A C++ header-only fixed-point math library. "fpm" stands for "fixed-point math".
It is designed to serve as a drop-in replacement for floating-point types and aims to provide as much of the standard library's functionality as possible with exclusively integers. fpm requires C++26.
fpm is designed to guard against accidental conversion to and from floats and supports many of the standard C++ maths functions, including trigonometry, power and logarithmic functions, with performance and accuracy generally comparable to alternative libraries.
There are several reasons why you can not or choose not to use floating-point math, but still want a similar type:
- Your target platform lacks an FPU, does not support floating-point operations or its floating-point operations are considerably slower than fixed-point integer operations.
- You require deterministic calculations.
If any of these reasons apply for you, and your problem domain has a clearly outlined range and required resolution, then fixed-point numbers might be a solution for you.
To use fpm, include its header <fpm/fixed.hpp> and use the fpm::fixed_16_16, fpm::fixed_24_8 or fpm::fixed_8_24
types as if they were native floating-pointer types:
#include <fpm/fixed.hpp> // For fpm::fixed_16_16
#include <fpm/fixed/math.hpp> // For fpm::cos
#include <fpm/fixed/ios.hpp> // For fpm::operator<< and fpm::operator>>
#include <iostream> // For std::cin, std::cout
int main()
{
std::cout << "Please input a number: ";
fpm::fixed_16_16 x;
std::cin >> x;
std::cout << "The cosine of " << x << " radians is: " << cos(x) << std::endl;
return 0;
}To use the fixed-point equivalents of the <math.h> functions such as sqrt, sin and log, include the header <fpm/fixed/math.hpp>.
To stream fixed-point values to or from streams, include the header <fpm/fixed/ios.hpp>.
To use them with std::format (without the dependency on streams), include the header <fpm/fixed/format.hpp>.
To store values in [0, 1) that wrap around, like an angle as a part of a full turn, include the header <fpm/fraction.hpp>.
Its trigonometry (for angles) is in <fpm/fraction/math.hpp>, and its conversions to and from text are in <fpm/fraction/charconv.hpp>,
<fpm/fraction/format.hpp> and <fpm/fraction/ios.hpp>.
For locale-independent, exact and constexpr conversions to and from text (fpm::to_chars, fpm::from_chars and fpm::to_string), include <fpm/fixed/charconv.hpp>.
Please refer to the documentation for detailed information how to use fpm, or skip straight to the performance or accuracy results.
This library is a work-in-progress. We welcome any contributions that improve the functional coverage or the performance or accuracy of the mathematical functions.
See the LICENSE file