FasterMath by Lokad

Author: Joannes Vermorel (Lokad, j.vermorel@lokad.com)

This library collects a short series of faster, but approximate, mathematical functions leveraging hardware intrinsics in .NET. The library maintains a relative precision of 1e-3 for the accelerated functions.

The library has no dependency and does not rely on memoization techniques. The goal is to make the most of the superscalar capabilities of modern CPUs, without burdening the cache or the garbage collector.

This library is licensed under the MIT license.

Requirements

• .NET Core 3.0+
• Modern CPU with AVX2

Getting started

To install with NuGet:

Install-Package Lokad.FasterMath

Usage:

using Lokad.Numerics;
	
var x = FxMath.Log(123f); // scalar
ReadOnlySpan<float> myInputs = .. ; 
Span<float> myResults = .. ;
FxMath.Log(myInputs, myResults); // SIMD-accelerated

Performance results

The S8 suffix indicates a SIMD implementation with Vector256<float>.

Method	Mean	Error	StdDev
Digamma_FxMath	8.1156 ns	0.1911 ns	0.2679 ns
Digamma_FxMath_S8	18.4599 ns	0.3741 ns	0.3674 ns
Exp_MathF	3.4134 ns	0.0962 ns	0.2210 ns
Exp_Math	14.5137 ns	0.2499 ns	0.2338 ns
Exp_FxMath	2.0275 ns	0.0706 ns	0.0918 ns
Exp_FxMath_S8	4.5711 ns	0.1207 ns	0.2297 ns
Log_MathF	3.9548 ns	0.1100 ns	0.2528 ns
Log_Math	11.2905 ns	0.1388 ns	0.1159 ns
Log_FxMath	2.7824 ns	0.0856 ns	0.1521 ns
Log_FxMath_S8	6.4883 ns	0.1236 ns	0.1563 ns
Log2_MathF	13.0202 ns	0.2853 ns	0.3172 ns
Log2_Math	17.1575 ns	0.3730 ns	0.7187 ns
Log2_FxMath	0.0444 ns	0.0252 ns	0.0447 ns
LogGamma_FxMath	15.8183 ns	0.3346 ns	0.3436 ns
LogGamma_FxMath_S8	28.8896 ns	0.6744 ns	1.0891 ns

Intel Core i9-8950HK CPU 2.90GHz (Coffee Lake), 1 CPU, 12 logical and 6 physical cores
.NET Core SDK=3.0.100
  [Host]     : .NET Core 3.0.0 (CoreCLR 4.700.19.46205, CoreFX 4.700.19.46214), X64 RyuJIT
  DefaultJob : .NET Core 3.0.0 (CoreCLR 4.700.19.46205, CoreFX 4.700.19.46214), X64 RyuJIT```