//===----------------------------------------------------------------------===// // // Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions. // See https://llvm.org/LICENSE.txt for license information. // SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception // //===----------------------------------------------------------------------===// // Copyright (c) Microsoft Corporation. // SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception // Copyright 2018 Ulf Adams // Copyright (c) Microsoft Corporation. All rights reserved. // Boost Software License - Version 1.0 - August 17th, 2003 // Permission is hereby granted, free of charge, to any person or organization // obtaining a copy of the software and accompanying documentation covered by // this license (the "Software") to use, reproduce, display, distribute, // execute, and transmit the Software, and to prepare derivative works of the // Software, and to permit third-parties to whom the Software is furnished to // do so, all subject to the following: // The copyright notices in the Software and this entire statement, including // the above license grant, this restriction and the following disclaimer, // must be included in all copies of the Software, in whole or in part, and // all derivative works of the Software, unless such copies or derivative // works are solely in the form of machine-executable object code generated by // a source language processor. // THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR // IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, // FITNESS FOR A PARTICULAR PURPOSE, TITLE AND NON-INFRINGEMENT. IN NO EVENT // SHALL THE COPYRIGHT HOLDERS OR ANYONE DISTRIBUTING THE SOFTWARE BE LIABLE // FOR ANY DAMAGES OR OTHER LIABILITY, WHETHER IN CONTRACT, TORT OR OTHERWISE, // ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER // DEALINGS IN THE SOFTWARE. // Avoid formatting to keep the changes with the original code minimal. // clang-format off #include "__config" #include "charconv" #include "include/ryu/common.h" #include "include/ryu/d2fixed.h" #include "include/ryu/d2s.h" #include "include/ryu/d2s_full_table.h" #include "include/ryu/d2s_intrinsics.h" #include "include/ryu/digit_table.h" #include "include/ryu/ryu.h" _LIBCPP_BEGIN_NAMESPACE_STD // We need a 64x128-bit multiplication and a subsequent 128-bit shift. // Multiplication: // The 64-bit factor is variable and passed in, the 128-bit factor comes // from a lookup table. We know that the 64-bit factor only has 55 // significant bits (i.e., the 9 topmost bits are zeros). The 128-bit // factor only has 124 significant bits (i.e., the 4 topmost bits are // zeros). // Shift: // In principle, the multiplication result requires 55 + 124 = 179 bits to // represent. However, we then shift this value to the right by __j, which is // at least __j >= 115, so the result is guaranteed to fit into 179 - 115 = 64 // bits. This means that we only need the topmost 64 significant bits of // the 64x128-bit multiplication. // // There are several ways to do this: // 1. Best case: the compiler exposes a 128-bit type. // We perform two 64x64-bit multiplications, add the higher 64 bits of the // lower result to the higher result, and shift by __j - 64 bits. // // We explicitly cast from 64-bit to 128-bit, so the compiler can tell // that these are only 64-bit inputs, and can map these to the best // possible sequence of assembly instructions. // x64 machines happen to have matching assembly instructions for // 64x64-bit multiplications and 128-bit shifts. // // 2. Second best case: the compiler exposes intrinsics for the x64 assembly // instructions mentioned in 1. // // 3. We only have 64x64 bit instructions that return the lower 64 bits of // the result, i.e., we have to use plain C. // Our inputs are less than the full width, so we have three options: // a. Ignore this fact and just implement the intrinsics manually. // b. Split both into 31-bit pieces, which guarantees no internal overflow, // but requires extra work upfront (unless we change the lookup table). // c. Split only the first factor into 31-bit pieces, which also guarantees // no internal overflow, but requires extra work since the intermediate // results are not perfectly aligned. #ifdef _LIBCPP_INTRINSIC128 [[nodiscard]] _LIBCPP_HIDE_FROM_ABI inline uint64_t __mulShift(const uint64_t __m, const uint64_t* const __mul, const int32_t __j) { // __m is maximum 55 bits uint64_t __high1; // 128 const uint64_t __low1 = __ryu_umul128(__m, __mul[1], &__high1); // 64 uint64_t __high0; // 64 (void) __ryu_umul128(__m, __mul[0], &__high0); // 0 const uint64_t __sum = __high0 + __low1; if (__sum < __high0) { ++__high1; // overflow into __high1 } return __ryu_shiftright128(__sum, __high1, static_cast(__j - 64)); } [[nodiscard]] _LIBCPP_HIDE_FROM_ABI inline uint64_t __mulShiftAll(const uint64_t __m, const uint64_t* const __mul, const int32_t __j, uint64_t* const __vp, uint64_t* const __vm, const uint32_t __mmShift) { *__vp = __mulShift(4 * __m + 2, __mul, __j); *__vm = __mulShift(4 * __m - 1 - __mmShift, __mul, __j); return __mulShift(4 * __m, __mul, __j); } #else // ^^^ intrinsics available ^^^ / vvv intrinsics unavailable vvv [[nodiscard]] _LIBCPP_HIDE_FROM_ABI inline _LIBCPP_ALWAYS_INLINE uint64_t __mulShiftAll(uint64_t __m, const uint64_t* const __mul, const int32_t __j, uint64_t* const __vp, uint64_t* const __vm, const uint32_t __mmShift) { // TRANSITION, VSO-634761 __m <<= 1; // __m is maximum 55 bits uint64_t __tmp; const uint64_t __lo = __ryu_umul128(__m, __mul[0], &__tmp); uint64_t __hi; const uint64_t __mid = __tmp + __ryu_umul128(__m, __mul[1], &__hi); __hi += __mid < __tmp; // overflow into __hi const uint64_t __lo2 = __lo + __mul[0]; const uint64_t __mid2 = __mid + __mul[1] + (__lo2 < __lo); const uint64_t __hi2 = __hi + (__mid2 < __mid); *__vp = __ryu_shiftright128(__mid2, __hi2, static_cast(__j - 64 - 1)); if (__mmShift == 1) { const uint64_t __lo3 = __lo - __mul[0]; const uint64_t __mid3 = __mid - __mul[1] - (__lo3 > __lo); const uint64_t __hi3 = __hi - (__mid3 > __mid); *__vm = __ryu_shiftright128(__mid3, __hi3, static_cast(__j - 64 - 1)); } else { const uint64_t __lo3 = __lo + __lo; const uint64_t __mid3 = __mid + __mid + (__lo3 < __lo); const uint64_t __hi3 = __hi + __hi + (__mid3 < __mid); const uint64_t __lo4 = __lo3 - __mul[0]; const uint64_t __mid4 = __mid3 - __mul[1] - (__lo4 > __lo3); const uint64_t __hi4 = __hi3 - (__mid4 > __mid3); *__vm = __ryu_shiftright128(__mid4, __hi4, static_cast(__j - 64)); } return __ryu_shiftright128(__mid, __hi, static_cast(__j - 64 - 1)); } #endif // ^^^ intrinsics unavailable ^^^ [[nodiscard]] _LIBCPP_HIDE_FROM_ABI inline uint32_t __decimalLength17(const uint64_t __v) { // This is slightly faster than a loop. // The average output length is 16.38 digits, so we check high-to-low. // Function precondition: __v is not an 18, 19, or 20-digit number. // (17 digits are sufficient for round-tripping.) _LIBCPP_ASSERT(__v < 100000000000000000u, ""); if (__v >= 10000000000000000u) { return 17; } if (__v >= 1000000000000000u) { return 16; } if (__v >= 100000000000000u) { return 15; } if (__v >= 10000000000000u) { return 14; } if (__v >= 1000000000000u) { return 13; } if (__v >= 100000000000u) { return 12; } if (__v >= 10000000000u) { return 11; } if (__v >= 1000000000u) { return 10; } if (__v >= 100000000u) { return 9; } if (__v >= 10000000u) { return 8; } if (__v >= 1000000u) { return 7; } if (__v >= 100000u) { return 6; } if (__v >= 10000u) { return 5; } if (__v >= 1000u) { return 4; } if (__v >= 100u) { return 3; } if (__v >= 10u) { return 2; } return 1; } // A floating decimal representing m * 10^e. struct __floating_decimal_64 { uint64_t __mantissa; int32_t __exponent; }; [[nodiscard]] _LIBCPP_HIDE_FROM_ABI inline __floating_decimal_64 __d2d(const uint64_t __ieeeMantissa, const uint32_t __ieeeExponent) { int32_t __e2; uint64_t __m2; if (__ieeeExponent == 0) { // We subtract 2 so that the bounds computation has 2 additional bits. __e2 = 1 - __DOUBLE_BIAS - __DOUBLE_MANTISSA_BITS - 2; __m2 = __ieeeMantissa; } else { __e2 = static_cast(__ieeeExponent) - __DOUBLE_BIAS - __DOUBLE_MANTISSA_BITS - 2; __m2 = (1ull << __DOUBLE_MANTISSA_BITS) | __ieeeMantissa; } const bool __even = (__m2 & 1) == 0; const bool __acceptBounds = __even; // Step 2: Determine the interval of valid decimal representations. const uint64_t __mv = 4 * __m2; // Implicit bool -> int conversion. True is 1, false is 0. const uint32_t __mmShift = __ieeeMantissa != 0 || __ieeeExponent <= 1; // We would compute __mp and __mm like this: // uint64_t __mp = 4 * __m2 + 2; // uint64_t __mm = __mv - 1 - __mmShift; // Step 3: Convert to a decimal power base using 128-bit arithmetic. uint64_t __vr, __vp, __vm; int32_t __e10; bool __vmIsTrailingZeros = false; bool __vrIsTrailingZeros = false; if (__e2 >= 0) { // I tried special-casing __q == 0, but there was no effect on performance. // This expression is slightly faster than max(0, __log10Pow2(__e2) - 1). const uint32_t __q = __log10Pow2(__e2) - (__e2 > 3); __e10 = static_cast(__q); const int32_t __k = __DOUBLE_POW5_INV_BITCOUNT + __pow5bits(static_cast(__q)) - 1; const int32_t __i = -__e2 + static_cast(__q) + __k; __vr = __mulShiftAll(__m2, __DOUBLE_POW5_INV_SPLIT[__q], __i, &__vp, &__vm, __mmShift); if (__q <= 21) { // This should use __q <= 22, but I think 21 is also safe. Smaller values // may still be safe, but it's more difficult to reason about them. // Only one of __mp, __mv, and __mm can be a multiple of 5, if any. const uint32_t __mvMod5 = static_cast(__mv) - 5 * static_cast(__div5(__mv)); if (__mvMod5 == 0) { __vrIsTrailingZeros = __multipleOfPowerOf5(__mv, __q); } else if (__acceptBounds) { // Same as min(__e2 + (~__mm & 1), __pow5Factor(__mm)) >= __q // <=> __e2 + (~__mm & 1) >= __q && __pow5Factor(__mm) >= __q // <=> true && __pow5Factor(__mm) >= __q, since __e2 >= __q. __vmIsTrailingZeros = __multipleOfPowerOf5(__mv - 1 - __mmShift, __q); } else { // Same as min(__e2 + 1, __pow5Factor(__mp)) >= __q. __vp -= __multipleOfPowerOf5(__mv + 2, __q); } } } else { // This expression is slightly faster than max(0, __log10Pow5(-__e2) - 1). const uint32_t __q = __log10Pow5(-__e2) - (-__e2 > 1); __e10 = static_cast(__q) + __e2; const int32_t __i = -__e2 - static_cast(__q); const int32_t __k = __pow5bits(__i) - __DOUBLE_POW5_BITCOUNT; const int32_t __j = static_cast(__q) - __k; __vr = __mulShiftAll(__m2, __DOUBLE_POW5_SPLIT[__i], __j, &__vp, &__vm, __mmShift); if (__q <= 1) { // {__vr,__vp,__vm} is trailing zeros if {__mv,__mp,__mm} has at least __q trailing 0 bits. // __mv = 4 * __m2, so it always has at least two trailing 0 bits. __vrIsTrailingZeros = true; if (__acceptBounds) { // __mm = __mv - 1 - __mmShift, so it has 1 trailing 0 bit iff __mmShift == 1. __vmIsTrailingZeros = __mmShift == 1; } else { // __mp = __mv + 2, so it always has at least one trailing 0 bit. --__vp; } } else if (__q < 63) { // TRANSITION(ulfjack): Use a tighter bound here. // We need to compute min(ntz(__mv), __pow5Factor(__mv) - __e2) >= __q - 1 // <=> ntz(__mv) >= __q - 1 && __pow5Factor(__mv) - __e2 >= __q - 1 // <=> ntz(__mv) >= __q - 1 (__e2 is negative and -__e2 >= __q) // <=> (__mv & ((1 << (__q - 1)) - 1)) == 0 // We also need to make sure that the left shift does not overflow. __vrIsTrailingZeros = __multipleOfPowerOf2(__mv, __q - 1); } } // Step 4: Find the shortest decimal representation in the interval of valid representations. int32_t __removed = 0; uint8_t __lastRemovedDigit = 0; uint64_t _Output; // On average, we remove ~2 digits. if (__vmIsTrailingZeros || __vrIsTrailingZeros) { // General case, which happens rarely (~0.7%). for (;;) { const uint64_t __vpDiv10 = __div10(__vp); const uint64_t __vmDiv10 = __div10(__vm); if (__vpDiv10 <= __vmDiv10) { break; } const uint32_t __vmMod10 = static_cast(__vm) - 10 * static_cast(__vmDiv10); const uint64_t __vrDiv10 = __div10(__vr); const uint32_t __vrMod10 = static_cast(__vr) - 10 * static_cast(__vrDiv10); __vmIsTrailingZeros &= __vmMod10 == 0; __vrIsTrailingZeros &= __lastRemovedDigit == 0; __lastRemovedDigit = static_cast(__vrMod10); __vr = __vrDiv10; __vp = __vpDiv10; __vm = __vmDiv10; ++__removed; } if (__vmIsTrailingZeros) { for (;;) { const uint64_t __vmDiv10 = __div10(__vm); const uint32_t __vmMod10 = static_cast(__vm) - 10 * static_cast(__vmDiv10); if (__vmMod10 != 0) { break; } const uint64_t __vpDiv10 = __div10(__vp); const uint64_t __vrDiv10 = __div10(__vr); const uint32_t __vrMod10 = static_cast(__vr) - 10 * static_cast(__vrDiv10); __vrIsTrailingZeros &= __lastRemovedDigit == 0; __lastRemovedDigit = static_cast(__vrMod10); __vr = __vrDiv10; __vp = __vpDiv10; __vm = __vmDiv10; ++__removed; } } if (__vrIsTrailingZeros && __lastRemovedDigit == 5 && __vr % 2 == 0) { // Round even if the exact number is .....50..0. __lastRemovedDigit = 4; } // We need to take __vr + 1 if __vr is outside bounds or we need to round up. _Output = __vr + ((__vr == __vm && (!__acceptBounds || !__vmIsTrailingZeros)) || __lastRemovedDigit >= 5); } else { // Specialized for the common case (~99.3%). Percentages below are relative to this. bool __roundUp = false; const uint64_t __vpDiv100 = __div100(__vp); const uint64_t __vmDiv100 = __div100(__vm); if (__vpDiv100 > __vmDiv100) { // Optimization: remove two digits at a time (~86.2%). const uint64_t __vrDiv100 = __div100(__vr); const uint32_t __vrMod100 = static_cast(__vr) - 100 * static_cast(__vrDiv100); __roundUp = __vrMod100 >= 50; __vr = __vrDiv100; __vp = __vpDiv100; __vm = __vmDiv100; __removed += 2; } // Loop iterations below (approximately), without optimization above: // 0: 0.03%, 1: 13.8%, 2: 70.6%, 3: 14.0%, 4: 1.40%, 5: 0.14%, 6+: 0.02% // Loop iterations below (approximately), with optimization above: // 0: 70.6%, 1: 27.8%, 2: 1.40%, 3: 0.14%, 4+: 0.02% for (;;) { const uint64_t __vpDiv10 = __div10(__vp); const uint64_t __vmDiv10 = __div10(__vm); if (__vpDiv10 <= __vmDiv10) { break; } const uint64_t __vrDiv10 = __div10(__vr); const uint32_t __vrMod10 = static_cast(__vr) - 10 * static_cast(__vrDiv10); __roundUp = __vrMod10 >= 5; __vr = __vrDiv10; __vp = __vpDiv10; __vm = __vmDiv10; ++__removed; } // We need to take __vr + 1 if __vr is outside bounds or we need to round up. _Output = __vr + (__vr == __vm || __roundUp); } const int32_t __exp = __e10 + __removed; __floating_decimal_64 __fd; __fd.__exponent = __exp; __fd.__mantissa = _Output; return __fd; } [[nodiscard]] _LIBCPP_HIDE_FROM_ABI inline to_chars_result __to_chars(char* const _First, char* const _Last, const __floating_decimal_64 __v, chars_format _Fmt, const double __f) { // Step 5: Print the decimal representation. uint64_t _Output = __v.__mantissa; int32_t _Ryu_exponent = __v.__exponent; const uint32_t __olength = __decimalLength17(_Output); int32_t _Scientific_exponent = _Ryu_exponent + static_cast(__olength) - 1; if (_Fmt == chars_format{}) { int32_t _Lower; int32_t _Upper; if (__olength == 1) { // Value | Fixed | Scientific // 1e-3 | "0.001" | "1e-03" // 1e4 | "10000" | "1e+04" _Lower = -3; _Upper = 4; } else { // Value | Fixed | Scientific // 1234e-7 | "0.0001234" | "1.234e-04" // 1234e5 | "123400000" | "1.234e+08" _Lower = -static_cast(__olength + 3); _Upper = 5; } if (_Lower <= _Ryu_exponent && _Ryu_exponent <= _Upper) { _Fmt = chars_format::fixed; } else { _Fmt = chars_format::scientific; } } else if (_Fmt == chars_format::general) { // C11 7.21.6.1 "The fprintf function"/8: // "Let P equal [...] 6 if the precision is omitted [...]. // Then, if a conversion with style E would have an exponent of X: // - if P > X >= -4, the conversion is with style f [...]. // - otherwise, the conversion is with style e [...]." if (-4 <= _Scientific_exponent && _Scientific_exponent < 6) { _Fmt = chars_format::fixed; } else { _Fmt = chars_format::scientific; } } if (_Fmt == chars_format::fixed) { // Example: _Output == 1729, __olength == 4 // _Ryu_exponent | Printed | _Whole_digits | _Total_fixed_length | Notes // --------------|----------|---------------|----------------------|--------------------------------------- // 2 | 172900 | 6 | _Whole_digits | Ryu can't be used for printing // 1 | 17290 | 5 | (sometimes adjusted) | when the trimmed digits are nonzero. // --------------|----------|---------------|----------------------|--------------------------------------- // 0 | 1729 | 4 | _Whole_digits | Unified length cases. // --------------|----------|---------------|----------------------|--------------------------------------- // -1 | 172.9 | 3 | __olength + 1 | This case can't happen for // -2 | 17.29 | 2 | | __olength == 1, but no additional // -3 | 1.729 | 1 | | code is needed to avoid it. // --------------|----------|---------------|----------------------|--------------------------------------- // -4 | 0.1729 | 0 | 2 - _Ryu_exponent | C11 7.21.6.1 "The fprintf function"/8: // -5 | 0.01729 | -1 | | "If a decimal-point character appears, // -6 | 0.001729 | -2 | | at least one digit appears before it." const int32_t _Whole_digits = static_cast(__olength) + _Ryu_exponent; uint32_t _Total_fixed_length; if (_Ryu_exponent >= 0) { // cases "172900" and "1729" _Total_fixed_length = static_cast(_Whole_digits); if (_Output == 1) { // Rounding can affect the number of digits. // For example, 1e23 is exactly "99999999999999991611392" which is 23 digits instead of 24. // We can use a lookup table to detect this and adjust the total length. static constexpr uint8_t _Adjustment[309] = { 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, 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, 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, 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, 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, 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, 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 }; _Total_fixed_length -= _Adjustment[_Ryu_exponent]; // _Whole_digits doesn't need to be adjusted because these cases won't refer to it later. } } else if (_Whole_digits > 0) { // case "17.29" _Total_fixed_length = __olength + 1; } else { // case "0.001729" _Total_fixed_length = static_cast(2 - _Ryu_exponent); } if (_Last - _First < static_cast(_Total_fixed_length)) { return { _Last, errc::value_too_large }; } char* _Mid; if (_Ryu_exponent > 0) { // case "172900" bool _Can_use_ryu; if (_Ryu_exponent > 22) { // 10^22 is the largest power of 10 that's exactly representable as a double. _Can_use_ryu = false; } else { // Ryu generated X: __v.__mantissa * 10^_Ryu_exponent // __v.__mantissa == 2^_Trailing_zero_bits * (__v.__mantissa >> _Trailing_zero_bits) // 10^_Ryu_exponent == 2^_Ryu_exponent * 5^_Ryu_exponent // _Trailing_zero_bits is [0, 56] (aside: because 2^56 is the largest power of 2 // with 17 decimal digits, which is double's round-trip limit.) // _Ryu_exponent is [1, 22]. // Normalization adds [2, 52] (aside: at least 2 because the pre-normalized mantissa is at least 5). // This adds up to [3, 130], which is well below double's maximum binary exponent 1023. // Therefore, we just need to consider (__v.__mantissa >> _Trailing_zero_bits) * 5^_Ryu_exponent. // If that product would exceed 53 bits, then X can't be exactly represented as a double. // (That's not a problem for round-tripping, because X is close enough to the original double, // but X isn't mathematically equal to the original double.) This requires a high-precision fallback. // If the product is 53 bits or smaller, then X can be exactly represented as a double (and we don't // need to re-synthesize it; the original double must have been X, because Ryu wouldn't produce the // same output for two different doubles X and Y). This allows Ryu's output to be used (zero-filled). // (2^53 - 1) / 5^0 (for indexing), (2^53 - 1) / 5^1, ..., (2^53 - 1) / 5^22 static constexpr uint64_t _Max_shifted_mantissa[23] = { 9007199254740991u, 1801439850948198u, 360287970189639u, 72057594037927u, 14411518807585u, 2882303761517u, 576460752303u, 115292150460u, 23058430092u, 4611686018u, 922337203u, 184467440u, 36893488u, 7378697u, 1475739u, 295147u, 59029u, 11805u, 2361u, 472u, 94u, 18u, 3u }; unsigned long _Trailing_zero_bits; #ifdef _LIBCPP_HAS_BITSCAN64 (void) _BitScanForward64(&_Trailing_zero_bits, __v.__mantissa); // __v.__mantissa is guaranteed nonzero #else // ^^^ 64-bit ^^^ / vvv 32-bit vvv const uint32_t _Low_mantissa = static_cast(__v.__mantissa); if (_Low_mantissa != 0) { (void) _BitScanForward(&_Trailing_zero_bits, _Low_mantissa); } else { const uint32_t _High_mantissa = static_cast(__v.__mantissa >> 32); // nonzero here (void) _BitScanForward(&_Trailing_zero_bits, _High_mantissa); _Trailing_zero_bits += 32; } #endif // ^^^ 32-bit ^^^ const uint64_t _Shifted_mantissa = __v.__mantissa >> _Trailing_zero_bits; _Can_use_ryu = _Shifted_mantissa <= _Max_shifted_mantissa[_Ryu_exponent]; } if (!_Can_use_ryu) { // Print the integer exactly. // Performance note: This will redundantly perform bounds checking. // Performance note: This will redundantly decompose the IEEE representation. return __d2fixed_buffered_n(_First, _Last, __f, 0); } // _Can_use_ryu // Print the decimal digits, left-aligned within [_First, _First + _Total_fixed_length). _Mid = _First + __olength; } else { // cases "1729", "17.29", and "0.001729" // Print the decimal digits, right-aligned within [_First, _First + _Total_fixed_length). _Mid = _First + _Total_fixed_length; } // We prefer 32-bit operations, even on 64-bit platforms. // We have at most 17 digits, and uint32_t can store 9 digits. // If _Output doesn't fit into uint32_t, we cut off 8 digits, // so the rest will fit into uint32_t. if ((_Output >> 32) != 0) { // Expensive 64-bit division. const uint64_t __q = __div1e8(_Output); uint32_t __output2 = static_cast(_Output - 100000000 * __q); _Output = __q; const uint32_t __c = __output2 % 10000; __output2 /= 10000; const uint32_t __d = __output2 % 10000; const uint32_t __c0 = (__c % 100) << 1; const uint32_t __c1 = (__c / 100) << 1; const uint32_t __d0 = (__d % 100) << 1; const uint32_t __d1 = (__d / 100) << 1; _VSTD::memcpy(_Mid -= 2, __DIGIT_TABLE + __c0, 2); _VSTD::memcpy(_Mid -= 2, __DIGIT_TABLE + __c1, 2); _VSTD::memcpy(_Mid -= 2, __DIGIT_TABLE + __d0, 2); _VSTD::memcpy(_Mid -= 2, __DIGIT_TABLE + __d1, 2); } uint32_t __output2 = static_cast(_Output); while (__output2 >= 10000) { #ifdef __clang__ // TRANSITION, LLVM-38217 const uint32_t __c = __output2 - 10000 * (__output2 / 10000); #else const uint32_t __c = __output2 % 10000; #endif __output2 /= 10000; const uint32_t __c0 = (__c % 100) << 1; const uint32_t __c1 = (__c / 100) << 1; _VSTD::memcpy(_Mid -= 2, __DIGIT_TABLE + __c0, 2); _VSTD::memcpy(_Mid -= 2, __DIGIT_TABLE + __c1, 2); } if (__output2 >= 100) { const uint32_t __c = (__output2 % 100) << 1; __output2 /= 100; _VSTD::memcpy(_Mid -= 2, __DIGIT_TABLE + __c, 2); } if (__output2 >= 10) { const uint32_t __c = __output2 << 1; _VSTD::memcpy(_Mid -= 2, __DIGIT_TABLE + __c, 2); } else { *--_Mid = static_cast('0' + __output2); } if (_Ryu_exponent > 0) { // case "172900" with _Can_use_ryu // Performance note: it might be more efficient to do this immediately after setting _Mid. _VSTD::memset(_First + __olength, '0', static_cast(_Ryu_exponent)); } else if (_Ryu_exponent == 0) { // case "1729" // Done! } else if (_Whole_digits > 0) { // case "17.29" // Performance note: moving digits might not be optimal. _VSTD::memmove(_First, _First + 1, static_cast(_Whole_digits)); _First[_Whole_digits] = '.'; } else { // case "0.001729" // Performance note: a larger memset() followed by overwriting '.' might be more efficient. _First[0] = '0'; _First[1] = '.'; _VSTD::memset(_First + 2, '0', static_cast(-_Whole_digits)); } return { _First + _Total_fixed_length, errc{} }; } const uint32_t _Total_scientific_length = __olength + (__olength > 1) // digits + possible decimal point + (-100 < _Scientific_exponent && _Scientific_exponent < 100 ? 4 : 5); // + scientific exponent if (_Last - _First < static_cast(_Total_scientific_length)) { return { _Last, errc::value_too_large }; } char* const __result = _First; // Print the decimal digits. uint32_t __i = 0; // We prefer 32-bit operations, even on 64-bit platforms. // We have at most 17 digits, and uint32_t can store 9 digits. // If _Output doesn't fit into uint32_t, we cut off 8 digits, // so the rest will fit into uint32_t. if ((_Output >> 32) != 0) { // Expensive 64-bit division. const uint64_t __q = __div1e8(_Output); uint32_t __output2 = static_cast(_Output) - 100000000 * static_cast(__q); _Output = __q; const uint32_t __c = __output2 % 10000; __output2 /= 10000; const uint32_t __d = __output2 % 10000; const uint32_t __c0 = (__c % 100) << 1; const uint32_t __c1 = (__c / 100) << 1; const uint32_t __d0 = (__d % 100) << 1; const uint32_t __d1 = (__d / 100) << 1; _VSTD::memcpy(__result + __olength - __i - 1, __DIGIT_TABLE + __c0, 2); _VSTD::memcpy(__result + __olength - __i - 3, __DIGIT_TABLE + __c1, 2); _VSTD::memcpy(__result + __olength - __i - 5, __DIGIT_TABLE + __d0, 2); _VSTD::memcpy(__result + __olength - __i - 7, __DIGIT_TABLE + __d1, 2); __i += 8; } uint32_t __output2 = static_cast(_Output); while (__output2 >= 10000) { #ifdef __clang__ // TRANSITION, LLVM-38217 const uint32_t __c = __output2 - 10000 * (__output2 / 10000); #else const uint32_t __c = __output2 % 10000; #endif __output2 /= 10000; const uint32_t __c0 = (__c % 100) << 1; const uint32_t __c1 = (__c / 100) << 1; _VSTD::memcpy(__result + __olength - __i - 1, __DIGIT_TABLE + __c0, 2); _VSTD::memcpy(__result + __olength - __i - 3, __DIGIT_TABLE + __c1, 2); __i += 4; } if (__output2 >= 100) { const uint32_t __c = (__output2 % 100) << 1; __output2 /= 100; _VSTD::memcpy(__result + __olength - __i - 1, __DIGIT_TABLE + __c, 2); __i += 2; } if (__output2 >= 10) { const uint32_t __c = __output2 << 1; // We can't use memcpy here: the decimal dot goes between these two digits. __result[2] = __DIGIT_TABLE[__c + 1]; __result[0] = __DIGIT_TABLE[__c]; } else { __result[0] = static_cast('0' + __output2); } // Print decimal point if needed. uint32_t __index; if (__olength > 1) { __result[1] = '.'; __index = __olength + 1; } else { __index = 1; } // Print the exponent. __result[__index++] = 'e'; if (_Scientific_exponent < 0) { __result[__index++] = '-'; _Scientific_exponent = -_Scientific_exponent; } else { __result[__index++] = '+'; } if (_Scientific_exponent >= 100) { const int32_t __c = _Scientific_exponent % 10; _VSTD::memcpy(__result + __index, __DIGIT_TABLE + 2 * (_Scientific_exponent / 10), 2); __result[__index + 2] = static_cast('0' + __c); __index += 3; } else { _VSTD::memcpy(__result + __index, __DIGIT_TABLE + 2 * _Scientific_exponent, 2); __index += 2; } return { _First + _Total_scientific_length, errc{} }; } [[nodiscard]] _LIBCPP_HIDE_FROM_ABI inline bool __d2d_small_int(const uint64_t __ieeeMantissa, const uint32_t __ieeeExponent, __floating_decimal_64* const __v) { const uint64_t __m2 = (1ull << __DOUBLE_MANTISSA_BITS) | __ieeeMantissa; const int32_t __e2 = static_cast(__ieeeExponent) - __DOUBLE_BIAS - __DOUBLE_MANTISSA_BITS; if (__e2 > 0) { // f = __m2 * 2^__e2 >= 2^53 is an integer. // Ignore this case for now. return false; } if (__e2 < -52) { // f < 1. return false; } // Since 2^52 <= __m2 < 2^53 and 0 <= -__e2 <= 52: 1 <= f = __m2 / 2^-__e2 < 2^53. // Test if the lower -__e2 bits of the significand are 0, i.e. whether the fraction is 0. const uint64_t __mask = (1ull << -__e2) - 1; const uint64_t __fraction = __m2 & __mask; if (__fraction != 0) { return false; } // f is an integer in the range [1, 2^53). // Note: __mantissa might contain trailing (decimal) 0's. // Note: since 2^53 < 10^16, there is no need to adjust __decimalLength17(). __v->__mantissa = __m2 >> -__e2; __v->__exponent = 0; return true; } [[nodiscard]] to_chars_result __d2s_buffered_n(char* const _First, char* const _Last, const double __f, const chars_format _Fmt) { // Step 1: Decode the floating-point number, and unify normalized and subnormal cases. const uint64_t __bits = __double_to_bits(__f); // Case distinction; exit early for the easy cases. if (__bits == 0) { if (_Fmt == chars_format::scientific) { if (_Last - _First < 5) { return { _Last, errc::value_too_large }; } _VSTD::memcpy(_First, "0e+00", 5); return { _First + 5, errc{} }; } // Print "0" for chars_format::fixed, chars_format::general, and chars_format{}. if (_First == _Last) { return { _Last, errc::value_too_large }; } *_First = '0'; return { _First + 1, errc{} }; } // Decode __bits into mantissa and exponent. const uint64_t __ieeeMantissa = __bits & ((1ull << __DOUBLE_MANTISSA_BITS) - 1); const uint32_t __ieeeExponent = static_cast(__bits >> __DOUBLE_MANTISSA_BITS); if (_Fmt == chars_format::fixed) { // const uint64_t _Mantissa2 = __ieeeMantissa | (1ull << __DOUBLE_MANTISSA_BITS); // restore implicit bit const int32_t _Exponent2 = static_cast(__ieeeExponent) - __DOUBLE_BIAS - __DOUBLE_MANTISSA_BITS; // bias and normalization // Normal values are equal to _Mantissa2 * 2^_Exponent2. // (Subnormals are different, but they'll be rejected by the _Exponent2 test here, so they can be ignored.) // For nonzero integers, _Exponent2 >= -52. (The minimum value occurs when _Mantissa2 * 2^_Exponent2 is 1. // In that case, _Mantissa2 is the implicit 1 bit followed by 52 zeros, so _Exponent2 is -52 to shift away // the zeros.) The dense range of exactly representable integers has negative or zero exponents // (as positive exponents make the range non-dense). For that dense range, Ryu will always be used: // every digit is necessary to uniquely identify the value, so Ryu must print them all. // Positive exponents are the non-dense range of exactly representable integers. This contains all of the values // for which Ryu can't be used (and a few Ryu-friendly values). We can save time by detecting positive // exponents here and skipping Ryu. Calling __d2fixed_buffered_n() with precision 0 is valid for all integers // (so it's okay if we call it with a Ryu-friendly value). if (_Exponent2 > 0) { return __d2fixed_buffered_n(_First, _Last, __f, 0); } } __floating_decimal_64 __v; const bool __isSmallInt = __d2d_small_int(__ieeeMantissa, __ieeeExponent, &__v); if (__isSmallInt) { // For small integers in the range [1, 2^53), __v.__mantissa might contain trailing (decimal) zeros. // For scientific notation we need to move these zeros into the exponent. // (This is not needed for fixed-point notation, so it might be beneficial to trim // trailing zeros in __to_chars only if needed - once fixed-point notation output is implemented.) for (;;) { const uint64_t __q = __div10(__v.__mantissa); const uint32_t __r = static_cast(__v.__mantissa) - 10 * static_cast(__q); if (__r != 0) { break; } __v.__mantissa = __q; ++__v.__exponent; } } else { __v = __d2d(__ieeeMantissa, __ieeeExponent); } return __to_chars(_First, _Last, __v, _Fmt, __f); } _LIBCPP_END_NAMESPACE_STD // clang-format on