niswegmann / small-matrix-inverse

SIMD optimised library for matrix inversion of 2x2, 3x3, and 4x4 matrices.

About

Small Matrix Inverse (SMI) is a portable, SIMD optimised library for matrix inversion of 2, 3, and 4 order (square) matrices. It is written in pure C99 combined with LLVM/SSE/NEON compiler intrinsics. The 4x4 routines are based on Intel's "Streaming SIMD Extensions - Inverse of 4x4 Matrix."

Why Another Library

What does SMI bring to the table that the existing open source scientific libraries lack? (E.g. Eigen, NT2, Blitz++.)

1. Hand-optimised SIMD routines for non-SSE architectures, such as ARM. (SMI targets all LLVM supported architectures.)
2. Hand-optimised SIMD routines for 2x2 and 3x3 inversion.
3. An easy-to-use, drag-and-drop, no-template-madness-WYSIWYG structure/interface.

Installation

Each matrix operation consists of a single C-function embedded in a header. Simply copy the relevant header (e.g. "invert2x2-llvm.h" or "invert4x4-sse.h") into your project.

Usage

SMI is straightforward to use. Include the appropriate header and you're good to go:

#include "invert4x4-llvm.h"
...
float M[16] __attribute__((aligned(16))) =
    {
        + 1.0f, + 2.0f, - 1.0f, + 3.0f,
        - 5.0f, + 1.0f, - 4.0f, - 2.0f,
        - 3.0f, + 8.0f, + 2.0f, - 4.0f,
        + 7.0f, - 9.0f, - 4.0f, - 6.0f
    };

float Minv[16] __attribute__((aligned(16)));

invert4x4(M, Minv);
...

Input matrices must be non-singular and can be in either row-major or column-major order -- it doesn't matter since for all non-singular matrices M transpose(invert(transpose(M))) is equal to invert(M). If the input matrix is singular, the result is undefined. For the sake of efficiency remember to align input and output buffers.

Supported Architectures

The goal is to support all commen architectures for 2x2, 3x3, and 4x4 matrices. LLVM covers both x86, x86-64, and ARMv7, but specialised versions for ARM NEON are planned.

For completeness there is also an 1x1 C-version.

Here's an overview of the currently supported architectures:

	C	LLVM	SSE	NEON
1x1	✓	-	-	-
2x2	✓	✓	-	-
3x3	✓	-	-	-
4x4	✓	✓	✓	-

Benchmark

SMI hasn't been proberly benchmarked yet. However, initial tests indicates a 50% to 100% performance increase over the matrix inverse routines in Apple's new SIMD library which targets 2x-, 3x-, and 4x- vectors/matrices.

Contributing

Send any comments, chocolate, and/or suggestions to [e-mail].

License

SMI is licenced under CC0 1.0 Universal.