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中文

fixed64

Cross-platform single-header modern C++ fixed-point arithmetic library.

requires c++11, recommands c++20

Features

  • 64-bits internal storage
  • tweakable fraction precision (QM.N)
  • protected from intermediatary overflows
  • support rounding and saturation
  • evaluated in compile time almostly(totally in c++20)

QuickStart

#include <iostream>
#include "fixed64.hpp"

int main(int argc, char* argv[]) 
{
    f64::fixed64<40> a = 1.23; // Q24.40

    std::cout << (a + 1);
    return 0;

}

Description

fixed64 is designed to find a balance between percision and performance. It is stored by int64. The target application scenario is physics engine，which has many distance calculation that cause the overflow on 32-bits fixed-point.

Contents

File

  • fixed64.hpp fixed-point header
  • trig_lut.hpp lut for sin, optional

Supported Functions

- Arithmetic: + - * / fmod sqrt
- Trigonometry: sin cos tan asin acos atan atan2
- Exponential: exp exp2 log log2 log10 pow
- Other: abs ceil floor round

Optimization

  • support hardware int128 (MSVC only)
  • support look-up table for trigonometric function
  • support speed up the multiplication and division with integer

Performance

see more in benchmark

Supported Switcher

#define FIXED_64_ENABLE_ROUNDING // apply rounding 
#define FIXED_64_ENABLE_OVERFLOW // checking overflow
#define FIXED_64_ENABLE_SATURATING // saturate result
#define FIXED_64_ENABLE_TRIG_LUT // use lut for trigonometric function
#define FIXED_64_FORCE_EVALUATE_IN_COMPILE_TIME //make all function be with constexpr, clz will use soft implemention
#define FIXED_64_ENABLE_FORCEINLINE // enable forceinline

Compare with other fixed-point arithmetic libraries

  • fpm good coding style,but has no overflow protection/alert, need to provide int128 as intermediate type by yourself
  • libfixmath64 gives me great inspiration. but it is c-style and can not evaluate fixed-point value in compile time.
  • fixmath I think the best one. support hardware int128, but need to include too many headers
  • fixed_point, fp perform incorrect result in multiply operation when the fraction has large bits(intermediatary overflow happens).

64位定点数

特性

  • 64位存储
  • 可变小数位精度
  • 越界保护/警告
  • 支持四舍五入和越界限制
  • 支持大部分函数的编译期计算（c++20全部支持）

快速上手

#include <iostream>
#include "fixed64.hpp"

int main(int argc, char* argv[]) 
{
    f64::fixed64<40> a = 1.23; // Q24.40

    std::cout << (a + 1);
    return 0;

}

简介

fixed64综合考虑了精度与性能的问题，使用了int64存储。个人的应用场景是物理引擎。物理引擎中存在大量距离计算，使用32位的定点数容易发生溢出。

内容

文件

  • fixed64.hpp 定点数头文件
  • trig_lut.hpp 三角函数查表文件，不是必须

支持的函数

- 算数操作: + - * / fmod sqrt
- 三角函数: sin cos tan asin acos atan atan2
- 指数函数: exp exp2 log log2 log10 pow
- 其他函数: abs ceil floor round

优化

  • 支持硬件int128加速计算（暂时只支持MSVC）
  • 支持三角函数查表
  • 支持与整型的乘除法加速

Performance

具体参考benchmark

开关

#define FIXED_64_ENABLE_ROUNDING // 使用四舍五入
#define FIXED_64_ENABLE_OVERFLOW // 使用越界检查
#define FIXED_64_ENABLE_SATURATING // 使用越界限制
#define FIXED_64_ENABLE_TRIG_LUT // 三角函数使用查表方法
#define FIXED_64_FORCE_EVALUATE_IN_COMPILE_TIME //强制使函数支持编译期运算，主要是改变clz的实现
#define FIXED_64_ENABLE_FORCEINLINE // 开启强制内联

与其他定点数库对比

  • fpm 优秀的代码风格，但是没有计算溢出检查，需要自己提供int128来支持64位的定点数实现。
  • libfixmath64 给我很大启发. 但是是C风格代码，缺少编译期运算支持。
  • fixmath 个人认为最好的定点数库. 支持硬件int128运算，但是头文件太多。
  • fixed_point, fp 这些库没有考虑当小数部分占位数较多时，乘除法计算中间值越界问题,这将导致计算结果错误。