### 39 releases (9 stable)

1.8.0 | Apr 20, 2021 |
---|---|

1.7.0 | Mar 25, 2021 |

1.6.0 | Feb 5, 2021 |

1.5.0 | Nov 5, 2020 |

0.1.4 | Nov 29, 2018 |

#**19** in Math

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# Fixed-point numbers

The *fixed* crate provides fixed-point numbers.

and`FixedI8`

are eight-bit fixed-point numbers.`FixedU8`

and`FixedI16`

are 16-bit fixed-point numbers.`FixedU16`

and`FixedI32`

are 32-bit fixed-point numbers.`FixedU32`

and`FixedI64`

are 64-bit fixed-point numbers.`FixedU64`

and`FixedI128`

are 128-bit fixed-point numbers.`FixedU128`

An *n*-bit fixed-point number has *f* =

fractional bits where
0 ≤ `Frac`*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

, and `i32``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* = 1/2^{n} 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

;
the plan is to to have a major version 2 with const generics instead when the
Rust compiler support for them is powerful enough.`Frac`

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

or`sqrt`

.`pow` - No trigonometric functions are provided, for example no

or`sin`

.`cos` - No other transcendental functions are provided, for example no

or`log`

.`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

and`From`

. These never fail (infallible) and do not lose any bits (lossless).`Into` - Infallible lossy conversions between fixed-point numbers and numeric
primitives are provided using the

and`LossyFrom`

traits. The source can have more fractional bits than the destination.`LossyInto` - Checked lossless conversions between fixed-point numbers and numeric
primitives are provided using the

and`LosslessTryFrom`

traits. The source cannot have more fractional bits than the destination.`LosslessTryInto` - Checked conversions between fixed-point numbers and numeric primitives are
provided using the

and`FromFixed`

traits, or using the`ToFixed`

and`from_num`

methods and their checked versions.`to_num` - Fixed-point numbers can be parsed from decimal strings using

, and from binary, octal and hexadecimal strings using the`FromStr`

,`from_str_binary`

and`from_str_octal`

methods. The result is rounded to the nearest, with ties rounded to even.`from_str_hex` - Fixed-point numbers can be converted to strings using

,`Display`

,`Binary`

,`Octal`

and`LowerHex`

. The output is rounded to the nearest, with ties rounded to even.`UpperHex`

## What’s new

### Version 1.8.0 news (2021-04-20)

- The following constants and method were added to all fixed-point numbers, to
the

trait, and to the`Fixed`

and`Wrapping`

wrappers:`Unwrapped` - The

constant was added to all fixed-point numbers that can represent the value 1.`ONE` - The following methods were added to all fixed-point numbers and to the

trait:`Fixed` - The following methods are now

functions:`const` - The following methods were added to all fixed-point numbers:
- Many methods were marked with the

attribute.`must_use`

### 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

is a 32-bit fixed-point signed number with 20 integer bits
and 12 fractional bits. It is an alias to `I20F12``FixedI32<U12>`

. The
unsigned counterpart would be

. Aliases are provided for all
combinations of integer and fractional bits adding up to a total of eight, 16,
32, 64 or 128 bits.`U20F12`

`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

means that `a`

is 3⁄16 instead of 1⁄5, leading to an inaccurate
result `a / 5`

`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

to `I4F4`

using `I4F12`

, as the
target type has the same number of integer bits and a larger number of
fractional bits. Converting from `From`

to `I4F12`

cannot use `I4F4`

as we
have less fractional bits, so we use `From`

instead.`from_num`

## 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 ``=` `"`1.8`"`

The *fixed* crate requires rustc version 1.50.0 or later.

## Optional features

The *fixed* crate has these optional feature:

, disabled by default. This provides serialization support for the fixed-point types. This feature requires the`serde`*serde*crate.

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

: currently the implementation of the`no_std`

trait for`Error`

.`ParseFixedError`

, disabled by default. Fixed-point numbers are serialized as strings showing the value when using human-readable formats. This feature requires the`serde-str`

and the`serde`

optional features.`std`**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 ``=` `"`1.8`"`
`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.

, disabled by default. This implements some traits from the`num-traits`*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.

, has no effect. Previously required for the cast traits from the`az`*az*crate. Now these cast traits are always provided.

, has no effect. Previously required for conversion to/from`f16`

and`f16`

. Now these conversions are always provided.`bf16`

## 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.

#### Dependencies

~610KB

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