Universal Numbers Library

Key Features

35+ Number Systems

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

IEEE-754 Out of the Box

half, single, duble, quad, octo – or fp16, fp32, fp64, fp128, fp256. The standard formats, already spelled for you.

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 -- a predefined alias, same as fp16
    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 -- a predefined alias, same as fp32
    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.

The Standard IEEE-754 Formats

cfloat can express any floating-point format, but most developers want one of the six the hardware already implements – and spelling those out by hand is where the mistakes happen. They are predefined, under both their word names and their fpNN names:

type	alias	bits	matches
quarter	fp8	8	IEEE interchange rule at 8 bits
half	fp16	16	IEEE-754 binary16
single	fp32	32	IEEE-754 binary32
duble	fp64	64	IEEE-754 binary64
quad	fp128	128	IEEE-754 binary128
octo	fp256	256	IEEE-754 binary256

single x = 1.0f;   // exactly binary32 -- no template parameters to get wrong
quad   z = 1.0;    // exactly binary128, on hardware that has never heard of it

See Standard IEEE types for the field widths, the two names that need a caveat, and how to choose between these and the faster extended-precision types.

Number Systems at a Glance

Static (Fixed-Size) Types

Category	Types
Integer & Fixed-Point	integer, fixpnt, dfixpnt, rational, positional
Standard IEEE-754	quarter/fp8, half/fp16, single/fp32, duble/fp64, quad/fp128, octo/fp256
Configurable Float	cfloat, bfloat16, areal, dfloat, hfloat
AI Quantization	microfloat, e8m0, mxfloat, nvblock
Unum Family	unum (Type I), unum2 (Type II), posit (Type III), takum
Logarithmic	lns, dbns
Interval & Uncertainty	interval, sorn, bisection, faithful
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 – expansion-based, precision set at compile time
Lazy Unbounded Real	elreal – refines on demand, no precision ceiling

Citation

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