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Daniel Lemire
João Paulo Magalhaes

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add_library(fast_float INTERFACE)
target_include_directories(fast_float INTERFACE "${CMAKE_CURRENT_SOURCE_DIR}/include")

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Eugene Golushkov
Maksim Kita
Marcin Wojdyr
Neal Richardson
Tim Paine
Fabio Pellacini
Lénárd Szolnoki
Jan Pharago
Maya Warrier
Taha Khokhar

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## fast_float number parsing library: 4x faster than strtod
[![Fuzzing Status](https://oss-fuzz-build-logs.storage.googleapis.com/badges/fast_float.svg)](https://bugs.chromium.org/p/oss-fuzz/issues/list?sort=-opened&can=1&q=proj:fast_float)
[![Ubuntu 22.04 CI (GCC 11)](https://github.com/fastfloat/fast_float/actions/workflows/ubuntu22.yml/badge.svg)](https://github.com/fastfloat/fast_float/actions/workflows/ubuntu22.yml)
The fast_float library provides fast header-only implementations for the C++ from_chars
functions for `float` and `double` types as well as integer types. These functions convert ASCII strings representing decimal values (e.g., `1.3e10`) into binary types. We provide exact rounding (including
round to even). In our experience, these `fast_float` functions many times faster than comparable number-parsing functions from existing C++ standard libraries.
Specifically, `fast_float` provides the following two functions to parse floating-point numbers with a C++17-like syntax (the library itself only requires C++11):
```C++
from_chars_result from_chars(const char* first, const char* last, float& value, ...);
from_chars_result from_chars(const char* first, const char* last, double& value, ...);
```
You can also parse integer types:
The return type (`from_chars_result`) is defined as the struct:
```C++
struct from_chars_result {
const char* ptr;
std::errc ec;
};
```
It parses the character sequence [first,last) for a number. It parses floating-point numbers expecting
a locale-independent format equivalent to the C++17 from_chars function.
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`).
It will parse infinity and nan values.
Example:
``` C++
#include "fast_float/fast_float.h"
#include <iostream>
int main() {
const std::string input = "3.1416 xyz ";
double result;
auto answer = fast_float::from_chars(input.data(), input.data()+input.size(), result);
if(answer.ec != std::errc()) { std::cerr << "parsing failure\n"; return EXIT_FAILURE; }
std::cout << "parsed the number " << result << std::endl;
return EXIT_SUCCESS;
}
```
You can parse delimited numbers:
```C++
const std::string input = "234532.3426362,7869234.9823,324562.645";
double result;
auto answer = fast_float::from_chars(input.data(), input.data()+input.size(), result);
if(answer.ec != std::errc()) {
// check error
}
// we have result == 234532.3426362.
if(answer.ptr[0] != ',') {
// unexpected delimiter
}
answer = fast_float::from_chars(answer.ptr + 1, input.data()+input.size(), result);
if(answer.ec != std::errc()) {
// check error
}
// we have result == 7869234.9823.
if(answer.ptr[0] != ',') {
// unexpected delimiter
}
answer = fast_float::from_chars(answer.ptr + 1, input.data()+input.size(), result);
if(answer.ec != std::errc()) {
// check error
}
// we have result == 324562.645.
```
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 allow the fixed point and scientific notation respectively.
The default is `fast_float::chars_format::general` which allows both `fixed` and `scientific`.
The library seeks to follow the C++17 (see [20.19.3](http://eel.is/c++draft/charconv.from.chars).(7.1)) specification.
* The `from_chars` function does not skip leading white-space characters.
* [A leading `+` sign](https://en.cppreference.com/w/cpp/utility/from_chars) is forbidden.
* It is generally impossible to represent a decimal value exactly as binary floating-point number (`float` and `double` types). We seek the nearest value. We round to an even mantissa when we are in-between two binary floating-point numbers.
Furthermore, we have the following restrictions:
* We only support `float` and `double` types at this time.
* We only support the decimal format: we do not support hexadecimal strings.
* For values that are either very large or very small (e.g., `1e9999`), we represent it using the infinity or negative infinity value and the returned `ec` is set to `std::errc::result_out_of_range`.
We support Visual Studio, macOS, Linux, freeBSD. We support big and little endian. We support 32-bit and 64-bit systems.
We assume that the rounding mode is set to nearest (`std::fegetround() == FE_TONEAREST`).
## Integer types
You can also parse integer types using different bases (e.g., 2, 10, 16). The following code will
print the number 22250738585072012 three times:
```C++
uint64_t i;
const char str[] = "22250738585072012";
auto answer = fast_float::from_chars(str, str + strlen(str), i);
if (answer.ec != std::errc()) {
std::cerr << "parsing failure\n";
return EXIT_FAILURE;
}
std::cout << "parsed the number "<< i << std::endl;
const char binstr[] = "1001111000011001110110111001001010110100111000110001100";
answer = fast_float::from_chars(binstr, binstr + strlen(binstr), i, 2);
if (answer.ec != std::errc()) {
std::cerr << "parsing failure\n";
return EXIT_FAILURE;
}
std::cout << "parsed the number "<< i << std::endl;
const char hexstr[] = "4f0cedc95a718c";
answer = fast_float::from_chars(hexstr, hexstr + strlen(hexstr), i, 16);
if (answer.ec != std::errc()) {
std::cerr << "parsing failure\n";
return EXIT_FAILURE;
}
std::cout << "parsed the number "<< i << std::endl;
```
## C++20: compile-time evaluation (constexpr)
In C++20, you may use `fast_float::from_chars` to parse strings
at compile-time, as in the following example:
```C++
// consteval forces compile-time evaluation of the function in C++20.
consteval double parse(std::string_view input) {
double result;
auto answer = fast_float::from_chars(input.data(), input.data()+input.size(), result);
if(answer.ec != std::errc()) { return -1.0; }
return result;
}
// This function should compile to a function which
// merely returns 3.1415.
constexpr double constexptest() {
return parse("3.1415 input");
}
```
## C++23: Fixed width floating-point types
The library also supports fixed-width floating-point types such as `std::float32_t` and `std::float64_t`. E.g., you can write:
```C++
std::float32_t result;
auto answer = fast_float::from_chars(f.data(), f.data() + f.size(), result);
``````
## Non-ASCII Inputs
We also support UTF-16 and UTF-32 inputs, as well as ASCII/UTF-8, as in the following example:
``` C++
#include "fast_float/fast_float.h"
#include <iostream>
int main() {
const std::u16string input = u"3.1416 xyz ";
double result;
auto answer = fast_float::from_chars(input.data(), input.data()+input.size(), result);
if(answer.ec != std::errc()) { std::cerr << "parsing failure\n"; return EXIT_FAILURE; }
std::cout << "parsed the number " << result << std::endl;
return EXIT_SUCCESS;
}
```
## Advanced options: using commas as decimal separator, JSON and Fortran
The C++ standard stipulate that `from_chars` has to be locale-independent. In
particular, the decimal separator has to be the period (`.`). However,
some users still want to use the `fast_float` library with in a locale-dependent
manner. Using a separate function called `from_chars_advanced`, we allow the users
to pass a `parse_options` instance which contains a custom decimal separator (e.g.,
the comma). You may use it as follows.
```C++
#include "fast_float/fast_float.h"
#include <iostream>
int main() {
const std::string input = "3,1416 xyz ";
double result;
fast_float::parse_options options{fast_float::chars_format::general, ','};
auto answer = fast_float::from_chars_advanced(input.data(), input.data()+input.size(), result, options);
if((answer.ec != std::errc()) || ((result != 3.1416))) { std::cerr << "parsing failure\n"; return EXIT_FAILURE; }
std::cout << "parsed the number " << result << std::endl;
return EXIT_SUCCESS;
}
```
You can also parse Fortran-like inputs:
```C++
#include "fast_float/fast_float.h"
#include <iostream>
int main() {
const std::string input = "1d+4";
double result;
fast_float::parse_options options{ fast_float::chars_format::fortran };
auto answer = fast_float::from_chars_advanced(input.data(), input.data()+input.size(), result, options);
if((answer.ec != std::errc()) || ((result != 10000))) { std::cerr << "parsing failure\n"; return EXIT_FAILURE; }
std::cout << "parsed the number " << result << std::endl;
return EXIT_SUCCESS;
}
```
You may also enforce the JSON format ([RFC 8259](https://datatracker.ietf.org/doc/html/rfc8259#section-6)):
```C++
#include "fast_float/fast_float.h"
#include <iostream>
int main() {
const std::string input = "+.1"; // not valid
double result;
fast_float::parse_options options{ fast_float::chars_format::json };
auto answer = fast_float::from_chars_advanced(input.data(), input.data()+input.size(), result, options);
if(answer.ec == std::errc()) { std::cerr << "should have failed\n"; return EXIT_FAILURE; }
return EXIT_SUCCESS;
}
```
By default the JSON format does not allow `inf`:
```C++
#include "fast_float/fast_float.h"
#include <iostream>
int main() {
const std::string input = "inf"; // not valid in JSON
double result;
fast_float::parse_options options{ fast_float::chars_format::json };
auto answer = fast_float::from_chars_advanced(input.data(), input.data()+input.size(), result, options);
if(answer.ec == std::errc()) { std::cerr << "should have failed\n"; return EXIT_FAILURE; }
}
```
You can allow it with a non-standard `json_or_infnan` variant:
```C++
#include "fast_float/fast_float.h"
#include <iostream>
int main() {
const std::string input = "inf"; // not valid in JSON but we allow it with json_or_infnan
double result;
fast_float::parse_options options{ fast_float::chars_format::json_or_infnan };
auto answer = fast_float::from_chars_advanced(input.data(), input.data()+input.size(), result, options);
if(answer.ec != std::errc() || (!std::isinf(result))) { std::cerr << "should have parsed infinity\n"; return EXIT_FAILURE; }
return EXIT_SUCCESS;
}
``````
## Relation With Other Work
The fast_float library is part of:
- GCC (as of version 12): the `from_chars` function in GCC relies on fast_float.
- [WebKit](https://github.com/WebKit/WebKit), the engine behind Safari (Apple's web browser)
The fastfloat algorithm is part of the [LLVM standard libraries](https://github.com/llvm/llvm-project/commit/87c016078ad72c46505461e4ff8bfa04819fe7ba).
There is a [derived implementation part of AdaCore](https://github.com/AdaCore/VSS).
The fast_float library provides a performance similar to that of the [fast_double_parser](https://github.com/lemire/fast_double_parser) library but using an updated algorithm reworked from the ground up, and while offering an API more in line with the expectations of C++ programmers. The fast_double_parser library is part of the [Microsoft LightGBM machine-learning framework](https://github.com/microsoft/LightGBM).
## References
- Daniel Lemire, [Number Parsing at a Gigabyte per Second](https://arxiv.org/abs/2101.11408), Software: Practice and Experience 51 (8), 2021.
- Noble Mushtak, Daniel Lemire, [Fast Number Parsing Without Fallback](https://arxiv.org/abs/2212.06644), Software: Practice and Experience 53 (7), 2023.
## Other programming languages
- [There is an R binding](https://github.com/eddelbuettel/rcppfastfloat) called `rcppfastfloat`.
- [There is a Rust port of the fast_float library](https://github.com/aldanor/fast-float-rust/) called `fast-float-rust`.
- [There is a Java port of the fast_float library](https://github.com/wrandelshofer/FastDoubleParser) called `FastDoubleParser`. It used for important systems such as [Jackson](https://github.com/FasterXML/jackson-core).
- [There is a C# port of the fast_float library](https://github.com/CarlVerret/csFastFloat) called `csFastFloat`.
## Users
The fast_float library is used by [Apache Arrow](https://github.com/apache/arrow/pull/8494) where it multiplied the number parsing speed by two or three times. It is also used by [ClickHouse](https://github.com/ClickHouse/ClickHouse) and by [Google Jsonnet](https://github.com/google/jsonnet). It is part of GCC (as of GCC 12). It is part of WebKit (Safari).
## How fast is it?
It can parse random floating-point numbers at a speed of 1 GB/s on some systems. We find that it is often twice as fast as the best available competitor, and many times faster than many standard-library implementations.
<img src="http://lemire.me/blog/wp-content/uploads/2020/11/fastfloat_speed.png" width="400">
```
$ ./build/benchmarks/benchmark
# parsing random integers in the range [0,1)
volume = 2.09808 MB
netlib : 271.18 MB/s (+/- 1.2 %) 12.93 Mfloat/s
doubleconversion : 225.35 MB/s (+/- 1.2 %) 10.74 Mfloat/s
strtod : 190.94 MB/s (+/- 1.6 %) 9.10 Mfloat/s
abseil : 430.45 MB/s (+/- 2.2 %) 20.52 Mfloat/s
fastfloat : 1042.38 MB/s (+/- 9.9 %) 49.68 Mfloat/s
```
See https://github.com/lemire/simple_fastfloat_benchmark for our benchmarking code.
## Video
[![Go Systems 2020](http://img.youtube.com/vi/AVXgvlMeIm4/0.jpg)](http://www.youtube.com/watch?v=AVXgvlMeIm4)<br />
## Using as a CMake dependency
This library is header-only by design. The CMake file provides the `fast_float` target
which is merely a pointer to the `include` directory.
If you drop the `fast_float` repository in your CMake project, you should be able to use
it in this manner:
```cmake
add_subdirectory(fast_float)
target_link_libraries(myprogram PUBLIC fast_float)
```
Or you may want to retrieve the dependency automatically if you have a sufficiently recent version of CMake (3.11 or better at least):
```cmake
FetchContent_Declare(
fast_float
GIT_REPOSITORY https://github.com/lemire/fast_float.git
GIT_TAG tags/v1.1.2
GIT_SHALLOW TRUE)
FetchContent_MakeAvailable(fast_float)
target_link_libraries(myprogram PUBLIC fast_float)
```
You should change the `GIT_TAG` line so that you recover the version you wish to use.
## Using as single header
The script `script/amalgamate.py` may be used to generate a single header
version of the library if so desired.
Just run the script from the root directory of this repository.
You can customize the license type and output file if desired as described in
the command line help.
You may directly download automatically generated single-header files:
https://github.com/fastfloat/fast_float/releases/download/v6.1.1/fast_float.h
## RFC 7159
If you need support for RFC 7159 (JSON standard), you may want to consider using the [fast_double_parser](https://github.com/lemire/fast_double_parser/) library instead.
## Credit
Though this work is inspired by many different people, this work benefited especially from exchanges with
Michael Eisel, who motivated the original research with his key insights, and with Nigel Tao who provided
invaluable feedback. Rémy Oudompheng first implemented a fast path we use in the case of long digits.
The library includes code adapted from Google Wuffs (written by Nigel Tao) which was originally published
under the Apache 2.0 license.
## License
<sup>
Licensed under either of <a href="LICENSE-APACHE">Apache License, Version
2.0</a> or <a href="LICENSE-MIT">MIT license</a> or <a href="LICENSE-BOOST">BOOST license</a> .
</sup>
<br>
<sub>
Unless you explicitly state otherwise, any contribution intentionally submitted
for inclusion in this repository by you, as defined in the Apache-2.0 license,
shall be triple licensed as above, without any additional terms or conditions.
</sub>

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#ifndef FASTFLOAT_ASCII_NUMBER_H
#define FASTFLOAT_ASCII_NUMBER_H
#include <cctype>
#include <cstdint>
#include <cstring>
#include <iterator>
#include <limits>
#include <type_traits>
#include "float_common.h"
#ifdef FASTFLOAT_SSE2
#include <emmintrin.h>
#endif
#ifdef FASTFLOAT_NEON
#include <arm_neon.h>
#endif
namespace fast_float {
template <typename UC>
fastfloat_really_inline constexpr bool has_simd_opt() {
#ifdef FASTFLOAT_HAS_SIMD
return std::is_same<UC, char16_t>::value;
#else
return false;
#endif
}
// Next function can be micro-optimized, but compilers are entirely
// able to optimize it well.
template <typename UC>
fastfloat_really_inline constexpr bool is_integer(UC c) noexcept {
return !(c > UC('9') || c < UC('0'));
}
fastfloat_really_inline constexpr 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;
}
// Read 8 UC into a u64. Truncates UC if not char.
template <typename UC>
fastfloat_really_inline FASTFLOAT_CONSTEXPR20
uint64_t read8_to_u64(const UC *chars) {
if (cpp20_and_in_constexpr() || !std::is_same<UC, char>::value) {
uint64_t val = 0;
for(int i = 0; i < 8; ++i) {
val |= uint64_t(uint8_t(*chars)) << (i*8);
++chars;
}
return val;
}
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;
}
#ifdef FASTFLOAT_SSE2
fastfloat_really_inline
uint64_t simd_read8_to_u64(const __m128i data) {
FASTFLOAT_SIMD_DISABLE_WARNINGS
const __m128i packed = _mm_packus_epi16(data, data);
#ifdef FASTFLOAT_64BIT
return uint64_t(_mm_cvtsi128_si64(packed));
#else
uint64_t value;
// Visual Studio + older versions of GCC don't support _mm_storeu_si64
_mm_storel_epi64(reinterpret_cast<__m128i*>(&value), packed);
return value;
#endif
FASTFLOAT_SIMD_RESTORE_WARNINGS
}
fastfloat_really_inline
uint64_t simd_read8_to_u64(const char16_t* chars) {
FASTFLOAT_SIMD_DISABLE_WARNINGS
return simd_read8_to_u64(_mm_loadu_si128(reinterpret_cast<const __m128i*>(chars)));
FASTFLOAT_SIMD_RESTORE_WARNINGS
}
#elif defined(FASTFLOAT_NEON)
fastfloat_really_inline
uint64_t simd_read8_to_u64(const uint16x8_t data) {
FASTFLOAT_SIMD_DISABLE_WARNINGS
uint8x8_t utf8_packed = vmovn_u16(data);
return vget_lane_u64(vreinterpret_u64_u8(utf8_packed), 0);
FASTFLOAT_SIMD_RESTORE_WARNINGS
}
fastfloat_really_inline
uint64_t simd_read8_to_u64(const char16_t* chars) {
FASTFLOAT_SIMD_DISABLE_WARNINGS
return simd_read8_to_u64(vld1q_u16(reinterpret_cast<const uint16_t*>(chars)));
FASTFLOAT_SIMD_RESTORE_WARNINGS
}
#endif // FASTFLOAT_SSE2
// MSVC SFINAE is broken pre-VS2017
#if defined(_MSC_VER) && _MSC_VER <= 1900
template <typename UC>
#else
template <typename UC, FASTFLOAT_ENABLE_IF(!has_simd_opt<UC>()) = 0>
#endif
// dummy for compile
uint64_t simd_read8_to_u64(UC const*) {
return 0;
}
fastfloat_really_inline FASTFLOAT_CONSTEXPR20
void write_u64(uint8_t *chars, uint64_t val) {
if (cpp20_and_in_constexpr()) {
for(int i = 0; i < 8; ++i) {
*chars = uint8_t(val);
val >>= 8;
++chars;
}
return;
}
#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 FASTFLOAT_CONSTEXPR14
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);
}
// Call this if chars are definitely 8 digits.
template <typename UC>
fastfloat_really_inline FASTFLOAT_CONSTEXPR20
uint32_t parse_eight_digits_unrolled(UC const * chars) noexcept {
if (cpp20_and_in_constexpr() || !has_simd_opt<UC>()) {
return parse_eight_digits_unrolled(read8_to_u64(chars)); // truncation okay
}
return parse_eight_digits_unrolled(simd_read8_to_u64(chars));
}
// credit @aqrit
fastfloat_really_inline constexpr bool is_made_of_eight_digits_fast(uint64_t val) noexcept {
return !((((val + 0x4646464646464646) | (val - 0x3030303030303030)) &
0x8080808080808080));
}
#ifdef FASTFLOAT_HAS_SIMD
// Call this if chars might not be 8 digits.
// Using this style (instead of is_made_of_eight_digits_fast() then parse_eight_digits_unrolled())
// ensures we don't load SIMD registers twice.
fastfloat_really_inline FASTFLOAT_CONSTEXPR20
bool simd_parse_if_eight_digits_unrolled(const char16_t* chars, uint64_t& i) noexcept {
if (cpp20_and_in_constexpr()) {
return false;
}
#ifdef FASTFLOAT_SSE2
FASTFLOAT_SIMD_DISABLE_WARNINGS
const __m128i data = _mm_loadu_si128(reinterpret_cast<const __m128i*>(chars));
// (x - '0') <= 9
// http://0x80.pl/articles/simd-parsing-int-sequences.html
const __m128i t0 = _mm_add_epi16(data, _mm_set1_epi16(32720));
const __m128i t1 = _mm_cmpgt_epi16(t0, _mm_set1_epi16(-32759));
if (_mm_movemask_epi8(t1) == 0) {
i = i * 100000000 + parse_eight_digits_unrolled(simd_read8_to_u64(data));
return true;
}
else return false;
FASTFLOAT_SIMD_RESTORE_WARNINGS
#elif defined(FASTFLOAT_NEON)
FASTFLOAT_SIMD_DISABLE_WARNINGS
const uint16x8_t data = vld1q_u16(reinterpret_cast<const uint16_t*>(chars));
// (x - '0') <= 9
// http://0x80.pl/articles/simd-parsing-int-sequences.html
const uint16x8_t t0 = vsubq_u16(data, vmovq_n_u16('0'));
const uint16x8_t mask = vcltq_u16(t0, vmovq_n_u16('9' - '0' + 1));
if (vminvq_u16(mask) == 0xFFFF) {
i = i * 100000000 + parse_eight_digits_unrolled(simd_read8_to_u64(data));
return true;
}
else return false;
FASTFLOAT_SIMD_RESTORE_WARNINGS
#else
(void)chars; (void)i;
return false;
#endif // FASTFLOAT_SSE2
}
#endif // FASTFLOAT_HAS_SIMD
// MSVC SFINAE is broken pre-VS2017
#if defined(_MSC_VER) && _MSC_VER <= 1900
template <typename UC>
#else
template <typename UC, FASTFLOAT_ENABLE_IF(!has_simd_opt<UC>()) = 0>
#endif
// dummy for compile
bool simd_parse_if_eight_digits_unrolled(UC const*, uint64_t&) {
return 0;
}
template <typename UC, FASTFLOAT_ENABLE_IF(!std::is_same<UC, char>::value) = 0>
fastfloat_really_inline FASTFLOAT_CONSTEXPR20
void loop_parse_if_eight_digits(const UC*& p, const UC* const pend, uint64_t& i) {
if (!has_simd_opt<UC>()) {
return;
}
while ((std::distance(p, pend) >= 8) && simd_parse_if_eight_digits_unrolled(p, i)) { // in rare cases, this will overflow, but that's ok
p += 8;
}
}
fastfloat_really_inline FASTFLOAT_CONSTEXPR20
void loop_parse_if_eight_digits(const char*& p, const char* const pend, uint64_t& i) {
// optimizes better than parse_if_eight_digits_unrolled() for UC = char.
while ((std::distance(p, pend) >= 8) && is_made_of_eight_digits_fast(read8_to_u64(p))) {
i = i * 100000000 + parse_eight_digits_unrolled(read8_to_u64(p)); // in rare cases, this will overflow, but that's ok
p += 8;
}
}
template <typename UC>
struct parsed_number_string_t {
int64_t exponent{0};
uint64_t mantissa{0};
UC const * lastmatch{nullptr};
bool negative{false};
bool valid{false};
bool too_many_digits{false};
// contains the range of the significant digits
span<const UC> integer{}; // non-nullable
span<const UC> fraction{}; // nullable
};
using byte_span = span<const char>;
using parsed_number_string = parsed_number_string_t<char>;
// Assuming that you use no more than 19 digits, this will
// parse an ASCII string.
template <typename UC>
fastfloat_really_inline FASTFLOAT_CONSTEXPR20
parsed_number_string_t<UC> parse_number_string(UC const *p, UC const * pend, parse_options_t<UC> options) noexcept {
chars_format const fmt = options.format;
UC const decimal_point = options.decimal_point;
parsed_number_string_t<UC> answer;
answer.valid = false;
answer.too_many_digits = false;
answer.negative = (*p == UC('-'));
#ifdef FASTFLOAT_ALLOWS_LEADING_PLUS // disabled by default
if ((*p == UC('-')) || (!(fmt & FASTFLOAT_JSONFMT) && *p == UC('+'))) {
#else
if (*p == UC('-')) { // C++17 20.19.3.(7.1) explicitly forbids '+' sign here
#endif
++p;
if (p == pend) {
return answer;
}
if (fmt & FASTFLOAT_JSONFMT) {
if (!is_integer(*p)) { // a sign must be followed by an integer
return answer;
}
} else {
if (!is_integer(*p) && (*p != decimal_point)) { // a sign must be followed by an integer or the dot
return answer;
}
}
}
UC const * 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 - UC('0')); // might overflow, we will handle the overflow later
++p;
}
UC const * const end_of_integer_part = p;
int64_t digit_count = int64_t(end_of_integer_part - start_digits);
answer.integer = span<const UC>(start_digits, size_t(digit_count));
if (fmt & FASTFLOAT_JSONFMT) {
// at least 1 digit in integer part, without leading zeros
if (digit_count == 0 || (start_digits[0] == UC('0') && digit_count > 1)) {
return answer;
}
}
int64_t exponent = 0;
const bool has_decimal_point = (p != pend) && (*p == decimal_point);
if (has_decimal_point) {
++p;
UC const * before = p;
// can occur at most twice without overflowing, but let it occur more, since
// for integers with many digits, digit parsing is the primary bottleneck.
loop_parse_if_eight_digits(p, pend, i);
while ((p != pend) && is_integer(*p)) {
uint8_t digit = uint8_t(*p - UC('0'));
++p;
i = i * 10 + digit; // in rare cases, this will overflow, but that's ok
}
exponent = before - p;
answer.fraction = span<const UC>(before, size_t(p - before));
digit_count -= exponent;
}
if (fmt & FASTFLOAT_JSONFMT) {
// at least 1 digit in fractional part
if (has_decimal_point && exponent == 0) {
return answer;
}
}
else if (digit_count == 0) { // we must have encountered at least one integer!
return answer;
}
int64_t exp_number = 0; // explicit exponential part
if ( ((fmt & chars_format::scientific) &&
(p != pend) &&
((UC('e') == *p) || (UC('E') == *p)))
||
((fmt & FASTFLOAT_FORTRANFMT) &&
(p != pend) &&
((UC('+') == *p) || (UC('-') == *p) || (UC('d') == *p) || (UC('D') == *p)))) {
UC const * location_of_e = p;
if ((UC('e') == *p) || (UC('E') == *p) || (UC('d') == *p) || (UC('D') == *p)) {
++p;
}
bool neg_exp = false;
if ((p != pend) && (UC('-') == *p)) {
neg_exp = true;
++p;
} else if ((p != pend) && (UC('+') == *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 - UC('0'));
if (exp_number < 0x10000000) {
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.
UC const * start = start_digits;
while ((start != pend) && (*start == UC('0') || *start == decimal_point)) {
if(*start == UC('0')) { digit_count --; }
start++;
}
if (digit_count > 19) {
answer.too_many_digits = true;
// Let us start again, this time, avoiding overflows.
// We don't need to check if is_integer, since we use the
// pre-tokenized spans from above.
i = 0;
p = answer.integer.ptr;
UC const* int_end = p + answer.integer.len();
const uint64_t minimal_nineteen_digit_integer{ 1000000000000000000 };
while ((i < minimal_nineteen_digit_integer) && (p != int_end)) {
i = i * 10 + uint64_t(*p - UC('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 = answer.fraction.ptr;
UC const* frac_end = p + answer.fraction.len();
while ((i < minimal_nineteen_digit_integer) && (p != frac_end)) {
i = i * 10 + uint64_t(*p - UC('0'));
++p;
}
exponent = answer.fraction.ptr - p + exp_number;
}
// We have now corrected both exponent and i, to a truncated value
}
}
answer.exponent = exponent;
answer.mantissa = i;
return answer;
}
template <typename T, typename UC>
fastfloat_really_inline FASTFLOAT_CONSTEXPR20
from_chars_result_t<UC> parse_int_string(UC const* p, UC const* pend, T& value, int base) {
from_chars_result_t<UC> answer;
UC const* const first = p;
bool negative = (*p == UC('-'));
if (!std::is_signed<T>::value && negative) {
answer.ec = std::errc::invalid_argument;
answer.ptr = first;
return answer;
}
#ifdef FASTFLOAT_ALLOWS_LEADING_PLUS // disabled by default
if ((*p == UC('-')) || (*p == UC('+'))) {
#else
if (*p == UC('-')) {
#endif
++p;
}
UC const* const start_num = p;
while (p!= pend && *p == UC('0')) {
++p;
}
const bool has_leading_zeros = p > start_num;
UC const* const start_digits = p;
uint64_t i = 0;
if (base == 10) {
loop_parse_if_eight_digits(p, pend, i); // use SIMD if possible
}
while (p != pend) {
uint8_t digit = ch_to_digit(*p);
if (digit >= base) {
break;
}
i = uint64_t(base) * i + digit; // might overflow, check this later
p++;
}
size_t digit_count = size_t(p - start_digits);
if (digit_count == 0) {
if (has_leading_zeros) {
value = 0;
answer.ec = std::errc();
answer.ptr = p;
}
else {
answer.ec = std::errc::invalid_argument;
answer.ptr = first;
}
return answer;
}
answer.ptr = p;
// check u64 overflow
size_t max_digits = max_digits_u64(base);
if (digit_count > max_digits) {
answer.ec = std::errc::result_out_of_range;
return answer;
}
// this check can be eliminated for all other types, but they will all require a max_digits(base) equivalent
if (digit_count == max_digits && i < min_safe_u64(base)) {
answer.ec = std::errc::result_out_of_range;
return answer;
}
// check other types overflow
if (!std::is_same<T, uint64_t>::value) {
if (i > uint64_t(std::numeric_limits<T>::max()) + uint64_t(negative)) {
answer.ec = std::errc::result_out_of_range;
return answer;
}
}
if (negative) {
#ifdef FASTFLOAT_VISUAL_STUDIO
#pragma warning(push)
#pragma warning(disable: 4146)
#endif
// this weird workaround is required because:
// - converting unsigned to signed when its value is greater than signed max is UB pre-C++23.
// - reinterpret_casting (~i + 1) would work, but it is not constexpr
// this is always optimized into a neg instruction (note: T is an integer type)
value = T(-std::numeric_limits<T>::max() - T(i - uint64_t(std::numeric_limits<T>::max())));
#ifdef FASTFLOAT_VISUAL_STUDIO
#pragma warning(pop)
#endif
}
else { value = T(i); }
answer.ec = std::errc();
return answer;
}
} // namespace fast_float
#endif

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#ifndef FASTFLOAT_BIGINT_H
#define FASTFLOAT_BIGINT_H
#include <algorithm>
#include <cstdint>
#include <climits>
#include <cstring>
#include "float_common.h"
namespace fast_float {
// the limb width: we want efficient multiplication of double the bits in
// limb, or for 64-bit limbs, at least 64-bit multiplication where we can
// extract the high and low parts efficiently. this is every 64-bit
// architecture except for sparc, which emulates 128-bit multiplication.
// we might have platforms where `CHAR_BIT` is not 8, so let's avoid
// doing `8 * sizeof(limb)`.
#if defined(FASTFLOAT_64BIT) && !defined(__sparc)
#define FASTFLOAT_64BIT_LIMB 1
typedef uint64_t limb;
constexpr size_t limb_bits = 64;
#else
#define FASTFLOAT_32BIT_LIMB
typedef uint32_t limb;
constexpr size_t limb_bits = 32;
#endif
typedef span<limb> limb_span;
// number of bits in a bigint. this needs to be at least the number
// of bits required to store the largest bigint, which is
// `log2(10**(digits + max_exp))`, or `log2(10**(767 + 342))`, or
// ~3600 bits, so we round to 4000.
constexpr size_t bigint_bits = 4000;
constexpr size_t bigint_limbs = bigint_bits / limb_bits;
// vector-like type that is allocated on the stack. the entire
// buffer is pre-allocated, and only the length changes.
template <uint16_t size>
struct stackvec {
limb data[size];
// we never need more than 150 limbs
uint16_t length{0};
stackvec() = default;
stackvec(const stackvec &) = delete;
stackvec &operator=(const stackvec &) = delete;
stackvec(stackvec &&) = delete;
stackvec &operator=(stackvec &&other) = delete;
// create stack vector from existing limb span.
FASTFLOAT_CONSTEXPR20 stackvec(limb_span s) {
FASTFLOAT_ASSERT(try_extend(s));
}
FASTFLOAT_CONSTEXPR14 limb& operator[](size_t index) noexcept {
FASTFLOAT_DEBUG_ASSERT(index < length);
return data[index];
}
FASTFLOAT_CONSTEXPR14 const limb& operator[](size_t index) const noexcept {
FASTFLOAT_DEBUG_ASSERT(index < length);
return data[index];
}
// index from the end of the container
FASTFLOAT_CONSTEXPR14 const limb& rindex(size_t index) const noexcept {
FASTFLOAT_DEBUG_ASSERT(index < length);
size_t rindex = length - index - 1;
return data[rindex];
}
// set the length, without bounds checking.
FASTFLOAT_CONSTEXPR14 void set_len(size_t len) noexcept {
length = uint16_t(len);
}
constexpr size_t len() const noexcept {
return length;
}
constexpr bool is_empty() const noexcept {
return length == 0;
}
constexpr size_t capacity() const noexcept {
return size;
}
// append item to vector, without bounds checking
FASTFLOAT_CONSTEXPR14 void push_unchecked(limb value) noexcept {
data[length] = value;
length++;
}
// append item to vector, returning if item was added
FASTFLOAT_CONSTEXPR14 bool try_push(limb value) noexcept {
if (len() < capacity()) {
push_unchecked(value);
return true;
} else {
return false;
}
}
// add items to the vector, from a span, without bounds checking
FASTFLOAT_CONSTEXPR20 void extend_unchecked(limb_span s) noexcept {
limb* ptr = data + length;
std::copy_n(s.ptr, s.len(), ptr);
set_len(len() + s.len());
}
// try to add items to the vector, returning if items were added
FASTFLOAT_CONSTEXPR20 bool try_extend(limb_span s) noexcept {
if (len() + s.len() <= capacity()) {
extend_unchecked(s);
return true;
} else {
return false;
}
}
// resize the vector, without bounds checking
// if the new size is longer than the vector, assign value to each
// appended item.
FASTFLOAT_CONSTEXPR20
void resize_unchecked(size_t new_len, limb value) noexcept {
if (new_len > len()) {
size_t count = new_len - len();
limb* first = data + len();
limb* last = first + count;
::std::fill(first, last, value);
set_len(new_len);
} else {
set_len(new_len);
}
}
// try to resize the vector, returning if the vector was resized.
FASTFLOAT_CONSTEXPR20 bool try_resize(size_t new_len, limb value) noexcept {
if (new_len > capacity()) {
return false;
} else {
resize_unchecked(new_len, value);
return true;
}
}
// check if any limbs are non-zero after the given index.
// this needs to be done in reverse order, since the index
// is relative to the most significant limbs.
FASTFLOAT_CONSTEXPR14 bool nonzero(size_t index) const noexcept {
while (index < len()) {
if (rindex(index) != 0) {
return true;
}
index++;
}
return false;
}
// normalize the big integer, so most-significant zero limbs are removed.
FASTFLOAT_CONSTEXPR14 void normalize() noexcept {
while (len() > 0 && rindex(0) == 0) {
length--;
}
}
};
fastfloat_really_inline FASTFLOAT_CONSTEXPR14
uint64_t empty_hi64(bool& truncated) noexcept {
truncated = false;
return 0;
}
fastfloat_really_inline FASTFLOAT_CONSTEXPR20
uint64_t uint64_hi64(uint64_t r0, bool& truncated) noexcept {
truncated = false;
int shl = leading_zeroes(r0);
return r0 << shl;
}
fastfloat_really_inline FASTFLOAT_CONSTEXPR20
uint64_t uint64_hi64(uint64_t r0, uint64_t r1, bool& truncated) noexcept {
int shl = leading_zeroes(r0);
if (shl == 0) {
truncated = r1 != 0;
return r0;
} else {
int shr = 64 - shl;
truncated = (r1 << shl) != 0;
return (r0 << shl) | (r1 >> shr);
}
}
fastfloat_really_inline FASTFLOAT_CONSTEXPR20
uint64_t uint32_hi64(uint32_t r0, bool& truncated) noexcept {
return uint64_hi64(r0, truncated);
}
fastfloat_really_inline FASTFLOAT_CONSTEXPR20
uint64_t uint32_hi64(uint32_t r0, uint32_t r1, bool& truncated) noexcept {
uint64_t x0 = r0;
uint64_t x1 = r1;
return uint64_hi64((x0 << 32) | x1, truncated);
}
fastfloat_really_inline FASTFLOAT_CONSTEXPR20
uint64_t uint32_hi64(uint32_t r0, uint32_t r1, uint32_t r2, bool& truncated) noexcept {
uint64_t x0 = r0;
uint64_t x1 = r1;
uint64_t x2 = r2;
return uint64_hi64(x0, (x1 << 32) | x2, truncated);
}
// add two small integers, checking for overflow.
// we want an efficient operation. for msvc, where
// we don't have built-in intrinsics, this is still
// pretty fast.
fastfloat_really_inline FASTFLOAT_CONSTEXPR20
limb scalar_add(limb x, limb y, bool& overflow) noexcept {
limb z;
// gcc and clang
#if defined(__has_builtin)
#if __has_builtin(__builtin_add_overflow)
if (!cpp20_and_in_constexpr()) {
overflow = __builtin_add_overflow(x, y, &z);
return z;
}
#endif
#endif
// generic, this still optimizes correctly on MSVC.
z = x + y;
overflow = z < x;
return z;
}
// multiply two small integers, getting both the high and low bits.
fastfloat_really_inline FASTFLOAT_CONSTEXPR20
limb scalar_mul(limb x, limb y, limb& carry) noexcept {
#ifdef FASTFLOAT_64BIT_LIMB
#if defined(__SIZEOF_INT128__)
// GCC and clang both define it as an extension.
__uint128_t z = __uint128_t(x) * __uint128_t(y) + __uint128_t(carry);
carry = limb(z >> limb_bits);
return limb(z);
#else
// fallback, no native 128-bit integer multiplication with carry.
// on msvc, this optimizes identically, somehow.
value128 z = full_multiplication(x, y);
bool overflow;
z.low = scalar_add(z.low, carry, overflow);
z.high += uint64_t(overflow); // cannot overflow
carry = z.high;
return z.low;
#endif
#else
uint64_t z = uint64_t(x) * uint64_t(y) + uint64_t(carry);
carry = limb(z >> limb_bits);
return limb(z);
#endif
}
// add scalar value to bigint starting from offset.
// used in grade school multiplication
template <uint16_t size>
inline FASTFLOAT_CONSTEXPR20
bool small_add_from(stackvec<size>& vec, limb y, size_t start) noexcept {
size_t index = start;
limb carry = y;
bool overflow;
while (carry != 0 && index < vec.len()) {
vec[index] = scalar_add(vec[index], carry, overflow);
carry = limb(overflow);
index += 1;
}
if (carry != 0) {
FASTFLOAT_TRY(vec.try_push(carry));
}
return true;
}
// add scalar value to bigint.
template <uint16_t size>
fastfloat_really_inline FASTFLOAT_CONSTEXPR20
bool small_add(stackvec<size>& vec, limb y) noexcept {
return small_add_from(vec, y, 0);
}
// multiply bigint by scalar value.
template <uint16_t size>
inline FASTFLOAT_CONSTEXPR20
bool small_mul(stackvec<size>& vec, limb y) noexcept {
limb carry = 0;
for (size_t index = 0; index < vec.len(); index++) {
vec[index] = scalar_mul(vec[index], y, carry);
}
if (carry != 0) {
FASTFLOAT_TRY(vec.try_push(carry));
}
return true;
}
// add bigint to bigint starting from index.
// used in grade school multiplication
template <uint16_t size>
FASTFLOAT_CONSTEXPR20
bool large_add_from(stackvec<size>& x, limb_span y, size_t start) noexcept {
// the effective x buffer is from `xstart..x.len()`, so exit early
// if we can't get that current range.
if (x.len() < start || y.len() > x.len() - start) {
FASTFLOAT_TRY(x.try_resize(y.len() + start, 0));
}
bool carry = false;
for (size_t index = 0; index < y.len(); index++) {
limb xi = x[index + start];
limb yi = y[index];
bool c1 = false;
bool c2 = false;
xi = scalar_add(xi, yi, c1);
if (carry) {
xi = scalar_add(xi, 1, c2);
}
x[index + start] = xi;
carry = c1 | c2;
}
// handle overflow
if (carry) {
FASTFLOAT_TRY(small_add_from(x, 1, y.len() + start));
}
return true;
}
// add bigint to bigint.
template <uint16_t size>
fastfloat_really_inline FASTFLOAT_CONSTEXPR20
bool large_add_from(stackvec<size>& x, limb_span y) noexcept {
return large_add_from(x, y, 0);
}
// grade-school multiplication algorithm
template <uint16_t size>
FASTFLOAT_CONSTEXPR20
bool long_mul(stackvec<size>& x, limb_span y) noexcept {
limb_span xs = limb_span(x.data, x.len());
stackvec<size> z(xs);
limb_span zs = limb_span(z.data, z.len());
if (y.len() != 0) {
limb y0 = y[0];
FASTFLOAT_TRY(small_mul(x, y0));
for (size_t index = 1; index < y.len(); index++) {
limb yi = y[index];
stackvec<size> zi;
if (yi != 0) {
// re-use the same buffer throughout
zi.set_len(0);
FASTFLOAT_TRY(zi.try_extend(zs));
FASTFLOAT_TRY(small_mul(zi, yi));
limb_span zis = limb_span(zi.data, zi.len());
FASTFLOAT_TRY(large_add_from(x, zis, index));
}
}
}
x.normalize();
return true;
}
// grade-school multiplication algorithm
template <uint16_t size>
FASTFLOAT_CONSTEXPR20
bool large_mul(stackvec<size>& x, limb_span y) noexcept {
if (y.len() == 1) {
FASTFLOAT_TRY(small_mul(x, y[0]));
} else {
FASTFLOAT_TRY(long_mul(x, y));
}
return true;
}
template <typename = void>
struct pow5_tables {
static constexpr uint32_t large_step = 135;
static constexpr uint64_t small_power_of_5[] = {
1UL, 5UL, 25UL, 125UL, 625UL, 3125UL, 15625UL, 78125UL, 390625UL,
1953125UL, 9765625UL, 48828125UL, 244140625UL, 1220703125UL,
6103515625UL, 30517578125UL, 152587890625UL, 762939453125UL,
3814697265625UL, 19073486328125UL, 95367431640625UL, 476837158203125UL,
2384185791015625UL, 11920928955078125UL, 59604644775390625UL,
298023223876953125UL, 1490116119384765625UL, 7450580596923828125UL,
};
#ifdef FASTFLOAT_64BIT_LIMB
constexpr static limb large_power_of_5[] = {
1414648277510068013UL, 9180637584431281687UL, 4539964771860779200UL,
10482974169319127550UL, 198276706040285095UL};
#else
constexpr static limb large_power_of_5[] = {
4279965485U, 329373468U, 4020270615U, 2137533757U, 4287402176U,
1057042919U, 1071430142U, 2440757623U, 381945767U, 46164893U};
#endif
};
template <typename T>
constexpr uint32_t pow5_tables<T>::large_step;
template <typename T>
constexpr uint64_t pow5_tables<T>::small_power_of_5[];
template <typename T>
constexpr limb pow5_tables<T>::large_power_of_5[];
// big integer type. implements a small subset of big integer
// arithmetic, using simple algorithms since asymptotically
// faster algorithms are slower for a small number of limbs.
// all operations assume the big-integer is normalized.
struct bigint : pow5_tables<> {
// storage of the limbs, in little-endian order.
stackvec<bigint_limbs> vec;
FASTFLOAT_CONSTEXPR20 bigint(): vec() {}
bigint(const bigint &) = delete;
bigint &operator=(const bigint &) = delete;
bigint(bigint &&) = delete;
bigint &operator=(bigint &&other) = delete;
FASTFLOAT_CONSTEXPR20 bigint(uint64_t value): vec() {
#ifdef FASTFLOAT_64BIT_LIMB
vec.push_unchecked(value);
#else
vec.push_unchecked(uint32_t(value));
vec.push_unchecked(uint32_t(value >> 32));
#endif
vec.normalize();
}
// get the high 64 bits from the vector, and if bits were truncated.
// this is to get the significant digits for the float.
FASTFLOAT_CONSTEXPR20 uint64_t hi64(bool& truncated) const noexcept {
#ifdef FASTFLOAT_64BIT_LIMB
if (vec.len() == 0) {
return empty_hi64(truncated);
} else if (vec.len() == 1) {
return uint64_hi64(vec.rindex(0), truncated);
} else {
uint64_t result = uint64_hi64(vec.rindex(0), vec.rindex(1), truncated);
truncated |= vec.nonzero(2);
return result;
}
#else
if (vec.len() == 0) {
return empty_hi64(truncated);
} else if (vec.len() == 1) {
return uint32_hi64(vec.rindex(0), truncated);
} else if (vec.len() == 2) {
return uint32_hi64(vec.rindex(0), vec.rindex(1), truncated);
} else {
uint64_t result = uint32_hi64(vec.rindex(0), vec.rindex(1), vec.rindex(2), truncated);
truncated |= vec.nonzero(3);
return result;
}
#endif
}
// compare two big integers, returning the large value.
// assumes both are normalized. if the return value is
// negative, other is larger, if the return value is
// positive, this is larger, otherwise they are equal.
// the limbs are stored in little-endian order, so we
// must compare the limbs in ever order.
FASTFLOAT_CONSTEXPR20 int compare(const bigint& other) const noexcept {
if (vec.len() > other.vec.len()) {
return 1;
} else if (vec.len() < other.vec.len()) {
return -1;
} else {
for (size_t index = vec.len(); index > 0; index--) {
limb xi = vec[index - 1];
limb yi = other.vec[index - 1];
if (xi > yi) {
return 1;
} else if (xi < yi) {
return -1;
}
}
return 0;
}
}
// shift left each limb n bits, carrying over to the new limb
// returns true if we were able to shift all the digits.
FASTFLOAT_CONSTEXPR20 bool shl_bits(size_t n) noexcept {
// Internally, for each item, we shift left by n, and add the previous
// right shifted limb-bits.
// For example, we transform (for u8) shifted left 2, to:
// b10100100 b01000010
// b10 b10010001 b00001000
FASTFLOAT_DEBUG_ASSERT(n != 0);
FASTFLOAT_DEBUG_ASSERT(n < sizeof(limb) * 8);
size_t shl = n;
size_t shr = limb_bits - shl;
limb prev = 0;
for (size_t index = 0; index < vec.len(); index++) {
limb xi = vec[index];
vec[index] = (xi << shl) | (prev >> shr);
prev = xi;
}
limb carry = prev >> shr;
if (carry != 0) {
return vec.try_push(carry);
}
return true;
}
// move the limbs left by `n` limbs.
FASTFLOAT_CONSTEXPR20 bool shl_limbs(size_t n) noexcept {
FASTFLOAT_DEBUG_ASSERT(n != 0);
if (n + vec.len() > vec.capacity()) {
return false;
} else if (!vec.is_empty()) {
// move limbs
limb* dst = vec.data + n;
const limb* src = vec.data;
std::copy_backward(src, src + vec.len(), dst + vec.len());
// fill in empty limbs
limb* first = vec.data;
limb* last = first + n;
::std::fill(first, last, 0);
vec.set_len(n + vec.len());
return true;
} else {
return true;
}
}
// move the limbs left by `n` bits.
FASTFLOAT_CONSTEXPR20 bool shl(size_t n) noexcept {
size_t rem = n % limb_bits;
size_t div = n / limb_bits;
if (rem != 0) {
FASTFLOAT_TRY(shl_bits(rem));
}
if (div != 0) {
FASTFLOAT_TRY(shl_limbs(div));
}
return true;
}
// get the number of leading zeros in the bigint.
FASTFLOAT_CONSTEXPR20 int ctlz() const noexcept {
if (vec.is_empty()) {
return 0;
} else {
#ifdef FASTFLOAT_64BIT_LIMB
return leading_zeroes(vec.rindex(0));
#else
// no use defining a specialized leading_zeroes for a 32-bit type.
uint64_t r0 = vec.rindex(0);
return leading_zeroes(r0 << 32);
#endif
}
}
// get the number of bits in the bigint.
FASTFLOAT_CONSTEXPR20 int bit_length() const noexcept {
int lz = ctlz();
return int(limb_bits * vec.len()) - lz;
}
FASTFLOAT_CONSTEXPR20 bool mul(limb y) noexcept {
return small_mul(vec, y);
}
FASTFLOAT_CONSTEXPR20 bool add(limb y) noexcept {
return small_add(vec, y);
}
// multiply as if by 2 raised to a power.
FASTFLOAT_CONSTEXPR20 bool pow2(uint32_t exp) noexcept {
return shl(exp);
}
// multiply as if by 5 raised to a power.
FASTFLOAT_CONSTEXPR20 bool pow5(uint32_t exp) noexcept {
// multiply by a power of 5
size_t large_length = sizeof(large_power_of_5) / sizeof(limb);
limb_span large = limb_span(large_power_of_5, large_length);
while (exp >= large_step) {
FASTFLOAT_TRY(large_mul(vec, large));
exp -= large_step;
}
#ifdef FASTFLOAT_64BIT_LIMB
uint32_t small_step = 27;
limb max_native = 7450580596923828125UL;
#else
uint32_t small_step = 13;
limb max_native = 1220703125U;
#endif
while (exp >= small_step) {
FASTFLOAT_TRY(small_mul(vec, max_native));
exp -= small_step;
}
if (exp != 0) {
// Work around clang bug https://godbolt.org/z/zedh7rrhc
// This is similar to https://github.com/llvm/llvm-project/issues/47746,
// except the workaround described there don't work here
FASTFLOAT_TRY(
small_mul(vec, limb(((void)small_power_of_5[0], small_power_of_5[exp])))
);
}
return true;
}
// multiply as if by 10 raised to a power.
FASTFLOAT_CONSTEXPR20 bool pow10(uint32_t exp) noexcept {
FASTFLOAT_TRY(pow5(exp));
return pow2(exp);
}
};
} // namespace fast_float
#endif

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#ifndef FASTFLOAT_CONSTEXPR_FEATURE_DETECT_H
#define FASTFLOAT_CONSTEXPR_FEATURE_DETECT_H
#ifdef __has_include
#if __has_include(<version>)
#include <version>
#endif
#endif
// Testing for https://wg21.link/N3652, adopted in C++14
#if __cpp_constexpr >= 201304
#define FASTFLOAT_CONSTEXPR14 constexpr
#else
#define FASTFLOAT_CONSTEXPR14
#endif
#if defined(__cpp_lib_bit_cast) && __cpp_lib_bit_cast >= 201806L
#define FASTFLOAT_HAS_BIT_CAST 1
#else
#define FASTFLOAT_HAS_BIT_CAST 0
#endif
#if defined(__cpp_lib_is_constant_evaluated) && __cpp_lib_is_constant_evaluated >= 201811L
#define FASTFLOAT_HAS_IS_CONSTANT_EVALUATED 1
#else
#define FASTFLOAT_HAS_IS_CONSTANT_EVALUATED 0
#endif
// Testing for relevant C++20 constexpr library features
#if FASTFLOAT_HAS_IS_CONSTANT_EVALUATED \
&& FASTFLOAT_HAS_BIT_CAST \
&& __cpp_lib_constexpr_algorithms >= 201806L /*For std::copy and std::fill*/
#define FASTFLOAT_CONSTEXPR20 constexpr
#define FASTFLOAT_IS_CONSTEXPR 1
#else
#define FASTFLOAT_CONSTEXPR20
#define FASTFLOAT_IS_CONSTEXPR 0
#endif
#endif // FASTFLOAT_CONSTEXPR_FEATURE_DETECT_H

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#ifndef FASTFLOAT_DECIMAL_TO_BINARY_H
#define FASTFLOAT_DECIMAL_TO_BINARY_H
#include "float_common.h"
#include "fast_table.h"
#include <cfloat>
#include <cinttypes>
#include <cmath>
#include <cstdint>
#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 FASTFLOAT_CONSTEXPR20
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)
*/
constexpr fastfloat_really_inline int32_t power(int32_t q) noexcept {
return (((152170 + 65536) * q) >> 16) + 63;
}
} // namespace detail
// create an adjusted mantissa, biased by the invalid power2
// for significant digits already multiplied by 10 ** q.
template <typename binary>
fastfloat_really_inline FASTFLOAT_CONSTEXPR14
adjusted_mantissa compute_error_scaled(int64_t q, uint64_t w, int lz) noexcept {
int hilz = int(w >> 63) ^ 1;
adjusted_mantissa answer;
answer.mantissa = w << hilz;
int bias = binary::mantissa_explicit_bits() - binary::minimum_exponent();
answer.power2 = int32_t(detail::power(int32_t(q)) + bias - hilz - lz - 62 + invalid_am_bias);
return answer;
}
// w * 10 ** q, without rounding the representation up.
// the power2 in the exponent will be adjusted by invalid_am_bias.
template <typename binary>
fastfloat_really_inline FASTFLOAT_CONSTEXPR20
adjusted_mantissa compute_error(int64_t q, uint64_t w) noexcept {
int lz = leading_zeroes(w);
w <<= lz;
value128 product = compute_product_approximation<binary::mantissa_explicit_bits() + 3>(q, w);
return compute_error_scaled<binary>(q, product.high, lz);
}
// 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 FASTFLOAT_CONSTEXPR20
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);
// The computed 'product' is always sufficient.
// Mathematical proof:
// Noble Mushtak and Daniel Lemire, Fast Number Parsing Without Fallback (to appear)
// See script/mushtak_lemire.py
// 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 = int32_t(detail::power(int32_t(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

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#ifndef FASTFLOAT_DIGIT_COMPARISON_H
#define FASTFLOAT_DIGIT_COMPARISON_H
#include <algorithm>
#include <cstdint>
#include <cstring>
#include <iterator>
#include "float_common.h"
#include "bigint.h"
#include "ascii_number.h"
namespace fast_float {
// 1e0 to 1e19
constexpr static uint64_t powers_of_ten_uint64[] = {
1UL, 10UL, 100UL, 1000UL, 10000UL, 100000UL, 1000000UL, 10000000UL, 100000000UL,
1000000000UL, 10000000000UL, 100000000000UL, 1000000000000UL, 10000000000000UL,
100000000000000UL, 1000000000000000UL, 10000000000000000UL, 100000000000000000UL,
1000000000000000000UL, 10000000000000000000UL};
// calculate the exponent, in scientific notation, of the number.
// this algorithm is not even close to optimized, but it has no practical
// effect on performance: in order to have a faster algorithm, we'd need
// to slow down performance for faster algorithms, and this is still fast.
template <typename UC>
fastfloat_really_inline FASTFLOAT_CONSTEXPR14
int32_t scientific_exponent(parsed_number_string_t<UC> & num) noexcept {
uint64_t mantissa = num.mantissa;
int32_t exponent = int32_t(num.exponent);
while (mantissa >= 10000) {
mantissa /= 10000;
exponent += 4;
}
while (mantissa >= 100) {
mantissa /= 100;
exponent += 2;
}
while (mantissa >= 10) {
mantissa /= 10;
exponent += 1;
}
return exponent;
}
// this converts a native floating-point number to an extended-precision float.
template <typename T>
fastfloat_really_inline FASTFLOAT_CONSTEXPR20
adjusted_mantissa to_extended(T value) noexcept {
using equiv_uint = typename binary_format<T>::equiv_uint;
constexpr equiv_uint exponent_mask = binary_format<T>::exponent_mask();
constexpr equiv_uint mantissa_mask = binary_format<T>::mantissa_mask();
constexpr equiv_uint hidden_bit_mask = binary_format<T>::hidden_bit_mask();
adjusted_mantissa am;
int32_t bias = binary_format<T>::mantissa_explicit_bits() - binary_format<T>::minimum_exponent();
equiv_uint bits;
#if FASTFLOAT_HAS_BIT_CAST
bits = std::bit_cast<equiv_uint>(value);
#else
::memcpy(&bits, &value, sizeof(T));
#endif
if ((bits & exponent_mask) == 0) {
// denormal
am.power2 = 1 - bias;
am.mantissa = bits & mantissa_mask;
} else {
// normal
am.power2 = int32_t((bits & exponent_mask) >> binary_format<T>::mantissa_explicit_bits());
am.power2 -= bias;
am.mantissa = (bits & mantissa_mask) | hidden_bit_mask;
}
return am;
}
// get the extended precision value of the halfway point between b and b+u.
// we are given a native float that represents b, so we need to adjust it
// halfway between b and b+u.
template <typename T>
fastfloat_really_inline FASTFLOAT_CONSTEXPR20
adjusted_mantissa to_extended_halfway(T value) noexcept {
adjusted_mantissa am = to_extended(value);
am.mantissa <<= 1;
am.mantissa += 1;
am.power2 -= 1;
return am;
}
// round an extended-precision float to the nearest machine float.
template <typename T, typename callback>
fastfloat_really_inline FASTFLOAT_CONSTEXPR14
void round(adjusted_mantissa& am, callback cb) noexcept {
int32_t mantissa_shift = 64 - binary_format<T>::mantissa_explicit_bits() - 1;
if (-am.power2 >= mantissa_shift) {
// have a denormal float
int32_t shift = -am.power2 + 1;
cb(am, std::min<int32_t>(shift, 64));
// check for round-up: if rounding-nearest carried us to the hidden bit.
am.power2 = (am.mantissa < (uint64_t(1) << binary_format<T>::mantissa_explicit_bits())) ? 0 : 1;
return;
}
// have a normal float, use the default shift.
cb(am, mantissa_shift);
// check for carry
if (am.mantissa >= (uint64_t(2) << binary_format<T>::mantissa_explicit_bits())) {
am.mantissa = (uint64_t(1) << binary_format<T>::mantissa_explicit_bits());
am.power2++;
}
// check for infinite: we could have carried to an infinite power
am.mantissa &= ~(uint64_t(1) << binary_format<T>::mantissa_explicit_bits());
if (am.power2 >= binary_format<T>::infinite_power()) {
am.power2 = binary_format<T>::infinite_power();
am.mantissa = 0;
}
}
template <typename callback>
fastfloat_really_inline FASTFLOAT_CONSTEXPR14
void round_nearest_tie_even(adjusted_mantissa& am, int32_t shift, callback cb) noexcept {
const uint64_t mask
= (shift == 64)
? UINT64_MAX
: (uint64_t(1) << shift) - 1;
const uint64_t halfway
= (shift == 0)
? 0
: uint64_t(1) << (shift - 1);
uint64_t truncated_bits = am.mantissa & mask;
bool is_above = truncated_bits > halfway;
bool is_halfway = truncated_bits == halfway;
// shift digits into position
if (shift == 64) {
am.mantissa = 0;
} else {
am.mantissa >>= shift;
}
am.power2 += shift;
bool is_odd = (am.mantissa & 1) == 1;
am.mantissa += uint64_t(cb(is_odd, is_halfway, is_above));
}
fastfloat_really_inline FASTFLOAT_CONSTEXPR14
void round_down(adjusted_mantissa& am, int32_t shift) noexcept {
if (shift == 64) {
am.mantissa = 0;
} else {
am.mantissa >>= shift;
}
am.power2 += shift;
}
template <typename UC>
fastfloat_really_inline FASTFLOAT_CONSTEXPR20
void skip_zeros(UC const * & first, UC const * last) noexcept {
uint64_t val;
while (!cpp20_and_in_constexpr() && std::distance(first, last) >= int_cmp_len<UC>()) {
::memcpy(&val, first, sizeof(uint64_t));
if (val != int_cmp_zeros<UC>()) {
break;
}
first += int_cmp_len<UC>();
}
while (first != last) {
if (*first != UC('0')) {
break;
}
first++;
}
}
// determine if any non-zero digits were truncated.
// all characters must be valid digits.
template <typename UC>
fastfloat_really_inline FASTFLOAT_CONSTEXPR20
bool is_truncated(UC const * first, UC const * last) noexcept {
// do 8-bit optimizations, can just compare to 8 literal 0s.
uint64_t val;
while (!cpp20_and_in_constexpr() && std::distance(first, last) >= int_cmp_len<UC>()) {
::memcpy(&val, first, sizeof(uint64_t));
if (val != int_cmp_zeros<UC>()) {
return true;
}
first += int_cmp_len<UC>();
}
while (first != last) {
if (*first != UC('0')) {
return true;
}
++first;
}
return false;
}
template <typename UC>
fastfloat_really_inline FASTFLOAT_CONSTEXPR20
bool is_truncated(span<const UC> s) noexcept {
return is_truncated(s.ptr, s.ptr + s.len());
}
template <typename UC>
fastfloat_really_inline FASTFLOAT_CONSTEXPR20
void parse_eight_digits(const UC*& p, limb& value, size_t& counter, size_t& count) noexcept {
value = value * 100000000 + parse_eight_digits_unrolled(p);
p += 8;
counter += 8;
count += 8;
}
template <typename UC>
fastfloat_really_inline FASTFLOAT_CONSTEXPR14
void parse_one_digit(UC const *& p, limb& value, size_t& counter, size_t& count) noexcept {
value = value * 10 + limb(*p - UC('0'));
p++;
counter++;
count++;
}
fastfloat_really_inline FASTFLOAT_CONSTEXPR20
void add_native(bigint& big, limb power, limb value) noexcept {
big.mul(power);
big.add(value);
}
fastfloat_really_inline FASTFLOAT_CONSTEXPR20
void round_up_bigint(bigint& big, size_t& count) noexcept {
// need to round-up the digits, but need to avoid rounding
// ....9999 to ...10000, which could cause a false halfway point.
add_native(big, 10, 1);
count++;
}
// parse the significant digits into a big integer
template <typename UC>
inline FASTFLOAT_CONSTEXPR20
void parse_mantissa(bigint& result, parsed_number_string_t<UC>& num, size_t max_digits, size_t& digits) noexcept {
// try to minimize the number of big integer and scalar multiplication.
// therefore, try to parse 8 digits at a time, and multiply by the largest
// scalar value (9 or 19 digits) for each step.
size_t counter = 0;
digits = 0;
limb value = 0;
#ifdef FASTFLOAT_64BIT_LIMB
size_t step = 19;
#else
size_t step = 9;
#endif
// process all integer digits.
UC const * p = num.integer.ptr;
UC const * pend = p + num.integer.len();
skip_zeros(p, pend);
// process all digits, in increments of step per loop
while (p != pend) {
while ((std::distance(p, pend) >= 8) && (step - counter >= 8) && (max_digits - digits >= 8)) {
parse_eight_digits(p, value, counter, digits);
}
while (counter < step && p != pend && digits < max_digits) {
parse_one_digit(p, value, counter, digits);
}
if (digits == max_digits) {
// add the temporary value, then check if we've truncated any digits
add_native(result, limb(powers_of_ten_uint64[counter]), value);
bool truncated = is_truncated(p, pend);
if (num.fraction.ptr != nullptr) {
truncated |= is_truncated(num.fraction);
}
if (truncated) {
round_up_bigint(result, digits);
}
return;
} else {
add_native(result, limb(powers_of_ten_uint64[counter]), value);
counter = 0;
value = 0;
}
}
// add our fraction digits, if they're available.
if (num.fraction.ptr != nullptr) {
p = num.fraction.ptr;
pend = p + num.fraction.len();
if (digits == 0) {
skip_zeros(p, pend);
}
// process all digits, in increments of step per loop
while (p != pend) {
while ((std::distance(p, pend) >= 8) && (step - counter >= 8) && (max_digits - digits >= 8)) {
parse_eight_digits(p, value, counter, digits);
}
while (counter < step && p != pend && digits < max_digits) {
parse_one_digit(p, value, counter, digits);
}
if (digits == max_digits) {
// add the temporary value, then check if we've truncated any digits
add_native(result, limb(powers_of_ten_uint64[counter]), value);
bool truncated = is_truncated(p, pend);
if (truncated) {
round_up_bigint(result, digits);
}
return;
} else {
add_native(result, limb(powers_of_ten_uint64[counter]), value);
counter = 0;
value = 0;
}
}
}
if (counter != 0) {
add_native(result, limb(powers_of_ten_uint64[counter]), value);
}
}
template <typename T>
inline FASTFLOAT_CONSTEXPR20
adjusted_mantissa positive_digit_comp(bigint& bigmant, int32_t exponent) noexcept {
FASTFLOAT_ASSERT(bigmant.pow10(uint32_t(exponent)));
adjusted_mantissa answer;
bool truncated;
answer.mantissa = bigmant.hi64(truncated);
int bias = binary_format<T>::mantissa_explicit_bits() - binary_format<T>::minimum_exponent();
answer.power2 = bigmant.bit_length() - 64 + bias;
round<T>(answer, [truncated](adjusted_mantissa& a, int32_t shift) {
round_nearest_tie_even(a, shift, [truncated](bool is_odd, bool is_halfway, bool is_above) -> bool {
return is_above || (is_halfway && truncated) || (is_odd && is_halfway);
});
});
return answer;
}
// the scaling here is quite simple: we have, for the real digits `m * 10^e`,
// and for the theoretical digits `n * 2^f`. Since `e` is always negative,
// to scale them identically, we do `n * 2^f * 5^-f`, so we now have `m * 2^e`.
// we then need to scale by `2^(f- e)`, and then the two significant digits
// are of the same magnitude.
template <typename T>
inline FASTFLOAT_CONSTEXPR20
adjusted_mantissa negative_digit_comp(bigint& bigmant, adjusted_mantissa am, int32_t exponent) noexcept {
bigint& real_digits = bigmant;
int32_t real_exp = exponent;
// get the value of `b`, rounded down, and get a bigint representation of b+h
adjusted_mantissa am_b = am;
// gcc7 buf: use a lambda to remove the noexcept qualifier bug with -Wnoexcept-type.
round<T>(am_b, [](adjusted_mantissa&a, int32_t shift) { round_down(a, shift); });
T b;
to_float(false, am_b, b);
adjusted_mantissa theor = to_extended_halfway(b);
bigint theor_digits(theor.mantissa);
int32_t theor_exp = theor.power2;
// scale real digits and theor digits to be same power.
int32_t pow2_exp = theor_exp - real_exp;
uint32_t pow5_exp = uint32_t(-real_exp);
if (pow5_exp != 0) {
FASTFLOAT_ASSERT(theor_digits.pow5(pow5_exp));
}
if (pow2_exp > 0) {
FASTFLOAT_ASSERT(theor_digits.pow2(uint32_t(pow2_exp)));
} else if (pow2_exp < 0) {
FASTFLOAT_ASSERT(real_digits.pow2(uint32_t(-pow2_exp)));
}
// compare digits, and use it to director rounding
int ord = real_digits.compare(theor_digits);
adjusted_mantissa answer = am;
round<T>(answer, [ord](adjusted_mantissa& a, int32_t shift) {
round_nearest_tie_even(a, shift, [ord](bool is_odd, bool _, bool __) -> bool {
(void)_; // not needed, since we've done our comparison
(void)__; // not needed, since we've done our comparison
if (ord > 0) {
return true;
} else if (ord < 0) {
return false;
} else {
return is_odd;
}
});
});
return answer;
}
// parse the significant digits as a big integer to unambiguously round the
// the significant digits. here, we are trying to determine how to round
// an extended float representation close to `b+h`, halfway between `b`
// (the float rounded-down) and `b+u`, the next positive float. this
// algorithm is always correct, and uses one of two approaches. when
// the exponent is positive relative to the significant digits (such as
// 1234), we create a big-integer representation, get the high 64-bits,
// determine if any lower bits are truncated, and use that to direct
// rounding. in case of a negative exponent relative to the significant
// digits (such as 1.2345), we create a theoretical representation of
// `b` as a big-integer type, scaled to the same binary exponent as
// the actual digits. we then compare the big integer representations
// of both, and use that to direct rounding.
template <typename T, typename UC>
inline FASTFLOAT_CONSTEXPR20
adjusted_mantissa digit_comp(parsed_number_string_t<UC>& num, adjusted_mantissa am) noexcept {
// remove the invalid exponent bias
am.power2 -= invalid_am_bias;
int32_t sci_exp = scientific_exponent(num);
size_t max_digits = binary_format<T>::max_digits();
size_t digits = 0;
bigint bigmant;
parse_mantissa(bigmant, num, max_digits, digits);
// can't underflow, since digits is at most max_digits.
int32_t exponent = sci_exp + 1 - int32_t(digits);
if (exponent >= 0) {
return positive_digit_comp<T>(bigmant, exponent);
} else {
return negative_digit_comp<T>(bigmant, am, exponent);
}
}
} // namespace fast_float
#endif

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#ifndef FASTFLOAT_FAST_FLOAT_H
#define FASTFLOAT_FAST_FLOAT_H
#include "float_common.h"
namespace fast_float {
/**
* 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 allow the fixed point and scientific notation respectively.
* The default is `fast_float::chars_format::general` which allows both `fixed` and `scientific`.
*/
template<typename T, typename UC = char, typename = FASTFLOAT_ENABLE_IF(is_supported_float_type<T>())>
FASTFLOAT_CONSTEXPR20
from_chars_result_t<UC> from_chars(UC const * first, UC const * 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, typename UC = char>
FASTFLOAT_CONSTEXPR20
from_chars_result_t<UC> from_chars_advanced(UC const * first, UC const * last,
T &value, parse_options_t<UC> options) noexcept;
/**
* from_chars for integer types.
*/
template <typename T, typename UC = char, typename = FASTFLOAT_ENABLE_IF(!is_supported_float_type<T>())>
FASTFLOAT_CONSTEXPR20
from_chars_result_t<UC> from_chars(UC const * first, UC const * last, T& value, int base = 10) noexcept;
} // namespace fast_float
#include "parse_number.h"
#endif // FASTFLOAT_FAST_FLOAT_H

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#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.
constexpr static uint64_t 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,
0xf7d88bc24209a565,0x1f225a7ca91a4226,
0x9ae757596946075f,0x3375788de9b06958,
0xc1a12d2fc3978937,0x52d6b1641c83ae,
0xf209787bb47d6b84,0xc0678c5dbd23a49a,
0x9745eb4d50ce6332,0xf840b7ba963646e0,
0xbd176620a501fbff,0xb650e5a93bc3d898,
0xec5d3fa8ce427aff,0xa3e51f138ab4cebe,
0x93ba47c980e98cdf,0xc66f336c36b10137,
0xb8a8d9bbe123f017,0xb80b0047445d4184,
0xe6d3102ad96cec1d,0xa60dc059157491e5,
0x9043ea1ac7e41392,0x87c89837ad68db2f,
0xb454e4a179dd1877,0x29babe4598c311fb,
0xe16a1dc9d8545e94,0xf4296dd6fef3d67a,
0x8ce2529e2734bb1d,0x1899e4a65f58660c,
0xb01ae745b101e9e4,0x5ec05dcff72e7f8f,
0xdc21a1171d42645d,0x76707543f4fa1f73,
0x899504ae72497eba,0x6a06494a791c53a8,
0xabfa45da0edbde69,0x487db9d17636892,
0xd6f8d7509292d603,0x45a9d2845d3c42b6,
0x865b86925b9bc5c2,0xb8a2392ba45a9b2,
0xa7f26836f282b732,0x8e6cac7768d7141e,
0xd1ef0244af2364ff,0x3207d795430cd926,
0x8335616aed761f1f,0x7f44e6bd49e807b8,
0xa402b9c5a8d3a6e7,0x5f16206c9c6209a6,
0xcd036837130890a1,0x36dba887c37a8c0f,
0x802221226be55a64,0xc2494954da2c9789,
0xa02aa96b06deb0fd,0xf2db9baa10b7bd6c,
0xc83553c5c8965d3d,0x6f92829494e5acc7,
0xfa42a8b73abbf48c,0xcb772339ba1f17f9,
0x9c69a97284b578d7,0xff2a760414536efb,
0xc38413cf25e2d70d,0xfef5138519684aba,
0xf46518c2ef5b8cd1,0x7eb258665fc25d69,
0x98bf2f79d5993802,0xef2f773ffbd97a61,
0xbeeefb584aff8603,0xaafb550ffacfd8fa,
0xeeaaba2e5dbf6784,0x95ba2a53f983cf38,
0x952ab45cfa97a0b2,0xdd945a747bf26183,
0xba756174393d88df,0x94f971119aeef9e4,
0xe912b9d1478ceb17,0x7a37cd5601aab85d,
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,
0xa59bc234db398c25,0x43fab9837e699095,
0xcf02b2c21207ef2e,0x94f967e45e03f4bb,
0x8161afb94b44f57d,0x1d1be0eebac278f5,
0xa1ba1ba79e1632dc,0x6462d92a69731732,
0xca28a291859bbf93,0x7d7b8f7503cfdcfe,
0xfcb2cb35e702af78,0x5cda735244c3d43e,
0x9defbf01b061adab,0x3a0888136afa64a7,
0xc56baec21c7a1916,0x88aaa1845b8fdd0,
0xf6c69a72a3989f5b,0x8aad549e57273d45,
0x9a3c2087a63f6399,0x36ac54e2f678864b,
0xc0cb28a98fcf3c7f,0x84576a1bb416a7dd,
0xf0fdf2d3f3c30b9f,0x656d44a2a11c51d5,
0x969eb7c47859e743,0x9f644ae5a4b1b325,
0xbc4665b596706114,0x873d5d9f0dde1fee,
0xeb57ff22fc0c7959,0xa90cb506d155a7ea,
0x9316ff75dd87cbd8,0x9a7f12442d588f2,
0xb7dcbf5354e9bece,0xc11ed6d538aeb2f,
0xe5d3ef282a242e81,0x8f1668c8a86da5fa,
0x8fa475791a569d10,0xf96e017d694487bc,
0xb38d92d760ec4455,0x37c981dcc395a9ac,
0xe070f78d3927556a,0x85bbe253f47b1417,
0x8c469ab843b89562,0x93956d7478ccec8e,
0xaf58416654a6babb,0x387ac8d1970027b2,
0xdb2e51bfe9d0696a,0x6997b05fcc0319e,
0x88fcf317f22241e2,0x441fece3bdf81f03,
0xab3c2fddeeaad25a,0xd527e81cad7626c3,
0xd60b3bd56a5586f1,0x8a71e223d8d3b074,
0x85c7056562757456,0xf6872d5667844e49,
0xa738c6bebb12d16c,0xb428f8ac016561db,
0xd106f86e69d785c7,0xe13336d701beba52,
0x82a45b450226b39c,0xecc0024661173473,
0xa34d721642b06084,0x27f002d7f95d0190,
0xcc20ce9bd35c78a5,0x31ec038df7b441f4,
0xff290242c83396ce,0x7e67047175a15271,
0x9f79a169bd203e41,0xf0062c6e984d386,
0xc75809c42c684dd1,0x52c07b78a3e60868,
0xf92e0c3537826145,0xa7709a56ccdf8a82,
0x9bbcc7a142b17ccb,0x88a66076400bb691,
0xc2abf989935ddbfe,0x6acff893d00ea435,
0xf356f7ebf83552fe,0x583f6b8c4124d43,
0x98165af37b2153de,0xc3727a337a8b704a,
0xbe1bf1b059e9a8d6,0x744f18c0592e4c5c,
0xeda2ee1c7064130c,0x1162def06f79df73,
0x9485d4d1c63e8be7,0x8addcb5645ac2ba8,
0xb9a74a0637ce2ee1,0x6d953e2bd7173692,
0xe8111c87c5c1ba99,0xc8fa8db6ccdd0437,
0x910ab1d4db9914a0,0x1d9c9892400a22a2,
0xb54d5e4a127f59c8,0x2503beb6d00cab4b,
0xe2a0b5dc971f303a,0x2e44ae64840fd61d,
0x8da471a9de737e24,0x5ceaecfed289e5d2,
0xb10d8e1456105dad,0x7425a83e872c5f47,
0xdd50f1996b947518,0xd12f124e28f77719,
0x8a5296ffe33cc92f,0x82bd6b70d99aaa6f,
0xace73cbfdc0bfb7b,0x636cc64d1001550b,
0xd8210befd30efa5a,0x3c47f7e05401aa4e,
0x8714a775e3e95c78,0x65acfaec34810a71,
0xa8d9d1535ce3b396,0x7f1839a741a14d0d,
0xd31045a8341ca07c,0x1ede48111209a050,
0x83ea2b892091e44d,0x934aed0aab460432,
0xa4e4b66b68b65d60,0xf81da84d5617853f,
0xce1de40642e3f4b9,0x36251260ab9d668e,
0x80d2ae83e9ce78f3,0xc1d72b7c6b426019,
0xa1075a24e4421730,0xb24cf65b8612f81f,
0xc94930ae1d529cfc,0xdee033f26797b627,
0xfb9b7cd9a4a7443c,0x169840ef017da3b1,
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,};
};
template <class unused>
constexpr uint64_t powers_template<unused>::power_of_five_128[number_of_entries];
using powers = powers_template<>;
} // namespace fast_float
#endif

767
3rdparty/fast_float/include/fast_float/float_common.h vendored Normal file
View File

@@ -0,0 +1,767 @@
#ifndef FASTFLOAT_FLOAT_COMMON_H
#define FASTFLOAT_FLOAT_COMMON_H
#include <cfloat>
#include <cstdint>
#include <cassert>
#include <cstring>
#include <type_traits>
#include <system_error>
#ifdef __has_include
#if __has_include(<stdfloat>) && (__cplusplus > 202002L || _MSVC_LANG > 202002L)
#include <stdfloat>
#endif
#endif
#include "constexpr_feature_detect.h"
namespace fast_float {
#define FASTFLOAT_JSONFMT (1 << 5)
#define FASTFLOAT_FORTRANFMT (1 << 6)
enum chars_format {
scientific = 1 << 0,
fixed = 1 << 2,
hex = 1 << 3,
no_infnan = 1 << 4,
// RFC 8259: https://datatracker.ietf.org/doc/html/rfc8259#section-6
json = FASTFLOAT_JSONFMT | fixed | scientific | no_infnan,
// Extension of RFC 8259 where, e.g., "inf" and "nan" are allowed.
json_or_infnan = FASTFLOAT_JSONFMT | fixed | scientific,
fortran = FASTFLOAT_FORTRANFMT | fixed | scientific,
general = fixed | scientific
};
template <typename UC>
struct from_chars_result_t {
UC const* ptr;
std::errc ec;
};
using from_chars_result = from_chars_result_t<char>;
template <typename UC>
struct parse_options_t {
constexpr explicit parse_options_t(chars_format fmt = chars_format::general,
UC dot = UC('.'))
: format(fmt), decimal_point(dot) {}
/** Which number formats are accepted */
chars_format format;
/** The character used as decimal point */
UC decimal_point;
};
using parse_options = parse_options_t<char>;
}
#if FASTFLOAT_HAS_BIT_CAST
#include <bit>
#endif
#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(__loongarch64) )
#define FASTFLOAT_64BIT 1
#elif (defined(__i386) || defined(__i386__) || defined(_M_IX86) \
|| defined(__arm__) || defined(_M_ARM) || defined(__ppc__) \
|| defined(__MINGW32__) || defined(__EMSCRIPTEN__))
#define FASTFLOAT_32BIT 1
#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 1
#elif SIZE_MAX == 0xffffffffffffffff
#define FASTFLOAT_64BIT 1
#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
#if defined __BYTE_ORDER__ && defined __ORDER_BIG_ENDIAN__
#define FASTFLOAT_IS_BIG_ENDIAN (__BYTE_ORDER__ == __ORDER_BIG_ENDIAN__)
#elif defined _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>
#elif defined(__MVS__)
#include <sys/endian.h>
#else
#ifdef __has_include
#if __has_include(<endian.h>)
#include <endian.h>
#endif //__has_include(<endian.h>)
#endif //__has_include
#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
#if defined(__SSE2__) || \
(defined(FASTFLOAT_VISUAL_STUDIO) && \
(defined(_M_AMD64) || defined(_M_X64) || (defined(_M_IX86_FP) && _M_IX86_FP == 2)))
#define FASTFLOAT_SSE2 1
#endif
#if defined(__aarch64__) || defined(_M_ARM64)
#define FASTFLOAT_NEON 1
#endif
#if defined(FASTFLOAT_SSE2) || defined(FASTFLOAT_NEON)
#define FASTFLOAT_HAS_SIMD 1
#endif
#if defined(__GNUC__)
// disable -Wcast-align=strict (GCC only)
#define FASTFLOAT_SIMD_DISABLE_WARNINGS \
_Pragma("GCC diagnostic push") \
_Pragma("GCC diagnostic ignored \"-Wcast-align\"")
#else
#define FASTFLOAT_SIMD_DISABLE_WARNINGS
#endif
#if defined(__GNUC__)
#define FASTFLOAT_SIMD_RESTORE_WARNINGS \
_Pragma("GCC diagnostic pop")
#else
#define FASTFLOAT_SIMD_RESTORE_WARNINGS
#endif
#ifdef FASTFLOAT_VISUAL_STUDIO
#define fastfloat_really_inline __forceinline
#else
#define fastfloat_really_inline inline __attribute__((always_inline))
#endif
#ifndef FASTFLOAT_ASSERT
#define FASTFLOAT_ASSERT(x) { ((void)(x)); }
#endif
#ifndef FASTFLOAT_DEBUG_ASSERT
#define FASTFLOAT_DEBUG_ASSERT(x) { ((void)(x)); }
#endif
// rust style `try!()` macro, or `?` operator
#define FASTFLOAT_TRY(x) { if (!(x)) return false; }
#define FASTFLOAT_ENABLE_IF(...) typename std::enable_if<(__VA_ARGS__), int>::type
namespace fast_float {
fastfloat_really_inline constexpr bool cpp20_and_in_constexpr() {
#if FASTFLOAT_HAS_IS_CONSTANT_EVALUATED
return std::is_constant_evaluated();
#else
return false;
#endif
}
template <typename T>
fastfloat_really_inline constexpr bool is_supported_float_type() {
return std::is_same<T, float>::value || std::is_same<T, double>::value
#if __STDCPP_FLOAT32_T__
|| std::is_same<T, std::float32_t>::value
#endif
#if __STDCPP_FLOAT64_T__
|| std::is_same<T, std::float64_t>::value
#endif
;
}
template <typename UC>
fastfloat_really_inline constexpr bool is_supported_char_type() {
return
std::is_same<UC, char>::value ||
std::is_same<UC, wchar_t>::value ||
std::is_same<UC, char16_t>::value ||
std::is_same<UC, char32_t>::value;
}
// Compares two ASCII strings in a case insensitive manner.
template <typename UC>
inline FASTFLOAT_CONSTEXPR14 bool
fastfloat_strncasecmp(UC const * input1, UC const * input2, size_t length) {
char running_diff{0};
for (size_t i = 0; i < length; ++i) {
running_diff |= (char(input1[i]) ^ char(input2[i]));
}
return (running_diff == 0) || (running_diff == 32);
}
#ifndef FLT_EVAL_METHOD
#error "FLT_EVAL_METHOD should be defined, please include cfloat."
#endif
// a pointer and a length to a contiguous block of memory
template <typename T>
struct span {
const T* ptr;
size_t length;
constexpr span(const T* _ptr, size_t _length) : ptr(_ptr), length(_length) {}
constexpr span() : ptr(nullptr), length(0) {}
constexpr size_t len() const noexcept {
return length;
}
FASTFLOAT_CONSTEXPR14 const T& operator[](size_t index) const noexcept {
FASTFLOAT_DEBUG_ASSERT(index < length);
return ptr[index];
}
};
struct value128 {
uint64_t low;
uint64_t high;
constexpr value128(uint64_t _low, uint64_t _high) : low(_low), high(_high) {}
constexpr value128() : low(0), high(0) {}
};
/* Helper C++14 constexpr generic implementation of leading_zeroes */
fastfloat_really_inline FASTFLOAT_CONSTEXPR14
int leading_zeroes_generic(uint64_t input_num, 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;
}
/* result might be undefined when input_num is zero */
fastfloat_really_inline FASTFLOAT_CONSTEXPR20
int leading_zeroes(uint64_t input_num) {
assert(input_num > 0);
if (cpp20_and_in_constexpr()) {
return leading_zeroes_generic(input_num);
}
#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
return leading_zeroes_generic(input_num);
#endif
#else
return __builtin_clzll(input_num);
#endif
}
// slow emulation routine for 32-bit
fastfloat_really_inline constexpr uint64_t emulu(uint32_t x, uint32_t y) {
return x * (uint64_t)y;
}
fastfloat_really_inline FASTFLOAT_CONSTEXPR14
uint64_t umul128_generic(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 = (uint64_t)(adbc < ad);
uint64_t lo = bd + (adbc << 32);
*hi = emulu((uint32_t)(ab >> 32), (uint32_t)(cd >> 32)) + (adbc >> 32) +
(adbc_carry << 32) + (uint64_t)(lo < bd);
return lo;
}
#ifdef FASTFLOAT_32BIT
// slow emulation routine for 32-bit
#if !defined(__MINGW64__)
fastfloat_really_inline FASTFLOAT_CONSTEXPR14
uint64_t _umul128(uint64_t ab, uint64_t cd, uint64_t *hi) {
return umul128_generic(ab, cd, hi);
}
#endif // !__MINGW64__
#endif // FASTFLOAT_32BIT
// compute 64-bit a*b
fastfloat_really_inline FASTFLOAT_CONSTEXPR20
value128 full_multiplication(uint64_t a, uint64_t b) {
if (cpp20_and_in_constexpr()) {
value128 answer;
answer.low = umul128_generic(a, b, &answer.high);
return answer;
}
value128 answer;
#if defined(_M_ARM64) && !defined(__MINGW32__)
// ARM64 has native support for 64-bit multiplications, no need to emulate
// But MinGW on ARM64 doesn't have native support for 64-bit multiplications
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) && defined(__SIZEOF_INT128__)
__uint128_t r = ((__uint128_t)a) * b;
answer.low = uint64_t(r);
answer.high = uint64_t(r >> 64);
#else
answer.low = umul128_generic(a, b, &answer.high);
#endif
return answer;
}
struct adjusted_mantissa {
uint64_t mantissa{0};
int32_t power2{0}; // a negative value indicates an invalid result
adjusted_mantissa() = default;
constexpr bool operator==(const adjusted_mantissa &o) const {
return mantissa == o.mantissa && power2 == o.power2;
}
constexpr bool operator!=(const adjusted_mantissa &o) const {
return mantissa != o.mantissa || power2 != o.power2;
}
};
// Bias so we can get the real exponent with an invalid adjusted_mantissa.
constexpr static int32_t invalid_am_bias = -0x8000;
// used for binary_format_lookup_tables<T>::max_mantissa
constexpr uint64_t constant_55555 = 5 * 5 * 5 * 5 * 5;
template <typename T, typename U = void>
struct binary_format_lookup_tables;
template <typename T> struct binary_format : binary_format_lookup_tables<T> {
using equiv_uint = typename std::conditional<sizeof(T) == 4, uint32_t, uint64_t>::type;
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(); // used when fegetround() == FE_TONEAREST
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(int64_t power);
static inline constexpr uint64_t max_mantissa_fast_path(); // used when fegetround() == FE_TONEAREST
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);
static inline constexpr size_t max_digits();
static inline constexpr equiv_uint exponent_mask();
static inline constexpr equiv_uint mantissa_mask();
static inline constexpr equiv_uint hidden_bit_mask();
};
template <typename U>
struct binary_format_lookup_tables<double, U> {
static constexpr double powers_of_ten[] = {
1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9, 1e10, 1e11,
1e12, 1e13, 1e14, 1e15, 1e16, 1e17, 1e18, 1e19, 1e20, 1e21, 1e22};
// Largest integer value v so that (5**index * v) <= 1<<53.
// 0x10000000000000 == 1 << 53
static constexpr uint64_t max_mantissa[] = {
0x10000000000000,
0x10000000000000 / 5,
0x10000000000000 / (5 * 5),
0x10000000000000 / (5 * 5 * 5),
0x10000000000000 / (5 * 5 * 5 * 5),
0x10000000000000 / (constant_55555),
0x10000000000000 / (constant_55555 * 5),
0x10000000000000 / (constant_55555 * 5 * 5),
0x10000000000000 / (constant_55555 * 5 * 5 * 5),
0x10000000000000 / (constant_55555 * 5 * 5 * 5 * 5),
0x10000000000000 / (constant_55555 * constant_55555),
0x10000000000000 / (constant_55555 * constant_55555 * 5),
0x10000000000000 / (constant_55555 * constant_55555 * 5 * 5),
0x10000000000000 / (constant_55555 * constant_55555 * 5 * 5 * 5),
0x10000000000000 / (constant_55555 * constant_55555 * constant_55555),
0x10000000000000 / (constant_55555 * constant_55555 * constant_55555 * 5),
0x10000000000000 / (constant_55555 * constant_55555 * constant_55555 * 5 * 5),
0x10000000000000 / (constant_55555 * constant_55555 * constant_55555 * 5 * 5 * 5),
0x10000000000000 / (constant_55555 * constant_55555 * constant_55555 * 5 * 5 * 5 * 5),
0x10000000000000 / (constant_55555 * constant_55555 * constant_55555 * constant_55555),
0x10000000000000 / (constant_55555 * constant_55555 * constant_55555 * constant_55555 * 5),
0x10000000000000 / (constant_55555 * constant_55555 * constant_55555 * constant_55555 * 5 * 5),
0x10000000000000 / (constant_55555 * constant_55555 * constant_55555 * constant_55555 * 5 * 5 * 5),
0x10000000000000 / (constant_55555 * constant_55555 * constant_55555 * constant_55555 * 5 * 5 * 5 * 5)};
};
template <typename U>
constexpr double binary_format_lookup_tables<double, U>::powers_of_ten[];
template <typename U>
constexpr uint64_t binary_format_lookup_tables<double, U>::max_mantissa[];
template <typename U>
struct binary_format_lookup_tables<float, U> {
static constexpr float powers_of_ten[] = {1e0f, 1e1f, 1e2f, 1e3f, 1e4f, 1e5f,
1e6f, 1e7f, 1e8f, 1e9f, 1e10f};
// Largest integer value v so that (5**index * v) <= 1<<24.
// 0x1000000 == 1<<24
static constexpr uint64_t max_mantissa[] = {
0x1000000,
0x1000000 / 5,
0x1000000 / (5 * 5),
0x1000000 / (5 * 5 * 5),
0x1000000 / (5 * 5 * 5 * 5),
0x1000000 / (constant_55555),
0x1000000 / (constant_55555 * 5),
0x1000000 / (constant_55555 * 5 * 5),
0x1000000 / (constant_55555 * 5 * 5 * 5),
0x1000000 / (constant_55555 * 5 * 5 * 5 * 5),
0x1000000 / (constant_55555 * constant_55555),
0x1000000 / (constant_55555 * constant_55555 * 5)};
};
template <typename U>
constexpr float binary_format_lookup_tables<float, U>::powers_of_ten[];
template <typename U>
constexpr uint64_t binary_format_lookup_tables<float, U>::max_mantissa[];
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>::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>::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<double>::max_mantissa_fast_path(int64_t power) {
// caller is responsible to ensure that
// power >= 0 && power <= 22
//
// Work around clang bug https://godbolt.org/z/zedh7rrhc
return (void)max_mantissa[0], max_mantissa[power];
}
template <> inline constexpr uint64_t binary_format<float>::max_mantissa_fast_path() {
return uint64_t(2) << mantissa_explicit_bits();
}
template <> inline constexpr uint64_t binary_format<float>::max_mantissa_fast_path(int64_t power) {
// caller is responsible to ensure that
// power >= 0 && power <= 10
//
// Work around clang bug https://godbolt.org/z/zedh7rrhc
return (void)max_mantissa[0], max_mantissa[power];
}
template <>
inline constexpr double binary_format<double>::exact_power_of_ten(int64_t power) {
// Work around clang bug https://godbolt.org/z/zedh7rrhc
return (void)powers_of_ten[0], powers_of_ten[power];
}
template <>
inline constexpr float binary_format<float>::exact_power_of_ten(int64_t power) {
// Work around clang bug https://godbolt.org/z/zedh7rrhc
return (void)powers_of_ten[0], powers_of_ten[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;
}
template <> inline constexpr size_t binary_format<double>::max_digits() {
return 769;
}
template <> inline constexpr size_t binary_format<float>::max_digits() {
return 114;
}
template <> inline constexpr binary_format<float>::equiv_uint
binary_format<float>::exponent_mask() {
return 0x7F800000;
}
template <> inline constexpr binary_format<double>::equiv_uint
binary_format<double>::exponent_mask() {
return 0x7FF0000000000000;
}
template <> inline constexpr binary_format<float>::equiv_uint
binary_format<float>::mantissa_mask() {
return 0x007FFFFF;
}
template <> inline constexpr binary_format<double>::equiv_uint
binary_format<double>::mantissa_mask() {
return 0x000FFFFFFFFFFFFF;
}
template <> inline constexpr binary_format<float>::equiv_uint
binary_format<float>::hidden_bit_mask() {
return 0x00800000;
}
template <> inline constexpr binary_format<double>::equiv_uint
binary_format<double>::hidden_bit_mask() {
return 0x0010000000000000;
}
template<typename T>
fastfloat_really_inline FASTFLOAT_CONSTEXPR20
void to_float(bool negative, adjusted_mantissa am, T &value) {
using fastfloat_uint = typename binary_format<T>::equiv_uint;
fastfloat_uint word = (fastfloat_uint)am.mantissa;
word |= fastfloat_uint(am.power2) << binary_format<T>::mantissa_explicit_bits();
word |= fastfloat_uint(negative) << binary_format<T>::sign_index();
#if FASTFLOAT_HAS_BIT_CAST
value = std::bit_cast<T>(word);
#else
::memcpy(&value, &word, sizeof(T));
#endif
}
#ifdef FASTFLOAT_SKIP_WHITE_SPACE // disabled by default
template <typename = void>
struct space_lut {
static constexpr bool value[] = {
0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0};
};
template <typename T>
constexpr bool space_lut<T>::value[];
inline constexpr bool is_space(uint8_t c) { return space_lut<>::value[c]; }
#endif
template<typename UC>
static constexpr uint64_t int_cmp_zeros()
{
static_assert((sizeof(UC) == 1) || (sizeof(UC) == 2) || (sizeof(UC) == 4), "Unsupported character size");
return (sizeof(UC) == 1) ? 0x3030303030303030 : (sizeof(UC) == 2) ? (uint64_t(UC('0')) << 48 | uint64_t(UC('0')) << 32 | uint64_t(UC('0')) << 16 | UC('0')) : (uint64_t(UC('0')) << 32 | UC('0'));
}
template<typename UC>
static constexpr int int_cmp_len()
{
return sizeof(uint64_t) / sizeof(UC);
}
template<typename UC>
static constexpr UC const * str_const_nan()
{
return nullptr;
}
template<>
constexpr char const * str_const_nan<char>()
{
return "nan";
}
template<>
constexpr wchar_t const * str_const_nan<wchar_t>()
{
return L"nan";
}
template<>
constexpr char16_t const * str_const_nan<char16_t>()
{
return u"nan";
}
template<>
constexpr char32_t const * str_const_nan<char32_t>()
{
return U"nan";
}
template<typename UC>
static constexpr UC const * str_const_inf()
{
return nullptr;
}
template<>
constexpr char const * str_const_inf<char>()
{
return "infinity";
}
template<>
constexpr wchar_t const * str_const_inf<wchar_t>()
{
return L"infinity";
}
template<>
constexpr char16_t const * str_const_inf<char16_t>()
{
return u"infinity";
}
template<>
constexpr char32_t const * str_const_inf<char32_t>()
{
return U"infinity";
}
template <typename = void>
struct int_luts {
static constexpr uint8_t chdigit[] = {
255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255,
255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255,
255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255,
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 255, 255, 255, 255, 255, 255,
255, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24,
25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 255, 255, 255, 255, 255,
255, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24,
25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 255, 255, 255, 255, 255,
255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255,
255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255,
255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255,
255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255,
255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255,
255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255,
255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255,
255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255
};
static constexpr size_t maxdigits_u64[] = {
64, 41, 32, 28, 25, 23, 22, 21,
20, 19, 18, 18, 17, 17, 16, 16,
16, 16, 15, 15, 15, 15, 14, 14,
14, 14, 14, 14, 14, 13, 13, 13,
13, 13, 13
};
static constexpr uint64_t min_safe_u64[] = {
9223372036854775808ull, 12157665459056928801ull, 4611686018427387904, 7450580596923828125, 4738381338321616896,
3909821048582988049, 9223372036854775808ull, 12157665459056928801ull, 10000000000000000000ull, 5559917313492231481,
2218611106740436992, 8650415919381337933, 2177953337809371136, 6568408355712890625, 1152921504606846976,
2862423051509815793, 6746640616477458432, 15181127029874798299ull, 1638400000000000000, 3243919932521508681,
6221821273427820544, 11592836324538749809ull, 876488338465357824, 1490116119384765625, 2481152873203736576,
4052555153018976267, 6502111422497947648, 10260628712958602189ull, 15943230000000000000ull, 787662783788549761,
1152921504606846976, 1667889514952984961, 2386420683693101056, 3379220508056640625, 4738381338321616896
};
};
template <typename T>
constexpr uint8_t int_luts<T>::chdigit[];
template <typename T>
constexpr size_t int_luts<T>::maxdigits_u64[];
template <typename T>
constexpr uint64_t int_luts<T>::min_safe_u64[];
template <typename UC>
fastfloat_really_inline
constexpr uint8_t ch_to_digit(UC c) { return int_luts<>::chdigit[static_cast<unsigned char>(c)]; }
fastfloat_really_inline
constexpr size_t max_digits_u64(int base) { return int_luts<>::maxdigits_u64[base - 2]; }
// If a u64 is exactly max_digits_u64() in length, this is
// the value below which it has definitely overflowed.
fastfloat_really_inline
constexpr uint64_t min_safe_u64(int base) { return int_luts<>::min_safe_u64[base - 2]; }
} // namespace fast_float
#endif

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#ifndef FASTFLOAT_PARSE_NUMBER_H
#define FASTFLOAT_PARSE_NUMBER_H
#include "ascii_number.h"
#include "decimal_to_binary.h"
#include "digit_comparison.h"
#include "float_common.h"
#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, typename UC>
from_chars_result_t<UC> FASTFLOAT_CONSTEXPR14
parse_infnan(UC const * first, UC const * last, T &value) noexcept {
from_chars_result_t<UC> answer{};
answer.ptr = first;
answer.ec = std::errc(); // be optimistic
bool minusSign = false;
if (*first == UC('-')) { // assume first < last, so dereference without checks; C++17 20.19.3.(7.1) explicitly forbids '+' here
minusSign = true;
++first;
}
#ifdef FASTFLOAT_ALLOWS_LEADING_PLUS // disabled by default
if (*first == UC('+')) {
++first;
}
#endif
if (last - first >= 3) {
if (fastfloat_strncasecmp(first, str_const_nan<UC>(), 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 == UC('(')) {
for(UC const * ptr = first + 1; ptr != last; ++ptr) {
if (*ptr == UC(')')) {
answer.ptr = ptr + 1; // valid nan(n-char-seq-opt)
break;
}
else if(!((UC('a') <= *ptr && *ptr <= UC('z')) || (UC('A') <= *ptr && *ptr <= UC('Z')) || (UC('0') <= *ptr && *ptr <= UC('9')) || *ptr == UC('_')))
break; // forbidden char, not nan(n-char-seq-opt)
}
}
return answer;
}
if (fastfloat_strncasecmp(first, str_const_inf<UC>(), 3)) {
if ((last - first >= 8) && fastfloat_strncasecmp(first + 3, str_const_inf<UC>() + 3, 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;
}
/**
* Returns true if the floating-pointing rounding mode is to 'nearest'.
* It is the default on most system. This function is meant to be inexpensive.
* Credit : @mwalcott3
*/
fastfloat_really_inline bool rounds_to_nearest() noexcept {
// https://lemire.me/blog/2020/06/26/gcc-not-nearest/
#if (FLT_EVAL_METHOD != 1) && (FLT_EVAL_METHOD != 0)
return false;
#endif
// See
// A fast function to check your floating-point rounding mode
// https://lemire.me/blog/2022/11/16/a-fast-function-to-check-your-floating-point-rounding-mode/
//
// This function is meant to be equivalent to :
// prior: #include <cfenv>
// return fegetround() == FE_TONEAREST;
// However, it is expected to be much faster than the fegetround()
// function call.
//
// The volatile keywoard prevents the compiler from computing the function
// at compile-time.
// There might be other ways to prevent compile-time optimizations (e.g., asm).
// The value does not need to be std::numeric_limits<float>::min(), any small
// value so that 1 + x should round to 1 would do (after accounting for excess
// precision, as in 387 instructions).
static volatile float fmin = std::numeric_limits<float>::min();
float fmini = fmin; // we copy it so that it gets loaded at most once.
//
// Explanation:
// Only when fegetround() == FE_TONEAREST do we have that
// fmin + 1.0f == 1.0f - fmin.
//
// FE_UPWARD:
// fmin + 1.0f > 1
// 1.0f - fmin == 1
//
// FE_DOWNWARD or FE_TOWARDZERO:
// fmin + 1.0f == 1
// 1.0f - fmin < 1
//
// Note: This may fail to be accurate if fast-math has been
// enabled, as rounding conventions may not apply.
#ifdef FASTFLOAT_VISUAL_STUDIO
# pragma warning(push)
// todo: is there a VS warning?
// see https://stackoverflow.com/questions/46079446/is-there-a-warning-for-floating-point-equality-checking-in-visual-studio-2013
#elif defined(__clang__)
# pragma clang diagnostic push
# pragma clang diagnostic ignored "-Wfloat-equal"
#elif defined(__GNUC__)
# pragma GCC diagnostic push
# pragma GCC diagnostic ignored "-Wfloat-equal"
#endif
return (fmini + 1.0f == 1.0f - fmini);
#ifdef FASTFLOAT_VISUAL_STUDIO
# pragma warning(pop)
#elif defined(__clang__)
# pragma clang diagnostic pop
#elif defined(__GNUC__)
# pragma GCC diagnostic pop
#endif
}
} // namespace detail
template <typename T>
struct from_chars_caller
{
template <typename UC>
FASTFLOAT_CONSTEXPR20
static from_chars_result_t<UC> call(UC const * first, UC const * last,
T &value, parse_options_t<UC> options) noexcept {
return from_chars_advanced(first, last, value, options);
}
};
#if __STDCPP_FLOAT32_T__ == 1
template <>
struct from_chars_caller<std::float32_t>
{
template <typename UC>
FASTFLOAT_CONSTEXPR20
static from_chars_result_t<UC> call(UC const * first, UC const * last,
std::float32_t &value, parse_options_t<UC> options) noexcept{
// if std::float32_t is defined, and we are in C++23 mode; macro set for float32;
// set value to float due to equivalence between float and float32_t
float val;
auto ret = from_chars_advanced(first, last, val, options);
value = val;
return ret;
}
};
#endif
#if __STDCPP_FLOAT64_T__ == 1
template <>
struct from_chars_caller<std::float64_t>
{
template <typename UC>
FASTFLOAT_CONSTEXPR20
static from_chars_result_t<UC> call(UC const * first, UC const * last,
std::float64_t &value, parse_options_t<UC> options) noexcept{
// if std::float64_t is defined, and we are in C++23 mode; macro set for float64;
// set value as double due to equivalence between double and float64_t
double val;
auto ret = from_chars_advanced(first, last, val, options);
value = val;
return ret;
}
};
#endif
template<typename T, typename UC, typename>
FASTFLOAT_CONSTEXPR20
from_chars_result_t<UC> from_chars(UC const * first, UC const * last,
T &value, chars_format fmt /*= chars_format::general*/) noexcept {
return from_chars_caller<T>::call(first, last, value, parse_options_t<UC>(fmt));
}
template<typename T, typename UC>
FASTFLOAT_CONSTEXPR20
from_chars_result_t<UC> from_chars_advanced(UC const * first, UC const * last,
T &value, parse_options_t<UC> options) noexcept {
static_assert (is_supported_float_type<T>(), "only some floating-point types are supported");
static_assert (is_supported_char_type<UC>(), "only char, wchar_t, char16_t and char32_t are supported");
from_chars_result_t<UC> answer;
#ifdef FASTFLOAT_SKIP_WHITE_SPACE // disabled by default
while ((first != last) && fast_float::is_space(uint8_t(*first))) {
first++;
}
#endif
if (first == last) {
answer.ec = std::errc::invalid_argument;
answer.ptr = first;
return answer;
}
parsed_number_string_t<UC> pns = parse_number_string<UC>(first, last, options);
if (!pns.valid) {
if (options.format & chars_format::no_infnan) {
answer.ec = std::errc::invalid_argument;
answer.ptr = first;
return answer;
} else {
return detail::parse_infnan(first, last, value);
}
}
answer.ec = std::errc(); // be optimistic
answer.ptr = pns.lastmatch;
// The implementation of the Clinger's fast path is convoluted because
// we want round-to-nearest in all cases, irrespective of the rounding mode
// selected on the thread.
// We proceed optimistically, assuming that detail::rounds_to_nearest() returns
// true.
if (binary_format<T>::min_exponent_fast_path() <= pns.exponent && pns.exponent <= binary_format<T>::max_exponent_fast_path() && !pns.too_many_digits) {
// Unfortunately, the conventional Clinger's fast path is only possible
// when the system rounds to the nearest float.
//
// We expect the next branch to almost always be selected.
// We could check it first (before the previous branch), but
// there might be performance advantages at having the check
// be last.
if(!cpp20_and_in_constexpr() && detail::rounds_to_nearest()) {
// We have that fegetround() == FE_TONEAREST.
// Next is Clinger's fast path.
if (pns.mantissa <=binary_format<T>::max_mantissa_fast_path()) {
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;
}
} else {
// We do not have that fegetround() == FE_TONEAREST.
// Next is a modified Clinger's fast path, inspired by Jakub Jelínek's proposal
if (pns.exponent >= 0 && pns.mantissa <=binary_format<T>::max_mantissa_fast_path(pns.exponent)) {
#if defined(__clang__) || defined(FASTFLOAT_32BIT)
// Clang may map 0 to -0.0 when fegetround() == FE_DOWNWARD
if(pns.mantissa == 0) {
value = pns.negative ? T(-0.) : T(0.);
return answer;
}
#endif
value = T(pns.mantissa) * 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 && am.power2 >= 0) {
if(am != compute_float<binary_format<T>>(pns.exponent, pns.mantissa + 1)) {
am = compute_error<binary_format<T>>(pns.exponent, pns.mantissa);
}
}
// 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 = digit_comp<T>(pns, am); }
to_float(pns.negative, am, value);
// Test for over/underflow.
if ((pns.mantissa != 0 && am.mantissa == 0 && am.power2 == 0) || am.power2 == binary_format<T>::infinite_power()) {
answer.ec = std::errc::result_out_of_range;
}
return answer;
}
template <typename T, typename UC, typename>
FASTFLOAT_CONSTEXPR20
from_chars_result_t<UC> from_chars(UC const* first, UC const* last, T& value, int base) noexcept {
static_assert (is_supported_char_type<UC>(), "only char, wchar_t, char16_t and char32_t are supported");
from_chars_result_t<UC> answer;
#ifdef FASTFLOAT_SKIP_WHITE_SPACE // disabled by default
while ((first != last) && fast_float::is_space(uint8_t(*first))) {
first++;
}
#endif
if (first == last || base < 2 || base > 36) {
answer.ec = std::errc::invalid_argument;
answer.ptr = first;
return answer;
}
return parse_int_string(first, last, value, base);
}
} // namespace fast_float
#endif

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#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 "ascii_number.h"
#include "decimal_to_binary.h"
#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;
constexpr 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;
constexpr 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;
}
constexpr uint32_t max_shift = 60;
constexpr uint32_t num_powers = 19;
constexpr 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