Fast Floating-Point Math

fast_fp provides a set of primitive types that support fast-math compiler optimizations for many operations. These optimizations allow the compiler to potentially generate faster code by relaxing some of the requirements of IEEE 754 floating-point arithmetic.

Examples

use fast_fp::{FF32, ff32};

// Construct instances of the fast type from std's type using the convenience
// wrapper `ff32` (or `ff64`)
let four = ff32(4.0);

// or using the `From`/`Into` trait
let five: FF32 = 5.0.into();

assert_eq!(four + five, ff32(9.0));

// Most ops are also implemented to work with std's floats too (including PartialEq).
// This makes working with literals easier.
assert_eq!(five + 6.0, 11.0);
assert_eq!(five * 2.0, 10.0);

// Functions can be made generic to accept std or fast types using `num-traits`
use num_traits::real::Real;
fn square<T: Real>(num: T) -> T {
    num * num
}
assert_eq!(square(3.0_f32), 9.0);
assert_eq!(square(five), 25.0);

// If the nalgebra feature (with version suffix) is enabled, interop with
// nalgebra is supported
# #[cfg(feature = "nalgebra_v029")]
use nalgebra_v029 as na;
# #[cfg(feature = "nalgebra_v029")]
assert_eq!(na::Matrix3::repeat(four).sum(), 36.0);

Caveats

Precision

The fast-math optimizations may result in different outputs than operations on the standard float primitives like f32, particularly where fine-grained precision is important. Fast-math may allow reordering operations in such a way that some precision is lost in the overall computation. Note that there are also cases where fast-math optimizations can improve precision, such as contracting separate multiplication and addition into a fused multiply-add operation.

Performance

Use of this crate's primitives may not be faster than the standard primitives in all cases. That may be because the generated code is slower in practice, or because of certain measures taken by this crate to prevent Undefined Behavior (in particular for comparison heavy code). Users should carefully measure and benchmark their code to understand whether they actually benefit from use of these types.

Finite Math

Many operations have the finite-math-only optimization flag enabled. With this flag, the user must ensure that operations on the fast types do not involve infinite or NaN values. If the arguments to an operation are, or the results of an operation would be, +inf, -inf, or NaN, then the operation's result value is unspecified. This crate goes to lengths to ensure that such an operation is not UB in the strict sense, but the output is free to be any representable value of the output type, and may not be a fixed value at all.

Building

fast_fp enables fast-math optimizations by calling C code which was compiled with these optimizations enabled; additionally, some LLVM IR is used to prevent triggering UB that is otherwise possible with these optimizations. As a consequence, building this crate requires clang to be installed and requires the final binary to be linked using cross-language LTO to achieve the performance benefits.

This LTO requires a version of clang compatible with the LLVM version used by rustc. To find the necessary LLVM version, check rustc's version info in verbose mode:

$ rustc -vV
rustc 1.56.0 (09c42c458 2021-10-18)
binary: rustc
commit-hash: 09c42c45858d5f3aedfa670698275303a3d19afa
commit-date: 2021-10-18
host: x86_64-unknown-linux-gnu
release: 1.56.0
LLVM version: 13.0.0 # <--- see the version here

Then build and link using a clang and lld with the corresponding version:

$ CC="clang-13" \
RUSTFLAGS="-Clinker-plugin-lto -Clinker=clang-13 -Clink-arg=-fuse-ld=lld-13" \
cargo build

For simplicity, these arguments can be stored in a cargo config file

[env]
CC = "clang-13"

[build]
rustflags = ["-Clinker-plugin-lto", "-Clinker=clang-13", "-Clink-arg=-fuse-ld=lld-13"]

Although rustc does not always use an official LLVM release version, it's typically close enough to be interoperable with the official clang and LLVM releases of the same version number.