Crate glam

Expand description

glam

glam is a simple and fast linear algebra library for games and graphics.

Features

f32 types
- vectors: Vec2, Vec3, Vec3A and Vec4
- square matrices: Mat2, Mat3, Mat3A and Mat4
- a quaternion type: Quat
- affine transformation types: Affine2 and Affine3A
f64 types
- vectors: DVec2, DVec3 and DVec4
- square matrices: DMat2, DMat3 and DMat4
- a quaternion type: DQuat
- affine transformation types: DAffine2 and DAffine3
i32 types
- vectors: IVec2, IVec3 and IVec4
u32 types
- vectors: UVec2, UVec3 and UVec4
bool types
- vectors: BVec2, BVec3 and BVec4

glam is built with SIMD in mind. Many f32 types use 128-bit SIMD vector types for storage and/or implementation. The use of SIMD generally enables better performance than using primitive numeric types such as f32.

Some glam types use SIMD for storage meaning they are 16 byte aligned, these types include Mat2, Mat3A, Mat4, Quat, Vec3A, Vec4, Affine2 an Affine3A. Types with an A suffix are a SIMD alternative to a scalar type, e.g. Vec3 uses f32 storage and Vec3A uses SIMD storage.

When SIMD is not available on the target the types will maintain 16 byte alignment and internal padding so that object sizes and layouts will not change between architectures. There are scalar math fallback implementations exist when SIMD is not available. It is intended to add support for other SIMD architectures once they appear in stable Rust.

Currently only SSE2 on x86/x86_64 is supported as this is what stable Rust supports.

Vec3A and Mat3A

Vec3A is a SIMD optimized version of the Vec3 type, which due to 16 byte alignment results in Vec3A containing 4 bytes of padding making it 16 bytes in size in total. Mat3A is composed of three Vec3A columns.

Type	`f32` bytes	Align bytes	Size bytes	Padding
`Vec3`	12	4	12	0
`Vec3A`	12	16	16	4
`Mat3`	36	4	36	0
`Mat3A`	36	16	48	12

Despite this wasted space the SIMD implementations tend to outperform f32 implementations in mathbench benchmarks.

glam treats Vec3 as the default 3D vector type and Vec3A a special case for optimization. When methods need to return a 3D vector they will generally return Vec3.

There are From trait implementations for converting from Vec4 to a Vec3A and between Vec3 and Vec3A (and vice versa).

use glam::{Vec3, Vec3A, Vec4};

let v4 = Vec4::new(1.0, 2.0, 3.0, 4.0);

// Convert from `Vec4` to `Vec3A`, this is a no-op if SIMD is supported.
let v3a = Vec3A::from(v4);
assert_eq!(Vec3A::new(1.0, 2.0, 3.0), v3a);

// Convert from `Vec3A` to `Vec3`.
let v3 = Vec3::from(v3a);
assert_eq!(Vec3::new(1.0, 2.0, 3.0), v3);

// Convert from `Vec3` to `Vec3A`.
let v3a = Vec3A::from(v3);
assert_eq!(Vec3A::new(1.0, 2.0, 3.0), v3a);

Affine2 and Affine3A

Affine2 and Affine3A are composed of a linear transform matrix and a vector translation. The represent 2D and 3D affine transformations which are commonly used in games.

The table below shows the performance advantage of Affine2 over Mat3A and Mat3A over Mat3.

operation	`Mat3`	`Mat3A`	`Affine2`
inverse	11.4±0.09ns	7.1±0.09ns	5.4±0.06ns
mul self	10.5±0.04ns	5.2±0.05ns	4.0±0.05ns
transform point2	2.7±0.02ns	2.7±0.03ns	2.8±0.04ns
transform vector2	2.6±0.01ns	2.6±0.03ns	2.3±0.02ns

Performance is much closer between Mat4 and Affine3A with the affine type being faster to invert.

operation	`Mat4`	`Affine3A`
inverse	15.9±0.11ns	10.8±0.06ns
mul self	7.3±0.05ns	7.0±0.06ns
transform point3	3.6±0.02ns	4.3±0.04ns
transform point3a	3.0±0.02ns	3.0±0.04ns
transform vector3	4.1±0.02ns	3.9±0.04ns
transform vector3a	2.8±0.02ns	2.8±0.02ns

Benchmarks were taken on an Intel Core i7-4710HQ.

Linear algebra conventions

glam interprets vectors as column matrices (also known as column vectors) meaning when transforming a vector with a matrix the matrix goes on the left.

use glam::{Mat3, Vec3};
let m = Mat3::IDENTITY;
let x = Vec3::X;
let v = m * x;
assert_eq!(v, x);

Matrices are stored in memory in column-major order.

All angles are in radians. Rust provides the f32::to_radians() and f64::to_radians() methods to convert from degrees.

Direct element access

Because some types may internally be implemented using SIMD types, direct access to vector elements is supported by implementing the Deref and DerefMut traits.

use glam::Vec3A;
let mut v = Vec3A::new(1.0, 2.0, 3.0);
assert_eq!(3.0, v.z);
v.z += 1.0;
assert_eq!(4.0, v.z);

glam assertions

glam does not enforce validity checks on method parameters at runtime. For example methods that require normalized vectors as input such as Quat::from_axis_angle(axis, angle) will not check that axis is a valid normalized vector. To help catch unintended misuse of glam the debug-glam-assert or glam-assert features can be enabled to add checks ensure that inputs to are valid.

Vector swizzles

glam vector types have functions allowing elements of vectors to be reordered, this includes creating a vector of a different size from the vectors elements.

The swizzle functions are implemented using traits to add them to each vector type. This is primarily because there are a lot of swizzle functions which can obfuscate the other vector functions in documentation and so on. The traits are Vec2Swizzles, Vec3Swizzles and Vec4Swizzles.

Note that the Vec3Swizzles implementation for Vec3A will return a Vec3A for 3 element swizzles, all other implementations will return Vec3.

use glam::{swizzles::*, Vec2, Vec3, Vec3A, Vec4};

let v = Vec4::new(1.0, 2.0, 3.0, 4.0);

// Reverse elements of `v`, if SIMD is supported this will use a vector shuffle.
let wzyx = v.wzyx();
assert_eq!(Vec4::new(4.0, 3.0, 2.0, 1.0), wzyx);

// Swizzle the yzw elements of `v` into a `Vec3`
let yzw = v.yzw();
assert_eq!(Vec3::new(2.0, 3.0, 4.0), yzw);

// To swizzle a `Vec4` into a `Vec3A` swizzle the `Vec4` first then convert to
// `Vec3A`. If SIMD is supported this will use a vector shuffle. The last
// element of the shuffled `Vec4` is ignored by the `Vec3A`.
let yzw = Vec3A::from(v.yzwx());
assert_eq!(Vec3A::new(2.0, 3.0, 4.0), yzw);

// You can swizzle from a `Vec4` to a `Vec2`
let xy = v.xy();
assert_eq!(Vec2::new(1.0, 2.0), xy);

// And back again
let yyxx = xy.yyxx();
assert_eq!(Vec4::new(2.0, 2.0, 1.0, 1.0), yyxx);

SIMD and scalar consistency

glam types implement serde Serialize and Deserialize traits to ensure that they will serialize and deserialize exactly the same whether or not SIMD support is being used.

The SIMD versions implement the core::fmt::Debug and core::fmt::Display traits so they print the same as the scalar version.

use glam::Vec4;
let a = Vec4::new(1.0, 2.0, 3.0, 4.0);
assert_eq!(format!("{}", a), "[1, 2, 3, 4]");

Feature gates

All glam dependencies are optional, however some are required for tests and benchmarks.

std - the default feature, has no dependencies.
approx - traits and macros for approximate float comparisons
bytemuck - for casting into slices of bytes
libm - required to compile with no_std
mint - for interoperating with other 3D math libraries
num-traits - required to compile no_std, will be included when enabling the libm feature
rand - implementations of Distribution trait for all glam types.
rkyv - implementations of Archive, Serialize and Deserialize for all glam types. Note that serialization is not interoperable with and without the scalar-math feature. It should work between all other builds of glam. Endian conversion is currently not supported
bytecheck - to perform archive validation when using the rkyv feature
serde - implementations of Serialize and Deserialize for all glam types. Note that serialization should work between builds of glam with and without SIMD enabled
scalar-math - disables SIMD support and uses native alignment for all types.
debug-glam-assert - adds assertions in debug builds which check the validity of parameters passed to glam to help catch runtime errors.
glam-assert - adds assertions to all builds which check the validity of parameters passed to glam to help catch runtime errors.
cuda - forces glam types to match expected cuda alignment
fast-math - By default, glam attempts to provide bit-for-bit identical results on all platforms. Using this feature will enable platform specific optimizations that may not be identical to other platforms. Intermediate libraries should not use this feature and defer the decision to the final binary build.
core-simd - enables SIMD support via the portable simd module. This is an unstable feature which requires a nightly Rust toolchain and std support.