13 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.
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 0.2.1 (unreleased)
- Bug fix: the
from_fixed
andfrom_int
methods (and their checked counterparts) could return wrong values for negative values. - Bug fix: display was using one fractional digit less than required, thus yielding the same output for diffent fixed-point numbers.
Version 0.2.0 news (2019-01-29)
- The new methods
from_fixed
,checked_from_fixed
,saturating_from_fixed
,wrapping_from_fixed
andoverflowing_from_fixed
were added. - The old method
from_int
was removed to be replaced. - The new methods
from_int
,checked_from_int
,saturating_from_int
,wrapping_from_int
andoverflowing_from_int
were added. - The new methods
from_float
,checked_from_float
,saturating_from_float
,wrapping_from_float
andoverflowing_from_float
were added. - The new method
to_float
was added. - The methods
from_f16
,from_f32
,from_f64
,to_f16
,to_f32
andto_f64
were deprecated. - The
to_int
method was fixed to truncate fractional bits as documented for negative values. - The new methods
ceil
,floor
,round
,checked_ceil
,checked_floor
,checked_round
,saturating_ceil
,saturating_floor
,saturating_round
,wrapping_ceil
,wrapping_floor
,wrapping_round
,overflowing_ceil
,overflowing_floor
andoverflowing_round
were added. - The methods
to_int_ceil
,to_int_floor
andto_int_round
were deprecated.
Version 0.1.6 news (2019-01-27)
- Optional serde support was added.
Version 0.1.5 news (2019-01-26)
- A new module
types
is available with aliases for all supported fixed-point numbers. - Lossless infallible conversions between fixed-point numbers and
numeric primitives are now supported using
From
andInto
.
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");
// convert to i32, taking the ceil
assert_eq!(six_and_third.ceil().to_int(), 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 = "0.2.0"
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 1.28.0 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 = "0.2.0"
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.