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Diffstat (limited to 'contrib/llvm-project/libcxx/src/ryu/d2s.cpp')
-rw-r--r-- | contrib/llvm-project/libcxx/src/ryu/d2s.cpp | 783 |
1 files changed, 783 insertions, 0 deletions
diff --git a/contrib/llvm-project/libcxx/src/ryu/d2s.cpp b/contrib/llvm-project/libcxx/src/ryu/d2s.cpp new file mode 100644 index 000000000000..32d617cb5532 --- /dev/null +++ b/contrib/llvm-project/libcxx/src/ryu/d2s.cpp @@ -0,0 +1,783 @@ +//===----------------------------------------------------------------------===// +// +// 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 <__assert> +#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<uint32_t>(__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<uint32_t>(__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<uint32_t>(__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<uint32_t>(__j - 64)); + } + + return __ryu_shiftright128(__mid, __hi, static_cast<uint32_t>(__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_INTERNAL(__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<int32_t>(__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<int32_t>(__q); + const int32_t __k = __DOUBLE_POW5_INV_BITCOUNT + __pow5bits(static_cast<int32_t>(__q)) - 1; + const int32_t __i = -__e2 + static_cast<int32_t>(__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<uint32_t>(__mv) - 5 * static_cast<uint32_t>(__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<int32_t>(__q) + __e2; + const int32_t __i = -__e2 - static_cast<int32_t>(__q); + const int32_t __k = __pow5bits(__i) - __DOUBLE_POW5_BITCOUNT; + const int32_t __j = static_cast<int32_t>(__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<uint32_t>(__vm) - 10 * static_cast<uint32_t>(__vmDiv10); + const uint64_t __vrDiv10 = __div10(__vr); + const uint32_t __vrMod10 = static_cast<uint32_t>(__vr) - 10 * static_cast<uint32_t>(__vrDiv10); + __vmIsTrailingZeros &= __vmMod10 == 0; + __vrIsTrailingZeros &= __lastRemovedDigit == 0; + __lastRemovedDigit = static_cast<uint8_t>(__vrMod10); + __vr = __vrDiv10; + __vp = __vpDiv10; + __vm = __vmDiv10; + ++__removed; + } + if (__vmIsTrailingZeros) { + for (;;) { + const uint64_t __vmDiv10 = __div10(__vm); + const uint32_t __vmMod10 = static_cast<uint32_t>(__vm) - 10 * static_cast<uint32_t>(__vmDiv10); + if (__vmMod10 != 0) { + break; + } + const uint64_t __vpDiv10 = __div10(__vp); + const uint64_t __vrDiv10 = __div10(__vr); + const uint32_t __vrMod10 = static_cast<uint32_t>(__vr) - 10 * static_cast<uint32_t>(__vrDiv10); + __vrIsTrailingZeros &= __lastRemovedDigit == 0; + __lastRemovedDigit = static_cast<uint8_t>(__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<uint32_t>(__vr) - 100 * static_cast<uint32_t>(__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<uint32_t>(__vr) - 10 * static_cast<uint32_t>(__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<int32_t>(__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<int32_t>(__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<int32_t>(__olength) + _Ryu_exponent; + + uint32_t _Total_fixed_length; + if (_Ryu_exponent >= 0) { // cases "172900" and "1729" + _Total_fixed_length = static_cast<uint32_t>(_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<uint32_t>(2 - _Ryu_exponent); + } + + if (_Last - _First < static_cast<ptrdiff_t>(_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<uint32_t>(__v.__mantissa); + if (_Low_mantissa != 0) { + (void) _BitScanForward(&_Trailing_zero_bits, _Low_mantissa); + } else { + const uint32_t _High_mantissa = static_cast<uint32_t>(__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<uint32_t>(_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; + + std::memcpy(_Mid -= 2, __DIGIT_TABLE + __c0, 2); + std::memcpy(_Mid -= 2, __DIGIT_TABLE + __c1, 2); + std::memcpy(_Mid -= 2, __DIGIT_TABLE + __d0, 2); + std::memcpy(_Mid -= 2, __DIGIT_TABLE + __d1, 2); + } + uint32_t __output2 = static_cast<uint32_t>(_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; + std::memcpy(_Mid -= 2, __DIGIT_TABLE + __c0, 2); + std::memcpy(_Mid -= 2, __DIGIT_TABLE + __c1, 2); + } + if (__output2 >= 100) { + const uint32_t __c = (__output2 % 100) << 1; + __output2 /= 100; + std::memcpy(_Mid -= 2, __DIGIT_TABLE + __c, 2); + } + if (__output2 >= 10) { + const uint32_t __c = __output2 << 1; + std::memcpy(_Mid -= 2, __DIGIT_TABLE + __c, 2); + } else { + *--_Mid = static_cast<char>('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. + std::memset(_First + __olength, '0', static_cast<size_t>(_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. + std::memmove(_First, _First + 1, static_cast<size_t>(_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] = '.'; + std::memset(_First + 2, '0', static_cast<size_t>(-_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<ptrdiff_t>(_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<uint32_t>(_Output) - 100000000 * static_cast<uint32_t>(__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; + std::memcpy(__result + __olength - __i - 1, __DIGIT_TABLE + __c0, 2); + std::memcpy(__result + __olength - __i - 3, __DIGIT_TABLE + __c1, 2); + std::memcpy(__result + __olength - __i - 5, __DIGIT_TABLE + __d0, 2); + std::memcpy(__result + __olength - __i - 7, __DIGIT_TABLE + __d1, 2); + __i += 8; + } + uint32_t __output2 = static_cast<uint32_t>(_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; + std::memcpy(__result + __olength - __i - 1, __DIGIT_TABLE + __c0, 2); + std::memcpy(__result + __olength - __i - 3, __DIGIT_TABLE + __c1, 2); + __i += 4; + } + if (__output2 >= 100) { + const uint32_t __c = (__output2 % 100) << 1; + __output2 /= 100; + std::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<char>('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; + std::memcpy(__result + __index, __DIGIT_TABLE + 2 * (_Scientific_exponent / 10), 2); + __result[__index + 2] = static_cast<char>('0' + __c); + __index += 3; + } else { + std::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<int32_t>(__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 }; + } + + std::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<uint32_t>(__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<int32_t>(__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<uint32_t>(__v.__mantissa) - 10 * static_cast<uint32_t>(__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 |