As discussed on issue #4819, I have created four new traits: `Algebraic`, `Trigonometric`, `Exponential` and `Hyperbolic`, and moved the appropriate methods into them from `Real`.
~~~rust
pub trait Algebraic {
fn pow(&self, n: Self) -> Self;
fn sqrt(&self) -> Self;
fn rsqrt(&self) -> Self;
fn cbrt(&self) -> Self;
fn hypot(&self, other: Self) -> Self;
}
pub trait Trigonometric {
fn sin(&self) -> Self;
fn cos(&self) -> Self;
fn tan(&self) -> Self;
fn asin(&self) -> Self;
fn acos(&self) -> Self;
fn atan(&self) -> Self;
fn atan2(&self, other: Self) -> Self;
}
pub trait Exponential {
fn exp(&self) -> Self;
fn exp2(&self) -> Self;
fn expm1(&self) -> Self;
fn log(&self) -> Self;
fn log2(&self) -> Self;
fn log10(&self) -> Self;
}
pub trait Hyperbolic: Exponential {
fn sinh(&self) -> Self;
fn cosh(&self) -> Self;
fn tanh(&self) -> Self;
}
~~~
There was some discussion over whether we should shorten the names, for example `Trig` and `Exp`. No abbreviations have been agreed on yet, but this could be considered in the future.
Additionally, `Integer::divisible_by` has been renamed to `Integer::is_multiple_of`.
After discussions on IRC and #4819, we have decided to revert this change. This is due to the traits expressing different ideas and because hyperbolic functions are not trivially implementable from exponential functions for floating-point types.
The Hyperbolic Functions are trivially implemented in terms of `exp`, so it's simpler to group them the Exponential trait. In the future these would have default implementations.
This is a temporary trait until we have default methods. We don't want to encumber all implementors of Ord by requiring them to implement these functions, but at the same time we want to be able to take advantage of the speed of the specific numeric functions (like the `fmin` and `fmax` intrinsics).
Having three traits for primitive ints/uints seemed rather excessive. If users wish to specify between them they can simply combine Int with either the Signed and Unsigned traits. For example: fn foo<T: Int + Signed>() { … }
'Natural' normally means 'positive integer' in mathematics. It is therefore strange to implement it on signed integer types. 'Integer' is probably a better choice.
This adds the following methods to ints and uints:
- div
- modulo
- div_mod
- quot_rem
- gcd
- lcm
- divisible_by
- is_even
- is_odd
I have not implemented Natural for BigInt and BigUInt because they're a little over my head.
This restores the trait that was lost in 216e85fadf. It will eventually be broken up into a more fine-grained trait hierarchy in the future once a design can be agreed upon.
This allows `TreeMap`/`TreeSet` to fully express their requirements and reduces the comparisons from ~1.5 per level to 1 which really helps for string keys.
I also added `ReverseIter` to the prelude exports because I forgot when I originally added it.
