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_intrinsics.h" 49 #include "include/ryu/digit_table.h" 50 #include "include/ryu/f2s.h" 51 #include "include/ryu/ryu.h" 52 53 _LIBCPP_BEGIN_NAMESPACE_STD 54 55 inline constexpr int __FLOAT_MANTISSA_BITS = 23; 56 inline constexpr int __FLOAT_EXPONENT_BITS = 8; 57 inline constexpr int __FLOAT_BIAS = 127; 58 59 inline constexpr int __FLOAT_POW5_INV_BITCOUNT = 59; 60 inline constexpr uint64_t __FLOAT_POW5_INV_SPLIT[31] = { 61 576460752303423489u, 461168601842738791u, 368934881474191033u, 295147905179352826u, 62 472236648286964522u, 377789318629571618u, 302231454903657294u, 483570327845851670u, 63 386856262276681336u, 309485009821345069u, 495176015714152110u, 396140812571321688u, 64 316912650057057351u, 507060240091291761u, 405648192073033409u, 324518553658426727u, 65 519229685853482763u, 415383748682786211u, 332306998946228969u, 531691198313966350u, 66 425352958651173080u, 340282366920938464u, 544451787073501542u, 435561429658801234u, 67 348449143727040987u, 557518629963265579u, 446014903970612463u, 356811923176489971u, 68 570899077082383953u, 456719261665907162u, 365375409332725730u 69 }; 70 inline constexpr int __FLOAT_POW5_BITCOUNT = 61; 71 inline constexpr uint64_t __FLOAT_POW5_SPLIT[47] = { 72 1152921504606846976u, 1441151880758558720u, 1801439850948198400u, 2251799813685248000u, 73 1407374883553280000u, 1759218604441600000u, 2199023255552000000u, 1374389534720000000u, 74 1717986918400000000u, 2147483648000000000u, 1342177280000000000u, 1677721600000000000u, 75 2097152000000000000u, 1310720000000000000u, 1638400000000000000u, 2048000000000000000u, 76 1280000000000000000u, 1600000000000000000u, 2000000000000000000u, 1250000000000000000u, 77 1562500000000000000u, 1953125000000000000u, 1220703125000000000u, 1525878906250000000u, 78 1907348632812500000u, 1192092895507812500u, 1490116119384765625u, 1862645149230957031u, 79 1164153218269348144u, 1455191522836685180u, 1818989403545856475u, 2273736754432320594u, 80 1421085471520200371u, 1776356839400250464u, 2220446049250313080u, 1387778780781445675u, 81 1734723475976807094u, 2168404344971008868u, 1355252715606880542u, 1694065894508600678u, 82 2117582368135750847u, 1323488980084844279u, 1654361225106055349u, 2067951531382569187u, 83 1292469707114105741u, 1615587133892632177u, 2019483917365790221u 84 }; 85 86 [[nodiscard]] _LIBCPP_HIDE_FROM_ABI inline uint32_t __pow5Factor(uint32_t __value) { 87 uint32_t __count = 0; 88 for (;;) { 89 _LIBCPP_ASSERT(__value != 0, ""); 90 const uint32_t __q = __value / 5; 91 const uint32_t __r = __value % 5; 92 if (__r != 0) { 93 break; 94 } 95 __value = __q; 96 ++__count; 97 } 98 return __count; 99 } 100 101 // Returns true if __value is divisible by 5^__p. 102 [[nodiscard]] _LIBCPP_HIDE_FROM_ABI inline bool __multipleOfPowerOf5(const uint32_t __value, const uint32_t __p) { 103 return __pow5Factor(__value) >= __p; 104 } 105 106 // Returns true if __value is divisible by 2^__p. 107 [[nodiscard]] _LIBCPP_HIDE_FROM_ABI inline bool __multipleOfPowerOf2(const uint32_t __value, const uint32_t __p) { 108 _LIBCPP_ASSERT(__value != 0, ""); 109 _LIBCPP_ASSERT(__p < 32, ""); 110 // __builtin_ctz doesn't appear to be faster here. 111 return (__value & ((1u << __p) - 1)) == 0; 112 } 113 114 [[nodiscard]] _LIBCPP_HIDE_FROM_ABI inline uint32_t __mulShift(const uint32_t __m, const uint64_t __factor, const int32_t __shift) { 115 _LIBCPP_ASSERT(__shift > 32, ""); 116 117 // The casts here help MSVC to avoid calls to the __allmul library 118 // function. 119 const uint32_t __factorLo = static_cast<uint32_t>(__factor); 120 const uint32_t __factorHi = static_cast<uint32_t>(__factor >> 32); 121 const uint64_t __bits0 = static_cast<uint64_t>(__m) * __factorLo; 122 const uint64_t __bits1 = static_cast<uint64_t>(__m) * __factorHi; 123 124 #ifndef _LIBCPP_64_BIT 125 // On 32-bit platforms we can avoid a 64-bit shift-right since we only 126 // need the upper 32 bits of the result and the shift value is > 32. 127 const uint32_t __bits0Hi = static_cast<uint32_t>(__bits0 >> 32); 128 uint32_t __bits1Lo = static_cast<uint32_t>(__bits1); 129 uint32_t __bits1Hi = static_cast<uint32_t>(__bits1 >> 32); 130 __bits1Lo += __bits0Hi; 131 __bits1Hi += (__bits1Lo < __bits0Hi); 132 const int32_t __s = __shift - 32; 133 return (__bits1Hi << (32 - __s)) | (__bits1Lo >> __s); 134 #else // ^^^ 32-bit ^^^ / vvv 64-bit vvv 135 const uint64_t __sum = (__bits0 >> 32) + __bits1; 136 const uint64_t __shiftedSum = __sum >> (__shift - 32); 137 _LIBCPP_ASSERT(__shiftedSum <= UINT32_MAX, ""); 138 return static_cast<uint32_t>(__shiftedSum); 139 #endif // ^^^ 64-bit ^^^ 140 } 141 142 [[nodiscard]] _LIBCPP_HIDE_FROM_ABI inline uint32_t __mulPow5InvDivPow2(const uint32_t __m, const uint32_t __q, const int32_t __j) { 143 return __mulShift(__m, __FLOAT_POW5_INV_SPLIT[__q], __j); 144 } 145 146 [[nodiscard]] _LIBCPP_HIDE_FROM_ABI inline uint32_t __mulPow5divPow2(const uint32_t __m, const uint32_t __i, const int32_t __j) { 147 return __mulShift(__m, __FLOAT_POW5_SPLIT[__i], __j); 148 } 149 150 // A floating decimal representing m * 10^e. 151 struct __floating_decimal_32 { 152 uint32_t __mantissa; 153 int32_t __exponent; 154 }; 155 156 [[nodiscard]] _LIBCPP_HIDE_FROM_ABI inline __floating_decimal_32 __f2d(const uint32_t __ieeeMantissa, const uint32_t __ieeeExponent) { 157 int32_t __e2; 158 uint32_t __m2; 159 if (__ieeeExponent == 0) { 160 // We subtract 2 so that the bounds computation has 2 additional bits. 161 __e2 = 1 - __FLOAT_BIAS - __FLOAT_MANTISSA_BITS - 2; 162 __m2 = __ieeeMantissa; 163 } else { 164 __e2 = static_cast<int32_t>(__ieeeExponent) - __FLOAT_BIAS - __FLOAT_MANTISSA_BITS - 2; 165 __m2 = (1u << __FLOAT_MANTISSA_BITS) | __ieeeMantissa; 166 } 167 const bool __even = (__m2 & 1) == 0; 168 const bool __acceptBounds = __even; 169 170 // Step 2: Determine the interval of valid decimal representations. 171 const uint32_t __mv = 4 * __m2; 172 const uint32_t __mp = 4 * __m2 + 2; 173 // Implicit bool -> int conversion. True is 1, false is 0. 174 const uint32_t __mmShift = __ieeeMantissa != 0 || __ieeeExponent <= 1; 175 const uint32_t __mm = 4 * __m2 - 1 - __mmShift; 176 177 // Step 3: Convert to a decimal power base using 64-bit arithmetic. 178 uint32_t __vr, __vp, __vm; 179 int32_t __e10; 180 bool __vmIsTrailingZeros = false; 181 bool __vrIsTrailingZeros = false; 182 uint8_t __lastRemovedDigit = 0; 183 if (__e2 >= 0) { 184 const uint32_t __q = __log10Pow2(__e2); 185 __e10 = static_cast<int32_t>(__q); 186 const int32_t __k = __FLOAT_POW5_INV_BITCOUNT + __pow5bits(static_cast<int32_t>(__q)) - 1; 187 const int32_t __i = -__e2 + static_cast<int32_t>(__q) + __k; 188 __vr = __mulPow5InvDivPow2(__mv, __q, __i); 189 __vp = __mulPow5InvDivPow2(__mp, __q, __i); 190 __vm = __mulPow5InvDivPow2(__mm, __q, __i); 191 if (__q != 0 && (__vp - 1) / 10 <= __vm / 10) { 192 // We need to know one removed digit even if we are not going to loop below. We could use 193 // __q = X - 1 above, except that would require 33 bits for the result, and we've found that 194 // 32-bit arithmetic is faster even on 64-bit machines. 195 const int32_t __l = __FLOAT_POW5_INV_BITCOUNT + __pow5bits(static_cast<int32_t>(__q - 1)) - 1; 196 __lastRemovedDigit = static_cast<uint8_t>(__mulPow5InvDivPow2(__mv, __q - 1, 197 -__e2 + static_cast<int32_t>(__q) - 1 + __l) % 10); 198 } 199 if (__q <= 9) { 200 // The largest power of 5 that fits in 24 bits is 5^10, but __q <= 9 seems to be safe as well. 201 // Only one of __mp, __mv, and __mm can be a multiple of 5, if any. 202 if (__mv % 5 == 0) { 203 __vrIsTrailingZeros = __multipleOfPowerOf5(__mv, __q); 204 } else if (__acceptBounds) { 205 __vmIsTrailingZeros = __multipleOfPowerOf5(__mm, __q); 206 } else { 207 __vp -= __multipleOfPowerOf5(__mp, __q); 208 } 209 } 210 } else { 211 const uint32_t __q = __log10Pow5(-__e2); 212 __e10 = static_cast<int32_t>(__q) + __e2; 213 const int32_t __i = -__e2 - static_cast<int32_t>(__q); 214 const int32_t __k = __pow5bits(__i) - __FLOAT_POW5_BITCOUNT; 215 int32_t __j = static_cast<int32_t>(__q) - __k; 216 __vr = __mulPow5divPow2(__mv, static_cast<uint32_t>(__i), __j); 217 __vp = __mulPow5divPow2(__mp, static_cast<uint32_t>(__i), __j); 218 __vm = __mulPow5divPow2(__mm, static_cast<uint32_t>(__i), __j); 219 if (__q != 0 && (__vp - 1) / 10 <= __vm / 10) { 220 __j = static_cast<int32_t>(__q) - 1 - (__pow5bits(__i + 1) - __FLOAT_POW5_BITCOUNT); 221 __lastRemovedDigit = static_cast<uint8_t>(__mulPow5divPow2(__mv, static_cast<uint32_t>(__i + 1), __j) % 10); 222 } 223 if (__q <= 1) { 224 // {__vr,__vp,__vm} is trailing zeros if {__mv,__mp,__mm} has at least __q trailing 0 bits. 225 // __mv = 4 * __m2, so it always has at least two trailing 0 bits. 226 __vrIsTrailingZeros = true; 227 if (__acceptBounds) { 228 // __mm = __mv - 1 - __mmShift, so it has 1 trailing 0 bit iff __mmShift == 1. 229 __vmIsTrailingZeros = __mmShift == 1; 230 } else { 231 // __mp = __mv + 2, so it always has at least one trailing 0 bit. 232 --__vp; 233 } 234 } else if (__q < 31) { // TRANSITION(ulfjack): Use a tighter bound here. 235 __vrIsTrailingZeros = __multipleOfPowerOf2(__mv, __q - 1); 236 } 237 } 238 239 // Step 4: Find the shortest decimal representation in the interval of valid representations. 240 int32_t __removed = 0; 241 uint32_t _Output; 242 if (__vmIsTrailingZeros || __vrIsTrailingZeros) { 243 // General case, which happens rarely (~4.0%). 244 while (__vp / 10 > __vm / 10) { 245 #ifdef __clang__ // TRANSITION, LLVM-23106 246 __vmIsTrailingZeros &= __vm - (__vm / 10) * 10 == 0; 247 #else 248 __vmIsTrailingZeros &= __vm % 10 == 0; 249 #endif 250 __vrIsTrailingZeros &= __lastRemovedDigit == 0; 251 __lastRemovedDigit = static_cast<uint8_t>(__vr % 10); 252 __vr /= 10; 253 __vp /= 10; 254 __vm /= 10; 255 ++__removed; 256 } 257 if (__vmIsTrailingZeros) { 258 while (__vm % 10 == 0) { 259 __vrIsTrailingZeros &= __lastRemovedDigit == 0; 260 __lastRemovedDigit = static_cast<uint8_t>(__vr % 10); 261 __vr /= 10; 262 __vp /= 10; 263 __vm /= 10; 264 ++__removed; 265 } 266 } 267 if (__vrIsTrailingZeros && __lastRemovedDigit == 5 && __vr % 2 == 0) { 268 // Round even if the exact number is .....50..0. 269 __lastRemovedDigit = 4; 270 } 271 // We need to take __vr + 1 if __vr is outside bounds or we need to round up. 272 _Output = __vr + ((__vr == __vm && (!__acceptBounds || !__vmIsTrailingZeros)) || __lastRemovedDigit >= 5); 273 } else { 274 // Specialized for the common case (~96.0%). Percentages below are relative to this. 275 // Loop iterations below (approximately): 276 // 0: 13.6%, 1: 70.7%, 2: 14.1%, 3: 1.39%, 4: 0.14%, 5+: 0.01% 277 while (__vp / 10 > __vm / 10) { 278 __lastRemovedDigit = static_cast<uint8_t>(__vr % 10); 279 __vr /= 10; 280 __vp /= 10; 281 __vm /= 10; 282 ++__removed; 283 } 284 // We need to take __vr + 1 if __vr is outside bounds or we need to round up. 285 _Output = __vr + (__vr == __vm || __lastRemovedDigit >= 5); 286 } 287 const int32_t __exp = __e10 + __removed; 288 289 __floating_decimal_32 __fd; 290 __fd.__exponent = __exp; 291 __fd.__mantissa = _Output; 292 return __fd; 293 } 294 295 [[nodiscard]] _LIBCPP_HIDE_FROM_ABI inline to_chars_result _Large_integer_to_chars(char* const _First, char* const _Last, 296 const uint32_t _Mantissa2, const int32_t _Exponent2) { 297 298 // Print the integer _Mantissa2 * 2^_Exponent2 exactly. 299 300 // For nonzero integers, _Exponent2 >= -23. (The minimum value occurs when _Mantissa2 * 2^_Exponent2 is 1. 301 // In that case, _Mantissa2 is the implicit 1 bit followed by 23 zeros, so _Exponent2 is -23 to shift away 302 // the zeros.) The dense range of exactly representable integers has negative or zero exponents 303 // (as positive exponents make the range non-dense). For that dense range, Ryu will always be used: 304 // every digit is necessary to uniquely identify the value, so Ryu must print them all. 305 306 // Positive exponents are the non-dense range of exactly representable integers. 307 // This contains all of the values for which Ryu can't be used (and a few Ryu-friendly values). 308 309 // Performance note: Long division appears to be faster than losslessly widening float to double and calling 310 // __d2fixed_buffered_n(). If __f2fixed_buffered_n() is implemented, it might be faster than long division. 311 312 _LIBCPP_ASSERT(_Exponent2 > 0, ""); 313 _LIBCPP_ASSERT(_Exponent2 <= 104, ""); // because __ieeeExponent <= 254 314 315 // Manually represent _Mantissa2 * 2^_Exponent2 as a large integer. _Mantissa2 is always 24 bits 316 // (due to the implicit bit), while _Exponent2 indicates a shift of at most 104 bits. 317 // 24 + 104 equals 128 equals 4 * 32, so we need exactly 4 32-bit elements. 318 // We use a little-endian representation, visualized like this: 319 320 // << left shift << 321 // most significant 322 // _Data[3] _Data[2] _Data[1] _Data[0] 323 // least significant 324 // >> right shift >> 325 326 constexpr uint32_t _Data_size = 4; 327 uint32_t _Data[_Data_size]{}; 328 329 // _Maxidx is the index of the most significant nonzero element. 330 uint32_t _Maxidx = ((24 + static_cast<uint32_t>(_Exponent2) + 31) / 32) - 1; 331 _LIBCPP_ASSERT(_Maxidx < _Data_size, ""); 332 333 const uint32_t _Bit_shift = static_cast<uint32_t>(_Exponent2) % 32; 334 if (_Bit_shift <= 8) { // _Mantissa2's 24 bits don't cross an element boundary 335 _Data[_Maxidx] = _Mantissa2 << _Bit_shift; 336 } else { // _Mantissa2's 24 bits cross an element boundary 337 _Data[_Maxidx - 1] = _Mantissa2 << _Bit_shift; 338 _Data[_Maxidx] = _Mantissa2 >> (32 - _Bit_shift); 339 } 340 341 // If Ryu hasn't determined the total output length, we need to buffer the digits generated from right to left 342 // by long division. The largest possible float is: 340'282346638'528859811'704183484'516925440 343 uint32_t _Blocks[4]; 344 int32_t _Filled_blocks = 0; 345 // From left to right, we're going to print: 346 // _Data[0] will be [1, 10] digits. 347 // Then if _Filled_blocks > 0: 348 // _Blocks[_Filled_blocks - 1], ..., _Blocks[0] will be 0-filled 9-digit blocks. 349 350 if (_Maxidx != 0) { // If the integer is actually large, perform long division. 351 // Otherwise, skip to printing _Data[0]. 352 for (;;) { 353 // Loop invariant: _Maxidx != 0 (i.e. the integer is actually large) 354 355 const uint32_t _Most_significant_elem = _Data[_Maxidx]; 356 const uint32_t _Initial_remainder = _Most_significant_elem % 1000000000; 357 const uint32_t _Initial_quotient = _Most_significant_elem / 1000000000; 358 _Data[_Maxidx] = _Initial_quotient; 359 uint64_t _Remainder = _Initial_remainder; 360 361 // Process less significant elements. 362 uint32_t _Idx = _Maxidx; 363 do { 364 --_Idx; // Initially, _Remainder is at most 10^9 - 1. 365 366 // Now, _Remainder is at most (10^9 - 1) * 2^32 + 2^32 - 1, simplified to 10^9 * 2^32 - 1. 367 _Remainder = (_Remainder << 32) | _Data[_Idx]; 368 369 // floor((10^9 * 2^32 - 1) / 10^9) == 2^32 - 1, so uint32_t _Quotient is lossless. 370 const uint32_t _Quotient = static_cast<uint32_t>(__div1e9(_Remainder)); 371 372 // _Remainder is at most 10^9 - 1 again. 373 // For uint32_t truncation, see the __mod1e9() comment in d2s_intrinsics.h. 374 _Remainder = static_cast<uint32_t>(_Remainder) - 1000000000u * _Quotient; 375 376 _Data[_Idx] = _Quotient; 377 } while (_Idx != 0); 378 379 // Store a 0-filled 9-digit block. 380 _Blocks[_Filled_blocks++] = static_cast<uint32_t>(_Remainder); 381 382 if (_Initial_quotient == 0) { // Is the large integer shrinking? 383 --_Maxidx; // log2(10^9) is 29.9, so we can't shrink by more than one element. 384 if (_Maxidx == 0) { 385 break; // We've finished long division. Now we need to print _Data[0]. 386 } 387 } 388 } 389 } 390 391 _LIBCPP_ASSERT(_Data[0] != 0, ""); 392 for (uint32_t _Idx = 1; _Idx < _Data_size; ++_Idx) { 393 _LIBCPP_ASSERT(_Data[_Idx] == 0, ""); 394 } 395 396 const uint32_t _Data_olength = _Data[0] >= 1000000000 ? 10 : __decimalLength9(_Data[0]); 397 const uint32_t _Total_fixed_length = _Data_olength + 9 * _Filled_blocks; 398 399 if (_Last - _First < static_cast<ptrdiff_t>(_Total_fixed_length)) { 400 return { _Last, errc::value_too_large }; 401 } 402 403 char* _Result = _First; 404 405 // Print _Data[0]. While it's up to 10 digits, 406 // which is more than Ryu generates, the code below can handle this. 407 __append_n_digits(_Data_olength, _Data[0], _Result); 408 _Result += _Data_olength; 409 410 // Print 0-filled 9-digit blocks. 411 for (int32_t _Idx = _Filled_blocks - 1; _Idx >= 0; --_Idx) { 412 __append_nine_digits(_Blocks[_Idx], _Result); 413 _Result += 9; 414 } 415 416 return { _Result, errc{} }; 417 } 418 419 [[nodiscard]] _LIBCPP_HIDE_FROM_ABI inline to_chars_result __to_chars(char* const _First, char* const _Last, const __floating_decimal_32 __v, 420 chars_format _Fmt, const uint32_t __ieeeMantissa, const uint32_t __ieeeExponent) { 421 // Step 5: Print the decimal representation. 422 uint32_t _Output = __v.__mantissa; 423 int32_t _Ryu_exponent = __v.__exponent; 424 const uint32_t __olength = __decimalLength9(_Output); 425 int32_t _Scientific_exponent = _Ryu_exponent + static_cast<int32_t>(__olength) - 1; 426 427 if (_Fmt == chars_format{}) { 428 int32_t _Lower; 429 int32_t _Upper; 430 431 if (__olength == 1) { 432 // Value | Fixed | Scientific 433 // 1e-3 | "0.001" | "1e-03" 434 // 1e4 | "10000" | "1e+04" 435 _Lower = -3; 436 _Upper = 4; 437 } else { 438 // Value | Fixed | Scientific 439 // 1234e-7 | "0.0001234" | "1.234e-04" 440 // 1234e5 | "123400000" | "1.234e+08" 441 _Lower = -static_cast<int32_t>(__olength + 3); 442 _Upper = 5; 443 } 444 445 if (_Lower <= _Ryu_exponent && _Ryu_exponent <= _Upper) { 446 _Fmt = chars_format::fixed; 447 } else { 448 _Fmt = chars_format::scientific; 449 } 450 } else if (_Fmt == chars_format::general) { 451 // C11 7.21.6.1 "The fprintf function"/8: 452 // "Let P equal [...] 6 if the precision is omitted [...]. 453 // Then, if a conversion with style E would have an exponent of X: 454 // - if P > X >= -4, the conversion is with style f [...]. 455 // - otherwise, the conversion is with style e [...]." 456 if (-4 <= _Scientific_exponent && _Scientific_exponent < 6) { 457 _Fmt = chars_format::fixed; 458 } else { 459 _Fmt = chars_format::scientific; 460 } 461 } 462 463 if (_Fmt == chars_format::fixed) { 464 // Example: _Output == 1729, __olength == 4 465 466 // _Ryu_exponent | Printed | _Whole_digits | _Total_fixed_length | Notes 467 // --------------|----------|---------------|----------------------|--------------------------------------- 468 // 2 | 172900 | 6 | _Whole_digits | Ryu can't be used for printing 469 // 1 | 17290 | 5 | (sometimes adjusted) | when the trimmed digits are nonzero. 470 // --------------|----------|---------------|----------------------|--------------------------------------- 471 // 0 | 1729 | 4 | _Whole_digits | Unified length cases. 472 // --------------|----------|---------------|----------------------|--------------------------------------- 473 // -1 | 172.9 | 3 | __olength + 1 | This case can't happen for 474 // -2 | 17.29 | 2 | | __olength == 1, but no additional 475 // -3 | 1.729 | 1 | | code is needed to avoid it. 476 // --------------|----------|---------------|----------------------|--------------------------------------- 477 // -4 | 0.1729 | 0 | 2 - _Ryu_exponent | C11 7.21.6.1 "The fprintf function"/8: 478 // -5 | 0.01729 | -1 | | "If a decimal-point character appears, 479 // -6 | 0.001729 | -2 | | at least one digit appears before it." 480 481 const int32_t _Whole_digits = static_cast<int32_t>(__olength) + _Ryu_exponent; 482 483 uint32_t _Total_fixed_length; 484 if (_Ryu_exponent >= 0) { // cases "172900" and "1729" 485 _Total_fixed_length = static_cast<uint32_t>(_Whole_digits); 486 if (_Output == 1) { 487 // Rounding can affect the number of digits. 488 // For example, 1e11f is exactly "99999997952" which is 11 digits instead of 12. 489 // We can use a lookup table to detect this and adjust the total length. 490 static constexpr uint8_t _Adjustment[39] = { 491 0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,1,1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,1,1,0,1,1,1 }; 492 _Total_fixed_length -= _Adjustment[_Ryu_exponent]; 493 // _Whole_digits doesn't need to be adjusted because these cases won't refer to it later. 494 } 495 } else if (_Whole_digits > 0) { // case "17.29" 496 _Total_fixed_length = __olength + 1; 497 } else { // case "0.001729" 498 _Total_fixed_length = static_cast<uint32_t>(2 - _Ryu_exponent); 499 } 500 501 if (_Last - _First < static_cast<ptrdiff_t>(_Total_fixed_length)) { 502 return { _Last, errc::value_too_large }; 503 } 504 505 char* _Mid; 506 if (_Ryu_exponent > 0) { // case "172900" 507 bool _Can_use_ryu; 508 509 if (_Ryu_exponent > 10) { // 10^10 is the largest power of 10 that's exactly representable as a float. 510 _Can_use_ryu = false; 511 } else { 512 // Ryu generated X: __v.__mantissa * 10^_Ryu_exponent 513 // __v.__mantissa == 2^_Trailing_zero_bits * (__v.__mantissa >> _Trailing_zero_bits) 514 // 10^_Ryu_exponent == 2^_Ryu_exponent * 5^_Ryu_exponent 515 516 // _Trailing_zero_bits is [0, 29] (aside: because 2^29 is the largest power of 2 517 // with 9 decimal digits, which is float's round-trip limit.) 518 // _Ryu_exponent is [1, 10]. 519 // Normalization adds [2, 23] (aside: at least 2 because the pre-normalized mantissa is at least 5). 520 // This adds up to [3, 62], which is well below float's maximum binary exponent 127. 521 522 // Therefore, we just need to consider (__v.__mantissa >> _Trailing_zero_bits) * 5^_Ryu_exponent. 523 524 // If that product would exceed 24 bits, then X can't be exactly represented as a float. 525 // (That's not a problem for round-tripping, because X is close enough to the original float, 526 // but X isn't mathematically equal to the original float.) This requires a high-precision fallback. 527 528 // If the product is 24 bits or smaller, then X can be exactly represented as a float (and we don't 529 // need to re-synthesize it; the original float must have been X, because Ryu wouldn't produce the 530 // same output for two different floats X and Y). This allows Ryu's output to be used (zero-filled). 531 532 // (2^24 - 1) / 5^0 (for indexing), (2^24 - 1) / 5^1, ..., (2^24 - 1) / 5^10 533 static constexpr uint32_t _Max_shifted_mantissa[11] = { 534 16777215, 3355443, 671088, 134217, 26843, 5368, 1073, 214, 42, 8, 1 }; 535 536 unsigned long _Trailing_zero_bits; 537 (void) _BitScanForward(&_Trailing_zero_bits, __v.__mantissa); // __v.__mantissa is guaranteed nonzero 538 const uint32_t _Shifted_mantissa = __v.__mantissa >> _Trailing_zero_bits; 539 _Can_use_ryu = _Shifted_mantissa <= _Max_shifted_mantissa[_Ryu_exponent]; 540 } 541 542 if (!_Can_use_ryu) { 543 const uint32_t _Mantissa2 = __ieeeMantissa | (1u << __FLOAT_MANTISSA_BITS); // restore implicit bit 544 const int32_t _Exponent2 = static_cast<int32_t>(__ieeeExponent) 545 - __FLOAT_BIAS - __FLOAT_MANTISSA_BITS; // bias and normalization 546 547 // Performance note: We've already called Ryu, so this will redundantly perform buffering and bounds checking. 548 return _Large_integer_to_chars(_First, _Last, _Mantissa2, _Exponent2); 549 } 550 551 // _Can_use_ryu 552 // Print the decimal digits, left-aligned within [_First, _First + _Total_fixed_length). 553 _Mid = _First + __olength; 554 } else { // cases "1729", "17.29", and "0.001729" 555 // Print the decimal digits, right-aligned within [_First, _First + _Total_fixed_length). 556 _Mid = _First + _Total_fixed_length; 557 } 558 559 while (_Output >= 10000) { 560 #ifdef __clang__ // TRANSITION, LLVM-38217 561 const uint32_t __c = _Output - 10000 * (_Output / 10000); 562 #else 563 const uint32_t __c = _Output % 10000; 564 #endif 565 _Output /= 10000; 566 const uint32_t __c0 = (__c % 100) << 1; 567 const uint32_t __c1 = (__c / 100) << 1; 568 _VSTD::memcpy(_Mid -= 2, __DIGIT_TABLE + __c0, 2); 569 _VSTD::memcpy(_Mid -= 2, __DIGIT_TABLE + __c1, 2); 570 } 571 if (_Output >= 100) { 572 const uint32_t __c = (_Output % 100) << 1; 573 _Output /= 100; 574 _VSTD::memcpy(_Mid -= 2, __DIGIT_TABLE + __c, 2); 575 } 576 if (_Output >= 10) { 577 const uint32_t __c = _Output << 1; 578 _VSTD::memcpy(_Mid -= 2, __DIGIT_TABLE + __c, 2); 579 } else { 580 *--_Mid = static_cast<char>('0' + _Output); 581 } 582 583 if (_Ryu_exponent > 0) { // case "172900" with _Can_use_ryu 584 // Performance note: it might be more efficient to do this immediately after setting _Mid. 585 _VSTD::memset(_First + __olength, '0', static_cast<size_t>(_Ryu_exponent)); 586 } else if (_Ryu_exponent == 0) { // case "1729" 587 // Done! 588 } else if (_Whole_digits > 0) { // case "17.29" 589 // Performance note: moving digits might not be optimal. 590 _VSTD::memmove(_First, _First + 1, static_cast<size_t>(_Whole_digits)); 591 _First[_Whole_digits] = '.'; 592 } else { // case "0.001729" 593 // Performance note: a larger memset() followed by overwriting '.' might be more efficient. 594 _First[0] = '0'; 595 _First[1] = '.'; 596 _VSTD::memset(_First + 2, '0', static_cast<size_t>(-_Whole_digits)); 597 } 598 599 return { _First + _Total_fixed_length, errc{} }; 600 } 601 602 const uint32_t _Total_scientific_length = 603 __olength + (__olength > 1) + 4; // digits + possible decimal point + scientific exponent 604 if (_Last - _First < static_cast<ptrdiff_t>(_Total_scientific_length)) { 605 return { _Last, errc::value_too_large }; 606 } 607 char* const __result = _First; 608 609 // Print the decimal digits. 610 uint32_t __i = 0; 611 while (_Output >= 10000) { 612 #ifdef __clang__ // TRANSITION, LLVM-38217 613 const uint32_t __c = _Output - 10000 * (_Output / 10000); 614 #else 615 const uint32_t __c = _Output % 10000; 616 #endif 617 _Output /= 10000; 618 const uint32_t __c0 = (__c % 100) << 1; 619 const uint32_t __c1 = (__c / 100) << 1; 620 _VSTD::memcpy(__result + __olength - __i - 1, __DIGIT_TABLE + __c0, 2); 621 _VSTD::memcpy(__result + __olength - __i - 3, __DIGIT_TABLE + __c1, 2); 622 __i += 4; 623 } 624 if (_Output >= 100) { 625 const uint32_t __c = (_Output % 100) << 1; 626 _Output /= 100; 627 _VSTD::memcpy(__result + __olength - __i - 1, __DIGIT_TABLE + __c, 2); 628 __i += 2; 629 } 630 if (_Output >= 10) { 631 const uint32_t __c = _Output << 1; 632 // We can't use memcpy here: the decimal dot goes between these two digits. 633 __result[2] = __DIGIT_TABLE[__c + 1]; 634 __result[0] = __DIGIT_TABLE[__c]; 635 } else { 636 __result[0] = static_cast<char>('0' + _Output); 637 } 638 639 // Print decimal point if needed. 640 uint32_t __index; 641 if (__olength > 1) { 642 __result[1] = '.'; 643 __index = __olength + 1; 644 } else { 645 __index = 1; 646 } 647 648 // Print the exponent. 649 __result[__index++] = 'e'; 650 if (_Scientific_exponent < 0) { 651 __result[__index++] = '-'; 652 _Scientific_exponent = -_Scientific_exponent; 653 } else { 654 __result[__index++] = '+'; 655 } 656 657 _VSTD::memcpy(__result + __index, __DIGIT_TABLE + 2 * _Scientific_exponent, 2); 658 __index += 2; 659 660 return { _First + _Total_scientific_length, errc{} }; 661 } 662 663 [[nodiscard]] to_chars_result __f2s_buffered_n(char* const _First, char* const _Last, const float __f, 664 const chars_format _Fmt) { 665 666 // Step 1: Decode the floating-point number, and unify normalized and subnormal cases. 667 const uint32_t __bits = __float_to_bits(__f); 668 669 // Case distinction; exit early for the easy cases. 670 if (__bits == 0) { 671 if (_Fmt == chars_format::scientific) { 672 if (_Last - _First < 5) { 673 return { _Last, errc::value_too_large }; 674 } 675 676 _VSTD::memcpy(_First, "0e+00", 5); 677 678 return { _First + 5, errc{} }; 679 } 680 681 // Print "0" for chars_format::fixed, chars_format::general, and chars_format{}. 682 if (_First == _Last) { 683 return { _Last, errc::value_too_large }; 684 } 685 686 *_First = '0'; 687 688 return { _First + 1, errc{} }; 689 } 690 691 // Decode __bits into mantissa and exponent. 692 const uint32_t __ieeeMantissa = __bits & ((1u << __FLOAT_MANTISSA_BITS) - 1); 693 const uint32_t __ieeeExponent = __bits >> __FLOAT_MANTISSA_BITS; 694 695 // When _Fmt == chars_format::fixed and the floating-point number is a large integer, 696 // it's faster to skip Ryu and immediately print the integer exactly. 697 if (_Fmt == chars_format::fixed) { 698 const uint32_t _Mantissa2 = __ieeeMantissa | (1u << __FLOAT_MANTISSA_BITS); // restore implicit bit 699 const int32_t _Exponent2 = static_cast<int32_t>(__ieeeExponent) 700 - __FLOAT_BIAS - __FLOAT_MANTISSA_BITS; // bias and normalization 701 702 // Normal values are equal to _Mantissa2 * 2^_Exponent2. 703 // (Subnormals are different, but they'll be rejected by the _Exponent2 test here, so they can be ignored.) 704 705 if (_Exponent2 > 0) { 706 return _Large_integer_to_chars(_First, _Last, _Mantissa2, _Exponent2); 707 } 708 } 709 710 const __floating_decimal_32 __v = __f2d(__ieeeMantissa, __ieeeExponent); 711 return __to_chars(_First, _Last, __v, _Fmt, __ieeeMantissa, __ieeeExponent); 712 } 713 714 _LIBCPP_END_NAMESPACE_STD 715 716 // clang-format on 717