//===----------------------------------------------------------------------===//
//
// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
// See https://llvm.org/LICENSE.txt for license information.
// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
//
//===----------------------------------------------------------------------===//
// Copyright (c) Microsoft Corporation.
// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
// Copyright 2018 Ulf Adams
// Copyright (c) Microsoft Corporation. All rights reserved.
// Boost Software License - Version 1.0 - August 17th, 2003
// Permission is hereby granted, free of charge, to any person or organization
// obtaining a copy of the software and accompanying documentation covered by
// this license (the "Software") to use, reproduce, display, distribute,
// execute, and transmit the Software, and to prepare derivative works of the
// Software, and to permit third-parties to whom the Software is furnished to
// do so, all subject to the following:
// The copyright notices in the Software and this entire statement, including
// the above license grant, this restriction and the following disclaimer,
// must be included in all copies of the Software, in whole or in part, and
// all derivative works of the Software, unless such copies or derivative
// works are solely in the form of machine-executable object code generated by
// a source language processor.
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
// FITNESS FOR A PARTICULAR PURPOSE, TITLE AND NON-INFRINGEMENT. IN NO EVENT
// SHALL THE COPYRIGHT HOLDERS OR ANYONE DISTRIBUTING THE SOFTWARE BE LIABLE
// FOR ANY DAMAGES OR OTHER LIABILITY, WHETHER IN CONTRACT, TORT OR OTHERWISE,
// ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
// DEALINGS IN THE SOFTWARE.
// Avoid formatting to keep the changes with the original code minimal.
// clang-format off
#include <__assert>
#include <__config>
#include <charconv>
#include "include/ryu/common.h"
#include "include/ryu/d2fixed.h"
#include "include/ryu/d2s_intrinsics.h"
#include "include/ryu/digit_table.h"
#include "include/ryu/f2s.h"
#include "include/ryu/ryu.h"
_LIBCPP_BEGIN_NAMESPACE_STD
inline constexpr int __FLOAT_MANTISSA_BITS = 23;
inline constexpr int __FLOAT_EXPONENT_BITS = 8;
inline constexpr int __FLOAT_BIAS = 127;
inline constexpr int __FLOAT_POW5_INV_BITCOUNT = 59;
inline constexpr uint64_t __FLOAT_POW5_INV_SPLIT[31] = {
576460752303423489u, 461168601842738791u, 368934881474191033u, 295147905179352826u,
472236648286964522u, 377789318629571618u, 302231454903657294u, 483570327845851670u,
386856262276681336u, 309485009821345069u, 495176015714152110u, 396140812571321688u,
316912650057057351u, 507060240091291761u, 405648192073033409u, 324518553658426727u,
519229685853482763u, 415383748682786211u, 332306998946228969u, 531691198313966350u,
425352958651173080u, 340282366920938464u, 544451787073501542u, 435561429658801234u,
348449143727040987u, 557518629963265579u, 446014903970612463u, 356811923176489971u,
570899077082383953u, 456719261665907162u, 365375409332725730u
};
inline constexpr int __FLOAT_POW5_BITCOUNT = 61;
inline constexpr uint64_t __FLOAT_POW5_SPLIT[47] = {
1152921504606846976u, 1441151880758558720u, 1801439850948198400u, 2251799813685248000u,
1407374883553280000u, 1759218604441600000u, 2199023255552000000u, 1374389534720000000u,
1717986918400000000u, 2147483648000000000u, 1342177280000000000u, 1677721600000000000u,
2097152000000000000u, 1310720000000000000u, 1638400000000000000u, 2048000000000000000u,
1280000000000000000u, 1600000000000000000u, 2000000000000000000u, 1250000000000000000u,
1562500000000000000u, 1953125000000000000u, 1220703125000000000u, 1525878906250000000u,
1907348632812500000u, 1192092895507812500u, 1490116119384765625u, 1862645149230957031u,
1164153218269348144u, 1455191522836685180u, 1818989403545856475u, 2273736754432320594u,
1421085471520200371u, 1776356839400250464u, 2220446049250313080u, 1387778780781445675u,
1734723475976807094u, 2168404344971008868u, 1355252715606880542u, 1694065894508600678u,
2117582368135750847u, 1323488980084844279u, 1654361225106055349u, 2067951531382569187u,
1292469707114105741u, 1615587133892632177u, 2019483917365790221u
};
[[nodiscard]] _LIBCPP_HIDE_FROM_ABI inline uint32_t __pow5Factor(uint32_t __value) {
uint32_t __count = 0;
for (;;) {
_LIBCPP_ASSERT_INTERNAL(__value != 0, "");
const uint32_t __q = __value / 5;
const uint32_t __r = __value % 5;
if (__r != 0) {
break;
}
__value = __q;
++__count;
}
return __count;
}
// Returns true if __value is divisible by 5^__p.
[[nodiscard]] _LIBCPP_HIDE_FROM_ABI inline bool __multipleOfPowerOf5(const uint32_t __value, const uint32_t __p) {
return __pow5Factor(__value) >= __p;
}
// Returns true if __value is divisible by 2^__p.
[[nodiscard]] _LIBCPP_HIDE_FROM_ABI inline bool __multipleOfPowerOf2(const uint32_t __value, const uint32_t __p) {
_LIBCPP_ASSERT_INTERNAL(__value != 0, "");
_LIBCPP_ASSERT_INTERNAL(__p < 32, "");
// __builtin_ctz doesn't appear to be faster here.
return (__value & ((1u << __p) - 1)) == 0;
}
[[nodiscard]] _LIBCPP_HIDE_FROM_ABI inline uint32_t __mulShift(const uint32_t __m, const uint64_t __factor, const int32_t __shift) {
_LIBCPP_ASSERT_INTERNAL(__shift > 32, "");
// The casts here help MSVC to avoid calls to the __allmul library
// function.
const uint32_t __factorLo = static_cast<uint32_t>(__factor);
const uint32_t __factorHi = static_cast<uint32_t>(__factor >> 32);
const uint64_t __bits0 = static_cast<uint64_t>(__m) * __factorLo;
const uint64_t __bits1 = static_cast<uint64_t>(__m) * __factorHi;
#ifndef _LIBCPP_64_BIT
// On 32-bit platforms we can avoid a 64-bit shift-right since we only
// need the upper 32 bits of the result and the shift value is > 32.
const uint32_t __bits0Hi = static_cast<uint32_t>(__bits0 >> 32);
uint32_t __bits1Lo = static_cast<uint32_t>(__bits1);
uint32_t __bits1Hi = static_cast<uint32_t>(__bits1 >> 32);
__bits1Lo += __bits0Hi;
__bits1Hi += (__bits1Lo < __bits0Hi);
const int32_t __s = __shift - 32;
return (__bits1Hi << (32 - __s)) | (__bits1Lo >> __s);
#else // ^^^ 32-bit ^^^ / vvv 64-bit vvv
const uint64_t __sum = (__bits0 >> 32) + __bits1;
const uint64_t __shiftedSum = __sum >> (__shift - 32);
_LIBCPP_ASSERT_INTERNAL(__shiftedSum <= UINT32_MAX, "");
return static_cast<uint32_t>(__shiftedSum);
#endif // ^^^ 64-bit ^^^
}
[[nodiscard]] _LIBCPP_HIDE_FROM_ABI inline uint32_t __mulPow5InvDivPow2(const uint32_t __m, const uint32_t __q, const int32_t __j) {
return __mulShift(__m, __FLOAT_POW5_INV_SPLIT[__q], __j);
}
[[nodiscard]] _LIBCPP_HIDE_FROM_ABI inline uint32_t __mulPow5divPow2(const uint32_t __m, const uint32_t __i, const int32_t __j) {
return __mulShift(__m, __FLOAT_POW5_SPLIT[__i], __j);
}
// A floating decimal representing m * 10^e.
struct __floating_decimal_32 {
uint32_t __mantissa;
int32_t __exponent;
};
[[nodiscard]] _LIBCPP_HIDE_FROM_ABI inline __floating_decimal_32 __f2d(const uint32_t __ieeeMantissa, const uint32_t __ieeeExponent) {
int32_t __e2;
uint32_t __m2;
if (__ieeeExponent == 0) {
// We subtract 2 so that the bounds computation has 2 additional bits.
__e2 = 1 - __FLOAT_BIAS - __FLOAT_MANTISSA_BITS - 2;
__m2 = __ieeeMantissa;
} else {
__e2 = static_cast<int32_t>(__ieeeExponent) - __FLOAT_BIAS - __FLOAT_MANTISSA_BITS - 2;
__m2 = (1u << __FLOAT_MANTISSA_BITS) | __ieeeMantissa;
}
const bool __even = (__m2 & 1) == 0;
const bool __acceptBounds = __even;
// Step 2: Determine the interval of valid decimal representations.
const uint32_t __mv = 4 * __m2;
const uint32_t __mp = 4 * __m2 + 2;
// Implicit bool -> int conversion. True is 1, false is 0.
const uint32_t __mmShift = __ieeeMantissa != 0 || __ieeeExponent <= 1;
const uint32_t __mm = 4 * __m2 - 1 - __mmShift;
// Step 3: Convert to a decimal power base using 64-bit arithmetic.
uint32_t __vr, __vp, __vm;
int32_t __e10;
bool __vmIsTrailingZeros = false;
bool __vrIsTrailingZeros = false;
uint8_t __lastRemovedDigit = 0;
if (__e2 >= 0) {
const uint32_t __q = __log10Pow2(__e2);
__e10 = static_cast<int32_t>(__q);
const int32_t __k = __FLOAT_POW5_INV_BITCOUNT + __pow5bits(static_cast<int32_t>(__q)) - 1;
const int32_t __i = -__e2 + static_cast<int32_t>(__q) + __k;
__vr = __mulPow5InvDivPow2(__mv, __q, __i);
__vp = __mulPow5InvDivPow2(__mp, __q, __i);
__vm = __mulPow5InvDivPow2(__mm, __q, __i);
if (__q != 0 && (__vp - 1) / 10 <= __vm / 10) {
// We need to know one removed digit even if we are not going to loop below. We could use
// __q = X - 1 above, except that would require 33 bits for the result, and we've found that
// 32-bit arithmetic is faster even on 64-bit machines.
const int32_t __l = __FLOAT_POW5_INV_BITCOUNT + __pow5bits(static_cast<int32_t>(__q - 1)) - 1;
__lastRemovedDigit = static_cast<uint8_t>(__mulPow5InvDivPow2(__mv, __q - 1,
-__e2 + static_cast<int32_t>(__q) - 1 + __l) % 10);
}
if (__q <= 9) {
// The largest power of 5 that fits in 24 bits is 5^10, but __q <= 9 seems to be safe as well.
// Only one of __mp, __mv, and __mm can be a multiple of 5, if any.
if (__mv % 5 == 0) {
__vrIsTrailingZeros = __multipleOfPowerOf5(__mv, __q);
} else if (__acceptBounds) {
__vmIsTrailingZeros = __multipleOfPowerOf5(__mm, __q);
} else {
__vp -= __multipleOfPowerOf5(__mp, __q);
}
}
} else {
const uint32_t __q = __log10Pow5(-__e2);
__e10 = static_cast<int32_t>(__q) + __e2;
const int32_t __i = -__e2 - static_cast<int32_t>(__q);
const int32_t __k = __pow5bits(__i) - __FLOAT_POW5_BITCOUNT;
int32_t __j = static_cast<int32_t>(__q) - __k;
__vr = __mulPow5divPow2(__mv, static_cast<uint32_t>(__i), __j);
__vp = __mulPow5divPow2(__mp, static_cast<uint32_t>(__i), __j);
__vm = __mulPow5divPow2(__mm, static_cast<uint32_t>(__i), __j);
if (__q != 0 && (__vp - 1) / 10 <= __vm / 10) {
__j = static_cast<int32_t>(__q) - 1 - (__pow5bits(__i + 1) - __FLOAT_POW5_BITCOUNT);
__lastRemovedDigit = static_cast<uint8_t>(__mulPow5divPow2(__mv, static_cast<uint32_t>(__i + 1), __j) % 10);
}
if (__q <= 1) {
// {__vr,__vp,__vm} is trailing zeros if {__mv,__mp,__mm} has at least __q trailing 0 bits.
// __mv = 4 * __m2, so it always has at least two trailing 0 bits.
__vrIsTrailingZeros = true;
if (__acceptBounds) {
// __mm = __mv - 1 - __mmShift, so it has 1 trailing 0 bit iff __mmShift == 1.
__vmIsTrailingZeros = __mmShift == 1;
} else {
// __mp = __mv + 2, so it always has at least one trailing 0 bit.
--__vp;
}
} else if (__q < 31) { // TRANSITION(ulfjack): Use a tighter bound here.
__vrIsTrailingZeros = __multipleOfPowerOf2(__mv, __q - 1);
}
}
// Step 4: Find the shortest decimal representation in the interval of valid representations.
int32_t __removed = 0;
uint32_t _Output;
if (__vmIsTrailingZeros || __vrIsTrailingZeros) {
// General case, which happens rarely (~4.0%).
while (__vp / 10 > __vm / 10) {
#ifdef __clang__ // TRANSITION, LLVM-23106
__vmIsTrailingZeros &= __vm - (__vm / 10) * 10 == 0;
#else
__vmIsTrailingZeros &= __vm % 10 == 0;
#endif
__vrIsTrailingZeros &= __lastRemovedDigit == 0;
__lastRemovedDigit = static_cast<uint8_t>(__vr % 10);
__vr /= 10;
__vp /= 10;
__vm /= 10;
++__removed;
}
if (__vmIsTrailingZeros) {
while (__vm % 10 == 0) {
__vrIsTrailingZeros &= __lastRemovedDigit == 0;
__lastRemovedDigit = static_cast<uint8_t>(__vr % 10);
__vr /= 10;
__vp /= 10;
__vm /= 10;
++__removed;
}
}
if (__vrIsTrailingZeros && __lastRemovedDigit == 5 && __vr % 2 == 0) {
// Round even if the exact number is .....50..0.
__lastRemovedDigit = 4;
}
// We need to take __vr + 1 if __vr is outside bounds or we need to round up.
_Output = __vr + ((__vr == __vm && (!__acceptBounds || !__vmIsTrailingZeros)) || __lastRemovedDigit >= 5);
} else {
// Specialized for the common case (~96.0%). Percentages below are relative to this.
// Loop iterations below (approximately):
// 0: 13.6%, 1: 70.7%, 2: 14.1%, 3: 1.39%, 4: 0.14%, 5+: 0.01%
while (__vp / 10 > __vm / 10) {
__lastRemovedDigit = static_cast<uint8_t>(__vr % 10);
__vr /= 10;
__vp /= 10;
__vm /= 10;
++__removed;
}
// We need to take __vr + 1 if __vr is outside bounds or we need to round up.
_Output = __vr + (__vr == __vm || __lastRemovedDigit >= 5);
}
const int32_t __exp = __e10 + __removed;
__floating_decimal_32 __fd;
__fd.__exponent = __exp;
__fd.__mantissa = _Output;
return __fd;
}
[[nodiscard]] _LIBCPP_HIDE_FROM_ABI inline to_chars_result _Large_integer_to_chars(char* const _First, char* const _Last,
const uint32_t _Mantissa2, const int32_t _Exponent2) {
// Print the integer _Mantissa2 * 2^_Exponent2 exactly.
// For nonzero integers, _Exponent2 >= -23. (The minimum value occurs when _Mantissa2 * 2^_Exponent2 is 1.
// In that case, _Mantissa2 is the implicit 1 bit followed by 23 zeros, so _Exponent2 is -23 to shift away
// the zeros.) The dense range of exactly representable integers has negative or zero exponents
// (as positive exponents make the range non-dense). For that dense range, Ryu will always be used:
// every digit is necessary to uniquely identify the value, so Ryu must print them all.
// Positive exponents are the non-dense range of exactly representable integers.
// This contains all of the values for which Ryu can't be used (and a few Ryu-friendly values).
// Performance note: Long division appears to be faster than losslessly widening float to double and calling
// __d2fixed_buffered_n(). If __f2fixed_buffered_n() is implemented, it might be faster than long division.
_LIBCPP_ASSERT_INTERNAL(_Exponent2 > 0, "");
_LIBCPP_ASSERT_INTERNAL(_Exponent2 <= 104, ""); // because __ieeeExponent <= 254
// Manually represent _Mantissa2 * 2^_Exponent2 as a large integer. _Mantissa2 is always 24 bits
// (due to the implicit bit), while _Exponent2 indicates a shift of at most 104 bits.
// 24 + 104 equals 128 equals 4 * 32, so we need exactly 4 32-bit elements.
// We use a little-endian representation, visualized like this:
// << left shift <<
// most significant
// _Data[3] _Data[2] _Data[1] _Data[0]
// least significant
// >> right shift >>
constexpr uint32_t _Data_size = 4;
uint32_t _Data[_Data_size]{};
// _Maxidx is the index of the most significant nonzero element.
uint32_t _Maxidx = ((24 + static_cast<uint32_t>(_Exponent2) + 31) / 32) - 1;
_LIBCPP_ASSERT_INTERNAL(_Maxidx < _Data_size, "");
const uint32_t _Bit_shift = static_cast<uint32_t>(_Exponent2) % 32;
if (_Bit_shift <= 8) { // _Mantissa2's 24 bits don't cross an element boundary
_Data[_Maxidx] = _Mantissa2 << _Bit_shift;
} else { // _Mantissa2's 24 bits cross an element boundary
_Data[_Maxidx - 1] = _Mantissa2 << _Bit_shift;
_Data[_Maxidx] = _Mantissa2 >> (32 - _Bit_shift);
}
// If Ryu hasn't determined the total output length, we need to buffer the digits generated from right to left
// by long division. The largest possible float is: 340'282346638'528859811'704183484'516925440
uint32_t _Blocks[4];
int32_t _Filled_blocks = 0;
// From left to right, we're going to print:
// _Data[0] will be [1, 10] digits.
// Then if _Filled_blocks > 0:
// _Blocks[_Filled_blocks - 1], ..., _Blocks[0] will be 0-filled 9-digit blocks.
if (_Maxidx != 0) { // If the integer is actually large, perform long division.
// Otherwise, skip to printing _Data[0].
for (;;) {
// Loop invariant: _Maxidx != 0 (i.e. the integer is actually large)
const uint32_t _Most_significant_elem = _Data[_Maxidx];
const uint32_t _Initial_remainder = _Most_significant_elem % 1000000000;
const uint32_t _Initial_quotient = _Most_significant_elem / 1000000000;
_Data[_Maxidx] = _Initial_quotient;
uint64_t _Remainder = _Initial_remainder;
// Process less significant elements.
uint32_t _Idx = _Maxidx;
do {
--_Idx; // Initially, _Remainder is at most 10^9 - 1.
// Now, _Remainder is at most (10^9 - 1) * 2^32 + 2^32 - 1, simplified to 10^9 * 2^32 - 1.
_Remainder = (_Remainder << 32) | _Data[_Idx];
// floor((10^9 * 2^32 - 1) / 10^9) == 2^32 - 1, so uint32_t _Quotient is lossless.
const uint32_t _Quotient = static_cast<uint32_t>(__div1e9(_Remainder));
// _Remainder is at most 10^9 - 1 again.
// For uint32_t truncation, see the __mod1e9() comment in d2s_intrinsics.h.
_Remainder = static_cast<uint32_t>(_Remainder) - 1000000000u * _Quotient;
_Data[_Idx] = _Quotient;
} while (_Idx != 0);
// Store a 0-filled 9-digit block.
_Blocks[_Filled_blocks++] = static_cast<uint32_t>(_Remainder);
if (_Initial_quotient == 0) { // Is the large integer shrinking?
--_Maxidx; // log2(10^9) is 29.9, so we can't shrink by more than one element.
if (_Maxidx == 0) {
break; // We've finished long division. Now we need to print _Data[0].
}
}
}
}
_LIBCPP_ASSERT_INTERNAL(_Data[0] != 0, "");
for (uint32_t _Idx = 1; _Idx < _Data_size; ++_Idx) {
_LIBCPP_ASSERT_INTERNAL(_Data[_Idx] == 0, "");
}
const uint32_t _Data_olength = _Data[0] >= 1000000000 ? 10 : __decimalLength9(_Data[0]);
const uint32_t _Total_fixed_length = _Data_olength + 9 * _Filled_blocks;
if (_Last - _First < static_cast<ptrdiff_t>(_Total_fixed_length)) {
return { _Last, errc::value_too_large };
}
char* _Result = _First;
// Print _Data[0]. While it's up to 10 digits,
// which is more than Ryu generates, the code below can handle this.
__append_n_digits(_Data_olength, _Data[0], _Result);
_Result += _Data_olength;
// Print 0-filled 9-digit blocks.
for (int32_t _Idx = _Filled_blocks - 1; _Idx >= 0; --_Idx) {
__append_nine_digits(_Blocks[_Idx], _Result);
_Result += 9;
}
return { _Result, errc{} };
}
[[nodiscard]] _LIBCPP_HIDE_FROM_ABI inline to_chars_result __to_chars(char* const _First, char* const _Last, const __floating_decimal_32 __v,
chars_format _Fmt, const uint32_t __ieeeMantissa, const uint32_t __ieeeExponent) {
// Step 5: Print the decimal representation.
uint32_t _Output = __v.__mantissa;
int32_t _Ryu_exponent = __v.__exponent;
const uint32_t __olength = __decimalLength9(_Output);
int32_t _Scientific_exponent = _Ryu_exponent + static_cast<int32_t>(__olength) - 1;
if (_Fmt == chars_format{}) {
int32_t _Lower;
int32_t _Upper;
if (__olength == 1) {
// Value | Fixed | Scientific
// 1e-3 | "0.001" | "1e-03"
// 1e4 | "10000" | "1e+04"
_Lower = -3;
_Upper = 4;
} else {
// Value | Fixed | Scientific
// 1234e-7 | "0.0001234" | "1.234e-04"
// 1234e5 | "123400000" | "1.234e+08"
_Lower = -static_cast<int32_t>(__olength + 3);
_Upper = 5;
}
if (_Lower <= _Ryu_exponent && _Ryu_exponent <= _Upper) {
_Fmt = chars_format::fixed;
} else {
_Fmt = chars_format::scientific;
}
} else if (_Fmt == chars_format::general) {
// C11 7.21.6.1 "The fprintf function"/8:
// "Let P equal [...] 6 if the precision is omitted [...].
// Then, if a conversion with style E would have an exponent of X:
// - if P > X >= -4, the conversion is with style f [...].
// - otherwise, the conversion is with style e [...]."
if (-4 <= _Scientific_exponent && _Scientific_exponent < 6) {
_Fmt = chars_format::fixed;
} else {
_Fmt = chars_format::scientific;
}
}
if (_Fmt == chars_format::fixed) {
// Example: _Output == 1729, __olength == 4
// _Ryu_exponent | Printed | _Whole_digits | _Total_fixed_length | Notes
// --------------|----------|---------------|----------------------|---------------------------------------
// 2 | 172900 | 6 | _Whole_digits | Ryu can't be used for printing
// 1 | 17290 | 5 | (sometimes adjusted) | when the trimmed digits are nonzero.
// --------------|----------|---------------|----------------------|---------------------------------------
// 0 | 1729 | 4 | _Whole_digits | Unified length cases.
// --------------|----------|---------------|----------------------|---------------------------------------
// -1 | 172.9 | 3 | __olength + 1 | This case can't happen for
// -2 | 17.29 | 2 | | __olength == 1, but no additional
// -3 | 1.729 | 1 | | code is needed to avoid it.
// --------------|----------|---------------|----------------------|---------------------------------------
// -4 | 0.1729 | 0 | 2 - _Ryu_exponent | C11 7.21.6.1 "The fprintf function"/8:
// -5 | 0.01729 | -1 | | "If a decimal-point character appears,
// -6 | 0.001729 | -2 | | at least one digit appears before it."
const int32_t _Whole_digits = static_cast<int32_t>(__olength) + _Ryu_exponent;
uint32_t _Total_fixed_length;
if (_Ryu_exponent >= 0) { // cases "172900" and "1729"
_Total_fixed_length = static_cast<uint32_t>(_Whole_digits);
if (_Output == 1) {
// Rounding can affect the number of digits.
// For example, 1e11f is exactly "99999997952" which is 11 digits instead of 12.
// We can use a lookup table to detect this and adjust the total length.
static constexpr uint8_t _Adjustment[39] = {
0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,1,1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,1,1,0,1,1,1 };
_Total_fixed_length -= _Adjustment[_Ryu_exponent];
// _Whole_digits doesn't need to be adjusted because these cases won't refer to it later.
}
} else if (_Whole_digits > 0) { // case "17.29"
_Total_fixed_length = __olength + 1;
} else { // case "0.001729"
_Total_fixed_length = static_cast<uint32_t>(2 - _Ryu_exponent);
}
if (_Last - _First < static_cast<ptrdiff_t>(_Total_fixed_length)) {
return { _Last, errc::value_too_large };
}
char* _Mid;
if (_Ryu_exponent > 0) { // case "172900"
bool _Can_use_ryu;
if (_Ryu_exponent > 10) { // 10^10 is the largest power of 10 that's exactly representable as a float.
_Can_use_ryu = false;
} else {
// Ryu generated X: __v.__mantissa * 10^_Ryu_exponent
// __v.__mantissa == 2^_Trailing_zero_bits * (__v.__mantissa >> _Trailing_zero_bits)
// 10^_Ryu_exponent == 2^_Ryu_exponent * 5^_Ryu_exponent
// _Trailing_zero_bits is [0, 29] (aside: because 2^29 is the largest power of 2
// with 9 decimal digits, which is float's round-trip limit.)
// _Ryu_exponent is [1, 10].
// Normalization adds [2, 23] (aside: at least 2 because the pre-normalized mantissa is at least 5).
// This adds up to [3, 62], which is well below float's maximum binary exponent 127.
// Therefore, we just need to consider (__v.__mantissa >> _Trailing_zero_bits) * 5^_Ryu_exponent.
// If that product would exceed 24 bits, then X can't be exactly represented as a float.
// (That's not a problem for round-tripping, because X is close enough to the original float,
// but X isn't mathematically equal to the original float.) This requires a high-precision fallback.
// If the product is 24 bits or smaller, then X can be exactly represented as a float (and we don't
// need to re-synthesize it; the original float must have been X, because Ryu wouldn't produce the
// same output for two different floats X and Y). This allows Ryu's output to be used (zero-filled).
// (2^24 - 1) / 5^0 (for indexing), (2^24 - 1) / 5^1, ..., (2^24 - 1) / 5^10
static constexpr uint32_t _Max_shifted_mantissa[11] = {
16777215, 3355443, 671088, 134217, 26843, 5368, 1073, 214, 42, 8, 1 };
unsigned long _Trailing_zero_bits;
(void) _BitScanForward(&_Trailing_zero_bits, __v.__mantissa); // __v.__mantissa is guaranteed nonzero
const uint32_t _Shifted_mantissa = __v.__mantissa >> _Trailing_zero_bits;
_Can_use_ryu = _Shifted_mantissa <= _Max_shifted_mantissa[_Ryu_exponent];
}
if (!_Can_use_ryu) {
const uint32_t _Mantissa2 = __ieeeMantissa | (1u << __FLOAT_MANTISSA_BITS); // restore implicit bit
const int32_t _Exponent2 = static_cast<int32_t>(__ieeeExponent)
- __FLOAT_BIAS - __FLOAT_MANTISSA_BITS; // bias and normalization
// Performance note: We've already called Ryu, so this will redundantly perform buffering and bounds checking.
return _Large_integer_to_chars(_First, _Last, _Mantissa2, _Exponent2);
}
// _Can_use_ryu
// Print the decimal digits, left-aligned within [_First, _First + _Total_fixed_length).
_Mid = _First + __olength;
} else { // cases "1729", "17.29", and "0.001729"
// Print the decimal digits, right-aligned within [_First, _First + _Total_fixed_length).
_Mid = _First + _Total_fixed_length;
}
while (_Output >= 10000) {
#ifdef __clang__ // TRANSITION, LLVM-38217
const uint32_t __c = _Output - 10000 * (_Output / 10000);
#else
const uint32_t __c = _Output % 10000;
#endif
_Output /= 10000;
const uint32_t __c0 = (__c % 100) << 1;
const uint32_t __c1 = (__c / 100) << 1;
std::memcpy(_Mid -= 2, __DIGIT_TABLE + __c0, 2);
std::memcpy(_Mid -= 2, __DIGIT_TABLE + __c1, 2);
}
if (_Output >= 100) {
const uint32_t __c = (_Output % 100) << 1;
_Output /= 100;
std::memcpy(_Mid -= 2, __DIGIT_TABLE + __c, 2);
}
if (_Output >= 10) {
const uint32_t __c = _Output << 1;
std::memcpy(_Mid -= 2, __DIGIT_TABLE + __c, 2);
} else {
*--_Mid = static_cast<char>('0' + _Output);
}
if (_Ryu_exponent > 0) { // case "172900" with _Can_use_ryu
// Performance note: it might be more efficient to do this immediately after setting _Mid.
std::memset(_First + __olength, '0', static_cast<size_t>(_Ryu_exponent));
} else if (_Ryu_exponent == 0) { // case "1729"
// Done!
} else if (_Whole_digits > 0) { // case "17.29"
// Performance note: moving digits might not be optimal.
std::memmove(_First, _First + 1, static_cast<size_t>(_Whole_digits));
_First[_Whole_digits] = '.';
} else { // case "0.001729"
// Performance note: a larger memset() followed by overwriting '.' might be more efficient.
_First[0] = '0';
_First[1] = '.';
std::memset(_First + 2, '0', static_cast<size_t>(-_Whole_digits));
}
return { _First + _Total_fixed_length, errc{} };
}
const uint32_t _Total_scientific_length =
__olength + (__olength > 1) + 4; // digits + possible decimal point + scientific exponent
if (_Last - _First < static_cast<ptrdiff_t>(_Total_scientific_length)) {
return { _Last, errc::value_too_large };
}
char* const __result = _First;
// Print the decimal digits.
uint32_t __i = 0;
while (_Output >= 10000) {
#ifdef __clang__ // TRANSITION, LLVM-38217
const uint32_t __c = _Output - 10000 * (_Output / 10000);
#else
const uint32_t __c = _Output % 10000;
#endif
_Output /= 10000;
const uint32_t __c0 = (__c % 100) << 1;
const uint32_t __c1 = (__c / 100) << 1;
std::memcpy(__result + __olength - __i - 1, __DIGIT_TABLE + __c0, 2);
std::memcpy(__result + __olength - __i - 3, __DIGIT_TABLE + __c1, 2);
__i += 4;
}
if (_Output >= 100) {
const uint32_t __c = (_Output % 100) << 1;
_Output /= 100;
std::memcpy(__result + __olength - __i - 1, __DIGIT_TABLE + __c, 2);
__i += 2;
}
if (_Output >= 10) {
const uint32_t __c = _Output << 1;
// We can't use memcpy here: the decimal dot goes between these two digits.
__result[2] = __DIGIT_TABLE[__c + 1];
__result[0] = __DIGIT_TABLE[__c];
} else {
__result[0] = static_cast<char>('0' + _Output);
}
// Print decimal point if needed.
uint32_t __index;
if (__olength > 1) {
__result[1] = '.';
__index = __olength + 1;
} else {
__index = 1;
}
// Print the exponent.
__result[__index++] = 'e';
if (_Scientific_exponent < 0) {
__result[__index++] = '-';
_Scientific_exponent = -_Scientific_exponent;
} else {
__result[__index++] = '+';
}
std::memcpy(__result + __index, __DIGIT_TABLE + 2 * _Scientific_exponent, 2);
__index += 2;
return { _First + _Total_scientific_length, errc{} };
}
[[nodiscard]] to_chars_result __f2s_buffered_n(char* const _First, char* const _Last, const float __f,
const chars_format _Fmt) {
// Step 1: Decode the floating-point number, and unify normalized and subnormal cases.
const uint32_t __bits = __float_to_bits(__f);
// Case distinction; exit early for the easy cases.
if (__bits == 0) {
if (_Fmt == chars_format::scientific) {
if (_Last - _First < 5) {
return { _Last, errc::value_too_large };
}
std::memcpy(_First, "0e+00", 5);
return { _First + 5, errc{} };
}
// Print "0" for chars_format::fixed, chars_format::general, and chars_format{}.
if (_First == _Last) {
return { _Last, errc::value_too_large };
}
*_First = '0';
return { _First + 1, errc{} };
}
// Decode __bits into mantissa and exponent.
const uint32_t __ieeeMantissa = __bits & ((1u << __FLOAT_MANTISSA_BITS) - 1);
const uint32_t __ieeeExponent = __bits >> __FLOAT_MANTISSA_BITS;
// When _Fmt == chars_format::fixed and the floating-point number is a large integer,
// it's faster to skip Ryu and immediately print the integer exactly.
if (_Fmt == chars_format::fixed) {
const uint32_t _Mantissa2 = __ieeeMantissa | (1u << __FLOAT_MANTISSA_BITS); // restore implicit bit
const int32_t _Exponent2 = static_cast<int32_t>(__ieeeExponent)
- __FLOAT_BIAS - __FLOAT_MANTISSA_BITS; // bias and normalization
// Normal values are equal to _Mantissa2 * 2^_Exponent2.
// (Subnormals are different, but they'll be rejected by the _Exponent2 test here, so they can be ignored.)
if (_Exponent2 > 0) {
return _Large_integer_to_chars(_First, _Last, _Mantissa2, _Exponent2);
}
}
const __floating_decimal_32 __v = __f2d(__ieeeMantissa, __ieeeExponent);
return __to_chars(_First, _Last, __v, _Fmt, __ieeeMantissa, __ieeeExponent);
}
_LIBCPP_END_NAMESPACE_STD
// clang-format on
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