Kolbe.LitMath 0.4.0

LitMath

A collection of AVX-256 accelerated mathematical functions for .NET

I rewrote Exp, Log, Sin and a few other useful functions using pure AVX intrinsics, so instead of doing one calculation per core, you can now do 4 doubles or 8 floats per core. I added the Sqrt, ERF function and a Normal Distribution CDF as well. On doubles, the following accuracies apply:

• Exp and Sqrt run at double precision limits
• ERF at 1e-13
• Sin and Cos at 1e-15
• Tan in $[0,\pi/4]$ at 2e-16
• ATan at 1e-10 (working on it)

There are examples in the benchmark and tests. But here is one to get you started anyway.

Calculate n $e^x$'s in chunks of 4 and store the result in y.

int n = 40;
Span<double> x = new Span<double>(Enumerable.Range(0 , n).Select(z => (double)z/n).ToArray());
Span<double> y = new Span<double>(new double[n]);
LitExp.Exp(ref x, ref y);

Parallel Processing

LitMath leverages SIMD for instruction level parallelism, but not compute cores. For array sizes large enough, it would be a really good idea to do multicore processing. There's an example called LitExpDoubleParallel in the ExpBenchmark.cs file to see one way to go about this.

Non-Math Things

Making a library like this involves reinventing the wheel so to speak on very basic concepts. LitUtilities includes methods like Max and Min and IfElse, which are key to many programming problems in AVX programming, because it needs to be branch-free.