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`.

10 files changed, 380 insertions, 258 deletions

diff --git a/src/libcore/core.rc b/src/libcore/core.rc
index dc3cd03dc20..f9a56f613d5 100644
--- a/src/libcore/core.rc
+++ b/src/libcore/core.rc
@@ -105,8 +105,9 @@ pub use old_iter::{ExtendedMutableIter};
 pub use iter::Times;
 
 pub use num::{Num, NumCast};
-pub use num::{Orderable, Signed, Unsigned, Integer};
-pub use num::{Round, Fractional, Real, RealExt};
+pub use num::{Orderable, Signed, Unsigned, Round};
+pub use num::{Algebraic, Trigonometric, Exponential, Hyperbolic};
+pub use num::{Integer, Fractional, Real, RealExt};
 pub use num::{Bitwise, BitCount, Bounded};
 pub use num::{Primitive, Int, Float};
 
diff --git a/src/libcore/num/f32.rs b/src/libcore/num/f32.rs
index ada47fb597e..e687f482fa9 100644
--- a/src/libcore/num/f32.rs
+++ b/src/libcore/num/f32.rs
@@ -11,7 +11,6 @@
 //! Operations and constants for `f32`
 
 use from_str;
-use libc::c_int;
 use num::{Zero, One, strconv};
 use prelude::*;
 
@@ -102,8 +101,8 @@ delegate!(
     fn sinh(n: c_float) -> c_float = c_float_utils::sinh,
     fn tan(n: c_float) -> c_float = c_float_utils::tan,
     fn tanh(n: c_float) -> c_float = c_float_utils::tanh,
-    fn tgamma(n: c_float) -> c_float = c_float_utils::tgamma)
-
+    fn tgamma(n: c_float) -> c_float = c_float_utils::tgamma
+)
 
 // These are not defined inside consts:: for consistency with
 // the integer types
@@ -368,154 +367,153 @@ impl Fractional for f32 {
     fn recip(&self) -> f32 { 1.0 / *self }
 }
 
-impl Real for f32 {
-    /// Archimedes' constant
+impl Algebraic for f32 {
     #[inline(always)]
-    fn pi() -> f32 { 3.14159265358979323846264338327950288 }
-
-    /// 2.0 * pi
-    #[inline(always)]
-    fn two_pi() -> f32 { 6.28318530717958647692528676655900576 }
-
-    /// pi / 2.0
-    #[inline(always)]
-    fn frac_pi_2() -> f32 { 1.57079632679489661923132169163975144 }
-
-    /// pi / 3.0
-    #[inline(always)]
-    fn frac_pi_3() -> f32 { 1.04719755119659774615421446109316763 }
+    fn pow(&self, n: f32) -> f32 { pow(*self, n) }
 
-    /// pi / 4.0
     #[inline(always)]
-    fn frac_pi_4() -> f32 { 0.785398163397448309615660845819875721 }
+    fn sqrt(&self) -> f32 { sqrt(*self) }
 
-    /// pi / 6.0
     #[inline(always)]
-    fn frac_pi_6() -> f32 { 0.52359877559829887307710723054658381 }
+    fn rsqrt(&self) -> f32 { self.sqrt().recip() }
 
-    /// pi / 8.0
     #[inline(always)]
-    fn frac_pi_8() -> f32 { 0.39269908169872415480783042290993786 }
+    fn cbrt(&self) -> f32 { cbrt(*self) }
 
-    /// 1 .0/ pi
     #[inline(always)]
-    fn frac_1_pi() -> f32 { 0.318309886183790671537767526745028724 }
+    fn hypot(&self, other: f32) -> f32 { hypot(*self, other) }
+}
 
-    /// 2.0 / pi
+impl Trigonometric for f32 {
     #[inline(always)]
-    fn frac_2_pi() -> f32 { 0.636619772367581343075535053490057448 }
+    fn sin(&self) -> f32 { sin(*self) }
 
-    /// 2.0 / sqrt(pi)
     #[inline(always)]
-    fn frac_2_sqrtpi() -> f32 { 1.12837916709551257389615890312154517 }
+    fn cos(&self) -> f32 { cos(*self) }
 
-    /// sqrt(2.0)
     #[inline(always)]
-    fn sqrt2() -> f32 { 1.41421356237309504880168872420969808 }
+    fn tan(&self) -> f32 { tan(*self) }
 
-    /// 1.0 / sqrt(2.0)
     #[inline(always)]
-    fn frac_1_sqrt2() -> f32 { 0.707106781186547524400844362104849039 }
+    fn asin(&self) -> f32 { asin(*self) }
 
-    /// Euler's number
     #[inline(always)]
-    fn e() -> f32 { 2.71828182845904523536028747135266250 }
+    fn acos(&self) -> f32 { acos(*self) }
 
-    /// log2(e)
     #[inline(always)]
-    fn log2_e() -> f32 { 1.44269504088896340735992468100189214 }
+    fn atan(&self) -> f32 { atan(*self) }
 
-    /// log10(e)
     #[inline(always)]
-    fn log10_e() -> f32 { 0.434294481903251827651128918916605082 }
+    fn atan2(&self, other: f32) -> f32 { atan2(*self, other) }
+}
 
-    /// log(2.0)
+impl Exponential for f32 {
     #[inline(always)]
-    fn log_2() -> f32 { 0.693147180559945309417232121458176568 }
+    fn exp(&self) -> f32 { exp(*self) }
 
-    /// log(10.0)
     #[inline(always)]
-    fn log_10() -> f32 { 2.30258509299404568401799145468436421 }
+    fn exp2(&self) -> f32 { exp2(*self) }
 
     #[inline(always)]
-    fn pow(&self, n: f32) -> f32 { pow(*self, n) }
+    fn expm1(&self) -> f32 { expm1(*self) }
 
     #[inline(always)]
-    fn exp(&self) -> f32 { exp(*self) }
+    fn log(&self) -> f32 { ln(*self) }
 
     #[inline(always)]
-    fn exp2(&self) -> f32 { exp2(*self) }
+    fn log2(&self) -> f32 { log2(*self) }
 
     #[inline(always)]
-    fn expm1(&self) -> f32 { expm1(*self) }
+    fn log10(&self) -> f32 { log10(*self) }
+}
 
+impl Hyperbolic for f32 {
     #[inline(always)]
-    fn ldexp(&self, n: int) -> f32 { ldexp(*self, n as c_int) }
+    fn sinh(&self) -> f32 { sinh(*self) }
 
     #[inline(always)]
-    fn log(&self) -> f32 { ln(*self) }
+    fn cosh(&self) -> f32 { cosh(*self) }
 
     #[inline(always)]
-    fn log2(&self) -> f32 { log2(*self) }
+    fn tanh(&self) -> f32 { tanh(*self) }
+}
 
+impl Real for f32 {
+    /// Archimedes' constant
     #[inline(always)]
-    fn log10(&self) -> f32 { log10(*self) }
+    fn pi() -> f32 { 3.14159265358979323846264338327950288 }
 
+    /// 2.0 * pi
     #[inline(always)]
-    fn log_radix(&self) -> f32 { log_radix(*self) as f32 }
+    fn two_pi() -> f32 { 6.28318530717958647692528676655900576 }
 
+    /// pi / 2.0
     #[inline(always)]
-    fn ilog_radix(&self) -> int { ilog_radix(*self) as int }
+    fn frac_pi_2() -> f32 { 1.57079632679489661923132169163975144 }
 
+    /// pi / 3.0
     #[inline(always)]
-    fn sqrt(&self) -> f32 { sqrt(*self) }
+    fn frac_pi_3() -> f32 { 1.04719755119659774615421446109316763 }
 
+    /// pi / 4.0
     #[inline(always)]
-    fn rsqrt(&self) -> f32 { self.sqrt().recip() }
+    fn frac_pi_4() -> f32 { 0.785398163397448309615660845819875721 }
 
+    /// pi / 6.0
     #[inline(always)]
-    fn cbrt(&self) -> f32 { cbrt(*self) }
+    fn frac_pi_6() -> f32 { 0.52359877559829887307710723054658381 }
 
-    /// Converts to degrees, assuming the number is in radians
+    /// pi / 8.0
     #[inline(always)]
-    fn to_degrees(&self) -> f32 { *self * (180.0 / Real::pi::<f32>()) }
+    fn frac_pi_8() -> f32 { 0.39269908169872415480783042290993786 }
 
-    /// Converts to radians, assuming the number is in degrees
+    /// 1 .0/ pi
     #[inline(always)]
-    fn to_radians(&self) -> f32 { *self * (Real::pi::<f32>() / 180.0) }
+    fn frac_1_pi() -> f32 { 0.318309886183790671537767526745028724 }
 
+    /// 2.0 / pi
     #[inline(always)]
-    fn hypot(&self, other: f32) -> f32 { hypot(*self, other) }
+    fn frac_2_pi() -> f32 { 0.636619772367581343075535053490057448 }
 
+    /// 2.0 / sqrt(pi)
     #[inline(always)]
-    fn sin(&self) -> f32 { sin(*self) }
+    fn frac_2_sqrtpi() -> f32 { 1.12837916709551257389615890312154517 }
 
+    /// sqrt(2.0)
     #[inline(always)]
-    fn cos(&self) -> f32 { cos(*self) }
+    fn sqrt2() -> f32 { 1.41421356237309504880168872420969808 }
 
+    /// 1.0 / sqrt(2.0)
     #[inline(always)]
-    fn tan(&self) -> f32 { tan(*self) }
+    fn frac_1_sqrt2() -> f32 { 0.707106781186547524400844362104849039 }
 
+    /// Euler's number
     #[inline(always)]
-    fn asin(&self) -> f32 { asin(*self) }
+    fn e() -> f32 { 2.71828182845904523536028747135266250 }
 
+    /// log2(e)
     #[inline(always)]
-    fn acos(&self) -> f32 { acos(*self) }
+    fn log2_e() -> f32 { 1.44269504088896340735992468100189214 }
 
+    /// log10(e)
     #[inline(always)]
-    fn atan(&self) -> f32 { atan(*self) }
+    fn log10_e() -> f32 { 0.434294481903251827651128918916605082 }
 
+    /// log(2.0)
     #[inline(always)]
-    fn atan2(&self, other: f32) -> f32 { atan2(*self, other) }
+    fn log_2() -> f32 { 0.693147180559945309417232121458176568 }
 
+    /// log(10.0)
     #[inline(always)]
-    fn sinh(&self) -> f32 { sinh(*self) }
+    fn log_10() -> f32 { 2.30258509299404568401799145468436421 }
 
+    /// Converts to degrees, assuming the number is in radians
     #[inline(always)]
-    fn cosh(&self) -> f32 { cosh(*self) }
+    fn to_degrees(&self) -> f32 { *self * (180.0 / Real::pi::<f32>()) }
 
+    /// Converts to radians, assuming the number is in degrees
     #[inline(always)]
-    fn tanh(&self) -> f32 { tanh(*self) }
+    fn to_radians(&self) -> f32 { *self * (Real::pi::<f32>() / 180.0) }
 }
 
 impl Bounded for f32 {
diff --git a/src/libcore/num/f64.rs b/src/libcore/num/f64.rs
index 07a29652e94..d00e6ae2c0d 100644
--- a/src/libcore/num/f64.rs
+++ b/src/libcore/num/f64.rs
@@ -109,7 +109,8 @@ delegate!(
     fn jn(i: c_int, n: c_double) -> c_double = c_double_utils::jn,
     fn y0(n: c_double) -> c_double = c_double_utils::y0,
     fn y1(n: c_double) -> c_double = c_double_utils::y1,
-    fn yn(i: c_int, n: c_double) -> c_double = c_double_utils::yn)
+    fn yn(i: c_int, n: c_double) -> c_double = c_double_utils::yn
+)
 
 // FIXME (#1433): obtain these in a different way
 
@@ -378,154 +379,153 @@ impl Fractional for f64 {
     fn recip(&self) -> f64 { 1.0 / *self }
 }
 
-impl Real for f64 {
-    /// Archimedes' constant
+impl Algebraic for f64 {
     #[inline(always)]
-    fn pi() -> f64 { 3.14159265358979323846264338327950288 }
-
-    /// 2.0 * pi
-    #[inline(always)]
-    fn two_pi() -> f64 { 6.28318530717958647692528676655900576 }
-
-    /// pi / 2.0
-    #[inline(always)]
-    fn frac_pi_2() -> f64 { 1.57079632679489661923132169163975144 }
+    fn pow(&self, n: f64) -> f64 { pow(*self, n) }
 
-    /// pi / 3.0
     #[inline(always)]
-    fn frac_pi_3() -> f64 { 1.04719755119659774615421446109316763 }
-
-    /// pi / 4.0
-    #[inline(always)]
-    fn frac_pi_4() -> f64 { 0.785398163397448309615660845819875721 }
+    fn sqrt(&self) -> f64 { sqrt(*self) }
 
-    /// pi / 6.0
     #[inline(always)]
-    fn frac_pi_6() -> f64 { 0.52359877559829887307710723054658381 }
+    fn rsqrt(&self) -> f64 { self.sqrt().recip() }
 
-    /// pi / 8.0
     #[inline(always)]
-    fn frac_pi_8() -> f64 { 0.39269908169872415480783042290993786 }
+    fn cbrt(&self) -> f64 { cbrt(*self) }
 
-    /// 1.0 / pi
     #[inline(always)]
-    fn frac_1_pi() -> f64 { 0.318309886183790671537767526745028724 }
+    fn hypot(&self, other: f64) -> f64 { hypot(*self, other) }
+}
 
-    /// 2.0 / pi
+impl Trigonometric for f64 {
     #[inline(always)]
-    fn frac_2_pi() -> f64 { 0.636619772367581343075535053490057448 }
+    fn sin(&self) -> f64 { sin(*self) }
 
-    /// 2.0 / sqrt(pi)
     #[inline(always)]
-    fn frac_2_sqrtpi() -> f64 { 1.12837916709551257389615890312154517 }
+    fn cos(&self) -> f64 { cos(*self) }
 
-    /// sqrt(2.0)
     #[inline(always)]
-    fn sqrt2() -> f64 { 1.41421356237309504880168872420969808 }
+    fn tan(&self) -> f64 { tan(*self) }
 
-    /// 1.0 / sqrt(2.0)
     #[inline(always)]
-    fn frac_1_sqrt2() -> f64 { 0.707106781186547524400844362104849039 }
+    fn asin(&self) -> f64 { asin(*self) }
 
-    /// Euler's number
     #[inline(always)]
-    fn e() -> f64 { 2.71828182845904523536028747135266250 }
+    fn acos(&self) -> f64 { acos(*self) }
 
-    /// log2(e)
     #[inline(always)]
-    fn log2_e() -> f64 { 1.44269504088896340735992468100189214 }
+    fn atan(&self) -> f64 { atan(*self) }
 
-    /// log10(e)
     #[inline(always)]
-    fn log10_e() -> f64 { 0.434294481903251827651128918916605082 }
+    fn atan2(&self, other: f64) -> f64 { atan2(*self, other) }
+}
 
-    /// log(2.0)
+impl Exponential for f64 {
     #[inline(always)]
-    fn log_2() -> f64 { 0.693147180559945309417232121458176568 }
+    fn exp(&self) -> f64 { exp(*self) }
 
-    /// log(10.0)
     #[inline(always)]
-    fn log_10() -> f64 { 2.30258509299404568401799145468436421 }
+    fn exp2(&self) -> f64 { exp2(*self) }
 
     #[inline(always)]
-    fn pow(&self, n: f64) -> f64 { pow(*self, n) }
+    fn expm1(&self) -> f64 { expm1(*self) }
 
     #[inline(always)]
-    fn exp(&self) -> f64 { exp(*self) }
+    fn log(&self) -> f64 { ln(*self) }
 
     #[inline(always)]
-    fn exp2(&self) -> f64 { exp2(*self) }
+    fn log2(&self) -> f64 { log2(*self) }
 
     #[inline(always)]
-    fn expm1(&self) -> f64 { expm1(*self) }
+    fn log10(&self) -> f64 { log10(*self) }
+}
 
+impl Hyperbolic for f64 {
     #[inline(always)]
-    fn ldexp(&self, n: int) -> f64 { ldexp(*self, n as c_int) }
+    fn sinh(&self) -> f64 { sinh(*self) }
 
     #[inline(always)]
-    fn log(&self) -> f64 { ln(*self) }
+    fn cosh(&self) -> f64 { cosh(*self) }
 
     #[inline(always)]
-    fn log2(&self) -> f64 { log2(*self) }
+    fn tanh(&self) -> f64 { tanh(*self) }
+}
 
+impl Real for f64 {
+    /// Archimedes' constant
     #[inline(always)]
-    fn log10(&self) -> f64 { log10(*self) }
+    fn pi() -> f64 { 3.14159265358979323846264338327950288 }
 
+    /// 2.0 * pi
     #[inline(always)]
-    fn log_radix(&self) -> f64 { log_radix(*self) }
+    fn two_pi() -> f64 { 6.28318530717958647692528676655900576 }
 
+    /// pi / 2.0
     #[inline(always)]
-    fn ilog_radix(&self) -> int { ilog_radix(*self) as int }
+    fn frac_pi_2() -> f64 { 1.57079632679489661923132169163975144 }
 
+    /// pi / 3.0
     #[inline(always)]
-    fn sqrt(&self) -> f64 { sqrt(*self) }
+    fn frac_pi_3() -> f64 { 1.04719755119659774615421446109316763 }
 
+    /// pi / 4.0
     #[inline(always)]
-    fn rsqrt(&self) -> f64 { self.sqrt().recip() }
+    fn frac_pi_4() -> f64 { 0.785398163397448309615660845819875721 }
 
+    /// pi / 6.0
     #[inline(always)]
-    fn cbrt(&self) -> f64 { cbrt(*self) }
+    fn frac_pi_6() -> f64 { 0.52359877559829887307710723054658381 }
 
-    /// Converts to degrees, assuming the number is in radians
+    /// pi / 8.0
     #[inline(always)]
-    fn to_degrees(&self) -> f64 { *self * (180.0 / Real::pi::<f64>()) }
+    fn frac_pi_8() -> f64 { 0.39269908169872415480783042290993786 }
 
-    /// Converts to radians, assuming the number is in degrees
+    /// 1.0 / pi
     #[inline(always)]
-    fn to_radians(&self) -> f64 { *self * (Real::pi::<f64>() / 180.0) }
+    fn frac_1_pi() -> f64 { 0.318309886183790671537767526745028724 }
 
+    /// 2.0 / pi
     #[inline(always)]
-    fn hypot(&self, other: f64) -> f64 { hypot(*self, other) }
+    fn frac_2_pi() -> f64 { 0.636619772367581343075535053490057448 }
 
+    /// 2.0 / sqrt(pi)
     #[inline(always)]
-    fn sin(&self) -> f64 { sin(*self) }
+    fn frac_2_sqrtpi() -> f64 { 1.12837916709551257389615890312154517 }
 
+    /// sqrt(2.0)
     #[inline(always)]
-    fn cos(&self) -> f64 { cos(*self) }
+    fn sqrt2() -> f64 { 1.41421356237309504880168872420969808 }
 
+    /// 1.0 / sqrt(2.0)
     #[inline(always)]
-    fn tan(&self) -> f64 { tan(*self) }
+    fn frac_1_sqrt2() -> f64 { 0.707106781186547524400844362104849039 }
 
+    /// Euler's number
     #[inline(always)]
-    fn asin(&self) -> f64 { asin(*self) }
+    fn e() -> f64 { 2.71828182845904523536028747135266250 }
 
+    /// log2(e)
     #[inline(always)]
-    fn acos(&self) -> f64 { acos(*self) }
+    fn log2_e() -> f64 { 1.44269504088896340735992468100189214 }
 
+    /// log10(e)
     #[inline(always)]
-    fn atan(&self) -> f64 { atan(*self) }
+    fn log10_e() -> f64 { 0.434294481903251827651128918916605082 }
 
+    /// log(2.0)
     #[inline(always)]
-    fn atan2(&self, other: f64) -> f64 { atan2(*self, other) }
+    fn log_2() -> f64 { 0.693147180559945309417232121458176568 }
 
+    /// log(10.0)
     #[inline(always)]
-    fn sinh(&self) -> f64 { sinh(*self) }
+    fn log_10() -> f64 { 2.30258509299404568401799145468436421 }
 
+    /// Converts to degrees, assuming the number is in radians
     #[inline(always)]
-    fn cosh(&self) -> f64 { cosh(*self) }
+    fn to_degrees(&self) -> f64 { *self * (180.0 / Real::pi::<f64>()) }
 
+    /// Converts to radians, assuming the number is in degrees
     #[inline(always)]
-    fn tanh(&self) -> f64 { tanh(*self) }
+    fn to_radians(&self) -> f64 { *self * (Real::pi::<f64>() / 180.0) }
 }
 
 impl RealExt for f64 {
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 {
diff --git a/src/libcore/num/int-template.rs b/src/libcore/num/int-template.rs
index 08df820a73d..ec38a32c039 100644
--- a/src/libcore/num/int-template.rs
+++ b/src/libcore/num/int-template.rs
@@ -406,11 +406,11 @@ impl Integer for T {
 
     /// Returns `true` if the number can be divided by `other` without leaving a remainder
     #[inline(always)]
-    fn divisible_by(&self, other: &T) -> bool { *self % *other == 0 }
+    fn is_multiple_of(&self, other: &T) -> bool { *self % *other == 0 }
 
     /// Returns `true` if the number is divisible by `2`
     #[inline(always)]
-    fn is_even(&self) -> bool { self.divisible_by(&2) }
+    fn is_even(&self) -> bool { self.is_multiple_of(&2) }
 
     /// Returns `true` if the number is not divisible by `2`
     #[inline(always)]
@@ -683,6 +683,42 @@ mod tests {
     }
 
     #[test]
+    fn test_multiple_of() {
+        assert!((6 as T).is_multiple_of(&(6 as T)));
+        assert!((6 as T).is_multiple_of(&(3 as T)));
+        assert!((6 as T).is_multiple_of(&(1 as T)));
+        assert!((-8 as T).is_multiple_of(&(4 as T)));
+        assert!((8 as T).is_multiple_of(&(-1 as T)));
+        assert!((-8 as T).is_multiple_of(&(-2 as T)));
+    }
+
+    #[test]
+    fn test_even() {
+        assert_eq!((-4 as T).is_even(), true);
+        assert_eq!((-3 as T).is_even(), false);
+        assert_eq!((-2 as T).is_even(), true);
+        assert_eq!((-1 as T).is_even(), false);
+        assert_eq!((0 as T).is_even(), true);
+        assert_eq!((1 as T).is_even(), false);
+        assert_eq!((2 as T).is_even(), true);
+        assert_eq!((3 as T).is_even(), false);
+        assert_eq!((4 as T).is_even(), true);
+    }
+
+    #[test]
+    fn test_odd() {
+        assert_eq!((-4 as T).is_odd(), false);
+        assert_eq!((-3 as T).is_odd(), true);
+        assert_eq!((-2 as T).is_odd(), false);
+        assert_eq!((-1 as T).is_odd(), true);
+        assert_eq!((0 as T).is_odd(), false);
+        assert_eq!((1 as T).is_odd(), true);
+        assert_eq!((2 as T).is_odd(), false);
+        assert_eq!((3 as T).is_odd(), true);
+        assert_eq!((4 as T).is_odd(), false);
+    }
+
+    #[test]
     fn test_bitcount() {
         assert_eq!((0b010101 as T).population_count(), 3);
     }
diff --git a/src/libcore/num/num.rs b/src/libcore/num/num.rs
index 0e2669a26b6..3e43ebfef12 100644
--- a/src/libcore/num/num.rs
+++ b/src/libcore/num/num.rs
@@ -85,7 +85,8 @@ pub trait Integer: Num
 
     fn gcd(&self, other: &Self) -> Self;
     fn lcm(&self, other: &Self) -> Self;
-    fn divisible_by(&self, other: &Self) -> bool;
+
+    fn is_multiple_of(&self, other: &Self) -> bool;
     fn is_even(&self) -> bool;
     fn is_odd(&self) -> bool;
 }
@@ -105,14 +106,47 @@ pub trait Fractional: Num
     fn recip(&self) -> Self;
 }
 
+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;
+}
+
 ///
 /// Defines constants and methods common to real numbers
 ///
 pub trait Real: Signed
-              + Fractional {
-    // FIXME (#5527): usages of `int` should be replaced with an associated
-    // integer type once these are implemented
-
+              + Fractional
+              + Algebraic
+              + Trigonometric
+              + Hyperbolic {
     // Common Constants
     // FIXME (#5527): These should be associated constants
     fn pi() -> Self;
@@ -133,41 +167,9 @@ pub trait Real: Signed
     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;
 }
 
 ///
diff --git a/src/libcore/num/uint-template.rs b/src/libcore/num/uint-template.rs
index af64660ad0c..3dfdd22c42d 100644
--- a/src/libcore/num/uint-template.rs
+++ b/src/libcore/num/uint-template.rs
@@ -238,11 +238,11 @@ impl Integer for T {
 
     /// Returns `true` if the number can be divided by `other` without leaving a remainder
     #[inline(always)]
-    fn divisible_by(&self, other: &T) -> bool { *self % *other == 0 }
+    fn is_multiple_of(&self, other: &T) -> bool { *self % *other == 0 }
 
     /// Returns `true` if the number is divisible by `2`
     #[inline(always)]
-    fn is_even(&self) -> bool { self.divisible_by(&2) }
+    fn is_even(&self) -> bool { self.is_multiple_of(&2) }
 
     /// Returns `true` if the number is not divisible by `2`
     #[inline(always)]
@@ -416,6 +416,31 @@ mod tests {
     }
 
     #[test]
+    fn test_multiple_of() {
+        assert!((6 as T).is_multiple_of(&(6 as T)));
+        assert!((6 as T).is_multiple_of(&(3 as T)));
+        assert!((6 as T).is_multiple_of(&(1 as T)));
+    }
+
+    #[test]
+    fn test_even() {
+        assert_eq!((0 as T).is_even(), true);
+        assert_eq!((1 as T).is_even(), false);
+        assert_eq!((2 as T).is_even(), true);
+        assert_eq!((3 as T).is_even(), false);
+        assert_eq!((4 as T).is_even(), true);
+    }
+
+    #[test]
+    fn test_odd() {
+        assert_eq!((0 as T).is_odd(), false);
+        assert_eq!((1 as T).is_odd(), true);
+        assert_eq!((2 as T).is_odd(), false);
+        assert_eq!((3 as T).is_odd(), true);
+        assert_eq!((4 as T).is_odd(), false);
+    }
+
+    #[test]
     fn test_bitwise() {
         assert_eq!(0b1110 as T, (0b1100 as T).bitor(&(0b1010 as T)));
         assert_eq!(0b1000 as T, (0b1100 as T).bitand(&(0b1010 as T)));
diff --git a/src/libcore/prelude.rs b/src/libcore/prelude.rs
index 41078fb8920..9a2e480ce6e 100644
--- a/src/libcore/prelude.rs
+++ b/src/libcore/prelude.rs
@@ -39,8 +39,9 @@ pub use old_iter::{CopyableIter, CopyableOrderedIter, CopyableNonstrictIter};
 pub use old_iter::{ExtendedMutableIter};
 pub use iter::Times;
 pub use num::{Num, NumCast};
-pub use num::{Orderable, Signed, Unsigned, Integer};
-pub use num::{Round, Fractional, Real, RealExt};
+pub use num::{Orderable, Signed, Unsigned, Round};
+pub use num::{Algebraic, Trigonometric, Exponential, Hyperbolic};
+pub use num::{Integer, Fractional, Real, RealExt};
 pub use num::{Bitwise, BitCount, Bounded};
 pub use num::{Primitive, Int, Float};
 pub use path::GenericPath;
diff --git a/src/libstd/num/bigint.rs b/src/libstd/num/bigint.rs
index 3ea94eababb..e97b3b5eeec 100644
--- a/src/libstd/num/bigint.rs
+++ b/src/libstd/num/bigint.rs
@@ -428,7 +428,7 @@ impl Integer for BigUint {
 
     /// Returns `true` if the number can be divided by `other` without leaving a remainder
     #[inline(always)]
-    fn divisible_by(&self, other: &BigUint) -> bool { (*self % *other).is_zero() }
+    fn is_multiple_of(&self, other: &BigUint) -> bool { (*self % *other).is_zero() }
 
     /// Returns `true` if the number is divisible by `2`
     #[inline(always)]
@@ -973,7 +973,7 @@ impl Integer for BigInt {
 
     /// Returns `true` if the number can be divided by `other` without leaving a remainder
     #[inline(always)]
-    fn divisible_by(&self, other: &BigInt) -> bool { self.data.divisible_by(&other.data) }
+    fn is_multiple_of(&self, other: &BigInt) -> bool { self.data.is_multiple_of(&other.data) }
 
     /// Returns `true` if the number is divisible by `2`
     #[inline(always)]
diff --git a/src/libstd/num/rational.rs b/src/libstd/num/rational.rs
index 34308988fa5..a7c170c1cd6 100644
--- a/src/libstd/num/rational.rs
+++ b/src/libstd/num/rational.rs
@@ -203,6 +203,9 @@ impl<T: Copy + Num + Ord>
     }
 }
 
+impl<T: Copy + Num + Ord>
+    Num for Ratio<T> {}
+
 /* Utils */
 impl<T: Copy + Num + Ord>
     Round for Ratio<T> {
@@ -242,6 +245,12 @@ impl<T: Copy + Num + Ord>
     }
 }
 
+impl<T: Copy + Num + Ord> Fractional for Ratio<T> {
+    #[inline]
+    fn recip(&self) -> Ratio<T> {
+        Ratio::new_raw(self.denom, self.numer)
+    }
+}
 
 /* String conversions */
 impl<T: ToStr> ToStr for Ratio<T> {
@@ -447,6 +456,15 @@ mod test {
     }
 
     #[test]
+    fn test_recip() {
+        assert_eq!(_1 * _1.recip(), _1);
+        assert_eq!(_2 * _2.recip(), _1);
+        assert_eq!(_1_2 * _1_2.recip(), _1);
+        assert_eq!(_3_2 * _3_2.recip(), _1);
+        assert_eq!(_neg1_2 * _neg1_2.recip(), _1);
+    }
+
+    #[test]
     fn test_to_from_str() {
         fn test(r: Rational, s: ~str) {
             assert_eq!(FromStr::from_str(s), Some(r));