The [fixed crate] provides fixed-point numbers.
FixedI8] and [FixedU8] are eight-bit fixed-point numbers.FixedI16] and [FixedU16] are 16-bit fixed-point numbers.FixedI32] and [FixedU32] are 32-bit fixed-point numbers.FixedI64] and [FixedU64] are 64-bit fixed-point numbers.FixedI128] and [FixedU128] are 128-bit fixed-point numbers.An n-bit fixed-point number has f = Frac fractional bits where
0 ≤ f ≤ n, and n − f integer bits. For example,
[FixedI32]\<[U24]> is a 32-bit signed fixed-point number with
n = 32 total bits, f = 24 fractional bits, and
n − f = 8 integer bits. [FixedI32]\<[U0]> behaves
like [i32], and [FixedU32]\<[U0]> behaves like [u32].
The difference between any two successive representable numbers is constant
throughout the possible range for a fixed-point number:
Δ = 1/2f. When f = 0, like in
[FixedI32]\<[U0]>, Δ = 1 because representable numbers are
integers, and the difference between two successive integers is 1. When
f = n, Δ = 1/2n and the value lies in the
range −0.5 ≤ x < 0.5 for signed numbers like
[FixedI32]\<[U32]>, and in the range 0 ≤ x < 1 for unsigned
numbers like [FixedU32]\<[U32]>.
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] instead when the
Rust compiler support for them is powerful enough.
The main features are
This crate does not provide decimal fixed-point numbers. For example 0.001 cannot be represented exactly, as it is 1/103. It is binary fractions like 1/24 (0.0625) that can be represented exactly, provided there are enough fractional bits.
This crate does not provide general analytic functions.
sqrt or pow.sin or cos.log or
exp.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 conversions supported cover the following cases.
From] and [Into]. These never fail
(infallible) and do not lose any bits (lossless).LossyFrom] and [LossyInto] traits.
The source can have more fractional bits than the destination.LosslessTryFrom] and
[LosslessTryInto] traits. The source cannot have more fractional bits than
the destination.FromFixed] and [ToFixed] traits, or using the
[from_num] and [to_num] methods and [their checked
versions][checked_from_num].az] casts are implemented for conversion between
fixed-point nubmers and numeric primitives.FromStr],
and from binary, octal and hexadecimal strings using the
[from_str_binary], [from_str_octal] and [from_str_hex] methods. The
result is rounded to the nearest, with ties rounded to even.Display],
[Binary], [Octal], [LowerHex] and [UpperHex]. The output is rounded
to the nearest, with ties rounded to even.bytemuck] bit casting
conversions can be used.{[Div][Div],[DivAssign][DivAssign],[Rem][Rem],[RemAssign][RemAssign]}\<[NonZeroU32][NonZeroU32]>
are now implemented for FixedU32, and similar for all other
unsigned fixed-point numbers.{[Rem][Rem],[RemAssign][RemAssign]}\<[NonZeroI32][NonZeroI32]>
are now implemented for FixedI32, and similar for all other
signed fixed-point numbers.arbitrary optional feature was added to implement the
Arbitrary trait provided by the [arbitrary crate] for all
fixed-point numbers ([issue 37]).Details on other releases can be found in [RELEASES.md].
```rust use fixed::types::I20F12;
// 19/3 = 6 1/3
let sixandthird = I20F12::fromnum(19) / 3;
// four decimal digits for 12 binary digits
asserteq!(sixandthird.tostring(), "6.3333");
// find the ceil and convert to i32
asserteq!(sixandthird.ceil().tonum::
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.
```rust use fixed::types::{I4F4, I4F12};
// −8 ≤ I4F4 < 8 with steps of 1/16 (~0.06) let a = I4F4::fromnum(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) asserteq!(ans1, I4F4::frombits((3 << 4) + 3)); asserteq!(ans1.to_string(), "3.2");
// −8 ≤ I4F12 < 8 with steps of 1/4096 (~0.0002) let widera = I4F12::from(a); let widerans = widera / 5 * 17; let ans2 = I4F4::fromnum(widerans); // now the answer is the much closer 3 6/16 (~3.4) asserteq!(ans2, I4F4::frombits((3 << 4) + 6)); asserteq!(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.
The [fixed-macro crate] provides a convenient macro to write down fixed-point constants literally in the code.
```rust 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); ```
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 = "1.10"
The fixed crate requires rustc version 1.53.0 or later.
The fixed crate has these optional feature:
arbitrary, disabled by default. This provides the generation of arbitrary
fixed-point numbers from raw, unstructured data. This feature requires the
[arbitrary 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 under
no_std: currently the implementation of the [Error] trait for
[ParseFixedError].serde-str, disabled by default. Fixed-point numbers are serialized as
strings showing the value when using human-readable formats. This feature
requires the serde and the std 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]:
toml
[dependencies.fixed]
version = "1.10"
features = ["serde"]
It is not considered a breaking change if the following 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.
num-traits, disabled by default. This implements some traits from the
[num-traits crate]. (The plan is to promote this to an optional feature
once the [num-traits crate] reaches version 1.0.0.)The following optional features are deprecated and may be removed in the next major version of the crate.
az, has no effect. Previously required for the [az] cast traits. Now
these cast traits are always provided.f16, has no effect. Previously required for conversion to/from [f16] and
[bf16]. Now these conversions are always provided.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.