auto merge of #14694 : aochagavia/rust/num-cleanup, r=alexcrichton
This commit is contained in:
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commit
5bf5cc605f
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@ -17,18 +17,16 @@ A `BigInt` is a combination of `BigUint` and `Sign`.
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*/
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use Integer;
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use rand::Rng;
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use std::cmp;
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use std::{cmp, fmt};
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use std::default::Default;
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use std::fmt;
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use std::from_str::FromStr;
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use std::num::CheckedDiv;
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use std::num::{Bitwise, ToPrimitive, FromPrimitive};
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use std::num::{Zero, One, ToStrRadix, FromStrRadix};
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use rand::Rng;
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use std::string::String;
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use std::uint;
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use std::{i64, u64};
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use std::{uint, i64, u64};
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/**
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A `BigDigit` is a `BigUint`'s composing element.
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@ -94,7 +92,7 @@ impl Eq for BigUint {}
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impl PartialOrd for BigUint {
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#[inline]
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fn lt(&self, other: &BigUint) -> bool {
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match self.cmp(other) { Less => true, _ => false}
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self.cmp(other) == Less
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}
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}
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@ -115,7 +113,7 @@ impl Ord for BigUint {
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impl Default for BigUint {
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#[inline]
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fn default() -> BigUint { BigUint::new(Vec::new()) }
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fn default() -> BigUint { Zero::zero() }
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}
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impl fmt::Show for BigUint {
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@ -605,7 +603,7 @@ impl_to_biguint!(u64, FromPrimitive::from_u64)
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impl ToStrRadix for BigUint {
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fn to_str_radix(&self, radix: uint) -> String {
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assert!(1 < radix && radix <= 16);
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assert!(1 < radix && radix <= 16, "The radix must be within (1, 16]");
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let (base, max_len) = get_radix_base(radix);
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if base == BigDigit::base {
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return fill_concat(self.data.as_slice(), radix, max_len)
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@ -645,8 +643,7 @@ impl ToStrRadix for BigUint {
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impl FromStrRadix for BigUint {
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/// Creates and initializes a `BigUint`.
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#[inline]
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fn from_str_radix(s: &str, radix: uint)
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-> Option<BigUint> {
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fn from_str_radix(s: &str, radix: uint) -> Option<BigUint> {
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BigUint::parse_bytes(s.as_bytes(), radix)
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}
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}
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@ -656,14 +653,11 @@ impl BigUint {
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///
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/// The digits are be in base 2^32.
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#[inline]
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pub fn new(v: Vec<BigDigit>) -> BigUint {
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pub fn new(mut digits: Vec<BigDigit>) -> BigUint {
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// omit trailing zeros
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let new_len = v.iter().rposition(|n| *n != 0).map_or(0, |p| p + 1);
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if new_len == v.len() { return BigUint { data: v }; }
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let mut v = v;
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v.truncate(new_len);
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return BigUint { data: v };
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let new_len = digits.iter().rposition(|n| *n != 0).map_or(0, |p| p + 1);
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digits.truncate(new_len);
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BigUint { data: digits }
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}
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/// Creates and initializes a `BigUint`.
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@ -671,7 +665,7 @@ impl BigUint {
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/// The digits are be in base 2^32.
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#[inline]
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pub fn from_slice(slice: &[BigDigit]) -> BigUint {
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return BigUint::new(Vec::from_slice(slice));
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BigUint::new(Vec::from_slice(slice))
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}
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/// Creates and initializes a `BigUint`.
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@ -768,7 +762,6 @@ impl BigUint {
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// `DoubleBigDigit` size dependent
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#[inline]
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fn get_radix_base(radix: uint) -> (DoubleBigDigit, uint) {
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assert!(1 < radix && radix <= 16);
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match radix {
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2 => (4294967296, 32),
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3 => (3486784401, 20),
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@ -785,7 +778,7 @@ fn get_radix_base(radix: uint) -> (DoubleBigDigit, uint) {
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14 => (1475789056, 8),
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15 => (2562890625, 8),
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16 => (4294967296, 8),
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_ => fail!()
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_ => fail!("The radix must be within (1, 16]")
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}
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}
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@ -815,7 +808,7 @@ pub struct BigInt {
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impl PartialEq for BigInt {
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#[inline]
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fn eq(&self, other: &BigInt) -> bool {
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match self.cmp(other) { Equal => true, _ => false }
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self.cmp(other) == Equal
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}
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}
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@ -824,7 +817,7 @@ impl Eq for BigInt {}
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impl PartialOrd for BigInt {
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#[inline]
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fn lt(&self, other: &BigInt) -> bool {
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match self.cmp(other) { Less => true, _ => false}
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self.cmp(other) == Less
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}
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}
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@ -844,7 +837,7 @@ impl Ord for BigInt {
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impl Default for BigInt {
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#[inline]
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fn default() -> BigInt { BigInt::new(Zero, Vec::new()) }
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fn default() -> BigInt { Zero::zero() }
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}
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impl fmt::Show for BigInt {
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@ -929,8 +922,7 @@ impl Add<BigInt, BigInt> for BigInt {
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match (self.sign, other.sign) {
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(Zero, _) => other.clone(),
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(_, Zero) => self.clone(),
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(Plus, Plus) => BigInt::from_biguint(Plus,
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self.data + other.data),
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(Plus, Plus) => BigInt::from_biguint(Plus, self.data + other.data),
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(Plus, Minus) => self - (-*other),
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(Minus, Plus) => other - (-*self),
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(Minus, Minus) => -((-self) + (-*other))
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@ -975,7 +967,7 @@ impl Div<BigInt, BigInt> for BigInt {
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#[inline]
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fn div(&self, other: &BigInt) -> BigInt {
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let (q, _) = self.div_rem(other);
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return q;
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q
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}
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}
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@ -983,7 +975,7 @@ impl Rem<BigInt, BigInt> for BigInt {
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#[inline]
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fn rem(&self, other: &BigInt) -> BigInt {
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let (_, r) = self.div_rem(other);
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return r;
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r
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}
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}
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@ -1045,13 +1037,13 @@ impl Integer for BigInt {
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#[inline]
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fn div_floor(&self, other: &BigInt) -> BigInt {
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let (d, _) = self.div_mod_floor(other);
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return d;
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d
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}
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#[inline]
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fn mod_floor(&self, other: &BigInt) -> BigInt {
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let (_, m) = self.div_mod_floor(other);
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return m;
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m
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}
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fn div_mod_floor(&self, other: &BigInt) -> (BigInt, BigInt) {
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@ -1265,7 +1257,7 @@ impl<R: Rng> RandBigInt for R {
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let final_digit: BigDigit = self.gen();
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data.push(final_digit >> (BigDigit::bits - rem));
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}
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return BigUint::new(data);
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BigUint::new(data)
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}
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fn gen_bigint(&mut self, bit_size: uint) -> BigInt {
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@ -1287,7 +1279,7 @@ impl<R: Rng> RandBigInt for R {
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} else {
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Minus
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};
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return BigInt::from_biguint(sign, biguint);
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BigInt::from_biguint(sign, biguint)
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}
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fn gen_biguint_below(&mut self, bound: &BigUint) -> BigUint {
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@ -1322,8 +1314,8 @@ impl BigInt {
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///
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/// The digits are be in base 2^32.
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#[inline]
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pub fn new(sign: Sign, v: Vec<BigDigit>) -> BigInt {
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BigInt::from_biguint(sign, BigUint::new(v))
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pub fn new(sign: Sign, digits: Vec<BigDigit>) -> BigInt {
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BigInt::from_biguint(sign, BigUint::new(digits))
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}
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/// Creates and initializes a `BigInt`.
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@ -1334,7 +1326,7 @@ impl BigInt {
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if sign == Zero || data.is_zero() {
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return BigInt { sign: Zero, data: Zero::zero() };
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}
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return BigInt { sign: sign, data: data };
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BigInt { sign: sign, data: data }
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}
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/// Creates and initializes a `BigInt`.
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@ -1344,8 +1336,7 @@ impl BigInt {
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}
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/// Creates and initializes a `BigInt`.
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pub fn parse_bytes(buf: &[u8], radix: uint)
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-> Option<BigInt> {
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pub fn parse_bytes(buf: &[u8], radix: uint) -> Option<BigInt> {
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if buf.is_empty() { return None; }
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let mut sign = Plus;
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let mut start = 0;
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@ -0,0 +1,411 @@
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// Copyright 2013-2014 The Rust Project Developers. See the COPYRIGHT
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// file at the top-level directory of this distribution and at
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// http://rust-lang.org/COPYRIGHT.
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//
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// Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or
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// http://www.apache.org/licenses/LICENSE-2.0> or the MIT license
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// <LICENSE-MIT or http://opensource.org/licenses/MIT>, at your
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// option. This file may not be copied, modified, or distributed
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// except according to those terms.
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//! Integer trait and functions
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pub trait Integer: Num + PartialOrd
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+ Div<Self, Self>
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+ Rem<Self, Self> {
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/// Simultaneous truncated integer division and modulus
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#[inline]
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fn div_rem(&self, other: &Self) -> (Self, Self) {
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(*self / *other, *self % *other)
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}
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/// Floored integer division
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///
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/// # Examples
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///
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/// ~~~
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/// # use num::Integer;
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/// assert!(( 8i).div_floor(& 3) == 2);
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/// assert!(( 8i).div_floor(&-3) == -3);
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/// assert!((-8i).div_floor(& 3) == -3);
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/// assert!((-8i).div_floor(&-3) == 2);
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///
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/// assert!(( 1i).div_floor(& 2) == 0);
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/// assert!(( 1i).div_floor(&-2) == -1);
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/// assert!((-1i).div_floor(& 2) == -1);
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/// assert!((-1i).div_floor(&-2) == 0);
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/// ~~~
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fn div_floor(&self, other: &Self) -> Self;
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/// Floored integer modulo, satisfying:
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///
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/// ~~~
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/// # use num::Integer;
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/// # let n = 1i; let d = 1i;
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/// assert!(n.div_floor(&d) * d + n.mod_floor(&d) == n)
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/// ~~~
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///
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/// # Examples
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///
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/// ~~~
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/// # use num::Integer;
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/// assert!(( 8i).mod_floor(& 3) == 2);
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/// assert!(( 8i).mod_floor(&-3) == -1);
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/// assert!((-8i).mod_floor(& 3) == 1);
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/// assert!((-8i).mod_floor(&-3) == -2);
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///
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/// assert!(( 1i).mod_floor(& 2) == 1);
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/// assert!(( 1i).mod_floor(&-2) == -1);
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/// assert!((-1i).mod_floor(& 2) == 1);
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/// assert!((-1i).mod_floor(&-2) == -1);
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/// ~~~
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fn mod_floor(&self, other: &Self) -> Self;
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/// Simultaneous floored integer division and modulus
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fn div_mod_floor(&self, other: &Self) -> (Self, Self) {
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(self.div_floor(other), self.mod_floor(other))
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}
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/// Greatest Common Divisor (GCD)
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fn gcd(&self, other: &Self) -> Self;
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/// Lowest Common Multiple (LCM)
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fn lcm(&self, other: &Self) -> Self;
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/// Returns `true` if `other` divides evenly into `self`
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fn divides(&self, other: &Self) -> bool;
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/// Returns `true` if the number is even
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fn is_even(&self) -> bool;
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/// Returns `true` if the number is odd
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fn is_odd(&self) -> bool;
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}
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/// Simultaneous integer division and modulus
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#[inline] pub fn div_rem<T: Integer>(x: T, y: T) -> (T, T) { x.div_rem(&y) }
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/// Floored integer division
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#[inline] pub fn div_floor<T: Integer>(x: T, y: T) -> T { x.div_floor(&y) }
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/// Floored integer modulus
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#[inline] pub fn mod_floor<T: Integer>(x: T, y: T) -> T { x.mod_floor(&y) }
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/// Simultaneous floored integer division and modulus
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#[inline] pub fn div_mod_floor<T: Integer>(x: T, y: T) -> (T, T) { x.div_mod_floor(&y) }
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/// Calculates the Greatest Common Divisor (GCD) of the number and `other`. The
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/// result is always positive.
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#[inline(always)] pub fn gcd<T: Integer>(x: T, y: T) -> T { x.gcd(&y) }
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/// Calculates the Lowest Common Multiple (LCM) of the number and `other`.
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#[inline(always)] pub fn lcm<T: Integer>(x: T, y: T) -> T { x.lcm(&y) }
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macro_rules! impl_integer_for_int {
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($T:ty, $test_mod:ident) => (
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impl Integer for $T {
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/// Floored integer division
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#[inline]
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fn div_floor(&self, other: &$T) -> $T {
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// Algorithm from [Daan Leijen. _Division and Modulus for Computer Scientists_,
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// December 2001](http://research.microsoft.com/pubs/151917/divmodnote-letter.pdf)
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match self.div_rem(other) {
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(d, r) if (r > 0 && *other < 0)
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|| (r < 0 && *other > 0) => d - 1,
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(d, _) => d,
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}
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}
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/// Floored integer modulo
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#[inline]
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fn mod_floor(&self, other: &$T) -> $T {
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// Algorithm from [Daan Leijen. _Division and Modulus for Computer Scientists_,
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// December 2001](http://research.microsoft.com/pubs/151917/divmodnote-letter.pdf)
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match *self % *other {
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r if (r > 0 && *other < 0)
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|| (r < 0 && *other > 0) => r + *other,
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r => r,
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}
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}
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/// Calculates `div_floor` and `mod_floor` simultaneously
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#[inline]
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fn div_mod_floor(&self, other: &$T) -> ($T,$T) {
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// Algorithm from [Daan Leijen. _Division and Modulus for Computer Scientists_,
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// December 2001](http://research.microsoft.com/pubs/151917/divmodnote-letter.pdf)
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match self.div_rem(other) {
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(d, r) if (r > 0 && *other < 0)
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|| (r < 0 && *other > 0) => (d - 1, r + *other),
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(d, r) => (d, r),
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}
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}
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/// Calculates the Greatest Common Divisor (GCD) of the number and
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/// `other`. The result is always positive.
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#[inline]
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fn gcd(&self, other: &$T) -> $T {
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// Use Euclid's algorithm
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let mut m = *self;
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let mut n = *other;
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while m != 0 {
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let temp = m;
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m = n % temp;
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n = temp;
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}
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n.abs()
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}
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/// Calculates the Lowest Common Multiple (LCM) of the number and
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/// `other`.
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#[inline]
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fn lcm(&self, other: &$T) -> $T {
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// should not have to recalculate abs
|
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((*self * *other) / self.gcd(other)).abs()
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}
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/// Returns `true` if the number can be divided by `other` without
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/// leaving a remainder
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#[inline]
|
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fn divides(&self, other: &$T) -> bool { *self % *other == 0 }
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/// Returns `true` if the number is divisible by `2`
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#[inline]
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fn is_even(&self) -> bool { self & 1 == 0 }
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/// Returns `true` if the number is not divisible by `2`
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#[inline]
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fn is_odd(&self) -> bool { !self.is_even() }
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}
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#[cfg(test)]
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mod $test_mod {
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use Integer;
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|
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/// Checks that the division rule holds for:
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///
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/// - `n`: numerator (dividend)
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/// - `d`: denominator (divisor)
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/// - `qr`: quotient and remainder
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#[cfg(test)]
|
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fn test_division_rule((n,d): ($T,$T), (q,r): ($T,$T)) {
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assert_eq!(d * q + r, n);
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}
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#[test]
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fn test_div_rem() {
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fn test_nd_dr(nd: ($T,$T), qr: ($T,$T)) {
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let (n,d) = nd;
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let separate_div_rem = (n / d, n % d);
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let combined_div_rem = n.div_rem(&d);
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assert_eq!(separate_div_rem, qr);
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assert_eq!(combined_div_rem, qr);
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test_division_rule(nd, separate_div_rem);
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test_division_rule(nd, combined_div_rem);
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}
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test_nd_dr(( 8, 3), ( 2, 2));
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test_nd_dr(( 8, -3), (-2, 2));
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test_nd_dr((-8, 3), (-2, -2));
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test_nd_dr((-8, -3), ( 2, -2));
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test_nd_dr(( 1, 2), ( 0, 1));
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test_nd_dr(( 1, -2), ( 0, 1));
|
||||
test_nd_dr((-1, 2), ( 0, -1));
|
||||
test_nd_dr((-1, -2), ( 0, -1));
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn test_div_mod_floor() {
|
||||
fn test_nd_dm(nd: ($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)
|
||||
|
|
@ -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<Self, Self>
|
||||
+ Rem<Self, Self> {
|
||||
/// 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<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) -> $T {
|
||||
// should not have to recalculate abs
|
||||
((*self * *other) / self.gcd(other)).abs()
|
||||
}
|
||||
|
||||
/// Returns `true` if the number can be divided by `other` without
|
||||
/// leaving a remainder
|
||||
#[inline]
|
||||
fn divides(&self, other: &$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;
|
||||
|
|
|
|||
Loading…
Reference in New Issue