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 <cstddef> 46 47 #include "include/ryu/common.h" 48 #include "include/ryu/d2fixed.h" 49 #include "include/ryu/d2s.h" 50 #include "include/ryu/d2s_full_table.h" 51 #include "include/ryu/d2s_intrinsics.h" 52 #include "include/ryu/digit_table.h" 53 #include "include/ryu/ryu.h" 54 55 _LIBCPP_BEGIN_NAMESPACE_STD 56 57 // We need a 64x128-bit multiplication and a subsequent 128-bit shift. 58 // Multiplication: 59 // The 64-bit factor is variable and passed in, the 128-bit factor comes 60 // from a lookup table. We know that the 64-bit factor only has 55 61 // significant bits (i.e., the 9 topmost bits are zeros). The 128-bit 62 // factor only has 124 significant bits (i.e., the 4 topmost bits are 63 // zeros). 64 // Shift: 65 // In principle, the multiplication result requires 55 + 124 = 179 bits to 66 // represent. However, we then shift this value to the right by __j, which is 67 // at least __j >= 115, so the result is guaranteed to fit into 179 - 115 = 64 68 // bits. This means that we only need the topmost 64 significant bits of 69 // the 64x128-bit multiplication. 70 // 71 // There are several ways to do this: 72 // 1. Best case: the compiler exposes a 128-bit type. 73 // We perform two 64x64-bit multiplications, add the higher 64 bits of the 74 // lower result to the higher result, and shift by __j - 64 bits. 75 // 76 // We explicitly cast from 64-bit to 128-bit, so the compiler can tell 77 // that these are only 64-bit inputs, and can map these to the best 78 // possible sequence of assembly instructions. 79 // x64 machines happen to have matching assembly instructions for 80 // 64x64-bit multiplications and 128-bit shifts. 81 // 82 // 2. Second best case: the compiler exposes intrinsics for the x64 assembly 83 // instructions mentioned in 1. 84 // 85 // 3. We only have 64x64 bit instructions that return the lower 64 bits of 86 // the result, i.e., we have to use plain C. 87 // Our inputs are less than the full width, so we have three options: 88 // a. Ignore this fact and just implement the intrinsics manually. 89 // b. Split both into 31-bit pieces, which guarantees no internal overflow, 90 // but requires extra work upfront (unless we change the lookup table). 91 // c. Split only the first factor into 31-bit pieces, which also guarantees 92 // no internal overflow, but requires extra work since the intermediate 93 // results are not perfectly aligned. 94 #ifdef _LIBCPP_INTRINSIC128 95 96 [[nodiscard]] _LIBCPP_HIDE_FROM_ABI inline uint64_t __mulShift(const uint64_t __m, const uint64_t* const __mul, const int32_t __j) { 97 // __m is maximum 55 bits 98 uint64_t __high1; // 128 99 const uint64_t __low1 = __ryu_umul128(__m, __mul[1], &__high1); // 64 100 uint64_t __high0; // 64 101 (void) __ryu_umul128(__m, __mul[0], &__high0); // 0 102 const uint64_t __sum = __high0 + __low1; 103 if (__sum < __high0) { 104 ++__high1; // overflow into __high1 105 } 106 return __ryu_shiftright128(__sum, __high1, static_cast<uint32_t>(__j - 64)); 107 } 108 109 [[nodiscard]] _LIBCPP_HIDE_FROM_ABI inline uint64_t __mulShiftAll(const uint64_t __m, const uint64_t* const __mul, const int32_t __j, 110 uint64_t* const __vp, uint64_t* const __vm, const uint32_t __mmShift) { 111 *__vp = __mulShift(4 * __m + 2, __mul, __j); 112 *__vm = __mulShift(4 * __m - 1 - __mmShift, __mul, __j); 113 return __mulShift(4 * __m, __mul, __j); 114 } 115 116 #else // ^^^ intrinsics available ^^^ / vvv intrinsics unavailable vvv 117 118 [[nodiscard]] _LIBCPP_HIDE_FROM_ABI inline _LIBCPP_ALWAYS_INLINE uint64_t __mulShiftAll(uint64_t __m, const uint64_t* const __mul, const int32_t __j, 119 uint64_t* const __vp, uint64_t* const __vm, const uint32_t __mmShift) { // TRANSITION, VSO-634761 120 __m <<= 1; 121 // __m is maximum 55 bits 122 uint64_t __tmp; 123 const uint64_t __lo = __ryu_umul128(__m, __mul[0], &__tmp); 124 uint64_t __hi; 125 const uint64_t __mid = __tmp + __ryu_umul128(__m, __mul[1], &__hi); 126 __hi += __mid < __tmp; // overflow into __hi 127 128 const uint64_t __lo2 = __lo + __mul[0]; 129 const uint64_t __mid2 = __mid + __mul[1] + (__lo2 < __lo); 130 const uint64_t __hi2 = __hi + (__mid2 < __mid); 131 *__vp = __ryu_shiftright128(__mid2, __hi2, static_cast<uint32_t>(__j - 64 - 1)); 132 133 if (__mmShift == 1) { 134 const uint64_t __lo3 = __lo - __mul[0]; 135 const uint64_t __mid3 = __mid - __mul[1] - (__lo3 > __lo); 136 const uint64_t __hi3 = __hi - (__mid3 > __mid); 137 *__vm = __ryu_shiftright128(__mid3, __hi3, static_cast<uint32_t>(__j - 64 - 1)); 138 } else { 139 const uint64_t __lo3 = __lo + __lo; 140 const uint64_t __mid3 = __mid + __mid + (__lo3 < __lo); 141 const uint64_t __hi3 = __hi + __hi + (__mid3 < __mid); 142 const uint64_t __lo4 = __lo3 - __mul[0]; 143 const uint64_t __mid4 = __mid3 - __mul[1] - (__lo4 > __lo3); 144 const uint64_t __hi4 = __hi3 - (__mid4 > __mid3); 145 *__vm = __ryu_shiftright128(__mid4, __hi4, static_cast<uint32_t>(__j - 64)); 146 } 147 148 return __ryu_shiftright128(__mid, __hi, static_cast<uint32_t>(__j - 64 - 1)); 149 } 150 151 #endif // ^^^ intrinsics unavailable ^^^ 152 153 [[nodiscard]] _LIBCPP_HIDE_FROM_ABI inline uint32_t __decimalLength17(const uint64_t __v) { 154 // This is slightly faster than a loop. 155 // The average output length is 16.38 digits, so we check high-to-low. 156 // Function precondition: __v is not an 18, 19, or 20-digit number. 157 // (17 digits are sufficient for round-tripping.) 158 _LIBCPP_ASSERT_INTERNAL(__v < 100000000000000000u, ""); 159 if (__v >= 10000000000000000u) { return 17; } 160 if (__v >= 1000000000000000u) { return 16; } 161 if (__v >= 100000000000000u) { return 15; } 162 if (__v >= 10000000000000u) { return 14; } 163 if (__v >= 1000000000000u) { return 13; } 164 if (__v >= 100000000000u) { return 12; } 165 if (__v >= 10000000000u) { return 11; } 166 if (__v >= 1000000000u) { return 10; } 167 if (__v >= 100000000u) { return 9; } 168 if (__v >= 10000000u) { return 8; } 169 if (__v >= 1000000u) { return 7; } 170 if (__v >= 100000u) { return 6; } 171 if (__v >= 10000u) { return 5; } 172 if (__v >= 1000u) { return 4; } 173 if (__v >= 100u) { return 3; } 174 if (__v >= 10u) { return 2; } 175 return 1; 176 } 177 178 // A floating decimal representing m * 10^e. 179 struct __floating_decimal_64 { 180 uint64_t __mantissa; 181 int32_t __exponent; 182 }; 183 184 [[nodiscard]] _LIBCPP_HIDE_FROM_ABI inline __floating_decimal_64 __d2d(const uint64_t __ieeeMantissa, const uint32_t __ieeeExponent) { 185 int32_t __e2; 186 uint64_t __m2; 187 if (__ieeeExponent == 0) { 188 // We subtract 2 so that the bounds computation has 2 additional bits. 189 __e2 = 1 - __DOUBLE_BIAS - __DOUBLE_MANTISSA_BITS - 2; 190 __m2 = __ieeeMantissa; 191 } else { 192 __e2 = static_cast<int32_t>(__ieeeExponent) - __DOUBLE_BIAS - __DOUBLE_MANTISSA_BITS - 2; 193 __m2 = (1ull << __DOUBLE_MANTISSA_BITS) | __ieeeMantissa; 194 } 195 const bool __even = (__m2 & 1) == 0; 196 const bool __acceptBounds = __even; 197 198 // Step 2: Determine the interval of valid decimal representations. 199 const uint64_t __mv = 4 * __m2; 200 // Implicit bool -> int conversion. True is 1, false is 0. 201 const uint32_t __mmShift = __ieeeMantissa != 0 || __ieeeExponent <= 1; 202 // We would compute __mp and __mm like this: 203 // uint64_t __mp = 4 * __m2 + 2; 204 // uint64_t __mm = __mv - 1 - __mmShift; 205 206 // Step 3: Convert to a decimal power base using 128-bit arithmetic. 207 uint64_t __vr, __vp, __vm; 208 int32_t __e10; 209 bool __vmIsTrailingZeros = false; 210 bool __vrIsTrailingZeros = false; 211 if (__e2 >= 0) { 212 // I tried special-casing __q == 0, but there was no effect on performance. 213 // This expression is slightly faster than max(0, __log10Pow2(__e2) - 1). 214 const uint32_t __q = __log10Pow2(__e2) - (__e2 > 3); 215 __e10 = static_cast<int32_t>(__q); 216 const int32_t __k = __DOUBLE_POW5_INV_BITCOUNT + __pow5bits(static_cast<int32_t>(__q)) - 1; 217 const int32_t __i = -__e2 + static_cast<int32_t>(__q) + __k; 218 __vr = __mulShiftAll(__m2, __DOUBLE_POW5_INV_SPLIT[__q], __i, &__vp, &__vm, __mmShift); 219 if (__q <= 21) { 220 // This should use __q <= 22, but I think 21 is also safe. Smaller values 221 // may still be safe, but it's more difficult to reason about them. 222 // Only one of __mp, __mv, and __mm can be a multiple of 5, if any. 223 const uint32_t __mvMod5 = static_cast<uint32_t>(__mv) - 5 * static_cast<uint32_t>(__div5(__mv)); 224 if (__mvMod5 == 0) { 225 __vrIsTrailingZeros = __multipleOfPowerOf5(__mv, __q); 226 } else if (__acceptBounds) { 227 // Same as min(__e2 + (~__mm & 1), __pow5Factor(__mm)) >= __q 228 // <=> __e2 + (~__mm & 1) >= __q && __pow5Factor(__mm) >= __q 229 // <=> true && __pow5Factor(__mm) >= __q, since __e2 >= __q. 230 __vmIsTrailingZeros = __multipleOfPowerOf5(__mv - 1 - __mmShift, __q); 231 } else { 232 // Same as min(__e2 + 1, __pow5Factor(__mp)) >= __q. 233 __vp -= __multipleOfPowerOf5(__mv + 2, __q); 234 } 235 } 236 } else { 237 // This expression is slightly faster than max(0, __log10Pow5(-__e2) - 1). 238 const uint32_t __q = __log10Pow5(-__e2) - (-__e2 > 1); 239 __e10 = static_cast<int32_t>(__q) + __e2; 240 const int32_t __i = -__e2 - static_cast<int32_t>(__q); 241 const int32_t __k = __pow5bits(__i) - __DOUBLE_POW5_BITCOUNT; 242 const int32_t __j = static_cast<int32_t>(__q) - __k; 243 __vr = __mulShiftAll(__m2, __DOUBLE_POW5_SPLIT[__i], __j, &__vp, &__vm, __mmShift); 244 if (__q <= 1) { 245 // {__vr,__vp,__vm} is trailing zeros if {__mv,__mp,__mm} has at least __q trailing 0 bits. 246 // __mv = 4 * __m2, so it always has at least two trailing 0 bits. 247 __vrIsTrailingZeros = true; 248 if (__acceptBounds) { 249 // __mm = __mv - 1 - __mmShift, so it has 1 trailing 0 bit iff __mmShift == 1. 250 __vmIsTrailingZeros = __mmShift == 1; 251 } else { 252 // __mp = __mv + 2, so it always has at least one trailing 0 bit. 253 --__vp; 254 } 255 } else if (__q < 63) { // TRANSITION(ulfjack): Use a tighter bound here. 256 // We need to compute min(ntz(__mv), __pow5Factor(__mv) - __e2) >= __q - 1 257 // <=> ntz(__mv) >= __q - 1 && __pow5Factor(__mv) - __e2 >= __q - 1 258 // <=> ntz(__mv) >= __q - 1 (__e2 is negative and -__e2 >= __q) 259 // <=> (__mv & ((1 << (__q - 1)) - 1)) == 0 260 // We also need to make sure that the left shift does not overflow. 261 __vrIsTrailingZeros = __multipleOfPowerOf2(__mv, __q - 1); 262 } 263 } 264 265 // Step 4: Find the shortest decimal representation in the interval of valid representations. 266 int32_t __removed = 0; 267 uint8_t __lastRemovedDigit = 0; 268 uint64_t _Output; 269 // On average, we remove ~2 digits. 270 if (__vmIsTrailingZeros || __vrIsTrailingZeros) { 271 // General case, which happens rarely (~0.7%). 272 for (;;) { 273 const uint64_t __vpDiv10 = __div10(__vp); 274 const uint64_t __vmDiv10 = __div10(__vm); 275 if (__vpDiv10 <= __vmDiv10) { 276 break; 277 } 278 const uint32_t __vmMod10 = static_cast<uint32_t>(__vm) - 10 * static_cast<uint32_t>(__vmDiv10); 279 const uint64_t __vrDiv10 = __div10(__vr); 280 const uint32_t __vrMod10 = static_cast<uint32_t>(__vr) - 10 * static_cast<uint32_t>(__vrDiv10); 281 __vmIsTrailingZeros &= __vmMod10 == 0; 282 __vrIsTrailingZeros &= __lastRemovedDigit == 0; 283 __lastRemovedDigit = static_cast<uint8_t>(__vrMod10); 284 __vr = __vrDiv10; 285 __vp = __vpDiv10; 286 __vm = __vmDiv10; 287 ++__removed; 288 } 289 if (__vmIsTrailingZeros) { 290 for (;;) { 291 const uint64_t __vmDiv10 = __div10(__vm); 292 const uint32_t __vmMod10 = static_cast<uint32_t>(__vm) - 10 * static_cast<uint32_t>(__vmDiv10); 293 if (__vmMod10 != 0) { 294 break; 295 } 296 const uint64_t __vpDiv10 = __div10(__vp); 297 const uint64_t __vrDiv10 = __div10(__vr); 298 const uint32_t __vrMod10 = static_cast<uint32_t>(__vr) - 10 * static_cast<uint32_t>(__vrDiv10); 299 __vrIsTrailingZeros &= __lastRemovedDigit == 0; 300 __lastRemovedDigit = static_cast<uint8_t>(__vrMod10); 301 __vr = __vrDiv10; 302 __vp = __vpDiv10; 303 __vm = __vmDiv10; 304 ++__removed; 305 } 306 } 307 if (__vrIsTrailingZeros && __lastRemovedDigit == 5 && __vr % 2 == 0) { 308 // Round even if the exact number is .....50..0. 309 __lastRemovedDigit = 4; 310 } 311 // We need to take __vr + 1 if __vr is outside bounds or we need to round up. 312 _Output = __vr + ((__vr == __vm && (!__acceptBounds || !__vmIsTrailingZeros)) || __lastRemovedDigit >= 5); 313 } else { 314 // Specialized for the common case (~99.3%). Percentages below are relative to this. 315 bool __roundUp = false; 316 const uint64_t __vpDiv100 = __div100(__vp); 317 const uint64_t __vmDiv100 = __div100(__vm); 318 if (__vpDiv100 > __vmDiv100) { // Optimization: remove two digits at a time (~86.2%). 319 const uint64_t __vrDiv100 = __div100(__vr); 320 const uint32_t __vrMod100 = static_cast<uint32_t>(__vr) - 100 * static_cast<uint32_t>(__vrDiv100); 321 __roundUp = __vrMod100 >= 50; 322 __vr = __vrDiv100; 323 __vp = __vpDiv100; 324 __vm = __vmDiv100; 325 __removed += 2; 326 } 327 // Loop iterations below (approximately), without optimization above: 328 // 0: 0.03%, 1: 13.8%, 2: 70.6%, 3: 14.0%, 4: 1.40%, 5: 0.14%, 6+: 0.02% 329 // Loop iterations below (approximately), with optimization above: 330 // 0: 70.6%, 1: 27.8%, 2: 1.40%, 3: 0.14%, 4+: 0.02% 331 for (;;) { 332 const uint64_t __vpDiv10 = __div10(__vp); 333 const uint64_t __vmDiv10 = __div10(__vm); 334 if (__vpDiv10 <= __vmDiv10) { 335 break; 336 } 337 const uint64_t __vrDiv10 = __div10(__vr); 338 const uint32_t __vrMod10 = static_cast<uint32_t>(__vr) - 10 * static_cast<uint32_t>(__vrDiv10); 339 __roundUp = __vrMod10 >= 5; 340 __vr = __vrDiv10; 341 __vp = __vpDiv10; 342 __vm = __vmDiv10; 343 ++__removed; 344 } 345 // We need to take __vr + 1 if __vr is outside bounds or we need to round up. 346 _Output = __vr + (__vr == __vm || __roundUp); 347 } 348 const int32_t __exp = __e10 + __removed; 349 350 __floating_decimal_64 __fd; 351 __fd.__exponent = __exp; 352 __fd.__mantissa = _Output; 353 return __fd; 354 } 355 356 [[nodiscard]] _LIBCPP_HIDE_FROM_ABI inline to_chars_result __to_chars(char* const _First, char* const _Last, const __floating_decimal_64 __v, 357 chars_format _Fmt, const double __f) { 358 // Step 5: Print the decimal representation. 359 uint64_t _Output = __v.__mantissa; 360 int32_t _Ryu_exponent = __v.__exponent; 361 const uint32_t __olength = __decimalLength17(_Output); 362 int32_t _Scientific_exponent = _Ryu_exponent + static_cast<int32_t>(__olength) - 1; 363 364 if (_Fmt == chars_format{}) { 365 int32_t _Lower; 366 int32_t _Upper; 367 368 if (__olength == 1) { 369 // Value | Fixed | Scientific 370 // 1e-3 | "0.001" | "1e-03" 371 // 1e4 | "10000" | "1e+04" 372 _Lower = -3; 373 _Upper = 4; 374 } else { 375 // Value | Fixed | Scientific 376 // 1234e-7 | "0.0001234" | "1.234e-04" 377 // 1234e5 | "123400000" | "1.234e+08" 378 _Lower = -static_cast<int32_t>(__olength + 3); 379 _Upper = 5; 380 } 381 382 if (_Lower <= _Ryu_exponent && _Ryu_exponent <= _Upper) { 383 _Fmt = chars_format::fixed; 384 } else { 385 _Fmt = chars_format::scientific; 386 } 387 } else if (_Fmt == chars_format::general) { 388 // C11 7.21.6.1 "The fprintf function"/8: 389 // "Let P equal [...] 6 if the precision is omitted [...]. 390 // Then, if a conversion with style E would have an exponent of X: 391 // - if P > X >= -4, the conversion is with style f [...]. 392 // - otherwise, the conversion is with style e [...]." 393 if (-4 <= _Scientific_exponent && _Scientific_exponent < 6) { 394 _Fmt = chars_format::fixed; 395 } else { 396 _Fmt = chars_format::scientific; 397 } 398 } 399 400 if (_Fmt == chars_format::fixed) { 401 // Example: _Output == 1729, __olength == 4 402 403 // _Ryu_exponent | Printed | _Whole_digits | _Total_fixed_length | Notes 404 // --------------|----------|---------------|----------------------|--------------------------------------- 405 // 2 | 172900 | 6 | _Whole_digits | Ryu can't be used for printing 406 // 1 | 17290 | 5 | (sometimes adjusted) | when the trimmed digits are nonzero. 407 // --------------|----------|---------------|----------------------|--------------------------------------- 408 // 0 | 1729 | 4 | _Whole_digits | Unified length cases. 409 // --------------|----------|---------------|----------------------|--------------------------------------- 410 // -1 | 172.9 | 3 | __olength + 1 | This case can't happen for 411 // -2 | 17.29 | 2 | | __olength == 1, but no additional 412 // -3 | 1.729 | 1 | | code is needed to avoid it. 413 // --------------|----------|---------------|----------------------|--------------------------------------- 414 // -4 | 0.1729 | 0 | 2 - _Ryu_exponent | C11 7.21.6.1 "The fprintf function"/8: 415 // -5 | 0.01729 | -1 | | "If a decimal-point character appears, 416 // -6 | 0.001729 | -2 | | at least one digit appears before it." 417 418 const int32_t _Whole_digits = static_cast<int32_t>(__olength) + _Ryu_exponent; 419 420 uint32_t _Total_fixed_length; 421 if (_Ryu_exponent >= 0) { // cases "172900" and "1729" 422 _Total_fixed_length = static_cast<uint32_t>(_Whole_digits); 423 if (_Output == 1) { 424 // Rounding can affect the number of digits. 425 // For example, 1e23 is exactly "99999999999999991611392" which is 23 digits instead of 24. 426 // We can use a lookup table to detect this and adjust the total length. 427 static constexpr uint8_t _Adjustment[309] = { 428 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,1,1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0, 429 1,1,0,0,1,0,1,1,1,0,0,0,0,1,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,1,1, 430 1,0,0,0,0,0,0,0,1,1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0,0,0,1,1,1,0,0,1,1,1,1,1,0,1,0,1,1,0,1, 431 1,0,0,0,0,0,0,0,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,1,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1, 432 0,1,0,1,0,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,1,1,1,1,0,1,0,1,1,0,0,0,1, 433 1,1,0,1,1,0,0,0,1,0,0,0,1,0,1,0,0,0,0,0,0,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0,0,0,0,1,1,0, 434 0,1,0,1,1,1,0,0,1,0,0,0,0,1,0,1,0,0,0,0,0,1,0,1,0,1,1,0,1,0,0,0,0,0,1,1,0,1,0 }; 435 _Total_fixed_length -= _Adjustment[_Ryu_exponent]; 436 // _Whole_digits doesn't need to be adjusted because these cases won't refer to it later. 437 } 438 } else if (_Whole_digits > 0) { // case "17.29" 439 _Total_fixed_length = __olength + 1; 440 } else { // case "0.001729" 441 _Total_fixed_length = static_cast<uint32_t>(2 - _Ryu_exponent); 442 } 443 444 if (_Last - _First < static_cast<ptrdiff_t>(_Total_fixed_length)) { 445 return { _Last, errc::value_too_large }; 446 } 447 448 char* _Mid; 449 if (_Ryu_exponent > 0) { // case "172900" 450 bool _Can_use_ryu; 451 452 if (_Ryu_exponent > 22) { // 10^22 is the largest power of 10 that's exactly representable as a double. 453 _Can_use_ryu = false; 454 } else { 455 // Ryu generated X: __v.__mantissa * 10^_Ryu_exponent 456 // __v.__mantissa == 2^_Trailing_zero_bits * (__v.__mantissa >> _Trailing_zero_bits) 457 // 10^_Ryu_exponent == 2^_Ryu_exponent * 5^_Ryu_exponent 458 459 // _Trailing_zero_bits is [0, 56] (aside: because 2^56 is the largest power of 2 460 // with 17 decimal digits, which is double's round-trip limit.) 461 // _Ryu_exponent is [1, 22]. 462 // Normalization adds [2, 52] (aside: at least 2 because the pre-normalized mantissa is at least 5). 463 // This adds up to [3, 130], which is well below double's maximum binary exponent 1023. 464 465 // Therefore, we just need to consider (__v.__mantissa >> _Trailing_zero_bits) * 5^_Ryu_exponent. 466 467 // If that product would exceed 53 bits, then X can't be exactly represented as a double. 468 // (That's not a problem for round-tripping, because X is close enough to the original double, 469 // but X isn't mathematically equal to the original double.) This requires a high-precision fallback. 470 471 // If the product is 53 bits or smaller, then X can be exactly represented as a double (and we don't 472 // need to re-synthesize it; the original double must have been X, because Ryu wouldn't produce the 473 // same output for two different doubles X and Y). This allows Ryu's output to be used (zero-filled). 474 475 // (2^53 - 1) / 5^0 (for indexing), (2^53 - 1) / 5^1, ..., (2^53 - 1) / 5^22 476 static constexpr uint64_t _Max_shifted_mantissa[23] = { 477 9007199254740991u, 1801439850948198u, 360287970189639u, 72057594037927u, 14411518807585u, 478 2882303761517u, 576460752303u, 115292150460u, 23058430092u, 4611686018u, 922337203u, 184467440u, 479 36893488u, 7378697u, 1475739u, 295147u, 59029u, 11805u, 2361u, 472u, 94u, 18u, 3u }; 480 481 unsigned long _Trailing_zero_bits; 482 #if _LIBCPP_HAS_BITSCAN64 483 (void) _BitScanForward64(&_Trailing_zero_bits, __v.__mantissa); // __v.__mantissa is guaranteed nonzero 484 #else // ^^^ 64-bit ^^^ / vvv 32-bit vvv 485 const uint32_t _Low_mantissa = static_cast<uint32_t>(__v.__mantissa); 486 if (_Low_mantissa != 0) { 487 (void) _BitScanForward(&_Trailing_zero_bits, _Low_mantissa); 488 } else { 489 const uint32_t _High_mantissa = static_cast<uint32_t>(__v.__mantissa >> 32); // nonzero here 490 (void) _BitScanForward(&_Trailing_zero_bits, _High_mantissa); 491 _Trailing_zero_bits += 32; 492 } 493 #endif // ^^^ 32-bit ^^^ 494 const uint64_t _Shifted_mantissa = __v.__mantissa >> _Trailing_zero_bits; 495 _Can_use_ryu = _Shifted_mantissa <= _Max_shifted_mantissa[_Ryu_exponent]; 496 } 497 498 if (!_Can_use_ryu) { 499 // Print the integer exactly. 500 // Performance note: This will redundantly perform bounds checking. 501 // Performance note: This will redundantly decompose the IEEE representation. 502 return __d2fixed_buffered_n(_First, _Last, __f, 0); 503 } 504 505 // _Can_use_ryu 506 // Print the decimal digits, left-aligned within [_First, _First + _Total_fixed_length). 507 _Mid = _First + __olength; 508 } else { // cases "1729", "17.29", and "0.001729" 509 // Print the decimal digits, right-aligned within [_First, _First + _Total_fixed_length). 510 _Mid = _First + _Total_fixed_length; 511 } 512 513 // We prefer 32-bit operations, even on 64-bit platforms. 514 // We have at most 17 digits, and uint32_t can store 9 digits. 515 // If _Output doesn't fit into uint32_t, we cut off 8 digits, 516 // so the rest will fit into uint32_t. 517 if ((_Output >> 32) != 0) { 518 // Expensive 64-bit division. 519 const uint64_t __q = __div1e8(_Output); 520 uint32_t __output2 = static_cast<uint32_t>(_Output - 100000000 * __q); 521 _Output = __q; 522 523 const uint32_t __c = __output2 % 10000; 524 __output2 /= 10000; 525 const uint32_t __d = __output2 % 10000; 526 const uint32_t __c0 = (__c % 100) << 1; 527 const uint32_t __c1 = (__c / 100) << 1; 528 const uint32_t __d0 = (__d % 100) << 1; 529 const uint32_t __d1 = (__d / 100) << 1; 530 531 std::memcpy(_Mid -= 2, __DIGIT_TABLE + __c0, 2); 532 std::memcpy(_Mid -= 2, __DIGIT_TABLE + __c1, 2); 533 std::memcpy(_Mid -= 2, __DIGIT_TABLE + __d0, 2); 534 std::memcpy(_Mid -= 2, __DIGIT_TABLE + __d1, 2); 535 } 536 uint32_t __output2 = static_cast<uint32_t>(_Output); 537 while (__output2 >= 10000) { 538 #ifdef __clang__ // TRANSITION, LLVM-38217 539 const uint32_t __c = __output2 - 10000 * (__output2 / 10000); 540 #else 541 const uint32_t __c = __output2 % 10000; 542 #endif 543 __output2 /= 10000; 544 const uint32_t __c0 = (__c % 100) << 1; 545 const uint32_t __c1 = (__c / 100) << 1; 546 std::memcpy(_Mid -= 2, __DIGIT_TABLE + __c0, 2); 547 std::memcpy(_Mid -= 2, __DIGIT_TABLE + __c1, 2); 548 } 549 if (__output2 >= 100) { 550 const uint32_t __c = (__output2 % 100) << 1; 551 __output2 /= 100; 552 std::memcpy(_Mid -= 2, __DIGIT_TABLE + __c, 2); 553 } 554 if (__output2 >= 10) { 555 const uint32_t __c = __output2 << 1; 556 std::memcpy(_Mid -= 2, __DIGIT_TABLE + __c, 2); 557 } else { 558 *--_Mid = static_cast<char>('0' + __output2); 559 } 560 561 if (_Ryu_exponent > 0) { // case "172900" with _Can_use_ryu 562 // Performance note: it might be more efficient to do this immediately after setting _Mid. 563 std::memset(_First + __olength, '0', static_cast<size_t>(_Ryu_exponent)); 564 } else if (_Ryu_exponent == 0) { // case "1729" 565 // Done! 566 } else if (_Whole_digits > 0) { // case "17.29" 567 // Performance note: moving digits might not be optimal. 568 std::memmove(_First, _First + 1, static_cast<size_t>(_Whole_digits)); 569 _First[_Whole_digits] = '.'; 570 } else { // case "0.001729" 571 // Performance note: a larger memset() followed by overwriting '.' might be more efficient. 572 _First[0] = '0'; 573 _First[1] = '.'; 574 std::memset(_First + 2, '0', static_cast<size_t>(-_Whole_digits)); 575 } 576 577 return { _First + _Total_fixed_length, errc{} }; 578 } 579 580 const uint32_t _Total_scientific_length = __olength + (__olength > 1) // digits + possible decimal point 581 + (-100 < _Scientific_exponent && _Scientific_exponent < 100 ? 4 : 5); // + scientific exponent 582 if (_Last - _First < static_cast<ptrdiff_t>(_Total_scientific_length)) { 583 return { _Last, errc::value_too_large }; 584 } 585 char* const __result = _First; 586 587 // Print the decimal digits. 588 uint32_t __i = 0; 589 // We prefer 32-bit operations, even on 64-bit platforms. 590 // We have at most 17 digits, and uint32_t can store 9 digits. 591 // If _Output doesn't fit into uint32_t, we cut off 8 digits, 592 // so the rest will fit into uint32_t. 593 if ((_Output >> 32) != 0) { 594 // Expensive 64-bit division. 595 const uint64_t __q = __div1e8(_Output); 596 uint32_t __output2 = static_cast<uint32_t>(_Output) - 100000000 * static_cast<uint32_t>(__q); 597 _Output = __q; 598 599 const uint32_t __c = __output2 % 10000; 600 __output2 /= 10000; 601 const uint32_t __d = __output2 % 10000; 602 const uint32_t __c0 = (__c % 100) << 1; 603 const uint32_t __c1 = (__c / 100) << 1; 604 const uint32_t __d0 = (__d % 100) << 1; 605 const uint32_t __d1 = (__d / 100) << 1; 606 std::memcpy(__result + __olength - __i - 1, __DIGIT_TABLE + __c0, 2); 607 std::memcpy(__result + __olength - __i - 3, __DIGIT_TABLE + __c1, 2); 608 std::memcpy(__result + __olength - __i - 5, __DIGIT_TABLE + __d0, 2); 609 std::memcpy(__result + __olength - __i - 7, __DIGIT_TABLE + __d1, 2); 610 __i += 8; 611 } 612 uint32_t __output2 = static_cast<uint32_t>(_Output); 613 while (__output2 >= 10000) { 614 #ifdef __clang__ // TRANSITION, LLVM-38217 615 const uint32_t __c = __output2 - 10000 * (__output2 / 10000); 616 #else 617 const uint32_t __c = __output2 % 10000; 618 #endif 619 __output2 /= 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 (__output2 >= 100) { 627 const uint32_t __c = (__output2 % 100) << 1; 628 __output2 /= 100; 629 std::memcpy(__result + __olength - __i - 1, __DIGIT_TABLE + __c, 2); 630 __i += 2; 631 } 632 if (__output2 >= 10) { 633 const uint32_t __c = __output2 << 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' + __output2); 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 if (_Scientific_exponent >= 100) { 660 const int32_t __c = _Scientific_exponent % 10; 661 std::memcpy(__result + __index, __DIGIT_TABLE + 2 * (_Scientific_exponent / 10), 2); 662 __result[__index + 2] = static_cast<char>('0' + __c); 663 __index += 3; 664 } else { 665 std::memcpy(__result + __index, __DIGIT_TABLE + 2 * _Scientific_exponent, 2); 666 __index += 2; 667 } 668 669 return { _First + _Total_scientific_length, errc{} }; 670 } 671 672 [[nodiscard]] _LIBCPP_HIDE_FROM_ABI inline bool __d2d_small_int(const uint64_t __ieeeMantissa, const uint32_t __ieeeExponent, 673 __floating_decimal_64* const __v) { 674 const uint64_t __m2 = (1ull << __DOUBLE_MANTISSA_BITS) | __ieeeMantissa; 675 const int32_t __e2 = static_cast<int32_t>(__ieeeExponent) - __DOUBLE_BIAS - __DOUBLE_MANTISSA_BITS; 676 677 if (__e2 > 0) { 678 // f = __m2 * 2^__e2 >= 2^53 is an integer. 679 // Ignore this case for now. 680 return false; 681 } 682 683 if (__e2 < -52) { 684 // f < 1. 685 return false; 686 } 687 688 // Since 2^52 <= __m2 < 2^53 and 0 <= -__e2 <= 52: 1 <= f = __m2 / 2^-__e2 < 2^53. 689 // Test if the lower -__e2 bits of the significand are 0, i.e. whether the fraction is 0. 690 const uint64_t __mask = (1ull << -__e2) - 1; 691 const uint64_t __fraction = __m2 & __mask; 692 if (__fraction != 0) { 693 return false; 694 } 695 696 // f is an integer in the range [1, 2^53). 697 // Note: __mantissa might contain trailing (decimal) 0's. 698 // Note: since 2^53 < 10^16, there is no need to adjust __decimalLength17(). 699 __v->__mantissa = __m2 >> -__e2; 700 __v->__exponent = 0; 701 return true; 702 } 703 704 [[nodiscard]] to_chars_result __d2s_buffered_n(char* const _First, char* const _Last, const double __f, 705 const chars_format _Fmt) { 706 707 // Step 1: Decode the floating-point number, and unify normalized and subnormal cases. 708 const uint64_t __bits = __double_to_bits(__f); 709 710 // Case distinction; exit early for the easy cases. 711 if (__bits == 0) { 712 if (_Fmt == chars_format::scientific) { 713 if (_Last - _First < 5) { 714 return { _Last, errc::value_too_large }; 715 } 716 717 std::memcpy(_First, "0e+00", 5); 718 719 return { _First + 5, errc{} }; 720 } 721 722 // Print "0" for chars_format::fixed, chars_format::general, and chars_format{}. 723 if (_First == _Last) { 724 return { _Last, errc::value_too_large }; 725 } 726 727 *_First = '0'; 728 729 return { _First + 1, errc{} }; 730 } 731 732 // Decode __bits into mantissa and exponent. 733 const uint64_t __ieeeMantissa = __bits & ((1ull << __DOUBLE_MANTISSA_BITS) - 1); 734 const uint32_t __ieeeExponent = static_cast<uint32_t>(__bits >> __DOUBLE_MANTISSA_BITS); 735 736 if (_Fmt == chars_format::fixed) { 737 // const uint64_t _Mantissa2 = __ieeeMantissa | (1ull << __DOUBLE_MANTISSA_BITS); // restore implicit bit 738 const int32_t _Exponent2 = static_cast<int32_t>(__ieeeExponent) 739 - __DOUBLE_BIAS - __DOUBLE_MANTISSA_BITS; // bias and normalization 740 741 // Normal values are equal to _Mantissa2 * 2^_Exponent2. 742 // (Subnormals are different, but they'll be rejected by the _Exponent2 test here, so they can be ignored.) 743 744 // For nonzero integers, _Exponent2 >= -52. (The minimum value occurs when _Mantissa2 * 2^_Exponent2 is 1. 745 // In that case, _Mantissa2 is the implicit 1 bit followed by 52 zeros, so _Exponent2 is -52 to shift away 746 // the zeros.) The dense range of exactly representable integers has negative or zero exponents 747 // (as positive exponents make the range non-dense). For that dense range, Ryu will always be used: 748 // every digit is necessary to uniquely identify the value, so Ryu must print them all. 749 750 // Positive exponents are the non-dense range of exactly representable integers. This contains all of the values 751 // for which Ryu can't be used (and a few Ryu-friendly values). We can save time by detecting positive 752 // exponents here and skipping Ryu. Calling __d2fixed_buffered_n() with precision 0 is valid for all integers 753 // (so it's okay if we call it with a Ryu-friendly value). 754 if (_Exponent2 > 0) { 755 return __d2fixed_buffered_n(_First, _Last, __f, 0); 756 } 757 } 758 759 __floating_decimal_64 __v; 760 const bool __isSmallInt = __d2d_small_int(__ieeeMantissa, __ieeeExponent, &__v); 761 if (__isSmallInt) { 762 // For small integers in the range [1, 2^53), __v.__mantissa might contain trailing (decimal) zeros. 763 // For scientific notation we need to move these zeros into the exponent. 764 // (This is not needed for fixed-point notation, so it might be beneficial to trim 765 // trailing zeros in __to_chars only if needed - once fixed-point notation output is implemented.) 766 for (;;) { 767 const uint64_t __q = __div10(__v.__mantissa); 768 const uint32_t __r = static_cast<uint32_t>(__v.__mantissa) - 10 * static_cast<uint32_t>(__q); 769 if (__r != 0) { 770 break; 771 } 772 __v.__mantissa = __q; 773 ++__v.__exponent; 774 } 775 } else { 776 __v = __d2d(__ieeeMantissa, __ieeeExponent); 777 } 778 779 return __to_chars(_First, _Last, __v, _Fmt, __f); 780 } 781 782 _LIBCPP_END_NAMESPACE_STD 783 784 // clang-format on 785