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chore: checkpoint before Python removal

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Sienna Meridian Satterwhite
2026-03-26 22:33:59 +00:00
parent 683cec9307
commit e568ddf82a
29972 changed files with 11269302 additions and 2 deletions
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195
vendor/serde_json/src/lexical/algorithm.rs vendored Normal file
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// 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)
}
}

218
vendor/serde_json/src/lexical/bhcomp.rs vendored Normal file
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// 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)
}
}

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vendor/serde_json/src/lexical/bignum.rs vendored Normal file
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// 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
}
}

82
vendor/serde_json/src/lexical/cached.rs vendored Normal file
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// 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()
}
}

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vendor/serde_json/src/lexical/cached_float80.rs vendored Normal file
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// 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
}

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vendor/serde_json/src/lexical/digit.rs vendored Normal file
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// 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),
}
}

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vendor/serde_json/src/lexical/errors.rs vendored Normal file
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// 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)
}
}

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// 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))
}
}

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// 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))
}
}

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// 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::*;

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// 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,
];

625
vendor/serde_json/src/lexical/large_powers64.rs vendored Normal file
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@@ -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,
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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,
];

884
vendor/serde_json/src/lexical/math.rs vendored Normal file
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@@ -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!(self.len() == 1);
let r0 = self[0] as u64;
u64_to_hi64_1(r0)
}
#[inline]
fn hi64_2(&self) -> (u64, bool) {
debug_assert!(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!(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);
}
}

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// 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};

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// 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)
}
}

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// 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,
)
}

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// 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);
}

46
vendor/serde_json/src/lexical/shift.rs vendored Normal file
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// 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;
}

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vendor/serde_json/src/lexical/small_powers.rs vendored Normal file
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// 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,
];