// Copyright 2020-2022 Junekey Jeon // // The contents of this file may be used under the terms of // the Apache License v2.0 with LLVM Exceptions. // // (See accompanying file LICENSE-Apache or copy at // https://llvm.org/foundation/relicensing/LICENSE.txt) // // Alternatively, the contents of this file may be used under the terms of // the Boost Software License, Version 1.0. // (See accompanying file LICENSE-Boost or copy at // https://www.boost.org/LICENSE_1_0.txt) // // Unless required by applicable law or agreed to in writing, this software // is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY // KIND, either express or implied. #pragma once #include "dragonbox_to_chars.h" #if defined(__GNUC__) || defined(__clang__) #define JKJ_FORCEINLINE inline __attribute__((always_inline)) #elif defined(_MSC_VER) #define JKJ_FORCEINLINE __forceinline #else #define JKJ_FORCEINLINE inline #endif namespace jkj::dragonbox { namespace to_chars_detail { // These "//"'s are to prevent clang-format to ruin this nice alignment. // Thanks to reddit user u/mcmcc: // https://www.reddit.com/r/cpp/comments/so3wx9/dragonbox_110_is_released_a_fast_floattostring/hw8z26r/?context=3 static constexpr char radix_100_table[] = { '0', '0', '0', '1', '0', '2', '0', '3', '0', '4', // '0', '5', '0', '6', '0', '7', '0', '8', '0', '9', // '1', '0', '1', '1', '1', '2', '1', '3', '1', '4', // '1', '5', '1', '6', '1', '7', '1', '8', '1', '9', // '2', '0', '2', '1', '2', '2', '2', '3', '2', '4', // '2', '5', '2', '6', '2', '7', '2', '8', '2', '9', // '3', '0', '3', '1', '3', '2', '3', '3', '3', '4', // '3', '5', '3', '6', '3', '7', '3', '8', '3', '9', // '4', '0', '4', '1', '4', '2', '4', '3', '4', '4', // '4', '5', '4', '6', '4', '7', '4', '8', '4', '9', // '5', '0', '5', '1', '5', '2', '5', '3', '5', '4', // '5', '5', '5', '6', '5', '7', '5', '8', '5', '9', // '6', '0', '6', '1', '6', '2', '6', '3', '6', '4', // '6', '5', '6', '6', '6', '7', '6', '8', '6', '9', // '7', '0', '7', '1', '7', '2', '7', '3', '7', '4', // '7', '5', '7', '6', '7', '7', '7', '8', '7', '9', // '8', '0', '8', '1', '8', '2', '8', '3', '8', '4', // '8', '5', '8', '6', '8', '7', '8', '8', '8', '9', // '9', '0', '9', '1', '9', '2', '9', '3', '9', '4', // '9', '5', '9', '6', '9', '7', '9', '8', '9', '9' // }; static constexpr char radix_100_head_table[] = { '0', '.', '1', '.', '2', '.', '3', '.', '4', '.', // '5', '.', '6', '.', '7', '.', '8', '.', '9', '.', // '1', '.', '1', '.', '1', '.', '1', '.', '1', '.', // '1', '.', '1', '.', '1', '.', '1', '.', '1', '.', // '2', '.', '2', '.', '2', '.', '2', '.', '2', '.', // '2', '.', '2', '.', '2', '.', '2', '.', '2', '.', // '3', '.', '3', '.', '3', '.', '3', '.', '3', '.', // '3', '.', '3', '.', '3', '.', '3', '.', '3', '.', // '4', '.', '4', '.', '4', '.', '4', '.', '4', '.', // '4', '.', '4', '.', '4', '.', '4', '.', '4', '.', // '5', '.', '5', '.', '5', '.', '5', '.', '5', '.', // '5', '.', '5', '.', '5', '.', '5', '.', '5', '.', // '6', '.', '6', '.', '6', '.', '6', '.', '6', '.', // '6', '.', '6', '.', '6', '.', '6', '.', '6', '.', // '7', '.', '7', '.', '7', '.', '7', '.', '7', '.', // '7', '.', '7', '.', '7', '.', '7', '.', '7', '.', // '8', '.', '8', '.', '8', '.', '8', '.', '8', '.', // '8', '.', '8', '.', '8', '.', '8', '.', '8', '.', // '9', '.', '9', '.', '9', '.', '9', '.', '9', '.', // '9', '.', '9', '.', '9', '.', '9', '.', '9', '.' // }; // These digit generation routines are inspired by James Anhalt's itoa algorithm: // https://github.com/jeaiii/itoa // The main idea is for given n, find y such that floor(10^k * y / 2^32) = n holds, // where k is an appropriate integer depending on the length of n. // For example, if n = 1234567, we set k = 6. In this case, we have // floor(y / 2^32) = 1, // floor(10^2 * ((10^0 * y) mod 2^32) / 2^32) = 23, // floor(10^2 * ((10^2 * y) mod 2^32) / 2^32) = 45, and // floor(10^2 * ((10^4 * y) mod 2^32) / 2^32) = 67. // See https://jk-jeon.github.io/posts/2022/02/jeaiii-algorithm/ for more explanation. JKJ_FORCEINLINE static void print_9_digits(std::uint32_t s32, int& exponent, char*& buffer) noexcept { // -- IEEE-754 binary32 // Since we do not cut trailing zeros in advance, s32 must be of 6~9 digits // unless the original input was subnormal. // In particular, when it is of 9 digits it shouldn't have any trailing zeros. // -- IEEE-754 binary64 // In this case, s32 must be of 7~9 digits unless the input is subnormal, // and it shouldn't have any trailing zeros if it is of 9 digits. if (s32 >= 1'0000'0000) { // 9 digits. // 1441151882 = ceil(2^57 / 1'0000'0000) + 1 auto prod = s32 * std::uint64_t(1441151882); prod >>= 25; std::memcpy(buffer, radix_100_head_table + std::uint32_t(prod >> 32) * 2, 2); prod = std::uint32_t(prod) * std::uint64_t(100); std::memcpy(buffer + 2, radix_100_table + std::uint32_t(prod >> 32) * 2, 2); prod = std::uint32_t(prod) * std::uint64_t(100); std::memcpy(buffer + 4, radix_100_table + std::uint32_t(prod >> 32) * 2, 2); prod = std::uint32_t(prod) * std::uint64_t(100); std::memcpy(buffer + 6, radix_100_table + std::uint32_t(prod >> 32) * 2, 2); prod = std::uint32_t(prod) * std::uint64_t(100); std::memcpy(buffer + 8, radix_100_table + std::uint32_t(prod >> 32) * 2, 2); exponent += 8; buffer += 10; } else if (s32 >= 100'0000) { // 7 or 8 digits. // 281474978 = ceil(2^48 / 100'0000) + 1 auto prod = s32 * std::uint64_t(281474978); prod >>= 16; auto two_digits = std::uint32_t(prod >> 32); // If s32 is of 8 digits, increase the exponent by 7. // Otherwise, increase it by 6. exponent += (6 + unsigned(two_digits >= 10)); // Write the first digit and the decimal point. std::memcpy(buffer, radix_100_head_table + two_digits * 2, 2); // This third character may be overwritten later but we don't care. buffer[2] = radix_100_table[two_digits * 2 + 1]; // Remaining 6 digits are all zero? if (std::uint32_t(prod) <= std::uint32_t((std::uint64_t(1) << 32) / 100'0000)) { // The number of characters actually written is: // 1, if only the first digit is nonzero, which means that either s32 is of 7 // digits or it is of 8 digits but the second digit is zero, or // 3, otherwise. // Note that buffer[2] is never zero if s32 is of 7 digits, because the input is // never zero. buffer += (1 + (unsigned(two_digits >= 10) & unsigned(buffer[2] > '0')) * 2); } else { // At least one of the remaining 6 digits are nonzero. // After this adjustment, now the first destination becomes buffer + 2. buffer += unsigned(two_digits >= 10); // Obtain the next two digits. prod = std::uint32_t(prod) * std::uint64_t(100); two_digits = std::uint32_t(prod >> 32); std::memcpy(buffer + 2, radix_100_table + two_digits * 2, 2); // Remaining 4 digits are all zero? if (std::uint32_t(prod) <= std::uint32_t((std::uint64_t(1) << 32) / 1'0000)) { buffer += (3 + unsigned(buffer[3] > '0')); } else { // At least one of the remaining 4 digits are nonzero. // Obtain the next two digits. prod = std::uint32_t(prod) * std::uint64_t(100); two_digits = std::uint32_t(prod >> 32); std::memcpy(buffer + 4, radix_100_table + two_digits * 2, 2); // Remaining 2 digits are all zero? if (std::uint32_t(prod) <= std::uint32_t((std::uint64_t(1) << 32) / 100)) { buffer += (5 + unsigned(buffer[5] > '0')); } else { // Obtain the last two digits. prod = std::uint32_t(prod) * std::uint64_t(100); two_digits = std::uint32_t(prod >> 32); std::memcpy(buffer + 6, radix_100_table + two_digits * 2, 2); buffer += (7 + unsigned(buffer[7] > '0')); } } } } else if (s32 >= 1'0000) { // 5 or 6 digits. // 429497 = ceil(2^32 / 1'0000) auto prod = s32 * std::uint64_t(429497); auto two_digits = std::uint32_t(prod >> 32); // If s32 is of 6 digits, increase the exponent by 5. // Otherwise, increase it by 4. exponent += (4 + unsigned(two_digits >= 10)); // Write the first digit and the decimal point. std::memcpy(buffer, radix_100_head_table + two_digits * 2, 2); // This third character may be overwritten later but we don't care. buffer[2] = radix_100_table[two_digits * 2 + 1]; // Remaining 4 digits are all zero? if (std::uint32_t(prod) <= std::uint32_t((std::uint64_t(1) << 32) / 1'0000)) { // The number of characters actually written is 1 or 3, similarly to the case of // 7 or 8 digits. buffer += (1 + (unsigned(two_digits >= 10) & unsigned(buffer[2] > '0')) * 2); } else { // At least one of the remaining 4 digits are nonzero. // After this adjustment, now the first destination becomes buffer + 2. buffer += unsigned(two_digits >= 10); // Obtain the next two digits. prod = std::uint32_t(prod) * std::uint64_t(100); two_digits = std::uint32_t(prod >> 32); std::memcpy(buffer + 2, radix_100_table + two_digits * 2, 2); // Remaining 2 digits are all zero? if (std::uint32_t(prod) <= std::uint32_t((std::uint64_t(1) << 32) / 100)) { buffer += (3 + unsigned(buffer[3] > '0')); } else { // Obtain the last two digits. prod = std::uint32_t(prod) * std::uint64_t(100); two_digits = std::uint32_t(prod >> 32); std::memcpy(buffer + 4, radix_100_table + two_digits * 2, 2); buffer += (5 + unsigned(buffer[5] > '0')); } } } else if (s32 >= 100) { // 3 or 4 digits. // 42949673 = ceil(2^32 / 100) auto prod = s32 * std::uint64_t(42949673); auto two_digits = std::uint32_t(prod >> 32); // If s32 is of 4 digits, increase the exponent by 3. // Otherwise, increase it by 2. exponent += (2 + int(two_digits >= 10)); // Write the first digit and the decimal point. std::memcpy(buffer, radix_100_head_table + two_digits * 2, 2); // This third character may be overwritten later but we don't care. buffer[2] = radix_100_table[two_digits * 2 + 1]; // Remaining 2 digits are all zero? if (std::uint32_t(prod) <= std::uint32_t((std::uint64_t(1) << 32) / 100)) { // The number of characters actually written is 1 or 3, similarly to the case of // 7 or 8 digits. buffer += (1 + (unsigned(two_digits >= 10) & unsigned(buffer[2] > '0')) * 2); } else { // At least one of the remaining 2 digits are nonzero. // After this adjustment, now the first destination becomes buffer + 2. buffer += unsigned(two_digits >= 10); // Obtain the last two digits. prod = std::uint32_t(prod) * std::uint64_t(100); two_digits = std::uint32_t(prod >> 32); std::memcpy(buffer + 2, radix_100_table + two_digits * 2, 2); buffer += (3 + unsigned(buffer[3] > '0')); } } else { // 1 or 2 digits. // If s32 is of 2 digits, increase the exponent by 1. exponent += int(s32 >= 10); // Write the first digit and the decimal point. std::memcpy(buffer, radix_100_head_table + s32 * 2, 2); // This third character may be overwritten later but we don't care. buffer[2] = radix_100_table[s32 * 2 + 1]; // The number of characters actually written is 1 or 3, similarly to the case of // 7 or 8 digits. buffer += (1 + (unsigned(s32 >= 10) & unsigned(buffer[2] > '0')) * 2); } } template <> char* to_chars>(std::uint32_t s32, int exponent, char* buffer) noexcept { // Print significand. print_9_digits(s32, exponent, buffer); // Print exponent and return if (exponent < 0) { std::memcpy(buffer, "E-", 2); buffer += 2; exponent = -exponent; } else if (exponent > 0) { buffer[0] = 'E'; buffer += 1; } else { return buffer; } if (exponent >= 10) { std::memcpy(buffer, &radix_100_table[exponent * 2], 2); buffer += 2; } else { buffer[0] = char('0' + exponent); buffer += 1; } return buffer; } template <> char* to_chars>(std::uint64_t const significand, int exponent, char* buffer) noexcept { // Print significand by decomposing it into a 9-digit block and a 8-digit block. std::uint32_t first_block, second_block; bool no_second_block; if (significand >= 1'0000'0000) { first_block = std::uint32_t(significand / 1'0000'0000); second_block = std::uint32_t(significand) - first_block * 1'0000'0000; exponent += 8; no_second_block = (second_block == 0); } else { first_block = std::uint32_t(significand); no_second_block = true; } if (no_second_block) { print_9_digits(first_block, exponent, buffer); } else { // We proceed similarly to print_9_digits(), but since we do not need to remove // trailing zeros, the procedure is a bit simpler. if (first_block >= 1'0000'0000) { // The input is of 17 digits, thus there should be no trailing zero at all. // The first block is of 9 digits. // 1441151882 = ceil(2^57 / 1'0000'0000) + 1 auto prod = first_block * std::uint64_t(1441151882); prod >>= 25; std::memcpy(buffer, radix_100_head_table + std::uint32_t(prod >> 32) * 2, 2); prod = std::uint32_t(prod) * std::uint64_t(100); std::memcpy(buffer + 2, radix_100_table + std::uint32_t(prod >> 32) * 2, 2); prod = std::uint32_t(prod) * std::uint64_t(100); std::memcpy(buffer + 4, radix_100_table + std::uint32_t(prod >> 32) * 2, 2); prod = std::uint32_t(prod) * std::uint64_t(100); std::memcpy(buffer + 6, radix_100_table + std::uint32_t(prod >> 32) * 2, 2); prod = std::uint32_t(prod) * std::uint64_t(100); std::memcpy(buffer + 8, radix_100_table + std::uint32_t(prod >> 32) * 2, 2); // The second block is of 8 digits. // 281474978 = ceil(2^48 / 100'0000) + 1 prod = second_block * std::uint64_t(281474978); prod >>= 16; prod += 1; std::memcpy(buffer + 10, radix_100_table + std::uint32_t(prod >> 32) * 2, 2); prod = std::uint32_t(prod) * std::uint64_t(100); std::memcpy(buffer + 12, radix_100_table + std::uint32_t(prod >> 32) * 2, 2); prod = std::uint32_t(prod) * std::uint64_t(100); std::memcpy(buffer + 14, radix_100_table + std::uint32_t(prod >> 32) * 2, 2); prod = std::uint32_t(prod) * std::uint64_t(100); std::memcpy(buffer + 16, radix_100_table + std::uint32_t(prod >> 32) * 2, 2); exponent += 8; buffer += 18; } else { if (first_block >= 100'0000) { // 7 or 8 digits. // 281474978 = ceil(2^48 / 100'0000) + 1 auto prod = first_block * std::uint64_t(281474978); prod >>= 16; auto two_digits = std::uint32_t(prod >> 32); std::memcpy(buffer, radix_100_head_table + two_digits * 2, 2); buffer[2] = radix_100_table[two_digits * 2 + 1]; exponent += (6 + unsigned(two_digits >= 10)); buffer += unsigned(two_digits >= 10); // Print remaining 6 digits. prod = std::uint32_t(prod) * std::uint64_t(100); std::memcpy(buffer + 2, radix_100_table + std::uint32_t(prod >> 32) * 2, 2); prod = std::uint32_t(prod) * std::uint64_t(100); std::memcpy(buffer + 4, radix_100_table + std::uint32_t(prod >> 32) * 2, 2); prod = std::uint32_t(prod) * std::uint64_t(100); std::memcpy(buffer + 6, radix_100_table + std::uint32_t(prod >> 32) * 2, 2); buffer += 8; } else if (first_block >= 1'0000) { // 5 or 6 digits. // 429497 = ceil(2^32 / 1'0000) auto prod = first_block * std::uint64_t(429497); auto two_digits = std::uint32_t(prod >> 32); std::memcpy(buffer, radix_100_head_table + two_digits * 2, 2); buffer[2] = radix_100_table[two_digits * 2 + 1]; exponent += (4 + unsigned(two_digits >= 10)); buffer += unsigned(two_digits >= 10); // Print remaining 4 digits. prod = std::uint32_t(prod) * std::uint64_t(100); std::memcpy(buffer + 2, radix_100_table + std::uint32_t(prod >> 32) * 2, 2); prod = std::uint32_t(prod) * std::uint64_t(100); std::memcpy(buffer + 4, radix_100_table + std::uint32_t(prod >> 32) * 2, 2); buffer += 6; } else if (first_block >= 100) { // 3 or 4 digits. // 42949673 = ceil(2^32 / 100) auto prod = first_block * std::uint64_t(42949673); auto two_digits = std::uint32_t(prod >> 32); std::memcpy(buffer, radix_100_head_table + two_digits * 2, 2); buffer[2] = radix_100_table[two_digits * 2 + 1]; exponent += (2 + unsigned(two_digits >= 10)); buffer += unsigned(two_digits >= 10); // Print remaining 2 digits. prod = std::uint32_t(prod) * std::uint64_t(100); std::memcpy(buffer + 2, radix_100_table + std::uint32_t(prod >> 32) * 2, 2); buffer += 4; } else { // 1 or 2 digits. std::memcpy(buffer, radix_100_head_table + first_block * 2, 2); buffer[2] = radix_100_table[first_block * 2 + 1]; exponent += unsigned(first_block >= 10); buffer += (2 + unsigned(first_block >= 10)); } // Next, print the second block. // The second block is of 8 digits, but we may have trailing zeros. // 281474978 = ceil(2^48 / 100'0000) + 1 auto prod = second_block * std::uint64_t(281474978); prod >>= 16; prod += 1; auto two_digits = std::uint32_t(prod >> 32); std::memcpy(buffer, radix_100_table + two_digits * 2, 2); // Remaining 6 digits are all zero? if (std::uint32_t(prod) <= std::uint32_t((std::uint64_t(1) << 32) / 100'0000)) { buffer += (1 + unsigned(buffer[1] > '0')); } else { // Obtain the next two digits. prod = std::uint32_t(prod) * std::uint64_t(100); two_digits = std::uint32_t(prod >> 32); std::memcpy(buffer + 2, radix_100_table + two_digits * 2, 2); // Remaining 4 digits are all zero? if (std::uint32_t(prod) <= std::uint32_t((std::uint64_t(1) << 32) / 1'0000)) { buffer += (3 + unsigned(buffer[3] > '0')); } else { // Obtain the next two digits. prod = std::uint32_t(prod) * std::uint64_t(100); two_digits = std::uint32_t(prod >> 32); std::memcpy(buffer + 4, radix_100_table + two_digits * 2, 2); // Remaining 2 digits are all zero? if (std::uint32_t(prod) <= std::uint32_t((std::uint64_t(1) << 32) / 100)) { buffer += (5 + unsigned(buffer[5] > '0')); } else { // Obtain the last two digits. prod = std::uint32_t(prod) * std::uint64_t(100); two_digits = std::uint32_t(prod >> 32); std::memcpy(buffer + 6, radix_100_table + two_digits * 2, 2); buffer += (7 + unsigned(buffer[7] > '0')); } } } } } // Print exponent and return if (exponent < 0) { std::memcpy(buffer, "E-", 2); buffer += 2; exponent = -exponent; } else if (exponent > 0) { buffer[0] = 'E'; buffer += 1; } else { return buffer; } if (exponent >= 100) { // d1 = exponent / 10; d2 = exponent % 10; // 6554 = ceil(2^16 / 10) auto prod = std::uint32_t(exponent) * std::uint32_t(6554); auto d1 = prod >> 16; prod = std::uint16_t(prod) * std::uint32_t(5); // * 10 auto d2 = prod >> 15; // >> 16 std::memcpy(buffer, &radix_100_table[d1 * 2], 2); buffer[2] = char('0' + d2); buffer += 3; } else if (exponent >= 10) { std::memcpy(buffer, &radix_100_table[exponent * 2], 2); buffer += 2; } else { buffer[0] = char('0' + exponent); buffer += 1; } return buffer; } } }