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, andFixedU128] 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:
From] or [Into] for the conversions that always work without
losing any bits.LossyFrom] and [LossyInto] can be used; these will
truncate any excess fractional bits in the source value.FromFixed] and [ToFixed] traits, or using the inherent methods
in the fixed-point types themselves.traits] module was added, with its traits [Fixed],
[FixedSigned], [FixedUnsigned], [FromFixed], [ToFixed],
[LossyFrom] and [LossyInto].saturating_neg] method was added to all fixed-point
numbers, and the [saturating_abs] method was added to signed
fixed-point numbers.consts] module was added.signum] method now wraps instead of panics in release mode.Int] and [Float] now have no provided
methods; the methods in the old implementation are new provided by
[FromFixed] and [ToFixed].isize] and [usize] were added.Details on other releases can be found in [RELEASES.md].
```rust // 20 integer bits, 12 fractional bits use fixed::types::I20F12;
// 19/3 = 6 1/3
let sixandthird = I20F12::fromint(19) / 3;
// four decimal digits for 12 binary digits
asserteq!(sixandthird.tostring(), "6.3333");
// find the ceil and convert to i32
asserteq!(sixandthird.ceil().toint::
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][.
The unsigned counterpart would be [FixedI32]<[frac::U12][frac::U12]>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.
```rust // −8 ≤ I4F4 < 8 with steps of 1/16 (about 0.06) use fixed::types::I4F4; let a = I4F4::fromint(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) asserteq!(ans1, I4F4::frombits((3 << 4) + 3)); asserteq!(ans1.to_string(), "3.19");
// −8 ≤ I4F12 < 8 with steps of 1/4096 (about 0.0002) use fixed::types::I4F12; let widera = I4F12::from(a); let widerans = widera / 5 * 17; let ans2 = I4F4::fromfixed(widerans); // now the answer is the much closer 3 6/16 (3.38) asserteq!(ans2, I4F4::frombits((3 << 4) + 6)); asserteq!(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.
The fixed crate is available on crates.io. To use it in your crate, add it as a dependency inside [Cargo.toml]:
toml
[dependencies]
fixed = "0.4.0"
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):
rust
extern crate fixed;
The fixed crate requires rustc version 1.31.0 or later.
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]:
toml
[dependencies.fixed]
version = "0.4.0"
features = ["f16", "serde"]
This crate is free software: you can redistribute it and/or modify it under the terms of either
at your option.
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.