Optimise the GCD implementations.

benches/gcd.rs

@@ -0,0 +1,176 @@
+//! Benchmark comparing the current GCD implemtation against an older one.
+
+#![feature(test)]
+
+extern crate num_integer;
+extern crate num_traits;
+extern crate test;
+
+use num_integer::Integer;
+use num_traits::{AsPrimitive, Bounded, Signed};
+use test::{black_box, Bencher};
+
+trait GcdOld: Integer {
+    fn gcd_old(&self, other: &Self) -> Self;
+}
+
+macro_rules! impl_gcd_old_for_isize {
+    ($T:ty) => {
+        impl GcdOld for $T {
+            /// Calculates the Greatest Common Divisor (GCD) of the number and
+            /// `other`. The result is always positive.
+            #[inline]
+            fn gcd_old(&self, other: &Self) -> Self {
+                // Use Stein's algorithm
+                let mut m = *self;
+                let mut n = *other;
+                if m == 0 || n == 0 {
+                    return (m | n).abs();
+                }
+
+                // find common factors of 2
+                let shift = (m | n).trailing_zeros();
+
+                // The algorithm needs positive numbers, but the minimum value
+                // can't be represented as a positive one.
+                // It's also a power of two, so the gcd can be
+                // calculated by bitshifting in that case
+
+                // Assuming two's complement, the number created by the shift
+                // is positive for all numbers except gcd = abs(min value)
+                // The call to .abs() causes a panic in debug mode
+                if m == Self::min_value() || n == Self::min_value() {
+                    return (1 << shift).abs();
+                }
+
+                // guaranteed to be positive now, rest like unsigned algorithm
+                m = m.abs();
+                n = n.abs();
+
+                // divide n and m by 2 until odd
+                // m inside loop
+                n >>= n.trailing_zeros();
+
+                while m != 0 {
+                    m >>= m.trailing_zeros();
+                    if n > m {
+                        std::mem::swap(&mut n, &mut m)
+                    }
+                    m -= n;
+                }
+
+                n << shift
+            }
+        }
+    };
+}
+
+impl_gcd_old_for_isize!(i8);
+impl_gcd_old_for_isize!(i16);
+impl_gcd_old_for_isize!(i32);
+impl_gcd_old_for_isize!(i64);
+impl_gcd_old_for_isize!(isize);
+impl_gcd_old_for_isize!(i128);
+
+macro_rules! impl_gcd_old_for_usize {
+    ($T:ty) => {
+        impl GcdOld for $T {
+            /// Calculates the Greatest Common Divisor (GCD) of the number and
+            /// `other`. The result is always positive.
+            #[inline]
+            fn gcd_old(&self, other: &Self) -> Self {
+                // Use Stein's algorithm
+                let mut m = *self;
+                let mut n = *other;
+                if m == 0 || n == 0 {
+                    return m | n;
+                }
+
+                // find common factors of 2
+                let shift = (m | n).trailing_zeros();
+
+                // divide n and m by 2 until odd
+                // m inside loop
+                n >>= n.trailing_zeros();
+
+                while m != 0 {
+                    m >>= m.trailing_zeros();
+                    if n > m {
+                        std::mem::swap(&mut n, &mut m)
+                    }
+                    m -= n;
+                }
+
+                n << shift
+            }
+        }
+    };
+}
+
+impl_gcd_old_for_usize!(u8);
+impl_gcd_old_for_usize!(u16);
+impl_gcd_old_for_usize!(u32);
+impl_gcd_old_for_usize!(u64);
+impl_gcd_old_for_usize!(usize);
+impl_gcd_old_for_usize!(u128);
+
+/// Return an iterator that yields all Fibonacci numbers fitting into a u128.
+fn fibonacci() -> impl Iterator<Item=u128> {
+    (0..185).scan((0, 1), |&mut (ref mut a, ref mut b), _| {
+        let tmp = *a;
+        *a = *b;
+        *b += tmp;
+        Some(*b)
+    })
+}
+
+fn run_bench<T: Integer + Bounded + Copy + 'static>(b: &mut Bencher, gcd: fn(&T, &T) -> T)
+where
+    T: AsPrimitive<u128>,
+    u128: AsPrimitive<T>,
+{
+    let max_value: u128 = T::max_value().as_();
+    let pairs: Vec<(T, T)> = fibonacci()
+        .collect::<Vec<_>>()
+        .windows(2)
+        .filter(|&pair| pair[0] <= max_value && pair[1] <= max_value)
+        .map(|pair| (pair[0].as_(), pair[1].as_()))
+        .collect();
+    b.iter(|| {
+        for &(ref m, ref n) in &pairs {
+            black_box(gcd(m, n));
+        }
+    });
+}
+
+macro_rules! bench_gcd {
+    ($T:ident) => {
+        mod $T {
+            use crate::{run_bench, GcdOld};
+            use num_integer::Integer;
+            use test::Bencher;
+
+            #[bench]
+            fn bench_gcd(b: &mut Bencher) {
+                run_bench(b, $T::gcd);
+            }
+
+            #[bench]
+            fn bench_gcd_old(b: &mut Bencher) {
+                run_bench(b, $T::gcd_old);
+            }
+        }
+    };
+}
+
+bench_gcd!(u8);
+bench_gcd!(u16);
+bench_gcd!(u32);
+bench_gcd!(u64);
+bench_gcd!(u128);
+
+bench_gcd!(i8);
+bench_gcd!(i16);
+bench_gcd!(i32);
+bench_gcd!(i64);
+bench_gcd!(i128);

src/lib.rs

@@ -23,7 +23,6 @@ extern crate std;
 extern crate num_traits as traits;
 
 use core::ops::Add;
-use core::mem;
 
 use traits::{Num, Signed};
 
@@ -275,16 +274,19 @@ macro_rules! impl_integer_for_isize {
                 n = n.abs();
 
                 // divide n and m by 2 until odd
-                // m inside loop
+                m >>= m.trailing_zeros();
                 n >>= n.trailing_zeros();
 
-                while m != 0 {
-                    m >>= m.trailing_zeros();
-                    if n > m { mem::swap(&mut n, &mut m) }
-                    m -= n;
+                while m != n {
+                    if m > n {
+                        m -= n;
+                        m >>= m.trailing_zeros();
+                    } else {
+                        n -= m;
+                        n >>= n.trailing_zeros();
+                    }
                 }
-
-                n << shift
+                m << shift
             }
 
             /// Calculates the Lowest Common Multiple (LCM) of the number and
@@ -537,16 +539,19 @@ macro_rules! impl_integer_for_usize {
                 let shift = (m | n).trailing_zeros();
 
                 // divide n and m by 2 until odd
-                // m inside loop
+                m >>= m.trailing_zeros();
                 n >>= n.trailing_zeros();
 
-                while m != 0 {
-                    m >>= m.trailing_zeros();
-                    if n > m { mem::swap(&mut n, &mut m) }
-                    m -= n;
+                while m != n {
+                    if m > n {
+                        m -= n;
+                        m >>= m.trailing_zeros();
+                    } else {
+                        n -= m;
+                        n >>= n.trailing_zeros();
+                    }
                 }
-
-                n << shift
+                m << shift
             }
 
             /// Calculates the Lowest Common Multiple (LCM) of the number and `other`.