Extract integer module
This commit is contained in:
Łukasz Jan Niemier
parent
4361521f5a
commit
f1a80857ee
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@ -21,6 +21,9 @@ serde = { version = "^0.7.0", optional = true }
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[dependencies.num-traits]
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path = "./traits"
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[dependencies.num-integer]
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path = "./integer"
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[dev-dependencies]
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# Some tests of non-rand functionality still use rand because the tests
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# themselves are randomized.
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@ -1,6 +1,7 @@
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[package]
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name = "integer"
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name = "num-integer"
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version = "0.1.0"
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authors = ["Łukasz Jan Niemier <lukasz@niemier.pl>"]
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[dependencies]
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[dependencies.num-traits]
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path = "../traits"
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@ -10,7 +10,9 @@
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//! Integer trait and functions.
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use {Num, Signed};
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extern crate num_traits as traits;
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use traits::{Num, Signed};
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pub trait Integer
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: Sized
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@ -179,7 +181,7 @@ macro_rules! impl_integer_for_isize {
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impl Integer for $T {
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/// Floored integer division
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#[inline]
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fn div_floor(&self, other: &$T) -> $T {
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fn div_floor(&self, other: &Self) -> Self {
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// Algorithm from [Daan Leijen. _Division and Modulus for Computer Scientists_,
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// December 2001](http://research.microsoft.com/pubs/151917/divmodnote-letter.pdf)
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match self.div_rem(other) {
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@ -191,7 +193,7 @@ macro_rules! impl_integer_for_isize {
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/// Floored integer modulo
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#[inline]
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fn mod_floor(&self, other: &$T) -> $T {
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fn mod_floor(&self, other: &Self) -> Self {
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// Algorithm from [Daan Leijen. _Division and Modulus for Computer Scientists_,
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// December 2001](http://research.microsoft.com/pubs/151917/divmodnote-letter.pdf)
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match *self % *other {
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@ -203,7 +205,7 @@ macro_rules! impl_integer_for_isize {
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/// Calculates `div_floor` and `mod_floor` simultaneously
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#[inline]
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fn div_mod_floor(&self, other: &$T) -> ($T,$T) {
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fn div_mod_floor(&self, other: &Self) -> (Self, Self) {
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// Algorithm from [Daan Leijen. _Division and Modulus for Computer Scientists_,
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// December 2001](http://research.microsoft.com/pubs/151917/divmodnote-letter.pdf)
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match self.div_rem(other) {
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@ -216,7 +218,7 @@ macro_rules! impl_integer_for_isize {
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/// Calculates the Greatest Common Divisor (GCD) of the number and
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/// `other`. The result is always positive.
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#[inline]
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fn gcd(&self, other: &$T) -> $T {
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fn gcd(&self, other: &Self) -> Self {
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// Use Stein's algorithm
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let mut m = *self;
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let mut n = *other;
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@ -233,7 +235,7 @@ macro_rules! impl_integer_for_isize {
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// Assuming two's complement, the number created by the shift
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// is positive for all numbers except gcd = abs(min value)
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// The call to .abs() causes a panic in debug mode
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if m == <$T>::min_value() || n == <$T>::min_value() {
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if m == Self::min_value() || n == Self::min_value() {
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return (1 << shift).abs()
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}
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@ -257,18 +259,22 @@ macro_rules! impl_integer_for_isize {
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/// Calculates the Lowest Common Multiple (LCM) of the number and
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/// `other`.
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#[inline]
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fn lcm(&self, other: &$T) -> $T {
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fn lcm(&self, other: &Self) -> Self {
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// should not have to recalculate abs
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((*self * *other) / self.gcd(other)).abs()
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}
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/// Deprecated, use `is_multiple_of` instead.
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#[inline]
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fn divides(&self, other: &$T) -> bool { return self.is_multiple_of(other); }
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fn divides(&self, other: &Self) -> bool {
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self.is_multiple_of(other)
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}
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/// Returns `true` if the number is a multiple of `other`.
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#[inline]
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fn is_multiple_of(&self, other: &$T) -> bool { *self % *other == 0 }
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fn is_multiple_of(&self, other: &Self) -> bool {
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*self % *other == 0
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}
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/// Returns `true` if the number is divisible by `2`
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#[inline]
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@ -280,7 +286,7 @@ macro_rules! impl_integer_for_isize {
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/// Simultaneous truncated integer division and modulus.
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#[inline]
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fn div_rem(&self, other: &$T) -> ($T, $T) {
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fn div_rem(&self, other: &Self) -> (Self, Self) {
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(*self / *other, *self % *other)
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}
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}
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@ -295,7 +301,7 @@ macro_rules! impl_integer_for_isize {
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/// - `d`: denominator (divisor)
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/// - `qr`: quotient and remainder
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#[cfg(test)]
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fn test_division_rule((n,d): ($T,$T), (q,r): ($T,$T)) {
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fn test_division_rule((n,d): ($T, $T), (q,r): ($T, $T)) {
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assert_eq!(d * q + r, n);
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}
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@ -475,15 +481,19 @@ macro_rules! impl_integer_for_usize {
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impl Integer for $T {
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/// Unsigned integer division. Returns the same result as `div` (`/`).
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#[inline]
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fn div_floor(&self, other: &$T) -> $T { *self / *other }
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fn div_floor(&self, other: &Self) -> Self {
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*self / *other
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}
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/// Unsigned integer modulo operation. Returns the same result as `rem` (`%`).
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#[inline]
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fn mod_floor(&self, other: &$T) -> $T { *self % *other }
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fn mod_floor(&self, other: &Self) -> Self {
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*self % *other
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}
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/// Calculates the Greatest Common Divisor (GCD) of the number and `other`
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#[inline]
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fn gcd(&self, other: &$T) -> $T {
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fn gcd(&self, other: &Self) -> Self {
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// Use Stein's algorithm
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let mut m = *self;
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let mut n = *other;
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@ -507,29 +517,37 @@ macro_rules! impl_integer_for_usize {
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/// Calculates the Lowest Common Multiple (LCM) of the number and `other`.
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#[inline]
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fn lcm(&self, other: &$T) -> $T {
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fn lcm(&self, other: &Self) -> Self {
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(*self * *other) / self.gcd(other)
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}
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/// Deprecated, use `is_multiple_of` instead.
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#[inline]
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fn divides(&self, other: &$T) -> bool { return self.is_multiple_of(other); }
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fn divides(&self, other: &Self) -> bool {
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self.is_multiple_of(other)
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}
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/// Returns `true` if the number is a multiple of `other`.
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#[inline]
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fn is_multiple_of(&self, other: &$T) -> bool { *self % *other == 0 }
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fn is_multiple_of(&self, other: &Self) -> bool {
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*self % *other == 0
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}
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/// Returns `true` if the number is divisible by `2`.
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#[inline]
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fn is_even(&self) -> bool { (*self) & 1 == 0 }
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fn is_even(&self) -> bool {
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*self % 2 == 0
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}
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/// Returns `true` if the number is not divisible by `2`.
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#[inline]
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fn is_odd(&self) -> bool { !(*self).is_even() }
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fn is_odd(&self) -> bool {
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!self.is_even()
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}
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/// Simultaneous truncated integer division and modulus.
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#[inline]
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fn div_rem(&self, other: &$T) -> ($T, $T) {
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fn div_rem(&self, other: &Self) -> (Self, Self) {
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(*self / *other, *self % *other)
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}
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}
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656
src/integer.rs
656
src/integer.rs
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@ -1,656 +0,0 @@
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// Copyright 2013-2014 The Rust Project Developers. See the COPYRIGHT
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// file at the top-level directory of this distribution and at
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// http://rust-lang.org/COPYRIGHT.
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//
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// Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or
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// http://www.apache.org/licenses/LICENSE-2.0> or the MIT license
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// <LICENSE-MIT or http://opensource.org/licenses/MIT>, at your
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// option. This file may not be copied, modified, or distributed
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// except according to those terms.
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//! Integer trait and functions.
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use {Num, Signed};
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pub trait Integer
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: Sized + Num + Ord
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{
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/// Floored integer division.
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///
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/// # Examples
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///
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/// ~~~
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/// # use num::Integer;
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/// assert!(( 8).div_floor(& 3) == 2);
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/// assert!(( 8).div_floor(&-3) == -3);
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/// assert!((-8).div_floor(& 3) == -3);
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/// assert!((-8).div_floor(&-3) == 2);
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///
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/// assert!(( 1).div_floor(& 2) == 0);
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/// assert!(( 1).div_floor(&-2) == -1);
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/// assert!((-1).div_floor(& 2) == -1);
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/// assert!((-1).div_floor(&-2) == 0);
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/// ~~~
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fn div_floor(&self, other: &Self) -> Self;
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/// Floored integer modulo, satisfying:
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///
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/// ~~~
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/// # use num::Integer;
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/// # let n = 1; let d = 1;
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/// assert!(n.div_floor(&d) * d + n.mod_floor(&d) == n)
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/// ~~~
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///
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/// # Examples
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///
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/// ~~~
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/// # use num::Integer;
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/// assert!(( 8).mod_floor(& 3) == 2);
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/// assert!(( 8).mod_floor(&-3) == -1);
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/// assert!((-8).mod_floor(& 3) == 1);
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/// assert!((-8).mod_floor(&-3) == -2);
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///
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/// assert!(( 1).mod_floor(& 2) == 1);
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/// assert!(( 1).mod_floor(&-2) == -1);
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/// assert!((-1).mod_floor(& 2) == 1);
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/// assert!((-1).mod_floor(&-2) == -1);
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/// ~~~
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fn mod_floor(&self, other: &Self) -> Self;
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/// Greatest Common Divisor (GCD).
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///
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/// # Examples
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///
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/// ~~~
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/// # use num::Integer;
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/// assert_eq!(6.gcd(&8), 2);
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/// assert_eq!(7.gcd(&3), 1);
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/// ~~~
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fn gcd(&self, other: &Self) -> Self;
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/// Lowest Common Multiple (LCM).
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///
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/// # Examples
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///
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/// ~~~
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/// # use num::Integer;
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/// assert_eq!(7.lcm(&3), 21);
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/// assert_eq!(2.lcm(&4), 4);
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/// ~~~
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fn lcm(&self, other: &Self) -> Self;
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/// Deprecated, use `is_multiple_of` instead.
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fn divides(&self, other: &Self) -> bool;
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/// Returns `true` if `other` is a multiple of `self`.
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///
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/// # Examples
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///
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/// ~~~
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/// # use num::Integer;
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/// assert_eq!(9.is_multiple_of(&3), true);
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/// assert_eq!(3.is_multiple_of(&9), false);
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/// ~~~
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fn is_multiple_of(&self, other: &Self) -> bool;
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/// Returns `true` if the number is even.
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///
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/// # Examples
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///
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/// ~~~
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/// # use num::Integer;
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/// assert_eq!(3.is_even(), false);
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/// assert_eq!(4.is_even(), true);
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/// ~~~
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fn is_even(&self) -> bool;
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/// Returns `true` if the number is odd.
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///
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/// # Examples
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///
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/// ~~~
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/// # use num::Integer;
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/// assert_eq!(3.is_odd(), true);
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/// assert_eq!(4.is_odd(), false);
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/// ~~~
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fn is_odd(&self) -> bool;
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/// Simultaneous truncated integer division and modulus.
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/// Returns `(quotient, remainder)`.
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///
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/// # Examples
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///
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/// ~~~
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/// # use num::Integer;
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/// assert_eq!(( 8).div_rem( &3), ( 2, 2));
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/// assert_eq!(( 8).div_rem(&-3), (-2, 2));
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/// assert_eq!((-8).div_rem( &3), (-2, -2));
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/// assert_eq!((-8).div_rem(&-3), ( 2, -2));
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///
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/// assert_eq!(( 1).div_rem( &2), ( 0, 1));
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/// assert_eq!(( 1).div_rem(&-2), ( 0, 1));
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/// assert_eq!((-1).div_rem( &2), ( 0, -1));
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/// assert_eq!((-1).div_rem(&-2), ( 0, -1));
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/// ~~~
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#[inline]
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fn div_rem(&self, other: &Self) -> (Self, Self);
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/// Simultaneous floored integer division and modulus.
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/// Returns `(quotient, remainder)`.
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///
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/// # Examples
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///
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/// ~~~
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/// # use num::Integer;
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/// assert_eq!(( 8).div_mod_floor( &3), ( 2, 2));
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/// assert_eq!(( 8).div_mod_floor(&-3), (-3, -1));
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/// assert_eq!((-8).div_mod_floor( &3), (-3, 1));
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/// assert_eq!((-8).div_mod_floor(&-3), ( 2, -2));
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///
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/// assert_eq!(( 1).div_mod_floor( &2), ( 0, 1));
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/// assert_eq!(( 1).div_mod_floor(&-2), (-1, -1));
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/// assert_eq!((-1).div_mod_floor( &2), (-1, 1));
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/// assert_eq!((-1).div_mod_floor(&-2), ( 0, -1));
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/// ~~~
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fn div_mod_floor(&self, other: &Self) -> (Self, Self) {
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(self.div_floor(other), self.mod_floor(other))
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}
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}
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/// Simultaneous integer division and modulus
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#[inline] pub fn div_rem<T: Integer>(x: T, y: T) -> (T, T) { x.div_rem(&y) }
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/// Floored integer division
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#[inline] pub fn div_floor<T: Integer>(x: T, y: T) -> T { x.div_floor(&y) }
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/// Floored integer modulus
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#[inline] pub fn mod_floor<T: Integer>(x: T, y: T) -> T { x.mod_floor(&y) }
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/// Simultaneous floored integer division and modulus
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#[inline] pub fn div_mod_floor<T: Integer>(x: T, y: T) -> (T, T) { x.div_mod_floor(&y) }
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/// Calculates the Greatest Common Divisor (GCD) of the number and `other`. The
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/// result is always positive.
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#[inline(always)] pub fn gcd<T: Integer>(x: T, y: T) -> T { x.gcd(&y) }
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/// Calculates the Lowest Common Multiple (LCM) of the number and `other`.
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#[inline(always)] pub fn lcm<T: Integer>(x: T, y: T) -> T { x.lcm(&y) }
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macro_rules! impl_integer_for_isize {
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($T:ty, $test_mod:ident) => (
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impl Integer for $T {
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/// Floored integer division
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#[inline]
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fn div_floor(&self, other: &$T) -> $T {
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// Algorithm from [Daan Leijen. _Division and Modulus for Computer Scientists_,
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// December 2001](http://research.microsoft.com/pubs/151917/divmodnote-letter.pdf)
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match self.div_rem(other) {
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(d, r) if (r > 0 && *other < 0)
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|| (r < 0 && *other > 0) => d - 1,
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(d, _) => d,
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}
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}
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/// Floored integer modulo
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#[inline]
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fn mod_floor(&self, other: &$T) -> $T {
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// Algorithm from [Daan Leijen. _Division and Modulus for Computer Scientists_,
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// December 2001](http://research.microsoft.com/pubs/151917/divmodnote-letter.pdf)
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match *self % *other {
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r if (r > 0 && *other < 0)
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|| (r < 0 && *other > 0) => r + *other,
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r => r,
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}
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}
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/// Calculates `div_floor` and `mod_floor` simultaneously
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#[inline]
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fn div_mod_floor(&self, other: &$T) -> ($T,$T) {
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// Algorithm from [Daan Leijen. _Division and Modulus for Computer Scientists_,
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// December 2001](http://research.microsoft.com/pubs/151917/divmodnote-letter.pdf)
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match self.div_rem(other) {
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(d, r) if (r > 0 && *other < 0)
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|| (r < 0 && *other > 0) => (d - 1, r + *other),
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(d, r) => (d, r),
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}
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}
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/// Calculates the Greatest Common Divisor (GCD) of the number and
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/// `other`. The result is always positive.
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#[inline]
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fn gcd(&self, other: &$T) -> $T {
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// Use Stein's algorithm
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let mut m = *self;
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let mut n = *other;
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if m == 0 || n == 0 { return (m | n).abs() }
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// find common factors of 2
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let shift = (m | n).trailing_zeros();
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// The algorithm needs positive numbers, but the minimum value
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// can't be represented as a positive one.
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// It's also a power of two, so the gcd can be
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// calculated by bitshifting in that case
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// Assuming two's complement, the number created by the shift
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// is positive for all numbers except gcd = abs(min value)
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// The call to .abs() causes a panic in debug mode
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if m == <$T>::min_value() || n == <$T>::min_value() {
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return (1 << shift).abs()
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}
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// guaranteed to be positive now, rest like unsigned algorithm
|
||||
m = m.abs();
|
||||
n = n.abs();
|
||||
|
||||
// divide n and m by 2 until odd
|
||||
// m inside loop
|
||||
n >>= n.trailing_zeros();
|
||||
|
||||
while m != 0 {
|
||||
m >>= m.trailing_zeros();
|
||||
if n > m { ::std::mem::swap(&mut n, &mut m) }
|
||||
m -= n;
|
||||
}
|
||||
|
||||
n << shift
|
||||
}
|
||||
|
||||
/// Calculates the Lowest Common Multiple (LCM) of the number and
|
||||
/// `other`.
|
||||
#[inline]
|
||||
fn lcm(&self, other: &$T) -> $T {
|
||||
// should not have to recalculate abs
|
||||
(*self * (*other / self.gcd(other))).abs()
|
||||
}
|
||||
|
||||
/// Deprecated, use `is_multiple_of` instead.
|
||||
#[inline]
|
||||
fn divides(&self, other: &$T) -> bool { return self.is_multiple_of(other); }
|
||||
|
||||
/// Returns `true` if the number is a multiple of `other`.
|
||||
#[inline]
|
||||
fn is_multiple_of(&self, other: &$T) -> bool { *self % *other == 0 }
|
||||
|
||||
/// Returns `true` if the number is divisible by `2`
|
||||
#[inline]
|
||||
fn is_even(&self) -> bool { (*self) & 1 == 0 }
|
||||
|
||||
/// Returns `true` if the number is not divisible by `2`
|
||||
#[inline]
|
||||
fn is_odd(&self) -> bool { !self.is_even() }
|
||||
|
||||
/// Simultaneous truncated integer division and modulus.
|
||||
#[inline]
|
||||
fn div_rem(&self, other: &$T) -> ($T, $T) {
|
||||
(*self / *other, *self % *other)
|
||||
}
|
||||
}
|
||||
|
||||
#[cfg(test)]
|
||||
mod $test_mod {
|
||||
use Integer;
|
||||
|
||||
/// Checks that the division rule holds for:
|
||||
///
|
||||
/// - `n`: numerator (dividend)
|
||||
/// - `d`: denominator (divisor)
|
||||
/// - `qr`: quotient and remainder
|
||||
#[cfg(test)]
|
||||
fn test_division_rule((n,d): ($T,$T), (q,r): ($T,$T)) {
|
||||
assert_eq!(d * q + r, n);
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn test_div_rem() {
|
||||
fn test_nd_dr(nd: ($T,$T), qr: ($T,$T)) {
|
||||
let (n,d) = nd;
|
||||
let separate_div_rem = (n / d, n % d);
|
||||
let combined_div_rem = n.div_rem(&d);
|
||||
|
||||
assert_eq!(separate_div_rem, qr);
|
||||
assert_eq!(combined_div_rem, qr);
|
||||
|
||||
test_division_rule(nd, separate_div_rem);
|
||||
test_division_rule(nd, combined_div_rem);
|
||||
}
|
||||
|
||||
test_nd_dr(( 8, 3), ( 2, 2));
|
||||
test_nd_dr(( 8, -3), (-2, 2));
|
||||
test_nd_dr((-8, 3), (-2, -2));
|
||||
test_nd_dr((-8, -3), ( 2, -2));
|
||||
|
||||
test_nd_dr(( 1, 2), ( 0, 1));
|
||||
test_nd_dr(( 1, -2), ( 0, 1));
|
||||
test_nd_dr((-1, 2), ( 0, -1));
|
||||
test_nd_dr((-1, -2), ( 0, -1));
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn test_div_mod_floor() {
|
||||
fn test_nd_dm(nd: ($T,$T), dm: ($T,$T)) {
|
||||
let (n,d) = nd;
|
||||
let separate_div_mod_floor = (n.div_floor(&d), n.mod_floor(&d));
|
||||
let combined_div_mod_floor = n.div_mod_floor(&d);
|
||||
|
||||
assert_eq!(separate_div_mod_floor, dm);
|
||||
assert_eq!(combined_div_mod_floor, dm);
|
||||
|
||||
test_division_rule(nd, separate_div_mod_floor);
|
||||
test_division_rule(nd, combined_div_mod_floor);
|
||||
}
|
||||
|
||||
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_gcd_cmp_with_euclidean() {
|
||||
fn euclidean_gcd(mut m: $T, mut n: $T) -> $T {
|
||||
while m != 0 {
|
||||
::std::mem::swap(&mut m, &mut n);
|
||||
m %= n;
|
||||
}
|
||||
|
||||
n.abs()
|
||||
}
|
||||
|
||||
// gcd(-128, b) = 128 is not representable as positive value
|
||||
// for i8
|
||||
for i in -127..127 {
|
||||
for j in -127..127 {
|
||||
assert_eq!(euclidean_gcd(i,j), i.gcd(&j));
|
||||
}
|
||||
}
|
||||
|
||||
// last value
|
||||
// FIXME: Use inclusive ranges for above loop when implemented
|
||||
let i = 127;
|
||||
for j in -127..127 {
|
||||
assert_eq!(euclidean_gcd(i,j), i.gcd(&j));
|
||||
}
|
||||
assert_eq!(127.gcd(&127), 127);
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn test_gcd_min_val() {
|
||||
let min = <$T>::min_value();
|
||||
let max = <$T>::max_value();
|
||||
let max_pow2 = max / 2 + 1;
|
||||
assert_eq!(min.gcd(&max), 1 as $T);
|
||||
assert_eq!(max.gcd(&min), 1 as $T);
|
||||
assert_eq!(min.gcd(&max_pow2), max_pow2);
|
||||
assert_eq!(max_pow2.gcd(&min), max_pow2);
|
||||
assert_eq!(min.gcd(&42), 2 as $T);
|
||||
assert_eq!((42 as $T).gcd(&min), 2 as $T);
|
||||
}
|
||||
|
||||
#[test]
|
||||
#[should_panic]
|
||||
fn test_gcd_min_val_min_val() {
|
||||
let min = <$T>::min_value();
|
||||
assert!(min.gcd(&min) >= 0);
|
||||
}
|
||||
|
||||
#[test]
|
||||
#[should_panic]
|
||||
fn test_gcd_min_val_0() {
|
||||
let min = <$T>::min_value();
|
||||
assert!(min.gcd(&0) >= 0);
|
||||
}
|
||||
|
||||
#[test]
|
||||
#[should_panic]
|
||||
fn test_gcd_0_min_val() {
|
||||
let min = <$T>::min_value();
|
||||
assert!((0 as $T).gcd(&min) >= 0);
|
||||
}
|
||||
|
||||
#[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_even() {
|
||||
assert_eq!((-4 as $T).is_even(), true);
|
||||
assert_eq!((-3 as $T).is_even(), false);
|
||||
assert_eq!((-2 as $T).is_even(), true);
|
||||
assert_eq!((-1 as $T).is_even(), false);
|
||||
assert_eq!((0 as $T).is_even(), true);
|
||||
assert_eq!((1 as $T).is_even(), false);
|
||||
assert_eq!((2 as $T).is_even(), true);
|
||||
assert_eq!((3 as $T).is_even(), false);
|
||||
assert_eq!((4 as $T).is_even(), true);
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn test_odd() {
|
||||
assert_eq!((-4 as $T).is_odd(), false);
|
||||
assert_eq!((-3 as $T).is_odd(), true);
|
||||
assert_eq!((-2 as $T).is_odd(), false);
|
||||
assert_eq!((-1 as $T).is_odd(), true);
|
||||
assert_eq!((0 as $T).is_odd(), false);
|
||||
assert_eq!((1 as $T).is_odd(), true);
|
||||
assert_eq!((2 as $T).is_odd(), false);
|
||||
assert_eq!((3 as $T).is_odd(), true);
|
||||
assert_eq!((4 as $T).is_odd(), false);
|
||||
}
|
||||
}
|
||||
)
|
||||
}
|
||||
|
||||
impl_integer_for_isize!(i8, test_integer_i8);
|
||||
impl_integer_for_isize!(i16, test_integer_i16);
|
||||
impl_integer_for_isize!(i32, test_integer_i32);
|
||||
impl_integer_for_isize!(i64, test_integer_i64);
|
||||
impl_integer_for_isize!(isize, test_integer_isize);
|
||||
|
||||
macro_rules! impl_integer_for_usize {
|
||||
($T:ty, $test_mod:ident) => (
|
||||
impl Integer for $T {
|
||||
/// Unsigned integer division. Returns the same result as `div` (`/`).
|
||||
#[inline]
|
||||
fn div_floor(&self, other: &$T) -> $T { *self / *other }
|
||||
|
||||
/// Unsigned integer modulo operation. Returns the same result as `rem` (`%`).
|
||||
#[inline]
|
||||
fn mod_floor(&self, other: &$T) -> $T { *self % *other }
|
||||
|
||||
/// Calculates the Greatest Common Divisor (GCD) of the number and `other`
|
||||
#[inline]
|
||||
fn gcd(&self, other: &$T) -> $T {
|
||||
// Use Stein's algorithm
|
||||
let mut m = *self;
|
||||
let mut n = *other;
|
||||
if m == 0 || n == 0 { return m | n }
|
||||
|
||||
// find common factors of 2
|
||||
let shift = (m | n).trailing_zeros();
|
||||
|
||||
// divide n and m by 2 until odd
|
||||
// m inside loop
|
||||
n >>= n.trailing_zeros();
|
||||
|
||||
while m != 0 {
|
||||
m >>= m.trailing_zeros();
|
||||
if n > m { ::std::mem::swap(&mut n, &mut m) }
|
||||
m -= n;
|
||||
}
|
||||
|
||||
n << shift
|
||||
}
|
||||
|
||||
/// Calculates the Lowest Common Multiple (LCM) of the number and `other`.
|
||||
#[inline]
|
||||
fn lcm(&self, other: &$T) -> $T {
|
||||
*self * (*other / self.gcd(other))
|
||||
}
|
||||
|
||||
/// Deprecated, use `is_multiple_of` instead.
|
||||
#[inline]
|
||||
fn divides(&self, other: &$T) -> bool { return self.is_multiple_of(other); }
|
||||
|
||||
/// Returns `true` if the number is a multiple of `other`.
|
||||
#[inline]
|
||||
fn is_multiple_of(&self, other: &$T) -> bool { *self % *other == 0 }
|
||||
|
||||
/// Returns `true` if the number is divisible by `2`.
|
||||
#[inline]
|
||||
fn is_even(&self) -> bool { (*self) & 1 == 0 }
|
||||
|
||||
/// Returns `true` if the number is not divisible by `2`.
|
||||
#[inline]
|
||||
fn is_odd(&self) -> bool { !(*self).is_even() }
|
||||
|
||||
/// Simultaneous truncated integer division and modulus.
|
||||
#[inline]
|
||||
fn div_rem(&self, other: &$T) -> ($T, $T) {
|
||||
(*self / *other, *self % *other)
|
||||
}
|
||||
}
|
||||
|
||||
#[cfg(test)]
|
||||
mod $test_mod {
|
||||
use Integer;
|
||||
|
||||
#[test]
|
||||
fn test_div_mod_floor() {
|
||||
assert_eq!((10 as $T).div_floor(&(3 as $T)), 3 as $T);
|
||||
assert_eq!((10 as $T).mod_floor(&(3 as $T)), 1 as $T);
|
||||
assert_eq!((10 as $T).div_mod_floor(&(3 as $T)), (3 as $T, 1 as $T));
|
||||
assert_eq!((5 as $T).div_floor(&(5 as $T)), 1 as $T);
|
||||
assert_eq!((5 as $T).mod_floor(&(5 as $T)), 0 as $T);
|
||||
assert_eq!((5 as $T).div_mod_floor(&(5 as $T)), (1 as $T, 0 as $T));
|
||||
assert_eq!((3 as $T).div_floor(&(7 as $T)), 0 as $T);
|
||||
assert_eq!((3 as $T).mod_floor(&(7 as $T)), 3 as $T);
|
||||
assert_eq!((3 as $T).div_mod_floor(&(7 as $T)), (0 as $T, 3 as $T));
|
||||
}
|
||||
|
||||
#[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_gcd_cmp_with_euclidean() {
|
||||
fn euclidean_gcd(mut m: $T, mut n: $T) -> $T {
|
||||
while m != 0 {
|
||||
::std::mem::swap(&mut m, &mut n);
|
||||
m %= n;
|
||||
}
|
||||
n
|
||||
}
|
||||
|
||||
for i in 0..255 {
|
||||
for j in 0..255 {
|
||||
assert_eq!(euclidean_gcd(i,j), i.gcd(&j));
|
||||
}
|
||||
}
|
||||
|
||||
// last value
|
||||
// FIXME: Use inclusive ranges for above loop when implemented
|
||||
let i = 255;
|
||||
for j in 0..255 {
|
||||
assert_eq!(euclidean_gcd(i,j), i.gcd(&j));
|
||||
}
|
||||
assert_eq!(255.gcd(&255), 255);
|
||||
}
|
||||
|
||||
#[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!((15 as $T).lcm(&17), 255 as $T);
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn test_is_multiple_of() {
|
||||
assert!((6 as $T).is_multiple_of(&(6 as $T)));
|
||||
assert!((6 as $T).is_multiple_of(&(3 as $T)));
|
||||
assert!((6 as $T).is_multiple_of(&(1 as $T)));
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn test_even() {
|
||||
assert_eq!((0 as $T).is_even(), true);
|
||||
assert_eq!((1 as $T).is_even(), false);
|
||||
assert_eq!((2 as $T).is_even(), true);
|
||||
assert_eq!((3 as $T).is_even(), false);
|
||||
assert_eq!((4 as $T).is_even(), true);
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn test_odd() {
|
||||
assert_eq!((0 as $T).is_odd(), false);
|
||||
assert_eq!((1 as $T).is_odd(), true);
|
||||
assert_eq!((2 as $T).is_odd(), false);
|
||||
assert_eq!((3 as $T).is_odd(), true);
|
||||
assert_eq!((4 as $T).is_odd(), false);
|
||||
}
|
||||
}
|
||||
)
|
||||
}
|
||||
|
||||
impl_integer_for_usize!(u8, test_integer_u8);
|
||||
impl_integer_for_usize!(u16, test_integer_u16);
|
||||
impl_integer_for_usize!(u32, test_integer_u32);
|
||||
impl_integer_for_usize!(u64, test_integer_u64);
|
||||
impl_integer_for_usize!(usize, test_integer_usize);
|
||||
|
||||
#[test]
|
||||
fn test_lcm_overflow() {
|
||||
macro_rules! check {
|
||||
($t:ty, $x:expr, $y:expr, $r:expr) => { {
|
||||
let x: $t = $x;
|
||||
let y: $t = $y;
|
||||
let o = x.checked_mul(y);
|
||||
assert!(o.is_none(),
|
||||
"sanity checking that {} input {} * {} overflows",
|
||||
stringify!($t), x, y);
|
||||
assert_eq!(x.lcm(&y), $r);
|
||||
assert_eq!(y.lcm(&x), $r);
|
||||
} }
|
||||
}
|
||||
|
||||
// Original bug (Issue #166)
|
||||
check!(i64, 46656000000000000, 600, 46656000000000000);
|
||||
|
||||
check!(i8, 0x40, 0x04, 0x40);
|
||||
check!(u8, 0x80, 0x02, 0x80);
|
||||
check!(i16, 0x40_00, 0x04, 0x40_00);
|
||||
check!(u16, 0x80_00, 0x02, 0x80_00);
|
||||
check!(i32, 0x4000_0000, 0x04, 0x4000_0000);
|
||||
check!(u32, 0x8000_0000, 0x02, 0x8000_0000);
|
||||
check!(i64, 0x4000_0000_0000_0000, 0x04, 0x4000_0000_0000_0000);
|
||||
check!(u64, 0x8000_0000_0000_0000, 0x02, 0x8000_0000_0000_0000);
|
||||
}
|
||||
|
|
@ -58,6 +58,7 @@
|
|||
html_playground_url = "http://play.rust-lang.org/")]
|
||||
|
||||
extern crate num_traits;
|
||||
extern crate num_integer;
|
||||
|
||||
#[cfg(feature = "rustc-serialize")]
|
||||
extern crate rustc_serialize;
|
||||
|
|
@ -92,7 +93,7 @@ use std::ops::{Mul};
|
|||
#[cfg(feature = "bigint")]
|
||||
pub mod bigint;
|
||||
pub mod complex;
|
||||
pub mod integer;
|
||||
pub mod integer { pub use num_integer::*; }
|
||||
pub mod iter;
|
||||
pub mod traits { pub use num_traits::*; }
|
||||
#[cfg(feature = "rational")]
|
||||
|
|
|
|||
Loading…
Reference in New Issue