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/*!
* Numerical type definitions.
*
* `Numeric` together with `where for<'a> &'a T: NumericRef<T>`
* expresses the operations in [`NumericByValue`] for
* all 4 combinations of by value and by reference. [`Numeric`]
* additionally adds some additional constraints only needed by value on an implementing
* type such as `PartialOrd`, [`ZeroOne`] and
* [`FromUsize`].
*/
use std::cmp::PartialOrd;
use std::iter::Sum;
use std::marker::Sized;
use std::num::Wrapping;
use std::ops::Add;
use std::ops::Div;
use std::ops::Mul;
use std::ops::Neg;
use std::ops::Sub;
/**
* A trait defining what a numeric type is in terms of by value
* numerical operations matrices need their types to support for
* math operations.
*
* The requirements are Add, Sub, Mul, Div, Neg and Sized. Note that
* unsigned integers do not implement Neg unless they are wrapped by
* [Wrapping](std::num::Wrapping).
*/
pub trait NumericByValue<Rhs = Self, Output = Self>:
Add<Rhs, Output = Output>
+ Sub<Rhs, Output = Output>
+ Mul<Rhs, Output = Output>
+ Div<Rhs, Output = Output>
+ Neg<Output = Output>
+ Sized
{
}
/**
* Anything which implements all the super traits will automatically implement this trait too.
* This covers primitives such as f32, f64, signed integers and
* [Wrapped unsigned integers](std::num::Wrapping)
* as well as [Traces](super::differentiation::Trace) and
* [Records](super::differentiation::Record) of those types.
*
* It will not include Matrix because Matrix does not implement Div.
* Similarly, unwrapped unsigned integers do not implement Neg so are not included.
*/
impl<T, Rhs, Output> NumericByValue<Rhs, Output> for T where
// Div is first here because Matrix does not implement it.
// if Add, Sub or Mul are first the rust compiler gets stuck
// in an infinite loop considering arbitarily nested matrix
// types, even though any level of nested Matrix types will
// never implement Div so shouldn't be considered for
// implementing NumericByValue
T: Div<Rhs, Output = Output>
+ Add<Rhs, Output = Output>
+ Sub<Rhs, Output = Output>
+ Mul<Rhs, Output = Output>
+ Neg<Output = Output>
+ Sized
{
}
/**
* The trait to define `&T op T` and `&T op &T` versions for NumericByValue
* based off the MIT/Apache 2.0 licensed code from num-traits 0.2.10:
*
* **This trait is not ever used directly for users of this library. You
* don't need to deal with it unless
* [implementing custom numeric types](super::using_custom_types)
* and even then it will be implemented automatically.**
*
* - [http://opensource.org/licenses/MIT](http://opensource.org/licenses/MIT)
* - [https://docs.rs/num-traits/0.2.10/src/num_traits/lib.rs.html#112](https://docs.rs/num-traits/0.2.10/src/num_traits/lib.rs.html#112)
*
* The trick is that all types implementing this trait will be references,
* so the first constraint expresses some &T which can be operated on with
* some right hand side type T to yield a value of type T.
*
* In a similar way the second constraint expresses `&T op &T -> T` operations
*/
pub trait NumericRef<T>:
// &T op T -> T
NumericByValue<T, T>
// &T op &T -> T
+ for<'a> NumericByValue<&'a T, T> {}
/**
* Anything which implements all the super traits will automatically implement this trait too.
* This covers primitives such as `&f32`, `&f64`, ie a type like `&u8` is `NumericRef<u8>`,
* as well as [Traces](super::differentiation::Trace) and
* [Records](super::differentiation::Record) of those types.
*/
impl<RefT, T> NumericRef<T> for RefT where
RefT: NumericByValue<T, T> + for<'a> NumericByValue<&'a T, T>
{
}
/**
* A general purpose numeric trait that defines all the behaviour numerical
* matrices need their types to support for math operations.
*
* This trait extends the constraints in [NumericByValue]
* to types which also support the operations with a right hand side type
* by reference, and adds some additional constraints needed only
* by value on types.
*
* When used together with [NumericRef] this
* expresses all 4 by value and by reference combinations for the
* operations using the following syntax:
*
* ```ignore
* fn function_name<T: Numeric>()
* where for<'a> &'a T: NumericRef<T> {
*
* }
* ```
*
* This pair of constraints is used nearly everywhere some numeric
* type is needed, so although this trait does not require reference
* type methods by itself, in practise you won't be able to call many
* functions in this library with a numeric type that doesn't.
*/
pub trait Numeric:
// T op T -> T
NumericByValue
// T op &T -> T
+ for<'a> NumericByValue<&'a Self>
+ Clone
+ ZeroOne
+ FromUsize
+ Sum
+ PartialOrd {}
/**
* All types implemeting the operations in NumericByValue with a right hand
* side type by reference are Numeric.
*
* This covers primitives such as f32, f64, signed integers and
* [Wrapped unsigned integers](std::num::Wrapping),
* as well as [Traces](super::differentiation::Trace) and
* [Records](super::differentiation::Record) of those types.
*/
impl<T> Numeric for T where
T: NumericByValue
+ for<'a> NumericByValue<&'a T>
+ Clone
+ ZeroOne
+ FromUsize
+ Sum
+ PartialOrd
{
}
/**
* A trait defining how to obtain 0 and 1 for every implementing type.
*
* The boilerplate implementations for primitives is performed with a macro.
* If a primitive type is missing from this list, please open an issue to add it in.
*/
pub trait ZeroOne: Sized {
fn zero() -> Self;
fn one() -> Self;
}
impl<T: ZeroOne> ZeroOne for Wrapping<T> {
#[inline]
fn zero() -> Wrapping<T> {
Wrapping(T::zero())
}
#[inline]
fn one() -> Wrapping<T> {
Wrapping(T::one())
}
}
macro_rules! zero_one_integral {
($T:ty) => {
impl ZeroOne for $T {
#[inline]
fn zero() -> $T {
0
}
#[inline]
fn one() -> $T {
1
}
}
};
}
macro_rules! zero_one_float {
($T:ty) => {
impl ZeroOne for $T {
#[inline]
fn zero() -> $T {
0.0
}
#[inline]
fn one() -> $T {
1.0
}
}
};
}
zero_one_integral!(u8);
zero_one_integral!(i8);
zero_one_integral!(u16);
zero_one_integral!(i16);
zero_one_integral!(u32);
zero_one_integral!(i32);
zero_one_integral!(u64);
zero_one_integral!(i64);
zero_one_integral!(u128);
zero_one_integral!(i128);
zero_one_float!(f32);
zero_one_float!(f64);
zero_one_integral!(usize);
zero_one_integral!(isize);
/**
* Specifies how to obtain an instance of this numeric type
* equal to the usize primitive. If the number is too large to
* represent in this type, `None` should be returned instead.
*
* The boilerplate implementations for primitives is performed with a macro.
* If a primitive type is missing from this list, please open an issue to add it in.
*/
pub trait FromUsize: Sized {
fn from_usize(n: usize) -> Option<Self>;
}
impl<T: FromUsize> FromUsize for Wrapping<T> {
fn from_usize(n: usize) -> Option<Wrapping<T>> {
Some(Wrapping(T::from_usize(n)?))
}
}
macro_rules! from_usize_integral {
($T:ty) => {
impl FromUsize for $T {
#[inline]
fn from_usize(n: usize) -> Option<$T> {
if n <= (<$T>::max_value() as usize) {
Some(n as $T)
} else {
None
}
}
}
};
}
macro_rules! from_usize_float {
($T:ty) => {
impl FromUsize for $T {
#[inline]
fn from_usize(n: usize) -> Option<$T> {
Some(n as $T)
}
}
};
}
from_usize_integral!(u8);
from_usize_integral!(i8);
from_usize_integral!(u16);
from_usize_integral!(i16);
from_usize_integral!(u32);
from_usize_integral!(i32);
from_usize_integral!(u64);
from_usize_integral!(i64);
from_usize_integral!(u128);
from_usize_integral!(i128);
from_usize_float!(f32);
from_usize_float!(f64);
from_usize_integral!(usize);
from_usize_integral!(isize);
/**
* Additional traits for more complex numerical operations on real numbers.
*/
pub mod extra {
/**
* A type which can be square rooted.
*
* This is implemented by `f32` and `f64` by value and by reference, as well as
* [Traces](super::super::differentiation::Trace)
* and [Records](super::super::differentiation::Record) of these.
*/
pub trait Sqrt {
type Output;
fn sqrt(self) -> Self::Output;
}
macro_rules! sqrt_float {
($T:ty) => {
impl Sqrt for $T {
type Output = $T;
#[inline]
fn sqrt(self) -> Self::Output {
self.sqrt()
}
}
impl Sqrt for &$T {
type Output = $T;
#[inline]
fn sqrt(self) -> Self::Output {
self.clone().sqrt()
}
}
};
}
sqrt_float!(f32);
sqrt_float!(f64);
/**
* A type which can compute e^self.
*
* This is implemented by `f32` and `f64` by value and by reference, as well as
* [Traces](super::super::differentiation::Trace)
* and [Records](super::super::differentiation::Record) of these.
*/
pub trait Exp {
type Output;
fn exp(self) -> Self::Output;
}
macro_rules! exp_float {
($T:ty) => {
impl Exp for $T {
type Output = $T;
#[inline]
fn exp(self) -> Self::Output {
self.exp()
}
}
impl Exp for &$T {
type Output = $T;
#[inline]
fn exp(self) -> Self::Output {
self.clone().exp()
}
}
};
}
exp_float!(f32);
exp_float!(f64);
/**
* A type which can compute self^rhs.
*
* This is implemented by `f32` and `f64` for all combinations of
* by value and by reference, as well as
* [Traces](super::super::differentiation::Trace)
* and [Records](super::super::differentiation::Record) of these.
*
* The Trace and Record implementations also implement versions with the other
* argument being a raw `f32` or `f64`, for convenience.
*/
pub trait Pow<Rhs = Self> {
type Output;
fn pow(self, rhs: Rhs) -> Self::Output;
}
macro_rules! pow_float {
($T:ty) => {
// T ^ T
impl Pow<$T> for $T {
type Output = $T;
#[inline]
fn pow(self, rhs: Self) -> Self::Output {
self.powf(rhs)
}
}
// T ^ &T
impl<'a> Pow<&'a $T> for $T {
type Output = $T;
#[inline]
fn pow(self, rhs: &Self) -> Self::Output {
self.powf(rhs.clone())
}
}
// &T ^ T
impl<'a> Pow<$T> for &'a $T {
type Output = $T;
#[inline]
fn pow(self, rhs: $T) -> Self::Output {
self.powf(rhs)
}
}
// &T ^ &T
impl<'a, 'b> Pow<&'b $T> for &'a $T {
type Output = $T;
#[inline]
fn pow(self, rhs: &$T) -> Self::Output {
self.powf(rhs.clone())
}
}
};
}
pow_float!(f32);
pow_float!(f64);
/**
* A type which can represent Pi.
*/
pub trait Pi {
fn pi() -> Self;
}
impl Pi for f32 {
fn pi() -> f32 {
std::f32::consts::PI
}
}
impl Pi for f64 {
fn pi() -> f64 {
std::f64::consts::PI
}
}
/**
* A type which can compute the natural logarithm of itself: ln(self).
*
* This is implemented by `f32` and `f64` by value and by reference, as well as
* [Traces](super::super::differentiation::Trace)
* and [Records](super::super::differentiation::Record) of these.
*/
pub trait Ln {
type Output;
fn ln(self) -> Self::Output;
}
macro_rules! ln_float {
($T:ty) => {
impl Ln for $T {
type Output = $T;
#[inline]
fn ln(self) -> Self::Output {
self.ln()
}
}
impl Ln for &$T {
type Output = $T;
#[inline]
fn ln(self) -> Self::Output {
self.clone().ln()
}
}
};
}
ln_float!(f32);
ln_float!(f64);
/**
* A type which can compute the sine of itself: sin(self)
*
* This is implemented by `f32` and `f64` by value and by reference, as well as
* [Traces](super::super::differentiation::Trace)
* and [Records](super::super::differentiation::Record) of these.
*/
pub trait Sin {
type Output;
fn sin(self) -> Self::Output;
}
macro_rules! sin_float {
($T:ty) => {
impl Sin for $T {
type Output = $T;
#[inline]
fn sin(self) -> Self::Output {
self.sin()
}
}
impl Sin for &$T {
type Output = $T;
#[inline]
fn sin(self) -> Self::Output {
self.clone().sin()
}
}
};
}
sin_float!(f32);
sin_float!(f64);
/**
* A type which can compute the cosine of itself: cos(self)
*
* This is implemented by `f32` and `f64` by value and by reference, as well as
* [Traces](super::super::differentiation::Trace)
* and [Records](super::super::differentiation::Record) of these.
*/
pub trait Cos {
type Output;
fn cos(self) -> Self::Output;
}
macro_rules! cos_float {
($T:ty) => {
impl Cos for $T {
type Output = $T;
#[inline]
fn cos(self) -> Self::Output {
self.cos()
}
}
impl Cos for &$T {
type Output = $T;
#[inline]
fn cos(self) -> Self::Output {
self.clone().cos()
}
}
};
}
cos_float!(f32);
cos_float!(f64);
/**
* A trait defining what a real number type is in terms of by value
* numerical operations needed on top of operations defined by Numeric
* for some functions.
*
* The requirements are Sqrt, Exp, Pow, Ln, Sin, Cos and Sized.
*/
pub trait RealByValue<Rhs = Self, Output = Self>:
Sqrt<Output = Output>
+ Exp<Output = Output>
+ Pow<Rhs, Output = Output>
+ Ln<Output = Output>
+ Sin<Output = Output>
+ Cos<Output = Output>
+ Sized
{
}
/**
* Anything which implements all the super traits will automatically implement this trait too.
* This covers primitives such as f32 & f64 as well as
* [Traces](super::super::differentiation::Trace) and
* [Records](super::super::differentiation::Record) of those types.
*/
impl<T, Rhs, Output> RealByValue<Rhs, Output> for T where
T: Sqrt<Output = Output>
+ Exp<Output = Output>
+ Pow<Rhs, Output = Output>
+ Ln<Output = Output>
+ Sin<Output = Output>
+ Cos<Output = Output>
+ Sized
{
}
/**
* The trait to define `&T op T` and `&T op &T` versions for RealByValue
* based off the MIT/Apache 2.0 licensed code from num-traits 0.2.10:
*
* **This trait is not ever used directly for users of this library. You
* don't need to deal with it unless
* [implementing custom numeric types](super::super::using_custom_types)
* and even then it will be implemented automatically.**
*
* - [http://opensource.org/licenses/MIT](http://opensource.org/licenses/MIT)
* - [https://docs.rs/num-traits/0.2.10/src/num_traits/lib.rs.html#112](https://docs.rs/num-traits/0.2.10/src/num_traits/lib.rs.html#112)
*
* The trick is that all types implementing this trait will be references,
* so the first constraint expresses some &T which can be operated on with
* some right hand side type T to yield a value of type T.
*
* In a similar way the second constraint expresses `&T op &T -> T` operations
*/
pub trait RealRef<T>:
// &T op T -> T
RealByValue<T, T>
// &T op &T -> T
+ for<'a> RealByValue<&'a T, T> {}
/**
* Anything which implements all the super traits will automatically implement this trait too.
* This covers primitives such as `&f32` & `&f64`, ie a type like `&f64` is `RealRef<&f64>`
* as well as [Traces](super::super::differentiation::Trace) and
* [Records](super::super::differentiation::Record) of those types.
*/
impl<RefT, T> RealRef<T> for RefT where RefT: RealByValue<T, T> + for<'a> RealByValue<&'a T, T> {}
/**
* A general purpose extension to the numeric trait that adds many operations needed
* for more complex math operations.
*
* This trait extends the constraints in [RealByValue]
* to types which also support the operations with a right hand side type
* by reference, and adds some additional constraints needed only
* by value on types.
*
* When used together with [RealRef] this
* expresses all 4 by value and by reference combinations for the
* operations using the following syntax:
*
* ```ignore
* fn function_name<T: Numeric + Real>()
* where for<'a> &'a T: NumericRef<T> + RealRef<T> {
*
* }
* ```
*
* This pair of constraints is used where any real number type is needed, so although
* this trait does not require reference type methods by itself, or re-require
* what is in Numeric, in practise you won't be able to call many
* functions in this library with a real type that doesn't.
*/
pub trait Real:
// T op T -> T
RealByValue
// T op &T -> T
+ for<'a> RealByValue<&'a Self>
+ Pi {}
/**
* All types implemeting the operations in RealByValue with a right hand
* side type by reference are Real.
*
* This covers primitives such as f32 & f64 as well as
* [Traces](super::super::differentiation::Trace) and
* [Records](super::super::differentiation::Record) of those types.
*/
impl<T> Real for T where T: RealByValue + for<'a> RealByValue<&'a T> + Pi {}
}