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Initial seeding from rust repo

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Aaron Turon 2014-09-16 10:35:35 -07:00
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/target
/Cargo.lock

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install:
- curl https://static.rust-lang.org/rustup.sh | sudo sh -
script:
- cargo build --verbose
- cargo test --verbose
env:
- LD_LIBRARY_PATH=/usr/local/lib

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[package]
name = "num"
version = "0.0.1"
authors = ["The Rust Project Developers"]
[lib]
name = "num"
plugin = true

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// Copyright 2013 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.
//! Complex numbers.
use std::fmt;
use std::num::{Zero, One, ToStrRadix};
// FIXME #1284: handle complex NaN & infinity etc. This
// probably doesn't map to C's _Complex correctly.
/// A complex number in Cartesian form.
#[deriving(PartialEq, Clone, Hash)]
pub struct Complex<T> {
/// Real portion of the complex number
pub re: T,
/// Imaginary portion of the complex number
pub im: T
}
pub type Complex32 = Complex<f32>;
pub type Complex64 = Complex<f64>;
impl<T: Clone + Num> Complex<T> {
/// Create a new Complex
#[inline]
pub fn new(re: T, im: T) -> Complex<T> {
Complex { re: re, im: im }
}
/// Returns the square of the norm (since `T` doesn't necessarily
/// have a sqrt function), i.e. `re^2 + im^2`.
#[inline]
pub fn norm_sqr(&self) -> T {
self.re * self.re + self.im * self.im
}
/// Returns the complex conjugate. i.e. `re - i im`
#[inline]
pub fn conj(&self) -> Complex<T> {
Complex::new(self.re.clone(), -self.im)
}
/// Multiplies `self` by the scalar `t`.
#[inline]
pub fn scale(&self, t: T) -> Complex<T> {
Complex::new(self.re * t, self.im * t)
}
/// Divides `self` by the scalar `t`.
#[inline]
pub fn unscale(&self, t: T) -> Complex<T> {
Complex::new(self.re / t, self.im / t)
}
/// Returns `1/self`
#[inline]
pub fn inv(&self) -> Complex<T> {
let norm_sqr = self.norm_sqr();
Complex::new(self.re / norm_sqr,
-self.im / norm_sqr)
}
}
impl<T: Clone + FloatMath> Complex<T> {
/// Calculate |self|
#[inline]
pub fn norm(&self) -> T {
self.re.hypot(self.im)
}
}
impl<T: Clone + FloatMath> Complex<T> {
/// Calculate the principal Arg of self.
#[inline]
pub fn arg(&self) -> T {
self.im.atan2(self.re)
}
/// Convert to polar form (r, theta), such that `self = r * exp(i
/// * theta)`
#[inline]
pub fn to_polar(&self) -> (T, T) {
(self.norm(), self.arg())
}
/// Convert a polar representation into a complex number.
#[inline]
pub fn from_polar(r: &T, theta: &T) -> Complex<T> {
Complex::new(*r * theta.cos(), *r * theta.sin())
}
}
/* arithmetic */
// (a + i b) + (c + i d) == (a + c) + i (b + d)
impl<T: Clone + Num> Add<Complex<T>, Complex<T>> for Complex<T> {
#[inline]
fn add(&self, other: &Complex<T>) -> Complex<T> {
Complex::new(self.re + other.re, self.im + other.im)
}
}
// (a + i b) - (c + i d) == (a - c) + i (b - d)
impl<T: Clone + Num> Sub<Complex<T>, Complex<T>> for Complex<T> {
#[inline]
fn sub(&self, other: &Complex<T>) -> Complex<T> {
Complex::new(self.re - other.re, self.im - other.im)
}
}
// (a + i b) * (c + i d) == (a*c - b*d) + i (a*d + b*c)
impl<T: Clone + Num> Mul<Complex<T>, Complex<T>> for Complex<T> {
#[inline]
fn mul(&self, other: &Complex<T>) -> Complex<T> {
Complex::new(self.re*other.re - self.im*other.im,
self.re*other.im + self.im*other.re)
}
}
// (a + i b) / (c + i d) == [(a + i b) * (c - i d)] / (c*c + d*d)
// == [(a*c + b*d) / (c*c + d*d)] + i [(b*c - a*d) / (c*c + d*d)]
impl<T: Clone + Num> Div<Complex<T>, Complex<T>> for Complex<T> {
#[inline]
fn div(&self, other: &Complex<T>) -> Complex<T> {
let norm_sqr = other.norm_sqr();
Complex::new((self.re*other.re + self.im*other.im) / norm_sqr,
(self.im*other.re - self.re*other.im) / norm_sqr)
}
}
impl<T: Clone + Num> Neg<Complex<T>> for Complex<T> {
#[inline]
fn neg(&self) -> Complex<T> {
Complex::new(-self.re, -self.im)
}
}
/* constants */
impl<T: Clone + Num> Zero for Complex<T> {
#[inline]
fn zero() -> Complex<T> {
Complex::new(Zero::zero(), Zero::zero())
}
#[inline]
fn is_zero(&self) -> bool {
self.re.is_zero() && self.im.is_zero()
}
}
impl<T: Clone + Num> One for Complex<T> {
#[inline]
fn one() -> Complex<T> {
Complex::new(One::one(), Zero::zero())
}
}
/* string conversions */
impl<T: fmt::Show + Num + PartialOrd> fmt::Show for Complex<T> {
fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
if self.im < Zero::zero() {
write!(f, "{}-{}i", self.re, -self.im)
} else {
write!(f, "{}+{}i", self.re, self.im)
}
}
}
impl<T: ToStrRadix + Num + PartialOrd> ToStrRadix for Complex<T> {
fn to_str_radix(&self, radix: uint) -> String {
if self.im < Zero::zero() {
format!("{}-{}i",
self.re.to_str_radix(radix),
(-self.im).to_str_radix(radix))
} else {
format!("{}+{}i",
self.re.to_str_radix(radix),
self.im.to_str_radix(radix))
}
}
}
#[cfg(test)]
mod test {
#![allow(non_uppercase_statics)]
use super::{Complex64, Complex};
use std::num::{Zero, One, Float};
use std::hash::hash;
pub static _0_0i : Complex64 = Complex { re: 0.0, im: 0.0 };
pub static _1_0i : Complex64 = Complex { re: 1.0, im: 0.0 };
pub static _1_1i : Complex64 = Complex { re: 1.0, im: 1.0 };
pub static _0_1i : Complex64 = Complex { re: 0.0, im: 1.0 };
pub static _neg1_1i : Complex64 = Complex { re: -1.0, im: 1.0 };
pub static _05_05i : Complex64 = Complex { re: 0.5, im: 0.5 };
pub static all_consts : [Complex64, .. 5] = [_0_0i, _1_0i, _1_1i, _neg1_1i, _05_05i];
#[test]
fn test_consts() {
// check our constants are what Complex::new creates
fn test(c : Complex64, r : f64, i: f64) {
assert_eq!(c, Complex::new(r,i));
}
test(_0_0i, 0.0, 0.0);
test(_1_0i, 1.0, 0.0);
test(_1_1i, 1.0, 1.0);
test(_neg1_1i, -1.0, 1.0);
test(_05_05i, 0.5, 0.5);
assert_eq!(_0_0i, Zero::zero());
assert_eq!(_1_0i, One::one());
}
#[test]
#[ignore(cfg(target_arch = "x86"))]
// FIXME #7158: (maybe?) currently failing on x86.
fn test_norm() {
fn test(c: Complex64, ns: f64) {
assert_eq!(c.norm_sqr(), ns);
assert_eq!(c.norm(), ns.sqrt())
}
test(_0_0i, 0.0);
test(_1_0i, 1.0);
test(_1_1i, 2.0);
test(_neg1_1i, 2.0);
test(_05_05i, 0.5);
}
#[test]
fn test_scale_unscale() {
assert_eq!(_05_05i.scale(2.0), _1_1i);
assert_eq!(_1_1i.unscale(2.0), _05_05i);
for &c in all_consts.iter() {
assert_eq!(c.scale(2.0).unscale(2.0), c);
}
}
#[test]
fn test_conj() {
for &c in all_consts.iter() {
assert_eq!(c.conj(), Complex::new(c.re, -c.im));
assert_eq!(c.conj().conj(), c);
}
}
#[test]
fn test_inv() {
assert_eq!(_1_1i.inv(), _05_05i.conj());
assert_eq!(_1_0i.inv(), _1_0i.inv());
}
#[test]
#[should_fail]
fn test_divide_by_zero_natural() {
let n = Complex::new(2i, 3i);
let d = Complex::new(0, 0);
let _x = n / d;
}
#[test]
#[should_fail]
#[ignore]
fn test_inv_zero() {
// FIXME #5736: should this really fail, or just NaN?
_0_0i.inv();
}
#[test]
fn test_arg() {
fn test(c: Complex64, arg: f64) {
assert!((c.arg() - arg).abs() < 1.0e-6)
}
test(_1_0i, 0.0);
test(_1_1i, 0.25 * Float::pi());
test(_neg1_1i, 0.75 * Float::pi());
test(_05_05i, 0.25 * Float::pi());
}
#[test]
fn test_polar_conv() {
fn test(c: Complex64) {
let (r, theta) = c.to_polar();
assert!((c - Complex::from_polar(&r, &theta)).norm() < 1e-6);
}
for &c in all_consts.iter() { test(c); }
}
mod arith {
use super::{_0_0i, _1_0i, _1_1i, _0_1i, _neg1_1i, _05_05i, all_consts};
use std::num::Zero;
#[test]
fn test_add() {
assert_eq!(_05_05i + _05_05i, _1_1i);
assert_eq!(_0_1i + _1_0i, _1_1i);
assert_eq!(_1_0i + _neg1_1i, _0_1i);
for &c in all_consts.iter() {
assert_eq!(_0_0i + c, c);
assert_eq!(c + _0_0i, c);
}
}
#[test]
fn test_sub() {
assert_eq!(_05_05i - _05_05i, _0_0i);
assert_eq!(_0_1i - _1_0i, _neg1_1i);
assert_eq!(_0_1i - _neg1_1i, _1_0i);
for &c in all_consts.iter() {
assert_eq!(c - _0_0i, c);
assert_eq!(c - c, _0_0i);
}
}
#[test]
fn test_mul() {
assert_eq!(_05_05i * _05_05i, _0_1i.unscale(2.0));
assert_eq!(_1_1i * _0_1i, _neg1_1i);
// i^2 & i^4
assert_eq!(_0_1i * _0_1i, -_1_0i);
assert_eq!(_0_1i * _0_1i * _0_1i * _0_1i, _1_0i);
for &c in all_consts.iter() {
assert_eq!(c * _1_0i, c);
assert_eq!(_1_0i * c, c);
}
}
#[test]
fn test_div() {
assert_eq!(_neg1_1i / _0_1i, _1_1i);
for &c in all_consts.iter() {
if c != Zero::zero() {
assert_eq!(c / c, _1_0i);
}
}
}
#[test]
fn test_neg() {
assert_eq!(-_1_0i + _0_1i, _neg1_1i);
assert_eq!((-_0_1i) * _0_1i, _1_0i);
for &c in all_consts.iter() {
assert_eq!(-(-c), c);
}
}
}
#[test]
fn test_to_string() {
fn test(c : Complex64, s: String) {
assert_eq!(c.to_string(), s);
}
test(_0_0i, "0+0i".to_string());
test(_1_0i, "1+0i".to_string());
test(_0_1i, "0+1i".to_string());
test(_1_1i, "1+1i".to_string());
test(_neg1_1i, "-1+1i".to_string());
test(-_neg1_1i, "1-1i".to_string());
test(_05_05i, "0.5+0.5i".to_string());
}
#[test]
fn test_hash() {
let a = Complex::new(0i32, 0i32);
let b = Complex::new(1i32, 0i32);
let c = Complex::new(0i32, 1i32);
assert!(hash(&a) != hash(&b));
assert!(hash(&b) != hash(&c));
assert!(hash(&c) != hash(&a));
}
}

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// 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.
pub trait Integer: Num + PartialOrd
+ Div<Self, Self>
+ Rem<Self, Self> {
/// Floored integer division.
///
/// # Examples
///
/// ~~~
/// # use num::Integer;
/// assert!(( 8i).div_floor(& 3) == 2);
/// assert!(( 8i).div_floor(&-3) == -3);
/// assert!((-8i).div_floor(& 3) == -3);
/// assert!((-8i).div_floor(&-3) == 2);
///
/// assert!(( 1i).div_floor(& 2) == 0);
/// assert!(( 1i).div_floor(&-2) == -1);
/// assert!((-1i).div_floor(& 2) == -1);
/// assert!((-1i).div_floor(&-2) == 0);
/// ~~~
fn div_floor(&self, other: &Self) -> Self;
/// Floored integer modulo, satisfying:
///
/// ~~~
/// # use num::Integer;
/// # let n = 1i; let d = 1i;
/// assert!(n.div_floor(&d) * d + n.mod_floor(&d) == n)
/// ~~~
///
/// # Examples
///
/// ~~~
/// # use num::Integer;
/// assert!(( 8i).mod_floor(& 3) == 2);
/// assert!(( 8i).mod_floor(&-3) == -1);
/// assert!((-8i).mod_floor(& 3) == 1);
/// assert!((-8i).mod_floor(&-3) == -2);
///
/// assert!(( 1i).mod_floor(& 2) == 1);
/// assert!(( 1i).mod_floor(&-2) == -1);
/// assert!((-1i).mod_floor(& 2) == 1);
/// assert!((-1i).mod_floor(&-2) == -1);
/// ~~~
fn mod_floor(&self, other: &Self) -> Self;
/// Greatest Common Divisor (GCD).
///
/// # Examples
///
/// ~~~
/// # use num::Integer;
/// assert_eq!(6i.gcd(&8), 2);
/// assert_eq!(7i.gcd(&3), 1);
/// ~~~
fn gcd(&self, other: &Self) -> Self;
/// Lowest Common Multiple (LCM).
///
/// # Examples
///
/// ~~~
/// # use num::Integer;
/// assert_eq!(7i.lcm(&3), 21);
/// assert_eq!(2i.lcm(&4), 4);
/// ~~~
fn lcm(&self, other: &Self) -> Self;
/// Deprecated, use `is_multiple_of` instead.
#[deprecated = "function renamed to `is_multiple_of`"]
fn divides(&self, other: &Self) -> bool;
/// Returns `true` if `other` is a multiple of `self`.
///
/// # Examples
///
/// ~~~
/// # use num::Integer;
/// assert_eq!(9i.is_multiple_of(&3), true);
/// assert_eq!(3i.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!(3i.is_even(), false);
/// assert_eq!(4i.is_even(), true);
/// ~~~
fn is_even(&self) -> bool;
/// Returns `true` if the number is odd.
///
/// # Examples
///
/// ~~~
/// # use num::Integer;
/// assert_eq!(3i.is_odd(), true);
/// assert_eq!(4i.is_odd(), false);
/// ~~~
fn is_odd(&self) -> bool;
/// Simultaneous truncated integer division and modulus.
/// Returns `(quotient, remainder)`.
///
/// # Examples
///
/// ~~~
/// # use num::Integer;
/// assert_eq!(( 8i).div_rem( &3), ( 2, 2));
/// assert_eq!(( 8i).div_rem(&-3), (-2, 2));
/// assert_eq!((-8i).div_rem( &3), (-2, -2));
/// assert_eq!((-8i).div_rem(&-3), ( 2, -2));
///
/// assert_eq!(( 1i).div_rem( &2), ( 0, 1));
/// assert_eq!(( 1i).div_rem(&-2), ( 0, 1));
/// assert_eq!((-1i).div_rem( &2), ( 0, -1));
/// assert_eq!((-1i).div_rem(&-2), ( 0, -1));
/// ~~~
#[inline]
fn div_rem(&self, other: &Self) -> (Self, Self) {
(*self / *other, *self % *other)
}
/// Simultaneous floored integer division and modulus.
/// Returns `(quotient, remainder)`.
///
/// # Examples
///
/// ~~~
/// # use num::Integer;
/// assert_eq!(( 8i).div_mod_floor( &3), ( 2, 2));
/// assert_eq!(( 8i).div_mod_floor(&-3), (-3, -1));
/// assert_eq!((-8i).div_mod_floor( &3), (-3, 1));
/// assert_eq!((-8i).div_mod_floor(&-3), ( 2, -2));
///
/// assert_eq!(( 1i).div_mod_floor( &2), ( 0, 1));
/// assert_eq!(( 1i).div_mod_floor(&-2), (-1, -1));
/// assert_eq!((-1i).div_mod_floor( &2), (-1, 1));
/// assert_eq!((-1i).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_int {
($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) -> $T {
// Use Euclid's algorithm
let mut m = *self;
let mut n = *other;
while m != 0 {
let temp = m;
m = n % temp;
n = temp;
}
n.abs()
}
/// Calculates the Lowest Common Multiple (LCM) of the number and
/// `other`.
#[inline]
fn lcm(&self, other: &$T) -> $T {
// should not have to recalculate abs
((*self * *other) / self.gcd(other)).abs()
}
/// Deprecated, use `is_multiple_of` instead.
#[deprecated = "function renamed to `is_multiple_of`"]
#[inline]
fn divides(&self, other: &$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() }
}
#[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_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 $T).is_odd(), false);
}
}
)
}
impl_integer_for_int!(i8, test_integer_i8)
impl_integer_for_int!(i16, test_integer_i16)
impl_integer_for_int!(i32, test_integer_i32)
impl_integer_for_int!(i64, test_integer_i64)
impl_integer_for_int!(int, test_integer_int)
macro_rules! impl_integer_for_uint {
($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) -> $T {
// Use Euclid's algorithm
let mut m = *self;
let mut n = *other;
while m != 0 {
let temp = m;
m = n % temp;
n = temp;
}
n
}
/// Calculates the Lowest Common Multiple (LCM) of the number and `other`.
#[inline]
fn lcm(&self, other: &$T) -> $T {
(*self * *other) / self.gcd(other)
}
/// Deprecated, use `is_multiple_of` instead.
#[deprecated = "function renamed to `is_multiple_of`"]
#[inline]
fn divides(&self, other: &$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() }
}
#[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_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!((99 as $T).lcm(&17), 1683 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_uint!(u8, test_integer_u8)
impl_integer_for_uint!(u16, test_integer_u16)
impl_integer_for_uint!(u32, test_integer_u32)
impl_integer_for_uint!(u64, test_integer_u64)
impl_integer_for_uint!(uint, test_integer_uint)

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// Copyright 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.
//! Simple numerics.
//!
//! This crate contains arbitrary-sized integer, rational, and complex types.
//!
//! ## Example
//!
//! This example uses the BigRational type and [Newton's method][newt] to
//! approximate a square root to arbitrary precision:
//!
//! ```
//! extern crate num;
//!
//! use num::bigint::BigInt;
//! use num::rational::{Ratio, BigRational};
//!
//! fn approx_sqrt(number: u64, iterations: uint) -> BigRational {
//! let start: Ratio<BigInt> = Ratio::from_integer(FromPrimitive::from_u64(number).unwrap());
//! let mut approx = start.clone();
//!
//! for _ in range(0, iterations) {
//! approx = (approx + (start / approx)) /
//! Ratio::from_integer(FromPrimitive::from_u64(2).unwrap());
//! }
//!
//! approx
//! }
//!
//! fn main() {
//! println!("{}", approx_sqrt(10, 4)); // prints 4057691201/1283082416
//! }
//! ```
//!
//! [newt]: https://en.wikipedia.org/wiki/Methods_of_computing_square_roots#Babylonian_method
#![feature(macro_rules)]
#![feature(default_type_params)]
#![crate_name = "num"]
#![experimental]
#![crate_type = "rlib"]
#![crate_type = "dylib"]
#![license = "MIT/ASL2"]
#![doc(html_logo_url = "http://www.rust-lang.org/logos/rust-logo-128x128-blk-v2.png",
html_favicon_url = "http://www.rust-lang.org/favicon.ico",
html_root_url = "http://doc.rust-lang.org/master/",
html_playground_url = "http://play.rust-lang.org/")]
#![allow(deprecated)] // from_str_radix
extern crate rand;
pub use bigint::{BigInt, BigUint};
pub use rational::{Rational, BigRational};
pub use complex::Complex;
pub use integer::Integer;
pub mod bigint;
pub mod complex;
pub mod integer;
pub mod rational;

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// 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.
//! Rational numbers
use Integer;
use std::cmp;
use std::fmt;
use std::from_str::FromStr;
use std::num;
use std::num::{Zero, One, ToStrRadix, FromStrRadix};
use bigint::{BigInt, BigUint, Sign, Plus, Minus};
/// Represents the ratio between 2 numbers.
#[deriving(Clone, Hash)]
#[allow(missing_doc)]
pub struct Ratio<T> {
numer: T,
denom: T
}
/// Alias for a `Ratio` of machine-sized integers.
pub type Rational = Ratio<int>;
pub type Rational32 = Ratio<i32>;
pub type Rational64 = Ratio<i64>;
/// Alias for arbitrary precision rationals.
pub type BigRational = Ratio<BigInt>;
impl<T: Clone + Integer + PartialOrd>
Ratio<T> {
/// Creates a ratio representing the integer `t`.
#[inline]
pub fn from_integer(t: T) -> Ratio<T> {
Ratio::new_raw(t, One::one())
}
/// Creates a ratio without checking for `denom == 0` or reducing.
#[inline]
pub fn new_raw(numer: T, denom: T) -> Ratio<T> {
Ratio { numer: numer, denom: denom }
}
/// Create a new Ratio. Fails if `denom == 0`.
#[inline]
pub fn new(numer: T, denom: T) -> Ratio<T> {
if denom == Zero::zero() {
fail!("denominator == 0");
}
let mut ret = Ratio::new_raw(numer, denom);
ret.reduce();
ret
}
/// Converts to an integer.
#[inline]
pub fn to_integer(&self) -> T {
self.trunc().numer
}
/// Gets an immutable reference to the numerator.
#[inline]
pub fn numer<'a>(&'a self) -> &'a T {
&self.numer
}
/// Gets an immutable reference to the denominator.
#[inline]
pub fn denom<'a>(&'a self) -> &'a T {
&self.denom
}
/// Returns true if the rational number is an integer (denominator is 1).
#[inline]
pub fn is_integer(&self) -> bool {
self.denom == One::one()
}
/// Put self into lowest terms, with denom > 0.
fn reduce(&mut self) {
let g : T = self.numer.gcd(&self.denom);
// FIXME(#5992): assignment operator overloads
// self.numer /= g;
self.numer = self.numer / g;
// FIXME(#5992): assignment operator overloads
// self.denom /= g;
self.denom = self.denom / g;
// keep denom positive!
if self.denom < Zero::zero() {
self.numer = -self.numer;
self.denom = -self.denom;
}
}
/// Returns a `reduce`d copy of self.
pub fn reduced(&self) -> Ratio<T> {
let mut ret = self.clone();
ret.reduce();
ret
}
/// Returns the reciprocal.
#[inline]
pub fn recip(&self) -> Ratio<T> {
Ratio::new_raw(self.denom.clone(), self.numer.clone())
}
/// Rounds towards minus infinity.
#[inline]
pub fn floor(&self) -> Ratio<T> {
if *self < Zero::zero() {
Ratio::from_integer((self.numer - self.denom + One::one()) / self.denom)
} else {
Ratio::from_integer(self.numer / self.denom)
}
}
/// Rounds towards plus infinity.
#[inline]
pub fn ceil(&self) -> Ratio<T> {
if *self < Zero::zero() {
Ratio::from_integer(self.numer / self.denom)
} else {
Ratio::from_integer((self.numer + self.denom - One::one()) / self.denom)
}
}
/// Rounds to the nearest integer. Rounds half-way cases away from zero.
#[inline]
pub fn round(&self) -> Ratio<T> {
if *self < Zero::zero() {
// a/b - 1/2 = (2*a - b)/(2*b)
Ratio::from_integer((self.numer + self.numer - self.denom) / (self.denom + self.denom))
} else {
// a/b + 1/2 = (2*a + b)/(2*b)
Ratio::from_integer((self.numer + self.numer + self.denom) / (self.denom + self.denom))
}
}
/// Rounds towards zero.
#[inline]
pub fn trunc(&self) -> Ratio<T> {
Ratio::from_integer(self.numer / self.denom)
}
/// Returns the fractional part of a number.
#[inline]
pub fn fract(&self) -> Ratio<T> {
Ratio::new_raw(self.numer % self.denom, self.denom.clone())
}
}
impl Ratio<BigInt> {
/// Converts a float into a rational number.
pub fn from_float<T: Float>(f: T) -> Option<BigRational> {
if !f.is_finite() {
return None;
}
let (mantissa, exponent, sign) = f.integer_decode();
let bigint_sign: Sign = if sign == 1 { Plus } else { Minus };
if exponent < 0 {
let one: BigInt = One::one();
let denom: BigInt = one << ((-exponent) as uint);
let numer: BigUint = FromPrimitive::from_u64(mantissa).unwrap();
Some(Ratio::new(BigInt::from_biguint(bigint_sign, numer), denom))
} else {
let mut numer: BigUint = FromPrimitive::from_u64(mantissa).unwrap();
numer = numer << (exponent as uint);
Some(Ratio::from_integer(BigInt::from_biguint(bigint_sign, numer)))
}
}
}
/* Comparisons */
// comparing a/b and c/d is the same as comparing a*d and b*c, so we
// abstract that pattern. The following macro takes a trait and either
// a comma-separated list of "method name -> return value" or just
// "method name" (return value is bool in that case)
macro_rules! cmp_impl {
(impl $imp:ident, $($method:ident),+) => {
cmp_impl!(impl $imp, $($method -> bool),+)
};
// return something other than a Ratio<T>
(impl $imp:ident, $($method:ident -> $res:ty),*) => {
impl<T: Mul<T,T> + $imp> $imp for Ratio<T> {
$(
#[inline]
fn $method(&self, other: &Ratio<T>) -> $res {
(self.numer * other.denom). $method (&(self.denom*other.numer))
}
)*
}
};
}
cmp_impl!(impl PartialEq, eq, ne)
cmp_impl!(impl PartialOrd, lt -> bool, gt -> bool, le -> bool, ge -> bool,
partial_cmp -> Option<cmp::Ordering>)
cmp_impl!(impl Eq, )
cmp_impl!(impl Ord, cmp -> cmp::Ordering)
/* Arithmetic */
// a/b * c/d = (a*c)/(b*d)
impl<T: Clone + Integer + PartialOrd>
Mul<Ratio<T>,Ratio<T>> for Ratio<T> {
#[inline]
fn mul(&self, rhs: &Ratio<T>) -> Ratio<T> {
Ratio::new(self.numer * rhs.numer, self.denom * rhs.denom)
}
}
// (a/b) / (c/d) = (a*d)/(b*c)
impl<T: Clone + Integer + PartialOrd>
Div<Ratio<T>,Ratio<T>> for Ratio<T> {
#[inline]
fn div(&self, rhs: &Ratio<T>) -> Ratio<T> {
Ratio::new(self.numer * rhs.denom, self.denom * rhs.numer)
}
}
// Abstracts the a/b `op` c/d = (a*d `op` b*d) / (b*d) pattern
macro_rules! arith_impl {
(impl $imp:ident, $method:ident) => {
impl<T: Clone + Integer + PartialOrd>
$imp<Ratio<T>,Ratio<T>> for Ratio<T> {
#[inline]
fn $method(&self, rhs: &Ratio<T>) -> Ratio<T> {
Ratio::new((self.numer * rhs.denom).$method(&(self.denom * rhs.numer)),
self.denom * rhs.denom)
}
}
}
}
// a/b + c/d = (a*d + b*c)/(b*d)
arith_impl!(impl Add, add)
// a/b - c/d = (a*d - b*c)/(b*d)
arith_impl!(impl Sub, sub)
// a/b % c/d = (a*d % b*c)/(b*d)
arith_impl!(impl Rem, rem)
impl<T: Clone + Integer + PartialOrd>
Neg<Ratio<T>> for Ratio<T> {
#[inline]
fn neg(&self) -> Ratio<T> {
Ratio::new_raw(-self.numer, self.denom.clone())
}
}
/* Constants */
impl<T: Clone + Integer + PartialOrd>
Zero for Ratio<T> {
#[inline]
fn zero() -> Ratio<T> {
Ratio::new_raw(Zero::zero(), One::one())
}
#[inline]
fn is_zero(&self) -> bool {
*self == Zero::zero()
}
}
impl<T: Clone + Integer + PartialOrd>
One for Ratio<T> {
#[inline]
fn one() -> Ratio<T> {
Ratio::new_raw(One::one(), One::one())
}
}
impl<T: Clone + Integer + PartialOrd>
Num for Ratio<T> {}
impl<T: Clone + Integer + PartialOrd>
num::Signed for Ratio<T> {
#[inline]
fn abs(&self) -> Ratio<T> {
if self.is_negative() { -self.clone() } else { self.clone() }
}
#[inline]
fn abs_sub(&self, other: &Ratio<T>) -> Ratio<T> {
if *self <= *other { Zero::zero() } else { *self - *other }
}
#[inline]
fn signum(&self) -> Ratio<T> {
if *self > Zero::zero() {
num::one()
} else if self.is_zero() {
num::zero()
} else {
- num::one::<Ratio<T>>()
}
}
#[inline]
fn is_positive(&self) -> bool { *self > Zero::zero() }
#[inline]
fn is_negative(&self) -> bool { *self < Zero::zero() }
}
/* String conversions */
impl<T: fmt::Show + Eq + One> fmt::Show for Ratio<T> {
/// Renders as `numer/denom`. If denom=1, renders as numer.
fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
if self.denom == One::one() {
write!(f, "{}", self.numer)
} else {
write!(f, "{}/{}", self.numer, self.denom)
}
}
}
impl<T: ToStrRadix> ToStrRadix for Ratio<T> {
/// Renders as `numer/denom` where the numbers are in base `radix`.
fn to_str_radix(&self, radix: uint) -> String {
format!("{}/{}",
self.numer.to_str_radix(radix),
self.denom.to_str_radix(radix))
}
}
impl<T: FromStr + Clone + Integer + PartialOrd>
FromStr for Ratio<T> {
/// Parses `numer/denom` or just `numer`.
fn from_str(s: &str) -> Option<Ratio<T>> {
let mut split = s.splitn(1, '/');
let num = split.next().and_then(|n| FromStr::from_str(n));
let den = split.next().or(Some("1")).and_then(|d| FromStr::from_str(d));
match (num, den) {
(Some(n), Some(d)) => Some(Ratio::new(n, d)),
_ => None
}
}
}
impl<T: FromStrRadix + Clone + Integer + PartialOrd>
FromStrRadix for Ratio<T> {
/// Parses `numer/denom` where the numbers are in base `radix`.
fn from_str_radix(s: &str, radix: uint) -> Option<Ratio<T>> {
let split: Vec<&str> = s.splitn(1, '/').collect();
if split.len() < 2 {
None
} else {
let a_option: Option<T> = FromStrRadix::from_str_radix(
*split.get(0),
radix);
a_option.and_then(|a| {
let b_option: Option<T> =
FromStrRadix::from_str_radix(*split.get(1), radix);
b_option.and_then(|b| {
Some(Ratio::new(a.clone(), b.clone()))
})
})
}
}
}
#[cfg(test)]
mod test {
use super::{Ratio, Rational, BigRational};
use std::num::{Zero, One, FromStrRadix, FromPrimitive, ToStrRadix};
use std::from_str::FromStr;
use std::hash::hash;
use std::num;
pub static _0 : Rational = Ratio { numer: 0, denom: 1};
pub static _1 : Rational = Ratio { numer: 1, denom: 1};
pub static _2: Rational = Ratio { numer: 2, denom: 1};
pub static _1_2: Rational = Ratio { numer: 1, denom: 2};
pub static _3_2: Rational = Ratio { numer: 3, denom: 2};
pub static _neg1_2: Rational = Ratio { numer: -1, denom: 2};
pub static _1_3: Rational = Ratio { numer: 1, denom: 3};
pub static _neg1_3: Rational = Ratio { numer: -1, denom: 3};
pub static _2_3: Rational = Ratio { numer: 2, denom: 3};
pub static _neg2_3: Rational = Ratio { numer: -2, denom: 3};
pub fn to_big(n: Rational) -> BigRational {
Ratio::new(
FromPrimitive::from_int(n.numer).unwrap(),
FromPrimitive::from_int(n.denom).unwrap()
)
}
#[test]
fn test_test_constants() {
// check our constants are what Ratio::new etc. would make.
assert_eq!(_0, Zero::zero());
assert_eq!(_1, One::one());
assert_eq!(_2, Ratio::from_integer(2i));
assert_eq!(_1_2, Ratio::new(1i,2i));
assert_eq!(_3_2, Ratio::new(3i,2i));
assert_eq!(_neg1_2, Ratio::new(-1i,2i));
}
#[test]
fn test_new_reduce() {
let one22 = Ratio::new(2i,2);
assert_eq!(one22, One::one());
}
#[test]
#[should_fail]
fn test_new_zero() {
let _a = Ratio::new(1i,0);
}
#[test]
fn test_cmp() {
assert!(_0 == _0 && _1 == _1);
assert!(_0 != _1 && _1 != _0);
assert!(_0 < _1 && !(_1 < _0));
assert!(_1 > _0 && !(_0 > _1));
assert!(_0 <= _0 && _1 <= _1);
assert!(_0 <= _1 && !(_1 <= _0));
assert!(_0 >= _0 && _1 >= _1);
assert!(_1 >= _0 && !(_0 >= _1));
}
#[test]
fn test_to_integer() {
assert_eq!(_0.to_integer(), 0);
assert_eq!(_1.to_integer(), 1);
assert_eq!(_2.to_integer(), 2);
assert_eq!(_1_2.to_integer(), 0);
assert_eq!(_3_2.to_integer(), 1);
assert_eq!(_neg1_2.to_integer(), 0);
}
#[test]
fn test_numer() {
assert_eq!(_0.numer(), &0);
assert_eq!(_1.numer(), &1);
assert_eq!(_2.numer(), &2);
assert_eq!(_1_2.numer(), &1);
assert_eq!(_3_2.numer(), &3);
assert_eq!(_neg1_2.numer(), &(-1));
}
#[test]
fn test_denom() {
assert_eq!(_0.denom(), &1);
assert_eq!(_1.denom(), &1);
assert_eq!(_2.denom(), &1);
assert_eq!(_1_2.denom(), &2);
assert_eq!(_3_2.denom(), &2);
assert_eq!(_neg1_2.denom(), &2);
}
#[test]
fn test_is_integer() {
assert!(_0.is_integer());
assert!(_1.is_integer());
assert!(_2.is_integer());
assert!(!_1_2.is_integer());
assert!(!_3_2.is_integer());
assert!(!_neg1_2.is_integer());
}
#[test]
fn test_show() {
assert_eq!(format!("{}", _2), "2".to_string());
assert_eq!(format!("{}", _1_2), "1/2".to_string());
assert_eq!(format!("{}", _0), "0".to_string());
assert_eq!(format!("{}", Ratio::from_integer(-2i)), "-2".to_string());
}
mod arith {
use super::{_0, _1, _2, _1_2, _3_2, _neg1_2, to_big};
use super::super::{Ratio, Rational};
#[test]
fn test_add() {
fn test(a: Rational, b: Rational, c: Rational) {
assert_eq!(a + b, c);
assert_eq!(to_big(a) + to_big(b), to_big(c));
}
test(_1, _1_2, _3_2);
test(_1, _1, _2);
test(_1_2, _3_2, _2);
test(_1_2, _neg1_2, _0);
}
#[test]
fn test_sub() {
fn test(a: Rational, b: Rational, c: Rational) {
assert_eq!(a - b, c);
assert_eq!(to_big(a) - to_big(b), to_big(c))
}
test(_1, _1_2, _1_2);
test(_3_2, _1_2, _1);
test(_1, _neg1_2, _3_2);
}
#[test]
fn test_mul() {
fn test(a: Rational, b: Rational, c: Rational) {
assert_eq!(a * b, c);
assert_eq!(to_big(a) * to_big(b), to_big(c))
}
test(_1, _1_2, _1_2);
test(_1_2, _3_2, Ratio::new(3i,4i));
test(_1_2, _neg1_2, Ratio::new(-1i, 4i));
}
#[test]
fn test_div() {
fn test(a: Rational, b: Rational, c: Rational) {
assert_eq!(a / b, c);
assert_eq!(to_big(a) / to_big(b), to_big(c))
}
test(_1, _1_2, _2);
test(_3_2, _1_2, _1 + _2);
test(_1, _neg1_2, _neg1_2 + _neg1_2 + _neg1_2 + _neg1_2);
}
#[test]
fn test_rem() {
fn test(a: Rational, b: Rational, c: Rational) {
assert_eq!(a % b, c);
assert_eq!(to_big(a) % to_big(b), to_big(c))
}
test(_3_2, _1, _1_2);
test(_2, _neg1_2, _0);
test(_1_2, _2, _1_2);
}
#[test]
fn test_neg() {
fn test(a: Rational, b: Rational) {
assert_eq!(-a, b);
assert_eq!(-to_big(a), to_big(b))
}
test(_0, _0);
test(_1_2, _neg1_2);
test(-_1, _1);
}
#[test]
fn test_zero() {
assert_eq!(_0 + _0, _0);
assert_eq!(_0 * _0, _0);
assert_eq!(_0 * _1, _0);
assert_eq!(_0 / _neg1_2, _0);
assert_eq!(_0 - _0, _0);
}
#[test]
#[should_fail]
fn test_div_0() {
let _a = _1 / _0;
}
}
#[test]
fn test_round() {
assert_eq!(_1_3.ceil(), _1);
assert_eq!(_1_3.floor(), _0);
assert_eq!(_1_3.round(), _0);
assert_eq!(_1_3.trunc(), _0);
assert_eq!(_neg1_3.ceil(), _0);
assert_eq!(_neg1_3.floor(), -_1);
assert_eq!(_neg1_3.round(), _0);
assert_eq!(_neg1_3.trunc(), _0);
assert_eq!(_2_3.ceil(), _1);
assert_eq!(_2_3.floor(), _0);
assert_eq!(_2_3.round(), _1);
assert_eq!(_2_3.trunc(), _0);
assert_eq!(_neg2_3.ceil(), _0);
assert_eq!(_neg2_3.floor(), -_1);
assert_eq!(_neg2_3.round(), -_1);
assert_eq!(_neg2_3.trunc(), _0);
assert_eq!(_1_2.ceil(), _1);
assert_eq!(_1_2.floor(), _0);
assert_eq!(_1_2.round(), _1);
assert_eq!(_1_2.trunc(), _0);
assert_eq!(_neg1_2.ceil(), _0);
assert_eq!(_neg1_2.floor(), -_1);
assert_eq!(_neg1_2.round(), -_1);
assert_eq!(_neg1_2.trunc(), _0);
assert_eq!(_1.ceil(), _1);
assert_eq!(_1.floor(), _1);
assert_eq!(_1.round(), _1);
assert_eq!(_1.trunc(), _1);
}
#[test]
fn test_fract() {
assert_eq!(_1.fract(), _0);
assert_eq!(_neg1_2.fract(), _neg1_2);
assert_eq!(_1_2.fract(), _1_2);
assert_eq!(_3_2.fract(), _1_2);
}
#[test]
fn test_recip() {
assert_eq!(_1 * _1.recip(), _1);
assert_eq!(_2 * _2.recip(), _1);
assert_eq!(_1_2 * _1_2.recip(), _1);
assert_eq!(_3_2 * _3_2.recip(), _1);
assert_eq!(_neg1_2 * _neg1_2.recip(), _1);
}
#[test]
fn test_to_from_str() {
fn test(r: Rational, s: String) {
assert_eq!(FromStr::from_str(s.as_slice()), Some(r));
assert_eq!(r.to_string(), s);
}
test(_1, "1".to_string());
test(_0, "0".to_string());
test(_1_2, "1/2".to_string());
test(_3_2, "3/2".to_string());
test(_2, "2".to_string());
test(_neg1_2, "-1/2".to_string());
}
#[test]
fn test_from_str_fail() {
fn test(s: &str) {
let rational: Option<Rational> = FromStr::from_str(s);
assert_eq!(rational, None);
}
let xs = ["0 /1", "abc", "", "1/", "--1/2","3/2/1"];
for &s in xs.iter() {
test(s);
}
}
#[test]
fn test_to_from_str_radix() {
fn test(r: Rational, s: String, n: uint) {
assert_eq!(FromStrRadix::from_str_radix(s.as_slice(), n),
Some(r));
assert_eq!(r.to_str_radix(n).to_string(), s);
}
fn test3(r: Rational, s: String) { test(r, s, 3) }
fn test16(r: Rational, s: String) { test(r, s, 16) }
test3(_1, "1/1".to_string());
test3(_0, "0/1".to_string());
test3(_1_2, "1/2".to_string());
test3(_3_2, "10/2".to_string());
test3(_2, "2/1".to_string());
test3(_neg1_2, "-1/2".to_string());
test3(_neg1_2 / _2, "-1/11".to_string());
test16(_1, "1/1".to_string());
test16(_0, "0/1".to_string());
test16(_1_2, "1/2".to_string());
test16(_3_2, "3/2".to_string());
test16(_2, "2/1".to_string());
test16(_neg1_2, "-1/2".to_string());
test16(_neg1_2 / _2, "-1/4".to_string());
test16(Ratio::new(13i,15i), "d/f".to_string());
test16(_1_2*_1_2*_1_2*_1_2, "1/10".to_string());
}
#[test]
fn test_from_str_radix_fail() {
fn test(s: &str) {
let radix: Option<Rational> = FromStrRadix::from_str_radix(s, 3);
assert_eq!(radix, None);
}
let xs = ["0 /1", "abc", "", "1/", "--1/2","3/2/1", "3/2"];
for &s in xs.iter() {
test(s);
}
}
#[test]
fn test_from_float() {
fn test<T: Float>(given: T, (numer, denom): (&str, &str)) {
let ratio: BigRational = Ratio::from_float(given).unwrap();
assert_eq!(ratio, Ratio::new(
FromStr::from_str(numer).unwrap(),
FromStr::from_str(denom).unwrap()));
}
// f32
test(3.14159265359f32, ("13176795", "4194304"));
test(2f32.powf(100.), ("1267650600228229401496703205376", "1"));
test(-2f32.powf(100.), ("-1267650600228229401496703205376", "1"));
test(1.0 / 2f32.powf(100.), ("1", "1267650600228229401496703205376"));
test(684729.48391f32, ("1369459", "2"));
test(-8573.5918555f32, ("-4389679", "512"));
// f64
test(3.14159265359f64, ("3537118876014453", "1125899906842624"));
test(2f64.powf(100.), ("1267650600228229401496703205376", "1"));
test(-2f64.powf(100.), ("-1267650600228229401496703205376", "1"));
test(684729.48391f64, ("367611342500051", "536870912"));
test(-8573.5918555f64, ("-4713381968463931", "549755813888"));
test(1.0 / 2f64.powf(100.), ("1", "1267650600228229401496703205376"));
}
#[test]
fn test_from_float_fail() {
use std::{f32, f64};
assert_eq!(Ratio::from_float(f32::NAN), None);
assert_eq!(Ratio::from_float(f32::INFINITY), None);
assert_eq!(Ratio::from_float(f32::NEG_INFINITY), None);
assert_eq!(Ratio::from_float(f64::NAN), None);
assert_eq!(Ratio::from_float(f64::INFINITY), None);
assert_eq!(Ratio::from_float(f64::NEG_INFINITY), None);
}
#[test]
fn test_signed() {
assert_eq!(_neg1_2.abs(), _1_2);
assert_eq!(_3_2.abs_sub(&_1_2), _1);
assert_eq!(_1_2.abs_sub(&_3_2), Zero::zero());
assert_eq!(_1_2.signum(), One::one());
assert_eq!(_neg1_2.signum(), - num::one::<Ratio<int>>());
assert!(_neg1_2.is_negative());
assert!(! _neg1_2.is_positive());
assert!(! _1_2.is_negative());
}
#[test]
fn test_hash() {
assert!(hash(&_0) != hash(&_1));
assert!(hash(&_0) != hash(&_3_2));
}
}