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Extract integer module

This commit is contained in:
Łukasz Jan Niemier 2016-02-17 18:51:28 +01:00
parent 4361521f5a
commit f1a80857ee
5 changed files with 46 additions and 679 deletions
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3
Cargo.toml
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@ -21,6 +21,9 @@ serde = { version = "^0.7.0", optional = true }
[dependencies.num-traits] [dependencies.num-traits]
path = "./traits" path = "./traits"
[dependencies.num-integer]
path = "./integer"
[dev-dependencies] [dev-dependencies]
# Some tests of non-rand functionality still use rand because the tests # Some tests of non-rand functionality still use rand because the tests
# themselves are randomized. # themselves are randomized.

5
integer/Cargo.toml
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@ -1,6 +1,7 @@
[package] [package]
name = "integer" name = "num-integer"
version = "0.1.0" version = "0.1.0"
authors = ["Łukasz Jan Niemier <lukasz@niemier.pl>"] authors = ["Łukasz Jan Niemier <lukasz@niemier.pl>"]
[dependencies] [dependencies.num-traits]
path = "../traits"

58
integer/src/lib.rs
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@ -10,7 +10,9 @@
//! Integer trait and functions. //! Integer trait and functions.
use {Num, Signed}; extern crate num_traits as traits;
use traits::{Num, Signed};
pub trait Integer pub trait Integer
: Sized : Sized
@ -179,7 +181,7 @@ macro_rules! impl_integer_for_isize {
impl Integer for $T { impl Integer for $T {
/// Floored integer division /// Floored integer division
#[inline] #[inline]
fn div_floor(&self, other: &$T) -> $T { fn div_floor(&self, other: &Self) -> Self {
// Algorithm from [Daan Leijen. _Division and Modulus for Computer Scientists_, // Algorithm from [Daan Leijen. _Division and Modulus for Computer Scientists_,
// December 2001](http://research.microsoft.com/pubs/151917/divmodnote-letter.pdf) // December 2001](http://research.microsoft.com/pubs/151917/divmodnote-letter.pdf)
match self.div_rem(other) { match self.div_rem(other) {
@ -191,7 +193,7 @@ macro_rules! impl_integer_for_isize {
/// Floored integer modulo /// Floored integer modulo
#[inline] #[inline]
fn mod_floor(&self, other: &$T) -> $T { fn mod_floor(&self, other: &Self) -> Self {
// Algorithm from [Daan Leijen. _Division and Modulus for Computer Scientists_, // Algorithm from [Daan Leijen. _Division and Modulus for Computer Scientists_,
// December 2001](http://research.microsoft.com/pubs/151917/divmodnote-letter.pdf) // December 2001](http://research.microsoft.com/pubs/151917/divmodnote-letter.pdf)
match *self % *other { match *self % *other {
@ -203,7 +205,7 @@ macro_rules! impl_integer_for_isize {
/// Calculates `div_floor` and `mod_floor` simultaneously /// Calculates `div_floor` and `mod_floor` simultaneously
#[inline] #[inline]
fn div_mod_floor(&self, other: &$T) -> ($T,$T) { fn div_mod_floor(&self, other: &Self) -> (Self, Self) {
// Algorithm from [Daan Leijen. _Division and Modulus for Computer Scientists_, // Algorithm from [Daan Leijen. _Division and Modulus for Computer Scientists_,
// December 2001](http://research.microsoft.com/pubs/151917/divmodnote-letter.pdf) // December 2001](http://research.microsoft.com/pubs/151917/divmodnote-letter.pdf)
match self.div_rem(other) { match self.div_rem(other) {
@ -216,7 +218,7 @@ macro_rules! impl_integer_for_isize {
/// Calculates the Greatest Common Divisor (GCD) of the number and /// Calculates the Greatest Common Divisor (GCD) of the number and
/// `other`. The result is always positive. /// `other`. The result is always positive.
#[inline] #[inline]
fn gcd(&self, other: &$T) -> $T { fn gcd(&self, other: &Self) -> Self {
// Use Stein's algorithm // Use Stein's algorithm
let mut m = *self; let mut m = *self;
let mut n = *other; let mut n = *other;
@ -233,7 +235,7 @@ macro_rules! impl_integer_for_isize {
// Assuming two's complement, the number created by the shift // Assuming two's complement, the number created by the shift
// is positive for all numbers except gcd = abs(min value) // is positive for all numbers except gcd = abs(min value)
// The call to .abs() causes a panic in debug mode // The call to .abs() causes a panic in debug mode
if m == <$T>::min_value() || n == <$T>::min_value() { if m == Self::min_value() || n == Self::min_value() {
return (1 << shift).abs() return (1 << shift).abs()
} }
@ -257,18 +259,22 @@ macro_rules! impl_integer_for_isize {
/// Calculates the Lowest Common Multiple (LCM) of the number and /// Calculates the Lowest Common Multiple (LCM) of the number and
/// `other`. /// `other`.
#[inline] #[inline]
fn lcm(&self, other: &$T) -> $T { fn lcm(&self, other: &Self) -> Self {
// should not have to recalculate abs // should not have to recalculate abs
((*self * *other) / self.gcd(other)).abs() ((*self * *other) / self.gcd(other)).abs()
} }
/// Deprecated, use `is_multiple_of` instead. /// Deprecated, use `is_multiple_of` instead.
#[inline] #[inline]
fn divides(&self, other: &$T) -> bool { return self.is_multiple_of(other); } fn divides(&self, other: &Self) -> bool {
self.is_multiple_of(other)
}
/// Returns `true` if the number is a multiple of `other`. /// Returns `true` if the number is a multiple of `other`.
#[inline] #[inline]
fn is_multiple_of(&self, other: &$T) -> bool { *self % *other == 0 } fn is_multiple_of(&self, other: &Self) -> bool {
*self % *other == 0
}
/// Returns `true` if the number is divisible by `2` /// Returns `true` if the number is divisible by `2`
#[inline] #[inline]
@ -280,7 +286,7 @@ macro_rules! impl_integer_for_isize {
/// Simultaneous truncated integer division and modulus. /// Simultaneous truncated integer division and modulus.
#[inline] #[inline]
fn div_rem(&self, other: &$T) -> ($T, $T) { fn div_rem(&self, other: &Self) -> (Self, Self) {
(*self / *other, *self % *other) (*self / *other, *self % *other)
} }
} }
@ -295,7 +301,7 @@ macro_rules! impl_integer_for_isize {
/// - `d`: denominator (divisor) /// - `d`: denominator (divisor)
/// - `qr`: quotient and remainder /// - `qr`: quotient and remainder
#[cfg(test)] #[cfg(test)]
fn test_division_rule((n,d): ($T,$T), (q,r): ($T,$T)) { fn test_division_rule((n,d): ($T, $T), (q,r): ($T, $T)) {
assert_eq!(d * q + r, n); assert_eq!(d * q + r, n);
} }
@ -475,15 +481,19 @@ macro_rules! impl_integer_for_usize {
impl Integer for $T { impl Integer for $T {
/// Unsigned integer division. Returns the same result as `div` (`/`). /// Unsigned integer division. Returns the same result as `div` (`/`).
#[inline] #[inline]
fn div_floor(&self, other: &$T) -> $T { *self / *other } fn div_floor(&self, other: &Self) -> Self {
*self / *other
}
/// Unsigned integer modulo operation. Returns the same result as `rem` (`%`). /// Unsigned integer modulo operation. Returns the same result as `rem` (`%`).
#[inline] #[inline]
fn mod_floor(&self, other: &$T) -> $T { *self % *other } fn mod_floor(&self, other: &Self) -> Self {
*self % *other
}
/// Calculates the Greatest Common Divisor (GCD) of the number and `other` /// Calculates the Greatest Common Divisor (GCD) of the number and `other`
#[inline] #[inline]
fn gcd(&self, other: &$T) -> $T { fn gcd(&self, other: &Self) -> Self {
// Use Stein's algorithm // Use Stein's algorithm
let mut m = *self; let mut m = *self;
let mut n = *other; let mut n = *other;
@ -507,29 +517,37 @@ macro_rules! impl_integer_for_usize {
/// Calculates the Lowest Common Multiple (LCM) of the number and `other`. /// Calculates the Lowest Common Multiple (LCM) of the number and `other`.
#[inline] #[inline]
fn lcm(&self, other: &$T) -> $T { fn lcm(&self, other: &Self) -> Self {
(*self * *other) / self.gcd(other) (*self * *other) / self.gcd(other)
} }
/// Deprecated, use `is_multiple_of` instead. /// Deprecated, use `is_multiple_of` instead.
#[inline] #[inline]
fn divides(&self, other: &$T) -> bool { return self.is_multiple_of(other); } fn divides(&self, other: &Self) -> bool {
self.is_multiple_of(other)
}
/// Returns `true` if the number is a multiple of `other`. /// Returns `true` if the number is a multiple of `other`.
#[inline] #[inline]
fn is_multiple_of(&self, other: &$T) -> bool { *self % *other == 0 } fn is_multiple_of(&self, other: &Self) -> bool {
*self % *other == 0
}
/// Returns `true` if the number is divisible by `2`. /// Returns `true` if the number is divisible by `2`.
#[inline] #[inline]
fn is_even(&self) -> bool { (*self) & 1 == 0 } fn is_even(&self) -> bool {
*self % 2 == 0
}
/// Returns `true` if the number is not divisible by `2`. /// Returns `true` if the number is not divisible by `2`.
#[inline] #[inline]
fn is_odd(&self) -> bool { !(*self).is_even() } fn is_odd(&self) -> bool {
!self.is_even()
}
/// Simultaneous truncated integer division and modulus. /// Simultaneous truncated integer division and modulus.
#[inline] #[inline]
fn div_rem(&self, other: &$T) -> ($T, $T) { fn div_rem(&self, other: &Self) -> (Self, Self) {
(*self / *other, *self % *other) (*self / *other, *self % *other)
} }
} }

656
src/integer.rs
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@ -1,656 +0,0 @@
// Copyright 2013-2014 The Rust Project Developers. See the COPYRIGHT
// file at the top-level directory of this distribution and at
// http://rust-lang.org/COPYRIGHT.
//
// Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or
// http://www.apache.org/licenses/LICENSE-2.0> or the MIT license
// <LICENSE-MIT or http://opensource.org/licenses/MIT>, at your
// option. This file may not be copied, modified, or distributed
// except according to those terms.
//! Integer trait and functions.
use {Num, Signed};
pub trait Integer
: Sized + Num + Ord
{
/// Floored integer division.
///
/// # Examples
///
/// ~~~
/// # use num::Integer;
/// assert!(( 8).div_floor(& 3) == 2);
/// assert!(( 8).div_floor(&-3) == -3);
/// assert!((-8).div_floor(& 3) == -3);
/// assert!((-8).div_floor(&-3) == 2);
///
/// assert!(( 1).div_floor(& 2) == 0);
/// assert!(( 1).div_floor(&-2) == -1);
/// assert!((-1).div_floor(& 2) == -1);
/// assert!((-1).div_floor(&-2) == 0);
/// ~~~
fn div_floor(&self, other: &Self) -> Self;
/// Floored integer modulo, satisfying:
///
/// ~~~
/// # use num::Integer;
/// # let n = 1; let d = 1;
/// assert!(n.div_floor(&d) * d + n.mod_floor(&d) == n)
/// ~~~
///
/// # Examples
///
/// ~~~
/// # use num::Integer;
/// assert!(( 8).mod_floor(& 3) == 2);
/// assert!(( 8).mod_floor(&-3) == -1);
/// assert!((-8).mod_floor(& 3) == 1);
/// assert!((-8).mod_floor(&-3) == -2);
///
/// assert!(( 1).mod_floor(& 2) == 1);
/// assert!(( 1).mod_floor(&-2) == -1);
/// assert!((-1).mod_floor(& 2) == 1);
/// assert!((-1).mod_floor(&-2) == -1);
/// ~~~
fn mod_floor(&self, other: &Self) -> Self;
/// Greatest Common Divisor (GCD).
///
/// # Examples
///
/// ~~~
/// # use num::Integer;
/// assert_eq!(6.gcd(&8), 2);
/// assert_eq!(7.gcd(&3), 1);
/// ~~~
fn gcd(&self, other: &Self) -> Self;
/// Lowest Common Multiple (LCM).
///
/// # Examples
///
/// ~~~
/// # use num::Integer;
/// assert_eq!(7.lcm(&3), 21);
/// assert_eq!(2.lcm(&4), 4);
/// ~~~
fn lcm(&self, other: &Self) -> Self;
/// Deprecated, use `is_multiple_of` instead.
fn divides(&self, other: &Self) -> bool;
/// Returns `true` if `other` is a multiple of `self`.
///
/// # Examples
///
/// ~~~
/// # use num::Integer;
/// assert_eq!(9.is_multiple_of(&3), true);
/// assert_eq!(3.is_multiple_of(&9), false);
/// ~~~
fn is_multiple_of(&self, other: &Self) -> bool;
/// Returns `true` if the number is even.
///
/// # Examples
///
/// ~~~
/// # use num::Integer;
/// assert_eq!(3.is_even(), false);
/// assert_eq!(4.is_even(), true);
/// ~~~
fn is_even(&self) -> bool;
/// Returns `true` if the number is odd.
///
/// # Examples
///
/// ~~~
/// # use num::Integer;
/// assert_eq!(3.is_odd(), true);
/// assert_eq!(4.is_odd(), false);
/// ~~~
fn is_odd(&self) -> bool;
/// Simultaneous truncated integer division and modulus.
/// Returns `(quotient, remainder)`.
///
/// # Examples
///
/// ~~~
/// # use num::Integer;
/// assert_eq!(( 8).div_rem( &3), ( 2, 2));
/// assert_eq!(( 8).div_rem(&-3), (-2, 2));
/// assert_eq!((-8).div_rem( &3), (-2, -2));
/// assert_eq!((-8).div_rem(&-3), ( 2, -2));
///
/// assert_eq!(( 1).div_rem( &2), ( 0, 1));
/// assert_eq!(( 1).div_rem(&-2), ( 0, 1));
/// assert_eq!((-1).div_rem( &2), ( 0, -1));
/// assert_eq!((-1).div_rem(&-2), ( 0, -1));
/// ~~~
#[inline]
fn div_rem(&self, other: &Self) -> (Self, Self);
/// Simultaneous floored integer division and modulus.
/// Returns `(quotient, remainder)`.
///
/// # Examples
///
/// ~~~
/// # use num::Integer;
/// assert_eq!(( 8).div_mod_floor( &3), ( 2, 2));
/// assert_eq!(( 8).div_mod_floor(&-3), (-3, -1));
/// assert_eq!((-8).div_mod_floor( &3), (-3, 1));
/// assert_eq!((-8).div_mod_floor(&-3), ( 2, -2));
///
/// assert_eq!(( 1).div_mod_floor( &2), ( 0, 1));
/// assert_eq!(( 1).div_mod_floor(&-2), (-1, -1));
/// assert_eq!((-1).div_mod_floor( &2), (-1, 1));
/// assert_eq!((-1).div_mod_floor(&-2), ( 0, -1));
/// ~~~
fn div_mod_floor(&self, other: &Self) -> (Self, Self) {
(self.div_floor(other), self.mod_floor(other))
}
}
/// Simultaneous integer division and modulus
#[inline] pub fn div_rem<T: Integer>(x: T, y: T) -> (T, T) { x.div_rem(&y) }
/// Floored integer division
#[inline] pub fn div_floor<T: Integer>(x: T, y: T) -> T { x.div_floor(&y) }
/// Floored integer modulus
#[inline] pub fn mod_floor<T: Integer>(x: T, y: T) -> T { x.mod_floor(&y) }
/// Simultaneous floored integer division and modulus
#[inline] pub fn div_mod_floor<T: Integer>(x: T, y: T) -> (T, T) { x.div_mod_floor(&y) }
/// Calculates the Greatest Common Divisor (GCD) of the number and `other`. The
/// result is always positive.
#[inline(always)] pub fn gcd<T: Integer>(x: T, y: T) -> T { x.gcd(&y) }
/// Calculates the Lowest Common Multiple (LCM) of the number and `other`.
#[inline(always)] pub fn lcm<T: Integer>(x: T, y: T) -> T { x.lcm(&y) }
macro_rules! impl_integer_for_isize {
($T:ty, $test_mod:ident) => (
impl Integer for $T {
/// Floored integer division
#[inline]
fn div_floor(&self, other: &$T) -> $T {
// Algorithm from [Daan Leijen. _Division and Modulus for Computer Scientists_,
// December 2001](http://research.microsoft.com/pubs/151917/divmodnote-letter.pdf)
match self.div_rem(other) {
(d, r) if (r > 0 && *other < 0)
|| (r < 0 && *other > 0) => d - 1,
(d, _) => d,
}
}
/// Floored integer modulo
#[inline]
fn mod_floor(&self, other: &$T) -> $T {
// Algorithm from [Daan Leijen. _Division and Modulus for Computer Scientists_,
// December 2001](http://research.microsoft.com/pubs/151917/divmodnote-letter.pdf)
match *self % *other {
r if (r > 0 && *other < 0)
|| (r < 0 && *other > 0) => r + *other,
r => r,
}
}
/// Calculates `div_floor` and `mod_floor` simultaneously
#[inline]
fn div_mod_floor(&self, other: &$T) -> ($T,$T) {
// Algorithm from [Daan Leijen. _Division and Modulus for Computer Scientists_,
// December 2001](http://research.microsoft.com/pubs/151917/divmodnote-letter.pdf)
match self.div_rem(other) {
(d, r) if (r > 0 && *other < 0)
|| (r < 0 && *other > 0) => (d - 1, r + *other),
(d, r) => (d, r),
}
}
/// Calculates the Greatest Common Divisor (GCD) of the number and
/// `other`. The result is always positive.
#[inline]
fn gcd(&self, other: &$T) -> $T {
// Use Stein's algorithm
let mut m = *self;
let mut n = *other;
if m == 0 || n == 0 { return (m | n).abs() }
// find common factors of 2
let shift = (m | n).trailing_zeros();
// The algorithm needs positive numbers, but the minimum value
// can't be represented as a positive one.
// It's also a power of two, so the gcd can be
// calculated by bitshifting in that case
// Assuming two's complement, the number created by the shift
// is positive for all numbers except gcd = abs(min value)
// The call to .abs() causes a panic in debug mode
if m == <$T>::min_value() || n == <$T>::min_value() {
return (1 << shift).abs()
}
// guaranteed to be positive now, rest like unsigned algorithm
m = m.abs();
n = n.abs();
// divide n and m by 2 until odd
// m inside loop
n >>= n.trailing_zeros();
while m != 0 {
m >>= m.trailing_zeros();
if n > m { ::std::mem::swap(&mut n, &mut m) }
m -= n;
}
n << shift
}
/// Calculates the Lowest Common Multiple (LCM) of the number and
/// `other`.
#[inline]
fn lcm(&self, other: &$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);
}

3
src/lib.rs
View File

@ -58,6 +58,7 @@
html_playground_url = "http://play.rust-lang.org/")] html_playground_url = "http://play.rust-lang.org/")]
extern crate num_traits; extern crate num_traits;
extern crate num_integer;
#[cfg(feature = "rustc-serialize")] #[cfg(feature = "rustc-serialize")]
extern crate rustc_serialize; extern crate rustc_serialize;
@ -92,7 +93,7 @@ use std::ops::{Mul};
#[cfg(feature = "bigint")] #[cfg(feature = "bigint")]
pub mod bigint; pub mod bigint;
pub mod complex; pub mod complex;
pub mod integer; pub mod integer { pub use num_integer::*; }
pub mod iter; pub mod iter;
pub mod traits { pub use num_traits::*; } pub mod traits { pub use num_traits::*; }
#[cfg(feature = "rational")] #[cfg(feature = "rational")]