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 46 #include "include/ryu/common.h" 47 #include "include/ryu/d2fixed.h" 48 #include "include/ryu/d2s.h" 49 #include "include/ryu/d2s_full_table.h" 50 #include "include/ryu/d2s_intrinsics.h" 51 #include "include/ryu/digit_table.h" 52 #include "include/ryu/ryu.h" 53 54 _LIBCPP_BEGIN_NAMESPACE_STD 55 56 // We need a 64x128-bit multiplication and a subsequent 128-bit shift. 57 // Multiplication: 58 // The 64-bit factor is variable and passed in, the 128-bit factor comes 59 // from a lookup table. We know that the 64-bit factor only has 55 60 // significant bits (i.e., the 9 topmost bits are zeros). The 128-bit 61 // factor only has 124 significant bits (i.e., the 4 topmost bits are 62 // zeros). 63 // Shift: 64 // In principle, the multiplication result requires 55 + 124 = 179 bits to 65 // represent. However, we then shift this value to the right by __j, which is 66 // at least __j >= 115, so the result is guaranteed to fit into 179 - 115 = 64 67 // bits. This means that we only need the topmost 64 significant bits of 68 // the 64x128-bit multiplication. 69 // 70 // There are several ways to do this: 71 // 1. Best case: the compiler exposes a 128-bit type. 72 // We perform two 64x64-bit multiplications, add the higher 64 bits of the 73 // lower result to the higher result, and shift by __j - 64 bits. 74 // 75 // We explicitly cast from 64-bit to 128-bit, so the compiler can tell 76 // that these are only 64-bit inputs, and can map these to the best 77 // possible sequence of assembly instructions. 78 // x64 machines happen to have matching assembly instructions for 79 // 64x64-bit multiplications and 128-bit shifts. 80 // 81 // 2. Second best case: the compiler exposes intrinsics for the x64 assembly 82 // instructions mentioned in 1. 83 // 84 // 3. We only have 64x64 bit instructions that return the lower 64 bits of 85 // the result, i.e., we have to use plain C. 86 // Our inputs are less than the full width, so we have three options: 87 // a. Ignore this fact and just implement the intrinsics manually. 88 // b. Split both into 31-bit pieces, which guarantees no internal overflow, 89 // but requires extra work upfront (unless we change the lookup table). 90 // c. Split only the first factor into 31-bit pieces, which also guarantees 91 // no internal overflow, but requires extra work since the intermediate 92 // results are not perfectly aligned. 93 #ifdef _LIBCPP_INTRINSIC128 94 95 [[nodiscard]] _LIBCPP_HIDE_FROM_ABI inline uint64_t __mulShift(const uint64_t __m, const uint64_t* const __mul, const int32_t __j) { 96 // __m is maximum 55 bits 97 uint64_t __high1; // 128 98 const uint64_t __low1 = __ryu_umul128(__m, __mul[1], &__high1); // 64 99 uint64_t __high0; // 64 100 (void) __ryu_umul128(__m, __mul[0], &__high0); // 0 101 const uint64_t __sum = __high0 + __low1; 102 if (__sum < __high0) { 103 ++__high1; // overflow into __high1 104 } 105 return __ryu_shiftright128(__sum, __high1, static_cast<uint32_t>(__j - 64)); 106 } 107 108 [[nodiscard]] _LIBCPP_HIDE_FROM_ABI inline uint64_t __mulShiftAll(const uint64_t __m, const uint64_t* const __mul, const int32_t __j, 109 uint64_t* const __vp, uint64_t* const __vm, const uint32_t __mmShift) { 110 *__vp = __mulShift(4 * __m + 2, __mul, __j); 111 *__vm = __mulShift(4 * __m - 1 - __mmShift, __mul, __j); 112 return __mulShift(4 * __m, __mul, __j); 113 } 114 115 #else // ^^^ intrinsics available ^^^ / vvv intrinsics unavailable vvv 116 117 [[nodiscard]] _LIBCPP_HIDE_FROM_ABI inline _LIBCPP_ALWAYS_INLINE uint64_t __mulShiftAll(uint64_t __m, const uint64_t* const __mul, const int32_t __j, 118 uint64_t* const __vp, uint64_t* const __vm, const uint32_t __mmShift) { // TRANSITION, VSO-634761 119 __m <<= 1; 120 // __m is maximum 55 bits 121 uint64_t __tmp; 122 const uint64_t __lo = __ryu_umul128(__m, __mul[0], &__tmp); 123 uint64_t __hi; 124 const uint64_t __mid = __tmp + __ryu_umul128(__m, __mul[1], &__hi); 125 __hi += __mid < __tmp; // overflow into __hi 126 127 const uint64_t __lo2 = __lo + __mul[0]; 128 const uint64_t __mid2 = __mid + __mul[1] + (__lo2 < __lo); 129 const uint64_t __hi2 = __hi + (__mid2 < __mid); 130 *__vp = __ryu_shiftright128(__mid2, __hi2, static_cast<uint32_t>(__j - 64 - 1)); 131 132 if (__mmShift == 1) { 133 const uint64_t __lo3 = __lo - __mul[0]; 134 const uint64_t __mid3 = __mid - __mul[1] - (__lo3 > __lo); 135 const uint64_t __hi3 = __hi - (__mid3 > __mid); 136 *__vm = __ryu_shiftright128(__mid3, __hi3, static_cast<uint32_t>(__j - 64 - 1)); 137 } else { 138 const uint64_t __lo3 = __lo + __lo; 139 const uint64_t __mid3 = __mid + __mid + (__lo3 < __lo); 140 const uint64_t __hi3 = __hi + __hi + (__mid3 < __mid); 141 const uint64_t __lo4 = __lo3 - __mul[0]; 142 const uint64_t __mid4 = __mid3 - __mul[1] - (__lo4 > __lo3); 143 const uint64_t __hi4 = __hi3 - (__mid4 > __mid3); 144 *__vm = __ryu_shiftright128(__mid4, __hi4, static_cast<uint32_t>(__j - 64)); 145 } 146 147 return __ryu_shiftright128(__mid, __hi, static_cast<uint32_t>(__j - 64 - 1)); 148 } 149 150 #endif // ^^^ intrinsics unavailable ^^^ 151 152 [[nodiscard]] _LIBCPP_HIDE_FROM_ABI inline uint32_t __decimalLength17(const uint64_t __v) { 153 // This is slightly faster than a loop. 154 // The average output length is 16.38 digits, so we check high-to-low. 155 // Function precondition: __v is not an 18, 19, or 20-digit number. 156 // (17 digits are sufficient for round-tripping.) 157 _LIBCPP_ASSERT_INTERNAL(__v < 100000000000000000u, ""); 158 if (__v >= 10000000000000000u) { return 17; } 159 if (__v >= 1000000000000000u) { return 16; } 160 if (__v >= 100000000000000u) { return 15; } 161 if (__v >= 10000000000000u) { return 14; } 162 if (__v >= 1000000000000u) { return 13; } 163 if (__v >= 100000000000u) { return 12; } 164 if (__v >= 10000000000u) { return 11; } 165 if (__v >= 1000000000u) { return 10; } 166 if (__v >= 100000000u) { return 9; } 167 if (__v >= 10000000u) { return 8; } 168 if (__v >= 1000000u) { return 7; } 169 if (__v >= 100000u) { return 6; } 170 if (__v >= 10000u) { return 5; } 171 if (__v >= 1000u) { return 4; } 172 if (__v >= 100u) { return 3; } 173 if (__v >= 10u) { return 2; } 174 return 1; 175 } 176 177 // A floating decimal representing m * 10^e. 178 struct __floating_decimal_64 { 179 uint64_t __mantissa; 180 int32_t __exponent; 181 }; 182 183 [[nodiscard]] _LIBCPP_HIDE_FROM_ABI inline __floating_decimal_64 __d2d(const uint64_t __ieeeMantissa, const uint32_t __ieeeExponent) { 184 int32_t __e2; 185 uint64_t __m2; 186 if (__ieeeExponent == 0) { 187 // We subtract 2 so that the bounds computation has 2 additional bits. 188 __e2 = 1 - __DOUBLE_BIAS - __DOUBLE_MANTISSA_BITS - 2; 189 __m2 = __ieeeMantissa; 190 } else { 191 __e2 = static_cast<int32_t>(__ieeeExponent) - __DOUBLE_BIAS - __DOUBLE_MANTISSA_BITS - 2; 192 __m2 = (1ull << __DOUBLE_MANTISSA_BITS) | __ieeeMantissa; 193 } 194 const bool __even = (__m2 & 1) == 0; 195 const bool __acceptBounds = __even; 196 197 // Step 2: Determine the interval of valid decimal representations. 198 const uint64_t __mv = 4 * __m2; 199 // Implicit bool -> int conversion. True is 1, false is 0. 200 const uint32_t __mmShift = __ieeeMantissa != 0 || __ieeeExponent <= 1; 201 // We would compute __mp and __mm like this: 202 // uint64_t __mp = 4 * __m2 + 2; 203 // uint64_t __mm = __mv - 1 - __mmShift; 204 205 // Step 3: Convert to a decimal power base using 128-bit arithmetic. 206 uint64_t __vr, __vp, __vm; 207 int32_t __e10; 208 bool __vmIsTrailingZeros = false; 209 bool __vrIsTrailingZeros = false; 210 if (__e2 >= 0) { 211 // I tried special-casing __q == 0, but there was no effect on performance. 212 // This expression is slightly faster than max(0, __log10Pow2(__e2) - 1). 213 const uint32_t __q = __log10Pow2(__e2) - (__e2 > 3); 214 __e10 = static_cast<int32_t>(__q); 215 const int32_t __k = __DOUBLE_POW5_INV_BITCOUNT + __pow5bits(static_cast<int32_t>(__q)) - 1; 216 const int32_t __i = -__e2 + static_cast<int32_t>(__q) + __k; 217 __vr = __mulShiftAll(__m2, __DOUBLE_POW5_INV_SPLIT[__q], __i, &__vp, &__vm, __mmShift); 218 if (__q <= 21) { 219 // This should use __q <= 22, but I think 21 is also safe. Smaller values 220 // may still be safe, but it's more difficult to reason about them. 221 // Only one of __mp, __mv, and __mm can be a multiple of 5, if any. 222 const uint32_t __mvMod5 = static_cast<uint32_t>(__mv) - 5 * static_cast<uint32_t>(__div5(__mv)); 223 if (__mvMod5 == 0) { 224 __vrIsTrailingZeros = __multipleOfPowerOf5(__mv, __q); 225 } else if (__acceptBounds) { 226 // Same as min(__e2 + (~__mm & 1), __pow5Factor(__mm)) >= __q 227 // <=> __e2 + (~__mm & 1) >= __q && __pow5Factor(__mm) >= __q 228 // <=> true && __pow5Factor(__mm) >= __q, since __e2 >= __q. 229 __vmIsTrailingZeros = __multipleOfPowerOf5(__mv - 1 - __mmShift, __q); 230 } else { 231 // Same as min(__e2 + 1, __pow5Factor(__mp)) >= __q. 232 __vp -= __multipleOfPowerOf5(__mv + 2, __q); 233 } 234 } 235 } else { 236 // This expression is slightly faster than max(0, __log10Pow5(-__e2) - 1). 237 const uint32_t __q = __log10Pow5(-__e2) - (-__e2 > 1); 238 __e10 = static_cast<int32_t>(__q) + __e2; 239 const int32_t __i = -__e2 - static_cast<int32_t>(__q); 240 const int32_t __k = __pow5bits(__i) - __DOUBLE_POW5_BITCOUNT; 241 const int32_t __j = static_cast<int32_t>(__q) - __k; 242 __vr = __mulShiftAll(__m2, __DOUBLE_POW5_SPLIT[__i], __j, &__vp, &__vm, __mmShift); 243 if (__q <= 1) { 244 // {__vr,__vp,__vm} is trailing zeros if {__mv,__mp,__mm} has at least __q trailing 0 bits. 245 // __mv = 4 * __m2, so it always has at least two trailing 0 bits. 246 __vrIsTrailingZeros = true; 247 if (__acceptBounds) { 248 // __mm = __mv - 1 - __mmShift, so it has 1 trailing 0 bit iff __mmShift == 1. 249 __vmIsTrailingZeros = __mmShift == 1; 250 } else { 251 // __mp = __mv + 2, so it always has at least one trailing 0 bit. 252 --__vp; 253 } 254 } else if (__q < 63) { // TRANSITION(ulfjack): Use a tighter bound here. 255 // We need to compute min(ntz(__mv), __pow5Factor(__mv) - __e2) >= __q - 1 256 // <=> ntz(__mv) >= __q - 1 && __pow5Factor(__mv) - __e2 >= __q - 1 257 // <=> ntz(__mv) >= __q - 1 (__e2 is negative and -__e2 >= __q) 258 // <=> (__mv & ((1 << (__q - 1)) - 1)) == 0 259 // We also need to make sure that the left shift does not overflow. 260 __vrIsTrailingZeros = __multipleOfPowerOf2(__mv, __q - 1); 261 } 262 } 263 264 // Step 4: Find the shortest decimal representation in the interval of valid representations. 265 int32_t __removed = 0; 266 uint8_t __lastRemovedDigit = 0; 267 uint64_t _Output; 268 // On average, we remove ~2 digits. 269 if (__vmIsTrailingZeros || __vrIsTrailingZeros) { 270 // General case, which happens rarely (~0.7%). 271 for (;;) { 272 const uint64_t __vpDiv10 = __div10(__vp); 273 const uint64_t __vmDiv10 = __div10(__vm); 274 if (__vpDiv10 <= __vmDiv10) { 275 break; 276 } 277 const uint32_t __vmMod10 = static_cast<uint32_t>(__vm) - 10 * static_cast<uint32_t>(__vmDiv10); 278 const uint64_t __vrDiv10 = __div10(__vr); 279 const uint32_t __vrMod10 = static_cast<uint32_t>(__vr) - 10 * static_cast<uint32_t>(__vrDiv10); 280 __vmIsTrailingZeros &= __vmMod10 == 0; 281 __vrIsTrailingZeros &= __lastRemovedDigit == 0; 282 __lastRemovedDigit = static_cast<uint8_t>(__vrMod10); 283 __vr = __vrDiv10; 284 __vp = __vpDiv10; 285 __vm = __vmDiv10; 286 ++__removed; 287 } 288 if (__vmIsTrailingZeros) { 289 for (;;) { 290 const uint64_t __vmDiv10 = __div10(__vm); 291 const uint32_t __vmMod10 = static_cast<uint32_t>(__vm) - 10 * static_cast<uint32_t>(__vmDiv10); 292 if (__vmMod10 != 0) { 293 break; 294 } 295 const uint64_t __vpDiv10 = __div10(__vp); 296 const uint64_t __vrDiv10 = __div10(__vr); 297 const uint32_t __vrMod10 = static_cast<uint32_t>(__vr) - 10 * static_cast<uint32_t>(__vrDiv10); 298 __vrIsTrailingZeros &= __lastRemovedDigit == 0; 299 __lastRemovedDigit = static_cast<uint8_t>(__vrMod10); 300 __vr = __vrDiv10; 301 __vp = __vpDiv10; 302 __vm = __vmDiv10; 303 ++__removed; 304 } 305 } 306 if (__vrIsTrailingZeros && __lastRemovedDigit == 5 && __vr % 2 == 0) { 307 // Round even if the exact number is .....50..0. 308 __lastRemovedDigit = 4; 309 } 310 // We need to take __vr + 1 if __vr is outside bounds or we need to round up. 311 _Output = __vr + ((__vr == __vm && (!__acceptBounds || !__vmIsTrailingZeros)) || __lastRemovedDigit >= 5); 312 } else { 313 // Specialized for the common case (~99.3%). Percentages below are relative to this. 314 bool __roundUp = false; 315 const uint64_t __vpDiv100 = __div100(__vp); 316 const uint64_t __vmDiv100 = __div100(__vm); 317 if (__vpDiv100 > __vmDiv100) { // Optimization: remove two digits at a time (~86.2%). 318 const uint64_t __vrDiv100 = __div100(__vr); 319 const uint32_t __vrMod100 = static_cast<uint32_t>(__vr) - 100 * static_cast<uint32_t>(__vrDiv100); 320 __roundUp = __vrMod100 >= 50; 321 __vr = __vrDiv100; 322 __vp = __vpDiv100; 323 __vm = __vmDiv100; 324 __removed += 2; 325 } 326 // Loop iterations below (approximately), without optimization above: 327 // 0: 0.03%, 1: 13.8%, 2: 70.6%, 3: 14.0%, 4: 1.40%, 5: 0.14%, 6+: 0.02% 328 // Loop iterations below (approximately), with optimization above: 329 // 0: 70.6%, 1: 27.8%, 2: 1.40%, 3: 0.14%, 4+: 0.02% 330 for (;;) { 331 const uint64_t __vpDiv10 = __div10(__vp); 332 const uint64_t __vmDiv10 = __div10(__vm); 333 if (__vpDiv10 <= __vmDiv10) { 334 break; 335 } 336 const uint64_t __vrDiv10 = __div10(__vr); 337 const uint32_t __vrMod10 = static_cast<uint32_t>(__vr) - 10 * static_cast<uint32_t>(__vrDiv10); 338 __roundUp = __vrMod10 >= 5; 339 __vr = __vrDiv10; 340 __vp = __vpDiv10; 341 __vm = __vmDiv10; 342 ++__removed; 343 } 344 // We need to take __vr + 1 if __vr is outside bounds or we need to round up. 345 _Output = __vr + (__vr == __vm || __roundUp); 346 } 347 const int32_t __exp = __e10 + __removed; 348 349 __floating_decimal_64 __fd; 350 __fd.__exponent = __exp; 351 __fd.__mantissa = _Output; 352 return __fd; 353 } 354 355 [[nodiscard]] _LIBCPP_HIDE_FROM_ABI inline to_chars_result __to_chars(char* const _First, char* const _Last, const __floating_decimal_64 __v, 356 chars_format _Fmt, const double __f) { 357 // Step 5: Print the decimal representation. 358 uint64_t _Output = __v.__mantissa; 359 int32_t _Ryu_exponent = __v.__exponent; 360 const uint32_t __olength = __decimalLength17(_Output); 361 int32_t _Scientific_exponent = _Ryu_exponent + static_cast<int32_t>(__olength) - 1; 362 363 if (_Fmt == chars_format{}) { 364 int32_t _Lower; 365 int32_t _Upper; 366 367 if (__olength == 1) { 368 // Value | Fixed | Scientific 369 // 1e-3 | "0.001" | "1e-03" 370 // 1e4 | "10000" | "1e+04" 371 _Lower = -3; 372 _Upper = 4; 373 } else { 374 // Value | Fixed | Scientific 375 // 1234e-7 | "0.0001234" | "1.234e-04" 376 // 1234e5 | "123400000" | "1.234e+08" 377 _Lower = -static_cast<int32_t>(__olength + 3); 378 _Upper = 5; 379 } 380 381 if (_Lower <= _Ryu_exponent && _Ryu_exponent <= _Upper) { 382 _Fmt = chars_format::fixed; 383 } else { 384 _Fmt = chars_format::scientific; 385 } 386 } else if (_Fmt == chars_format::general) { 387 // C11 7.21.6.1 "The fprintf function"/8: 388 // "Let P equal [...] 6 if the precision is omitted [...]. 389 // Then, if a conversion with style E would have an exponent of X: 390 // - if P > X >= -4, the conversion is with style f [...]. 391 // - otherwise, the conversion is with style e [...]." 392 if (-4 <= _Scientific_exponent && _Scientific_exponent < 6) { 393 _Fmt = chars_format::fixed; 394 } else { 395 _Fmt = chars_format::scientific; 396 } 397 } 398 399 if (_Fmt == chars_format::fixed) { 400 // Example: _Output == 1729, __olength == 4 401 402 // _Ryu_exponent | Printed | _Whole_digits | _Total_fixed_length | Notes 403 // --------------|----------|---------------|----------------------|--------------------------------------- 404 // 2 | 172900 | 6 | _Whole_digits | Ryu can't be used for printing 405 // 1 | 17290 | 5 | (sometimes adjusted) | when the trimmed digits are nonzero. 406 // --------------|----------|---------------|----------------------|--------------------------------------- 407 // 0 | 1729 | 4 | _Whole_digits | Unified length cases. 408 // --------------|----------|---------------|----------------------|--------------------------------------- 409 // -1 | 172.9 | 3 | __olength + 1 | This case can't happen for 410 // -2 | 17.29 | 2 | | __olength == 1, but no additional 411 // -3 | 1.729 | 1 | | code is needed to avoid it. 412 // --------------|----------|---------------|----------------------|--------------------------------------- 413 // -4 | 0.1729 | 0 | 2 - _Ryu_exponent | C11 7.21.6.1 "The fprintf function"/8: 414 // -5 | 0.01729 | -1 | | "If a decimal-point character appears, 415 // -6 | 0.001729 | -2 | | at least one digit appears before it." 416 417 const int32_t _Whole_digits = static_cast<int32_t>(__olength) + _Ryu_exponent; 418 419 uint32_t _Total_fixed_length; 420 if (_Ryu_exponent >= 0) { // cases "172900" and "1729" 421 _Total_fixed_length = static_cast<uint32_t>(_Whole_digits); 422 if (_Output == 1) { 423 // Rounding can affect the number of digits. 424 // For example, 1e23 is exactly "99999999999999991611392" which is 23 digits instead of 24. 425 // We can use a lookup table to detect this and adjust the total length. 426 static constexpr uint8_t _Adjustment[309] = { 427 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, 428 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, 429 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, 430 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, 431 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, 432 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, 433 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 }; 434 _Total_fixed_length -= _Adjustment[_Ryu_exponent]; 435 // _Whole_digits doesn't need to be adjusted because these cases won't refer to it later. 436 } 437 } else if (_Whole_digits > 0) { // case "17.29" 438 _Total_fixed_length = __olength + 1; 439 } else { // case "0.001729" 440 _Total_fixed_length = static_cast<uint32_t>(2 - _Ryu_exponent); 441 } 442 443 if (_Last - _First < static_cast<ptrdiff_t>(_Total_fixed_length)) { 444 return { _Last, errc::value_too_large }; 445 } 446 447 char* _Mid; 448 if (_Ryu_exponent > 0) { // case "172900" 449 bool _Can_use_ryu; 450 451 if (_Ryu_exponent > 22) { // 10^22 is the largest power of 10 that's exactly representable as a double. 452 _Can_use_ryu = false; 453 } else { 454 // Ryu generated X: __v.__mantissa * 10^_Ryu_exponent 455 // __v.__mantissa == 2^_Trailing_zero_bits * (__v.__mantissa >> _Trailing_zero_bits) 456 // 10^_Ryu_exponent == 2^_Ryu_exponent * 5^_Ryu_exponent 457 458 // _Trailing_zero_bits is [0, 56] (aside: because 2^56 is the largest power of 2 459 // with 17 decimal digits, which is double's round-trip limit.) 460 // _Ryu_exponent is [1, 22]. 461 // Normalization adds [2, 52] (aside: at least 2 because the pre-normalized mantissa is at least 5). 462 // This adds up to [3, 130], which is well below double's maximum binary exponent 1023. 463 464 // Therefore, we just need to consider (__v.__mantissa >> _Trailing_zero_bits) * 5^_Ryu_exponent. 465 466 // If that product would exceed 53 bits, then X can't be exactly represented as a double. 467 // (That's not a problem for round-tripping, because X is close enough to the original double, 468 // but X isn't mathematically equal to the original double.) This requires a high-precision fallback. 469 470 // If the product is 53 bits or smaller, then X can be exactly represented as a double (and we don't 471 // need to re-synthesize it; the original double must have been X, because Ryu wouldn't produce the 472 // same output for two different doubles X and Y). This allows Ryu's output to be used (zero-filled). 473 474 // (2^53 - 1) / 5^0 (for indexing), (2^53 - 1) / 5^1, ..., (2^53 - 1) / 5^22 475 static constexpr uint64_t _Max_shifted_mantissa[23] = { 476 9007199254740991u, 1801439850948198u, 360287970189639u, 72057594037927u, 14411518807585u, 477 2882303761517u, 576460752303u, 115292150460u, 23058430092u, 4611686018u, 922337203u, 184467440u, 478 36893488u, 7378697u, 1475739u, 295147u, 59029u, 11805u, 2361u, 472u, 94u, 18u, 3u }; 479 480 unsigned long _Trailing_zero_bits; 481 #ifdef _LIBCPP_HAS_BITSCAN64 482 (void) _BitScanForward64(&_Trailing_zero_bits, __v.__mantissa); // __v.__mantissa is guaranteed nonzero 483 #else // ^^^ 64-bit ^^^ / vvv 32-bit vvv 484 const uint32_t _Low_mantissa = static_cast<uint32_t>(__v.__mantissa); 485 if (_Low_mantissa != 0) { 486 (void) _BitScanForward(&_Trailing_zero_bits, _Low_mantissa); 487 } else { 488 const uint32_t _High_mantissa = static_cast<uint32_t>(__v.__mantissa >> 32); // nonzero here 489 (void) _BitScanForward(&_Trailing_zero_bits, _High_mantissa); 490 _Trailing_zero_bits += 32; 491 } 492 #endif // ^^^ 32-bit ^^^ 493 const uint64_t _Shifted_mantissa = __v.__mantissa >> _Trailing_zero_bits; 494 _Can_use_ryu = _Shifted_mantissa <= _Max_shifted_mantissa[_Ryu_exponent]; 495 } 496 497 if (!_Can_use_ryu) { 498 // Print the integer exactly. 499 // Performance note: This will redundantly perform bounds checking. 500 // Performance note: This will redundantly decompose the IEEE representation. 501 return __d2fixed_buffered_n(_First, _Last, __f, 0); 502 } 503 504 // _Can_use_ryu 505 // Print the decimal digits, left-aligned within [_First, _First + _Total_fixed_length). 506 _Mid = _First + __olength; 507 } else { // cases "1729", "17.29", and "0.001729" 508 // Print the decimal digits, right-aligned within [_First, _First + _Total_fixed_length). 509 _Mid = _First + _Total_fixed_length; 510 } 511 512 // We prefer 32-bit operations, even on 64-bit platforms. 513 // We have at most 17 digits, and uint32_t can store 9 digits. 514 // If _Output doesn't fit into uint32_t, we cut off 8 digits, 515 // so the rest will fit into uint32_t. 516 if ((_Output >> 32) != 0) { 517 // Expensive 64-bit division. 518 const uint64_t __q = __div1e8(_Output); 519 uint32_t __output2 = static_cast<uint32_t>(_Output - 100000000 * __q); 520 _Output = __q; 521 522 const uint32_t __c = __output2 % 10000; 523 __output2 /= 10000; 524 const uint32_t __d = __output2 % 10000; 525 const uint32_t __c0 = (__c % 100) << 1; 526 const uint32_t __c1 = (__c / 100) << 1; 527 const uint32_t __d0 = (__d % 100) << 1; 528 const uint32_t __d1 = (__d / 100) << 1; 529 530 std::memcpy(_Mid -= 2, __DIGIT_TABLE + __c0, 2); 531 std::memcpy(_Mid -= 2, __DIGIT_TABLE + __c1, 2); 532 std::memcpy(_Mid -= 2, __DIGIT_TABLE + __d0, 2); 533 std::memcpy(_Mid -= 2, __DIGIT_TABLE + __d1, 2); 534 } 535 uint32_t __output2 = static_cast<uint32_t>(_Output); 536 while (__output2 >= 10000) { 537 #ifdef __clang__ // TRANSITION, LLVM-38217 538 const uint32_t __c = __output2 - 10000 * (__output2 / 10000); 539 #else 540 const uint32_t __c = __output2 % 10000; 541 #endif 542 __output2 /= 10000; 543 const uint32_t __c0 = (__c % 100) << 1; 544 const uint32_t __c1 = (__c / 100) << 1; 545 std::memcpy(_Mid -= 2, __DIGIT_TABLE + __c0, 2); 546 std::memcpy(_Mid -= 2, __DIGIT_TABLE + __c1, 2); 547 } 548 if (__output2 >= 100) { 549 const uint32_t __c = (__output2 % 100) << 1; 550 __output2 /= 100; 551 std::memcpy(_Mid -= 2, __DIGIT_TABLE + __c, 2); 552 } 553 if (__output2 >= 10) { 554 const uint32_t __c = __output2 << 1; 555 std::memcpy(_Mid -= 2, __DIGIT_TABLE + __c, 2); 556 } else { 557 *--_Mid = static_cast<char>('0' + __output2); 558 } 559 560 if (_Ryu_exponent > 0) { // case "172900" with _Can_use_ryu 561 // Performance note: it might be more efficient to do this immediately after setting _Mid. 562 std::memset(_First + __olength, '0', static_cast<size_t>(_Ryu_exponent)); 563 } else if (_Ryu_exponent == 0) { // case "1729" 564 // Done! 565 } else if (_Whole_digits > 0) { // case "17.29" 566 // Performance note: moving digits might not be optimal. 567 std::memmove(_First, _First + 1, static_cast<size_t>(_Whole_digits)); 568 _First[_Whole_digits] = '.'; 569 } else { // case "0.001729" 570 // Performance note: a larger memset() followed by overwriting '.' might be more efficient. 571 _First[0] = '0'; 572 _First[1] = '.'; 573 std::memset(_First + 2, '0', static_cast<size_t>(-_Whole_digits)); 574 } 575 576 return { _First + _Total_fixed_length, errc{} }; 577 } 578 579 const uint32_t _Total_scientific_length = __olength + (__olength > 1) // digits + possible decimal point 580 + (-100 < _Scientific_exponent && _Scientific_exponent < 100 ? 4 : 5); // + scientific exponent 581 if (_Last - _First < static_cast<ptrdiff_t>(_Total_scientific_length)) { 582 return { _Last, errc::value_too_large }; 583 } 584 char* const __result = _First; 585 586 // Print the decimal digits. 587 uint32_t __i = 0; 588 // We prefer 32-bit operations, even on 64-bit platforms. 589 // We have at most 17 digits, and uint32_t can store 9 digits. 590 // If _Output doesn't fit into uint32_t, we cut off 8 digits, 591 // so the rest will fit into uint32_t. 592 if ((_Output >> 32) != 0) { 593 // Expensive 64-bit division. 594 const uint64_t __q = __div1e8(_Output); 595 uint32_t __output2 = static_cast<uint32_t>(_Output) - 100000000 * static_cast<uint32_t>(__q); 596 _Output = __q; 597 598 const uint32_t __c = __output2 % 10000; 599 __output2 /= 10000; 600 const uint32_t __d = __output2 % 10000; 601 const uint32_t __c0 = (__c % 100) << 1; 602 const uint32_t __c1 = (__c / 100) << 1; 603 const uint32_t __d0 = (__d % 100) << 1; 604 const uint32_t __d1 = (__d / 100) << 1; 605 std::memcpy(__result + __olength - __i - 1, __DIGIT_TABLE + __c0, 2); 606 std::memcpy(__result + __olength - __i - 3, __DIGIT_TABLE + __c1, 2); 607 std::memcpy(__result + __olength - __i - 5, __DIGIT_TABLE + __d0, 2); 608 std::memcpy(__result + __olength - __i - 7, __DIGIT_TABLE + __d1, 2); 609 __i += 8; 610 } 611 uint32_t __output2 = static_cast<uint32_t>(_Output); 612 while (__output2 >= 10000) { 613 #ifdef __clang__ // TRANSITION, LLVM-38217 614 const uint32_t __c = __output2 - 10000 * (__output2 / 10000); 615 #else 616 const uint32_t __c = __output2 % 10000; 617 #endif 618 __output2 /= 10000; 619 const uint32_t __c0 = (__c % 100) << 1; 620 const uint32_t __c1 = (__c / 100) << 1; 621 std::memcpy(__result + __olength - __i - 1, __DIGIT_TABLE + __c0, 2); 622 std::memcpy(__result + __olength - __i - 3, __DIGIT_TABLE + __c1, 2); 623 __i += 4; 624 } 625 if (__output2 >= 100) { 626 const uint32_t __c = (__output2 % 100) << 1; 627 __output2 /= 100; 628 std::memcpy(__result + __olength - __i - 1, __DIGIT_TABLE + __c, 2); 629 __i += 2; 630 } 631 if (__output2 >= 10) { 632 const uint32_t __c = __output2 << 1; 633 // We can't use memcpy here: the decimal dot goes between these two digits. 634 __result[2] = __DIGIT_TABLE[__c + 1]; 635 __result[0] = __DIGIT_TABLE[__c]; 636 } else { 637 __result[0] = static_cast<char>('0' + __output2); 638 } 639 640 // Print decimal point if needed. 641 uint32_t __index; 642 if (__olength > 1) { 643 __result[1] = '.'; 644 __index = __olength + 1; 645 } else { 646 __index = 1; 647 } 648 649 // Print the exponent. 650 __result[__index++] = 'e'; 651 if (_Scientific_exponent < 0) { 652 __result[__index++] = '-'; 653 _Scientific_exponent = -_Scientific_exponent; 654 } else { 655 __result[__index++] = '+'; 656 } 657 658 if (_Scientific_exponent >= 100) { 659 const int32_t __c = _Scientific_exponent % 10; 660 std::memcpy(__result + __index, __DIGIT_TABLE + 2 * (_Scientific_exponent / 10), 2); 661 __result[__index + 2] = static_cast<char>('0' + __c); 662 __index += 3; 663 } else { 664 std::memcpy(__result + __index, __DIGIT_TABLE + 2 * _Scientific_exponent, 2); 665 __index += 2; 666 } 667 668 return { _First + _Total_scientific_length, errc{} }; 669 } 670 671 [[nodiscard]] _LIBCPP_HIDE_FROM_ABI inline bool __d2d_small_int(const uint64_t __ieeeMantissa, const uint32_t __ieeeExponent, 672 __floating_decimal_64* const __v) { 673 const uint64_t __m2 = (1ull << __DOUBLE_MANTISSA_BITS) | __ieeeMantissa; 674 const int32_t __e2 = static_cast<int32_t>(__ieeeExponent) - __DOUBLE_BIAS - __DOUBLE_MANTISSA_BITS; 675 676 if (__e2 > 0) { 677 // f = __m2 * 2^__e2 >= 2^53 is an integer. 678 // Ignore this case for now. 679 return false; 680 } 681 682 if (__e2 < -52) { 683 // f < 1. 684 return false; 685 } 686 687 // Since 2^52 <= __m2 < 2^53 and 0 <= -__e2 <= 52: 1 <= f = __m2 / 2^-__e2 < 2^53. 688 // Test if the lower -__e2 bits of the significand are 0, i.e. whether the fraction is 0. 689 const uint64_t __mask = (1ull << -__e2) - 1; 690 const uint64_t __fraction = __m2 & __mask; 691 if (__fraction != 0) { 692 return false; 693 } 694 695 // f is an integer in the range [1, 2^53). 696 // Note: __mantissa might contain trailing (decimal) 0's. 697 // Note: since 2^53 < 10^16, there is no need to adjust __decimalLength17(). 698 __v->__mantissa = __m2 >> -__e2; 699 __v->__exponent = 0; 700 return true; 701 } 702 703 [[nodiscard]] to_chars_result __d2s_buffered_n(char* const _First, char* const _Last, const double __f, 704 const chars_format _Fmt) { 705 706 // Step 1: Decode the floating-point number, and unify normalized and subnormal cases. 707 const uint64_t __bits = __double_to_bits(__f); 708 709 // Case distinction; exit early for the easy cases. 710 if (__bits == 0) { 711 if (_Fmt == chars_format::scientific) { 712 if (_Last - _First < 5) { 713 return { _Last, errc::value_too_large }; 714 } 715 716 std::memcpy(_First, "0e+00", 5); 717 718 return { _First + 5, errc{} }; 719 } 720 721 // Print "0" for chars_format::fixed, chars_format::general, and chars_format{}. 722 if (_First == _Last) { 723 return { _Last, errc::value_too_large }; 724 } 725 726 *_First = '0'; 727 728 return { _First + 1, errc{} }; 729 } 730 731 // Decode __bits into mantissa and exponent. 732 const uint64_t __ieeeMantissa = __bits & ((1ull << __DOUBLE_MANTISSA_BITS) - 1); 733 const uint32_t __ieeeExponent = static_cast<uint32_t>(__bits >> __DOUBLE_MANTISSA_BITS); 734 735 if (_Fmt == chars_format::fixed) { 736 // const uint64_t _Mantissa2 = __ieeeMantissa | (1ull << __DOUBLE_MANTISSA_BITS); // restore implicit bit 737 const int32_t _Exponent2 = static_cast<int32_t>(__ieeeExponent) 738 - __DOUBLE_BIAS - __DOUBLE_MANTISSA_BITS; // bias and normalization 739 740 // Normal values are equal to _Mantissa2 * 2^_Exponent2. 741 // (Subnormals are different, but they'll be rejected by the _Exponent2 test here, so they can be ignored.) 742 743 // For nonzero integers, _Exponent2 >= -52. (The minimum value occurs when _Mantissa2 * 2^_Exponent2 is 1. 744 // In that case, _Mantissa2 is the implicit 1 bit followed by 52 zeros, so _Exponent2 is -52 to shift away 745 // the zeros.) The dense range of exactly representable integers has negative or zero exponents 746 // (as positive exponents make the range non-dense). For that dense range, Ryu will always be used: 747 // every digit is necessary to uniquely identify the value, so Ryu must print them all. 748 749 // Positive exponents are the non-dense range of exactly representable integers. This contains all of the values 750 // for which Ryu can't be used (and a few Ryu-friendly values). We can save time by detecting positive 751 // exponents here and skipping Ryu. Calling __d2fixed_buffered_n() with precision 0 is valid for all integers 752 // (so it's okay if we call it with a Ryu-friendly value). 753 if (_Exponent2 > 0) { 754 return __d2fixed_buffered_n(_First, _Last, __f, 0); 755 } 756 } 757 758 __floating_decimal_64 __v; 759 const bool __isSmallInt = __d2d_small_int(__ieeeMantissa, __ieeeExponent, &__v); 760 if (__isSmallInt) { 761 // For small integers in the range [1, 2^53), __v.__mantissa might contain trailing (decimal) zeros. 762 // For scientific notation we need to move these zeros into the exponent. 763 // (This is not needed for fixed-point notation, so it might be beneficial to trim 764 // trailing zeros in __to_chars only if needed - once fixed-point notation output is implemented.) 765 for (;;) { 766 const uint64_t __q = __div10(__v.__mantissa); 767 const uint32_t __r = static_cast<uint32_t>(__v.__mantissa) - 10 * static_cast<uint32_t>(__q); 768 if (__r != 0) { 769 break; 770 } 771 __v.__mantissa = __q; 772 ++__v.__exponent; 773 } 774 } else { 775 __v = __d2d(__ieeeMantissa, __ieeeExponent); 776 } 777 778 return __to_chars(_First, _Last, __v, _Fmt, __f); 779 } 780 781 _LIBCPP_END_NAMESPACE_STD 782 783 // clang-format on 784