rust/src/libstd/num/bigint.rs
2013-05-10 18:38:54 +09:00

1973 lines
61 KiB
Rust

// 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.
*/
#[deny(deprecated_mutable_fields)];
use core::cmp::{Eq, Ord, TotalEq, TotalOrd, Ordering, Less, Equal, Greater};
use core::num::{IntConvertible, Zero, One, ToStrRadix, FromStrRadix};
/**
A BigDigit is a BigUint's composing element.
A BigDigit is half the size of machine word size.
*/
#[cfg(target_arch = "x86")]
#[cfg(target_arch = "arm")]
#[cfg(target_arch = "mips")]
pub type BigDigit = u16;
/**
A BigDigit is a BigUint's composing element.
A BigDigit is half the size of machine word size.
*/
#[cfg(target_arch = "x86_64")]
pub type BigDigit = u32;
pub mod BigDigit {
use bigint::BigDigit;
#[cfg(target_arch = "x86")]
#[cfg(target_arch = "arm")]
#[cfg(target_arch = "mips")]
pub static bits: uint = 16;
#[cfg(target_arch = "x86_64")]
pub static bits: uint = 32;
pub static base: uint = 1 << bits;
priv static hi_mask: uint = (-1 as uint) << bits;
priv static lo_mask: uint = (-1 as uint) >> bits;
#[inline(always)]
priv fn get_hi(n: uint) -> BigDigit { (n >> bits) as BigDigit }
#[inline(always)]
priv fn get_lo(n: uint) -> BigDigit { (n & lo_mask) as BigDigit }
/// Split one machine sized unsigned integer into two BigDigits.
#[inline(always)]
pub fn from_uint(n: uint) -> (BigDigit, BigDigit) {
(get_hi(n), get_lo(n))
}
/// Join two BigDigits into one machine sized unsigned integer
#[inline(always)]
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(always)]
fn eq(&self, other: &BigUint) -> bool { self.equals(other) }
#[inline(always)]
fn ne(&self, other: &BigUint) -> bool { !self.equals(other) }
}
impl TotalEq for BigUint {
#[inline(always)]
fn equals(&self, other: &BigUint) -> bool {
match self.cmp(other) { Equal => true, _ => false }
}
}
impl Ord for BigUint {
#[inline(always)]
fn lt(&self, other: &BigUint) -> bool {
match self.cmp(other) { Less => true, _ => false}
}
#[inline(always)]
fn le(&self, other: &BigUint) -> bool {
match self.cmp(other) { Less | Equal => true, _ => false }
}
#[inline(always)]
fn ge(&self, other: &BigUint) -> bool {
match self.cmp(other) { Greater | Equal => true, _ => false }
}
#[inline(always)]
fn gt(&self, other: &BigUint) -> bool {
match self.cmp(other) { Greater => true, _ => false }
}
}
impl TotalOrd for BigUint {
#[inline(always)]
fn cmp(&self, other: &BigUint) -> Ordering {
let s_len = self.data.len(), o_len = other.data.len();
if s_len < o_len { return Less; }
if s_len > o_len { return Greater; }
for self.data.eachi_reverse |i, elm| {
match (*elm, other.data[i]) {
(l, r) if l < r => return Less,
(l, r) if l > r => return Greater,
_ => loop
};
}
return Equal;
}
}
impl ToStr for BigUint {
#[inline(always)]
fn to_str(&self) -> ~str { self.to_str_radix(10) }
}
impl FromStr for BigUint {
#[inline(always)]
fn from_str(s: &str) -> Option<BigUint> {
FromStrRadix::from_str_radix(s, 10)
}
}
impl Shl<uint, BigUint> for BigUint {
#[inline(always)]
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(always)]
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(always)]
fn zero() -> BigUint { BigUint::new(~[]) }
#[inline(always)]
fn is_zero(&self) -> bool { self.data.is_empty() }
}
impl One for BigUint {
#[inline(always)]
fn one() -> BigUint { BigUint::new(~[1]) }
}
impl Unsigned for BigUint {}
impl Add<BigUint, BigUint> for BigUint {
#[inline(always)]
fn add(&self, other: &BigUint) -> BigUint {
let new_len = uint::max(self.data.len(), other.data.len());
let mut carry = 0;
let 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 { return BigUint::new(sum) };
return BigUint::new(sum + [carry]);
}
}
impl Sub<BigUint, BigUint> for BigUint {
#[inline(always)]
fn sub(&self, other: &BigUint) -> BigUint {
let new_len = uint::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!(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 = self.data.len(), o_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 = uint::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);
#[inline(always)]
fn mul_digit(a: &BigUint, n: BigDigit) -> BigUint {
if n == 0 { return Zero::zero(); }
if n == 1 { return copy *a; }
let mut carry = 0;
let prod = do vec::map(a.data) |ai| {
let (hi, lo) = BigDigit::from_uint(
(*ai as uint) * (n as uint) + (carry as uint)
);
carry = hi;
lo
};
if carry == 0 { return BigUint::new(prod) };
return BigUint::new(prod + [carry]);
}
#[inline(always)]
fn cut_at(a: &BigUint, n: uint) -> (BigUint, BigUint) {
let mid = uint::min(a.data.len(), n);
return (BigUint::from_slice(vec::slice(a.data, mid,
a.data.len())),
BigUint::from_slice(vec::slice(a.data, 0, mid)));
}
#[inline(always)]
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(always)]
fn div(&self, other: &BigUint) -> BigUint {
let (q, _) = self.div_rem(other);
return q;
}
}
impl Rem<BigUint, BigUint> for BigUint {
#[inline(always)]
fn rem(&self, other: &BigUint) -> BigUint {
let (_, r) = self.div_rem(other);
return r;
}
}
impl Neg<BigUint> for BigUint {
#[inline(always)]
fn neg(&self) -> BigUint { fail!() }
}
impl Integer for BigUint {
#[inline(always)]
fn div_rem(&self, other: &BigUint) -> (BigUint, BigUint) {
self.div_mod_floor(other)
}
#[inline(always)]
fn div_floor(&self, other: &BigUint) -> BigUint {
let (d, _) = self.div_mod_floor(other);
return d;
}
#[inline(always)]
fn mod_floor(&self, other: &BigUint) -> BigUint {
let (_, m) = self.div_mod_floor(other);
return m;
}
#[inline(always)]
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 (copy *self, Zero::zero()); }
match self.cmp(other) {
Less => return (Zero::zero(), copy *self),
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);
#[inline(always)]
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 mut (d0, d_unit, b_unit) = div_estimate(&m, &b, n);
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);
}
#[inline(always)]
fn div_estimate(a: &BigUint, b: &BigUint, n: uint)
-> (BigUint, BigUint, BigUint) {
if a.data.len() < n {
return (Zero::zero(), Zero::zero(), copy *a);
}
let an = vec::slice(a.data, a.data.len() - n, a.data.len());
let bn = *b.data.last();
let mut d = ~[];
let mut carry = 0;
for an.each_reverse |elt| {
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(), copy *b);
}
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(always)]
fn gcd(&self, other: &BigUint) -> BigUint {
// Use Euclid's algorithm
let mut m = copy *self, n = copy *other;
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(always)]
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(always)]
fn is_multiple_of(&self, other: &BigUint) -> bool { (*self % *other).is_zero() }
/// Returns `true` if the number is divisible by `2`
#[inline(always)]
fn is_even(&self) -> bool {
// Considering only the last digit.
if self.data.is_empty() {
true
} else {
self.data.last().is_even()
}
}
/// Returns `true` if the number is not divisible by `2`
#[inline(always)]
fn is_odd(&self) -> bool { !self.is_even() }
}
impl IntConvertible for BigUint {
#[inline(always)]
fn to_int(&self) -> int {
uint::min(self.to_uint(), int::max_value as uint) as int
}
#[inline(always)]
fn from_int(n: int) -> BigUint {
if (n < 0) { Zero::zero() } else { BigUint::from_uint(n as uint) }
}
}
impl ToStrRadix for BigUint {
#[inline(always)]
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(copy *self, base), radix, max_len);
#[inline(always)]
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 += [m0.to_uint() as BigDigit];
m = d;
}
if !m.is_zero() {
result += [m.to_uint() as BigDigit];
}
return result;
}
#[inline(always)]
fn fill_concat(v: &[BigDigit], radix: uint, l: uint) -> ~str {
if v.is_empty() { return ~"0" }
let s = str::concat(vec::reversed(v).map(|n| {
let s = uint::to_str_radix(*n as uint, radix);
str::from_chars(vec::from_elem(l - s.len(), '0')) + s
}));
str::trim_left_chars(s, ['0']).to_owned()
}
}
}
impl FromStrRadix for BigUint {
/// Creates and initializes an BigUint.
#[inline(always)]
pub fn from_str_radix(s: &str, radix: uint)
-> Option<BigUint> {
BigUint::parse_bytes(str::to_bytes(s), radix)
}
}
impl BigUint {
/// Creates and initializes an BigUint.
#[inline(always)]
pub fn new(v: ~[BigDigit]) -> BigUint {
// omit trailing zeros
let new_len = v.rposition(|n| *n != 0).map_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(always)]
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(always)]
pub fn from_slice(slice: &[BigDigit]) -> BigUint {
return BigUint::new(vec::to_owned(slice));
}
/// Creates and initializes an BigUint.
#[inline(always)]
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 = uint::max(end, unit_len) - unit_len;
match uint::parse_bytes(vec::slice(buf, 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;
}
}
#[inline(always)]
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(always)]
priv fn shl_unit(&self, n_unit: uint) -> BigUint {
if n_unit == 0 || self.is_zero() { return copy *self; }
return BigUint::new(vec::from_elem(n_unit, 0) + self.data);
}
#[inline(always)]
priv fn shl_bits(&self, n_bits: uint) -> BigUint {
if n_bits == 0 || self.is_zero() { return copy *self; }
let mut carry = 0;
let shifted = do vec::map(self.data) |elem| {
let (hi, lo) = BigDigit::from_uint(
(*elem as uint) << n_bits | (carry as uint)
);
carry = hi;
lo
};
if carry == 0 { return BigUint::new(shifted); }
return BigUint::new(shifted + [carry]);
}
#[inline(always)]
priv fn shr_unit(&self, n_unit: uint) -> BigUint {
if n_unit == 0 { return copy *self; }
if self.data.len() < n_unit { return Zero::zero(); }
return BigUint::from_slice(
vec::slice(self.data, n_unit, self.data.len())
);
}
#[inline(always)]
priv fn shr_bits(&self, n_bits: uint) -> BigUint {
if n_bits == 0 || self.data.is_empty() { return copy *self; }
let mut borrow = 0;
let mut shifted = ~[];
for self.data.each_reverse |elem| {
shifted = ~[(*elem >> n_bits) | borrow] + shifted;
borrow = *elem << (BigDigit::bits - n_bits);
}
return BigUint::new(shifted);
}
}
#[cfg(target_arch = "x86_64")]
#[inline(always)]
priv 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_arch = "arm")]
#[cfg(target_arch = "x86")]
#[cfg(target_arch = "mips")]
#[inline(always)]
priv 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(always)]
fn lt(&self, other: &Sign) -> bool {
match self.cmp(other) { Less => true, _ => false}
}
#[inline(always)]
fn le(&self, other: &Sign) -> bool {
match self.cmp(other) { Less | Equal => true, _ => false }
}
#[inline(always)]
fn ge(&self, other: &Sign) -> bool {
match self.cmp(other) { Greater | Equal => true, _ => false }
}
#[inline(always)]
fn gt(&self, other: &Sign) -> bool {
match self.cmp(other) { Greater => true, _ => false }
}
}
impl TotalOrd for Sign {
#[inline(always)]
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(always)]
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(always)]
fn eq(&self, other: &BigInt) -> bool { self.equals(other) }
#[inline(always)]
fn ne(&self, other: &BigInt) -> bool { !self.equals(other) }
}
impl TotalEq for BigInt {
#[inline(always)]
fn equals(&self, other: &BigInt) -> bool {
match self.cmp(other) { Equal => true, _ => false }
}
}
impl Ord for BigInt {
#[inline(always)]
fn lt(&self, other: &BigInt) -> bool {
match self.cmp(other) { Less => true, _ => false}
}
#[inline(always)]
fn le(&self, other: &BigInt) -> bool {
match self.cmp(other) { Less | Equal => true, _ => false }
}
#[inline(always)]
fn ge(&self, other: &BigInt) -> bool {
match self.cmp(other) { Greater | Equal => true, _ => false }
}
#[inline(always)]
fn gt(&self, other: &BigInt) -> bool {
match self.cmp(other) { Greater => true, _ => false }
}
}
impl TotalOrd for BigInt {
#[inline(always)]
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(always)]
fn to_str(&self) -> ~str { self.to_str_radix(10) }
}
impl FromStr for BigInt {
#[inline(always)]
fn from_str(s: &str) -> Option<BigInt> {
FromStrRadix::from_str_radix(s, 10)
}
}
impl Shl<uint, BigInt> for BigInt {
#[inline(always)]
fn shl(&self, rhs: &uint) -> BigInt {
BigInt::from_biguint(self.sign, self.data << *rhs)
}
}
impl Shr<uint, BigInt> for BigInt {
#[inline(always)]
fn shr(&self, rhs: &uint) -> BigInt {
BigInt::from_biguint(self.sign, self.data >> *rhs)
}
}
impl Zero for BigInt {
#[inline(always)]
fn zero() -> BigInt {
BigInt::from_biguint(Zero, Zero::zero())
}
#[inline(always)]
fn is_zero(&self) -> bool { self.sign == Zero }
}
impl One for BigInt {
#[inline(always)]
fn one() -> BigInt {
BigInt::from_biguint(Plus, One::one())
}
}
impl Signed for BigInt {
#[inline(always)]
fn abs(&self) -> BigInt {
match self.sign {
Plus | Zero => self.clone(),
Minus => BigInt::from_biguint(Plus, self.data.clone())
}
}
#[inline(always)]
fn abs_sub(&self, other: &BigInt) -> BigInt {
if *self <= *other { Zero::zero() } else { *self - *other }
}
#[inline(always)]
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(always)]
fn is_positive(&self) -> bool { self.sign == Plus }
#[inline(always)]
fn is_negative(&self) -> bool { self.sign == Minus }
}
impl Add<BigInt, BigInt> for BigInt {
#[inline(always)]
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(always)]
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(always)]
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(always)]
fn div(&self, other: &BigInt) -> BigInt {
let (q, _) = self.div_rem(other);
return q;
}
}
impl Rem<BigInt, BigInt> for BigInt {
#[inline(always)]
fn rem(&self, other: &BigInt) -> BigInt {
let (_, r) = self.div_rem(other);
return r;
}
}
impl Neg<BigInt> for BigInt {
#[inline(always)]
fn neg(&self) -> BigInt {
BigInt::from_biguint(self.sign.neg(), self.data.clone())
}
}
impl Integer for BigInt {
#[inline(always)]
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(always)]
fn div_floor(&self, other: &BigInt) -> BigInt {
let (d, _) = self.div_mod_floor(other);
return d;
}
#[inline(always)]
fn mod_floor(&self, other: &BigInt) -> BigInt {
let (_, m) = self.div_mod_floor(other);
return m;
}
#[inline(always)]
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),
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(always)]
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(always)]
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(always)]
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(always)]
fn is_even(&self) -> bool { self.data.is_even() }
/// Returns `true` if the number is not divisible by `2`
#[inline(always)]
fn is_odd(&self) -> bool { self.data.is_odd() }
}
impl IntConvertible for BigInt {
#[inline(always)]
fn to_int(&self) -> int {
match self.sign {
Plus => uint::min(self.to_uint(), int::max_value as uint) as int,
Zero => 0,
Minus => uint::min((-self).to_uint(),
(int::max_value as uint) + 1) as int
}
}
#[inline(always)]
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(always)]
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(always)]
fn from_str_radix(s: &str, radix: uint)
-> Option<BigInt> {
BigInt::parse_bytes(str::to_bytes(s), radix)
}
}
pub impl BigInt {
/// Creates and initializes an BigInt.
#[inline(always)]
pub fn new(sign: Sign, v: ~[BigDigit]) -> BigInt {
BigInt::from_biguint(sign, BigUint::new(v))
}
/// Creates and initializes an BigInt.
#[inline(always)]
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(always)]
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(always)]
pub fn from_slice(sign: Sign, slice: &[BigDigit]) -> BigInt {
BigInt::from_biguint(sign, BigUint::from_slice(slice))
}
/// Creates and initializes an BigInt.
#[inline(always)]
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(vec::slice(buf, start, buf.len()), radix)
.map_consume(|bu| BigInt::from_biguint(sign, bu));
}
#[inline(always)]
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 core::num::{IntConvertible, Zero, One, FromStrRadix};
use core::cmp::{Less, Equal, Greater};
#[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 = [ &[], &[1], &[2], &[-1], &[0, 1], &[2, 1], &[1, 1, 1] ]
.map(|v| BigUint::from_slice(*v));
for data.eachi |i, ni| {
for vec::slice(data, i, data.len()).eachi |j0, nj| {
let j = j0 + i;
if i == j {
assert_eq!(ni.cmp(nj), Equal);
assert_eq!(nj.cmp(ni), Equal);
assert!(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(v: ~[BigDigit], shift: uint, ans: ~[BigDigit]) {
assert!(BigUint::new(v) << shift == BigUint::new(ans));
}
check(~[], 3, ~[]);
check(~[1, 1, 1], 3, ~[1 << 3, 1 << 3, 1 << 3]);
check(~[1 << (BigDigit::bits - 2)], 2, ~[0, 1]);
check(~[1 << (BigDigit::bits - 2)], 3, ~[0, 2]);
check(~[1 << (BigDigit::bits - 2)], 3 + BigDigit::bits, ~[0, 0, 2]);
test_shl_bits();
#[cfg(target_arch = "x86_64")]
fn test_shl_bits() {
check(~[0x7654_3210, 0xfedc_ba98,
0x7654_3210, 0xfedc_ba98], 4,
~[0x6543_2100, 0xedcb_a987,
0x6543_210f, 0xedcb_a987, 0xf]);
check(~[0x2222_1111, 0x4444_3333,
0x6666_5555, 0x8888_7777], 16,
~[0x1111_0000, 0x3333_2222,
0x5555_4444, 0x7777_6666, 0x8888]);
}
#[cfg(target_arch = "arm")]
#[cfg(target_arch = "x86")]
#[cfg(target_arch = "mips")]
fn test_shl_bits() {
check(~[0x3210, 0x7654, 0xba98, 0xfedc,
0x3210, 0x7654, 0xba98, 0xfedc], 4,
~[0x2100, 0x6543, 0xa987, 0xedcb,
0x210f, 0x6543, 0xa987, 0xedcb, 0xf]);
check(~[0x1111, 0x2222, 0x3333, 0x4444,
0x5555, 0x6666, 0x7777, 0x8888], 16,
~[0x0000, 0x1111, 0x2222, 0x3333,
0x4444, 0x5555, 0x6666, 0x7777, 0x8888]);
}
}
#[test]
#[ignore(cfg(target_arch = "x86"))]
#[ignore(cfg(target_arch = "arm"))]
#[ignore(cfg(target_arch = "mips"))]
fn test_shr() {
fn check(v: ~[BigDigit], shift: uint, ans: ~[BigDigit]) {
assert!(BigUint::new(v) >> shift == BigUint::new(ans));
}
check(~[], 3, ~[]);
check(~[1, 1, 1], 3,
~[1 << (BigDigit::bits - 3), 1 << (BigDigit::bits - 3)]);
check(~[1 << 2], 2, ~[1]);
check(~[1, 2], 3, ~[1 << (BigDigit::bits - 2)]);
check(~[1, 1, 2], 3 + BigDigit::bits, ~[1 << (BigDigit::bits - 2)]);
check(~[0, 1], 1, ~[0x80000000]);
test_shr_bits();
#[cfg(target_arch = "x86_64")]
fn test_shr_bits() {
check(~[0x6543_2100, 0xedcb_a987,
0x6543_210f, 0xedcb_a987, 0xf], 4,
~[0x7654_3210, 0xfedc_ba98,
0x7654_3210, 0xfedc_ba98]);
check(~[0x1111_0000, 0x3333_2222,
0x5555_4444, 0x7777_6666, 0x8888], 16,
~[0x2222_1111, 0x4444_3333,
0x6666_5555, 0x8888_7777]);
}
#[cfg(target_arch = "arm")]
#[cfg(target_arch = "x86")]
#[cfg(target_arch = "mips")]
fn test_shr_bits() {
check(~[0x2100, 0x6543, 0xa987, 0xedcb,
0x210f, 0x6543, 0xa987, 0xedcb, 0xf], 4,
~[0x3210, 0x7654, 0xba98, 0xfedc,
0x3210, 0x7654, 0xba98, 0xfedc]);
check(~[0x0000, 0x1111, 0x2222, 0x3333,
0x4444, 0x5555, 0x6666, 0x7777, 0x8888], 16,
~[0x1111, 0x2222, 0x3333, 0x4444,
0x5555, 0x6666, 0x7777, 0x8888]);
}
}
#[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!(BigUint::new(~[0, -1]).to_int() == int::max_value);
assert!(BigUint::new(~[0, 0, 1]).to_int() == int::max_value);
assert!(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!(BigUint::new(~[0, 0, 1]).to_uint() == uint::max_value);
assert!(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 sum_triples.each |elm| {
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 sum_triples.each |elm| {
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 mul_triples.each |elm| {
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 div_rem_quadruples.each |elm| {
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 mul_triples.each |elm| {
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!(c.div_rem(&a) == (b.clone(), Zero::zero()));
}
if !b.is_zero() {
assert!(c.div_rem(&b) == (a.clone(), Zero::zero()));
}
}
for div_rem_quadruples.each |elm| {
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);
}
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() {
for to_str_pairs().each |num_pair| {
let &(n, rs) = num_pair;
for rs.each |str_pair| {
let &(radix, str) = str_pair;
assert!(n.to_str_radix(radix) == str);
}
}
}
#[test]
fn test_from_str_radix() {
for to_str_pairs().each |num_pair| {
let &(n, rs) = num_pair;
for rs.each |str_pair| {
let &(radix, str) = str_pair;
assert_eq!(&n, &FromStrRadix::from_str_radix(str, radix).get());
}
}
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 uint::range(2, n + 1) |i| {
// 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!(n == ans);
}
check(3, "6");
check(10, "3628800");
check(20, "2432902008176640000");
check(30, "265252859812191058636308480000000");
}
}
#[cfg(test)]
mod bigint_tests {
use super::*;
use core::cmp::{Less, Equal, Greater};
use core::num::{IntConvertible, Zero, One, FromStrRadix};
#[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!(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], &[1, 1], &[2, 1], &[1, 1, 1] ];
let mut nums = vec::reversed(vs)
.map(|s| BigInt::from_slice(Minus, *s));
nums.push(Zero::zero());
nums.push_all_move(vs.map(|s| BigInt::from_slice(Plus, *s)));
for nums.eachi |i, ni| {
for vec::slice(nums, i, nums.len()).eachi |j0, nj| {
let j = i + j0;
if i == j {
assert_eq!(ni.cmp(nj), Equal);
assert_eq!(nj.cmp(ni), Equal);
assert!(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 sum_triples.each |elm| {
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 sum_triples.each |elm| {
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 mul_triples.each |elm| {
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 div_rem_quadruples.each |elm| {
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!(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 mul_triples.each |elm| {
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 div_rem_quadruples.each |elm| {
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!(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 mul_triples.each |elm| {
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 div_rem_quadruples.each |elm| {
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(|&n| IntConvertible::from_int::<BigInt>(n));
assert!(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!(-Zero::zero::<BigInt>() == Zero::zero::<BigInt>());
}
}