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AQuery/server/dragonbox/dragonbox_to_chars.hpp

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// 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<float, default_float_traits<float>>(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<double, default_float_traits<double>>(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;
}
}
}