# Welcome to Universal!¶

Universal is a header-only C++17/20 template library for mixed-precision algorithm design and optimization. It contains plug-in replacements for native arithmetic types, parameterized in terms of precision, dynamic range, sampling profile, and rounding algorithms. The number systems provided in Universal enable algorithm development that optimizes performance and energy efficiency by tailoring the number systems to the requirements of the algorithm.

The motivation to find improvements to IEEE floating-point had been brewing in the HPC community since the late 90’s. Most algorithms had become memory bound and computational scientists were looking for alternatives that provided more granularity in precision and dynamic range to extract more performance from the memory and networking subsystems. Even though the inefficiency of IEEE floating-point had been measured and agreed upon in the HPC community, it was the commercial demands of Deep Learning that provided the incentive to replace IEEE-754 with alternatives, such as half-floats, bfloats, TensorFloats, and DeepFloats. These alternatives are tailored to the application and yield speed-ups of two to three orders of magnitude, making it possible to scale AI deep learning algorithms to ever more capable and accurate solutions. Other computational science and engineering algorithms, such as Krylov solvers, Iso Geometric Analysis, N-Body problems, multi-grid methods, fast multipole methods, etc all stand to benefit from mixed-precision optimization, and Universal is providing the foundation for this new class of computational science and engineering performance.

The basic use pattern is as simple as:

```
#include <universal/number/posit/posit>
template<typename Real>
Real MyKernel(const Real& a, const Real& b) {
return a * b; // replace this with your kernel computation
}
constexpr double pi = 3.14159265358979323846;
int main() {
using Real = sw::universal::posit<32,2>;
Real a = sqrt(2);
Real b = pi;
std::cout << "Result: " << MyKernel(a, b) << std::endl;
}
```

The library contains integers, decimals, fixed-points, rationals, linear floats, tapered floats, logarithmic, interval and adaptive-precision integers and floats. There are example number system skeletons to get you started quickly if you desire to add your own, which is highly encouraged.