auto merge of #6041 : bjz/rust/numeric-traits, r=brson

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

~~~rust
pub trait Signed: Num
                + Neg<Self> {
    fn abs(&self) -> Self;
    fn signum(&self) -> Self;
    fn is_positive(&self) -> bool;
    fn is_negative(&self) -> bool;
}

pub trait Unsigned: Num {}

pub trait Natural: Num
                 + Ord
                 + Quot<Self,Self>
                 + Rem<Self,Self> {
    fn div(&self, other: Self) -> Self;
    fn modulo(&self, other: Self) -> Self;
    fn div_mod(&self, other: Self) -> (Self,Self);
    fn quot_rem(&self, other: Self) -> (Self,Self);

    fn gcd(&self, other: Self) -> Self;
    fn lcm(&self, other: Self) -> Self;
    fn divisible_by(&self, other: Self) -> bool;
    fn is_even(&self) -> bool;
    fn is_odd(&self) -> bool;
}
~~~

I have not implemented `Natural` for `BigInt` and `BigUInt` because they're a little over my head. Help with this would be most appreciated.

15 files changed, 671 insertions, 188 deletions

diff --git a/src/libcore/core.rc b/src/libcore/core.rc
index b0a3939db73..61fbf98a7c6 100644
--- a/src/libcore/core.rc
+++ b/src/libcore/core.rc
@@ -105,7 +105,7 @@ pub use iter::{BaseIter, ExtendedIter, EqIter, CopyableIter};
 pub use iter::{CopyableOrderedIter, CopyableNonstrictIter, Times};
 pub use iter::{ExtendedMutableIter};
 
-pub use num::{Num, NumCast};
+pub use num::{Num, Signed, Unsigned, Natural, NumCast};
 pub use ptr::Ptr;
 pub use to_str::ToStr;
 pub use clone::Clone;
diff --git a/src/libcore/num/f32.rs b/src/libcore/num/f32.rs
index 62004710196..5d663844e5b 100644
--- a/src/libcore/num/f32.rs
+++ b/src/libcore/num/f32.rs
@@ -11,6 +11,7 @@
 //! Operations and constants for `f32`
 
 use num::strconv;
+use num::Signed;
 use num;
 use option::Option;
 use from_str;
@@ -163,38 +164,6 @@ pub fn gt(x: f32, y: f32) -> bool { return x > y; }
 // FIXME (#1999): replace the predicates below with llvm intrinsics or
 // calls to the libmath macros in the rust runtime for performance.
 
-/// Returns true if `x` is a positive number, including +0.0f320 and +Infinity
-#[inline(always)]
-pub fn is_positive(x: f32) -> bool {
-    x > 0.0f32 || (1.0f32/x) == infinity
-}
-
-/// Returns true if `x` is a negative number, including -0.0f320 and -Infinity
-#[inline(always)]
-pub fn is_negative(x: f32) -> bool {
-    x < 0.0f32 || (1.0f32/x) == neg_infinity
-}
-
-/**
- * Returns true if `x` is a negative number, including -0.0f320 and -Infinity
- *
- * This is the same as `f32::is_negative`.
- */
-#[inline(always)]
-pub fn is_nonpositive(x: f32) -> bool {
-  return x < 0.0f32 || (1.0f32/x) == neg_infinity;
-}
-
-/**
- * Returns true if `x` is a positive number, including +0.0f320 and +Infinity
- *
- * This is the same as `f32::is_positive`.)
- */
-#[inline(always)]
-pub fn is_nonnegative(x: f32) -> bool {
-  return x > 0.0f32 || (1.0f32/x) == infinity;
-}
-
 /// Returns true if `x` is a zero number (positive or negative zero)
 #[inline(always)]
 pub fn is_zero(x: f32) -> bool {
@@ -260,11 +229,6 @@ pub mod consts {
 }
 
 #[inline(always)]
-pub fn signbit(x: f32) -> int {
-    if is_negative(x) { return 1; } else { return 0; }
-}
-
-#[inline(always)]
 pub fn logarithm(n: f32, b: f32) -> f32 {
     return log2(n) / log2(b);
 }
@@ -351,15 +315,41 @@ impl Neg<f32> for f32 {
     fn neg(&self) -> f32 { -*self }
 }
 
+impl Signed for f32 {
+    /// Computes the absolute value. Returns `NaN` if the number is `NaN`.
+    #[inline(always)]
+    fn abs(&self) -> f32 { abs(*self) }
+
+    /**
+     * # Returns
+     *
+     * - `1.0` if the number is positive, `+0.0` or `infinity`
+     * - `-1.0` if the number is negative, `-0.0` or `neg_infinity`
+     * - `NaN` if the number is `NaN`
+     */
+    #[inline(always)]
+    fn signum(&self) -> f32 {
+        if is_NaN(*self) { NaN } else { copysign(1.0, *self) }
+    }
+
+    /// Returns `true` if the number is positive, including `+0.0` and `infinity`
+    #[inline(always)]
+    fn is_positive(&self) -> bool { *self > 0.0 || (1.0 / *self) == infinity }
+
+    /// Returns `true` if the number is negative, including `-0.0` and `neg_infinity`
+    #[inline(always)]
+    fn is_negative(&self) -> bool { *self < 0.0 || (1.0 / *self) == neg_infinity }
+}
+
 impl num::Round for f32 {
     #[inline(always)]
     fn round(&self, mode: num::RoundMode) -> f32 {
         match mode {
             num::RoundDown                           => floor(*self),
             num::RoundUp                             => ceil(*self),
-            num::RoundToZero   if is_negative(*self) => ceil(*self),
+            num::RoundToZero   if self.is_negative() => ceil(*self),
             num::RoundToZero                         => floor(*self),
-            num::RoundFromZero if is_negative(*self) => floor(*self),
+            num::RoundFromZero if self.is_negative() => floor(*self),
             num::RoundFromZero                       => ceil(*self)
         }
     }
@@ -370,7 +360,7 @@ impl num::Round for f32 {
     fn ceil(&self) -> f32 { ceil(*self) }
     #[inline(always)]
     fn fract(&self) -> f32 {
-        if is_negative(*self) {
+        if self.is_negative() {
             (*self) - ceil(*self)
         } else {
             (*self) - floor(*self)
@@ -595,6 +585,50 @@ impl num::FromStrRadix for f32 {
     }
 }
 
+#[cfg(test)]
+mod tests {
+    use f32::*;
+
+    #[test]
+    pub fn test_signed() {
+        assert_eq!(infinity.abs(), infinity);
+        assert_eq!(1f32.abs(), 1f32);
+        assert_eq!(0f32.abs(), 0f32);
+        assert_eq!((-0f32).abs(), 0f32);
+        assert_eq!((-1f32).abs(), 1f32);
+        assert_eq!(neg_infinity.abs(), infinity);
+        assert_eq!((1f32/neg_infinity).abs(), 0f32);
+        assert!(is_NaN(NaN.abs()));
+
+        assert_eq!(infinity.signum(), 1f32);
+        assert_eq!(1f32.signum(), 1f32);
+        assert_eq!(0f32.signum(), 1f32);
+        assert_eq!((-0f32).signum(), -1f32);
+        assert_eq!((-1f32).signum(), -1f32);
+        assert_eq!(neg_infinity.signum(), -1f32);
+        assert_eq!((1f32/neg_infinity).signum(), -1f32);
+        assert!(is_NaN(NaN.signum()));
+
+        assert!(infinity.is_positive());
+        assert!(1f32.is_positive());
+        assert!(0f32.is_positive());
+        assert!(!(-0f32).is_positive());
+        assert!(!(-1f32).is_positive());
+        assert!(!neg_infinity.is_positive());
+        assert!(!(1f32/neg_infinity).is_positive());
+        assert!(!NaN.is_positive());
+
+        assert!(!infinity.is_negative());
+        assert!(!1f32.is_negative());
+        assert!(!0f32.is_negative());
+        assert!((-0f32).is_negative());
+        assert!((-1f32).is_negative());
+        assert!(neg_infinity.is_negative());
+        assert!((1f32/neg_infinity).is_negative());
+        assert!(!NaN.is_negative());
+    }
+}
+
 //
 // Local Variables:
 // mode: rust
diff --git a/src/libcore/num/f64.rs b/src/libcore/num/f64.rs
index 4762c395a25..48f23fe8ba9 100644
--- a/src/libcore/num/f64.rs
+++ b/src/libcore/num/f64.rs
@@ -11,6 +11,7 @@
 //! Operations and constants for `f64`
 
 use num::strconv;
+use num::Signed;
 use num;
 use option::Option;
 use to_str;
@@ -183,36 +184,6 @@ pub fn ge(x: f64, y: f64) -> bool { return x >= y; }
 #[inline(always)]
 pub fn gt(x: f64, y: f64) -> bool { return x > y; }
 
-/// Returns true if `x` is a positive number, including +0.0f640 and +Infinity
-#[inline(always)]
-pub fn is_positive(x: f64) -> bool
-    { return x > 0.0f64 || (1.0f64/x) == infinity; }
-
-/// Returns true if `x` is a negative number, including -0.0f640 and -Infinity
-#[inline(always)]
-pub fn is_negative(x: f64) -> bool
-    { return x < 0.0f64 || (1.0f64/x) == neg_infinity; }
-
-/**
- * Returns true if `x` is a negative number, including -0.0f640 and -Infinity
- *
- * This is the same as `f64::is_negative`.
- */
-#[inline(always)]
-pub fn is_nonpositive(x: f64) -> bool {
-  return x < 0.0f64 || (1.0f64/x) == neg_infinity;
-}
-
-/**
- * Returns true if `x` is a positive number, including +0.0f640 and +Infinity
- *
- * This is the same as `f64::positive`.
- */
-#[inline(always)]
-pub fn is_nonnegative(x: f64) -> bool {
-  return x > 0.0f64 || (1.0f64/x) == infinity;
-}
-
 /// Returns true if `x` is a zero number (positive or negative zero)
 #[inline(always)]
 pub fn is_zero(x: f64) -> bool {
@@ -279,11 +250,6 @@ pub mod consts {
 }
 
 #[inline(always)]
-pub fn signbit(x: f64) -> int {
-    if is_negative(x) { return 1; } else { return 0; }
-}
-
-#[inline(always)]
 pub fn logarithm(n: f64, b: f64) -> f64 {
     return log2(n) / log2(b);
 }
@@ -357,15 +323,41 @@ impl Neg<f64> for f64 {
     fn neg(&self) -> f64 { -*self }
 }
 
+impl Signed for f64 {
+    /// Computes the absolute value. Returns `NaN` if the number is `NaN`.
+    #[inline(always)]
+    fn abs(&self) -> f64 { abs(*self) }
+
+    /**
+     * # Returns
+     *
+     * - `1.0` if the number is positive, `+0.0` or `infinity`
+     * - `-1.0` if the number is negative, `-0.0` or `neg_infinity`
+     * - `NaN` if the number is `NaN`
+     */
+    #[inline(always)]
+    fn signum(&self) -> f64 {
+        if is_NaN(*self) { NaN } else { copysign(1.0, *self) }
+    }
+
+    /// Returns `true` if the number is positive, including `+0.0` and `infinity`
+    #[inline(always)]
+    fn is_positive(&self) -> bool { *self > 0.0 || (1.0 / *self) == infinity }
+
+    /// Returns `true` if the number is negative, including `-0.0` and `neg_infinity`
+    #[inline(always)]
+    fn is_negative(&self) -> bool { *self < 0.0 || (1.0 / *self) == neg_infinity }
+}
+
 impl num::Round for f64 {
     #[inline(always)]
     fn round(&self, mode: num::RoundMode) -> f64 {
         match mode {
             num::RoundDown                           => floor(*self),
             num::RoundUp                             => ceil(*self),
-            num::RoundToZero   if is_negative(*self) => ceil(*self),
+            num::RoundToZero   if self.is_negative() => ceil(*self),
             num::RoundToZero                         => floor(*self),
-            num::RoundFromZero if is_negative(*self) => floor(*self),
+            num::RoundFromZero if self.is_negative() => floor(*self),
             num::RoundFromZero                       => ceil(*self)
         }
     }
@@ -376,7 +368,7 @@ impl num::Round for f64 {
     fn ceil(&self) -> f64 { ceil(*self) }
     #[inline(always)]
     fn fract(&self) -> f64 {
-        if is_negative(*self) {
+        if self.is_negative() {
             (*self) - ceil(*self)
         } else {
             (*self) - floor(*self)
@@ -601,6 +593,50 @@ impl num::FromStrRadix for f64 {
     }
 }
 
+#[cfg(test)]
+mod tests {
+    use f64::*;
+
+    #[test]
+    pub fn test_signed() {
+        assert_eq!(infinity.abs(), infinity);
+        assert_eq!(1f64.abs(), 1f64);
+        assert_eq!(0f64.abs(), 0f64);
+        assert_eq!((-0f64).abs(), 0f64);
+        assert_eq!((-1f64).abs(), 1f64);
+        assert_eq!(neg_infinity.abs(), infinity);
+        assert_eq!((1f64/neg_infinity).abs(), 0f64);
+        assert!(is_NaN(NaN.abs()));
+
+        assert_eq!(infinity.signum(), 1f64);
+        assert_eq!(1f64.signum(), 1f64);
+        assert_eq!(0f64.signum(), 1f64);
+        assert_eq!((-0f64).signum(), -1f64);
+        assert_eq!((-1f64).signum(), -1f64);
+        assert_eq!(neg_infinity.signum(), -1f64);
+        assert_eq!((1f64/neg_infinity).signum(), -1f64);
+        assert!(is_NaN(NaN.signum()));
+
+        assert!(infinity.is_positive());
+        assert!(1f64.is_positive());
+        assert!(0f64.is_positive());
+        assert!(!(-0f64).is_positive());
+        assert!(!(-1f64).is_positive());
+        assert!(!neg_infinity.is_positive());
+        assert!(!(1f64/neg_infinity).is_positive());
+        assert!(!NaN.is_positive());
+
+        assert!(!infinity.is_negative());
+        assert!(!1f64.is_negative());
+        assert!(!0f64.is_negative());
+        assert!((-0f64).is_negative());
+        assert!((-1f64).is_negative());
+        assert!(neg_infinity.is_negative());
+        assert!((1f64/neg_infinity).is_negative());
+        assert!(!NaN.is_negative());
+    }
+}
+
 //
 // Local Variables:
 // mode: rust
diff --git a/src/libcore/num/float.rs b/src/libcore/num/float.rs
index c5c1e52a14c..036d295943c 100644
--- a/src/libcore/num/float.rs
+++ b/src/libcore/num/float.rs
@@ -22,6 +22,7 @@
 
 use f64;
 use num::strconv;
+use num::Signed;
 use num;
 use option::Option;
 use to_str;
@@ -42,7 +43,6 @@ pub use f64::{erf, erfc, exp, expm1, exp2, abs_sub};
 pub use f64::{mul_add, fmax, fmin, nextafter, frexp, hypot, ldexp};
 pub use f64::{lgamma, ln, log_radix, ln1p, log10, log2, ilog_radix};
 pub use f64::{modf, pow, powi, round, sinh, tanh, tgamma, trunc};
-pub use f64::signbit;
 pub use f64::{j0, j1, jn, y0, y1, yn};
 
 pub static NaN: float = 0.0/0.0;
@@ -349,14 +349,6 @@ pub fn pow_with_uint(base: uint, pow: uint) -> float {
 }
 
 #[inline(always)]
-pub fn is_positive(x: float) -> bool { f64::is_positive(x as f64) }
-#[inline(always)]
-pub fn is_negative(x: float) -> bool { f64::is_negative(x as f64) }
-#[inline(always)]
-pub fn is_nonpositive(x: float) -> bool { f64::is_nonpositive(x as f64) }
-#[inline(always)]
-pub fn is_nonnegative(x: float) -> bool { f64::is_nonnegative(x as f64) }
-#[inline(always)]
 pub fn is_zero(x: float) -> bool { f64::is_zero(x as f64) }
 #[inline(always)]
 pub fn is_infinite(x: float) -> bool { f64::is_infinite(x as f64) }
@@ -428,11 +420,11 @@ impl num::Round for float {
                 => f64::floor(*self as f64) as float,
             num::RoundUp
                 => f64::ceil(*self as f64) as float,
-            num::RoundToZero   if is_negative(*self)
+            num::RoundToZero   if self.is_negative()
                 => f64::ceil(*self as f64) as float,
             num::RoundToZero
                 => f64::floor(*self as f64) as float,
-            num::RoundFromZero if is_negative(*self)
+            num::RoundFromZero if self.is_negative()
                 => f64::floor(*self as f64) as float,
             num::RoundFromZero
                 => f64::ceil(*self as f64) as float
@@ -445,7 +437,7 @@ impl num::Round for float {
     fn ceil(&self) -> float { f64::ceil(*self as f64) as float}
     #[inline(always)]
     fn fract(&self) -> float {
-        if is_negative(*self) {
+        if self.is_negative() {
             (*self) - (f64::ceil(*self as f64) as float)
         } else {
             (*self) - (f64::floor(*self as f64) as float)
@@ -501,10 +493,76 @@ impl Neg<float> for float {
     fn neg(&self) -> float { -*self }
 }
 
+impl Signed for float {
+    /// Computes the absolute value. Returns `NaN` if the number is `NaN`.
+    #[inline(always)]
+    fn abs(&self) -> float { abs(*self) }
+
+    /**
+     * # Returns
+     *
+     * - `1.0` if the number is positive, `+0.0` or `infinity`
+     * - `-1.0` if the number is negative, `-0.0` or `neg_infinity`
+     * - `NaN` if the number is NaN
+     */
+    #[inline(always)]
+    fn signum(&self) -> float {
+        if is_NaN(*self) { NaN } else { f64::copysign(1.0, *self as f64) as float }
+    }
+
+    /// Returns `true` if the number is positive, including `+0.0` and `infinity`
+    #[inline(always)]
+    fn is_positive(&self) -> bool { *self > 0.0 || (1.0 / *self) == infinity }
+
+    /// Returns `true` if the number is negative, including `-0.0` and `neg_infinity`
+    #[inline(always)]
+    fn is_negative(&self) -> bool { *self < 0.0 || (1.0 / *self) == neg_infinity }
+}
+
 #[cfg(test)]
 mod tests {
     use super::*;
     use prelude::*;
+
+    #[test]
+    pub fn test_signed() {
+        assert_eq!(infinity.abs(), infinity);
+        assert_eq!(1f.abs(), 1f);
+        assert_eq!(0f.abs(), 0f);
+        assert_eq!((-0f).abs(), 0f);
+        assert_eq!((-1f).abs(), 1f);
+        assert_eq!(neg_infinity.abs(), infinity);
+        assert_eq!((1f/neg_infinity).abs(), 0f);
+        assert!(is_NaN(NaN.abs()));
+
+        assert_eq!(infinity.signum(), 1f);
+        assert_eq!(1f.signum(), 1f);
+        assert_eq!(0f.signum(), 1f);
+        assert_eq!((-0f).signum(), -1f);
+        assert_eq!((-1f).signum(), -1f);
+        assert_eq!(neg_infinity.signum(), -1f);
+        assert_eq!((1f/neg_infinity).signum(), -1f);
+        assert!(is_NaN(NaN.signum()));
+
+        assert!(infinity.is_positive());
+        assert!(1f.is_positive());
+        assert!(0f.is_positive());
+        assert!(!(-0f).is_positive());
+        assert!(!(-1f).is_positive());
+        assert!(!neg_infinity.is_positive());
+        assert!(!(1f/neg_infinity).is_positive());
+        assert!(!NaN.is_positive());
+
+        assert!(!infinity.is_negative());
+        assert!(!1f.is_negative());
+        assert!(!0f.is_negative());
+        assert!((-0f).is_negative());
+        assert!((-1f).is_negative());
+        assert!(neg_infinity.is_negative());
+        assert!((1f/neg_infinity).is_negative());
+        assert!(!NaN.is_negative());
+    }
+
     #[test]
     pub fn test_to_str_exact_do_decimal() {
         let s = to_str_exact(5.0, 4u);
@@ -538,11 +596,11 @@ mod tests {
         }
         // note: -0 == 0, hence these slightly more complex tests
         match from_str(~"-0") {
-            Some(v) if is_zero(v) => assert!(is_negative(v)),
+            Some(v) if is_zero(v) => assert!(v.is_negative()),
             _ => fail!()
         }
         match from_str(~"0") {
-            Some(v) if is_zero(v) => assert!(is_positive(v)),
+            Some(v) if is_zero(v) => assert!(v.is_positive()),
             _ => fail!()
         }
 
@@ -585,11 +643,11 @@ mod tests {
         }
         // note: -0 == 0, hence these slightly more complex tests
         match from_str_hex(~"-0") {
-            Some(v) if is_zero(v) => assert!(is_negative(v)),
+            Some(v) if is_zero(v) => assert!(v.is_negative()),
             _ => fail!()
         }
         match from_str_hex(~"0") {
-            Some(v) if is_zero(v) => assert!(is_positive(v)),
+            Some(v) if is_zero(v) => assert!(v.is_positive()),
             _ => fail!()
         }
         assert_eq!(from_str_hex(~"e"), Some(14.));
@@ -642,50 +700,6 @@ mod tests {
     }
 
     #[test]
-    pub fn test_positive() {
-        assert!(is_positive(infinity));
-        assert!(is_positive(1.));
-        assert!(is_positive(0.));
-        assert!(!is_positive(-1.));
-        assert!(!is_positive(neg_infinity));
-        assert!(!is_positive(1./neg_infinity));
-        assert!(!is_positive(NaN));
-    }
-
-    #[test]
-    pub fn test_negative() {
-        assert!(!is_negative(infinity));
-        assert!(!is_negative(1.));
-        assert!(!is_negative(0.));
-        assert!(is_negative(-1.));
-        assert!(is_negative(neg_infinity));
-        assert!(is_negative(1./neg_infinity));
-        assert!(!is_negative(NaN));
-    }
-
-    #[test]
-    pub fn test_nonpositive() {
-        assert!(!is_nonpositive(infinity));
-        assert!(!is_nonpositive(1.));
-        assert!(!is_nonpositive(0.));
-        assert!(is_nonpositive(-1.));
-        assert!(is_nonpositive(neg_infinity));
-        assert!(is_nonpositive(1./neg_infinity));
-        assert!(!is_nonpositive(NaN));
-    }
-
-    #[test]
-    pub fn test_nonnegative() {
-        assert!(is_nonnegative(infinity));
-        assert!(is_nonnegative(1.));
-        assert!(is_nonnegative(0.));
-        assert!(!is_nonnegative(-1.));
-        assert!(!is_nonnegative(neg_infinity));
-        assert!(!is_nonnegative(1./neg_infinity));
-        assert!(!is_nonnegative(NaN));
-    }
-
-    #[test]
     pub fn test_to_str_inf() {
         assert_eq!(to_str_digits(infinity, 10u), ~"inf");
         assert_eq!(to_str_digits(-infinity, 10u), ~"-inf");
diff --git a/src/libcore/num/int-template.rs b/src/libcore/num/int-template.rs
index 684083f53e9..426ed8a8b0f 100644
--- a/src/libcore/num/int-template.rs
+++ b/src/libcore/num/int-template.rs
@@ -14,6 +14,7 @@ use to_str::ToStr;
 use from_str::FromStr;
 use num::{ToStrRadix, FromStrRadix};
 use num::strconv;
+use num::Signed;
 use num;
 use prelude::*;
 
@@ -70,15 +71,6 @@ pub fn ge(x: T, y: T) -> bool { x >= y }
 #[inline(always)]
 pub fn gt(x: T, y: T) -> bool { x > y }
 
-#[inline(always)]
-pub fn is_positive(x: T) -> bool { x > 0 as T }
-#[inline(always)]
-pub fn is_negative(x: T) -> bool { x < 0 as T }
-#[inline(always)]
-pub fn is_nonpositive(x: T) -> bool { x <= 0 as T }
-#[inline(always)]
-pub fn is_nonnegative(x: T) -> bool { x >= 0 as T }
-
 /**
  * Iterate over the range [`lo`..`hi`)
  *
@@ -139,9 +131,7 @@ pub fn compl(i: T) -> T {
 
 /// Computes the absolute value
 #[inline(always)]
-pub fn abs(i: T) -> T {
-    if is_negative(i) { -i } else { i }
-}
+pub fn abs(i: T) -> T { i.abs() }
 
 #[cfg(notest)]
 impl Ord for T {
@@ -201,6 +191,24 @@ impl Div<T,T> for T {
 #[cfg(stage2,notest)]
 #[cfg(stage3,notest)]
 impl Quot<T,T> for T {
+    /**
+     * Returns the integer quotient, truncated towards 0. As this behaviour reflects
+     * the underlying machine implementation it is more efficient than `Natural::div`.
+     *
+     * # Examples
+     *
+     * ~~~
+     * assert!( 8 /  3 ==  2);
+     * assert!( 8 / -3 == -2);
+     * assert!(-8 /  3 == -2);
+     * assert!(-8 / -3 ==  2);
+
+     * assert!( 1 /  2 ==  0);
+     * assert!( 1 / -2 ==  0);
+     * assert!(-1 /  2 ==  0);
+     * assert!(-1 / -2 ==  0);
+     * ~~~
+     */
     #[inline(always)]
     fn quot(&self, other: &T) -> T { *self / *other }
 }
@@ -215,6 +223,27 @@ impl Modulo<T,T> for T {
 #[cfg(stage2,notest)]
 #[cfg(stage3,notest)]
 impl Rem<T,T> for T {
+    /**
+     * Returns the integer remainder after division, satisfying:
+     *
+     * ~~~
+     * assert!((n / d) * d + (n % d) == n)
+     * ~~~
+     *
+     * # Examples
+     *
+     * ~~~
+     * assert!( 8 %  3 ==  2);
+     * assert!( 8 % -3 ==  2);
+     * assert!(-8 %  3 == -2);
+     * assert!(-8 % -3 == -2);
+
+     * assert!( 1 %  2 ==  1);
+     * assert!( 1 % -2 ==  1);
+     * assert!(-1 %  2 == -1);
+     * assert!(-1 % -2 == -1);
+     * ~~~
+     */
     #[inline(always)]
     fn rem(&self, other: &T) -> T { *self % *other }
 }
@@ -225,6 +254,155 @@ impl Neg<T> for T {
     fn neg(&self) -> T { -*self }
 }
 
+impl Signed for T {
+    /// Computes the absolute value
+    #[inline(always)]
+    fn abs(&self) -> T {
+        if self.is_negative() { -*self } else { *self }
+    }
+
+    /**
+     * # Returns
+     *
+     * - `0` if the number is zero
+     * - `1` if the number is positive
+     * - `-1` if the number is negative
+     */
+    #[inline(always)]
+    fn signum(&self) -> T {
+        match *self {
+            n if n > 0 =>  1,
+            0          =>  0,
+            _          => -1,
+        }
+    }
+
+    /// Returns true if the number is positive
+    #[inline(always)]
+    fn is_positive(&self) -> bool { *self > 0 }
+
+    /// Returns true if the number is negative
+    #[inline(always)]
+    fn is_negative(&self) -> bool { *self < 0 }
+}
+
+impl Natural for T {
+    /**
+     * Floored integer division
+     *
+     * # Examples
+     *
+     * ~~~
+     * assert!(( 8).div( 3) ==  2);
+     * assert!(( 8).div(-3) == -3);
+     * assert!((-8).div( 3) == -3);
+     * assert!((-8).div(-3) ==  2);
+     *
+     * assert!(( 1).div( 2) ==  0);
+     * assert!(( 1).div(-2) == -1);
+     * assert!((-1).div( 2) == -1);
+     * assert!((-1).div(-2) ==  0);
+     * ~~~
+     */
+    #[inline(always)]
+    fn div(&self, other: T) -> T {
+        // Algorithm from [Daan Leijen. _Division and Modulus for Computer Scientists_,
+        // December 2001](http://research.microsoft.com/pubs/151917/divmodnote-letter.pdf)
+        match self.quot_rem(other) {
+            (q, r) if (r > 0 && other < 0)
+                   || (r < 0 && other > 0) => q - 1,
+            (q, _)                         => q,
+        }
+    }
+
+    /**
+     * Integer modulo, satisfying:
+     *
+     * ~~~
+     * assert!(n.div(d) * d + n.modulo(d) == n)
+     * ~~~
+     *
+     * # Examples
+     *
+     * ~~~
+     * assert!(( 8).modulo( 3) ==  2);
+     * assert!(( 8).modulo(-3) == -1);
+     * assert!((-8).modulo( 3) ==  1);
+     * assert!((-8).modulo(-3) == -2);
+     *
+     * assert!(( 1).modulo( 2) ==  1);
+     * assert!(( 1).modulo(-2) == -1);
+     * assert!((-1).modulo( 2) ==  1);
+     * assert!((-1).modulo(-2) == -1);
+     * ~~~
+     */
+    #[inline(always)]
+    fn modulo(&self, other: T) -> T {
+        // Algorithm from [Daan Leijen. _Division and Modulus for Computer Scientists_,
+        // December 2001](http://research.microsoft.com/pubs/151917/divmodnote-letter.pdf)
+        match *self % other {
+            r if (r > 0 && other < 0)
+              || (r < 0 && other > 0) => r + other,
+            r                         => r,
+        }
+    }
+
+    /// Calculates `div` and `modulo` simultaneously
+    #[inline(always)]
+    fn div_mod(&self, other: T) -> (T,T) {
+        // Algorithm from [Daan Leijen. _Division and Modulus for Computer Scientists_,
+        // December 2001](http://research.microsoft.com/pubs/151917/divmodnote-letter.pdf)
+        match self.quot_rem(other) {
+            (q, r) if (r > 0 && other < 0)
+                   || (r < 0 && other > 0) => (q - 1, r + other),
+            (q, r)                         => (q, r),
+        }
+    }
+
+    /// Calculates `quot` (`\`) and `rem` (`%`) simultaneously
+    #[inline(always)]
+    fn quot_rem(&self, other: T) -> (T,T) {
+        (*self / other, *self % other)
+    }
+
+    /**
+     * Calculates the Greatest Common Divisor (GCD) of the number and `other`
+     *
+     * The result is always positive
+     */
+    #[inline(always)]
+    fn gcd(&self, other: T) -> T {
+        // Use Euclid's algorithm
+        let mut m = *self, n = other;
+        while m != 0 {
+            let temp = m;
+            m = n % temp;
+            n = temp;
+        }
+        n.abs()
+    }
+
+    /**
+     * Calculates the Lowest Common Multiple (LCM) of the number and `other`
+     */
+    #[inline(always)]
+    fn lcm(&self, other: T) -> T {
+        ((*self * other) / self.gcd(other)).abs() // should not have to recaluculate abs
+    }
+
+    /// 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 }
+
+    /// Returns `true` if the number is divisible by `2`
+    #[inline(always)]
+    fn is_even(&self) -> bool { self.divisible_by(2) }
+
+    /// Returns `true` if the number is not divisible by `2`
+    #[inline(always)]
+    fn is_odd(&self) -> bool { !self.is_even() }
+}
+
 #[cfg(notest)]
 impl BitOr<T,T> for T {
     #[inline(always)]
@@ -345,6 +523,117 @@ mod tests {
     use prelude::*;
 
     #[test]
+    pub fn test_signed() {
+        assert_eq!((1 as T).abs(), 1 as T);
+        assert_eq!((0 as T).abs(), 0 as T);
+        assert_eq!((-1 as T).abs(), 1 as T);
+
+        assert_eq!((1 as T).signum(), 1 as T);
+        assert_eq!((0 as T).signum(), 0 as T);
+        assert_eq!((-0 as T).signum(), 0 as T);
+        assert_eq!((-1 as T).signum(), -1 as T);
+
+        assert!((1 as T).is_positive());
+        assert!(!(0 as T).is_positive());
+        assert!(!(-0 as T).is_positive());
+        assert!(!(-1 as T).is_positive());
+
+        assert!(!(1 as T).is_negative());
+        assert!(!(0 as T).is_negative());
+        assert!(!(-0 as T).is_negative());
+        assert!((-1 as T).is_negative());
+    }
+
+    /**
+     * Checks that the division rule holds for:
+     *
+     * - `n`: numerator (dividend)
+     * - `d`: denominator (divisor)
+     * - `qr`: quotient and remainder
+     */
+    #[cfg(test)]
+    fn test_division_rule(nd: (T,T), qr: (T,T)) {
+        let (n,d) = nd,
+            (q,r) = qr;
+
+        assert_eq!(d * q + r, n);
+    }
+
+    #[test]
+    fn test_quot_rem() {
+        fn test_nd_qr(nd: (T,T), qr: (T,T)) {
+            let (n,d) = nd;
+            let separate_quot_rem = (n / d, n % d);
+            let combined_quot_rem = n.quot_rem(d);
+
+            assert_eq!(separate_quot_rem, qr);
+            assert_eq!(combined_quot_rem, qr);
+
+            test_division_rule(nd, separate_quot_rem);
+            test_division_rule(nd, combined_quot_rem);
+        }
+
+        test_nd_qr(( 8,  3), ( 2,  2));
+        test_nd_qr(( 8, -3), (-2,  2));
+        test_nd_qr((-8,  3), (-2, -2));
+        test_nd_qr((-8, -3), ( 2, -2));
+
+        test_nd_qr(( 1,  2), ( 0,  1));
+        test_nd_qr(( 1, -2), ( 0,  1));
+        test_nd_qr((-1,  2), ( 0, -1));
+        test_nd_qr((-1, -2), ( 0, -1));
+    }
+
+    #[test]
+    fn test_div_mod() {
+        fn test_nd_dm(nd: (T,T), dm: (T,T)) {
+            let (n,d) = nd;
+            let separate_div_mod = (n.div(d), n.modulo(d));
+            let combined_div_mod = n.div_mod(d);
+
+            assert_eq!(separate_div_mod, dm);
+            assert_eq!(combined_div_mod, dm);
+
+            test_division_rule(nd, separate_div_mod);
+            test_division_rule(nd, combined_div_mod);
+        }
+
+        test_nd_dm(( 8,  3), ( 2,  2));
+        test_nd_dm(( 8, -3), (-3, -1));
+        test_nd_dm((-8,  3), (-3,  1));
+        test_nd_dm((-8, -3), ( 2, -2));
+
+        test_nd_dm(( 1,  2), ( 0,  1));
+        test_nd_dm(( 1, -2), (-1, -1));
+        test_nd_dm((-1,  2), (-1,  1));
+        test_nd_dm((-1, -2), ( 0, -1));
+    }
+
+    #[test]
+    fn test_gcd() {
+        assert_eq!((10 as T).gcd(2), 2 as T);
+        assert_eq!((10 as T).gcd(3), 1 as T);
+        assert_eq!((0 as T).gcd(3), 3 as T);
+        assert_eq!((3 as T).gcd(3), 3 as T);
+        assert_eq!((56 as T).gcd(42), 14 as T);
+        assert_eq!((3 as T).gcd(-3), 3 as T);
+        assert_eq!((-6 as T).gcd(3), 3 as T);
+        assert_eq!((-4 as T).gcd(-2), 2 as T);
+    }
+
+    #[test]
+    fn test_lcm() {
+        assert_eq!((1 as T).lcm(0), 0 as T);
+        assert_eq!((0 as T).lcm(1), 0 as T);
+        assert_eq!((1 as T).lcm(1), 1 as T);
+        assert_eq!((-1 as T).lcm(1), 1 as T);
+        assert_eq!((1 as T).lcm(-1), 1 as T);
+        assert_eq!((-1 as T).lcm(-1), 1 as T);
+        assert_eq!((8 as T).lcm(9), 72 as T);
+        assert_eq!((11 as T).lcm(5), 55 as T);
+    }
+
+    #[test]
     fn test_bitwise_ops() {
         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/num/num.rs b/src/libcore/num/num.rs
index a0ff510cde7..577bb3f0f15 100644
--- a/src/libcore/num/num.rs
+++ b/src/libcore/num/num.rs
@@ -60,10 +60,37 @@ pub trait One {
     fn one() -> Self;
 }
 
+pub trait Signed: Num
+                + Neg<Self> {
+    fn abs(&self) -> Self;
+    fn signum(&self) -> Self;
+    fn is_positive(&self) -> bool;
+    fn is_negative(&self) -> bool;
+}
+
+pub trait Unsigned: Num {}
+
+// This should be moved into the default implementation for Signed::abs
 pub fn abs<T:Ord + Zero + Neg<T>>(v: T) -> T {
     if v < Zero::zero() { v.neg() } else { v }
 }
 
+pub trait Natural: Num
+                 + Ord
+                 + Quot<Self,Self>
+                 + Rem<Self,Self> {
+    fn div(&self, other: Self) -> Self;
+    fn modulo(&self, other: Self) -> Self;
+    fn div_mod(&self, other: Self) -> (Self,Self);
+    fn quot_rem(&self, other: Self) -> (Self,Self);
+
+    fn gcd(&self, other: Self) -> Self;
+    fn lcm(&self, other: Self) -> Self;
+    fn divisible_by(&self, other: Self) -> bool;
+    fn is_even(&self) -> bool;
+    fn is_odd(&self) -> bool;
+}
+
 pub trait Round {
     fn round(&self, mode: RoundMode) -> Self;
 
diff --git a/src/libcore/num/uint-template.rs b/src/libcore/num/uint-template.rs
index 4bb93907a3a..a0da84a8c53 100644
--- a/src/libcore/num/uint-template.rs
+++ b/src/libcore/num/uint-template.rs
@@ -15,6 +15,7 @@ use to_str::ToStr;
 use from_str::FromStr;
 use num::{ToStrRadix, FromStrRadix};
 use num::strconv;
+use num::Unsigned;
 use num;
 use option::Option;
 use prelude::*;
@@ -52,15 +53,6 @@ pub fn ge(x: T, y: T) -> bool { x >= y }
 pub fn gt(x: T, y: T) -> bool { x > y }
 
 #[inline(always)]
-pub fn is_positive(x: T) -> bool { x > 0 as T }
-#[inline(always)]
-pub fn is_negative(x: T) -> bool { x < 0 as T }
-#[inline(always)]
-pub fn is_nonpositive(x: T) -> bool { x <= 0 as T }
-#[inline(always)]
-pub fn is_nonnegative(x: T) -> bool { x >= 0 as T }
-
-#[inline(always)]
 /**
  * Iterate over the range [`start`,`start`+`step`..`stop`)
  *
@@ -190,6 +182,61 @@ impl Neg<T> for T {
     fn neg(&self) -> T { -*self }
 }
 
+impl Unsigned for T {}
+
+impl Natural for T {
+    /// Unsigned integer division. Returns the same result as `quot` (`/`).
+    #[inline(always)]
+    fn div(&self, other: T) -> T { *self / other }
+
+    /// Unsigned integer modulo operation. Returns the same result as `rem` (`%`).
+    #[inline(always)]
+    fn modulo(&self, other: T) -> T { *self / other }
+
+    /// Calculates `div` and `modulo` simultaneously
+    #[inline(always)]
+    fn div_mod(&self, other: T) -> (T,T) {
+        (*self / other, *self % other)
+    }
+
+    /// Calculates `quot` (`\`) and `rem` (`%`) simultaneously
+    #[inline(always)]
+    fn quot_rem(&self, other: T) -> (T,T) {
+        (*self / other, *self % other)
+    }
+
+    /// Calculates the Greatest Common Divisor (GCD) of the number and `other`
+    #[inline(always)]
+    fn gcd(&self, other: T) -> T {
+        // Use Euclid's algorithm
+        let mut m = *self, n = other;
+        while m != 0 {
+            let temp = m;
+            m = n % temp;
+            n = temp;
+        }
+        n
+    }
+
+    /// Calculates the Lowest Common Multiple (LCM) of the number and `other`
+    #[inline(always)]
+    fn lcm(&self, other: T) -> T {
+        (*self * other) / self.gcd(other)
+    }
+
+    /// 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 }
+
+    /// Returns `true` if the number is divisible by `2`
+    #[inline(always)]
+    fn is_even(&self) -> bool { self.divisible_by(2) }
+
+    /// Returns `true` if the number is not divisible by `2`
+    #[inline(always)]
+    fn is_odd(&self) -> bool { !self.is_even() }
+}
+
 #[cfg(notest)]
 impl BitOr<T,T> for T {
     #[inline(always)]
@@ -310,6 +357,25 @@ mod tests {
     use prelude::*;
 
     #[test]
+    fn test_gcd() {
+        assert_eq!((10 as T).gcd(2), 2 as T);
+        assert_eq!((10 as T).gcd(3), 1 as T);
+        assert_eq!((0 as T).gcd(3), 3 as T);
+        assert_eq!((3 as T).gcd(3), 3 as T);
+        assert_eq!((56 as T).gcd(42), 14 as T);
+    }
+
+    #[test]
+    fn test_lcm() {
+        assert_eq!((1 as T).lcm(0), 0 as T);
+        assert_eq!((0 as T).lcm(1), 0 as T);
+        assert_eq!((1 as T).lcm(1), 1 as T);
+        assert_eq!((8 as T).lcm(9), 72 as T);
+        assert_eq!((11 as T).lcm(5), 55 as T);
+        assert_eq!((99 as T).lcm(17), 1683 as T);
+    }
+
+    #[test]
     fn test_bitwise_ops() {
         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 15aa6c78ed6..03e6065a85c 100644
--- a/src/libcore/prelude.rs
+++ b/src/libcore/prelude.rs
@@ -39,7 +39,7 @@ pub use hash::Hash;
 pub use iter::{BaseIter, ReverseIter, MutableIter, ExtendedIter, EqIter};
 pub use iter::{CopyableIter, CopyableOrderedIter, CopyableNonstrictIter};
 pub use iter::{Times, ExtendedMutableIter};
-pub use num::{Num, NumCast};
+pub use num::{Num, Signed, Unsigned, Natural, NumCast};
 pub use path::GenericPath;
 pub use path::Path;
 pub use path::PosixPath;
diff --git a/src/librustc/middle/const_eval.rs b/src/librustc/middle/const_eval.rs
index c1cc01ed05a..d3619a24767 100644
--- a/src/librustc/middle/const_eval.rs
+++ b/src/librustc/middle/const_eval.rs
@@ -299,9 +299,9 @@ pub fn eval_const_expr_partial(tcx: middle::ty::ctxt, e: @expr)
               add => Ok(const_int(a + b)),
               subtract => Ok(const_int(a - b)),
               mul => Ok(const_int(a * b)),
-              quot if b == 0 => Err(~"quotient zero"),
+              quot if b == 0 => Err(~"attempted quotient with a divisor of zero"),
               quot => Ok(const_int(a / b)),
-              rem if b == 0 => Err(~"remainder zero"),
+              rem if b == 0 => Err(~"attempted remainder with a divisor of zero"),
               rem => Ok(const_int(a % b)),
               and | bitand => Ok(const_int(a & b)),
               or | bitor => Ok(const_int(a | b)),
@@ -321,9 +321,9 @@ pub fn eval_const_expr_partial(tcx: middle::ty::ctxt, e: @expr)
               add => Ok(const_uint(a + b)),
               subtract => Ok(const_uint(a - b)),
               mul => Ok(const_uint(a * b)),
-              quot if b == 0 => Err(~"quotient zero"),
+              quot if b == 0 => Err(~"attempted quotient with a divisor of zero"),
               quot => Ok(const_uint(a / b)),
-              rem if b == 0 => Err(~"remainder zero"),
+              rem if b == 0 => Err(~"attempted remainder with a divisor of zero"),
               rem => Ok(const_uint(a % b)),
               and | bitand => Ok(const_uint(a & b)),
               or | bitor => Ok(const_uint(a | b)),
diff --git a/src/librustc/middle/trans/base.rs b/src/librustc/middle/trans/base.rs
index da87568b3d0..de64441fd95 100644
--- a/src/librustc/middle/trans/base.rs
+++ b/src/librustc/middle/trans/base.rs
@@ -785,9 +785,9 @@ pub fn cast_shift_rhs(op: ast::binop,
 pub fn fail_if_zero(cx: block, span: span, quotrem: ast::binop,
                     rhs: ValueRef, rhs_t: ty::t) -> block {
     let text = if quotrem == ast::quot {
-        @~"quotient zero"
+        @~"attempted quotient with a divisor of zero"
     } else {
-        @~"remainder zero"
+        @~"attempted remainder with a divisor of zero"
     };
     let is_zero = match ty::get(rhs_t).sty {
       ty::ty_int(t) => {
diff --git a/src/libstd/num/bigint.rs b/src/libstd/num/bigint.rs
index ee9749af532..5f0fd76640a 100644
--- a/src/libstd/num/bigint.rs
+++ b/src/libstd/num/bigint.rs
@@ -154,6 +154,8 @@ impl One for BigUint {
     pub fn one() -> BigUint { BigUint::new(~[1]) }
 }
 
+impl Unsigned for BigUint {}
+
 impl Add<BigUint, BigUint> for BigUint {
     fn add(&self, other: &BigUint) -> BigUint {
         let new_len = uint::max(self.data.len(), other.data.len());
@@ -469,11 +471,8 @@ pub impl BigUint {
     }
 
     fn is_zero(&self) -> bool { self.data.is_empty() }
+
     fn is_not_zero(&self) -> bool { !self.data.is_empty() }
-    fn is_positive(&self) -> bool { self.is_not_zero() }
-    fn is_negative(&self) -> bool { false }
-    fn is_nonpositive(&self) -> bool { self.is_zero() }
-    fn is_nonnegative(&self) -> bool { true }
 
     fn to_uint(&self) -> uint {
         match self.data.len() {
@@ -693,6 +692,27 @@ impl One for BigInt {
     }
 }
 
+impl Signed for BigInt {
+    fn abs(&self) -> BigInt {
+        match self.sign {
+            Plus | Zero => copy *self,
+            Minus => BigInt::from_biguint(Plus, copy self.data)
+        }
+    }
+
+    fn signum(&self) -> BigInt {
+        match self.sign {
+            Plus  => BigInt::from_biguint(Plus, One::one()),
+            Minus => BigInt::from_biguint(Minus, One::one()),
+            Zero  => Zero::zero(),
+        }
+    }
+
+    fn is_positive(&self) -> bool { self.sign == Plus }
+
+    fn is_negative(&self) -> bool { self.sign == Minus }
+}
+
 impl Add<BigInt, BigInt> for BigInt {
     fn add(&self, other: &BigInt) -> BigInt {
         match (self.sign, other.sign) {
@@ -888,11 +908,8 @@ pub impl BigInt {
     }
 
     fn is_zero(&self) -> bool { self.sign == Zero }
+
     fn is_not_zero(&self) -> bool { self.sign != Zero }
-    fn is_positive(&self) -> bool { self.sign == Plus }
-    fn is_negative(&self) -> bool { self.sign == Minus }
-    fn is_nonpositive(&self) -> bool { self.sign != Plus }
-    fn is_nonnegative(&self) -> bool { self.sign != Minus }
 
     fn to_uint(&self) -> uint {
         match self.sign {
diff --git a/src/test/compile-fail/eval-enum.rs b/src/test/compile-fail/eval-enum.rs
index d368f9d6769..01233419579 100644
--- a/src/test/compile-fail/eval-enum.rs
+++ b/src/test/compile-fail/eval-enum.rs
@@ -1,6 +1,6 @@
 enum test {
-    quot_zero = 1/0, //~ERROR expected constant: quotient zero
-    rem_zero = 1%0  //~ERROR expected constant: remainder zero
+    quot_zero = 1/0, //~ERROR expected constant: attempted quotient with a divisor of zero
+    rem_zero = 1%0  //~ERROR expected constant: attempted remainder with a divisor of zero
 }
 
 fn main() {}
diff --git a/src/test/run-fail/divide-by-zero.rs b/src/test/run-fail/divide-by-zero.rs
index 7a17dd02415..d4f3828ea71 100644
--- a/src/test/run-fail/divide-by-zero.rs
+++ b/src/test/run-fail/divide-by-zero.rs
@@ -8,7 +8,7 @@
 // option. This file may not be copied, modified, or distributed
 // except according to those terms.
 
-// error-pattern:quotient zero
+// error-pattern:attempted quotient with a divisor of zero
 fn main() {
     let y = 0;
     let z = 1 / y;
diff --git a/src/test/run-fail/mod-zero.rs b/src/test/run-fail/mod-zero.rs
index c379a8fc65f..b3e083c77fb 100644
--- a/src/test/run-fail/mod-zero.rs
+++ b/src/test/run-fail/mod-zero.rs
@@ -8,7 +8,7 @@
 // option. This file may not be copied, modified, or distributed
 // except according to those terms.
 
-// error-pattern:remainder zero
+// error-pattern:attempted remainder with a divisor of zero
 fn main() {
     let y = 0;
     let z = 1 % y;
diff --git a/src/test/run-pass/block-arg.rs b/src/test/run-pass/block-arg.rs
index 4fecbd4e956..93c44b8faa1 100644
--- a/src/test/run-pass/block-arg.rs
+++ b/src/test/run-pass/block-arg.rs
@@ -18,28 +18,28 @@ pub fn main() {
     }
 
     // Usable at all:
-    let mut any_negative = do vec::any(v) |e| { float::is_negative(*e) };
+    let mut any_negative = do vec::any(v) |e| { e.is_negative() };
     assert!(any_negative);
 
     // Higher precedence than assignments:
-    any_negative = do vec::any(v) |e| { float::is_negative(*e) };
+    any_negative = do vec::any(v) |e| { e.is_negative() };
     assert!(any_negative);
 
     // Higher precedence than unary operations:
-    let abs_v = do vec::map(v) |e| { float::abs(*e) };
-    assert!(do vec::all(abs_v) |e| { float::is_nonnegative(*e) });
-    assert!(!do vec::any(abs_v) |e| { float::is_negative(*e) });
+    let abs_v = do vec::map(v) |e| { e.abs() };
+    assert!(do vec::all(abs_v) |e| { e.is_positive() });
+    assert!(!do vec::any(abs_v) |e| { e.is_negative() });
 
     // Usable in funny statement-like forms:
-    if !do vec::any(v) |e| { float::is_positive(*e) } {
+    if !do vec::any(v) |e| { e.is_positive() } {
         assert!(false);
     }
-    match do vec::all(v) |e| { float::is_negative(*e) } {
+    match do vec::all(v) |e| { e.is_negative() } {
         true => { fail!(~"incorrect answer."); }
         false => { }
     }
     match 3 {
-      _ if do vec::any(v) |e| { float::is_negative(*e) } => {
+      _ if do vec::any(v) |e| { e.is_negative() } => {
       }
       _ => {
         fail!(~"wrong answer.");
@@ -56,7 +56,7 @@ pub fn main() {
 
     // In the tail of a block
     let w =
-        if true { do vec::any(abs_v) |e| { float::is_nonnegative(*e) } }
+        if true { do vec::any(abs_v) |e| { e.is_positive() } }
       else { false };
     assert!(w);
 }