719 lines · cpp
1//===----------------------------------------------------------------------===//2//3// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.4// See https://llvm.org/LICENSE.txt for license information.5// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception6//7//===----------------------------------------------------------------------===//8 9// Copyright (c) Microsoft Corporation.10// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception11 12// Copyright 2018 Ulf Adams13// Copyright (c) Microsoft Corporation. All rights reserved.14 15// Boost Software License - Version 1.0 - August 17th, 200316 17// Permission is hereby granted, free of charge, to any person or organization18// obtaining a copy of the software and accompanying documentation covered by19// this license (the "Software") to use, reproduce, display, distribute,20// execute, and transmit the Software, and to prepare derivative works of the21// Software, and to permit third-parties to whom the Software is furnished to22// do so, all subject to the following:23 24// The copyright notices in the Software and this entire statement, including25// the above license grant, this restriction and the following disclaimer,26// must be included in all copies of the Software, in whole or in part, and27// all derivative works of the Software, unless such copies or derivative28// works are solely in the form of machine-executable object code generated by29// a source language processor.30 31// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR32// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,33// FITNESS FOR A PARTICULAR PURPOSE, TITLE AND NON-INFRINGEMENT. IN NO EVENT34// SHALL THE COPYRIGHT HOLDERS OR ANYONE DISTRIBUTING THE SOFTWARE BE LIABLE35// FOR ANY DAMAGES OR OTHER LIABILITY, WHETHER IN CONTRACT, TORT OR OTHERWISE,36// ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER37// DEALINGS IN THE SOFTWARE.38 39// Avoid formatting to keep the changes with the original code minimal.40// clang-format off41 42#include <__assert>43#include <__config>44#include <charconv>45#include <cstdint>46#include <cstddef>47 48#include "include/ryu/common.h"49#include "include/ryu/d2fixed.h"50#include "include/ryu/d2s_intrinsics.h"51#include "include/ryu/digit_table.h"52#include "include/ryu/f2s.h"53#include "include/ryu/ryu.h"54 55_LIBCPP_BEGIN_NAMESPACE_STD56 57inline constexpr int __FLOAT_MANTISSA_BITS = 23;58inline constexpr int __FLOAT_EXPONENT_BITS = 8;59inline constexpr int __FLOAT_BIAS = 127;60 61inline constexpr int __FLOAT_POW5_INV_BITCOUNT = 59;62inline constexpr uint64_t __FLOAT_POW5_INV_SPLIT[31] = {63 576460752303423489u, 461168601842738791u, 368934881474191033u, 295147905179352826u,64 472236648286964522u, 377789318629571618u, 302231454903657294u, 483570327845851670u,65 386856262276681336u, 309485009821345069u, 495176015714152110u, 396140812571321688u,66 316912650057057351u, 507060240091291761u, 405648192073033409u, 324518553658426727u,67 519229685853482763u, 415383748682786211u, 332306998946228969u, 531691198313966350u,68 425352958651173080u, 340282366920938464u, 544451787073501542u, 435561429658801234u,69 348449143727040987u, 557518629963265579u, 446014903970612463u, 356811923176489971u,70 570899077082383953u, 456719261665907162u, 365375409332725730u71};72inline constexpr int __FLOAT_POW5_BITCOUNT = 61;73inline constexpr uint64_t __FLOAT_POW5_SPLIT[47] = {74 1152921504606846976u, 1441151880758558720u, 1801439850948198400u, 2251799813685248000u,75 1407374883553280000u, 1759218604441600000u, 2199023255552000000u, 1374389534720000000u,76 1717986918400000000u, 2147483648000000000u, 1342177280000000000u, 1677721600000000000u,77 2097152000000000000u, 1310720000000000000u, 1638400000000000000u, 2048000000000000000u,78 1280000000000000000u, 1600000000000000000u, 2000000000000000000u, 1250000000000000000u,79 1562500000000000000u, 1953125000000000000u, 1220703125000000000u, 1525878906250000000u,80 1907348632812500000u, 1192092895507812500u, 1490116119384765625u, 1862645149230957031u,81 1164153218269348144u, 1455191522836685180u, 1818989403545856475u, 2273736754432320594u,82 1421085471520200371u, 1776356839400250464u, 2220446049250313080u, 1387778780781445675u,83 1734723475976807094u, 2168404344971008868u, 1355252715606880542u, 1694065894508600678u,84 2117582368135750847u, 1323488980084844279u, 1654361225106055349u, 2067951531382569187u,85 1292469707114105741u, 1615587133892632177u, 2019483917365790221u86};87 88[[nodiscard]] _LIBCPP_HIDE_FROM_ABI inline uint32_t __pow5Factor(uint32_t __value) {89 uint32_t __count = 0;90 for (;;) {91 _LIBCPP_ASSERT_INTERNAL(__value != 0, "");92 const uint32_t __q = __value / 5;93 const uint32_t __r = __value % 5;94 if (__r != 0) {95 break;96 }97 __value = __q;98 ++__count;99 }100 return __count;101}102 103// Returns true if __value is divisible by 5^__p.104[[nodiscard]] _LIBCPP_HIDE_FROM_ABI inline bool __multipleOfPowerOf5(const uint32_t __value, const uint32_t __p) {105 return __pow5Factor(__value) >= __p;106}107 108// Returns true if __value is divisible by 2^__p.109[[nodiscard]] _LIBCPP_HIDE_FROM_ABI inline bool __multipleOfPowerOf2(const uint32_t __value, const uint32_t __p) {110 _LIBCPP_ASSERT_INTERNAL(__value != 0, "");111 _LIBCPP_ASSERT_INTERNAL(__p < 32, "");112 // __builtin_ctz doesn't appear to be faster here.113 return (__value & ((1u << __p) - 1)) == 0;114}115 116[[nodiscard]] _LIBCPP_HIDE_FROM_ABI inline uint32_t __mulShift(const uint32_t __m, const uint64_t __factor, const int32_t __shift) {117 _LIBCPP_ASSERT_INTERNAL(__shift > 32, "");118 119 // The casts here help MSVC to avoid calls to the __allmul library120 // function.121 const uint32_t __factorLo = static_cast<uint32_t>(__factor);122 const uint32_t __factorHi = static_cast<uint32_t>(__factor >> 32);123 const uint64_t __bits0 = static_cast<uint64_t>(__m) * __factorLo;124 const uint64_t __bits1 = static_cast<uint64_t>(__m) * __factorHi;125 126#ifndef _LIBCPP_64_BIT127 // On 32-bit platforms we can avoid a 64-bit shift-right since we only128 // need the upper 32 bits of the result and the shift value is > 32.129 const uint32_t __bits0Hi = static_cast<uint32_t>(__bits0 >> 32);130 uint32_t __bits1Lo = static_cast<uint32_t>(__bits1);131 uint32_t __bits1Hi = static_cast<uint32_t>(__bits1 >> 32);132 __bits1Lo += __bits0Hi;133 __bits1Hi += (__bits1Lo < __bits0Hi);134 const int32_t __s = __shift - 32;135 return (__bits1Hi << (32 - __s)) | (__bits1Lo >> __s);136#else // ^^^ 32-bit ^^^ / vvv 64-bit vvv137 const uint64_t __sum = (__bits0 >> 32) + __bits1;138 const uint64_t __shiftedSum = __sum >> (__shift - 32);139 _LIBCPP_ASSERT_INTERNAL(__shiftedSum <= UINT32_MAX, "");140 return static_cast<uint32_t>(__shiftedSum);141#endif // ^^^ 64-bit ^^^142}143 144[[nodiscard]] _LIBCPP_HIDE_FROM_ABI inline uint32_t __mulPow5InvDivPow2(const uint32_t __m, const uint32_t __q, const int32_t __j) {145 return __mulShift(__m, __FLOAT_POW5_INV_SPLIT[__q], __j);146}147 148[[nodiscard]] _LIBCPP_HIDE_FROM_ABI inline uint32_t __mulPow5divPow2(const uint32_t __m, const uint32_t __i, const int32_t __j) {149 return __mulShift(__m, __FLOAT_POW5_SPLIT[__i], __j);150}151 152// A floating decimal representing m * 10^e.153struct __floating_decimal_32 {154 uint32_t __mantissa;155 int32_t __exponent;156};157 158[[nodiscard]] _LIBCPP_HIDE_FROM_ABI inline __floating_decimal_32 __f2d(const uint32_t __ieeeMantissa, const uint32_t __ieeeExponent) {159 int32_t __e2;160 uint32_t __m2;161 if (__ieeeExponent == 0) {162 // We subtract 2 so that the bounds computation has 2 additional bits.163 __e2 = 1 - __FLOAT_BIAS - __FLOAT_MANTISSA_BITS - 2;164 __m2 = __ieeeMantissa;165 } else {166 __e2 = static_cast<int32_t>(__ieeeExponent) - __FLOAT_BIAS - __FLOAT_MANTISSA_BITS - 2;167 __m2 = (1u << __FLOAT_MANTISSA_BITS) | __ieeeMantissa;168 }169 const bool __even = (__m2 & 1) == 0;170 const bool __acceptBounds = __even;171 172 // Step 2: Determine the interval of valid decimal representations.173 const uint32_t __mv = 4 * __m2;174 const uint32_t __mp = 4 * __m2 + 2;175 // Implicit bool -> int conversion. True is 1, false is 0.176 const uint32_t __mmShift = __ieeeMantissa != 0 || __ieeeExponent <= 1;177 const uint32_t __mm = 4 * __m2 - 1 - __mmShift;178 179 // Step 3: Convert to a decimal power base using 64-bit arithmetic.180 uint32_t __vr, __vp, __vm;181 int32_t __e10;182 bool __vmIsTrailingZeros = false;183 bool __vrIsTrailingZeros = false;184 uint8_t __lastRemovedDigit = 0;185 if (__e2 >= 0) {186 const uint32_t __q = __log10Pow2(__e2);187 __e10 = static_cast<int32_t>(__q);188 const int32_t __k = __FLOAT_POW5_INV_BITCOUNT + __pow5bits(static_cast<int32_t>(__q)) - 1;189 const int32_t __i = -__e2 + static_cast<int32_t>(__q) + __k;190 __vr = __mulPow5InvDivPow2(__mv, __q, __i);191 __vp = __mulPow5InvDivPow2(__mp, __q, __i);192 __vm = __mulPow5InvDivPow2(__mm, __q, __i);193 if (__q != 0 && (__vp - 1) / 10 <= __vm / 10) {194 // We need to know one removed digit even if we are not going to loop below. We could use195 // __q = X - 1 above, except that would require 33 bits for the result, and we've found that196 // 32-bit arithmetic is faster even on 64-bit machines.197 const int32_t __l = __FLOAT_POW5_INV_BITCOUNT + __pow5bits(static_cast<int32_t>(__q - 1)) - 1;198 __lastRemovedDigit = static_cast<uint8_t>(__mulPow5InvDivPow2(__mv, __q - 1,199 -__e2 + static_cast<int32_t>(__q) - 1 + __l) % 10);200 }201 if (__q <= 9) {202 // The largest power of 5 that fits in 24 bits is 5^10, but __q <= 9 seems to be safe as well.203 // Only one of __mp, __mv, and __mm can be a multiple of 5, if any.204 if (__mv % 5 == 0) {205 __vrIsTrailingZeros = __multipleOfPowerOf5(__mv, __q);206 } else if (__acceptBounds) {207 __vmIsTrailingZeros = __multipleOfPowerOf5(__mm, __q);208 } else {209 __vp -= __multipleOfPowerOf5(__mp, __q);210 }211 }212 } else {213 const uint32_t __q = __log10Pow5(-__e2);214 __e10 = static_cast<int32_t>(__q) + __e2;215 const int32_t __i = -__e2 - static_cast<int32_t>(__q);216 const int32_t __k = __pow5bits(__i) - __FLOAT_POW5_BITCOUNT;217 int32_t __j = static_cast<int32_t>(__q) - __k;218 __vr = __mulPow5divPow2(__mv, static_cast<uint32_t>(__i), __j);219 __vp = __mulPow5divPow2(__mp, static_cast<uint32_t>(__i), __j);220 __vm = __mulPow5divPow2(__mm, static_cast<uint32_t>(__i), __j);221 if (__q != 0 && (__vp - 1) / 10 <= __vm / 10) {222 __j = static_cast<int32_t>(__q) - 1 - (__pow5bits(__i + 1) - __FLOAT_POW5_BITCOUNT);223 __lastRemovedDigit = static_cast<uint8_t>(__mulPow5divPow2(__mv, static_cast<uint32_t>(__i + 1), __j) % 10);224 }225 if (__q <= 1) {226 // {__vr,__vp,__vm} is trailing zeros if {__mv,__mp,__mm} has at least __q trailing 0 bits.227 // __mv = 4 * __m2, so it always has at least two trailing 0 bits.228 __vrIsTrailingZeros = true;229 if (__acceptBounds) {230 // __mm = __mv - 1 - __mmShift, so it has 1 trailing 0 bit iff __mmShift == 1.231 __vmIsTrailingZeros = __mmShift == 1;232 } else {233 // __mp = __mv + 2, so it always has at least one trailing 0 bit.234 --__vp;235 }236 } else if (__q < 31) { // TRANSITION(ulfjack): Use a tighter bound here.237 __vrIsTrailingZeros = __multipleOfPowerOf2(__mv, __q - 1);238 }239 }240 241 // Step 4: Find the shortest decimal representation in the interval of valid representations.242 int32_t __removed = 0;243 uint32_t _Output;244 if (__vmIsTrailingZeros || __vrIsTrailingZeros) {245 // General case, which happens rarely (~4.0%).246 while (__vp / 10 > __vm / 10) {247#ifdef __clang__ // TRANSITION, LLVM-23106248 __vmIsTrailingZeros &= __vm - (__vm / 10) * 10 == 0;249#else250 __vmIsTrailingZeros &= __vm % 10 == 0;251#endif252 __vrIsTrailingZeros &= __lastRemovedDigit == 0;253 __lastRemovedDigit = static_cast<uint8_t>(__vr % 10);254 __vr /= 10;255 __vp /= 10;256 __vm /= 10;257 ++__removed;258 }259 if (__vmIsTrailingZeros) {260 while (__vm % 10 == 0) {261 __vrIsTrailingZeros &= __lastRemovedDigit == 0;262 __lastRemovedDigit = static_cast<uint8_t>(__vr % 10);263 __vr /= 10;264 __vp /= 10;265 __vm /= 10;266 ++__removed;267 }268 }269 if (__vrIsTrailingZeros && __lastRemovedDigit == 5 && __vr % 2 == 0) {270 // Round even if the exact number is .....50..0.271 __lastRemovedDigit = 4;272 }273 // We need to take __vr + 1 if __vr is outside bounds or we need to round up.274 _Output = __vr + ((__vr == __vm && (!__acceptBounds || !__vmIsTrailingZeros)) || __lastRemovedDigit >= 5);275 } else {276 // Specialized for the common case (~96.0%). Percentages below are relative to this.277 // Loop iterations below (approximately):278 // 0: 13.6%, 1: 70.7%, 2: 14.1%, 3: 1.39%, 4: 0.14%, 5+: 0.01%279 while (__vp / 10 > __vm / 10) {280 __lastRemovedDigit = static_cast<uint8_t>(__vr % 10);281 __vr /= 10;282 __vp /= 10;283 __vm /= 10;284 ++__removed;285 }286 // We need to take __vr + 1 if __vr is outside bounds or we need to round up.287 _Output = __vr + (__vr == __vm || __lastRemovedDigit >= 5);288 }289 const int32_t __exp = __e10 + __removed;290 291 __floating_decimal_32 __fd;292 __fd.__exponent = __exp;293 __fd.__mantissa = _Output;294 return __fd;295}296 297[[nodiscard]] _LIBCPP_HIDE_FROM_ABI inline to_chars_result _Large_integer_to_chars(char* const _First, char* const _Last,298 const uint32_t _Mantissa2, const int32_t _Exponent2) {299 300 // Print the integer _Mantissa2 * 2^_Exponent2 exactly.301 302 // For nonzero integers, _Exponent2 >= -23. (The minimum value occurs when _Mantissa2 * 2^_Exponent2 is 1.303 // In that case, _Mantissa2 is the implicit 1 bit followed by 23 zeros, so _Exponent2 is -23 to shift away304 // the zeros.) The dense range of exactly representable integers has negative or zero exponents305 // (as positive exponents make the range non-dense). For that dense range, Ryu will always be used:306 // every digit is necessary to uniquely identify the value, so Ryu must print them all.307 308 // Positive exponents are the non-dense range of exactly representable integers.309 // This contains all of the values for which Ryu can't be used (and a few Ryu-friendly values).310 311 // Performance note: Long division appears to be faster than losslessly widening float to double and calling312 // __d2fixed_buffered_n(). If __f2fixed_buffered_n() is implemented, it might be faster than long division.313 314 _LIBCPP_ASSERT_INTERNAL(_Exponent2 > 0, "");315 _LIBCPP_ASSERT_INTERNAL(_Exponent2 <= 104, ""); // because __ieeeExponent <= 254316 317 // Manually represent _Mantissa2 * 2^_Exponent2 as a large integer. _Mantissa2 is always 24 bits318 // (due to the implicit bit), while _Exponent2 indicates a shift of at most 104 bits.319 // 24 + 104 equals 128 equals 4 * 32, so we need exactly 4 32-bit elements.320 // We use a little-endian representation, visualized like this:321 322 // << left shift <<323 // most significant324 // _Data[3] _Data[2] _Data[1] _Data[0]325 // least significant326 // >> right shift >>327 328 constexpr uint32_t _Data_size = 4;329 uint32_t _Data[_Data_size]{};330 331 // _Maxidx is the index of the most significant nonzero element.332 uint32_t _Maxidx = ((24 + static_cast<uint32_t>(_Exponent2) + 31) / 32) - 1;333 _LIBCPP_ASSERT_INTERNAL(_Maxidx < _Data_size, "");334 335 const uint32_t _Bit_shift = static_cast<uint32_t>(_Exponent2) % 32;336 if (_Bit_shift <= 8) { // _Mantissa2's 24 bits don't cross an element boundary337 _Data[_Maxidx] = _Mantissa2 << _Bit_shift;338 } else { // _Mantissa2's 24 bits cross an element boundary339 _Data[_Maxidx - 1] = _Mantissa2 << _Bit_shift;340 _Data[_Maxidx] = _Mantissa2 >> (32 - _Bit_shift);341 }342 343 // If Ryu hasn't determined the total output length, we need to buffer the digits generated from right to left344 // by long division. The largest possible float is: 340'282346638'528859811'704183484'516925440345 uint32_t _Blocks[4];346 int32_t _Filled_blocks = 0;347 // From left to right, we're going to print:348 // _Data[0] will be [1, 10] digits.349 // Then if _Filled_blocks > 0:350 // _Blocks[_Filled_blocks - 1], ..., _Blocks[0] will be 0-filled 9-digit blocks.351 352 if (_Maxidx != 0) { // If the integer is actually large, perform long division.353 // Otherwise, skip to printing _Data[0].354 for (;;) {355 // Loop invariant: _Maxidx != 0 (i.e. the integer is actually large)356 357 const uint32_t _Most_significant_elem = _Data[_Maxidx];358 const uint32_t _Initial_remainder = _Most_significant_elem % 1000000000;359 const uint32_t _Initial_quotient = _Most_significant_elem / 1000000000;360 _Data[_Maxidx] = _Initial_quotient;361 uint64_t _Remainder = _Initial_remainder;362 363 // Process less significant elements.364 uint32_t _Idx = _Maxidx;365 do {366 --_Idx; // Initially, _Remainder is at most 10^9 - 1.367 368 // Now, _Remainder is at most (10^9 - 1) * 2^32 + 2^32 - 1, simplified to 10^9 * 2^32 - 1.369 _Remainder = (_Remainder << 32) | _Data[_Idx];370 371 // floor((10^9 * 2^32 - 1) / 10^9) == 2^32 - 1, so uint32_t _Quotient is lossless.372 const uint32_t _Quotient = static_cast<uint32_t>(__div1e9(_Remainder));373 374 // _Remainder is at most 10^9 - 1 again.375 // For uint32_t truncation, see the __mod1e9() comment in d2s_intrinsics.h.376 _Remainder = static_cast<uint32_t>(_Remainder) - 1000000000u * _Quotient;377 378 _Data[_Idx] = _Quotient;379 } while (_Idx != 0);380 381 // Store a 0-filled 9-digit block.382 _Blocks[_Filled_blocks++] = static_cast<uint32_t>(_Remainder);383 384 if (_Initial_quotient == 0) { // Is the large integer shrinking?385 --_Maxidx; // log2(10^9) is 29.9, so we can't shrink by more than one element.386 if (_Maxidx == 0) {387 break; // We've finished long division. Now we need to print _Data[0].388 }389 }390 }391 }392 393 _LIBCPP_ASSERT_INTERNAL(_Data[0] != 0, "");394 for (uint32_t _Idx = 1; _Idx < _Data_size; ++_Idx) {395 _LIBCPP_ASSERT_INTERNAL(_Data[_Idx] == 0, "");396 }397 398 const uint32_t _Data_olength = _Data[0] >= 1000000000 ? 10 : __decimalLength9(_Data[0]);399 const uint32_t _Total_fixed_length = _Data_olength + 9 * _Filled_blocks;400 401 if (_Last - _First < static_cast<ptrdiff_t>(_Total_fixed_length)) {402 return { _Last, errc::value_too_large };403 }404 405 char* _Result = _First;406 407 // Print _Data[0]. While it's up to 10 digits,408 // which is more than Ryu generates, the code below can handle this.409 __append_n_digits(_Data_olength, _Data[0], _Result);410 _Result += _Data_olength;411 412 // Print 0-filled 9-digit blocks.413 for (int32_t _Idx = _Filled_blocks - 1; _Idx >= 0; --_Idx) {414 __append_nine_digits(_Blocks[_Idx], _Result);415 _Result += 9;416 }417 418 return { _Result, errc{} };419}420 421[[nodiscard]] _LIBCPP_HIDE_FROM_ABI inline to_chars_result __to_chars(char* const _First, char* const _Last, const __floating_decimal_32 __v,422 chars_format _Fmt, const uint32_t __ieeeMantissa, const uint32_t __ieeeExponent) {423 // Step 5: Print the decimal representation.424 uint32_t _Output = __v.__mantissa;425 int32_t _Ryu_exponent = __v.__exponent;426 const uint32_t __olength = __decimalLength9(_Output);427 int32_t _Scientific_exponent = _Ryu_exponent + static_cast<int32_t>(__olength) - 1;428 429 if (_Fmt == chars_format{}) {430 int32_t _Lower;431 int32_t _Upper;432 433 if (__olength == 1) {434 // Value | Fixed | Scientific435 // 1e-3 | "0.001" | "1e-03"436 // 1e4 | "10000" | "1e+04"437 _Lower = -3;438 _Upper = 4;439 } else {440 // Value | Fixed | Scientific441 // 1234e-7 | "0.0001234" | "1.234e-04"442 // 1234e5 | "123400000" | "1.234e+08"443 _Lower = -static_cast<int32_t>(__olength + 3);444 _Upper = 5;445 }446 447 if (_Lower <= _Ryu_exponent && _Ryu_exponent <= _Upper) {448 _Fmt = chars_format::fixed;449 } else {450 _Fmt = chars_format::scientific;451 }452 } else if (_Fmt == chars_format::general) {453 // C11 7.21.6.1 "The fprintf function"/8:454 // "Let P equal [...] 6 if the precision is omitted [...].455 // Then, if a conversion with style E would have an exponent of X:456 // - if P > X >= -4, the conversion is with style f [...].457 // - otherwise, the conversion is with style e [...]."458 if (-4 <= _Scientific_exponent && _Scientific_exponent < 6) {459 _Fmt = chars_format::fixed;460 } else {461 _Fmt = chars_format::scientific;462 }463 }464 465 if (_Fmt == chars_format::fixed) {466 // Example: _Output == 1729, __olength == 4467 468 // _Ryu_exponent | Printed | _Whole_digits | _Total_fixed_length | Notes469 // --------------|----------|---------------|----------------------|---------------------------------------470 // 2 | 172900 | 6 | _Whole_digits | Ryu can't be used for printing471 // 1 | 17290 | 5 | (sometimes adjusted) | when the trimmed digits are nonzero.472 // --------------|----------|---------------|----------------------|---------------------------------------473 // 0 | 1729 | 4 | _Whole_digits | Unified length cases.474 // --------------|----------|---------------|----------------------|---------------------------------------475 // -1 | 172.9 | 3 | __olength + 1 | This case can't happen for476 // -2 | 17.29 | 2 | | __olength == 1, but no additional477 // -3 | 1.729 | 1 | | code is needed to avoid it.478 // --------------|----------|---------------|----------------------|---------------------------------------479 // -4 | 0.1729 | 0 | 2 - _Ryu_exponent | C11 7.21.6.1 "The fprintf function"/8:480 // -5 | 0.01729 | -1 | | "If a decimal-point character appears,481 // -6 | 0.001729 | -2 | | at least one digit appears before it."482 483 const int32_t _Whole_digits = static_cast<int32_t>(__olength) + _Ryu_exponent;484 485 uint32_t _Total_fixed_length;486 if (_Ryu_exponent >= 0) { // cases "172900" and "1729"487 _Total_fixed_length = static_cast<uint32_t>(_Whole_digits);488 if (_Output == 1) {489 // Rounding can affect the number of digits.490 // For example, 1e11f is exactly "99999997952" which is 11 digits instead of 12.491 // We can use a lookup table to detect this and adjust the total length.492 static constexpr uint8_t _Adjustment[39] = {493 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 };494 _Total_fixed_length -= _Adjustment[_Ryu_exponent];495 // _Whole_digits doesn't need to be adjusted because these cases won't refer to it later.496 }497 } else if (_Whole_digits > 0) { // case "17.29"498 _Total_fixed_length = __olength + 1;499 } else { // case "0.001729"500 _Total_fixed_length = static_cast<uint32_t>(2 - _Ryu_exponent);501 }502 503 if (_Last - _First < static_cast<ptrdiff_t>(_Total_fixed_length)) {504 return { _Last, errc::value_too_large };505 }506 507 char* _Mid;508 if (_Ryu_exponent > 0) { // case "172900"509 bool _Can_use_ryu;510 511 if (_Ryu_exponent > 10) { // 10^10 is the largest power of 10 that's exactly representable as a float.512 _Can_use_ryu = false;513 } else {514 // Ryu generated X: __v.__mantissa * 10^_Ryu_exponent515 // __v.__mantissa == 2^_Trailing_zero_bits * (__v.__mantissa >> _Trailing_zero_bits)516 // 10^_Ryu_exponent == 2^_Ryu_exponent * 5^_Ryu_exponent517 518 // _Trailing_zero_bits is [0, 29] (aside: because 2^29 is the largest power of 2519 // with 9 decimal digits, which is float's round-trip limit.)520 // _Ryu_exponent is [1, 10].521 // Normalization adds [2, 23] (aside: at least 2 because the pre-normalized mantissa is at least 5).522 // This adds up to [3, 62], which is well below float's maximum binary exponent 127.523 524 // Therefore, we just need to consider (__v.__mantissa >> _Trailing_zero_bits) * 5^_Ryu_exponent.525 526 // If that product would exceed 24 bits, then X can't be exactly represented as a float.527 // (That's not a problem for round-tripping, because X is close enough to the original float,528 // but X isn't mathematically equal to the original float.) This requires a high-precision fallback.529 530 // If the product is 24 bits or smaller, then X can be exactly represented as a float (and we don't531 // need to re-synthesize it; the original float must have been X, because Ryu wouldn't produce the532 // same output for two different floats X and Y). This allows Ryu's output to be used (zero-filled).533 534 // (2^24 - 1) / 5^0 (for indexing), (2^24 - 1) / 5^1, ..., (2^24 - 1) / 5^10535 static constexpr uint32_t _Max_shifted_mantissa[11] = {536 16777215, 3355443, 671088, 134217, 26843, 5368, 1073, 214, 42, 8, 1 };537 538 unsigned long _Trailing_zero_bits;539 (void) _BitScanForward(&_Trailing_zero_bits, __v.__mantissa); // __v.__mantissa is guaranteed nonzero540 const uint32_t _Shifted_mantissa = __v.__mantissa >> _Trailing_zero_bits;541 _Can_use_ryu = _Shifted_mantissa <= _Max_shifted_mantissa[_Ryu_exponent];542 }543 544 if (!_Can_use_ryu) {545 const uint32_t _Mantissa2 = __ieeeMantissa | (1u << __FLOAT_MANTISSA_BITS); // restore implicit bit546 const int32_t _Exponent2 = static_cast<int32_t>(__ieeeExponent)547 - __FLOAT_BIAS - __FLOAT_MANTISSA_BITS; // bias and normalization548 549 // Performance note: We've already called Ryu, so this will redundantly perform buffering and bounds checking.550 return _Large_integer_to_chars(_First, _Last, _Mantissa2, _Exponent2);551 }552 553 // _Can_use_ryu554 // Print the decimal digits, left-aligned within [_First, _First + _Total_fixed_length).555 _Mid = _First + __olength;556 } else { // cases "1729", "17.29", and "0.001729"557 // Print the decimal digits, right-aligned within [_First, _First + _Total_fixed_length).558 _Mid = _First + _Total_fixed_length;559 }560 561 while (_Output >= 10000) {562#ifdef __clang__ // TRANSITION, LLVM-38217563 const uint32_t __c = _Output - 10000 * (_Output / 10000);564#else565 const uint32_t __c = _Output % 10000;566#endif567 _Output /= 10000;568 const uint32_t __c0 = (__c % 100) << 1;569 const uint32_t __c1 = (__c / 100) << 1;570 std::memcpy(_Mid -= 2, __DIGIT_TABLE + __c0, 2);571 std::memcpy(_Mid -= 2, __DIGIT_TABLE + __c1, 2);572 }573 if (_Output >= 100) {574 const uint32_t __c = (_Output % 100) << 1;575 _Output /= 100;576 std::memcpy(_Mid -= 2, __DIGIT_TABLE + __c, 2);577 }578 if (_Output >= 10) {579 const uint32_t __c = _Output << 1;580 std::memcpy(_Mid -= 2, __DIGIT_TABLE + __c, 2);581 } else {582 *--_Mid = static_cast<char>('0' + _Output);583 }584 585 if (_Ryu_exponent > 0) { // case "172900" with _Can_use_ryu586 // Performance note: it might be more efficient to do this immediately after setting _Mid.587 std::memset(_First + __olength, '0', static_cast<size_t>(_Ryu_exponent));588 } else if (_Ryu_exponent == 0) { // case "1729"589 // Done!590 } else if (_Whole_digits > 0) { // case "17.29"591 // Performance note: moving digits might not be optimal.592 std::memmove(_First, _First + 1, static_cast<size_t>(_Whole_digits));593 _First[_Whole_digits] = '.';594 } else { // case "0.001729"595 // Performance note: a larger memset() followed by overwriting '.' might be more efficient.596 _First[0] = '0';597 _First[1] = '.';598 std::memset(_First + 2, '0', static_cast<size_t>(-_Whole_digits));599 }600 601 return { _First + _Total_fixed_length, errc{} };602 }603 604 const uint32_t _Total_scientific_length =605 __olength + (__olength > 1) + 4; // digits + possible decimal point + scientific exponent606 if (_Last - _First < static_cast<ptrdiff_t>(_Total_scientific_length)) {607 return { _Last, errc::value_too_large };608 }609 char* const __result = _First;610 611 // Print the decimal digits.612 uint32_t __i = 0;613 while (_Output >= 10000) {614#ifdef __clang__ // TRANSITION, LLVM-38217615 const uint32_t __c = _Output - 10000 * (_Output / 10000);616#else617 const uint32_t __c = _Output % 10000;618#endif619 _Output /= 10000;620 const uint32_t __c0 = (__c % 100) << 1;621 const uint32_t __c1 = (__c / 100) << 1;622 std::memcpy(__result + __olength - __i - 1, __DIGIT_TABLE + __c0, 2);623 std::memcpy(__result + __olength - __i - 3, __DIGIT_TABLE + __c1, 2);624 __i += 4;625 }626 if (_Output >= 100) {627 const uint32_t __c = (_Output % 100) << 1;628 _Output /= 100;629 std::memcpy(__result + __olength - __i - 1, __DIGIT_TABLE + __c, 2);630 __i += 2;631 }632 if (_Output >= 10) {633 const uint32_t __c = _Output << 1;634 // We can't use memcpy here: the decimal dot goes between these two digits.635 __result[2] = __DIGIT_TABLE[__c + 1];636 __result[0] = __DIGIT_TABLE[__c];637 } else {638 __result[0] = static_cast<char>('0' + _Output);639 }640 641 // Print decimal point if needed.642 uint32_t __index;643 if (__olength > 1) {644 __result[1] = '.';645 __index = __olength + 1;646 } else {647 __index = 1;648 }649 650 // Print the exponent.651 __result[__index++] = 'e';652 if (_Scientific_exponent < 0) {653 __result[__index++] = '-';654 _Scientific_exponent = -_Scientific_exponent;655 } else {656 __result[__index++] = '+';657 }658 659 std::memcpy(__result + __index, __DIGIT_TABLE + 2 * _Scientific_exponent, 2);660 __index += 2;661 662 return { _First + _Total_scientific_length, errc{} };663}664 665[[nodiscard]] to_chars_result __f2s_buffered_n(char* const _First, char* const _Last, const float __f,666 const chars_format _Fmt) {667 668 // Step 1: Decode the floating-point number, and unify normalized and subnormal cases.669 const uint32_t __bits = __float_to_bits(__f);670 671 // Case distinction; exit early for the easy cases.672 if (__bits == 0) {673 if (_Fmt == chars_format::scientific) {674 if (_Last - _First < 5) {675 return { _Last, errc::value_too_large };676 }677 678 std::memcpy(_First, "0e+00", 5);679 680 return { _First + 5, errc{} };681 }682 683 // Print "0" for chars_format::fixed, chars_format::general, and chars_format{}.684 if (_First == _Last) {685 return { _Last, errc::value_too_large };686 }687 688 *_First = '0';689 690 return { _First + 1, errc{} };691 }692 693 // Decode __bits into mantissa and exponent.694 const uint32_t __ieeeMantissa = __bits & ((1u << __FLOAT_MANTISSA_BITS) - 1);695 const uint32_t __ieeeExponent = __bits >> __FLOAT_MANTISSA_BITS;696 697 // When _Fmt == chars_format::fixed and the floating-point number is a large integer,698 // it's faster to skip Ryu and immediately print the integer exactly.699 if (_Fmt == chars_format::fixed) {700 const uint32_t _Mantissa2 = __ieeeMantissa | (1u << __FLOAT_MANTISSA_BITS); // restore implicit bit701 const int32_t _Exponent2 = static_cast<int32_t>(__ieeeExponent)702 - __FLOAT_BIAS - __FLOAT_MANTISSA_BITS; // bias and normalization703 704 // Normal values are equal to _Mantissa2 * 2^_Exponent2.705 // (Subnormals are different, but they'll be rejected by the _Exponent2 test here, so they can be ignored.)706 707 if (_Exponent2 > 0) {708 return _Large_integer_to_chars(_First, _Last, _Mantissa2, _Exponent2);709 }710 }711 712 const __floating_decimal_32 __v = __f2d(__ieeeMantissa, __ieeeExponent);713 return __to_chars(_First, _Last, __v, _Fmt, __ieeeMantissa, __ieeeExponent);714}715 716_LIBCPP_END_NAMESPACE_STD717 718// clang-format on719