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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.
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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.