mozilla/rust — pull request #6048 by bjz (2013-04-24 22:53:19+00:00)
Title: Add Fractional, Real, and RealExt traits. Rename Natural trait to Integer.

As part of the numeric trait reform (see issue #4819), I have added the following traits to `core::num` and implemented them for floating point types:

~~~rust

pub trait Fractional: Num
+ Ord
+ Quot {
fn recip(&self) -> Self;
}

pub trait Real: Signed
+ Fractional {
// Common Constants
fn pi() -> Self;
fn two_pi() -> Self;
fn frac_pi_2() -> Self;
fn frac_pi_3() -> Self;
fn frac_pi_4() -> Self;
fn frac_pi_6() -> Self;
fn frac_pi_8() -> Self;
fn frac_1_pi() -> Self;
fn frac_2_pi() -> Self;
fn frac_2_sqrtpi() -> Self;
fn sqrt2() -> Self;
fn frac_1_sqrt2() -> Self;
fn e() -> Self;
fn log2_e() -> Self;
fn log10_e() -> Self;
fn log_2() -> Self;
fn log_10() -> Self;

// Rounding operations
fn floor(&self) -> Self;
fn ceil(&self) -> Self;
fn round(&self) -> Self;
fn trunc(&self) -> Self;
fn fract(&self) -> Self;

// Exponential functions
fn pow(&self, n: Self) -> Self;
fn exp(&self) -> Self;
fn exp2(&self) -> Self;
fn expm1(&self) -> Self;
fn ldexp(&self, n: int) -> Self;
fn log(&self) -> Self;
fn log2(&self) -> Self;
fn log10(&self) -> Self;
fn log_radix(&self) -> Self;
fn ilog_radix(&self) -> int;
fn sqrt(&self) -> Self;
fn rsqrt(&self) -> Self;
fn cbrt(&self) -> Self;

// Angular conversions
fn to_degrees(&self) -> Self;
fn to_radians(&self) -> Self;

// Triganomic functions
fn hypot(&self, other: Self) -> Self;
fn sin(&self) -> Self;
fn cos(&self) -> Self;
fn tan(&self) -> Self;

// Inverse triganomic functions
fn asin(&self) -> Self;
fn acos(&self) -> Self;
fn atan(&self) -> Self;
fn atan2(&self, other: Self) -> Self;

// Hyperbolic triganomic functions
fn sinh(&self) -> Self;
fn cosh(&self) -> Self;
fn tanh(&self) -> Self;
}

/// Methods that are harder to implement and not commonly used.
pub trait RealExt: Real {
// Gamma functions
fn lgamma(&self) -> (int, Self);
fn tgamma(&self) -> Self;

// Bessel functions
fn j0(&self) -> Self;
fn j1(&self) -> Self;
fn jn(&self, n: int) -> Self;
fn y0(&self) -> Self;
fn y1(&self) -> Self;
fn yn(&self, n: int) -> Self;
}
~~~

The constants in `Real` could be [associated items](http://smallcultfollowing.com/babysteps/blog/2013/04/03/associated-items-continued/) in the future (see issue #5527). At the moment I have left the constants in {float|f32|f64}::consts in case folks need to access these at compile time. There are also instances of `int` in `Real` and `RealExt`. In the future these could be replaced with an associated `INTEGER` type on `Real`.

`Natural` has also been renamed to `Integer`. This is because `Natural` normally means 'positive integer' in mathematics. It is therefore strange to implement it on signed integer types. `Integer` is probably a better choice.

I have also switched some of the `Integer` methods to take borrowed pointers as arguments. This brings them in line with the `Quot` and `Rem` traits, and is be better for large Integer types like `BigInt` and `BigUint` because they don't need to be copied unnecessarily.

There has also been considerable discussion on the mailing list and IRC about the renaming of the `Div` and `Modulo` traits to `Quot` and `Rem`. Depending on the outcome of these discussions they might be renamed again.