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Diffstat (limited to 'contrib/llvm-project/libcxx/src/ryu/f2s.cpp')
| -rw-r--r-- | contrib/llvm-project/libcxx/src/ryu/f2s.cpp | 716 |
1 files changed, 716 insertions, 0 deletions
diff --git a/contrib/llvm-project/libcxx/src/ryu/f2s.cpp b/contrib/llvm-project/libcxx/src/ryu/f2s.cpp new file mode 100644 index 000000000000..f42fbd68c91d --- /dev/null +++ b/contrib/llvm-project/libcxx/src/ryu/f2s.cpp @@ -0,0 +1,716 @@ +//===----------------------------------------------------------------------===// +// +// 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_intrinsics.h" +#include "include/ryu/digit_table.h" +#include "include/ryu/f2s.h" +#include "include/ryu/ryu.h" + +_LIBCPP_BEGIN_NAMESPACE_STD + +inline constexpr int __FLOAT_MANTISSA_BITS = 23; +inline constexpr int __FLOAT_EXPONENT_BITS = 8; +inline constexpr int __FLOAT_BIAS = 127; + +inline constexpr int __FLOAT_POW5_INV_BITCOUNT = 59; +inline constexpr uint64_t __FLOAT_POW5_INV_SPLIT[31] = { + 576460752303423489u, 461168601842738791u, 368934881474191033u, 295147905179352826u, + 472236648286964522u, 377789318629571618u, 302231454903657294u, 483570327845851670u, + 386856262276681336u, 309485009821345069u, 495176015714152110u, 396140812571321688u, + 316912650057057351u, 507060240091291761u, 405648192073033409u, 324518553658426727u, + 519229685853482763u, 415383748682786211u, 332306998946228969u, 531691198313966350u, + 425352958651173080u, 340282366920938464u, 544451787073501542u, 435561429658801234u, + 348449143727040987u, 557518629963265579u, 446014903970612463u, 356811923176489971u, + 570899077082383953u, 456719261665907162u, 365375409332725730u +}; +inline constexpr int __FLOAT_POW5_BITCOUNT = 61; +inline constexpr uint64_t __FLOAT_POW5_SPLIT[47] = { + 1152921504606846976u, 1441151880758558720u, 1801439850948198400u, 2251799813685248000u, + 1407374883553280000u, 1759218604441600000u, 2199023255552000000u, 1374389534720000000u, + 1717986918400000000u, 2147483648000000000u, 1342177280000000000u, 1677721600000000000u, + 2097152000000000000u, 1310720000000000000u, 1638400000000000000u, 2048000000000000000u, + 1280000000000000000u, 1600000000000000000u, 2000000000000000000u, 1250000000000000000u, + 1562500000000000000u, 1953125000000000000u, 1220703125000000000u, 1525878906250000000u, + 1907348632812500000u, 1192092895507812500u, 1490116119384765625u, 1862645149230957031u, + 1164153218269348144u, 1455191522836685180u, 1818989403545856475u, 2273736754432320594u, + 1421085471520200371u, 1776356839400250464u, 2220446049250313080u, 1387778780781445675u, + 1734723475976807094u, 2168404344971008868u, 1355252715606880542u, 1694065894508600678u, + 2117582368135750847u, 1323488980084844279u, 1654361225106055349u, 2067951531382569187u, + 1292469707114105741u, 1615587133892632177u, 2019483917365790221u +}; + +[[nodiscard]] _LIBCPP_HIDE_FROM_ABI inline uint32_t __pow5Factor(uint32_t __value) { + uint32_t __count = 0; + for (;;) { + _LIBCPP_ASSERT_INTERNAL(__value != 0, ""); + const uint32_t __q = __value / 5; + const uint32_t __r = __value % 5; + if (__r != 0) { + break; + } + __value = __q; + ++__count; + } + return __count; +} + +// Returns true if __value is divisible by 5^__p. +[[nodiscard]] _LIBCPP_HIDE_FROM_ABI inline bool __multipleOfPowerOf5(const uint32_t __value, const uint32_t __p) { + return __pow5Factor(__value) >= __p; +} + +// Returns true if __value is divisible by 2^__p. +[[nodiscard]] _LIBCPP_HIDE_FROM_ABI inline bool __multipleOfPowerOf2(const uint32_t __value, const uint32_t __p) { + _LIBCPP_ASSERT_INTERNAL(__value != 0, ""); + _LIBCPP_ASSERT_INTERNAL(__p < 32, ""); + // __builtin_ctz doesn't appear to be faster here. + return (__value & ((1u << __p) - 1)) == 0; +} + +[[nodiscard]] _LIBCPP_HIDE_FROM_ABI inline uint32_t __mulShift(const uint32_t __m, const uint64_t __factor, const int32_t __shift) { + _LIBCPP_ASSERT_INTERNAL(__shift > 32, ""); + + // The casts here help MSVC to avoid calls to the __allmul library + // function. + const uint32_t __factorLo = static_cast<uint32_t>(__factor); + const uint32_t __factorHi = static_cast<uint32_t>(__factor >> 32); + const uint64_t __bits0 = static_cast<uint64_t>(__m) * __factorLo; + const uint64_t __bits1 = static_cast<uint64_t>(__m) * __factorHi; + +#ifndef _LIBCPP_64_BIT + // On 32-bit platforms we can avoid a 64-bit shift-right since we only + // need the upper 32 bits of the result and the shift value is > 32. + const uint32_t __bits0Hi = static_cast<uint32_t>(__bits0 >> 32); + uint32_t __bits1Lo = static_cast<uint32_t>(__bits1); + uint32_t __bits1Hi = static_cast<uint32_t>(__bits1 >> 32); + __bits1Lo += __bits0Hi; + __bits1Hi += (__bits1Lo < __bits0Hi); + const int32_t __s = __shift - 32; + return (__bits1Hi << (32 - __s)) | (__bits1Lo >> __s); +#else // ^^^ 32-bit ^^^ / vvv 64-bit vvv + const uint64_t __sum = (__bits0 >> 32) + __bits1; + const uint64_t __shiftedSum = __sum >> (__shift - 32); + _LIBCPP_ASSERT_INTERNAL(__shiftedSum <= UINT32_MAX, ""); + return static_cast<uint32_t>(__shiftedSum); +#endif // ^^^ 64-bit ^^^ +} + +[[nodiscard]] _LIBCPP_HIDE_FROM_ABI inline uint32_t __mulPow5InvDivPow2(const uint32_t __m, const uint32_t __q, const int32_t __j) { + return __mulShift(__m, __FLOAT_POW5_INV_SPLIT[__q], __j); +} + +[[nodiscard]] _LIBCPP_HIDE_FROM_ABI inline uint32_t __mulPow5divPow2(const uint32_t __m, const uint32_t __i, const int32_t __j) { + return __mulShift(__m, __FLOAT_POW5_SPLIT[__i], __j); +} + +// A floating decimal representing m * 10^e. +struct __floating_decimal_32 { + uint32_t __mantissa; + int32_t __exponent; +}; + +[[nodiscard]] _LIBCPP_HIDE_FROM_ABI inline __floating_decimal_32 __f2d(const uint32_t __ieeeMantissa, const uint32_t __ieeeExponent) { + int32_t __e2; + uint32_t __m2; + if (__ieeeExponent == 0) { + // We subtract 2 so that the bounds computation has 2 additional bits. + __e2 = 1 - __FLOAT_BIAS - __FLOAT_MANTISSA_BITS - 2; + __m2 = __ieeeMantissa; + } else { + __e2 = static_cast<int32_t>(__ieeeExponent) - __FLOAT_BIAS - __FLOAT_MANTISSA_BITS - 2; + __m2 = (1u << __FLOAT_MANTISSA_BITS) | __ieeeMantissa; + } + const bool __even = (__m2 & 1) == 0; + const bool __acceptBounds = __even; + + // Step 2: Determine the interval of valid decimal representations. + const uint32_t __mv = 4 * __m2; + const uint32_t __mp = 4 * __m2 + 2; + // Implicit bool -> int conversion. True is 1, false is 0. + const uint32_t __mmShift = __ieeeMantissa != 0 || __ieeeExponent <= 1; + const uint32_t __mm = 4 * __m2 - 1 - __mmShift; + + // Step 3: Convert to a decimal power base using 64-bit arithmetic. + uint32_t __vr, __vp, __vm; + int32_t __e10; + bool __vmIsTrailingZeros = false; + bool __vrIsTrailingZeros = false; + uint8_t __lastRemovedDigit = 0; + if (__e2 >= 0) { + const uint32_t __q = __log10Pow2(__e2); + __e10 = static_cast<int32_t>(__q); + const int32_t __k = __FLOAT_POW5_INV_BITCOUNT + __pow5bits(static_cast<int32_t>(__q)) - 1; + const int32_t __i = -__e2 + static_cast<int32_t>(__q) + __k; + __vr = __mulPow5InvDivPow2(__mv, __q, __i); + __vp = __mulPow5InvDivPow2(__mp, __q, __i); + __vm = __mulPow5InvDivPow2(__mm, __q, __i); + if (__q != 0 && (__vp - 1) / 10 <= __vm / 10) { + // We need to know one removed digit even if we are not going to loop below. We could use + // __q = X - 1 above, except that would require 33 bits for the result, and we've found that + // 32-bit arithmetic is faster even on 64-bit machines. + const int32_t __l = __FLOAT_POW5_INV_BITCOUNT + __pow5bits(static_cast<int32_t>(__q - 1)) - 1; + __lastRemovedDigit = static_cast<uint8_t>(__mulPow5InvDivPow2(__mv, __q - 1, + -__e2 + static_cast<int32_t>(__q) - 1 + __l) % 10); + } + if (__q <= 9) { + // The largest power of 5 that fits in 24 bits is 5^10, but __q <= 9 seems to be safe as well. + // Only one of __mp, __mv, and __mm can be a multiple of 5, if any. + if (__mv % 5 == 0) { + __vrIsTrailingZeros = __multipleOfPowerOf5(__mv, __q); + } else if (__acceptBounds) { + __vmIsTrailingZeros = __multipleOfPowerOf5(__mm, __q); + } else { + __vp -= __multipleOfPowerOf5(__mp, __q); + } + } + } else { + const uint32_t __q = __log10Pow5(-__e2); + __e10 = static_cast<int32_t>(__q) + __e2; + const int32_t __i = -__e2 - static_cast<int32_t>(__q); + const int32_t __k = __pow5bits(__i) - __FLOAT_POW5_BITCOUNT; + int32_t __j = static_cast<int32_t>(__q) - __k; + __vr = __mulPow5divPow2(__mv, static_cast<uint32_t>(__i), __j); + __vp = __mulPow5divPow2(__mp, static_cast<uint32_t>(__i), __j); + __vm = __mulPow5divPow2(__mm, static_cast<uint32_t>(__i), __j); + if (__q != 0 && (__vp - 1) / 10 <= __vm / 10) { + __j = static_cast<int32_t>(__q) - 1 - (__pow5bits(__i + 1) - __FLOAT_POW5_BITCOUNT); + __lastRemovedDigit = static_cast<uint8_t>(__mulPow5divPow2(__mv, static_cast<uint32_t>(__i + 1), __j) % 10); + } + 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 < 31) { // TRANSITION(ulfjack): Use a tighter bound here. + __vrIsTrailingZeros = __multipleOfPowerOf2(__mv, __q - 1); + } + } + + // Step 4: Find the shortest decimal representation in the interval of valid representations. + int32_t __removed = 0; + uint32_t _Output; + if (__vmIsTrailingZeros || __vrIsTrailingZeros) { + // General case, which happens rarely (~4.0%). + while (__vp / 10 > __vm / 10) { +#ifdef __clang__ // TRANSITION, LLVM-23106 + __vmIsTrailingZeros &= __vm - (__vm / 10) * 10 == 0; +#else + __vmIsTrailingZeros &= __vm % 10 == 0; +#endif + __vrIsTrailingZeros &= __lastRemovedDigit == 0; + __lastRemovedDigit = static_cast<uint8_t>(__vr % 10); + __vr /= 10; + __vp /= 10; + __vm /= 10; + ++__removed; + } + if (__vmIsTrailingZeros) { + while (__vm % 10 == 0) { + __vrIsTrailingZeros &= __lastRemovedDigit == 0; + __lastRemovedDigit = static_cast<uint8_t>(__vr % 10); + __vr /= 10; + __vp /= 10; + __vm /= 10; + ++__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 (~96.0%). Percentages below are relative to this. + // Loop iterations below (approximately): + // 0: 13.6%, 1: 70.7%, 2: 14.1%, 3: 1.39%, 4: 0.14%, 5+: 0.01% + while (__vp / 10 > __vm / 10) { + __lastRemovedDigit = static_cast<uint8_t>(__vr % 10); + __vr /= 10; + __vp /= 10; + __vm /= 10; + ++__removed; + } + // We need to take __vr + 1 if __vr is outside bounds or we need to round up. + _Output = __vr + (__vr == __vm || __lastRemovedDigit >= 5); + } + const int32_t __exp = __e10 + __removed; + + __floating_decimal_32 __fd; + __fd.__exponent = __exp; + __fd.__mantissa = _Output; + return __fd; +} + +[[nodiscard]] _LIBCPP_HIDE_FROM_ABI inline to_chars_result _Large_integer_to_chars(char* const _First, char* const _Last, + const uint32_t _Mantissa2, const int32_t _Exponent2) { + + // Print the integer _Mantissa2 * 2^_Exponent2 exactly. + + // For nonzero integers, _Exponent2 >= -23. (The minimum value occurs when _Mantissa2 * 2^_Exponent2 is 1. + // In that case, _Mantissa2 is the implicit 1 bit followed by 23 zeros, so _Exponent2 is -23 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). + + // Performance note: Long division appears to be faster than losslessly widening float to double and calling + // __d2fixed_buffered_n(). If __f2fixed_buffered_n() is implemented, it might be faster than long division. + + _LIBCPP_ASSERT_INTERNAL(_Exponent2 > 0, ""); + _LIBCPP_ASSERT_INTERNAL(_Exponent2 <= 104, ""); // because __ieeeExponent <= 254 + + // Manually represent _Mantissa2 * 2^_Exponent2 as a large integer. _Mantissa2 is always 24 bits + // (due to the implicit bit), while _Exponent2 indicates a shift of at most 104 bits. + // 24 + 104 equals 128 equals 4 * 32, so we need exactly 4 32-bit elements. + // We use a little-endian representation, visualized like this: + + // << left shift << + // most significant + // _Data[3] _Data[2] _Data[1] _Data[0] + // least significant + // >> right shift >> + + constexpr uint32_t _Data_size = 4; + uint32_t _Data[_Data_size]{}; + + // _Maxidx is the index of the most significant nonzero element. + uint32_t _Maxidx = ((24 + static_cast<uint32_t>(_Exponent2) + 31) / 32) - 1; + _LIBCPP_ASSERT_INTERNAL(_Maxidx < _Data_size, ""); + + const uint32_t _Bit_shift = static_cast<uint32_t>(_Exponent2) % 32; + if (_Bit_shift <= 8) { // _Mantissa2's 24 bits don't cross an element boundary + _Data[_Maxidx] = _Mantissa2 << _Bit_shift; + } else { // _Mantissa2's 24 bits cross an element boundary + _Data[_Maxidx - 1] = _Mantissa2 << _Bit_shift; + _Data[_Maxidx] = _Mantissa2 >> (32 - _Bit_shift); + } + + // If Ryu hasn't determined the total output length, we need to buffer the digits generated from right to left + // by long division. The largest possible float is: 340'282346638'528859811'704183484'516925440 + uint32_t _Blocks[4]; + int32_t _Filled_blocks = 0; + // From left to right, we're going to print: + // _Data[0] will be [1, 10] digits. + // Then if _Filled_blocks > 0: + // _Blocks[_Filled_blocks - 1], ..., _Blocks[0] will be 0-filled 9-digit blocks. + + if (_Maxidx != 0) { // If the integer is actually large, perform long division. + // Otherwise, skip to printing _Data[0]. + for (;;) { + // Loop invariant: _Maxidx != 0 (i.e. the integer is actually large) + + const uint32_t _Most_significant_elem = _Data[_Maxidx]; + const uint32_t _Initial_remainder = _Most_significant_elem % 1000000000; + const uint32_t _Initial_quotient = _Most_significant_elem / 1000000000; + _Data[_Maxidx] = _Initial_quotient; + uint64_t _Remainder = _Initial_remainder; + + // Process less significant elements. + uint32_t _Idx = _Maxidx; + do { + --_Idx; // Initially, _Remainder is at most 10^9 - 1. + + // Now, _Remainder is at most (10^9 - 1) * 2^32 + 2^32 - 1, simplified to 10^9 * 2^32 - 1. + _Remainder = (_Remainder << 32) | _Data[_Idx]; + + // floor((10^9 * 2^32 - 1) / 10^9) == 2^32 - 1, so uint32_t _Quotient is lossless. + const uint32_t _Quotient = static_cast<uint32_t>(__div1e9(_Remainder)); + + // _Remainder is at most 10^9 - 1 again. + // For uint32_t truncation, see the __mod1e9() comment in d2s_intrinsics.h. + _Remainder = static_cast<uint32_t>(_Remainder) - 1000000000u * _Quotient; + + _Data[_Idx] = _Quotient; + } while (_Idx != 0); + + // Store a 0-filled 9-digit block. + _Blocks[_Filled_blocks++] = static_cast<uint32_t>(_Remainder); + + if (_Initial_quotient == 0) { // Is the large integer shrinking? + --_Maxidx; // log2(10^9) is 29.9, so we can't shrink by more than one element. + if (_Maxidx == 0) { + break; // We've finished long division. Now we need to print _Data[0]. + } + } + } + } + + _LIBCPP_ASSERT_INTERNAL(_Data[0] != 0, ""); + for (uint32_t _Idx = 1; _Idx < _Data_size; ++_Idx) { + _LIBCPP_ASSERT_INTERNAL(_Data[_Idx] == 0, ""); + } + + const uint32_t _Data_olength = _Data[0] >= 1000000000 ? 10 : __decimalLength9(_Data[0]); + const uint32_t _Total_fixed_length = _Data_olength + 9 * _Filled_blocks; + + if (_Last - _First < static_cast<ptrdiff_t>(_Total_fixed_length)) { + return { _Last, errc::value_too_large }; + } + + char* _Result = _First; + + // Print _Data[0]. While it's up to 10 digits, + // which is more than Ryu generates, the code below can handle this. + __append_n_digits(_Data_olength, _Data[0], _Result); + _Result += _Data_olength; + + // Print 0-filled 9-digit blocks. + for (int32_t _Idx = _Filled_blocks - 1; _Idx >= 0; --_Idx) { + __append_nine_digits(_Blocks[_Idx], _Result); + _Result += 9; + } + + return { _Result, errc{} }; +} + +[[nodiscard]] _LIBCPP_HIDE_FROM_ABI inline to_chars_result __to_chars(char* const _First, char* const _Last, const __floating_decimal_32 __v, + chars_format _Fmt, const uint32_t __ieeeMantissa, const uint32_t __ieeeExponent) { + // Step 5: Print the decimal representation. + uint32_t _Output = __v.__mantissa; + int32_t _Ryu_exponent = __v.__exponent; + const uint32_t __olength = __decimalLength9(_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, 1e11f is exactly "99999997952" which is 11 digits instead of 12. + // We can use a lookup table to detect this and adjust the total length. + static constexpr uint8_t _Adjustment[39] = { + 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 }; + _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 > 10) { // 10^10 is the largest power of 10 that's exactly representable as a float. + _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, 29] (aside: because 2^29 is the largest power of 2 + // with 9 decimal digits, which is float's round-trip limit.) + // _Ryu_exponent is [1, 10]. + // Normalization adds [2, 23] (aside: at least 2 because the pre-normalized mantissa is at least 5). + // This adds up to [3, 62], which is well below float's maximum binary exponent 127. + + // Therefore, we just need to consider (__v.__mantissa >> _Trailing_zero_bits) * 5^_Ryu_exponent. + + // If that product would exceed 24 bits, then X can't be exactly represented as a float. + // (That's not a problem for round-tripping, because X is close enough to the original float, + // but X isn't mathematically equal to the original float.) This requires a high-precision fallback. + + // If the product is 24 bits or smaller, then X can be exactly represented as a float (and we don't + // need to re-synthesize it; the original float must have been X, because Ryu wouldn't produce the + // same output for two different floats X and Y). This allows Ryu's output to be used (zero-filled). + + // (2^24 - 1) / 5^0 (for indexing), (2^24 - 1) / 5^1, ..., (2^24 - 1) / 5^10 + static constexpr uint32_t _Max_shifted_mantissa[11] = { + 16777215, 3355443, 671088, 134217, 26843, 5368, 1073, 214, 42, 8, 1 }; + + unsigned long _Trailing_zero_bits; + (void) _BitScanForward(&_Trailing_zero_bits, __v.__mantissa); // __v.__mantissa is guaranteed nonzero + const uint32_t _Shifted_mantissa = __v.__mantissa >> _Trailing_zero_bits; + _Can_use_ryu = _Shifted_mantissa <= _Max_shifted_mantissa[_Ryu_exponent]; + } + + if (!_Can_use_ryu) { + const uint32_t _Mantissa2 = __ieeeMantissa | (1u << __FLOAT_MANTISSA_BITS); // restore implicit bit + const int32_t _Exponent2 = static_cast<int32_t>(__ieeeExponent) + - __FLOAT_BIAS - __FLOAT_MANTISSA_BITS; // bias and normalization + + // Performance note: We've already called Ryu, so this will redundantly perform buffering and bounds checking. + return _Large_integer_to_chars(_First, _Last, _Mantissa2, _Exponent2); + } + + // _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; + } + + while (_Output >= 10000) { +#ifdef __clang__ // TRANSITION, LLVM-38217 + const uint32_t __c = _Output - 10000 * (_Output / 10000); +#else + const uint32_t __c = _Output % 10000; +#endif + _Output /= 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 (_Output >= 100) { + const uint32_t __c = (_Output % 100) << 1; + _Output /= 100; + std::memcpy(_Mid -= 2, __DIGIT_TABLE + __c, 2); + } + if (_Output >= 10) { + const uint32_t __c = _Output << 1; + std::memcpy(_Mid -= 2, __DIGIT_TABLE + __c, 2); + } else { + *--_Mid = static_cast<char>('0' + _Output); + } + + 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) + 4; // digits + possible decimal point + 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; + while (_Output >= 10000) { +#ifdef __clang__ // TRANSITION, LLVM-38217 + const uint32_t __c = _Output - 10000 * (_Output / 10000); +#else + const uint32_t __c = _Output % 10000; +#endif + _Output /= 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 (_Output >= 100) { + const uint32_t __c = (_Output % 100) << 1; + _Output /= 100; + std::memcpy(__result + __olength - __i - 1, __DIGIT_TABLE + __c, 2); + __i += 2; + } + if (_Output >= 10) { + const uint32_t __c = _Output << 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' + _Output); + } + + // 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++] = '+'; + } + + std::memcpy(__result + __index, __DIGIT_TABLE + 2 * _Scientific_exponent, 2); + __index += 2; + + return { _First + _Total_scientific_length, errc{} }; +} + +[[nodiscard]] to_chars_result __f2s_buffered_n(char* const _First, char* const _Last, const float __f, + const chars_format _Fmt) { + + // Step 1: Decode the floating-point number, and unify normalized and subnormal cases. + const uint32_t __bits = __float_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 uint32_t __ieeeMantissa = __bits & ((1u << __FLOAT_MANTISSA_BITS) - 1); + const uint32_t __ieeeExponent = __bits >> __FLOAT_MANTISSA_BITS; + + // When _Fmt == chars_format::fixed and the floating-point number is a large integer, + // it's faster to skip Ryu and immediately print the integer exactly. + if (_Fmt == chars_format::fixed) { + const uint32_t _Mantissa2 = __ieeeMantissa | (1u << __FLOAT_MANTISSA_BITS); // restore implicit bit + const int32_t _Exponent2 = static_cast<int32_t>(__ieeeExponent) + - __FLOAT_BIAS - __FLOAT_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.) + + if (_Exponent2 > 0) { + return _Large_integer_to_chars(_First, _Last, _Mantissa2, _Exponent2); + } + } + + const __floating_decimal_32 __v = __f2d(__ieeeMantissa, __ieeeExponent); + return __to_chars(_First, _Last, __v, _Fmt, __ieeeMantissa, __ieeeExponent); +} + +_LIBCPP_END_NAMESPACE_STD + +// clang-format on |