### 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

**6,477** downloads per month

Used in **24** crates
(13 directly)

**MIT/Apache**

1MB

17K
SLoC

# 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`

These types can have

fractional bits, where
0 ≤ `Frac`

≤ `Frac`*n* and *n* is the total number of bits. When

= 0, the fixed-point number behaves like an `Frac`*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

; the plan is to to have a major version 2 with const
generics when they are supported by the Rust compiler.`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 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 1.5.0 news (2020-11-05)

- The

method was added to all fixed-point numbers up to 64 bits wide (issue 25).`wide_mul` - Unwrapped methods for arithmetic together with the

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`

.)`unwrapped` - The

feature was added. (This was previously an experimental feature.)`serde-str` - For the experimental feature

, some missing supertraits were added to`num-traits`

.`FixedOptionalFeatures` - Bug fix: multiplication of

was panicking when multiplying some large negative numbers (issue 26).`FixedI128`

### Version 1.4.0 news (2020-10-22)

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

trait, and to the`Fixed`

wrapper:`Wrapping` - For the experimental feature

, the following traits were implemented where applicable (issue 23):`num-traits` - For the experimental feature

, serialization in human-readable formats was made more convenient to write manually (issue 24). This makes it incompatible with the version in 1.3.0.`serde-str`

### Version 1.3.0 news (2020-10-15)

- The

implementation on fixed-point numbers now accepts an rhs fixed-point number with a different number of fractional bits from`MulAssign`

.`self` - The following methods were added to all fixed-point types, to the

trait, and to the`Fixed`

wrapper:`Wrapping` - The new experimental feature

was added, providing arithmetic methods that panic on overflow even when debug assertions are disabled.`unwrapped` - The new experimental feature

was added, which makes serialization use the number’s value in human-readable formats.`serde-str`

### 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 ``=` `"`1.5`"`

The *fixed* crate requires rustc version 1.44.0 or later.

## Optional features

The *fixed* crate has these optional feature:

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

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

and`f16`

. This features requires the`bf16`*half*crate.

, 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 ``=` `"`1.5`"`
`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:

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