740401,
+    17505030673829275878,
+    1291290830058928444,
+    14856191690683232796,
+    8916773426496500052,
+    10152003807578858265,
+    13104441193763861714,
+    649395,
+];
+const POW5_13: [u64; 149] = [
+    15308384451594534913,
+    17913664074042735335,
+    6115977719198531863,
+    5794980608663993169,
+    16544350702855106930,
+    9253787637781258566,
+    4977988951675168190,
+    9087837664087448770,
+    2098480401110016986,
+    15474332540882100712,
+    14042133997396540944,
+    1090855284423485362,
+    12639956485351058381,
+    1454115676006639319,
+    3180465001342538023,
+    14649076551958697729,
+    9801292446545910916,
+    13552201410826594004,
+    6101141927469189381,
+    1881431857880609316,
+    4907847477899433595,
+    8714572486973123228,
+    3514969632331374520,
+    11667642286891470094,
+    2391499697425323350,
+    17486585679659076043,
+    18267223761882105642,
+    2886610765822313148,
+    9302834862968900288,
+    15246507846733637044,
+    15924227519624562840,
+    9743741243284697760,
+    3159780987244964246,
+    7304816812369628428,
+    17584602612559717809,
+    4146812420657846766,
+    14525415362681041515,
+    8477630142371600195,
+    4380695748062263745,
+    12119915994367943173,
+    16970630866565485122,
+    4332724980155264503,
+    8079943140620527639,
+    1687908087554405626,
+    17051081099834002166,
+    12638146269730763230,
+    11883749876933445771,
+    4662462156371383785,
+    4796962238316531176,
+    3325504751659868927,
+    6469595803187862550,
+    5852556621152583005,
+    9229334792448387881,
+    17979733373938620709,
+    13951623534175792756,
+    17075879371091039277,
+    14212246479457938037,
+    4008999959804158260,
+    2414266395366403722,
+    3252733766253918247,
+    6382678985007829216,
+    2245927470982310841,
+    13790724502051307301,
+    13116936866733148041,
+    9718402891306794538,
+    13516274400356104875,
+    17859223875778049403,
+    4396895129099725471,
+    3563053650368467915,
+    12176845952536972668,
+    3492050964335269015,
+    2740656767075170753,
+    4409704077614761919,
+    10237775279597492710,
+    3314206875098230827,
+    16437361028114095448,
+    12361736225407656572,
+    16792510651790145480,
+    11449053143229929935,
+    18336641737580333136,
+    6558939822118891088,
+    4606255756908155300,
+    2360792578991605004,
+    160428430149144538,
+    11644861220729221511,
+    10785178451159739786,
+    14923560618031934681,
+    1902620814992781610,
+    14064076995338910412,
+    11547019064112212657,
+    16847481479966225734,
+    8331994491163145469,
+    11739712981738851885,
+    8008309968651120619,
+    10266969595459035264,
+    15175153381217702033,
+    12208659352573720245,
+    7714061140750342961,
+    2892831567213510541,
+    15453714249045017319,
+    71020323573871677,
+    15431137995750602633,
+    5659146884637671933,
+    5998809010488554503,
+    16552192379299157850,
+    1192197967194298797,
+    16157555793424861524,
+    10929371590994640255,
+    3194469143425738352,
+    6651586784672005225,
+    11062427140788057791,
+    6834443579468668318,
+    16421563197797455922,
+    6251046422506172884,
+    13952303462156793860,
+    16632486601871393224,
+    11313454360291325172,
+    5587835232504462834,
+    3105197524618514637,
+    18268568531031972989,
+    2397205535804309313,
+    59413027864729597,
+    11869878125348715710,
+    12592801707270523266,
+    8070632061321113656,
+    18403647807860650811,
+    267109013517069093,
+    6537214311028855260,
+    5220826919973709902,
+    3448740582779163661,
+    16822239213112884941,
+    5975299384311048185,
+    10294433804430712138,
+    4739856055412448774,
+    12057273038326387897,
+    13119002941950056609,
+    3354445304051737058,
+    13592813067499314594,
+    3890182464434078629,
+    17820384357466425060,
+    9785228118969879380,
+    1778431746734556271,
+    10075313876350055029,
+    13994048489400919028,
+    17948287074199726448,
+    2815088342305858722,
+    2676626035777198370,
+    1174257960026283968,
+    421714788677,
+];
+const POW5_14: [u64; 298] = [
+    11471884475673051137,
+    8902860357476377573,
+    13350296775839230505,
+    10609191786344608888,
+    7261211985859587338,
+    11439672689354862964,
+    16789708072300570627,
+    4607056528866348430,
+    3202978990421512997,
+    2024899620433984146,
+    17666950207239811774,
+    4233228489390288200,
+    9137580478688460738,
+    4060411066587388546,
+    11119949806060600124,
+    867715462473090103,
+    14382394941384869610,
+    4856042377419278489,
+    8265605599571137921,
+    538981667666252469,
+    4270263388700786523,
+    3281140600308898503,
+    4121392524544394174,
+    2077884106245940229,
+    9773041957329767574,
+    7550623316597646685,
+    8611033926449791714,
+    18137922955420802793,
+    2796546741236224013,
+    15477096484628446761,
+    9517540128113714010,
+    9471917970500821378,
+    15938570248662483124,
+    5228016831978462619,
+    15720991252586974501,
+    7662829825220776698,
+    17328310068068434348,
+    3371736428170309730,
+    3803724952191098855,
+    13115926536504376719,
+    16752571196153442257,
+    16540185467776259880,
+    3432518182450051120,
+    5880364967211798870,
+    12355748840305392783,
+    14196090758536469575,
+    7370123524686686319,
+    6819740424617592686,
+    13037938013537368753,
+    15029273671291927100,
+    3671312928327205696,
+    7473228676544792780,
+    17234079691312938123,
+    14164740848093544419,
+    13169904779481875902,
+    7179036968465894054,
+    8244653688947194445,
+    17179797746073799490,
+    5591970751047577674,
+    17530550506268329742,
+    5965746721852312330,
+    1604149463243472865,
+    7734199791463116918,
+    11305790396015856714,
+    4441196105025505137,
+    13046431581185664762,
+    124776524294606713,
+    1134521334706523966,
+    11671728093344476434,
+    14103440020972933148,
+    3966727403013869059,
+    9828094508409132821,
+    4355682486381147287,
+    10261407143988481234,
+    3800455155249557199,
+    12700901937937547500,
+    18184475466894579360,
+    13267691151779895412,
+    4714157123477697445,
+    10770360171308585263,
+    9083344917597998040,
+    12078649873810212155,
+    18218989082046199377,
+    4454285072780637351,
+    5287307245618354742,
+    16042289702059031730,
+    4131926574212754010,
+    217692071448455473,
+    3624845916216282093,
+    2901203491797614218,
+    6679177724033967080,
+    44561358851332790,
+    9094639944041587162,
+    13690915012276084311,
+    1408896670826320686,
+    5359130319612337580,
+    6148412925099835601,
+    5211368532286409612,
+    11386360825549027374,
+    16895182466965795071,
+    3392940493846427241,
+    438089879085393580,
+    4783928372776399972,
+    6278117363595909959,
+    12569481049412674733,
+    15648622492570893902,
+    1966316336235305115,
+    1603775390515993547,
+    13576113010204316709,
+    10821754650102840474,
+    18198222517222903152,
+    6966163076615302988,
+    1373932372410129684,
+    3285839581819684990,
+    30177575069719475,
+    16447047871247307061,
+    11618654126674833808,
+    990072222556306872,
+    1260682336135768017,
+    13862055046689532489,
+    15668483092844698432,
+    1879572630092764264,
+    13912027797058626108,
+    6231679788219816920,
+    13857858054844167403,
+    18101470072534728857,
+    4144579812461609229,
+    7048589655616599284,
+    9946956499532694630,
+    9771303850109874038,
+    6477823708780339765,
+    17526247621747041971,
+    13525995675852669549,
+    3928768291901239810,
+    8094153383078124544,
+    11214278667728965552,
+    11251547162596832610,
+    5964946855123292381,
+    3622548288590237903,
+    13469765967150053587,
+    17798986288523466082,
+    14684592818807932259,
+    16724077276802963921,
+    7119877993753121290,
+    1864571304902781632,
+    12871984921385213812,
+    9065447042604670298,
+    3987130777300360550,
+    6890545752116901685,
+    17275341711601865750,
+    6296474927799264658,
+    1257436973037243463,
+    13854281781965301421,
+    1657132483318662716,
+    17309399540017292849,
+    12808111630089217242,
+    1098489625264462071,
+    14010458905686364135,
+    16134414519481621220,
+    14288255900328821475,
+    3469093466388187882,
+    15982710881468295872,
+    4056765540058056052,
+    15945176389096104089,
+    8625339365793505375,
+    12316179968863788913,
+    15334123773538054321,
+    9536238824220581765,
+    16080825720106203271,
+    6235695225418121745,
+    12035192956458019349,
+    3235835166714703698,
+    5348960676912581218,
+    15315062772709464647,
+    17335089708021308662,
+    16855855317958414409,
+    2369751139431140406,
+    3693542588628609043,
+    7350405893393987577,
+    17402072586341663801,
+    7007897690013647122,
+    15671767872059304758,
+    9259490518292347915,
+    14836045474406130394,
+    4654005815464502513,
+    6487825998330548401,
+    7013356660323385022,
+    7136200343936679946,
+    15341236858676437716,
+    3657357368867197449,
+    12621075530054608378,
+    5603868621997066972,
+    7683447656788439942,
+    450883379216880060,
+    14291494350184945047,
+    5466258454997635048,
+    14206933098432772126,
+    4775870327277641692,
+    1864430798867181939,
+    13748978265070608793,
+    12250822864261576589,
+    12561896977498605296,
+    16060949594257359328,
+    17775189113543311529,
+    11835965177892927035,
+    4218664174878121437,
+    3499000902478111683,
+    15169853304359126294,
+    7076121963053575143,
+    832652347668916805,
+    1292148207755194737,
+    7556838978364207852,
+    5904021986723518500,
+    4610244652288570024,
+    4526508363195533871,
+    746120481022614726,
+    737965197247830486,
+    4006266184415762653,
+    9272188239892688050,
+    15346235246415709678,
+    11850675997347533184,
+    11181059668610842701,
+    6687857983250662774,
+    2908718488661492818,
+    4828337780126983225,
+    18071738646453002184,
+    12790187227727197880,
+    17602483480871623153,
+    12523532189621855977,
+    10598805712727696716,
+    2179787555896149376,
+    2242193929457337594,
+    14908923241136742532,
+    8369182018012550027,
+    13385381554043022324,
+    3332327430110633913,
+    16138090784046208492,
+    16172324607469047339,
+    8279089815915615244,
+    12872906602736235247,
+    10894545290539475621,
+    15428756545851905023,
+    4155747980686992922,
+    4074479178894544043,
+    66083965608603584,
+    13873786284662268377,
+    8861183628277687555,
+    12119497911296021430,
+    2154012318305274287,
+    15490706314503067312,
+    13643145488710608367,
+    672340241093017103,
+    6039493278284091973,
+    9679797700977436461,
+    18070795828318171174,
+    2188146431134935377,
+    5247392385741514952,
+    1852539214842869734,
+    12235621681634112739,
+    8812930319623534062,
+    5585597406294108629,
+    11312989214475901864,
+    1547377291787797995,
+    8641748937186208205,
+    12518148659168623694,
+    6611379197521520985,
+    18096591571068008576,
+    15087021227100112139,
+    13058454842015958418,
+    1473584652966833794,
+    4387660670140018168,
+    8452836916843525402,
+    14376083294443363955,
+    13998026203969090659,
+    611968444648172645,
+    990232438801273845,
+    18001186324715561929,
+    13470591857250177501,
+    14881554140239420091,
+    16696367836720124495,
+    6328076032778459673,
+    17027497695968504616,
+    10192245646262428833,
+    8282482589527318647,
+    4319014353374321425,
+    14134087271041670980,
+    5060230880114618599,
+    13179509240430058600,
+    3903514232614801894,
+    17774749744702165255,
+    15448635507030969726,
+    15983775238358480209,
+    14542832143965487887,
+    9385618098039514666,
+    14431419612662304843,
+    730863073501675978,
+    16750118380379734815,
+    9640,
+];
+
+pub(crate) const POW5: [&[u64]; 14] = [
+    &POW5_1, &POW5_2, &POW5_3, &POW5_4, &POW5_5, &POW5_6, &POW5_7, &POW5_8, &POW5_9, &POW5_10,
+    &POW5_11, &POW5_12, &POW5_13, &POW5_14,
+];
@@ -0,0 +1,884 @@
+// Adapted from https://github.com/Alexhuszagh/rust-lexical.
+
+//! Building-blocks for arbitrary-precision math.
+//!
+//! These algorithms assume little-endian order for the large integer
+//! buffers, so for a `vec![0, 1, 2, 3]`, `3` is the most significant limb,
+//! and `0` is the least significant limb.
+
+use super::large_powers;
+use super::num::*;
+use super::small_powers::*;
+use alloc::vec::Vec;
+use core::{cmp, iter, mem};
+
+// ALIASES
+// -------
+
+//  Type for a single limb of the big integer.
+//
+//  A limb is analogous to a digit in base10, except, it stores 32-bit
+//  or 64-bit numbers instead.
+//
+//  This should be all-known 64-bit platforms supported by Rust.
+//      https://forge.rust-lang.org/platform-support.html
+//
+//  Platforms where native 128-bit multiplication is explicitly supported:
+//      - x86_64 (Supported via `MUL`).
+//      - mips64 (Supported via `DMULTU`, which `HI` and `LO` can be read-from).
+//
+//  Platforms where native 64-bit multiplication is supported and
+//  you can extract hi-lo for 64-bit multiplications.
+//      aarch64 (Requires `UMULH` and `MUL` to capture high and low bits).
+//      powerpc64 (Requires `MULHDU` and `MULLD` to capture high and low bits).
+//
+//  Platforms where native 128-bit multiplication is not supported,
+//  requiring software emulation.
+//      sparc64 (`UMUL` only supported double-word arguments).
+
+// 32-BIT LIMB
+#[cfg(fast_arithmetic = "32")]
+pub type Limb = u32;
+
+#[cfg(fast_arithmetic = "32")]
+pub const POW5_LIMB: &[Limb] = &POW5_32;
+
+#[cfg(fast_arithmetic = "32")]
+pub const POW10_LIMB: &[Limb] = &POW10_32;
+
+#[cfg(fast_arithmetic = "32")]
+type Wide = u64;
+
+// 64-BIT LIMB
+#[cfg(fast_arithmetic = "64")]
+pub type Limb = u64;
+
+#[cfg(fast_arithmetic = "64")]
+pub const POW5_LIMB: &[Limb] = &POW5_64;
+
+#[cfg(fast_arithmetic = "64")]
+pub const POW10_LIMB: &[Limb] = &POW10_64;
+
+#[cfg(fast_arithmetic = "64")]
+type Wide = u128;
+
+/// Cast to limb type.
+#[inline]
+pub(crate) fn as_limb<T: Integer>(t: T) -> Limb {
+    Limb::as_cast(t)
+}
+
+/// Cast to wide type.
+#[inline]
+fn as_wide<T: Integer>(t: T) -> Wide {
+    Wide::as_cast(t)
+}
+
+// SPLIT
+// -----
+
+/// Split u64 into limbs, in little-endian order.
+#[inline]
+#[cfg(fast_arithmetic = "32")]
+fn split_u64(x: u64) -> [Limb; 2] {
+    [as_limb(x), as_limb(x >> 32)]
+}
+
+/// Split u64 into limbs, in little-endian order.
+#[inline]
+#[cfg(fast_arithmetic = "64")]
+fn split_u64(x: u64) -> [Limb; 1] {
+    [as_limb(x)]
+}
+
+// HI64
+// ----
+
+// NONZERO
+
+/// Check if any of the remaining bits are non-zero.
+#[inline]
+pub fn nonzero<T: Integer>(x: &[T], rindex: usize) -> bool {
+    let len = x.len();
+    let slc = &x[..len - rindex];
+    slc.iter().rev().any(|&x| x != T::ZERO)
+}
+
+/// Shift 64-bit integer to high 64-bits.
+#[inline]
+fn u64_to_hi64_1(r0: u64) -> (u64, bool) {
+    debug_assert!(r0 != 0);
+    let ls = r0.leading_zeros();
+    (r0 << ls, false)
+}
+
+/// Shift 2 64-bit integers to high 64-bits.
+#[inline]
+fn u64_to_hi64_2(r0: u64, r1: u64) -> (u64, bool) {
+    debug_assert!(r0 != 0);
+    let ls = r0.leading_zeros();
+    let rs = 64 - ls;
+    let v = match ls {
+        0 => r0,
+        _ => (r0 << ls) | (r1 >> rs),
+    };
+    let n = r1 << ls != 0;
+    (v, n)
+}
+
+/// Trait to export the high 64-bits from a little-endian slice.
+trait Hi64<T>: AsRef<[T]> {
+    /// Get the hi64 bits from a 1-limb slice.
+    fn hi64_1(&self) -> (u64, bool);
+
+    /// Get the hi64 bits from a 2-limb slice.
+    fn hi64_2(&self) -> (u64, bool);
+
+    /// Get the hi64 bits from a 3-limb slice.
+    fn hi64_3(&self) -> (u64, bool);
+
+    /// High-level exporter to extract the high 64 bits from a little-endian slice.
+    #[inline]
+    fn hi64(&self) -> (u64, bool) {
+        match self.as_ref().len() {
+            0 => (0, false),
+            1 => self.hi64_1(),
+            2 => self.hi64_2(),
+            _ => self.hi64_3(),
+        }
+    }
+}
+
+impl Hi64<u32> for [u32] {
+    #[inline]
+    fn hi64_1(&self) -> (u64, bool) {
+        debug_assert_eq!(self.len(), 1);
+        let r0 = self[0] as u64;
+        u64_to_hi64_1(r0)
+    }
+
+    #[inline]
+    fn hi64_2(&self) -> (u64, bool) {
+        debug_assert_eq!(self.len(), 2);
+        let r0 = (self[1] as u64) << 32;
+        let r1 = self[0] as u64;
+        u64_to_hi64_1(r0 | r1)
+    }
+
+    #[inline]
+    fn hi64_3(&self) -> (u64, bool) {
+        debug_assert!(self.len() >= 3);
+        let r0 = self[self.len() - 1] as u64;
+        let r1 = (self[self.len() - 2] as u64) << 32;
+        let r2 = self[self.len() - 3] as u64;
+        let (v, n) = u64_to_hi64_2(r0, r1 | r2);
+        (v, n || nonzero(self, 3))
+    }
+}
+
+impl Hi64<u64> for [u64] {
+    #[inline]
+    fn hi64_1(&self) -> (u64, bool) {
+        debug_assert_eq!(self.len(), 1);
+        let r0 = self[0];
+        u64_to_hi64_1(r0)
+    }
+
+    #[inline]
+    fn hi64_2(&self) -> (u64, bool) {
+        debug_assert!(self.len() >= 2);
+        let r0 = self[self.len() - 1];
+        let r1 = self[self.len() - 2];
+        let (v, n) = u64_to_hi64_2(r0, r1);
+        (v, n || nonzero(self, 2))
+    }
+
+    #[inline]
+    fn hi64_3(&self) -> (u64, bool) {
+        self.hi64_2()
+    }
+}
+
+// SCALAR
+// ------
+
+// Scalar-to-scalar operations, for building-blocks for arbitrary-precision
+// operations.
+
+mod scalar {
+    use super::*;
+
+    // ADDITION
+
+    /// Add two small integers and return the resulting value and if overflow happens.
+    #[inline]
+    pub fn add(x: Limb, y: Limb) -> (Limb, bool) {
+        x.overflowing_add(y)
+    }
+
+    /// AddAssign two small integers and return if overflow happens.
+    #[inline]
+    pub fn iadd(x: &mut Limb, y: Limb) -> bool {
+        let t = add(*x, y);
+        *x = t.0;
+        t.1
+    }
+
+    // SUBTRACTION
+
+    /// Subtract two small integers and return the resulting value and if overflow happens.
+    #[inline]
+    pub fn sub(x: Limb, y: Limb) -> (Limb, bool) {
+        x.overflowing_sub(y)
+    }
+
+    /// SubAssign two small integers and return if overflow happens.
+    #[inline]
+    pub fn isub(x: &mut Limb, y: Limb) -> bool {
+        let t = sub(*x, y);
+        *x = t.0;
+        t.1
+    }
+
+    // MULTIPLICATION
+
+    /// Multiply two small integers (with carry) (and return the overflow contribution).
+    ///
+    /// Returns the (low, high) components.
+    #[inline]
+    pub fn mul(x: Limb, y: Limb, carry: Limb) -> (Limb, Limb) {
+        // Cannot overflow, as long as wide is 2x as wide. This is because
+        // the following is always true:
+        // `Wide::max_value() - (Narrow::max_value() * Narrow::max_value()) >= Narrow::max_value()`
+        let z: Wide = as_wide(x) * as_wide(y) + as_wide(carry);
+        let bits = mem::size_of::<Limb>() * 8;
+        (as_limb(z), as_limb(z >> bits))
+    }
+
+    /// Multiply two small integers (with carry) (and return if overflow happens).
+    #[inline]
+    pub fn imul(x: &mut Limb, y: Limb, carry: Limb) -> Limb {
+        let t = mul(*x, y, carry);
+        *x = t.0;
+        t.1
+    }
+} // scalar
+
+// SMALL
+// -----
+
+// Large-to-small operations, to modify a big integer from a native scalar.
+
+mod small {
+    use super::*;
+
+    // ADDITION
+
+    /// Implied AddAssign implementation for adding a small integer to bigint.
+    ///
+    /// Allows us to choose a start-index in x to store, to allow incrementing
+    /// from a non-zero start.
+    #[inline]
+    pub fn iadd_impl(x: &mut Vec<Limb>, y: Limb, xstart: usize) {
+        if x.len() <= xstart {
+            x.push(y);
+        } else {
+            // Initial add
+            let mut carry = scalar::iadd(&mut x[xstart], y);
+
+            // Increment until overflow stops occurring.
+            let mut size = xstart + 1;
+            while carry && size < x.len() {
+                carry = scalar::iadd(&mut x[size], 1);
+                size += 1;
+            }
+
+            // If we overflowed the buffer entirely, need to add 1 to the end
+            // of the buffer.
+            if carry {
+                x.push(1);
+            }
+        }
+    }
+
+    /// AddAssign small integer to bigint.
+    #[inline]
+    pub fn iadd(x: &mut Vec<Limb>, y: Limb) {
+        iadd_impl(x, y, 0);
+    }
+
+    // SUBTRACTION
+
+    /// SubAssign small integer to bigint.
+    /// Does not do overflowing subtraction.
+    #[inline]
+    pub fn isub_impl(x: &mut Vec<Limb>, y: Limb, xstart: usize) {
+        debug_assert!(x.len() > xstart && (x[xstart] >= y || x.len() > xstart + 1));
+
+        // Initial subtraction
+        let mut carry = scalar::isub(&mut x[xstart], y);
+
+        // Increment until overflow stops occurring.
+        let mut size = xstart + 1;
+        while carry && size < x.len() {
+            carry = scalar::isub(&mut x[size], 1);
+            size += 1;
+        }
+        normalize(x);
+    }
+
+    // MULTIPLICATION
+
+    /// MulAssign small integer to bigint.
+    #[inline]
+    pub fn imul(x: &mut Vec<Limb>, y: Limb) {
+        // Multiply iteratively over all elements, adding the carry each time.
+        let mut carry: Limb = 0;
+        for xi in &mut *x {
+            carry = scalar::imul(xi, y, carry);
+        }
+
+        // Overflow of value, add to end.
+        if carry != 0 {
+            x.push(carry);
+        }
+    }
+
+    /// Mul small integer to bigint.
+    #[inline]
+    pub fn mul(x: &[Limb], y: Limb) -> Vec<Limb> {
+        let mut z = Vec::<Limb>::default();
+        z.extend_from_slice(x);
+        imul(&mut z, y);
+        z
+    }
+
+    /// MulAssign by a power.
+    ///
+    /// Theoretically...
+    ///
+    /// Use an exponentiation by squaring method, since it reduces the time
+    /// complexity of the multiplication to ~`O(log(n))` for the squaring,
+    /// and `O(n*m)` for the result. Since `m` is typically a lower-order
+    /// factor, this significantly reduces the number of multiplications
+    /// we need to do. Iteratively multiplying by small powers follows
+    /// the nth triangular number series, which scales as `O(p^2)`, but
+    /// where `p` is `n+m`. In short, it scales very poorly.
+    ///
+    /// Practically....
+    ///
+    /// Exponentiation by Squaring:
+    ///     running 2 tests
+    ///     test bigcomp_f32_lexical ... bench:       1,018 ns/iter (+/- 78)
+    ///     test bigcomp_f64_lexical ... bench:       3,639 ns/iter (+/- 1,007)
+    ///
+    /// Exponentiation by Iterative Small Powers:
+    ///     running 2 tests
+    ///     test bigcomp_f32_lexical ... bench:         518 ns/iter (+/- 31)
+    ///     test bigcomp_f64_lexical ... bench:         583 ns/iter (+/- 47)
+    ///
+    /// Exponentiation by Iterative Large Powers (of 2):
+    ///     running 2 tests
+    ///     test bigcomp_f32_lexical ... bench:         671 ns/iter (+/- 31)
+    ///     test bigcomp_f64_lexical ... bench:       1,394 ns/iter (+/- 47)
+    ///
+    /// Even using worst-case scenarios, exponentiation by squaring is
+    /// significantly slower for our workloads. Just multiply by small powers,
+    /// in simple cases, and use precalculated large powers in other cases.
+    pub fn imul_pow5(x: &mut Vec<Limb>, n: u32) {
+        use super::large::KARATSUBA_CUTOFF;
+
+        let small_powers = POW5_LIMB;
+        let large_powers = large_powers::POW5;
+
+        if n == 0 {
+            // No exponent, just return.
+            // The 0-index of the large powers is `2^0`, which is 1, so we want
+            // to make sure we don't take that path with a literal 0.
+            return;
+        }
+
+        // We want to use the asymptotically faster algorithm if we're going
+        // to be using Karabatsu multiplication sometime during the result,
+        // otherwise, just use exponentiation by squaring.
+        let bit_length = 32 - n.leading_zeros() as usize;
+        debug_assert!(bit_length != 0 && bit_length <= large_powers.len());
+        if x.len() + large_powers[bit_length - 1].len() < 2 * KARATSUBA_CUTOFF {
+            // We can use iterative small powers to make this faster for the
+            // easy cases.
+
+            // Multiply by the largest small power until n < step.
+            let step = small_powers.len() - 1;
+            let power = small_powers[step];
+            let mut n = n as usize;
+            while n >= step {
+                imul(x, power);
+                n -= step;
+            }
+
+            // Multiply by the remainder.
+            imul(x, small_powers[n]);
+        } else {
+            // In theory, this code should be asymptotically a lot faster,
+            // in practice, our small::imul seems to be the limiting step,
+            // and large imul is slow as well.
+
+            // Multiply by higher order powers.
+            let mut idx: usize = 0;
+            let mut bit: usize = 1;
+            let mut n = n as usize;
+            while n != 0 {
+                if n & bit != 0 {
+                    debug_assert!(idx < large_powers.len());
+                    large::imul(x, large_powers[idx]);
+                    n ^= bit;
+                }
+                idx += 1;
+                bit <<= 1;
+            }
+        }
+    }
+
+    // BIT LENGTH
+
+    /// Get number of leading zero bits in the storage.
+    #[inline]
+    pub fn leading_zeros(x: &[Limb]) -> usize {
+        x.last().map_or(0, |x| x.leading_zeros() as usize)
+    }
+
+    /// Calculate the bit-length of the big-integer.
+    #[inline]
+    pub fn bit_length(x: &[Limb]) -> usize {
+        let bits = mem::size_of::<Limb>() * 8;
+        // Avoid overflowing, calculate via total number of bits
+        // minus leading zero bits.
+        let nlz = leading_zeros(x);
+        bits.checked_mul(x.len())
+            .map_or_else(usize::max_value, |v| v - nlz)
+    }
+
+    // SHL
+
+    /// Shift-left bits inside a buffer.
+    ///
+    /// Assumes `n < Limb::BITS`, IE, internally shifting bits.
+    #[inline]
+    pub fn ishl_bits(x: &mut Vec<Limb>, n: usize) {
+        // Need to shift by the number of `bits % Limb::BITS)`.
+        let bits = mem::size_of::<Limb>() * 8;
+        debug_assert!(n < bits);
+        if n == 0 {
+            return;
+        }
+
+        // Internally, for each item, we shift left by n, and add the previous
+        // right shifted limb-bits.
+        // For example, we transform (for u8) shifted left 2, to:
+        //      b10100100 b01000010
+        //      b10 b10010001 b00001000
+        let rshift = bits - n;
+        let lshift = n;
+        let mut prev: Limb = 0;
+        for xi in &mut *x {
+            let tmp = *xi;
+            *xi <<= lshift;
+            *xi |= prev >> rshift;
+            prev = tmp;
+        }
+
+        // Always push the carry, even if it creates a non-normal result.
+        let carry = prev >> rshift;
+        if carry != 0 {
+            x.push(carry);
+        }
+    }
+
+    /// Shift-left `n` digits inside a buffer.
+    ///
+    /// Assumes `n` is not 0.
+    #[inline]
+    pub fn ishl_limbs(x: &mut Vec<Limb>, n: usize) {
+        debug_assert!(n != 0);
+        if !x.is_empty() {
+            x.reserve(n);
+            x.splice(..0, iter::repeat(0).take(n));
+        }
+    }
+
+    /// Shift-left buffer by n bits.
+    #[inline]
+    pub fn ishl(x: &mut Vec<Limb>, n: usize) {
+        let bits = mem::size_of::<Limb>() * 8;
+        // Need to pad with zeros for the number of `bits / Limb::BITS`,
+        // and shift-left with carry for `bits % Limb::BITS`.
+        let rem = n % bits;
+        let div = n / bits;
+        ishl_bits(x, rem);
+        if div != 0 {
+            ishl_limbs(x, div);
+        }
+    }
+
+    // NORMALIZE
+
+    /// Normalize the container by popping any leading zeros.
+    #[inline]
+    pub fn normalize(x: &mut Vec<Limb>) {
+        // Remove leading zero if we cause underflow. Since we're dividing
+        // by a small power, we have at max 1 int removed.
+        while x.last() == Some(&0) {
+            x.pop();
+        }
+    }
+} // small
+
+// LARGE
+// -----
+
+// Large-to-large operations, to modify a big integer from a native scalar.
+
+mod large {
+    use super::*;
+
+    // RELATIVE OPERATORS
+
+    /// Compare `x` to `y`, in little-endian order.
+    #[inline]
+    pub fn compare(x: &[Limb], y: &[Limb]) -> cmp::Ordering {
+        if x.len() > y.len() {
+            cmp::Ordering::Greater
+        } else if x.len() < y.len() {
+            cmp::Ordering::Less
+        } else {
+            let iter = x.iter().rev().zip(y.iter().rev());
+            for (&xi, &yi) in iter {
+                if xi > yi {
+                    return cmp::Ordering::Greater;
+                } else if xi < yi {
+                    return cmp::Ordering::Less;
+                }
+            }
+            // Equal case.
+            cmp::Ordering::Equal
+        }
+    }
+
+    /// Check if x is less than y.
+    #[inline]
+    pub fn less(x: &[Limb], y: &[Limb]) -> bool {
+        compare(x, y) == cmp::Ordering::Less
+    }
+
+    /// Check if x is greater than or equal to y.
+    #[inline]
+    pub fn greater_equal(x: &[Limb], y: &[Limb]) -> bool {
+        !less(x, y)
+    }
+
+    // ADDITION
+
+    /// Implied AddAssign implementation for bigints.
+    ///
+    /// Allows us to choose a start-index in x to store, so we can avoid
+    /// padding the buffer with zeros when not needed, optimized for vectors.
+    pub fn iadd_impl(x: &mut Vec<Limb>, y: &[Limb], xstart: usize) {
+        // The effective x buffer is from `xstart..x.len()`, so we need to treat
+        // that as the current range. If the effective y buffer is longer, need
+        // to resize to that, + the start index.
+        if y.len() > x.len() - xstart {
+            x.resize(y.len() + xstart, 0);
+        }
+
+        // Iteratively add elements from y to x.
+        let mut carry = false;
+        for (xi, yi) in x[xstart..].iter_mut().zip(y.iter()) {
+            // Only one op of the two can overflow, since we added at max
+            // Limb::max_value() + Limb::max_value(). Add the previous carry,
+            // and store the current carry for the next.
+            let mut tmp = scalar::iadd(xi, *yi);
+            if carry {
+                tmp |= scalar::iadd(xi, 1);
+            }
+            carry = tmp;
+        }
+
+        // Overflow from the previous bit.
+        if carry {
+            small::iadd_impl(x, 1, y.len() + xstart);
+        }
+    }
+
+    /// AddAssign bigint to bigint.
+    #[inline]
+    pub fn iadd(x: &mut Vec<Limb>, y: &[Limb]) {
+        iadd_impl(x, y, 0);
+    }
+
+    /// Add bigint to bigint.
+    #[inline]
+    pub fn add(x: &[Limb], y: &[Limb]) -> Vec<Limb> {
+        let mut z = Vec::<Limb>::default();
+        z.extend_from_slice(x);
+        iadd(&mut z, y);
+        z
+    }
+
+    // SUBTRACTION
+
+    /// SubAssign bigint to bigint.
+    pub fn isub(x: &mut Vec<Limb>, y: &[Limb]) {
+        // Basic underflow checks.
+        debug_assert!(greater_equal(x, y));
+
+        // Iteratively add elements from y to x.
+        let mut carry = false;
+        for (xi, yi) in x.iter_mut().zip(y.iter()) {
+            // Only one op of the two can overflow, since we added at max
+            // Limb::max_value() + Limb::max_value(). Add the previous carry,
+            // and store the current carry for the next.
+            let mut tmp = scalar::isub(xi, *yi);
+            if carry {
+                tmp |= scalar::isub(xi, 1);
+            }
+            carry = tmp;
+        }
+
+        if carry {
+            small::isub_impl(x, 1, y.len());
+        } else {
+            small::normalize(x);
+        }
+    }
+
+    // MULTIPLICATION
+
+    /// Number of digits to bottom-out to asymptotically slow algorithms.
+    ///
+    /// Karatsuba tends to out-perform long-multiplication at ~320-640 bits,
+    /// so we go halfway, while Newton division tends to out-perform
+    /// Algorithm D at ~1024 bits. We can toggle this for optimal performance.
+    pub const KARATSUBA_CUTOFF: usize = 32;
+
+    /// Grade-school multiplication algorithm.
+    ///
+    /// Slow, naive algorithm, using limb-bit bases and just shifting left for
+    /// each iteration. This could be optimized with numerous other algorithms,
+    /// but it's extremely simple, and works in O(n*m) time, which is fine
+    /// by me. Each iteration, of which there are `m` iterations, requires
+    /// `n` multiplications, and `n` additions, or grade-school multiplication.
+    fn long_mul(x: &[Limb], y: &[Limb]) -> Vec<Limb> {
+        // Using the immutable value, multiply by all the scalars in y, using
+        // the algorithm defined above. Use a single buffer to avoid
+        // frequent reallocations. Handle the first case to avoid a redundant
+        // addition, since we know y.len() >= 1.
+        let mut z: Vec<Limb> = small::mul(x, y[0]);
+        z.resize(x.len() + y.len(), 0);
+
+        // Handle the iterative cases.
+        for (i, &yi) in y[1..].iter().enumerate() {
+            let zi: Vec<Limb> = small::mul(x, yi);
+            iadd_impl(&mut z, &zi, i + 1);
+        }
+
+        small::normalize(&mut z);
+
+        z
+    }
+
+    /// Split two buffers into halfway, into (lo, hi).
+    #[inline]
+    pub fn karatsuba_split(z: &[Limb], m: usize) -> (&[Limb], &[Limb]) {
+        (&z[..m], &z[m..])
+    }
+
+    /// Karatsuba multiplication algorithm with roughly equal input sizes.
+    ///
+    /// Assumes `y.len() >= x.len()`.
+    fn karatsuba_mul(x: &[Limb], y: &[Limb]) -> Vec<Limb> {
+        if y.len() <= KARATSUBA_CUTOFF {
+            // Bottom-out to long division for small cases.
+            long_mul(x, y)
+        } else if x.len() < y.len() / 2 {
+            karatsuba_uneven_mul(x, y)
+        } else {
+            // Do our 3 multiplications.
+            let m = y.len() / 2;
+            let (xl, xh) = karatsuba_split(x, m);
+            let (yl, yh) = karatsuba_split(y, m);
+            let sumx = add(xl, xh);
+            let sumy = add(yl, yh);
+            let z0 = karatsuba_mul(xl, yl);
+            let mut z1 = karatsuba_mul(&sumx, &sumy);
+            let z2 = karatsuba_mul(xh, yh);
+            // Properly scale z1, which is `z1 - z2 - zo`.
+            isub(&mut z1, &z2);
+            isub(&mut z1, &z0);
+
+            // Create our result, which is equal to, in little-endian order:
+            // [z0, z1 - z2 - z0, z2]
+            //  z1 must be shifted m digits (2^(32m)) over.
+            //  z2 must be shifted 2*m digits (2^(64m)) over.
+            let len = z0.len().max(m + z1.len()).max(2 * m + z2.len());
+            let mut result = z0;
+            result.reserve_exact(len - result.len());
+            iadd_impl(&mut result, &z1, m);
+            iadd_impl(&mut result, &z2, 2 * m);
+
+            result
+        }
+    }
+
+    /// Karatsuba multiplication algorithm where y is substantially larger than x.
+    ///
+    /// Assumes `y.len() >= x.len()`.
+    fn karatsuba_uneven_mul(x: &[Limb], mut y: &[Limb]) -> Vec<Limb> {
+        let mut result = Vec::<Limb>::default();
+        result.resize(x.len() + y.len(), 0);
+
+        // This effectively is like grade-school multiplication between
+        // two numbers, except we're using splits on `y`, and the intermediate
+        // step is a Karatsuba multiplication.
+        let mut start = 0;
+        while !y.is_empty() {
+            let m = x.len().min(y.len());
+            let (yl, yh) = karatsuba_split(y, m);
+            let prod = karatsuba_mul(x, yl);
+            iadd_impl(&mut result, &prod, start);
+            y = yh;
+            start += m;
+        }
+        small::normalize(&mut result);
+
+        result
+    }
+
+    /// Forwarder to the proper Karatsuba algorithm.
+    #[inline]
+    fn karatsuba_mul_fwd(x: &[Limb], y: &[Limb]) -> Vec<Limb> {
+        if x.len() < y.len() {
+            karatsuba_mul(x, y)
+        } else {
+            karatsuba_mul(y, x)
+        }
+    }
+
+    /// MulAssign bigint to bigint.
+    #[inline]
+    pub fn imul(x: &mut Vec<Limb>, y: &[Limb]) {
+        if y.len() == 1 {
+            small::imul(x, y[0]);
+        } else {
+            // We're not really in a condition where using Karatsuba
+            // multiplication makes sense, so we're just going to use long
+            // division. ~20% speedup compared to:
+            //      *x = karatsuba_mul_fwd(x, y);
+            *x = karatsuba_mul_fwd(x, y);
+        }
+    }
+} // large
+
+// TRAITS
+// ------
+
+/// Traits for shared operations for big integers.
+///
+/// None of these are implemented using normal traits, since these
+/// are very expensive operations, and we want to deliberately
+/// and explicitly use these functions.
+pub(crate) trait Math: Clone + Sized + Default {
+    // DATA
+
+    /// Get access to the underlying data
+    fn data(&self) -> &Vec<Limb>;
+
+    /// Get access to the underlying data
+    fn data_mut(&mut self) -> &mut Vec<Limb>;
+
+    // RELATIVE OPERATIONS
+
+    /// Compare self to y.
+    #[inline]
+    fn compare(&self, y: &Self) -> cmp::Ordering {
+        large::compare(self.data(), y.data())
+    }
+
+    // PROPERTIES
+
+    /// Get the high 64-bits from the bigint and if there are remaining bits.
+    #[inline]
+    fn hi64(&self) -> (u64, bool) {
+        self.data().as_slice().hi64()
+    }
+
+    /// Calculate the bit-length of the big-integer.
+    /// Returns usize::max_value() if the value overflows,
+    /// IE, if `self.data().len() > usize::max_value() / 8`.
+    #[inline]
+    fn bit_length(&self) -> usize {
+        small::bit_length(self.data())
+    }
+
+    // INTEGER CONVERSIONS
+
+    /// Create new big integer from u64.
+    #[inline]
+    fn from_u64(x: u64) -> Self {
+        let mut v = Self::default();
+        let slc = split_u64(x);
+        v.data_mut().extend_from_slice(&slc);
+        v.normalize();
+        v
+    }
+
+    // NORMALIZE
+
+    /// Normalize the integer, so any leading zero values are removed.
+    #[inline]
+    fn normalize(&mut self) {
+        small::normalize(self.data_mut());
+    }
+
+    // ADDITION
+
+    /// AddAssign small integer.
+    #[inline]
+    fn iadd_small(&mut self, y: Limb) {
+        small::iadd(self.data_mut(), y);
+    }
+
+    // MULTIPLICATION
+
+    /// MulAssign small integer.
+    #[inline]
+    fn imul_small(&mut self, y: Limb) {
+        small::imul(self.data_mut(), y);
+    }
+
+    /// Multiply by a power of 2.
+    #[inline]
+    fn imul_pow2(&mut self, n: u32) {
+        self.ishl(n as usize);
+    }
+
+    /// Multiply by a power of 5.
+    #[inline]
+    fn imul_pow5(&mut self, n: u32) {
+        small::imul_pow5(self.data_mut(), n);
+    }
+
+    /// MulAssign by a power of 10.
+    #[inline]
+    fn imul_pow10(&mut self, n: u32) {
+        self.imul_pow5(n);
+        self.imul_pow2(n);
+    }
+
+    // SHIFTS
+
+    /// Shift-left the entire buffer n bits.
+    #[inline]
+    fn ishl(&mut self, n: usize) {
+        small::ishl(self.data_mut(), n);
+    }
+}
@@ -0,0 +1,38 @@
+// The code in this module is derived from the `lexical` crate by @Alexhuszagh
+// which the author condensed into this minimal subset for use in serde_json.
+// For the serde_json use case we care more about reliably round tripping all
+// possible floating point values than about parsing any arbitrarily long string
+// of digits with perfect accuracy, as the latter would take a high cost in
+// compile time and performance.
+//
+// Dual licensed as MIT and Apache 2.0 just like the rest of serde_json, but
+// copyright Alexander Huszagh.
+
+//! Fast, minimal float-parsing algorithm.
+
+// MODULES
+pub(crate) mod algorithm;
+mod bhcomp;
+mod bignum;
+mod cached;
+mod cached_float80;
+mod digit;
+mod errors;
+pub(crate) mod exponent;
+pub(crate) mod float;
+mod large_powers;
+pub(crate) mod math;
+pub(crate) mod num;
+pub(crate) mod parse;
+pub(crate) mod rounding;
+mod shift;
+mod small_powers;
+
+#[cfg(fast_arithmetic = "32")]
+mod large_powers32;
+
+#[cfg(fast_arithmetic = "64")]
+mod large_powers64;
+
+// API
+pub use self::parse::{parse_concise_float, parse_truncated_float};
@@ -0,0 +1,421 @@
+// Adapted from https://github.com/Alexhuszagh/rust-lexical.
+
+//! Utilities for Rust numbers.
+
+use core::ops;
+
+/// Precalculated values of radix**i for i in range [0, arr.len()-1].
+/// Each value can be **exactly** represented as that type.
+const F32_POW10: [f32; 11] = [
+    1.0,
+    10.0,
+    100.0,
+    1000.0,
+    10000.0,
+    100000.0,
+    1000000.0,
+    10000000.0,
+    100000000.0,
+    1000000000.0,
+    10000000000.0,
+];
+
+/// Precalculated values of radix**i for i in range [0, arr.len()-1].
+/// Each value can be **exactly** represented as that type.
+const F64_POW10: [f64; 23] = [
+    1.0,
+    10.0,
+    100.0,
+    1000.0,
+    10000.0,
+    100000.0,
+    1000000.0,
+    10000000.0,
+    100000000.0,
+    1000000000.0,
+    10000000000.0,
+    100000000000.0,
+    1000000000000.0,
+    10000000000000.0,
+    100000000000000.0,
+    1000000000000000.0,
+    10000000000000000.0,
+    100000000000000000.0,
+    1000000000000000000.0,
+    10000000000000000000.0,
+    100000000000000000000.0,
+    1000000000000000000000.0,
+    10000000000000000000000.0,
+];
+
+/// Type that can be converted to primitive with `as`.
+pub trait AsPrimitive: Sized + Copy + PartialOrd {
+    fn as_u32(self) -> u32;
+    fn as_u64(self) -> u64;
+    fn as_u128(self) -> u128;
+    fn as_usize(self) -> usize;
+    fn as_f32(self) -> f32;
+    fn as_f64(self) -> f64;
+}
+
+macro_rules! as_primitive_impl {
+    ($($ty:ident)*) => {
+        $(
+            impl AsPrimitive for $ty {
+                #[inline]
+                fn as_u32(self) -> u32 {
+                    self as u32
+                }
+
+                #[inline]
+                fn as_u64(self) -> u64 {
+                    self as u64
+                }
+
+                #[inline]
+                fn as_u128(self) -> u128 {
+                    self as u128
+                }
+
+                #[inline]
+                fn as_usize(self) -> usize {
+                    self as usize
+                }
+
+                #[inline]
+                fn as_f32(self) -> f32 {
+                    self as f32
+                }
+
+                #[inline]
+                fn as_f64(self) -> f64 {
+                    self as f64
+                }
+            }
+        )*
+    };
+}
+
+as_primitive_impl! { u32 u64 u128 usize f32 f64 }
+
+/// An interface for casting between machine scalars.
+pub trait AsCast: AsPrimitive {
+    /// Creates a number from another value that can be converted into
+    /// a primitive via the `AsPrimitive` trait.
+    fn as_cast<N: AsPrimitive>(n: N) -> Self;
+}
+
+macro_rules! as_cast_impl {
+    ($ty:ident, $method:ident) => {
+        impl AsCast for $ty {
+            #[inline]
+            fn as_cast<N: AsPrimitive>(n: N) -> Self {
+                n.$method()
+            }
+        }
+    };
+}
+
+as_cast_impl!(u32, as_u32);
+as_cast_impl!(u64, as_u64);
+as_cast_impl!(u128, as_u128);
+as_cast_impl!(usize, as_usize);
+as_cast_impl!(f32, as_f32);
+as_cast_impl!(f64, as_f64);
+
+/// Numerical type trait.
+pub trait Number: AsCast + ops::Add<Output = Self> {}
+
+macro_rules! number_impl {
+    ($($ty:ident)*) => {
+        $(
+            impl Number for $ty {}
+        )*
+    };
+}
+
+number_impl! { u32 u64 u128 usize f32 f64 }
+
+/// Defines a trait that supports integral operations.
+pub trait Integer: Number + ops::BitAnd<Output = Self> + ops::Shr<i32, Output = Self> {
+    const ZERO: Self;
+}
+
+macro_rules! integer_impl {
+    ($($ty:tt)*) => {
+        $(
+            impl Integer for $ty {
+                const ZERO: Self = 0;
+            }
+        )*
+    };
+}
+
+integer_impl! { u32 u64 u128 usize }
+
+/// Type trait for the mantissa type.
+pub trait Mantissa: Integer {
+    /// Mask to extract the high bits from the integer.
+    const HIMASK: Self;
+    /// Mask to extract the low bits from the integer.
+    const LOMASK: Self;
+    /// Full size of the integer, in bits.
+    const FULL: i32;
+    /// Half size of the integer, in bits.
+    const HALF: i32 = Self::FULL / 2;
+}
+
+impl Mantissa for u64 {
+    const HIMASK: u64 = 0xFFFFFFFF00000000;
+    const LOMASK: u64 = 0x00000000FFFFFFFF;
+    const FULL: i32 = 64;
+}
+
+/// Get exact exponent limit for radix.
+pub trait Float: Number {
+    /// Unsigned type of the same size.
+    type Unsigned: Integer;
+
+    /// Literal zero.
+    const ZERO: Self;
+    /// Maximum number of digits that can contribute in the mantissa.
+    ///
+    /// 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))`
+    ///
+    /// This was used to calculate the maximum number of digits for [2, 36].
+    const MAX_DIGITS: usize;
+
+    // MASKS
+
+    /// Bitmask for the exponent, including the hidden bit.
+    const EXPONENT_MASK: Self::Unsigned;
+    /// Bitmask for the hidden bit in exponent, which is an implicit 1 in the fraction.
+    const HIDDEN_BIT_MASK: Self::Unsigned;
+    /// Bitmask for the mantissa (fraction), excluding the hidden bit.
+    const MANTISSA_MASK: Self::Unsigned;
+
+    // PROPERTIES
+
+    /// Positive infinity as bits.
+    const INFINITY_BITS: Self::Unsigned;
+    /// Size of the significand (mantissa) without hidden bit.
+    const MANTISSA_SIZE: i32;
+    /// Bias of the exponent
+    const EXPONENT_BIAS: i32;
+    /// Exponent portion of a denormal float.
+    const DENORMAL_EXPONENT: i32;
+    /// Maximum exponent value in float.
+    const MAX_EXPONENT: i32;
+
+    // ROUNDING
+
+    /// Default number of bits to shift (or 64 - mantissa size - 1).
+    const DEFAULT_SHIFT: i32;
+    /// Mask to determine if a full-carry occurred (1 in bit above hidden bit).
+    const CARRY_MASK: u64;
+
+    /// Get min and max exponent limits (exact) from radix.
+    fn exponent_limit() -> (i32, i32);
+
+    /// Get the number of digits that can be shifted from exponent to mantissa.
+    fn mantissa_limit() -> i32;
+
+    // Re-exported methods from std.
+    fn pow10(self, n: i32) -> Self;
+    fn from_bits(u: Self::Unsigned) -> Self;
+    fn to_bits(self) -> Self::Unsigned;
+    fn is_sign_positive(self) -> bool;
+
+    /// Returns true if the float is a denormal.
+    #[inline]
+    fn is_denormal(self) -> bool {
+        self.to_bits() & Self::EXPONENT_MASK == Self::Unsigned::ZERO
+    }
+
+    /// Returns true if the float is a NaN or Infinite.
+    #[inline]
+    fn is_special(self) -> bool {
+        self.to_bits() & Self::EXPONENT_MASK == Self::EXPONENT_MASK
+    }
+
+    /// Returns true if the float is infinite.
+    #[inline]
+    fn is_inf(self) -> bool {
+        self.is_special() && (self.to_bits() & Self::MANTISSA_MASK) == Self::Unsigned::ZERO
+    }
+
+    /// Get exponent component from the float.
+    #[inline]
+    fn exponent(self) -> i32 {
+        if self.is_denormal() {
+            return Self::DENORMAL_EXPONENT;
+        }
+
+        let bits = self.to_bits();
+        let biased_e = ((bits & Self::EXPONENT_MASK) >> Self::MANTISSA_SIZE).as_u32();
+        biased_e as i32 - Self::EXPONENT_BIAS
+    }
+
+    /// Get mantissa (significand) component from float.
+    #[inline]
+    fn mantissa(self) -> Self::Unsigned {
+        let bits = self.to_bits();
+        let s = bits & Self::MANTISSA_MASK;
+        if !self.is_denormal() {
+            s + Self::HIDDEN_BIT_MASK
+        } else {
+            s
+        }
+    }
+
+    /// Get next greater float for a positive float.
+    /// Value must be >= 0.0 and < INFINITY.
+    #[inline]
+    fn next_positive(self) -> Self {
+        debug_assert!(self.is_sign_positive() && !self.is_inf());
+        Self::from_bits(self.to_bits() + Self::Unsigned::as_cast(1u32))
+    }
+
+    /// Round a positive number to even.
+    #[inline]
+    fn round_positive_even(self) -> Self {
+        if self.mantissa() & Self::Unsigned::as_cast(1u32) == Self::Unsigned::as_cast(1u32) {
+            self.next_positive()
+        } else {
+            self
+        }
+    }
+}
+
+impl Float for f32 {
+    type Unsigned = u32;
+
+    const ZERO: f32 = 0.0;
+    const MAX_DIGITS: usize = 114;
+    const EXPONENT_MASK: u32 = 0x7F800000;
+    const HIDDEN_BIT_MASK: u32 = 0x00800000;
+    const MANTISSA_MASK: u32 = 0x007FFFFF;
+    const INFINITY_BITS: u32 = 0x7F800000;
+    const MANTISSA_SIZE: i32 = 23;
+    const EXPONENT_BIAS: i32 = 127 + Self::MANTISSA_SIZE;
+    const DENORMAL_EXPONENT: i32 = 1 - Self::EXPONENT_BIAS;
+    const MAX_EXPONENT: i32 = 0xFF - Self::EXPONENT_BIAS;
+    const DEFAULT_SHIFT: i32 = u64::FULL - f32::MANTISSA_SIZE - 1;
+    const CARRY_MASK: u64 = 0x1000000;
+
+    #[inline]
+    fn exponent_limit() -> (i32, i32) {
+        (-10, 10)
+    }
+
+    #[inline]
+    fn mantissa_limit() -> i32 {
+        7
+    }
+
+    #[inline]
+    fn pow10(self, n: i32) -> f32 {
+        // Check the exponent is within bounds in debug builds.
+        debug_assert!({
+            let (min, max) = Self::exponent_limit();
+            n >= min && n <= max
+        });
+
+        if n > 0 {
+            self * F32_POW10[n as usize]
+        } else {
+            self / F32_POW10[-n as usize]
+        }
+    }
+
+    #[inline]
+    fn from_bits(u: u32) -> f32 {
+        f32::from_bits(u)
+    }
+
+    #[inline]
+    fn to_bits(self) -> u32 {
+        f32::to_bits(self)
+    }
+
+    #[inline]
+    fn is_sign_positive(self) -> bool {
+        f32::is_sign_positive(self)
+    }
+}
+
+impl Float for f64 {
+    type Unsigned = u64;
+
+    const ZERO: f64 = 0.0;
+    const MAX_DIGITS: usize = 769;
+    const EXPONENT_MASK: u64 = 0x7FF0000000000000;
+    const HIDDEN_BIT_MASK: u64 = 0x0010000000000000;
+    const MANTISSA_MASK: u64 = 0x000FFFFFFFFFFFFF;
+    const INFINITY_BITS: u64 = 0x7FF0000000000000;
+    const MANTISSA_SIZE: i32 = 52;
+    const EXPONENT_BIAS: i32 = 1023 + Self::MANTISSA_SIZE;
+    const DENORMAL_EXPONENT: i32 = 1 - Self::EXPONENT_BIAS;
+    const MAX_EXPONENT: i32 = 0x7FF - Self::EXPONENT_BIAS;
+    const DEFAULT_SHIFT: i32 = u64::FULL - f64::MANTISSA_SIZE - 1;
+    const CARRY_MASK: u64 = 0x20000000000000;
+
+    #[inline]
+    fn exponent_limit() -> (i32, i32) {
+        (-22, 22)
+    }
+
+    #[inline]
+    fn mantissa_limit() -> i32 {
+        15
+    }
+
+    #[inline]
+    fn pow10(self, n: i32) -> f64 {
+        // Check the exponent is within bounds in debug builds.
+        debug_assert!({
+            let (min, max) = Self::exponent_limit();
+            n >= min && n <= max
+        });
+
+        if n > 0 {
+            self * F64_POW10[n as usize]
+        } else {
+            self / F64_POW10[-n as usize]
+        }
+    }
+
+    #[inline]
+    fn from_bits(u: u64) -> f64 {
+        f64::from_bits(u)
+    }
+
+    #[inline]
+    fn to_bits(self) -> u64 {
+        f64::to_bits(self)
+    }
+
+    #[inline]
+    fn is_sign_positive(self) -> bool {
+        f64::is_sign_positive(self)
+    }
+}
@@ -0,0 +1,83 @@
+// Adapted from https://github.com/Alexhuszagh/rust-lexical.
+
+use super::algorithm::*;
+use super::bhcomp::*;
+use super::digit::*;
+use super::exponent::*;
+use super::num::*;
+
+// PARSERS
+// -------
+
+/// Parse float for which the entire integer and fraction parts fit into a 64
+/// bit mantissa.
+pub fn parse_concise_float<F>(mantissa: u64, mant_exp: i32) -> F
+where
+    F: Float,
+{
+    if let Some(float) = fast_path(mantissa, mant_exp) {
+        return float;
+    }
+
+    // Moderate path (use an extended 80-bit representation).
+    let truncated = false;
+    let (fp, valid) = moderate_path::<F>(mantissa, mant_exp, truncated);
+    if valid {
+        return fp.into_float::<F>();
+    }
+
+    let b = fp.into_downward_float::<F>();
+    if b.is_special() {
+        // We have a non-finite number, we get to leave early.
+        return b;
+    }
+
+    // Slow path, fast path didn't work.
+    let mut buffer = itoa::Buffer::new();
+    let integer = buffer.format(mantissa).as_bytes();
+    let fraction = &[];
+    bhcomp(b, integer, fraction, mant_exp)
+}
+
+/// Parse float from extracted float components.
+///
+/// * `integer`     - Slice containing the integer digits.
+/// * `fraction`    - Slice containing the fraction digits.
+/// * `exponent`    - Parsed, 32-bit exponent.
+///
+/// Precondition: The integer must not have leading zeros.
+pub fn parse_truncated_float<F>(integer: &[u8], mut fraction: &[u8], exponent: i32) -> F
+where
+    F: Float,
+{
+    // Trim trailing zeroes from the fraction part.
+    while fraction.last() == Some(&b'0') {
+        fraction = &fraction[..fraction.len() - 1];
+    }
+
+    // Calculate the number of truncated digits.
+    let mut truncated = 0;
+    let mut mantissa: u64 = 0;
+    let mut iter = integer.iter().chain(fraction);
+    for &c in &mut iter {
+        mantissa = match add_digit(mantissa, to_digit(c).unwrap()) {
+            Some(v) => v,
+            None => {
+                truncated = 1 + iter.count();
+                break;
+            }
+        };
+    }
+
+    let mant_exp = mantissa_exponent(exponent, fraction.len(), truncated);
+    let is_truncated = true;
+
+    fallback_path(
+        integer,
+        fraction,
+        mantissa,
+        exponent,
+        mant_exp,
+        is_truncated,
+    )
+}
@@ -0,0 +1,231 @@
+// Adapted from https://github.com/Alexhuszagh/rust-lexical.
+
+//! Defines rounding schemes for floating-point numbers.
+
+use super::float::ExtendedFloat;
+use super::num::*;
+use super::shift::*;
+use core::mem;
+
+// MASKS
+
+/// Calculate a scalar factor of 2 above the halfway point.
+#[inline]
+pub(crate) fn nth_bit(n: u64) -> u64 {
+    let bits: u64 = mem::size_of::<u64>() as u64 * 8;
+    debug_assert!(n < bits, "nth_bit() overflow in shl.");
+
+    1 << n
+}
+
+/// Generate a bitwise mask for the lower `n` bits.
+#[inline]
+pub(crate) fn lower_n_mask(n: u64) -> u64 {
+    let bits: u64 = mem::size_of::<u64>() as u64 * 8;
+    debug_assert!(n <= bits, "lower_n_mask() overflow in shl.");
+
+    if n == bits {
+        u64::MAX
+    } else {
+        (1 << n) - 1
+    }
+}
+
+/// Calculate the halfway point for the lower `n` bits.
+#[inline]
+pub(crate) fn lower_n_halfway(n: u64) -> u64 {
+    let bits: u64 = mem::size_of::<u64>() as u64 * 8;
+    debug_assert!(n <= bits, "lower_n_halfway() overflow in shl.");
+
+    if n == 0 {
+        0
+    } else {
+        nth_bit(n - 1)
+    }
+}
+
+/// Calculate a bitwise mask with `n` 1 bits starting at the `bit` position.
+#[inline]
+pub(crate) fn internal_n_mask(bit: u64, n: u64) -> u64 {
+    let bits: u64 = mem::size_of::<u64>() as u64 * 8;
+    debug_assert!(bit <= bits, "internal_n_halfway() overflow in shl.");
+    debug_assert!(n <= bits, "internal_n_halfway() overflow in shl.");
+    debug_assert!(bit >= n, "internal_n_halfway() overflow in sub.");
+
+    lower_n_mask(bit) ^ lower_n_mask(bit - n)
+}
+
+// NEAREST ROUNDING
+
+// Shift right N-bytes and round to the nearest.
+//
+// Return if we are above halfway and if we are halfway.
+#[inline]
+pub(crate) fn round_nearest(fp: &mut ExtendedFloat, shift: i32) -> (bool, bool) {
+    // Extract the truncated bits using mask.
+    // Calculate if the value of the truncated bits are either above
+    // the mid-way point, or equal to it.
+    //
+    // For example, for 4 truncated bytes, the mask would be b1111
+    // and the midway point would be b1000.
+    let mask: u64 = lower_n_mask(shift as u64);
+    let halfway: u64 = lower_n_halfway(shift as u64);
+
+    let truncated_bits = fp.mant & mask;
+    let is_above = truncated_bits > halfway;
+    let is_halfway = truncated_bits == halfway;
+
+    // Bit shift so the leading bit is in the hidden bit.
+    overflowing_shr(fp, shift);
+
+    (is_above, is_halfway)
+}
+
+// Tie rounded floating point to event.
+#[inline]
+pub(crate) fn tie_even(fp: &mut ExtendedFloat, is_above: bool, is_halfway: bool) {
+    // Extract the last bit after shifting (and determine if it is odd).
+    let is_odd = fp.mant & 1 == 1;
+
+    // Calculate if we need to roundup.
+    // We need to roundup if we are above halfway, or if we are odd
+    // and at half-way (need to tie-to-even).
+    if is_above || (is_odd && is_halfway) {
+        fp.mant += 1;
+    }
+}
+
+// Shift right N-bytes and round nearest, tie-to-even.
+//
+// Floating-point arithmetic uses round to nearest, ties to even,
+// which rounds to the nearest value, if the value is halfway in between,
+// round to an even value.
+#[inline]
+pub(crate) fn round_nearest_tie_even(fp: &mut ExtendedFloat, shift: i32) {
+    let (is_above, is_halfway) = round_nearest(fp, shift);
+    tie_even(fp, is_above, is_halfway);
+}
+
+// DIRECTED ROUNDING
+
+// Shift right N-bytes and round towards a direction.
+//
+// Return if we have any truncated bytes.
+#[inline]
+fn round_toward(fp: &mut ExtendedFloat, shift: i32) -> bool {
+    let mask: u64 = lower_n_mask(shift as u64);
+    let truncated_bits = fp.mant & mask;
+
+    // Bit shift so the leading bit is in the hidden bit.
+    overflowing_shr(fp, shift);
+
+    truncated_bits != 0
+}
+
+// Round down.
+#[inline]
+fn downard(_: &mut ExtendedFloat, _: bool) {}
+
+// Shift right N-bytes and round toward zero.
+//
+// Floating-point arithmetic defines round toward zero, which rounds
+// towards positive zero.
+#[inline]
+pub(crate) fn round_downward(fp: &mut ExtendedFloat, shift: i32) {
+    // Bit shift so the leading bit is in the hidden bit.
+    // No rounding schemes, so we just ignore everything else.
+    let is_truncated = round_toward(fp, shift);
+    downard(fp, is_truncated);
+}
+
+// ROUND TO FLOAT
+
+// Shift the ExtendedFloat fraction to the fraction bits in a native float.
+//
+// Floating-point arithmetic uses round to nearest, ties to even,
+// which rounds to the nearest value, if the value is halfway in between,
+// round to an even value.
+#[inline]
+pub(crate) fn round_to_float<F, Algorithm>(fp: &mut ExtendedFloat, algorithm: Algorithm)
+where
+    F: Float,
+    Algorithm: FnOnce(&mut ExtendedFloat, i32),
+{
+    // Calculate the difference to allow a single calculation
+    // rather than a loop, to minimize the number of ops required.
+    // This does underflow detection.
+    let final_exp = fp.exp + F::DEFAULT_SHIFT;
+    if final_exp < F::DENORMAL_EXPONENT {
+        // We would end up with a denormal exponent, try to round to more
+        // digits. Only shift right if we can avoid zeroing out the value,
+        // which requires the exponent diff to be < M::BITS. The value
+        // is already normalized, so we shouldn't have any issue zeroing
+        // out the value.
+        let diff = F::DENORMAL_EXPONENT - fp.exp;
+        if diff <= u64::FULL {
+            // We can avoid underflow, can get a valid representation.
+            algorithm(fp, diff);
+        } else {
+            // Certain underflow, assign literal 0s.
+            fp.mant = 0;
+            fp.exp = 0;
+        }
+    } else {
+        algorithm(fp, F::DEFAULT_SHIFT);
+    }
+
+    if fp.mant & F::CARRY_MASK == F::CARRY_MASK {
+        // Roundup carried over to 1 past the hidden bit.
+        shr(fp, 1);
+    }
+}
+
+// AVOID OVERFLOW/UNDERFLOW
+
+// Avoid overflow for large values, shift left as needed.
+//
+// Shift until a 1-bit is in the hidden bit, if the mantissa is not 0.
+#[inline]
+pub(crate) fn avoid_overflow<F>(fp: &mut ExtendedFloat)
+where
+    F: Float,
+{
+    // Calculate the difference to allow a single calculation
+    // rather than a loop, minimizing the number of ops required.
+    if fp.exp >= F::MAX_EXPONENT {
+        let diff = fp.exp - F::MAX_EXPONENT;
+        if diff <= F::MANTISSA_SIZE {
+            // Our overflow mask needs to start at the hidden bit, or at
+            // `F::MANTISSA_SIZE+1`, and needs to have `diff+1` bits set,
+            // to see if our value overflows.
+            let bit = (F::MANTISSA_SIZE + 1) as u64;
+            let n = (diff + 1) as u64;
+            let mask = internal_n_mask(bit, n);
+            if (fp.mant & mask) == 0 {
+                // If we have no 1-bit in the hidden-bit position,
+                // which is index 0, we need to shift 1.
+                let shift = diff + 1;
+                shl(fp, shift);
+            }
+        }
+    }
+}
+
+// ROUND TO NATIVE
+
+// Round an extended-precision float to a native float representation.
+#[inline]
+pub(crate) fn round_to_native<F, Algorithm>(fp: &mut ExtendedFloat, algorithm: Algorithm)
+where
+    F: Float,
+    Algorithm: FnOnce(&mut ExtendedFloat, i32),
+{
+    // Shift all the way left, to ensure a consistent representation.
+    // The following right-shifts do not work for a non-normalized number.
+    fp.normalize();
+
+    // Round so the fraction is in a native mantissa representation,
+    // and avoid overflow/underflow.
+    round_to_float::<F, _>(fp, algorithm);
+    avoid_overflow::<F>(fp);
+}
@@ -0,0 +1,46 @@
+// Adapted from https://github.com/Alexhuszagh/rust-lexical.
+
+//! Bit-shift helpers.
+
+use super::float::ExtendedFloat;
+use core::mem;
+
+// Shift extended-precision float right `shift` bytes.
+#[inline]
+pub(crate) fn shr(fp: &mut ExtendedFloat, shift: i32) {
+    let bits: u64 = mem::size_of::<u64>() as u64 * 8;
+    debug_assert!((shift as u64) < bits, "shr() overflow in shift right.");
+
+    fp.mant >>= shift;
+    fp.exp += shift;
+}
+
+// Shift extended-precision float right `shift` bytes.
+//
+// Accepts when the shift is the same as the type size, and
+// sets the value to 0.
+#[inline]
+pub(crate) fn overflowing_shr(fp: &mut ExtendedFloat, shift: i32) {
+    let bits: u64 = mem::size_of::<u64>() as u64 * 8;
+    debug_assert!(
+        (shift as u64) <= bits,
+        "overflowing_shr() overflow in shift right."
+    );
+
+    fp.mant = if shift as u64 == bits {
+        0
+    } else {
+        fp.mant >> shift
+    };
+    fp.exp += shift;
+}
+
+// Shift extended-precision float left `shift` bytes.
+#[inline]
+pub(crate) fn shl(fp: &mut ExtendedFloat, shift: i32) {
+    let bits: u64 = mem::size_of::<u64>() as u64 * 8;
+    debug_assert!((shift as u64) < bits, "shl() overflow in shift left.");
+
+    fp.mant <<= shift;
+    fp.exp -= shift;
+}
@@ -0,0 +1,70 @@
+// Adapted from https://github.com/Alexhuszagh/rust-lexical.
+
+//! Pre-computed small powers.
+
+// 32 BIT
+#[cfg(fast_arithmetic = "32")]
+pub(crate) const POW5_32: [u32; 14] = [
+    1, 5, 25, 125, 625, 3125, 15625, 78125, 390625, 1953125, 9765625, 48828125, 244140625,
+    1220703125,
+];
+
+#[cfg(fast_arithmetic = "32")]
+pub(crate) const POW10_32: [u32; 10] = [
+    1, 10, 100, 1000, 10000, 100000, 1000000, 10000000, 100000000, 1000000000,
+];
+
+// 64 BIT
+#[cfg(fast_arithmetic = "64")]
+pub(crate) const POW5_64: [u64; 28] = [
+    1,
+    5,
+    25,
+    125,
+    625,
+    3125,
+    15625,
+    78125,
+    390625,
+    1953125,
+    9765625,
+    48828125,
+    244140625,
+    1220703125,
+    6103515625,
+    30517578125,
+    152587890625,
+    762939453125,
+    3814697265625,
+    19073486328125,
+    95367431640625,
+    476837158203125,
+    2384185791015625,
+    11920928955078125,
+    59604644775390625,
+    298023223876953125,
+    1490116119384765625,
+    7450580596923828125,
+];
+pub(crate) const POW10_64: [u64; 20] = [
+    1,
+    10,
+    100,
+    1000,
+    10000,
+    100000,
+    1000000,
+    10000000,
+    100000000,
+    1000000000,
+    10000000000,
+    100000000000,
+    1000000000000,
+    10000000000000,
+    100000000000000,
+    1000000000000000,
+    10000000000000000,
+    100000000000000000,
+    1000000000000000000,
+    10000000000000000000,
+];