https://github.com/blockworks-foundation/fixed

Fork of 'fixed' library from https://gitlab.com/tspiteri/fixed with patches from cram
https://github.com/blockworks-foundation/fixed
Last synced: about 2 months ago
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Fork of 'fixed' library from https://gitlab.com/tspiteri/fixed with patches from cram
Host: GitHub
URL: https://github.com/blockworks-foundation/fixed
Owner: blockworks-foundation
License: apache-2.0
Created: 2023-09-13T08:26:07.000Z (over 1 year ago)
Default Branch: master
Last Pushed: 2023-09-13T08:35:39.000Z (over 1 year ago)
Last Synced: 2025-01-26T15:32:25.147Z (4 months ago)
Language: Rust
Size: 1.89 MB
Stars: 0
Watchers: 2
Forks: 1
Open Issues: 0
Metadata Files:
- Readme: README.md
- License: LICENSE-APACHE
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README

        

# Fixed-point numbers

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 = 1/2^f. 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

  * Representation of binary 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 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.

  * No algebraic functions are provided, for example no `sqrt` or `pow`.

  * No trigonometric functions are provided, for example no `sin` or `cos`.

  * No other transcendental functions are provided, for example no `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 [*fixed-sqrt* crate] provides the square root operation.

  * The [*cordic* crate] provides various functions implemented using the

    [CORDIC] algorithm.

The conversions supported cover the following cases.

  * Infallible lossless conversions between fixed-point numbers and numeric

    primitives are provided using [`From`] and [`Into`]. 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`] and [`LossyInto`] 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`] and

    [`LosslessTryInto`] 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`] and [`ToFixed`] traits, or using the

    [`from_num`] and [`to_num`] methods and [their checked

    versions][`checked_from_num`].

  * Additionally, [`az`] casts are implemented for conversion between

    fixed-point nubmers and numeric primitives.

  * Fixed-point numbers can be parsed from decimal strings using [`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.

  * Fixed-point numbers can be converted to strings using [`Display`],

    [`Binary`], [`Octal`], [`LowerHex`] and [`UpperHex`]. The output is rounded

    to the nearest, with ties rounded to even.

  * All fixed-point numbers are plain old data, so [`bytemuck`] bit casting

    conversions can be used.

## What’s new

### Version 1.11.0 news (unreleased)

  * The following methods were added to all fixed-point numbers, to the

    [`Fixed`][tf-1-11] trait, and to the [`Wrapping`][w-1-11] and

    [`Unwrapped`][u-1-11] wrappers:

      * [`lerp`][f-l-1-11]

      * [`inv_lerp`][f-il-1-11]

  * The following methods were added to all fixed-point numbers and to the

    [`Fixed`][tf-1-11] trait:

      * [`checked_lerp`][f-cl-1-11], [`saturating_lerp`][f-sl-1-11],

        [`wrapping_lerp`][f-wl-1-11], [`unwrapped_lerp`][f-ul-1-11],

        [`overflowing_lerp`][f-ol-1-11]

      * [`checked_inv_lerp`][f-cil-1-11], [`saturating_inv_lerp`][f-sil-1-11],

        [`wrapping_inv_lerp`][f-wil-1-11], [`unwrapped_inv_lerp`][f-uil-1-11],

        [`overflowing_inv_lerp`][f-oil-1-11]

  * The [*typenum* crate] dependency was updated to [version

    1.14][typenum-1-14].

  * The [`LeEqU8`][leu8-1-11], [`LeEqU16`][leu16-1-11], [`LeEqU32`][leu32-1-11],

    [`LeEqU64`][leu64-1-11] and [`LeEqU128`][leu128-1-11] traits no longer have

    a direct `'static` constraint, as it is a constraint of their supertrait

    [`Unsigned`][uns-1-11] since typenum [version 1.14][typenum-1-14]. This

    fixes a potential compatibility issue introduced in version 1.9.0.

[f-cil-1-11]: https://tspiteri.gitlab.io/fixed/dev/fixed/struct.FixedI32.html#method.checked_inv_lerp

[f-cl-1-11]: https://tspiteri.gitlab.io/fixed/dev/fixed/struct.FixedI32.html#method.checked_lerp

[f-il-1-11]: https://tspiteri.gitlab.io/fixed/dev/fixed/struct.FixedI32.html#method.inv_lerp

[f-l-1-11]: https://tspiteri.gitlab.io/fixed/dev/fixed/struct.FixedI32.html#method.lerp

[f-oil-1-11]: https://tspiteri.gitlab.io/fixed/dev/fixed/struct.FixedI32.html#method.overflowing_inv_lerp

[f-ol-1-11]: https://tspiteri.gitlab.io/fixed/dev/fixed/struct.FixedI32.html#method.overflowing_lerp

[f-sil-1-11]: https://tspiteri.gitlab.io/fixed/dev/fixed/struct.FixedI32.html#method.saturating_inv_lerp

[f-sl-1-11]: https://tspiteri.gitlab.io/fixed/dev/fixed/struct.FixedI32.html#method.saturating_lerp

[f-uil-1-11]: https://tspiteri.gitlab.io/fixed/dev/fixed/struct.FixedI32.html#method.unwrapped_inv_lerp

[f-ul-1-11]: https://tspiteri.gitlab.io/fixed/dev/fixed/struct.FixedI32.html#method.unwrapped_lerp

[f-wil-1-11]: https://tspiteri.gitlab.io/fixed/dev/fixed/struct.FixedI32.html#method.wrapping_inv_lerp

[f-wl-1-11]: https://tspiteri.gitlab.io/fixed/dev/fixed/struct.FixedI32.html#method.wrapping_lerp

[leu128-1-11]: https://tspiteri.gitlab.io/fixed/dev/fixed/types/extra/trait.LeEqU128.html

[leu16-1-11]: https://tspiteri.gitlab.io/fixed/dev/fixed/types/extra/trait.LeEqU16.html

[leu32-1-11]: https://tspiteri.gitlab.io/fixed/dev/fixed/types/extra/trait.LeEqU32.html

[leu64-1-11]: https://tspiteri.gitlab.io/fixed/dev/fixed/types/extra/trait.LeEqU64.html

[leu8-1-11]: https://tspiteri.gitlab.io/fixed/dev/fixed/types/extra/trait.LeEqU8.html

[tf-1-11]: https://tspiteri.gitlab.io/fixed/dev/fixed/traits/trait.Fixed.html

[typenum-1-14]: https://docs.rs/typenum/~1.14/typenum/index.html

[u-1-11]: https://tspiteri.gitlab.io/fixed/dev/fixed/struct.Unwrapped.html

[uns-1-11]: https://tspiteri.gitlab.io/fixed/dev/fixed/types/extra/trait.Unsigned.html

[w-1-11]: https://tspiteri.gitlab.io/fixed/dev/fixed/struct.Wrapping.html

### Version 1.10.0 news (2021-08-23)

  * The crate now requires rustc version 1.53.0 or later.

  * {[Div][`Div`],[DivAssign][`DivAssign`],[Rem][`Rem`],[RemAssign][`RemAssign`]}\<[NonZeroU32][`NonZeroU32`]>

    are now implemented for [`FixedU32`][fu-1-10], and similar for all other

    unsigned fixed-point numbers.

  * {[Rem][`Rem`],[RemAssign][`RemAssign`]}\<[NonZeroI32][`NonZeroI32`]>

    are now implemented for [`FixedI32`][fi-1-10], and similar for all other

    signed fixed-point numbers.

  * The new [`arbitrary`][feat-1-10] optional feature was added to implement the

    [`Arbitrary`][a-a-1] trait provided by the [*arbitrary* crate] for all

    fixed-point numbers ([issue 37]).

[`DivAssign`]: https://doc.rust-lang.org/nightly/core/ops/trait.DivAssign.html

[`Div`]: https://doc.rust-lang.org/nightly/core/ops/trait.Div.html

[`NonZeroI32`]: https://doc.rust-lang.org/nightly/core/num/struct.NonZeroI32.html

[`NonZeroU32`]: https://doc.rust-lang.org/nightly/core/num/struct.NonZeroU32.html

[`RemAssign`]: https://doc.rust-lang.org/nightly/core/ops/trait.RemAssign.html

[`Rem`]: https://doc.rust-lang.org/nightly/core/ops/trait.Rem.html

[a-a-1]: https://docs.rs/arbitrary/^1/arbitrary/trait.Arbitrary.html

[feat-1-10]: https://docs.rs/fixed/~1.10/fixed/index.html#optional-features

[fi-1-10]: https://docs.rs/fixed/~1.10/fixed/struct.FixedI32.html

[fu-1-10]: https://docs.rs/fixed/~1.10/fixed/struct.FixedU32.html

[issue 37]: https://gitlab.com/tspiteri/fixed/-/issues/37

### Other releases

Details on other releases can be found in [*RELEASES.md*].

[*RELEASES.md*]: https://gitlab.com/tspiteri/fixed/blob/master/RELEASES.md

## Quick examples

```rust

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::(), 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.

```rust

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.

```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);

```

## Using the *fixed* crate

The *fixed* crate is available on [crates.io][*fixed* crate]. 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.

## Optional features

The *fixed* crate has these optional feature:

 1. `arbitrary`, disabled by default. This provides the generation of arbitrary

    fixed-point numbers from raw, unstructured data. This feature requires the

    [*arbitrary* crate].

 2. `serde`, disabled by default. This provides serialization support for the

    fixed-point types. This feature requires the [*serde* crate].

 3. `std`, disabled by default. This is for features that are not possible under

    `no_std`: currently the implementation of the [`Error`] trait for

    [`ParseFixedError`].

 4. `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"]

```

## Experimental optional features

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.

 1. `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.)

## Deprecated optional features

The following optional features are deprecated and may be removed in the next

major version of the crate.

 1. `az`, has no effect. Previously required for the [`az`] cast traits. Now

    these cast traits are always provided.

 2. `f16`, has no effect. Previously required for conversion to/from [`f16`] and

    [`bf16`]. Now these conversions are always provided.

## 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][LICENSE-APACHE] or

  * the [MIT License][LICENSE-MIT]

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.

[*Cargo.toml*]: https://doc.rust-lang.org/cargo/guide/dependencies.html

[*arbitrary* crate]: https://crates.io/crates/arbitrary

[*cordic* crate]: https://crates.io/crates/cordic

[*fixed* crate]: https://crates.io/crates/fixed

[*fixed-macro* crate]: https://crates.io/crates/fixed-macro

[*fixed-sqrt* crate]: https://crates.io/crates/fixed-sqrt

[*half* crate]: https://crates.io/crates/half

[*num-traits* crate]: https://crates.io/crates/num-traits

[*serde* crate]: https://crates.io/crates/serde

[*typenum* crate]: https://crates.io/crates/typenum

[CORDIC]: https://en.wikipedia.org/wiki/CORDIC

[FixedI32]: https://docs.rs/fixed/~1.10/fixed/struct.FixedI32.html

[FixedU32]: https://docs.rs/fixed/~1.10/fixed/struct.FixedU32.html

[LICENSE-APACHE]: https://www.apache.org/licenses/LICENSE-2.0

[LICENSE-MIT]: https://opensource.org/licenses/MIT

[U0]: https://docs.rs/fixed/~1.10/fixed/types/extra/type.U0.html

[U12]: https://docs.rs/fixed/~1.10/fixed/types/extra/type.U12.html

[U24]: https://docs.rs/fixed/~1.10/fixed/types/extra/type.U24.html

[U32]: https://docs.rs/fixed/~1.10/fixed/types/extra/type.U32.html

[`Binary`]: https://doc.rust-lang.org/nightly/core/fmt/trait.Binary.html

[`Display`]: https://doc.rust-lang.org/nightly/core/fmt/trait.Display.html

[`Error`]: https://doc.rust-lang.org/nightly/std/error/trait.Error.html

[`FixedI128`]: https://docs.rs/fixed/~1.10/fixed/struct.FixedI128.html

[`FixedI16`]: https://docs.rs/fixed/~1.10/fixed/struct.FixedI16.html

[`FixedI32`]: https://docs.rs/fixed/~1.10/fixed/struct.FixedI32.html

[`FixedI64`]: https://docs.rs/fixed/~1.10/fixed/struct.FixedI64.html

[`FixedI8`]: https://docs.rs/fixed/~1.10/fixed/struct.FixedI8.html

[`FixedU128`]: https://docs.rs/fixed/~1.10/fixed/struct.FixedU128.html

[`FixedU16`]: https://docs.rs/fixed/~1.10/fixed/struct.FixedU16.html

[`FixedU32`]: https://docs.rs/fixed/~1.10/fixed/struct.FixedU32.html

[`FixedU64`]: https://docs.rs/fixed/~1.10/fixed/struct.FixedU64.html

[`FixedU8`]: https://docs.rs/fixed/~1.10/fixed/struct.FixedU8.html

[`FromFixed`]: https://docs.rs/fixed/~1.10/fixed/traits/trait.FromFixed.html

[`FromStr`]: https://doc.rust-lang.org/nightly/core/str/trait.FromStr.html

[`From`]: https://doc.rust-lang.org/nightly/core/convert/trait.From.html

[`I20F12`]: https://docs.rs/fixed/~1.10/fixed/types/type.I20F12.html

[`I4F12`]: https://docs.rs/fixed/~1.10/fixed/types/type.I4F12.html

[`I4F4`]: https://docs.rs/fixed/~1.10/fixed/types/type.I4F4.html

[`Into`]: https://doc.rust-lang.org/nightly/core/convert/trait.Into.html

[`LosslessTryFrom`]: https://docs.rs/fixed/~1.10/fixed/traits/trait.LosslessTryFrom.html

[`LosslessTryInto`]: https://docs.rs/fixed/~1.10/fixed/traits/trait.LosslessTryInto.html

[`LossyFrom`]: https://docs.rs/fixed/~1.10/fixed/traits/trait.LossyFrom.html

[`LossyInto`]: https://docs.rs/fixed/~1.10/fixed/traits/trait.LossyInto.html

[`LowerHex`]: https://doc.rust-lang.org/nightly/core/fmt/trait.LowerHex.html

[`Octal`]: https://doc.rust-lang.org/nightly/core/fmt/trait.Octal.html

[`ParseFixedError`]: https://docs.rs/fixed/~1.10/fixed/struct.ParseFixedError.html

[`ToFixed`]: https://docs.rs/fixed/~1.10/fixed/traits/trait.ToFixed.html

[`U20F12`]: https://docs.rs/fixed/~1.10/fixed/types/type.U20F12.html

[`UpperHex`]: https://doc.rust-lang.org/nightly/core/fmt/trait.UpperHex.html

[`az`]: https://docs.rs/az/^1/az/index.html

[`bf16`]: https://docs.rs/half/^1/half/struct.bf16.html

[`bytemuck`]: https://docs.rs/bytemuck/^1/bytemuck/index.html

[`checked_from_num`]: https://docs.rs/fixed/~1.10/fixed/struct.FixedI32.html#method.checked_from_num

[`f16`]: https://docs.rs/half/^1/half/struct.f16.html

[`from_num`]: https://docs.rs/fixed/~1.10/fixed/struct.FixedI32.html#method.from_num

[`from_str_binary`]: https://docs.rs/fixed/~1.10/fixed/struct.FixedI32.html#method.from_str_binary

[`from_str_hex`]: https://docs.rs/fixed/~1.10/fixed/struct.FixedI32.html#method.from_str_hex

[`from_str_octal`]: https://docs.rs/fixed/~1.10/fixed/struct.FixedI32.html#method.from_str_octal

[`i32`]: https://doc.rust-lang.org/nightly/std/primitive.i32.html

[`to_num`]: https://docs.rs/fixed/~1.10/fixed/struct.FixedI32.html#method.to_num

[`u32`]: https://doc.rust-lang.org/nightly/std/primitive.u32.html

[const generics]: https://github.com/rust-lang/rust/issues/44580
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