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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) }