Universal Numbers Library

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

#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):

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

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

Category	Types
Adaptive Integer	einteger
Adaptive Decimal	edecimal
Adaptive Rational	erational
Adaptive Float	efloat
Adaptive Real	ereal

Citation

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