Crate substrate_fixed[−][src]

Fixed-point numbers

The fixed crate provides fixed-point numbers.

These types can have Frac fractional bits, where 0 ≤ Frac ≤ n and n is the total number of bits. When Frac = 0, the fixed-point number behaves like an n-bit integer. When Frac = n, the value x lies in the range −0.5 ≤ x < 0.5 for signed numbers, and in the range 0 ≤ x < 1 for unsigned numbers.

Currently the typenum crate is used for the fractional bit count Frac; it is planned to move to const generics when they are supported by the Rust compiler.

The main features are

This crate does not provide general analytic functions.

These functions are not provided because different implementations can have different trade-offs, for example trading some correctness for speed. Implementations can be provided in other crates.

The conversions supported cover the following cases.

Quick examples

use substrate_fixed::types::I20F12;

// 19/3 = 6 1/3
let six_and_third = I20F12::from_num(19) / 3;
// four decimal digits for 12 binary digits
assert_eq!(six_and_third.to_string(), "6.3333");
// find the ceil and convert to i32
assert_eq!(six_and_third.ceil().to_num::<i32>(), 7);
// we can also compare directly to integers
assert_eq!(six_and_third.ceil(), 7);

The type I20F12 is a 32-bit fixed-point signed number with 20 integer bits and 12 fractional bits. It is an alias to FixedI32<U12>. The unsigned counterpart would be U20F12. Aliases are provided for all combinations of integer and fractional bits adding up to a total of eight, 16, 32, 64 or 128 bits.

use substrate_fixed::types::{I4F4, I4F12};

// −8 ≤ I4F4 < 8 with steps of 1/16 (~0.06)
let a = I4F4::from_num(1);
// multiplication and division by integers are possible
let ans1 = a / 5 * 17;
// 1 / 5 × 17 = 3 2/5 (3.4), but we get 3 3/16 (~3.2)
assert_eq!(ans1, I4F4::from_bits((3 << 4) + 3));
assert_eq!(ans1.to_string(), "3.2");

// −8 ≤ I4F12 < 8 with steps of 1/4096 (~0.0002)
let wider_a = I4F12::from(a);
let wider_ans = wider_a / 5 * 17;
let ans2 = I4F4::from_num(wider_ans);
// now the answer is the much closer 3 6/16 (~3.4)
assert_eq!(ans2, I4F4::from_bits((3 << 4) + 6));
assert_eq!(ans2.to_string(), "3.4");

The second example shows some precision and conversion issues. The low precision of a means that a / 5 is 3⁄16 instead of 1⁄5, leading to an inaccurate result ans1 = 3 3⁄16 (~3.2). With a higher precision, we get wider_a / 5 equal to 819⁄4096, leading to a more accurate intermediate result wider_ans = 3 1635⁄4096. When we convert back to four fractional bits, we get ans2 = 3 6⁄16 (~3.4).

Note that we can convert from I4F4 to I4F12 using From, as the target type has the same number of integer bits and a larger number of fractional bits. Converting from I4F12 to I4F4 cannot use From as we have less fractional bits, so we use from_num instead.

Using the fixed crate

The fixed crate is available on crates.io. To use it in your crate, add it as a dependency inside Cargo.toml:

[dependencies]
fixed = "0.5.4"

The fixed crate requires rustc version 1.39.0 or later.

Optional features

The fixed crate has four optional feature:

  1. az, disabled by default. This implements the cast traits provided by the az crate.
  2. f16, disabled by default. This provides conversion to/from f16 and bf16. This features requires the half crate.
  3. serde, disabled by default. This provides serialization support for the fixed-point types. This feature requires the serde crate.
  4. std, disabled by default. This is for features that are not possible under no_std: currently the implementation of the Error trait for ParseFixedError.

To enable features, you can add the dependency like this to Cargo.toml:

[dependencies.fixed]
version = "0.5.4"
features = ["f16", "serde"]

License

This crate is free software: you can redistribute it and/or modify it under the terms of either

at your option.

Contribution

Unless you explicitly state otherwise, any contribution intentionally submitted for inclusion in the work by you, as defined in the Apache License, Version 2.0, shall be dual licensed as above, without any additional terms or conditions.

Modules

consts

This module contains constants.

prelude

A prelude for users of the fixed crate.

traits

This module contains traits.

transcendental

This module contains transcendental functions.

types

This module provides type aliases for all supported fixed-point numbers.

Structs

FixedI8

An eight-bit fixed-point signed number with Frac fractional bits.

FixedI16

A 16-bit fixed-point signed number with Frac fractional bits.

FixedI32

A 32-bit fixed-point signed number with Frac fractional bits.

FixedI64

A 64-bit fixed-point signed number with Frac fractional bits.

FixedI128

A 128-bit fixed-point signed number with Frac fractional bits.

FixedU8

An eight-bit fixed-point unsigned number with Frac fractional bits.

FixedU16

A 16-bit fixed-point unsigned number with Frac fractional bits.

FixedU32

A 32-bit fixed-point unsigned number with Frac fractional bits.

FixedU64

A 64-bit fixed-point unsigned number with Frac fractional bits.

FixedU128

A 128-bit fixed-point unsigned number with Frac fractional bits.

ParseFixedError

An error which can be returned when parsing a fixed-point number.

Wrapping

Provides intentionally wrapped arithmetic on fixed-point numbers.