36 releases (6 stable)

1.5.0 Nov 5, 2020
1.2.0 Sep 2, 2020
1.1.0 Jul 21, 2020
0.5.7 May 11, 2020
0.1.4 Nov 29, 2018

#20 in Math

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Fixed-point numbers

The fixed crate provides 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 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 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.
  • 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 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 feature unwrapped.)
  • The serde-str feature was added. (This was previously an experimental feature.)
  • For the experimental feature num-traits, some missing supertraits were added to FixedOptionalFeatures.
  • Bug fix: multiplication of FixedI128 was panicking when multiplying some large negative numbers (issue 26).

Version 1.4.0 news (2020-10-22)

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 from self.
  • The following methods were added to all fixed-point types, to the Fixed trait, and to the Wrapping 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:

fixed = "1.5"

The fixed crate requires rustc version 1.44.0 or later.

Optional features

The fixed crate has these 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.
  5. 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:

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:

  1. 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.)


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.