Skip to content
Universal Numbers Library

Universal Numbers Library

Alternatives to native integer and floating-point for mixed-precision algorithm development and optimization. Tailored arithmetic for Deep Learning, DSP, HPC, and embedded applications.
Get StartedView on GitHub

Key Features

Section titled “Key Features”

30+ Number Systems

Integers, fixed-point, classic floats, posits, logarithmic, interval, multi-precision, AI quantization formats, and more.

Header-Only

No external dependencies. Just #include and go. Pure C++20 templates.

Plug-in Replacement

Template your algorithms once, switch arithmetic types freely with zero code changes.

Comprehensive Testing

Exhaustive regression suites for every type. CI on GCC, Clang, and MSVC.

Quick Example

Section titled “Quick Example”
#include <iostream>
#include <universal/number/cfloat/cfloat.hpp>


template<typename Real>
Real MyKernel(const Real& a, const Real& b) {
    return a * b;
}


int main() {
    using namespace sw::universal;


    // half-precision IEEE-754
    half ha = sqrt(2);
    half hb = 3.14159265358979;
    half hc = MyKernel(ha, hb);
    std::cout << "Result: " << hc << '\n';
    std::cout << "Bits  : " << to_binary(hc) << " : " << color_print(hc) << '\n';


    // single-precision IEEE-754
    single fa = sqrt(2);
    single fb = 3.14159265358979;
    single fc = MyKernel(fa, fb);
    std::cout << "Result: " << fc << std::endl;
    std::cout << "Bits  : " << to_binary(fc) << " : " << color_print(fc) << std::endl;
}

To compile (assuming Universal is cloned to ./universal):

Terminal window
g++ -std=c++20 -I universal/include/sw -o kernel kernel.cpp

The library requires C++20 and is header-only with no external dependencies. The include path points to include/sw/ because headers use #include <universal/...> paths.

Number Systems at a Glance

Section titled “Number Systems at a Glance”

Static (Fixed-Size) Types

Section titled “Static (Fixed-Size) Types”
Category Types
Integer & Fixed-Point integer, fixpnt, dfixpnt, rational
Configurable Float cfloat, bfloat16, areal, dfloat, hfloat
AI Quantization microfloat, e8m0, mxfloat, nvblock
Unum Family unum1, unum2, posit, takum
Logarithmic lns, dbns
Interval valid, interval, sorn
Extended Precision dd, qd, dd_cascade, td_cascade, qd_cascade
Kulisch Super-Accumulator quire for half, float, double, cfloat, posit, fixpnt, lns, dbns, integer

Adaptive (Elastic) Precision Types

Section titled “Adaptive (Elastic) Precision Types”
Category Types
Adaptive Integer einteger
Adaptive Decimal edecimal
Adaptive Rational erational
Adaptive Float efloat
Adaptive Real ereal

Citation

Section titled “Citation”

Please cite our JOSS paper if you use Universal in your work.