C++ Math Library Test

Introduction

This repository contains some simple tests between different C++ math libraries that I wrote during the process of selecting a math library to use for game development.

At the time of writing, the libraries tested are:

• Eigen
• GLM
• CML

These choices are largely influenced by reading their websites and posts at the Game Development StackExchange site:

• Best C Math Library for Game Engine?
• High Performance Math Library for Vector And Matrix Calculations
• Complete Math Library for use in OpenGL ES 2.0 Game?

This project uses CMake and has been tested on Mac OS X Lion and Android (android-9 platform version, including armeabi, armeabi-v7a and armeabi-v7a with NEON).

Requirements

My requirements are:

• C++
• Matrix operations
• Vector operations
• Complex number support
• Quarternian operations
• Cross-platform, easy to compile on different platforms with different compilers.
• Fast. SIMD instruction support is preferred.
• Easy to use and understand.
• Permissive license. Accreditation is perfectly fine. Forcing distribution of source code isn't.

Libraries Overview

This section contains my notes to help understand the design choices and advantages and disadvantages of each library. It is fairly long so has been moved to LIBRARIES.md. This section also contains licensing information for each library.

Things Tested

• Matrix operations - addition, multiplication

Things Yet To Test

This is for gaming applications. Features that I can think of that need testing are:

• Matrix operations - including addition, subtraction, multiplication, inversion, transposition, translation, rotation, scale
• Vector operations - cross/dot product, normalisation, zeroing, magnitude, length2, scalar operands, normal calculation
• Euler angle + Quarternion operations - rotation, interpolation, conversion, inversion, multiplication
• Coordinate system conversion (Cartesian, spherical)
• Random numbers - generator speed, period, statistical randomness
• Possibly noise generation
• Ease of integration with gl functions like glTranslate()

Running the tests

git clone git@github.com:mfoo/Math-Library-Test.git MathTest
cd MathTest
mkdir build
cd build
cmake ..
make

To run the tests on Android you will need the Android NDK and android-cmake. For Ant you will need to specify your Android SDK location in android/local.properties. I have included prebuilt libraries for armeabi and armeabi-v7a so if you don't want to compile them yourself you can skip straight to the ant commants.

git clone git@github.com:mfoo/Math-Library-Test.git MathTest
cd MathTest
mkdir build
cd build
cmake-android ..
make
cd ../android
ant debug
ant installd

Results

So far I've tested matrix addition and multiplication. src/Main.cpp contains code that will generate two lists of 1 million 4x4 float matrices for each library, populate them with random float values, and then add each one from the first column to the second. It will then do the same for multiplication. It will repeat this step 10 times and print out how long it took for each library.

Results for each library vary greatly with architecture and optimisation level. I have tested standard GCC build on Mac OS X Lion as well as an SSE enabled build, and armeabi, armeabi-v7a and armeabi-v7a with NEON instructions for Android.

Note that all tests use the -O2 GCC optimisation flag except the non-SSE laptop build which uses -O0.

Results for addition and multiplication are shown below. Note that the laptop I'm using is an i7 2.2ghz early 2011 MacBook Pro and the Android device is a Stock HTC Desire (2.2) with a 1 GHz Qualcomm QSD8250. All times are in milliseconds.

                        laptop  laptop (SSE)  armeabi  armeabi-v7a  armeabi-v7a with neon
Eigen additions         8065    30            9944     2181         2145
Eigen multiplications   22404   86            59460    5143         5113
GLM additions           2375    76            10256    1506         1407
GLM multiplications     7337    400           59008    2189         3108
CML additions           12336   96            9587     2885         2996
CML multiplications     21603   551           58399    5306         5280

The first column for the laptop doesn't have any compile-time optimisations and is included purely for interest. From the other results, Eigen seems to be the fastest for these operations, but GLM is the fastest on the HTC Desire with both ABIs.

Despite GLM being faster on the mobile devices, I am more inclined to use Eigen due to its speed on the tested Intel CPU and its much better documentation and more active community.