What every programmer should know about memory

I found a pretty good document written by Ulrich Drepper about CPUs, caches and memory. The document can found here. Understanding the CPU and memory architecture of a modern computer is essential to writing fast code.

Updates license terms

I updated the license for code examples given on this page. They are now released under the MIT license, which grants everyone to use all examples free of charge in any non-commercial or commercial project. More details can be found on the Terms of Usage page.

Efficient Processing of Arrays using SSE/SIMD and C++ Functors

This post is about how to write beautiful SIMD/SSE code that is easy to debug and maintain, yet allows to produce optimal code with zero overhead. It builds upon existing posts such as the Template based vector library and How to unroll a loop in C++. Here we present a pattern that is fully based on functors and similar to array processing in the Standard Template Library (STL).
Given one or multiple array of values (such as float, double, int, etc.), we want to process the array element wise. For example, we want to scale and add the value of an input array and add that to the output array. This is exactly the behavior of the ?AXPY method of the BLAS linear algebra library:

Y = A*X + Y

Note that this special function is just a running example (we will use the single precision datatype float, thus our function of interest is called saxpy). The underlying concept is true for any element-wise array function.

Calculating the Length of a 3D Vector using SSE

This article explains how to calculate the length of a single 3D float vector stored in a SSE register. The length or norm of a vector is defined as the square root of the dot product of the vector with itself:

|v| = length3(v) = sqrt(v.x^2 + v.y^2 + v.z^2)

A single SSE register can be used to hold a 3D vector (the highest 32 bits are unused). In a previous article we show how to load a struct containing 3 float values into a SSE register. You may as well use the _mm_setr_ps(x, y, z, 0) intrinsic. SSE4 introduced the DPPS instruction (accessible via the _mm_dp_ps intrinsic) which allows to calculate the dot product of up to four float values. We will now use this intrinsic to calculate the length of a 3D vector with minimal instructions.

Template based vector library with SSE support

This article explains how to set up a vector math library that performs mathematical operations on arbitrary sized float arrays or vectors. It can handle aligned and unaligned pointers with minimal code overhead but optimal runtime performance. This is achieved through template functions and compile-time arguments.
This tutorial is based on a simple code example: adding two arrays and storing the result in a third array. Step by step, we will introduce loop SSE intrinsics, loop unrolling and functor based concepts which allow to build a library with different operations.

Simple vector3 class with SSE support

In this post we show how to write a simple class which represents a 3D vector which uses SSE operations for fast calculations. The class stores three float values (x, y and z) and implements all basic vector operators such as add, subtract, multiply, divide, cross product, dot product and length calculations. It uses aligned 128-bit memory which allows to use SSE intrinsics directly. In addition, it overloads the new and delete operators for arrays which allows to create multiple instances of vector3.

Fast 3D-vector matrix transformation using SSE4

In this blog-post we'd like to show how to efficiently transform multiple 3D vectors using an affine transformation matrix. Each vector has three coordinates (x, y and z) and the matrix consists of three rows each with 4 elements (3 for rotation/scale + 1 for translation). In order to multiply a 3-element vector with a 3x4 matrix, we add an additional 1 at the end of the 3D vector: