palette/num.rs
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//! Traits for abstracting over numeric types.
//!
//! These traits describe various numeric properties and operations. They are
//! similar in purpose to the immensely helpful traits in
//! [`num-traits`](https://crates.io/crates/num-traits/), but the structure is
//! different. The philosophy behind this module is to focus on capabilities,
//! rather than categories, and to assume as little as possible. Within reason.
//!
//! Instead of having large traits with a lot of methods and dependencies, each
//! operation (or group of operations), are separated into their own traits.
//! This allows number types to have partial compatibility by only implementing
//! some of the traits, and new methods can be added as new traits without
//! affecting old functionality.
use core::ops::{Add, Div, Mul, Neg, Sub};
use crate::bool_mask::HasBoolMask;
#[cfg(all(not(feature = "std"), feature = "libm"))]
mod libm;
#[cfg(feature = "wide")]
mod wide;
/// Numbers that belong to the real number set. It's both a semantic marker and
/// provides a constructor for number constants.
pub trait Real {
/// Create a number from an `f64` value, mainly for converting constants.
#[must_use]
fn from_f64(n: f64) -> Self;
}
/// Trait for creating a vectorized value from a scalar value.
pub trait FromScalar {
/// The scalar type that is stored in each lane of `Self`. Scalar types
/// should set this to equal `Self`.
type Scalar;
/// Create a new vectorized value where each lane is `scalar`. This
/// corresponds to `splat` for SIMD types.
#[must_use]
fn from_scalar(scalar: Self::Scalar) -> Self;
}
/// Conversion from an array of scalars to a vectorized value.
pub trait FromScalarArray<const N: usize>: FromScalar {
/// Creates a vectorized value from an array of scalars.
#[must_use]
fn from_array(scalars: [Self::Scalar; N]) -> Self;
}
/// Conversion from a vectorized value to an array of scalars.
pub trait IntoScalarArray<const N: usize>: FromScalar {
/// Creates an array of scalars from a vectorized value.
#[must_use]
fn into_array(self) -> [Self::Scalar; N];
}
/// Methods for the value `0`.
pub trait Zero {
/// Create a new `0` value.
#[must_use]
fn zero() -> Self;
}
/// Methods for the value `1`.
pub trait One {
/// Create a new `1` value.
#[must_use]
fn one() -> Self;
}
/// A helper trait that collects arithmetic traits under one name.
pub trait Arithmetics
where
Self: Add<Output = Self>
+ Sub<Output = Self>
+ Mul<Output = Self>
+ Div<Output = Self>
+ Neg<Output = Self>
+ Sized,
for<'a> Self: Add<&'a Self, Output = Self>
+ Sub<&'a Self, Output = Self>
+ Mul<&'a Self, Output = Self>
+ Div<&'a Self, Output = Self>,
{
}
impl<T> Arithmetics for T
where
T: Add<Output = Self>
+ Sub<Output = Self>
+ Mul<Output = Self>
+ Div<Output = Self>
+ Neg<Output = Self>
+ Sized,
for<'a> Self: Add<&'a Self, Output = Self>
+ Sub<&'a Self, Output = Self>
+ Mul<&'a Self, Output = Self>
+ Div<&'a Self, Output = Self>,
{
}
/// Methods for getting the largest or smallest of two values.
pub trait MinMax: Sized {
/// Return the smallest of `self` and `other`.
#[must_use]
fn min(self, other: Self) -> Self;
/// Return the largest of `self` and `other`.
#[must_use]
fn max(self, other: Self) -> Self;
/// Return a pair of `self` and `other`, where the smallest is the first
/// value and the largest is the second.
#[must_use]
fn min_max(self, other: Self) -> (Self, Self);
}
/// Trigonometry methods and their inverses.
pub trait Trigonometry: Sized {
/// Compute the sine of `self` (in radians).
#[must_use]
fn sin(self) -> Self;
/// Compute the cosine of `self` (in radians).
#[must_use]
fn cos(self) -> Self;
/// Simultaneously compute the sine and cosine of `self` (in radians).
/// Returns `(sin(self), cos(self))`.
#[must_use]
fn sin_cos(self) -> (Self, Self);
/// Compute the tangent of `self` (in radians).
#[must_use]
fn tan(self) -> Self;
/// Compute the arcsine in radians of `self`.
#[must_use]
fn asin(self) -> Self;
/// Compute the arccosine in radians of `self`.
#[must_use]
fn acos(self) -> Self;
/// Compute the arctangent in radians of `self`.
#[must_use]
fn atan(self) -> Self;
/// Compute the arctangent in radians of `self` (y) and `other` (x).
#[must_use]
fn atan2(self, other: Self) -> Self;
}
/// Method for getting the absolute value of a number.
pub trait Abs {
/// Returns the absolute value of `self`.
#[must_use]
fn abs(self) -> Self;
}
/// Method for getting the square root of a number.
pub trait Sqrt {
/// Returns the square root of `self`.
#[must_use]
fn sqrt(self) -> Self;
}
/// Method for getting the cube root of a number.
pub trait Cbrt {
/// Returns the cube root of `self`.
#[must_use]
fn cbrt(self) -> Self;
}
/// Method for raising a number by a real number exponent.
///
/// The name "powf" is kept for familiarity, even though the exponent doesn't
/// have to be a floating point number.
pub trait Powf {
/// Return `self` raised to the power of `exp`.
#[must_use]
fn powf(self, exp: Self) -> Self;
}
/// Method for raising a number by a signed integer exponent.
pub trait Powi {
/// Return `self` raised to the power of `exp`.
#[must_use]
fn powi(self, exp: i32) -> Self;
}
/// Method for raising a number by a n unsigned integer exponent.
pub trait Powu {
/// Return `self` raised to the power of `exp`.
#[must_use]
fn powu(self, exp: u32) -> Self;
}
/// Method for calculating `1 / x`.
pub trait Recip {
/// Return `1 / self`.
#[must_use]
fn recip(self) -> Self;
}
/// Methods for calculating `e ^ x`,
pub trait Exp {
/// Return `e ^ self`.
#[must_use]
fn exp(self) -> Self;
}
/// Methods for checking if a number can be used as a divisor.
pub trait IsValidDivisor: HasBoolMask {
/// Return `true` if `self` can be used as a divisor in `x / self`.
///
/// This checks that division by `self` will result in a finite and defined
/// value. Integers check for `self != 0`, while floating point types call
/// [`is_normal`][std::primitive::f32::is_normal].
#[must_use]
fn is_valid_divisor(&self) -> Self::Mask;
}
/// Methods for calculating the lengths of a hypotenuse.
pub trait Hypot {
/// Returns the length of the hypotenuse formed by `self` and `other`, i.e.
/// `sqrt(self * self + other * other)`.
#[must_use]
fn hypot(self, other: Self) -> Self;
}
/// Methods for rounding numbers to integers.
pub trait Round {
/// Return the nearest integer to `self`. Round half-way cases away from 0.0.
#[must_use]
fn round(self) -> Self;
/// Return the largest integer less than or equal to `self`.
#[must_use]
fn floor(self) -> Self;
/// Return the smallest integer greater than or equal to `self`.
#[must_use]
fn ceil(self) -> Self;
}
/// Trait for clamping a value.
pub trait Clamp {
/// Clamp self to be within the range `[min, max]`.
#[must_use]
fn clamp(self, min: Self, max: Self) -> Self;
/// Clamp self to be within the range `[min, ∞)`.
#[must_use]
fn clamp_min(self, min: Self) -> Self;
/// Clamp self to be within the range `(-∞, max]`.
#[must_use]
fn clamp_max(self, max: Self) -> Self;
}
/// Assigning trait for clamping a value.
pub trait ClampAssign {
/// Clamp self to be within the range `[min, max]`.
fn clamp_assign(&mut self, min: Self, max: Self);
/// Clamp self to be within the range `[min, ∞)`.
fn clamp_min_assign(&mut self, min: Self);
/// Clamp self to be within the range `(-∞, max]`.
fn clamp_max_assign(&mut self, max: Self);
}
/// Combined multiplication and addition operation.
pub trait MulAdd {
/// Multiplies self with `m` and add `a`, as in `(self * m) + a`.
#[must_use]
fn mul_add(self, m: Self, a: Self) -> Self;
}
/// Combined multiplication and subtraction operation.
pub trait MulSub {
/// Multiplies self with `m` and subtract `s`, as in `(self * m) - s`.
#[must_use]
fn mul_sub(self, m: Self, s: Self) -> Self;
}
/// Saturating addition operation.
pub trait SaturatingAdd<Rhs = Self> {
/// The resulting type.
type Output;
/// Returns the sum of `self` and `other`, but saturates instead of overflowing.
#[must_use]
fn saturating_add(self, other: Rhs) -> Self::Output;
}
/// Saturating subtraction operation.
pub trait SaturatingSub<Rhs = Self> {
/// The resulting type.
type Output;
/// Returns the difference of `self` and `other`, but saturates instead of overflowing.
#[must_use]
fn saturating_sub(self, other: Rhs) -> Self::Output;
}
/// Trait for getting a number that represents the sign of `self`.
pub trait Signum {
/// Returns a number that represents the sign of `self`. For floating point:
///
/// * `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
fn signum(self) -> Self;
}
/// Trait for getting the natural logarithm of `self`.
pub trait Ln {
/// Returns the natural logarithm of `self`.
fn ln(self) -> Self;
}
macro_rules! impl_uint {
($($ty: ident),+) => {
$(
impl FromScalar for $ty {
type Scalar = Self;
#[inline]
fn from_scalar(scalar: Self) -> Self {
scalar
}
}
impl FromScalarArray<1> for $ty {
#[inline]
fn from_array(scalars: [Self; 1]) -> Self {
let [scalar] = scalars;
scalar
}
}
impl IntoScalarArray<1> for $ty {
#[inline]
fn into_array(self) -> [Self; 1] {
[self]
}
}
impl Zero for $ty {
#[inline]
fn zero() -> Self {
0
}
}
impl One for $ty {
#[inline]
fn one() -> Self {
1
}
}
impl MinMax for $ty {
#[inline]
fn min(self, other: Self) -> Self {
core::cmp::Ord::min(self, other)
}
#[inline]
fn max(self, other: Self) -> Self {
core::cmp::Ord::max(self, other)
}
#[inline]
fn min_max(self, other: Self) -> (Self, Self) {
if self > other {
(other, self)
} else {
(self, other)
}
}
}
impl Powu for $ty {
#[inline]
fn powu(self, exp: u32) -> Self {
pow(self, exp)
}
}
impl IsValidDivisor for $ty {
#[inline]
fn is_valid_divisor(&self) -> bool {
*self != 0
}
}
impl Clamp for $ty {
#[inline]
fn clamp(self, min: Self, max: Self) -> Self {
core::cmp::Ord::clamp(self, min, max)
}
#[inline]
fn clamp_min(self, min: Self) -> Self {
core::cmp::Ord::max(self, min)
}
#[inline]
fn clamp_max(self, max: Self) -> Self {
core::cmp::Ord::min(self, max)
}
}
impl ClampAssign for $ty {
#[inline]
fn clamp_assign(&mut self, min: Self, max: Self) {
*self = core::cmp::Ord::clamp(*self, min, max);
}
#[inline]
fn clamp_min_assign(&mut self, min: Self) {
*self = core::cmp::Ord::max(*self, min);
}
#[inline]
fn clamp_max_assign(&mut self, max: Self) {
*self = core::cmp::Ord::min(*self, max);
}
}
impl MulAdd for $ty {
#[inline]
fn mul_add(self, m: Self, a: Self) -> Self {
(self * m) + a
}
}
impl MulSub for $ty {
#[inline]
fn mul_sub(self, m: Self, s: Self) -> Self {
(self * m) - s
}
}
impl SaturatingAdd for $ty {
type Output = $ty;
#[inline]
fn saturating_add(self, other: Self) -> Self{
<$ty>::saturating_add(self, other)
}
}
impl SaturatingSub for $ty {
type Output = $ty;
#[inline]
fn saturating_sub(self, other: Self) -> Self{
<$ty>::saturating_sub(self, other)
}
}
)+
};
}
macro_rules! impl_float {
($($ty: ident),+) => {
$(
impl Real for $ty {
#[inline]
fn from_f64(n: f64) -> $ty {
n as $ty
}
}
impl FromScalar for $ty {
type Scalar = Self;
#[inline]
fn from_scalar(scalar: Self) -> Self {
scalar
}
}
impl FromScalarArray<1> for $ty {
#[inline]
fn from_array(scalars: [Self; 1]) -> Self {
let [scalar] = scalars;
scalar
}
}
impl IntoScalarArray<1> for $ty {
#[inline]
fn into_array(self) -> [Self; 1] {
[self]
}
}
impl Zero for $ty {
#[inline]
fn zero() -> Self {
0.0
}
}
impl One for $ty {
#[inline]
fn one() -> Self {
1.0
}
}
impl MinMax for $ty {
#[inline]
fn max(self, other: Self) -> Self {
$ty::max(self, other)
}
#[inline]
fn min(self, other: Self) -> Self {
$ty::min(self, other)
}
#[inline]
fn min_max(self, other: Self) -> (Self, Self) {
if self > other {
(other, self)
} else {
(self, other)
}
}
}
impl Powu for $ty {
#[inline]
fn powu(self, exp: u32) -> Self {
pow(self, exp)
}
}
impl IsValidDivisor for $ty {
#[inline]
fn is_valid_divisor(&self) -> bool {
$ty::is_normal(*self)
}
}
#[cfg(any(feature = "std", all(test, not(feature = "libm"))))]
impl Trigonometry for $ty {
#[inline]
fn sin(self) -> Self {
$ty::sin(self)
}
#[inline]
fn cos(self) -> Self {
$ty::cos(self)
}
#[inline]
fn sin_cos(self) -> (Self, Self) {
$ty::sin_cos(self)
}
#[inline]
fn tan(self) -> Self {
$ty::tan(self)
}
#[inline]
fn asin(self) -> Self {
$ty::asin(self)
}
#[inline]
fn acos(self) -> Self {
$ty::acos(self)
}
#[inline]
fn atan(self) -> Self {
$ty::atan(self)
}
#[inline]
fn atan2(self, other: Self) -> Self {
$ty::atan2(self, other)
}
}
#[cfg(any(feature = "std", all(test, not(feature = "libm"))))]
impl Abs for $ty {
#[inline]
fn abs(self) -> Self {
$ty::abs(self)
}
}
#[cfg(any(feature = "std", all(test, not(feature = "libm"))))]
impl Sqrt for $ty {
#[inline]
fn sqrt(self) -> Self {
$ty::sqrt(self)
}
}
#[cfg(any(feature = "std", all(test, not(feature = "libm"))))]
impl Cbrt for $ty {
#[inline]
fn cbrt(self) -> Self {
$ty::cbrt(self)
}
}
#[cfg(any(feature = "std", all(test, not(feature = "libm"))))]
impl Powf for $ty {
#[inline]
fn powf(self, exp: Self) -> Self {
$ty::powf(self, exp)
}
}
#[cfg(any(feature = "std", all(test, not(feature = "libm"))))]
impl Powi for $ty {
#[inline]
fn powi(self, exp: i32) -> Self {
$ty::powi(self, exp)
}
}
#[cfg(any(feature = "std", all(test, not(feature = "libm"))))]
impl Recip for $ty {
#[inline]
fn recip(self) -> Self {
$ty::recip(self)
}
}
#[cfg(any(feature = "std", all(test, not(feature = "libm"))))]
impl Exp for $ty {
#[inline]
fn exp(self) -> Self {
$ty::exp(self)
}
}
#[cfg(any(feature = "std", all(test, not(feature = "libm"))))]
impl Hypot for $ty {
#[inline]
fn hypot(self, other: Self) -> Self {
$ty::hypot(self, other)
}
}
#[cfg(any(feature = "std", all(test, not(feature = "libm"))))]
impl Round for $ty {
#[inline]
fn round(self) -> Self {
$ty::round(self)
}
#[inline]
fn floor(self) -> Self {
$ty::floor(self)
}
#[inline]
fn ceil(self) -> Self {
$ty::ceil(self)
}
}
impl Clamp for $ty {
#[inline]
fn clamp(self, min: Self, max: Self) -> Self {
$ty::clamp(self, min, max)
}
#[inline]
fn clamp_min(self, min: Self) -> Self {
$ty::max(self, min)
}
#[inline]
fn clamp_max(self, max: Self) -> Self {
$ty::min(self, max)
}
}
impl ClampAssign for $ty {
#[inline]
fn clamp_assign(&mut self, min: Self, max: Self) {
*self = $ty::clamp(*self, min, max);
}
#[inline]
fn clamp_min_assign(&mut self, min: Self) {
*self = $ty::max(*self, min);
}
#[inline]
fn clamp_max_assign(&mut self, max: Self) {
*self = $ty::min(*self, max);
}
}
#[cfg(any(feature = "std", all(test, not(feature = "libm"))))]
impl MulAdd for $ty {
#[inline]
fn mul_add(self, m: Self, a: Self) -> Self {
$ty::mul_add(self, m, a)
}
}
impl MulSub for $ty {
#[inline]
fn mul_sub(self, m: Self, s: Self) -> Self {
(self * m) - s
}
}
#[cfg(any(feature = "std", all(test, not(feature = "libm"))))]
impl Signum for $ty {
#[inline]
fn signum(self) -> Self {
$ty::signum(self)
}
}
#[cfg(any(feature = "std", all(test, not(feature = "libm"))))]
impl Ln for $ty {
#[inline]
fn ln(self) -> Self {
$ty::ln(self)
}
}
)+
};
}
impl_uint!(u8, u16, u32, u64, u128);
impl_float!(f32, f64);
/// "borrowed" from num_traits
///
/// Raises a value to the power of exp, using exponentiation by squaring.
///
/// Note that `0⁰` (`pow(0, 0)`) returns `1`. Mathematically this is undefined.
//
// # Example
//
// ```rust
// use num_traits::pow;
//
// assert_eq!(pow(2i8, 4), 16);
// assert_eq!(pow(6u8, 3), 216);
// assert_eq!(pow(0u8, 0), 1); // Be aware if this case affects you
// ```
#[inline]
fn pow<T: Clone + One + Mul<T, Output = T>>(mut base: T, mut exp: u32) -> T {
if exp == 0 {
return T::one();
}
while exp & 1 == 0 {
base = base.clone() * base;
exp >>= 1;
}
if exp == 1 {
return base;
}
let mut acc = base.clone();
while exp > 1 {
exp >>= 1;
base = base.clone() * base;
if exp & 1 == 1 {
acc = acc * base.clone();
}
}
acc
}
/// Trait for lanewise comparison of two values.
///
/// This is similar to `PartialEq` and `PartialOrd`, except that it returns a
/// Boolean mask instead of `bool` or [`Ordering`][core::cmp::Ordering].
pub trait PartialCmp: HasBoolMask {
/// Compares `self < other`.
#[must_use]
fn lt(&self, other: &Self) -> Self::Mask;
/// Compares `self <= other`.
#[must_use]
fn lt_eq(&self, other: &Self) -> Self::Mask;
/// Compares `self == other`.
#[must_use]
fn eq(&self, other: &Self) -> Self::Mask;
/// Compares `self != other`.
#[must_use]
fn neq(&self, other: &Self) -> Self::Mask;
/// Compares `self >= other`.
#[must_use]
fn gt_eq(&self, other: &Self) -> Self::Mask;
/// Compares `self > other`.
#[must_use]
fn gt(&self, other: &Self) -> Self::Mask;
}
macro_rules! impl_partial_cmp {
($($ty:ident),+) => {
$(
impl PartialCmp for $ty {
#[inline]
fn lt(&self, other: &Self) -> Self::Mask {
self < other
}
#[inline]
fn lt_eq(&self, other: &Self) -> Self::Mask {
self <= other
}
#[inline]
fn eq(&self, other: &Self) -> Self::Mask {
self == other
}
#[inline]
fn neq(&self, other: &Self) -> Self::Mask {
self != other
}
#[inline]
fn gt_eq(&self, other: &Self) -> Self::Mask {
self >= other
}
#[inline]
fn gt(&self, other: &Self) -> Self::Mask {
self > other
}
}
)+
};
}
impl_partial_cmp!(u8, u16, u32, u64, u128, i8, i16, i32, i64, i128, f32, f64);