9.8 KiB
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, 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:
- All lossless infallible conversions between fixed-point numbers
and numeric primitives are implemented. That is, you can use
From
orInto
for the conversions that always work without losing any bits. - For infallible conversions that are not lossless because the
source type may have more fractional bits than the destination
type,
LossyFrom
andLossyInto
can be used; these will truncate any excess fractional bits in the source value. - Checked conversions are provided between all types using the
FromFixed
andToFixed
traits, or using the inherent methods in the fixed-point types themselves.
What’s new
Version 0.4.0 news (2019-08-08)
- The fixed crate now requires rustc version 1.31.0 or later.
- The
traits
module was added, with its traitsFixed
,FixedSigned
,FixedUnsigned
,FromFixed
,ToFixed
,LossyFrom
andLossyInto
. - The
saturating_neg
method was added to all fixed-point numbers, and thesaturating_abs
method was added to signed fixed-point numbers. - The
consts
module was added. - The
signum
method now wraps instead of panics in release mode.
Incompatible changes
- The sealed traits
Int
andFloat
now have no provided methods; the methods in the old implementation are new provided byFromFixed
andToFixed
. - Deprecated methods were removed.
Contributors
Version 0.3.3 news (2019-06-27)
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 = "0.4.0"
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):
extern crate fixed;
The fixed crate requires rustc version 1.31.0 or later.
Optional features
The fixed crate has two optional feature:
f16
, disabled by default. This provides conversion to/fromf16
. 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 = "0.4.0"
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.