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BambuStudio/fast_float/fast_float.h

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初始化
2024-12-20 06:44:50 +00:00
// fast_float by Daniel Lemire
// fast_float by João Paulo Magalhaes
// with contributions from Eugene Golushkov
// with contributions from Maksim Kita
// with contributions from Marcin Wojdyr
// with contributions from Neal Richardson
// with contributions from Tim Paine
// with contributions from Fabio Pellacini
// Permission is hereby granted, free of charge, to any
// person obtaining a copy of this software and associated
// documentation files (the "Software"), to deal in the
// Software without restriction, including without
// limitation the rights to use, copy, modify, merge,
// publish, distribute, sublicense, and/or sell copies of
// the Software, and to permit persons to whom the Software
// is furnished to do so, subject to the following
// conditions:
//
// The above copyright notice and this permission notice
// shall be included in all copies or substantial portions
// of the Software.
//
// 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 AND NONINFRINGEMENT. IN NO EVENT
// SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY
// CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION
// OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR
// IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
// DEALINGS IN THE SOFTWARE.
#ifndef FASTFLOAT_FAST_FLOAT_H
#define FASTFLOAT_FAST_FLOAT_H
#include <system_error>
namespace fast_float {
enum chars_format {
scientific = 1<<0,
fixed = 1<<2,
hex = 1<<3,
general = fixed | scientific
};
struct from_chars_result {
const char *ptr;
std::errc ec;
};
struct parse_options {
explicit parse_options(chars_format fmt = chars_format::general,
char dot = '.')
: format(fmt), decimal_point(dot) {}
/** Which number formats are accepted */
chars_format format;
/** The character used as decimal point */
char decimal_point;
};
/**
* This function parses the character sequence [first,last) for a number. It parses floating-point numbers expecting
* a locale-indepent format equivalent to what is used by std::strtod in the default ("C") locale.
* The resulting floating-point value is the closest floating-point values (using either float or double),
* using the "round to even" convention for values that would otherwise fall right in-between two values.
* That is, we provide exact parsing according to the IEEE standard.
*
* Given a successful parse, the pointer (`ptr`) in the returned value is set to point right after the
* parsed number, and the `value` referenced is set to the parsed value. In case of error, the returned
* `ec` contains a representative error, otherwise the default (`std::errc()`) value is stored.
*
* The implementation does not throw and does not allocate memory (e.g., with `new` or `malloc`).
*
* Like the C++17 standard, the `fast_float::from_chars` functions take an optional last argument of
* the type `fast_float::chars_format`. It is a bitset value: we check whether
* `fmt & fast_float::chars_format::fixed` and `fmt & fast_float::chars_format::scientific` are set
* to determine whether we allowe the fixed point and scientific notation respectively.
* The default is `fast_float::chars_format::general` which allows both `fixed` and `scientific`.
*/
template<typename T>
from_chars_result from_chars(const char *first, const char *last,
T &value, chars_format fmt = chars_format::general) noexcept;
/**
* Like from_chars, but accepts an `options` argument to govern number parsing.
*/
template<typename T>
from_chars_result from_chars_advanced(const char *first, const char *last,
T &value, parse_options options) noexcept;
}
#endif // FASTFLOAT_FAST_FLOAT_H
#ifndef FASTFLOAT_FLOAT_COMMON_H
#define FASTFLOAT_FLOAT_COMMON_H
#include <cfloat>
#include <cstdint>
#include <cassert>
#if (defined(__x86_64) || defined(__x86_64__) || defined(_M_X64) \
|| defined(__amd64) || defined(__aarch64__) || defined(_M_ARM64) \
|| defined(__MINGW64__) \
|| defined(__s390x__) \
|| (defined(__ppc64__) || defined(__PPC64__) || defined(__ppc64le__) || defined(__PPC64LE__)) \
|| defined(__EMSCRIPTEN__))
#define FASTFLOAT_64BIT
#elif (defined(__i386) || defined(__i386__) || defined(_M_IX86) \
|| defined(__arm__) || defined(_M_ARM) \
|| defined(__MINGW32__))
#define FASTFLOAT_32BIT
#else
// Need to check incrementally, since SIZE_MAX is a size_t, avoid overflow.
// We can never tell the register width, but the SIZE_MAX is a good approximation.
// UINTPTR_MAX and INTPTR_MAX are optional, so avoid them for max portability.
#if SIZE_MAX == 0xffff
#error Unknown platform (16-bit, unsupported)
#elif SIZE_MAX == 0xffffffff
#define FASTFLOAT_32BIT
#elif SIZE_MAX == 0xffffffffffffffff
#define FASTFLOAT_64BIT
#else
#error Unknown platform (not 32-bit, not 64-bit?)
#endif
#endif
#if ((defined(_WIN32) || defined(_WIN64)) && !defined(__clang__))
#include <intrin.h>
#endif
#if defined(_MSC_VER) && !defined(__clang__)
#define FASTFLOAT_VISUAL_STUDIO 1
#endif
#ifdef _WIN32
#define FASTFLOAT_IS_BIG_ENDIAN 0
#else
#if defined(__APPLE__) || defined(__FreeBSD__)
#include <machine/endian.h>
#elif defined(sun) || defined(__sun)
#include <sys/byteorder.h>
#else
#include <endian.h>
#endif
#
#ifndef __BYTE_ORDER__
// safe choice
#define FASTFLOAT_IS_BIG_ENDIAN 0
#endif
#
#ifndef __ORDER_LITTLE_ENDIAN__
// safe choice
#define FASTFLOAT_IS_BIG_ENDIAN 0
#endif
#
#if __BYTE_ORDER__ == __ORDER_LITTLE_ENDIAN__
#define FASTFLOAT_IS_BIG_ENDIAN 0
#else
#define FASTFLOAT_IS_BIG_ENDIAN 1
#endif
#endif
#ifdef FASTFLOAT_VISUAL_STUDIO
#define fastfloat_really_inline __forceinline
#else
#define fastfloat_really_inline inline __attribute__((always_inline))
#endif
namespace fast_float {
// Compares two ASCII strings in a case insensitive manner.
inline bool fastfloat_strncasecmp(const char *input1, const char *input2,
size_t length) {
char running_diff{0};
for (size_t i = 0; i < length; i++) {
running_diff |= (input1[i] ^ input2[i]);
}
return (running_diff == 0) || (running_diff == 32);
}
#ifndef FLT_EVAL_METHOD
#error "FLT_EVAL_METHOD should be defined, please include cfloat."
#endif
namespace {
constexpr uint32_t max_digits = 768;
constexpr uint32_t max_digit_without_overflow = 19;
constexpr int32_t decimal_point_range = 2047;
} // namespace
struct value128 {
uint64_t low;
uint64_t high;
value128(uint64_t _low, uint64_t _high) : low(_low), high(_high) {}
value128() : low(0), high(0) {}
};
/* result might be undefined when input_num is zero */
fastfloat_really_inline int leading_zeroes(uint64_t input_num) {
assert(input_num > 0);
#ifdef FASTFLOAT_VISUAL_STUDIO
#if defined(_M_X64) || defined(_M_ARM64)
unsigned long leading_zero = 0;
// Search the mask data from most significant bit (MSB)
// to least significant bit (LSB) for a set bit (1).
_BitScanReverse64(&leading_zero, input_num);
return (int)(63 - leading_zero);
#else
int last_bit = 0;
if(input_num & uint64_t(0xffffffff00000000)) input_num >>= 32, last_bit |= 32;
if(input_num & uint64_t( 0xffff0000)) input_num >>= 16, last_bit |= 16;
if(input_num & uint64_t( 0xff00)) input_num >>= 8, last_bit |= 8;
if(input_num & uint64_t( 0xf0)) input_num >>= 4, last_bit |= 4;
if(input_num & uint64_t( 0xc)) input_num >>= 2, last_bit |= 2;
if(input_num & uint64_t( 0x2)) input_num >>= 1, last_bit |= 1;
return 63 - last_bit;
#endif
#else
return __builtin_clzll(input_num);
#endif
}
#ifdef FASTFLOAT_32BIT
// slow emulation routine for 32-bit
fastfloat_really_inline uint64_t emulu(uint32_t x, uint32_t y) {
return x * (uint64_t)y;
}
// slow emulation routine for 32-bit
#if !defined(__MINGW64__)
fastfloat_really_inline uint64_t _umul128(uint64_t ab, uint64_t cd,
uint64_t *hi) {
uint64_t ad = emulu((uint32_t)(ab >> 32), (uint32_t)cd);
uint64_t bd = emulu((uint32_t)ab, (uint32_t)cd);
uint64_t adbc = ad + emulu((uint32_t)ab, (uint32_t)(cd >> 32));
uint64_t adbc_carry = !!(adbc < ad);
uint64_t lo = bd + (adbc << 32);
*hi = emulu((uint32_t)(ab >> 32), (uint32_t)(cd >> 32)) + (adbc >> 32) +
(adbc_carry << 32) + !!(lo < bd);
return lo;
}
#endif // !__MINGW64__
#endif // FASTFLOAT_32BIT
// compute 64-bit a*b
fastfloat_really_inline value128 full_multiplication(uint64_t a,
uint64_t b) {
value128 answer;
#ifdef _M_ARM64
// ARM64 has native support for 64-bit multiplications, no need to emulate
answer.high = __umulh(a, b);
answer.low = a * b;
#elif defined(FASTFLOAT_32BIT) || (defined(_WIN64) && !defined(__clang__))
answer.low = _umul128(a, b, &answer.high); // _umul128 not available on ARM64
#elif defined(FASTFLOAT_64BIT)
__uint128_t r = ((__uint128_t)a) * b;
answer.low = uint64_t(r);
answer.high = uint64_t(r >> 64);
#else
#error Not implemented
#endif
return answer;
}
struct adjusted_mantissa {
uint64_t mantissa{0};
int power2{0}; // a negative value indicates an invalid result
adjusted_mantissa() = default;
bool operator==(const adjusted_mantissa &o) const {
return mantissa == o.mantissa && power2 == o.power2;
}
bool operator!=(const adjusted_mantissa &o) const {
return mantissa != o.mantissa || power2 != o.power2;
}
};
struct decimal {
uint32_t num_digits{0};
int32_t decimal_point{0};
bool negative{false};
bool truncated{false};
uint8_t digits[max_digits];
decimal() = default;
// Copies are not allowed since this is a fat object.
decimal(const decimal &) = delete;
// Copies are not allowed since this is a fat object.
decimal &operator=(const decimal &) = delete;
// Moves are allowed:
decimal(decimal &&) = default;
decimal &operator=(decimal &&other) = default;
};
constexpr static double powers_of_ten_double[] = {
1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9, 1e10, 1e11,
1e12, 1e13, 1e14, 1e15, 1e16, 1e17, 1e18, 1e19, 1e20, 1e21, 1e22};
constexpr static float powers_of_ten_float[] = {1e0, 1e1, 1e2, 1e3, 1e4, 1e5,
1e6, 1e7, 1e8, 1e9, 1e10};
template <typename T> struct binary_format {
static inline constexpr int mantissa_explicit_bits();
static inline constexpr int minimum_exponent();
static inline constexpr int infinite_power();
static inline constexpr int sign_index();
static inline constexpr int min_exponent_fast_path();
static inline constexpr int max_exponent_fast_path();
static inline constexpr int max_exponent_round_to_even();
static inline constexpr int min_exponent_round_to_even();
static inline constexpr uint64_t max_mantissa_fast_path();
static inline constexpr int largest_power_of_ten();
static inline constexpr int smallest_power_of_ten();
static inline constexpr T exact_power_of_ten(int64_t power);
};
template <> inline constexpr int binary_format<double>::mantissa_explicit_bits() {
return 52;
}
template <> inline constexpr int binary_format<float>::mantissa_explicit_bits() {
return 23;
}
template <> inline constexpr int binary_format<double>::max_exponent_round_to_even() {
return 23;
}
template <> inline constexpr int binary_format<float>::max_exponent_round_to_even() {
return 10;
}
template <> inline constexpr int binary_format<double>::min_exponent_round_to_even() {
return -4;
}
template <> inline constexpr int binary_format<float>::min_exponent_round_to_even() {
return -17;
}
template <> inline constexpr int binary_format<double>::minimum_exponent() {
return -1023;
}
template <> inline constexpr int binary_format<float>::minimum_exponent() {
return -127;
}
template <> inline constexpr int binary_format<double>::infinite_power() {
return 0x7FF;
}
template <> inline constexpr int binary_format<float>::infinite_power() {
return 0xFF;
}
template <> inline constexpr int binary_format<double>::sign_index() { return 63; }
template <> inline constexpr int binary_format<float>::sign_index() { return 31; }
template <> inline constexpr int binary_format<double>::min_exponent_fast_path() {
#if (FLT_EVAL_METHOD != 1) && (FLT_EVAL_METHOD != 0)
return 0;
#else
return -22;
#endif
}
template <> inline constexpr int binary_format<float>::min_exponent_fast_path() {
#if (FLT_EVAL_METHOD != 1) && (FLT_EVAL_METHOD != 0)
return 0;
#else
return -10;
#endif
}
template <> inline constexpr int binary_format<double>::max_exponent_fast_path() {
return 22;
}
template <> inline constexpr int binary_format<float>::max_exponent_fast_path() {
return 10;
}
template <> inline constexpr uint64_t binary_format<double>::max_mantissa_fast_path() {
return uint64_t(2) << mantissa_explicit_bits();
}
template <> inline constexpr uint64_t binary_format<float>::max_mantissa_fast_path() {
return uint64_t(2) << mantissa_explicit_bits();
}
template <>
inline constexpr double binary_format<double>::exact_power_of_ten(int64_t power) {
return powers_of_ten_double[power];
}
template <>
inline constexpr float binary_format<float>::exact_power_of_ten(int64_t power) {
return powers_of_ten_float[power];
}
template <>
inline constexpr int binary_format<double>::largest_power_of_ten() {
return 308;
}
template <>
inline constexpr int binary_format<float>::largest_power_of_ten() {
return 38;
}
template <>
inline constexpr int binary_format<double>::smallest_power_of_ten() {
return -342;
}
template <>
inline constexpr int binary_format<float>::smallest_power_of_ten() {
return -65;
}
} // namespace fast_float
// for convenience:
template<class OStream>
inline OStream& operator<<(OStream &out, const fast_float::decimal &d) {
out << "0.";
for (size_t i = 0; i < d.num_digits; i++) {
out << int32_t(d.digits[i]);
}
out << " * 10 ** " << d.decimal_point;
return out;
}
#endif
#ifndef FASTFLOAT_ASCII_NUMBER_H
#define FASTFLOAT_ASCII_NUMBER_H
#include <cstdio>
#include <cctype>
#include <cstdint>
#include <cstring>
namespace fast_float {
// Next function can be micro-optimized, but compilers are entirely
// able to optimize it well.
fastfloat_really_inline bool is_integer(char c) noexcept { return c >= '0' && c <= '9'; }
fastfloat_really_inline uint64_t byteswap(uint64_t val) {
return (val & 0xFF00000000000000) >> 56
| (val & 0x00FF000000000000) >> 40
| (val & 0x0000FF0000000000) >> 24
| (val & 0x000000FF00000000) >> 8
| (val & 0x00000000FF000000) << 8
| (val & 0x0000000000FF0000) << 24
| (val & 0x000000000000FF00) << 40
| (val & 0x00000000000000FF) << 56;
}
fastfloat_really_inline uint64_t read_u64(const char *chars) {
uint64_t val;
::memcpy(&val, chars, sizeof(uint64_t));
#if FASTFLOAT_IS_BIG_ENDIAN == 1
// Need to read as-if the number was in little-endian order.
val = byteswap(val);
#endif
return val;
}
fastfloat_really_inline void write_u64(uint8_t *chars, uint64_t val) {
#if FASTFLOAT_IS_BIG_ENDIAN == 1
// Need to read as-if the number was in little-endian order.
val = byteswap(val);
#endif
::memcpy(chars, &val, sizeof(uint64_t));
}
// credit @aqrit
fastfloat_really_inline uint32_t parse_eight_digits_unrolled(uint64_t val) {
const uint64_t mask = 0x000000FF000000FF;
const uint64_t mul1 = 0x000F424000000064; // 100 + (1000000ULL << 32)
const uint64_t mul2 = 0x0000271000000001; // 1 + (10000ULL << 32)
val -= 0x3030303030303030;
val = (val * 10) + (val >> 8); // val = (val * 2561) >> 8;
val = (((val & mask) * mul1) + (((val >> 16) & mask) * mul2)) >> 32;
return uint32_t(val);
}
fastfloat_really_inline uint32_t parse_eight_digits_unrolled(const char *chars) noexcept {
return parse_eight_digits_unrolled(read_u64(chars));
}
// credit @aqrit
fastfloat_really_inline bool is_made_of_eight_digits_fast(uint64_t val) noexcept {
return !((((val + 0x4646464646464646) | (val - 0x3030303030303030)) &
0x8080808080808080));
}
fastfloat_really_inline bool is_made_of_eight_digits_fast(const char *chars) noexcept {
return is_made_of_eight_digits_fast(read_u64(chars));
}
struct parsed_number_string {
int64_t exponent;
uint64_t mantissa;
const char *lastmatch;
bool negative;
bool valid;
bool too_many_digits;
};
// Assuming that you use no more than 19 digits, this will
// parse an ASCII string.
fastfloat_really_inline
parsed_number_string parse_number_string(const char *p, const char *pend, parse_options options) noexcept {
const chars_format fmt = options.format;
const char decimal_point = options.decimal_point;
parsed_number_string answer;
answer.valid = false;
answer.too_many_digits = false;
answer.negative = (*p == '-');
if (*p == '-') { // C++17 20.19.3.(7.1) explicitly forbids '+' sign here
++p;
if (p == pend) {
return answer;
}
if (!is_integer(*p) && (*p != decimal_point)) { // a sign must be followed by an integer or the dot
return answer;
}
}
const char *const start_digits = p;
uint64_t i = 0; // an unsigned int avoids signed overflows (which are bad)
while ((p != pend) && is_integer(*p)) {
// a multiplication by 10 is cheaper than an arbitrary integer
// multiplication
i = 10 * i +
uint64_t(*p - '0'); // might overflow, we will handle the overflow later
++p;
}
const char *const end_of_integer_part = p;
int64_t digit_count = int64_t(end_of_integer_part - start_digits);
int64_t exponent = 0;
if ((p != pend) && (*p == decimal_point)) {
++p;
// Fast approach only tested under little endian systems
if ((p + 8 <= pend) && is_made_of_eight_digits_fast(p)) {
i = i * 100000000 + parse_eight_digits_unrolled(p); // in rare cases, this will overflow, but that's ok
p += 8;
if ((p + 8 <= pend) && is_made_of_eight_digits_fast(p)) {
i = i * 100000000 + parse_eight_digits_unrolled(p); // in rare cases, this will overflow, but that's ok
p += 8;
}
}
while ((p != pend) && is_integer(*p)) {
uint8_t digit = uint8_t(*p - '0');
++p;
i = i * 10 + digit; // in rare cases, this will overflow, but that's ok
}
exponent = end_of_integer_part + 1 - p;
digit_count -= exponent;
}
// we must have encountered at least one integer!
if (digit_count == 0) {
return answer;
}
int64_t exp_number = 0; // explicit exponential part
if ((fmt & chars_format::scientific) && (p != pend) && (('e' == *p) || ('E' == *p))) {
const char * location_of_e = p;
++p;
bool neg_exp = false;
if ((p != pend) && ('-' == *p)) {
neg_exp = true;
++p;
} else if ((p != pend) && ('+' == *p)) { // '+' on exponent is allowed by C++17 20.19.3.(7.1)
++p;
}
if ((p == pend) || !is_integer(*p)) {
if(!(fmt & chars_format::fixed)) {
// We are in error.
return answer;
}
// Otherwise, we will be ignoring the 'e'.
p = location_of_e;
} else {
while ((p != pend) && is_integer(*p)) {
uint8_t digit = uint8_t(*p - '0');
if (exp_number < 0x10000) {
exp_number = 10 * exp_number + digit;
}
++p;
}
if(neg_exp) { exp_number = - exp_number; }
exponent += exp_number;
}
} else {
// If it scientific and not fixed, we have to bail out.
if((fmt & chars_format::scientific) && !(fmt & chars_format::fixed)) { return answer; }
}
answer.lastmatch = p;
answer.valid = true;
// If we frequently had to deal with long strings of digits,
// we could extend our code by using a 128-bit integer instead
// of a 64-bit integer. However, this is uncommon.
//
// We can deal with up to 19 digits.
if (digit_count > 19) { // this is uncommon
// It is possible that the integer had an overflow.
// We have to handle the case where we have 0.0000somenumber.
// We need to be mindful of the case where we only have zeroes...
// E.g., 0.000000000...000.
const char *start = start_digits;
while ((start != pend) && (*start == '0' || *start == decimal_point)) {
if(*start == '0') { digit_count --; }
start++;
}
if (digit_count > 19) {
answer.too_many_digits = true;
// Let us start again, this time, avoiding overflows.
i = 0;
p = start_digits;
const uint64_t minimal_nineteen_digit_integer{1000000000000000000};
while((i < minimal_nineteen_digit_integer) && (p != pend) && is_integer(*p)) {
i = i * 10 + uint64_t(*p - '0');
++p;
}
if (i >= minimal_nineteen_digit_integer) { // We have a big integers
exponent = end_of_integer_part - p + exp_number;
} else { // We have a value with a fractional component.
p++; // skip the dot
const char *first_after_period = p;
while((i < minimal_nineteen_digit_integer) && (p != pend) && is_integer(*p)) {
i = i * 10 + uint64_t(*p - '0');
++p;
}
exponent = first_after_period - p + exp_number;
}
// We have now corrected both exponent and i, to a truncated value
}
}
answer.exponent = exponent;
answer.mantissa = i;
return answer;
}
// This should always succeed since it follows a call to parse_number_string
// This function could be optimized. In particular, we could stop after 19 digits
// and try to bail out. Furthermore, we should be able to recover the computed
// exponent from the pass in parse_number_string.
fastfloat_really_inline decimal parse_decimal(const char *p, const char *pend, parse_options options) noexcept {
const char decimal_point = options.decimal_point;
decimal answer;
answer.num_digits = 0;
answer.decimal_point = 0;
answer.truncated = false;
answer.negative = (*p == '-');
if (*p == '-') { // C++17 20.19.3.(7.1) explicitly forbids '+' sign here
++p;
}
// skip leading zeroes
while ((p != pend) && (*p == '0')) {
++p;
}
while ((p != pend) && is_integer(*p)) {
if (answer.num_digits < max_digits) {
answer.digits[answer.num_digits] = uint8_t(*p - '0');
}
answer.num_digits++;
++p;
}
if ((p != pend) && (*p == decimal_point)) {
++p;
const char *first_after_period = p;
// if we have not yet encountered a zero, we have to skip it as well
if(answer.num_digits == 0) {
// skip zeros
while ((p != pend) && (*p == '0')) {
++p;
}
}
// We expect that this loop will often take the bulk of the running time
// because when a value has lots of digits, these digits often
while ((p + 8 <= pend) && (answer.num_digits + 8 < max_digits)) {
uint64_t val = read_u64(p);
if(! is_made_of_eight_digits_fast(val)) { break; }
// We have eight digits, process them in one go!
val -= 0x3030303030303030;
write_u64(answer.digits + answer.num_digits, val);
answer.num_digits += 8;
p += 8;
}
while ((p != pend) && is_integer(*p)) {
if (answer.num_digits < max_digits) {
answer.digits[answer.num_digits] = uint8_t(*p - '0');
}
answer.num_digits++;
++p;
}
answer.decimal_point = int32_t(first_after_period - p);
}
// We want num_digits to be the number of significant digits, excluding
// leading *and* trailing zeros! Otherwise the truncated flag later is
// going to be misleading.
if(answer.num_digits > 0) {
// We potentially need the answer.num_digits > 0 guard because we
// prune leading zeros. So with answer.num_digits > 0, we know that
// we have at least one non-zero digit.
const char *preverse = p - 1;
int32_t trailing_zeros = 0;
while ((*preverse == '0') || (*preverse == decimal_point)) {
if(*preverse == '0') { trailing_zeros++; };
--preverse;
}
answer.decimal_point += int32_t(answer.num_digits);
answer.num_digits -= uint32_t(trailing_zeros);
}
if(answer.num_digits > max_digits) {
answer.truncated = true;
answer.num_digits = max_digits;
}
if ((p != pend) && (('e' == *p) || ('E' == *p))) {
++p;
bool neg_exp = false;
if ((p != pend) && ('-' == *p)) {
neg_exp = true;
++p;
} else if ((p != pend) && ('+' == *p)) { // '+' on exponent is allowed by C++17 20.19.3.(7.1)
++p;
}
int32_t exp_number = 0; // exponential part
while ((p != pend) && is_integer(*p)) {
uint8_t digit = uint8_t(*p - '0');
if (exp_number < 0x10000) {
exp_number = 10 * exp_number + digit;
}
++p;
}
answer.decimal_point += (neg_exp ? -exp_number : exp_number);
}
// In very rare cases, we may have fewer than 19 digits, we want to be able to reliably
// assume that all digits up to max_digit_without_overflow have been initialized.
for(uint32_t i = answer.num_digits; i < max_digit_without_overflow; i++) { answer.digits[i] = 0; }
return answer;
}
} // namespace fast_float
#endif
#ifndef FASTFLOAT_FAST_TABLE_H
#define FASTFLOAT_FAST_TABLE_H
#include <cstdint>
namespace fast_float {
/**
* When mapping numbers from decimal to binary,
* we go from w * 10^q to m * 2^p but we have
* 10^q = 5^q * 2^q, so effectively
* we are trying to match
* w * 2^q * 5^q to m * 2^p. Thus the powers of two
* are not a concern since they can be represented
* exactly using the binary notation, only the powers of five
* affect the binary significand.
*/
/**
* The smallest non-zero float (binary64) is 2^−1074.
* We take as input numbers of the form w x 10^q where w < 2^64.
* We have that w * 10^-343 < 2^(64-344) 5^-343 < 2^-1076.
* However, we have that
* (2^64-1) * 10^-342 = (2^64-1) * 2^-342 * 5^-342 > 2^−1074.
* Thus it is possible for a number of the form w * 10^-342 where
* w is a 64-bit value to be a non-zero floating-point number.
*********
* Any number of form w * 10^309 where w>= 1 is going to be
* infinite in binary64 so we never need to worry about powers
* of 5 greater than 308.
*/
template <class unused = void>
struct powers_template {
constexpr static int smallest_power_of_five = binary_format<double>::smallest_power_of_ten();
constexpr static int largest_power_of_five = binary_format<double>::largest_power_of_ten();
constexpr static int number_of_entries = 2 * (largest_power_of_five - smallest_power_of_five + 1);
// Powers of five from 5^-342 all the way to 5^308 rounded toward one.
static const uint64_t power_of_five_128[number_of_entries];
};
template <class unused>
const uint64_t powers_template<unused>::power_of_five_128[number_of_entries] = {
0xeef453d6923bd65a,0x113faa2906a13b3f,
0x9558b4661b6565f8,0x4ac7ca59a424c507,
0xbaaee17fa23ebf76,0x5d79bcf00d2df649,
0xe95a99df8ace6f53,0xf4d82c2c107973dc,
0x91d8a02bb6c10594,0x79071b9b8a4be869,
0xb64ec836a47146f9,0x9748e2826cdee284,
0xe3e27a444d8d98b7,0xfd1b1b2308169b25,
0x8e6d8c6ab0787f72,0xfe30f0f5e50e20f7,
0xb208ef855c969f4f,0xbdbd2d335e51a935,
0xde8b2b66b3bc4723,0xad2c788035e61382,
0x8b16fb203055ac76,0x4c3bcb5021afcc31,
0xaddcb9e83c6b1793,0xdf4abe242a1bbf3d,
0xd953e8624b85dd78,0xd71d6dad34a2af0d,
0x87d4713d6f33aa6b,0x8672648c40e5ad68,
0xa9c98d8ccb009506,0x680efdaf511f18c2,
0xd43bf0effdc0ba48,0x212bd1b2566def2,
0x84a57695fe98746d,0x14bb630f7604b57,
0xa5ced43b7e3e9188,0x419ea3bd35385e2d,
0xcf42894a5dce35ea,0x52064cac828675b9,
0x818995ce7aa0e1b2,0x7343efebd1940993,
0xa1ebfb4219491a1f,0x1014ebe6c5f90bf8,
0xca66fa129f9b60a6,0xd41a26e077774ef6,
0xfd00b897478238d0,0x8920b098955522b4,
0x9e20735e8cb16382,0x55b46e5f5d5535b0,
0xc5a890362fddbc62,0xeb2189f734aa831d,
0xf712b443bbd52b7b,0xa5e9ec7501d523e4,
0x9a6bb0aa55653b2d,0x47b233c92125366e,
0xc1069cd4eabe89f8,0x999ec0bb696e840a,
0xf148440a256e2c76,0xc00670ea43ca250d,
0x96cd2a865764dbca,0x380406926a5e5728,
0xbc807527ed3e12bc,0xc605083704f5ecf2,
0xeba09271e88d976b,0xf7864a44c633682e,
0x93445b8731587ea3,0x7ab3ee6afbe0211d,
0xb8157268fdae9e4c,0x5960ea05bad82964,
0xe61acf033d1a45df,0x6fb92487298e33bd,
0x8fd0c16206306bab,0xa5d3b6d479f8e056,
0xb3c4f1ba87bc8696,0x8f48a4899877186c,
0xe0b62e2929aba83c,0x331acdabfe94de87,
0x8c71dcd9ba0b4925,0x9ff0c08b7f1d0b14,
0xaf8e5410288e1b6f,0x7ecf0ae5ee44dd9,
0xdb71e91432b1a24a,0xc9e82cd9f69d6150,
0x892731ac9faf056e,0xbe311c083a225cd2,
0xab70fe17c79ac6ca,0x6dbd630a48aaf406,
0xd64d3d9db981787d,0x92cbbccdad5b108,
0x85f0468293f0eb4e,0x25bbf56008c58ea5,
0xa76c582338ed2621,0xaf2af2b80af6f24e,
0xd1476e2c07286faa,0x1af5af660db4aee1,
0x82cca4db847945ca,0x50d98d9fc890ed4d,
0xa37fce126597973c,0xe50ff107bab528a0,
0xcc5fc196fefd7d0c,0x1e53ed49a96272c8,
0xff77b1fcbebcdc4f,0x25e8e89c13bb0f7a,
0x9faacf3df73609b1,0x77b191618c54e9ac,
0xc795830d75038c1d,0xd59df5b9ef6a2417,
0xf97ae3d0d2446f25,0x4b0573286b44ad1d,
0x9becce62836ac577,0x4ee367f9430aec32,
0xc2e801fb244576d5,0x229c41f793cda73f,
0xf3a20279ed56d48a,0x6b43527578c1110f,
0x9845418c345644d6,0x830a13896b78aaa9,
0xbe5691ef416bd60c,0x23cc986bc656d553,
0xedec366b11c6cb8f,0x2cbfbe86b7ec8aa8,
0x94b3a202eb1c3f39,0x7bf7d71432f3d6a9,
0xb9e08a83a5e34f07,0xdaf5ccd93fb0cc53,
0xe858ad248f5c22c9,0xd1b3400f8f9cff68,
0x91376c36d99995be,0x23100809b9c21fa1,
0xb58547448ffffb2d,0xabd40a0c2832a78a,
0xe2e69915b3fff9f9,0x16c90c8f323f516c,
0x8dd01fad907ffc3b,0xae3da7d97f6792e3,
0xb1442798f49ffb4a,0x99cd11cfdf41779c,
0xdd95317f31c7fa1d,0x40405643d711d583,
0x8a7d3eef7f1cfc52,0x482835ea666b2572,
0xad1c8eab5ee43b66,0xda3243650005eecf,
0xd863b256369d4a40,0x90bed43e40076a82,
0x873e4f75e2224e68,0x5a7744a6e804a291,
0xa90de3535aaae202,0x711515d0a205cb36,
0xd3515c2831559a83,0xd5a5b44ca873e03,
0x8412d9991ed58091,0xe858790afe9486c2,
0xa5178fff668ae0b6,0x626e974dbe39a872,
0xce5d73ff402d98e3,0xfb0a3d212dc8128f,
0x80fa687f881c7f8e,0x7ce66634bc9d0b99,
0xa139029f6a239f72,0x1c1fffc1ebc44e80,
0xc987434744ac874e,0xa327ffb266b56220,
0xfbe9141915d7a922,0x4bf1ff9f0062baa8,
0x9d71ac8fada6c9b5,0x6f773fc3603db4a9,
0xc4ce17b399107c22,0xcb550fb4384d21d3,
0xf6019da07f549b2b,0x7e2a53a146606a48,
0x99c102844f94e0fb,0x2eda7444cbfc426d,
0xc0314325637a1939,0xfa911155fefb5308,
0xf03d93eebc589f88,0x793555ab7eba27ca,
0x96267c7535b763b5,0x4bc1558b2f3458de,
0xbbb01b9283253ca2,0x9eb1aaedfb016f16,
0xea9c227723ee8bcb,0x465e15a979c1cadc,
0x92a1958a7675175f,0xbfacd89ec191ec9,
0xb749faed14125d36,0xcef980ec671f667b,
0xe51c79a85916f484,0x82b7e12780e7401a,
0x8f31cc0937ae58d2,0xd1b2ecb8b0908810,
0xb2fe3f0b8599ef07,0x861fa7e6dcb4aa15,
0xdfbdcece67006ac9,0x67a791e093e1d49a,
0x8bd6a141006042bd,0xe0c8bb2c5c6d24e0,
0xaecc49914078536d,0x58fae9f773886e18,
0xda7f5bf590966848,0xaf39a475506a899e,
0x888f99797a5e012d,0x6d8406c952429603,
0xaab37fd7d8f58178,0xc8e5087ba6d33b83,
0xd5605fcdcf32e1d6,0xfb1e4a9a90880a64,
0x855c3be0a17fcd26,0x5cf2eea09a55067f,
0xa6b34ad8c9dfc06f,0xf42faa48c0ea481e,
0xd0601d8efc57b08b,0xf13b94daf124da26,
0x823c12795db6ce57,0x76c53d08d6b70858,
0xa2cb1717b52481ed,0x54768c4b0c64ca6e,
0xcb7ddcdda26da268,0xa9942f5dcf7dfd09,
0xfe5d54150b090b02,0xd3f93b35435d7c4c,
0x9efa548d26e5a6e1,0xc47bc5014a1a6daf,
0xc6b8e9b0709f109a,0x359ab6419ca1091b,
0xf867241c8cc6d4c0,0xc30163d203c94b62,
0x9b407691d7fc44f8,0x79e0de63425dcf1d,
0xc21094364dfb5636,0x985915fc12f542e4,
0xf294b943e17a2bc4,0x3e6f5b7b17b2939d,
0x979cf3ca6cec5b5a,0xa705992ceecf9c42,
0xbd8430bd08277231,0x50c6ff782a838353,
0xece53cec4a314ebd,0xa4f8bf5635246428,
0x940f4613ae5ed136,0x871b7795e136be99,
0xb913179899f68584,0x28e2557b59846e3f,
0xe757dd7ec07426e5,0x331aeada2fe589cf,
0x9096ea6f3848984f,0x3ff0d2c85def7621,
0xb4bca50b065abe63,0xfed077a756b53a9,
0xe1ebce4dc7f16dfb,0xd3e8495912c62894,
0x8d3360f09cf6e4bd,0x64712dd7abbbd95c,
0xb080392cc4349dec,0xbd8d794d96aacfb3,
0xdca04777f541c567,0xecf0d7a0fc5583a0,
0x89e42caaf9491b60,0xf41686c49db57244,
0xac5d37d5b79b6239,0x311c2875c522ced5,
0xd77485cb25823ac7,0x7d633293366b828b,
0x86a8d39ef77164bc,0xae5dff9c02033197,
0xa8530886b54dbdeb,0xd9f57f830283fdfc,
0xd267caa862a12d66,0xd072df63c324fd7b,
0x8380dea93da4bc60,0x4247cb9e59f71e6d,
0xa46116538d0deb78,0x52d9be85f074e608,
0xcd795be870516656,0x67902e276c921f8b,
0x806bd9714632dff6,0xba1cd8a3db53b6,
0xa086cfcd97bf97f3,0x80e8a40eccd228a4,
0xc8a883c0fdaf7df0,0x6122cd128006b2cd,
0xfad2a4b13d1b5d6c,0x796b805720085f81,
0x9cc3a6eec6311a63,0xcbe3303674053bb0,
0xc3f490aa77bd60fc,0xbedbfc4411068a9c,
0xf4f1b4d515acb93b,0xee92fb5515482d44,
0x991711052d8bf3c5,0x751bdd152d4d1c4a,
0xbf5cd54678eef0b6,0xd262d45a78a0635d,
0xef340a98172aace4,0x86fb897116c87c34,
0x9580869f0e7aac0e,0xd45d35e6ae3d4da0,
0xbae0a846d2195712,0x8974836059cca109,
0xe998d258869facd7,0x2bd1a438703fc94b,
0x91ff83775423cc06,0x7b6306a34627ddcf,
0xb67f6455292cbf08,0x1a3bc84c17b1d542,
0xe41f3d6a7377eeca,0x20caba5f1d9e4a93,
0x8e938662882af53e,0x547eb47b7282ee9c,
0xb23867fb2a35b28d,0xe99e619a4f23aa43,
0xdec681f9f4c31f31,0x6405fa00e2ec94d4,
0x8b3c113c38f9f37e,0xde83bc408dd3dd04,
0xae0b158b4738705e,0x9624ab50b148d445,
0xd98ddaee19068c76,0x3badd624dd9b0957,
0x87f8a8d4cfa417c9,0xe54ca5d70a80e5d6,
0xa9f6d30a038d1dbc,0x5e9fcf4ccd211f4c,
0xd47487cc8470652b,0x7647c3200069671f,
0x84c8d4dfd2c63f3b,0x29ecd9f40041e073,
0xa5fb0a17c777cf09,0xf468107100525890,
0xcf79cc9db955c2cc,0x7182148d4066eeb4,
0x81ac1fe293d599bf,0xc6f14cd848405530,
0xa21727db38cb002f,0xb8ada00e5a506a7c,
0xca9cf1d206fdc03b,0xa6d90811f0e4851c,
0xfd442e4688bd304a,0x908f4a166d1da663,
0x9e4a9cec15763e2e,0x9a598e4e043287fe,
0xc5dd44271ad3cdba,0x40eff1e1853f29fd,
0xf7549530e188c128,0xd12bee59e68ef47c,
0x9a94dd3e8cf578b9,0x82bb74f8301958ce,
0xc13a148e3032d6e7,0xe36a52363c1faf01,
0xf18899b1bc3f8ca1,0xdc44e6c3cb279ac1,
0x96f5600f15a7b7e5,0x29ab103a5ef8c0b9,
0xbcb2b812db11a5de,0x7415d448f6b6f0e7,
0xebdf661791d60f56,0x111b495b3464ad21,
0x936b9fcebb25c995,0xcab10dd900beec34,
0xb84687c269ef3bfb,0x3d5d514f40eea742,
0xe65829b3046b0afa,0xcb4a5a3112a5112,
0x8ff71a0fe2c2e6dc,0x47f0e785eaba72ab,
0xb3f4e093db73a093,0x59ed216765690f56,
0xe0f218b8d25088b8,0x306869c13ec3532c,
0x8c974f7383725573,0x1e414218c73a13fb,
0xafbd2350644eeacf,0xe5d1929ef90898fa,
0xdbac6c247d62a583,0xdf45f746b74abf39,
0x894bc396ce5da772,0x6b8bba8c328eb783,
0xab9eb47c81f5114f,0x66ea92f3f326564,
0xd686619ba27255a2,0xc80a537b0efefebd,
0x8613fd0145877585,0xbd06742ce95f5f36,
0xa798fc4196e952e7,0x2c48113823b73704,
0xd17f3b51fca3a7a0,0xf75a15862ca504c5,
0x82ef85133de648c4,0x9a984d73dbe722fb,
0xa3ab66580d5fdaf5,0xc13e60d0d2e0ebba,
0xcc963fee10b7d1b3,0x318df905079926a8,
0xffbbcfe994e5c61f,0xfdf17746497f7052,
0x9fd561f1fd0f9bd3,0xfeb6ea8bedefa633,
0xc7caba6e7c5382c8,0xfe64a52ee96b8fc0,
0xf9bd690a1b68637b,0x3dfdce7aa3c673b0,
0x9c1661a651213e2d,0x6bea10ca65c084e,
0xc31bfa0fe5698db8,0x486e494fcff30a62,
0xf3e2f893dec3f126,0x5a89dba3c3efccfa,
0x986ddb5c6b3a76b7,0xf89629465a75e01c,
0xbe89523386091465,0xf6bbb397f1135823,
0xee2ba6c0678b597f,0x746aa07ded582e2c,
0x94db483840b717ef,0xa8c2a44eb4571cdc,
0xba121a4650e4ddeb,0x92f34d62616ce413,
0xe896a0d7e51e1566,0x77b020baf9c81d17,
0x915e2486ef32cd60,0xace1474dc1d122e,
0xb5b5ada8aaff80b8,0xd819992132456ba,
0xe3231912d5bf60e6,0x10e1fff697ed6c69,
0x8df5efabc5979c8f,0xca8d3ffa1ef463c1,
0xb1736b96b6fd83b3,0xbd308ff8a6b17cb2,
0xddd0467c64bce4a0,0xac7cb3f6d05ddbde,
0x8aa22c0dbef60ee4,0x6bcdf07a423aa96b,
0xad4ab7112eb3929d,0x86c16c98d2c953c6,
0xd89d64d57a607744,0xe871c7bf077ba8b7,
0x87625f056c7c4a8b,0x11471cd764ad4972,
0xa93af6c6c79b5d2d,0xd598e40d3dd89bcf,
0xd389b47879823479,0x4aff1d108d4ec2c3,
0x843610cb4bf160cb,0xcedf722a585139ba,
0xa54394fe1eedb8fe,0xc2974eb4ee658828,
0xce947a3da6a9273e,0x733d226229feea32,
0x811ccc668829b887,0x806357d5a3f525f,
0xa163ff802a3426a8,0xca07c2dcb0cf26f7,
0xc9bcff6034c13052,0xfc89b393dd02f0b5,
0xfc2c3f3841f17c67,0xbbac2078d443ace2,
0x9d9ba7832936edc0,0xd54b944b84aa4c0d,
0xc5029163f384a931,0xa9e795e65d4df11,
0xf64335bcf065d37d,0x4d4617b5ff4a16d5,
0x99ea0196163fa42e,0x504bced1bf8e4e45,
0xc06481fb9bcf8d39,0xe45ec2862f71e1d6,
0xf07da27a82c37088,0x5d767327bb4e5a4c,
0x964e858c91ba2655,0x3a6a07f8d510f86f,
0xbbe226efb628afea,0x890489f70a55368b,
0xeadab0aba3b2dbe5,0x2b45ac74ccea842e,
0x92c8ae6b464fc96f,0x3b0b8bc90012929d,
0xb77ada0617e3bbcb,0x9ce6ebb40173744,
0xe55990879ddcaabd,0xcc420a6a101d0515,
0x8f57fa54c2a9eab6,0x9fa946824a12232d,
0xb32df8e9f3546564,0x47939822dc96abf9,
0xdff9772470297ebd,0x59787e2b93bc56f7,
0x8bfbea76c619ef36,0x57eb4edb3c55b65a,
0xaefae51477a06b03,0xede622920b6b23f1,
0xdab99e59958885c4,0xe95fab368e45eced,
0x88b402f7fd75539b,0x11dbcb0218ebb414,
0xaae103b5fcd2a881,0xd652bdc29f26a119,
0xd59944a37c0752a2,0x4be76d3346f0495f,
0x857fcae62d8493a5,0x6f70a4400c562ddb,
0xa6dfbd9fb8e5b88e,0xcb4ccd500f6bb952,
0xd097ad07a71f26b2,0x7e2000a41346a7a7,
0x825ecc24c873782f,0x8ed400668c0c28c8,
0xa2f67f2dfa90563b,0x728900802f0f32fa,
0xcbb41ef979346bca,0x4f2b40a03ad2ffb9,
0xfea126b7d78186bc,0xe2f610c84987bfa8,
0x9f24b832e6b0f436,0xdd9ca7d2df4d7c9,
0xc6ede63fa05d3143,0x91503d1c79720dbb,
0xf8a95fcf88747d94,0x75a44c6397ce912a,
0x9b69dbe1b548ce7c,0xc986afbe3ee11aba,
0xc24452da229b021b,0xfbe85badce996168,
0xf2d56790ab41c2a2,0xfae27299423fb9c3,
0x97c560ba6b0919a5,0xdccd879fc967d41a,
0xbdb6b8e905cb600f,0x5400e987bbc1c920,
0xed246723473e3813,0x290123e9aab23b68,
0x9436c0760c86e30b,0xf9a0b6720aaf6521,
0xb94470938fa89bce,0xf808e40e8d5b3e69,
0xe7958cb87392c2c2,0xb60b1d1230b20e04,
0x90bd77f3483bb9b9,0xb1c6f22b5e6f48c2,
0xb4ecd5f01a4aa828,0x1e38aeb6360b1af3,
0xe2280b6c20dd5232,0x25c6da63c38de1b0,
0x8d590723948a535f,0x579c487e5a38ad0e,
0xb0af48ec79ace837,0x2d835a9df0c6d851,
0xdcdb1b2798182244,0xf8e431456cf88e65,
0x8a08f0f8bf0f156b,0x1b8e9ecb641b58ff,
0xac8b2d36eed2dac5,0xe272467e3d222f3f,
0xd7adf884aa879177,0x5b0ed81dcc6abb0f,
0x86ccbb52ea94baea,0x98e947129fc2b4e9,
0xa87fea27a539e9a5,0x3f2398d747b36224,
0xd29fe4b18e88640e,0x8eec7f0d19a03aad,
0x83a3eeeef9153e89,0x1953cf68300424ac,
0xa48ceaaab75a8e2b,0x5fa8c3423c052dd7,
0xcdb02555653131b6,0x3792f412cb06794d,
0x808e17555f3ebf11,0xe2bbd88bbee40bd0,
0xa0b19d2ab70e6ed6,0x5b6aceaeae9d0ec4,
0xc8de047564d20a8b,0xf245825a5a445275,
0xfb158592be068d2e,0xeed6e2f0f0d56712,
0x9ced737bb6c4183d,0x55464dd69685606b,
0xc428d05aa4751e4c,0xaa97e14c3c26b886,
0xf53304714d9265df,0xd53dd99f4b3066a8,
0x993fe2c6d07b7fab,0xe546a8038efe4029,
0xbf8fdb78849a5f96,0xde98520472bdd033,
0xef73d256a5c0f77c,0x963e66858f6d4440,
0x95a8637627989aad,0xdde7001379a44aa8,
0xbb127c53b17ec159,0x5560c018580d5d52,
0xe9d71b689dde71af,0xaab8f01e6e10b4a6,
0x9226712162ab070d,0xcab3961304ca70e8,
0xb6b00d69bb55c8d1,0x3d607b97c5fd0d22,
0xe45c10c42a2b3b05,0x8cb89a7db77c506a,
0x8eb98a7a9a5b04e3,0x77f3608e92adb242,
0xb267ed1940f1c61c,0x55f038b237591ed3,
0xdf01e85f912e37a3,0x6b6c46dec52f6688,
0x8b61313bbabce2c6,0x2323ac4b3b3da015,
0xae397d8aa96c1b77,0xabec975e0a0d081a,
0xd9c7dced53c72255,0x96e7bd358c904a21,
0x881cea14545c7575,0x7e50d64177da2e54,
0xaa242499697392d2,0xdde50bd1d5d0b9e9,
0xd4ad2dbfc3d07787,0x955e4ec64b44e864,
0x84ec3c97da624ab4,0xbd5af13bef0b113e,
0xa6274bbdd0fadd61,0xecb1ad8aeacdd58e,
0xcfb11ead453994ba,0x67de18eda5814af2,
0x81ceb32c4b43fcf4,0x80eacf948770ced7,
0xa2425ff75e14fc31,0xa1258379a94d028d,
0xcad2f7f5359a3b3e,0x96ee45813a04330,
0xfd87b5f28300ca0d,0x8bca9d6e188853fc,
0x9e74d1b791e07e48,0x775ea264cf55347e,
0xc612062576589dda,0x95364afe032a819e,
0xf79687aed3eec551,0x3a83ddbd83f52205,
0x9abe14cd44753b52,0xc4926a9672793543,
0xc16d9a0095928a27,0x75b7053c0f178294,
0xf1c90080baf72cb1,0x5324c68b12dd6339,
0x971da05074da7bee,0xd3f6fc16ebca5e04,
0xbce5086492111aea,0x88f4bb1ca6bcf585,
0xec1e4a7db69561a5,0x2b31e9e3d06c32e6,
0x9392ee8e921d5d07,0x3aff322e62439fd0,
0xb877aa3236a4b449,0x9befeb9fad487c3,
0xe69594bec44de15b,0x4c2ebe687989a9b4,
0x901d7cf73ab0acd9,0xf9d37014bf60a11,
0xb424dc35095cd80f,0x538484c19ef38c95,
0xe12e13424bb40e13,0x2865a5f206b06fba,
0x8cbccc096f5088cb,0xf93f87b7442e45d4,
0xafebff0bcb24aafe,0xf78f69a51539d749,
0xdbe6fecebdedd5be,0xb573440e5a884d1c,
0x89705f4136b4a597,0x31680a88f8953031,
0xabcc77118461cefc,0xfdc20d2b36ba7c3e,
0xd6bf94d5e57a42bc,0x3d32907604691b4d,
0x8637bd05af6c69b5,0xa63f9a49c2c1b110,
0xa7c5ac471b478423,0xfcf80dc33721d54,
0xd1b71758e219652b,0xd3c36113404ea4a9,
0x83126e978d4fdf3b,0x645a1cac083126ea,
0xa3d70a3d70a3d70a,0x3d70a3d70a3d70a4,
0xcccccccccccccccc,0xcccccccccccccccd,
0x8000000000000000,0x0,
0xa000000000000000,0x0,
0xc800000000000000,0x0,
0xfa00000000000000,0x0,
0x9c40000000000000,0x0,
0xc350000000000000,0x0,
0xf424000000000000,0x0,
0x9896800000000000,0x0,
0xbebc200000000000,0x0,
0xee6b280000000000,0x0,
0x9502f90000000000,0x0,
0xba43b74000000000,0x0,
0xe8d4a51000000000,0x0,
0x9184e72a00000000,0x0,
0xb5e620f480000000,0x0,
0xe35fa931a0000000,0x0,
0x8e1bc9bf04000000,0x0,
0xb1a2bc2ec5000000,0x0,
0xde0b6b3a76400000,0x0,
0x8ac7230489e80000,0x0,
0xad78ebc5ac620000,0x0,
0xd8d726b7177a8000,0x0,
0x878678326eac9000,0x0,
0xa968163f0a57b400,0x0,
0xd3c21bcecceda100,0x0,
0x84595161401484a0,0x0,
0xa56fa5b99019a5c8,0x0,
0xcecb8f27f4200f3a,0x0,
0x813f3978f8940984,0x4000000000000000,
0xa18f07d736b90be5,0x5000000000000000,
0xc9f2c9cd04674ede,0xa400000000000000,
0xfc6f7c4045812296,0x4d00000000000000,
0x9dc5ada82b70b59d,0xf020000000000000,
0xc5371912364ce305,0x6c28000000000000,
0xf684df56c3e01bc6,0xc732000000000000,
0x9a130b963a6c115c,0x3c7f400000000000,
0xc097ce7bc90715b3,0x4b9f100000000000,
0xf0bdc21abb48db20,0x1e86d40000000000,
0x96769950b50d88f4,0x1314448000000000,
0xbc143fa4e250eb31,0x17d955a000000000,
0xeb194f8e1ae525fd,0x5dcfab0800000000,
0x92efd1b8d0cf37be,0x5aa1cae500000000,
0xb7abc627050305ad,0xf14a3d9e40000000,
0xe596b7b0c643c719,0x6d9ccd05d0000000,
0x8f7e32ce7bea5c6f,0xe4820023a2000000,
0xb35dbf821ae4f38b,0xdda2802c8a800000,
0xe0352f62a19e306e,0xd50b2037ad200000,
0x8c213d9da502de45,0x4526f422cc340000,
0xaf298d050e4395d6,0x9670b12b7f410000,
0xdaf3f04651d47b4c,0x3c0cdd765f114000,
0x88d8762bf324cd0f,0xa5880a69fb6ac800,
0xab0e93b6efee0053,0x8eea0d047a457a00,
0xd5d238a4abe98068,0x72a4904598d6d880,
0x85a36366eb71f041,0x47a6da2b7f864750,
0xa70c3c40a64e6c51,0x999090b65f67d924,
0xd0cf4b50cfe20765,0xfff4b4e3f741cf6d,
0x82818f1281ed449f,0xbff8f10e7a8921a4,
0xa321f2d7226895c7,0xaff72d52192b6a0d,
0xcbea6f8ceb02bb39,0x9bf4f8a69f764490,
0xfee50b7025c36a08,0x2f236d04753d5b4,
0x9f4f2726179a2245,0x1d762422c946590,
0xc722f0ef9d80aad6,0x424d3ad2b7b97ef5,
0xf8ebad2b84e0d58b,0xd2e0898765a7deb2,
0x9b934c3b330c8577,0x63cc55f49f88eb2f,
0xc2781f49ffcfa6d5,0x3cbf6b71c76b25fb,
0xf316271c7fc3908a,0x8bef464e3945ef7a,
0x97edd871cfda3a56,0x97758bf0e3cbb5ac,
0xbde94e8e43d0c8ec,0x3d52eeed1cbea317,
0xed63a231d4c4fb27,0x4ca7aaa863ee4bdd,
0x945e455f24fb1cf8,0x8fe8caa93e74ef6a,
0xb975d6b6ee39e436,0xb3e2fd538e122b44,
0xe7d34c64a9c85d44,0x60dbbca87196b616,
0x90e40fbeea1d3a4a,0xbc8955e946fe31cd,
0xb51d13aea4a488dd,0x6babab6398bdbe41,
0xe264589a4dcdab14,0xc696963c7eed2dd1,
0x8d7eb76070a08aec,0xfc1e1de5cf543ca2,
0xb0de65388cc8ada8,0x3b25a55f43294bcb,
0xdd15fe86affad912,0x49ef0eb713f39ebe,
0x8a2dbf142dfcc7ab,0x6e3569326c784337,
0xacb92ed9397bf996,0x49c2c37f07965404,
0xd7e77a8f87daf7fb,0xdc33745ec97be906,
0x86f0ac99b4e8dafd,0x69a028bb3ded71a3,
0xa8acd7c0222311bc,0xc40832ea0d68ce0c,
0xd2d80db02aabd62b,0xf50a3fa490c30190,
0x83c7088e1aab65db,0x792667c6da79e0fa,
0xa4b8cab1a1563f52,0x577001b891185938,
0xcde6fd5e09abcf26,0xed4c0226b55e6f86,
0x80b05e5ac60b6178,0x544f8158315b05b4,
0xa0dc75f1778e39d6,0x696361ae3db1c721,
0xc913936dd571c84c,0x3bc3a19cd1e38e9,
0xfb5878494ace3a5f,0x4ab48a04065c723,
0x9d174b2dcec0e47b,0x62eb0d64283f9c76,
0xc45d1df942711d9a,0x3ba5d0bd324f8394,
0xf5746577930d6500,0xca8f44ec7ee36479,
0x9968bf6abbe85f20,0x7e998b13cf4e1ecb,
0xbfc2ef456ae276e8,0x9e3fedd8c321a67e,
0xefb3ab16c59b14a2,0xc5cfe94ef3ea101e,
0x95d04aee3b80ece5,0xbba1f1d158724a12,
0xbb445da9ca61281f,0x2a8a6e45ae8edc97,
0xea1575143cf97226,0xf52d09d71a3293bd,
0x924d692ca61be758,0x593c2626705f9c56,
0xb6e0c377cfa2e12e,0x6f8b2fb00c77836c,
0xe498f455c38b997a,0xb6dfb9c0f956447,
0x8edf98b59a373fec,0x4724bd4189bd5eac,
0xb2977ee300c50fe7,0x58edec91ec2cb657,
0xdf3d5e9bc0f653e1,0x2f2967b66737e3ed,
0x8b865b215899f46c,0xbd79e0d20082ee74,
0xae67f1e9aec07187,0xecd8590680a3aa11,
0xda01ee641a708de9,0xe80e6f4820cc9495,
0x884134fe908658b2,0x3109058d147fdcdd,
0xaa51823e34a7eede,0xbd4b46f0599fd415,
0xd4e5e2cdc1d1ea96,0x6c9e18ac7007c91a,
0x850fadc09923329e,0x3e2cf6bc604ddb0,
0xa6539930bf6bff45,0x84db8346b786151c,
0xcfe87f7cef46ff16,0xe612641865679a63,
0x81f14fae158c5f6e,0x4fcb7e8f3f60c07e,
0xa26da3999aef7749,0xe3be5e330f38f09d,
0xcb090c8001ab551c,0x5cadf5bfd3072cc5,
0xfdcb4fa002162a63,0x73d9732fc7c8f7f6,
0x9e9f11c4014dda7e,0x2867e7fddcdd9afa,
0xc646d63501a1511d,0xb281e1fd541501b8,
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0x9ae757596946075f,0x3375788de9b06958,
0xc1a12d2fc3978937,0x52d6b1641c83ae,
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0x93ba47c980e98cdf,0xc66f336c36b10137,
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0xb454e4a179dd1877,0x29babe4598c311fb,
0xe16a1dc9d8545e94,0xf4296dd6fef3d67a,
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0xb01ae745b101e9e4,0x5ec05dcff72e7f8f,
0xdc21a1171d42645d,0x76707543f4fa1f73,
0x899504ae72497eba,0x6a06494a791c53a8,
0xabfa45da0edbde69,0x487db9d17636892,
0xd6f8d7509292d603,0x45a9d2845d3c42b6,
0x865b86925b9bc5c2,0xb8a2392ba45a9b2,
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0xd1ef0244af2364ff,0x3207d795430cd926,
0x8335616aed761f1f,0x7f44e6bd49e807b8,
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0xcd036837130890a1,0x36dba887c37a8c0f,
0x802221226be55a64,0xc2494954da2c9789,
0xa02aa96b06deb0fd,0xf2db9baa10b7bd6c,
0xc83553c5c8965d3d,0x6f92829494e5acc7,
0xfa42a8b73abbf48c,0xcb772339ba1f17f9,
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0xc38413cf25e2d70d,0xfef5138519684aba,
0xf46518c2ef5b8cd1,0x7eb258665fc25d69,
0x98bf2f79d5993802,0xef2f773ffbd97a61,
0xbeeefb584aff8603,0xaafb550ffacfd8fa,
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0x952ab45cfa97a0b2,0xdd945a747bf26183,
0xba756174393d88df,0x94f971119aeef9e4,
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0x91abb422ccb812ee,0xac62e055c10ab33a,
0xb616a12b7fe617aa,0x577b986b314d6009,
0xe39c49765fdf9d94,0xed5a7e85fda0b80b,
0x8e41ade9fbebc27d,0x14588f13be847307,
0xb1d219647ae6b31c,0x596eb2d8ae258fc8,
0xde469fbd99a05fe3,0x6fca5f8ed9aef3bb,
0x8aec23d680043bee,0x25de7bb9480d5854,
0xada72ccc20054ae9,0xaf561aa79a10ae6a,
0xd910f7ff28069da4,0x1b2ba1518094da04,
0x87aa9aff79042286,0x90fb44d2f05d0842,
0xa99541bf57452b28,0x353a1607ac744a53,
0xd3fa922f2d1675f2,0x42889b8997915ce8,
0x847c9b5d7c2e09b7,0x69956135febada11,
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0xcf02b2c21207ef2e,0x94f967e45e03f4bb,
0x8161afb94b44f57d,0x1d1be0eebac278f5,
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0xca28a291859bbf93,0x7d7b8f7503cfdcfe,
0xfcb2cb35e702af78,0x5cda735244c3d43e,
0x9defbf01b061adab,0x3a0888136afa64a7,
0xc56baec21c7a1916,0x88aaa1845b8fdd0,
0xf6c69a72a3989f5b,0x8aad549e57273d45,
0x9a3c2087a63f6399,0x36ac54e2f678864b,
0xc0cb28a98fcf3c7f,0x84576a1bb416a7dd,
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0xeb57ff22fc0c7959,0xa90cb506d155a7ea,
0x9316ff75dd87cbd8,0x9a7f12442d588f2,
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0xe5d3ef282a242e81,0x8f1668c8a86da5fa,
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0xb38d92d760ec4455,0x37c981dcc395a9ac,
0xe070f78d3927556a,0x85bbe253f47b1417,
0x8c469ab843b89562,0x93956d7478ccec8e,
0xaf58416654a6babb,0x387ac8d1970027b2,
0xdb2e51bfe9d0696a,0x6997b05fcc0319e,
0x88fcf317f22241e2,0x441fece3bdf81f03,
0xab3c2fddeeaad25a,0xd527e81cad7626c3,
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0x85c7056562757456,0xf6872d5667844e49,
0xa738c6bebb12d16c,0xb428f8ac016561db,
0xd106f86e69d785c7,0xe13336d701beba52,
0x82a45b450226b39c,0xecc0024661173473,
0xa34d721642b06084,0x27f002d7f95d0190,
0xcc20ce9bd35c78a5,0x31ec038df7b441f4,
0xff290242c83396ce,0x7e67047175a15271,
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0xc75809c42c684dd1,0x52c07b78a3e60868,
0xf92e0c3537826145,0xa7709a56ccdf8a82,
0x9bbcc7a142b17ccb,0x88a66076400bb691,
0xc2abf989935ddbfe,0x6acff893d00ea435,
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0x98165af37b2153de,0xc3727a337a8b704a,
0xbe1bf1b059e9a8d6,0x744f18c0592e4c5c,
0xeda2ee1c7064130c,0x1162def06f79df73,
0x9485d4d1c63e8be7,0x8addcb5645ac2ba8,
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0x910ab1d4db9914a0,0x1d9c9892400a22a2,
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0xe2a0b5dc971f303a,0x2e44ae64840fd61d,
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0xb10d8e1456105dad,0x7425a83e872c5f47,
0xdd50f1996b947518,0xd12f124e28f77719,
0x8a5296ffe33cc92f,0x82bd6b70d99aaa6f,
0xace73cbfdc0bfb7b,0x636cc64d1001550b,
0xd8210befd30efa5a,0x3c47f7e05401aa4e,
0x8714a775e3e95c78,0x65acfaec34810a71,
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0xd31045a8341ca07c,0x1ede48111209a050,
0x83ea2b892091e44d,0x934aed0aab460432,
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0xce1de40642e3f4b9,0x36251260ab9d668e,
0x80d2ae83e9ce78f3,0xc1d72b7c6b426019,
0xa1075a24e4421730,0xb24cf65b8612f81f,
0xc94930ae1d529cfc,0xdee033f26797b627,
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0x9d412e0806e88aa5,0x8e1f289560ee864e,
0xc491798a08a2ad4e,0xf1a6f2bab92a27e2,
0xf5b5d7ec8acb58a2,0xae10af696774b1db,
0x9991a6f3d6bf1765,0xacca6da1e0a8ef29,
0xbff610b0cc6edd3f,0x17fd090a58d32af3,
0xeff394dcff8a948e,0xddfc4b4cef07f5b0,
0x95f83d0a1fb69cd9,0x4abdaf101564f98e,
0xbb764c4ca7a4440f,0x9d6d1ad41abe37f1,
0xea53df5fd18d5513,0x84c86189216dc5ed,
0x92746b9be2f8552c,0x32fd3cf5b4e49bb4,
0xb7118682dbb66a77,0x3fbc8c33221dc2a1,
0xe4d5e82392a40515,0xfabaf3feaa5334a,
0x8f05b1163ba6832d,0x29cb4d87f2a7400e,
0xb2c71d5bca9023f8,0x743e20e9ef511012,
0xdf78e4b2bd342cf6,0x914da9246b255416,
0x8bab8eefb6409c1a,0x1ad089b6c2f7548e,
0xae9672aba3d0c320,0xa184ac2473b529b1,
0xda3c0f568cc4f3e8,0xc9e5d72d90a2741e,
0x8865899617fb1871,0x7e2fa67c7a658892,
0xaa7eebfb9df9de8d,0xddbb901b98feeab7,
0xd51ea6fa85785631,0x552a74227f3ea565,
0x8533285c936b35de,0xd53a88958f87275f,
0xa67ff273b8460356,0x8a892abaf368f137,
0xd01fef10a657842c,0x2d2b7569b0432d85,
0x8213f56a67f6b29b,0x9c3b29620e29fc73,
0xa298f2c501f45f42,0x8349f3ba91b47b8f,
0xcb3f2f7642717713,0x241c70a936219a73,
0xfe0efb53d30dd4d7,0xed238cd383aa0110,
0x9ec95d1463e8a506,0xf4363804324a40aa,
0xc67bb4597ce2ce48,0xb143c6053edcd0d5,
0xf81aa16fdc1b81da,0xdd94b7868e94050a,
0x9b10a4e5e9913128,0xca7cf2b4191c8326,
0xc1d4ce1f63f57d72,0xfd1c2f611f63a3f0,
0xf24a01a73cf2dccf,0xbc633b39673c8cec,
0x976e41088617ca01,0xd5be0503e085d813,
0xbd49d14aa79dbc82,0x4b2d8644d8a74e18,
0xec9c459d51852ba2,0xddf8e7d60ed1219e,
0x93e1ab8252f33b45,0xcabb90e5c942b503,
0xb8da1662e7b00a17,0x3d6a751f3b936243,
0xe7109bfba19c0c9d,0xcc512670a783ad4,
0x906a617d450187e2,0x27fb2b80668b24c5,
0xb484f9dc9641e9da,0xb1f9f660802dedf6,
0xe1a63853bbd26451,0x5e7873f8a0396973,
0x8d07e33455637eb2,0xdb0b487b6423e1e8,
0xb049dc016abc5e5f,0x91ce1a9a3d2cda62,
0xdc5c5301c56b75f7,0x7641a140cc7810fb,
0x89b9b3e11b6329ba,0xa9e904c87fcb0a9d,
0xac2820d9623bf429,0x546345fa9fbdcd44,
0xd732290fbacaf133,0xa97c177947ad4095,
0x867f59a9d4bed6c0,0x49ed8eabcccc485d,
0xa81f301449ee8c70,0x5c68f256bfff5a74,
0xd226fc195c6a2f8c,0x73832eec6fff3111,
0x83585d8fd9c25db7,0xc831fd53c5ff7eab,
0xa42e74f3d032f525,0xba3e7ca8b77f5e55,
0xcd3a1230c43fb26f,0x28ce1bd2e55f35eb,
0x80444b5e7aa7cf85,0x7980d163cf5b81b3,
0xa0555e361951c366,0xd7e105bcc332621f,
0xc86ab5c39fa63440,0x8dd9472bf3fefaa7,
0xfa856334878fc150,0xb14f98f6f0feb951,
0x9c935e00d4b9d8d2,0x6ed1bf9a569f33d3,
0xc3b8358109e84f07,0xa862f80ec4700c8,
0xf4a642e14c6262c8,0xcd27bb612758c0fa,
0x98e7e9cccfbd7dbd,0x8038d51cb897789c,
0xbf21e44003acdd2c,0xe0470a63e6bd56c3,
0xeeea5d5004981478,0x1858ccfce06cac74,
0x95527a5202df0ccb,0xf37801e0c43ebc8,
0xbaa718e68396cffd,0xd30560258f54e6ba,
0xe950df20247c83fd,0x47c6b82ef32a2069,
0x91d28b7416cdd27e,0x4cdc331d57fa5441,
0xb6472e511c81471d,0xe0133fe4adf8e952,
0xe3d8f9e563a198e5,0x58180fddd97723a6,
0x8e679c2f5e44ff8f,0x570f09eaa7ea7648,};
using powers = powers_template<>;
}
#endif
#ifndef FASTFLOAT_DECIMAL_TO_BINARY_H
#define FASTFLOAT_DECIMAL_TO_BINARY_H
#include <cfloat>
#include <cinttypes>
#include <cmath>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
namespace fast_float {
// This will compute or rather approximate w * 5**q and return a pair of 64-bit words approximating
// the result, with the "high" part corresponding to the most significant bits and the
// low part corresponding to the least significant bits.
//
template <int bit_precision>
fastfloat_really_inline
value128 compute_product_approximation(int64_t q, uint64_t w) {
const int index = 2 * int(q - powers::smallest_power_of_five);
// For small values of q, e.g., q in [0,27], the answer is always exact because
// The line value128 firstproduct = full_multiplication(w, power_of_five_128[index]);
// gives the exact answer.
value128 firstproduct = full_multiplication(w, powers::power_of_five_128[index]);
static_assert((bit_precision >= 0) && (bit_precision <= 64), " precision should be in (0,64]");
constexpr uint64_t precision_mask = (bit_precision < 64) ?
(uint64_t(0xFFFFFFFFFFFFFFFF) >> bit_precision)
: uint64_t(0xFFFFFFFFFFFFFFFF);
if((firstproduct.high & precision_mask) == precision_mask) { // could further guard with (lower + w < lower)
// regarding the second product, we only need secondproduct.high, but our expectation is that the compiler will optimize this extra work away if needed.
value128 secondproduct = full_multiplication(w, powers::power_of_five_128[index + 1]);
firstproduct.low += secondproduct.high;
if(secondproduct.high > firstproduct.low) {
firstproduct.high++;
}
}
return firstproduct;
}
namespace detail {
/**
* For q in (0,350), we have that
* f = (((152170 + 65536) * q ) >> 16);
* is equal to
* floor(p) + q
* where
* p = log(5**q)/log(2) = q * log(5)/log(2)
*
* For negative values of q in (-400,0), we have that
* f = (((152170 + 65536) * q ) >> 16);
* is equal to
* -ceil(p) + q
* where
* p = log(5**-q)/log(2) = -q * log(5)/log(2)
*/
fastfloat_really_inline int power(int q) noexcept {
return (((152170 + 65536) * q) >> 16) + 63;
}
} // namespace detail
// w * 10 ** q
// The returned value should be a valid ieee64 number that simply need to be packed.
// However, in some very rare cases, the computation will fail. In such cases, we
// return an adjusted_mantissa with a negative power of 2: the caller should recompute
// in such cases.
template <typename binary>
fastfloat_really_inline
adjusted_mantissa compute_float(int64_t q, uint64_t w) noexcept {
adjusted_mantissa answer;
if ((w == 0) || (q < binary::smallest_power_of_ten())) {
answer.power2 = 0;
answer.mantissa = 0;
// result should be zero
return answer;
}
if (q > binary::largest_power_of_ten()) {
// we want to get infinity:
answer.power2 = binary::infinite_power();
answer.mantissa = 0;
return answer;
}
// At this point in time q is in [powers::smallest_power_of_five, powers::largest_power_of_five].
// We want the most significant bit of i to be 1. Shift if needed.
int lz = leading_zeroes(w);
w <<= lz;
// The required precision is binary::mantissa_explicit_bits() + 3 because
// 1. We need the implicit bit
// 2. We need an extra bit for rounding purposes
// 3. We might lose a bit due to the "upperbit" routine (result too small, requiring a shift)
value128 product = compute_product_approximation<binary::mantissa_explicit_bits() + 3>(q, w);
if(product.low == 0xFFFFFFFFFFFFFFFF) { // could guard it further
// In some very rare cases, this could happen, in which case we might need a more accurate
// computation that what we can provide cheaply. This is very, very unlikely.
//
const bool inside_safe_exponent = (q >= -27) && (q <= 55); // always good because 5**q <2**128 when q>=0,
// and otherwise, for q<0, we have 5**-q<2**64 and the 128-bit reciprocal allows for exact computation.
if(!inside_safe_exponent) {
answer.power2 = -1; // This (a negative value) indicates an error condition.
return answer;
}
}
// The "compute_product_approximation" function can be slightly slower than a branchless approach:
// value128 product = compute_product(q, w);
// but in practice, we can win big with the compute_product_approximation if its additional branch
// is easily predicted. Which is best is data specific.
int upperbit = int(product.high >> 63);
answer.mantissa = product.high >> (upperbit + 64 - binary::mantissa_explicit_bits() - 3);
answer.power2 = int(detail::power(int(q)) + upperbit - lz - binary::minimum_exponent());
if (answer.power2 <= 0) { // we have a subnormal?
// Here have that answer.power2 <= 0 so -answer.power2 >= 0
if(-answer.power2 + 1 >= 64) { // if we have more than 64 bits below the minimum exponent, you have a zero for sure.
answer.power2 = 0;
answer.mantissa = 0;
// result should be zero
return answer;
}
// next line is safe because -answer.power2 + 1 < 64
answer.mantissa >>= -answer.power2 + 1;
// Thankfully, we can't have both "round-to-even" and subnormals because
// "round-to-even" only occurs for powers close to 0.
answer.mantissa += (answer.mantissa & 1); // round up
answer.mantissa >>= 1;
// There is a weird scenario where we don't have a subnormal but just.
// Suppose we start with 2.2250738585072013e-308, we end up
// with 0x3fffffffffffff x 2^-1023-53 which is technically subnormal
// whereas 0x40000000000000 x 2^-1023-53 is normal. Now, we need to round
// up 0x3fffffffffffff x 2^-1023-53 and once we do, we are no longer
// subnormal, but we can only know this after rounding.
// So we only declare a subnormal if we are smaller than the threshold.
answer.power2 = (answer.mantissa < (uint64_t(1) << binary::mantissa_explicit_bits())) ? 0 : 1;
return answer;
}
// usually, we round *up*, but if we fall right in between and and we have an
// even basis, we need to round down
// We are only concerned with the cases where 5**q fits in single 64-bit word.
if ((product.low <= 1) && (q >= binary::min_exponent_round_to_even()) && (q <= binary::max_exponent_round_to_even()) &&
((answer.mantissa & 3) == 1) ) { // we may fall between two floats!
// To be in-between two floats we need that in doing
// answer.mantissa = product.high >> (upperbit + 64 - binary::mantissa_explicit_bits() - 3);
// ... we dropped out only zeroes. But if this happened, then we can go back!!!
if((answer.mantissa << (upperbit + 64 - binary::mantissa_explicit_bits() - 3)) == product.high) {
answer.mantissa &= ~uint64_t(1); // flip it so that we do not round up
}
}
answer.mantissa += (answer.mantissa & 1); // round up
answer.mantissa >>= 1;
if (answer.mantissa >= (uint64_t(2) << binary::mantissa_explicit_bits())) {
answer.mantissa = (uint64_t(1) << binary::mantissa_explicit_bits());
answer.power2++; // undo previous addition
}
answer.mantissa &= ~(uint64_t(1) << binary::mantissa_explicit_bits());
if (answer.power2 >= binary::infinite_power()) { // infinity
answer.power2 = binary::infinite_power();
answer.mantissa = 0;
}
return answer;
}
} // namespace fast_float
#endif
#ifndef FASTFLOAT_ASCII_NUMBER_H
#define FASTFLOAT_ASCII_NUMBER_H
#include <cstdio>
#include <cctype>
#include <cstdint>
#include <cstring>
namespace fast_float {
// Next function can be micro-optimized, but compilers are entirely
// able to optimize it well.
fastfloat_really_inline bool is_integer(char c) noexcept { return c >= '0' && c <= '9'; }
fastfloat_really_inline uint64_t byteswap(uint64_t val) {
return (val & 0xFF00000000000000) >> 56
| (val & 0x00FF000000000000) >> 40
| (val & 0x0000FF0000000000) >> 24
| (val & 0x000000FF00000000) >> 8
| (val & 0x00000000FF000000) << 8
| (val & 0x0000000000FF0000) << 24
| (val & 0x000000000000FF00) << 40
| (val & 0x00000000000000FF) << 56;
}
fastfloat_really_inline uint64_t read_u64(const char *chars) {
uint64_t val;
::memcpy(&val, chars, sizeof(uint64_t));
#if FASTFLOAT_IS_BIG_ENDIAN == 1
// Need to read as-if the number was in little-endian order.
val = byteswap(val);
#endif
return val;
}
fastfloat_really_inline void write_u64(uint8_t *chars, uint64_t val) {
#if FASTFLOAT_IS_BIG_ENDIAN == 1
// Need to read as-if the number was in little-endian order.
val = byteswap(val);
#endif
::memcpy(chars, &val, sizeof(uint64_t));
}
// credit @aqrit
fastfloat_really_inline uint32_t parse_eight_digits_unrolled(uint64_t val) {
const uint64_t mask = 0x000000FF000000FF;
const uint64_t mul1 = 0x000F424000000064; // 100 + (1000000ULL << 32)
const uint64_t mul2 = 0x0000271000000001; // 1 + (10000ULL << 32)
val -= 0x3030303030303030;
val = (val * 10) + (val >> 8); // val = (val * 2561) >> 8;
val = (((val & mask) * mul1) + (((val >> 16) & mask) * mul2)) >> 32;
return uint32_t(val);
}
fastfloat_really_inline uint32_t parse_eight_digits_unrolled(const char *chars) noexcept {
return parse_eight_digits_unrolled(read_u64(chars));
}
// credit @aqrit
fastfloat_really_inline bool is_made_of_eight_digits_fast(uint64_t val) noexcept {
return !((((val + 0x4646464646464646) | (val - 0x3030303030303030)) &
0x8080808080808080));
}
fastfloat_really_inline bool is_made_of_eight_digits_fast(const char *chars) noexcept {
return is_made_of_eight_digits_fast(read_u64(chars));
}
struct parsed_number_string {
int64_t exponent;
uint64_t mantissa;
const char *lastmatch;
bool negative;
bool valid;
bool too_many_digits;
};
// Assuming that you use no more than 19 digits, this will
// parse an ASCII string.
fastfloat_really_inline
parsed_number_string parse_number_string(const char *p, const char *pend, parse_options options) noexcept {
const chars_format fmt = options.format;
const char decimal_point = options.decimal_point;
parsed_number_string answer;
answer.valid = false;
answer.too_many_digits = false;
answer.negative = (*p == '-');
if (*p == '-') { // C++17 20.19.3.(7.1) explicitly forbids '+' sign here
++p;
if (p == pend) {
return answer;
}
if (!is_integer(*p) && (*p != decimal_point)) { // a sign must be followed by an integer or the dot
return answer;
}
}
const char *const start_digits = p;
uint64_t i = 0; // an unsigned int avoids signed overflows (which are bad)
while ((p != pend) && is_integer(*p)) {
// a multiplication by 10 is cheaper than an arbitrary integer
// multiplication
i = 10 * i +
uint64_t(*p - '0'); // might overflow, we will handle the overflow later
++p;
}
const char *const end_of_integer_part = p;
int64_t digit_count = int64_t(end_of_integer_part - start_digits);
int64_t exponent = 0;
if ((p != pend) && (*p == decimal_point)) {
++p;
// Fast approach only tested under little endian systems
if ((p + 8 <= pend) && is_made_of_eight_digits_fast(p)) {
i = i * 100000000 + parse_eight_digits_unrolled(p); // in rare cases, this will overflow, but that's ok
p += 8;
if ((p + 8 <= pend) && is_made_of_eight_digits_fast(p)) {
i = i * 100000000 + parse_eight_digits_unrolled(p); // in rare cases, this will overflow, but that's ok
p += 8;
}
}
while ((p != pend) && is_integer(*p)) {
uint8_t digit = uint8_t(*p - '0');
++p;
i = i * 10 + digit; // in rare cases, this will overflow, but that's ok
}
exponent = end_of_integer_part + 1 - p;
digit_count -= exponent;
}
// we must have encountered at least one integer!
if (digit_count == 0) {
return answer;
}
int64_t exp_number = 0; // explicit exponential part
if ((fmt & chars_format::scientific) && (p != pend) && (('e' == *p) || ('E' == *p))) {
const char * location_of_e = p;
++p;
bool neg_exp = false;
if ((p != pend) && ('-' == *p)) {
neg_exp = true;
++p;
} else if ((p != pend) && ('+' == *p)) { // '+' on exponent is allowed by C++17 20.19.3.(7.1)
++p;
}
if ((p == pend) || !is_integer(*p)) {
if(!(fmt & chars_format::fixed)) {
// We are in error.
return answer;
}
// Otherwise, we will be ignoring the 'e'.
p = location_of_e;
} else {
while ((p != pend) && is_integer(*p)) {
uint8_t digit = uint8_t(*p - '0');
if (exp_number < 0x10000) {
exp_number = 10 * exp_number + digit;
}
++p;
}
if(neg_exp) { exp_number = - exp_number; }
exponent += exp_number;
}
} else {
// If it scientific and not fixed, we have to bail out.
if((fmt & chars_format::scientific) && !(fmt & chars_format::fixed)) { return answer; }
}
answer.lastmatch = p;
answer.valid = true;
// If we frequently had to deal with long strings of digits,
// we could extend our code by using a 128-bit integer instead
// of a 64-bit integer. However, this is uncommon.
//
// We can deal with up to 19 digits.
if (digit_count > 19) { // this is uncommon
// It is possible that the integer had an overflow.
// We have to handle the case where we have 0.0000somenumber.
// We need to be mindful of the case where we only have zeroes...
// E.g., 0.000000000...000.
const char *start = start_digits;
while ((start != pend) && (*start == '0' || *start == decimal_point)) {
if(*start == '0') { digit_count --; }
start++;
}
if (digit_count > 19) {
answer.too_many_digits = true;
// Let us start again, this time, avoiding overflows.
i = 0;
p = start_digits;
const uint64_t minimal_nineteen_digit_integer{1000000000000000000};
while((i < minimal_nineteen_digit_integer) && (p != pend) && is_integer(*p)) {
i = i * 10 + uint64_t(*p - '0');
++p;
}
if (i >= minimal_nineteen_digit_integer) { // We have a big integers
exponent = end_of_integer_part - p + exp_number;
} else { // We have a value with a fractional component.
p++; // skip the dot
const char *first_after_period = p;
while((i < minimal_nineteen_digit_integer) && (p != pend) && is_integer(*p)) {
i = i * 10 + uint64_t(*p - '0');
++p;
}
exponent = first_after_period - p + exp_number;
}
// We have now corrected both exponent and i, to a truncated value
}
}
answer.exponent = exponent;
answer.mantissa = i;
return answer;
}
// This should always succeed since it follows a call to parse_number_string
// This function could be optimized. In particular, we could stop after 19 digits
// and try to bail out. Furthermore, we should be able to recover the computed
// exponent from the pass in parse_number_string.
fastfloat_really_inline decimal parse_decimal(const char *p, const char *pend, parse_options options) noexcept {
const char decimal_point = options.decimal_point;
decimal answer;
answer.num_digits = 0;
answer.decimal_point = 0;
answer.truncated = false;
answer.negative = (*p == '-');
if (*p == '-') { // C++17 20.19.3.(7.1) explicitly forbids '+' sign here
++p;
}
// skip leading zeroes
while ((p != pend) && (*p == '0')) {
++p;
}
while ((p != pend) && is_integer(*p)) {
if (answer.num_digits < max_digits) {
answer.digits[answer.num_digits] = uint8_t(*p - '0');
}
answer.num_digits++;
++p;
}
if ((p != pend) && (*p == decimal_point)) {
++p;
const char *first_after_period = p;
// if we have not yet encountered a zero, we have to skip it as well
if(answer.num_digits == 0) {
// skip zeros
while ((p != pend) && (*p == '0')) {
++p;
}
}
// We expect that this loop will often take the bulk of the running time
// because when a value has lots of digits, these digits often
while ((p + 8 <= pend) && (answer.num_digits + 8 < max_digits)) {
uint64_t val = read_u64(p);
if(! is_made_of_eight_digits_fast(val)) { break; }
// We have eight digits, process them in one go!
val -= 0x3030303030303030;
write_u64(answer.digits + answer.num_digits, val);
answer.num_digits += 8;
p += 8;
}
while ((p != pend) && is_integer(*p)) {
if (answer.num_digits < max_digits) {
answer.digits[answer.num_digits] = uint8_t(*p - '0');
}
answer.num_digits++;
++p;
}
answer.decimal_point = int32_t(first_after_period - p);
}
// We want num_digits to be the number of significant digits, excluding
// leading *and* trailing zeros! Otherwise the truncated flag later is
// going to be misleading.
if(answer.num_digits > 0) {
// We potentially need the answer.num_digits > 0 guard because we
// prune leading zeros. So with answer.num_digits > 0, we know that
// we have at least one non-zero digit.
const char *preverse = p - 1;
int32_t trailing_zeros = 0;
while ((*preverse == '0') || (*preverse == decimal_point)) {
if(*preverse == '0') { trailing_zeros++; };
--preverse;
}
answer.decimal_point += int32_t(answer.num_digits);
answer.num_digits -= uint32_t(trailing_zeros);
}
if(answer.num_digits > max_digits) {
answer.truncated = true;
answer.num_digits = max_digits;
}
if ((p != pend) && (('e' == *p) || ('E' == *p))) {
++p;
bool neg_exp = false;
if ((p != pend) && ('-' == *p)) {
neg_exp = true;
++p;
} else if ((p != pend) && ('+' == *p)) { // '+' on exponent is allowed by C++17 20.19.3.(7.1)
++p;
}
int32_t exp_number = 0; // exponential part
while ((p != pend) && is_integer(*p)) {
uint8_t digit = uint8_t(*p - '0');
if (exp_number < 0x10000) {
exp_number = 10 * exp_number + digit;
}
++p;
}
answer.decimal_point += (neg_exp ? -exp_number : exp_number);
}
// In very rare cases, we may have fewer than 19 digits, we want to be able to reliably
// assume that all digits up to max_digit_without_overflow have been initialized.
for(uint32_t i = answer.num_digits; i < max_digit_without_overflow; i++) { answer.digits[i] = 0; }
return answer;
}
} // namespace fast_float
#endif
#ifndef FASTFLOAT_GENERIC_DECIMAL_TO_BINARY_H
#define FASTFLOAT_GENERIC_DECIMAL_TO_BINARY_H
/**
* This code is meant to handle the case where we have more than 19 digits.
*
* It is based on work by Nigel Tao (at https://github.com/google/wuffs/)
* who credits Ken Thompson for the design (via a reference to the Go source
* code).
*
* Rob Pike suggested that this algorithm be called "Simple Decimal Conversion".
*
* It is probably not very fast but it is a fallback that should almost never
* be used in real life. Though it is not fast, it is "easily" understood and debugged.
**/
#include <cstdint>
namespace fast_float {
namespace detail {
// remove all final zeroes
inline void trim(decimal &h) {
while ((h.num_digits > 0) && (h.digits[h.num_digits - 1] == 0)) {
h.num_digits--;
}
}
inline uint32_t number_of_digits_decimal_left_shift(const decimal &h, uint32_t shift) {
shift &= 63;
const static uint16_t number_of_digits_decimal_left_shift_table[65] = {
0x0000, 0x0800, 0x0801, 0x0803, 0x1006, 0x1009, 0x100D, 0x1812, 0x1817,
0x181D, 0x2024, 0x202B, 0x2033, 0x203C, 0x2846, 0x2850, 0x285B, 0x3067,
0x3073, 0x3080, 0x388E, 0x389C, 0x38AB, 0x38BB, 0x40CC, 0x40DD, 0x40EF,
0x4902, 0x4915, 0x4929, 0x513E, 0x5153, 0x5169, 0x5180, 0x5998, 0x59B0,
0x59C9, 0x61E3, 0x61FD, 0x6218, 0x6A34, 0x6A50, 0x6A6D, 0x6A8B, 0x72AA,
0x72C9, 0x72E9, 0x7B0A, 0x7B2B, 0x7B4D, 0x8370, 0x8393, 0x83B7, 0x83DC,
0x8C02, 0x8C28, 0x8C4F, 0x9477, 0x949F, 0x94C8, 0x9CF2, 0x051C, 0x051C,
0x051C, 0x051C,
};
uint32_t x_a = number_of_digits_decimal_left_shift_table[shift];
uint32_t x_b = number_of_digits_decimal_left_shift_table[shift + 1];
uint32_t num_new_digits = x_a >> 11;
uint32_t pow5_a = 0x7FF & x_a;
uint32_t pow5_b = 0x7FF & x_b;
const static uint8_t
number_of_digits_decimal_left_shift_table_powers_of_5[0x051C] = {
5, 2, 5, 1, 2, 5, 6, 2, 5, 3, 1, 2, 5, 1, 5, 6, 2, 5, 7, 8, 1, 2, 5, 3,
9, 0, 6, 2, 5, 1, 9, 5, 3, 1, 2, 5, 9, 7, 6, 5, 6, 2, 5, 4, 8, 8, 2, 8,
1, 2, 5, 2, 4, 4, 1, 4, 0, 6, 2, 5, 1, 2, 2, 0, 7, 0, 3, 1, 2, 5, 6, 1,
0, 3, 5, 1, 5, 6, 2, 5, 3, 0, 5, 1, 7, 5, 7, 8, 1, 2, 5, 1, 5, 2, 5, 8,
7, 8, 9, 0, 6, 2, 5, 7, 6, 2, 9, 3, 9, 4, 5, 3, 1, 2, 5, 3, 8, 1, 4, 6,
9, 7, 2, 6, 5, 6, 2, 5, 1, 9, 0, 7, 3, 4, 8, 6, 3, 2, 8, 1, 2, 5, 9, 5,
3, 6, 7, 4, 3, 1, 6, 4, 0, 6, 2, 5, 4, 7, 6, 8, 3, 7, 1, 5, 8, 2, 0, 3,
1, 2, 5, 2, 3, 8, 4, 1, 8, 5, 7, 9, 1, 0, 1, 5, 6, 2, 5, 1, 1, 9, 2, 0,
9, 2, 8, 9, 5, 5, 0, 7, 8, 1, 2, 5, 5, 9, 6, 0, 4, 6, 4, 4, 7, 7, 5, 3,
9, 0, 6, 2, 5, 2, 9, 8, 0, 2, 3, 2, 2, 3, 8, 7, 6, 9, 5, 3, 1, 2, 5, 1,
4, 9, 0, 1, 1, 6, 1, 1, 9, 3, 8, 4, 7, 6, 5, 6, 2, 5, 7, 4, 5, 0, 5, 8,
0, 5, 9, 6, 9, 2, 3, 8, 2, 8, 1, 2, 5, 3, 7, 2, 5, 2, 9, 0, 2, 9, 8, 4,
6, 1, 9, 1, 4, 0, 6, 2, 5, 1, 8, 6, 2, 6, 4, 5, 1, 4, 9, 2, 3, 0, 9, 5,
7, 0, 3, 1, 2, 5, 9, 3, 1, 3, 2, 2, 5, 7, 4, 6, 1, 5, 4, 7, 8, 5, 1, 5,
6, 2, 5, 4, 6, 5, 6, 6, 1, 2, 8, 7, 3, 0, 7, 7, 3, 9, 2, 5, 7, 8, 1, 2,
5, 2, 3, 2, 8, 3, 0, 6, 4, 3, 6, 5, 3, 8, 6, 9, 6, 2, 8, 9, 0, 6, 2, 5,
1, 1, 6, 4, 1, 5, 3, 2, 1, 8, 2, 6, 9, 3, 4, 8, 1, 4, 4, 5, 3, 1, 2, 5,
5, 8, 2, 0, 7, 6, 6, 0, 9, 1, 3, 4, 6, 7, 4, 0, 7, 2, 2, 6, 5, 6, 2, 5,
2, 9, 1, 0, 3, 8, 3, 0, 4, 5, 6, 7, 3, 3, 7, 0, 3, 6, 1, 3, 2, 8, 1, 2,
5, 1, 4, 5, 5, 1, 9, 1, 5, 2, 2, 8, 3, 6, 6, 8, 5, 1, 8, 0, 6, 6, 4, 0,
6, 2, 5, 7, 2, 7, 5, 9, 5, 7, 6, 1, 4, 1, 8, 3, 4, 2, 5, 9, 0, 3, 3, 2,
0, 3, 1, 2, 5, 3, 6, 3, 7, 9, 7, 8, 8, 0, 7, 0, 9, 1, 7, 1, 2, 9, 5, 1,
6, 6, 0, 1, 5, 6, 2, 5, 1, 8, 1, 8, 9, 8, 9, 4, 0, 3, 5, 4, 5, 8, 5, 6,
4, 7, 5, 8, 3, 0, 0, 7, 8, 1, 2, 5, 9, 0, 9, 4, 9, 4, 7, 0, 1, 7, 7, 2,
9, 2, 8, 2, 3, 7, 9, 1, 5, 0, 3, 9, 0, 6, 2, 5, 4, 5, 4, 7, 4, 7, 3, 5,
0, 8, 8, 6, 4, 6, 4, 1, 1, 8, 9, 5, 7, 5, 1, 9, 5, 3, 1, 2, 5, 2, 2, 7,
3, 7, 3, 6, 7, 5, 4, 4, 3, 2, 3, 2, 0, 5, 9, 4, 7, 8, 7, 5, 9, 7, 6, 5,
6, 2, 5, 1, 1, 3, 6, 8, 6, 8, 3, 7, 7, 2, 1, 6, 1, 6, 0, 2, 9, 7, 3, 9,
3, 7, 9, 8, 8, 2, 8, 1, 2, 5, 5, 6, 8, 4, 3, 4, 1, 8, 8, 6, 0, 8, 0, 8,
0, 1, 4, 8, 6, 9, 6, 8, 9, 9, 4, 1, 4, 0, 6, 2, 5, 2, 8, 4, 2, 1, 7, 0,
9, 4, 3, 0, 4, 0, 4, 0, 0, 7, 4, 3, 4, 8, 4, 4, 9, 7, 0, 7, 0, 3, 1, 2,
5, 1, 4, 2, 1, 0, 8, 5, 4, 7, 1, 5, 2, 0, 2, 0, 0, 3, 7, 1, 7, 4, 2, 2,
4, 8, 5, 3, 5, 1, 5, 6, 2, 5, 7, 1, 0, 5, 4, 2, 7, 3, 5, 7, 6, 0, 1, 0,
0, 1, 8, 5, 8, 7, 1, 1, 2, 4, 2, 6, 7, 5, 7, 8, 1, 2, 5, 3, 5, 5, 2, 7,
1, 3, 6, 7, 8, 8, 0, 0, 5, 0, 0, 9, 2, 9, 3, 5, 5, 6, 2, 1, 3, 3, 7, 8,
9, 0, 6, 2, 5, 1, 7, 7, 6, 3, 5, 6, 8, 3, 9, 4, 0, 0, 2, 5, 0, 4, 6, 4,
6, 7, 7, 8, 1, 0, 6, 6, 8, 9, 4, 5, 3, 1, 2, 5, 8, 8, 8, 1, 7, 8, 4, 1,
9, 7, 0, 0, 1, 2, 5, 2, 3, 2, 3, 3, 8, 9, 0, 5, 3, 3, 4, 4, 7, 2, 6, 5,
6, 2, 5, 4, 4, 4, 0, 8, 9, 2, 0, 9, 8, 5, 0, 0, 6, 2, 6, 1, 6, 1, 6, 9,
4, 5, 2, 6, 6, 7, 2, 3, 6, 3, 2, 8, 1, 2, 5, 2, 2, 2, 0, 4, 4, 6, 0, 4,
9, 2, 5, 0, 3, 1, 3, 0, 8, 0, 8, 4, 7, 2, 6, 3, 3, 3, 6, 1, 8, 1, 6, 4,
0, 6, 2, 5, 1, 1, 1, 0, 2, 2, 3, 0, 2, 4, 6, 2, 5, 1, 5, 6, 5, 4, 0, 4,
2, 3, 6, 3, 1, 6, 6, 8, 0, 9, 0, 8, 2, 0, 3, 1, 2, 5, 5, 5, 5, 1, 1, 1,
5, 1, 2, 3, 1, 2, 5, 7, 8, 2, 7, 0, 2, 1, 1, 8, 1, 5, 8, 3, 4, 0, 4, 5,
4, 1, 0, 1, 5, 6, 2, 5, 2, 7, 7, 5, 5, 5, 7, 5, 6, 1, 5, 6, 2, 8, 9, 1,
3, 5, 1, 0, 5, 9, 0, 7, 9, 1, 7, 0, 2, 2, 7, 0, 5, 0, 7, 8, 1, 2, 5, 1,
3, 8, 7, 7, 7, 8, 7, 8, 0, 7, 8, 1, 4, 4, 5, 6, 7, 5, 5, 2, 9, 5, 3, 9,
5, 8, 5, 1, 1, 3, 5, 2, 5, 3, 9, 0, 6, 2, 5, 6, 9, 3, 8, 8, 9, 3, 9, 0,
3, 9, 0, 7, 2, 2, 8, 3, 7, 7, 6, 4, 7, 6, 9, 7, 9, 2, 5, 5, 6, 7, 6, 2,
6, 9, 5, 3, 1, 2, 5, 3, 4, 6, 9, 4, 4, 6, 9, 5, 1, 9, 5, 3, 6, 1, 4, 1,
8, 8, 8, 2, 3, 8, 4, 8, 9, 6, 2, 7, 8, 3, 8, 1, 3, 4, 7, 6, 5, 6, 2, 5,
1, 7, 3, 4, 7, 2, 3, 4, 7, 5, 9, 7, 6, 8, 0, 7, 0, 9, 4, 4, 1, 1, 9, 2,
4, 4, 8, 1, 3, 9, 1, 9, 0, 6, 7, 3, 8, 2, 8, 1, 2, 5, 8, 6, 7, 3, 6, 1,
7, 3, 7, 9, 8, 8, 4, 0, 3, 5, 4, 7, 2, 0, 5, 9, 6, 2, 2, 4, 0, 6, 9, 5,
9, 5, 3, 3, 6, 9, 1, 4, 0, 6, 2, 5,
};
const uint8_t *pow5 =
&number_of_digits_decimal_left_shift_table_powers_of_5[pow5_a];
uint32_t i = 0;
uint32_t n = pow5_b - pow5_a;
for (; i < n; i++) {
if (i >= h.num_digits) {
return num_new_digits - 1;
} else if (h.digits[i] == pow5[i]) {
continue;
} else if (h.digits[i] < pow5[i]) {
return num_new_digits - 1;
} else {
return num_new_digits;
}
}
return num_new_digits;
}
inline uint64_t round(decimal &h) {
if ((h.num_digits == 0) || (h.decimal_point < 0)) {
return 0;
} else if (h.decimal_point > 18) {
return UINT64_MAX;
}
// at this point, we know that h.decimal_point >= 0
uint32_t dp = uint32_t(h.decimal_point);
uint64_t n = 0;
for (uint32_t i = 0; i < dp; i++) {
n = (10 * n) + ((i < h.num_digits) ? h.digits[i] : 0);
}
bool round_up = false;
if (dp < h.num_digits) {
round_up = h.digits[dp] >= 5; // normally, we round up
// but we may need to round to even!
if ((h.digits[dp] == 5) && (dp + 1 == h.num_digits)) {
round_up = h.truncated || ((dp > 0) && (1 & h.digits[dp - 1]));
}
}
if (round_up) {
n++;
}
return n;
}
// computes h * 2^-shift
inline void decimal_left_shift(decimal &h, uint32_t shift) {
if (h.num_digits == 0) {
return;
}
uint32_t num_new_digits = number_of_digits_decimal_left_shift(h, shift);
int32_t read_index = int32_t(h.num_digits - 1);
uint32_t write_index = h.num_digits - 1 + num_new_digits;
uint64_t n = 0;
while (read_index >= 0) {
n += uint64_t(h.digits[read_index]) << shift;
uint64_t quotient = n / 10;
uint64_t remainder = n - (10 * quotient);
if (write_index < max_digits) {
h.digits[write_index] = uint8_t(remainder);
} else if (remainder > 0) {
h.truncated = true;
}
n = quotient;
write_index--;
read_index--;
}
while (n > 0) {
uint64_t quotient = n / 10;
uint64_t remainder = n - (10 * quotient);
if (write_index < max_digits) {
h.digits[write_index] = uint8_t(remainder);
} else if (remainder > 0) {
h.truncated = true;
}
n = quotient;
write_index--;
}
h.num_digits += num_new_digits;
if (h.num_digits > max_digits) {
h.num_digits = max_digits;
}
h.decimal_point += int32_t(num_new_digits);
trim(h);
}
// computes h * 2^shift
inline void decimal_right_shift(decimal &h, uint32_t shift) {
uint32_t read_index = 0;
uint32_t write_index = 0;
uint64_t n = 0;
while ((n >> shift) == 0) {
if (read_index < h.num_digits) {
n = (10 * n) + h.digits[read_index++];
} else if (n == 0) {
return;
} else {
while ((n >> shift) == 0) {
n = 10 * n;
read_index++;
}
break;
}
}
h.decimal_point -= int32_t(read_index - 1);
if (h.decimal_point < -decimal_point_range) { // it is zero
h.num_digits = 0;
h.decimal_point = 0;
h.negative = false;
h.truncated = false;
return;
}
uint64_t mask = (uint64_t(1) << shift) - 1;
while (read_index < h.num_digits) {
uint8_t new_digit = uint8_t(n >> shift);
n = (10 * (n & mask)) + h.digits[read_index++];
h.digits[write_index++] = new_digit;
}
while (n > 0) {
uint8_t new_digit = uint8_t(n >> shift);
n = 10 * (n & mask);
if (write_index < max_digits) {
h.digits[write_index++] = new_digit;
} else if (new_digit > 0) {
h.truncated = true;
}
}
h.num_digits = write_index;
trim(h);
}
} // namespace detail
template <typename binary>
adjusted_mantissa compute_float(decimal &d) {
adjusted_mantissa answer;
if (d.num_digits == 0) {
// should be zero
answer.power2 = 0;
answer.mantissa = 0;
return answer;
}
// At this point, going further, we can assume that d.num_digits > 0.
//
// We want to guard against excessive decimal point values because
// they can result in long running times. Indeed, we do
// shifts by at most 60 bits. We have that log(10**400)/log(2**60) ~= 22
// which is fine, but log(10**299995)/log(2**60) ~= 16609 which is not
// fine (runs for a long time).
//
if(d.decimal_point < -324) {
// We have something smaller than 1e-324 which is always zero
// in binary64 and binary32.
// It should be zero.
answer.power2 = 0;
answer.mantissa = 0;
return answer;
} else if(d.decimal_point >= 310) {
// We have something at least as large as 0.1e310 which is
// always infinite.
answer.power2 = binary::infinite_power();
answer.mantissa = 0;
return answer;
}
static const uint32_t max_shift = 60;
static const uint32_t num_powers = 19;
static const uint8_t decimal_powers[19] = {
0, 3, 6, 9, 13, 16, 19, 23, 26, 29, //
33, 36, 39, 43, 46, 49, 53, 56, 59, //
};
int32_t exp2 = 0;
while (d.decimal_point > 0) {
uint32_t n = uint32_t(d.decimal_point);
uint32_t shift = (n < num_powers) ? decimal_powers[n] : max_shift;
detail::decimal_right_shift(d, shift);
if (d.decimal_point < -decimal_point_range) {
// should be zero
answer.power2 = 0;
answer.mantissa = 0;
return answer;
}
exp2 += int32_t(shift);
}
// We shift left toward [1/2 ... 1].
while (d.decimal_point <= 0) {
uint32_t shift;
if (d.decimal_point == 0) {
if (d.digits[0] >= 5) {
break;
}
shift = (d.digits[0] < 2) ? 2 : 1;
} else {
uint32_t n = uint32_t(-d.decimal_point);
shift = (n < num_powers) ? decimal_powers[n] : max_shift;
}
detail::decimal_left_shift(d, shift);
if (d.decimal_point > decimal_point_range) {
// we want to get infinity:
answer.power2 = binary::infinite_power();
answer.mantissa = 0;
return answer;
}
exp2 -= int32_t(shift);
}
// We are now in the range [1/2 ... 1] but the binary format uses [1 ... 2].
exp2--;
constexpr int32_t minimum_exponent = binary::minimum_exponent();
while ((minimum_exponent + 1) > exp2) {
uint32_t n = uint32_t((minimum_exponent + 1) - exp2);
if (n > max_shift) {
n = max_shift;
}
detail::decimal_right_shift(d, n);
exp2 += int32_t(n);
}
if ((exp2 - minimum_exponent) >= binary::infinite_power()) {
answer.power2 = binary::infinite_power();
answer.mantissa = 0;
return answer;
}
const int mantissa_size_in_bits = binary::mantissa_explicit_bits() + 1;
detail::decimal_left_shift(d, mantissa_size_in_bits);
uint64_t mantissa = detail::round(d);
// It is possible that we have an overflow, in which case we need
// to shift back.
if(mantissa >= (uint64_t(1) << mantissa_size_in_bits)) {
detail::decimal_right_shift(d, 1);
exp2 += 1;
mantissa = detail::round(d);
if ((exp2 - minimum_exponent) >= binary::infinite_power()) {
answer.power2 = binary::infinite_power();
answer.mantissa = 0;
return answer;
}
}
answer.power2 = exp2 - binary::minimum_exponent();
if(mantissa < (uint64_t(1) << binary::mantissa_explicit_bits())) { answer.power2--; }
answer.mantissa = mantissa & ((uint64_t(1) << binary::mantissa_explicit_bits()) - 1);
return answer;
}
template <typename binary>
adjusted_mantissa parse_long_mantissa(const char *first, const char* last, parse_options options) {
decimal d = parse_decimal(first, last, options);
return compute_float<binary>(d);
}
} // namespace fast_float
#endif
#ifndef FASTFLOAT_PARSE_NUMBER_H
#define FASTFLOAT_PARSE_NUMBER_H
#include <cassert>
#include <cmath>
#include <cstring>
#include <limits>
#include <system_error>
namespace fast_float {
namespace detail {
/**
* Special case +inf, -inf, nan, infinity, -infinity.
* The case comparisons could be made much faster given that we know that the
* strings a null-free and fixed.
**/
template <typename T>
from_chars_result parse_infnan(const char *first, const char *last, T &value) noexcept {
from_chars_result answer;
answer.ptr = first;
answer.ec = std::errc(); // be optimistic
bool minusSign = false;
if (*first == '-') { // assume first < last, so dereference without checks; C++17 20.19.3.(7.1) explicitly forbids '+' here
minusSign = true;
++first;
}
if (last - first >= 3) {
if (fastfloat_strncasecmp(first, "nan", 3)) {
answer.ptr = (first += 3);
value = minusSign ? -std::numeric_limits<T>::quiet_NaN() : std::numeric_limits<T>::quiet_NaN();
// Check for possible nan(n-char-seq-opt), C++17 20.19.3.7, C11 7.20.1.3.3. At least MSVC produces nan(ind) and nan(snan).
if(first != last && *first == '(') {
for(const char* ptr = first + 1; ptr != last; ++ptr) {
if (*ptr == ')') {
answer.ptr = ptr + 1; // valid nan(n-char-seq-opt)
break;
}
else if(!(('a' <= *ptr && *ptr <= 'z') || ('A' <= *ptr && *ptr <= 'Z') || ('0' <= *ptr && *ptr <= '9') || *ptr == '_'))
break; // forbidden char, not nan(n-char-seq-opt)
}
}
return answer;
}
if (fastfloat_strncasecmp(first, "inf", 3)) {
if ((last - first >= 8) && fastfloat_strncasecmp(first + 3, "inity", 5)) {
answer.ptr = first + 8;
} else {
answer.ptr = first + 3;
}
value = minusSign ? -std::numeric_limits<T>::infinity() : std::numeric_limits<T>::infinity();
return answer;
}
}
answer.ec = std::errc::invalid_argument;
return answer;
}
template<typename T>
fastfloat_really_inline void to_float(bool negative, adjusted_mantissa am, T &value) {
uint64_t word = am.mantissa;
word |= uint64_t(am.power2) << binary_format<T>::mantissa_explicit_bits();
word = negative
? word | (uint64_t(1) << binary_format<T>::sign_index()) : word;
#if FASTFLOAT_IS_BIG_ENDIAN == 1
if (std::is_same<T, float>::value) {
::memcpy(&value, (char *)&word + 4, sizeof(T)); // extract value at offset 4-7 if float on big-endian
} else {
::memcpy(&value, &word, sizeof(T));
}
#else
// For little-endian systems:
::memcpy(&value, &word, sizeof(T));
#endif
}
} // namespace detail
template<typename T>
from_chars_result from_chars(const char *first, const char *last,
T &value, chars_format fmt /*= chars_format::general*/) noexcept {
return from_chars_advanced(first, last, value, parse_options{fmt});
}
template<typename T>
from_chars_result from_chars_advanced(const char *first, const char *last,
T &value, parse_options options) noexcept {
static_assert (std::is_same<T, double>::value || std::is_same<T, float>::value, "only float and double are supported");
from_chars_result answer;
if (first == last) {
answer.ec = std::errc::invalid_argument;
answer.ptr = first;
return answer;
}
parsed_number_string pns = parse_number_string(first, last, options);
if (!pns.valid) {
return detail::parse_infnan(first, last, value);
}
answer.ec = std::errc(); // be optimistic
answer.ptr = pns.lastmatch;
// Next is Clinger's fast path.
if (binary_format<T>::min_exponent_fast_path() <= pns.exponent && pns.exponent <= binary_format<T>::max_exponent_fast_path() && pns.mantissa <=binary_format<T>::max_mantissa_fast_path() && !pns.too_many_digits) {
value = T(pns.mantissa);
if (pns.exponent < 0) { value = value / binary_format<T>::exact_power_of_ten(-pns.exponent); }
else { value = value * binary_format<T>::exact_power_of_ten(pns.exponent); }
if (pns.negative) { value = -value; }
return answer;
}
adjusted_mantissa am = compute_float<binary_format<T>>(pns.exponent, pns.mantissa);
if(pns.too_many_digits) {
if(am != compute_float<binary_format<T>>(pns.exponent, pns.mantissa + 1)) {
am.power2 = -1; // value is invalid.
}
}
// If we called compute_float<binary_format<T>>(pns.exponent, pns.mantissa) and we have an invalid power (am.power2 < 0),
// then we need to go the long way around again. This is very uncommon.
if(am.power2 < 0) { am = parse_long_mantissa<binary_format<T>>(first, last, options); }
detail::to_float(pns.negative, am, value);
return answer;
}
} // namespace fast_float
#endif