byzhang / aarith

An arbitrary precision number library for C++

Aarith: An Arbitrary Precision Number Library

Aarith is a header-only, arbitrary precision number library for C++. It is intended to be used as a drop-in replacement of the native data types.

Aarith currently supports

• IEEE 754 like floating-point numbers of arbitrary bit-width for both, the exponent and the mantissa
• Two's complement integers of arbitrary bit-width (signed and unsigned)

Read the full documentation

Installation

Copy the contents of this repository into a <destination> folder and include Aarith in your CMake build using:

add_subdirectory(<destination>)

You can then link your target <targetname> against Aarith with:

target_link_libraries(<targetname> PUBLIC aarith::Library)

Usage Example

Aarith is intended to be used as a drop-in replacement for the native data types. You only need to include the headers and can start using Aarith immediately:

#include <aarith/float.hpp>
#include <aarith/integer.hpp>

int main()
{
    using namespace aarith;
    uint64_t a = 10, b = 20;
    uinteger<64> a_ = 10, b_ = 20;
    std::cout << "a + b = " << (a + b) << "\n";
    std::cout << "a_+ b_ = " << (a_ + b_) << "\n";

    float x=3.0F, y=2.5F;
    floating_point<8,23> x_{3.0F}, y_{2.5F};
    std::cout << "x + y = " << (x * y) << "\n";
    std::cout << "x_+ y_ = " << (x_ * y_) << "\n";
}

This gives the expected output of

$ ./arithmetic_example
a + b = 30
a_+ b_ = 30
x * y = 7.5
x_* y_ = 7.5

To make usage of Aarith more convenient, the following type aliases are shipped with Aarith:

using half_precision = floating_point<5, 10, uint64_t>;
using single_precision = floating_point<8, 23, uint64_t>;
using double_precison = floating_point<11, 52, uint64_t>;
using quadruple_precision = floating_point<15, 112, uint64_t>;
using bfloat16 = floating_point<8, 7, uint64_t>;
using tensorfloat32 = floating_point<8, 10, uint64_t>;

Further examples for how to use aarith can be found in the examples and experiments folders (the tests can also give a good idea of how to use aarith).

We also refer the interested user to the publication listed below.

License

Aarith does use a license! At some point in time, we will even tell you which one

Publication

If you use Aarith (e.g., in your publication), please cite

Oliver Keszocze, Marcel Brand, Christian Heidorn, und Jürgen Teich. „Aarith: An Arbitrary Precision Number Library“, In: ACM/SIGAPP Symposium On Applied Computing (SAC'21). March 2021.

Bibtex:

@inproceedings{Keszocze2021,
  title = {Aarith: {{An Arbitrary Precision Number Library}}},
  booktitle = {ACM/SIGAPP Symposium On Applied Computing},
  author = {Keszocze, Oliver and Brand, Marcel and Heidorn, Christian and Teich, Jürgen},
  date = {2021-03},
  location = {{Virtual Event, South Korea}},
  series = {{{SAC}}'21}
}