Import 'num-integer' crate version 0.2.11
Change-Id: I43f7b6de8a4ffae1f721423fce67e56c2137701e
diff --git a/benches/average.rs b/benches/average.rs
new file mode 100644
index 0000000..05d824c
--- /dev/null
+++ b/benches/average.rs
@@ -0,0 +1,414 @@
+//! Benchmark sqrt and cbrt
+
+#![feature(test)]
+
+extern crate num_integer;
+extern crate num_traits;
+extern crate test;
+
+use num_integer::Integer;
+use num_traits::{AsPrimitive, PrimInt, WrappingAdd, WrappingMul};
+use std::cmp::{max, min};
+use std::fmt::Debug;
+use test::{black_box, Bencher};
+
+// --- Utilities for RNG ----------------------------------------------------
+
+trait BenchInteger: Integer + PrimInt + WrappingAdd + WrappingMul + 'static {}
+
+impl<T> BenchInteger for T where T: Integer + PrimInt + WrappingAdd + WrappingMul + 'static {}
+
+// Simple PRNG so we don't have to worry about rand compatibility
+fn lcg<T>(x: T) -> T
+where
+ u32: AsPrimitive<T>,
+ T: BenchInteger,
+{
+ // LCG parameters from Numerical Recipes
+ // (but we're applying it to arbitrary sizes)
+ const LCG_A: u32 = 1664525;
+ const LCG_C: u32 = 1013904223;
+ x.wrapping_mul(&LCG_A.as_()).wrapping_add(&LCG_C.as_())
+}
+
+// --- Alt. Implementations -------------------------------------------------
+
+trait NaiveAverage {
+ fn naive_average_ceil(&self, other: &Self) -> Self;
+ fn naive_average_floor(&self, other: &Self) -> Self;
+}
+
+trait UncheckedAverage {
+ fn unchecked_average_ceil(&self, other: &Self) -> Self;
+ fn unchecked_average_floor(&self, other: &Self) -> Self;
+}
+
+trait ModuloAverage {
+ fn modulo_average_ceil(&self, other: &Self) -> Self;
+ fn modulo_average_floor(&self, other: &Self) -> Self;
+}
+
+macro_rules! naive_average {
+ ($T:ident) => {
+ impl super::NaiveAverage for $T {
+ fn naive_average_floor(&self, other: &$T) -> $T {
+ match self.checked_add(*other) {
+ Some(z) => z.div_floor(&2),
+ None => {
+ if self > other {
+ let diff = self - other;
+ other + diff.div_floor(&2)
+ } else {
+ let diff = other - self;
+ self + diff.div_floor(&2)
+ }
+ }
+ }
+ }
+ fn naive_average_ceil(&self, other: &$T) -> $T {
+ match self.checked_add(*other) {
+ Some(z) => z.div_ceil(&2),
+ None => {
+ if self > other {
+ let diff = self - other;
+ self - diff.div_floor(&2)
+ } else {
+ let diff = other - self;
+ other - diff.div_floor(&2)
+ }
+ }
+ }
+ }
+ }
+ };
+}
+
+macro_rules! unchecked_average {
+ ($T:ident) => {
+ impl super::UncheckedAverage for $T {
+ fn unchecked_average_floor(&self, other: &$T) -> $T {
+ self.wrapping_add(*other) / 2
+ }
+ fn unchecked_average_ceil(&self, other: &$T) -> $T {
+ (self.wrapping_add(*other) / 2).wrapping_add(1)
+ }
+ }
+ };
+}
+
+macro_rules! modulo_average {
+ ($T:ident) => {
+ impl super::ModuloAverage for $T {
+ fn modulo_average_ceil(&self, other: &$T) -> $T {
+ let (q1, r1) = self.div_mod_floor(&2);
+ let (q2, r2) = other.div_mod_floor(&2);
+ q1 + q2 + (r1 | r2)
+ }
+ fn modulo_average_floor(&self, other: &$T) -> $T {
+ let (q1, r1) = self.div_mod_floor(&2);
+ let (q2, r2) = other.div_mod_floor(&2);
+ q1 + q2 + (r1 * r2)
+ }
+ }
+ };
+}
+
+// --- Bench functions ------------------------------------------------------
+
+fn bench_unchecked<T, F>(b: &mut Bencher, v: &[(T, T)], f: F)
+where
+ T: Integer + Debug + Copy,
+ F: Fn(&T, &T) -> T,
+{
+ b.iter(|| {
+ for (x, y) in v {
+ black_box(f(x, y));
+ }
+ });
+}
+
+fn bench_ceil<T, F>(b: &mut Bencher, v: &[(T, T)], f: F)
+where
+ T: Integer + Debug + Copy,
+ F: Fn(&T, &T) -> T,
+{
+ for &(i, j) in v {
+ let rt = f(&i, &j);
+ let (a, b) = (min(i, j), max(i, j));
+ // if both number are the same sign, check rt is in the middle
+ if (a < T::zero()) == (b < T::zero()) {
+ if (b - a).is_even() {
+ assert_eq!(rt - a, b - rt);
+ } else {
+ assert_eq!(rt - a, b - rt + T::one());
+ }
+ // if both number have a different sign,
+ } else {
+ if (a + b).is_even() {
+ assert_eq!(rt, (a + b) / (T::one() + T::one()))
+ } else {
+ assert_eq!(rt, (a + b + T::one()) / (T::one() + T::one()))
+ }
+ }
+ }
+ bench_unchecked(b, v, f);
+}
+
+fn bench_floor<T, F>(b: &mut Bencher, v: &[(T, T)], f: F)
+where
+ T: Integer + Debug + Copy,
+ F: Fn(&T, &T) -> T,
+{
+ for &(i, j) in v {
+ let rt = f(&i, &j);
+ let (a, b) = (min(i, j), max(i, j));
+ // if both number are the same sign, check rt is in the middle
+ if (a < T::zero()) == (b < T::zero()) {
+ if (b - a).is_even() {
+ assert_eq!(rt - a, b - rt);
+ } else {
+ assert_eq!(rt - a + T::one(), b - rt);
+ }
+ // if both number have a different sign,
+ } else {
+ if (a + b).is_even() {
+ assert_eq!(rt, (a + b) / (T::one() + T::one()))
+ } else {
+ assert_eq!(rt, (a + b - T::one()) / (T::one() + T::one()))
+ }
+ }
+ }
+ bench_unchecked(b, v, f);
+}
+
+// --- Bench implementation -------------------------------------------------
+
+macro_rules! bench_average {
+ ($($T:ident),*) => {$(
+ mod $T {
+ use test::Bencher;
+ use num_integer::{Average, Integer};
+ use super::{UncheckedAverage, NaiveAverage, ModuloAverage};
+ use super::{bench_ceil, bench_floor, bench_unchecked};
+
+ naive_average!($T);
+ unchecked_average!($T);
+ modulo_average!($T);
+
+ const SIZE: $T = 30;
+
+ fn overflowing() -> Vec<($T, $T)> {
+ (($T::max_value()-SIZE)..$T::max_value())
+ .flat_map(|x| -> Vec<_> {
+ (($T::max_value()-100)..($T::max_value()-100+SIZE))
+ .map(|y| (x, y))
+ .collect()
+ })
+ .collect()
+ }
+
+ fn small() -> Vec<($T, $T)> {
+ (0..SIZE)
+ .flat_map(|x| -> Vec<_> {(0..SIZE).map(|y| (x, y)).collect()})
+ .collect()
+ }
+
+ fn rand() -> Vec<($T, $T)> {
+ small()
+ .into_iter()
+ .map(|(x, y)| (super::lcg(x), super::lcg(y)))
+ .collect()
+ }
+
+ mod ceil {
+
+ use super::*;
+
+ mod small {
+
+ use super::*;
+
+ #[bench]
+ fn optimized(b: &mut Bencher) {
+ let v = small();
+ bench_ceil(b, &v, |x: &$T, y: &$T| x.average_ceil(y));
+ }
+
+ #[bench]
+ fn naive(b: &mut Bencher) {
+ let v = small();
+ bench_ceil(b, &v, |x: &$T, y: &$T| x.naive_average_ceil(y));
+ }
+
+ #[bench]
+ fn unchecked(b: &mut Bencher) {
+ let v = small();
+ bench_unchecked(b, &v, |x: &$T, y: &$T| x.unchecked_average_ceil(y));
+ }
+
+ #[bench]
+ fn modulo(b: &mut Bencher) {
+ let v = small();
+ bench_ceil(b, &v, |x: &$T, y: &$T| x.modulo_average_ceil(y));
+ }
+ }
+
+ mod overflowing {
+
+ use super::*;
+
+ #[bench]
+ fn optimized(b: &mut Bencher) {
+ let v = overflowing();
+ bench_ceil(b, &v, |x: &$T, y: &$T| x.average_ceil(y));
+ }
+
+ #[bench]
+ fn naive(b: &mut Bencher) {
+ let v = overflowing();
+ bench_ceil(b, &v, |x: &$T, y: &$T| x.naive_average_ceil(y));
+ }
+
+ #[bench]
+ fn unchecked(b: &mut Bencher) {
+ let v = overflowing();
+ bench_unchecked(b, &v, |x: &$T, y: &$T| x.unchecked_average_ceil(y));
+ }
+
+ #[bench]
+ fn modulo(b: &mut Bencher) {
+ let v = overflowing();
+ bench_ceil(b, &v, |x: &$T, y: &$T| x.modulo_average_ceil(y));
+ }
+ }
+
+ mod rand {
+
+ use super::*;
+
+ #[bench]
+ fn optimized(b: &mut Bencher) {
+ let v = rand();
+ bench_ceil(b, &v, |x: &$T, y: &$T| x.average_ceil(y));
+ }
+
+ #[bench]
+ fn naive(b: &mut Bencher) {
+ let v = rand();
+ bench_ceil(b, &v, |x: &$T, y: &$T| x.naive_average_ceil(y));
+ }
+
+ #[bench]
+ fn unchecked(b: &mut Bencher) {
+ let v = rand();
+ bench_unchecked(b, &v, |x: &$T, y: &$T| x.unchecked_average_ceil(y));
+ }
+
+ #[bench]
+ fn modulo(b: &mut Bencher) {
+ let v = rand();
+ bench_ceil(b, &v, |x: &$T, y: &$T| x.modulo_average_ceil(y));
+ }
+ }
+
+ }
+
+ mod floor {
+
+ use super::*;
+
+ mod small {
+
+ use super::*;
+
+ #[bench]
+ fn optimized(b: &mut Bencher) {
+ let v = small();
+ bench_floor(b, &v, |x: &$T, y: &$T| x.average_floor(y));
+ }
+
+ #[bench]
+ fn naive(b: &mut Bencher) {
+ let v = small();
+ bench_floor(b, &v, |x: &$T, y: &$T| x.naive_average_floor(y));
+ }
+
+ #[bench]
+ fn unchecked(b: &mut Bencher) {
+ let v = small();
+ bench_unchecked(b, &v, |x: &$T, y: &$T| x.unchecked_average_floor(y));
+ }
+
+ #[bench]
+ fn modulo(b: &mut Bencher) {
+ let v = small();
+ bench_floor(b, &v, |x: &$T, y: &$T| x.modulo_average_floor(y));
+ }
+ }
+
+ mod overflowing {
+
+ use super::*;
+
+ #[bench]
+ fn optimized(b: &mut Bencher) {
+ let v = overflowing();
+ bench_floor(b, &v, |x: &$T, y: &$T| x.average_floor(y));
+ }
+
+ #[bench]
+ fn naive(b: &mut Bencher) {
+ let v = overflowing();
+ bench_floor(b, &v, |x: &$T, y: &$T| x.naive_average_floor(y));
+ }
+
+ #[bench]
+ fn unchecked(b: &mut Bencher) {
+ let v = overflowing();
+ bench_unchecked(b, &v, |x: &$T, y: &$T| x.unchecked_average_floor(y));
+ }
+
+ #[bench]
+ fn modulo(b: &mut Bencher) {
+ let v = overflowing();
+ bench_floor(b, &v, |x: &$T, y: &$T| x.modulo_average_floor(y));
+ }
+ }
+
+ mod rand {
+
+ use super::*;
+
+ #[bench]
+ fn optimized(b: &mut Bencher) {
+ let v = rand();
+ bench_floor(b, &v, |x: &$T, y: &$T| x.average_floor(y));
+ }
+
+ #[bench]
+ fn naive(b: &mut Bencher) {
+ let v = rand();
+ bench_floor(b, &v, |x: &$T, y: &$T| x.naive_average_floor(y));
+ }
+
+ #[bench]
+ fn unchecked(b: &mut Bencher) {
+ let v = rand();
+ bench_unchecked(b, &v, |x: &$T, y: &$T| x.unchecked_average_floor(y));
+ }
+
+ #[bench]
+ fn modulo(b: &mut Bencher) {
+ let v = rand();
+ bench_floor(b, &v, |x: &$T, y: &$T| x.modulo_average_floor(y));
+ }
+ }
+
+ }
+
+ }
+ )*}
+}
+
+bench_average!(i8, i16, i32, i64, i128, isize);
+bench_average!(u8, u16, u32, u64, u128, usize);
diff --git a/benches/gcd.rs b/benches/gcd.rs
new file mode 100644
index 0000000..082d5ee
--- /dev/null
+++ b/benches/gcd.rs
@@ -0,0 +1,176 @@
+//! Benchmark comparing the current GCD implemtation against an older one.
+
+#![feature(test)]
+
+extern crate num_integer;
+extern crate num_traits;
+extern crate test;
+
+use num_integer::Integer;
+use num_traits::{AsPrimitive, Bounded, Signed};
+use test::{black_box, Bencher};
+
+trait GcdOld: Integer {
+ fn gcd_old(&self, other: &Self) -> Self;
+}
+
+macro_rules! impl_gcd_old_for_isize {
+ ($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);
diff --git a/benches/roots.rs b/benches/roots.rs
new file mode 100644
index 0000000..7f67278
--- /dev/null
+++ b/benches/roots.rs
@@ -0,0 +1,170 @@
+//! Benchmark sqrt and cbrt
+
+#![feature(test)]
+
+extern crate num_integer;
+extern crate num_traits;
+extern crate test;
+
+use num_integer::Integer;
+use num_traits::checked_pow;
+use num_traits::{AsPrimitive, PrimInt, WrappingAdd, WrappingMul};
+use test::{black_box, Bencher};
+
+trait BenchInteger: Integer + PrimInt + WrappingAdd + WrappingMul + 'static {}
+
+impl<T> BenchInteger for T where T: Integer + PrimInt + WrappingAdd + WrappingMul + 'static {}
+
+fn bench<T, F>(b: &mut Bencher, v: &[T], f: F, n: u32)
+where
+ T: BenchInteger,
+ F: Fn(&T) -> T,
+{
+ // Pre-validate the results...
+ for i in v {
+ let rt = f(i);
+ if *i >= T::zero() {
+ let rt1 = rt + T::one();
+ assert!(rt.pow(n) <= *i);
+ if let Some(x) = checked_pow(rt1, n as usize) {
+ assert!(*i < x);
+ }
+ } else {
+ let rt1 = rt - T::one();
+ assert!(rt < T::zero());
+ assert!(*i <= rt.pow(n));
+ if let Some(x) = checked_pow(rt1, n as usize) {
+ assert!(x < *i);
+ }
+ };
+ }
+
+ // Now just run as fast as we can!
+ b.iter(|| {
+ for i in v {
+ black_box(f(i));
+ }
+ });
+}
+
+// Simple PRNG so we don't have to worry about rand compatibility
+fn lcg<T>(x: T) -> T
+where
+ u32: AsPrimitive<T>,
+ T: BenchInteger,
+{
+ // LCG parameters from Numerical Recipes
+ // (but we're applying it to arbitrary sizes)
+ const LCG_A: u32 = 1664525;
+ const LCG_C: u32 = 1013904223;
+ x.wrapping_mul(&LCG_A.as_()).wrapping_add(&LCG_C.as_())
+}
+
+fn bench_rand<T, F>(b: &mut Bencher, f: F, n: u32)
+where
+ u32: AsPrimitive<T>,
+ T: BenchInteger,
+ F: Fn(&T) -> T,
+{
+ let mut x: T = 3u32.as_();
+ let v: Vec<T> = (0..1000)
+ .map(|_| {
+ x = lcg(x);
+ x
+ })
+ .collect();
+ bench(b, &v, f, n);
+}
+
+fn bench_rand_pos<T, F>(b: &mut Bencher, f: F, n: u32)
+where
+ u32: AsPrimitive<T>,
+ T: BenchInteger,
+ F: Fn(&T) -> T,
+{
+ let mut x: T = 3u32.as_();
+ let v: Vec<T> = (0..1000)
+ .map(|_| {
+ x = lcg(x);
+ while x < T::zero() {
+ x = lcg(x);
+ }
+ x
+ })
+ .collect();
+ bench(b, &v, f, n);
+}
+
+fn bench_small<T, F>(b: &mut Bencher, f: F, n: u32)
+where
+ u32: AsPrimitive<T>,
+ T: BenchInteger,
+ F: Fn(&T) -> T,
+{
+ let v: Vec<T> = (0..1000).map(|i| i.as_()).collect();
+ bench(b, &v, f, n);
+}
+
+fn bench_small_pos<T, F>(b: &mut Bencher, f: F, n: u32)
+where
+ u32: AsPrimitive<T>,
+ T: BenchInteger,
+ F: Fn(&T) -> T,
+{
+ let v: Vec<T> = (0..1000)
+ .map(|i| i.as_().mod_floor(&T::max_value()))
+ .collect();
+ bench(b, &v, f, n);
+}
+
+macro_rules! bench_roots {
+ ($($T:ident),*) => {$(
+ mod $T {
+ use test::Bencher;
+ use num_integer::Roots;
+
+ #[bench]
+ fn sqrt_rand(b: &mut Bencher) {
+ ::bench_rand_pos(b, $T::sqrt, 2);
+ }
+
+ #[bench]
+ fn sqrt_small(b: &mut Bencher) {
+ ::bench_small_pos(b, $T::sqrt, 2);
+ }
+
+ #[bench]
+ fn cbrt_rand(b: &mut Bencher) {
+ ::bench_rand(b, $T::cbrt, 3);
+ }
+
+ #[bench]
+ fn cbrt_small(b: &mut Bencher) {
+ ::bench_small(b, $T::cbrt, 3);
+ }
+
+ #[bench]
+ fn fourth_root_rand(b: &mut Bencher) {
+ ::bench_rand_pos(b, |x: &$T| x.nth_root(4), 4);
+ }
+
+ #[bench]
+ fn fourth_root_small(b: &mut Bencher) {
+ ::bench_small_pos(b, |x: &$T| x.nth_root(4), 4);
+ }
+
+ #[bench]
+ fn fifth_root_rand(b: &mut Bencher) {
+ ::bench_rand(b, |x: &$T| x.nth_root(5), 5);
+ }
+
+ #[bench]
+ fn fifth_root_small(b: &mut Bencher) {
+ ::bench_small(b, |x: &$T| x.nth_root(5), 5);
+ }
+ }
+ )*}
+}
+
+bench_roots!(i8, i16, i32, i64, i128);
+bench_roots!(u8, u16, u32, u64, u128);