DLAL: Dacite Linear Algebra Library

A work-in-progress header-only vector/matrix/quaternion library for Dacite.

Specifically intended for graphics related mathematics, transforms, etc.

Requirements

Compiler

Compiler	Version
Clang	>= 8
Apple Clang	>= 11

GCC is not yet supported as we use the ext_vector_type extension. Further, we currently only support machines with SSE4.1 instructions.

Test

Building the test suite requires:

Package	Version
GLM	>= 0.9.2

We use GLM to help verify operation correctness.

Building

As a header only library, no build is technically required. See installation. A cmake file is provided to build the testing suite and documentation.

Installation

Copy the contents of include into your source tree, or git submodule it into your own repo. If you wish to use a single header, there is a single_include directory containing a single header that can be copied into your source directory.

Usage

All types are in the dct namespace. See each sub-heading for modules.

Vector

vec.h provides the vec<class T, int N> core SIMD vector class (where T is the component type, and N is the component count), and some handy typedefs of the format: [i, d][M]vec(C).

• The optional prefix indicates type, where i for signed integer, d for double precision. No prefix is reserved for the common single precision floating point case.
• The optional second prefix M indicates component bit size.
• C indicates the number of components, 1 to 4.

This type does not provide size guarantees; it is intended to provide as much performance as possible, thus some vectors may have odd sizes. As an example, vec3 has the same byte size as vec4.

Most GLSL-like operations are supported. Trig functions are accessed with: vec_trig.h

packed_vec.h provides size-stable versions of the same vectors, and supports more types and sizes. It, however, does not have any mathematics support; it is intended to be used only as a storage format.

Matrix

mat.h provides the mat<class T, size_t C, size_t R> core matrix class (where T is the cell type, C is the column count, R is the row count).

Typedefs include

• mat2, a floating point 2x2 matrix
• mat3, a floating point 3x3 matrix
• mat4, a floating point 4x4 matrix

Common GLSL-like matrix operations, including inversion, are accessed using: mat_operations.h

Common matrix transformation operations are accessed using: mat_transforms.h

As with vectors, this type has no size guarantees. Use the packed_mat from the packed_mat.h header for predictably sized matrices.

Quaternion

#include <quat.h>

Provides the quaternion<class T> core quaternion class (where T is the component type).

Typedefs include

• quat, a floating point quaternion
• dquat, a double precision floating point quaternion

Transformation Matrix

tmatrix.h provides TMatrix, an abstraction for mat4, with the objective to help construct and work with transformation matrices. For example, the default constructor initializes to the identity. Also includes perspective matrix builders.

Todo

• Finish accellerating the common typedefs in vec and mat.
• Clean up cmake
• Improve the test suite
• Improve GLSL-like conformance
• Find a good way to test codegen output to verify instructions