2019-01-26 13:02:58 -08:00
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<!-- Copyright © 2018–2019 Trevor Spiteri -->
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2018-08-09 11:02:34 -07:00
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copyright notice and this notice are preserved. This file is offered
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as-is, without any warranty. -->
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# Fixed-point numbers
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2018-08-10 11:30:03 -07:00
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The [*fixed* crate] provides fixed-point numbers. Currently it uses
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the [*typenum* crate] for the fractional bit count; it is planned to
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move to [const generics] when they are implemented by the Rust
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2018-08-10 08:45:08 -07:00
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compiler.
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2018-08-09 11:02:34 -07:00
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2018-08-10 11:43:53 -07:00
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The crate provides the following types:
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* [`FixedI8`] is a signed eight-bit fixed-point number,
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* [`FixedI16`] is a signed 16-bit fixed-point number,
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* [`FixedI32`] is a signed 32-bit fixed-point number,
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* [`FixedI64`] is a signed 64-bit fixed-point number,
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* [`FixedI128`] is a signed 128-bit fixed-point number,
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* [`FixedU8`] is an unsigned eight-bit fixed-point number,
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* [`FixedU16`] is an unsigned 16-bit fixed-point number,
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* [`FixedU32`] is an unsigned 32-bit fixed-point number,
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* [`FixedU64`] is an unsigned 64-bit fixed-point number, and
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* [`FixedU128`] is an unsigned 128-bit fixed-point number.
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All fixed-point numbers can have `Frac` fractional bits, where `Frac`
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can have any value from 0 up to and including the size of the number
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in bits. When `Frac` is 0, the fixed-point number behaves like an
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integer. When `Frac` is equal to the number of bits, the value of the
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fixed-point number lies in the range −0.5 ≤ *x* < 0.5 for signed
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fixed-point numbers, and in the range 0 ≤ *x* < 1 for unsigned
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fixed-point numbers.
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2019-01-26 12:16:20 -08:00
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All lossless infallible conversions between fixed-point numbers and
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numeric primitives are implemented. That is, you can use [`From`] or
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[`Into`] for the conversions that always work without losing any bits.
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2018-08-10 11:57:59 -07:00
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## What’s new
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2019-01-28 18:35:42 -08:00
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### Version 0.2.0 news (2019-01-29)
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2019-01-28 13:43:43 -08:00
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* The new methods [`from_fixed`], [`checked_from_fixed`],
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[`saturating_from_fixed`], [`wrapping_from_fixed`] and
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[`overflowing_from_fixed`] were added.
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* The old method [`from_int`] was removed to be replaced.
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* The new methods [`from_int`], [`checked_from_int`],
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[`saturating_from_int`], [`wrapping_from_int`] and
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[`overflowing_from_int`] were added.
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* The new methods [`from_float`], [`checked_from_float`],
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[`saturating_from_float`], [`wrapping_from_float`] and
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[`overflowing_from_float`] were added.
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* The new method [`to_float`] was added.
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* The methods [`from_f16`], [`from_f32`], [`from_f64`], [`to_f16`],
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[`to_f32`] and [`to_f64`] were deprecated.
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* The [`to_int`] method was fixed to truncate fractional bits as
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documented for negative values.
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* The new methods [`ceil`], [`floor`], [`round`], [`checked_ceil`],
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[`checked_floor`], [`checked_round`], [`saturating_ceil`],
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[`saturating_floor`], [`saturating_round`], [`wrapping_ceil`],
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[`wrapping_floor`], [`wrapping_round`], [`overflowing_ceil`],
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[`overflowing_floor`] and [`overflowing_round`] were added.
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* The methods [`to_int_ceil`], [`to_int_floor`] and [`to_int_round`]
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were deprecated.
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2019-01-27 19:30:56 -08:00
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[`ceil`]: https://docs.rs/fixed/0.2.0/fixed/struct.FixedI32.html#method.ceil
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[`checked_ceil`]: https://docs.rs/fixed/0.2.0/fixed/struct.FixedI32.html#method.checked_ceil
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[`checked_floor`]: https://docs.rs/fixed/0.2.0/fixed/struct.FixedI32.html#method.checked_floor
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[`checked_from_fixed`]: https://docs.rs/fixed/0.2.0/fixed/struct.FixedI32.html#method.checked_from_fixed
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[`checked_from_float`]: https://docs.rs/fixed/0.2.0/fixed/struct.FixedI32.html#method.checked_from_float
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[`checked_from_int`]: https://docs.rs/fixed/0.2.0/fixed/struct.FixedI32.html#method.checked_from_int
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[`checked_round`]: https://docs.rs/fixed/0.2.0/fixed/struct.FixedI32.html#method.checked_round
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[`floor`]: https://docs.rs/fixed/0.2.0/fixed/struct.FixedI32.html#method.floor
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[`from_f16`]: https://docs.rs/fixed/0.2.0/fixed/struct.FixedI32.html#method.from_f16
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[`from_f32`]: https://docs.rs/fixed/0.2.0/fixed/struct.FixedI32.html#method.from_f32
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[`from_f64`]: https://docs.rs/fixed/0.2.0/fixed/struct.FixedI32.html#method.from_f64
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[`from_fixed`]: https://docs.rs/fixed/0.2.0/fixed/struct.FixedI32.html#method.from_fixed
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[`from_float`]: https://docs.rs/fixed/0.2.0/fixed/struct.FixedI32.html#method.from_float
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[`from_int`]: https://docs.rs/fixed/0.2.0/fixed/struct.FixedI32.html#method.from_int
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[`from_int`]: https://docs.rs/fixed/0.2.0/fixed/struct.FixedI32.html#method.from_int
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[`overflowing_ceil`]: https://docs.rs/fixed/0.2.0/fixed/struct.FixedI32.html#method.overflowing_ceil
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[`overflowing_floor`]: https://docs.rs/fixed/0.2.0/fixed/struct.FixedI32.html#method.overflowing_floor
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[`overflowing_from_fixed`]: https://docs.rs/fixed/0.2.0/fixed/struct.FixedI32.html#method.overflowing_from_fixed
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[`overflowing_from_float`]: https://docs.rs/fixed/0.2.0/fixed/struct.FixedI32.html#method.overflowing_from_float
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[`overflowing_from_int`]: https://docs.rs/fixed/0.2.0/fixed/struct.FixedI32.html#method.overflowing_from_int
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[`overflowing_round`]: https://docs.rs/fixed/0.2.0/fixed/struct.FixedI32.html#method.overflowing_round
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[`round`]: https://docs.rs/fixed/0.2.0/fixed/struct.FixedI32.html#method.round
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[`saturating_ceil`]: https://docs.rs/fixed/0.2.0/fixed/struct.FixedI32.html#method.saturating_ceil
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[`saturating_floor`]: https://docs.rs/fixed/0.2.0/fixed/struct.FixedI32.html#method.saturating_floor
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[`saturating_from_fixed`]: https://docs.rs/fixed/0.2.0/fixed/struct.FixedI32.html#method.saturating_from_fixed
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[`saturating_from_float`]: https://docs.rs/fixed/0.2.0/fixed/struct.FixedI32.html#method.saturating_from_float
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[`saturating_from_int`]: https://docs.rs/fixed/0.2.0/fixed/struct.FixedI32.html#method.saturating_from_int
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[`saturating_round`]: https://docs.rs/fixed/0.2.0/fixed/struct.FixedI32.html#method.saturating_round
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[`to_f16`]: https://docs.rs/fixed/0.2.0/fixed/struct.FixedI32.html#method.to_f16
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[`to_f32`]: https://docs.rs/fixed/0.2.0/fixed/struct.FixedI32.html#method.to_f32
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[`to_f64`]: https://docs.rs/fixed/0.2.0/fixed/struct.FixedI32.html#method.to_f64
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[`to_float`]: https://docs.rs/fixed/0.2.0/fixed/struct.FixedI32.html#method.to_float
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[`to_int_ceil`]: https://docs.rs/fixed/0.2.0/fixed/struct.FixedI32.html#method.to_int_ceil
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[`to_int_floor`]: https://docs.rs/fixed/0.2.0/fixed/struct.FixedI32.html#method.to_int_floor
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[`to_int_round`]: https://docs.rs/fixed/0.2.0/fixed/struct.FixedI32.html#method.to_int_round
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[`to_int`]: https://docs.rs/fixed/0.2.0/fixed/struct.FixedI32.html#method.to_int
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[`wrapping_ceil`]: https://docs.rs/fixed/0.2.0/fixed/struct.FixedI32.html#method.wrapping_ceil
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[`wrapping_floor`]: https://docs.rs/fixed/0.2.0/fixed/struct.FixedI32.html#method.wrapping_floor
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[`wrapping_from_fixed`]: https://docs.rs/fixed/0.2.0/fixed/struct.FixedI32.html#method.wrapping_from_fixed
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[`wrapping_from_float`]: https://docs.rs/fixed/0.2.0/fixed/struct.FixedI32.html#method.wrapping_from_float
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[`wrapping_from_int`]: https://docs.rs/fixed/0.2.0/fixed/struct.FixedI32.html#method.wrapping_from_int
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[`wrapping_round`]: https://docs.rs/fixed/0.2.0/fixed/struct.FixedI32.html#method.wrapping_round
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2019-01-27 18:41:44 -08:00
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### Version 0.1.6 news (2019-01-27)
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2019-01-26 15:39:24 -08:00
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* Optional [serde][*serde* crate] support was added.
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2019-01-27 18:41:44 -08:00
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### Version 0.1.5 news (2019-01-26)
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2019-01-26 13:22:18 -08:00
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* A new module [`types`] is available with aliases for all supported
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fixed-point numbers.
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* Lossless infallible conversions between fixed-point numbers and
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2019-01-26 12:44:34 -08:00
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numeric primitives are now supported using [`From`] and [`Into`].
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2019-01-26 12:16:20 -08:00
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2019-01-28 18:35:42 -08:00
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[`types`]: https://docs.rs/fixed/0.2.0/fixed/types/index.html
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2018-11-03 09:23:18 -07:00
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2018-08-10 11:57:59 -07:00
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### Other releases
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Details on other releases can be found in [*RELEASES.md*].
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[*RELEASES.md*]: https://gitlab.com/tspiteri/fixed/blob/master/RELEASES.md
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2018-08-11 08:33:31 -07:00
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## Quick example
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```rust
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// 20 integer bits, 12 fractional bits
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use fixed::types::I20F12;
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2018-08-11 08:49:36 -07:00
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// 19/3 = 6 1/3
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let six_and_third = I20F12::from_int(19) / 3;
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// four decimal digits for 12 binary digits
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assert_eq!(six_and_third.to_string(), "6.3333");
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// convert to i32, taking the ceil
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assert_eq!(six_and_third.ceil().to_int(), 7);
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```
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2019-01-26 13:22:18 -08:00
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The type [`I20F12`] is a 32-bit fixed-point signed number with 20
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integer bits and 12 fractional bits. It is an alias to
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[`FixedI32<frac::U12>`][`FixedI32`]. The unsigned counterpart would be
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[`U20F12`]. Aliases are provided for all combinations of integer and
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fractional bits adding up to a total of eight, 16, 32, 64 or 128 bits.
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2018-08-10 11:30:03 -07:00
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## Using the *fixed* crate
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The *fixed* crate is available on [crates.io][*fixed* crate]. To use
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it in your crate, add it as a dependency inside [*Cargo.toml*]:
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```toml
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[dependencies]
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fixed = "0.2.0"
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```
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2019-01-26 13:02:58 -08:00
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If you are using the 2015 Rust edition, you also need to declare it by
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adding this to your crate root (usually *lib.rs* or *main.rs*):
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```rust
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extern crate fixed;
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```
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2018-08-13 03:10:53 -07:00
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The *fixed* crate requires rustc version 1.28.0 or later.
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2018-08-23 04:12:32 -07:00
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## Optional features
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The *fixed* crate has two optional feature:
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1. `f16`, disabled by default. This provides conversion to/from
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[`f16`]. This features requires the [*half* crate].
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2. `serde`, disabled by default. This provides serialization support
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for the fixed-point types. This feature requires the
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[*serde* crate].
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2019-01-26 15:39:24 -08:00
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To enable features, you can add the dependency like this to
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[*Cargo.toml*]:
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```toml
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[dependencies.fixed]
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version = "0.2.0"
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features = ["f16", "serde"]
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```
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2018-08-10 02:13:42 -07:00
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## License
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2018-08-10 02:34:17 -07:00
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This crate is free software: you can redistribute it and/or modify it
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under the terms of either
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* the [Apache License, Version 2.0][LICENSE-APACHE] or
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* the [MIT License][LICENSE-MIT]
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at your option.
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### Contribution
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Unless you explicitly state otherwise, any contribution intentionally
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submitted for inclusion in the work by you, as defined in the Apache
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License, Version 2.0, shall be dual licensed as above, without any
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additional terms or conditions.
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[*Cargo.toml*]: https://doc.rust-lang.org/cargo/guide/dependencies.html
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[*fixed* crate]: https://crates.io/crates/fixed
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[*half* crate]: https://crates.io/crates/half
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[*serde* crate]: https://crates.io/crates/serde
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[*typenum* crate]: https://crates.io/crates/typenum
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[LICENSE-APACHE]: https://www.apache.org/licenses/LICENSE-2.0
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[LICENSE-MIT]: https://opensource.org/licenses/MIT
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[`FixedI128`]: https://docs.rs/fixed/0.2.0/fixed/struct.FixedI128.html
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[`FixedI16`]: https://docs.rs/fixed/0.2.0/fixed/struct.FixedI16.html
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[`FixedI32`]: https://docs.rs/fixed/0.2.0/fixed/struct.FixedI32.html
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[`FixedI64`]: https://docs.rs/fixed/0.2.0/fixed/struct.FixedI64.html
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[`FixedI8`]: https://docs.rs/fixed/0.2.0/fixed/struct.FixedI8.html
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[`FixedU128`]: https://docs.rs/fixed/0.2.0/fixed/struct.FixedU128.html
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[`FixedU16`]: https://docs.rs/fixed/0.2.0/fixed/struct.FixedU16.html
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[`FixedU32`]: https://docs.rs/fixed/0.2.0/fixed/struct.FixedU32.html
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[`FixedU64`]: https://docs.rs/fixed/0.2.0/fixed/struct.FixedU64.html
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[`FixedU8`]: https://docs.rs/fixed/0.2.0/fixed/struct.FixedU8.html
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2019-01-26 12:16:20 -08:00
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[`From`]: https://doc.rust-lang.org/nightly/std/convert/trait.From.html
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2019-01-28 18:35:42 -08:00
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[`I20F12`]: https://docs.rs/fixed/0.2.0/fixed/types/type.I20F12.html
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2019-01-26 12:16:20 -08:00
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[`Into`]: https://doc.rust-lang.org/nightly/std/convert/trait.Into.html
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2019-01-28 18:35:42 -08:00
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[`U20F12`]: https://docs.rs/fixed/0.2.0/fixed/types/type.U20F12.html
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2018-08-23 04:12:32 -07:00
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[`f16`]: https://docs.rs/half/^1/half/struct.f16.html
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2018-08-09 11:02:34 -07:00
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[const generics]: https://github.com/rust-lang/rust/issues/44580
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