### 20 unstable releases (4 breaking)

✓ Uses Rust 2018 edition

new 0.4.4 | Aug 24, 2019 |
---|---|

0.3.3 | Jun 27, 2019 |

0.3.2 | Feb 27, 2019 |

0.1.4 | Nov 29, 2018 |

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# Fixed-point numbers

The *fixed* crate provides fixed-point numbers. Currently it uses
the *typenum* crate for the fractional bit count; it is planned to
move to const generics when they are implemented by the Rust
compiler.

The crate provides the following types:

is a signed eight-bit fixed-point number,`FixedI8`

is a signed 16-bit fixed-point number,`FixedI16`

is a signed 32-bit fixed-point number,`FixedI32`

is a signed 64-bit fixed-point number,`FixedI64`

is a signed 128-bit fixed-point number,`FixedI128`

is an unsigned eight-bit fixed-point number,`FixedU8`

is an unsigned 16-bit fixed-point number,`FixedU16`

is an unsigned 32-bit fixed-point number,`FixedU32`

is an unsigned 64-bit fixed-point number, and`FixedU64`

is an unsigned 128-bit fixed-point number.`FixedU128`

All fixed-point numbers can have

fractional bits, where `Frac`

can have any value from 0 up to and including the size of the number
in bits. When `Frac`

is 0, the fixed-point number behaves like an
integer. When `Frac`

is equal to the number of bits, the value of the
fixed-point number lies in the range −0.5 ≤ `Frac`*x* < 0.5 for signed
fixed-point numbers, and in the range 0 ≤ *x* < 1 for unsigned
fixed-point numbers.

Various conversion methods are available:

- All lossless infallible conversions between fixed-point numbers
and numeric primitives are implemented. You can use

or`From`

for conversions that always work without losing any bits.`Into` - For lossy infallible conversions between fixed-point numbers and
numeric primitives, where the source type may have more fractional
bits than the destination type, the

and`LossyFrom`

traits can be used. Excess fractional bits are truncated.`LossyInto` - Checked conversions are provided between fixed-point numbers and
numeric primitives 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

, or from binary, octal or hexadecimal using the`FromStr`

,`from_str_binary`

or`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 0.4.3 news (2019-08-20)

- The
*fixed*crate now requires rustc version 1.34.0 or later. - The precision argument is no longer ignored when formatting fixed-point numbers; precision should now be handled the same as for primitive floating-point numbers in the standard library.
- Parsing strings now rounds to the nearest with ties rounded to even.
- Checked versions of string parsing methods are now available as
inherent methods to all fixed-point numbers, and as methods in the

trait.`Fixed`

now has methods for parsing with wrapping, including an implementation of`Wrapping`

.`FromStr`- The following methods are now

functions:`const`

,`min_value`

,`max_value`

,`from_bits``to_bits`

,`count_ones`

,`count_zeros`

,`leading_zeros``trailing_zeros`

,`rotate_left``rotate_right`

,`wrapping_neg`

,`wrapping_add`

,`wrapping_sub`

,`wrapping_mul_int`

,`wrapping_shl``wrapping_shr`

,`overflowing_neg`

,`overflowing_add`

,`overflowing_sub`

,`overflowing_mul_int`

,`overflowing_shl``overflowing_shr`

,`is_positive``is_negative`

- The associated constants

and`INT_NBITS`

were added.`FRAC_NBITS` - The reexports in the

module and the`frac`

traits were moved into the new`LeEqU``*`

module.`types`extra`::`

### Version 0.4.2 news (2019-08-16)

- The new methods

and`from_num`

together with their checked versions were added to all fixed-point numbers.`to_num` - The methods

,`from_fixed`

,`to_fixed`

,`from_int`

,`to_int`

, and`from_float`

, and their checked versions, were deprecated.`to_float` - The new method

was added to the`from_num`

wrapper.`Wrapping` - Bug fix: parsing of decimal fractions was fixed to give correctly rounded results for long decimal fraction strings, for example with four fractional bits, 0.96874999… (just below 31⁄32) and 0.96875 (31⁄32) are now parsed correctly as 0.9375 (15⁄16) and 1.0.

### Version 0.4.1 news (2019-08-12)

- All fixed-point types now implement

.`FromStr` - The methods

,`from_str_binary`

and`from_str_octal`

were added.`from_str_hex`

### Version 0.4.0 news (2019-08-08)

- The
*fixed*crate now requires rustc version 1.31.0 or later. - The

module was added, with its traits`traits`

,`Fixed`

,`FixedSigned`

,`FixedUnsigned`

,`FromFixed`

,`ToFixed`

and`LossyFrom`

.`LossyInto` - The

method was added to all fixed-point numbers, and the`saturating_neg`

method was added to signed fixed-point numbers.`saturating_abs` - The

module was added.`consts` - The

method now wraps instead of panics in release mode.`signum`

#### Incompatible changes

- The sealed traits

and`Int`

now have no provided methods; the methods in the old implementation are new provided by`Float`

and`FromFixed`

.`ToFixed` - Deprecated methods were removed.

#### Contributors

### Other releases

Details on other releases can be found in *RELEASES.md*.

## Quick examples

`//` 20 integer bits, 12 fractional bits
`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`

`//` −8 ≤ I4F4 < 8 with steps of 1/16 (~0.06)
`use` `fixed``::``types``::``I4F4``;`
`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)
`use` `fixed``::``types``::``I4F12``;`
`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`

## 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 ``=` `"`0.4.3`"`

The *fixed* crate requires rustc version 1.34.0 or later.

## Optional features

The *fixed* crate has two optional feature:

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

. This features requires the`f16`*half*crate.

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

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

`[``dependencies.fixed``]`
`version ``=` `"`0.4.3`"`
`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.