19 KiB
Fixed-point numbers
The fixed crate provides fixed-point numbers.
FixedI8
andFixedU8
are eight-bit fixed-point numbers.FixedI16
andFixedU16
are 16-bit fixed-point numbers.FixedI32
andFixedU32
are 32-bit fixed-point numbers.FixedI64
andFixedU64
are 64-bit fixed-point numbers.FixedI128
andFixedU128
are 128-bit fixed-point numbers.
These types can have Frac
fractional bits, where
0 ≤ Frac
≤ n and n is the total number of bits. When
Frac
= 0, the fixed-point number behaves like an n-bit
integer. When Frac
= n, the value x lies in the range
−0.5 ≤ x < 0.5 for signed numbers, and in the range
0 ≤ x < 1 for unsigned numbers.
In version 1 the typenum crate is used for the fractional bit
count Frac
; the plan is to to have a major version 2 with const
generics when they are supported by the Rust compiler.
The main features are
- Representation of fixed-point numbers up to 128 bits wide.
- Conversions between fixed-point numbers and numeric primitives.
- Comparisons between fixed-point numbers and numeric primitives.
- Parsing from strings in decimal, binary, octal and hexadecimal.
- Display as decimal, binary, octal and hexadecimal.
- Arithmetic and logic operations.
This crate does not provide general analytic functions.
- No algebraic functions are provided, for example no
sqrt
orpow
. - No trigonometric functions are provided, for example no
sin
orcos
. - No other transcendental functions are provided, for example no
log
orexp
.
These functions are not provided because different implementations can have different trade-offs, for example trading some correctness for speed. Implementations can be provided in other crates.
- The fixed-sqrt crate provides the square root operation.
The conversions supported cover the following cases.
- Infallible lossless conversions between fixed-point numbers and
numeric primitives are provided using
From
andInto
. These never fail (infallible) and do not lose any bits (lossless). - Infallible lossy conversions between fixed-point numbers and
numeric primitives are provided using the
LossyFrom
andLossyInto
traits. The source can have more fractional bits than the destination. - Checked lossless conversions between fixed-point numbers and
numeric primitives are provided using the
LosslessTryFrom
andLosslessTryInto
traits. The source cannot have more fractional bits than the destination. - Checked conversions between fixed-point numbers and numeric
primitives are provided using the
FromFixed
andToFixed
traits, or using thefrom_num
andto_num
methods and their checked versions. - Fixed-point numbers can be parsed from decimal strings using
FromStr
, and from binary, octal and hexadecimal strings using thefrom_str_binary
,from_str_octal
andfrom_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
andUpperHex
. The output is rounded to the nearest, with ties rounded to even.
What’s new
Version 1.6.0 news (unreleased)
- The crate now requires rustc version 1.47.0 or later.
- The following methods are now
const
functions: - The
unwrapped_to_fixed
method was added to theToFixed
trait. - The
unwrapped_from_fixed
method was added to theFromFixed
trait.
Version 1.5.0 news (2020-11-05)
- The
wide_mul
method was added to all fixed-point numbers up to 64 bits wide (issue 25). - Unwrapped methods for arithmetic together with the
Unwrapped
wrapper were added. Unwrapped methods panic on overflow, even when debug assertions are disabled, similar to how wrapping methods will wrap around even when debug assertions are enabled. (This was previously an experimental featureunwrapped
.) - The
serde-str
feature was added. (This was previously an experimental feature.) - For the experimental feature
num-traits
, some missing supertraits were added toFixedOptionalFeatures
. - Bug fix: multiplication of
FixedI128
was panicking when multiplying some large negative numbers (issue 26).
Version 1.4.0 news (2020-10-22)
- The following methods were added to all fixed-point types, to the
Fixed
trait, and to theWrapping
wrapper: - For the experimental feature
num-traits
, the following traits were implemented where applicable (issue 23): - For the experimental feature
serde-str
, serialization in human-readable formats was made more convenient to write manually (issue 24). This makes it incompatible with the version in 1.3.0.
Version 1.3.0 news (2020-10-15)
- The
MulAssign
implementation on fixed-point numbers now accepts an rhs fixed-point number with a different number of fractional bits fromself
. - The following methods were added to all fixed-point types, to the
Fixed
trait, and to theWrapping
wrapper: - The new experimental feature
unwrapped
was added, providing arithmetic methods that panic on overflow even when debug assertions are disabled. - The new experimental feature
serde-str
was added, which makes serialization use the number’s value in human-readable formats.
Other releases
Details on other releases can be found in RELEASES.md.
Quick examples
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.
use fixed::types::{I4F4, I4F12};
// −8 ≤ I4F4 < 8 with steps of 1/16 (~0.06)
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)
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.
Writing fixed-point constants and values literally
The fixed-macro crate provides a convenient macro to write down fixed-point constants literally in the code.
use fixed::types::I16F16;
use fixed_macro::fixed;
const NUM1: I16F16 = fixed!(12.75: I16F16);
let num2 = NUM1 + fixed!(13.125: I16F16);
assert_eq!(num2, 25.875);
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 = "1.5"
The fixed crate requires rustc version 1.47.0 or later.
Optional features
The fixed crate has these optional feature:
az
, disabled by default. This implements the cast traits provided by the az crate.f16
, disabled by default. This provides conversion to/fromf16
andbf16
. 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.std
, disabled by default. This is for features that are not possible underno_std
: currently the implementation of theError
trait forParseFixedError
.serde-str
, disabled by default. Fixed-point numbers are serialized as strings showing the value when using human-readable formats. This feature requires theserde
and thestd
optional features. Warning: numbers serialized when this feature is enabled cannot be deserialized when this feature is disabled, and vice versa.
To enable features, you can add the dependency like this to Cargo.toml:
[dependencies.fixed]
version = "1.5"
features = ["f16", "serde"]
Experimental optional features
It is not considered a breaking change if experimental features are removed. The removal of experimental features would however require a minor version bump. Similarly, on a minor version bump, optional dependencies can be updated to an incompatible newer version.
There is one experimental feature:
num-traits
, disabled by default. This implements some traits from the num-traits crate. (The plan is to upgrade this to an optional feature once the num-traits crate reaches version 1.0.0.)
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.