1 files changed, 78 insertions, 0 deletions
diff --git a/src/average.rs b/src/average.rs
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+++ b/src/average.rs
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+use core::ops::{BitAnd, BitOr, BitXor, Shr};
+use Integer;
+
+/// Provides methods to compute the average of two integers, without overflows.
+pub trait Average: Integer {
+    /// Returns the ceiling value of the average of `self` and `other`.
+    /// -- `⌈(self + other)/2⌉`
+    ///
+    /// # Examples
+    ///
+    /// ```
+    /// use num_integer::Average;
+    ///
+    /// assert_eq!(( 3).average_ceil(&10),  7);
+    /// assert_eq!((-2).average_ceil(&-5), -3);
+    /// assert_eq!(( 4).average_ceil(& 4),  4);
+    ///
+    /// assert_eq!(u8::max_value().average_ceil(&2), 129);
+    /// assert_eq!(i8::min_value().average_ceil(&-1), -64);
+    /// assert_eq!(i8::min_value().average_ceil(&i8::max_value()), 0);
+    /// ```
+    ///
+    fn average_ceil(&self, other: &Self) -> Self;
+
+    /// Returns the floor value of the average of `self` and `other`.
+    /// -- `⌊(self + other)/2⌋`
+    ///
+    /// # Examples
+    ///
+    /// ```
+    /// use num_integer::Average;
+    ///
+    /// assert_eq!(( 3).average_floor(&10),  6);
+    /// assert_eq!((-2).average_floor(&-5), -4);
+    /// assert_eq!(( 4).average_floor(& 4),  4);
+    ///
+    /// assert_eq!(u8::max_value().average_floor(&2), 128);
+    /// assert_eq!(i8::min_value().average_floor(&-1), -65);
+    /// assert_eq!(i8::min_value().average_floor(&i8::max_value()), -1);
+    /// ```
+    ///
+    fn average_floor(&self, other: &Self) -> Self;
+}
+
+impl<I> Average for I
+where
+    I: Integer + Shr<usize, Output = I>,
+    for<'a, 'b> &'a I:
+        BitAnd<&'b I, Output = I> + BitOr<&'b I, Output = I> + BitXor<&'b I, Output = I>,
+{
+    // The Henry Gordon Dietz implementation as shown in the Hacker's Delight,
+    // see http://aggregate.org/MAGIC/#Average%20of%20Integers
+
+    /// Returns the floor value of the average of `self` and `other`.
+    #[inline]
+    fn average_floor(&self, other: &I) -> I {
+        (self & other) + ((self ^ other) >> 1)
+    }
+
+    /// Returns the ceil value of the average of `self` and `other`.
+    #[inline]
+    fn average_ceil(&self, other: &I) -> I {
+        (self | other) - ((self ^ other) >> 1)
+    }
+}
+
+/// Returns the floor value of the average of `x` and `y` --
+/// see [Average::average_floor](trait.Average.html#tymethod.average_floor).
+#[inline]
+pub fn average_floor<T: Average>(x: T, y: T) -> T {
+    x.average_floor(&y)
+}
+/// Returns the ceiling value of the average of `x` and `y` --
+/// see [Average::average_ceil](trait.Average.html#tymethod.average_ceil).
+#[inline]
+pub fn average_ceil<T: Average>(x: T, y: T) -> T {
+    x.average_ceil(&y)
+}