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-exception 6// 7//===----------------------------------------------------------------------===// 8 9// Copyright (c) Microsoft Corporation. 10// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception 11 12// Copyright 2018 Ulf Adams 13// Copyright (c) Microsoft Corporation. All rights reserved. 14 15// Boost Software License - Version 1.0 - August 17th, 2003 16 17// Permission is hereby granted, free of charge, to any person or organization 18// obtaining a copy of the software and accompanying documentation covered by 19// this license (the "Software") to use, reproduce, display, distribute, 20// execute, and transmit the Software, and to prepare derivative works of the 21// Software, and to permit third-parties to whom the Software is furnished to 22// do so, all subject to the following: 23 24// The copyright notices in the Software and this entire statement, including 25// 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, and 27// all derivative works of the Software, unless such copies or derivative 28// works are solely in the form of machine-executable object code generated by 29// a source language processor. 30 31// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR 32// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, 33// FITNESS FOR A PARTICULAR PURPOSE, TITLE AND NON-INFRINGEMENT. IN NO EVENT 34// SHALL THE COPYRIGHT HOLDERS OR ANYONE DISTRIBUTING THE SOFTWARE BE LIABLE 35// 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 OTHER 37// DEALINGS IN THE SOFTWARE. 38 39// Avoid formatting to keep the changes with the original code minimal. 40// clang-format off 41 42#include <__assert> 43#include <__config> 44#include <charconv> 45#include <cstring> 46 47#include "include/ryu/common.h" 48#include "include/ryu/d2fixed.h" 49#include "include/ryu/d2fixed_full_table.h" 50#include "include/ryu/d2s.h" 51#include "include/ryu/d2s_intrinsics.h" 52#include "include/ryu/digit_table.h" 53 54_LIBCPP_BEGIN_NAMESPACE_STD 55 56inline constexpr int __POW10_ADDITIONAL_BITS = 120; 57 58#ifdef _LIBCPP_INTRINSIC128 59// Returns the low 64 bits of the high 128 bits of the 256-bit product of a and b. 60[[nodiscard]] _LIBCPP_HIDE_FROM_ABI inline uint64_t __umul256_hi128_lo64( 61 const uint64_t __aHi, const uint64_t __aLo, const uint64_t __bHi, const uint64_t __bLo) { 62 uint64_t __b00Hi; 63 const uint64_t __b00Lo = __ryu_umul128(__aLo, __bLo, &__b00Hi); 64 uint64_t __b01Hi; 65 const uint64_t __b01Lo = __ryu_umul128(__aLo, __bHi, &__b01Hi); 66 uint64_t __b10Hi; 67 const uint64_t __b10Lo = __ryu_umul128(__aHi, __bLo, &__b10Hi); 68 uint64_t __b11Hi; 69 const uint64_t __b11Lo = __ryu_umul128(__aHi, __bHi, &__b11Hi); 70 (void) __b00Lo; // unused 71 (void) __b11Hi; // unused 72 const uint64_t __temp1Lo = __b10Lo + __b00Hi; 73 const uint64_t __temp1Hi = __b10Hi + (__temp1Lo < __b10Lo); 74 const uint64_t __temp2Lo = __b01Lo + __temp1Lo; 75 const uint64_t __temp2Hi = __b01Hi + (__temp2Lo < __b01Lo); 76 return __b11Lo + __temp1Hi + __temp2Hi; 77} 78 79[[nodiscard]] _LIBCPP_HIDE_FROM_ABI inline uint32_t __uint128_mod1e9(const uint64_t __vHi, const uint64_t __vLo) { 80 // After multiplying, we're going to shift right by 29, then truncate to uint32_t. 81 // This means that we need only 29 + 32 = 61 bits, so we can truncate to uint64_t before shifting. 82 const uint64_t __multiplied = __umul256_hi128_lo64(__vHi, __vLo, 0x89705F4136B4A597u, 0x31680A88F8953031u); 83 84 // For uint32_t truncation, see the __mod1e9() comment in d2s_intrinsics.h. 85 const uint32_t __shifted = static_cast<uint32_t>(__multiplied >> 29); 86 87 return static_cast<uint32_t>(__vLo) - 1000000000 * __shifted; 88} 89#endif // ^^^ intrinsics available ^^^ 90 91[[nodiscard]] _LIBCPP_HIDE_FROM_ABI inline uint32_t __mulShift_mod1e9(const uint64_t __m, const uint64_t* const __mul, const int32_t __j) { 92 uint64_t __high0; // 64 93 const uint64_t __low0 = __ryu_umul128(__m, __mul[0], &__high0); // 0 94 uint64_t __high1; // 128 95 const uint64_t __low1 = __ryu_umul128(__m, __mul[1], &__high1); // 64 96 uint64_t __high2; // 192 97 const uint64_t __low2 = __ryu_umul128(__m, __mul[2], &__high2); // 128 98 const uint64_t __s0low = __low0; // 0 99 (void) __s0low; // unused 100 const uint64_t __s0high = __low1 + __high0; // 64 101 const uint32_t __c1 = __s0high < __low1; 102 const uint64_t __s1low = __low2 + __high1 + __c1; // 128 103 const uint32_t __c2 = __s1low < __low2; // __high1 + __c1 can't overflow, so compare against __low2 104 const uint64_t __s1high = __high2 + __c2; // 192 105 _LIBCPP_ASSERT_INTERNAL(__j >= 128, ""); 106 _LIBCPP_ASSERT_INTERNAL(__j <= 180, ""); 107#ifdef _LIBCPP_INTRINSIC128 108 const uint32_t __dist = static_cast<uint32_t>(__j - 128); // __dist: [0, 52] 109 const uint64_t __shiftedhigh = __s1high >> __dist; 110 const uint64_t __shiftedlow = __ryu_shiftright128(__s1low, __s1high, __dist); 111 return __uint128_mod1e9(__shiftedhigh, __shiftedlow); 112#else // ^^^ intrinsics available ^^^ / vvv intrinsics unavailable vvv 113 if (__j < 160) { // __j: [128, 160) 114 const uint64_t __r0 = __mod1e9(__s1high); 115 const uint64_t __r1 = __mod1e9((__r0 << 32) | (__s1low >> 32)); 116 const uint64_t __r2 = ((__r1 << 32) | (__s1low & 0xffffffff)); 117 return __mod1e9(__r2 >> (__j - 128)); 118 } else { // __j: [160, 192) 119 const uint64_t __r0 = __mod1e9(__s1high); 120 const uint64_t __r1 = ((__r0 << 32) | (__s1low >> 32)); 121 return __mod1e9(__r1 >> (__j - 160)); 122 } 123#endif // ^^^ intrinsics unavailable ^^^ 124} 125 126void __append_n_digits(const uint32_t __olength, uint32_t __digits, char* const __result) { 127 uint32_t __i = 0; 128 while (__digits >= 10000) { 129#ifdef __clang__ // TRANSITION, LLVM-38217 130 const uint32_t __c = __digits - 10000 * (__digits / 10000); 131#else 132 const uint32_t __c = __digits % 10000; 133#endif 134 __digits /= 10000; 135 const uint32_t __c0 = (__c % 100) << 1; 136 const uint32_t __c1 = (__c / 100) << 1; 137 std::memcpy(__result + __olength - __i - 2, __DIGIT_TABLE + __c0, 2); 138 std::memcpy(__result + __olength - __i - 4, __DIGIT_TABLE + __c1, 2); 139 __i += 4; 140 } 141 if (__digits >= 100) { 142 const uint32_t __c = (__digits % 100) << 1; 143 __digits /= 100; 144 std::memcpy(__result + __olength - __i - 2, __DIGIT_TABLE + __c, 2); 145 __i += 2; 146 } 147 if (__digits >= 10) { 148 const uint32_t __c = __digits << 1; 149 std::memcpy(__result + __olength - __i - 2, __DIGIT_TABLE + __c, 2); 150 } else { 151 __result[0] = static_cast<char>('0' + __digits); 152 } 153} 154 155_LIBCPP_HIDE_FROM_ABI inline void __append_d_digits(const uint32_t __olength, uint32_t __digits, char* const __result) { 156 uint32_t __i = 0; 157 while (__digits >= 10000) { 158#ifdef __clang__ // TRANSITION, LLVM-38217 159 const uint32_t __c = __digits - 10000 * (__digits / 10000); 160#else 161 const uint32_t __c = __digits % 10000; 162#endif 163 __digits /= 10000; 164 const uint32_t __c0 = (__c % 100) << 1; 165 const uint32_t __c1 = (__c / 100) << 1; 166 std::memcpy(__result + __olength + 1 - __i - 2, __DIGIT_TABLE + __c0, 2); 167 std::memcpy(__result + __olength + 1 - __i - 4, __DIGIT_TABLE + __c1, 2); 168 __i += 4; 169 } 170 if (__digits >= 100) { 171 const uint32_t __c = (__digits % 100) << 1; 172 __digits /= 100; 173 std::memcpy(__result + __olength + 1 - __i - 2, __DIGIT_TABLE + __c, 2); 174 __i += 2; 175 } 176 if (__digits >= 10) { 177 const uint32_t __c = __digits << 1; 178 __result[2] = __DIGIT_TABLE[__c + 1]; 179 __result[1] = '.'; 180 __result[0] = __DIGIT_TABLE[__c]; 181 } else { 182 __result[1] = '.'; 183 __result[0] = static_cast<char>('0' + __digits); 184 } 185} 186 187_LIBCPP_HIDE_FROM_ABI inline void __append_c_digits(const uint32_t __count, uint32_t __digits, char* const __result) { 188 uint32_t __i = 0; 189 for (; __i < __count - 1; __i += 2) { 190 const uint32_t __c = (__digits % 100) << 1; 191 __digits /= 100; 192 std::memcpy(__result + __count - __i - 2, __DIGIT_TABLE + __c, 2); 193 } 194 if (__i < __count) { 195 const char __c = static_cast<char>('0' + (__digits % 10)); 196 __result[__count - __i - 1] = __c; 197 } 198} 199 200void __append_nine_digits(uint32_t __digits, char* const __result) { 201 if (__digits == 0) { 202 std::memset(__result, '0', 9); 203 return; 204 } 205 206 for (uint32_t __i = 0; __i < 5; __i += 4) { 207#ifdef __clang__ // TRANSITION, LLVM-38217 208 const uint32_t __c = __digits - 10000 * (__digits / 10000); 209#else 210 const uint32_t __c = __digits % 10000; 211#endif 212 __digits /= 10000; 213 const uint32_t __c0 = (__c % 100) << 1; 214 const uint32_t __c1 = (__c / 100) << 1; 215 std::memcpy(__result + 7 - __i, __DIGIT_TABLE + __c0, 2); 216 std::memcpy(__result + 5 - __i, __DIGIT_TABLE + __c1, 2); 217 } 218 __result[0] = static_cast<char>('0' + __digits); 219} 220 221[[nodiscard]] _LIBCPP_HIDE_FROM_ABI inline uint32_t __indexForExponent(const uint32_t __e) { 222 return (__e + 15) / 16; 223} 224 225[[nodiscard]] _LIBCPP_HIDE_FROM_ABI inline uint32_t __pow10BitsForIndex(const uint32_t __idx) { 226 return 16 * __idx + __POW10_ADDITIONAL_BITS; 227} 228 229[[nodiscard]] _LIBCPP_HIDE_FROM_ABI inline uint32_t __lengthForIndex(const uint32_t __idx) { 230 // +1 for ceil, +16 for mantissa, +8 to round up when dividing by 9 231 return (__log10Pow2(16 * static_cast<int32_t>(__idx)) + 1 + 16 + 8) / 9; 232} 233 234[[nodiscard]] to_chars_result __d2fixed_buffered_n(char* _First, char* const _Last, const double __d, 235 const uint32_t __precision) { 236 char* const _Original_first = _First; 237 238 const uint64_t __bits = __double_to_bits(__d); 239 240 // Case distinction; exit early for the easy cases. 241 if (__bits == 0) { 242 const int32_t _Total_zero_length = 1 // leading zero 243 + static_cast<int32_t>(__precision != 0) // possible decimal point 244 + static_cast<int32_t>(__precision); // zeroes after decimal point 245 246 if (_Last - _First < _Total_zero_length) { 247 return { _Last, errc::value_too_large }; 248 } 249 250 *_First++ = '0'; 251 if (__precision > 0) { 252 *_First++ = '.'; 253 std::memset(_First, '0', __precision); 254 _First += __precision; 255 } 256 return { _First, errc{} }; 257 } 258 259 // Decode __bits into mantissa and exponent. 260 const uint64_t __ieeeMantissa = __bits & ((1ull << __DOUBLE_MANTISSA_BITS) - 1); 261 const uint32_t __ieeeExponent = static_cast<uint32_t>(__bits >> __DOUBLE_MANTISSA_BITS); 262 263 int32_t __e2; 264 uint64_t __m2; 265 if (__ieeeExponent == 0) { 266 __e2 = 1 - __DOUBLE_BIAS - __DOUBLE_MANTISSA_BITS; 267 __m2 = __ieeeMantissa; 268 } else { 269 __e2 = static_cast<int32_t>(__ieeeExponent) - __DOUBLE_BIAS - __DOUBLE_MANTISSA_BITS; 270 __m2 = (1ull << __DOUBLE_MANTISSA_BITS) | __ieeeMantissa; 271 } 272 273 bool __nonzero = false; 274 if (__e2 >= -52) { 275 const uint32_t __idx = __e2 < 0 ? 0 : __indexForExponent(static_cast<uint32_t>(__e2)); 276 const uint32_t __p10bits = __pow10BitsForIndex(__idx); 277 const int32_t __len = static_cast<int32_t>(__lengthForIndex(__idx)); 278 for (int32_t __i = __len - 1; __i >= 0; --__i) { 279 const uint32_t __j = __p10bits - __e2; 280 // Temporary: __j is usually around 128, and by shifting a bit, we push it to 128 or above, which is 281 // a slightly faster code path in __mulShift_mod1e9. Instead, we can just increase the multipliers. 282 const uint32_t __digits = __mulShift_mod1e9(__m2 << 8, __POW10_SPLIT[__POW10_OFFSET[__idx] + __i], 283 static_cast<int32_t>(__j + 8)); 284 if (__nonzero) { 285 if (_Last - _First < 9) { 286 return { _Last, errc::value_too_large }; 287 } 288 __append_nine_digits(__digits, _First); 289 _First += 9; 290 } else if (__digits != 0) { 291 const uint32_t __olength = __decimalLength9(__digits); 292 if (_Last - _First < static_cast<ptrdiff_t>(__olength)) { 293 return { _Last, errc::value_too_large }; 294 } 295 __append_n_digits(__olength, __digits, _First); 296 _First += __olength; 297 __nonzero = true; 298 } 299 } 300 } 301 if (!__nonzero) { 302 if (_First == _Last) { 303 return { _Last, errc::value_too_large }; 304 } 305 *_First++ = '0'; 306 } 307 if (__precision > 0) { 308 if (_First == _Last) { 309 return { _Last, errc::value_too_large }; 310 } 311 *_First++ = '.'; 312 } 313 if (__e2 < 0) { 314 const int32_t __idx = -__e2 / 16; 315 const uint32_t __blocks = __precision / 9 + 1; 316 // 0 = don't round up; 1 = round up unconditionally; 2 = round up if odd. 317 int __roundUp = 0; 318 uint32_t __i = 0; 319 if (__blocks <= __MIN_BLOCK_2[__idx]) { 320 __i = __blocks; 321 if (_Last - _First < static_cast<ptrdiff_t>(__precision)) { 322 return { _Last, errc::value_too_large }; 323 } 324 std::memset(_First, '0', __precision); 325 _First += __precision; 326 } else if (__i < __MIN_BLOCK_2[__idx]) { 327 __i = __MIN_BLOCK_2[__idx]; 328 if (_Last - _First < static_cast<ptrdiff_t>(9 * __i)) { 329 return { _Last, errc::value_too_large }; 330 } 331 std::memset(_First, '0', 9 * __i); 332 _First += 9 * __i; 333 } 334 for (; __i < __blocks; ++__i) { 335 const int32_t __j = __ADDITIONAL_BITS_2 + (-__e2 - 16 * __idx); 336 const uint32_t __p = __POW10_OFFSET_2[__idx] + __i - __MIN_BLOCK_2[__idx]; 337 if (__p >= __POW10_OFFSET_2[__idx + 1]) { 338 // If the remaining digits are all 0, then we might as well use memset. 339 // No rounding required in this case. 340 const uint32_t __fill = __precision - 9 * __i; 341 if (_Last - _First < static_cast<ptrdiff_t>(__fill)) { 342 return { _Last, errc::value_too_large }; 343 } 344 std::memset(_First, '0', __fill); 345 _First += __fill; 346 break; 347 } 348 // Temporary: __j is usually around 128, and by shifting a bit, we push it to 128 or above, which is 349 // a slightly faster code path in __mulShift_mod1e9. Instead, we can just increase the multipliers. 350 uint32_t __digits = __mulShift_mod1e9(__m2 << 8, __POW10_SPLIT_2[__p], __j + 8); 351 if (__i < __blocks - 1) { 352 if (_Last - _First < 9) { 353 return { _Last, errc::value_too_large }; 354 } 355 __append_nine_digits(__digits, _First); 356 _First += 9; 357 } else { 358 const uint32_t __maximum = __precision - 9 * __i; 359 uint32_t __lastDigit = 0; 360 for (uint32_t __k = 0; __k < 9 - __maximum; ++__k) { 361 __lastDigit = __digits % 10; 362 __digits /= 10; 363 } 364 if (__lastDigit != 5) { 365 __roundUp = __lastDigit > 5; 366 } else { 367 // Is m * 10^(additionalDigits + 1) / 2^(-__e2) integer? 368 const int32_t __requiredTwos = -__e2 - static_cast<int32_t>(__precision) - 1; 369 const bool __trailingZeros = __requiredTwos <= 0 370 || (__requiredTwos < 60 && __multipleOfPowerOf2(__m2, static_cast<uint32_t>(__requiredTwos))); 371 __roundUp = __trailingZeros ? 2 : 1; 372 } 373 if (__maximum > 0) { 374 if (_Last - _First < static_cast<ptrdiff_t>(__maximum)) { 375 return { _Last, errc::value_too_large }; 376 } 377 __append_c_digits(__maximum, __digits, _First); 378 _First += __maximum; 379 } 380 break; 381 } 382 } 383 if (__roundUp != 0) { 384 char* _Round = _First; 385 char* _Dot = _Last; 386 while (true) { 387 if (_Round == _Original_first) { 388 _Round[0] = '1'; 389 if (_Dot != _Last) { 390 _Dot[0] = '0'; 391 _Dot[1] = '.'; 392 } 393 if (_First == _Last) { 394 return { _Last, errc::value_too_large }; 395 } 396 *_First++ = '0'; 397 break; 398 } 399 --_Round; 400 const char __c = _Round[0]; 401 if (__c == '.') { 402 _Dot = _Round; 403 } else if (__c == '9') { 404 _Round[0] = '0'; 405 __roundUp = 1; 406 } else { 407 if (__roundUp == 1 || __c % 2 != 0) { 408 _Round[0] = __c + 1; 409 } 410 break; 411 } 412 } 413 } 414 } else { 415 if (_Last - _First < static_cast<ptrdiff_t>(__precision)) { 416 return { _Last, errc::value_too_large }; 417 } 418 std::memset(_First, '0', __precision); 419 _First += __precision; 420 } 421 return { _First, errc{} }; 422} 423 424[[nodiscard]] to_chars_result __d2exp_buffered_n(char* _First, char* const _Last, const double __d, 425 uint32_t __precision) { 426 char* const _Original_first = _First; 427 428 const uint64_t __bits = __double_to_bits(__d); 429 430 // Case distinction; exit early for the easy cases. 431 if (__bits == 0) { 432 const int32_t _Total_zero_length = 1 // leading zero 433 + static_cast<int32_t>(__precision != 0) // possible decimal point 434 + static_cast<int32_t>(__precision) // zeroes after decimal point 435 + 4; // "e+00" 436 if (_Last - _First < _Total_zero_length) { 437 return { _Last, errc::value_too_large }; 438 } 439 *_First++ = '0'; 440 if (__precision > 0) { 441 *_First++ = '.'; 442 std::memset(_First, '0', __precision); 443 _First += __precision; 444 } 445 std::memcpy(_First, "e+00", 4); 446 _First += 4; 447 return { _First, errc{} }; 448 } 449 450 // Decode __bits into mantissa and exponent. 451 const uint64_t __ieeeMantissa = __bits & ((1ull << __DOUBLE_MANTISSA_BITS) - 1); 452 const uint32_t __ieeeExponent = static_cast<uint32_t>(__bits >> __DOUBLE_MANTISSA_BITS); 453 454 int32_t __e2; 455 uint64_t __m2; 456 if (__ieeeExponent == 0) { 457 __e2 = 1 - __DOUBLE_BIAS - __DOUBLE_MANTISSA_BITS; 458 __m2 = __ieeeMantissa; 459 } else { 460 __e2 = static_cast<int32_t>(__ieeeExponent) - __DOUBLE_BIAS - __DOUBLE_MANTISSA_BITS; 461 __m2 = (1ull << __DOUBLE_MANTISSA_BITS) | __ieeeMantissa; 462 } 463 464 const bool __printDecimalPoint = __precision > 0; 465 ++__precision; 466 uint32_t __digits = 0; 467 uint32_t __printedDigits = 0; 468 uint32_t __availableDigits = 0; 469 int32_t __exp = 0; 470 if (__e2 >= -52) { 471 const uint32_t __idx = __e2 < 0 ? 0 : __indexForExponent(static_cast<uint32_t>(__e2)); 472 const uint32_t __p10bits = __pow10BitsForIndex(__idx); 473 const int32_t __len = static_cast<int32_t>(__lengthForIndex(__idx)); 474 for (int32_t __i = __len - 1; __i >= 0; --__i) { 475 const uint32_t __j = __p10bits - __e2; 476 // Temporary: __j is usually around 128, and by shifting a bit, we push it to 128 or above, which is 477 // a slightly faster code path in __mulShift_mod1e9. Instead, we can just increase the multipliers. 478 __digits = __mulShift_mod1e9(__m2 << 8, __POW10_SPLIT[__POW10_OFFSET[__idx] + __i], 479 static_cast<int32_t>(__j + 8)); 480 if (__printedDigits != 0) { 481 if (__printedDigits + 9 > __precision) { 482 __availableDigits = 9; 483 break; 484 } 485 if (_Last - _First < 9) { 486 return { _Last, errc::value_too_large }; 487 } 488 __append_nine_digits(__digits, _First); 489 _First += 9; 490 __printedDigits += 9; 491 } else if (__digits != 0) { 492 __availableDigits = __decimalLength9(__digits); 493 __exp = __i * 9 + static_cast<int32_t>(__availableDigits) - 1; 494 if (__availableDigits > __precision) { 495 break; 496 } 497 if (__printDecimalPoint) { 498 if (_Last - _First < static_cast<ptrdiff_t>(__availableDigits + 1)) { 499 return { _Last, errc::value_too_large }; 500 } 501 __append_d_digits(__availableDigits, __digits, _First); 502 _First += __availableDigits + 1; // +1 for decimal point 503 } else { 504 if (_First == _Last) { 505 return { _Last, errc::value_too_large }; 506 } 507 *_First++ = static_cast<char>('0' + __digits); 508 } 509 __printedDigits = __availableDigits; 510 __availableDigits = 0; 511 } 512 } 513 } 514 515 if (__e2 < 0 && __availableDigits == 0) { 516 const int32_t __idx = -__e2 / 16; 517 for (int32_t __i = __MIN_BLOCK_2[__idx]; __i < 200; ++__i) { 518 const int32_t __j = __ADDITIONAL_BITS_2 + (-__e2 - 16 * __idx); 519 const uint32_t __p = __POW10_OFFSET_2[__idx] + static_cast<uint32_t>(__i) - __MIN_BLOCK_2[__idx]; 520 // Temporary: __j is usually around 128, and by shifting a bit, we push it to 128 or above, which is 521 // a slightly faster code path in __mulShift_mod1e9. Instead, we can just increase the multipliers. 522 __digits = (__p >= __POW10_OFFSET_2[__idx + 1]) ? 0 : __mulShift_mod1e9(__m2 << 8, __POW10_SPLIT_2[__p], __j + 8); 523 if (__printedDigits != 0) { 524 if (__printedDigits + 9 > __precision) { 525 __availableDigits = 9; 526 break; 527 } 528 if (_Last - _First < 9) { 529 return { _Last, errc::value_too_large }; 530 } 531 __append_nine_digits(__digits, _First); 532 _First += 9; 533 __printedDigits += 9; 534 } else if (__digits != 0) { 535 __availableDigits = __decimalLength9(__digits); 536 __exp = -(__i + 1) * 9 + static_cast<int32_t>(__availableDigits) - 1; 537 if (__availableDigits > __precision) { 538 break; 539 } 540 if (__printDecimalPoint) { 541 if (_Last - _First < static_cast<ptrdiff_t>(__availableDigits + 1)) { 542 return { _Last, errc::value_too_large }; 543 } 544 __append_d_digits(__availableDigits, __digits, _First); 545 _First += __availableDigits + 1; // +1 for decimal point 546 } else { 547 if (_First == _Last) { 548 return { _Last, errc::value_too_large }; 549 } 550 *_First++ = static_cast<char>('0' + __digits); 551 } 552 __printedDigits = __availableDigits; 553 __availableDigits = 0; 554 } 555 } 556 } 557 558 const uint32_t __maximum = __precision - __printedDigits; 559 if (__availableDigits == 0) { 560 __digits = 0; 561 } 562 uint32_t __lastDigit = 0; 563 if (__availableDigits > __maximum) { 564 for (uint32_t __k = 0; __k < __availableDigits - __maximum; ++__k) { 565 __lastDigit = __digits % 10; 566 __digits /= 10; 567 } 568 } 569 // 0 = don't round up; 1 = round up unconditionally; 2 = round up if odd. 570 int __roundUp = 0; 571 if (__lastDigit != 5) { 572 __roundUp = __lastDigit > 5; 573 } else { 574 // Is m * 2^__e2 * 10^(__precision + 1 - __exp) integer? 575 // __precision was already increased by 1, so we don't need to write + 1 here. 576 const int32_t __rexp = static_cast<int32_t>(__precision) - __exp; 577 const int32_t __requiredTwos = -__e2 - __rexp; 578 bool __trailingZeros = __requiredTwos <= 0 579 || (__requiredTwos < 60 && __multipleOfPowerOf2(__m2, static_cast<uint32_t>(__requiredTwos))); 580 if (__rexp < 0) { 581 const int32_t __requiredFives = -__rexp; 582 __trailingZeros = __trailingZeros && __multipleOfPowerOf5(__m2, static_cast<uint32_t>(__requiredFives)); 583 } 584 __roundUp = __trailingZeros ? 2 : 1; 585 } 586 if (__printedDigits != 0) { 587 if (_Last - _First < static_cast<ptrdiff_t>(__maximum)) { 588 return { _Last, errc::value_too_large }; 589 } 590 if (__digits == 0) { 591 std::memset(_First, '0', __maximum); 592 } else { 593 __append_c_digits(__maximum, __digits, _First); 594 } 595 _First += __maximum; 596 } else { 597 if (__printDecimalPoint) { 598 if (_Last - _First < static_cast<ptrdiff_t>(__maximum + 1)) { 599 return { _Last, errc::value_too_large }; 600 } 601 __append_d_digits(__maximum, __digits, _First); 602 _First += __maximum + 1; // +1 for decimal point 603 } else { 604 if (_First == _Last) { 605 return { _Last, errc::value_too_large }; 606 } 607 *_First++ = static_cast<char>('0' + __digits); 608 } 609 } 610 if (__roundUp != 0) { 611 char* _Round = _First; 612 while (true) { 613 if (_Round == _Original_first) { 614 _Round[0] = '1'; 615 ++__exp; 616 break; 617 } 618 --_Round; 619 const char __c = _Round[0]; 620 if (__c == '.') { 621 // Keep going. 622 } else if (__c == '9') { 623 _Round[0] = '0'; 624 __roundUp = 1; 625 } else { 626 if (__roundUp == 1 || __c % 2 != 0) { 627 _Round[0] = __c + 1; 628 } 629 break; 630 } 631 } 632 } 633 634 char _Sign_character; 635 636 if (__exp < 0) { 637 _Sign_character = '-'; 638 __exp = -__exp; 639 } else { 640 _Sign_character = '+'; 641 } 642 643 const int _Exponent_part_length = __exp >= 100 644 ? 5 // "e+NNN" 645 : 4; // "e+NN" 646 647 if (_Last - _First < _Exponent_part_length) { 648 return { _Last, errc::value_too_large }; 649 } 650 651 *_First++ = 'e'; 652 *_First++ = _Sign_character; 653 654 if (__exp >= 100) { 655 const int32_t __c = __exp % 10; 656 std::memcpy(_First, __DIGIT_TABLE + 2 * (__exp / 10), 2); 657 _First[2] = static_cast<char>('0' + __c); 658 _First += 3; 659 } else { 660 std::memcpy(_First, __DIGIT_TABLE + 2 * __exp, 2); 661 _First += 2; 662 } 663 664 return { _First, errc{} }; 665} 666 667_LIBCPP_END_NAMESPACE_STD 668 669// clang-format on 670