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 when the Rust
compiler’s [generic_const_exprs feature] is ready and stabilized. An [alpha
version] is already available.
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 numbers 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.TRY_ONE associated constant was added to the
Fixed trait.TRY_NEG_ONE associated constant was added to the
FixedSigned trait.const_from_fixed and const_from_int
methods were added to all fixed-point numbers.const_fixed_from_int macro is now deprecated.F128
struct:
F128 now implements [From] for conversions from [f64],
[f32], f16 and bf16.fixed::f128::consts
module was added with F128 basic mathematical constants.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 parsing methods are available as const functions.
```rust use fixed::types::I16F16;
const TWELVEPOINT75: I16F16 = I16F16::unwrappedfromstr("12.75"); // 1.1 binary is 1.5 decimal const ONEPOINT5: I16F16 = I16F16::unwrappedfromstrbinary("1.1"); // 12.75 + 1.5 = 14.25 let sum = TWELVEPOINT75 + ONEPOINT5; asserteq!(sum, 14.25); ```
The [fixed-macro crate] is an alternative which provides a convenient macro to write down fixed-point constants literally in the code. It supports underscores as separators, scientific notation, and binary/octal/hexadecimal integers, but it does not support binary/octal/hexadecimal fractions as they cannot be parsed by the Rust compiler.
```rust use fixed::types::I16F16; use fixed_macro::fixed;
// 0.1275e2 is 12.75 const NUM1: I16F16 = fixed!(0.1275e2: I16F16); // 11 binary is 3 decimal let num2 = NUM1 + fixed!(0b11: I16F16); // 12.75 + 3 = 15.75 asserteq!(num2, 15.75); ```
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 = "1.20"
The fixed crate requires rustc version 1.61.0 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 = "1.20"
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.
borsh, disabled by default. This implements serialization and
deserialization using the [borsh crate]. (The plan is to promote this to
an optional feature once the [borsh crate] reaches version 1.0.0.)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 will 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.