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auto merge of #6048 : bjz/rust/numeric-traits, r=pcwalton
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 Round { fn floor(&self) -> Self; fn ceil(&self) -> Self; fn round(&self) -> Self; fn trunc(&self) -> Self; fn fract(&self) -> Self; } pub trait Fractional: Num + Ord + Round + Quot<Self,Self> { 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; // 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.
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