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Signed-off-by: Valentin Popov <valentin@popov.link>
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Valentin Popov
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# THIS FILE IS AUTOMATICALLY GENERATED BY CARGO
#
# When uploading crates to the registry Cargo will automatically
# "normalize" Cargo.toml files for maximal compatibility
# with all versions of Cargo and also rewrite `path` dependencies
# to registry (e.g., crates.io) dependencies.
#
# If you are reading this file be aware that the original Cargo.toml
# will likely look very different (and much more reasonable).
# See Cargo.toml.orig for the original contents.
[package]
edition = "2018"
rust-version = "1.31"
name = "num-traits"
version = "0.2.17"
authors = ["The Rust Project Developers"]
build = "build.rs"
exclude = [
"/bors.toml",
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]
description = "Numeric traits for generic mathematics"
homepage = "https://github.com/rust-num/num-traits"
documentation = "https://docs.rs/num-traits"
readme = "README.md"
keywords = [
"mathematics",
"numerics",
]
categories = [
"algorithms",
"science",
"no-std",
]
license = "MIT OR Apache-2.0"
repository = "https://github.com/rust-num/num-traits"
[package.metadata.docs.rs]
features = ["std"]
rustdoc-args = ["--generate-link-to-definition"]
[dependencies.libm]
version = "0.2.0"
optional = true
[build-dependencies.autocfg]
version = "1"
[features]
default = ["std"]
i128 = []
std = []

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Copyright (c) 2014 The Rust Project Developers
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# num-traits
[![crate](https://img.shields.io/crates/v/num-traits.svg)](https://crates.io/crates/num-traits)
[![documentation](https://docs.rs/num-traits/badge.svg)](https://docs.rs/num-traits)
[![minimum rustc 1.31](https://img.shields.io/badge/rustc-1.31+-red.svg)](https://rust-lang.github.io/rfcs/2495-min-rust-version.html)
[![build status](https://github.com/rust-num/num-traits/workflows/master/badge.svg)](https://github.com/rust-num/num-traits/actions)
Numeric traits for generic mathematics in Rust.
## Usage
Add this to your `Cargo.toml`:
```toml
[dependencies]
num-traits = "0.2"
```
## Features
This crate can be used without the standard library (`#![no_std]`) by disabling
the default `std` feature. Use this in `Cargo.toml`:
```toml
[dependencies.num-traits]
version = "0.2"
default-features = false
# features = ["libm"] # <--- Uncomment if you wish to use `Float` and `Real` without `std`
```
The `Float` and `Real` traits are only available when either `std` or `libm` is enabled.
The `FloatCore` trait is always available. `MulAdd` and `MulAddAssign` for `f32`
and `f64` also require `std` or `libm`, as do implementations of signed and floating-
point exponents in `Pow`.
## Releases
Release notes are available in [RELEASES.md](RELEASES.md).
## Compatibility
The `num-traits` crate is tested for rustc 1.31 and greater.
## License
Licensed under either of
* [Apache License, Version 2.0](http://www.apache.org/licenses/LICENSE-2.0)
* [MIT license](http://opensource.org/licenses/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-2.0 license, shall be
dual licensed as above, without any additional terms or conditions.

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# Release 0.2.17 (2023-10-07)
- [Fix a doc warning about custom classes with newer rustdoc.][286]
**Contributors**: @robamu
[286]: https://github.com/rust-num/num-traits/pull/286
# Release 0.2.16 (2023-07-20)
- [Upgrade to 2018 edition, **MSRV 1.31**][240]
- [The new `ToBytes` and `FromBytes` traits][224] convert to and from byte
representations of a value, with little, big, and native-endian options.
- [The new `Float::is_subnormal` method checks for subnormal values][279], with
a non-zero magnitude that is less than the normal minimum positive value.
- Several other improvements to documentation and testing.
**Contributors**: @ctrlcctrlv, @cuviper, @flier, @GuillaumeGomez, @kaidokert,
@rs017991, @vicsn
[224]: https://github.com/rust-num/num-traits/pull/224
[240]: https://github.com/rust-num/num-traits/pull/240
[279]: https://github.com/rust-num/num-traits/pull/279
# Release 0.2.15 (2022-05-02)
- [The new `Euclid` trait calculates Euclidean division][195], where the
remainder is always positive or zero.
- [The new `LowerBounded` and `UpperBounded` traits][210] separately describe
types with lower and upper bounds. These traits are automatically implemented
for all fully-`Bounded` types.
- [The new `Float::copysign` method copies the sign of the argument][207] to
to the magnitude of `self`.
- [The new `PrimInt::leading_ones` and `trailing_ones` methods][205] are the
complement of the existing methods that count zero bits.
- [The new `PrimInt::reverse_bits` method reverses the order of all bits][202]
of a primitive integer.
- [Improved `Num::from_str_radix` for floats][201], also [ignoring case][214].
- [`Float` and `FloatCore` use more from `libm`][196] when that is enabled.
**Contributors**: @alion02, @clarfonthey, @cuviper, @ElectronicRU,
@ibraheemdev, @SparrowLii, @sshilovsky, @tspiteri, @XAMPPRocky, @Xiretza
[195]: https://github.com/rust-num/num-traits/pull/195
[196]: https://github.com/rust-num/num-traits/pull/196
[201]: https://github.com/rust-num/num-traits/pull/201
[202]: https://github.com/rust-num/num-traits/pull/202
[205]: https://github.com/rust-num/num-traits/pull/205
[207]: https://github.com/rust-num/num-traits/pull/207
[210]: https://github.com/rust-num/num-traits/pull/210
[214]: https://github.com/rust-num/num-traits/pull/214
# Release 0.2.14 (2020-10-29)
- Clarify the license specification as "MIT OR Apache-2.0".
**Contributors**: @cuviper
# Release 0.2.13 (2020-10-29)
- [The new `OverflowingAdd`, `OverflowingSub`, and `OverflowingMul` traits][180]
return a tuple with the operation result and a `bool` indicating overflow.
- [The "i128" feature now overrides compiler probes for that support][185].
This may fix scenarios where `autocfg` probing doesn't work properly.
- [Casts from large `f64` values to `f32` now saturate to infinity][186]. They
previously returned `None` because that was once thought to be undefined
behavior, but [rust#15536] resolved that such casts are fine.
- [`Num::from_str_radix` documents requirements for radix support][192], which
are now more relaxed than previously implied. It is suggested to accept at
least `2..=36` without panicking, but `Err` may be returned otherwise.
**Contributors**: @cuviper, @Enet4, @KaczuH, @martin-t, @newpavlov
[180]: https://github.com/rust-num/num-traits/pull/180
[185]: https://github.com/rust-num/num-traits/pull/185
[186]: https://github.com/rust-num/num-traits/pull/186
[192]: https://github.com/rust-num/num-traits/issues/192
[rust#15536]: https://github.com/rust-lang/rust/issues/15536
# Release 0.2.12 (2020-06-11)
- [The new `WrappingNeg` trait][153] will wrap the result if it exceeds the
boundary of the type, e.g. `i32::MIN.wrapping_neg() == i32::MIN`.
- [The new `SaturatingAdd`, `SaturatingSub`, and `SaturatingMul` traits][165]
will saturate at the numeric bounds if the operation would overflow. These
soft-deprecate the existing `Saturating` trait that only has addition and
subtraction methods.
- [Added new constants for logarithms, `FloatConst::{LOG10_2, LOG2_10}`][171].
**Contributors**: @cuviper, @ocstl, @trepetti, @vallentin
[153]: https://github.com/rust-num/num-traits/pull/153
[165]: https://github.com/rust-num/num-traits/pull/165
[171]: https://github.com/rust-num/num-traits/pull/171
# Release 0.2.11 (2020-01-09)
- [Added the full circle constant τ as `FloatConst::TAU`][145].
- [Updated the `autocfg` build dependency to 1.0][148].
**Contributors**: @cuviper, @m-ou-se
[145]: https://github.com/rust-num/num-traits/pull/145
[148]: https://github.com/rust-num/num-traits/pull/148
# Release 0.2.10 (2019-11-22)
- [Updated the `libm` dependency to 0.2][144].
**Contributors**: @CryZe
[144]: https://github.com/rust-num/num-traits/pull/144
# Release 0.2.9 (2019-11-12)
- [A new optional `libm` dependency][99] enables the `Float` and `Real` traits
in `no_std` builds.
- [The new `clamp_min` and `clamp_max`][122] limit minimum and maximum values
while preserving input `NAN`s.
- [Fixed a panic in floating point `from_str_radix` on invalid signs][126].
- Miscellaneous documentation updates.
**Contributors**: @cuviper, @dingelish, @HeroicKatora, @jturner314, @ocstl,
@Shnatsel, @termoshtt, @waywardmonkeys, @yoanlcq
[99]: https://github.com/rust-num/num-traits/pull/99
[122]: https://github.com/rust-num/num-traits/pull/122
[126]: https://github.com/rust-num/num-traits/pull/126
# Release 0.2.8 (2019-05-21)
- [Fixed feature detection on `no_std` targets][116].
**Contributors**: @cuviper
[116]: https://github.com/rust-num/num-traits/pull/116
# Release 0.2.7 (2019-05-20)
- [Documented when `CheckedShl` and `CheckedShr` return `None`][90].
- [The new `Zero::set_zero` and `One::set_one`][104] will set values to their
identities in place, possibly optimized better than direct assignment.
- [Documented general features and intentions of `PrimInt`][108].
**Contributors**: @cuviper, @dvdhrm, @ignatenkobrain, @lcnr, @samueltardieu
[90]: https://github.com/rust-num/num-traits/pull/90
[104]: https://github.com/rust-num/num-traits/pull/104
[108]: https://github.com/rust-num/num-traits/pull/108
# Release 0.2.6 (2018-09-13)
- [Documented that `pow(0, 0)` returns `1`][79]. Mathematically, this is not
strictly defined, but the current behavior is a pragmatic choice that has
precedent in Rust `core` for the primitives and in many other languages.
- [The new `WrappingShl` and `WrappingShr` traits][81] will wrap the shift count
if it exceeds the bit size of the type.
**Contributors**: @cuviper, @edmccard, @meltinglava
[79]: https://github.com/rust-num/num-traits/pull/79
[81]: https://github.com/rust-num/num-traits/pull/81
# Release 0.2.5 (2018-06-20)
- [Documentation for `mul_add` now clarifies that it's not always faster.][70]
- [The default methods in `FromPrimitive` and `ToPrimitive` are more robust.][73]
**Contributors**: @cuviper, @frewsxcv
[70]: https://github.com/rust-num/num-traits/pull/70
[73]: https://github.com/rust-num/num-traits/pull/73
# Release 0.2.4 (2018-05-11)
- [Support for 128-bit integers is now automatically detected and enabled.][69]
Setting the `i128` crate feature now causes the build script to panic if such
support is not detected.
**Contributors**: @cuviper
[69]: https://github.com/rust-num/num-traits/pull/69
# Release 0.2.3 (2018-05-10)
- [The new `CheckedNeg` and `CheckedRem` traits][63] perform checked `Neg` and
`Rem`, returning `Some(output)` or `None` on overflow.
- [The `no_std` implementation of `FloatCore::to_degrees` for `f32`][61] now
uses a constant for greater accuracy, mirroring [rust#47919]. (With `std` it
just calls the inherent `f32::to_degrees` in the standard library.)
- [The new `MulAdd` and `MulAddAssign` traits][59] perform a fused multiply-
add. For integer types this is just a convenience, but for floating point
types this produces a more accurate result than the separate operations.
- [All applicable traits are now implemented for 128-bit integers][60] starting
with Rust 1.26, enabled by the new `i128` crate feature. The `FromPrimitive`
and `ToPrimitive` traits now also have corresponding 128-bit methods, which
default to converting via 64-bit integers for compatibility.
**Contributors**: @cuviper, @LEXUGE, @regexident, @vks
[59]: https://github.com/rust-num/num-traits/pull/59
[60]: https://github.com/rust-num/num-traits/pull/60
[61]: https://github.com/rust-num/num-traits/pull/61
[63]: https://github.com/rust-num/num-traits/pull/63
[rust#47919]: https://github.com/rust-lang/rust/pull/47919
# Release 0.2.2 (2018-03-18)
- [Casting from floating point to integers now returns `None` on overflow][52],
avoiding [rustc's undefined behavior][rust-10184]. This applies to the `cast`
function and the traits `NumCast`, `FromPrimitive`, and `ToPrimitive`.
**Contributors**: @apopiak, @cuviper, @dbarella
[52]: https://github.com/rust-num/num-traits/pull/52
[rust-10184]: https://github.com/rust-lang/rust/issues/10184
# Release 0.2.1 (2018-03-01)
- [The new `FloatCore` trait][32] offers a subset of `Float` for `#![no_std]` use.
[This includes everything][41] except the transcendental functions and FMA.
- [The new `Inv` trait][37] returns the multiplicative inverse, or reciprocal.
- [The new `Pow` trait][37] performs exponentiation, much like the existing `pow`
function, but with generic exponent types.
- [The new `One::is_one` method][39] tests if a value equals 1. Implementers
should override this method if there's a more efficient way to check for 1,
rather than comparing with a temporary `one()`.
**Contributors**: @clarcharr, @cuviper, @vks
[32]: https://github.com/rust-num/num-traits/pull/32
[37]: https://github.com/rust-num/num-traits/pull/37
[39]: https://github.com/rust-num/num-traits/pull/39
[41]: https://github.com/rust-num/num-traits/pull/41
# Release 0.2.0 (2018-02-06)
- **breaking change**: [There is now a `std` feature][30], enabled by default, along
with the implication that building *without* this feature makes this a
`#![no_std]` crate.
- The `Float` and `Real` traits are only available when `std` is enabled.
- Otherwise, the API is unchanged, and num-traits 0.1.43 now re-exports its
items from num-traits 0.2 for compatibility (the [semver-trick]).
**Contributors**: @cuviper, @termoshtt, @vks
[semver-trick]: https://github.com/dtolnay/semver-trick
[30]: https://github.com/rust-num/num-traits/pull/30
# Release 0.1.43 (2018-02-06)
- All items are now [re-exported from num-traits 0.2][31] for compatibility.
[31]: https://github.com/rust-num/num-traits/pull/31
# Release 0.1.42 (2018-01-22)
- [num-traits now has its own source repository][num-356] at [rust-num/num-traits][home].
- [`ParseFloatError` now implements `Display`][22].
- [The new `AsPrimitive` trait][17] implements generic casting with the `as` operator.
- [The new `CheckedShl` and `CheckedShr` traits][21] implement generic
support for the `checked_shl` and `checked_shr` methods on primitive integers.
- [The new `Real` trait][23] offers a subset of `Float` functionality that may be applicable to more
types, with a blanket implementation for all existing `T: Float` types.
Thanks to @cuviper, @Enet4, @fabianschuiki, @svartalf, and @yoanlcq for their contributions!
[home]: https://github.com/rust-num/num-traits
[num-356]: https://github.com/rust-num/num/pull/356
[17]: https://github.com/rust-num/num-traits/pull/17
[21]: https://github.com/rust-num/num-traits/pull/21
[22]: https://github.com/rust-num/num-traits/pull/22
[23]: https://github.com/rust-num/num-traits/pull/23
# Prior releases
No prior release notes were kept. Thanks all the same to the many
contributors that have made this crate what it is!

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use std::env;
fn main() {
let ac = autocfg::new();
ac.emit_expression_cfg(
"unsafe { 1f64.to_int_unchecked::<i32>() }",
"has_to_int_unchecked",
);
ac.emit_expression_cfg("1u32.reverse_bits()", "has_reverse_bits");
ac.emit_expression_cfg("1u32.trailing_ones()", "has_leading_trailing_ones");
ac.emit_expression_cfg("1u32.div_euclid(1u32)", "has_div_euclid");
if env::var_os("CARGO_FEATURE_STD").is_some() {
ac.emit_expression_cfg("1f64.copysign(-1f64)", "has_copysign");
}
ac.emit_expression_cfg("1f64.is_subnormal()", "has_is_subnormal");
ac.emit_expression_cfg("1u32.to_ne_bytes()", "has_int_to_from_bytes");
ac.emit_expression_cfg("3.14f64.to_ne_bytes()", "has_float_to_from_bytes");
autocfg::rerun_path("build.rs");
}

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use core::num::Wrapping;
use core::{f32, f64};
use core::{i128, i16, i32, i64, i8, isize};
use core::{u128, u16, u32, u64, u8, usize};
/// Numbers which have upper and lower bounds
pub trait Bounded {
// FIXME (#5527): These should be associated constants
/// Returns the smallest finite number this type can represent
fn min_value() -> Self;
/// Returns the largest finite number this type can represent
fn max_value() -> Self;
}
/// Numbers which have lower bounds
pub trait LowerBounded {
/// Returns the smallest finite number this type can represent
fn min_value() -> Self;
}
// FIXME: With a major version bump, this should be a supertrait instead
impl<T: Bounded> LowerBounded for T {
fn min_value() -> T {
Bounded::min_value()
}
}
/// Numbers which have upper bounds
pub trait UpperBounded {
/// Returns the largest finite number this type can represent
fn max_value() -> Self;
}
// FIXME: With a major version bump, this should be a supertrait instead
impl<T: Bounded> UpperBounded for T {
fn max_value() -> T {
Bounded::max_value()
}
}
macro_rules! bounded_impl {
($t:ty, $min:expr, $max:expr) => {
impl Bounded for $t {
#[inline]
fn min_value() -> $t {
$min
}
#[inline]
fn max_value() -> $t {
$max
}
}
};
}
bounded_impl!(usize, usize::MIN, usize::MAX);
bounded_impl!(u8, u8::MIN, u8::MAX);
bounded_impl!(u16, u16::MIN, u16::MAX);
bounded_impl!(u32, u32::MIN, u32::MAX);
bounded_impl!(u64, u64::MIN, u64::MAX);
bounded_impl!(u128, u128::MIN, u128::MAX);
bounded_impl!(isize, isize::MIN, isize::MAX);
bounded_impl!(i8, i8::MIN, i8::MAX);
bounded_impl!(i16, i16::MIN, i16::MAX);
bounded_impl!(i32, i32::MIN, i32::MAX);
bounded_impl!(i64, i64::MIN, i64::MAX);
bounded_impl!(i128, i128::MIN, i128::MAX);
impl<T: Bounded> Bounded for Wrapping<T> {
fn min_value() -> Self {
Wrapping(T::min_value())
}
fn max_value() -> Self {
Wrapping(T::max_value())
}
}
bounded_impl!(f32, f32::MIN, f32::MAX);
macro_rules! for_each_tuple_ {
( $m:ident !! ) => (
$m! { }
);
( $m:ident !! $h:ident, $($t:ident,)* ) => (
$m! { $h $($t)* }
for_each_tuple_! { $m !! $($t,)* }
);
}
macro_rules! for_each_tuple {
($m:ident) => {
for_each_tuple_! { $m !! A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, }
};
}
macro_rules! bounded_tuple {
( $($name:ident)* ) => (
impl<$($name: Bounded,)*> Bounded for ($($name,)*) {
#[inline]
fn min_value() -> Self {
($($name::min_value(),)*)
}
#[inline]
fn max_value() -> Self {
($($name::max_value(),)*)
}
}
);
}
for_each_tuple!(bounded_tuple);
bounded_impl!(f64, f64::MIN, f64::MAX);
#[test]
fn wrapping_bounded() {
macro_rules! test_wrapping_bounded {
($($t:ty)+) => {
$(
assert_eq!(<Wrapping<$t> as Bounded>::min_value().0, <$t>::min_value());
assert_eq!(<Wrapping<$t> as Bounded>::max_value().0, <$t>::max_value());
)+
};
}
test_wrapping_bounded!(usize u8 u16 u32 u64 isize i8 i16 i32 i64);
}
#[test]
fn wrapping_bounded_i128() {
macro_rules! test_wrapping_bounded {
($($t:ty)+) => {
$(
assert_eq!(<Wrapping<$t> as Bounded>::min_value().0, <$t>::min_value());
assert_eq!(<Wrapping<$t> as Bounded>::max_value().0, <$t>::max_value());
)+
};
}
test_wrapping_bounded!(u128 i128);
}
#[test]
fn wrapping_is_bounded() {
fn require_bounded<T: Bounded>(_: &T) {}
require_bounded(&Wrapping(42_u32));
require_bounded(&Wrapping(-42));
}

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use core::mem::size_of;
use core::num::Wrapping;
use core::{f32, f64};
use core::{i128, i16, i32, i64, i8, isize};
use core::{u128, u16, u32, u64, u8, usize};
/// A generic trait for converting a value to a number.
///
/// A value can be represented by the target type when it lies within
/// the range of scalars supported by the target type.
/// For example, a negative integer cannot be represented by an unsigned
/// integer type, and an `i64` with a very high magnitude might not be
/// convertible to an `i32`.
/// On the other hand, conversions with possible precision loss or truncation
/// are admitted, like an `f32` with a decimal part to an integer type, or
/// even a large `f64` saturating to `f32` infinity.
pub trait ToPrimitive {
/// Converts the value of `self` to an `isize`. If the value cannot be
/// represented by an `isize`, then `None` is returned.
#[inline]
fn to_isize(&self) -> Option<isize> {
self.to_i64().as_ref().and_then(ToPrimitive::to_isize)
}
/// Converts the value of `self` to an `i8`. If the value cannot be
/// represented by an `i8`, then `None` is returned.
#[inline]
fn to_i8(&self) -> Option<i8> {
self.to_i64().as_ref().and_then(ToPrimitive::to_i8)
}
/// Converts the value of `self` to an `i16`. If the value cannot be
/// represented by an `i16`, then `None` is returned.
#[inline]
fn to_i16(&self) -> Option<i16> {
self.to_i64().as_ref().and_then(ToPrimitive::to_i16)
}
/// Converts the value of `self` to an `i32`. If the value cannot be
/// represented by an `i32`, then `None` is returned.
#[inline]
fn to_i32(&self) -> Option<i32> {
self.to_i64().as_ref().and_then(ToPrimitive::to_i32)
}
/// Converts the value of `self` to an `i64`. If the value cannot be
/// represented by an `i64`, then `None` is returned.
fn to_i64(&self) -> Option<i64>;
/// Converts the value of `self` to an `i128`. If the value cannot be
/// represented by an `i128` (`i64` under the default implementation), then
/// `None` is returned.
///
/// The default implementation converts through `to_i64()`. Types implementing
/// this trait should override this method if they can represent a greater range.
#[inline]
fn to_i128(&self) -> Option<i128> {
self.to_i64().map(From::from)
}
/// Converts the value of `self` to a `usize`. If the value cannot be
/// represented by a `usize`, then `None` is returned.
#[inline]
fn to_usize(&self) -> Option<usize> {
self.to_u64().as_ref().and_then(ToPrimitive::to_usize)
}
/// Converts the value of `self` to a `u8`. If the value cannot be
/// represented by a `u8`, then `None` is returned.
#[inline]
fn to_u8(&self) -> Option<u8> {
self.to_u64().as_ref().and_then(ToPrimitive::to_u8)
}
/// Converts the value of `self` to a `u16`. If the value cannot be
/// represented by a `u16`, then `None` is returned.
#[inline]
fn to_u16(&self) -> Option<u16> {
self.to_u64().as_ref().and_then(ToPrimitive::to_u16)
}
/// Converts the value of `self` to a `u32`. If the value cannot be
/// represented by a `u32`, then `None` is returned.
#[inline]
fn to_u32(&self) -> Option<u32> {
self.to_u64().as_ref().and_then(ToPrimitive::to_u32)
}
/// Converts the value of `self` to a `u64`. If the value cannot be
/// represented by a `u64`, then `None` is returned.
fn to_u64(&self) -> Option<u64>;
/// Converts the value of `self` to a `u128`. If the value cannot be
/// represented by a `u128` (`u64` under the default implementation), then
/// `None` is returned.
///
/// The default implementation converts through `to_u64()`. Types implementing
/// this trait should override this method if they can represent a greater range.
#[inline]
fn to_u128(&self) -> Option<u128> {
self.to_u64().map(From::from)
}
/// Converts the value of `self` to an `f32`. Overflows may map to positive
/// or negative inifinity, otherwise `None` is returned if the value cannot
/// be represented by an `f32`.
#[inline]
fn to_f32(&self) -> Option<f32> {
self.to_f64().as_ref().and_then(ToPrimitive::to_f32)
}
/// Converts the value of `self` to an `f64`. Overflows may map to positive
/// or negative inifinity, otherwise `None` is returned if the value cannot
/// be represented by an `f64`.
///
/// The default implementation tries to convert through `to_i64()`, and
/// failing that through `to_u64()`. Types implementing this trait should
/// override this method if they can represent a greater range.
#[inline]
fn to_f64(&self) -> Option<f64> {
match self.to_i64() {
Some(i) => i.to_f64(),
None => self.to_u64().as_ref().and_then(ToPrimitive::to_f64),
}
}
}
macro_rules! impl_to_primitive_int_to_int {
($SrcT:ident : $( $(#[$cfg:meta])* fn $method:ident -> $DstT:ident ; )*) => {$(
#[inline]
$(#[$cfg])*
fn $method(&self) -> Option<$DstT> {
let min = $DstT::MIN as $SrcT;
let max = $DstT::MAX as $SrcT;
if size_of::<$SrcT>() <= size_of::<$DstT>() || (min <= *self && *self <= max) {
Some(*self as $DstT)
} else {
None
}
}
)*}
}
macro_rules! impl_to_primitive_int_to_uint {
($SrcT:ident : $( $(#[$cfg:meta])* fn $method:ident -> $DstT:ident ; )*) => {$(
#[inline]
$(#[$cfg])*
fn $method(&self) -> Option<$DstT> {
let max = $DstT::MAX as $SrcT;
if 0 <= *self && (size_of::<$SrcT>() <= size_of::<$DstT>() || *self <= max) {
Some(*self as $DstT)
} else {
None
}
}
)*}
}
macro_rules! impl_to_primitive_int {
($T:ident) => {
impl ToPrimitive for $T {
impl_to_primitive_int_to_int! { $T:
fn to_isize -> isize;
fn to_i8 -> i8;
fn to_i16 -> i16;
fn to_i32 -> i32;
fn to_i64 -> i64;
fn to_i128 -> i128;
}
impl_to_primitive_int_to_uint! { $T:
fn to_usize -> usize;
fn to_u8 -> u8;
fn to_u16 -> u16;
fn to_u32 -> u32;
fn to_u64 -> u64;
fn to_u128 -> u128;
}
#[inline]
fn to_f32(&self) -> Option<f32> {
Some(*self as f32)
}
#[inline]
fn to_f64(&self) -> Option<f64> {
Some(*self as f64)
}
}
};
}
impl_to_primitive_int!(isize);
impl_to_primitive_int!(i8);
impl_to_primitive_int!(i16);
impl_to_primitive_int!(i32);
impl_to_primitive_int!(i64);
impl_to_primitive_int!(i128);
macro_rules! impl_to_primitive_uint_to_int {
($SrcT:ident : $( $(#[$cfg:meta])* fn $method:ident -> $DstT:ident ; )*) => {$(
#[inline]
$(#[$cfg])*
fn $method(&self) -> Option<$DstT> {
let max = $DstT::MAX as $SrcT;
if size_of::<$SrcT>() < size_of::<$DstT>() || *self <= max {
Some(*self as $DstT)
} else {
None
}
}
)*}
}
macro_rules! impl_to_primitive_uint_to_uint {
($SrcT:ident : $( $(#[$cfg:meta])* fn $method:ident -> $DstT:ident ; )*) => {$(
#[inline]
$(#[$cfg])*
fn $method(&self) -> Option<$DstT> {
let max = $DstT::MAX as $SrcT;
if size_of::<$SrcT>() <= size_of::<$DstT>() || *self <= max {
Some(*self as $DstT)
} else {
None
}
}
)*}
}
macro_rules! impl_to_primitive_uint {
($T:ident) => {
impl ToPrimitive for $T {
impl_to_primitive_uint_to_int! { $T:
fn to_isize -> isize;
fn to_i8 -> i8;
fn to_i16 -> i16;
fn to_i32 -> i32;
fn to_i64 -> i64;
fn to_i128 -> i128;
}
impl_to_primitive_uint_to_uint! { $T:
fn to_usize -> usize;
fn to_u8 -> u8;
fn to_u16 -> u16;
fn to_u32 -> u32;
fn to_u64 -> u64;
fn to_u128 -> u128;
}
#[inline]
fn to_f32(&self) -> Option<f32> {
Some(*self as f32)
}
#[inline]
fn to_f64(&self) -> Option<f64> {
Some(*self as f64)
}
}
};
}
impl_to_primitive_uint!(usize);
impl_to_primitive_uint!(u8);
impl_to_primitive_uint!(u16);
impl_to_primitive_uint!(u32);
impl_to_primitive_uint!(u64);
impl_to_primitive_uint!(u128);
macro_rules! impl_to_primitive_float_to_float {
($SrcT:ident : $( fn $method:ident -> $DstT:ident ; )*) => {$(
#[inline]
fn $method(&self) -> Option<$DstT> {
// We can safely cast all values, whether NaN, +-inf, or finite.
// Finite values that are reducing size may saturate to +-inf.
Some(*self as $DstT)
}
)*}
}
#[cfg(has_to_int_unchecked)]
macro_rules! float_to_int_unchecked {
// SAFETY: Must not be NaN or infinite; must be representable as the integer after truncating.
// We already checked that the float is in the exclusive range `(MIN-1, MAX+1)`.
($float:expr => $int:ty) => {
unsafe { $float.to_int_unchecked::<$int>() }
};
}
#[cfg(not(has_to_int_unchecked))]
macro_rules! float_to_int_unchecked {
($float:expr => $int:ty) => {
$float as $int
};
}
macro_rules! impl_to_primitive_float_to_signed_int {
($f:ident : $( $(#[$cfg:meta])* fn $method:ident -> $i:ident ; )*) => {$(
#[inline]
$(#[$cfg])*
fn $method(&self) -> Option<$i> {
// Float as int truncates toward zero, so we want to allow values
// in the exclusive range `(MIN-1, MAX+1)`.
if size_of::<$f>() > size_of::<$i>() {
// With a larger size, we can represent the range exactly.
const MIN_M1: $f = $i::MIN as $f - 1.0;
const MAX_P1: $f = $i::MAX as $f + 1.0;
if *self > MIN_M1 && *self < MAX_P1 {
return Some(float_to_int_unchecked!(*self => $i));
}
} else {
// We can't represent `MIN-1` exactly, but there's no fractional part
// at this magnitude, so we can just use a `MIN` inclusive boundary.
const MIN: $f = $i::MIN as $f;
// We can't represent `MAX` exactly, but it will round up to exactly
// `MAX+1` (a power of two) when we cast it.
const MAX_P1: $f = $i::MAX as $f;
if *self >= MIN && *self < MAX_P1 {
return Some(float_to_int_unchecked!(*self => $i));
}
}
None
}
)*}
}
macro_rules! impl_to_primitive_float_to_unsigned_int {
($f:ident : $( $(#[$cfg:meta])* fn $method:ident -> $u:ident ; )*) => {$(
#[inline]
$(#[$cfg])*
fn $method(&self) -> Option<$u> {
// Float as int truncates toward zero, so we want to allow values
// in the exclusive range `(-1, MAX+1)`.
if size_of::<$f>() > size_of::<$u>() {
// With a larger size, we can represent the range exactly.
const MAX_P1: $f = $u::MAX as $f + 1.0;
if *self > -1.0 && *self < MAX_P1 {
return Some(float_to_int_unchecked!(*self => $u));
}
} else {
// We can't represent `MAX` exactly, but it will round up to exactly
// `MAX+1` (a power of two) when we cast it.
// (`u128::MAX as f32` is infinity, but this is still ok.)
const MAX_P1: $f = $u::MAX as $f;
if *self > -1.0 && *self < MAX_P1 {
return Some(float_to_int_unchecked!(*self => $u));
}
}
None
}
)*}
}
macro_rules! impl_to_primitive_float {
($T:ident) => {
impl ToPrimitive for $T {
impl_to_primitive_float_to_signed_int! { $T:
fn to_isize -> isize;
fn to_i8 -> i8;
fn to_i16 -> i16;
fn to_i32 -> i32;
fn to_i64 -> i64;
fn to_i128 -> i128;
}
impl_to_primitive_float_to_unsigned_int! { $T:
fn to_usize -> usize;
fn to_u8 -> u8;
fn to_u16 -> u16;
fn to_u32 -> u32;
fn to_u64 -> u64;
fn to_u128 -> u128;
}
impl_to_primitive_float_to_float! { $T:
fn to_f32 -> f32;
fn to_f64 -> f64;
}
}
};
}
impl_to_primitive_float!(f32);
impl_to_primitive_float!(f64);
/// A generic trait for converting a number to a value.
///
/// A value can be represented by the target type when it lies within
/// the range of scalars supported by the target type.
/// For example, a negative integer cannot be represented by an unsigned
/// integer type, and an `i64` with a very high magnitude might not be
/// convertible to an `i32`.
/// On the other hand, conversions with possible precision loss or truncation
/// are admitted, like an `f32` with a decimal part to an integer type, or
/// even a large `f64` saturating to `f32` infinity.
pub trait FromPrimitive: Sized {
/// Converts an `isize` to return an optional value of this type. If the
/// value cannot be represented by this type, then `None` is returned.
#[inline]
fn from_isize(n: isize) -> Option<Self> {
n.to_i64().and_then(FromPrimitive::from_i64)
}
/// Converts an `i8` to return an optional value of this type. If the
/// value cannot be represented by this type, then `None` is returned.
#[inline]
fn from_i8(n: i8) -> Option<Self> {
FromPrimitive::from_i64(From::from(n))
}
/// Converts an `i16` to return an optional value of this type. If the
/// value cannot be represented by this type, then `None` is returned.
#[inline]
fn from_i16(n: i16) -> Option<Self> {
FromPrimitive::from_i64(From::from(n))
}
/// Converts an `i32` to return an optional value of this type. If the
/// value cannot be represented by this type, then `None` is returned.
#[inline]
fn from_i32(n: i32) -> Option<Self> {
FromPrimitive::from_i64(From::from(n))
}
/// Converts an `i64` to return an optional value of this type. If the
/// value cannot be represented by this type, then `None` is returned.
fn from_i64(n: i64) -> Option<Self>;
/// Converts an `i128` to return an optional value of this type. If the
/// value cannot be represented by this type, then `None` is returned.
///
/// The default implementation converts through `from_i64()`. Types implementing
/// this trait should override this method if they can represent a greater range.
#[inline]
fn from_i128(n: i128) -> Option<Self> {
n.to_i64().and_then(FromPrimitive::from_i64)
}
/// Converts a `usize` to return an optional value of this type. If the
/// value cannot be represented by this type, then `None` is returned.
#[inline]
fn from_usize(n: usize) -> Option<Self> {
n.to_u64().and_then(FromPrimitive::from_u64)
}
/// Converts an `u8` to return an optional value of this type. If the
/// value cannot be represented by this type, then `None` is returned.
#[inline]
fn from_u8(n: u8) -> Option<Self> {
FromPrimitive::from_u64(From::from(n))
}
/// Converts an `u16` to return an optional value of this type. If the
/// value cannot be represented by this type, then `None` is returned.
#[inline]
fn from_u16(n: u16) -> Option<Self> {
FromPrimitive::from_u64(From::from(n))
}
/// Converts an `u32` to return an optional value of this type. If the
/// value cannot be represented by this type, then `None` is returned.
#[inline]
fn from_u32(n: u32) -> Option<Self> {
FromPrimitive::from_u64(From::from(n))
}
/// Converts an `u64` to return an optional value of this type. If the
/// value cannot be represented by this type, then `None` is returned.
fn from_u64(n: u64) -> Option<Self>;
/// Converts an `u128` to return an optional value of this type. If the
/// value cannot be represented by this type, then `None` is returned.
///
/// The default implementation converts through `from_u64()`. Types implementing
/// this trait should override this method if they can represent a greater range.
#[inline]
fn from_u128(n: u128) -> Option<Self> {
n.to_u64().and_then(FromPrimitive::from_u64)
}
/// Converts a `f32` to return an optional value of this type. If the
/// value cannot be represented by this type, then `None` is returned.
#[inline]
fn from_f32(n: f32) -> Option<Self> {
FromPrimitive::from_f64(From::from(n))
}
/// Converts a `f64` to return an optional value of this type. If the
/// value cannot be represented by this type, then `None` is returned.
///
/// The default implementation tries to convert through `from_i64()`, and
/// failing that through `from_u64()`. Types implementing this trait should
/// override this method if they can represent a greater range.
#[inline]
fn from_f64(n: f64) -> Option<Self> {
match n.to_i64() {
Some(i) => FromPrimitive::from_i64(i),
None => n.to_u64().and_then(FromPrimitive::from_u64),
}
}
}
macro_rules! impl_from_primitive {
($T:ty, $to_ty:ident) => {
#[allow(deprecated)]
impl FromPrimitive for $T {
#[inline]
fn from_isize(n: isize) -> Option<$T> {
n.$to_ty()
}
#[inline]
fn from_i8(n: i8) -> Option<$T> {
n.$to_ty()
}
#[inline]
fn from_i16(n: i16) -> Option<$T> {
n.$to_ty()
}
#[inline]
fn from_i32(n: i32) -> Option<$T> {
n.$to_ty()
}
#[inline]
fn from_i64(n: i64) -> Option<$T> {
n.$to_ty()
}
#[inline]
fn from_i128(n: i128) -> Option<$T> {
n.$to_ty()
}
#[inline]
fn from_usize(n: usize) -> Option<$T> {
n.$to_ty()
}
#[inline]
fn from_u8(n: u8) -> Option<$T> {
n.$to_ty()
}
#[inline]
fn from_u16(n: u16) -> Option<$T> {
n.$to_ty()
}
#[inline]
fn from_u32(n: u32) -> Option<$T> {
n.$to_ty()
}
#[inline]
fn from_u64(n: u64) -> Option<$T> {
n.$to_ty()
}
#[inline]
fn from_u128(n: u128) -> Option<$T> {
n.$to_ty()
}
#[inline]
fn from_f32(n: f32) -> Option<$T> {
n.$to_ty()
}
#[inline]
fn from_f64(n: f64) -> Option<$T> {
n.$to_ty()
}
}
};
}
impl_from_primitive!(isize, to_isize);
impl_from_primitive!(i8, to_i8);
impl_from_primitive!(i16, to_i16);
impl_from_primitive!(i32, to_i32);
impl_from_primitive!(i64, to_i64);
impl_from_primitive!(i128, to_i128);
impl_from_primitive!(usize, to_usize);
impl_from_primitive!(u8, to_u8);
impl_from_primitive!(u16, to_u16);
impl_from_primitive!(u32, to_u32);
impl_from_primitive!(u64, to_u64);
impl_from_primitive!(u128, to_u128);
impl_from_primitive!(f32, to_f32);
impl_from_primitive!(f64, to_f64);
macro_rules! impl_to_primitive_wrapping {
($( $(#[$cfg:meta])* fn $method:ident -> $i:ident ; )*) => {$(
#[inline]
$(#[$cfg])*
fn $method(&self) -> Option<$i> {
(self.0).$method()
}
)*}
}
impl<T: ToPrimitive> ToPrimitive for Wrapping<T> {
impl_to_primitive_wrapping! {
fn to_isize -> isize;
fn to_i8 -> i8;
fn to_i16 -> i16;
fn to_i32 -> i32;
fn to_i64 -> i64;
fn to_i128 -> i128;
fn to_usize -> usize;
fn to_u8 -> u8;
fn to_u16 -> u16;
fn to_u32 -> u32;
fn to_u64 -> u64;
fn to_u128 -> u128;
fn to_f32 -> f32;
fn to_f64 -> f64;
}
}
macro_rules! impl_from_primitive_wrapping {
($( $(#[$cfg:meta])* fn $method:ident ( $i:ident ); )*) => {$(
#[inline]
$(#[$cfg])*
fn $method(n: $i) -> Option<Self> {
T::$method(n).map(Wrapping)
}
)*}
}
impl<T: FromPrimitive> FromPrimitive for Wrapping<T> {
impl_from_primitive_wrapping! {
fn from_isize(isize);
fn from_i8(i8);
fn from_i16(i16);
fn from_i32(i32);
fn from_i64(i64);
fn from_i128(i128);
fn from_usize(usize);
fn from_u8(u8);
fn from_u16(u16);
fn from_u32(u32);
fn from_u64(u64);
fn from_u128(u128);
fn from_f32(f32);
fn from_f64(f64);
}
}
/// Cast from one machine scalar to another.
///
/// # Examples
///
/// ```
/// # use num_traits as num;
/// let twenty: f32 = num::cast(0x14).unwrap();
/// assert_eq!(twenty, 20f32);
/// ```
///
#[inline]
pub fn cast<T: NumCast, U: NumCast>(n: T) -> Option<U> {
NumCast::from(n)
}
/// An interface for casting between machine scalars.
pub trait NumCast: Sized + ToPrimitive {
/// Creates a number from another value that can be converted into
/// a primitive via the `ToPrimitive` trait. If the source value cannot be
/// represented by the target type, then `None` is returned.
///
/// A value can be represented by the target type when it lies within
/// the range of scalars supported by the target type.
/// For example, a negative integer cannot be represented by an unsigned
/// integer type, and an `i64` with a very high magnitude might not be
/// convertible to an `i32`.
/// On the other hand, conversions with possible precision loss or truncation
/// are admitted, like an `f32` with a decimal part to an integer type, or
/// even a large `f64` saturating to `f32` infinity.
fn from<T: ToPrimitive>(n: T) -> Option<Self>;
}
macro_rules! impl_num_cast {
($T:ty, $conv:ident) => {
impl NumCast for $T {
#[inline]
#[allow(deprecated)]
fn from<N: ToPrimitive>(n: N) -> Option<$T> {
// `$conv` could be generated using `concat_idents!`, but that
// macro seems to be broken at the moment
n.$conv()
}
}
};
}
impl_num_cast!(u8, to_u8);
impl_num_cast!(u16, to_u16);
impl_num_cast!(u32, to_u32);
impl_num_cast!(u64, to_u64);
impl_num_cast!(u128, to_u128);
impl_num_cast!(usize, to_usize);
impl_num_cast!(i8, to_i8);
impl_num_cast!(i16, to_i16);
impl_num_cast!(i32, to_i32);
impl_num_cast!(i64, to_i64);
impl_num_cast!(i128, to_i128);
impl_num_cast!(isize, to_isize);
impl_num_cast!(f32, to_f32);
impl_num_cast!(f64, to_f64);
impl<T: NumCast> NumCast for Wrapping<T> {
fn from<U: ToPrimitive>(n: U) -> Option<Self> {
T::from(n).map(Wrapping)
}
}
/// A generic interface for casting between machine scalars with the
/// `as` operator, which admits narrowing and precision loss.
/// Implementers of this trait `AsPrimitive` should behave like a primitive
/// numeric type (e.g. a newtype around another primitive), and the
/// intended conversion must never fail.
///
/// # Examples
///
/// ```
/// # use num_traits::AsPrimitive;
/// let three: i32 = (3.14159265f32).as_();
/// assert_eq!(three, 3);
/// ```
///
/// # Safety
///
/// **In Rust versions before 1.45.0**, some uses of the `as` operator were not entirely safe.
/// In particular, it was undefined behavior if
/// a truncated floating point value could not fit in the target integer
/// type ([#10184](https://github.com/rust-lang/rust/issues/10184)).
///
/// ```ignore
/// # use num_traits::AsPrimitive;
/// let x: u8 = (1.04E+17).as_(); // UB
/// ```
///
pub trait AsPrimitive<T>: 'static + Copy
where
T: 'static + Copy,
{
/// Convert a value to another, using the `as` operator.
fn as_(self) -> T;
}
macro_rules! impl_as_primitive {
(@ $T: ty => $(#[$cfg:meta])* impl $U: ty ) => {
$(#[$cfg])*
impl AsPrimitive<$U> for $T {
#[inline] fn as_(self) -> $U { self as $U }
}
};
(@ $T: ty => { $( $U: ty ),* } ) => {$(
impl_as_primitive!(@ $T => impl $U);
)*};
($T: ty => { $( $U: ty ),* } ) => {
impl_as_primitive!(@ $T => { $( $U ),* });
impl_as_primitive!(@ $T => { u8, u16, u32, u64, u128, usize });
impl_as_primitive!(@ $T => { i8, i16, i32, i64, i128, isize });
};
}
impl_as_primitive!(u8 => { char, f32, f64 });
impl_as_primitive!(i8 => { f32, f64 });
impl_as_primitive!(u16 => { f32, f64 });
impl_as_primitive!(i16 => { f32, f64 });
impl_as_primitive!(u32 => { f32, f64 });
impl_as_primitive!(i32 => { f32, f64 });
impl_as_primitive!(u64 => { f32, f64 });
impl_as_primitive!(i64 => { f32, f64 });
impl_as_primitive!(u128 => { f32, f64 });
impl_as_primitive!(i128 => { f32, f64 });
impl_as_primitive!(usize => { f32, f64 });
impl_as_primitive!(isize => { f32, f64 });
impl_as_primitive!(f32 => { f32, f64 });
impl_as_primitive!(f64 => { f32, f64 });
impl_as_primitive!(char => { char });
impl_as_primitive!(bool => {});

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use core::num::Wrapping;
use core::ops::{Add, Mul};
/// Defines an additive identity element for `Self`.
///
/// # Laws
///
/// ```text
/// a + 0 = a ∀ a ∈ Self
/// 0 + a = a ∀ a ∈ Self
/// ```
pub trait Zero: Sized + Add<Self, Output = Self> {
/// Returns the additive identity element of `Self`, `0`.
/// # Purity
///
/// This function should return the same result at all times regardless of
/// external mutable state, for example values stored in TLS or in
/// `static mut`s.
// This cannot be an associated constant, because of bignums.
fn zero() -> Self;
/// Sets `self` to the additive identity element of `Self`, `0`.
fn set_zero(&mut self) {
*self = Zero::zero();
}
/// Returns `true` if `self` is equal to the additive identity.
fn is_zero(&self) -> bool;
}
macro_rules! zero_impl {
($t:ty, $v:expr) => {
impl Zero for $t {
#[inline]
fn zero() -> $t {
$v
}
#[inline]
fn is_zero(&self) -> bool {
*self == $v
}
}
};
}
zero_impl!(usize, 0);
zero_impl!(u8, 0);
zero_impl!(u16, 0);
zero_impl!(u32, 0);
zero_impl!(u64, 0);
zero_impl!(u128, 0);
zero_impl!(isize, 0);
zero_impl!(i8, 0);
zero_impl!(i16, 0);
zero_impl!(i32, 0);
zero_impl!(i64, 0);
zero_impl!(i128, 0);
zero_impl!(f32, 0.0);
zero_impl!(f64, 0.0);
impl<T: Zero> Zero for Wrapping<T>
where
Wrapping<T>: Add<Output = Wrapping<T>>,
{
fn is_zero(&self) -> bool {
self.0.is_zero()
}
fn set_zero(&mut self) {
self.0.set_zero();
}
fn zero() -> Self {
Wrapping(T::zero())
}
}
/// Defines a multiplicative identity element for `Self`.
///
/// # Laws
///
/// ```text
/// a * 1 = a ∀ a ∈ Self
/// 1 * a = a ∀ a ∈ Self
/// ```
pub trait One: Sized + Mul<Self, Output = Self> {
/// Returns the multiplicative identity element of `Self`, `1`.
///
/// # Purity
///
/// This function should return the same result at all times regardless of
/// external mutable state, for example values stored in TLS or in
/// `static mut`s.
// This cannot be an associated constant, because of bignums.
fn one() -> Self;
/// Sets `self` to the multiplicative identity element of `Self`, `1`.
fn set_one(&mut self) {
*self = One::one();
}
/// Returns `true` if `self` is equal to the multiplicative identity.
///
/// For performance reasons, it's best to implement this manually.
/// After a semver bump, this method will be required, and the
/// `where Self: PartialEq` bound will be removed.
#[inline]
fn is_one(&self) -> bool
where
Self: PartialEq,
{
*self == Self::one()
}
}
macro_rules! one_impl {
($t:ty, $v:expr) => {
impl One for $t {
#[inline]
fn one() -> $t {
$v
}
#[inline]
fn is_one(&self) -> bool {
*self == $v
}
}
};
}
one_impl!(usize, 1);
one_impl!(u8, 1);
one_impl!(u16, 1);
one_impl!(u32, 1);
one_impl!(u64, 1);
one_impl!(u128, 1);
one_impl!(isize, 1);
one_impl!(i8, 1);
one_impl!(i16, 1);
one_impl!(i32, 1);
one_impl!(i64, 1);
one_impl!(i128, 1);
one_impl!(f32, 1.0);
one_impl!(f64, 1.0);
impl<T: One> One for Wrapping<T>
where
Wrapping<T>: Mul<Output = Wrapping<T>>,
{
fn set_one(&mut self) {
self.0.set_one();
}
fn one() -> Self {
Wrapping(T::one())
}
}
// Some helper functions provided for backwards compatibility.
/// Returns the additive identity, `0`.
#[inline(always)]
pub fn zero<T: Zero>() -> T {
Zero::zero()
}
/// Returns the multiplicative identity, `1`.
#[inline(always)]
pub fn one<T: One>() -> T {
One::one()
}
#[test]
fn wrapping_identities() {
macro_rules! test_wrapping_identities {
($($t:ty)+) => {
$(
assert_eq!(zero::<$t>(), zero::<Wrapping<$t>>().0);
assert_eq!(one::<$t>(), one::<Wrapping<$t>>().0);
assert_eq!((0 as $t).is_zero(), Wrapping(0 as $t).is_zero());
assert_eq!((1 as $t).is_zero(), Wrapping(1 as $t).is_zero());
)+
};
}
test_wrapping_identities!(isize i8 i16 i32 i64 usize u8 u16 u32 u64);
}
#[test]
fn wrapping_is_zero() {
fn require_zero<T: Zero>(_: &T) {}
require_zero(&Wrapping(42));
}
#[test]
fn wrapping_is_one() {
fn require_one<T: One>(_: &T) {}
require_one(&Wrapping(42));
}

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use core::ops::{BitAnd, BitOr, BitXor, Not, Shl, Shr};
use crate::bounds::Bounded;
use crate::ops::checked::*;
use crate::ops::saturating::Saturating;
use crate::{Num, NumCast};
/// Generic trait for primitive integers.
///
/// The `PrimInt` trait is an abstraction over the builtin primitive integer types (e.g., `u8`,
/// `u32`, `isize`, `i128`, ...). It inherits the basic numeric traits and extends them with
/// bitwise operators and non-wrapping arithmetic.
///
/// The trait explicitly inherits `Copy`, `Eq`, `Ord`, and `Sized`. The intention is that all
/// types implementing this trait behave like primitive types that are passed by value by default
/// and behave like builtin integers. Furthermore, the types are expected to expose the integer
/// value in binary representation and support bitwise operators. The standard bitwise operations
/// (e.g., bitwise-and, bitwise-or, right-shift, left-shift) are inherited and the trait extends
/// these with introspective queries (e.g., `PrimInt::count_ones()`, `PrimInt::leading_zeros()`),
/// bitwise combinators (e.g., `PrimInt::rotate_left()`), and endianness converters (e.g.,
/// `PrimInt::to_be()`).
///
/// All `PrimInt` types are expected to be fixed-width binary integers. The width can be queried
/// via `T::zero().count_zeros()`. The trait currently lacks a way to query the width at
/// compile-time.
///
/// While a default implementation for all builtin primitive integers is provided, the trait is in
/// no way restricted to these. Other integer types that fulfil the requirements are free to
/// implement the trait was well.
///
/// This trait and many of the method names originate in the unstable `core::num::Int` trait from
/// the rust standard library. The original trait was never stabilized and thus removed from the
/// standard library.
pub trait PrimInt:
Sized
+ Copy
+ Num
+ NumCast
+ Bounded
+ PartialOrd
+ Ord
+ Eq
+ Not<Output = Self>
+ BitAnd<Output = Self>
+ BitOr<Output = Self>
+ BitXor<Output = Self>
+ Shl<usize, Output = Self>
+ Shr<usize, Output = Self>
+ CheckedAdd<Output = Self>
+ CheckedSub<Output = Self>
+ CheckedMul<Output = Self>
+ CheckedDiv<Output = Self>
+ Saturating
{
/// Returns the number of ones in the binary representation of `self`.
///
/// # Examples
///
/// ```
/// use num_traits::PrimInt;
///
/// let n = 0b01001100u8;
///
/// assert_eq!(n.count_ones(), 3);
/// ```
fn count_ones(self) -> u32;
/// Returns the number of zeros in the binary representation of `self`.
///
/// # Examples
///
/// ```
/// use num_traits::PrimInt;
///
/// let n = 0b01001100u8;
///
/// assert_eq!(n.count_zeros(), 5);
/// ```
fn count_zeros(self) -> u32;
/// Returns the number of leading ones in the binary representation
/// of `self`.
///
/// # Examples
///
/// ```
/// use num_traits::PrimInt;
///
/// let n = 0xF00Du16;
///
/// assert_eq!(n.leading_ones(), 4);
/// ```
fn leading_ones(self) -> u32 {
(!self).leading_zeros()
}
/// Returns the number of leading zeros in the binary representation
/// of `self`.
///
/// # Examples
///
/// ```
/// use num_traits::PrimInt;
///
/// let n = 0b0101000u16;
///
/// assert_eq!(n.leading_zeros(), 10);
/// ```
fn leading_zeros(self) -> u32;
/// Returns the number of trailing ones in the binary representation
/// of `self`.
///
/// # Examples
///
/// ```
/// use num_traits::PrimInt;
///
/// let n = 0xBEEFu16;
///
/// assert_eq!(n.trailing_ones(), 4);
/// ```
fn trailing_ones(self) -> u32 {
(!self).trailing_zeros()
}
/// Returns the number of trailing zeros in the binary representation
/// of `self`.
///
/// # Examples
///
/// ```
/// use num_traits::PrimInt;
///
/// let n = 0b0101000u16;
///
/// assert_eq!(n.trailing_zeros(), 3);
/// ```
fn trailing_zeros(self) -> u32;
/// Shifts the bits to the left by a specified amount, `n`, wrapping
/// the truncated bits to the end of the resulting integer.
///
/// # Examples
///
/// ```
/// use num_traits::PrimInt;
///
/// let n = 0x0123456789ABCDEFu64;
/// let m = 0x3456789ABCDEF012u64;
///
/// assert_eq!(n.rotate_left(12), m);
/// ```
fn rotate_left(self, n: u32) -> Self;
/// Shifts the bits to the right by a specified amount, `n`, wrapping
/// the truncated bits to the beginning of the resulting integer.
///
/// # Examples
///
/// ```
/// use num_traits::PrimInt;
///
/// let n = 0x0123456789ABCDEFu64;
/// let m = 0xDEF0123456789ABCu64;
///
/// assert_eq!(n.rotate_right(12), m);
/// ```
fn rotate_right(self, n: u32) -> Self;
/// Shifts the bits to the left by a specified amount, `n`, filling
/// zeros in the least significant bits.
///
/// This is bitwise equivalent to signed `Shl`.
///
/// # Examples
///
/// ```
/// use num_traits::PrimInt;
///
/// let n = 0x0123456789ABCDEFu64;
/// let m = 0x3456789ABCDEF000u64;
///
/// assert_eq!(n.signed_shl(12), m);
/// ```
fn signed_shl(self, n: u32) -> Self;
/// Shifts the bits to the right by a specified amount, `n`, copying
/// the "sign bit" in the most significant bits even for unsigned types.
///
/// This is bitwise equivalent to signed `Shr`.
///
/// # Examples
///
/// ```
/// use num_traits::PrimInt;
///
/// let n = 0xFEDCBA9876543210u64;
/// let m = 0xFFFFEDCBA9876543u64;
///
/// assert_eq!(n.signed_shr(12), m);
/// ```
fn signed_shr(self, n: u32) -> Self;
/// Shifts the bits to the left by a specified amount, `n`, filling
/// zeros in the least significant bits.
///
/// This is bitwise equivalent to unsigned `Shl`.
///
/// # Examples
///
/// ```
/// use num_traits::PrimInt;
///
/// let n = 0x0123456789ABCDEFi64;
/// let m = 0x3456789ABCDEF000i64;
///
/// assert_eq!(n.unsigned_shl(12), m);
/// ```
fn unsigned_shl(self, n: u32) -> Self;
/// Shifts the bits to the right by a specified amount, `n`, filling
/// zeros in the most significant bits.
///
/// This is bitwise equivalent to unsigned `Shr`.
///
/// # Examples
///
/// ```
/// use num_traits::PrimInt;
///
/// let n = -8i8; // 0b11111000
/// let m = 62i8; // 0b00111110
///
/// assert_eq!(n.unsigned_shr(2), m);
/// ```
fn unsigned_shr(self, n: u32) -> Self;
/// Reverses the byte order of the integer.
///
/// # Examples
///
/// ```
/// use num_traits::PrimInt;
///
/// let n = 0x0123456789ABCDEFu64;
/// let m = 0xEFCDAB8967452301u64;
///
/// assert_eq!(n.swap_bytes(), m);
/// ```
fn swap_bytes(self) -> Self;
/// Reverses the order of bits in the integer.
///
/// The least significant bit becomes the most significant bit, second least-significant bit
/// becomes second most-significant bit, etc.
///
/// # Examples
///
/// ```
/// use num_traits::PrimInt;
///
/// let n = 0x12345678u32;
/// let m = 0x1e6a2c48u32;
///
/// assert_eq!(n.reverse_bits(), m);
/// assert_eq!(0u32.reverse_bits(), 0);
/// ```
fn reverse_bits(self) -> Self {
reverse_bits_fallback(self)
}
/// Convert an integer from big endian to the target's endianness.
///
/// On big endian this is a no-op. On little endian the bytes are swapped.
///
/// # Examples
///
/// ```
/// use num_traits::PrimInt;
///
/// let n = 0x0123456789ABCDEFu64;
///
/// if cfg!(target_endian = "big") {
/// assert_eq!(u64::from_be(n), n)
/// } else {
/// assert_eq!(u64::from_be(n), n.swap_bytes())
/// }
/// ```
fn from_be(x: Self) -> Self;
/// Convert an integer from little endian to the target's endianness.
///
/// On little endian this is a no-op. On big endian the bytes are swapped.
///
/// # Examples
///
/// ```
/// use num_traits::PrimInt;
///
/// let n = 0x0123456789ABCDEFu64;
///
/// if cfg!(target_endian = "little") {
/// assert_eq!(u64::from_le(n), n)
/// } else {
/// assert_eq!(u64::from_le(n), n.swap_bytes())
/// }
/// ```
fn from_le(x: Self) -> Self;
/// Convert `self` to big endian from the target's endianness.
///
/// On big endian this is a no-op. On little endian the bytes are swapped.
///
/// # Examples
///
/// ```
/// use num_traits::PrimInt;
///
/// let n = 0x0123456789ABCDEFu64;
///
/// if cfg!(target_endian = "big") {
/// assert_eq!(n.to_be(), n)
/// } else {
/// assert_eq!(n.to_be(), n.swap_bytes())
/// }
/// ```
fn to_be(self) -> Self;
/// Convert `self` to little endian from the target's endianness.
///
/// On little endian this is a no-op. On big endian the bytes are swapped.
///
/// # Examples
///
/// ```
/// use num_traits::PrimInt;
///
/// let n = 0x0123456789ABCDEFu64;
///
/// if cfg!(target_endian = "little") {
/// assert_eq!(n.to_le(), n)
/// } else {
/// assert_eq!(n.to_le(), n.swap_bytes())
/// }
/// ```
fn to_le(self) -> Self;
/// Raises self to the power of `exp`, using exponentiation by squaring.
///
/// # Examples
///
/// ```
/// use num_traits::PrimInt;
///
/// assert_eq!(2i32.pow(4), 16);
/// ```
fn pow(self, exp: u32) -> Self;
}
fn one_per_byte<P: PrimInt>() -> P {
// i8, u8: return 0x01
// i16, u16: return 0x0101 = (0x01 << 8) | 0x01
// i32, u32: return 0x01010101 = (0x0101 << 16) | 0x0101
// ...
let mut ret = P::one();
let mut shift = 8;
let mut b = ret.count_zeros() >> 3;
while b != 0 {
ret = (ret << shift) | ret;
shift <<= 1;
b >>= 1;
}
ret
}
fn reverse_bits_fallback<P: PrimInt>(i: P) -> P {
let rep_01: P = one_per_byte();
let rep_03 = (rep_01 << 1) | rep_01;
let rep_05 = (rep_01 << 2) | rep_01;
let rep_0f = (rep_03 << 2) | rep_03;
let rep_33 = (rep_03 << 4) | rep_03;
let rep_55 = (rep_05 << 4) | rep_05;
// code above only used to determine rep_0f, rep_33, rep_55;
// optimizer should be able to do it in compile time
let mut ret = i.swap_bytes();
ret = ((ret & rep_0f) << 4) | ((ret >> 4) & rep_0f);
ret = ((ret & rep_33) << 2) | ((ret >> 2) & rep_33);
ret = ((ret & rep_55) << 1) | ((ret >> 1) & rep_55);
ret
}
macro_rules! prim_int_impl {
($T:ty, $S:ty, $U:ty) => {
impl PrimInt for $T {
#[inline]
fn count_ones(self) -> u32 {
<$T>::count_ones(self)
}
#[inline]
fn count_zeros(self) -> u32 {
<$T>::count_zeros(self)
}
#[cfg(has_leading_trailing_ones)]
#[inline]
fn leading_ones(self) -> u32 {
<$T>::leading_ones(self)
}
#[inline]
fn leading_zeros(self) -> u32 {
<$T>::leading_zeros(self)
}
#[cfg(has_leading_trailing_ones)]
#[inline]
fn trailing_ones(self) -> u32 {
<$T>::trailing_ones(self)
}
#[inline]
fn trailing_zeros(self) -> u32 {
<$T>::trailing_zeros(self)
}
#[inline]
fn rotate_left(self, n: u32) -> Self {
<$T>::rotate_left(self, n)
}
#[inline]
fn rotate_right(self, n: u32) -> Self {
<$T>::rotate_right(self, n)
}
#[inline]
fn signed_shl(self, n: u32) -> Self {
((self as $S) << n) as $T
}
#[inline]
fn signed_shr(self, n: u32) -> Self {
((self as $S) >> n) as $T
}
#[inline]
fn unsigned_shl(self, n: u32) -> Self {
((self as $U) << n) as $T
}
#[inline]
fn unsigned_shr(self, n: u32) -> Self {
((self as $U) >> n) as $T
}
#[inline]
fn swap_bytes(self) -> Self {
<$T>::swap_bytes(self)
}
#[cfg(has_reverse_bits)]
#[inline]
fn reverse_bits(self) -> Self {
<$T>::reverse_bits(self)
}
#[inline]
fn from_be(x: Self) -> Self {
<$T>::from_be(x)
}
#[inline]
fn from_le(x: Self) -> Self {
<$T>::from_le(x)
}
#[inline]
fn to_be(self) -> Self {
<$T>::to_be(self)
}
#[inline]
fn to_le(self) -> Self {
<$T>::to_le(self)
}
#[inline]
fn pow(self, exp: u32) -> Self {
<$T>::pow(self, exp)
}
}
};
}
// prim_int_impl!(type, signed, unsigned);
prim_int_impl!(u8, i8, u8);
prim_int_impl!(u16, i16, u16);
prim_int_impl!(u32, i32, u32);
prim_int_impl!(u64, i64, u64);
prim_int_impl!(u128, i128, u128);
prim_int_impl!(usize, isize, usize);
prim_int_impl!(i8, i8, u8);
prim_int_impl!(i16, i16, u16);
prim_int_impl!(i32, i32, u32);
prim_int_impl!(i64, i64, u64);
prim_int_impl!(i128, i128, u128);
prim_int_impl!(isize, isize, usize);
#[cfg(test)]
mod tests {
use crate::int::PrimInt;
#[test]
pub fn reverse_bits() {
use core::{i16, i32, i64, i8};
assert_eq!(
PrimInt::reverse_bits(0x0123_4567_89ab_cdefu64),
0xf7b3_d591_e6a2_c480
);
assert_eq!(PrimInt::reverse_bits(0i8), 0);
assert_eq!(PrimInt::reverse_bits(-1i8), -1);
assert_eq!(PrimInt::reverse_bits(1i8), i8::MIN);
assert_eq!(PrimInt::reverse_bits(i8::MIN), 1);
assert_eq!(PrimInt::reverse_bits(-2i8), i8::MAX);
assert_eq!(PrimInt::reverse_bits(i8::MAX), -2);
assert_eq!(PrimInt::reverse_bits(0i16), 0);
assert_eq!(PrimInt::reverse_bits(-1i16), -1);
assert_eq!(PrimInt::reverse_bits(1i16), i16::MIN);
assert_eq!(PrimInt::reverse_bits(i16::MIN), 1);
assert_eq!(PrimInt::reverse_bits(-2i16), i16::MAX);
assert_eq!(PrimInt::reverse_bits(i16::MAX), -2);
assert_eq!(PrimInt::reverse_bits(0i32), 0);
assert_eq!(PrimInt::reverse_bits(-1i32), -1);
assert_eq!(PrimInt::reverse_bits(1i32), i32::MIN);
assert_eq!(PrimInt::reverse_bits(i32::MIN), 1);
assert_eq!(PrimInt::reverse_bits(-2i32), i32::MAX);
assert_eq!(PrimInt::reverse_bits(i32::MAX), -2);
assert_eq!(PrimInt::reverse_bits(0i64), 0);
assert_eq!(PrimInt::reverse_bits(-1i64), -1);
assert_eq!(PrimInt::reverse_bits(1i64), i64::MIN);
assert_eq!(PrimInt::reverse_bits(i64::MIN), 1);
assert_eq!(PrimInt::reverse_bits(-2i64), i64::MAX);
assert_eq!(PrimInt::reverse_bits(i64::MAX), -2);
}
#[test]
pub fn reverse_bits_i128() {
use core::i128;
assert_eq!(PrimInt::reverse_bits(0i128), 0);
assert_eq!(PrimInt::reverse_bits(-1i128), -1);
assert_eq!(PrimInt::reverse_bits(1i128), i128::MIN);
assert_eq!(PrimInt::reverse_bits(i128::MIN), 1);
assert_eq!(PrimInt::reverse_bits(-2i128), i128::MAX);
assert_eq!(PrimInt::reverse_bits(i128::MAX), -2);
}
}

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@ -0,0 +1,635 @@
// Copyright 2013-2014 The Rust Project Developers. See the COPYRIGHT
// file at the top-level directory of this distribution and at
// http://rust-lang.org/COPYRIGHT.
//
// Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or
// http://www.apache.org/licenses/LICENSE-2.0> or the MIT license
// <LICENSE-MIT or http://opensource.org/licenses/MIT>, at your
// option. This file may not be copied, modified, or distributed
// except according to those terms.
//! Numeric traits for generic mathematics
//!
//! ## Compatibility
//!
//! The `num-traits` crate is tested for rustc 1.31 and greater.
#![doc(html_root_url = "https://docs.rs/num-traits/0.2")]
#![deny(unconditional_recursion)]
#![no_std]
// Need to explicitly bring the crate in for inherent float methods
#[cfg(feature = "std")]
extern crate std;
use core::fmt;
use core::num::Wrapping;
use core::ops::{Add, Div, Mul, Rem, Sub};
use core::ops::{AddAssign, DivAssign, MulAssign, RemAssign, SubAssign};
pub use crate::bounds::Bounded;
#[cfg(any(feature = "std", feature = "libm"))]
pub use crate::float::Float;
pub use crate::float::FloatConst;
// pub use real::{FloatCore, Real}; // NOTE: Don't do this, it breaks `use num_traits::*;`.
pub use crate::cast::{cast, AsPrimitive, FromPrimitive, NumCast, ToPrimitive};
pub use crate::identities::{one, zero, One, Zero};
pub use crate::int::PrimInt;
pub use crate::ops::bytes::{FromBytes, ToBytes};
pub use crate::ops::checked::{
CheckedAdd, CheckedDiv, CheckedMul, CheckedNeg, CheckedRem, CheckedShl, CheckedShr, CheckedSub,
};
pub use crate::ops::euclid::{CheckedEuclid, Euclid};
pub use crate::ops::inv::Inv;
pub use crate::ops::mul_add::{MulAdd, MulAddAssign};
pub use crate::ops::saturating::{Saturating, SaturatingAdd, SaturatingMul, SaturatingSub};
pub use crate::ops::wrapping::{
WrappingAdd, WrappingMul, WrappingNeg, WrappingShl, WrappingShr, WrappingSub,
};
pub use crate::pow::{checked_pow, pow, Pow};
pub use crate::sign::{abs, abs_sub, signum, Signed, Unsigned};
#[macro_use]
mod macros;
pub mod bounds;
pub mod cast;
pub mod float;
pub mod identities;
pub mod int;
pub mod ops;
pub mod pow;
pub mod real;
pub mod sign;
/// The base trait for numeric types, covering `0` and `1` values,
/// comparisons, basic numeric operations, and string conversion.
pub trait Num: PartialEq + Zero + One + NumOps {
type FromStrRadixErr;
/// Convert from a string and radix (typically `2..=36`).
///
/// # Examples
///
/// ```rust
/// use num_traits::Num;
///
/// let result = <i32 as Num>::from_str_radix("27", 10);
/// assert_eq!(result, Ok(27));
///
/// let result = <i32 as Num>::from_str_radix("foo", 10);
/// assert!(result.is_err());
/// ```
///
/// # Supported radices
///
/// The exact range of supported radices is at the discretion of each type implementation. For
/// primitive integers, this is implemented by the inherent `from_str_radix` methods in the
/// standard library, which **panic** if the radix is not in the range from 2 to 36. The
/// implementation in this crate for primitive floats is similar.
///
/// For third-party types, it is suggested that implementations should follow suit and at least
/// accept `2..=36` without panicking, but an `Err` may be returned for any unsupported radix.
/// It's possible that a type might not even support the common radix 10, nor any, if string
/// parsing doesn't make sense for that type.
fn from_str_radix(str: &str, radix: u32) -> Result<Self, Self::FromStrRadixErr>;
}
/// Generic trait for types implementing basic numeric operations
///
/// This is automatically implemented for types which implement the operators.
pub trait NumOps<Rhs = Self, Output = Self>:
Add<Rhs, Output = Output>
+ Sub<Rhs, Output = Output>
+ Mul<Rhs, Output = Output>
+ Div<Rhs, Output = Output>
+ Rem<Rhs, Output = Output>
{
}
impl<T, Rhs, Output> NumOps<Rhs, Output> for T where
T: Add<Rhs, Output = Output>
+ Sub<Rhs, Output = Output>
+ Mul<Rhs, Output = Output>
+ Div<Rhs, Output = Output>
+ Rem<Rhs, Output = Output>
{
}
/// The trait for `Num` types which also implement numeric operations taking
/// the second operand by reference.
///
/// This is automatically implemented for types which implement the operators.
pub trait NumRef: Num + for<'r> NumOps<&'r Self> {}
impl<T> NumRef for T where T: Num + for<'r> NumOps<&'r T> {}
/// The trait for `Num` references which implement numeric operations, taking the
/// second operand either by value or by reference.
///
/// This is automatically implemented for all types which implement the operators. It covers
/// every type implementing the operations though, regardless of it being a reference or
/// related to `Num`.
pub trait RefNum<Base>: NumOps<Base, Base> + for<'r> NumOps<&'r Base, Base> {}
impl<T, Base> RefNum<Base> for T where T: NumOps<Base, Base> + for<'r> NumOps<&'r Base, Base> {}
/// Generic trait for types implementing numeric assignment operators (like `+=`).
///
/// This is automatically implemented for types which implement the operators.
pub trait NumAssignOps<Rhs = Self>:
AddAssign<Rhs> + SubAssign<Rhs> + MulAssign<Rhs> + DivAssign<Rhs> + RemAssign<Rhs>
{
}
impl<T, Rhs> NumAssignOps<Rhs> for T where
T: AddAssign<Rhs> + SubAssign<Rhs> + MulAssign<Rhs> + DivAssign<Rhs> + RemAssign<Rhs>
{
}
/// The trait for `Num` types which also implement assignment operators.
///
/// This is automatically implemented for types which implement the operators.
pub trait NumAssign: Num + NumAssignOps {}
impl<T> NumAssign for T where T: Num + NumAssignOps {}
/// The trait for `NumAssign` types which also implement assignment operations
/// taking the second operand by reference.
///
/// This is automatically implemented for types which implement the operators.
pub trait NumAssignRef: NumAssign + for<'r> NumAssignOps<&'r Self> {}
impl<T> NumAssignRef for T where T: NumAssign + for<'r> NumAssignOps<&'r T> {}
macro_rules! int_trait_impl {
($name:ident for $($t:ty)*) => ($(
impl $name for $t {
type FromStrRadixErr = ::core::num::ParseIntError;
#[inline]
fn from_str_radix(s: &str, radix: u32)
-> Result<Self, ::core::num::ParseIntError>
{
<$t>::from_str_radix(s, radix)
}
}
)*)
}
int_trait_impl!(Num for usize u8 u16 u32 u64 u128);
int_trait_impl!(Num for isize i8 i16 i32 i64 i128);
impl<T: Num> Num for Wrapping<T>
where
Wrapping<T>: NumOps,
{
type FromStrRadixErr = T::FromStrRadixErr;
fn from_str_radix(str: &str, radix: u32) -> Result<Self, Self::FromStrRadixErr> {
T::from_str_radix(str, radix).map(Wrapping)
}
}
#[derive(Debug)]
pub enum FloatErrorKind {
Empty,
Invalid,
}
// FIXME: core::num::ParseFloatError is stable in 1.0, but opaque to us,
// so there's not really any way for us to reuse it.
#[derive(Debug)]
pub struct ParseFloatError {
pub kind: FloatErrorKind,
}
impl fmt::Display for ParseFloatError {
fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
let description = match self.kind {
FloatErrorKind::Empty => "cannot parse float from empty string",
FloatErrorKind::Invalid => "invalid float literal",
};
description.fmt(f)
}
}
fn str_to_ascii_lower_eq_str(a: &str, b: &str) -> bool {
a.len() == b.len()
&& a.bytes().zip(b.bytes()).all(|(a, b)| {
let a_to_ascii_lower = a | (((b'A' <= a && a <= b'Z') as u8) << 5);
a_to_ascii_lower == b
})
}
// FIXME: The standard library from_str_radix on floats was deprecated, so we're stuck
// with this implementation ourselves until we want to make a breaking change.
// (would have to drop it from `Num` though)
macro_rules! float_trait_impl {
($name:ident for $($t:ident)*) => ($(
impl $name for $t {
type FromStrRadixErr = ParseFloatError;
fn from_str_radix(src: &str, radix: u32)
-> Result<Self, Self::FromStrRadixErr>
{
use self::FloatErrorKind::*;
use self::ParseFloatError as PFE;
// Special case radix 10 to use more accurate standard library implementation
if radix == 10 {
return src.parse().map_err(|_| PFE {
kind: if src.is_empty() { Empty } else { Invalid },
});
}
// Special values
if str_to_ascii_lower_eq_str(src, "inf")
|| str_to_ascii_lower_eq_str(src, "infinity")
{
return Ok(core::$t::INFINITY);
} else if str_to_ascii_lower_eq_str(src, "-inf")
|| str_to_ascii_lower_eq_str(src, "-infinity")
{
return Ok(core::$t::NEG_INFINITY);
} else if str_to_ascii_lower_eq_str(src, "nan") {
return Ok(core::$t::NAN);
} else if str_to_ascii_lower_eq_str(src, "-nan") {
return Ok(-core::$t::NAN);
}
fn slice_shift_char(src: &str) -> Option<(char, &str)> {
let mut chars = src.chars();
Some((chars.next()?, chars.as_str()))
}
let (is_positive, src) = match slice_shift_char(src) {
None => return Err(PFE { kind: Empty }),
Some(('-', "")) => return Err(PFE { kind: Empty }),
Some(('-', src)) => (false, src),
Some((_, _)) => (true, src),
};
// The significand to accumulate
let mut sig = if is_positive { 0.0 } else { -0.0 };
// Necessary to detect overflow
let mut prev_sig = sig;
let mut cs = src.chars().enumerate();
// Exponent prefix and exponent index offset
let mut exp_info = None::<(char, usize)>;
// Parse the integer part of the significand
for (i, c) in cs.by_ref() {
match c.to_digit(radix) {
Some(digit) => {
// shift significand one digit left
sig *= radix as $t;
// add/subtract current digit depending on sign
if is_positive {
sig += (digit as isize) as $t;
} else {
sig -= (digit as isize) as $t;
}
// Detect overflow by comparing to last value, except
// if we've not seen any non-zero digits.
if prev_sig != 0.0 {
if is_positive && sig <= prev_sig
{ return Ok(core::$t::INFINITY); }
if !is_positive && sig >= prev_sig
{ return Ok(core::$t::NEG_INFINITY); }
// Detect overflow by reversing the shift-and-add process
if is_positive && (prev_sig != (sig - digit as $t) / radix as $t)
{ return Ok(core::$t::INFINITY); }
if !is_positive && (prev_sig != (sig + digit as $t) / radix as $t)
{ return Ok(core::$t::NEG_INFINITY); }
}
prev_sig = sig;
},
None => match c {
'e' | 'E' | 'p' | 'P' => {
exp_info = Some((c, i + 1));
break; // start of exponent
},
'.' => {
break; // start of fractional part
},
_ => {
return Err(PFE { kind: Invalid });
},
},
}
}
// If we are not yet at the exponent parse the fractional
// part of the significand
if exp_info.is_none() {
let mut power = 1.0;
for (i, c) in cs.by_ref() {
match c.to_digit(radix) {
Some(digit) => {
// Decrease power one order of magnitude
power /= radix as $t;
// add/subtract current digit depending on sign
sig = if is_positive {
sig + (digit as $t) * power
} else {
sig - (digit as $t) * power
};
// Detect overflow by comparing to last value
if is_positive && sig < prev_sig
{ return Ok(core::$t::INFINITY); }
if !is_positive && sig > prev_sig
{ return Ok(core::$t::NEG_INFINITY); }
prev_sig = sig;
},
None => match c {
'e' | 'E' | 'p' | 'P' => {
exp_info = Some((c, i + 1));
break; // start of exponent
},
_ => {
return Err(PFE { kind: Invalid });
},
},
}
}
}
// Parse and calculate the exponent
let exp = match exp_info {
Some((c, offset)) => {
let base = match c {
'E' | 'e' if radix == 10 => 10.0,
'P' | 'p' if radix == 16 => 2.0,
_ => return Err(PFE { kind: Invalid }),
};
// Parse the exponent as decimal integer
let src = &src[offset..];
let (is_positive, exp) = match slice_shift_char(src) {
Some(('-', src)) => (false, src.parse::<usize>()),
Some(('+', src)) => (true, src.parse::<usize>()),
Some((_, _)) => (true, src.parse::<usize>()),
None => return Err(PFE { kind: Invalid }),
};
#[cfg(feature = "std")]
fn pow(base: $t, exp: usize) -> $t {
Float::powi(base, exp as i32)
}
// otherwise uses the generic `pow` from the root
match (is_positive, exp) {
(true, Ok(exp)) => pow(base, exp),
(false, Ok(exp)) => 1.0 / pow(base, exp),
(_, Err(_)) => return Err(PFE { kind: Invalid }),
}
},
None => 1.0, // no exponent
};
Ok(sig * exp)
}
}
)*)
}
float_trait_impl!(Num for f32 f64);
/// A value bounded by a minimum and a maximum
///
/// If input is less than min then this returns min.
/// If input is greater than max then this returns max.
/// Otherwise this returns input.
///
/// **Panics** in debug mode if `!(min <= max)`.
#[inline]
pub fn clamp<T: PartialOrd>(input: T, min: T, max: T) -> T {
debug_assert!(min <= max, "min must be less than or equal to max");
if input < min {
min
} else if input > max {
max
} else {
input
}
}
/// A value bounded by a minimum value
///
/// If input is less than min then this returns min.
/// Otherwise this returns input.
/// `clamp_min(std::f32::NAN, 1.0)` preserves `NAN` different from `f32::min(std::f32::NAN, 1.0)`.
///
/// **Panics** in debug mode if `!(min == min)`. (This occurs if `min` is `NAN`.)
#[inline]
#[allow(clippy::eq_op)]
pub fn clamp_min<T: PartialOrd>(input: T, min: T) -> T {
debug_assert!(min == min, "min must not be NAN");
if input < min {
min
} else {
input
}
}
/// A value bounded by a maximum value
///
/// If input is greater than max then this returns max.
/// Otherwise this returns input.
/// `clamp_max(std::f32::NAN, 1.0)` preserves `NAN` different from `f32::max(std::f32::NAN, 1.0)`.
///
/// **Panics** in debug mode if `!(max == max)`. (This occurs if `max` is `NAN`.)
#[inline]
#[allow(clippy::eq_op)]
pub fn clamp_max<T: PartialOrd>(input: T, max: T) -> T {
debug_assert!(max == max, "max must not be NAN");
if input > max {
max
} else {
input
}
}
#[test]
fn clamp_test() {
// Int test
assert_eq!(1, clamp(1, -1, 2));
assert_eq!(-1, clamp(-2, -1, 2));
assert_eq!(2, clamp(3, -1, 2));
assert_eq!(1, clamp_min(1, -1));
assert_eq!(-1, clamp_min(-2, -1));
assert_eq!(-1, clamp_max(1, -1));
assert_eq!(-2, clamp_max(-2, -1));
// Float test
assert_eq!(1.0, clamp(1.0, -1.0, 2.0));
assert_eq!(-1.0, clamp(-2.0, -1.0, 2.0));
assert_eq!(2.0, clamp(3.0, -1.0, 2.0));
assert_eq!(1.0, clamp_min(1.0, -1.0));
assert_eq!(-1.0, clamp_min(-2.0, -1.0));
assert_eq!(-1.0, clamp_max(1.0, -1.0));
assert_eq!(-2.0, clamp_max(-2.0, -1.0));
assert!(clamp(::core::f32::NAN, -1.0, 1.0).is_nan());
assert!(clamp_min(::core::f32::NAN, 1.0).is_nan());
assert!(clamp_max(::core::f32::NAN, 1.0).is_nan());
}
#[test]
#[should_panic]
#[cfg(debug_assertions)]
fn clamp_nan_min() {
clamp(0., ::core::f32::NAN, 1.);
}
#[test]
#[should_panic]
#[cfg(debug_assertions)]
fn clamp_nan_max() {
clamp(0., -1., ::core::f32::NAN);
}
#[test]
#[should_panic]
#[cfg(debug_assertions)]
fn clamp_nan_min_max() {
clamp(0., ::core::f32::NAN, ::core::f32::NAN);
}
#[test]
#[should_panic]
#[cfg(debug_assertions)]
fn clamp_min_nan_min() {
clamp_min(0., ::core::f32::NAN);
}
#[test]
#[should_panic]
#[cfg(debug_assertions)]
fn clamp_max_nan_max() {
clamp_max(0., ::core::f32::NAN);
}
#[test]
fn from_str_radix_unwrap() {
// The Result error must impl Debug to allow unwrap()
let i: i32 = Num::from_str_radix("0", 10).unwrap();
assert_eq!(i, 0);
let f: f32 = Num::from_str_radix("0.0", 10).unwrap();
assert_eq!(f, 0.0);
}
#[test]
fn from_str_radix_multi_byte_fail() {
// Ensure parsing doesn't panic, even on invalid sign characters
assert!(f32::from_str_radix("™0.2", 10).is_err());
// Even when parsing the exponent sign
assert!(f32::from_str_radix("0.2E™1", 10).is_err());
}
#[test]
fn from_str_radix_ignore_case() {
assert_eq!(
f32::from_str_radix("InF", 16).unwrap(),
::core::f32::INFINITY
);
assert_eq!(
f32::from_str_radix("InfinitY", 16).unwrap(),
::core::f32::INFINITY
);
assert_eq!(
f32::from_str_radix("-InF", 8).unwrap(),
::core::f32::NEG_INFINITY
);
assert_eq!(
f32::from_str_radix("-InfinitY", 8).unwrap(),
::core::f32::NEG_INFINITY
);
assert!(f32::from_str_radix("nAn", 4).unwrap().is_nan());
assert!(f32::from_str_radix("-nAn", 4).unwrap().is_nan());
}
#[test]
fn wrapping_is_num() {
fn require_num<T: Num>(_: &T) {}
require_num(&Wrapping(42_u32));
require_num(&Wrapping(-42));
}
#[test]
fn wrapping_from_str_radix() {
macro_rules! test_wrapping_from_str_radix {
($($t:ty)+) => {
$(
for &(s, r) in &[("42", 10), ("42", 2), ("-13.0", 10), ("foo", 10)] {
let w = Wrapping::<$t>::from_str_radix(s, r).map(|w| w.0);
assert_eq!(w, <$t as Num>::from_str_radix(s, r));
}
)+
};
}
test_wrapping_from_str_radix!(usize u8 u16 u32 u64 isize i8 i16 i32 i64);
}
#[test]
fn check_num_ops() {
fn compute<T: Num + Copy>(x: T, y: T) -> T {
x * y / y % y + y - y
}
assert_eq!(compute(1, 2), 1)
}
#[test]
fn check_numref_ops() {
fn compute<T: NumRef>(x: T, y: &T) -> T {
x * y / y % y + y - y
}
assert_eq!(compute(1, &2), 1)
}
#[test]
fn check_refnum_ops() {
fn compute<T: Copy>(x: &T, y: T) -> T
where
for<'a> &'a T: RefNum<T>,
{
&(&(&(&(x * y) / y) % y) + y) - y
}
assert_eq!(compute(&1, 2), 1)
}
#[test]
fn check_refref_ops() {
fn compute<T>(x: &T, y: &T) -> T
where
for<'a> &'a T: RefNum<T>,
{
&(&(&(&(x * y) / y) % y) + y) - y
}
assert_eq!(compute(&1, &2), 1)
}
#[test]
fn check_numassign_ops() {
fn compute<T: NumAssign + Copy>(mut x: T, y: T) -> T {
x *= y;
x /= y;
x %= y;
x += y;
x -= y;
x
}
assert_eq!(compute(1, 2), 1)
}
#[test]
fn check_numassignref_ops() {
fn compute<T: NumAssignRef + Copy>(mut x: T, y: &T) -> T {
x *= y;
x /= y;
x %= y;
x += y;
x -= y;
x
}
assert_eq!(compute(1, &2), 1)
}

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// not all are used in all features configurations
#![allow(unused)]
/// Forward a method to an inherent method or a base trait method.
macro_rules! forward {
($( Self :: $method:ident ( self $( , $arg:ident : $ty:ty )* ) -> $ret:ty ; )*)
=> {$(
#[inline]
fn $method(self $( , $arg : $ty )* ) -> $ret {
Self::$method(self $( , $arg )* )
}
)*};
($( $base:ident :: $method:ident ( self $( , $arg:ident : $ty:ty )* ) -> $ret:ty ; )*)
=> {$(
#[inline]
fn $method(self $( , $arg : $ty )* ) -> $ret {
<Self as $base>::$method(self $( , $arg )* )
}
)*};
($( $base:ident :: $method:ident ( $( $arg:ident : $ty:ty ),* ) -> $ret:ty ; )*)
=> {$(
#[inline]
fn $method( $( $arg : $ty ),* ) -> $ret {
<Self as $base>::$method( $( $arg ),* )
}
)*};
($( $imp:path as $method:ident ( self $( , $arg:ident : $ty:ty )* ) -> $ret:ty ; )*)
=> {$(
#[inline]
fn $method(self $( , $arg : $ty )* ) -> $ret {
$imp(self $( , $arg )* )
}
)*};
}
macro_rules! constant {
($( $method:ident () -> $ret:expr ; )*)
=> {$(
#[inline]
fn $method() -> Self {
$ret
}
)*};
}

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use core::borrow::{Borrow, BorrowMut};
use core::cmp::{Eq, Ord, PartialEq, PartialOrd};
use core::fmt::Debug;
use core::hash::Hash;
#[cfg(not(has_int_to_from_bytes))]
use core::mem::transmute;
pub trait NumBytes:
Debug
+ AsRef<[u8]>
+ AsMut<[u8]>
+ PartialEq
+ Eq
+ PartialOrd
+ Ord
+ Hash
+ Borrow<[u8]>
+ BorrowMut<[u8]>
{
}
impl<T> NumBytes for T where
T: Debug
+ AsRef<[u8]>
+ AsMut<[u8]>
+ PartialEq
+ Eq
+ PartialOrd
+ Ord
+ Hash
+ Borrow<[u8]>
+ BorrowMut<[u8]>
+ ?Sized
{
}
pub trait ToBytes {
type Bytes: NumBytes;
/// Return the memory representation of this number as a byte array in big-endian byte order.
///
/// # Examples
///
/// ```
/// use num_traits::ToBytes;
///
/// let bytes = ToBytes::to_be_bytes(&0x12345678u32);
/// assert_eq!(bytes, [0x12, 0x34, 0x56, 0x78]);
/// ```
fn to_be_bytes(&self) -> Self::Bytes;
/// Return the memory representation of this number as a byte array in little-endian byte order.
///
/// # Examples
///
/// ```
/// use num_traits::ToBytes;
///
/// let bytes = ToBytes::to_le_bytes(&0x12345678u32);
/// assert_eq!(bytes, [0x78, 0x56, 0x34, 0x12]);
/// ```
fn to_le_bytes(&self) -> Self::Bytes;
/// Return the memory representation of this number as a byte array in native byte order.
///
/// As the target platform's native endianness is used,
/// portable code should use [`to_be_bytes`] or [`to_le_bytes`], as appropriate, instead.
///
/// [`to_be_bytes`]: #method.to_be_bytes
/// [`to_le_bytes`]: #method.to_le_bytes
///
/// # Examples
///
/// ```
/// use num_traits::ToBytes;
///
/// #[cfg(target_endian = "big")]
/// let expected = [0x12, 0x34, 0x56, 0x78];
///
/// #[cfg(target_endian = "little")]
/// let expected = [0x78, 0x56, 0x34, 0x12];
///
/// let bytes = ToBytes::to_ne_bytes(&0x12345678u32);
/// assert_eq!(bytes, expected)
/// ```
fn to_ne_bytes(&self) -> Self::Bytes {
#[cfg(target_endian = "big")]
let bytes = self.to_be_bytes();
#[cfg(target_endian = "little")]
let bytes = self.to_le_bytes();
bytes
}
}
pub trait FromBytes: Sized {
type Bytes: NumBytes + ?Sized;
/// Create a number from its representation as a byte array in big endian.
///
/// # Examples
///
/// ```
/// use num_traits::FromBytes;
///
/// let value: u32 = FromBytes::from_be_bytes(&[0x12, 0x34, 0x56, 0x78]);
/// assert_eq!(value, 0x12345678);
/// ```
fn from_be_bytes(bytes: &Self::Bytes) -> Self;
/// Create a number from its representation as a byte array in little endian.
///
/// # Examples
///
/// ```
/// use num_traits::FromBytes;
///
/// let value: u32 = FromBytes::from_le_bytes(&[0x78, 0x56, 0x34, 0x12]);
/// assert_eq!(value, 0x12345678);
/// ```
fn from_le_bytes(bytes: &Self::Bytes) -> Self;
/// Create a number from its memory representation as a byte array in native endianness.
///
/// As the target platform's native endianness is used,
/// portable code likely wants to use [`from_be_bytes`] or [`from_le_bytes`], as appropriate instead.
///
/// [`from_be_bytes`]: #method.from_be_bytes
/// [`from_le_bytes`]: #method.from_le_bytes
///
/// # Examples
///
/// ```
/// use num_traits::FromBytes;
///
/// #[cfg(target_endian = "big")]
/// let bytes = [0x12, 0x34, 0x56, 0x78];
///
/// #[cfg(target_endian = "little")]
/// let bytes = [0x78, 0x56, 0x34, 0x12];
///
/// let value: u32 = FromBytes::from_ne_bytes(&bytes);
/// assert_eq!(value, 0x12345678)
/// ```
fn from_ne_bytes(bytes: &Self::Bytes) -> Self {
#[cfg(target_endian = "big")]
let this = Self::from_be_bytes(bytes);
#[cfg(target_endian = "little")]
let this = Self::from_le_bytes(bytes);
this
}
}
macro_rules! float_to_from_bytes_impl {
($T:ty, $L:expr) => {
#[cfg(has_float_to_from_bytes)]
impl ToBytes for $T {
type Bytes = [u8; $L];
#[inline]
fn to_be_bytes(&self) -> Self::Bytes {
<$T>::to_be_bytes(*self)
}
#[inline]
fn to_le_bytes(&self) -> Self::Bytes {
<$T>::to_le_bytes(*self)
}
#[inline]
fn to_ne_bytes(&self) -> Self::Bytes {
<$T>::to_ne_bytes(*self)
}
}
#[cfg(has_float_to_from_bytes)]
impl FromBytes for $T {
type Bytes = [u8; $L];
#[inline]
fn from_be_bytes(bytes: &Self::Bytes) -> Self {
<$T>::from_be_bytes(*bytes)
}
#[inline]
fn from_le_bytes(bytes: &Self::Bytes) -> Self {
<$T>::from_le_bytes(*bytes)
}
#[inline]
fn from_ne_bytes(bytes: &Self::Bytes) -> Self {
<$T>::from_ne_bytes(*bytes)
}
}
#[cfg(not(has_float_to_from_bytes))]
impl ToBytes for $T {
type Bytes = [u8; $L];
#[inline]
fn to_be_bytes(&self) -> Self::Bytes {
ToBytes::to_be_bytes(&self.to_bits())
}
#[inline]
fn to_le_bytes(&self) -> Self::Bytes {
ToBytes::to_le_bytes(&self.to_bits())
}
#[inline]
fn to_ne_bytes(&self) -> Self::Bytes {
ToBytes::to_ne_bytes(&self.to_bits())
}
}
#[cfg(not(has_float_to_from_bytes))]
impl FromBytes for $T {
type Bytes = [u8; $L];
#[inline]
fn from_be_bytes(bytes: &Self::Bytes) -> Self {
Self::from_bits(FromBytes::from_be_bytes(bytes))
}
#[inline]
fn from_le_bytes(bytes: &Self::Bytes) -> Self {
Self::from_bits(FromBytes::from_le_bytes(bytes))
}
#[inline]
fn from_ne_bytes(bytes: &Self::Bytes) -> Self {
Self::from_bits(FromBytes::from_ne_bytes(bytes))
}
}
};
}
macro_rules! int_to_from_bytes_impl {
($T:ty, $L:expr) => {
#[cfg(has_int_to_from_bytes)]
impl ToBytes for $T {
type Bytes = [u8; $L];
#[inline]
fn to_be_bytes(&self) -> Self::Bytes {
<$T>::to_be_bytes(*self)
}
#[inline]
fn to_le_bytes(&self) -> Self::Bytes {
<$T>::to_le_bytes(*self)
}
#[inline]
fn to_ne_bytes(&self) -> Self::Bytes {
<$T>::to_ne_bytes(*self)
}
}
#[cfg(has_int_to_from_bytes)]
impl FromBytes for $T {
type Bytes = [u8; $L];
#[inline]
fn from_be_bytes(bytes: &Self::Bytes) -> Self {
<$T>::from_be_bytes(*bytes)
}
#[inline]
fn from_le_bytes(bytes: &Self::Bytes) -> Self {
<$T>::from_le_bytes(*bytes)
}
#[inline]
fn from_ne_bytes(bytes: &Self::Bytes) -> Self {
<$T>::from_ne_bytes(*bytes)
}
}
#[cfg(not(has_int_to_from_bytes))]
impl ToBytes for $T {
type Bytes = [u8; $L];
#[inline]
fn to_be_bytes(&self) -> Self::Bytes {
<$T as ToBytes>::to_ne_bytes(&<$T>::to_be(*self))
}
#[inline]
fn to_le_bytes(&self) -> Self::Bytes {
<$T as ToBytes>::to_ne_bytes(&<$T>::to_le(*self))
}
#[inline]
fn to_ne_bytes(&self) -> Self::Bytes {
unsafe { transmute(*self) }
}
}
#[cfg(not(has_int_to_from_bytes))]
impl FromBytes for $T {
type Bytes = [u8; $L];
#[inline]
fn from_be_bytes(bytes: &Self::Bytes) -> Self {
Self::from_be(<Self as FromBytes>::from_ne_bytes(bytes))
}
#[inline]
fn from_le_bytes(bytes: &Self::Bytes) -> Self {
Self::from_le(<Self as FromBytes>::from_ne_bytes(bytes))
}
#[inline]
fn from_ne_bytes(bytes: &Self::Bytes) -> Self {
unsafe { transmute(*bytes) }
}
}
};
}
int_to_from_bytes_impl!(u8, 1);
int_to_from_bytes_impl!(u16, 2);
int_to_from_bytes_impl!(u32, 4);
int_to_from_bytes_impl!(u64, 8);
int_to_from_bytes_impl!(u128, 16);
#[cfg(target_pointer_width = "64")]
int_to_from_bytes_impl!(usize, 8);
#[cfg(target_pointer_width = "32")]
int_to_from_bytes_impl!(usize, 4);
int_to_from_bytes_impl!(i8, 1);
int_to_from_bytes_impl!(i16, 2);
int_to_from_bytes_impl!(i32, 4);
int_to_from_bytes_impl!(i64, 8);
int_to_from_bytes_impl!(i128, 16);
#[cfg(target_pointer_width = "64")]
int_to_from_bytes_impl!(isize, 8);
#[cfg(target_pointer_width = "32")]
int_to_from_bytes_impl!(isize, 4);
float_to_from_bytes_impl!(f32, 4);
float_to_from_bytes_impl!(f64, 8);
#[cfg(test)]
mod tests {
use super::*;
macro_rules! check_to_from_bytes {
($( $ty:ty )+) => {$({
let n = 1;
let be = <$ty as ToBytes>::to_be_bytes(&n);
let le = <$ty as ToBytes>::to_le_bytes(&n);
let ne = <$ty as ToBytes>::to_ne_bytes(&n);
assert_eq!(*be.last().unwrap(), 1);
assert_eq!(*le.first().unwrap(), 1);
if cfg!(target_endian = "big") {
assert_eq!(*ne.last().unwrap(), 1);
} else {
assert_eq!(*ne.first().unwrap(), 1);
}
assert_eq!(<$ty as FromBytes>::from_be_bytes(&be), n);
assert_eq!(<$ty as FromBytes>::from_le_bytes(&le), n);
if cfg!(target_endian = "big") {
assert_eq!(<$ty as FromBytes>::from_ne_bytes(&be), n);
} else {
assert_eq!(<$ty as FromBytes>::from_ne_bytes(&le), n);
}
})+}
}
#[test]
fn convert_between_int_and_bytes() {
check_to_from_bytes!(u8 u16 u32 u64 u128 usize);
check_to_from_bytes!(i8 i16 i32 i64 i128 isize);
}
#[test]
fn convert_between_float_and_bytes() {
macro_rules! check_to_from_bytes {
($( $ty:ty )+) => {$(
let n: $ty = 3.14;
let be = <$ty as ToBytes>::to_be_bytes(&n);
let le = <$ty as ToBytes>::to_le_bytes(&n);
let ne = <$ty as ToBytes>::to_ne_bytes(&n);
assert_eq!(<$ty as FromBytes>::from_be_bytes(&be), n);
assert_eq!(<$ty as FromBytes>::from_le_bytes(&le), n);
if cfg!(target_endian = "big") {
assert_eq!(ne, be);
assert_eq!(<$ty as FromBytes>::from_ne_bytes(&be), n);
} else {
assert_eq!(ne, le);
assert_eq!(<$ty as FromBytes>::from_ne_bytes(&le), n);
}
)+}
}
check_to_from_bytes!(f32 f64);
}
}

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use core::ops::{Add, Div, Mul, Rem, Shl, Shr, Sub};
/// Performs addition that returns `None` instead of wrapping around on
/// overflow.
pub trait CheckedAdd: Sized + Add<Self, Output = Self> {
/// Adds two numbers, checking for overflow. If overflow happens, `None` is
/// returned.
fn checked_add(&self, v: &Self) -> Option<Self>;
}
macro_rules! checked_impl {
($trait_name:ident, $method:ident, $t:ty) => {
impl $trait_name for $t {
#[inline]
fn $method(&self, v: &$t) -> Option<$t> {
<$t>::$method(*self, *v)
}
}
};
}
checked_impl!(CheckedAdd, checked_add, u8);
checked_impl!(CheckedAdd, checked_add, u16);
checked_impl!(CheckedAdd, checked_add, u32);
checked_impl!(CheckedAdd, checked_add, u64);
checked_impl!(CheckedAdd, checked_add, usize);
checked_impl!(CheckedAdd, checked_add, u128);
checked_impl!(CheckedAdd, checked_add, i8);
checked_impl!(CheckedAdd, checked_add, i16);
checked_impl!(CheckedAdd, checked_add, i32);
checked_impl!(CheckedAdd, checked_add, i64);
checked_impl!(CheckedAdd, checked_add, isize);
checked_impl!(CheckedAdd, checked_add, i128);
/// Performs subtraction that returns `None` instead of wrapping around on underflow.
pub trait CheckedSub: Sized + Sub<Self, Output = Self> {
/// Subtracts two numbers, checking for underflow. If underflow happens,
/// `None` is returned.
fn checked_sub(&self, v: &Self) -> Option<Self>;
}
checked_impl!(CheckedSub, checked_sub, u8);
checked_impl!(CheckedSub, checked_sub, u16);
checked_impl!(CheckedSub, checked_sub, u32);
checked_impl!(CheckedSub, checked_sub, u64);
checked_impl!(CheckedSub, checked_sub, usize);
checked_impl!(CheckedSub, checked_sub, u128);
checked_impl!(CheckedSub, checked_sub, i8);
checked_impl!(CheckedSub, checked_sub, i16);
checked_impl!(CheckedSub, checked_sub, i32);
checked_impl!(CheckedSub, checked_sub, i64);
checked_impl!(CheckedSub, checked_sub, isize);
checked_impl!(CheckedSub, checked_sub, i128);
/// Performs multiplication that returns `None` instead of wrapping around on underflow or
/// overflow.
pub trait CheckedMul: Sized + Mul<Self, Output = Self> {
/// Multiplies two numbers, checking for underflow or overflow. If underflow
/// or overflow happens, `None` is returned.
fn checked_mul(&self, v: &Self) -> Option<Self>;
}
checked_impl!(CheckedMul, checked_mul, u8);
checked_impl!(CheckedMul, checked_mul, u16);
checked_impl!(CheckedMul, checked_mul, u32);
checked_impl!(CheckedMul, checked_mul, u64);
checked_impl!(CheckedMul, checked_mul, usize);
checked_impl!(CheckedMul, checked_mul, u128);
checked_impl!(CheckedMul, checked_mul, i8);
checked_impl!(CheckedMul, checked_mul, i16);
checked_impl!(CheckedMul, checked_mul, i32);
checked_impl!(CheckedMul, checked_mul, i64);
checked_impl!(CheckedMul, checked_mul, isize);
checked_impl!(CheckedMul, checked_mul, i128);
/// Performs division that returns `None` instead of panicking on division by zero and instead of
/// wrapping around on underflow and overflow.
pub trait CheckedDiv: Sized + Div<Self, Output = Self> {
/// Divides two numbers, checking for underflow, overflow and division by
/// zero. If any of that happens, `None` is returned.
fn checked_div(&self, v: &Self) -> Option<Self>;
}
checked_impl!(CheckedDiv, checked_div, u8);
checked_impl!(CheckedDiv, checked_div, u16);
checked_impl!(CheckedDiv, checked_div, u32);
checked_impl!(CheckedDiv, checked_div, u64);
checked_impl!(CheckedDiv, checked_div, usize);
checked_impl!(CheckedDiv, checked_div, u128);
checked_impl!(CheckedDiv, checked_div, i8);
checked_impl!(CheckedDiv, checked_div, i16);
checked_impl!(CheckedDiv, checked_div, i32);
checked_impl!(CheckedDiv, checked_div, i64);
checked_impl!(CheckedDiv, checked_div, isize);
checked_impl!(CheckedDiv, checked_div, i128);
/// Performs an integral remainder that returns `None` instead of panicking on division by zero and
/// instead of wrapping around on underflow and overflow.
pub trait CheckedRem: Sized + Rem<Self, Output = Self> {
/// Finds the remainder of dividing two numbers, checking for underflow, overflow and division
/// by zero. If any of that happens, `None` is returned.
///
/// # Examples
///
/// ```
/// use num_traits::CheckedRem;
/// use std::i32::MIN;
///
/// assert_eq!(CheckedRem::checked_rem(&10, &7), Some(3));
/// assert_eq!(CheckedRem::checked_rem(&10, &-7), Some(3));
/// assert_eq!(CheckedRem::checked_rem(&-10, &7), Some(-3));
/// assert_eq!(CheckedRem::checked_rem(&-10, &-7), Some(-3));
///
/// assert_eq!(CheckedRem::checked_rem(&10, &0), None);
///
/// assert_eq!(CheckedRem::checked_rem(&MIN, &1), Some(0));
/// assert_eq!(CheckedRem::checked_rem(&MIN, &-1), None);
/// ```
fn checked_rem(&self, v: &Self) -> Option<Self>;
}
checked_impl!(CheckedRem, checked_rem, u8);
checked_impl!(CheckedRem, checked_rem, u16);
checked_impl!(CheckedRem, checked_rem, u32);
checked_impl!(CheckedRem, checked_rem, u64);
checked_impl!(CheckedRem, checked_rem, usize);
checked_impl!(CheckedRem, checked_rem, u128);
checked_impl!(CheckedRem, checked_rem, i8);
checked_impl!(CheckedRem, checked_rem, i16);
checked_impl!(CheckedRem, checked_rem, i32);
checked_impl!(CheckedRem, checked_rem, i64);
checked_impl!(CheckedRem, checked_rem, isize);
checked_impl!(CheckedRem, checked_rem, i128);
macro_rules! checked_impl_unary {
($trait_name:ident, $method:ident, $t:ty) => {
impl $trait_name for $t {
#[inline]
fn $method(&self) -> Option<$t> {
<$t>::$method(*self)
}
}
};
}
/// Performs negation that returns `None` if the result can't be represented.
pub trait CheckedNeg: Sized {
/// Negates a number, returning `None` for results that can't be represented, like signed `MIN`
/// values that can't be positive, or non-zero unsigned values that can't be negative.
///
/// # Examples
///
/// ```
/// use num_traits::CheckedNeg;
/// use std::i32::MIN;
///
/// assert_eq!(CheckedNeg::checked_neg(&1_i32), Some(-1));
/// assert_eq!(CheckedNeg::checked_neg(&-1_i32), Some(1));
/// assert_eq!(CheckedNeg::checked_neg(&MIN), None);
///
/// assert_eq!(CheckedNeg::checked_neg(&0_u32), Some(0));
/// assert_eq!(CheckedNeg::checked_neg(&1_u32), None);
/// ```
fn checked_neg(&self) -> Option<Self>;
}
checked_impl_unary!(CheckedNeg, checked_neg, u8);
checked_impl_unary!(CheckedNeg, checked_neg, u16);
checked_impl_unary!(CheckedNeg, checked_neg, u32);
checked_impl_unary!(CheckedNeg, checked_neg, u64);
checked_impl_unary!(CheckedNeg, checked_neg, usize);
checked_impl_unary!(CheckedNeg, checked_neg, u128);
checked_impl_unary!(CheckedNeg, checked_neg, i8);
checked_impl_unary!(CheckedNeg, checked_neg, i16);
checked_impl_unary!(CheckedNeg, checked_neg, i32);
checked_impl_unary!(CheckedNeg, checked_neg, i64);
checked_impl_unary!(CheckedNeg, checked_neg, isize);
checked_impl_unary!(CheckedNeg, checked_neg, i128);
/// Performs a left shift that returns `None` on shifts larger than
/// or equal to the type width.
pub trait CheckedShl: Sized + Shl<u32, Output = Self> {
/// Checked shift left. Computes `self << rhs`, returning `None`
/// if `rhs` is larger than or equal to the number of bits in `self`.
///
/// ```
/// use num_traits::CheckedShl;
///
/// let x: u16 = 0x0001;
///
/// assert_eq!(CheckedShl::checked_shl(&x, 0), Some(0x0001));
/// assert_eq!(CheckedShl::checked_shl(&x, 1), Some(0x0002));
/// assert_eq!(CheckedShl::checked_shl(&x, 15), Some(0x8000));
/// assert_eq!(CheckedShl::checked_shl(&x, 16), None);
/// ```
fn checked_shl(&self, rhs: u32) -> Option<Self>;
}
macro_rules! checked_shift_impl {
($trait_name:ident, $method:ident, $t:ty) => {
impl $trait_name for $t {
#[inline]
fn $method(&self, rhs: u32) -> Option<$t> {
<$t>::$method(*self, rhs)
}
}
};
}
checked_shift_impl!(CheckedShl, checked_shl, u8);
checked_shift_impl!(CheckedShl, checked_shl, u16);
checked_shift_impl!(CheckedShl, checked_shl, u32);
checked_shift_impl!(CheckedShl, checked_shl, u64);
checked_shift_impl!(CheckedShl, checked_shl, usize);
checked_shift_impl!(CheckedShl, checked_shl, u128);
checked_shift_impl!(CheckedShl, checked_shl, i8);
checked_shift_impl!(CheckedShl, checked_shl, i16);
checked_shift_impl!(CheckedShl, checked_shl, i32);
checked_shift_impl!(CheckedShl, checked_shl, i64);
checked_shift_impl!(CheckedShl, checked_shl, isize);
checked_shift_impl!(CheckedShl, checked_shl, i128);
/// Performs a right shift that returns `None` on shifts larger than
/// or equal to the type width.
pub trait CheckedShr: Sized + Shr<u32, Output = Self> {
/// Checked shift right. Computes `self >> rhs`, returning `None`
/// if `rhs` is larger than or equal to the number of bits in `self`.
///
/// ```
/// use num_traits::CheckedShr;
///
/// let x: u16 = 0x8000;
///
/// assert_eq!(CheckedShr::checked_shr(&x, 0), Some(0x8000));
/// assert_eq!(CheckedShr::checked_shr(&x, 1), Some(0x4000));
/// assert_eq!(CheckedShr::checked_shr(&x, 15), Some(0x0001));
/// assert_eq!(CheckedShr::checked_shr(&x, 16), None);
/// ```
fn checked_shr(&self, rhs: u32) -> Option<Self>;
}
checked_shift_impl!(CheckedShr, checked_shr, u8);
checked_shift_impl!(CheckedShr, checked_shr, u16);
checked_shift_impl!(CheckedShr, checked_shr, u32);
checked_shift_impl!(CheckedShr, checked_shr, u64);
checked_shift_impl!(CheckedShr, checked_shr, usize);
checked_shift_impl!(CheckedShr, checked_shr, u128);
checked_shift_impl!(CheckedShr, checked_shr, i8);
checked_shift_impl!(CheckedShr, checked_shr, i16);
checked_shift_impl!(CheckedShr, checked_shr, i32);
checked_shift_impl!(CheckedShr, checked_shr, i64);
checked_shift_impl!(CheckedShr, checked_shr, isize);
checked_shift_impl!(CheckedShr, checked_shr, i128);

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vendor/num-traits/src/ops/euclid.rs vendored Normal file
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use core::ops::{Div, Rem};
pub trait Euclid: Sized + Div<Self, Output = Self> + Rem<Self, Output = Self> {
/// Calculates Euclidean division, the matching method for `rem_euclid`.
///
/// This computes the integer `n` such that
/// `self = n * v + self.rem_euclid(v)`.
/// In other words, the result is `self / v` rounded to the integer `n`
/// such that `self >= n * v`.
///
/// # Examples
///
/// ```
/// use num_traits::Euclid;
///
/// let a: i32 = 7;
/// let b: i32 = 4;
/// assert_eq!(Euclid::div_euclid(&a, &b), 1); // 7 > 4 * 1
/// assert_eq!(Euclid::div_euclid(&-a, &b), -2); // -7 >= 4 * -2
/// assert_eq!(Euclid::div_euclid(&a, &-b), -1); // 7 >= -4 * -1
/// assert_eq!(Euclid::div_euclid(&-a, &-b), 2); // -7 >= -4 * 2
/// ```
fn div_euclid(&self, v: &Self) -> Self;
/// Calculates the least nonnegative remainder of `self (mod v)`.
///
/// In particular, the return value `r` satisfies `0.0 <= r < v.abs()` in
/// most cases. However, due to a floating point round-off error it can
/// result in `r == v.abs()`, violating the mathematical definition, if
/// `self` is much smaller than `v.abs()` in magnitude and `self < 0.0`.
/// This result is not an element of the function's codomain, but it is the
/// closest floating point number in the real numbers and thus fulfills the
/// property `self == self.div_euclid(v) * v + self.rem_euclid(v)`
/// approximatively.
///
/// # Examples
///
/// ```
/// use num_traits::Euclid;
///
/// let a: i32 = 7;
/// let b: i32 = 4;
/// assert_eq!(Euclid::rem_euclid(&a, &b), 3);
/// assert_eq!(Euclid::rem_euclid(&-a, &b), 1);
/// assert_eq!(Euclid::rem_euclid(&a, &-b), 3);
/// assert_eq!(Euclid::rem_euclid(&-a, &-b), 1);
/// ```
fn rem_euclid(&self, v: &Self) -> Self;
}
macro_rules! euclid_forward_impl {
($($t:ty)*) => {$(
#[cfg(has_div_euclid)]
impl Euclid for $t {
#[inline]
fn div_euclid(&self, v: &$t) -> Self {
<$t>::div_euclid(*self, *v)
}
#[inline]
fn rem_euclid(&self, v: &$t) -> Self {
<$t>::rem_euclid(*self, *v)
}
}
)*}
}
macro_rules! euclid_int_impl {
($($t:ty)*) => {$(
euclid_forward_impl!($t);
#[cfg(not(has_div_euclid))]
impl Euclid for $t {
#[inline]
fn div_euclid(&self, v: &$t) -> Self {
let q = self / v;
if self % v < 0 {
return if *v > 0 { q - 1 } else { q + 1 }
}
q
}
#[inline]
fn rem_euclid(&self, v: &$t) -> Self {
let r = self % v;
if r < 0 {
if *v < 0 {
r - v
} else {
r + v
}
} else {
r
}
}
}
)*}
}
macro_rules! euclid_uint_impl {
($($t:ty)*) => {$(
euclid_forward_impl!($t);
#[cfg(not(has_div_euclid))]
impl Euclid for $t {
#[inline]
fn div_euclid(&self, v: &$t) -> Self {
self / v
}
#[inline]
fn rem_euclid(&self, v: &$t) -> Self {
self % v
}
}
)*}
}
euclid_int_impl!(isize i8 i16 i32 i64 i128);
euclid_uint_impl!(usize u8 u16 u32 u64 u128);
#[cfg(all(has_div_euclid, feature = "std"))]
euclid_forward_impl!(f32 f64);
#[cfg(not(all(has_div_euclid, feature = "std")))]
impl Euclid for f32 {
#[inline]
fn div_euclid(&self, v: &f32) -> f32 {
let q = <f32 as crate::float::FloatCore>::trunc(self / v);
if self % v < 0.0 {
return if *v > 0.0 { q - 1.0 } else { q + 1.0 };
}
q
}
#[inline]
fn rem_euclid(&self, v: &f32) -> f32 {
let r = self % v;
if r < 0.0 {
r + <f32 as crate::float::FloatCore>::abs(*v)
} else {
r
}
}
}
#[cfg(not(all(has_div_euclid, feature = "std")))]
impl Euclid for f64 {
#[inline]
fn div_euclid(&self, v: &f64) -> f64 {
let q = <f64 as crate::float::FloatCore>::trunc(self / v);
if self % v < 0.0 {
return if *v > 0.0 { q - 1.0 } else { q + 1.0 };
}
q
}
#[inline]
fn rem_euclid(&self, v: &f64) -> f64 {
let r = self % v;
if r < 0.0 {
r + <f64 as crate::float::FloatCore>::abs(*v)
} else {
r
}
}
}
pub trait CheckedEuclid: Euclid {
/// Performs euclid division that returns `None` instead of panicking on division by zero
/// and instead of wrapping around on underflow and overflow.
fn checked_div_euclid(&self, v: &Self) -> Option<Self>;
/// Finds the euclid remainder of dividing two numbers, checking for underflow, overflow and
/// division by zero. If any of that happens, `None` is returned.
fn checked_rem_euclid(&self, v: &Self) -> Option<Self>;
}
macro_rules! checked_euclid_forward_impl {
($($t:ty)*) => {$(
#[cfg(has_div_euclid)]
impl CheckedEuclid for $t {
#[inline]
fn checked_div_euclid(&self, v: &$t) -> Option<Self> {
<$t>::checked_div_euclid(*self, *v)
}
#[inline]
fn checked_rem_euclid(&self, v: &$t) -> Option<Self> {
<$t>::checked_rem_euclid(*self, *v)
}
}
)*}
}
macro_rules! checked_euclid_int_impl {
($($t:ty)*) => {$(
checked_euclid_forward_impl!($t);
#[cfg(not(has_div_euclid))]
impl CheckedEuclid for $t {
#[inline]
fn checked_div_euclid(&self, v: &$t) -> Option<$t> {
if *v == 0 || (*self == Self::min_value() && *v == -1) {
None
} else {
Some(Euclid::div_euclid(self, v))
}
}
#[inline]
fn checked_rem_euclid(&self, v: &$t) -> Option<$t> {
if *v == 0 || (*self == Self::min_value() && *v == -1) {
None
} else {
Some(Euclid::rem_euclid(self, v))
}
}
}
)*}
}
macro_rules! checked_euclid_uint_impl {
($($t:ty)*) => {$(
checked_euclid_forward_impl!($t);
#[cfg(not(has_div_euclid))]
impl CheckedEuclid for $t {
#[inline]
fn checked_div_euclid(&self, v: &$t) -> Option<$t> {
if *v == 0 {
None
} else {
Some(Euclid::div_euclid(self, v))
}
}
#[inline]
fn checked_rem_euclid(&self, v: &$t) -> Option<$t> {
if *v == 0 {
None
} else {
Some(Euclid::rem_euclid(self, v))
}
}
}
)*}
}
checked_euclid_int_impl!(isize i8 i16 i32 i64 i128);
checked_euclid_uint_impl!(usize u8 u16 u32 u64 u128);
#[cfg(test)]
mod tests {
use super::*;
#[test]
fn euclid_unsigned() {
macro_rules! test_euclid {
($($t:ident)+) => {
$(
{
let x: $t = 10;
let y: $t = 3;
assert_eq!(Euclid::div_euclid(&x, &y), 3);
assert_eq!(Euclid::rem_euclid(&x, &y), 1);
}
)+
};
}
test_euclid!(usize u8 u16 u32 u64);
}
#[test]
fn euclid_signed() {
macro_rules! test_euclid {
($($t:ident)+) => {
$(
{
let x: $t = 10;
let y: $t = -3;
assert_eq!(Euclid::div_euclid(&x, &y), -3);
assert_eq!(Euclid::div_euclid(&-x, &y), 4);
assert_eq!(Euclid::rem_euclid(&x, &y), 1);
assert_eq!(Euclid::rem_euclid(&-x, &y), 2);
let x: $t = $t::min_value() + 1;
let y: $t = -1;
assert_eq!(Euclid::div_euclid(&x, &y), $t::max_value());
}
)+
};
}
test_euclid!(isize i8 i16 i32 i64 i128);
}
#[test]
fn euclid_float() {
macro_rules! test_euclid {
($($t:ident)+) => {
$(
{
let x: $t = 12.1;
let y: $t = 3.2;
assert!(Euclid::div_euclid(&x, &y) * y + Euclid::rem_euclid(&x, &y) - x
<= 46.4 * <$t as crate::float::FloatCore>::epsilon());
assert!(Euclid::div_euclid(&x, &-y) * -y + Euclid::rem_euclid(&x, &-y) - x
<= 46.4 * <$t as crate::float::FloatCore>::epsilon());
assert!(Euclid::div_euclid(&-x, &y) * y + Euclid::rem_euclid(&-x, &y) + x
<= 46.4 * <$t as crate::float::FloatCore>::epsilon());
assert!(Euclid::div_euclid(&-x, &-y) * -y + Euclid::rem_euclid(&-x, &-y) + x
<= 46.4 * <$t as crate::float::FloatCore>::epsilon());
}
)+
};
}
test_euclid!(f32 f64);
}
#[test]
fn euclid_checked() {
macro_rules! test_euclid_checked {
($($t:ident)+) => {
$(
{
assert_eq!(CheckedEuclid::checked_div_euclid(&$t::min_value(), &-1), None);
assert_eq!(CheckedEuclid::checked_rem_euclid(&$t::min_value(), &-1), None);
assert_eq!(CheckedEuclid::checked_div_euclid(&1, &0), None);
assert_eq!(CheckedEuclid::checked_rem_euclid(&1, &0), None);
}
)+
};
}
test_euclid_checked!(isize i8 i16 i32 i64 i128);
}
}

47
vendor/num-traits/src/ops/inv.rs vendored Normal file
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/// Unary operator for retrieving the multiplicative inverse, or reciprocal, of a value.
pub trait Inv {
/// The result after applying the operator.
type Output;
/// Returns the multiplicative inverse of `self`.
///
/// # Examples
///
/// ```
/// use std::f64::INFINITY;
/// use num_traits::Inv;
///
/// assert_eq!(7.0.inv() * 7.0, 1.0);
/// assert_eq!((-0.0).inv(), -INFINITY);
/// ```
fn inv(self) -> Self::Output;
}
impl Inv for f32 {
type Output = f32;
#[inline]
fn inv(self) -> f32 {
1.0 / self
}
}
impl Inv for f64 {
type Output = f64;
#[inline]
fn inv(self) -> f64 {
1.0 / self
}
}
impl<'a> Inv for &'a f32 {
type Output = f32;
#[inline]
fn inv(self) -> f32 {
1.0 / *self
}
}
impl<'a> Inv for &'a f64 {
type Output = f64;
#[inline]
fn inv(self) -> f64 {
1.0 / *self
}
}

8
vendor/num-traits/src/ops/mod.rs vendored Normal file
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@ -0,0 +1,8 @@
pub mod bytes;
pub mod checked;
pub mod euclid;
pub mod inv;
pub mod mul_add;
pub mod overflowing;
pub mod saturating;
pub mod wrapping;

149
vendor/num-traits/src/ops/mul_add.rs vendored Normal file
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/// Fused multiply-add. Computes `(self * a) + b` with only one rounding
/// error, yielding a more accurate result than an unfused multiply-add.
///
/// Using `mul_add` can be more performant than an unfused multiply-add if
/// the target architecture has a dedicated `fma` CPU instruction.
///
/// Note that `A` and `B` are `Self` by default, but this is not mandatory.
///
/// # Example
///
/// ```
/// use std::f32;
///
/// let m = 10.0_f32;
/// let x = 4.0_f32;
/// let b = 60.0_f32;
///
/// // 100.0
/// let abs_difference = (m.mul_add(x, b) - (m*x + b)).abs();
///
/// assert!(abs_difference <= 100.0 * f32::EPSILON);
/// ```
pub trait MulAdd<A = Self, B = Self> {
/// The resulting type after applying the fused multiply-add.
type Output;
/// Performs the fused multiply-add operation `(self * a) + b`
fn mul_add(self, a: A, b: B) -> Self::Output;
}
/// The fused multiply-add assignment operation `*self = (*self * a) + b`
pub trait MulAddAssign<A = Self, B = Self> {
/// Performs the fused multiply-add assignment operation `*self = (*self * a) + b`
fn mul_add_assign(&mut self, a: A, b: B);
}
#[cfg(any(feature = "std", feature = "libm"))]
impl MulAdd<f32, f32> for f32 {
type Output = Self;
#[inline]
fn mul_add(self, a: Self, b: Self) -> Self::Output {
<Self as crate::Float>::mul_add(self, a, b)
}
}
#[cfg(any(feature = "std", feature = "libm"))]
impl MulAdd<f64, f64> for f64 {
type Output = Self;
#[inline]
fn mul_add(self, a: Self, b: Self) -> Self::Output {
<Self as crate::Float>::mul_add(self, a, b)
}
}
macro_rules! mul_add_impl {
($trait_name:ident for $($t:ty)*) => {$(
impl $trait_name for $t {
type Output = Self;
#[inline]
fn mul_add(self, a: Self, b: Self) -> Self::Output {
(self * a) + b
}
}
)*}
}
mul_add_impl!(MulAdd for isize i8 i16 i32 i64 i128);
mul_add_impl!(MulAdd for usize u8 u16 u32 u64 u128);
#[cfg(any(feature = "std", feature = "libm"))]
impl MulAddAssign<f32, f32> for f32 {
#[inline]
fn mul_add_assign(&mut self, a: Self, b: Self) {
*self = <Self as crate::Float>::mul_add(*self, a, b)
}
}
#[cfg(any(feature = "std", feature = "libm"))]
impl MulAddAssign<f64, f64> for f64 {
#[inline]
fn mul_add_assign(&mut self, a: Self, b: Self) {
*self = <Self as crate::Float>::mul_add(*self, a, b)
}
}
macro_rules! mul_add_assign_impl {
($trait_name:ident for $($t:ty)*) => {$(
impl $trait_name for $t {
#[inline]
fn mul_add_assign(&mut self, a: Self, b: Self) {
*self = (*self * a) + b
}
}
)*}
}
mul_add_assign_impl!(MulAddAssign for isize i8 i16 i32 i64 i128);
mul_add_assign_impl!(MulAddAssign for usize u8 u16 u32 u64 u128);
#[cfg(test)]
mod tests {
use super::*;
#[test]
fn mul_add_integer() {
macro_rules! test_mul_add {
($($t:ident)+) => {
$(
{
let m: $t = 2;
let x: $t = 3;
let b: $t = 4;
assert_eq!(MulAdd::mul_add(m, x, b), (m*x + b));
}
)+
};
}
test_mul_add!(usize u8 u16 u32 u64 isize i8 i16 i32 i64);
}
#[test]
#[cfg(feature = "std")]
fn mul_add_float() {
macro_rules! test_mul_add {
($($t:ident)+) => {
$(
{
use core::$t;
let m: $t = 12.0;
let x: $t = 3.4;
let b: $t = 5.6;
let abs_difference = (MulAdd::mul_add(m, x, b) - (m*x + b)).abs();
assert!(abs_difference <= 46.4 * $t::EPSILON);
}
)+
};
}
test_mul_add!(f32 f64);
}
}

96
vendor/num-traits/src/ops/overflowing.rs vendored Normal file
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@ -0,0 +1,96 @@
use core::ops::{Add, Mul, Sub};
use core::{i128, i16, i32, i64, i8, isize};
use core::{u128, u16, u32, u64, u8, usize};
macro_rules! overflowing_impl {
($trait_name:ident, $method:ident, $t:ty) => {
impl $trait_name for $t {
#[inline]
fn $method(&self, v: &Self) -> (Self, bool) {
<$t>::$method(*self, *v)
}
}
};
}
/// Performs addition with a flag for overflow.
pub trait OverflowingAdd: Sized + Add<Self, Output = Self> {
/// Returns a tuple of the sum along with a boolean indicating whether an arithmetic overflow would occur.
/// If an overflow would have occurred then the wrapped value is returned.
fn overflowing_add(&self, v: &Self) -> (Self, bool);
}
overflowing_impl!(OverflowingAdd, overflowing_add, u8);
overflowing_impl!(OverflowingAdd, overflowing_add, u16);
overflowing_impl!(OverflowingAdd, overflowing_add, u32);
overflowing_impl!(OverflowingAdd, overflowing_add, u64);
overflowing_impl!(OverflowingAdd, overflowing_add, usize);
overflowing_impl!(OverflowingAdd, overflowing_add, u128);
overflowing_impl!(OverflowingAdd, overflowing_add, i8);
overflowing_impl!(OverflowingAdd, overflowing_add, i16);
overflowing_impl!(OverflowingAdd, overflowing_add, i32);
overflowing_impl!(OverflowingAdd, overflowing_add, i64);
overflowing_impl!(OverflowingAdd, overflowing_add, isize);
overflowing_impl!(OverflowingAdd, overflowing_add, i128);
/// Performs substraction with a flag for overflow.
pub trait OverflowingSub: Sized + Sub<Self, Output = Self> {
/// Returns a tuple of the difference along with a boolean indicating whether an arithmetic overflow would occur.
/// If an overflow would have occurred then the wrapped value is returned.
fn overflowing_sub(&self, v: &Self) -> (Self, bool);
}
overflowing_impl!(OverflowingSub, overflowing_sub, u8);
overflowing_impl!(OverflowingSub, overflowing_sub, u16);
overflowing_impl!(OverflowingSub, overflowing_sub, u32);
overflowing_impl!(OverflowingSub, overflowing_sub, u64);
overflowing_impl!(OverflowingSub, overflowing_sub, usize);
overflowing_impl!(OverflowingSub, overflowing_sub, u128);
overflowing_impl!(OverflowingSub, overflowing_sub, i8);
overflowing_impl!(OverflowingSub, overflowing_sub, i16);
overflowing_impl!(OverflowingSub, overflowing_sub, i32);
overflowing_impl!(OverflowingSub, overflowing_sub, i64);
overflowing_impl!(OverflowingSub, overflowing_sub, isize);
overflowing_impl!(OverflowingSub, overflowing_sub, i128);
/// Performs multiplication with a flag for overflow.
pub trait OverflowingMul: Sized + Mul<Self, Output = Self> {
/// Returns a tuple of the product along with a boolean indicating whether an arithmetic overflow would occur.
/// If an overflow would have occurred then the wrapped value is returned.
fn overflowing_mul(&self, v: &Self) -> (Self, bool);
}
overflowing_impl!(OverflowingMul, overflowing_mul, u8);
overflowing_impl!(OverflowingMul, overflowing_mul, u16);
overflowing_impl!(OverflowingMul, overflowing_mul, u32);
overflowing_impl!(OverflowingMul, overflowing_mul, u64);
overflowing_impl!(OverflowingMul, overflowing_mul, usize);
overflowing_impl!(OverflowingMul, overflowing_mul, u128);
overflowing_impl!(OverflowingMul, overflowing_mul, i8);
overflowing_impl!(OverflowingMul, overflowing_mul, i16);
overflowing_impl!(OverflowingMul, overflowing_mul, i32);
overflowing_impl!(OverflowingMul, overflowing_mul, i64);
overflowing_impl!(OverflowingMul, overflowing_mul, isize);
overflowing_impl!(OverflowingMul, overflowing_mul, i128);
#[test]
fn test_overflowing_traits() {
fn overflowing_add<T: OverflowingAdd>(a: T, b: T) -> (T, bool) {
a.overflowing_add(&b)
}
fn overflowing_sub<T: OverflowingSub>(a: T, b: T) -> (T, bool) {
a.overflowing_sub(&b)
}
fn overflowing_mul<T: OverflowingMul>(a: T, b: T) -> (T, bool) {
a.overflowing_mul(&b)
}
assert_eq!(overflowing_add(5i16, 2), (7, false));
assert_eq!(overflowing_add(i16::MAX, 1), (i16::MIN, true));
assert_eq!(overflowing_sub(5i16, 2), (3, false));
assert_eq!(overflowing_sub(i16::MIN, 1), (i16::MAX, true));
assert_eq!(overflowing_mul(5i16, 2), (10, false));
assert_eq!(overflowing_mul(1_000_000_000i32, 10), (1410065408, true));
}

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use core::ops::{Add, Mul, Sub};
/// Saturating math operations. Deprecated, use `SaturatingAdd`, `SaturatingSub` and
/// `SaturatingMul` instead.
pub trait Saturating {
/// Saturating addition operator.
/// Returns a+b, saturating at the numeric bounds instead of overflowing.
fn saturating_add(self, v: Self) -> Self;
/// Saturating subtraction operator.
/// Returns a-b, saturating at the numeric bounds instead of overflowing.
fn saturating_sub(self, v: Self) -> Self;
}
macro_rules! deprecated_saturating_impl {
($trait_name:ident for $($t:ty)*) => {$(
impl $trait_name for $t {
#[inline]
fn saturating_add(self, v: Self) -> Self {
Self::saturating_add(self, v)
}
#[inline]
fn saturating_sub(self, v: Self) -> Self {
Self::saturating_sub(self, v)
}
}
)*}
}
deprecated_saturating_impl!(Saturating for isize i8 i16 i32 i64 i128);
deprecated_saturating_impl!(Saturating for usize u8 u16 u32 u64 u128);
macro_rules! saturating_impl {
($trait_name:ident, $method:ident, $t:ty) => {
impl $trait_name for $t {
#[inline]
fn $method(&self, v: &Self) -> Self {
<$t>::$method(*self, *v)
}
}
};
}
/// Performs addition that saturates at the numeric bounds instead of overflowing.
pub trait SaturatingAdd: Sized + Add<Self, Output = Self> {
/// Saturating addition. Computes `self + other`, saturating at the relevant high or low boundary of
/// the type.
fn saturating_add(&self, v: &Self) -> Self;
}
saturating_impl!(SaturatingAdd, saturating_add, u8);
saturating_impl!(SaturatingAdd, saturating_add, u16);
saturating_impl!(SaturatingAdd, saturating_add, u32);
saturating_impl!(SaturatingAdd, saturating_add, u64);
saturating_impl!(SaturatingAdd, saturating_add, usize);
saturating_impl!(SaturatingAdd, saturating_add, u128);
saturating_impl!(SaturatingAdd, saturating_add, i8);
saturating_impl!(SaturatingAdd, saturating_add, i16);
saturating_impl!(SaturatingAdd, saturating_add, i32);
saturating_impl!(SaturatingAdd, saturating_add, i64);
saturating_impl!(SaturatingAdd, saturating_add, isize);
saturating_impl!(SaturatingAdd, saturating_add, i128);
/// Performs subtraction that saturates at the numeric bounds instead of overflowing.
pub trait SaturatingSub: Sized + Sub<Self, Output = Self> {
/// Saturating subtraction. Computes `self - other`, saturating at the relevant high or low boundary of
/// the type.
fn saturating_sub(&self, v: &Self) -> Self;
}
saturating_impl!(SaturatingSub, saturating_sub, u8);
saturating_impl!(SaturatingSub, saturating_sub, u16);
saturating_impl!(SaturatingSub, saturating_sub, u32);
saturating_impl!(SaturatingSub, saturating_sub, u64);
saturating_impl!(SaturatingSub, saturating_sub, usize);
saturating_impl!(SaturatingSub, saturating_sub, u128);
saturating_impl!(SaturatingSub, saturating_sub, i8);
saturating_impl!(SaturatingSub, saturating_sub, i16);
saturating_impl!(SaturatingSub, saturating_sub, i32);
saturating_impl!(SaturatingSub, saturating_sub, i64);
saturating_impl!(SaturatingSub, saturating_sub, isize);
saturating_impl!(SaturatingSub, saturating_sub, i128);
/// Performs multiplication that saturates at the numeric bounds instead of overflowing.
pub trait SaturatingMul: Sized + Mul<Self, Output = Self> {
/// Saturating multiplication. Computes `self * other`, saturating at the relevant high or low boundary of
/// the type.
fn saturating_mul(&self, v: &Self) -> Self;
}
saturating_impl!(SaturatingMul, saturating_mul, u8);
saturating_impl!(SaturatingMul, saturating_mul, u16);
saturating_impl!(SaturatingMul, saturating_mul, u32);
saturating_impl!(SaturatingMul, saturating_mul, u64);
saturating_impl!(SaturatingMul, saturating_mul, usize);
saturating_impl!(SaturatingMul, saturating_mul, u128);
saturating_impl!(SaturatingMul, saturating_mul, i8);
saturating_impl!(SaturatingMul, saturating_mul, i16);
saturating_impl!(SaturatingMul, saturating_mul, i32);
saturating_impl!(SaturatingMul, saturating_mul, i64);
saturating_impl!(SaturatingMul, saturating_mul, isize);
saturating_impl!(SaturatingMul, saturating_mul, i128);
// TODO: add SaturatingNeg for signed integer primitives once the saturating_neg() API is stable.
#[test]
fn test_saturating_traits() {
fn saturating_add<T: SaturatingAdd>(a: T, b: T) -> T {
a.saturating_add(&b)
}
fn saturating_sub<T: SaturatingSub>(a: T, b: T) -> T {
a.saturating_sub(&b)
}
fn saturating_mul<T: SaturatingMul>(a: T, b: T) -> T {
a.saturating_mul(&b)
}
assert_eq!(saturating_add(255, 1), 255u8);
assert_eq!(saturating_add(127, 1), 127i8);
assert_eq!(saturating_add(-128, -1), -128i8);
assert_eq!(saturating_sub(0, 1), 0u8);
assert_eq!(saturating_sub(-128, 1), -128i8);
assert_eq!(saturating_sub(127, -1), 127i8);
assert_eq!(saturating_mul(255, 2), 255u8);
assert_eq!(saturating_mul(127, 2), 127i8);
assert_eq!(saturating_mul(-128, 2), -128i8);
}

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use core::num::Wrapping;
use core::ops::{Add, Mul, Neg, Shl, Shr, Sub};
macro_rules! wrapping_impl {
($trait_name:ident, $method:ident, $t:ty) => {
impl $trait_name for $t {
#[inline]
fn $method(&self, v: &Self) -> Self {
<$t>::$method(*self, *v)
}
}
};
($trait_name:ident, $method:ident, $t:ty, $rhs:ty) => {
impl $trait_name<$rhs> for $t {
#[inline]
fn $method(&self, v: &$rhs) -> Self {
<$t>::$method(*self, *v)
}
}
};
}
/// Performs addition that wraps around on overflow.
pub trait WrappingAdd: Sized + Add<Self, Output = Self> {
/// Wrapping (modular) addition. Computes `self + other`, wrapping around at the boundary of
/// the type.
fn wrapping_add(&self, v: &Self) -> Self;
}
wrapping_impl!(WrappingAdd, wrapping_add, u8);
wrapping_impl!(WrappingAdd, wrapping_add, u16);
wrapping_impl!(WrappingAdd, wrapping_add, u32);
wrapping_impl!(WrappingAdd, wrapping_add, u64);
wrapping_impl!(WrappingAdd, wrapping_add, usize);
wrapping_impl!(WrappingAdd, wrapping_add, u128);
wrapping_impl!(WrappingAdd, wrapping_add, i8);
wrapping_impl!(WrappingAdd, wrapping_add, i16);
wrapping_impl!(WrappingAdd, wrapping_add, i32);
wrapping_impl!(WrappingAdd, wrapping_add, i64);
wrapping_impl!(WrappingAdd, wrapping_add, isize);
wrapping_impl!(WrappingAdd, wrapping_add, i128);
/// Performs subtraction that wraps around on overflow.
pub trait WrappingSub: Sized + Sub<Self, Output = Self> {
/// Wrapping (modular) subtraction. Computes `self - other`, wrapping around at the boundary
/// of the type.
fn wrapping_sub(&self, v: &Self) -> Self;
}
wrapping_impl!(WrappingSub, wrapping_sub, u8);
wrapping_impl!(WrappingSub, wrapping_sub, u16);
wrapping_impl!(WrappingSub, wrapping_sub, u32);
wrapping_impl!(WrappingSub, wrapping_sub, u64);
wrapping_impl!(WrappingSub, wrapping_sub, usize);
wrapping_impl!(WrappingSub, wrapping_sub, u128);
wrapping_impl!(WrappingSub, wrapping_sub, i8);
wrapping_impl!(WrappingSub, wrapping_sub, i16);
wrapping_impl!(WrappingSub, wrapping_sub, i32);
wrapping_impl!(WrappingSub, wrapping_sub, i64);
wrapping_impl!(WrappingSub, wrapping_sub, isize);
wrapping_impl!(WrappingSub, wrapping_sub, i128);
/// Performs multiplication that wraps around on overflow.
pub trait WrappingMul: Sized + Mul<Self, Output = Self> {
/// Wrapping (modular) multiplication. Computes `self * other`, wrapping around at the boundary
/// of the type.
fn wrapping_mul(&self, v: &Self) -> Self;
}
wrapping_impl!(WrappingMul, wrapping_mul, u8);
wrapping_impl!(WrappingMul, wrapping_mul, u16);
wrapping_impl!(WrappingMul, wrapping_mul, u32);
wrapping_impl!(WrappingMul, wrapping_mul, u64);
wrapping_impl!(WrappingMul, wrapping_mul, usize);
wrapping_impl!(WrappingMul, wrapping_mul, u128);
wrapping_impl!(WrappingMul, wrapping_mul, i8);
wrapping_impl!(WrappingMul, wrapping_mul, i16);
wrapping_impl!(WrappingMul, wrapping_mul, i32);
wrapping_impl!(WrappingMul, wrapping_mul, i64);
wrapping_impl!(WrappingMul, wrapping_mul, isize);
wrapping_impl!(WrappingMul, wrapping_mul, i128);
macro_rules! wrapping_unary_impl {
($trait_name:ident, $method:ident, $t:ty) => {
impl $trait_name for $t {
#[inline]
fn $method(&self) -> $t {
<$t>::$method(*self)
}
}
};
}
/// Performs a negation that does not panic.
pub trait WrappingNeg: Sized {
/// Wrapping (modular) negation. Computes `-self`,
/// wrapping around at the boundary of the type.
///
/// Since unsigned types do not have negative equivalents
/// all applications of this function will wrap (except for `-0`).
/// For values smaller than the corresponding signed type's maximum
/// the result is the same as casting the corresponding signed value.
/// Any larger values are equivalent to `MAX + 1 - (val - MAX - 1)` where
/// `MAX` is the corresponding signed type's maximum.
///
/// ```
/// use num_traits::WrappingNeg;
///
/// assert_eq!(100i8.wrapping_neg(), -100);
/// assert_eq!((-100i8).wrapping_neg(), 100);
/// assert_eq!((-128i8).wrapping_neg(), -128); // wrapped!
/// ```
fn wrapping_neg(&self) -> Self;
}
wrapping_unary_impl!(WrappingNeg, wrapping_neg, u8);
wrapping_unary_impl!(WrappingNeg, wrapping_neg, u16);
wrapping_unary_impl!(WrappingNeg, wrapping_neg, u32);
wrapping_unary_impl!(WrappingNeg, wrapping_neg, u64);
wrapping_unary_impl!(WrappingNeg, wrapping_neg, usize);
wrapping_unary_impl!(WrappingNeg, wrapping_neg, u128);
wrapping_unary_impl!(WrappingNeg, wrapping_neg, i8);
wrapping_unary_impl!(WrappingNeg, wrapping_neg, i16);
wrapping_unary_impl!(WrappingNeg, wrapping_neg, i32);
wrapping_unary_impl!(WrappingNeg, wrapping_neg, i64);
wrapping_unary_impl!(WrappingNeg, wrapping_neg, isize);
wrapping_unary_impl!(WrappingNeg, wrapping_neg, i128);
macro_rules! wrapping_shift_impl {
($trait_name:ident, $method:ident, $t:ty) => {
impl $trait_name for $t {
#[inline]
fn $method(&self, rhs: u32) -> $t {
<$t>::$method(*self, rhs)
}
}
};
}
/// Performs a left shift that does not panic.
pub trait WrappingShl: Sized + Shl<usize, Output = Self> {
/// Panic-free bitwise shift-left; yields `self << mask(rhs)`,
/// where `mask` removes any high order bits of `rhs` that would
/// cause the shift to exceed the bitwidth of the type.
///
/// ```
/// use num_traits::WrappingShl;
///
/// let x: u16 = 0x0001;
///
/// assert_eq!(WrappingShl::wrapping_shl(&x, 0), 0x0001);
/// assert_eq!(WrappingShl::wrapping_shl(&x, 1), 0x0002);
/// assert_eq!(WrappingShl::wrapping_shl(&x, 15), 0x8000);
/// assert_eq!(WrappingShl::wrapping_shl(&x, 16), 0x0001);
/// ```
fn wrapping_shl(&self, rhs: u32) -> Self;
}
wrapping_shift_impl!(WrappingShl, wrapping_shl, u8);
wrapping_shift_impl!(WrappingShl, wrapping_shl, u16);
wrapping_shift_impl!(WrappingShl, wrapping_shl, u32);
wrapping_shift_impl!(WrappingShl, wrapping_shl, u64);
wrapping_shift_impl!(WrappingShl, wrapping_shl, usize);
wrapping_shift_impl!(WrappingShl, wrapping_shl, u128);
wrapping_shift_impl!(WrappingShl, wrapping_shl, i8);
wrapping_shift_impl!(WrappingShl, wrapping_shl, i16);
wrapping_shift_impl!(WrappingShl, wrapping_shl, i32);
wrapping_shift_impl!(WrappingShl, wrapping_shl, i64);
wrapping_shift_impl!(WrappingShl, wrapping_shl, isize);
wrapping_shift_impl!(WrappingShl, wrapping_shl, i128);
/// Performs a right shift that does not panic.
pub trait WrappingShr: Sized + Shr<usize, Output = Self> {
/// Panic-free bitwise shift-right; yields `self >> mask(rhs)`,
/// where `mask` removes any high order bits of `rhs` that would
/// cause the shift to exceed the bitwidth of the type.
///
/// ```
/// use num_traits::WrappingShr;
///
/// let x: u16 = 0x8000;
///
/// assert_eq!(WrappingShr::wrapping_shr(&x, 0), 0x8000);
/// assert_eq!(WrappingShr::wrapping_shr(&x, 1), 0x4000);
/// assert_eq!(WrappingShr::wrapping_shr(&x, 15), 0x0001);
/// assert_eq!(WrappingShr::wrapping_shr(&x, 16), 0x8000);
/// ```
fn wrapping_shr(&self, rhs: u32) -> Self;
}
wrapping_shift_impl!(WrappingShr, wrapping_shr, u8);
wrapping_shift_impl!(WrappingShr, wrapping_shr, u16);
wrapping_shift_impl!(WrappingShr, wrapping_shr, u32);
wrapping_shift_impl!(WrappingShr, wrapping_shr, u64);
wrapping_shift_impl!(WrappingShr, wrapping_shr, usize);
wrapping_shift_impl!(WrappingShr, wrapping_shr, u128);
wrapping_shift_impl!(WrappingShr, wrapping_shr, i8);
wrapping_shift_impl!(WrappingShr, wrapping_shr, i16);
wrapping_shift_impl!(WrappingShr, wrapping_shr, i32);
wrapping_shift_impl!(WrappingShr, wrapping_shr, i64);
wrapping_shift_impl!(WrappingShr, wrapping_shr, isize);
wrapping_shift_impl!(WrappingShr, wrapping_shr, i128);
// Well this is a bit funny, but all the more appropriate.
impl<T: WrappingAdd> WrappingAdd for Wrapping<T>
where
Wrapping<T>: Add<Output = Wrapping<T>>,
{
fn wrapping_add(&self, v: &Self) -> Self {
Wrapping(self.0.wrapping_add(&v.0))
}
}
impl<T: WrappingSub> WrappingSub for Wrapping<T>
where
Wrapping<T>: Sub<Output = Wrapping<T>>,
{
fn wrapping_sub(&self, v: &Self) -> Self {
Wrapping(self.0.wrapping_sub(&v.0))
}
}
impl<T: WrappingMul> WrappingMul for Wrapping<T>
where
Wrapping<T>: Mul<Output = Wrapping<T>>,
{
fn wrapping_mul(&self, v: &Self) -> Self {
Wrapping(self.0.wrapping_mul(&v.0))
}
}
impl<T: WrappingNeg> WrappingNeg for Wrapping<T>
where
Wrapping<T>: Neg<Output = Wrapping<T>>,
{
fn wrapping_neg(&self) -> Self {
Wrapping(self.0.wrapping_neg())
}
}
impl<T: WrappingShl> WrappingShl for Wrapping<T>
where
Wrapping<T>: Shl<usize, Output = Wrapping<T>>,
{
fn wrapping_shl(&self, rhs: u32) -> Self {
Wrapping(self.0.wrapping_shl(rhs))
}
}
impl<T: WrappingShr> WrappingShr for Wrapping<T>
where
Wrapping<T>: Shr<usize, Output = Wrapping<T>>,
{
fn wrapping_shr(&self, rhs: u32) -> Self {
Wrapping(self.0.wrapping_shr(rhs))
}
}
#[test]
fn test_wrapping_traits() {
fn wrapping_add<T: WrappingAdd>(a: T, b: T) -> T {
a.wrapping_add(&b)
}
fn wrapping_sub<T: WrappingSub>(a: T, b: T) -> T {
a.wrapping_sub(&b)
}
fn wrapping_mul<T: WrappingMul>(a: T, b: T) -> T {
a.wrapping_mul(&b)
}
fn wrapping_neg<T: WrappingNeg>(a: T) -> T {
a.wrapping_neg()
}
fn wrapping_shl<T: WrappingShl>(a: T, b: u32) -> T {
a.wrapping_shl(b)
}
fn wrapping_shr<T: WrappingShr>(a: T, b: u32) -> T {
a.wrapping_shr(b)
}
assert_eq!(wrapping_add(255, 1), 0u8);
assert_eq!(wrapping_sub(0, 1), 255u8);
assert_eq!(wrapping_mul(255, 2), 254u8);
assert_eq!(wrapping_neg(255), 1u8);
assert_eq!(wrapping_shl(255, 8), 255u8);
assert_eq!(wrapping_shr(255, 8), 255u8);
assert_eq!(wrapping_add(255, 1), (Wrapping(255u8) + Wrapping(1u8)).0);
assert_eq!(wrapping_sub(0, 1), (Wrapping(0u8) - Wrapping(1u8)).0);
assert_eq!(wrapping_mul(255, 2), (Wrapping(255u8) * Wrapping(2u8)).0);
assert_eq!(wrapping_neg(255), (-Wrapping(255u8)).0);
assert_eq!(wrapping_shl(255, 8), (Wrapping(255u8) << 8).0);
assert_eq!(wrapping_shr(255, 8), (Wrapping(255u8) >> 8).0);
}
#[test]
fn wrapping_is_wrappingadd() {
fn require_wrappingadd<T: WrappingAdd>(_: &T) {}
require_wrappingadd(&Wrapping(42));
}
#[test]
fn wrapping_is_wrappingsub() {
fn require_wrappingsub<T: WrappingSub>(_: &T) {}
require_wrappingsub(&Wrapping(42));
}
#[test]
fn wrapping_is_wrappingmul() {
fn require_wrappingmul<T: WrappingMul>(_: &T) {}
require_wrappingmul(&Wrapping(42));
}
#[test]
fn wrapping_is_wrappingneg() {
fn require_wrappingneg<T: WrappingNeg>(_: &T) {}
require_wrappingneg(&Wrapping(42));
}
#[test]
fn wrapping_is_wrappingshl() {
fn require_wrappingshl<T: WrappingShl>(_: &T) {}
require_wrappingshl(&Wrapping(42));
}
#[test]
fn wrapping_is_wrappingshr() {
fn require_wrappingshr<T: WrappingShr>(_: &T) {}
require_wrappingshr(&Wrapping(42));
}

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use crate::{CheckedMul, One};
use core::num::Wrapping;
use core::ops::Mul;
/// Binary operator for raising a value to a power.
pub trait Pow<RHS> {
/// The result after applying the operator.
type Output;
/// Returns `self` to the power `rhs`.
///
/// # Examples
///
/// ```
/// use num_traits::Pow;
/// assert_eq!(Pow::pow(10u32, 2u32), 100);
/// ```
fn pow(self, rhs: RHS) -> Self::Output;
}
macro_rules! pow_impl {
($t:ty) => {
pow_impl!($t, u8);
pow_impl!($t, usize);
// FIXME: these should be possible
// pow_impl!($t, u16);
// pow_impl!($t, u32);
// pow_impl!($t, u64);
};
($t:ty, $rhs:ty) => {
pow_impl!($t, $rhs, usize, pow);
};
($t:ty, $rhs:ty, $desired_rhs:ty, $method:expr) => {
impl Pow<$rhs> for $t {
type Output = $t;
#[inline]
fn pow(self, rhs: $rhs) -> $t {
($method)(self, <$desired_rhs>::from(rhs))
}
}
impl<'a> Pow<&'a $rhs> for $t {
type Output = $t;
#[inline]
fn pow(self, rhs: &'a $rhs) -> $t {
($method)(self, <$desired_rhs>::from(*rhs))
}
}
impl<'a> Pow<$rhs> for &'a $t {
type Output = $t;
#[inline]
fn pow(self, rhs: $rhs) -> $t {
($method)(*self, <$desired_rhs>::from(rhs))
}
}
impl<'a, 'b> Pow<&'a $rhs> for &'b $t {
type Output = $t;
#[inline]
fn pow(self, rhs: &'a $rhs) -> $t {
($method)(*self, <$desired_rhs>::from(*rhs))
}
}
};
}
pow_impl!(u8, u8, u32, u8::pow);
pow_impl!(u8, u16, u32, u8::pow);
pow_impl!(u8, u32, u32, u8::pow);
pow_impl!(u8, usize);
pow_impl!(i8, u8, u32, i8::pow);
pow_impl!(i8, u16, u32, i8::pow);
pow_impl!(i8, u32, u32, i8::pow);
pow_impl!(i8, usize);
pow_impl!(u16, u8, u32, u16::pow);
pow_impl!(u16, u16, u32, u16::pow);
pow_impl!(u16, u32, u32, u16::pow);
pow_impl!(u16, usize);
pow_impl!(i16, u8, u32, i16::pow);
pow_impl!(i16, u16, u32, i16::pow);
pow_impl!(i16, u32, u32, i16::pow);
pow_impl!(i16, usize);
pow_impl!(u32, u8, u32, u32::pow);
pow_impl!(u32, u16, u32, u32::pow);
pow_impl!(u32, u32, u32, u32::pow);
pow_impl!(u32, usize);
pow_impl!(i32, u8, u32, i32::pow);
pow_impl!(i32, u16, u32, i32::pow);
pow_impl!(i32, u32, u32, i32::pow);
pow_impl!(i32, usize);
pow_impl!(u64, u8, u32, u64::pow);
pow_impl!(u64, u16, u32, u64::pow);
pow_impl!(u64, u32, u32, u64::pow);
pow_impl!(u64, usize);
pow_impl!(i64, u8, u32, i64::pow);
pow_impl!(i64, u16, u32, i64::pow);
pow_impl!(i64, u32, u32, i64::pow);
pow_impl!(i64, usize);
pow_impl!(u128, u8, u32, u128::pow);
pow_impl!(u128, u16, u32, u128::pow);
pow_impl!(u128, u32, u32, u128::pow);
pow_impl!(u128, usize);
pow_impl!(i128, u8, u32, i128::pow);
pow_impl!(i128, u16, u32, i128::pow);
pow_impl!(i128, u32, u32, i128::pow);
pow_impl!(i128, usize);
pow_impl!(usize, u8, u32, usize::pow);
pow_impl!(usize, u16, u32, usize::pow);
pow_impl!(usize, u32, u32, usize::pow);
pow_impl!(usize, usize);
pow_impl!(isize, u8, u32, isize::pow);
pow_impl!(isize, u16, u32, isize::pow);
pow_impl!(isize, u32, u32, isize::pow);
pow_impl!(isize, usize);
pow_impl!(Wrapping<u8>);
pow_impl!(Wrapping<i8>);
pow_impl!(Wrapping<u16>);
pow_impl!(Wrapping<i16>);
pow_impl!(Wrapping<u32>);
pow_impl!(Wrapping<i32>);
pow_impl!(Wrapping<u64>);
pow_impl!(Wrapping<i64>);
pow_impl!(Wrapping<u128>);
pow_impl!(Wrapping<i128>);
pow_impl!(Wrapping<usize>);
pow_impl!(Wrapping<isize>);
// FIXME: these should be possible
// pow_impl!(u8, u64);
// pow_impl!(i16, u64);
// pow_impl!(i8, u64);
// pow_impl!(u16, u64);
// pow_impl!(u32, u64);
// pow_impl!(i32, u64);
// pow_impl!(u64, u64);
// pow_impl!(i64, u64);
// pow_impl!(usize, u64);
// pow_impl!(isize, u64);
#[cfg(any(feature = "std", feature = "libm"))]
mod float_impls {
use super::Pow;
use crate::Float;
pow_impl!(f32, i8, i32, <f32 as Float>::powi);
pow_impl!(f32, u8, i32, <f32 as Float>::powi);
pow_impl!(f32, i16, i32, <f32 as Float>::powi);
pow_impl!(f32, u16, i32, <f32 as Float>::powi);
pow_impl!(f32, i32, i32, <f32 as Float>::powi);
pow_impl!(f64, i8, i32, <f64 as Float>::powi);
pow_impl!(f64, u8, i32, <f64 as Float>::powi);
pow_impl!(f64, i16, i32, <f64 as Float>::powi);
pow_impl!(f64, u16, i32, <f64 as Float>::powi);
pow_impl!(f64, i32, i32, <f64 as Float>::powi);
pow_impl!(f32, f32, f32, <f32 as Float>::powf);
pow_impl!(f64, f32, f64, <f64 as Float>::powf);
pow_impl!(f64, f64, f64, <f64 as Float>::powf);
}
/// Raises a value to the power of exp, using exponentiation by squaring.
///
/// Note that `0⁰` (`pow(0, 0)`) returns `1`. Mathematically this is undefined.
///
/// # Example
///
/// ```rust
/// use num_traits::pow;
///
/// assert_eq!(pow(2i8, 4), 16);
/// assert_eq!(pow(6u8, 3), 216);
/// assert_eq!(pow(0u8, 0), 1); // Be aware if this case affects you
/// ```
#[inline]
pub fn pow<T: Clone + One + Mul<T, Output = T>>(mut base: T, mut exp: usize) -> T {
if exp == 0 {
return T::one();
}
while exp & 1 == 0 {
base = base.clone() * base;
exp >>= 1;
}
if exp == 1 {
return base;
}
let mut acc = base.clone();
while exp > 1 {
exp >>= 1;
base = base.clone() * base;
if exp & 1 == 1 {
acc = acc * base.clone();
}
}
acc
}
/// Raises a value to the power of exp, returning `None` if an overflow occurred.
///
/// Note that `0⁰` (`checked_pow(0, 0)`) returns `Some(1)`. Mathematically this is undefined.
///
/// Otherwise same as the `pow` function.
///
/// # Example
///
/// ```rust
/// use num_traits::checked_pow;
///
/// assert_eq!(checked_pow(2i8, 4), Some(16));
/// assert_eq!(checked_pow(7i8, 8), None);
/// assert_eq!(checked_pow(7u32, 8), Some(5_764_801));
/// assert_eq!(checked_pow(0u32, 0), Some(1)); // Be aware if this case affect you
/// ```
#[inline]
pub fn checked_pow<T: Clone + One + CheckedMul>(mut base: T, mut exp: usize) -> Option<T> {
if exp == 0 {
return Some(T::one());
}
while exp & 1 == 0 {
base = base.checked_mul(&base)?;
exp >>= 1;
}
if exp == 1 {
return Some(base);
}
let mut acc = base.clone();
while exp > 1 {
exp >>= 1;
base = base.checked_mul(&base)?;
if exp & 1 == 1 {
acc = acc.checked_mul(&base)?;
}
}
Some(acc)
}

834
vendor/num-traits/src/real.rs vendored Normal file
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@ -0,0 +1,834 @@
#![cfg(any(feature = "std", feature = "libm"))]
use core::ops::Neg;
use crate::{Float, Num, NumCast};
// NOTE: These doctests have the same issue as those in src/float.rs.
// They're testing the inherent methods directly, and not those of `Real`.
/// A trait for real number types that do not necessarily have
/// floating-point-specific characteristics such as NaN and infinity.
///
/// See [this Wikipedia article](https://en.wikipedia.org/wiki/Real_data_type)
/// for a list of data types that could meaningfully implement this trait.
///
/// This trait is only available with the `std` feature, or with the `libm` feature otherwise.
pub trait Real: Num + Copy + NumCast + PartialOrd + Neg<Output = Self> {
/// Returns the smallest finite value that this type can represent.
///
/// ```
/// use num_traits::real::Real;
/// use std::f64;
///
/// let x: f64 = Real::min_value();
///
/// assert_eq!(x, f64::MIN);
/// ```
fn min_value() -> Self;
/// Returns the smallest positive, normalized value that this type can represent.
///
/// ```
/// use num_traits::real::Real;
/// use std::f64;
///
/// let x: f64 = Real::min_positive_value();
///
/// assert_eq!(x, f64::MIN_POSITIVE);
/// ```
fn min_positive_value() -> Self;
/// Returns epsilon, a small positive value.
///
/// ```
/// use num_traits::real::Real;
/// use std::f64;
///
/// let x: f64 = Real::epsilon();
///
/// assert_eq!(x, f64::EPSILON);
/// ```
///
/// # Panics
///
/// The default implementation will panic if `f32::EPSILON` cannot
/// be cast to `Self`.
fn epsilon() -> Self;
/// Returns the largest finite value that this type can represent.
///
/// ```
/// use num_traits::real::Real;
/// use std::f64;
///
/// let x: f64 = Real::max_value();
/// assert_eq!(x, f64::MAX);
/// ```
fn max_value() -> Self;
/// Returns the largest integer less than or equal to a number.
///
/// ```
/// use num_traits::real::Real;
///
/// let f = 3.99;
/// let g = 3.0;
///
/// assert_eq!(f.floor(), 3.0);
/// assert_eq!(g.floor(), 3.0);
/// ```
fn floor(self) -> Self;
/// Returns the smallest integer greater than or equal to a number.
///
/// ```
/// use num_traits::real::Real;
///
/// let f = 3.01;
/// let g = 4.0;
///
/// assert_eq!(f.ceil(), 4.0);
/// assert_eq!(g.ceil(), 4.0);
/// ```
fn ceil(self) -> Self;
/// Returns the nearest integer to a number. Round half-way cases away from
/// `0.0`.
///
/// ```
/// use num_traits::real::Real;
///
/// let f = 3.3;
/// let g = -3.3;
///
/// assert_eq!(f.round(), 3.0);
/// assert_eq!(g.round(), -3.0);
/// ```
fn round(self) -> Self;
/// Return the integer part of a number.
///
/// ```
/// use num_traits::real::Real;
///
/// let f = 3.3;
/// let g = -3.7;
///
/// assert_eq!(f.trunc(), 3.0);
/// assert_eq!(g.trunc(), -3.0);
/// ```
fn trunc(self) -> Self;
/// Returns the fractional part of a number.
///
/// ```
/// use num_traits::real::Real;
///
/// let x = 3.5;
/// let y = -3.5;
/// let abs_difference_x = (x.fract() - 0.5).abs();
/// let abs_difference_y = (y.fract() - (-0.5)).abs();
///
/// assert!(abs_difference_x < 1e-10);
/// assert!(abs_difference_y < 1e-10);
/// ```
fn fract(self) -> Self;
/// Computes the absolute value of `self`. Returns `Float::nan()` if the
/// number is `Float::nan()`.
///
/// ```
/// use num_traits::real::Real;
/// use std::f64;
///
/// let x = 3.5;
/// let y = -3.5;
///
/// let abs_difference_x = (x.abs() - x).abs();
/// let abs_difference_y = (y.abs() - (-y)).abs();
///
/// assert!(abs_difference_x < 1e-10);
/// assert!(abs_difference_y < 1e-10);
///
/// assert!(::num_traits::Float::is_nan(f64::NAN.abs()));
/// ```
fn abs(self) -> Self;
/// Returns a number that represents the sign of `self`.
///
/// - `1.0` if the number is positive, `+0.0` or `Float::infinity()`
/// - `-1.0` if the number is negative, `-0.0` or `Float::neg_infinity()`
/// - `Float::nan()` if the number is `Float::nan()`
///
/// ```
/// use num_traits::real::Real;
/// use std::f64;
///
/// let f = 3.5;
///
/// assert_eq!(f.signum(), 1.0);
/// assert_eq!(f64::NEG_INFINITY.signum(), -1.0);
///
/// assert!(f64::NAN.signum().is_nan());
/// ```
fn signum(self) -> Self;
/// Returns `true` if `self` is positive, including `+0.0`,
/// `Float::infinity()`, and with newer versions of Rust `f64::NAN`.
///
/// ```
/// use num_traits::real::Real;
/// use std::f64;
///
/// let neg_nan: f64 = -f64::NAN;
///
/// let f = 7.0;
/// let g = -7.0;
///
/// assert!(f.is_sign_positive());
/// assert!(!g.is_sign_positive());
/// assert!(!neg_nan.is_sign_positive());
/// ```
fn is_sign_positive(self) -> bool;
/// Returns `true` if `self` is negative, including `-0.0`,
/// `Float::neg_infinity()`, and with newer versions of Rust `-f64::NAN`.
///
/// ```
/// use num_traits::real::Real;
/// use std::f64;
///
/// let nan: f64 = f64::NAN;
///
/// let f = 7.0;
/// let g = -7.0;
///
/// assert!(!f.is_sign_negative());
/// assert!(g.is_sign_negative());
/// assert!(!nan.is_sign_negative());
/// ```
fn is_sign_negative(self) -> bool;
/// Fused multiply-add. Computes `(self * a) + b` with only one rounding
/// error, yielding a more accurate result than an unfused multiply-add.
///
/// Using `mul_add` can be more performant than an unfused multiply-add if
/// the target architecture has a dedicated `fma` CPU instruction.
///
/// ```
/// use num_traits::real::Real;
///
/// let m = 10.0;
/// let x = 4.0;
/// let b = 60.0;
///
/// // 100.0
/// let abs_difference = (m.mul_add(x, b) - (m*x + b)).abs();
///
/// assert!(abs_difference < 1e-10);
/// ```
fn mul_add(self, a: Self, b: Self) -> Self;
/// Take the reciprocal (inverse) of a number, `1/x`.
///
/// ```
/// use num_traits::real::Real;
///
/// let x = 2.0;
/// let abs_difference = (x.recip() - (1.0/x)).abs();
///
/// assert!(abs_difference < 1e-10);
/// ```
fn recip(self) -> Self;
/// Raise a number to an integer power.
///
/// Using this function is generally faster than using `powf`
///
/// ```
/// use num_traits::real::Real;
///
/// let x = 2.0;
/// let abs_difference = (x.powi(2) - x*x).abs();
///
/// assert!(abs_difference < 1e-10);
/// ```
fn powi(self, n: i32) -> Self;
/// Raise a number to a real number power.
///
/// ```
/// use num_traits::real::Real;
///
/// let x = 2.0;
/// let abs_difference = (x.powf(2.0) - x*x).abs();
///
/// assert!(abs_difference < 1e-10);
/// ```
fn powf(self, n: Self) -> Self;
/// Take the square root of a number.
///
/// Returns NaN if `self` is a negative floating-point number.
///
/// # Panics
///
/// If the implementing type doesn't support NaN, this method should panic if `self < 0`.
///
/// ```
/// use num_traits::real::Real;
///
/// let positive = 4.0;
/// let negative = -4.0;
///
/// let abs_difference = (positive.sqrt() - 2.0).abs();
///
/// assert!(abs_difference < 1e-10);
/// assert!(::num_traits::Float::is_nan(negative.sqrt()));
/// ```
fn sqrt(self) -> Self;
/// Returns `e^(self)`, (the exponential function).
///
/// ```
/// use num_traits::real::Real;
///
/// let one = 1.0;
/// // e^1
/// let e = one.exp();
///
/// // ln(e) - 1 == 0
/// let abs_difference = (e.ln() - 1.0).abs();
///
/// assert!(abs_difference < 1e-10);
/// ```
fn exp(self) -> Self;
/// Returns `2^(self)`.
///
/// ```
/// use num_traits::real::Real;
///
/// let f = 2.0;
///
/// // 2^2 - 4 == 0
/// let abs_difference = (f.exp2() - 4.0).abs();
///
/// assert!(abs_difference < 1e-10);
/// ```
fn exp2(self) -> Self;
/// Returns the natural logarithm of the number.
///
/// # Panics
///
/// If `self <= 0` and this type does not support a NaN representation, this function should panic.
///
/// ```
/// use num_traits::real::Real;
///
/// let one = 1.0;
/// // e^1
/// let e = one.exp();
///
/// // ln(e) - 1 == 0
/// let abs_difference = (e.ln() - 1.0).abs();
///
/// assert!(abs_difference < 1e-10);
/// ```
fn ln(self) -> Self;
/// Returns the logarithm of the number with respect to an arbitrary base.
///
/// # Panics
///
/// If `self <= 0` and this type does not support a NaN representation, this function should panic.
///
/// ```
/// use num_traits::real::Real;
///
/// let ten = 10.0;
/// let two = 2.0;
///
/// // log10(10) - 1 == 0
/// let abs_difference_10 = (ten.log(10.0) - 1.0).abs();
///
/// // log2(2) - 1 == 0
/// let abs_difference_2 = (two.log(2.0) - 1.0).abs();
///
/// assert!(abs_difference_10 < 1e-10);
/// assert!(abs_difference_2 < 1e-10);
/// ```
fn log(self, base: Self) -> Self;
/// Returns the base 2 logarithm of the number.
///
/// # Panics
///
/// If `self <= 0` and this type does not support a NaN representation, this function should panic.
///
/// ```
/// use num_traits::real::Real;
///
/// let two = 2.0;
///
/// // log2(2) - 1 == 0
/// let abs_difference = (two.log2() - 1.0).abs();
///
/// assert!(abs_difference < 1e-10);
/// ```
fn log2(self) -> Self;
/// Returns the base 10 logarithm of the number.
///
/// # Panics
///
/// If `self <= 0` and this type does not support a NaN representation, this function should panic.
///
///
/// ```
/// use num_traits::real::Real;
///
/// let ten = 10.0;
///
/// // log10(10) - 1 == 0
/// let abs_difference = (ten.log10() - 1.0).abs();
///
/// assert!(abs_difference < 1e-10);
/// ```
fn log10(self) -> Self;
/// Converts radians to degrees.
///
/// ```
/// use std::f64::consts;
///
/// let angle = consts::PI;
///
/// let abs_difference = (angle.to_degrees() - 180.0).abs();
///
/// assert!(abs_difference < 1e-10);
/// ```
fn to_degrees(self) -> Self;
/// Converts degrees to radians.
///
/// ```
/// use std::f64::consts;
///
/// let angle = 180.0_f64;
///
/// let abs_difference = (angle.to_radians() - consts::PI).abs();
///
/// assert!(abs_difference < 1e-10);
/// ```
fn to_radians(self) -> Self;
/// Returns the maximum of the two numbers.
///
/// ```
/// use num_traits::real::Real;
///
/// let x = 1.0;
/// let y = 2.0;
///
/// assert_eq!(x.max(y), y);
/// ```
fn max(self, other: Self) -> Self;
/// Returns the minimum of the two numbers.
///
/// ```
/// use num_traits::real::Real;
///
/// let x = 1.0;
/// let y = 2.0;
///
/// assert_eq!(x.min(y), x);
/// ```
fn min(self, other: Self) -> Self;
/// The positive difference of two numbers.
///
/// * If `self <= other`: `0:0`
/// * Else: `self - other`
///
/// ```
/// use num_traits::real::Real;
///
/// let x = 3.0;
/// let y = -3.0;
///
/// let abs_difference_x = (x.abs_sub(1.0) - 2.0).abs();
/// let abs_difference_y = (y.abs_sub(1.0) - 0.0).abs();
///
/// assert!(abs_difference_x < 1e-10);
/// assert!(abs_difference_y < 1e-10);
/// ```
fn abs_sub(self, other: Self) -> Self;
/// Take the cubic root of a number.
///
/// ```
/// use num_traits::real::Real;
///
/// let x = 8.0;
///
/// // x^(1/3) - 2 == 0
/// let abs_difference = (x.cbrt() - 2.0).abs();
///
/// assert!(abs_difference < 1e-10);
/// ```
fn cbrt(self) -> Self;
/// Calculate the length of the hypotenuse of a right-angle triangle given
/// legs of length `x` and `y`.
///
/// ```
/// use num_traits::real::Real;
///
/// let x = 2.0;
/// let y = 3.0;
///
/// // sqrt(x^2 + y^2)
/// let abs_difference = (x.hypot(y) - (x.powi(2) + y.powi(2)).sqrt()).abs();
///
/// assert!(abs_difference < 1e-10);
/// ```
fn hypot(self, other: Self) -> Self;
/// Computes the sine of a number (in radians).
///
/// ```
/// use num_traits::real::Real;
/// use std::f64;
///
/// let x = f64::consts::PI/2.0;
///
/// let abs_difference = (x.sin() - 1.0).abs();
///
/// assert!(abs_difference < 1e-10);
/// ```
fn sin(self) -> Self;
/// Computes the cosine of a number (in radians).
///
/// ```
/// use num_traits::real::Real;
/// use std::f64;
///
/// let x = 2.0*f64::consts::PI;
///
/// let abs_difference = (x.cos() - 1.0).abs();
///
/// assert!(abs_difference < 1e-10);
/// ```
fn cos(self) -> Self;
/// Computes the tangent of a number (in radians).
///
/// ```
/// use num_traits::real::Real;
/// use std::f64;
///
/// let x = f64::consts::PI/4.0;
/// let abs_difference = (x.tan() - 1.0).abs();
///
/// assert!(abs_difference < 1e-14);
/// ```
fn tan(self) -> Self;
/// Computes the arcsine of a number. Return value is in radians in
/// the range [-pi/2, pi/2] or NaN if the number is outside the range
/// [-1, 1].
///
/// # Panics
///
/// If this type does not support a NaN representation, this function should panic
/// if the number is outside the range [-1, 1].
///
/// ```
/// use num_traits::real::Real;
/// use std::f64;
///
/// let f = f64::consts::PI / 2.0;
///
/// // asin(sin(pi/2))
/// let abs_difference = (f.sin().asin() - f64::consts::PI / 2.0).abs();
///
/// assert!(abs_difference < 1e-10);
/// ```
fn asin(self) -> Self;
/// Computes the arccosine of a number. Return value is in radians in
/// the range [0, pi] or NaN if the number is outside the range
/// [-1, 1].
///
/// # Panics
///
/// If this type does not support a NaN representation, this function should panic
/// if the number is outside the range [-1, 1].
///
/// ```
/// use num_traits::real::Real;
/// use std::f64;
///
/// let f = f64::consts::PI / 4.0;
///
/// // acos(cos(pi/4))
/// let abs_difference = (f.cos().acos() - f64::consts::PI / 4.0).abs();
///
/// assert!(abs_difference < 1e-10);
/// ```
fn acos(self) -> Self;
/// Computes the arctangent of a number. Return value is in radians in the
/// range [-pi/2, pi/2];
///
/// ```
/// use num_traits::real::Real;
///
/// let f = 1.0;
///
/// // atan(tan(1))
/// let abs_difference = (f.tan().atan() - 1.0).abs();
///
/// assert!(abs_difference < 1e-10);
/// ```
fn atan(self) -> Self;
/// Computes the four quadrant arctangent of `self` (`y`) and `other` (`x`).
///
/// * `x = 0`, `y = 0`: `0`
/// * `x >= 0`: `arctan(y/x)` -> `[-pi/2, pi/2]`
/// * `y >= 0`: `arctan(y/x) + pi` -> `(pi/2, pi]`
/// * `y < 0`: `arctan(y/x) - pi` -> `(-pi, -pi/2)`
///
/// ```
/// use num_traits::real::Real;
/// use std::f64;
///
/// let pi = f64::consts::PI;
/// // All angles from horizontal right (+x)
/// // 45 deg counter-clockwise
/// let x1 = 3.0;
/// let y1 = -3.0;
///
/// // 135 deg clockwise
/// let x2 = -3.0;
/// let y2 = 3.0;
///
/// let abs_difference_1 = (y1.atan2(x1) - (-pi/4.0)).abs();
/// let abs_difference_2 = (y2.atan2(x2) - 3.0*pi/4.0).abs();
///
/// assert!(abs_difference_1 < 1e-10);
/// assert!(abs_difference_2 < 1e-10);
/// ```
fn atan2(self, other: Self) -> Self;
/// Simultaneously computes the sine and cosine of the number, `x`. Returns
/// `(sin(x), cos(x))`.
///
/// ```
/// use num_traits::real::Real;
/// use std::f64;
///
/// let x = f64::consts::PI/4.0;
/// let f = x.sin_cos();
///
/// let abs_difference_0 = (f.0 - x.sin()).abs();
/// let abs_difference_1 = (f.1 - x.cos()).abs();
///
/// assert!(abs_difference_0 < 1e-10);
/// assert!(abs_difference_0 < 1e-10);
/// ```
fn sin_cos(self) -> (Self, Self);
/// Returns `e^(self) - 1` in a way that is accurate even if the
/// number is close to zero.
///
/// ```
/// use num_traits::real::Real;
///
/// let x = 7.0;
///
/// // e^(ln(7)) - 1
/// let abs_difference = (x.ln().exp_m1() - 6.0).abs();
///
/// assert!(abs_difference < 1e-10);
/// ```
fn exp_m1(self) -> Self;
/// Returns `ln(1+n)` (natural logarithm) more accurately than if
/// the operations were performed separately.
///
/// # Panics
///
/// If this type does not support a NaN representation, this function should panic
/// if `self-1 <= 0`.
///
/// ```
/// use num_traits::real::Real;
/// use std::f64;
///
/// let x = f64::consts::E - 1.0;
///
/// // ln(1 + (e - 1)) == ln(e) == 1
/// let abs_difference = (x.ln_1p() - 1.0).abs();
///
/// assert!(abs_difference < 1e-10);
/// ```
fn ln_1p(self) -> Self;
/// Hyperbolic sine function.
///
/// ```
/// use num_traits::real::Real;
/// use std::f64;
///
/// let e = f64::consts::E;
/// let x = 1.0;
///
/// let f = x.sinh();
/// // Solving sinh() at 1 gives `(e^2-1)/(2e)`
/// let g = (e*e - 1.0)/(2.0*e);
/// let abs_difference = (f - g).abs();
///
/// assert!(abs_difference < 1e-10);
/// ```
fn sinh(self) -> Self;
/// Hyperbolic cosine function.
///
/// ```
/// use num_traits::real::Real;
/// use std::f64;
///
/// let e = f64::consts::E;
/// let x = 1.0;
/// let f = x.cosh();
/// // Solving cosh() at 1 gives this result
/// let g = (e*e + 1.0)/(2.0*e);
/// let abs_difference = (f - g).abs();
///
/// // Same result
/// assert!(abs_difference < 1.0e-10);
/// ```
fn cosh(self) -> Self;
/// Hyperbolic tangent function.
///
/// ```
/// use num_traits::real::Real;
/// use std::f64;
///
/// let e = f64::consts::E;
/// let x = 1.0;
///
/// let f = x.tanh();
/// // Solving tanh() at 1 gives `(1 - e^(-2))/(1 + e^(-2))`
/// let g = (1.0 - e.powi(-2))/(1.0 + e.powi(-2));
/// let abs_difference = (f - g).abs();
///
/// assert!(abs_difference < 1.0e-10);
/// ```
fn tanh(self) -> Self;
/// Inverse hyperbolic sine function.
///
/// ```
/// use num_traits::real::Real;
///
/// let x = 1.0;
/// let f = x.sinh().asinh();
///
/// let abs_difference = (f - x).abs();
///
/// assert!(abs_difference < 1.0e-10);
/// ```
fn asinh(self) -> Self;
/// Inverse hyperbolic cosine function.
///
/// ```
/// use num_traits::real::Real;
///
/// let x = 1.0;
/// let f = x.cosh().acosh();
///
/// let abs_difference = (f - x).abs();
///
/// assert!(abs_difference < 1.0e-10);
/// ```
fn acosh(self) -> Self;
/// Inverse hyperbolic tangent function.
///
/// ```
/// use num_traits::real::Real;
/// use std::f64;
///
/// let e = f64::consts::E;
/// let f = e.tanh().atanh();
///
/// let abs_difference = (f - e).abs();
///
/// assert!(abs_difference < 1.0e-10);
/// ```
fn atanh(self) -> Self;
}
impl<T: Float> Real for T {
forward! {
Float::min_value() -> Self;
Float::min_positive_value() -> Self;
Float::epsilon() -> Self;
Float::max_value() -> Self;
}
forward! {
Float::floor(self) -> Self;
Float::ceil(self) -> Self;
Float::round(self) -> Self;
Float::trunc(self) -> Self;
Float::fract(self) -> Self;
Float::abs(self) -> Self;
Float::signum(self) -> Self;
Float::is_sign_positive(self) -> bool;
Float::is_sign_negative(self) -> bool;
Float::mul_add(self, a: Self, b: Self) -> Self;
Float::recip(self) -> Self;
Float::powi(self, n: i32) -> Self;
Float::powf(self, n: Self) -> Self;
Float::sqrt(self) -> Self;
Float::exp(self) -> Self;
Float::exp2(self) -> Self;
Float::ln(self) -> Self;
Float::log(self, base: Self) -> Self;
Float::log2(self) -> Self;
Float::log10(self) -> Self;
Float::to_degrees(self) -> Self;
Float::to_radians(self) -> Self;
Float::max(self, other: Self) -> Self;
Float::min(self, other: Self) -> Self;
Float::abs_sub(self, other: Self) -> Self;
Float::cbrt(self) -> Self;
Float::hypot(self, other: Self) -> Self;
Float::sin(self) -> Self;
Float::cos(self) -> Self;
Float::tan(self) -> Self;
Float::asin(self) -> Self;
Float::acos(self) -> Self;
Float::atan(self) -> Self;
Float::atan2(self, other: Self) -> Self;
Float::sin_cos(self) -> (Self, Self);
Float::exp_m1(self) -> Self;
Float::ln_1p(self) -> Self;
Float::sinh(self) -> Self;
Float::cosh(self) -> Self;
Float::tanh(self) -> Self;
Float::asinh(self) -> Self;
Float::acosh(self) -> Self;
Float::atanh(self) -> Self;
}
}

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use core::num::Wrapping;
use core::ops::Neg;
use crate::float::FloatCore;
use crate::Num;
/// Useful functions for signed numbers (i.e. numbers that can be negative).
pub trait Signed: Sized + Num + Neg<Output = Self> {
/// Computes the absolute value.
///
/// For `f32` and `f64`, `NaN` will be returned if the number is `NaN`.
///
/// For signed integers, `::MIN` will be returned if the number is `::MIN`.
fn abs(&self) -> Self;
/// The positive difference of two numbers.
///
/// Returns `zero` if the number is less than or equal to `other`, otherwise the difference
/// between `self` and `other` is returned.
fn abs_sub(&self, other: &Self) -> Self;
/// Returns the sign of the number.
///
/// For `f32` and `f64`:
///
/// * `1.0` if the number is positive, `+0.0` or `INFINITY`
/// * `-1.0` if the number is negative, `-0.0` or `NEG_INFINITY`
/// * `NaN` if the number is `NaN`
///
/// For signed integers:
///
/// * `0` if the number is zero
/// * `1` if the number is positive
/// * `-1` if the number is negative
fn signum(&self) -> Self;
/// Returns true if the number is positive and false if the number is zero or negative.
fn is_positive(&self) -> bool;
/// Returns true if the number is negative and false if the number is zero or positive.
fn is_negative(&self) -> bool;
}
macro_rules! signed_impl {
($($t:ty)*) => ($(
impl Signed for $t {
#[inline]
fn abs(&self) -> $t {
if self.is_negative() { -*self } else { *self }
}
#[inline]
fn abs_sub(&self, other: &$t) -> $t {
if *self <= *other { 0 } else { *self - *other }
}
#[inline]
fn signum(&self) -> $t {
match *self {
n if n > 0 => 1,
0 => 0,
_ => -1,
}
}
#[inline]
fn is_positive(&self) -> bool { *self > 0 }
#[inline]
fn is_negative(&self) -> bool { *self < 0 }
}
)*)
}
signed_impl!(isize i8 i16 i32 i64 i128);
impl<T: Signed> Signed for Wrapping<T>
where
Wrapping<T>: Num + Neg<Output = Wrapping<T>>,
{
#[inline]
fn abs(&self) -> Self {
Wrapping(self.0.abs())
}
#[inline]
fn abs_sub(&self, other: &Self) -> Self {
Wrapping(self.0.abs_sub(&other.0))
}
#[inline]
fn signum(&self) -> Self {
Wrapping(self.0.signum())
}
#[inline]
fn is_positive(&self) -> bool {
self.0.is_positive()
}
#[inline]
fn is_negative(&self) -> bool {
self.0.is_negative()
}
}
macro_rules! signed_float_impl {
($t:ty) => {
impl Signed for $t {
/// Computes the absolute value. Returns `NAN` if the number is `NAN`.
#[inline]
fn abs(&self) -> $t {
FloatCore::abs(*self)
}
/// The positive difference of two numbers. Returns `0.0` if the number is
/// less than or equal to `other`, otherwise the difference between`self`
/// and `other` is returned.
#[inline]
fn abs_sub(&self, other: &$t) -> $t {
if *self <= *other {
0.
} else {
*self - *other
}
}
/// # Returns
///
/// - `1.0` if the number is positive, `+0.0` or `INFINITY`
/// - `-1.0` if the number is negative, `-0.0` or `NEG_INFINITY`
/// - `NAN` if the number is NaN
#[inline]
fn signum(&self) -> $t {
FloatCore::signum(*self)
}
/// Returns `true` if the number is positive, including `+0.0` and `INFINITY`
#[inline]
fn is_positive(&self) -> bool {
FloatCore::is_sign_positive(*self)
}
/// Returns `true` if the number is negative, including `-0.0` and `NEG_INFINITY`
#[inline]
fn is_negative(&self) -> bool {
FloatCore::is_sign_negative(*self)
}
}
};
}
signed_float_impl!(f32);
signed_float_impl!(f64);
/// Computes the absolute value.
///
/// For `f32` and `f64`, `NaN` will be returned if the number is `NaN`
///
/// For signed integers, `::MIN` will be returned if the number is `::MIN`.
#[inline(always)]
pub fn abs<T: Signed>(value: T) -> T {
value.abs()
}
/// The positive difference of two numbers.
///
/// Returns zero if `x` is less than or equal to `y`, otherwise the difference
/// between `x` and `y` is returned.
#[inline(always)]
pub fn abs_sub<T: Signed>(x: T, y: T) -> T {
x.abs_sub(&y)
}
/// Returns the sign of the number.
///
/// For `f32` and `f64`:
///
/// * `1.0` if the number is positive, `+0.0` or `INFINITY`
/// * `-1.0` if the number is negative, `-0.0` or `NEG_INFINITY`
/// * `NaN` if the number is `NaN`
///
/// For signed integers:
///
/// * `0` if the number is zero
/// * `1` if the number is positive
/// * `-1` if the number is negative
#[inline(always)]
pub fn signum<T: Signed>(value: T) -> T {
value.signum()
}
/// A trait for values which cannot be negative
pub trait Unsigned: Num {}
macro_rules! empty_trait_impl {
($name:ident for $($t:ty)*) => ($(
impl $name for $t {}
)*)
}
empty_trait_impl!(Unsigned for usize u8 u16 u32 u64 u128);
impl<T: Unsigned> Unsigned for Wrapping<T> where Wrapping<T>: Num {}
#[test]
fn unsigned_wrapping_is_unsigned() {
fn require_unsigned<T: Unsigned>(_: &T) {}
require_unsigned(&Wrapping(42_u32));
}
#[test]
fn signed_wrapping_is_signed() {
fn require_signed<T: Signed>(_: &T) {}
require_signed(&Wrapping(-42));
}

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//! Tests of `num_traits::cast`.
#![cfg_attr(not(feature = "std"), no_std)]
use num_traits::cast::*;
use num_traits::Bounded;
use core::{f32, f64};
use core::{i128, i16, i32, i64, i8, isize};
use core::{u128, u16, u32, u64, u8, usize};
use core::fmt::Debug;
use core::mem;
use core::num::Wrapping;
#[test]
fn to_primitive_float() {
let f32_toolarge = 1e39f64;
assert_eq!(f32_toolarge.to_f32(), Some(f32::INFINITY));
assert_eq!((-f32_toolarge).to_f32(), Some(f32::NEG_INFINITY));
assert_eq!((f32::MAX as f64).to_f32(), Some(f32::MAX));
assert_eq!((-f32::MAX as f64).to_f32(), Some(-f32::MAX));
assert_eq!(f64::INFINITY.to_f32(), Some(f32::INFINITY));
assert_eq!((f64::NEG_INFINITY).to_f32(), Some(f32::NEG_INFINITY));
assert!((f64::NAN).to_f32().map_or(false, |f| f.is_nan()));
}
#[test]
fn wrapping_to_primitive() {
macro_rules! test_wrapping_to_primitive {
($($t:ty)+) => {
$({
let i: $t = 0;
let w = Wrapping(i);
assert_eq!(i.to_u8(), w.to_u8());
assert_eq!(i.to_u16(), w.to_u16());
assert_eq!(i.to_u32(), w.to_u32());
assert_eq!(i.to_u64(), w.to_u64());
assert_eq!(i.to_usize(), w.to_usize());
assert_eq!(i.to_i8(), w.to_i8());
assert_eq!(i.to_i16(), w.to_i16());
assert_eq!(i.to_i32(), w.to_i32());
assert_eq!(i.to_i64(), w.to_i64());
assert_eq!(i.to_isize(), w.to_isize());
assert_eq!(i.to_f32(), w.to_f32());
assert_eq!(i.to_f64(), w.to_f64());
})+
};
}
test_wrapping_to_primitive!(usize u8 u16 u32 u64 isize i8 i16 i32 i64);
}
#[test]
fn wrapping_is_toprimitive() {
fn require_toprimitive<T: ToPrimitive>(_: &T) {}
require_toprimitive(&Wrapping(42));
}
#[test]
fn wrapping_is_fromprimitive() {
fn require_fromprimitive<T: FromPrimitive>(_: &T) {}
require_fromprimitive(&Wrapping(42));
}
#[test]
fn wrapping_is_numcast() {
fn require_numcast<T: NumCast>(_: &T) {}
require_numcast(&Wrapping(42));
}
#[test]
fn as_primitive() {
let x: f32 = (1.625f64).as_();
assert_eq!(x, 1.625f32);
let x: f32 = (3.14159265358979323846f64).as_();
assert_eq!(x, 3.1415927f32);
let x: u8 = (768i16).as_();
assert_eq!(x, 0);
}
#[test]
fn float_to_integer_checks_overflow() {
// This will overflow an i32
let source: f64 = 1.0e+123f64;
// Expect the overflow to be caught
assert_eq!(cast::<f64, i32>(source), None);
}
#[test]
fn cast_to_int_checks_overflow() {
let big_f: f64 = 1.0e123;
let normal_f: f64 = 1.0;
let small_f: f64 = -1.0e123;
assert_eq!(None, cast::<f64, isize>(big_f));
assert_eq!(None, cast::<f64, i8>(big_f));
assert_eq!(None, cast::<f64, i16>(big_f));
assert_eq!(None, cast::<f64, i32>(big_f));
assert_eq!(None, cast::<f64, i64>(big_f));
assert_eq!(Some(normal_f as isize), cast::<f64, isize>(normal_f));
assert_eq!(Some(normal_f as i8), cast::<f64, i8>(normal_f));
assert_eq!(Some(normal_f as i16), cast::<f64, i16>(normal_f));
assert_eq!(Some(normal_f as i32), cast::<f64, i32>(normal_f));
assert_eq!(Some(normal_f as i64), cast::<f64, i64>(normal_f));
assert_eq!(None, cast::<f64, isize>(small_f));
assert_eq!(None, cast::<f64, i8>(small_f));
assert_eq!(None, cast::<f64, i16>(small_f));
assert_eq!(None, cast::<f64, i32>(small_f));
assert_eq!(None, cast::<f64, i64>(small_f));
}
#[test]
fn cast_to_unsigned_int_checks_overflow() {
let big_f: f64 = 1.0e123;
let normal_f: f64 = 1.0;
let small_f: f64 = -1.0e123;
assert_eq!(None, cast::<f64, usize>(big_f));
assert_eq!(None, cast::<f64, u8>(big_f));
assert_eq!(None, cast::<f64, u16>(big_f));
assert_eq!(None, cast::<f64, u32>(big_f));
assert_eq!(None, cast::<f64, u64>(big_f));
assert_eq!(Some(normal_f as usize), cast::<f64, usize>(normal_f));
assert_eq!(Some(normal_f as u8), cast::<f64, u8>(normal_f));
assert_eq!(Some(normal_f as u16), cast::<f64, u16>(normal_f));
assert_eq!(Some(normal_f as u32), cast::<f64, u32>(normal_f));
assert_eq!(Some(normal_f as u64), cast::<f64, u64>(normal_f));
assert_eq!(None, cast::<f64, usize>(small_f));
assert_eq!(None, cast::<f64, u8>(small_f));
assert_eq!(None, cast::<f64, u16>(small_f));
assert_eq!(None, cast::<f64, u32>(small_f));
assert_eq!(None, cast::<f64, u64>(small_f));
}
#[test]
fn cast_to_i128_checks_overflow() {
let big_f: f64 = 1.0e123;
let normal_f: f64 = 1.0;
let small_f: f64 = -1.0e123;
assert_eq!(None, cast::<f64, i128>(big_f));
assert_eq!(None, cast::<f64, u128>(big_f));
assert_eq!(Some(normal_f as i128), cast::<f64, i128>(normal_f));
assert_eq!(Some(normal_f as u128), cast::<f64, u128>(normal_f));
assert_eq!(None, cast::<f64, i128>(small_f));
assert_eq!(None, cast::<f64, u128>(small_f));
}
#[cfg(feature = "std")]
fn dbg(args: ::core::fmt::Arguments<'_>) {
println!("{}", args);
}
#[cfg(not(feature = "std"))]
fn dbg(_: ::core::fmt::Arguments) {}
// Rust 1.8 doesn't handle cfg on macros correctly
macro_rules! dbg { ($($tok:tt)*) => { dbg(format_args!($($tok)*)) } }
macro_rules! float_test_edge {
($f:ident -> $($t:ident)+) => { $({
dbg!("testing cast edge cases for {} -> {}", stringify!($f), stringify!($t));
let small = if $t::MIN == 0 || mem::size_of::<$t>() < mem::size_of::<$f>() {
$t::MIN as $f - 1.0
} else {
($t::MIN as $f).raw_inc().floor()
};
let fmin = small.raw_dec();
dbg!(" testing min {}\n\tvs. {:.0}\n\tand {:.0}", $t::MIN, fmin, small);
assert_eq!(Some($t::MIN), cast::<$f, $t>($t::MIN as $f));
assert_eq!(Some($t::MIN), cast::<$f, $t>(fmin));
assert_eq!(None, cast::<$f, $t>(small));
let (max, large) = if mem::size_of::<$t>() < mem::size_of::<$f>() {
($t::MAX, $t::MAX as $f + 1.0)
} else {
let large = $t::MAX as $f; // rounds up!
let max = large.raw_dec() as $t; // the next smallest possible
assert_eq!(max.count_ones(), $f::MANTISSA_DIGITS);
(max, large)
};
let fmax = large.raw_dec();
dbg!(" testing max {}\n\tvs. {:.0}\n\tand {:.0}", max, fmax, large);
assert_eq!(Some(max), cast::<$f, $t>(max as $f));
assert_eq!(Some(max), cast::<$f, $t>(fmax));
assert_eq!(None, cast::<$f, $t>(large));
dbg!(" testing non-finite values");
assert_eq!(None, cast::<$f, $t>($f::NAN));
assert_eq!(None, cast::<$f, $t>($f::INFINITY));
assert_eq!(None, cast::<$f, $t>($f::NEG_INFINITY));
})+}
}
trait RawOffset: Sized {
fn raw_inc(self) -> Self;
fn raw_dec(self) -> Self;
}
impl RawOffset for f32 {
fn raw_inc(self) -> Self {
Self::from_bits(self.to_bits() + 1)
}
fn raw_dec(self) -> Self {
Self::from_bits(self.to_bits() - 1)
}
}
impl RawOffset for f64 {
fn raw_inc(self) -> Self {
Self::from_bits(self.to_bits() + 1)
}
fn raw_dec(self) -> Self {
Self::from_bits(self.to_bits() - 1)
}
}
#[test]
fn cast_float_to_int_edge_cases() {
float_test_edge!(f32 -> isize i8 i16 i32 i64);
float_test_edge!(f32 -> usize u8 u16 u32 u64);
float_test_edge!(f64 -> isize i8 i16 i32 i64);
float_test_edge!(f64 -> usize u8 u16 u32 u64);
}
#[test]
fn cast_float_to_i128_edge_cases() {
float_test_edge!(f32 -> i128 u128);
float_test_edge!(f64 -> i128 u128);
}
macro_rules! int_test_edge {
($f:ident -> { $($t:ident)+ } with $BigS:ident $BigU:ident ) => { $({
#[allow(arithmetic_overflow)] // https://github.com/rust-lang/rust/issues/109731
fn test_edge() {
dbg!("testing cast edge cases for {} -> {}", stringify!($f), stringify!($t));
match ($f::MIN as $BigS).cmp(&($t::MIN as $BigS)) {
Greater => {
assert_eq!(Some($f::MIN as $t), cast::<$f, $t>($f::MIN));
}
Equal => {
assert_eq!(Some($t::MIN), cast::<$f, $t>($f::MIN));
}
Less => {
let min = $t::MIN as $f;
assert_eq!(Some($t::MIN), cast::<$f, $t>(min));
assert_eq!(None, cast::<$f, $t>(min - 1));
}
}
match ($f::MAX as $BigU).cmp(&($t::MAX as $BigU)) {
Greater => {
let max = $t::MAX as $f;
assert_eq!(Some($t::MAX), cast::<$f, $t>(max));
assert_eq!(None, cast::<$f, $t>(max + 1));
}
Equal => {
assert_eq!(Some($t::MAX), cast::<$f, $t>($f::MAX));
}
Less => {
assert_eq!(Some($f::MAX as $t), cast::<$f, $t>($f::MAX));
}
}
}
test_edge();
})+}
}
#[test]
fn cast_int_to_int_edge_cases() {
use core::cmp::Ordering::*;
macro_rules! test_edge {
($( $from:ident )+) => { $({
int_test_edge!($from -> { isize i8 i16 i32 i64 } with i64 u64);
int_test_edge!($from -> { usize u8 u16 u32 u64 } with i64 u64);
})+}
}
test_edge!(isize i8 i16 i32 i64);
test_edge!(usize u8 u16 u32 u64);
}
#[test]
fn cast_int_to_128_edge_cases() {
use core::cmp::Ordering::*;
macro_rules! test_edge {
($( $t:ident )+) => {
$(
int_test_edge!($t -> { i128 u128 } with i128 u128);
)+
int_test_edge!(i128 -> { $( $t )+ } with i128 u128);
int_test_edge!(u128 -> { $( $t )+ } with i128 u128);
}
}
test_edge!(isize i8 i16 i32 i64 i128);
test_edge!(usize u8 u16 u32 u64 u128);
}
#[test]
fn newtype_from_primitive() {
#[derive(PartialEq, Debug)]
struct New<T>(T);
// minimal impl
impl<T: FromPrimitive> FromPrimitive for New<T> {
fn from_i64(n: i64) -> Option<Self> {
T::from_i64(n).map(New)
}
fn from_u64(n: u64) -> Option<Self> {
T::from_u64(n).map(New)
}
}
macro_rules! assert_eq_from {
($( $from:ident )+) => {$(
assert_eq!(T::$from(Bounded::min_value()).map(New),
New::<T>::$from(Bounded::min_value()));
assert_eq!(T::$from(Bounded::max_value()).map(New),
New::<T>::$from(Bounded::max_value()));
)+}
}
fn check<T: PartialEq + Debug + FromPrimitive>() {
assert_eq_from!(from_i8 from_i16 from_i32 from_i64 from_isize);
assert_eq_from!(from_u8 from_u16 from_u32 from_u64 from_usize);
assert_eq_from!(from_f32 from_f64);
}
macro_rules! check {
($( $ty:ty )+) => {$( check::<$ty>(); )+}
}
check!(i8 i16 i32 i64 isize);
check!(u8 u16 u32 u64 usize);
}
#[test]
fn newtype_to_primitive() {
#[derive(PartialEq, Debug)]
struct New<T>(T);
// minimal impl
impl<T: ToPrimitive> ToPrimitive for New<T> {
fn to_i64(&self) -> Option<i64> {
self.0.to_i64()
}
fn to_u64(&self) -> Option<u64> {
self.0.to_u64()
}
}
macro_rules! assert_eq_to {
($( $to:ident )+) => {$(
assert_eq!(T::$to(&Bounded::min_value()),
New::<T>::$to(&New(Bounded::min_value())));
assert_eq!(T::$to(&Bounded::max_value()),
New::<T>::$to(&New(Bounded::max_value())));
)+}
}
fn check<T: PartialEq + Debug + Bounded + ToPrimitive>() {
assert_eq_to!(to_i8 to_i16 to_i32 to_i64 to_isize);
assert_eq_to!(to_u8 to_u16 to_u32 to_u64 to_usize);
assert_eq_to!(to_f32 to_f64);
}
macro_rules! check {
($( $ty:ty )+) => {$( check::<$ty>(); )+}
}
check!(i8 i16 i32 i64 isize);
check!(u8 u16 u32 u64 usize);
}