glam/

lib.rs

/*!
# glam

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

## Features

* [`f32`](mod@f32) types
  * vectors: [`Vec2`], [`Vec3`], [`Vec3A`] and [`Vec4`]
  * square matrices: [`Mat2`], [`Mat3`], [`Mat3A`] and [`Mat4`]
  * a quaternion type: [`Quat`]
  * affine transformation types: [`Affine2`], [`Affine3`] and [`Affine3A`]
* [`f64`](mod@f64) types
  * vectors: [`DVec2`], [`DVec3`] and [`DVec4`]
  * square matrices: [`DMat2`], [`DMat3`] and [`DMat4`]
  * a quaternion type: [`DQuat`]
  * affine transformation types: [`DAffine2`] and [`DAffine3`]
* [`i8`](mod@i8) types
  * vectors: [`I8Vec2`], [`I8Vec3`] and [`I8Vec4`]
* [`u8`](mod@u8) types
  * vectors: [`U8Vec2`], [`U8Vec3`] and [`U8Vec4`]
* [`i16`](mod@i16) types
  * vectors: [`I16Vec2`], [`I16Vec3`] and [`I16Vec4`]
* [`u16`](mod@u16) types
  * vectors: [`U16Vec2`], [`U16Vec3`] and [`U16Vec4`]
* [`i32`](mod@i32) types
  * vectors: [`IVec2`], [`IVec3`] and [`IVec4`]
* [`u32`](mod@u32) types
  * vectors: [`UVec2`], [`UVec3`] and [`UVec4`]
* [`i64`](mod@i64) types
  * vectors: [`I64Vec2`], [`I64Vec3`] and [`I64Vec4`]
* [`u64`](mod@u64) types
  * vectors: [`U64Vec2`], [`U64Vec3`] and [`U64Vec4`]
* [`isize`](mod@isize) types
  * vectors: [`ISizeVec2`], [`ISizeVec3`] and [`ISizeVec4`]
* [`usize`](mod@usize) types
  * vectors: [`USizeVec2`], [`USizeVec3`] and [`USizeVec4`]
* [`bool`](mod@bool) types
  * vectors: [`BVec2`], [`BVec3`] and [`BVec4`]

## SIMD

`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, NEON on Aarch64, and simd128 on WASM are supported.

## 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**](https://github.com/bitshifter/mathbench-rs) 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.
// We use an explicit method here instead of a From impl as data is lost in the conversion.
let v3a = Vec3A::from_vec4(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, Affine3 and Affine3A

`Affine2`, `Affine3` 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.

`Affine3` is composed from `Vec3` and `Mat3` whereas `Affine3A` is composed from `Mat3A` and
`Vec3A`. `Affine3A` will generally be faster but is 16 byte aligned and 64 btyes verses `Affine3`
which is 48 bytes.

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);
```

[`Deref`]: https://doc.rust-lang.org/std/ops/trait.Deref.html
[`DerefMut`]: https://doc.rust-lang.org/std/ops/trait.DerefMut.html

## 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_vec4(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]");
```

## Optional features

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

* `approx` - traits and macros for approximate float comparisons
* `arbitrary` - implementations of `Arbitrary` trait for all `glam` types.
* `bytemuck` - for casting into slices of bytes
* `encase` - `encase` trait implementations for `glam` types.
* `libm` - uses `libm` math functions instead of `std`
* `mint` - for interoperating with other 3D math libraries
* `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
* `speedy` - implementations of `speedy`'s `Readable` and `Writable` for all `glam` types.
* `zerocopy` - implementations of zerocopy traits for safe transmutes.

## Feature gates

* `std` - the default feature, has no dependencies.
* `nostd-libm` - uses `libm` math functions if `std` is not available
* `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.

## Minimum Supported Rust Version (MSRV)

The minimum supported Rust version is `1.68.2`.

*/
#![doc(html_root_url = "https://docs.rs/glam/0.31.1")]
#![cfg_attr(not(feature = "std"), no_std)]
#![cfg_attr(target_arch = "spirv", feature(repr_simd))]
#![cfg_attr(target_arch = "wasm64", feature(simd_wasm64))]
#![deny(
    rust_2018_compatibility,
    rust_2018_idioms,
    future_incompatible,
    nonstandard_style
)]
// clippy doesn't like `to_array(&self)`
#![allow(clippy::wrong_self_convention)]
#![cfg_attr(
    all(feature = "core-simd", not(feature = "scalar-math")),
    feature(portable_simd)
)]

#[cfg(all(
    not(feature = "std"),
    not(feature = "libm"),
    not(feature = "nostd-libm")
))]
compile_error!(
    "You must specify a math backend. Consider enabling either `std`, `libm`, or `nostd-libm`."
);

#[macro_use]
mod macros;

mod align16;
mod deref;
mod euler;
mod features;

#[cfg(all(
    target_arch = "aarch64",
    not(any(feature = "core-simd", feature = "scalar-math"))
))]
mod neon;

#[cfg(target_arch = "spirv")]
mod spirv;

#[cfg(all(
    target_feature = "sse2",
    not(any(feature = "core-simd", feature = "scalar-math"))
))]
mod sse2;

#[cfg(all(
    target_feature = "simd128",
    not(any(feature = "core-simd", feature = "scalar-math"))
))]
mod wasm;

#[cfg(all(feature = "core-simd", not(feature = "scalar-math")))]
mod coresimd;

#[cfg(all(
    target_feature = "sse2",
    not(any(feature = "core-simd", feature = "scalar-math"))
))]
use align16::Align16;

/** `bool` vector mask types. */
pub mod bool;
pub use self::bool::*;

/** `f32` vector, quaternion and matrix types. */
pub mod f32;
pub use self::f32::*;

/** `f64` vector, quaternion and matrix types. */
pub mod f64;
pub use self::f64::*;

/** `i8` vector types. */
pub mod i8;
pub use self::i8::*;

/** `u8` vector types. */
pub mod u8;
pub use self::u8::*;

/** `i16` vector types. */
pub mod i16;
pub use self::i16::*;

/** `u16` vector types. */
pub mod u16;
pub use self::u16::*;

/** `i32` vector types. */
pub mod i32;
pub use self::i32::*;

/** `u32` vector types. */
pub mod u32;
pub use self::u32::*;

/** `i64` vector types. */
pub mod i64;
pub use self::i64::*;

/** `u64` vector types. */
pub mod u64;
pub use self::u64::*;

/** `usize` vector types. */
pub mod usize;
pub use self::usize::*;

/** `isize` vector types. */
pub mod isize;
pub use self::isize::*;

/** Traits adding swizzle methods to all vector types. */
pub mod swizzles;
pub use self::swizzles::{Vec2Swizzles, Vec3Swizzles, Vec4Swizzles};

/** Rotation Helper */
pub use euler::EulerRot;

/** A trait for extending [`prim@f32`] and [`prim@f64`] with extra methods. */
mod float;
pub use float::FloatExt;