zlm

Comptime-generic linear algebra library for Zig. Built for graphics programming — supports Vulkan, OpenGL, GLSL, and HLSL conventions with no hidden defaults.

Usage

const zlm = @import("zlm").init(.{ .graphics_api = .vulkan, .shader_lang = .glsl });

const Vec3 = zlm.Vec3(f32);
const Mat4 = zlm.Mat4(f32);

const eye = Vec3.init(0, 0, 5);
const target = Vec3.init(0, 0, 0);
const up = Vec3.init(0, 1, 0);

const view = Mat4.lookAt(eye, target, up);
const proj = Mat4.perspective(std.math.pi / 4.0, 16.0 / 9.0, 0.1, 100.0);
const vp = Mat4.mul(proj, view);

Multiple APIs in one project

If your engine supports both Vulkan and OpenGL via an RHI abstraction, you can use both configs in the same compilation unit:

const zlm = @import("zlm");
const vk = zlm.init(.{ .graphics_api = .vulkan, .shader_lang = .glsl });
const gl = zlm.init(.{ .graphics_api = .opengl, .shader_lang = .glsl });

// both available in the same file
const proj_vk = vk.Mat4(f32).perspective(fov, aspect, near, far);
const proj_gl = gl.Mat4(f32).perspective(fov, aspect, near, far);

Mixed precision

Scalar type is per-type, so you can mix precisions freely:

const zlm = @import("zlm").init(.{ .graphics_api = .vulkan, .shader_lang = .glsl });

const pos = zlm.Vec3(f32).init(1, 2, 3);
const view = zlm.Mat4(f64).lookAt(...);

Configuration

graphics_api

Affects projection matrices only.

	Y direction	Depth range
.vulkan	flipped (clip Y points down)	[0, 1]
.opengl	standard	[-1, 1]

lookAt is API-agnostic.

shader_lang

Affects matrix memory layout.

	Layout
.glsl	column-major (m[col * rows + row])
.hlsl	row-major (m[row * cols + col])

Types

Vectors

• Vec2(T) — 2-component vector: add, sub, scale, dot, length, normalize
• Vec3(T) — 3-component vector: add, sub, scale, dot, length, normalize, cross
• Vec4(T) — 4-component vector: add, sub, scale, dot, length, normalize

Matrices

All matrix types support: add, sub, scale, transpose, mul.

Type	Size	Extra ops
Mat2(T)	2x2	identity, trace, determinant, inverse
Mat3(T)	3x3	identity, trace, determinant, inverse
Mat4(T)	4x4	identity, trace, determinant, inverse, perspective, lookAt
Mat2x3(T)	2 cols, 3 rows	—
Mat2x4(T)	2 cols, 4 rows	—
Mat3x2(T)	3 cols, 2 rows	—
Mat3x4(T)	3 cols, 4 rows	—
Mat4x2(T)	4 cols, 2 rows	—
Mat4x3(T)	4 cols, 3 rows	—

mul supports cross-type multiplication — a Mat3x4 times a Mat4x2 returns a Mat3x2 (dimensions checked at comptime).

Building

Requires Zig 0.16.0.

zig build bench    # run benchmarks

Benchmarks

1 billion iterations per test, ReleaseFast, Vulkan/GLSL config.

Vec2

Operation	f16	f32	f64	f128
add	0.57 ns	0.57 ns	0.57 ns	13.86 ns
sub	0.61 ns	0.57 ns	0.57 ns	20.97 ns
scale	0.57 ns	0.57 ns	0.57 ns	15.49 ns
dot	0.57 ns	0.26 ns	0.27 ns	28.26 ns
length	0.57 ns	0.27 ns	0.26 ns	65.86 ns
normalize	0.57 ns	0.57 ns	0.57 ns	121.16 ns

Vec3

Operation	f16	f32	f64	f128
add	0.57 ns	0.57 ns	0.56 ns	20.46 ns
sub	0.56 ns	0.57 ns	0.56 ns	31.98 ns
scale	0.57 ns	0.56 ns	0.57 ns	23.01 ns
dot	0.56 ns	0.25 ns	0.26 ns	49.75 ns
length	0.57 ns	0.26 ns	0.26 ns	86.60 ns
normalize	0.57 ns	0.57 ns	0.56 ns	148.16 ns
cross	0.57 ns	0.56 ns	0.57 ns	88.57 ns

Vec4

Operation	f16	f32	f64	f128
add	0.57 ns	0.56 ns	0.63 ns	27.11 ns
sub	0.57 ns	0.57 ns	0.63 ns	41.04 ns
scale	0.56 ns	0.56 ns	0.64 ns	30.30 ns
dot	0.57 ns	0.26 ns	0.26 ns	68.53 ns
length	0.57 ns	0.27 ns	0.26 ns	106.64 ns
normalize	0.57 ns	0.57 ns	0.63 ns	175.96 ns

Mat2

Operation	f16	f32	f64	f128
mul	0.57 ns	0.56 ns	0.63 ns	88.92 ns
determinant	0.56 ns	0.26 ns	0.25 ns	18.34 ns
inverse	0.57 ns	0.57 ns	0.63 ns	74.11 ns

Mat3

Operation	f16	f32	f64	f128
mul	0.63 ns	0.63 ns	1.14 ns	301.40 ns
determinant	0.57 ns	0.27 ns	0.27 ns	83.71 ns
inverse	0.63 ns	0.64 ns	1.14 ns	319.04 ns

Mat4

Operation	f64
mul	1.51 ns
perspective	1.52 ns
lookAt	1.33 ns