# Crate fixed[−][src]

# 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.

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 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 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.

## 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*:

```
[dependencies]
fixed = "1.6"
```

The *fixed* crate requires rustc version 1.47.0 or later.

## Optional features

The *fixed* crate has these optional feature:

`az`

, disabled by default. This implements the cast traits provided by the*az*crate.`f16`

, disabled by default. This provides conversion to/from`f16`

and`bf16`

. This features requires the*half*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*:

```
[dependencies.fixed]
version = "1.6"
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:

`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.)

## 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.

## Modules

consts | Mathematical constants. |

prelude | A prelude to import useful traits. |

traits | Traits for conversions and for generic use of fixed-point numbers. |

types | Type aliases for all supported fixed-point numbers. |

## Macros

const_fixed_from_int | Defines constant fixed-point numbers from integer expressions. |

## Structs

FixedI8 | An eight-bit fixed-point signed number with |

FixedI16 | A 16-bit fixed-point signed number with |

FixedI32 | A 32-bit fixed-point signed number with |

FixedI64 | A 64-bit fixed-point signed number with |

FixedI128 | A 128-bit fixed-point signed number with |

FixedU8 | An eight-bit fixed-point unsigned number with |

FixedU16 | A 16-bit fixed-point unsigned number with |

FixedU32 | A 32-bit fixed-point unsigned number with |

FixedU64 | A 64-bit fixed-point unsigned number with |

FixedU128 | A 128-bit fixed-point unsigned number with |

ParseFixedError | An error which can be returned when parsing a fixed-point number. |

Unwrapped | Provides arithmetic operations that panic on overflow even when debug assertions are disabled. |

Wrapping | Provides intentionally wrapped arithmetic on fixed-point numbers. |

## Enums

RadixParseFixedError | An error which can be returned when parsing a fixed-point number with a given radix. |