auto merge of #11412 : bjz/rust/num-cleanups, r=alexcrichton

The methods contained in `std::num::{Algebraic, Trigonometric, Exponential, Hyperbolic}` have now been moved into `std::num::Real`. This is part of an ongoing effort to simplify `std::num` (see issue #10387).

`std::num::RealExt` has also been removed from the prelude because it is not a commonly used trait.

r? @alexcrichton

Author: bors

src/libextra/num/complex.rs

@@ -11,7 +11,6 @@
 
 //! Complex numbers.
 
-
 use std::num::{Zero,One,ToStrRadix};
 
 // FIXME #1284: handle complex NaN & infinity etc. This
@@ -78,15 +77,15 @@ impl<T: Clone + Num> Cmplx<T> {
     }
 }
 
-impl<T: Clone + Algebraic + Num> Cmplx<T> {
+impl<T: Clone + Real> Cmplx<T> {
     /// Calculate |self|
     #[inline]
     pub fn norm(&self) -> T {
         self.re.hypot(&self.im)
     }
 }
 
-impl<T: Clone + Trigonometric + Algebraic + Num> Cmplx<T> {
+impl<T: Clone + Real> Cmplx<T> {
     /// Calculate the principal Arg of self.
     #[inline]
     pub fn arg(&self) -> T {

src/libextra/num/rational.rs

@@ -105,6 +105,12 @@ impl<T: Clone + Integer + Ord>
         ret.reduce();
         ret
     }
+
+    /// Return the reciprocal
+    #[inline]
+    pub fn recip(&self) -> Ratio<T> {
+        Ratio::new_raw(self.denom.clone(), self.numer.clone())
+    }
 }
 
 impl Ratio<BigInt> {
@@ -288,13 +294,6 @@ impl<T: Clone + Integer + Ord>
     }
 }
 
-impl<T: Clone + Integer + Ord> Fractional for Ratio<T> {
-    #[inline]
-    fn recip(&self) -> Ratio<T> {
-        Ratio::new_raw(self.denom.clone(), self.numer.clone())
-    }
-}
-
 /* String conversions */
 impl<T: ToStr> ToStr for Ratio<T> {
     /// Renders as `numer/denom`.

src/libstd/num/f32.rs

@@ -331,13 +331,79 @@ impl Round for f32 {
     fn fract(&self) -> f32 { *self - self.trunc() }
 }
 
-impl Fractional for f32 {
+impl Real for f32 {
+    /// Archimedes' constant
+    #[inline]
+    fn pi() -> f32 { 3.14159265358979323846264338327950288 }
+
+    /// 2.0 * pi
+    #[inline]
+    fn two_pi() -> f32 { 6.28318530717958647692528676655900576 }
+
+    /// pi / 2.0
+    #[inline]
+    fn frac_pi_2() -> f32 { 1.57079632679489661923132169163975144 }
+
+    /// pi / 3.0
+    #[inline]
+    fn frac_pi_3() -> f32 { 1.04719755119659774615421446109316763 }
+
+    /// pi / 4.0
+    #[inline]
+    fn frac_pi_4() -> f32 { 0.785398163397448309615660845819875721 }
+
+    /// pi / 6.0
+    #[inline]
+    fn frac_pi_6() -> f32 { 0.52359877559829887307710723054658381 }
+
+    /// pi / 8.0
+    #[inline]
+    fn frac_pi_8() -> f32 { 0.39269908169872415480783042290993786 }
+
+    /// 1 .0/ pi
+    #[inline]
+    fn frac_1_pi() -> f32 { 0.318309886183790671537767526745028724 }
+
+    /// 2.0 / pi
+    #[inline]
+    fn frac_2_pi() -> f32 { 0.636619772367581343075535053490057448 }
+
+    /// 2.0 / sqrt(pi)
+    #[inline]
+    fn frac_2_sqrtpi() -> f32 { 1.12837916709551257389615890312154517 }
+
+    /// sqrt(2.0)
+    #[inline]
+    fn sqrt2() -> f32 { 1.41421356237309504880168872420969808 }
+
+    /// 1.0 / sqrt(2.0)
+    #[inline]
+    fn frac_1_sqrt2() -> f32 { 0.707106781186547524400844362104849039 }
+
+    /// Euler's number
+    #[inline]
+    fn e() -> f32 { 2.71828182845904523536028747135266250 }
+
+    /// log2(e)
+    #[inline]
+    fn log2_e() -> f32 { 1.44269504088896340735992468100189214 }
+
+    /// log10(e)
+    #[inline]
+    fn log10_e() -> f32 { 0.434294481903251827651128918916605082 }
+
+    /// ln(2.0)
+    #[inline]
+    fn ln_2() -> f32 { 0.693147180559945309417232121458176568 }
+
+    /// ln(10.0)
+    #[inline]
+    fn ln_10() -> f32 { 2.30258509299404568401799145468436421 }
+
     /// The reciprocal (multiplicative inverse) of the number
     #[inline]
     fn recip(&self) -> f32 { 1.0 / *self }
-}
 
-impl Algebraic for f32 {
     #[inline]
     fn pow(&self, n: &f32) -> f32 { pow(*self, *n) }
 
@@ -352,9 +418,7 @@ impl Algebraic for f32 {
 
     #[inline]
     fn hypot(&self, other: &f32) -> f32 { hypot(*self, *other) }
-}
 
-impl Trigonometric for f32 {
     #[inline]
     fn sin(&self) -> f32 { sin(*self) }
 
@@ -381,9 +445,7 @@ impl Trigonometric for f32 {
     fn sin_cos(&self) -> (f32, f32) {
         (self.sin(), self.cos())
     }
-}
 
-impl Exponential for f32 {
     /// Returns the exponential of the number
     #[inline]
     fn exp(&self) -> f32 { exp(*self) }
@@ -407,9 +469,7 @@ impl Exponential for f32 {
     /// Returns the base 10 logarithm of the number
     #[inline]
     fn log10(&self) -> f32 { log10(*self) }
-}
 
-impl Hyperbolic for f32 {
     #[inline]
     fn sinh(&self) -> f32 { sinh(*self) }
 
@@ -469,76 +529,6 @@ impl Hyperbolic for f32 {
     fn atanh(&self) -> f32 {
         0.5 * ((2.0 * *self) / (1.0 - *self)).ln_1p()
     }
-}
-
-impl Real for f32 {
-    /// Archimedes' constant
-    #[inline]
-    fn pi() -> f32 { 3.14159265358979323846264338327950288 }
-
-    /// 2.0 * pi
-    #[inline]
-    fn two_pi() -> f32 { 6.28318530717958647692528676655900576 }
-
-    /// pi / 2.0
-    #[inline]
-    fn frac_pi_2() -> f32 { 1.57079632679489661923132169163975144 }
-
-    /// pi / 3.0
-    #[inline]
-    fn frac_pi_3() -> f32 { 1.04719755119659774615421446109316763 }
-
-    /// pi / 4.0
-    #[inline]
-    fn frac_pi_4() -> f32 { 0.785398163397448309615660845819875721 }
-
-    /// pi / 6.0
-    #[inline]
-    fn frac_pi_6() -> f32 { 0.52359877559829887307710723054658381 }
-
-    /// pi / 8.0
-    #[inline]
-    fn frac_pi_8() -> f32 { 0.39269908169872415480783042290993786 }
-
-    /// 1 .0/ pi
-    #[inline]
-    fn frac_1_pi() -> f32 { 0.318309886183790671537767526745028724 }
-
-    /// 2.0 / pi
-    #[inline]
-    fn frac_2_pi() -> f32 { 0.636619772367581343075535053490057448 }
-
-    /// 2.0 / sqrt(pi)
-    #[inline]
-    fn frac_2_sqrtpi() -> f32 { 1.12837916709551257389615890312154517 }
-
-    /// sqrt(2.0)
-    #[inline]
-    fn sqrt2() -> f32 { 1.41421356237309504880168872420969808 }
-
-    /// 1.0 / sqrt(2.0)
-    #[inline]
-    fn frac_1_sqrt2() -> f32 { 0.707106781186547524400844362104849039 }
-
-    /// Euler's number
-    #[inline]
-    fn e() -> f32 { 2.71828182845904523536028747135266250 }
-
-    /// log2(e)
-    #[inline]
-    fn log2_e() -> f32 { 1.44269504088896340735992468100189214 }
-
-    /// log10(e)
-    #[inline]
-    fn log10_e() -> f32 { 0.434294481903251827651128918916605082 }
-
-    /// ln(2.0)
-    #[inline]
-    fn ln_2() -> f32 { 0.693147180559945309417232121458176568 }
-
-    /// ln(10.0)
-    #[inline]
-    fn ln_10() -> f32 { 2.30258509299404568401799145468436421 }
 
     /// Converts to degrees, assuming the number is in radians
     #[inline]