diff --git a/src/libnum/bigint.rs b/src/libnum/bigint.rs index 67501c9795d..0933301970d 100644 --- a/src/libnum/bigint.rs +++ b/src/libnum/bigint.rs @@ -17,18 +17,16 @@ A `BigInt` is a combination of `BigUint` and `Sign`. */ use Integer; +use rand::Rng; -use std::cmp; +use std::{cmp, fmt}; use std::default::Default; -use std::fmt; use std::from_str::FromStr; use std::num::CheckedDiv; use std::num::{Bitwise, ToPrimitive, FromPrimitive}; use std::num::{Zero, One, ToStrRadix, FromStrRadix}; -use rand::Rng; use std::string::String; -use std::uint; -use std::{i64, u64}; +use std::{uint, i64, u64}; /** A `BigDigit` is a `BigUint`'s composing element. @@ -94,7 +92,7 @@ impl Eq for BigUint {} impl PartialOrd for BigUint { #[inline] fn lt(&self, other: &BigUint) -> bool { - match self.cmp(other) { Less => true, _ => false} + self.cmp(other) == Less } } @@ -115,7 +113,7 @@ impl Ord for BigUint { impl Default for BigUint { #[inline] - fn default() -> BigUint { BigUint::new(Vec::new()) } + fn default() -> BigUint { Zero::zero() } } impl fmt::Show for BigUint { @@ -605,7 +603,7 @@ impl_to_biguint!(u64, FromPrimitive::from_u64) impl ToStrRadix for BigUint { fn to_str_radix(&self, radix: uint) -> String { - assert!(1 < radix && radix <= 16); + assert!(1 < radix && radix <= 16, "The radix must be within (1, 16]"); let (base, max_len) = get_radix_base(radix); if base == BigDigit::base { return fill_concat(self.data.as_slice(), radix, max_len) @@ -645,8 +643,7 @@ impl ToStrRadix for BigUint { impl FromStrRadix for BigUint { /// Creates and initializes a `BigUint`. #[inline] - fn from_str_radix(s: &str, radix: uint) - -> Option { + fn from_str_radix(s: &str, radix: uint) -> Option { BigUint::parse_bytes(s.as_bytes(), radix) } } @@ -656,14 +653,11 @@ impl BigUint { /// /// The digits are be in base 2^32. #[inline] - pub fn new(v: Vec) -> BigUint { + pub fn new(mut digits: Vec) -> BigUint { // omit trailing zeros - let new_len = v.iter().rposition(|n| *n != 0).map_or(0, |p| p + 1); - - if new_len == v.len() { return BigUint { data: v }; } - let mut v = v; - v.truncate(new_len); - return BigUint { data: v }; + let new_len = digits.iter().rposition(|n| *n != 0).map_or(0, |p| p + 1); + digits.truncate(new_len); + BigUint { data: digits } } /// Creates and initializes a `BigUint`. @@ -671,7 +665,7 @@ impl BigUint { /// The digits are be in base 2^32. #[inline] pub fn from_slice(slice: &[BigDigit]) -> BigUint { - return BigUint::new(Vec::from_slice(slice)); + BigUint::new(Vec::from_slice(slice)) } /// Creates and initializes a `BigUint`. @@ -768,7 +762,6 @@ impl BigUint { // `DoubleBigDigit` size dependent #[inline] fn get_radix_base(radix: uint) -> (DoubleBigDigit, uint) { - assert!(1 < radix && radix <= 16); match radix { 2 => (4294967296, 32), 3 => (3486784401, 20), @@ -785,7 +778,7 @@ fn get_radix_base(radix: uint) -> (DoubleBigDigit, uint) { 14 => (1475789056, 8), 15 => (2562890625, 8), 16 => (4294967296, 8), - _ => fail!() + _ => fail!("The radix must be within (1, 16]") } } @@ -815,7 +808,7 @@ pub struct BigInt { impl PartialEq for BigInt { #[inline] fn eq(&self, other: &BigInt) -> bool { - match self.cmp(other) { Equal => true, _ => false } + self.cmp(other) == Equal } } @@ -824,7 +817,7 @@ impl Eq for BigInt {} impl PartialOrd for BigInt { #[inline] fn lt(&self, other: &BigInt) -> bool { - match self.cmp(other) { Less => true, _ => false} + self.cmp(other) == Less } } @@ -844,7 +837,7 @@ impl Ord for BigInt { impl Default for BigInt { #[inline] - fn default() -> BigInt { BigInt::new(Zero, Vec::new()) } + fn default() -> BigInt { Zero::zero() } } impl fmt::Show for BigInt { @@ -929,8 +922,7 @@ impl Add for BigInt { match (self.sign, other.sign) { (Zero, _) => other.clone(), (_, Zero) => self.clone(), - (Plus, Plus) => BigInt::from_biguint(Plus, - self.data + other.data), + (Plus, Plus) => BigInt::from_biguint(Plus, self.data + other.data), (Plus, Minus) => self - (-*other), (Minus, Plus) => other - (-*self), (Minus, Minus) => -((-self) + (-*other)) @@ -975,7 +967,7 @@ impl Div for BigInt { #[inline] fn div(&self, other: &BigInt) -> BigInt { let (q, _) = self.div_rem(other); - return q; + q } } @@ -983,7 +975,7 @@ impl Rem for BigInt { #[inline] fn rem(&self, other: &BigInt) -> BigInt { let (_, r) = self.div_rem(other); - return r; + r } } @@ -1045,13 +1037,13 @@ impl Integer for BigInt { #[inline] fn div_floor(&self, other: &BigInt) -> BigInt { let (d, _) = self.div_mod_floor(other); - return d; + d } #[inline] fn mod_floor(&self, other: &BigInt) -> BigInt { let (_, m) = self.div_mod_floor(other); - return m; + m } fn div_mod_floor(&self, other: &BigInt) -> (BigInt, BigInt) { @@ -1265,7 +1257,7 @@ impl RandBigInt for R { let final_digit: BigDigit = self.gen(); data.push(final_digit >> (BigDigit::bits - rem)); } - return BigUint::new(data); + BigUint::new(data) } fn gen_bigint(&mut self, bit_size: uint) -> BigInt { @@ -1287,7 +1279,7 @@ impl RandBigInt for R { } else { Minus }; - return BigInt::from_biguint(sign, biguint); + BigInt::from_biguint(sign, biguint) } fn gen_biguint_below(&mut self, bound: &BigUint) -> BigUint { @@ -1322,8 +1314,8 @@ impl BigInt { /// /// The digits are be in base 2^32. #[inline] - pub fn new(sign: Sign, v: Vec) -> BigInt { - BigInt::from_biguint(sign, BigUint::new(v)) + pub fn new(sign: Sign, digits: Vec) -> BigInt { + BigInt::from_biguint(sign, BigUint::new(digits)) } /// Creates and initializes a `BigInt`. @@ -1334,7 +1326,7 @@ impl BigInt { if sign == Zero || data.is_zero() { return BigInt { sign: Zero, data: Zero::zero() }; } - return BigInt { sign: sign, data: data }; + BigInt { sign: sign, data: data } } /// Creates and initializes a `BigInt`. @@ -1344,8 +1336,7 @@ impl BigInt { } /// Creates and initializes a `BigInt`. - pub fn parse_bytes(buf: &[u8], radix: uint) - -> Option { + pub fn parse_bytes(buf: &[u8], radix: uint) -> Option { if buf.is_empty() { return None; } let mut sign = Plus; let mut start = 0; diff --git a/src/libnum/integer.rs b/src/libnum/integer.rs new file mode 100644 index 00000000000..d958d40d3d1 --- /dev/null +++ b/src/libnum/integer.rs @@ -0,0 +1,411 @@ +// 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 or the MIT license +// , 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 + + Rem { + /// Simultaneous truncated integer division and modulus + #[inline] + fn div_rem(&self, other: &Self) -> (Self, Self) { + (*self / *other, *self % *other) + } + + /// 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; + + /// Simultaneous floored integer division and modulus + fn div_mod_floor(&self, other: &Self) -> (Self, Self) { + (self.div_floor(other), self.mod_floor(other)) + } + + /// Greatest Common Divisor (GCD) + fn gcd(&self, other: &Self) -> Self; + + /// Lowest Common Multiple (LCM) + fn lcm(&self, other: &Self) -> Self; + + /// Returns `true` if `other` divides evenly into `self` + fn divides(&self, other: &Self) -> bool; + + /// Returns `true` if the number is even + fn is_even(&self) -> bool; + + /// Returns `true` if the number is odd + fn is_odd(&self) -> bool; +} + +/// Simultaneous integer division and modulus +#[inline] pub fn div_rem(x: T, y: T) -> (T, T) { x.div_rem(&y) } +/// Floored integer division +#[inline] pub fn div_floor(x: T, y: T) -> T { x.div_floor(&y) } +/// Floored integer modulus +#[inline] pub fn mod_floor(x: T, y: T) -> T { x.mod_floor(&y) } +/// Simultaneous floored integer division and modulus +#[inline] pub fn div_mod_floor(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(x: T, y: T) -> T { x.gcd(&y) } +/// Calculates the Lowest Common Multiple (LCM) of the number and `other`. +#[inline(always)] pub fn lcm(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) -> $T { + // should not have to recalculate abs + ((*self * *other) / self.gcd(other)).abs() + } + + /// Returns `true` if the number can be divided by `other` without + /// leaving a remainder + #[inline] + fn divides(&self, other: &$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) -> $T { + (*self * *other) / self.gcd(other) + } + + /// Returns `true` if the number can be divided by `other` without leaving a remainder + #[inline] + fn divides(&self, other: &$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_divides() { + assert!((6 as $T).divides(&(6 as $T))); + assert!((6 as $T).divides(&(3 as $T))); + assert!((6 as $T).divides(&(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) diff --git a/src/libnum/lib.rs b/src/libnum/lib.rs index fae21e80f30..709882c87ce 100644 --- a/src/libnum/lib.rs +++ b/src/libnum/lib.rs @@ -57,406 +57,12 @@ 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 rational; pub mod complex; - -pub trait Integer: Num + PartialOrd - + Div - + Rem { - /// Simultaneous truncated integer division and modulus - #[inline] - fn div_rem(&self, other: &Self) -> (Self, Self) { - (*self / *other, *self % *other) - } - - /// 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; - - /// Simultaneous floored integer division and modulus - fn div_mod_floor(&self, other: &Self) -> (Self, Self) { - (self.div_floor(other), self.mod_floor(other)) - } - - /// Greatest Common Divisor (GCD) - fn gcd(&self, other: &Self) -> Self; - - /// Lowest Common Multiple (LCM) - fn lcm(&self, other: &Self) -> Self; - - /// Returns `true` if `other` divides evenly into `self` - fn divides(&self, other: &Self) -> bool; - - /// Returns `true` if the number is even - fn is_even(&self) -> bool; - - /// Returns `true` if the number is odd - fn is_odd(&self) -> bool; -} - -/// Simultaneous integer division and modulus -#[inline] pub fn div_rem(x: T, y: T) -> (T, T) { x.div_rem(&y) } -/// Floored integer division -#[inline] pub fn div_floor(x: T, y: T) -> T { x.div_floor(&y) } -/// Floored integer modulus -#[inline] pub fn mod_floor(x: T, y: T) -> T { x.mod_floor(&y) } -/// Simultaneous floored integer division and modulus -#[inline] pub fn div_mod_floor(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(x: T, y: T) -> T { x.gcd(&y) } -/// Calculates the Lowest Common Multiple (LCM) of the number and `other`. -#[inline(always)] pub fn lcm(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) -> $T { - // should not have to recalculate abs - ((*self * *other) / self.gcd(other)).abs() - } - - /// Returns `true` if the number can be divided by `other` without - /// leaving a remainder - #[inline] - fn divides(&self, other: &$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) -> $T { - (*self * *other) / self.gcd(other) - } - - /// Returns `true` if the number can be divided by `other` without leaving a remainder - #[inline] - fn divides(&self, other: &$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_divides() { - assert!((6 as $T).divides(&(6 as $T))); - assert!((6 as $T).divides(&(3 as $T))); - assert!((6 as $T).divides(&(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) +pub mod integer; +pub mod rational;