Fixed-point numbers

The fixed crate provides fixed-point numbers. Currently it uses the typenum crate for the fractional bit count; it is planned to move to const generics when they are implemented by the Rust compiler.

The crate provides the following types:

FixedI8 is a signed eight-bit fixed-point number,
FixedI16 is a signed 16-bit fixed-point number,
FixedI32 is a signed 32-bit fixed-point number,
FixedI64 is a signed 64-bit fixed-point number,
FixedI128 is a signed 128-bit fixed-point number,
FixedU8 is an unsigned eight-bit fixed-point number,
FixedU16 is an unsigned 16-bit fixed-point number,
FixedU32 is an unsigned 32-bit fixed-point number,
FixedU64 is an unsigned 64-bit fixed-point number, and
FixedU128 is an unsigned 128-bit fixed-point number.

All fixed-point numbers can have Frac fractional bits, where Frac can have any value from 0 up to and including the size of the number in bits. When Frac is 0, the fixed-point number behaves like an integer. When Frac is equal to the number of bits, the value of the fixed-point number lies in the range −0.5 ≤ x < 0.5 for signed fixed-point numbers, and in the range 0 ≤ x < 1 for unsigned fixed-point numbers.

All lossless infallible conversions between fixed-point numbers and numeric primitives are implemented. That is, you can use From or Into for the conversions that always work without losing any bits.

What’s new

Version 0.3.3 news (2019-06-27)

Conversions to/from isize and usize were added.

Version 0.3.2 news (2019-02-27)

The Wrapping wrapper was added.

Version 0.3.1 news (2019-02-07)

Reimplement From<bool> for all fixed-point types which can represent the integer 1. This was inadvertently removed in 0.3.0.

Version 0.3.0 news (2019-02-03)

Highlights

Every fixed-point type now supports conversion to/from all primitive number types, including checked versions of the conversions.
Every fixed-point type now supports comparisons with all primitive number types.

Incompatible changes

The method to_int was changed; now its return type is generic.
The Int trait implementation for bool was removed.

Other changes

The new method to_fixed was added.
Checked versions of to_fixed and to_int were added.
The methods from_fixed and to_fixed, and their checked versions, were added to the Int trait.
The method from_fixed, and the method to_fixed and its checked versions, were added to the Float trait.
The methods int_bits and frac_bits were deprecated and replaced by the methods int_nbits and frac_nbits.

Other releases

Details on other releases can be found in RELEASES.md.

Quick examples

// 20 integer bits, 12 fractional bits
use fixed::types::I20F12;

// 19/3 = 6 1/3
let six_and_third = I20F12::from_int(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_int::<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<frac::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.

// −8 ≤ I4F4 < 8 with steps of 1/16 (about 0.06)
use fixed::types::I4F4;
let a = I4F4::from_int(1);
// multiplication and division by integers is possible
let ans1 = a / 5 * 17;
// 1 / 5 × 17 = 3 2/5 (3.4), but we get 3 3/16 (3.19)
assert_eq!(ans1, I4F4::from_bits((3 << 4) + 3));
assert_eq!(ans1.to_string(), "3.19");

// −8 ≤ I4F12 < 8 with steps of 1/4096 (about 0.0002)
use fixed::types::I4F12;
let wider_a = I4F12::from(a);
let wider_ans = wider_a / 5 * 17;
let ans2 = I4F4::from_fixed(wider_ans);
// now the answer is the much closer 3 6/16 (3.38)
assert_eq!(ans2, I4F4::from_bits((3 << 4) + 6));
assert_eq!(ans2.to_string(), "3.38");

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 (3.19). 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 (3.38).

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_fixed 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 = "0.3.3"

If you are using the 2015 Rust edition, you also need to declare it by adding this to your crate root (usually lib.rs or main.rs):

extern crate fixed;

The fixed crate requires rustc version 1.28.0 or later.

Optional features

The fixed crate has two optional feature:

f16, disabled by default. This provides conversion to/from f16. This features requires the half crate.
serde, disabled by default. This provides serialization support for the fixed-point types. This feature requires the serde crate.

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

[dependencies.fixed]
version = "0.3.3"
features = ["f16", "serde"]

License

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

the Apache License, Version 2.0 or
the MIT License

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.

fixed 0.3.3