Ben {chmark} Adams benaadams

Unexpected Uses for the Galois Field Affine Transformation Instruction

Intel added the Galois Field instruction set (GFNI) extensions to their Sunny Cove and Tremont cores. What’s particularly interesting is that GFNI is the only new SIMD extension that came with SSE and VEX/AVX encodings (in addition to EVEX/AVX512), to allow it to be supported on all future Intel cores, including those which don’t support AVX512 (such as the Atom line, as well as Celeron/Pentium branded “big” cores).

I suspect GFNI was aimed at accelerating SM4 encryption, however, one of the instructions can be used for many other purposes. The extension includes three instructions, but of particular interest here is the Affine Transformation (GF2P8AFFINEQB), aka bit-matrix multiply, instruction.

There have been various articles which discuss out-of-band

Count Leading/Trailing Zero Bits (Byte-wise)

Counting the trailing zero bit count (TZCNT) can be done by isolating the lowest bit, then depositing this into the appropriate locations for the count. The leading zero bit count (LZCNT) can be done by reversing bits, then computing the TZCNT.

__m128i _mm_tzcnt_epi8(__m128i a) {
	// isolate lowest bit
	a = _mm_andnot_si128(_mm_add_epi8(a, _mm_set1_epi8(0xff)), a);
	// convert lowest bit to index

These links no longer work. Springer have pulled the free plug.

Graduate texts in mathematics

duplicates = multiple editions

A Classical Introduction to Modern Number Theory, Kenneth Ireland Michael Rosen

What forces layout / reflow

All of the below properties or methods, when requested/called in JavaScript, will trigger the browser to synchronously calculate the style and layout*. This is also called reflow or layout thrashing, and is common performance bottleneck.

Generally, all APIs that synchronously provide layout metrics will trigger forced reflow / layout. Read on for additional cases and details.

Element APIs

Getting box metrics

elem.offsetLeft, elem.offsetTop, elem.offsetWidth, elem.offsetHeight, elem.offsetParent

Memory Optimization (Christer Ericson, GDC 2003)
http://realtimecollisiondetection.net/pubs/GDC03_Ericson_Memory_Optimization.ppt

Cache coherency primer (Fabian Giesen)
https://fgiesen.wordpress.com/2014/07/07/cache-coherency/

Code Clinic 2015: How to Write Code the Compiler Can Actually Optimize (Mike Acton)
http://gdcvault.com/play/1021866/Code-Clinic-2015-How-to

Please consider using http://lygia.xyz instead of copy/pasting this functions. It expand suport for voronoi, voronoise, fbm, noise, worley, noise, derivatives and much more, through simple file dependencies. Take a look to https://github.com/patriciogonzalezvivo/lygia/tree/main/generative

Generic 1,2,3 Noise

float rand(float n){return fract(sin(n) * 43758.5453123);}

float noise(float p){
	float fl = floor(p);
  float fc = fract(p);

	/*
	The MIT License (MIT)

	Copyright (c) 2018 Eric Arnebäck

	Permission is hereby granted, free of charge, to any person obtaining a copy
	of this software and associated documentation files (the "Software"), to deal
	in the Software without restriction, including without limitation the rights
	to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
	copies of the Software, and to permit persons to whom the Software is

	Latency Comparison Numbers
	--------------------------
	L1 cache reference/hit 1.5 ns 4 cycles
	Floating-point add/mult/FMA operation 1.5 ns 4 cycles
	L2 cache reference/hit 5 ns 12 ~ 17 cycles
	Branch mispredict 6 ns 15 ~ 20 cycles
	L3 cache hit (unshared cache line) 16 ns 42 cycles
	L3 cache hit (shared line in another core) 25 ns 65 cycles
	Mutex lock/unlock 25 ns
	L3 cache hit (modified in another core) 29 ns 75 cycles

	// The following code is licensed under the MIT license: https://gist.github.com/TheRealMJP/bc503b0b87b643d3505d41eab8b332ae

	// Samples a texture with Catmull-Rom filtering, using 9 texture fetches instead of 16.
	// See http://vec3.ca/bicubic-filtering-in-fewer-taps/ for more details
	float4 SampleTextureCatmullRom(in Texture2D<float4> tex, in SamplerState linearSampler, in float2 uv, in float2 texSize)
	{
	// We're going to sample a a 4x4 grid of texels surrounding the target UV coordinate. We'll do this by rounding
	// down the sample location to get the exact center of our "starting" texel. The starting texel will be at
	// location [1, 1] in the grid, where [0, 0] is the top left corner.
	float2 samplePos = uv * texSize;

	using System;
	using System.Runtime.CompilerServices;
	using System.Runtime.InteropServices;

	namespace ConsoleApp2
	{
	public unsafe class UnmanagedArray<T>
	where T : struct
	{
	private static IntPtr _value;