auto merge of #6110 : bjz/rust/numeric-traits, r=pcwalton

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`.

1 files changed, 110 insertions, 69 deletions

diff --git a/src/libcore/num/float.rs b/src/libcore/num/float.rs
index ef0adee884b..3aa8848cdbe 100644
--- a/src/libcore/num/float.rs
+++ b/src/libcore/num/float.rs
@@ -453,154 +453,195 @@ impl Fractional for float {
     fn recip(&self) -> float { 1.0 / *self }
 }
 
-impl Real for float {
-    /// Archimedes' constant
-    #[inline(always)]
-    fn pi() -> float { 3.14159265358979323846264338327950288 }
-
-    /// 2.0 * pi
-    #[inline(always)]
-    fn two_pi() -> float { 6.28318530717958647692528676655900576 }
-
-    /// pi / 2.0
-    #[inline(always)]
-    fn frac_pi_2() -> float { 1.57079632679489661923132169163975144 }
-
-    /// pi / 3.0
+impl Algebraic for float {
     #[inline(always)]
-    fn frac_pi_3() -> float { 1.04719755119659774615421446109316763 }
+    fn pow(&self, n: float) -> float {
+        (*self as f64).pow(n as f64) as float
+    }
 
-    /// pi / 4.0
     #[inline(always)]
-    fn frac_pi_4() -> float { 0.785398163397448309615660845819875721 }
+    fn sqrt(&self) -> float {
+        (*self as f64).sqrt() as float
+    }
 
-    /// pi / 6.0
     #[inline(always)]
-    fn frac_pi_6() -> float { 0.52359877559829887307710723054658381 }
+    fn rsqrt(&self) -> float {
+        (*self as f64).rsqrt() as float
+    }
 
-    /// pi / 8.0
     #[inline(always)]
-    fn frac_pi_8() -> float { 0.39269908169872415480783042290993786 }
+    fn cbrt(&self) -> float {
+        (*self as f64).cbrt() as float
+    }
 
-    /// 1.0 / pi
     #[inline(always)]
-    fn frac_1_pi() -> float { 0.318309886183790671537767526745028724 }
+    fn hypot(&self, other: float) -> float {
+        (*self as f64).hypot(other as f64) as float
+    }
+}
 
-    /// 2.0 / pi
+impl Trigonometric for float {
     #[inline(always)]
-    fn frac_2_pi() -> float { 0.636619772367581343075535053490057448 }
+    fn sin(&self) -> float {
+        (*self as f64).sin() as float
+    }
 
-    /// 2 .0/ sqrt(pi)
     #[inline(always)]
-    fn frac_2_sqrtpi() -> float { 1.12837916709551257389615890312154517 }
+    fn cos(&self) -> float {
+        (*self as f64).cos() as float
+    }
 
-    /// sqrt(2.0)
     #[inline(always)]
-    fn sqrt2() -> float { 1.41421356237309504880168872420969808 }
+    fn tan(&self) -> float {
+        (*self as f64).tan() as float
+    }
 
-    /// 1.0 / sqrt(2.0)
     #[inline(always)]
-    fn frac_1_sqrt2() -> float { 0.707106781186547524400844362104849039 }
+    fn asin(&self) -> float {
+        (*self as f64).asin() as float
+    }
 
-    /// Euler's number
     #[inline(always)]
-    fn e() -> float { 2.71828182845904523536028747135266250 }
+    fn acos(&self) -> float {
+        (*self as f64).acos() as float
+    }
 
-    /// log2(e)
     #[inline(always)]
-    fn log2_e() -> float { 1.44269504088896340735992468100189214 }
+    fn atan(&self) -> float {
+        (*self as f64).atan() as float
+    }
 
-    /// log10(e)
     #[inline(always)]
-    fn log10_e() -> float { 0.434294481903251827651128918916605082 }
+    fn atan2(&self, other: float) -> float {
+        (*self as f64).atan2(other as f64) as float
+    }
+}
 
-    /// log(2.0)
+impl Exponential for float {
     #[inline(always)]
-    fn log_2() -> float { 0.693147180559945309417232121458176568 }
+    fn exp(&self) -> float {
+        (*self as f64).exp() as float
+    }
 
-    /// log(10.0)
     #[inline(always)]
-    fn log_10() -> float { 2.30258509299404568401799145468436421 }
+    fn exp2(&self) -> float {
+        (*self as f64).exp2() as float
+    }
 
     #[inline(always)]
-    fn pow(&self, n: float) -> float { pow(*self as f64, n as f64) as float }
+    fn expm1(&self) -> float {
+        (*self as f64).expm1() as float
+    }
 
     #[inline(always)]
-    fn exp(&self) -> float { exp(*self as f64) as float }
+    fn log(&self) -> float {
+        (*self as f64).log() as float
+    }
 
     #[inline(always)]
-    fn exp2(&self) -> float { exp2(*self as f64) as float }
+    fn log2(&self) -> float {
+        (*self as f64).log2() as float
+    }
 
     #[inline(always)]
-    fn expm1(&self) -> float { expm1(*self as f64) as float }
+    fn log10(&self) -> float {
+        (*self as f64).log10() as float
+    }
+}
 
+impl Hyperbolic for float {
     #[inline(always)]
-    fn ldexp(&self, n: int) -> float { ldexp(*self as f64, n as c_int) as float }
+    fn sinh(&self) -> float {
+        (*self as f64).sinh() as float
+    }
 
     #[inline(always)]
-    fn log(&self) -> float { ln(*self as f64) as float }
+    fn cosh(&self) -> float {
+        (*self as f64).cosh() as float
+    }
 
     #[inline(always)]
-    fn log2(&self) -> float { log2(*self as f64) as float }
+    fn tanh(&self) -> float {
+        (*self as f64).tanh() as float
+    }
+}
 
+impl Real for float {
+    /// Archimedes' constant
     #[inline(always)]
-    fn log10(&self) -> float { log10(*self as f64) as float }
+    fn pi() -> float { 3.14159265358979323846264338327950288 }
 
+    /// 2.0 * pi
     #[inline(always)]
-    fn log_radix(&self) -> float { log_radix(*self as f64) as float }
+    fn two_pi() -> float { 6.28318530717958647692528676655900576 }
 
+    /// pi / 2.0
     #[inline(always)]
-    fn ilog_radix(&self) -> int { ilog_radix(*self as f64) as int }
+    fn frac_pi_2() -> float { 1.57079632679489661923132169163975144 }
 
+    /// pi / 3.0
     #[inline(always)]
-    fn sqrt(&self) -> float { sqrt(*self) }
+    fn frac_pi_3() -> float { 1.04719755119659774615421446109316763 }
 
+    /// pi / 4.0
     #[inline(always)]
-    fn rsqrt(&self) -> float { self.sqrt().recip() }
+    fn frac_pi_4() -> float { 0.785398163397448309615660845819875721 }
 
+    /// pi / 6.0
     #[inline(always)]
-    fn cbrt(&self) -> float { cbrt(*self as f64) as float }
+    fn frac_pi_6() -> float { 0.52359877559829887307710723054658381 }
 
-    /// Converts to degrees, assuming the number is in radians
+    /// pi / 8.0
     #[inline(always)]
-    fn to_degrees(&self) -> float { *self * (180.0 / Real::pi::<float>()) }
+    fn frac_pi_8() -> float { 0.39269908169872415480783042290993786 }
 
-    /// Converts to radians, assuming the number is in degrees
+    /// 1.0 / pi
     #[inline(always)]
-    fn to_radians(&self) -> float { *self * (Real::pi::<float>() / 180.0) }
+    fn frac_1_pi() -> float { 0.318309886183790671537767526745028724 }
 
+    /// 2.0 / pi
     #[inline(always)]
-    fn hypot(&self, other: float) -> float { hypot(*self as f64, other as f64) as float }
+    fn frac_2_pi() -> float { 0.636619772367581343075535053490057448 }
 
+    /// 2 .0/ sqrt(pi)
     #[inline(always)]
-    fn sin(&self) -> float { sin(*self) }
+    fn frac_2_sqrtpi() -> float { 1.12837916709551257389615890312154517 }
 
+    /// sqrt(2.0)
     #[inline(always)]
-    fn cos(&self) -> float { cos(*self) }
+    fn sqrt2() -> float { 1.41421356237309504880168872420969808 }
 
+    /// 1.0 / sqrt(2.0)
     #[inline(always)]
-    fn tan(&self) -> float { tan(*self) }
+    fn frac_1_sqrt2() -> float { 0.707106781186547524400844362104849039 }
 
+    /// Euler's number
     #[inline(always)]
-    fn asin(&self) -> float { asin(*self as f64) as float }
+    fn e() -> float { 2.71828182845904523536028747135266250 }
 
+    /// log2(e)
     #[inline(always)]
-    fn acos(&self) -> float { acos(*self as f64) as float }
+    fn log2_e() -> float { 1.44269504088896340735992468100189214 }
 
+    /// log10(e)
     #[inline(always)]
-    fn atan(&self) -> float { atan(*self) }
+    fn log10_e() -> float { 0.434294481903251827651128918916605082 }
 
+    /// log(2.0)
     #[inline(always)]
-    fn atan2(&self, other: float) -> float { atan2(*self as f64, other as f64) as float }
+    fn log_2() -> float { 0.693147180559945309417232121458176568 }
 
+    /// log(10.0)
     #[inline(always)]
-    fn sinh(&self) -> float { sinh(*self as f64) as float }
+    fn log_10() -> float { 2.30258509299404568401799145468436421 }
 
+    /// Converts to degrees, assuming the number is in radians
     #[inline(always)]
-    fn cosh(&self) -> float { cosh(*self as f64) as float }
+    fn to_degrees(&self) -> float { (*self as f64).to_degrees() as float }
 
+    /// Converts to radians, assuming the number is in degrees
     #[inline(always)]
-    fn tanh(&self) -> float { tanh(*self as f64) as float }
+    fn to_radians(&self) -> float { (*self as f64).to_radians() as float }
 }
 
 impl RealExt for float {