# 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:

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.

## 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 = "0.3.2"
``````

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:

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 = "0.3.2"
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

 frac This module reexports items from the typenum crate. sealed This module contains sealed traits. types This module provides type aliases for all supported fixed-point numbers.

## Structs

 FixedI8 An eight-bit fixed-point signed integer with `Frac` fractional bits. FixedI16 A 16-bit fixed-point signed integer with `Frac` fractional bits. FixedI32 A 32-bit fixed-point signed integer with `Frac` fractional bits. FixedI64 A 64-bit fixed-point signed integer with `Frac` fractional bits. FixedI128 A 128-bit fixed-point signed integer with `Frac` fractional bits. FixedU8 An eight-bit fixed-point unsigned integer with `Frac` fractional bits. FixedU16 A 16-bit fixed-point unsigned integer with `Frac` fractional bits. FixedU32 A 32-bit fixed-point unsigned integer with `Frac` fractional bits. FixedU64 A 64-bit fixed-point unsigned integer with `Frac` fractional bits. FixedU128 A 128-bit fixed-point unsigned integer with `Frac` fractional bits. Wrapping Provides intentionally wrapped arithmetic on fixed-point numbers.