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Merge #31 

31: Re-export all items from num-traits 0.2 r=cuviper a=cuviper
This commit is contained in:
bors[bot] 2018-02-07 01:22:25 +00:00
parent 3716330128 b8fb4b0c2b
commit c9727a6051
17 changed files with 71 additions and 4486 deletions
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1
.travis.yml
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@ -14,6 +14,7 @@ notifications:
branches: branches:
only: only:
- master - master
- num-traits-0.1.x
- next - next
- staging - staging
- trying - trying

8
Cargo.toml
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@ -8,7 +8,11 @@ categories = [ "algorithms", "science" ]
license = "MIT/Apache-2.0" license = "MIT/Apache-2.0"
repository = "https://github.com/rust-num/num-traits" repository = "https://github.com/rust-num/num-traits"
name = "num-traits" name = "num-traits"
version = "0.1.42" version = "0.1.43"
readme = "README.md" readme = "README.md"
[dependencies] [lib]
doctest = false # multiple rlib candidates for `num_traits` found
[dependencies.num-traits]
version = "0.2.0"

3
README.md
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@ -6,6 +6,9 @@
Numeric traits for generic mathematics in Rust. Numeric traits for generic mathematics in Rust.
This version of the crate only exists to re-export compatible
items from `num-traits` 0.2. Please consider updating!
## Usage ## Usage
Add this to your `Cargo.toml`: Add this to your `Cargo.toml`:

17
RELEASES.md
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@ -1,3 +1,20 @@
# Release 0.2.0
- **breaking change**: There is now a `std` feature, 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
# Release 0.1.43
- All items are now re-exported from num-traits 0.2 for compatibility.
# Release 0.1.42 # Release 0.1.42
- [num-traits now has its own source repository][num-356] at [rust-num/num-traits][home]. - [num-traits now has its own source repository][num-356] at [rust-num/num-traits][home].

99
src/bounds.rs
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@ -1,99 +0,0 @@
use std::{usize, u8, u16, u32, u64};
use std::{isize, i8, i16, i32, i64};
use std::{f32, f64};
use std::num::Wrapping;
/// 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;
}
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!(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);
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>::min_value().0, <$t>::min_value());
assert_eq!(Wrapping::<$t>::max_value().0, <$t>::max_value());
)+
};
}
test_wrapping_bounded!(usize u8 u16 u32 u64 isize i8 i16 i32 i64);
}
#[test]
fn wrapping_is_bounded() {
fn require_bounded<T: Bounded>(_: &T) {}
require_bounded(&Wrapping(42_u32));
require_bounded(&Wrapping(-42));
}

591
src/cast.rs
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@ -1,591 +0,0 @@
use std::mem::size_of;
use std::num::Wrapping;
use identities::Zero;
use bounds::Bounded;
/// A generic trait for converting a value to a number.
pub trait ToPrimitive {
/// Converts the value of `self` to an `isize`.
#[inline]
fn to_isize(&self) -> Option<isize> {
self.to_i64().and_then(|x| x.to_isize())
}
/// Converts the value of `self` to an `i8`.
#[inline]
fn to_i8(&self) -> Option<i8> {
self.to_i64().and_then(|x| x.to_i8())
}
/// Converts the value of `self` to an `i16`.
#[inline]
fn to_i16(&self) -> Option<i16> {
self.to_i64().and_then(|x| x.to_i16())
}
/// Converts the value of `self` to an `i32`.
#[inline]
fn to_i32(&self) -> Option<i32> {
self.to_i64().and_then(|x| x.to_i32())
}
/// Converts the value of `self` to an `i64`.
fn to_i64(&self) -> Option<i64>;
/// Converts the value of `self` to a `usize`.
#[inline]
fn to_usize(&self) -> Option<usize> {
self.to_u64().and_then(|x| x.to_usize())
}
/// Converts the value of `self` to an `u8`.
#[inline]
fn to_u8(&self) -> Option<u8> {
self.to_u64().and_then(|x| x.to_u8())
}
/// Converts the value of `self` to an `u16`.
#[inline]
fn to_u16(&self) -> Option<u16> {
self.to_u64().and_then(|x| x.to_u16())
}
/// Converts the value of `self` to an `u32`.
#[inline]
fn to_u32(&self) -> Option<u32> {
self.to_u64().and_then(|x| x.to_u32())
}
/// Converts the value of `self` to an `u64`.
#[inline]
fn to_u64(&self) -> Option<u64>;
/// Converts the value of `self` to an `f32`.
#[inline]
fn to_f32(&self) -> Option<f32> {
self.to_f64().and_then(|x| x.to_f32())
}
/// Converts the value of `self` to an `f64`.
#[inline]
fn to_f64(&self) -> Option<f64> {
self.to_i64().and_then(|x| x.to_f64())
}
}
macro_rules! impl_to_primitive_int_to_int {
($SrcT:ty, $DstT:ty, $slf:expr) => (
{
if size_of::<$SrcT>() <= size_of::<$DstT>() {
Some($slf as $DstT)
} else {
let n = $slf as i64;
let min_value: $DstT = Bounded::min_value();
let max_value: $DstT = Bounded::max_value();
if min_value as i64 <= n && n <= max_value as i64 {
Some($slf as $DstT)
} else {
None
}
}
}
)
}
macro_rules! impl_to_primitive_int_to_uint {
($SrcT:ty, $DstT:ty, $slf:expr) => (
{
let zero: $SrcT = Zero::zero();
let max_value: $DstT = Bounded::max_value();
if zero <= $slf && $slf as u64 <= max_value as u64 {
Some($slf as $DstT)
} else {
None
}
}
)
}
macro_rules! impl_to_primitive_int {
($T:ty) => (
impl ToPrimitive for $T {
#[inline]
fn to_isize(&self) -> Option<isize> { impl_to_primitive_int_to_int!($T, isize, *self) }
#[inline]
fn to_i8(&self) -> Option<i8> { impl_to_primitive_int_to_int!($T, i8, *self) }
#[inline]
fn to_i16(&self) -> Option<i16> { impl_to_primitive_int_to_int!($T, i16, *self) }
#[inline]
fn to_i32(&self) -> Option<i32> { impl_to_primitive_int_to_int!($T, i32, *self) }
#[inline]
fn to_i64(&self) -> Option<i64> { impl_to_primitive_int_to_int!($T, i64, *self) }
#[inline]
fn to_usize(&self) -> Option<usize> { impl_to_primitive_int_to_uint!($T, usize, *self) }
#[inline]
fn to_u8(&self) -> Option<u8> { impl_to_primitive_int_to_uint!($T, u8, *self) }
#[inline]
fn to_u16(&self) -> Option<u16> { impl_to_primitive_int_to_uint!($T, u16, *self) }
#[inline]
fn to_u32(&self) -> Option<u32> { impl_to_primitive_int_to_uint!($T, u32, *self) }
#[inline]
fn to_u64(&self) -> Option<u64> { impl_to_primitive_int_to_uint!($T, u64, *self) }
#[inline]
fn to_f32(&self) -> Option<f32> { Some(*self as f32) }
#[inline]
fn to_f64(&self) -> Option<f64> { Some(*self as f64) }
}
)
}
impl_to_primitive_int!(isize);
impl_to_primitive_int!(i8);
impl_to_primitive_int!(i16);
impl_to_primitive_int!(i32);
impl_to_primitive_int!(i64);
macro_rules! impl_to_primitive_uint_to_int {
($DstT:ty, $slf:expr) => (
{
let max_value: $DstT = Bounded::max_value();
if $slf as u64 <= max_value as u64 {
Some($slf as $DstT)
} else {
None
}
}
)
}
macro_rules! impl_to_primitive_uint_to_uint {
($SrcT:ty, $DstT:ty, $slf:expr) => (
{
if size_of::<$SrcT>() <= size_of::<$DstT>() {
Some($slf as $DstT)
} else {
let zero: $SrcT = Zero::zero();
let max_value: $DstT = Bounded::max_value();
if zero <= $slf && $slf as u64 <= max_value as u64 {
Some($slf as $DstT)
} else {
None
}
}
}
)
}
macro_rules! impl_to_primitive_uint {
($T:ty) => (
impl ToPrimitive for $T {
#[inline]
fn to_isize(&self) -> Option<isize> { impl_to_primitive_uint_to_int!(isize, *self) }
#[inline]
fn to_i8(&self) -> Option<i8> { impl_to_primitive_uint_to_int!(i8, *self) }
#[inline]
fn to_i16(&self) -> Option<i16> { impl_to_primitive_uint_to_int!(i16, *self) }
#[inline]
fn to_i32(&self) -> Option<i32> { impl_to_primitive_uint_to_int!(i32, *self) }
#[inline]
fn to_i64(&self) -> Option<i64> { impl_to_primitive_uint_to_int!(i64, *self) }
#[inline]
fn to_usize(&self) -> Option<usize> {
impl_to_primitive_uint_to_uint!($T, usize, *self)
}
#[inline]
fn to_u8(&self) -> Option<u8> { impl_to_primitive_uint_to_uint!($T, u8, *self) }
#[inline]
fn to_u16(&self) -> Option<u16> { impl_to_primitive_uint_to_uint!($T, u16, *self) }
#[inline]
fn to_u32(&self) -> Option<u32> { impl_to_primitive_uint_to_uint!($T, u32, *self) }
#[inline]
fn to_u64(&self) -> Option<u64> { impl_to_primitive_uint_to_uint!($T, u64, *self) }
#[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);
macro_rules! impl_to_primitive_float_to_float {
($SrcT:ident, $DstT:ident, $slf:expr) => (
if size_of::<$SrcT>() <= size_of::<$DstT>() {
Some($slf as $DstT)
} else {
// Make sure the value is in range for the cast.
// NaN and +-inf are cast as they are.
let n = $slf as f64;
let max_value: $DstT = ::std::$DstT::MAX;
if !n.is_finite() || (-max_value as f64 <= n && n <= max_value as f64) {
Some($slf as $DstT)
} else {
None
}
}
)
}
macro_rules! impl_to_primitive_float {
($T:ident) => (
impl ToPrimitive for $T {
#[inline]
fn to_isize(&self) -> Option<isize> { Some(*self as isize) }
#[inline]
fn to_i8(&self) -> Option<i8> { Some(*self as i8) }
#[inline]
fn to_i16(&self) -> Option<i16> { Some(*self as i16) }
#[inline]
fn to_i32(&self) -> Option<i32> { Some(*self as i32) }
#[inline]
fn to_i64(&self) -> Option<i64> { Some(*self as i64) }
#[inline]
fn to_usize(&self) -> Option<usize> { Some(*self as usize) }
#[inline]
fn to_u8(&self) -> Option<u8> { Some(*self as u8) }
#[inline]
fn to_u16(&self) -> Option<u16> { Some(*self as u16) }
#[inline]
fn to_u32(&self) -> Option<u32> { Some(*self as u32) }
#[inline]
fn to_u64(&self) -> Option<u64> { Some(*self as u64) }
#[inline]
fn to_f32(&self) -> Option<f32> { impl_to_primitive_float_to_float!($T, f32, *self) }
#[inline]
fn to_f64(&self) -> Option<f64> { impl_to_primitive_float_to_float!($T, f64, *self) }
}
)
}
impl_to_primitive_float!(f32);
impl_to_primitive_float!(f64);
/// A generic trait for converting a number to a value.
pub trait FromPrimitive: Sized {
/// Convert an `isize` to return an optional value of this type. If the
/// value cannot be represented by this value, the `None` is returned.
#[inline]
fn from_isize(n: isize) -> Option<Self> {
FromPrimitive::from_i64(n as i64)
}
/// Convert an `i8` to return an optional value of this type. If the
/// type cannot be represented by this value, the `None` is returned.
#[inline]
fn from_i8(n: i8) -> Option<Self> {
FromPrimitive::from_i64(n as i64)
}
/// Convert an `i16` to return an optional value of this type. If the
/// type cannot be represented by this value, the `None` is returned.
#[inline]
fn from_i16(n: i16) -> Option<Self> {
FromPrimitive::from_i64(n as i64)
}
/// Convert an `i32` to return an optional value of this type. If the
/// type cannot be represented by this value, the `None` is returned.
#[inline]
fn from_i32(n: i32) -> Option<Self> {
FromPrimitive::from_i64(n as i64)
}
/// Convert an `i64` to return an optional value of this type. If the
/// type cannot be represented by this value, the `None` is returned.
fn from_i64(n: i64) -> Option<Self>;
/// Convert a `usize` to return an optional value of this type. If the
/// type cannot be represented by this value, the `None` is returned.
#[inline]
fn from_usize(n: usize) -> Option<Self> {
FromPrimitive::from_u64(n as u64)
}
/// Convert an `u8` to return an optional value of this type. If the
/// type cannot be represented by this value, the `None` is returned.
#[inline]
fn from_u8(n: u8) -> Option<Self> {
FromPrimitive::from_u64(n as u64)
}
/// Convert an `u16` to return an optional value of this type. If the
/// type cannot be represented by this value, the `None` is returned.
#[inline]
fn from_u16(n: u16) -> Option<Self> {
FromPrimitive::from_u64(n as u64)
}
/// Convert an `u32` to return an optional value of this type. If the
/// type cannot be represented by this value, the `None` is returned.
#[inline]
fn from_u32(n: u32) -> Option<Self> {
FromPrimitive::from_u64(n as u64)
}
/// Convert an `u64` to return an optional value of this type. If the
/// type cannot be represented by this value, the `None` is returned.
fn from_u64(n: u64) -> Option<Self>;
/// Convert a `f32` to return an optional value of this type. If the
/// type cannot be represented by this value, the `None` is returned.
#[inline]
fn from_f32(n: f32) -> Option<Self> {
FromPrimitive::from_f64(n as f64)
}
/// Convert a `f64` to return an optional value of this type. If the
/// type cannot be represented by this value, the `None` is returned.
#[inline]
fn from_f64(n: f64) -> Option<Self> {
FromPrimitive::from_i64(n as i64)
}
}
macro_rules! impl_from_primitive {
($T:ty, $to_ty:ident) => (
#[allow(deprecated)]
impl FromPrimitive for $T {
#[inline] fn from_i8(n: i8) -> Option<$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.$to_ty() }
#[inline] fn from_u8(n: u8) -> Option<$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.$to_ty() }
#[inline] fn from_f32(n: f32) -> Option<$T> { n.$to_ty() }
#[inline] fn from_f64(n: f64) -> Option<$T> { n.$to_ty() }
}
)
}
impl_from_primitive!(isize, to_isize);
impl_from_primitive!(i8, to_i8);
impl_from_primitive!(i16, to_i16);
impl_from_primitive!(i32, to_i32);
impl_from_primitive!(i64, to_i64);
impl_from_primitive!(usize, to_usize);
impl_from_primitive!(u8, to_u8);
impl_from_primitive!(u16, to_u16);
impl_from_primitive!(u32, to_u32);
impl_from_primitive!(u64, to_u64);
impl_from_primitive!(f32, to_f32);
impl_from_primitive!(f64, to_f64);
impl<T: ToPrimitive> ToPrimitive for Wrapping<T> {
fn to_i64(&self) -> Option<i64> { self.0.to_i64() }
fn to_u64(&self) -> Option<u64> { self.0.to_u64() }
}
impl<T: FromPrimitive> FromPrimitive for Wrapping<T> {
fn from_u64(n: u64) -> Option<Self> { T::from_u64(n).map(Wrapping) }
fn from_i64(n: i64) -> Option<Self> { T::from_i64(n).map(Wrapping) }
}
/// Cast from one machine scalar to another.
///
/// # Examples
///
/// ```
/// # use num_traits as num;
/// let twenty: f32 = num::cast(0x14).unwrap();
/// assert_eq!(twenty, 20f32);
/// ```
///
#[inline]
pub fn cast<T: NumCast, U: NumCast>(n: T) -> Option<U> {
NumCast::from(n)
}
/// An interface for casting between machine scalars.
pub trait NumCast: Sized + ToPrimitive {
/// Creates a number from another value that can be converted into
/// a primitive via the `ToPrimitive` trait.
fn from<T: ToPrimitive>(n: T) -> Option<Self>;
}
macro_rules! impl_num_cast {
($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!(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!(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
///
/// Currently, some uses of the `as` operator are not entirely safe.
/// In particular, it is undefined behavior if:
///
/// - A truncated floating point value cannot 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
/// ```
///
/// - Or a floating point value does not fit in another floating
/// point type ([#15536](https://github.com/rust-lang/rust/issues/15536)).
///
/// ```ignore
/// # use num_traits::AsPrimitive;
/// let x: f32 = (1e300f64).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 => $( $U: ty ),* ) => {
$(
impl AsPrimitive<$U> for $T {
#[inline] fn as_(self) -> $U { self as $U }
}
)*
};
}
impl_as_primitive!(u8 => char, u8, i8, u16, i16, u32, i32, u64, isize, usize, i64, f32, f64);
impl_as_primitive!(i8 => u8, i8, u16, i16, u32, i32, u64, isize, usize, i64, f32, f64);
impl_as_primitive!(u16 => u8, i8, u16, i16, u32, i32, u64, isize, usize, i64, f32, f64);
impl_as_primitive!(i16 => u8, i8, u16, i16, u32, i32, u64, isize, usize, i64, f32, f64);
impl_as_primitive!(u32 => u8, i8, u16, i16, u32, i32, u64, isize, usize, i64, f32, f64);
impl_as_primitive!(i32 => u8, i8, u16, i16, u32, i32, u64, isize, usize, i64, f32, f64);
impl_as_primitive!(u64 => u8, i8, u16, i16, u32, i32, u64, isize, usize, i64, f32, f64);
impl_as_primitive!(i64 => u8, i8, u16, i16, u32, i32, u64, isize, usize, i64, f32, f64);
impl_as_primitive!(usize => u8, i8, u16, i16, u32, i32, u64, isize, usize, i64, f32, f64);
impl_as_primitive!(isize => u8, i8, u16, i16, u32, i32, u64, isize, usize, i64, f32, f64);
impl_as_primitive!(f32 => u8, i8, u16, i16, u32, i32, u64, isize, usize, i64, f32, f64);
impl_as_primitive!(f64 => u8, i8, u16, i16, u32, i32, u64, isize, usize, i64, f32, f64);
impl_as_primitive!(char => char, u8, i8, u16, i16, u32, i32, u64, isize, usize, i64);
impl_as_primitive!(bool => u8, i8, u16, i16, u32, i32, u64, isize, usize, i64);
#[test]
fn to_primitive_float() {
use std::f32;
use std::f64;
let f32_toolarge = 1e39f64;
assert_eq!(f32_toolarge.to_f32(), None);
assert_eq!((f32::MAX as f64).to_f32(), Some(f32::MAX));
assert_eq!((-f32::MAX as f64).to_f32(), Some(-f32::MAX));
assert_eq!(f64::INFINITY.to_f32(), Some(f32::INFINITY));
assert_eq!((f64::NEG_INFINITY).to_f32(), Some(f32::NEG_INFINITY));
assert!((f64::NAN).to_f32().map_or(false, |f| f.is_nan()));
}
#[test]
fn wrapping_to_primitive() {
macro_rules! test_wrapping_to_primitive {
($($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);
}

1344
src/float.rs
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148
src/identities.rs
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@ -1,148 +0,0 @@
use std::ops::{Add, Mul};
use std::num::Wrapping;
/// Defines an additive identity element for `Self`.
pub trait Zero: Sized + Add<Self, Output = Self> {
/// Returns the additive identity element of `Self`, `0`.
///
/// # Laws
///
/// ```{.text}
/// a + 0 = a ∀ a ∈ Self
/// 0 + a = a ∀ a ∈ Self
/// ```
///
/// # 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.
// FIXME (#5527): This should be an associated constant
fn zero() -> Self;
/// Returns `true` if `self` is equal to the additive identity.
#[inline]
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 == $v }
}
}
}
zero_impl!(usize, 0usize);
zero_impl!(u8, 0u8);
zero_impl!(u16, 0u16);
zero_impl!(u32, 0u32);
zero_impl!(u64, 0u64);
zero_impl!(isize, 0isize);
zero_impl!(i8, 0i8);
zero_impl!(i16, 0i16);
zero_impl!(i32, 0i32);
zero_impl!(i64, 0i64);
zero_impl!(f32, 0.0f32);
zero_impl!(f64, 0.0f64);
impl<T: Zero> Zero for Wrapping<T> where Wrapping<T>: Add<Output=Wrapping<T>> {
fn is_zero(&self) -> bool {
self.0.is_zero()
}
fn zero() -> Self {
Wrapping(T::zero())
}
}
/// Defines a multiplicative identity element for `Self`.
pub trait One: Sized + Mul<Self, Output = Self> {
/// Returns the multiplicative identity element of `Self`, `1`.
///
/// # Laws
///
/// ```{.text}
/// a * 1 = a ∀ a ∈ Self
/// 1 * a = a ∀ a ∈ Self
/// ```
///
/// # Purity
///
/// This function should return the same result at all times regardless of
/// external mutable state, for example values stored in TLS or in
/// `static mut`s.
// FIXME (#5527): This should be an associated constant
fn one() -> Self;
}
macro_rules! one_impl {
($t:ty, $v:expr) => {
impl One for $t {
#[inline]
fn one() -> $t { $v }
}
}
}
one_impl!(usize, 1usize);
one_impl!(u8, 1u8);
one_impl!(u16, 1u16);
one_impl!(u32, 1u32);
one_impl!(u64, 1u64);
one_impl!(isize, 1isize);
one_impl!(i8, 1i8);
one_impl!(i16, 1i16);
one_impl!(i32, 1i32);
one_impl!(i64, 1i64);
one_impl!(f32, 1.0f32);
one_impl!(f64, 1.0f64);
impl<T: One> One for Wrapping<T> where Wrapping<T>: Mul<Output=Wrapping<T>> {
fn one() -> Self {
Wrapping(T::one())
}
}
// Some helper functions provided for backwards compatibility.
/// Returns the additive identity, `0`.
#[inline(always)] pub fn zero<T: Zero>() -> T { Zero::zero() }
/// Returns the multiplicative identity, `1`.
#[inline(always)] pub fn one<T: One>() -> T { One::one() }
#[test]
fn wrapping_identities() {
macro_rules! test_wrapping_identities {
($($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));
}

376
src/int.rs
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@ -1,376 +0,0 @@
use std::ops::{Not, BitAnd, BitOr, BitXor, Shl, Shr};
use {Num, NumCast};
use bounds::Bounded;
use ops::checked::*;
use ops::saturating::Saturating;
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 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 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 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 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 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 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 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 amount, `n`, filling
/// zeros in the most significant bits.
///
/// This is bitwise equivalent to unsigned `Shr`.
///
/// # Examples
///
/// ```
/// use num_traits::PrimInt;
///
/// let n = 0xFEDCBA9876543210i64;
/// let m = 0x000FEDCBA9876543i64;
///
/// assert_eq!(n.unsigned_shr(12), 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;
/// 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;
}
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 {
<$T>::count_zeros(self)
}
#[inline]
fn leading_zeros(self) -> u32 {
<$T>::leading_zeros(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)
}
#[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!(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!(isize, isize, usize);

449
src/lib.rs
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@ -9,441 +9,80 @@
// except according to those terms. // except according to those terms.
//! Numeric traits for generic mathematics //! Numeric traits for generic mathematics
//!
//! This version of the crate only exists to re-export compatible
//! items from num-traits 0.2. Please consider updating!
#![doc(html_root_url = "https://docs.rs/num-traits/0.1")] #![doc(html_root_url = "https://docs.rs/num-traits/0.1")]
use std::ops::{Add, Sub, Mul, Div, Rem}; extern crate num_traits;
use std::ops::{AddAssign, SubAssign, MulAssign, DivAssign, RemAssign};
use std::num::Wrapping;
use std::fmt;
pub use bounds::Bounded; pub use bounds::Bounded;
pub use float::{Float, FloatConst}; pub use float::{Float, FloatConst};
// pub use real::Real; // NOTE: Don't do this, it breaks `use num_traits::*;`. // pub use real::Real; // NOTE: Don't do this, it breaks `use num_traits::*;`.
pub use identities::{Zero, One, zero, one}; pub use identities::{Zero, One, zero, one};
pub use ops::checked::*; pub use ops::checked::{CheckedAdd, CheckedSub, CheckedMul, CheckedDiv, CheckedShl, CheckedShr};
pub use ops::wrapping::*; pub use ops::wrapping::{WrappingAdd, WrappingMul, WrappingSub};
pub use ops::saturating::Saturating; pub use ops::saturating::Saturating;
pub use sign::{Signed, Unsigned, abs, abs_sub, signum}; pub use sign::{Signed, Unsigned, abs, abs_sub, signum};
pub use cast::*; pub use cast::{AsPrimitive, FromPrimitive, ToPrimitive, NumCast, cast};
pub use int::PrimInt; pub use int::PrimInt;
pub use pow::{pow, checked_pow}; pub use pow::{pow, checked_pow};
pub mod identities;
pub mod sign;
pub mod ops;
pub mod bounds;
pub mod float;
pub mod real;
pub mod cast;
pub mod int;
pub mod pow;
/// The base trait for numeric types, covering `0` and `1` values, // Re-exports from num-traits 0.2!
/// comparisons, basic numeric operations, and string conversion.
pub trait Num: PartialEq + Zero + One + NumOps
{
type FromStrRadixErr;
/// Convert from a string and radix <= 36. pub use num_traits::{Num, NumOps, NumRef, RefNum};
/// pub use num_traits::{NumAssignOps, NumAssign, NumAssignRef};
/// # Examples pub use num_traits::{FloatErrorKind, ParseFloatError};
/// pub use num_traits::clamp;
/// ```rust
/// use num_traits::Num; // Note: the module structure is explicitly re-created, rather than re-exporting en masse,
/// // so we won't expose any items that may be added later in the new version.
/// let result = <i32 as Num>::from_str_radix("27", 10);
/// assert_eq!(result, Ok(27)); pub mod identities {
/// pub use num_traits::identities::{Zero, One, zero, one};
/// let result = <i32 as Num>::from_str_radix("foo", 10);
/// assert!(result.is_err());
/// ```
fn from_str_radix(str: &str, radix: u32) -> Result<Self, Self::FromStrRadixErr>;
} }
/// The trait for types implementing basic numeric operations pub mod sign {
/// pub use num_traits::sign::{Signed, Unsigned, abs, abs_sub, signum};
/// 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 references which implement numeric operations, taking the
/// second operand either by value or by reference.
///
/// This is automatically implemented for types which implement the operators.
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> {}
/// The 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 $t {
type FromStrRadixErr = ::std::num::ParseIntError;
#[inline]
fn from_str_radix(s: &str, radix: u32)
-> Result<Self, ::std::num::ParseIntError>
{
<$t>::from_str_radix(s, radix)
}
}
)*)
} }
int_trait_impl!(Num for usize u8 u16 u32 u64 isize i8 i16 i32 i64);
impl<T: Num> Num for Wrapping<T> pub mod ops {
where Wrapping<T>: pub mod saturating {
Add<Output = Wrapping<T>> + Sub<Output = Wrapping<T>> pub use num_traits::ops::saturating::Saturating;
+ Mul<Output = Wrapping<T>> + Div<Output = Wrapping<T>> + Rem<Output = Wrapping<T>> }
{
type FromStrRadixErr = T::FromStrRadixErr; pub mod checked {
fn from_str_radix(str: &str, radix: u32) -> Result<Self, Self::FromStrRadixErr> { pub use num_traits::ops::checked::{CheckedAdd, CheckedSub, CheckedMul, CheckedDiv,
T::from_str_radix(str, radix).map(Wrapping) CheckedShl, CheckedShr};
}
pub mod wrapping {
pub use num_traits::ops::wrapping::{WrappingAdd, WrappingMul, WrappingSub};
} }
} }
pub mod bounds {
#[derive(Debug)] pub use num_traits::bounds::Bounded;
pub enum FloatErrorKind {
Empty,
Invalid,
}
// FIXME: std::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 { pub mod float {
fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result { pub use num_traits::float::{Float, FloatConst};
let description = match self.kind {
FloatErrorKind::Empty => "cannot parse float from empty string",
FloatErrorKind::Invalid => "invalid float literal",
};
description.fmt(f)
}
} }
// FIXME: The standard library from_str_radix on floats was deprecated, so we're stuck pub mod real {
// with this implementation ourselves until we want to make a breaking change. pub use num_traits::real::Real;
// (would have to drop it from `Num` though)
macro_rules! float_trait_impl {
($name:ident for $($t:ty)*) => ($(
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 values
match src {
"inf" => return Ok(Float::infinity()),
"-inf" => return Ok(Float::neg_infinity()),
"NaN" => return Ok(Float::nan()),
_ => {},
}
fn slice_shift_char(src: &str) -> Option<(char, &str)> {
src.chars().nth(0).map(|ch| (ch, &src[1..]))
}
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 = sig * (radix as $t);
// add/subtract current digit depending on sign
if is_positive {
sig = sig + ((digit as isize) as $t);
} else {
sig = 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(Float::infinity()); }
if !is_positive && sig >= prev_sig
{ return Ok(Float::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(Float::infinity()); }
if !is_positive && (prev_sig != (sig + digit as $t) / radix as $t)
{ return Ok(Float::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 = 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(Float::infinity()); }
if !is_positive && sig > prev_sig
{ return Ok(Float::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 }),
};
match (is_positive, exp) {
(true, Ok(exp)) => base.powi(exp as i32),
(false, Ok(exp)) => 1.0 / base.powi(exp as i32),
(_, 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.
#[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
}
} }
#[test] pub mod cast {
fn clamp_test() { pub use num_traits::cast::{AsPrimitive, FromPrimitive, ToPrimitive, NumCast, cast};
// Int test
assert_eq!(1, clamp(1, -1, 2));
assert_eq!(-1, clamp(-2, -1, 2));
assert_eq!(2, clamp(3, -1, 2));
// 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));
} }
#[test] pub mod int {
fn from_str_radix_unwrap() { pub use num_traits::int::PrimInt;
// 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] pub mod pow {
fn wrapping_is_num() { pub use num_traits::pow::{pow, checked_pow};
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)
}
// TODO test `NumAssignRef`, but even the standard numeric types don't
// implement this yet. (see rust pr41336)

162
src/ops/checked.rs
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@ -1,162 +0,0 @@
use std::ops::{Add, Sub, Mul, Div, Shl, Shr};
/// 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, 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);
/// 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, 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);
/// 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, 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);
/// 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, 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);
/// Performs a left shift that returns `None` on overflow.
pub trait CheckedShl: Sized + Shl<u32, Output=Self> {
/// Shifts a number to the left, checking for overflow. If overflow happens,
/// `None` is returned.
///
/// ```
/// 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, 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);
/// Performs a right shift that returns `None` on overflow.
pub trait CheckedShr: Sized + Shr<u32, Output=Self> {
/// Shifts a number to the left, checking for overflow. If overflow happens,
/// `None` is returned.
///
/// ```
/// 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, 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);

3
src/ops/mod.rs
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@ -1,3 +0,0 @@
pub mod saturating;
pub mod checked;
pub mod wrapping;

28
src/ops/saturating.rs
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@ -1,28 +0,0 @@
/// Saturating math operations
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! 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)
}
}
)*}
}
saturating_impl!(Saturating for isize usize i8 u8 i16 u16 i32 u32 i64 u64);

127
src/ops/wrapping.rs
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@ -1,127 +0,0 @@
use std::ops::{Add, Sub, Mul};
use std::num::Wrapping;
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, 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);
/// 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, 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);
/// 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, 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);
// 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))
}
}
#[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) }
assert_eq!(wrapping_add(255, 1), 0u8);
assert_eq!(wrapping_sub(0, 1), 255u8);
assert_eq!(wrapping_mul(255, 2), 254u8);
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);
}
#[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));
}

73
src/pow.rs
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@ -1,73 +0,0 @@
use std::ops::Mul;
use {One, CheckedMul};
/// Raises a value to the power of exp, using exponentiation by squaring.
///
/// # Example
///
/// ```rust
/// use num_traits::pow;
///
/// assert_eq!(pow(2i8, 4), 16);
/// assert_eq!(pow(6u8, 3), 216);
/// ```
#[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.
///
/// 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));
/// ```
#[inline]
pub fn checked_pow<T: Clone + One + CheckedMul>(mut base: T, mut exp: usize) -> Option<T> {
if exp == 0 { return Some(T::one()) }
macro_rules! optry {
( $ expr : expr ) => {
if let Some(val) = $expr { val } else { return None }
}
}
while exp & 1 == 0 {
base = optry!(base.checked_mul(&base));
exp >>= 1;
}
if exp == 1 { return Some(base) }
let mut acc = base.clone();
while exp > 1 {
exp >>= 1;
base = optry!(base.checked_mul(&base));
if exp & 1 == 1 {
acc = optry!(acc.checked_mul(&base));
}
}
Some(acc)
}

924
src/real.rs
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@ -1,924 +0,0 @@
use std::ops::Neg;
use {Num, NumCast, Float};
// 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.
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. This produces a more accurate result with better performance than
/// a separate multiplication operation followed by an add.
///
/// ```
/// 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 {
fn min_value() -> Self {
Self::min_value()
}
fn min_positive_value() -> Self {
Self::min_positive_value()
}
fn epsilon() -> Self {
Self::epsilon()
}
fn max_value() -> Self {
Self::max_value()
}
fn floor(self) -> Self {
self.floor()
}
fn ceil(self) -> Self {
self.ceil()
}
fn round(self) -> Self {
self.round()
}
fn trunc(self) -> Self {
self.trunc()
}
fn fract(self) -> Self {
self.fract()
}
fn abs(self) -> Self {
self.abs()
}
fn signum(self) -> Self {
self.signum()
}
fn is_sign_positive(self) -> bool {
self.is_sign_positive()
}
fn is_sign_negative(self) -> bool {
self.is_sign_negative()
}
fn mul_add(self, a: Self, b: Self) -> Self {
self.mul_add(a, b)
}
fn recip(self) -> Self {
self.recip()
}
fn powi(self, n: i32) -> Self {
self.powi(n)
}
fn powf(self, n: Self) -> Self {
self.powf(n)
}
fn sqrt(self) -> Self {
self.sqrt()
}
fn exp(self) -> Self {
self.exp()
}
fn exp2(self) -> Self {
self.exp2()
}
fn ln(self) -> Self {
self.ln()
}
fn log(self, base: Self) -> Self {
self.log(base)
}
fn log2(self) -> Self {
self.log2()
}
fn log10(self) -> Self {
self.log10()
}
fn to_degrees(self) -> Self {
self.to_degrees()
}
fn to_radians(self) -> Self {
self.to_radians()
}
fn max(self, other: Self) -> Self {
self.max(other)
}
fn min(self, other: Self) -> Self {
self.min(other)
}
fn abs_sub(self, other: Self) -> Self {
self.abs_sub(other)
}
fn cbrt(self) -> Self {
self.cbrt()
}
fn hypot(self, other: Self) -> Self {
self.hypot(other)
}
fn sin(self) -> Self {
self.sin()
}
fn cos(self) -> Self {
self.cos()
}
fn tan(self) -> Self {
self.tan()
}
fn asin(self) -> Self {
self.asin()
}
fn acos(self) -> Self {
self.acos()
}
fn atan(self) -> Self {
self.atan()
}
fn atan2(self, other: Self) -> Self {
self.atan2(other)
}
fn sin_cos(self) -> (Self, Self) {
self.sin_cos()
}
fn exp_m1(self) -> Self {
self.exp_m1()
}
fn ln_1p(self) -> Self {
self.ln_1p()
}
fn sinh(self) -> Self {
self.sinh()
}
fn cosh(self) -> Self {
self.cosh()
}
fn tanh(self) -> Self {
self.tanh()
}
fn asinh(self) -> Self {
self.asinh()
}
fn acosh(self) -> Self {
self.acosh()
}
fn atanh(self) -> Self {
self.atanh()
}
}

204
src/sign.rs
View File

@ -1,204 +0,0 @@
use std::ops::Neg;
use std::{f32, f64};
use std::num::Wrapping;
use 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) -> $t {
match *self {
n if n > 0 => 1,
0 => 0,
_ => -1,
}
}
#[inline]
fn is_positive(&self) -> bool { *self > 0 }
#[inline]
fn is_negative(&self) -> bool { *self < 0 }
}
)*)
}
signed_impl!(isize i8 i16 i32 i64);
impl<T: Signed> Signed for Wrapping<T> where Wrapping<T>: Num + Neg<Output=Wrapping<T>>
{
#[inline]
fn abs(&self) -> Self {
Wrapping(self.0.abs())
}
#[inline]
fn abs_sub(&self, other: &Self) -> Self {
Wrapping(self.0.abs_sub(&other.0))
}
#[inline]
fn signum(&self) -> Self {
Wrapping(self.0.signum())
}
#[inline]
fn is_positive(&self) -> bool { self.0.is_positive() }
#[inline]
fn is_negative(&self) -> bool { self.0.is_negative() }
}
macro_rules! signed_float_impl {
($t:ty, $nan:expr, $inf:expr, $neg_inf:expr) => {
impl Signed for $t {
/// Computes the absolute value. Returns `NAN` if the number is `NAN`.
#[inline]
fn abs(&self) -> $t {
<$t>::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]
#[allow(deprecated)]
fn abs_sub(&self, other: &$t) -> $t {
<$t>::abs_sub(*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) -> $t {
<$t>::signum(*self)
}
/// Returns `true` if the number is positive, including `+0.0` and `INFINITY`
#[inline]
fn is_positive(&self) -> bool { *self > 0.0 || (1.0 / *self) == $inf }
/// Returns `true` if the number is negative, including `-0.0` and `NEG_INFINITY`
#[inline]
fn is_negative(&self) -> bool { *self < 0.0 || (1.0 / *self) == $neg_inf }
}
}
}
signed_float_impl!(f32, f32::NAN, f32::INFINITY, f32::NEG_INFINITY);
signed_float_impl!(f64, f64::NAN, f64::INFINITY, f64::NEG_INFINITY);
/// Computes the absolute value.
///
/// For `f32` and `f64`, `NaN` will be returned if the number is `NaN`
///
/// For signed integers, `::MIN` will be returned if the number is `::MIN`.
#[inline(always)]
pub fn abs<T: Signed>(value: T) -> T {
value.abs()
}
/// The positive difference of two numbers.
///
/// Returns zero if `x` is less than or equal to `y`, otherwise the difference
/// between `x` and `y` is returned.
#[inline(always)]
pub fn abs_sub<T: Signed>(x: T, y: T) -> T {
x.abs_sub(&y)
}
/// Returns the sign of the number.
///
/// For `f32` and `f64`:
///
/// * `1.0` if the number is positive, `+0.0` or `INFINITY`
/// * `-1.0` if the number is negative, `-0.0` or `NEG_INFINITY`
/// * `NaN` if the number is `NaN`
///
/// For signed integers:
///
/// * `0` if the number is zero
/// * `1` if the number is positive
/// * `-1` if the number is negative
#[inline(always)] pub fn signum<T: Signed>(value: T) -> T { value.signum() }
/// A trait for values which cannot be negative
pub trait Unsigned: Num {}
macro_rules! empty_trait_impl {
($name:ident for $($t:ty)*) => ($(
impl $name for $t {}
)*)
}
empty_trait_impl!(Unsigned for usize u8 u16 u32 u64);
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));
}
/*
// Commenting this out since it doesn't compile on Rust 1.8,
// because on this version Wrapping doesn't implement Neg and therefore can't
// implement Signed.
#[test]
fn signed_wrapping_is_signed() {
fn require_signed<T: Signed>(_: &T) {}
require_signed(&Wrapping(-42));
}
*/