user0/rust
1
0
Fork 0
Code Issues Pull requests Projects Releases Packages Wiki Activity Actions
rust/src/libextra/num/bigint.rs
gifnksm f8f17a39ce bigint: fix wrong benchmark fn name
2013-08-26 20:27:20 +09:00

2029 lines
62 KiB
Rust
Raw Blame History

// 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.
/*!
A Big integer (signed version: BigInt, unsigned version: BigUint).
A BigUint is represented as an array of BigDigits.
A BigInt is a combination of BigUint and Sign.
*/
#[allow(missing_doc)];
#[allow(non_uppercase_statics)];
use std::cmp::{Eq, Ord, TotalEq, TotalOrd, Ordering, Less, Equal, Greater};
use std::int;
use std::num;
use std::num::{IntConvertible, Zero, One, ToStrRadix, FromStrRadix, Orderable};
use std::str;
use std::uint;
use std::vec;
/**
A BigDigit is a BigUint's composing element.
A BigDigit is half the size of machine word size.
*/
#[cfg(target_word_size = "32")]
pub type BigDigit = u16;
/**
A BigDigit is a BigUint's composing element.
A BigDigit is half the size of machine word size.
*/
#[cfg(target_word_size = "64")]
pub type BigDigit = u32;
pub static ZERO_BIG_DIGIT: BigDigit = 0;
pub mod BigDigit {
use bigint::BigDigit;
#[cfg(target_word_size = "32")]
pub static bits: uint = 16;
#[cfg(target_word_size = "64")]
pub static bits: uint = 32;
pub static base: uint = 1 << bits;
static hi_mask: uint = (-1 as uint) << bits;
static lo_mask: uint = (-1 as uint) >> bits;
#[inline]
fn get_hi(n: uint) -> BigDigit { (n >> bits) as BigDigit }
#[inline]
fn get_lo(n: uint) -> BigDigit { (n & lo_mask) as BigDigit }
/// Split one machine sized unsigned integer into two BigDigits.
#[inline]
pub fn from_uint(n: uint) -> (BigDigit, BigDigit) {
(get_hi(n), get_lo(n))
}
/// Join two BigDigits into one machine sized unsigned integer
#[inline]
pub fn to_uint(hi: BigDigit, lo: BigDigit) -> uint {
(lo as uint) | ((hi as uint) << bits)
}
}
/**
A big unsigned integer type.
A BigUint-typed value BigUint { data: @[a, b, c] } represents a number
(a + b * BigDigit::base + c * BigDigit::base^2).
*/
#[deriving(Clone)]
pub struct BigUint {
priv data: ~[BigDigit]
}
impl Eq for BigUint {
#[inline]
fn eq(&self, other: &BigUint) -> bool { self.equals(other) }
}
impl TotalEq for BigUint {
#[inline]
fn equals(&self, other: &BigUint) -> bool {
match self.cmp(other) { Equal => true, _ => false }
}
}
impl Ord for BigUint {
#[inline]
fn lt(&self, other: &BigUint) -> bool {
match self.cmp(other) { Less => true, _ => false}
}
}
impl TotalOrd for BigUint {
#[inline]
fn cmp(&self, other: &BigUint) -> Ordering {
let (s_len, o_len) = (self.data.len(), other.data.len());
if s_len < o_len { return Less; }
if s_len > o_len { return Greater; }
for (&self_i, &other_i) in self.data.rev_iter().zip(other.data.rev_iter()) {
cond!((self_i < other_i) { return Less; }
(self_i > other_i) { return Greater; })
}
return Equal;
}
}
impl ToStr for BigUint {
#[inline]
fn to_str(&self) -> ~str { self.to_str_radix(10) }
}
impl FromStr for BigUint {
#[inline]
fn from_str(s: &str) -> Option<BigUint> {
FromStrRadix::from_str_radix(s, 10)
}
}
impl Num for BigUint {}
impl Orderable for BigUint {
#[inline]
fn min(&self, other: &BigUint) -> BigUint {
if self < other { self.clone() } else { other.clone() }
}
#[inline]
fn max(&self, other: &BigUint) -> BigUint {
if self > other { self.clone() } else { other.clone() }
}
#[inline]
fn clamp(&self, mn: &BigUint, mx: &BigUint) -> BigUint {
if self > mx { mx.clone() } else
if self < mn { mn.clone() } else { self.clone() }
}
}
impl Shl<uint, BigUint> for BigUint {
#[inline]
fn shl(&self, rhs: &uint) -> BigUint {
let n_unit = *rhs / BigDigit::bits;
let n_bits = *rhs % BigDigit::bits;
return self.shl_unit(n_unit).shl_bits(n_bits);
}
}
impl Shr<uint, BigUint> for BigUint {
#[inline]
fn shr(&self, rhs: &uint) -> BigUint {
let n_unit = *rhs / BigDigit::bits;
let n_bits = *rhs % BigDigit::bits;
return self.shr_unit(n_unit).shr_bits(n_bits);
}
}
impl Zero for BigUint {
#[inline]
fn zero() -> BigUint { BigUint::new(~[]) }
#[inline]
fn is_zero(&self) -> bool { self.data.is_empty() }
}
impl One for BigUint {
#[inline]
fn one() -> BigUint { BigUint::new(~[1]) }
}
impl Unsigned for BigUint {}
impl Add<BigUint, BigUint> for BigUint {
fn add(&self, other: &BigUint) -> BigUint {
let new_len = num::max(self.data.len(), other.data.len());
let mut carry = 0;
let mut sum = do vec::from_fn(new_len) |i| {
let ai = if i < self.data.len() { self.data[i] } else { 0 };
let bi = if i < other.data.len() { other.data[i] } else { 0 };
let (hi, lo) = BigDigit::from_uint(
(ai as uint) + (bi as uint) + (carry as uint)
);
carry = hi;
lo
};
if carry != 0 { sum.push(carry); }
return BigUint::new(sum);
}
}
impl Sub<BigUint, BigUint> for BigUint {
fn sub(&self, other: &BigUint) -> BigUint {
let new_len = num::max(self.data.len(), other.data.len());
let mut borrow = 0;
let diff = do vec::from_fn(new_len) |i| {
let ai = if i < self.data.len() { self.data[i] } else { 0 };
let bi = if i < other.data.len() { other.data[i] } else { 0 };
let (hi, lo) = BigDigit::from_uint(
(BigDigit::base) +
(ai as uint) - (bi as uint) - (borrow as uint)
);
/*
hi * (base) + lo == 1*(base) + ai - bi - borrow
=> ai - bi - borrow < 0 <=> hi == 0
*/
borrow = if hi == 0 { 1 } else { 0 };
lo
};
assert_eq!(borrow, 0); // <=> assert!((self >= other));
return BigUint::new(diff);
}
}
impl Mul<BigUint, BigUint> for BigUint {
fn mul(&self, other: &BigUint) -> BigUint {
if self.is_zero() || other.is_zero() { return Zero::zero(); }
let (s_len, o_len) = (self.data.len(), other.data.len());
if s_len == 1 { return mul_digit(other, self.data[0]); }
if o_len == 1 { return mul_digit(self, other.data[0]); }
// Using Karatsuba multiplication
// (a1 * base + a0) * (b1 * base + b0)
// = a1*b1 * base^2 +
// (a1*b1 + a0*b0 - (a1-b0)*(b1-a0)) * base +
// a0*b0
let half_len = num::max(s_len, o_len) / 2;
let (sHi, sLo) = cut_at(self, half_len);
let (oHi, oLo) = cut_at(other, half_len);
let ll = sLo * oLo;
let hh = sHi * oHi;
let mm = {
let (s1, n1) = sub_sign(sHi, sLo);
let (s2, n2) = sub_sign(oHi, oLo);
match (s1, s2) {
(Equal, _) | (_, Equal) => hh + ll,
(Less, Greater) | (Greater, Less) => hh + ll + (n1 * n2),
(Less, Less) | (Greater, Greater) => hh + ll - (n1 * n2)
}
};
return ll + mm.shl_unit(half_len) + hh.shl_unit(half_len * 2);
fn mul_digit(a: &BigUint, n: BigDigit) -> BigUint {
if n == 0 { return Zero::zero(); }
if n == 1 { return (*a).clone(); }
let mut carry = 0;
let mut prod = do a.data.iter().map |ai| {
let (hi, lo) = BigDigit::from_uint(
(*ai as uint) * (n as uint) + (carry as uint)
);
carry = hi;
lo
}.collect::<~[BigDigit]>();
if carry != 0 { prod.push(carry); }
return BigUint::new(prod);
}
#[inline]
fn cut_at(a: &BigUint, n: uint) -> (BigUint, BigUint) {
let mid = num::min(a.data.len(), n);
return (BigUint::from_slice(a.data.slice(mid, a.data.len())),
BigUint::from_slice(a.data.slice(0, mid)));
}
#[inline]
fn sub_sign(a: BigUint, b: BigUint) -> (Ordering, BigUint) {
match a.cmp(&b) {
Less => (Less, b - a),
Greater => (Greater, a - b),
_ => (Equal, Zero::zero())
}
}
}
}
impl Div<BigUint, BigUint> for BigUint {
#[inline]
fn div(&self, other: &BigUint) -> BigUint {
let (q, _) = self.div_rem(other);
return q;
}
}
impl Rem<BigUint, BigUint> for BigUint {
#[inline]
fn rem(&self, other: &BigUint) -> BigUint {
let (_, r) = self.div_rem(other);
return r;
}
}
impl Neg<BigUint> for BigUint {
#[inline]
fn neg(&self) -> BigUint { fail!() }
}
impl Integer for BigUint {
#[inline]
fn div_rem(&self, other: &BigUint) -> (BigUint, BigUint) {
self.div_mod_floor(other)
}
#[inline]
fn div_floor(&self, other: &BigUint) -> BigUint {
let (d, _) = self.div_mod_floor(other);
return d;
}
#[inline]
fn mod_floor(&self, other: &BigUint) -> BigUint {
let (_, m) = self.div_mod_floor(other);
return m;
}
fn div_mod_floor(&self, other: &BigUint) -> (BigUint, BigUint) {
if other.is_zero() { fail!() }
if self.is_zero() { return (Zero::zero(), Zero::zero()); }
if *other == One::one() { return ((*self).clone(), Zero::zero()); }
match self.cmp(other) {
Less => return (Zero::zero(), (*self).clone()),
Equal => return (One::one(), Zero::zero()),
Greater => {} // Do nothing
}
let mut shift = 0;
let mut n = *other.data.last();
while n < (1 << BigDigit::bits - 2) {
n <<= 1;
shift += 1;
}
assert!(shift < BigDigit::bits);
let (d, m) = div_mod_floor_inner(self << shift, other << shift);
return (d, m >> shift);
fn div_mod_floor_inner(a: BigUint, b: BigUint) -> (BigUint, BigUint) {
let mut m = a;
let mut d = Zero::zero::<BigUint>();
let mut n = 1;
while m >= b {
let (d0, d_unit, b_unit) = div_estimate(&m, &b, n);
let mut d0 = d0;
let mut prod = b * d0;
while prod > m {
// FIXME(#6050): overloaded operators force moves with generic types
// d0 -= d_unit
d0 = d0 - d_unit;
// FIXME(#6050): overloaded operators force moves with generic types
// prod = prod - b_unit;
prod = prod - b_unit
}
if d0.is_zero() {
n = 2;
loop;
}
n = 1;
// FIXME(#6102): Assignment operator for BigInt causes ICE
// d += d0;
d = d + d0;
// FIXME(#6102): Assignment operator for BigInt causes ICE
// m -= prod;
m = m - prod;
}
return (d, m);
}
fn div_estimate(a: &BigUint, b: &BigUint, n: uint)
-> (BigUint, BigUint, BigUint) {
if a.data.len() < n {
return (Zero::zero(), Zero::zero(), (*a).clone());
}
let an = a.data.slice(a.data.len() - n, a.data.len());
let bn = *b.data.last();
let mut d = ~[];
let mut carry = 0;
for elt in an.rev_iter() {
let ai = BigDigit::to_uint(carry, *elt);
let di = ai / (bn as uint);
assert!(di < BigDigit::base);
carry = (ai % (bn as uint)) as BigDigit;
d = ~[di as BigDigit] + d;
}
let shift = (a.data.len() - an.len()) - (b.data.len() - 1);
if shift == 0 {
return (BigUint::new(d), One::one(), (*b).clone());
}
return (BigUint::from_slice(d).shl_unit(shift),
One::one::<BigUint>().shl_unit(shift),
b.shl_unit(shift));
}
}
/**
* Calculates the Greatest Common Divisor (GCD) of the number and `other`
*
* The result is always positive
*/
#[inline]
fn gcd(&self, other: &BigUint) -> BigUint {
// Use Euclid's algorithm
let mut m = (*self).clone();
let mut n = (*other).clone();
while !m.is_zero() {
let temp = m;
m = n % temp;
n = temp;
}
return n;
}
/**
* Calculates the Lowest Common Multiple (LCM) of the number and `other`
*/
#[inline]
fn lcm(&self, other: &BigUint) -> BigUint { ((*self * *other) / self.gcd(other)) }
/// Returns `true` if the number can be divided by `other` without leaving a remainder
#[inline]
fn is_multiple_of(&self, other: &BigUint) -> bool { (*self % *other).is_zero() }
/// Returns `true` if the number is divisible by `2`
#[inline]
fn is_even(&self) -> bool {
// Considering only the last digit.
if self.data.is_empty() {
true
} else {
self.data[0].is_even()
}
}
/// Returns `true` if the number is not divisible by `2`
#[inline]
fn is_odd(&self) -> bool { !self.is_even() }
}
impl IntConvertible for BigUint {
#[inline]
fn to_int(&self) -> int {
num::min(self.to_uint(), int::max_value as uint) as int
}
#[inline]
fn from_int(n: int) -> BigUint {
if (n < 0) { Zero::zero() } else { BigUint::from_uint(n as uint) }
}
}
impl ToStrRadix for BigUint {
fn to_str_radix(&self, radix: uint) -> ~str {
assert!(1 < radix && radix <= 16);
let (base, max_len) = get_radix_base(radix);
if base == BigDigit::base {
return fill_concat(self.data, radix, max_len)
}
return fill_concat(convert_base((*self).clone(), base), radix, max_len);
fn convert_base(n: BigUint, base: uint) -> ~[BigDigit] {
let divider = BigUint::from_uint(base);
let mut result = ~[];
let mut m = n;
while m > divider {
let (d, m0) = m.div_mod_floor(&divider);
result.push(m0.to_uint() as BigDigit);
m = d;
}
if !m.is_zero() {
result.push(m.to_uint() as BigDigit);
}
return result;
}
fn fill_concat(v: &[BigDigit], radix: uint, l: uint) -> ~str {
if v.is_empty() { return ~"0" }
let mut s = str::with_capacity(v.len() * l);
for n in v.rev_iter() {
let ss = (*n as uint).to_str_radix(radix);
s.push_str("0".repeat(l - ss.len()));
s.push_str(ss);
}
s.trim_left_chars(&'0').to_owned()
}
}
}
impl FromStrRadix for BigUint {
/// Creates and initializes an BigUint.
#[inline]
fn from_str_radix(s: &str, radix: uint)
-> Option<BigUint> {
BigUint::parse_bytes(s.as_bytes(), radix)
}
}
impl BigUint {
/// Creates and initializes an BigUint.
#[inline]
pub fn new(v: ~[BigDigit]) -> BigUint {
// omit trailing zeros
let new_len = v.rposition(|n| *n != 0).map_move_default(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 };
}
/// Creates and initializes an BigUint.
#[inline]
pub fn from_uint(n: uint) -> BigUint {
match BigDigit::from_uint(n) {
(0, 0) => Zero::zero(),
(0, n0) => BigUint::new(~[n0]),
(n1, n0) => BigUint::new(~[n0, n1])
}
}
/// Creates and initializes an BigUint.
#[inline]
pub fn from_slice(slice: &[BigDigit]) -> BigUint {
return BigUint::new(slice.to_owned());
}
/// Creates and initializes an BigUint.
pub fn parse_bytes(buf: &[u8], radix: uint)
-> Option<BigUint> {
let (base, unit_len) = get_radix_base(radix);
let base_num: BigUint = BigUint::from_uint(base);
let mut end = buf.len();
let mut n: BigUint = Zero::zero();
let mut power: BigUint = One::one();
loop {
let start = num::max(end, unit_len) - unit_len;
match uint::parse_bytes(buf.slice(start, end), radix) {
// FIXME(#6102): Assignment operator for BigInt causes ICE
// Some(d) => n += BigUint::from_uint(d) * power,
Some(d) => n = n + BigUint::from_uint(d) * power,
None => return None
}
if end <= unit_len {
return Some(n);
}
end -= unit_len;
// FIXME(#6050): overloaded operators force moves with generic types
// power *= base_num;
power = power * base_num;
}
}
/// Converts this big integer into a uint, returning the uint::max_value if
/// it's too large to fit in a uint.
#[inline]
pub fn to_uint(&self) -> uint {
match self.data.len() {
0 => 0,
1 => self.data[0] as uint,
2 => BigDigit::to_uint(self.data[1], self.data[0]),
_ => uint::max_value
}
}
#[inline]
fn shl_unit(&self, n_unit: uint) -> BigUint {
if n_unit == 0 || self.is_zero() { return (*self).clone(); }
return BigUint::new(vec::from_elem(n_unit, ZERO_BIG_DIGIT)
+ self.data);
}
#[inline]
fn shl_bits(&self, n_bits: uint) -> BigUint {
if n_bits == 0 || self.is_zero() { return (*self).clone(); }
let mut carry = 0;
let mut shifted = do self.data.iter().map |elem| {
let (hi, lo) = BigDigit::from_uint(
(*elem as uint) << n_bits | (carry as uint)
);
carry = hi;
lo
}.collect::<~[BigDigit]>();
if carry != 0 { shifted.push(carry); }
return BigUint::new(shifted);
}
#[inline]
fn shr_unit(&self, n_unit: uint) -> BigUint {
if n_unit == 0 { return (*self).clone(); }
if self.data.len() < n_unit { return Zero::zero(); }
return BigUint::from_slice(
self.data.slice(n_unit, self.data.len())
);
}
#[inline]
fn shr_bits(&self, n_bits: uint) -> BigUint {
if n_bits == 0 || self.data.is_empty() { return (*self).clone(); }
let mut borrow = 0;
let mut shifted = ~[];
for elem in self.data.rev_iter() {
shifted = ~[(*elem >> n_bits) | borrow] + shifted;
borrow = *elem << (BigDigit::bits - n_bits);
}
return BigUint::new(shifted);
}
}
#[cfg(target_word_size = "64")]
#[inline]
fn get_radix_base(radix: uint) -> (uint, uint) {
assert!(1 < radix && radix <= 16);
match radix {
2 => (4294967296, 32),
3 => (3486784401, 20),
4 => (4294967296, 16),
5 => (1220703125, 13),
6 => (2176782336, 12),
7 => (1977326743, 11),
8 => (1073741824, 10),
9 => (3486784401, 10),
10 => (1000000000, 9),
11 => (2357947691, 9),
12 => (429981696, 8),
13 => (815730721, 8),
14 => (1475789056, 8),
15 => (2562890625, 8),
16 => (4294967296, 8),
_ => fail!()
}
}
#[cfg(target_word_size = "32")]
#[inline]
fn get_radix_base(radix: uint) -> (uint, uint) {
assert!(1 < radix && radix <= 16);
match radix {
2 => (65536, 16),
3 => (59049, 10),
4 => (65536, 8),
5 => (15625, 6),
6 => (46656, 6),
7 => (16807, 5),
8 => (32768, 5),
9 => (59049, 5),
10 => (10000, 4),
11 => (14641, 4),
12 => (20736, 4),
13 => (28561, 4),
14 => (38416, 4),
15 => (50625, 4),
16 => (65536, 4),
_ => fail!()
}
}
/// A Sign is a BigInt's composing element.
#[deriving(Eq, Clone)]
pub enum Sign { Minus, Zero, Plus }
impl Ord for Sign {
#[inline]
fn lt(&self, other: &Sign) -> bool {
match self.cmp(other) { Less => true, _ => false}
}
}
impl TotalEq for Sign {
#[inline]
fn equals(&self, other: &Sign) -> bool { *self == *other }
}
impl TotalOrd for Sign {
#[inline]
fn cmp(&self, other: &Sign) -> Ordering {
match (*self, *other) {
(Minus, Minus) | (Zero, Zero) | (Plus, Plus) => Equal,
(Minus, Zero) | (Minus, Plus) | (Zero, Plus) => Less,
_ => Greater
}
}
}
impl Neg<Sign> for Sign {
/// Negate Sign value.
#[inline]
fn neg(&self) -> Sign {
match *self {
Minus => Plus,
Zero => Zero,
Plus => Minus
}
}
}
/// A big signed integer type.
#[deriving(Clone)]
pub struct BigInt {
priv sign: Sign,
priv data: BigUint
}
impl Eq for BigInt {
#[inline]
fn eq(&self, other: &BigInt) -> bool { self.equals(other) }
}
impl TotalEq for BigInt {
#[inline]
fn equals(&self, other: &BigInt) -> bool {
match self.cmp(other) { Equal => true, _ => false }
}
}
impl Ord for BigInt {
#[inline]
fn lt(&self, other: &BigInt) -> bool {
match self.cmp(other) { Less => true, _ => false}
}
}
impl TotalOrd for BigInt {
#[inline]
fn cmp(&self, other: &BigInt) -> Ordering {
let scmp = self.sign.cmp(&other.sign);
if scmp != Equal { return scmp; }
match self.sign {
Zero => Equal,
Plus => self.data.cmp(&other.data),
Minus => other.data.cmp(&self.data),
}
}
}
impl ToStr for BigInt {
#[inline]
fn to_str(&self) -> ~str { self.to_str_radix(10) }
}
impl FromStr for BigInt {
#[inline]
fn from_str(s: &str) -> Option<BigInt> {
FromStrRadix::from_str_radix(s, 10)
}
}
impl Num for BigInt {}
impl Orderable for BigInt {
#[inline]
fn min(&self, other: &BigInt) -> BigInt {
if self < other { self.clone() } else { other.clone() }
}
#[inline]
fn max(&self, other: &BigInt) -> BigInt {
if self > other { self.clone() } else { other.clone() }
}
#[inline]
fn clamp(&self, mn: &BigInt, mx: &BigInt) -> BigInt {
if self > mx { mx.clone() } else
if self < mn { mn.clone() } else { self.clone() }
}
}
impl Shl<uint, BigInt> for BigInt {
#[inline]
fn shl(&self, rhs: &uint) -> BigInt {
BigInt::from_biguint(self.sign, self.data << *rhs)
}
}
impl Shr<uint, BigInt> for BigInt {
#[inline]
fn shr(&self, rhs: &uint) -> BigInt {
BigInt::from_biguint(self.sign, self.data >> *rhs)
}
}
impl Zero for BigInt {
#[inline]
fn zero() -> BigInt {
BigInt::from_biguint(Zero, Zero::zero())
}
#[inline]
fn is_zero(&self) -> bool { self.sign == Zero }
}
impl One for BigInt {
#[inline]
fn one() -> BigInt {
BigInt::from_biguint(Plus, One::one())
}
}
impl Signed for BigInt {
#[inline]
fn abs(&self) -> BigInt {
match self.sign {
Plus | Zero => self.clone(),
Minus => BigInt::from_biguint(Plus, self.data.clone())
}
}
#[inline]
fn abs_sub(&self, other: &BigInt) -> BigInt {
if *self <= *other { Zero::zero() } else { *self - *other }
}
#[inline]
fn signum(&self) -> BigInt {
match self.sign {
Plus => BigInt::from_biguint(Plus, One::one()),
Minus => BigInt::from_biguint(Minus, One::one()),
Zero => Zero::zero(),
}
}
#[inline]
fn is_positive(&self) -> bool { self.sign == Plus }
#[inline]
fn is_negative(&self) -> bool { self.sign == Minus }
}
impl Add<BigInt, BigInt> for BigInt {
#[inline]
fn add(&self, other: &BigInt) -> BigInt {
match (self.sign, other.sign) {
(Zero, _) => other.clone(),
(_, Zero) => self.clone(),
(Plus, Plus) => BigInt::from_biguint(Plus,
self.data + other.data),
(Plus, Minus) => self - (-*other),
(Minus, Plus) => other - (-*self),
(Minus, Minus) => -((-self) + (-*other))
}
}
}
impl Sub<BigInt, BigInt> for BigInt {
#[inline]
fn sub(&self, other: &BigInt) -> BigInt {
match (self.sign, other.sign) {
(Zero, _) => -other,
(_, Zero) => self.clone(),
(Plus, Plus) => match self.data.cmp(&other.data) {
Less => BigInt::from_biguint(Minus, other.data - self.data),
Greater => BigInt::from_biguint(Plus, self.data - other.data),
Equal => Zero::zero()
},
(Plus, Minus) => self + (-*other),
(Minus, Plus) => -((-self) + *other),
(Minus, Minus) => (-other) - (-*self)
}
}
}
impl Mul<BigInt, BigInt> for BigInt {
#[inline]
fn mul(&self, other: &BigInt) -> BigInt {
match (self.sign, other.sign) {
(Zero, _) | (_, Zero) => Zero::zero(),
(Plus, Plus) | (Minus, Minus) => {
BigInt::from_biguint(Plus, self.data * other.data)
},
(Plus, Minus) | (Minus, Plus) => {
BigInt::from_biguint(Minus, self.data * other.data)
}
}
}
}
impl Div<BigInt, BigInt> for BigInt {
#[inline]
fn div(&self, other: &BigInt) -> BigInt {
let (q, _) = self.div_rem(other);
return q;
}
}
impl Rem<BigInt, BigInt> for BigInt {
#[inline]
fn rem(&self, other: &BigInt) -> BigInt {
let (_, r) = self.div_rem(other);
return r;
}
}
impl Neg<BigInt> for BigInt {
#[inline]
fn neg(&self) -> BigInt {
BigInt::from_biguint(self.sign.neg(), self.data.clone())
}
}
impl Integer for BigInt {
#[inline]
fn div_rem(&self, other: &BigInt) -> (BigInt, BigInt) {
// r.sign == self.sign
let (d_ui, r_ui) = self.data.div_mod_floor(&other.data);
let d = BigInt::from_biguint(Plus, d_ui);
let r = BigInt::from_biguint(Plus, r_ui);
match (self.sign, other.sign) {
(_, Zero) => fail!(),
(Plus, Plus) | (Zero, Plus) => ( d, r),
(Plus, Minus) | (Zero, Minus) => (-d, r),
(Minus, Plus) => (-d, -r),
(Minus, Minus) => ( d, -r)
}
}
#[inline]
fn div_floor(&self, other: &BigInt) -> BigInt {
let (d, _) = self.div_mod_floor(other);
return d;
}
#[inline]
fn mod_floor(&self, other: &BigInt) -> BigInt {
let (_, m) = self.div_mod_floor(other);
return m;
}
fn div_mod_floor(&self, other: &BigInt) -> (BigInt, BigInt) {
// m.sign == other.sign
let (d_ui, m_ui) = self.data.div_rem(&other.data);
let d = BigInt::from_biguint(Plus, d_ui);
let m = BigInt::from_biguint(Plus, m_ui);
match (self.sign, other.sign) {
(_, Zero) => fail!(),
(Plus, Plus) | (Zero, Plus) => (d, m),
(Plus, Minus) | (Zero, Minus) => if m.is_zero() {
(-d, Zero::zero())
} else {
(-d - One::one(), m + *other)
},
(Minus, Plus) => if m.is_zero() {
(-d, Zero::zero())
} else {
(-d - One::one(), other - m)
},
(Minus, Minus) => (d, -m)
}
}
/**
* Calculates the Greatest Common Divisor (GCD) of the number and `other`
*
* The result is always positive
*/
#[inline]
fn gcd(&self, other: &BigInt) -> BigInt {
BigInt::from_biguint(Plus, self.data.gcd(&other.data))
}
/**
* Calculates the Lowest Common Multiple (LCM) of the number and `other`
*/
#[inline]
fn lcm(&self, other: &BigInt) -> BigInt {
BigInt::from_biguint(Plus, self.data.lcm(&other.data))
}
/// Returns `true` if the number can be divided by `other` without leaving a remainder
#[inline]
fn is_multiple_of(&self, other: &BigInt) -> bool { self.data.is_multiple_of(&other.data) }
/// Returns `true` if the number is divisible by `2`
#[inline]
fn is_even(&self) -> bool { self.data.is_even() }
/// Returns `true` if the number is not divisible by `2`
#[inline]
fn is_odd(&self) -> bool { self.data.is_odd() }
}
impl IntConvertible for BigInt {
#[inline]
fn to_int(&self) -> int {
match self.sign {
Plus => num::min(self.to_uint(), int::max_value as uint) as int,
Zero => 0,
Minus => num::min((-self).to_uint(),
(int::max_value as uint) + 1) as int
}
}
#[inline]
fn from_int(n: int) -> BigInt {
if n > 0 {
return BigInt::from_biguint(Plus, BigUint::from_uint(n as uint));
}
if n < 0 {
return BigInt::from_biguint(
Minus, BigUint::from_uint(uint::max_value - (n as uint) + 1)
);
}
return Zero::zero();
}
}
impl ToStrRadix for BigInt {
#[inline]
fn to_str_radix(&self, radix: uint) -> ~str {
match self.sign {
Plus => self.data.to_str_radix(radix),
Zero => ~"0",
Minus => ~"-" + self.data.to_str_radix(radix)
}
}
}
impl FromStrRadix for BigInt {
/// Creates and initializes an BigInt.
#[inline]
fn from_str_radix(s: &str, radix: uint) -> Option<BigInt> {
BigInt::parse_bytes(s.as_bytes(), radix)
}
}
impl BigInt {
/// Creates and initializes an BigInt.
#[inline]
pub fn new(sign: Sign, v: ~[BigDigit]) -> BigInt {
BigInt::from_biguint(sign, BigUint::new(v))
}
/// Creates and initializes an BigInt.
#[inline]
pub fn from_biguint(sign: Sign, data: BigUint) -> BigInt {
if sign == Zero || data.is_zero() {
return BigInt { sign: Zero, data: Zero::zero() };
}
return BigInt { sign: sign, data: data };
}
/// Creates and initializes an BigInt.
#[inline]
pub fn from_uint(n: uint) -> BigInt {
if n == 0 { return Zero::zero(); }
return BigInt::from_biguint(Plus, BigUint::from_uint(n));
}
/// Creates and initializes an BigInt.
#[inline]
pub fn from_slice(sign: Sign, slice: &[BigDigit]) -> BigInt {
BigInt::from_biguint(sign, BigUint::from_slice(slice))
}
/// Creates and initializes an BigInt.
pub fn parse_bytes(buf: &[u8], radix: uint)
-> Option<BigInt> {
if buf.is_empty() { return None; }
let mut sign = Plus;
let mut start = 0;
if buf[0] == ('-' as u8) {
sign = Minus;
start = 1;
}
return BigUint::parse_bytes(buf.slice(start, buf.len()), radix)
.map_move(|bu| BigInt::from_biguint(sign, bu));
}
#[inline]
pub fn to_uint(&self) -> uint {
match self.sign {
Plus => self.data.to_uint(),
Zero => 0,
Minus => 0
}
}
}
#[cfg(test)]
mod biguint_tests {
use super::*;
use std::cmp::{Less, Equal, Greater};
use std::int;
use std::num::{IntConvertible, Zero, One, FromStrRadix};
use std::str;
use std::uint;
use std::vec;
#[test]
fn test_from_slice() {
fn check(slice: &[BigDigit], data: &[BigDigit]) {
assert!(data == BigUint::from_slice(slice).data);
}
check([1], [1]);
check([0, 0, 0], []);
check([1, 2, 0, 0], [1, 2]);
check([0, 0, 1, 2], [0, 0, 1, 2]);
check([0, 0, 1, 2, 0, 0], [0, 0, 1, 2]);
check([-1], [-1]);
}
#[test]
fn test_cmp() {
let data: ~[BigUint] = [ &[], &[1], &[2], &[-1], &[0, 1], &[2, 1], &[1, 1, 1] ]
.map(|v| BigUint::from_slice(*v));
for (i, ni) in data.iter().enumerate() {
for (j0, nj) in data.slice(i, data.len()).iter().enumerate() {
let j = j0 + i;
if i == j {
assert_eq!(ni.cmp(nj), Equal);
assert_eq!(nj.cmp(ni), Equal);
assert_eq!(ni, nj);
assert!(!(ni != nj));
assert!(ni <= nj);
assert!(ni >= nj);
assert!(!(ni < nj));
assert!(!(ni > nj));
} else {
assert_eq!(ni.cmp(nj), Less);
assert_eq!(nj.cmp(ni), Greater);
assert!(!(ni == nj));
assert!(ni != nj);
assert!(ni <= nj);
assert!(!(ni >= nj));
assert!(ni < nj);
assert!(!(ni > nj));
assert!(!(nj <= ni));
assert!(nj >= ni);
assert!(!(nj < ni));
assert!(nj > ni);
}
}
}
}
#[test]
fn test_shl() {
fn check(s: &str, shift: uint, ans: &str) {
let bu = (FromStrRadix::from_str_radix::<BigUint>(s, 16).unwrap() << shift)
.to_str_radix(16);
assert_eq!(bu.as_slice(), ans);
}
check("0", 3, "0");
check("1", 3, "8");
check("1" + "0000" + "0000" + "0000" + "0001" + "0000" + "0000" + "0000" + "0001", 3,
"8" + "0000" + "0000" + "0000" + "0008" + "0000" + "0000" + "0000" + "0008");
check("1" + "0000" + "0001" + "0000" + "0001", 2,
"4" + "0000" + "0004" + "0000" + "0004");
check("1" + "0001" + "0001", 1,
"2" + "0002" + "0002");
check("" + "4000" + "0000" + "0000" + "0000", 3,
"2" + "0000" + "0000" + "0000" + "0000");
check("" + "4000" + "0000", 2,
"1" + "0000" + "0000");
check("" + "4000", 2,
"1" + "0000");
check("" + "4000" + "0000" + "0000" + "0000", 67,
"2" + "0000" + "0000" + "0000" + "0000" + "0000" + "0000" + "0000" + "0000");
check("" + "4000" + "0000", 35,
"2" + "0000" + "0000" + "0000" + "0000");
check("" + "4000", 19,
"2" + "0000" + "0000");
check("" + "fedc" + "ba98" + "7654" + "3210" + "fedc" + "ba98" + "7654" + "3210", 4,
"f" + "edcb" + "a987" + "6543" + "210f" + "edcb" + "a987" + "6543" + "2100");
check("88887777666655554444333322221111", 16,
"888877776666555544443333222211110000");
}
#[test]
fn test_shr() {
fn check(s: &str, shift: uint, ans: &str) {
let bu = (FromStrRadix::from_str_radix::<BigUint>(s, 16).unwrap() >> shift)
.to_str_radix(16);
assert_eq!(bu.as_slice(), ans);
}
check("0", 3, "0");
check("f", 3, "1");
check("1" + "0000" + "0000" + "0000" + "0001" + "0000" + "0000" + "0000" + "0001", 3,
"" + "2000" + "0000" + "0000" + "0000" + "2000" + "0000" + "0000" + "0000");
check("1" + "0000" + "0001" + "0000" + "0001", 2,
"" + "4000" + "0000" + "4000" + "0000");
check("1" + "0001" + "0001", 1,
"" + "8000" + "8000");
check("2" + "0000" + "0000" + "0000" + "0001" + "0000" + "0000" + "0000" + "0001", 67,
"" + "4000" + "0000" + "0000" + "0000");
check("2" + "0000" + "0001" + "0000" + "0001", 35,
"" + "4000" + "0000");
check("2" + "0001" + "0001", 19,
"" + "4000");
check("1" + "0000" + "0000" + "0000" + "0000", 1,
"" + "8000" + "0000" + "0000" + "0000");
check("1" + "0000" + "0000", 1,
"" + "8000" + "0000");
check("1" + "0000", 1,
"" + "8000");
check("f" + "edcb" + "a987" + "6543" + "210f" + "edcb" + "a987" + "6543" + "2100", 4,
"" + "fedc" + "ba98" + "7654" + "3210" + "fedc" + "ba98" + "7654" + "3210");
check("888877776666555544443333222211110000", 16,
"88887777666655554444333322221111");
}
#[test]
fn test_convert_int() {
fn check(v: ~[BigDigit], i: int) {
let b = BigUint::new(v);
assert!(b == IntConvertible::from_int(i));
assert!(b.to_int() == i);
}
check(~[], 0);
check(~[1], 1);
check(~[-1], (uint::max_value >> BigDigit::bits) as int);
check(~[ 0, 1], ((uint::max_value >> BigDigit::bits) + 1) as int);
check(~[-1, -1 >> 1], int::max_value);
assert_eq!(BigUint::new(~[0, -1]).to_int(), int::max_value);
assert_eq!(BigUint::new(~[0, 0, 1]).to_int(), int::max_value);
assert_eq!(BigUint::new(~[0, 0, -1]).to_int(), int::max_value);
}
#[test]
fn test_convert_uint() {
fn check(v: ~[BigDigit], u: uint) {
let b = BigUint::new(v);
assert!(b == BigUint::from_uint(u));
assert!(b.to_uint() == u);
}
check(~[], 0);
check(~[ 1], 1);
check(~[-1], uint::max_value >> BigDigit::bits);
check(~[ 0, 1], (uint::max_value >> BigDigit::bits) + 1);
check(~[ 0, -1], uint::max_value << BigDigit::bits);
check(~[-1, -1], uint::max_value);
assert_eq!(BigUint::new(~[0, 0, 1]).to_uint(), uint::max_value);
assert_eq!(BigUint::new(~[0, 0, -1]).to_uint(), uint::max_value);
}
static sum_triples: &'static [(&'static [BigDigit],
&'static [BigDigit],
&'static [BigDigit])] = &[
(&[], &[], &[]),
(&[], &[ 1], &[ 1]),
(&[ 1], &[ 1], &[ 2]),
(&[ 1], &[ 1, 1], &[ 2, 1]),
(&[ 1], &[-1], &[ 0, 1]),
(&[ 1], &[-1, -1], &[ 0, 0, 1]),
(&[-1, -1], &[-1, -1], &[-2, -1, 1]),
(&[ 1, 1, 1], &[-1, -1], &[ 0, 1, 2]),
(&[ 2, 2, 1], &[-1, -2], &[ 1, 1, 2])
];
#[test]
fn test_add() {
for elm in sum_triples.iter() {
let (aVec, bVec, cVec) = *elm;
let a = BigUint::from_slice(aVec);
let b = BigUint::from_slice(bVec);
let c = BigUint::from_slice(cVec);
assert!(a + b == c);
assert!(b + a == c);
}
}
#[test]
fn test_sub() {
for elm in sum_triples.iter() {
let (aVec, bVec, cVec) = *elm;
let a = BigUint::from_slice(aVec);
let b = BigUint::from_slice(bVec);
let c = BigUint::from_slice(cVec);
assert!(c - a == b);
assert!(c - b == a);
}
}
static mul_triples: &'static [(&'static [BigDigit],
&'static [BigDigit],
&'static [BigDigit])] = &[
(&[], &[], &[]),
(&[], &[ 1], &[]),
(&[ 2], &[], &[]),
(&[ 1], &[ 1], &[1]),
(&[ 2], &[ 3], &[ 6]),
(&[ 1], &[ 1, 1, 1], &[1, 1, 1]),
(&[ 1, 2, 3], &[ 3], &[ 3, 6, 9]),
(&[ 1, 1, 1], &[-1], &[-1, -1, -1]),
(&[ 1, 2, 3], &[-1], &[-1, -2, -2, 2]),
(&[ 1, 2, 3, 4], &[-1], &[-1, -2, -2, -2, 3]),
(&[-1], &[-1], &[ 1, -2]),
(&[-1, -1], &[-1], &[ 1, -1, -2]),
(&[-1, -1, -1], &[-1], &[ 1, -1, -1, -2]),
(&[-1, -1, -1, -1], &[-1], &[ 1, -1, -1, -1, -2]),
(&[-1/2 + 1], &[ 2], &[ 0, 1]),
(&[0, -1/2 + 1], &[ 2], &[ 0, 0, 1]),
(&[ 1, 2], &[ 1, 2, 3], &[1, 4, 7, 6]),
(&[-1, -1], &[-1, -1, -1], &[1, 0, -1, -2, -1]),
(&[-1, -1, -1], &[-1, -1, -1, -1], &[1, 0, 0, -1, -2, -1, -1]),
(&[ 0, 0, 1], &[ 1, 2, 3], &[0, 0, 1, 2, 3]),
(&[ 0, 0, 1], &[ 0, 0, 0, 1], &[0, 0, 0, 0, 0, 1])
];
static div_rem_quadruples: &'static [(&'static [BigDigit],
&'static [BigDigit],
&'static [BigDigit],
&'static [BigDigit])]
= &[
(&[ 1], &[ 2], &[], &[1]),
(&[ 1, 1], &[ 2], &[-1/2+1], &[1]),
(&[ 1, 1, 1], &[ 2], &[-1/2+1, -1/2+1], &[1]),
(&[ 0, 1], &[-1], &[1], &[1]),
(&[-1, -1], &[-2], &[2, 1], &[3])
];
#[test]
fn test_mul() {
for elm in mul_triples.iter() {
let (aVec, bVec, cVec) = *elm;
let a = BigUint::from_slice(aVec);
let b = BigUint::from_slice(bVec);
let c = BigUint::from_slice(cVec);
assert!(a * b == c);
assert!(b * a == c);
}
for elm in div_rem_quadruples.iter() {
let (aVec, bVec, cVec, dVec) = *elm;
let a = BigUint::from_slice(aVec);
let b = BigUint::from_slice(bVec);
let c = BigUint::from_slice(cVec);
let d = BigUint::from_slice(dVec);
assert!(a == b * c + d);
assert!(a == c * b + d);
}
}
#[test]
fn test_div_rem() {
for elm in mul_triples.iter() {
let (aVec, bVec, cVec) = *elm;
let a = BigUint::from_slice(aVec);
let b = BigUint::from_slice(bVec);
let c = BigUint::from_slice(cVec);
if !a.is_zero() {
assert_eq!(c.div_rem(&a), (b.clone(), Zero::zero()));
}
if !b.is_zero() {
assert_eq!(c.div_rem(&b), (a.clone(), Zero::zero()));
}
}
for elm in div_rem_quadruples.iter() {
let (aVec, bVec, cVec, dVec) = *elm;
let a = BigUint::from_slice(aVec);
let b = BigUint::from_slice(bVec);
let c = BigUint::from_slice(cVec);
let d = BigUint::from_slice(dVec);
if !b.is_zero() { assert!(a.div_rem(&b) == (c, d)); }
}
}
#[test]
fn test_gcd() {
fn check(a: uint, b: uint, c: uint) {
let big_a = BigUint::from_uint(a);
let big_b = BigUint::from_uint(b);
let big_c = BigUint::from_uint(c);
assert_eq!(big_a.gcd(&big_b), big_c);
}
check(10, 2, 2);
check(10, 3, 1);
check(0, 3, 3);
check(3, 3, 3);
check(56, 42, 14);
}
#[test]
fn test_lcm() {
fn check(a: uint, b: uint, c: uint) {
let big_a = BigUint::from_uint(a);
let big_b = BigUint::from_uint(b);
let big_c = BigUint::from_uint(c);
assert_eq!(big_a.lcm(&big_b), big_c);
}
check(1, 0, 0);
check(0, 1, 0);
check(1, 1, 1);
check(8, 9, 72);
check(11, 5, 55);
check(99, 17, 1683);
}
#[test]
fn test_is_even() {
assert!(FromStr::from_str::<BigUint>("1").unwrap().is_odd());
assert!(FromStr::from_str::<BigUint>("2").unwrap().is_even());
assert!(FromStr::from_str::<BigUint>("1000").unwrap().is_even());
assert!(FromStr::from_str::<BigUint>("1000000000000000000000").unwrap().is_even());
assert!(FromStr::from_str::<BigUint>("1000000000000000000001").unwrap().is_odd());
assert!((BigUint::from_uint(1) << 64).is_even());
assert!(((BigUint::from_uint(1) << 64) + BigUint::from_uint(1)).is_odd());
}
fn to_str_pairs() -> ~[ (BigUint, ~[(uint, ~str)]) ] {
let bits = BigDigit::bits;
~[( Zero::zero(), ~[
(2, ~"0"), (3, ~"0")
]), ( BigUint::from_slice([ 0xff ]), ~[
(2, ~"11111111"),
(3, ~"100110"),
(4, ~"3333"),
(5, ~"2010"),
(6, ~"1103"),
(7, ~"513"),
(8, ~"377"),
(9, ~"313"),
(10, ~"255"),
(11, ~"212"),
(12, ~"193"),
(13, ~"168"),
(14, ~"143"),
(15, ~"120"),
(16, ~"ff")
]), ( BigUint::from_slice([ 0xfff ]), ~[
(2, ~"111111111111"),
(4, ~"333333"),
(16, ~"fff")
]), ( BigUint::from_slice([ 1, 2 ]), ~[
(2,
~"10" +
str::from_chars(vec::from_elem(bits - 1, '0')) + "1"),
(4,
~"2" +
str::from_chars(vec::from_elem(bits / 2 - 1, '0')) + "1"),
(10, match bits {
32 => ~"8589934593", 16 => ~"131073", _ => fail!()
}),
(16,
~"2" +
str::from_chars(vec::from_elem(bits / 4 - 1, '0')) + "1")
]), ( BigUint::from_slice([ 1, 2, 3 ]), ~[
(2,
~"11" +
str::from_chars(vec::from_elem(bits - 2, '0')) + "10" +
str::from_chars(vec::from_elem(bits - 1, '0')) + "1"),
(4,
~"3" +
str::from_chars(vec::from_elem(bits / 2 - 1, '0')) + "2" +
str::from_chars(vec::from_elem(bits / 2 - 1, '0')) + "1"),
(10, match bits {
32 => ~"55340232229718589441",
16 => ~"12885032961",
_ => fail!()
}),
(16, ~"3" +
str::from_chars(vec::from_elem(bits / 4 - 1, '0')) + "2" +
str::from_chars(vec::from_elem(bits / 4 - 1, '0')) + "1")
]) ]
}
#[test]
fn test_to_str_radix() {
let r = to_str_pairs();
for num_pair in r.iter() {
let &(ref n, ref rs) = num_pair;
for str_pair in rs.iter() {
let &(ref radix, ref str) = str_pair;
assert_eq!(&n.to_str_radix(*radix), str);
}
}
}
#[test]
fn test_from_str_radix() {
let r = to_str_pairs();
for num_pair in r.iter() {
let &(ref n, ref rs) = num_pair;
for str_pair in rs.iter() {
let &(ref radix, ref str) = str_pair;
assert_eq!(n, &FromStrRadix::from_str_radix(*str, *radix).unwrap());
}
}
assert_eq!(FromStrRadix::from_str_radix::<BigUint>("Z", 10), None);
assert_eq!(FromStrRadix::from_str_radix::<BigUint>("_", 2), None);
assert_eq!(FromStrRadix::from_str_radix::<BigUint>("-1", 10), None);
}
#[test]
fn test_factor() {
fn factor(n: uint) -> BigUint {
let mut f= One::one::<BigUint>();
for i in range(2, n + 1) {
// FIXME(#6102): Assignment operator for BigInt causes ICE
// f *= BigUint::from_uint(i);
f = f * BigUint::from_uint(i);
}
return f;
}
fn check(n: uint, s: &str) {
let n = factor(n);
let ans = match FromStrRadix::from_str_radix(s, 10) {
Some(x) => x, None => fail!()
};
assert_eq!(n, ans);
}
check(3, "6");
check(10, "3628800");
check(20, "2432902008176640000");
check(30, "265252859812191058636308480000000");
}
}
#[cfg(test)]
mod bigint_tests {
use super::*;
use std::cmp::{Less, Equal, Greater};
use std::int;
use std::num::{IntConvertible, Zero, One, FromStrRadix};
use std::uint;
#[test]
fn test_from_biguint() {
fn check(inp_s: Sign, inp_n: uint, ans_s: Sign, ans_n: uint) {
let inp = BigInt::from_biguint(inp_s, BigUint::from_uint(inp_n));
let ans = BigInt { sign: ans_s, data: BigUint::from_uint(ans_n)};
assert_eq!(inp, ans);
}
check(Plus, 1, Plus, 1);
check(Plus, 0, Zero, 0);
check(Minus, 1, Minus, 1);
check(Zero, 1, Zero, 0);
}
#[test]
fn test_cmp() {
let vs = [ &[2 as BigDigit], &[1, 1], &[2, 1], &[1, 1, 1] ];
let mut nums = ~[];
for s in vs.rev_iter() {
nums.push(BigInt::from_slice(Minus, *s));
}
nums.push(Zero::zero());
nums.push_all_move(vs.map(|s| BigInt::from_slice(Plus, *s)));
for (i, ni) in nums.iter().enumerate() {
for (j0, nj) in nums.slice(i, nums.len()).iter().enumerate() {
let j = i + j0;
if i == j {
assert_eq!(ni.cmp(nj), Equal);
assert_eq!(nj.cmp(ni), Equal);
assert_eq!(ni, nj);
assert!(!(ni != nj));
assert!(ni <= nj);
assert!(ni >= nj);
assert!(!(ni < nj));
assert!(!(ni > nj));
} else {
assert_eq!(ni.cmp(nj), Less);
assert_eq!(nj.cmp(ni), Greater);
assert!(!(ni == nj));
assert!(ni != nj);
assert!(ni <= nj);
assert!(!(ni >= nj));
assert!(ni < nj);
assert!(!(ni > nj));
assert!(!(nj <= ni));
assert!(nj >= ni);
assert!(!(nj < ni));
assert!(nj > ni);
}
}
}
}
#[test]
fn test_convert_int() {
fn check(b: BigInt, i: int) {
assert!(b == IntConvertible::from_int(i));
assert!(b.to_int() == i);
}
check(Zero::zero(), 0);
check(One::one(), 1);
check(BigInt::from_biguint(
Plus, BigUint::from_uint(int::max_value as uint)
), int::max_value);
assert!(BigInt::from_biguint(
Plus, BigUint::from_uint(int::max_value as uint + 1)
).to_int() == int::max_value);
assert!(BigInt::from_biguint(
Plus, BigUint::new(~[1, 2, 3])
).to_int() == int::max_value);
check(BigInt::from_biguint(
Minus, BigUint::from_uint(-int::min_value as uint)
), int::min_value);
assert!(BigInt::from_biguint(
Minus, BigUint::from_uint(-int::min_value as uint + 1)
).to_int() == int::min_value);
assert!(BigInt::from_biguint(
Minus, BigUint::new(~[1, 2, 3])
).to_int() == int::min_value);
}
#[test]
fn test_convert_uint() {
fn check(b: BigInt, u: uint) {
assert!(b == BigInt::from_uint(u));
assert!(b.to_uint() == u);
}
check(Zero::zero(), 0);
check(One::one(), 1);
check(
BigInt::from_biguint(Plus, BigUint::from_uint(uint::max_value)),
uint::max_value);
assert!(BigInt::from_biguint(
Plus, BigUint::new(~[1, 2, 3])
).to_uint() == uint::max_value);
assert!(BigInt::from_biguint(
Minus, BigUint::from_uint(uint::max_value)
).to_uint() == 0);
assert!(BigInt::from_biguint(
Minus, BigUint::new(~[1, 2, 3])
).to_uint() == 0);
}
static sum_triples: &'static [(&'static [BigDigit],
&'static [BigDigit],
&'static [BigDigit])] = &[
(&[], &[], &[]),
(&[], &[ 1], &[ 1]),
(&[ 1], &[ 1], &[ 2]),
(&[ 1], &[ 1, 1], &[ 2, 1]),
(&[ 1], &[-1], &[ 0, 1]),
(&[ 1], &[-1, -1], &[ 0, 0, 1]),
(&[-1, -1], &[-1, -1], &[-2, -1, 1]),
(&[ 1, 1, 1], &[-1, -1], &[ 0, 1, 2]),
(&[ 2, 2, 1], &[-1, -2], &[ 1, 1, 2])
];
#[test]
fn test_add() {
for elm in sum_triples.iter() {
let (aVec, bVec, cVec) = *elm;
let a = BigInt::from_slice(Plus, aVec);
let b = BigInt::from_slice(Plus, bVec);
let c = BigInt::from_slice(Plus, cVec);
assert!(a + b == c);
assert!(b + a == c);
assert!(c + (-a) == b);
assert!(c + (-b) == a);
assert!(a + (-c) == (-b));
assert!(b + (-c) == (-a));
assert!((-a) + (-b) == (-c))
assert!(a + (-a) == Zero::zero());
}
}
#[test]
fn test_sub() {
for elm in sum_triples.iter() {
let (aVec, bVec, cVec) = *elm;
let a = BigInt::from_slice(Plus, aVec);
let b = BigInt::from_slice(Plus, bVec);
let c = BigInt::from_slice(Plus, cVec);
assert!(c - a == b);
assert!(c - b == a);
assert!((-b) - a == (-c))
assert!((-a) - b == (-c))
assert!(b - (-a) == c);
assert!(a - (-b) == c);
assert!((-c) - (-a) == (-b));
assert!(a - a == Zero::zero());
}
}
static mul_triples: &'static [(&'static [BigDigit],
&'static [BigDigit],
&'static [BigDigit])] = &[
(&[], &[], &[]),
(&[], &[ 1], &[]),
(&[ 2], &[], &[]),
(&[ 1], &[ 1], &[1]),
(&[ 2], &[ 3], &[ 6]),
(&[ 1], &[ 1, 1, 1], &[1, 1, 1]),
(&[ 1, 2, 3], &[ 3], &[ 3, 6, 9]),
(&[ 1, 1, 1], &[-1], &[-1, -1, -1]),
(&[ 1, 2, 3], &[-1], &[-1, -2, -2, 2]),
(&[ 1, 2, 3, 4], &[-1], &[-1, -2, -2, -2, 3]),
(&[-1], &[-1], &[ 1, -2]),
(&[-1, -1], &[-1], &[ 1, -1, -2]),
(&[-1, -1, -1], &[-1], &[ 1, -1, -1, -2]),
(&[-1, -1, -1, -1], &[-1], &[ 1, -1, -1, -1, -2]),
(&[-1/2 + 1], &[ 2], &[ 0, 1]),
(&[0, -1/2 + 1], &[ 2], &[ 0, 0, 1]),
(&[ 1, 2], &[ 1, 2, 3], &[1, 4, 7, 6]),
(&[-1, -1], &[-1, -1, -1], &[1, 0, -1, -2, -1]),
(&[-1, -1, -1], &[-1, -1, -1, -1], &[1, 0, 0, -1, -2, -1, -1]),
(&[ 0, 0, 1], &[ 1, 2, 3], &[0, 0, 1, 2, 3]),
(&[ 0, 0, 1], &[ 0, 0, 0, 1], &[0, 0, 0, 0, 0, 1])
];
static div_rem_quadruples: &'static [(&'static [BigDigit],
&'static [BigDigit],
&'static [BigDigit],
&'static [BigDigit])]
= &[
(&[ 1], &[ 2], &[], &[1]),
(&[ 1, 1], &[ 2], &[-1/2+1], &[1]),
(&[ 1, 1, 1], &[ 2], &[-1/2+1, -1/2+1], &[1]),
(&[ 0, 1], &[-1], &[1], &[1]),
(&[-1, -1], &[-2], &[2, 1], &[3])
];
#[test]
fn test_mul() {
for elm in mul_triples.iter() {
let (aVec, bVec, cVec) = *elm;
let a = BigInt::from_slice(Plus, aVec);
let b = BigInt::from_slice(Plus, bVec);
let c = BigInt::from_slice(Plus, cVec);
assert!(a * b == c);
assert!(b * a == c);
assert!((-a) * b == -c);
assert!((-b) * a == -c);
}
for elm in div_rem_quadruples.iter() {
let (aVec, bVec, cVec, dVec) = *elm;
let a = BigInt::from_slice(Plus, aVec);
let b = BigInt::from_slice(Plus, bVec);
let c = BigInt::from_slice(Plus, cVec);
let d = BigInt::from_slice(Plus, dVec);
assert!(a == b * c + d);
assert!(a == c * b + d);
}
}
#[test]
fn test_div_mod_floor() {
fn check_sub(a: &BigInt, b: &BigInt, ans_d: &BigInt, ans_m: &BigInt) {
let (d, m) = a.div_mod_floor(b);
if !m.is_zero() {
assert_eq!(m.sign, b.sign);
}
assert!(m.abs() <= b.abs());
assert!(*a == b * d + m);
assert!(d == *ans_d);
assert!(m == *ans_m);
}
fn check(a: &BigInt, b: &BigInt, d: &BigInt, m: &BigInt) {
if m.is_zero() {
check_sub(a, b, d, m);
check_sub(a, &b.neg(), &d.neg(), m);
check_sub(&a.neg(), b, &d.neg(), m);
check_sub(&a.neg(), &b.neg(), d, m);
} else {
check_sub(a, b, d, m);
check_sub(a, &b.neg(), &(d.neg() - One::one()), &(m - *b));
check_sub(&a.neg(), b, &(d.neg() - One::one()), &(b - *m));
check_sub(&a.neg(), &b.neg(), d, &m.neg());
}
}
for elm in mul_triples.iter() {
let (aVec, bVec, cVec) = *elm;
let a = BigInt::from_slice(Plus, aVec);
let b = BigInt::from_slice(Plus, bVec);
let c = BigInt::from_slice(Plus, cVec);
if !a.is_zero() { check(&c, &a, &b, &Zero::zero()); }
if !b.is_zero() { check(&c, &b, &a, &Zero::zero()); }
}
for elm in div_rem_quadruples.iter() {
let (aVec, bVec, cVec, dVec) = *elm;
let a = BigInt::from_slice(Plus, aVec);
let b = BigInt::from_slice(Plus, bVec);
let c = BigInt::from_slice(Plus, cVec);
let d = BigInt::from_slice(Plus, dVec);
if !b.is_zero() {
check(&a, &b, &c, &d);
}
}
}
#[test]
fn test_div_rem() {
fn check_sub(a: &BigInt, b: &BigInt, ans_q: &BigInt, ans_r: &BigInt) {
let (q, r) = a.div_rem(b);
if !r.is_zero() {
assert_eq!(r.sign, a.sign);
}
assert!(r.abs() <= b.abs());
assert!(*a == b * q + r);
assert!(q == *ans_q);
assert!(r == *ans_r);
}
fn check(a: &BigInt, b: &BigInt, q: &BigInt, r: &BigInt) {
check_sub(a, b, q, r);
check_sub(a, &b.neg(), &q.neg(), r);
check_sub(&a.neg(), b, &q.neg(), &r.neg());
check_sub(&a.neg(), &b.neg(), q, &r.neg());
}
for elm in mul_triples.iter() {
let (aVec, bVec, cVec) = *elm;
let a = BigInt::from_slice(Plus, aVec);
let b = BigInt::from_slice(Plus, bVec);
let c = BigInt::from_slice(Plus, cVec);
if !a.is_zero() { check(&c, &a, &b, &Zero::zero()); }
if !b.is_zero() { check(&c, &b, &a, &Zero::zero()); }
}
for elm in div_rem_quadruples.iter() {
let (aVec, bVec, cVec, dVec) = *elm;
let a = BigInt::from_slice(Plus, aVec);
let b = BigInt::from_slice(Plus, bVec);
let c = BigInt::from_slice(Plus, cVec);
let d = BigInt::from_slice(Plus, dVec);
if !b.is_zero() {
check(&a, &b, &c, &d);
}
}
}
#[test]
fn test_gcd() {
fn check(a: int, b: int, c: int) {
let big_a: BigInt = IntConvertible::from_int(a);
let big_b: BigInt = IntConvertible::from_int(b);
let big_c: BigInt = IntConvertible::from_int(c);
assert_eq!(big_a.gcd(&big_b), big_c);
}
check(10, 2, 2);
check(10, 3, 1);
check(0, 3, 3);
check(3, 3, 3);
check(56, 42, 14);
check(3, -3, 3);
check(-6, 3, 3);
check(-4, -2, 2);
}
#[test]
fn test_lcm() {
fn check(a: int, b: int, c: int) {
let big_a: BigInt = IntConvertible::from_int(a);
let big_b: BigInt = IntConvertible::from_int(b);
let big_c: BigInt = IntConvertible::from_int(c);
assert_eq!(big_a.lcm(&big_b), big_c);
}
check(1, 0, 0);
check(0, 1, 0);
check(1, 1, 1);
check(-1, 1, 1);
check(1, -1, 1);
check(-1, -1, 1);
check(8, 9, 72);
check(11, 5, 55);
}
#[test]
fn test_abs_sub() {
assert_eq!((-One::one::<BigInt>()).abs_sub(&One::one()), Zero::zero());
assert_eq!(One::one::<BigInt>().abs_sub(&One::one()), Zero::zero());
assert_eq!(One::one::<BigInt>().abs_sub(&Zero::zero()), One::one());
assert_eq!(One::one::<BigInt>().abs_sub(&-One::one::<BigInt>()),
IntConvertible::from_int(2));
}
#[test]
fn test_to_str_radix() {
fn check(n: int, ans: &str) {
assert!(ans == IntConvertible::from_int::<BigInt>(n).to_str_radix(10));
}
check(10, "10");
check(1, "1");
check(0, "0");
check(-1, "-1");
check(-10, "-10");
}
#[test]
fn test_from_str_radix() {
fn check(s: &str, ans: Option<int>) {
let ans = ans.map_move(|n| IntConvertible::from_int::<BigInt>(n));
assert_eq!(FromStrRadix::from_str_radix(s, 10), ans);
}
check("10", Some(10));
check("1", Some(1));
check("0", Some(0));
check("-1", Some(-1));
check("-10", Some(-10));
check("Z", None);
check("_", None);
}
#[test]
fn test_neg() {
assert!(-BigInt::new(Plus, ~[1, 1, 1]) ==
BigInt::new(Minus, ~[1, 1, 1]));
assert!(-BigInt::new(Minus, ~[1, 1, 1]) ==
BigInt::new(Plus, ~[1, 1, 1]));
assert_eq!(-Zero::zero::<BigInt>(), Zero::zero::<BigInt>());
}
}
#[cfg(test)]
mod bench {
use super::*;
use std::{iterator, util};
use std::num::{Zero, One};
use extra::test::BenchHarness;
fn factorial(n: uint) -> BigUint {
let mut f = One::one::<BigUint>();
for i in iterator::range_inclusive(1, n) {
f = f * BigUint::from_uint(i);
}
f
}
fn fib(n: uint) -> BigUint {
let mut f0 = Zero::zero::<BigUint>();
let mut f1 = One::one::<BigUint>();
for _ in range(0, n) {
let f2 = f0 + f1;
f0 = util::replace(&mut f1, f2);
}
f0
}
#[bench]
fn factorial_100(bh: &mut BenchHarness) {
do bh.iter { factorial(100); }
}
#[bench]
fn fib_100(bh: &mut BenchHarness) {
do bh.iter { fib(100); }
}
#[bench]
fn to_str(bh: &mut BenchHarness) {
let fac = factorial(100);
let fib = fib(100);
do bh.iter { fac.to_str(); }
do bh.iter { fib.to_str(); }
}
}
Reference in a new issue View git blame Copy permalink