//===----------------------------------------------------------------------===// // // 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 #include #include "include/ryu/common.h" #include "include/ryu/d2fixed.h" #include "include/ryu/d2fixed_full_table.h" #include "include/ryu/d2s.h" #include "include/ryu/d2s_intrinsics.h" #include "include/ryu/digit_table.h" _LIBCPP_BEGIN_NAMESPACE_STD inline constexpr int __POW10_ADDITIONAL_BITS = 120; #ifdef _LIBCPP_INTRINSIC128 // Returns the low 64 bits of the high 128 bits of the 256-bit product of a and b. [[nodiscard]] _LIBCPP_HIDE_FROM_ABI inline uint64_t __umul256_hi128_lo64( const uint64_t __aHi, const uint64_t __aLo, const uint64_t __bHi, const uint64_t __bLo) { uint64_t __b00Hi; const uint64_t __b00Lo = __ryu_umul128(__aLo, __bLo, &__b00Hi); uint64_t __b01Hi; const uint64_t __b01Lo = __ryu_umul128(__aLo, __bHi, &__b01Hi); uint64_t __b10Hi; const uint64_t __b10Lo = __ryu_umul128(__aHi, __bLo, &__b10Hi); uint64_t __b11Hi; const uint64_t __b11Lo = __ryu_umul128(__aHi, __bHi, &__b11Hi); (void) __b00Lo; // unused (void) __b11Hi; // unused const uint64_t __temp1Lo = __b10Lo + __b00Hi; const uint64_t __temp1Hi = __b10Hi + (__temp1Lo < __b10Lo); const uint64_t __temp2Lo = __b01Lo + __temp1Lo; const uint64_t __temp2Hi = __b01Hi + (__temp2Lo < __b01Lo); return __b11Lo + __temp1Hi + __temp2Hi; } [[nodiscard]] _LIBCPP_HIDE_FROM_ABI inline uint32_t __uint128_mod1e9(const uint64_t __vHi, const uint64_t __vLo) { // After multiplying, we're going to shift right by 29, then truncate to uint32_t. // This means that we need only 29 + 32 = 61 bits, so we can truncate to uint64_t before shifting. const uint64_t __multiplied = __umul256_hi128_lo64(__vHi, __vLo, 0x89705F4136B4A597u, 0x31680A88F8953031u); // For uint32_t truncation, see the __mod1e9() comment in d2s_intrinsics.h. const uint32_t __shifted = static_cast(__multiplied >> 29); return static_cast(__vLo) - 1000000000 * __shifted; } #endif // ^^^ intrinsics available ^^^ [[nodiscard]] _LIBCPP_HIDE_FROM_ABI inline uint32_t __mulShift_mod1e9(const uint64_t __m, const uint64_t* const __mul, const int32_t __j) { uint64_t __high0; // 64 const uint64_t __low0 = __ryu_umul128(__m, __mul[0], &__high0); // 0 uint64_t __high1; // 128 const uint64_t __low1 = __ryu_umul128(__m, __mul[1], &__high1); // 64 uint64_t __high2; // 192 const uint64_t __low2 = __ryu_umul128(__m, __mul[2], &__high2); // 128 const uint64_t __s0low = __low0; // 0 (void) __s0low; // unused const uint64_t __s0high = __low1 + __high0; // 64 const uint32_t __c1 = __s0high < __low1; const uint64_t __s1low = __low2 + __high1 + __c1; // 128 const uint32_t __c2 = __s1low < __low2; // __high1 + __c1 can't overflow, so compare against __low2 const uint64_t __s1high = __high2 + __c2; // 192 _LIBCPP_ASSERT_UNCATEGORIZED(__j >= 128, ""); _LIBCPP_ASSERT_UNCATEGORIZED(__j <= 180, ""); #ifdef _LIBCPP_INTRINSIC128 const uint32_t __dist = static_cast(__j - 128); // __dist: [0, 52] const uint64_t __shiftedhigh = __s1high >> __dist; const uint64_t __shiftedlow = __ryu_shiftright128(__s1low, __s1high, __dist); return __uint128_mod1e9(__shiftedhigh, __shiftedlow); #else // ^^^ intrinsics available ^^^ / vvv intrinsics unavailable vvv if (__j < 160) { // __j: [128, 160) const uint64_t __r0 = __mod1e9(__s1high); const uint64_t __r1 = __mod1e9((__r0 << 32) | (__s1low >> 32)); const uint64_t __r2 = ((__r1 << 32) | (__s1low & 0xffffffff)); return __mod1e9(__r2 >> (__j - 128)); } else { // __j: [160, 192) const uint64_t __r0 = __mod1e9(__s1high); const uint64_t __r1 = ((__r0 << 32) | (__s1low >> 32)); return __mod1e9(__r1 >> (__j - 160)); } #endif // ^^^ intrinsics unavailable ^^^ } void __append_n_digits(const uint32_t __olength, uint32_t __digits, char* const __result) { uint32_t __i = 0; while (__digits >= 10000) { #ifdef __clang__ // TRANSITION, LLVM-38217 const uint32_t __c = __digits - 10000 * (__digits / 10000); #else const uint32_t __c = __digits % 10000; #endif __digits /= 10000; const uint32_t __c0 = (__c % 100) << 1; const uint32_t __c1 = (__c / 100) << 1; std::memcpy(__result + __olength - __i - 2, __DIGIT_TABLE + __c0, 2); std::memcpy(__result + __olength - __i - 4, __DIGIT_TABLE + __c1, 2); __i += 4; } if (__digits >= 100) { const uint32_t __c = (__digits % 100) << 1; __digits /= 100; std::memcpy(__result + __olength - __i - 2, __DIGIT_TABLE + __c, 2); __i += 2; } if (__digits >= 10) { const uint32_t __c = __digits << 1; std::memcpy(__result + __olength - __i - 2, __DIGIT_TABLE + __c, 2); } else { __result[0] = static_cast('0' + __digits); } } _LIBCPP_HIDE_FROM_ABI inline void __append_d_digits(const uint32_t __olength, uint32_t __digits, char* const __result) { uint32_t __i = 0; while (__digits >= 10000) { #ifdef __clang__ // TRANSITION, LLVM-38217 const uint32_t __c = __digits - 10000 * (__digits / 10000); #else const uint32_t __c = __digits % 10000; #endif __digits /= 10000; const uint32_t __c0 = (__c % 100) << 1; const uint32_t __c1 = (__c / 100) << 1; std::memcpy(__result + __olength + 1 - __i - 2, __DIGIT_TABLE + __c0, 2); std::memcpy(__result + __olength + 1 - __i - 4, __DIGIT_TABLE + __c1, 2); __i += 4; } if (__digits >= 100) { const uint32_t __c = (__digits % 100) << 1; __digits /= 100; std::memcpy(__result + __olength + 1 - __i - 2, __DIGIT_TABLE + __c, 2); __i += 2; } if (__digits >= 10) { const uint32_t __c = __digits << 1; __result[2] = __DIGIT_TABLE[__c + 1]; __result[1] = '.'; __result[0] = __DIGIT_TABLE[__c]; } else { __result[1] = '.'; __result[0] = static_cast('0' + __digits); } } _LIBCPP_HIDE_FROM_ABI inline void __append_c_digits(const uint32_t __count, uint32_t __digits, char* const __result) { uint32_t __i = 0; for (; __i < __count - 1; __i += 2) { const uint32_t __c = (__digits % 100) << 1; __digits /= 100; std::memcpy(__result + __count - __i - 2, __DIGIT_TABLE + __c, 2); } if (__i < __count) { const char __c = static_cast('0' + (__digits % 10)); __result[__count - __i - 1] = __c; } } void __append_nine_digits(uint32_t __digits, char* const __result) { if (__digits == 0) { std::memset(__result, '0', 9); return; } for (uint32_t __i = 0; __i < 5; __i += 4) { #ifdef __clang__ // TRANSITION, LLVM-38217 const uint32_t __c = __digits - 10000 * (__digits / 10000); #else const uint32_t __c = __digits % 10000; #endif __digits /= 10000; const uint32_t __c0 = (__c % 100) << 1; const uint32_t __c1 = (__c / 100) << 1; std::memcpy(__result + 7 - __i, __DIGIT_TABLE + __c0, 2); std::memcpy(__result + 5 - __i, __DIGIT_TABLE + __c1, 2); } __result[0] = static_cast('0' + __digits); } [[nodiscard]] _LIBCPP_HIDE_FROM_ABI inline uint32_t __indexForExponent(const uint32_t __e) { return (__e + 15) / 16; } [[nodiscard]] _LIBCPP_HIDE_FROM_ABI inline uint32_t __pow10BitsForIndex(const uint32_t __idx) { return 16 * __idx + __POW10_ADDITIONAL_BITS; } [[nodiscard]] _LIBCPP_HIDE_FROM_ABI inline uint32_t __lengthForIndex(const uint32_t __idx) { // +1 for ceil, +16 for mantissa, +8 to round up when dividing by 9 return (__log10Pow2(16 * static_cast(__idx)) + 1 + 16 + 8) / 9; } [[nodiscard]] to_chars_result __d2fixed_buffered_n(char* _First, char* const _Last, const double __d, const uint32_t __precision) { char* const _Original_first = _First; const uint64_t __bits = __double_to_bits(__d); // Case distinction; exit early for the easy cases. if (__bits == 0) { const int32_t _Total_zero_length = 1 // leading zero + static_cast(__precision != 0) // possible decimal point + static_cast(__precision); // zeroes after decimal point if (_Last - _First < _Total_zero_length) { return { _Last, errc::value_too_large }; } *_First++ = '0'; if (__precision > 0) { *_First++ = '.'; std::memset(_First, '0', __precision); _First += __precision; } return { _First, 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); int32_t __e2; uint64_t __m2; if (__ieeeExponent == 0) { __e2 = 1 - __DOUBLE_BIAS - __DOUBLE_MANTISSA_BITS; __m2 = __ieeeMantissa; } else { __e2 = static_cast(__ieeeExponent) - __DOUBLE_BIAS - __DOUBLE_MANTISSA_BITS; __m2 = (1ull << __DOUBLE_MANTISSA_BITS) | __ieeeMantissa; } bool __nonzero = false; if (__e2 >= -52) { const uint32_t __idx = __e2 < 0 ? 0 : __indexForExponent(static_cast(__e2)); const uint32_t __p10bits = __pow10BitsForIndex(__idx); const int32_t __len = static_cast(__lengthForIndex(__idx)); for (int32_t __i = __len - 1; __i >= 0; --__i) { const uint32_t __j = __p10bits - __e2; // Temporary: __j is usually around 128, and by shifting a bit, we push it to 128 or above, which is // a slightly faster code path in __mulShift_mod1e9. Instead, we can just increase the multipliers. const uint32_t __digits = __mulShift_mod1e9(__m2 << 8, __POW10_SPLIT[__POW10_OFFSET[__idx] + __i], static_cast(__j + 8)); if (__nonzero) { if (_Last - _First < 9) { return { _Last, errc::value_too_large }; } __append_nine_digits(__digits, _First); _First += 9; } else if (__digits != 0) { const uint32_t __olength = __decimalLength9(__digits); if (_Last - _First < static_cast(__olength)) { return { _Last, errc::value_too_large }; } __append_n_digits(__olength, __digits, _First); _First += __olength; __nonzero = true; } } } if (!__nonzero) { if (_First == _Last) { return { _Last, errc::value_too_large }; } *_First++ = '0'; } if (__precision > 0) { if (_First == _Last) { return { _Last, errc::value_too_large }; } *_First++ = '.'; } if (__e2 < 0) { const int32_t __idx = -__e2 / 16; const uint32_t __blocks = __precision / 9 + 1; // 0 = don't round up; 1 = round up unconditionally; 2 = round up if odd. int __roundUp = 0; uint32_t __i = 0; if (__blocks <= __MIN_BLOCK_2[__idx]) { __i = __blocks; if (_Last - _First < static_cast(__precision)) { return { _Last, errc::value_too_large }; } std::memset(_First, '0', __precision); _First += __precision; } else if (__i < __MIN_BLOCK_2[__idx]) { __i = __MIN_BLOCK_2[__idx]; if (_Last - _First < static_cast(9 * __i)) { return { _Last, errc::value_too_large }; } std::memset(_First, '0', 9 * __i); _First += 9 * __i; } for (; __i < __blocks; ++__i) { const int32_t __j = __ADDITIONAL_BITS_2 + (-__e2 - 16 * __idx); const uint32_t __p = __POW10_OFFSET_2[__idx] + __i - __MIN_BLOCK_2[__idx]; if (__p >= __POW10_OFFSET_2[__idx + 1]) { // If the remaining digits are all 0, then we might as well use memset. // No rounding required in this case. const uint32_t __fill = __precision - 9 * __i; if (_Last - _First < static_cast(__fill)) { return { _Last, errc::value_too_large }; } std::memset(_First, '0', __fill); _First += __fill; break; } // Temporary: __j is usually around 128, and by shifting a bit, we push it to 128 or above, which is // a slightly faster code path in __mulShift_mod1e9. Instead, we can just increase the multipliers. uint32_t __digits = __mulShift_mod1e9(__m2 << 8, __POW10_SPLIT_2[__p], __j + 8); if (__i < __blocks - 1) { if (_Last - _First < 9) { return { _Last, errc::value_too_large }; } __append_nine_digits(__digits, _First); _First += 9; } else { const uint32_t __maximum = __precision - 9 * __i; uint32_t __lastDigit = 0; for (uint32_t __k = 0; __k < 9 - __maximum; ++__k) { __lastDigit = __digits % 10; __digits /= 10; } if (__lastDigit != 5) { __roundUp = __lastDigit > 5; } else { // Is m * 10^(additionalDigits + 1) / 2^(-__e2) integer? const int32_t __requiredTwos = -__e2 - static_cast(__precision) - 1; const bool __trailingZeros = __requiredTwos <= 0 || (__requiredTwos < 60 && __multipleOfPowerOf2(__m2, static_cast(__requiredTwos))); __roundUp = __trailingZeros ? 2 : 1; } if (__maximum > 0) { if (_Last - _First < static_cast(__maximum)) { return { _Last, errc::value_too_large }; } __append_c_digits(__maximum, __digits, _First); _First += __maximum; } break; } } if (__roundUp != 0) { char* _Round = _First; char* _Dot = _Last; while (true) { if (_Round == _Original_first) { _Round[0] = '1'; if (_Dot != _Last) { _Dot[0] = '0'; _Dot[1] = '.'; } if (_First == _Last) { return { _Last, errc::value_too_large }; } *_First++ = '0'; break; } --_Round; const char __c = _Round[0]; if (__c == '.') { _Dot = _Round; } else if (__c == '9') { _Round[0] = '0'; __roundUp = 1; } else { if (__roundUp == 1 || __c % 2 != 0) { _Round[0] = __c + 1; } break; } } } } else { if (_Last - _First < static_cast(__precision)) { return { _Last, errc::value_too_large }; } std::memset(_First, '0', __precision); _First += __precision; } return { _First, errc{} }; } [[nodiscard]] to_chars_result __d2exp_buffered_n(char* _First, char* const _Last, const double __d, uint32_t __precision) { char* const _Original_first = _First; const uint64_t __bits = __double_to_bits(__d); // Case distinction; exit early for the easy cases. if (__bits == 0) { const int32_t _Total_zero_length = 1 // leading zero + static_cast(__precision != 0) // possible decimal point + static_cast(__precision) // zeroes after decimal point + 4; // "e+00" if (_Last - _First < _Total_zero_length) { return { _Last, errc::value_too_large }; } *_First++ = '0'; if (__precision > 0) { *_First++ = '.'; std::memset(_First, '0', __precision); _First += __precision; } std::memcpy(_First, "e+00", 4); _First += 4; return { _First, 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); int32_t __e2; uint64_t __m2; if (__ieeeExponent == 0) { __e2 = 1 - __DOUBLE_BIAS - __DOUBLE_MANTISSA_BITS; __m2 = __ieeeMantissa; } else { __e2 = static_cast(__ieeeExponent) - __DOUBLE_BIAS - __DOUBLE_MANTISSA_BITS; __m2 = (1ull << __DOUBLE_MANTISSA_BITS) | __ieeeMantissa; } const bool __printDecimalPoint = __precision > 0; ++__precision; uint32_t __digits = 0; uint32_t __printedDigits = 0; uint32_t __availableDigits = 0; int32_t __exp = 0; if (__e2 >= -52) { const uint32_t __idx = __e2 < 0 ? 0 : __indexForExponent(static_cast(__e2)); const uint32_t __p10bits = __pow10BitsForIndex(__idx); const int32_t __len = static_cast(__lengthForIndex(__idx)); for (int32_t __i = __len - 1; __i >= 0; --__i) { const uint32_t __j = __p10bits - __e2; // Temporary: __j is usually around 128, and by shifting a bit, we push it to 128 or above, which is // a slightly faster code path in __mulShift_mod1e9. Instead, we can just increase the multipliers. __digits = __mulShift_mod1e9(__m2 << 8, __POW10_SPLIT[__POW10_OFFSET[__idx] + __i], static_cast(__j + 8)); if (__printedDigits != 0) { if (__printedDigits + 9 > __precision) { __availableDigits = 9; break; } if (_Last - _First < 9) { return { _Last, errc::value_too_large }; } __append_nine_digits(__digits, _First); _First += 9; __printedDigits += 9; } else if (__digits != 0) { __availableDigits = __decimalLength9(__digits); __exp = __i * 9 + static_cast(__availableDigits) - 1; if (__availableDigits > __precision) { break; } if (__printDecimalPoint) { if (_Last - _First < static_cast(__availableDigits + 1)) { return { _Last, errc::value_too_large }; } __append_d_digits(__availableDigits, __digits, _First); _First += __availableDigits + 1; // +1 for decimal point } else { if (_First == _Last) { return { _Last, errc::value_too_large }; } *_First++ = static_cast('0' + __digits); } __printedDigits = __availableDigits; __availableDigits = 0; } } } if (__e2 < 0 && __availableDigits == 0) { const int32_t __idx = -__e2 / 16; for (int32_t __i = __MIN_BLOCK_2[__idx]; __i < 200; ++__i) { const int32_t __j = __ADDITIONAL_BITS_2 + (-__e2 - 16 * __idx); const uint32_t __p = __POW10_OFFSET_2[__idx] + static_cast(__i) - __MIN_BLOCK_2[__idx]; // Temporary: __j is usually around 128, and by shifting a bit, we push it to 128 or above, which is // a slightly faster code path in __mulShift_mod1e9. Instead, we can just increase the multipliers. __digits = (__p >= __POW10_OFFSET_2[__idx + 1]) ? 0 : __mulShift_mod1e9(__m2 << 8, __POW10_SPLIT_2[__p], __j + 8); if (__printedDigits != 0) { if (__printedDigits + 9 > __precision) { __availableDigits = 9; break; } if (_Last - _First < 9) { return { _Last, errc::value_too_large }; } __append_nine_digits(__digits, _First); _First += 9; __printedDigits += 9; } else if (__digits != 0) { __availableDigits = __decimalLength9(__digits); __exp = -(__i + 1) * 9 + static_cast(__availableDigits) - 1; if (__availableDigits > __precision) { break; } if (__printDecimalPoint) { if (_Last - _First < static_cast(__availableDigits + 1)) { return { _Last, errc::value_too_large }; } __append_d_digits(__availableDigits, __digits, _First); _First += __availableDigits + 1; // +1 for decimal point } else { if (_First == _Last) { return { _Last, errc::value_too_large }; } *_First++ = static_cast('0' + __digits); } __printedDigits = __availableDigits; __availableDigits = 0; } } } const uint32_t __maximum = __precision - __printedDigits; if (__availableDigits == 0) { __digits = 0; } uint32_t __lastDigit = 0; if (__availableDigits > __maximum) { for (uint32_t __k = 0; __k < __availableDigits - __maximum; ++__k) { __lastDigit = __digits % 10; __digits /= 10; } } // 0 = don't round up; 1 = round up unconditionally; 2 = round up if odd. int __roundUp = 0; if (__lastDigit != 5) { __roundUp = __lastDigit > 5; } else { // Is m * 2^__e2 * 10^(__precision + 1 - __exp) integer? // __precision was already increased by 1, so we don't need to write + 1 here. const int32_t __rexp = static_cast(__precision) - __exp; const int32_t __requiredTwos = -__e2 - __rexp; bool __trailingZeros = __requiredTwos <= 0 || (__requiredTwos < 60 && __multipleOfPowerOf2(__m2, static_cast(__requiredTwos))); if (__rexp < 0) { const int32_t __requiredFives = -__rexp; __trailingZeros = __trailingZeros && __multipleOfPowerOf5(__m2, static_cast(__requiredFives)); } __roundUp = __trailingZeros ? 2 : 1; } if (__printedDigits != 0) { if (_Last - _First < static_cast(__maximum)) { return { _Last, errc::value_too_large }; } if (__digits == 0) { std::memset(_First, '0', __maximum); } else { __append_c_digits(__maximum, __digits, _First); } _First += __maximum; } else { if (__printDecimalPoint) { if (_Last - _First < static_cast(__maximum + 1)) { return { _Last, errc::value_too_large }; } __append_d_digits(__maximum, __digits, _First); _First += __maximum + 1; // +1 for decimal point } else { if (_First == _Last) { return { _Last, errc::value_too_large }; } *_First++ = static_cast('0' + __digits); } } if (__roundUp != 0) { char* _Round = _First; while (true) { if (_Round == _Original_first) { _Round[0] = '1'; ++__exp; break; } --_Round; const char __c = _Round[0]; if (__c == '.') { // Keep going. } else if (__c == '9') { _Round[0] = '0'; __roundUp = 1; } else { if (__roundUp == 1 || __c % 2 != 0) { _Round[0] = __c + 1; } break; } } } char _Sign_character; if (__exp < 0) { _Sign_character = '-'; __exp = -__exp; } else { _Sign_character = '+'; } const int _Exponent_part_length = __exp >= 100 ? 5 // "e+NNN" : 4; // "e+NN" if (_Last - _First < _Exponent_part_length) { return { _Last, errc::value_too_large }; } *_First++ = 'e'; *_First++ = _Sign_character; if (__exp >= 100) { const int32_t __c = __exp % 10; std::memcpy(_First, __DIGIT_TABLE + 2 * (__exp / 10), 2); _First[2] = static_cast('0' + __c); _First += 3; } else { std::memcpy(_First, __DIGIT_TABLE + 2 * __exp, 2); _First += 2; } return { _First, errc{} }; } _LIBCPP_END_NAMESPACE_STD // clang-format on