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.

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.

Currently the [typenum crate] is used for the fractional bit count Frac; it is planned to move to [const generics] in version 2 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 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 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 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].
• 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.

What’s new

Version 0.5.6 news (2020-05-01)

This release is meant to be the last release before version 1.0.0: The plan is that the only differences between 0.5.6 and 1.0.0 will be dependency updates and the removal of deprecated items.

Other news in this release:

• The following method were added to signed fixed-point types and to the FixedSigned trait:
  • checked_signum, saturating_signum, wrapping_signum, overflowing_signum
• The LossyFrom and LossyInto traits were added to the prelude.
• Casts deprecated in version 0.3.1 of the az crate were marked as deprecated.

Other releases

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

Quick examples

```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::(), 7); // we can also compare directly to integers asserteq!(sixandthird.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][FixedI32]<[U12][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.

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]:

toml [dependencies] fixed = "0.5.6"

The fixed crate requires rustc version 1.39.0 or later.

Optional features

The fixed crate has four optional feature:

1. az, disabled by default. This implements the cast traits provided by the [az crate].
2. f16, disabled by default. This provides conversion to/from [f16] and [bf16]. This features requires the [half crate].
3. serde, disabled by default. This provides serialization support for the fixed-point types. This feature requires the [serde crate].
4. std, disabled by default. This is for features that are not possible under no_std: currently the implementation of the [Error] trait for [ParseFixedError].

To enable features, you can add the dependency like this to [Cargo.toml]:

toml [dependencies.fixed] version = "0.5.6" 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.