zmath

SIMD math library for game developers

Tested on x86_64 and AArch64.

Provides ~140 optimized routines and ~70 extensive tests.

Can be used with any graphics API.

Documentation can be found here.

Benchamrks can be found here.

An intro article can be found here.

Getting started

Example build.zig

pub fn build(b: *std.Build) void {
    const exe = b.addExecutable(.{ ... });

    const zmath = b.dependency("zmath", .{});
    exe.root_module.addImport("zmath", zmath.module("root"));
}

Now in your code you may import and use zmath:

const zm = @import("zmath");

pub fn main() !void {
    //
    // OpenGL/Vulkan example
    //
    const object_to_world = zm.rotationY(..);
    const world_to_view = zm.lookAtRh(
        zm.f32x4(3.0, 3.0, 3.0, 1.0), // eye position
        zm.f32x4(0.0, 0.0, 0.0, 1.0), // focus point
        zm.f32x4(0.0, 1.0, 0.0, 0.0), // up direction ('w' coord is zero because this is a vector not a point)
    );
    // `perspectiveFovRhGl` produces Z values in [-1.0, 1.0] range (Vulkan app should use `perspectiveFovRh`)
    const view_to_clip = zm.perspectiveFovRhGl(0.25 * math.pi, aspect_ratio, 0.1, 20.0);

    const object_to_view = zm.mul(object_to_world, world_to_view);
    const object_to_clip = zm.mul(object_to_view, view_to_clip);

    // Transposition is needed because GLSL uses column-major matrices by default
    gl.uniformMatrix4fv(0, 1, gl.TRUE, zm.arrNPtr(&object_to_clip));
    
    // In GLSL: gl_Position = vec4(in_position, 1.0) * object_to_clip;
    
    //
    // DirectX example
    //
    const object_to_world = zm.rotationY(..);
    const world_to_view = zm.lookAtLh(
        zm.f32x4(3.0, 3.0, -3.0, 1.0), // eye position
        zm.f32x4(0.0, 0.0, 0.0, 1.0), // focus point
        zm.f32x4(0.0, 1.0, 0.0, 0.0), // up direction ('w' coord is zero because this is a vector not a point)
    );
    const view_to_clip = zm.perspectiveFovLh(0.25 * math.pi, aspect_ratio, 0.1, 20.0);

    const object_to_view = zm.mul(object_to_world, world_to_view);
    const object_to_clip = zm.mul(object_to_view, view_to_clip);
    
    // Transposition is needed because HLSL uses column-major matrices by default
    const mem = allocateUploadMemory(...);
    zm.storeMat(mem, zm.transpose(object_to_clip));
    
    // In HLSL: out_position_sv = mul(float4(in_position, 1.0), object_to_clip);
    
    //
    // 'WASD' camera movement example
    //
    {
        const speed = zm.f32x4s(10.0);
        const delta_time = zm.f32x4s(demo.frame_stats.delta_time);
        const transform = zm.mul(zm.rotationX(demo.camera.pitch), zm.rotationY(demo.camera.yaw));
        var forward = zm.normalize3(zm.mul(zm.f32x4(0.0, 0.0, 1.0, 0.0), transform));

        zm.storeArr3(&demo.camera.forward, forward);

        const right = speed * delta_time * zm.normalize3(zm.cross3(zm.f32x4(0.0, 1.0, 0.0, 0.0), forward));
        forward = speed * delta_time * forward;

        var cam_pos = zm.loadArr3(demo.camera.position);

        if (keyDown('W')) {
            cam_pos += forward;
        } else if (keyDown('S')) {
            cam_pos -= forward;
        }
        if (keyDown('D')) {
            cam_pos += right;
        } else if (keyDown('A')) {
            cam_pos -= right;
        }

        zm.storeArr3(&demo.camera.position, cam_pos);
    }
   
    //
    // SIMD wave equation solver example (works with vector width 4, 8 and 16)
    // 'T' can be F32x4, F32x8 or F32x16
    //
    var z_index: i32 = 0;
    while (z_index < grid_size) : (z_index += 1) {
        const z = scale * @intToFloat(f32, z_index - grid_size / 2);
        const vz = zm.splat(T, z);

        var x_index: i32 = 0;
        while (x_index < grid_size) : (x_index += zm.veclen(T)) {
            const x = scale * @intToFloat(f32, x_index - grid_size / 2);
            const vx = zm.splat(T, x) + voffset * zm.splat(T, scale);

            const d = zm.sqrt(vx * vx + vz * vz);
            const vy = zm.sin(d - vtime);

            const index = @intCast(usize, x_index + z_index * grid_size);
            zm.store(xslice[index..], vx, 0);
            zm.store(yslice[index..], vy, 0);
            zm.store(zslice[index..], vz, 0);
        }
    }
}