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.

Various conversion methods are available:

• All lossless infallible conversions between fixed-point numbers and numeric primitives are implemented. You can use From or Into for conversions that always work without losing any bits.
• For lossy infallible conversions between fixed-point numbers and numeric primitives, where the source type may have more fractional bits than the destination type, the LossyFrom and LossyInto traits can be used. Excess fractional bits are truncated.
• Checked conversions are provided between fixed-point numbers and numeric primitives using the FromFixed and ToFixed traits, or using the from_num and to_num methods and their checked versions.
• Fixed-point numbers can be parsed from decimal strings using FromStr, or from binary, octal or hexadecimal using the from_str_binary, from_str_octal or from_str_hex methods. The result is rounded to the nearest, with ties rounded to even.
• Fixed-point numbers can be converted to strings using Display, Binary, Octal, LowerHex and UpperHex. The output is rounded to the nearest, with ties rounded to even.

Quick examples

// 20 integer bits, 12 fractional bits
use 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.

// −8 ≤ I4F4 < 8 with steps of 1/16 (~0.06)
use fixed::types::I4F4;
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)
use fixed::types::I4F12;
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 = "0.4.3"

The fixed crate requires rustc version 1.34.0 or later.

Optional features

The fixed crate has two optional feature:

1. f16, disabled by default. This provides conversion to/from f16. This features requires the half crate.
2. 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 = "0.4.3"
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.