484 lines
24 KiB
Markdown
484 lines
24 KiB
Markdown
<!-- Copyright © 2018–2021 Trevor Spiteri -->
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<!-- Copying and distribution of this file, with or without
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modification, are permitted in any medium without royalty provided the
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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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The [*fixed* crate] provides fixed-point numbers.
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* [`FixedI8`] and [`FixedU8`] are eight-bit fixed-point numbers.
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* [`FixedI16`] and [`FixedU16`] are 16-bit fixed-point numbers.
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* [`FixedI32`] and [`FixedU32`] are 32-bit fixed-point numbers.
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* [`FixedI64`] and [`FixedU64`] are 64-bit fixed-point numbers.
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* [`FixedI128`] and [`FixedU128`] are 128-bit fixed-point numbers.
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These types can have <i>f</i> = `Frac` fractional bits, where
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0 ≤ <i>f</i> ≤ <i>n</i> and <i>n</i> is the total number of bits. For
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example, [`FixedI32<Frac>`][`FixedI32`] is a 32-bit signed fixed-point
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number with <i>n</i> = 32. The value <i>x</i> can lie in the range
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−2<sup><i>n</i> − <i>f</i> − 1</sup> ≤ <i>x</i> < 2<sup><i>n</i> − <i>f</i> − 1</sup>
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for signed numbers, and in the range
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0 ≤ <i>x</i> < 2<sup><i>n</i> − <i>f</i></sup> for unsigned numbers.
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The difference between successive numbers is constant throughout the
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range: <i>Δ</i> = 2<sup>−<i>f</i></sup>.
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When <i>f</i> = 0, <i>Δ</i> = 1 and the fixed-point number behaves
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like an <i>n</i>-bit integer with the value lying in the range
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−2<sup><i>n</i> − 1</sup> ≤ <i>x</i> < 2<sup><i>n</i> − 1</sup> for
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signed numbers, and in the range 0 ≤ <i>x</i> < 2<sup><i>n</i></sup>
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for unsigned numbers. When <i>f</i> = <i>n</i>,
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<i>Δ</i> = 2<sup>−<i>n</i></sup> and the value lies in the range
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−0.5 ≤ <i>x</i> < 0.5 for signed numbers, and in the range
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0 ≤ <i>x</i> < 1 for unsigned numbers.
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In version 1 the [*typenum* crate] is used for the fractional bit
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count `Frac`; the plan is to to have a major version 2 with [const
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generics] instead when the Rust compiler support for them is powerful
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enough.
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The main features are
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* Representation of fixed-point numbers up to 128 bits wide.
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* Conversions between fixed-point numbers and numeric primitives.
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* Comparisons between fixed-point numbers and numeric primitives.
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* Parsing from strings in decimal, binary, octal and hexadecimal.
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* Display as decimal, binary, octal and hexadecimal.
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* Arithmetic and logic operations.
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This crate does *not* provide general analytic functions.
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* No algebraic functions are provided, for example no `sqrt` or
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`pow`.
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* No trigonometric functions are provided, for example no `sin` or
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`cos`.
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* No other transcendental functions are provided, for example no
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`log` or `exp`.
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These functions are not provided because different implementations can
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have different trade-offs, for example trading some correctness for
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speed. Implementations can be provided in other crates.
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* The [*fixed-sqrt* crate] provides the square root operation.
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* The [*cordic* crate] provides various functions implemented using
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the [CORDIC] algorithm.
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The conversions supported cover the following cases.
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* Infallible lossless conversions between fixed-point numbers and
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numeric primitives are provided using [`From`] and [`Into`]. These
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never fail (infallible) and do not lose any bits (lossless).
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* Infallible lossy conversions between fixed-point numbers and
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numeric primitives are provided using the [`LossyFrom`] and
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[`LossyInto`] traits. The source can have more fractional bits
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than the destination.
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* Checked lossless conversions between fixed-point numbers and
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numeric primitives are provided using the [`LosslessTryFrom`] and
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[`LosslessTryInto`] traits. The source cannot have more fractional
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bits than the destination.
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* Checked conversions between fixed-point numbers and numeric
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primitives are provided using the [`FromFixed`] and [`ToFixed`]
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traits, or using the [`from_num`] and [`to_num`] methods and
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[their checked versions][`checked_from_num`].
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* Fixed-point numbers can be parsed from decimal strings using
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[`FromStr`], and from binary, octal and hexadecimal strings using
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the [`from_str_binary`], [`from_str_octal`] and [`from_str_hex`]
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methods. The result is rounded to the nearest, with ties rounded
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to even.
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* Fixed-point numbers can be converted to strings using [`Display`],
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[`Binary`], [`Octal`], [`LowerHex`] and [`UpperHex`]. The output
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is rounded to the nearest, with ties rounded to even.
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## What’s new
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### Version 1.8.0 news (unreleased)
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* The following constants were added to all fixed-point numbers, to
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the [`Fixed`][tf-1-8] trait, and to the [`Wrapping`][w-1-8] and
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[`Unwrapped`][u-1-8] wrappers:
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* [`ZERO`][f-z-1-8], [`DELTA`][f-d-1-8]
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* The [`ONE`][f-o-1-8] constant was added to all fixed-point numbers
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that can represent the value 1.
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* The following methods were added to all fixed-point numbers and to
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the [`Fixed`][tf-1-8] trait:
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* [`saturating_div_euclid_int`][f-sdei-1-8],
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[`saturating_rem_euclid_int`][f-srei-1-8]
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* [`unwrapped_rem`][f-ur-1-8],
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[`unwrapped_rem_euclid`][f-ure-1-8]
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* [`unwrapped_rem_int`][f-uri-1-8]
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* The following methods are now `const` functions:
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* [`checked_rem`][f-cr-1-8]
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* [`rem_euclid`][f-re-1-8], [`checked_rem_euclid`][f-cre-1-8]
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* [`checked_div_int`][f-cdi-1-8],
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[`wrapping_div_int`][f-wdi-1-8],
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[`overflowing_div_int`][f-odi-1-8]
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* The following methods were added to all fixed-point numbers:
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* [`const_not`][f-cn-1-8]
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* [`const_bitand`][f-cba-1-8], [`const_bitor`][f-cbo-1-8],
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[`const_bitxor`][f-cbx-1-8]
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* Many methods were marked with the `must_use` attribute.
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[f-cba-1-8]: https://tspiteri.gitlab.io/fixed/dev/fixed/struct.FixedI32.html#method.const_bitand
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[f-cbo-1-8]: https://tspiteri.gitlab.io/fixed/dev/fixed/struct.FixedI32.html#method.const_bitor
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[f-cbx-1-8]: https://tspiteri.gitlab.io/fixed/dev/fixed/struct.FixedI32.html#method.const_bitxor
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[f-cdi-1-8]: https://tspiteri.gitlab.io/fixed/dev/fixed/struct.FixedI32.html#method.checked_div_int
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[f-cn-1-8]: https://tspiteri.gitlab.io/fixed/dev/fixed/struct.FixedI32.html#method.const_not
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[f-cr-1-8]: https://tspiteri.gitlab.io/fixed/dev/fixed/struct.FixedI32.html#method.checked_rem
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[f-cre-1-8]: https://tspiteri.gitlab.io/fixed/dev/fixed/struct.FixedI32.html#method.checked_rem_euclid
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[f-d-1-8]: https://tspiteri.gitlab.io/fixed/dev/fixed/struct.FixedI32.html#associatedconstant.DELTA
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[f-o-1-8]: https://tspiteri.gitlab.io/fixed/dev/fixed/struct.FixedI32.html#associatedconstant.ONE
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[f-odi-1-8]: https://tspiteri.gitlab.io/fixed/dev/fixed/struct.FixedI32.html#method.overflowing_div_int
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[f-re-1-8]: https://tspiteri.gitlab.io/fixed/dev/fixed/struct.FixedI32.html#method.rem_euclid
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[f-sdei-1-8]: https://tspiteri.gitlab.io/fixed/dev/fixed/struct.FixedI32.html#method.saturating_div_euclid_int
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[f-srei-1-8]: https://tspiteri.gitlab.io/fixed/dev/fixed/struct.FixedI32.html#method.saturating_rem_euclid_int
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[f-ur-1-8]: https://tspiteri.gitlab.io/fixed/dev/fixed/struct.FixedI32.html#method.unwrapped_rem
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[f-ure-1-8]: https://tspiteri.gitlab.io/fixed/dev/fixed/struct.FixedI32.html#method.unwrapped_rem_euclid
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[f-uri-1-8]: https://tspiteri.gitlab.io/fixed/dev/fixed/struct.FixedI32.html#method.unwrapped_rem_int
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[f-wdi-1-8]: https://tspiteri.gitlab.io/fixed/dev/fixed/struct.FixedI32.html#method.wrapping_div_int
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[f-z-1-8]: https://tspiteri.gitlab.io/fixed/dev/fixed/struct.FixedI32.html#associatedconstant.ZERO
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[tf-1-8]: https://tspiteri.gitlab.io/fixed/dev/fixed/traits/trait.Fixed.html
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[u-1-8]: https://tspiteri.gitlab.io/fixed/dev/fixed/struct.Unwrapped.html
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[w-1-8]: https://tspiteri.gitlab.io/fixed/dev/fixed/struct.Wrapping.html
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### Version 1.7.0 news (2021-03-25)
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* The crate now requires rustc version 1.50.0 or later.
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* The following methods are now `const` functions:
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* [`next_power_of_two`][f-npot-1-7],
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[`checked_next_power_of_two`][f-cnpot-1-7],
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[`wrapping_next_power_of_two`][f-wnpot-1-7]
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* The following constant and methods were added to all fixed-point
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numbers, to the [`Fixed`][tf-1-7] trait, and to the
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[`Wrapping`][w-1-7] and [`Unwrapped`][u-1-7] wrappers:
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* [`IS_SIGNED`][f-is-1-7]
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* [`from_be`][f-fb-1-7], [`from_le`][f-fl-1-7]
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* [`to_be`][f-tb-1-7], [`to_le`][f-tl-1-7]
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* [`swap_bytes`][f-sb-1-7]
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* [`reverse_bits`][f-rb-1-7]
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* [`mean`][f-m-1-7]
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* The following methods were added to the [`Wrapping`][w-1-7] and
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[`Unwrapped`][u-1-7] wrappers:
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* [`from_be_bytes`][f-fbb-1-7], [`from_le_bytes`][f-flb-1-7],
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[`from_ne_bytes`][f-fnb-1-7]
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* [`to_be_bytes`][f-tbb-1-7], [`to_le_bytes`][f-tlb-1-7],
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[`to_ne_bytes`][f-tnb-1-7]
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* The following methods were added to all unsigned fixed-point
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types, to the [`FixedUnsigned`][tfu-1-7] trait, and to the
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[`Wrapping`][w-1-7] and [`Unwrapped`][u-1-7] wrappers for unsigned
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numbers:
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* [`significant_bits`][f-signi-1-7]
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* [`highest_one`][f-ho-1-7]
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* The [`signed_bits`][f-signe-1-7] method was added to all signed
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fixed-point types, to the [`FixedSigned`][tfs-1-7] trait, and to
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the [`Wrapping`][w-1-7] and [`Unwrapped`][u-1-7] wrappers for
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signed numbers.
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* The following constants, which are available in other programming
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language standard libraries, were added to the [`consts`][c-1-7]
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module and as associated constants to fixed-point types:
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* [`SQRT_PI`][c-rp-1-7] (Go), [`FRAC_1_SQRT_PI`][c-1rp-1-7] (C++)
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* [`SQRT_3`][c-r3-1-7] (C++), [`FRAC_1_SQRT_3`][c-1r3-1-7] (C++)
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* [`SQRT_E`][c-re-1-7] (Go)
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* [`SQRT_PHI`][c-rf-1-7] (Go)
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* [`GAMMA`][c-g-1-7] (C++)
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* [`CATALAN`][c-c-1-7] (Julia)
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* [`Sum`] and [`Product`] are now supertraits of the
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[`Fixed`][tf-1-7] trait.
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* The [`F128Bits`][f128-1-7] type was added to support conversions
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and comparisons between fixed-point numbers and *binary128*
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floating-point numbers.
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* The features that previously required the [`az`][feat-dep-1-7] and
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[`f16`][feat-dep-1-7] optional features are now always provided.
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The [`az`][feat-dep-1-7] and [`f16`][feat-dep-1-7] optional
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features are now deprecated and have no effect.
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* For the experimental feature [`num-traits`][feat-exp-1-7], the
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following traits were implemented for all fixed-point numbers:
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* [`OverflowingAdd`][nt-0-2-oa], [`OverflowingSub`][nt-0-2-os],
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[`OverflowingMul`][nt-0-2-om]
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[`Product`]: https://doc.rust-lang.org/nightly/core/iter/trait.Product.html
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[`Sum`]: https://doc.rust-lang.org/nightly/core/iter/trait.Sum.html
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[c-1-7]: https://docs.rs/fixed/~1.7/fixed/consts/index.html
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[c-1r3-1-7]: https://docs.rs/fixed/~1.7/fixed/consts/constant.FRAC_1_SQRT_3.html
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[c-1rp-1-7]: https://docs.rs/fixed/~1.7/fixed/consts/constant.FRAC_1_SQRT_PI.html
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[c-c-1-7]: https://docs.rs/fixed/~1.7/fixed/consts/constant.CATALAN.html
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[c-g-1-7]: https://docs.rs/fixed/~1.7/fixed/consts/constant.GAMMA.html
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[c-r3-1-7]: https://docs.rs/fixed/~1.7/fixed/consts/constant.SQRT_3.html
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[c-re-1-7]: https://docs.rs/fixed/~1.7/fixed/consts/constant.SQRT_E.html
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[c-rf-1-7]: https://docs.rs/fixed/~1.7/fixed/consts/constant.SQRT_PHI.html
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[c-rp-1-7]: https://docs.rs/fixed/~1.7/fixed/consts/constant.SQRT_PI.html
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[f-cnpot-1-7]: https://docs.rs/fixed/~1.7/fixed/struct.FixedU32.html#method.checked_next_power_of_two
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[f-fb-1-7]: https://docs.rs/fixed/~1.7/fixed/struct.FixedI32.html#method.from_be
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[f-fbb-1-7]: https://docs.rs/fixed/~1.7/fixed/struct.FixedI32.html#method.from_be_bytes
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[f-fl-1-7]: https://docs.rs/fixed/~1.7/fixed/struct.FixedI32.html#method.from_le
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[f-flb-1-7]: https://docs.rs/fixed/~1.7/fixed/struct.FixedI32.html#method.from_le_bytes
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[f-fnb-1-7]: https://docs.rs/fixed/~1.7/fixed/struct.FixedI32.html#method.from_ne_bytes
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[f-ho-1-7]: https://docs.rs/fixed/~1.7/fixed/struct.FixedU32.html#method.highest_one
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[f-is-1-7]: https://docs.rs/fixed/~1.7/fixed/struct.FixedI32.html#associatedconstant.IS_SIGNED
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[f-m-1-7]: https://docs.rs/fixed/~1.7/fixed/struct.FixedI32.html#method.mean
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[f-npot-1-7]: https://docs.rs/fixed/~1.7/fixed/struct.FixedU32.html#method.next_power_of_two
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[f-rb-1-7]: https://docs.rs/fixed/~1.7/fixed/struct.FixedI32.html#method.reverse_bits
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[f-sb-1-7]: https://docs.rs/fixed/~1.7/fixed/struct.FixedI32.html#method.swap_bytes
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[f-signe-1-7]: https://docs.rs/fixed/~1.7/fixed/struct.FixedI32.html#method.signed_bits
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[f-signi-1-7]: https://docs.rs/fixed/~1.7/fixed/struct.FixedU32.html#method.significant_bits
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[f-tb-1-7]: https://docs.rs/fixed/~1.7/fixed/struct.FixedI32.html#method.to_be
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[f-tbb-1-7]: https://docs.rs/fixed/~1.7/fixed/struct.FixedI32.html#method.to_be_bytes
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[f-tl-1-7]: https://docs.rs/fixed/~1.7/fixed/struct.FixedI32.html#method.to_le
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[f-tlb-1-7]: https://docs.rs/fixed/~1.7/fixed/struct.FixedI32.html#method.to_le_bytes
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[f-tnb-1-7]: https://docs.rs/fixed/~1.7/fixed/struct.FixedI32.html#method.to_ne_bytes
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[f-wnpot-1-7]: https://docs.rs/fixed/~1.7/fixed/struct.FixedU32.html#method.wrapping_next_power_of_two
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[f128-1-7]: https://docs.rs/fixed/~1.7/fixed/struct.F128Bits.html
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[feat-dep-1-7]: https://docs.rs/fixed/~1.7/fixed/#deprecated-optional-features
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[feat-exp-1-7]: https://docs.rs/fixed/~1.7/fixed/#experimental-optional-features
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[nt-0-2-oa]: https://docs.rs/num-traits/^0.2/num_traits/ops/overflowing/trait.OverflowingAdd.html
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[nt-0-2-om]: https://docs.rs/num-traits/^0.2/num_traits/ops/overflowing/trait.OverflowingMul.html
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[nt-0-2-os]: https://docs.rs/num-traits/^0.2/num_traits/ops/overflowing/trait.OverflowingSub.html
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[tf-1-7]: https://docs.rs/fixed/~1.7/fixed/traits/trait.Fixed.html
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[tfs-1-7]: https://docs.rs/fixed/~1.7/fixed/traits/trait.FixedSigned.html
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[tfu-1-7]: https://docs.rs/fixed/~1.7/fixed/traits/trait.FixedUnsigned.html
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[u-1-7]: https://docs.rs/fixed/~1.7/fixed/struct.Unwrapped.html
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[w-1-7]: https://docs.rs/fixed/~1.7/fixed/struct.Wrapping.html
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### Version 1.6.0 news (2021-02-05)
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* The crate now requires rustc version 1.47.0 or later.
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* The optional [*az* crate] dependency was updated to
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[version 1.1][az-1-1].
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* The [`unsigned_abs`][f-ua-1-6] method was added to all signed
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fixed-point types and to the [`FixedSigned`][tfs-1-6] trait.
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* The following methods are now `const` functions:
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* [`checked_neg`][f-cn-1-6], [`checked_add`][f-cad-1-6],
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[`checked_sub`][f-cs-1-6], [`checked_mul_int`][f-cmi-1-6],
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[`checked_shl`][f-cshl-1-6], [`checked_shr`][f-cshr-1-6],
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[`checked_abs`][f-cab-1-6]
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* The [`unwrapped_to_fixed`][f-utf-1-6] method was added to the
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[`ToFixed`][f-tf-1-6] trait.
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* The [`unwrapped_from_fixed`][f-uff-1-6] method was added to the
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[`FromFixed`][f-ff-1-6] trait.
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[*az* crate]: https://crates.io/crates/az
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[az-1-1]: https://docs.rs/az/~1.1/az/index.html
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[f-cab-1-6]: https://docs.rs/fixed/~1.6/fixed/struct.FixedI32.html#method.checked_abs
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[f-cad-1-6]: https://docs.rs/fixed/~1.6/fixed/struct.FixedI32.html#method.checked_add
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[f-cmi-1-6]: https://docs.rs/fixed/~1.6/fixed/struct.FixedI32.html#method.checked_mul_int
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[f-cn-1-6]: https://docs.rs/fixed/~1.6/fixed/struct.FixedI32.html#method.checked_neg
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[f-cs-1-6]: https://docs.rs/fixed/~1.6/fixed/struct.FixedI32.html#method.checked_sub
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[f-cshl-1-6]: https://docs.rs/fixed/~1.6/fixed/struct.FixedI32.html#method.checked_shl
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[f-cshr-1-6]: https://docs.rs/fixed/~1.6/fixed/struct.FixedI32.html#method.checked_shr
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[f-ff-1-6]: https://docs.rs/fixed/~1.6/fixed/traits/trait.FromFixed.html
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[f-tf-1-6]: https://docs.rs/fixed/~1.6/fixed/traits/trait.ToFixed.html
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[f-ua-1-6]: https://docs.rs/fixed/~1.6/fixed/struct.FixedI32.html#method.unsigned_abs
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[f-uff-1-6]: https://docs.rs/fixed/~1.6/fixed/traits/trait.FromFixed.html#method.unwrapped_from_fixed
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[f-utf-1-6]: https://docs.rs/fixed/~1.6/fixed/traits/trait.ToFixed.html#method.unwrapped_to_fixed
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[tfs-1-6]: https://docs.rs/fixed/~1.6/fixed/traits/trait.FixedSigned.html
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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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|
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## Quick examples
|
||
|
||
```rust
|
||
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
|
||
<code>[FixedI32][`FixedI32`]<[U12][`U12`]></code>. 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.
|
||
|
||
```rust
|
||
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.
|
||
|
||
```rust
|
||
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][*fixed* crate]. To use
|
||
it in your crate, add it as a dependency inside [*Cargo.toml*]:
|
||
|
||
```toml
|
||
[dependencies]
|
||
fixed = "1.7"
|
||
```
|
||
|
||
The *fixed* crate requires rustc version 1.50.0 or later.
|
||
|
||
## Optional features
|
||
|
||
The *fixed* crate has these optional feature:
|
||
|
||
1. `serde`, disabled by default. This provides serialization support
|
||
for the fixed-point types. This feature requires the
|
||
[*serde* crate].
|
||
2. `std`, disabled by default. This is for features that are not
|
||
possible under `no_std`: currently the implementation of the
|
||
[`Error`] trait for [`ParseFixedError`].
|
||
3. `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*]:
|
||
|
||
```toml
|
||
[dependencies.fixed]
|
||
version = "1.7"
|
||
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.
|
||
|
||
1. `num-traits`, disabled by default. This implements some traits
|
||
from the [*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.
|
||
|
||
1. `az`, has no effect. Previously required to enable the cast traits
|
||
provided by the [*az* crate]. Now these cast traits are always
|
||
provided.
|
||
2. `f16`, has no effect. Previously required to provide conversion
|
||
to/from [`f16`] and [`bf16`]. Now these conversions are always
|
||
provided.
|
||
|
||
## 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][LICENSE-APACHE] or
|
||
* the [MIT License][LICENSE-MIT]
|
||
|
||
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.
|
||
|
||
[*Cargo.toml*]: https://doc.rust-lang.org/cargo/guide/dependencies.html
|
||
[*az* crate]: https://crates.io/crates/az
|
||
[*cordic* crate]: https://crates.io/crates/cordic
|
||
[*fixed* crate]: https://crates.io/crates/fixed
|
||
[*fixed-macro* crate]: https://crates.io/crates/fixed-macro
|
||
[*fixed-sqrt* crate]: https://crates.io/crates/fixed-sqrt
|
||
[*half* crate]: https://crates.io/crates/half
|
||
[*num-traits* crate]: https://crates.io/crates/num-traits
|
||
[*serde* crate]: https://crates.io/crates/serde
|
||
[*typenum* crate]: https://crates.io/crates/typenum
|
||
[CORDIC]: https://en.wikipedia.org/wiki/CORDIC
|
||
[LICENSE-APACHE]: https://www.apache.org/licenses/LICENSE-2.0
|
||
[LICENSE-MIT]: https://opensource.org/licenses/MIT
|
||
[`Binary`]: https://doc.rust-lang.org/nightly/core/fmt/trait.Binary.html
|
||
[`Display`]: https://doc.rust-lang.org/nightly/core/fmt/trait.Display.html
|
||
[`Error`]: https://doc.rust-lang.org/nightly/std/error/trait.Error.html
|
||
[`FixedI128`]: https://docs.rs/fixed/~1.7/fixed/struct.FixedI128.html
|
||
[`FixedI16`]: https://docs.rs/fixed/~1.7/fixed/struct.FixedI16.html
|
||
[`FixedI32`]: https://docs.rs/fixed/~1.7/fixed/struct.FixedI32.html
|
||
[`FixedI64`]: https://docs.rs/fixed/~1.7/fixed/struct.FixedI64.html
|
||
[`FixedI8`]: https://docs.rs/fixed/~1.7/fixed/struct.FixedI8.html
|
||
[`FixedU128`]: https://docs.rs/fixed/~1.7/fixed/struct.FixedU128.html
|
||
[`FixedU16`]: https://docs.rs/fixed/~1.7/fixed/struct.FixedU16.html
|
||
[`FixedU32`]: https://docs.rs/fixed/~1.7/fixed/struct.FixedU32.html
|
||
[`FixedU64`]: https://docs.rs/fixed/~1.7/fixed/struct.FixedU64.html
|
||
[`FixedU8`]: https://docs.rs/fixed/~1.7/fixed/struct.FixedU8.html
|
||
[`FromFixed`]: https://docs.rs/fixed/~1.7/fixed/traits/trait.FromFixed.html
|
||
[`FromStr`]: https://doc.rust-lang.org/nightly/core/str/trait.FromStr.html
|
||
[`From`]: https://doc.rust-lang.org/nightly/core/convert/trait.From.html
|
||
[`I20F12`]: https://docs.rs/fixed/~1.7/fixed/types/type.I20F12.html
|
||
[`I4F12`]: https://docs.rs/fixed/~1.7/fixed/types/type.I4F12.html
|
||
[`I4F4`]: https://docs.rs/fixed/~1.7/fixed/types/type.I4F4.html
|
||
[`Into`]: https://doc.rust-lang.org/nightly/core/convert/trait.Into.html
|
||
[`LosslessTryFrom`]: https://docs.rs/fixed/~1.7/fixed/traits/trait.LosslessTryFrom.html
|
||
[`LosslessTryInto`]: https://docs.rs/fixed/~1.7/fixed/traits/trait.LosslessTryInto.html
|
||
[`LossyFrom`]: https://docs.rs/fixed/~1.7/fixed/traits/trait.LossyFrom.html
|
||
[`LossyInto`]: https://docs.rs/fixed/~1.7/fixed/traits/trait.LossyInto.html
|
||
[`LowerHex`]: https://doc.rust-lang.org/nightly/core/fmt/trait.LowerHex.html
|
||
[`Octal`]: https://doc.rust-lang.org/nightly/core/fmt/trait.Octal.html
|
||
[`ParseFixedError`]: https://docs.rs/fixed/~1.7/fixed/struct.ParseFixedError.html
|
||
[`ToFixed`]: https://docs.rs/fixed/~1.7/fixed/traits/trait.ToFixed.html
|
||
[`U12`]: https://docs.rs/fixed/~1.7/fixed/types/extra/type.U12.html
|
||
[`U20F12`]: https://docs.rs/fixed/~1.7/fixed/types/type.U20F12.html
|
||
[`UpperHex`]: https://doc.rust-lang.org/nightly/core/fmt/trait.UpperHex.html
|
||
[`bf16`]: https://docs.rs/half/^1/half/struct.bf16.html
|
||
[`checked_from_num`]: https://docs.rs/fixed/~1.7/fixed/struct.FixedI32.html#method.checked_from_num
|
||
[`f16`]: https://docs.rs/half/^1/half/struct.f16.html
|
||
[`from_num`]: https://docs.rs/fixed/~1.7/fixed/struct.FixedI32.html#method.from_num
|
||
[`from_str_binary`]: https://docs.rs/fixed/~1.7/fixed/struct.FixedI32.html#method.from_str_binary
|
||
[`from_str_hex`]: https://docs.rs/fixed/~1.7/fixed/struct.FixedI32.html#method.from_str_hex
|
||
[`from_str_octal`]: https://docs.rs/fixed/~1.7/fixed/struct.FixedI32.html#method.from_str_octal
|
||
[`to_num`]: https://docs.rs/fixed/~1.7/fixed/struct.FixedI32.html#method.to_num
|
||
[const generics]: https://github.com/rust-lang/rust/issues/44580
|