dep: Add fast_float
This commit is contained in:
Connor McLaughlin
parent
591ac15612
commit
81383afc50
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@ -17,6 +17,7 @@ add_subdirectory(soundtouch)
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add_subdirectory(tinyxml2)
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add_subdirectory(tinyxml2)
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add_subdirectory(googletest)
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add_subdirectory(googletest)
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add_subdirectory(cpuinfo)
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add_subdirectory(cpuinfo)
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add_subdirectory(fast_float)
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if(ENABLE_CUBEB)
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if(ENABLE_CUBEB)
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add_subdirectory(cubeb)
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add_subdirectory(cubeb)
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@ -0,0 +1,2 @@
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Daniel Lemire
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João Paulo Magalhaes
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@ -0,0 +1,3 @@
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add_library(fast_float INTERFACE)
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target_include_directories(fast_float INTERFACE "${CMAKE_CURRENT_SOURCE_DIR}/include")
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@ -0,0 +1,6 @@
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Eugene Golushkov
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Maksim Kita
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Marcin Wojdyr
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Neal Richardson
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Tim Paine
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Fabio Pellacini
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@ -0,0 +1,190 @@
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Apache License
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Version 2.0, January 2004
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http://www.apache.org/licenses/
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END OF TERMS AND CONDITIONS
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Copyright 2021 The fast_float authors
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Licensed under the Apache License, Version 2.0 (the "License");
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you may not use this file except in compliance with the License.
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@ -0,0 +1,27 @@
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MIT License
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Copyright (c) 2021 The fast_float authors
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The above copyright notice and this permission notice
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shall be included in all copies or substantial portions
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THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF
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DEALINGS IN THE SOFTWARE.
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@ -0,0 +1,247 @@
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## fast_float number parsing library: 4x faster than strtod
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The fast_float library provides fast header-only implementations for the C++ from_chars
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functions for `float` and `double` types. These functions convert ASCII strings representing
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decimal values (e.g., `1.3e10`) into binary types. We provide exact rounding (including
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round to even). In our experience, these `fast_float` functions many times faster than comparable number-parsing functions from existing C++ standard libraries.
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Specifically, `fast_float` provides the following two functions with a C++17-like syntax (the library itself only requires C++11):
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```C++
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from_chars_result from_chars(const char* first, const char* last, float& value, ...);
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from_chars_result from_chars(const char* first, const char* last, double& value, ...);
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```
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The return type (`from_chars_result`) is defined as the struct:
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```C++
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struct from_chars_result {
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const char* ptr;
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std::errc ec;
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};
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```
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It parses the character sequence [first,last) for a number. It parses floating-point numbers expecting
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a locale-independent format equivalent to the C++17 from_chars function.
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The resulting floating-point value is the closest floating-point values (using either float or double),
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using the "round to even" convention for values that would otherwise fall right in-between two values.
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That is, we provide exact parsing according to the IEEE standard.
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Given a successful parse, the pointer (`ptr`) in the returned value is set to point right after the
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parsed number, and the `value` referenced is set to the parsed value. In case of error, the returned
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`ec` contains a representative error, otherwise the default (`std::errc()`) value is stored.
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The implementation does not throw and does not allocate memory (e.g., with `new` or `malloc`).
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It will parse infinity and nan values.
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Example:
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``` C++
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#include "fast_float/fast_float.h"
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#include <iostream>
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int main() {
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const std::string input = "3.1416 xyz ";
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double result;
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auto answer = fast_float::from_chars(input.data(), input.data()+input.size(), result);
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if(answer.ec != std::errc()) { std::cerr << "parsing failure\n"; return EXIT_FAILURE; }
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std::cout << "parsed the number " << result << std::endl;
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return EXIT_SUCCESS;
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}
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```
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Like the C++17 standard, the `fast_float::from_chars` functions take an optional last argument of
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the type `fast_float::chars_format`. It is a bitset value: we check whether
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`fmt & fast_float::chars_format::fixed` and `fmt & fast_float::chars_format::scientific` are set
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to determine whether we allow the fixed point and scientific notation respectively.
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The default is `fast_float::chars_format::general` which allows both `fixed` and `scientific`.
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The library seeks to follow the C++17 (see [20.19.3](http://eel.is/c++draft/charconv.from.chars).(7.1)) specification.
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* The `from_chars` function does not skip leading white-space characters.
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* [A leading `+` sign](https://en.cppreference.com/w/cpp/utility/from_chars) is forbidden.
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* 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.
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Furthermore, we have the following restrictions:
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* We only support `float` and `double` types at this time.
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* We only support the decimal format: we do not support hexadecimal strings.
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* For values that are either very large or very small (e.g., `1e9999`), we represent it using the infinity or negative infinity value.
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We support Visual Studio, macOS, Linux, freeBSD. We support big and little endian. We support 32-bit and 64-bit systems.
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We assume that the rounding mode is set to nearest (`std::fegetround() == FE_TONEAREST`).
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## Using commas as decimal separator
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The C++ standard stipulate that `from_chars` has to be locale-independent. In
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particular, the decimal separator has to be the period (`.`). However,
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some users still want to use the `fast_float` library with in a locale-dependent
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manner. Using a separate function called `from_chars_advanced`, we allow the users
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to pass a `parse_options` instance which contains a custom decimal separator (e.g.,
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the comma). You may use it as follows.
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```C++
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#include "fast_float/fast_float.h"
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#include <iostream>
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int main() {
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const std::string input = "3,1416 xyz ";
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double result;
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fast_float::parse_options options{fast_float::chars_format::general, ','};
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auto answer = fast_float::from_chars_advanced(input.data(), input.data()+input.size(), result, options);
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if((answer.ec != std::errc()) || ((result != 3.1416))) { std::cerr << "parsing failure\n"; return EXIT_FAILURE; }
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std::cout << "parsed the number " << result << std::endl;
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return EXIT_SUCCESS;
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}
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```
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You can parse delimited numbers:
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```C++
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const std::string input = "234532.3426362,7869234.9823,324562.645";
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double result;
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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.
|
||||||
|
```
|
||||||
|
|
||||||
|
|
||||||
|
## 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).
|
||||||
|
|
||||||
|
## Reference
|
||||||
|
|
||||||
|
- Daniel Lemire, [Number Parsing at a Gigabyte per Second](https://arxiv.org/abs/2101.11408), Software: Practice and Experience 51 (8), 2021.
|
||||||
|
|
||||||
|
## 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 [Yandex ClickHouse](https://github.com/ClickHouse/ClickHouse) and by [Google Jsonnet](https://github.com/google/jsonnet).
|
||||||
|
|
||||||
|
|
||||||
|
## 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
|
||||||
|
|
||||||
|
[](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/v3.4.0/fast_float.h
|
||||||
|
|
||||||
|
## 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> at your option.
|
||||||
|
</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 dual licensed as above, without any additional terms or conditions.
|
||||||
|
</sub>
|
||||||
|
|
@ -0,0 +1,227 @@
|
||||||
|
#ifndef FASTFLOAT_ASCII_NUMBER_H
|
||||||
|
#define FASTFLOAT_ASCII_NUMBER_H
|
||||||
|
|
||||||
|
#include <cctype>
|
||||||
|
#include <cstdint>
|
||||||
|
#include <cstring>
|
||||||
|
#include <iterator>
|
||||||
|
|
||||||
|
#include "float_common.h"
|
||||||
|
|
||||||
|
namespace fast_float {
|
||||||
|
|
||||||
|
// Next function can be micro-optimized, but compilers are entirely
|
||||||
|
// able to optimize it well.
|
||||||
|
fastfloat_really_inline bool is_integer(char c) noexcept { return c >= '0' && c <= '9'; }
|
||||||
|
|
||||||
|
fastfloat_really_inline uint64_t byteswap(uint64_t val) {
|
||||||
|
return (val & 0xFF00000000000000) >> 56
|
||||||
|
| (val & 0x00FF000000000000) >> 40
|
||||||
|
| (val & 0x0000FF0000000000) >> 24
|
||||||
|
| (val & 0x000000FF00000000) >> 8
|
||||||
|
| (val & 0x00000000FF000000) << 8
|
||||||
|
| (val & 0x0000000000FF0000) << 24
|
||||||
|
| (val & 0x000000000000FF00) << 40
|
||||||
|
| (val & 0x00000000000000FF) << 56;
|
||||||
|
}
|
||||||
|
|
||||||
|
fastfloat_really_inline uint64_t read_u64(const char *chars) {
|
||||||
|
uint64_t val;
|
||||||
|
::memcpy(&val, chars, sizeof(uint64_t));
|
||||||
|
#if FASTFLOAT_IS_BIG_ENDIAN == 1
|
||||||
|
// Need to read as-if the number was in little-endian order.
|
||||||
|
val = byteswap(val);
|
||||||
|
#endif
|
||||||
|
return val;
|
||||||
|
}
|
||||||
|
|
||||||
|
fastfloat_really_inline void write_u64(uint8_t *chars, uint64_t val) {
|
||||||
|
#if FASTFLOAT_IS_BIG_ENDIAN == 1
|
||||||
|
// Need to read as-if the number was in little-endian order.
|
||||||
|
val = byteswap(val);
|
||||||
|
#endif
|
||||||
|
::memcpy(chars, &val, sizeof(uint64_t));
|
||||||
|
}
|
||||||
|
|
||||||
|
// credit @aqrit
|
||||||
|
fastfloat_really_inline uint32_t parse_eight_digits_unrolled(uint64_t val) {
|
||||||
|
const uint64_t mask = 0x000000FF000000FF;
|
||||||
|
const uint64_t mul1 = 0x000F424000000064; // 100 + (1000000ULL << 32)
|
||||||
|
const uint64_t mul2 = 0x0000271000000001; // 1 + (10000ULL << 32)
|
||||||
|
val -= 0x3030303030303030;
|
||||||
|
val = (val * 10) + (val >> 8); // val = (val * 2561) >> 8;
|
||||||
|
val = (((val & mask) * mul1) + (((val >> 16) & mask) * mul2)) >> 32;
|
||||||
|
return uint32_t(val);
|
||||||
|
}
|
||||||
|
|
||||||
|
fastfloat_really_inline uint32_t parse_eight_digits_unrolled(const char *chars) noexcept {
|
||||||
|
return parse_eight_digits_unrolled(read_u64(chars));
|
||||||
|
}
|
||||||
|
|
||||||
|
// credit @aqrit
|
||||||
|
fastfloat_really_inline bool is_made_of_eight_digits_fast(uint64_t val) noexcept {
|
||||||
|
return !((((val + 0x4646464646464646) | (val - 0x3030303030303030)) &
|
||||||
|
0x8080808080808080));
|
||||||
|
}
|
||||||
|
|
||||||
|
fastfloat_really_inline bool is_made_of_eight_digits_fast(const char *chars) noexcept {
|
||||||
|
return is_made_of_eight_digits_fast(read_u64(chars));
|
||||||
|
}
|
||||||
|
|
||||||
|
typedef span<const char> byte_span;
|
||||||
|
|
||||||
|
struct parsed_number_string {
|
||||||
|
int64_t exponent{0};
|
||||||
|
uint64_t mantissa{0};
|
||||||
|
const char *lastmatch{nullptr};
|
||||||
|
bool negative{false};
|
||||||
|
bool valid{false};
|
||||||
|
bool too_many_digits{false};
|
||||||
|
// contains the range of the significant digits
|
||||||
|
byte_span integer{}; // non-nullable
|
||||||
|
byte_span fraction{}; // nullable
|
||||||
|
};
|
||||||
|
|
||||||
|
// Assuming that you use no more than 19 digits, this will
|
||||||
|
// parse an ASCII string.
|
||||||
|
fastfloat_really_inline
|
||||||
|
parsed_number_string parse_number_string(const char *p, const char *pend, parse_options options) noexcept {
|
||||||
|
const chars_format fmt = options.format;
|
||||||
|
const char decimal_point = options.decimal_point;
|
||||||
|
|
||||||
|
parsed_number_string answer;
|
||||||
|
answer.valid = false;
|
||||||
|
answer.too_many_digits = false;
|
||||||
|
answer.negative = (*p == '-');
|
||||||
|
if (*p == '-') { // C++17 20.19.3.(7.1) explicitly forbids '+' sign here
|
||||||
|
++p;
|
||||||
|
if (p == pend) {
|
||||||
|
return answer;
|
||||||
|
}
|
||||||
|
if (!is_integer(*p) && (*p != decimal_point)) { // a sign must be followed by an integer or the dot
|
||||||
|
return answer;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
const char *const start_digits = p;
|
||||||
|
|
||||||
|
uint64_t i = 0; // an unsigned int avoids signed overflows (which are bad)
|
||||||
|
|
||||||
|
while ((p != pend) && is_integer(*p)) {
|
||||||
|
// a multiplication by 10 is cheaper than an arbitrary integer
|
||||||
|
// multiplication
|
||||||
|
i = 10 * i +
|
||||||
|
uint64_t(*p - '0'); // might overflow, we will handle the overflow later
|
||||||
|
++p;
|
||||||
|
}
|
||||||
|
const char *const end_of_integer_part = p;
|
||||||
|
int64_t digit_count = int64_t(end_of_integer_part - start_digits);
|
||||||
|
answer.integer = byte_span(start_digits, size_t(digit_count));
|
||||||
|
int64_t exponent = 0;
|
||||||
|
if ((p != pend) && (*p == decimal_point)) {
|
||||||
|
++p;
|
||||||
|
const char* 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.
|
||||||
|
while ((std::distance(p, pend) >= 8) && is_made_of_eight_digits_fast(p)) {
|
||||||
|
i = i * 100000000 + parse_eight_digits_unrolled(p); // in rare cases, this will overflow, but that's ok
|
||||||
|
p += 8;
|
||||||
|
}
|
||||||
|
while ((p != pend) && is_integer(*p)) {
|
||||||
|
uint8_t digit = uint8_t(*p - '0');
|
||||||
|
++p;
|
||||||
|
i = i * 10 + digit; // in rare cases, this will overflow, but that's ok
|
||||||
|
}
|
||||||
|
exponent = before - p;
|
||||||
|
answer.fraction = byte_span(before, size_t(p - before));
|
||||||
|
digit_count -= exponent;
|
||||||
|
}
|
||||||
|
// we must have encountered at least one integer!
|
||||||
|
if (digit_count == 0) {
|
||||||
|
return answer;
|
||||||
|
}
|
||||||
|
int64_t exp_number = 0; // explicit exponential part
|
||||||
|
if ((fmt & chars_format::scientific) && (p != pend) && (('e' == *p) || ('E' == *p))) {
|
||||||
|
const char * location_of_e = p;
|
||||||
|
++p;
|
||||||
|
bool neg_exp = false;
|
||||||
|
if ((p != pend) && ('-' == *p)) {
|
||||||
|
neg_exp = true;
|
||||||
|
++p;
|
||||||
|
} else if ((p != pend) && ('+' == *p)) { // '+' on exponent is allowed by C++17 20.19.3.(7.1)
|
||||||
|
++p;
|
||||||
|
}
|
||||||
|
if ((p == pend) || !is_integer(*p)) {
|
||||||
|
if(!(fmt & chars_format::fixed)) {
|
||||||
|
// We are in error.
|
||||||
|
return answer;
|
||||||
|
}
|
||||||
|
// Otherwise, we will be ignoring the 'e'.
|
||||||
|
p = location_of_e;
|
||||||
|
} else {
|
||||||
|
while ((p != pend) && is_integer(*p)) {
|
||||||
|
uint8_t digit = uint8_t(*p - '0');
|
||||||
|
if (exp_number < 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.
|
||||||
|
const char *start = start_digits;
|
||||||
|
while ((start != pend) && (*start == '0' || *start == decimal_point)) {
|
||||||
|
if(*start == '0') { digit_count --; }
|
||||||
|
start++;
|
||||||
|
}
|
||||||
|
if (digit_count > 19) {
|
||||||
|
answer.too_many_digits = true;
|
||||||
|
// Let us start again, this time, avoiding overflows.
|
||||||
|
// We don't need to check if is_integer, since we use the
|
||||||
|
// pre-tokenized spans from above.
|
||||||
|
i = 0;
|
||||||
|
p = answer.integer.ptr;
|
||||||
|
const char* 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 - '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;
|
||||||
|
const char* frac_end = p + answer.fraction.len();
|
||||||
|
while((i < minimal_nineteen_digit_integer) && (p != frac_end)) {
|
||||||
|
i = i * 10 + uint64_t(*p - '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;
|
||||||
|
}
|
||||||
|
|
||||||
|
} // namespace fast_float
|
||||||
|
|
||||||
|
#endif
|
||||||
|
|
@ -0,0 +1,590 @@
|
||||||
|
#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.
|
||||||
|
stackvec(limb_span s) {
|
||||||
|
FASTFLOAT_ASSERT(try_extend(s));
|
||||||
|
}
|
||||||
|
|
||||||
|
limb& operator[](size_t index) noexcept {
|
||||||
|
FASTFLOAT_DEBUG_ASSERT(index < length);
|
||||||
|
return data[index];
|
||||||
|
}
|
||||||
|
const limb& operator[](size_t index) const noexcept {
|
||||||
|
FASTFLOAT_DEBUG_ASSERT(index < length);
|
||||||
|
return data[index];
|
||||||
|
}
|
||||||
|
// index from the end of the container
|
||||||
|
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.
|
||||||
|
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
|
||||||
|
void push_unchecked(limb value) noexcept {
|
||||||
|
data[length] = value;
|
||||||
|
length++;
|
||||||
|
}
|
||||||
|
// append item to vector, returning if item was added
|
||||||
|
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
|
||||||
|
void extend_unchecked(limb_span s) noexcept {
|
||||||
|
limb* ptr = data + length;
|
||||||
|
::memcpy((void*)ptr, (const void*)s.ptr, sizeof(limb) * s.len());
|
||||||
|
set_len(len() + s.len());
|
||||||
|
}
|
||||||
|
// try to add items to the vector, returning if items were added
|
||||||
|
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.
|
||||||
|
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.
|
||||||
|
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.
|
||||||
|
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.
|
||||||
|
void normalize() noexcept {
|
||||||
|
while (len() > 0 && rindex(0) == 0) {
|
||||||
|
length--;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
};
|
||||||
|
|
||||||
|
fastfloat_really_inline
|
||||||
|
uint64_t empty_hi64(bool& truncated) noexcept {
|
||||||
|
truncated = false;
|
||||||
|
return 0;
|
||||||
|
}
|
||||||
|
|
||||||
|
fastfloat_really_inline
|
||||||
|
uint64_t uint64_hi64(uint64_t r0, bool& truncated) noexcept {
|
||||||
|
truncated = false;
|
||||||
|
int shl = leading_zeroes(r0);
|
||||||
|
return r0 << shl;
|
||||||
|
}
|
||||||
|
|
||||||
|
fastfloat_really_inline
|
||||||
|
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
|
||||||
|
uint64_t uint32_hi64(uint32_t r0, bool& truncated) noexcept {
|
||||||
|
return uint64_hi64(r0, truncated);
|
||||||
|
}
|
||||||
|
|
||||||
|
fastfloat_really_inline
|
||||||
|
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
|
||||||
|
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
|
||||||
|
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)
|
||||||
|
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
|
||||||
|
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 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 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 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>
|
||||||
|
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 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>
|
||||||
|
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>
|
||||||
|
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;
|
||||||
|
}
|
||||||
|
|
||||||
|
// 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 {
|
||||||
|
// storage of the limbs, in little-endian order.
|
||||||
|
stackvec<bigint_limbs> vec;
|
||||||
|
|
||||||
|
bigint(): vec() {}
|
||||||
|
bigint(const bigint &) = delete;
|
||||||
|
bigint &operator=(const bigint &) = delete;
|
||||||
|
bigint(bigint &&) = delete;
|
||||||
|
bigint &operator=(bigint &&other) = delete;
|
||||||
|
|
||||||
|
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.
|
||||||
|
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.
|
||||||
|
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.
|
||||||
|
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.
|
||||||
|
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;
|
||||||
|
::memmove(dst, src, sizeof(limb) * 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.
|
||||||
|
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.
|
||||||
|
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.
|
||||||
|
int bit_length() const noexcept {
|
||||||
|
int lz = ctlz();
|
||||||
|
return int(limb_bits * vec.len()) - lz;
|
||||||
|
}
|
||||||
|
|
||||||
|
bool mul(limb y) noexcept {
|
||||||
|
return small_mul(vec, y);
|
||||||
|
}
|
||||||
|
|
||||||
|
bool add(limb y) noexcept {
|
||||||
|
return small_add(vec, y);
|
||||||
|
}
|
||||||
|
|
||||||
|
// multiply as if by 2 raised to a power.
|
||||||
|
bool pow2(uint32_t exp) noexcept {
|
||||||
|
return shl(exp);
|
||||||
|
}
|
||||||
|
|
||||||
|
// multiply as if by 5 raised to a power.
|
||||||
|
bool pow5(uint32_t exp) noexcept {
|
||||||
|
// multiply by a power of 5
|
||||||
|
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
|
||||||
|
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) {
|
||||||
|
FASTFLOAT_TRY(small_mul(vec, limb(small_power_of_5[exp])));
|
||||||
|
}
|
||||||
|
|
||||||
|
return true;
|
||||||
|
}
|
||||||
|
|
||||||
|
// multiply as if by 10 raised to a power.
|
||||||
|
bool pow10(uint32_t exp) noexcept {
|
||||||
|
FASTFLOAT_TRY(pow5(exp));
|
||||||
|
return pow2(exp);
|
||||||
|
}
|
||||||
|
};
|
||||||
|
|
||||||
|
} // namespace fast_float
|
||||||
|
|
||||||
|
#endif
|
||||||
|
|
@ -0,0 +1,194 @@
|
||||||
|
#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
|
||||||
|
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
|
||||||
|
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
|
||||||
|
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
|
||||||
|
adjusted_mantissa compute_float(int64_t q, uint64_t w) noexcept {
|
||||||
|
adjusted_mantissa answer;
|
||||||
|
if ((w == 0) || (q < binary::smallest_power_of_ten())) {
|
||||||
|
answer.power2 = 0;
|
||||||
|
answer.mantissa = 0;
|
||||||
|
// result should be zero
|
||||||
|
return answer;
|
||||||
|
}
|
||||||
|
if (q > binary::largest_power_of_ten()) {
|
||||||
|
// we want to get infinity:
|
||||||
|
answer.power2 = binary::infinite_power();
|
||||||
|
answer.mantissa = 0;
|
||||||
|
return answer;
|
||||||
|
}
|
||||||
|
// At this point in time q is in [powers::smallest_power_of_five, powers::largest_power_of_five].
|
||||||
|
|
||||||
|
// We want the most significant bit of i to be 1. Shift if needed.
|
||||||
|
int lz = leading_zeroes(w);
|
||||||
|
w <<= lz;
|
||||||
|
|
||||||
|
// The required precision is binary::mantissa_explicit_bits() + 3 because
|
||||||
|
// 1. We need the implicit bit
|
||||||
|
// 2. We need an extra bit for rounding purposes
|
||||||
|
// 3. We might lose a bit due to the "upperbit" routine (result too small, requiring a shift)
|
||||||
|
|
||||||
|
value128 product = compute_product_approximation<binary::mantissa_explicit_bits() + 3>(q, w);
|
||||||
|
if(product.low == 0xFFFFFFFFFFFFFFFF) { // could guard it further
|
||||||
|
// In some very rare cases, this could happen, in which case we might need a more accurate
|
||||||
|
// computation that what we can provide cheaply. This is very, very unlikely.
|
||||||
|
//
|
||||||
|
const bool inside_safe_exponent = (q >= -27) && (q <= 55); // always good because 5**q <2**128 when q>=0,
|
||||||
|
// and otherwise, for q<0, we have 5**-q<2**64 and the 128-bit reciprocal allows for exact computation.
|
||||||
|
if(!inside_safe_exponent) {
|
||||||
|
return compute_error_scaled<binary>(q, product.high, lz);
|
||||||
|
}
|
||||||
|
}
|
||||||
|
// 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
|
||||||
|
|
@ -0,0 +1,407 @@
|
||||||
|
#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.
|
||||||
|
fastfloat_really_inline int32_t scientific_exponent(parsed_number_string& 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 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;
|
||||||
|
::memcpy(&bits, &value, sizeof(T));
|
||||||
|
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 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 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
|
||||||
|
void round_nearest_tie_even(adjusted_mantissa& am, int32_t shift, callback cb) noexcept {
|
||||||
|
uint64_t mask;
|
||||||
|
uint64_t halfway;
|
||||||
|
if (shift == 64) {
|
||||||
|
mask = UINT64_MAX;
|
||||||
|
} else {
|
||||||
|
mask = (uint64_t(1) << shift) - 1;
|
||||||
|
}
|
||||||
|
if (shift == 0) {
|
||||||
|
halfway = 0;
|
||||||
|
} else {
|
||||||
|
halfway = 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 void round_down(adjusted_mantissa& am, int32_t shift) noexcept {
|
||||||
|
if (shift == 64) {
|
||||||
|
am.mantissa = 0;
|
||||||
|
} else {
|
||||||
|
am.mantissa >>= shift;
|
||||||
|
}
|
||||||
|
am.power2 += shift;
|
||||||
|
}
|
||||||
|
|
||||||
|
fastfloat_really_inline void skip_zeros(const char*& first, const char* last) noexcept {
|
||||||
|
uint64_t val;
|
||||||
|
while (std::distance(first, last) >= 8) {
|
||||||
|
::memcpy(&val, first, sizeof(uint64_t));
|
||||||
|
if (val != 0x3030303030303030) {
|
||||||
|
break;
|
||||||
|
}
|
||||||
|
first += 8;
|
||||||
|
}
|
||||||
|
while (first != last) {
|
||||||
|
if (*first != '0') {
|
||||||
|
break;
|
||||||
|
}
|
||||||
|
first++;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
// determine if any non-zero digits were truncated.
|
||||||
|
// all characters must be valid digits.
|
||||||
|
fastfloat_really_inline bool is_truncated(const char* first, const char* last) noexcept {
|
||||||
|
// do 8-bit optimizations, can just compare to 8 literal 0s.
|
||||||
|
uint64_t val;
|
||||||
|
while (std::distance(first, last) >= 8) {
|
||||||
|
::memcpy(&val, first, sizeof(uint64_t));
|
||||||
|
if (val != 0x3030303030303030) {
|
||||||
|
return true;
|
||||||
|
}
|
||||||
|
first += 8;
|
||||||
|
}
|
||||||
|
while (first != last) {
|
||||||
|
if (*first != '0') {
|
||||||
|
return true;
|
||||||
|
}
|
||||||
|
first++;
|
||||||
|
}
|
||||||
|
return false;
|
||||||
|
}
|
||||||
|
|
||||||
|
fastfloat_really_inline bool is_truncated(byte_span s) noexcept {
|
||||||
|
return is_truncated(s.ptr, s.ptr + s.len());
|
||||||
|
}
|
||||||
|
|
||||||
|
fastfloat_really_inline
|
||||||
|
void parse_eight_digits(const char*& p, limb& value, size_t& counter, size_t& count) noexcept {
|
||||||
|
value = value * 100000000 + parse_eight_digits_unrolled(p);
|
||||||
|
p += 8;
|
||||||
|
counter += 8;
|
||||||
|
count += 8;
|
||||||
|
}
|
||||||
|
|
||||||
|
fastfloat_really_inline
|
||||||
|
void parse_one_digit(const char*& p, limb& value, size_t& counter, size_t& count) noexcept {
|
||||||
|
value = value * 10 + limb(*p - '0');
|
||||||
|
p++;
|
||||||
|
counter++;
|
||||||
|
count++;
|
||||||
|
}
|
||||||
|
|
||||||
|
fastfloat_really_inline
|
||||||
|
void add_native(bigint& big, limb power, limb value) noexcept {
|
||||||
|
big.mul(power);
|
||||||
|
big.add(value);
|
||||||
|
}
|
||||||
|
|
||||||
|
fastfloat_really_inline 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
|
||||||
|
inline void parse_mantissa(bigint& result, parsed_number_string& 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.
|
||||||
|
const char* p = num.integer.ptr;
|
||||||
|
const char* 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 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 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>
|
||||||
|
inline adjusted_mantissa digit_comp(parsed_number_string& 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
|
||||||
|
|
@ -0,0 +1,63 @@
|
||||||
|
#ifndef FASTFLOAT_FAST_FLOAT_H
|
||||||
|
#define FASTFLOAT_FAST_FLOAT_H
|
||||||
|
|
||||||
|
#include <system_error>
|
||||||
|
|
||||||
|
namespace fast_float {
|
||||||
|
enum chars_format {
|
||||||
|
scientific = 1<<0,
|
||||||
|
fixed = 1<<2,
|
||||||
|
hex = 1<<3,
|
||||||
|
general = fixed | scientific
|
||||||
|
};
|
||||||
|
|
||||||
|
|
||||||
|
struct from_chars_result {
|
||||||
|
const char *ptr;
|
||||||
|
std::errc ec;
|
||||||
|
};
|
||||||
|
|
||||||
|
struct parse_options {
|
||||||
|
constexpr explicit parse_options(chars_format fmt = chars_format::general,
|
||||||
|
char dot = '.')
|
||||||
|
: format(fmt), decimal_point(dot) {}
|
||||||
|
|
||||||
|
/** Which number formats are accepted */
|
||||||
|
chars_format format;
|
||||||
|
/** The character used as decimal point */
|
||||||
|
char decimal_point;
|
||||||
|
};
|
||||||
|
|
||||||
|
/**
|
||||||
|
* This function parses the character sequence [first,last) for a number. It parses floating-point numbers expecting
|
||||||
|
* a locale-indepent format equivalent to what is used by std::strtod in the default ("C") locale.
|
||||||
|
* The resulting floating-point value is the closest floating-point values (using either float or double),
|
||||||
|
* using the "round to even" convention for values that would otherwise fall right in-between two values.
|
||||||
|
* That is, we provide exact parsing according to the IEEE standard.
|
||||||
|
*
|
||||||
|
* Given a successful parse, the pointer (`ptr`) in the returned value is set to point right after the
|
||||||
|
* parsed number, and the `value` referenced is set to the parsed value. In case of error, the returned
|
||||||
|
* `ec` contains a representative error, otherwise the default (`std::errc()`) value is stored.
|
||||||
|
*
|
||||||
|
* The implementation does not throw and does not allocate memory (e.g., with `new` or `malloc`).
|
||||||
|
*
|
||||||
|
* Like the C++17 standard, the `fast_float::from_chars` functions take an optional last argument of
|
||||||
|
* the type `fast_float::chars_format`. It is a bitset value: we check whether
|
||||||
|
* `fmt & fast_float::chars_format::fixed` and `fmt & fast_float::chars_format::scientific` are set
|
||||||
|
* to determine whether we 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>
|
||||||
|
from_chars_result from_chars(const char *first, const char *last,
|
||||||
|
T &value, chars_format fmt = chars_format::general) noexcept;
|
||||||
|
|
||||||
|
/**
|
||||||
|
* Like from_chars, but accepts an `options` argument to govern number parsing.
|
||||||
|
*/
|
||||||
|
template<typename T>
|
||||||
|
from_chars_result from_chars_advanced(const char *first, const char *last,
|
||||||
|
T &value, parse_options options) noexcept;
|
||||||
|
|
||||||
|
} // namespace fast_float
|
||||||
|
#include "parse_number.h"
|
||||||
|
#endif // FASTFLOAT_FAST_FLOAT_H
|
||||||
|
|
@ -0,0 +1,699 @@
|
||||||
|
#ifndef FASTFLOAT_FAST_TABLE_H
|
||||||
|
#define FASTFLOAT_FAST_TABLE_H
|
||||||
|
|
||||||
|
#include <cstdint>
|
||||||
|
|
||||||
|
namespace fast_float {
|
||||||
|
|
||||||
|
/**
|
||||||
|
* When mapping numbers from decimal to binary,
|
||||||
|
* we go from w * 10^q to m * 2^p but we have
|
||||||
|
* 10^q = 5^q * 2^q, so effectively
|
||||||
|
* we are trying to match
|
||||||
|
* w * 2^q * 5^q to m * 2^p. Thus the powers of two
|
||||||
|
* are not a concern since they can be represented
|
||||||
|
* exactly using the binary notation, only the powers of five
|
||||||
|
* affect the binary significand.
|
||||||
|
*/
|
||||||
|
|
||||||
|
/**
|
||||||
|
* The smallest non-zero float (binary64) is 2^-1074.
|
||||||
|
* We take as input numbers of the form w x 10^q where w < 2^64.
|
||||||
|
* We have that w * 10^-343 < 2^(64-344) 5^-343 < 2^-1076.
|
||||||
|
* However, we have that
|
||||||
|
* (2^64-1) * 10^-342 = (2^64-1) * 2^-342 * 5^-342 > 2^-1074.
|
||||||
|
* Thus it is possible for a number of the form w * 10^-342 where
|
||||||
|
* w is a 64-bit value to be a non-zero floating-point number.
|
||||||
|
*********
|
||||||
|
* Any number of form w * 10^309 where w>= 1 is going to be
|
||||||
|
* infinite in binary64 so we never need to worry about powers
|
||||||
|
* of 5 greater than 308.
|
||||||
|
*/
|
||||||
|
template <class unused = void>
|
||||||
|
struct powers_template {
|
||||||
|
|
||||||
|
constexpr static int smallest_power_of_five = binary_format<double>::smallest_power_of_ten();
|
||||||
|
constexpr static int largest_power_of_five = binary_format<double>::largest_power_of_ten();
|
||||||
|
constexpr static int number_of_entries = 2 * (largest_power_of_five - smallest_power_of_five + 1);
|
||||||
|
// Powers of five from 5^-342 all the way to 5^308 rounded toward one.
|
||||||
|
static const uint64_t power_of_five_128[number_of_entries];
|
||||||
|
};
|
||||||
|
|
||||||
|
template <class unused>
|
||||||
|
const uint64_t powers_template<unused>::power_of_five_128[number_of_entries] = {
|
||||||
|
0xeef453d6923bd65a,0x113faa2906a13b3f,
|
||||||
|
0x9558b4661b6565f8,0x4ac7ca59a424c507,
|
||||||
|
0xbaaee17fa23ebf76,0x5d79bcf00d2df649,
|
||||||
|
0xe95a99df8ace6f53,0xf4d82c2c107973dc,
|
||||||
|
0x91d8a02bb6c10594,0x79071b9b8a4be869,
|
||||||
|
0xb64ec836a47146f9,0x9748e2826cdee284,
|
||||||
|
0xe3e27a444d8d98b7,0xfd1b1b2308169b25,
|
||||||
|
0x8e6d8c6ab0787f72,0xfe30f0f5e50e20f7,
|
||||||
|
0xb208ef855c969f4f,0xbdbd2d335e51a935,
|
||||||
|
0xde8b2b66b3bc4723,0xad2c788035e61382,
|
||||||
|
0x8b16fb203055ac76,0x4c3bcb5021afcc31,
|
||||||
|
0xaddcb9e83c6b1793,0xdf4abe242a1bbf3d,
|
||||||
|
0xd953e8624b85dd78,0xd71d6dad34a2af0d,
|
||||||
|
0x87d4713d6f33aa6b,0x8672648c40e5ad68,
|
||||||
|
0xa9c98d8ccb009506,0x680efdaf511f18c2,
|
||||||
|
0xd43bf0effdc0ba48,0x212bd1b2566def2,
|
||||||
|
0x84a57695fe98746d,0x14bb630f7604b57,
|
||||||
|
0xa5ced43b7e3e9188,0x419ea3bd35385e2d,
|
||||||
|
0xcf42894a5dce35ea,0x52064cac828675b9,
|
||||||
|
0x818995ce7aa0e1b2,0x7343efebd1940993,
|
||||||
|
0xa1ebfb4219491a1f,0x1014ebe6c5f90bf8,
|
||||||
|
0xca66fa129f9b60a6,0xd41a26e077774ef6,
|
||||||
|
0xfd00b897478238d0,0x8920b098955522b4,
|
||||||
|
0x9e20735e8cb16382,0x55b46e5f5d5535b0,
|
||||||
|
0xc5a890362fddbc62,0xeb2189f734aa831d,
|
||||||
|
0xf712b443bbd52b7b,0xa5e9ec7501d523e4,
|
||||||
|
0x9a6bb0aa55653b2d,0x47b233c92125366e,
|
||||||
|
0xc1069cd4eabe89f8,0x999ec0bb696e840a,
|
||||||
|
0xf148440a256e2c76,0xc00670ea43ca250d,
|
||||||
|
0x96cd2a865764dbca,0x380406926a5e5728,
|
||||||
|
0xbc807527ed3e12bc,0xc605083704f5ecf2,
|
||||||
|
0xeba09271e88d976b,0xf7864a44c633682e,
|
||||||
|
0x93445b8731587ea3,0x7ab3ee6afbe0211d,
|
||||||
|
0xb8157268fdae9e4c,0x5960ea05bad82964,
|
||||||
|
0xe61acf033d1a45df,0x6fb92487298e33bd,
|
||||||
|
0x8fd0c16206306bab,0xa5d3b6d479f8e056,
|
||||||
|
0xb3c4f1ba87bc8696,0x8f48a4899877186c,
|
||||||
|
0xe0b62e2929aba83c,0x331acdabfe94de87,
|
||||||
|
0x8c71dcd9ba0b4925,0x9ff0c08b7f1d0b14,
|
||||||
|
0xaf8e5410288e1b6f,0x7ecf0ae5ee44dd9,
|
||||||
|
0xdb71e91432b1a24a,0xc9e82cd9f69d6150,
|
||||||
|
0x892731ac9faf056e,0xbe311c083a225cd2,
|
||||||
|
0xab70fe17c79ac6ca,0x6dbd630a48aaf406,
|
||||||
|
0xd64d3d9db981787d,0x92cbbccdad5b108,
|
||||||
|
0x85f0468293f0eb4e,0x25bbf56008c58ea5,
|
||||||
|
0xa76c582338ed2621,0xaf2af2b80af6f24e,
|
||||||
|
0xd1476e2c07286faa,0x1af5af660db4aee1,
|
||||||
|
0x82cca4db847945ca,0x50d98d9fc890ed4d,
|
||||||
|
0xa37fce126597973c,0xe50ff107bab528a0,
|
||||||
|
0xcc5fc196fefd7d0c,0x1e53ed49a96272c8,
|
||||||
|
0xff77b1fcbebcdc4f,0x25e8e89c13bb0f7a,
|
||||||
|
0x9faacf3df73609b1,0x77b191618c54e9ac,
|
||||||
|
0xc795830d75038c1d,0xd59df5b9ef6a2417,
|
||||||
|
0xf97ae3d0d2446f25,0x4b0573286b44ad1d,
|
||||||
|
0x9becce62836ac577,0x4ee367f9430aec32,
|
||||||
|
0xc2e801fb244576d5,0x229c41f793cda73f,
|
||||||
|
0xf3a20279ed56d48a,0x6b43527578c1110f,
|
||||||
|
0x9845418c345644d6,0x830a13896b78aaa9,
|
||||||
|
0xbe5691ef416bd60c,0x23cc986bc656d553,
|
||||||
|
0xedec366b11c6cb8f,0x2cbfbe86b7ec8aa8,
|
||||||
|
0x94b3a202eb1c3f39,0x7bf7d71432f3d6a9,
|
||||||
|
0xb9e08a83a5e34f07,0xdaf5ccd93fb0cc53,
|
||||||
|
0xe858ad248f5c22c9,0xd1b3400f8f9cff68,
|
||||||
|
0x91376c36d99995be,0x23100809b9c21fa1,
|
||||||
|
0xb58547448ffffb2d,0xabd40a0c2832a78a,
|
||||||
|
0xe2e69915b3fff9f9,0x16c90c8f323f516c,
|
||||||
|
0x8dd01fad907ffc3b,0xae3da7d97f6792e3,
|
||||||
|
0xb1442798f49ffb4a,0x99cd11cfdf41779c,
|
||||||
|
0xdd95317f31c7fa1d,0x40405643d711d583,
|
||||||
|
0x8a7d3eef7f1cfc52,0x482835ea666b2572,
|
||||||
|
0xad1c8eab5ee43b66,0xda3243650005eecf,
|
||||||
|
0xd863b256369d4a40,0x90bed43e40076a82,
|
||||||
|
0x873e4f75e2224e68,0x5a7744a6e804a291,
|
||||||
|
0xa90de3535aaae202,0x711515d0a205cb36,
|
||||||
|
0xd3515c2831559a83,0xd5a5b44ca873e03,
|
||||||
|
0x8412d9991ed58091,0xe858790afe9486c2,
|
||||||
|
0xa5178fff668ae0b6,0x626e974dbe39a872,
|
||||||
|
0xce5d73ff402d98e3,0xfb0a3d212dc8128f,
|
||||||
|
0x80fa687f881c7f8e,0x7ce66634bc9d0b99,
|
||||||
|
0xa139029f6a239f72,0x1c1fffc1ebc44e80,
|
||||||
|
0xc987434744ac874e,0xa327ffb266b56220,
|
||||||
|
0xfbe9141915d7a922,0x4bf1ff9f0062baa8,
|
||||||
|
0x9d71ac8fada6c9b5,0x6f773fc3603db4a9,
|
||||||
|
0xc4ce17b399107c22,0xcb550fb4384d21d3,
|
||||||
|
0xf6019da07f549b2b,0x7e2a53a146606a48,
|
||||||
|
0x99c102844f94e0fb,0x2eda7444cbfc426d,
|
||||||
|
0xc0314325637a1939,0xfa911155fefb5308,
|
||||||
|
0xf03d93eebc589f88,0x793555ab7eba27ca,
|
||||||
|
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0x881cea14545c7575,0x7e50d64177da2e54,
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0xaa242499697392d2,0xdde50bd1d5d0b9e9,
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0xd4ad2dbfc3d07787,0x955e4ec64b44e864,
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0x84ec3c97da624ab4,0xbd5af13bef0b113e,
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0xa6274bbdd0fadd61,0xecb1ad8aeacdd58e,
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0xcfb11ead453994ba,0x67de18eda5814af2,
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0x81ceb32c4b43fcf4,0x80eacf948770ced7,
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0xa2425ff75e14fc31,0xa1258379a94d028d,
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0xcad2f7f5359a3b3e,0x96ee45813a04330,
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0xfd87b5f28300ca0d,0x8bca9d6e188853fc,
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0x9e74d1b791e07e48,0x775ea264cf55347e,
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0xc612062576589dda,0x95364afe032a819e,
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0xf79687aed3eec551,0x3a83ddbd83f52205,
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0x9abe14cd44753b52,0xc4926a9672793543,
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0xc16d9a0095928a27,0x75b7053c0f178294,
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0xf1c90080baf72cb1,0x5324c68b12dd6339,
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0x971da05074da7bee,0xd3f6fc16ebca5e04,
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0xbce5086492111aea,0x88f4bb1ca6bcf585,
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0xec1e4a7db69561a5,0x2b31e9e3d06c32e6,
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0x9392ee8e921d5d07,0x3aff322e62439fd0,
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0xb877aa3236a4b449,0x9befeb9fad487c3,
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0xe69594bec44de15b,0x4c2ebe687989a9b4,
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0x901d7cf73ab0acd9,0xf9d37014bf60a11,
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0xb424dc35095cd80f,0x538484c19ef38c95,
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0xe12e13424bb40e13,0x2865a5f206b06fba,
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0x8cbccc096f5088cb,0xf93f87b7442e45d4,
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0xdbe6fecebdedd5be,0xb573440e5a884d1c,
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0x89705f4136b4a597,0x31680a88f8953031,
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0xabcc77118461cefc,0xfdc20d2b36ba7c3e,
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0xd6bf94d5e57a42bc,0x3d32907604691b4d,
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0xa7c5ac471b478423,0xfcf80dc33721d54,
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0xd1b71758e219652b,0xd3c36113404ea4a9,
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0x83126e978d4fdf3b,0x645a1cac083126ea,
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0xa3d70a3d70a3d70a,0x3d70a3d70a3d70a4,
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0xcccccccccccccccc,0xcccccccccccccccd,
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0x8000000000000000,0x0,
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0xa000000000000000,0x0,
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0xc800000000000000,0x0,
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0xfa00000000000000,0x0,
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0x9c40000000000000,0x0,
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0xc350000000000000,0x0,
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0xf424000000000000,0x0,
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0x9896800000000000,0x0,
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0xbebc200000000000,0x0,
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0xee6b280000000000,0x0,
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0x9502f90000000000,0x0,
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0xba43b74000000000,0x0,
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0xe8d4a51000000000,0x0,
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0x9184e72a00000000,0x0,
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0xb5e620f480000000,0x0,
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0xe35fa931a0000000,0x0,
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0x8e1bc9bf04000000,0x0,
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0xb1a2bc2ec5000000,0x0,
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0xde0b6b3a76400000,0x0,
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0x8ac7230489e80000,0x0,
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0xad78ebc5ac620000,0x0,
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0xd8d726b7177a8000,0x0,
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0x878678326eac9000,0x0,
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0xa968163f0a57b400,0x0,
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0xd3c21bcecceda100,0x0,
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0x84595161401484a0,0x0,
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0xa56fa5b99019a5c8,0x0,
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0xcecb8f27f4200f3a,0x0,
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0x813f3978f8940984,0x4000000000000000,
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0xa18f07d736b90be5,0x5000000000000000,
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0xc9f2c9cd04674ede,0xa400000000000000,
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0xfc6f7c4045812296,0x4d00000000000000,
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0x9dc5ada82b70b59d,0xf020000000000000,
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0xc5371912364ce305,0x6c28000000000000,
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0xf684df56c3e01bc6,0xc732000000000000,
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0x9a130b963a6c115c,0x3c7f400000000000,
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0xc097ce7bc90715b3,0x4b9f100000000000,
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0xf0bdc21abb48db20,0x1e86d40000000000,
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0x96769950b50d88f4,0x1314448000000000,
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0xbc143fa4e250eb31,0x17d955a000000000,
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0xeb194f8e1ae525fd,0x5dcfab0800000000,
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0x92efd1b8d0cf37be,0x5aa1cae500000000,
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0xb7abc627050305ad,0xf14a3d9e40000000,
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0xe596b7b0c643c719,0x6d9ccd05d0000000,
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0x8f7e32ce7bea5c6f,0xe4820023a2000000,
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0xb35dbf821ae4f38b,0xdda2802c8a800000,
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0xe0352f62a19e306e,0xd50b2037ad200000,
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0x8c213d9da502de45,0x4526f422cc340000,
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0xaf298d050e4395d6,0x9670b12b7f410000,
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0xdaf3f04651d47b4c,0x3c0cdd765f114000,
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0xd5d238a4abe98068,0x72a4904598d6d880,
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0xd0cf4b50cfe20765,0xfff4b4e3f741cf6d,
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0xc2781f49ffcfa6d5,0x3cbf6b71c76b25fb,
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0xbde94e8e43d0c8ec,0x3d52eeed1cbea317,
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0x945e455f24fb1cf8,0x8fe8caa93e74ef6a,
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0xb975d6b6ee39e436,0xb3e2fd538e122b44,
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0xe7d34c64a9c85d44,0x60dbbca87196b616,
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0xb51d13aea4a488dd,0x6babab6398bdbe41,
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0xe264589a4dcdab14,0xc696963c7eed2dd1,
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0x8d7eb76070a08aec,0xfc1e1de5cf543ca2,
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0xb0de65388cc8ada8,0x3b25a55f43294bcb,
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0xdd15fe86affad912,0x49ef0eb713f39ebe,
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0x8a2dbf142dfcc7ab,0x6e3569326c784337,
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0xd7e77a8f87daf7fb,0xdc33745ec97be906,
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0xd2d80db02aabd62b,0xf50a3fa490c30190,
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0x83c7088e1aab65db,0x792667c6da79e0fa,
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0xcde6fd5e09abcf26,0xed4c0226b55e6f86,
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0x9d174b2dcec0e47b,0x62eb0d64283f9c76,
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0xf5746577930d6500,0xca8f44ec7ee36479,
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0xb6e0c377cfa2e12e,0x6f8b2fb00c77836c,
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0xe498f455c38b997a,0xb6dfb9c0f956447,
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0xb2977ee300c50fe7,0x58edec91ec2cb657,
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0xdf3d5e9bc0f653e1,0x2f2967b66737e3ed,
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0x8b865b215899f46c,0xbd79e0d20082ee74,
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0xda01ee641a708de9,0xe80e6f4820cc9495,
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0x884134fe908658b2,0x3109058d147fdcdd,
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0xaa51823e34a7eede,0xbd4b46f0599fd415,
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0xd4e5e2cdc1d1ea96,0x6c9e18ac7007c91a,
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0x850fadc09923329e,0x3e2cf6bc604ddb0,
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0xa6539930bf6bff45,0x84db8346b786151c,
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0xcfe87f7cef46ff16,0xe612641865679a63,
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0x81f14fae158c5f6e,0x4fcb7e8f3f60c07e,
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0xa26da3999aef7749,0xe3be5e330f38f09d,
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0xcb090c8001ab551c,0x5cadf5bfd3072cc5,
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0xfdcb4fa002162a63,0x73d9732fc7c8f7f6,
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0x9e9f11c4014dda7e,0x2867e7fddcdd9afa,
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0xc646d63501a1511d,0xb281e1fd541501b8,
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0xf7d88bc24209a565,0x1f225a7ca91a4226,
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0x9ae757596946075f,0x3375788de9b06958,
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0xc1a12d2fc3978937,0x52d6b1641c83ae,
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0xf209787bb47d6b84,0xc0678c5dbd23a49a,
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0x9745eb4d50ce6332,0xf840b7ba963646e0,
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0xbd176620a501fbff,0xb650e5a93bc3d898,
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0xec5d3fa8ce427aff,0xa3e51f138ab4cebe,
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0x93ba47c980e98cdf,0xc66f336c36b10137,
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0xb8a8d9bbe123f017,0xb80b0047445d4184,
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0xe6d3102ad96cec1d,0xa60dc059157491e5,
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0x9043ea1ac7e41392,0x87c89837ad68db2f,
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0xb454e4a179dd1877,0x29babe4598c311fb,
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0xe16a1dc9d8545e94,0xf4296dd6fef3d67a,
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0x8ce2529e2734bb1d,0x1899e4a65f58660c,
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0xb01ae745b101e9e4,0x5ec05dcff72e7f8f,
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0xdc21a1171d42645d,0x76707543f4fa1f73,
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0x899504ae72497eba,0x6a06494a791c53a8,
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0xabfa45da0edbde69,0x487db9d17636892,
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0xd6f8d7509292d603,0x45a9d2845d3c42b6,
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0x865b86925b9bc5c2,0xb8a2392ba45a9b2,
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0xa7f26836f282b732,0x8e6cac7768d7141e,
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0xd1ef0244af2364ff,0x3207d795430cd926,
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0x8335616aed761f1f,0x7f44e6bd49e807b8,
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0xa402b9c5a8d3a6e7,0x5f16206c9c6209a6,
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0xcd036837130890a1,0x36dba887c37a8c0f,
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0x802221226be55a64,0xc2494954da2c9789,
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0xa02aa96b06deb0fd,0xf2db9baa10b7bd6c,
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0xc83553c5c8965d3d,0x6f92829494e5acc7,
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0xfa42a8b73abbf48c,0xcb772339ba1f17f9,
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0x9c69a97284b578d7,0xff2a760414536efb,
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0xc38413cf25e2d70d,0xfef5138519684aba,
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0xf46518c2ef5b8cd1,0x7eb258665fc25d69,
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0x98bf2f79d5993802,0xef2f773ffbd97a61,
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0xbeeefb584aff8603,0xaafb550ffacfd8fa,
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0xeeaaba2e5dbf6784,0x95ba2a53f983cf38,
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0x952ab45cfa97a0b2,0xdd945a747bf26183,
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0xba756174393d88df,0x94f971119aeef9e4,
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0xe912b9d1478ceb17,0x7a37cd5601aab85d,
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0x91abb422ccb812ee,0xac62e055c10ab33a,
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0xb616a12b7fe617aa,0x577b986b314d6009,
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0xe39c49765fdf9d94,0xed5a7e85fda0b80b,
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0x8e41ade9fbebc27d,0x14588f13be847307,
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0xb1d219647ae6b31c,0x596eb2d8ae258fc8,
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0xde469fbd99a05fe3,0x6fca5f8ed9aef3bb,
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0x8aec23d680043bee,0x25de7bb9480d5854,
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0xada72ccc20054ae9,0xaf561aa79a10ae6a,
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0xd910f7ff28069da4,0x1b2ba1518094da04,
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0x87aa9aff79042286,0x90fb44d2f05d0842,
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0xa99541bf57452b28,0x353a1607ac744a53,
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0xd3fa922f2d1675f2,0x42889b8997915ce8,
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0x847c9b5d7c2e09b7,0x69956135febada11,
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0xa59bc234db398c25,0x43fab9837e699095,
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0xcf02b2c21207ef2e,0x94f967e45e03f4bb,
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0x8161afb94b44f57d,0x1d1be0eebac278f5,
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0xa1ba1ba79e1632dc,0x6462d92a69731732,
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0xca28a291859bbf93,0x7d7b8f7503cfdcfe,
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0xfcb2cb35e702af78,0x5cda735244c3d43e,
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0x9defbf01b061adab,0x3a0888136afa64a7,
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0xc56baec21c7a1916,0x88aaa1845b8fdd0,
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0xf6c69a72a3989f5b,0x8aad549e57273d45,
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0x9a3c2087a63f6399,0x36ac54e2f678864b,
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0xc0cb28a98fcf3c7f,0x84576a1bb416a7dd,
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0xf0fdf2d3f3c30b9f,0x656d44a2a11c51d5,
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0x969eb7c47859e743,0x9f644ae5a4b1b325,
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0xbc4665b596706114,0x873d5d9f0dde1fee,
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0xeb57ff22fc0c7959,0xa90cb506d155a7ea,
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0x9316ff75dd87cbd8,0x9a7f12442d588f2,
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0xb7dcbf5354e9bece,0xc11ed6d538aeb2f,
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0xe5d3ef282a242e81,0x8f1668c8a86da5fa,
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|
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,};
|
||||||
|
using powers = powers_template<>;
|
||||||
|
|
||||||
|
} // namespace fast_float
|
||||||
|
|
||||||
|
#endif
|
||||||
|
|
@ -0,0 +1,458 @@
|
||||||
|
#ifndef FASTFLOAT_FLOAT_COMMON_H
|
||||||
|
#define FASTFLOAT_FLOAT_COMMON_H
|
||||||
|
|
||||||
|
#include <cfloat>
|
||||||
|
#include <cstdint>
|
||||||
|
#include <cassert>
|
||||||
|
#include <cstring>
|
||||||
|
#include <type_traits>
|
||||||
|
|
||||||
|
#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__)) )
|
||||||
|
#define FASTFLOAT_64BIT 1
|
||||||
|
#elif (defined(__i386) || defined(__i386__) || defined(_M_IX86) \
|
||||||
|
|| defined(__arm__) || defined(_M_ARM) \
|
||||||
|
|| 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>
|
||||||
|
#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
|
||||||
|
|
||||||
|
#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) { if (!(x)) abort(); }
|
||||||
|
#endif
|
||||||
|
|
||||||
|
#ifndef FASTFLOAT_DEBUG_ASSERT
|
||||||
|
#include <cassert>
|
||||||
|
#define FASTFLOAT_DEBUG_ASSERT(x) assert(x)
|
||||||
|
#endif
|
||||||
|
|
||||||
|
// rust style `try!()` macro, or `?` operator
|
||||||
|
#define FASTFLOAT_TRY(x) { if (!(x)) return false; }
|
||||||
|
|
||||||
|
namespace fast_float {
|
||||||
|
|
||||||
|
// Compares two ASCII strings in a case insensitive manner.
|
||||||
|
inline bool fastfloat_strncasecmp(const char *input1, const char *input2,
|
||||||
|
size_t length) {
|
||||||
|
char running_diff{0};
|
||||||
|
for (size_t i = 0; i < length; i++) {
|
||||||
|
running_diff |= (input1[i] ^ input2[i]);
|
||||||
|
}
|
||||||
|
return (running_diff == 0) || (running_diff == 32);
|
||||||
|
}
|
||||||
|
|
||||||
|
#ifndef FLT_EVAL_METHOD
|
||||||
|
#error "FLT_EVAL_METHOD should be defined, please include cfloat."
|
||||||
|
#endif
|
||||||
|
|
||||||
|
// a pointer and a length to a contiguous block of memory
|
||||||
|
template <typename T>
|
||||||
|
struct span {
|
||||||
|
const T* ptr;
|
||||||
|
size_t length;
|
||||||
|
span(const T* _ptr, size_t _length) : ptr(_ptr), length(_length) {}
|
||||||
|
span() : ptr(nullptr), length(0) {}
|
||||||
|
|
||||||
|
constexpr size_t len() const noexcept {
|
||||||
|
return length;
|
||||||
|
}
|
||||||
|
|
||||||
|
const T& operator[](size_t index) const noexcept {
|
||||||
|
FASTFLOAT_DEBUG_ASSERT(index < length);
|
||||||
|
return ptr[index];
|
||||||
|
}
|
||||||
|
};
|
||||||
|
|
||||||
|
struct value128 {
|
||||||
|
uint64_t low;
|
||||||
|
uint64_t high;
|
||||||
|
value128(uint64_t _low, uint64_t _high) : low(_low), high(_high) {}
|
||||||
|
value128() : low(0), high(0) {}
|
||||||
|
};
|
||||||
|
|
||||||
|
/* result might be undefined when input_num is zero */
|
||||||
|
fastfloat_really_inline int leading_zeroes(uint64_t input_num) {
|
||||||
|
assert(input_num > 0);
|
||||||
|
#ifdef FASTFLOAT_VISUAL_STUDIO
|
||||||
|
#if defined(_M_X64) || defined(_M_ARM64)
|
||||||
|
unsigned long leading_zero = 0;
|
||||||
|
// Search the mask data from most significant bit (MSB)
|
||||||
|
// to least significant bit (LSB) for a set bit (1).
|
||||||
|
_BitScanReverse64(&leading_zero, input_num);
|
||||||
|
return (int)(63 - leading_zero);
|
||||||
|
#else
|
||||||
|
int last_bit = 0;
|
||||||
|
if(input_num & uint64_t(0xffffffff00000000)) input_num >>= 32, last_bit |= 32;
|
||||||
|
if(input_num & uint64_t( 0xffff0000)) input_num >>= 16, last_bit |= 16;
|
||||||
|
if(input_num & uint64_t( 0xff00)) input_num >>= 8, last_bit |= 8;
|
||||||
|
if(input_num & uint64_t( 0xf0)) input_num >>= 4, last_bit |= 4;
|
||||||
|
if(input_num & uint64_t( 0xc)) input_num >>= 2, last_bit |= 2;
|
||||||
|
if(input_num & uint64_t( 0x2)) input_num >>= 1, last_bit |= 1;
|
||||||
|
return 63 - last_bit;
|
||||||
|
#endif
|
||||||
|
#else
|
||||||
|
return __builtin_clzll(input_num);
|
||||||
|
#endif
|
||||||
|
}
|
||||||
|
|
||||||
|
#ifdef FASTFLOAT_32BIT
|
||||||
|
|
||||||
|
// slow emulation routine for 32-bit
|
||||||
|
fastfloat_really_inline uint64_t emulu(uint32_t x, uint32_t y) {
|
||||||
|
return x * (uint64_t)y;
|
||||||
|
}
|
||||||
|
|
||||||
|
// slow emulation routine for 32-bit
|
||||||
|
#if !defined(__MINGW64__)
|
||||||
|
fastfloat_really_inline uint64_t _umul128(uint64_t ab, uint64_t cd,
|
||||||
|
uint64_t *hi) {
|
||||||
|
uint64_t ad = emulu((uint32_t)(ab >> 32), (uint32_t)cd);
|
||||||
|
uint64_t bd = emulu((uint32_t)ab, (uint32_t)cd);
|
||||||
|
uint64_t adbc = ad + emulu((uint32_t)ab, (uint32_t)(cd >> 32));
|
||||||
|
uint64_t adbc_carry = !!(adbc < ad);
|
||||||
|
uint64_t lo = bd + (adbc << 32);
|
||||||
|
*hi = emulu((uint32_t)(ab >> 32), (uint32_t)(cd >> 32)) + (adbc >> 32) +
|
||||||
|
(adbc_carry << 32) + !!(lo < bd);
|
||||||
|
return lo;
|
||||||
|
}
|
||||||
|
#endif // !__MINGW64__
|
||||||
|
|
||||||
|
#endif // FASTFLOAT_32BIT
|
||||||
|
|
||||||
|
|
||||||
|
// compute 64-bit a*b
|
||||||
|
fastfloat_really_inline value128 full_multiplication(uint64_t a,
|
||||||
|
uint64_t b) {
|
||||||
|
value128 answer;
|
||||||
|
#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)
|
||||||
|
__uint128_t r = ((__uint128_t)a) * b;
|
||||||
|
answer.low = uint64_t(r);
|
||||||
|
answer.high = uint64_t(r >> 64);
|
||||||
|
#else
|
||||||
|
#error Not implemented
|
||||||
|
#endif
|
||||||
|
return answer;
|
||||||
|
}
|
||||||
|
|
||||||
|
struct adjusted_mantissa {
|
||||||
|
uint64_t mantissa{0};
|
||||||
|
int32_t power2{0}; // a negative value indicates an invalid result
|
||||||
|
adjusted_mantissa() = default;
|
||||||
|
bool operator==(const adjusted_mantissa &o) const {
|
||||||
|
return mantissa == o.mantissa && power2 == o.power2;
|
||||||
|
}
|
||||||
|
bool operator!=(const adjusted_mantissa &o) const {
|
||||||
|
return mantissa != o.mantissa || power2 != o.power2;
|
||||||
|
}
|
||||||
|
};
|
||||||
|
|
||||||
|
// Bias so we can get the real exponent with an invalid adjusted_mantissa.
|
||||||
|
constexpr static int32_t invalid_am_bias = -0x8000;
|
||||||
|
|
||||||
|
constexpr static double powers_of_ten_double[] = {
|
||||||
|
1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9, 1e10, 1e11,
|
||||||
|
1e12, 1e13, 1e14, 1e15, 1e16, 1e17, 1e18, 1e19, 1e20, 1e21, 1e22};
|
||||||
|
constexpr static float powers_of_ten_float[] = {1e0f, 1e1f, 1e2f, 1e3f, 1e4f, 1e5f,
|
||||||
|
1e6f, 1e7f, 1e8f, 1e9f, 1e10f};
|
||||||
|
// used for max_mantissa_double and max_mantissa_float
|
||||||
|
constexpr uint64_t constant_55555 = 5 * 5 * 5 * 5 * 5;
|
||||||
|
// Largest integer value v so that (5**index * v) <= 1<<53.
|
||||||
|
// 0x10000000000000 == 1 << 53
|
||||||
|
constexpr static uint64_t max_mantissa_double[] = {
|
||||||
|
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)};
|
||||||
|
// Largest integer value v so that (5**index * v) <= 1<<24.
|
||||||
|
// 0x1000000 == 1<<24
|
||||||
|
constexpr static uint64_t max_mantissa_float[] = {
|
||||||
|
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 T> struct binary_format {
|
||||||
|
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 <> 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
|
||||||
|
//
|
||||||
|
return max_mantissa_double[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
|
||||||
|
//
|
||||||
|
return max_mantissa_float[power];
|
||||||
|
}
|
||||||
|
|
||||||
|
template <>
|
||||||
|
inline constexpr double binary_format<double>::exact_power_of_ten(int64_t power) {
|
||||||
|
return powers_of_ten_double[power];
|
||||||
|
}
|
||||||
|
template <>
|
||||||
|
inline constexpr float binary_format<float>::exact_power_of_ten(int64_t power) {
|
||||||
|
|
||||||
|
return powers_of_ten_float[power];
|
||||||
|
}
|
||||||
|
|
||||||
|
|
||||||
|
template <>
|
||||||
|
inline constexpr int binary_format<double>::largest_power_of_ten() {
|
||||||
|
return 308;
|
||||||
|
}
|
||||||
|
template <>
|
||||||
|
inline constexpr int binary_format<float>::largest_power_of_ten() {
|
||||||
|
return 38;
|
||||||
|
}
|
||||||
|
|
||||||
|
template <>
|
||||||
|
inline constexpr int binary_format<double>::smallest_power_of_ten() {
|
||||||
|
return -342;
|
||||||
|
}
|
||||||
|
template <>
|
||||||
|
inline constexpr int binary_format<float>::smallest_power_of_ten() {
|
||||||
|
return -65;
|
||||||
|
}
|
||||||
|
|
||||||
|
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 void to_float(bool negative, adjusted_mantissa am, T &value) {
|
||||||
|
uint64_t word = am.mantissa;
|
||||||
|
word |= uint64_t(am.power2) << binary_format<T>::mantissa_explicit_bits();
|
||||||
|
word = negative
|
||||||
|
? word | (uint64_t(1) << binary_format<T>::sign_index()) : word;
|
||||||
|
#if FASTFLOAT_IS_BIG_ENDIAN == 1
|
||||||
|
if (std::is_same<T, float>::value) {
|
||||||
|
::memcpy(&value, (char *)&word + 4, sizeof(T)); // extract value at offset 4-7 if float on big-endian
|
||||||
|
} else {
|
||||||
|
::memcpy(&value, &word, sizeof(T));
|
||||||
|
}
|
||||||
|
#else
|
||||||
|
// For little-endian systems:
|
||||||
|
::memcpy(&value, &word, sizeof(T));
|
||||||
|
#endif
|
||||||
|
}
|
||||||
|
|
||||||
|
} // namespace fast_float
|
||||||
|
|
||||||
|
#endif
|
||||||
|
|
@ -0,0 +1,205 @@
|
||||||
|
#ifndef FASTFLOAT_PARSE_NUMBER_H
|
||||||
|
#define FASTFLOAT_PARSE_NUMBER_H
|
||||||
|
|
||||||
|
#include "ascii_number.h"
|
||||||
|
#include "decimal_to_binary.h"
|
||||||
|
#include "digit_comparison.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>
|
||||||
|
from_chars_result parse_infnan(const char *first, const char *last, T &value) noexcept {
|
||||||
|
from_chars_result answer;
|
||||||
|
answer.ptr = first;
|
||||||
|
answer.ec = std::errc(); // be optimistic
|
||||||
|
bool minusSign = false;
|
||||||
|
if (*first == '-') { // assume first < last, so dereference without checks; C++17 20.19.3.(7.1) explicitly forbids '+' here
|
||||||
|
minusSign = true;
|
||||||
|
++first;
|
||||||
|
}
|
||||||
|
if (last - first >= 3) {
|
||||||
|
if (fastfloat_strncasecmp(first, "nan", 3)) {
|
||||||
|
answer.ptr = (first += 3);
|
||||||
|
value = minusSign ? -std::numeric_limits<T>::quiet_NaN() : std::numeric_limits<T>::quiet_NaN();
|
||||||
|
// Check for possible nan(n-char-seq-opt), C++17 20.19.3.7, C11 7.20.1.3.3. At least MSVC produces nan(ind) and nan(snan).
|
||||||
|
if(first != last && *first == '(') {
|
||||||
|
for(const char* ptr = first + 1; ptr != last; ++ptr) {
|
||||||
|
if (*ptr == ')') {
|
||||||
|
answer.ptr = ptr + 1; // valid nan(n-char-seq-opt)
|
||||||
|
break;
|
||||||
|
}
|
||||||
|
else if(!(('a' <= *ptr && *ptr <= 'z') || ('A' <= *ptr && *ptr <= 'Z') || ('0' <= *ptr && *ptr <= '9') || *ptr == '_'))
|
||||||
|
break; // forbidden char, not nan(n-char-seq-opt)
|
||||||
|
}
|
||||||
|
}
|
||||||
|
return answer;
|
||||||
|
}
|
||||||
|
if (fastfloat_strncasecmp(first, "inf", 3)) {
|
||||||
|
if ((last - first >= 8) && fastfloat_strncasecmp(first + 3, "inity", 5)) {
|
||||||
|
answer.ptr = first + 8;
|
||||||
|
} else {
|
||||||
|
answer.ptr = first + 3;
|
||||||
|
}
|
||||||
|
value = minusSign ? -std::numeric_limits<T>::infinity() : std::numeric_limits<T>::infinity();
|
||||||
|
return answer;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
answer.ec = std::errc::invalid_argument;
|
||||||
|
return answer;
|
||||||
|
}
|
||||||
|
|
||||||
|
/**
|
||||||
|
* 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 {
|
||||||
|
// 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.
|
||||||
|
#if 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);
|
||||||
|
#if 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>
|
||||||
|
from_chars_result from_chars(const char *first, const char *last,
|
||||||
|
T &value, chars_format fmt /*= chars_format::general*/) noexcept {
|
||||||
|
return from_chars_advanced(first, last, value, parse_options{fmt});
|
||||||
|
}
|
||||||
|
|
||||||
|
template<typename T>
|
||||||
|
from_chars_result from_chars_advanced(const char *first, const char *last,
|
||||||
|
T &value, parse_options options) noexcept {
|
||||||
|
|
||||||
|
static_assert (std::is_same<T, double>::value || std::is_same<T, float>::value, "only float and double are supported");
|
||||||
|
|
||||||
|
|
||||||
|
from_chars_result answer;
|
||||||
|
if (first == last) {
|
||||||
|
answer.ec = std::errc::invalid_argument;
|
||||||
|
answer.ptr = first;
|
||||||
|
return answer;
|
||||||
|
}
|
||||||
|
parsed_number_string pns = parse_number_string(first, last, options);
|
||||||
|
if (!pns.valid) {
|
||||||
|
return detail::parse_infnan(first, last, value);
|
||||||
|
}
|
||||||
|
answer.ec = std::errc(); // be optimistic
|
||||||
|
answer.ptr = pns.lastmatch;
|
||||||
|
// 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(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__)
|
||||||
|
// Clang may map 0 to -0.0 when fegetround() == FE_DOWNWARD
|
||||||
|
if(pns.mantissa == 0) {
|
||||||
|
value = 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);
|
||||||
|
return answer;
|
||||||
|
}
|
||||||
|
|
||||||
|
} // namespace fast_float
|
||||||
|
|
||||||
|
#endif
|
||||||
|
|
@ -0,0 +1,360 @@
|
||||||
|
#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
|
||||||
Loading…
Reference in New Issue