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num-traits/src/bigint.rs

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// Copyright 2013-2014 The Rust Project Developers. See the COPYRIGHT
// file at the top-level directory of this distribution and at
// http://rust-lang.org/COPYRIGHT.
//
// Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or
// http://www.apache.org/licenses/LICENSE-2.0> or the MIT license
// <LICENSE-MIT or http://opensource.org/licenses/MIT>, at your
// option. This file may not be copied, modified, or distributed
// except according to those terms.
//! A Big integer (signed version: `BigInt`, unsigned version: `BigUint`).
//!
//! A `BigUint` is represented as an array of `BigDigit`s.
//! A `BigInt` is a combination of `BigUint` and `Sign`.
//!
//! Common numerical operations are overloaded, so we can treat them
//! the same way we treat other numbers.
//!
//! ## Example
//!
//! ```rust
//! use num::bigint::BigUint;
//! use std::num::{Zero, One};
//! use std::mem::replace;
//!
//! // Calculate large fibonacci numbers.
//! fn fib(n: uint) -> BigUint {
//! let mut f0: BigUint = Zero::zero();
//! let mut f1: BigUint = One::one();
//! for _ in range(0, n) {
//! let f2 = f0 + f1;
//! // This is a low cost way of swapping f0 with f1 and f1 with f2.
//! f0 = replace(&mut f1, f2);
//! }
//! f0
//! }
//!
//! // This is a very large number.
//! println!("fib(1000) = {}", fib(1000));
//! ```
//!
//! It's easy to generate large random numbers:
//!
//! ```rust
//! use num::bigint::{ToBigInt, RandBigInt};
//! use std::rand;
//!
//! let mut rng = rand::task_rng();
//! let a = rng.gen_bigint(1000u);
//!
//! let low = -10000i.to_bigint().unwrap();
//! let high = 10000i.to_bigint().unwrap();
//! let b = rng.gen_bigint_range(&low, &high);
//!
//! // Probably an even larger number.
//! println!("{}", a * b);
//! ```
use Integer;
use rand::Rng;
use std::{cmp, fmt, hash};
use std::default::Default;
use std::from_str::FromStr;
use std::num::CheckedDiv;
use std::num::{ToPrimitive, FromPrimitive};
use std::num::{Zero, One, ToStrRadix, FromStrRadix};
use std::string::String;
use std::{uint, i64, u64};
/// A `BigDigit` is a `BigUint`'s composing element.
pub type BigDigit = u32;
/// A `DoubleBigDigit` is the internal type used to do the computations. Its
/// size is the double of the size of `BigDigit`.
pub type DoubleBigDigit = u64;
pub static ZERO_BIG_DIGIT: BigDigit = 0;
static ZERO_VEC: [BigDigit, ..1] = [ZERO_BIG_DIGIT];
#[allow(non_snake_case)]
pub mod BigDigit {
use super::BigDigit;
use super::DoubleBigDigit;
// `DoubleBigDigit` size dependent
pub static bits: uint = 32;
pub static base: DoubleBigDigit = 1 << bits;
static lo_mask: DoubleBigDigit = (-1 as DoubleBigDigit) >> bits;
#[inline]
fn get_hi(n: DoubleBigDigit) -> BigDigit { (n >> bits) as BigDigit }
#[inline]
fn get_lo(n: DoubleBigDigit) -> BigDigit { (n & lo_mask) as BigDigit }
/// Split one `DoubleBigDigit` into two `BigDigit`s.
#[inline]
pub fn from_doublebigdigit(n: DoubleBigDigit) -> (BigDigit, BigDigit) {
(get_hi(n), get_lo(n))
}
/// Join two `BigDigit`s into one `DoubleBigDigit`
#[inline]
pub fn to_doublebigdigit(hi: BigDigit, lo: BigDigit) -> DoubleBigDigit {
(lo as DoubleBigDigit) | ((hi as DoubleBigDigit) << bits)
}
}
/// A big unsigned integer type.
///
/// A `BigUint`-typed value `BigUint { data: vec!(a, b, c) }` represents a number
/// `(a + b * BigDigit::base + c * BigDigit::base^2)`.
#[deriving(Clone)]
pub struct BigUint {
data: Vec<BigDigit>
}
impl PartialEq for BigUint {
#[inline]
fn eq(&self, other: &BigUint) -> bool {
match self.cmp(other) { Equal => true, _ => false }
}
}
impl Eq for BigUint {}
impl PartialOrd for BigUint {
#[inline]
fn partial_cmp(&self, other: &BigUint) -> Option<Ordering> {
Some(self.cmp(other))
}
}
impl Ord 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.iter().rev().zip(other.data.iter().rev()) {
if self_i < other_i { return Less; }
if self_i > other_i { return Greater; }
}
return Equal;
}
}
impl Default for BigUint {
#[inline]
fn default() -> BigUint { Zero::zero() }
}
impl<S: hash::Writer> hash::Hash<S> for BigUint {
fn hash(&self, state: &mut S) {
// hash 0 in case it's all 0's
0u32.hash(state);
let mut found_first_value = false;
for elem in self.data.iter().rev() {
// don't hash any leading 0's, they shouldn't affect the hash
if found_first_value || *elem != 0 {
found_first_value = true;
elem.hash(state);
}
}
}
}
impl fmt::Show for BigUint {
fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
write!(f, "{}", 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 BitAnd<BigUint, BigUint> for BigUint {
fn bitand(&self, other: &BigUint) -> BigUint {
BigUint::new(self.data.iter().zip(other.data.iter()).map(|(ai, bi)| *ai & *bi).collect())
}
}
impl BitOr<BigUint, BigUint> for BigUint {
fn bitor(&self, other: &BigUint) -> BigUint {
let zeros = ZERO_VEC.iter().cycle();
let (a, b) = if self.data.len() > other.data.len() { (self, other) } else { (other, self) };
let ored = a.data.iter().zip(b.data.iter().chain(zeros)).map(
|(ai, bi)| *ai | *bi
).collect();
return BigUint::new(ored);
}
}
impl BitXor<BigUint, BigUint> for BigUint {
fn bitxor(&self, other: &BigUint) -> BigUint {
let zeros = ZERO_VEC.iter().cycle();
let (a, b) = if self.data.len() > other.data.len() { (self, other) } else { (other, self) };
let xored = a.data.iter().zip(b.data.iter().chain(zeros)).map(
|(ai, bi)| *ai ^ *bi
).collect();
return BigUint::new(xored);
}
}
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(Vec::new()) }
#[inline]
fn is_zero(&self) -> bool { self.data.is_empty() }
}
impl One for BigUint {
#[inline]
fn one() -> BigUint { BigUint::new(vec!(1)) }
}
impl Unsigned for BigUint {}
impl Add<BigUint, BigUint> for BigUint {
fn add(&self, other: &BigUint) -> BigUint {
let zeros = ZERO_VEC.iter().cycle();
let (a, b) = if self.data.len() > other.data.len() { (self, other) } else { (other, self) };
let mut carry = 0;
let mut sum: Vec<BigDigit> = a.data.iter().zip(b.data.iter().chain(zeros)).map(|(ai, bi)| {
let (hi, lo) = BigDigit::from_doublebigdigit(
(*ai as DoubleBigDigit) + (*bi as DoubleBigDigit) + (carry as DoubleBigDigit));
carry = hi;
lo
}).collect();
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 = cmp::max(self.data.len(), other.data.len());
let zeros = ZERO_VEC.iter().cycle();
let (a, b) = (self.data.iter().chain(zeros.clone()), other.data.iter().chain(zeros));
let mut borrow = 0i;
let diff: Vec<BigDigit> = a.take(new_len).zip(b).map(|(ai, bi)| {
let (hi, lo) = BigDigit::from_doublebigdigit(
BigDigit::base
+ (*ai as DoubleBigDigit)
- (*bi as DoubleBigDigit)
- (borrow as DoubleBigDigit)
);
/*
hi * (base) + lo == 1*(base) + ai - bi - borrow
=> ai - bi - borrow < 0 <=> hi == 0
*/
borrow = if hi == 0 { 1 } else { 0 };
lo
}).collect();
assert!(borrow == 0,
"Cannot subtract other from self because other is larger than self.");
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.as_slice()[0]); }
if o_len == 1 { return mul_digit(self, other.data.as_slice()[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 = cmp::max(s_len, o_len) / 2;
let (s_hi, s_lo) = cut_at(self, half_len);
let (o_hi, o_lo) = cut_at(other, half_len);
let ll = s_lo * o_lo;
let hh = s_hi * o_hi;
let mm = {
let (s1, n1) = sub_sign(s_hi, s_lo);
let (s2, n2) = sub_sign(o_hi, o_lo);
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: Vec<BigDigit> = a.data.iter().map(|ai| {
let (hi, lo) = BigDigit::from_doublebigdigit(
(*ai as DoubleBigDigit) * (n as DoubleBigDigit) + (carry as DoubleBigDigit)
);
carry = hi;
lo
}).collect();
if carry != 0 { prod.push(carry); }
return BigUint::new(prod);
}
#[inline]
fn cut_at(a: &BigUint, n: uint) -> (BigUint, BigUint) {
let mid = cmp::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 CheckedAdd for BigUint {
#[inline]
fn checked_add(&self, v: &BigUint) -> Option<BigUint> {
return Some(self.add(v));
}
}
impl CheckedSub for BigUint {
#[inline]
fn checked_sub(&self, v: &BigUint) -> Option<BigUint> {
if *self < *v {
return None;
}
return Some(self.sub(v));
}
}
impl CheckedMul for BigUint {
#[inline]
fn checked_mul(&self, v: &BigUint) -> Option<BigUint> {
return Some(self.mul(v));
}
}
impl CheckedDiv for BigUint {
#[inline]
fn checked_div(&self, v: &BigUint) -> Option<BigUint> {
if v.is_zero() {
return None;
}
return Some(self.div(v));
}
}
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().unwrap();
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: BigUint = Zero::zero();
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(#5992): assignment operator overloads
// d0 -= d_unit
d0 = d0 - d_unit;
// FIXME(#5992): assignment operator overloads
// prod -= b_unit;
prod = prod - b_unit
}
if d0.is_zero() {
n = 2;
continue;
}
n = 1;
// FIXME(#5992): assignment operator overloads
// d += d0;
d = d + d0;
// FIXME(#5992): assignment operator overloads
// 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.tailn(a.data.len() - n);
let bn = *b.data.last().unwrap();
let mut d = Vec::with_capacity(an.len());
let mut carry = 0;
for elt in an.iter().rev() {
let ai = BigDigit::to_doublebigdigit(carry, *elt);
let di = ai / (bn as DoubleBigDigit);
assert!(di < BigDigit::base);
carry = (ai % (bn as DoubleBigDigit)) as BigDigit;
d.push(di as BigDigit)
}
d.reverse();
let shift = (a.data.len() - an.len()) - (b.data.len() - 1);
if shift == 0 {
return (BigUint::new(d), One::one(), (*b).clone());
}
let one: BigUint = One::one();
return (BigUint::new(d).shl_unit(shift),
one.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)) }
/// Deprecated, use `is_multiple_of` instead.
#[deprecated = "function renamed to `is_multiple_of`"]
#[inline]
fn divides(&self, other: &BigUint) -> bool { return self.is_multiple_of(other); }
/// Returns `true` if the number is a multiple of `other`.
#[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.
match self.data.as_slice().head() {
Some(x) => x.is_even(),
None => true
}
}
/// Returns `true` if the number is not divisible by `2`.
#[inline]
fn is_odd(&self) -> bool { !self.is_even() }
}
impl ToPrimitive for BigUint {
#[inline]
fn to_i64(&self) -> Option<i64> {
self.to_u64().and_then(|n| {
// If top bit of u64 is set, it's too large to convert to i64.
if n >> 63 == 0 {
Some(n as i64)
} else {
None
}
})
}
// `DoubleBigDigit` size dependent
#[inline]
fn to_u64(&self) -> Option<u64> {
match self.data.len() {
0 => Some(0),
1 => Some(self.data.as_slice()[0] as u64),
2 => Some(BigDigit::to_doublebigdigit(self.data.as_slice()[1], self.data.as_slice()[0])
as u64),
_ => None
}
}
}
impl FromPrimitive for BigUint {
#[inline]
fn from_i64(n: i64) -> Option<BigUint> {
if n > 0 {
FromPrimitive::from_u64(n as u64)
} else if n == 0 {
Some(Zero::zero())
} else {
None
}
}
// `DoubleBigDigit` size dependent
#[inline]
fn from_u64(n: u64) -> Option<BigUint> {
let n = match BigDigit::from_doublebigdigit(n) {
(0, 0) => Zero::zero(),
(0, n0) => BigUint::new(vec!(n0)),
(n1, n0) => BigUint::new(vec!(n0, n1))
};
Some(n)
}
}
/// A generic trait for converting a value to a `BigUint`.
pub trait ToBigUint {
/// Converts the value of `self` to a `BigUint`.
fn to_biguint(&self) -> Option<BigUint>;
}
impl ToBigUint for BigInt {
#[inline]
fn to_biguint(&self) -> Option<BigUint> {
if self.sign == Plus {
Some(self.data.clone())
} else if self.sign == Zero {
Some(Zero::zero())
} else {
None
}
}
}
impl ToBigUint for BigUint {
#[inline]
fn to_biguint(&self) -> Option<BigUint> {
Some(self.clone())
}
}
macro_rules! impl_to_biguint(
($T:ty, $from_ty:path) => {
impl ToBigUint for $T {
#[inline]
fn to_biguint(&self) -> Option<BigUint> {
$from_ty(*self)
}
}
}
)
impl_to_biguint!(int, FromPrimitive::from_int)
impl_to_biguint!(i8, FromPrimitive::from_i8)
impl_to_biguint!(i16, FromPrimitive::from_i16)
impl_to_biguint!(i32, FromPrimitive::from_i32)
impl_to_biguint!(i64, FromPrimitive::from_i64)
impl_to_biguint!(uint, FromPrimitive::from_uint)
impl_to_biguint!(u8, FromPrimitive::from_u8)
impl_to_biguint!(u16, FromPrimitive::from_u16)
impl_to_biguint!(u32, FromPrimitive::from_u32)
impl_to_biguint!(u64, FromPrimitive::from_u64)
impl ToStrRadix for BigUint {
fn to_str_radix(&self, radix: uint) -> String {
assert!(1 < radix && radix <= 16, "The radix must be within (1, 16]");
let (base, max_len) = get_radix_base(radix);
if base == BigDigit::base {
return fill_concat(self.data.as_slice(), radix, max_len)
}
return fill_concat(convert_base(self, base).as_slice(), radix, max_len);
fn convert_base(n: &BigUint, base: DoubleBigDigit) -> Vec<BigDigit> {
let divider = base.to_biguint().unwrap();
let mut result = Vec::new();
let mut m = n.clone();
while m >= divider {
let (d, m0) = m.div_mod_floor(&divider);
result.push(m0.to_uint().unwrap() as BigDigit);
m = d;
}
if !m.is_zero() {
result.push(m.to_uint().unwrap() as BigDigit);
}
return result;
}
fn fill_concat(v: &[BigDigit], radix: uint, l: uint) -> String {
if v.is_empty() {
return "0".to_string()
}
let mut s = String::with_capacity(v.len() * l);
for n in v.iter().rev() {
let ss = (*n as uint).to_str_radix(radix);
s.push_str("0".repeat(l - ss.len()).as_slice());
s.push_str(ss.as_slice());
}
s.as_slice().trim_left_chars('0').to_string()
}
}
}
impl FromStrRadix for BigUint {
/// Creates and initializes a `BigUint`.
#[inline]
fn from_str_radix(s: &str, radix: uint) -> Option<BigUint> {
BigUint::parse_bytes(s.as_bytes(), radix)
}
}
impl BigUint {
/// Creates and initializes a `BigUint`.
///
/// The digits are be in base 2^32.
#[inline]
pub fn new(mut digits: Vec<BigDigit>) -> BigUint {
// omit trailing zeros
let new_len = digits.iter().rposition(|n| *n != 0).map_or(0, |p| p + 1);
digits.truncate(new_len);
BigUint { data: digits }
}
/// Creates and initializes a `BigUint`.
///
/// The digits are be in base 2^32.
#[inline]
pub fn from_slice(slice: &[BigDigit]) -> BigUint {
BigUint::new(Vec::from_slice(slice))
}
/// Creates and initializes a `BigUint`.
pub fn parse_bytes(buf: &[u8], radix: uint) -> Option<BigUint> {
let (base, unit_len) = get_radix_base(radix);
let base_num = match base.to_biguint() {
Some(base_num) => base_num,
None => { return None; }
};
let mut end = buf.len();
let mut n: BigUint = Zero::zero();
let mut power: BigUint = One::one();
loop {
let start = cmp::max(end, unit_len) - unit_len;
match uint::parse_bytes(buf.slice(start, end), radix) {
Some(d) => {
let d: Option<BigUint> = FromPrimitive::from_uint(d);
match d {
Some(d) => {
// FIXME(#5992): assignment operator overloads
// n += d * power;
n = n + d * power;
}
None => { return None; }
}
}
None => { return None; }
}
if end <= unit_len {
return Some(n);
}
end -= unit_len;
// FIXME(#5992): assignment operator overloads
// power *= base_num;
power = power * base_num;
}
}
#[inline]
fn shl_unit(&self, n_unit: uint) -> BigUint {
if n_unit == 0 || self.is_zero() { return (*self).clone(); }
BigUint::new(Vec::from_elem(n_unit, ZERO_BIG_DIGIT).append(self.data.as_slice()))
}
#[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: Vec<BigDigit> = self.data.iter().map(|elem| {
let (hi, lo) = BigDigit::from_doublebigdigit(
(*elem as DoubleBigDigit) << n_bits | (carry as DoubleBigDigit)
);
carry = hi;
lo
}).collect();
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_rev = Vec::with_capacity(self.data.len());
for elem in self.data.iter().rev() {
shifted_rev.push((*elem >> n_bits) | borrow);
borrow = *elem << (BigDigit::bits - n_bits);
}
let shifted = { shifted_rev.reverse(); shifted_rev };
return BigUint::new(shifted);
}
/// Determines the fewest bits necessary to express the `BigUint`.
pub fn bits(&self) -> uint {
if self.is_zero() { return 0; }
let zeros = self.data.last().unwrap().leading_zeros();
return self.data.len()*BigDigit::bits - zeros;
}
}
// `DoubleBigDigit` size dependent
#[inline]
fn get_radix_base(radix: uint) -> (DoubleBigDigit, uint) {
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!("The radix must be within (1, 16]")
}
}
/// A Sign is a `BigInt`'s composing element.
#[deriving(PartialEq, PartialOrd, Eq, Ord, Clone, Show)]
pub enum Sign { Minus, Zero, Plus }
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 {
sign: Sign,
data: BigUint
}
impl PartialEq for BigInt {
#[inline]
fn eq(&self, other: &BigInt) -> bool {
self.cmp(other) == Equal
}
}
impl Eq for BigInt {}
impl PartialOrd for BigInt {
#[inline]
fn partial_cmp(&self, other: &BigInt) -> Option<Ordering> {
Some(self.cmp(other))
}
}
impl Ord 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 Default for BigInt {
#[inline]
fn default() -> BigInt { Zero::zero() }
}
impl fmt::Show for BigInt {
fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
write!(f, "{}", self.to_str_radix(10))
}
}
impl<S: hash::Writer> hash::Hash<S> for BigInt {
fn hash(&self, state: &mut S) {
(self.sign == Plus).hash(state);
self.data.hash(state);
}
}
impl FromStr for BigInt {
#[inline]
fn from_str(s: &str) -> Option<BigInt> {
FromStrRadix::from_str_radix(s, 10)
}
}
impl Num for BigInt {}
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);
q
}
}
impl Rem<BigInt, BigInt> for BigInt {
#[inline]
fn rem(&self, other: &BigInt) -> BigInt {
let (_, r) = self.div_rem(other);
r
}
}
impl Neg<BigInt> for BigInt {
#[inline]
fn neg(&self) -> BigInt {
BigInt::from_biguint(self.sign.neg(), self.data.clone())
}
}
impl CheckedAdd for BigInt {
#[inline]
fn checked_add(&self, v: &BigInt) -> Option<BigInt> {
return Some(self.add(v));
}
}
impl CheckedSub for BigInt {
#[inline]
fn checked_sub(&self, v: &BigInt) -> Option<BigInt> {
return Some(self.sub(v));
}
}
impl CheckedMul for BigInt {
#[inline]
fn checked_mul(&self, v: &BigInt) -> Option<BigInt> {
return Some(self.mul(v));
}
}
impl CheckedDiv for BigInt {
#[inline]
fn checked_div(&self, v: &BigInt) -> Option<BigInt> {
if v.is_zero() {
return None;
}
return Some(self.div(v));
}
}
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);
d
}
#[inline]
fn mod_floor(&self, other: &BigInt) -> BigInt {
let (_, m) = self.div_mod_floor(other);
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))
}
/// Deprecated, use `is_multiple_of` instead.
#[deprecated = "function renamed to `is_multiple_of`"]
#[inline]
fn divides(&self, other: &BigInt) -> bool { return self.is_multiple_of(other); }
/// Returns `true` if the number is a multiple of `other`.
#[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 ToPrimitive for BigInt {
#[inline]
fn to_i64(&self) -> Option<i64> {
match self.sign {
Plus => self.data.to_i64(),
Zero => Some(0),
Minus => {
self.data.to_u64().and_then(|n| {
let m: u64 = 1 << 63;
if n < m {
Some(-(n as i64))
} else if n == m {
Some(i64::MIN)
} else {
None
}
})
}
}
}
#[inline]
fn to_u64(&self) -> Option<u64> {
match self.sign {
Plus => self.data.to_u64(),
Zero => Some(0),
Minus => None
}
}
}
impl FromPrimitive for BigInt {
#[inline]
fn from_i64(n: i64) -> Option<BigInt> {
if n > 0 {
FromPrimitive::from_u64(n as u64).and_then(|n| {
Some(BigInt::from_biguint(Plus, n))
})
} else if n < 0 {
FromPrimitive::from_u64(u64::MAX - (n as u64) + 1).and_then(
|n| {
Some(BigInt::from_biguint(Minus, n))
})
} else {
Some(Zero::zero())
}
}
#[inline]
fn from_u64(n: u64) -> Option<BigInt> {
if n == 0 {
Some(Zero::zero())
} else {
FromPrimitive::from_u64(n).and_then(|n| {
Some(BigInt::from_biguint(Plus, n))
})
}
}
}
/// A generic trait for converting a value to a `BigInt`.
pub trait ToBigInt {
/// Converts the value of `self` to a `BigInt`.
fn to_bigint(&self) -> Option<BigInt>;
}
impl ToBigInt for BigInt {
#[inline]
fn to_bigint(&self) -> Option<BigInt> {
Some(self.clone())
}
}
impl ToBigInt for BigUint {
#[inline]
fn to_bigint(&self) -> Option<BigInt> {
if self.is_zero() {
Some(Zero::zero())
} else {
Some(BigInt { sign: Plus, data: self.clone() })
}
}
}
macro_rules! impl_to_bigint(
($T:ty, $from_ty:path) => {
impl ToBigInt for $T {
#[inline]
fn to_bigint(&self) -> Option<BigInt> {
$from_ty(*self)
}
}
}
)
impl_to_bigint!(int, FromPrimitive::from_int)
impl_to_bigint!(i8, FromPrimitive::from_i8)
impl_to_bigint!(i16, FromPrimitive::from_i16)
impl_to_bigint!(i32, FromPrimitive::from_i32)
impl_to_bigint!(i64, FromPrimitive::from_i64)
impl_to_bigint!(uint, FromPrimitive::from_uint)
impl_to_bigint!(u8, FromPrimitive::from_u8)
impl_to_bigint!(u16, FromPrimitive::from_u16)
impl_to_bigint!(u32, FromPrimitive::from_u32)
impl_to_bigint!(u64, FromPrimitive::from_u64)
impl ToStrRadix for BigInt {
#[inline]
fn to_str_radix(&self, radix: uint) -> String {
match self.sign {
Plus => self.data.to_str_radix(radix),
Zero => "0".to_string(),
Minus => format!("-{}", self.data.to_str_radix(radix)),
}
}
}
impl FromStrRadix for BigInt {
/// Creates and initializes a BigInt.
#[inline]
fn from_str_radix(s: &str, radix: uint) -> Option<BigInt> {
BigInt::parse_bytes(s.as_bytes(), radix)
}
}
pub trait RandBigInt {
/// Generate a random `BigUint` of the given bit size.
fn gen_biguint(&mut self, bit_size: uint) -> BigUint;
/// Generate a random BigInt of the given bit size.
fn gen_bigint(&mut self, bit_size: uint) -> BigInt;
/// Generate a random `BigUint` less than the given bound. Fails
/// when the bound is zero.
fn gen_biguint_below(&mut self, bound: &BigUint) -> BigUint;
/// Generate a random `BigUint` within the given range. The lower
/// bound is inclusive; the upper bound is exclusive. Fails when
/// the upper bound is not greater than the lower bound.
fn gen_biguint_range(&mut self, lbound: &BigUint, ubound: &BigUint) -> BigUint;
/// Generate a random `BigInt` within the given range. The lower
/// bound is inclusive; the upper bound is exclusive. Fails when
/// the upper bound is not greater than the lower bound.
fn gen_bigint_range(&mut self, lbound: &BigInt, ubound: &BigInt) -> BigInt;
}
impl<R: Rng> RandBigInt for R {
fn gen_biguint(&mut self, bit_size: uint) -> BigUint {
let (digits, rem) = bit_size.div_rem(&BigDigit::bits);
let mut data = Vec::with_capacity(digits+1);
for _ in range(0, digits) {
data.push(self.gen());
}
if rem > 0 {
let final_digit: BigDigit = self.gen();
data.push(final_digit >> (BigDigit::bits - rem));
}
BigUint::new(data)
}
fn gen_bigint(&mut self, bit_size: uint) -> BigInt {
// Generate a random BigUint...
let biguint = self.gen_biguint(bit_size);
// ...and then randomly assign it a Sign...
let sign = if biguint.is_zero() {
// ...except that if the BigUint is zero, we need to try
// again with probability 0.5. This is because otherwise,
// the probability of generating a zero BigInt would be
// double that of any other number.
if self.gen() {
return self.gen_bigint(bit_size);
} else {
Zero
}
} else if self.gen() {
Plus
} else {
Minus
};
BigInt::from_biguint(sign, biguint)
}
fn gen_biguint_below(&mut self, bound: &BigUint) -> BigUint {
assert!(!bound.is_zero());
let bits = bound.bits();
loop {
let n = self.gen_biguint(bits);
if n < *bound { return n; }
}
}
fn gen_biguint_range(&mut self,
lbound: &BigUint,
ubound: &BigUint)
-> BigUint {
assert!(*lbound < *ubound);
return *lbound + self.gen_biguint_below(&(*ubound - *lbound));
}
fn gen_bigint_range(&mut self,
lbound: &BigInt,
ubound: &BigInt)
-> BigInt {
assert!(*lbound < *ubound);
let delta = (*ubound - *lbound).to_biguint().unwrap();
return *lbound + self.gen_biguint_below(&delta).to_bigint().unwrap();
}
}
impl BigInt {
/// Creates and initializes a BigInt.
///
/// The digits are be in base 2^32.
#[inline]
pub fn new(sign: Sign, digits: Vec<BigDigit>) -> BigInt {
BigInt::from_biguint(sign, BigUint::new(digits))
}
/// Creates and initializes a `BigInt`.
///
/// The digits are be in base 2^32.
#[inline]
pub fn from_biguint(sign: Sign, data: BigUint) -> BigInt {
if sign == Zero || data.is_zero() {
return BigInt { sign: Zero, data: Zero::zero() };
}
BigInt { sign: sign, data: data }
}
/// Creates and initializes a `BigInt`.
#[inline]
pub fn from_slice(sign: Sign, slice: &[BigDigit]) -> BigInt {
BigInt::from_biguint(sign, BigUint::from_slice(slice))
}
/// Creates and initializes a `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] == b'-' {
sign = Minus;
start = 1;
}
return BigUint::parse_bytes(buf.slice(start, buf.len()), radix)
.map(|bu| BigInt::from_biguint(sign, bu));
}
/// Converts this `BigInt` into a `BigUint`, if it's not negative.
#[inline]
pub fn to_biguint(&self) -> Option<BigUint> {
match self.sign {
Plus => Some(self.data.clone()),
Zero => Some(Zero::zero()),
Minus => None
}
}
}
#[cfg(test)]
mod biguint_tests {
use Integer;
use super::{BigDigit, BigUint, ToBigUint};
use super::{Plus, BigInt, RandBigInt, ToBigInt};
use std::cmp::{Less, Equal, Greater};
use std::from_str::FromStr;
use std::i64;
use std::num::{Zero, One, FromStrRadix, ToStrRadix};
use std::num::{ToPrimitive, FromPrimitive};
use std::num::CheckedDiv;
use std::rand::task_rng;
use std::u64;
use std::hash::hash;
#[test]
fn test_from_slice() {
fn check(slice: &[BigDigit], data: &[BigDigit]) {
assert!(data == BigUint::from_slice(slice).data.as_slice());
}
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: [&[_], ..7] = [ &[], &[1], &[2], &[-1], &[0, 1], &[2, 1], &[1, 1, 1] ];
let data: Vec<BigUint> = data.iter().map(|v| BigUint::from_slice(*v)).collect();
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_hash() {
let a = BigUint::new(vec!());
let b = BigUint::new(vec!(0));
let c = BigUint::new(vec!(1));
let d = BigUint::new(vec!(1,0,0,0,0,0));
let e = BigUint::new(vec!(0,0,0,0,0,1));
assert!(hash(&a) == hash(&b));
assert!(hash(&b) != hash(&c));
assert!(hash(&c) == hash(&d));
assert!(hash(&d) != hash(&e));
}
#[test]
fn test_bitand() {
fn check(left: &[BigDigit],
right: &[BigDigit],
expected: &[BigDigit]) {
assert_eq!(BigUint::from_slice(left) & BigUint::from_slice(right),
BigUint::from_slice(expected));
}
check([], [], []);
check([268, 482, 17],
[964, 54],
[260, 34]);
}
#[test]
fn test_bitor() {
fn check(left: &[BigDigit],
right: &[BigDigit],
expected: &[BigDigit]) {
assert_eq!(BigUint::from_slice(left) | BigUint::from_slice(right),
BigUint::from_slice(expected));
}
check([], [], []);
check([268, 482, 17],
[964, 54],
[972, 502, 17]);
}
#[test]
fn test_bitxor() {
fn check(left: &[BigDigit],
right: &[BigDigit],
expected: &[BigDigit]) {
assert_eq!(BigUint::from_slice(left) ^ BigUint::from_slice(right),
BigUint::from_slice(expected));
}
check([], [], []);
check([268, 482, 17],
[964, 54],
[712, 468, 17]);
}
#[test]
fn test_shl() {
fn check(s: &str, shift: uint, ans: &str) {
let opt_biguint: Option<BigUint> = FromStrRadix::from_str_radix(s, 16);
let bu = (opt_biguint.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 opt_biguint: Option<BigUint> =
FromStrRadix::from_str_radix(s, 16);
let bu = (opt_biguint.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");
}
// `DoubleBigDigit` size dependent
#[test]
fn test_convert_i64() {
fn check(b1: BigUint, i: i64) {
let b2: BigUint = FromPrimitive::from_i64(i).unwrap();
assert!(b1 == b2);
assert!(b1.to_i64().unwrap() == i);
}
check(Zero::zero(), 0);
check(One::one(), 1);
check(i64::MAX.to_biguint().unwrap(), i64::MAX);
check(BigUint::new(vec!( )), 0);
check(BigUint::new(vec!( 1 )), (1 << (0*BigDigit::bits)));
check(BigUint::new(vec!(-1 )), (1 << (1*BigDigit::bits)) - 1);
check(BigUint::new(vec!( 0, 1 )), (1 << (1*BigDigit::bits)));
check(BigUint::new(vec!(-1, -1 >> 1)), i64::MAX);
assert_eq!(i64::MIN.to_biguint(), None);
assert_eq!(BigUint::new(vec!(-1, -1 )).to_i64(), None);
assert_eq!(BigUint::new(vec!( 0, 0, 1)).to_i64(), None);
assert_eq!(BigUint::new(vec!(-1, -1, -1)).to_i64(), None);
}
// `DoubleBigDigit` size dependent
#[test]
fn test_convert_u64() {
fn check(b1: BigUint, u: u64) {
let b2: BigUint = FromPrimitive::from_u64(u).unwrap();
assert!(b1 == b2);
assert!(b1.to_u64().unwrap() == u);
}
check(Zero::zero(), 0);
check(One::one(), 1);
check(u64::MIN.to_biguint().unwrap(), u64::MIN);
check(u64::MAX.to_biguint().unwrap(), u64::MAX);
check(BigUint::new(vec!( )), 0);
check(BigUint::new(vec!( 1 )), (1 << (0*BigDigit::bits)));
check(BigUint::new(vec!(-1 )), (1 << (1*BigDigit::bits)) - 1);
check(BigUint::new(vec!( 0, 1)), (1 << (1*BigDigit::bits)));
check(BigUint::new(vec!(-1, -1)), u64::MAX);
assert_eq!(BigUint::new(vec!( 0, 0, 1)).to_u64(), None);
assert_eq!(BigUint::new(vec!(-1, -1, -1)).to_u64(), None);
}
#[test]
fn test_convert_to_bigint() {
fn check(n: BigUint, ans: BigInt) {
assert_eq!(n.to_bigint().unwrap(), ans);
assert_eq!(n.to_bigint().unwrap().to_biguint().unwrap(), n);
}
check(Zero::zero(), Zero::zero());
check(BigUint::new(vec!(1,2,3)),
BigInt::from_biguint(Plus, BigUint::new(vec!(1,2,3))));
}
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 (a_vec, b_vec, c_vec) = *elm;
let a = BigUint::from_slice(a_vec);
let b = BigUint::from_slice(b_vec);
let c = BigUint::from_slice(c_vec);
assert!(a + b == c);
assert!(b + a == c);
}
}
#[test]
fn test_sub() {
for elm in sum_triples.iter() {
let (a_vec, b_vec, c_vec) = *elm;
let a = BigUint::from_slice(a_vec);
let b = BigUint::from_slice(b_vec);
let c = BigUint::from_slice(c_vec);
assert!(c - a == b);
assert!(c - b == a);
}
}
#[test]
#[should_fail]
fn test_sub_fail_on_underflow() {
let (a, b) : (BigUint, BigUint) = (Zero::zero(), One::one());
a - b;
}
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 (a_vec, b_vec, c_vec) = *elm;
let a = BigUint::from_slice(a_vec);
let b = BigUint::from_slice(b_vec);
let c = BigUint::from_slice(c_vec);
assert!(a * b == c);
assert!(b * a == c);
}
for elm in div_rem_quadruples.iter() {
let (a_vec, b_vec, c_vec, d_vec) = *elm;
let a = BigUint::from_slice(a_vec);
let b = BigUint::from_slice(b_vec);
let c = BigUint::from_slice(c_vec);
let d = BigUint::from_slice(d_vec);
assert!(a == b * c + d);
assert!(a == c * b + d);
}
}
#[test]
fn test_div_rem() {
for elm in mul_triples.iter() {
let (a_vec, b_vec, c_vec) = *elm;
let a = BigUint::from_slice(a_vec);
let b = BigUint::from_slice(b_vec);
let c = BigUint::from_slice(c_vec);
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 (a_vec, b_vec, c_vec, d_vec) = *elm;
let a = BigUint::from_slice(a_vec);
let b = BigUint::from_slice(b_vec);
let c = BigUint::from_slice(c_vec);
let d = BigUint::from_slice(d_vec);
if !b.is_zero() { assert!(a.div_rem(&b) == (c, d)); }
}
}
#[test]
fn test_checked_add() {
for elm in sum_triples.iter() {
let (a_vec, b_vec, c_vec) = *elm;
let a = BigUint::from_slice(a_vec);
let b = BigUint::from_slice(b_vec);
let c = BigUint::from_slice(c_vec);
assert!(a.checked_add(&b).unwrap() == c);
assert!(b.checked_add(&a).unwrap() == c);
}
}
#[test]
fn test_checked_sub() {
for elm in sum_triples.iter() {
let (a_vec, b_vec, c_vec) = *elm;
let a = BigUint::from_slice(a_vec);
let b = BigUint::from_slice(b_vec);
let c = BigUint::from_slice(c_vec);
assert!(c.checked_sub(&a).unwrap() == b);
assert!(c.checked_sub(&b).unwrap() == a);
if a > c {
assert!(a.checked_sub(&c).is_none());
}
if b > c {
assert!(b.checked_sub(&c).is_none());
}
}
}
#[test]
fn test_checked_mul() {
for elm in mul_triples.iter() {
let (a_vec, b_vec, c_vec) = *elm;
let a = BigUint::from_slice(a_vec);
let b = BigUint::from_slice(b_vec);
let c = BigUint::from_slice(c_vec);
assert!(a.checked_mul(&b).unwrap() == c);
assert!(b.checked_mul(&a).unwrap() == c);
}
for elm in div_rem_quadruples.iter() {
let (a_vec, b_vec, c_vec, d_vec) = *elm;
let a = BigUint::from_slice(a_vec);
let b = BigUint::from_slice(b_vec);
let c = BigUint::from_slice(c_vec);
let d = BigUint::from_slice(d_vec);
assert!(a == b.checked_mul(&c).unwrap() + d);
assert!(a == c.checked_mul(&b).unwrap() + d);
}
}
#[test]
fn test_checked_div() {
for elm in mul_triples.iter() {
let (a_vec, b_vec, c_vec) = *elm;
let a = BigUint::from_slice(a_vec);
let b = BigUint::from_slice(b_vec);
let c = BigUint::from_slice(c_vec);
if !a.is_zero() {
assert!(c.checked_div(&a).unwrap() == b);
}
if !b.is_zero() {
assert!(c.checked_div(&b).unwrap() == a);
}
assert!(c.checked_div(&Zero::zero()).is_none());
}
}
#[test]
fn test_gcd() {
fn check(a: uint, b: uint, c: uint) {
let big_a: BigUint = FromPrimitive::from_uint(a).unwrap();
let big_b: BigUint = FromPrimitive::from_uint(b).unwrap();
let big_c: BigUint = FromPrimitive::from_uint(c).unwrap();
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 = FromPrimitive::from_uint(a).unwrap();
let big_b: BigUint = FromPrimitive::from_uint(b).unwrap();
let big_c: BigUint = FromPrimitive::from_uint(c).unwrap();
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() {
let one: BigUint = FromStr::from_str("1").unwrap();
let two: BigUint = FromStr::from_str("2").unwrap();
let thousand: BigUint = FromStr::from_str("1000").unwrap();
let big: BigUint = FromStr::from_str("1000000000000000000000").unwrap();
let bigger: BigUint = FromStr::from_str("1000000000000000000001").unwrap();
assert!(one.is_odd());
assert!(two.is_even());
assert!(thousand.is_even());
assert!(big.is_even());
assert!(bigger.is_odd());
assert!((one << 64).is_even());
assert!(((one << 64) + one).is_odd());
}
fn to_str_pairs() -> Vec<(BigUint, Vec<(uint, String)>)> {
let bits = BigDigit::bits;
vec!(( Zero::zero(), vec!(
(2, "0".to_string()), (3, "0".to_string())
)), ( BigUint::from_slice([ 0xff ]), vec!(
(2, "11111111".to_string()),
(3, "100110".to_string()),
(4, "3333".to_string()),
(5, "2010".to_string()),
(6, "1103".to_string()),
(7, "513".to_string()),
(8, "377".to_string()),
(9, "313".to_string()),
(10, "255".to_string()),
(11, "212".to_string()),
(12, "193".to_string()),
(13, "168".to_string()),
(14, "143".to_string()),
(15, "120".to_string()),
(16, "ff".to_string())
)), ( BigUint::from_slice([ 0xfff ]), vec!(
(2, "111111111111".to_string()),
(4, "333333".to_string()),
(16, "fff".to_string())
)), ( BigUint::from_slice([ 1, 2 ]), vec!(
(2,
format!("10{}1", "0".repeat(bits - 1))),
(4,
format!("2{}1", "0".repeat(bits / 2 - 1))),
(10, match bits {
32 => "8589934593".to_string(),
16 => "131073".to_string(),
_ => fail!()
}),
(16,
format!("2{}1", "0".repeat(bits / 4 - 1)))
)), ( BigUint::from_slice([ 1, 2, 3 ]), vec!(
(2,
format!("11{}10{}1",
"0".repeat(bits - 2),
"0".repeat(bits - 1))),
(4,
format!("3{}2{}1",
"0".repeat(bits / 2 - 1),
"0".repeat(bits / 2 - 1))),
(10, match bits {
32 => "55340232229718589441".to_string(),
16 => "12885032961".to_string(),
_ => fail!()
}),
(16,
format!("3{}2{}1",
"0".repeat(bits / 4 - 1),
"0".repeat(bits / 4 - 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).as_slice(),
str.as_slice());
}
}
}
#[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.as_slice(),
*radix).unwrap());
}
}
let zed: Option<BigUint> = FromStrRadix::from_str_radix("Z", 10);
assert_eq!(zed, None);
let blank: Option<BigUint> = FromStrRadix::from_str_radix("_", 2);
assert_eq!(blank, None);
let minus_one: Option<BigUint> = FromStrRadix::from_str_radix("-1",
10);
assert_eq!(minus_one, None);
}
#[test]
fn test_factor() {
fn factor(n: uint) -> BigUint {
let mut f: BigUint = One::one();
for i in range(2, n + 1) {
// FIXME(#5992): assignment operator overloads
// f *= FromPrimitive::from_uint(i);
f = f * FromPrimitive::from_uint(i).unwrap();
}
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");
}
#[test]
fn test_bits() {
assert_eq!(BigUint::new(vec!(0,0,0,0)).bits(), 0);
let n: BigUint = FromPrimitive::from_uint(0).unwrap();
assert_eq!(n.bits(), 0);
let n: BigUint = FromPrimitive::from_uint(1).unwrap();
assert_eq!(n.bits(), 1);
let n: BigUint = FromPrimitive::from_uint(3).unwrap();
assert_eq!(n.bits(), 2);
let n: BigUint = FromStrRadix::from_str_radix("4000000000", 16).unwrap();
assert_eq!(n.bits(), 39);
let one: BigUint = One::one();
assert_eq!((one << 426).bits(), 427);
}
#[test]
fn test_rand() {
let mut rng = task_rng();
let _n: BigUint = rng.gen_biguint(137);
assert!(rng.gen_biguint(0).is_zero());
}
#[test]
fn test_rand_range() {
let mut rng = task_rng();
for _ in range(0u, 10) {
assert_eq!(rng.gen_bigint_range(&FromPrimitive::from_uint(236).unwrap(),
&FromPrimitive::from_uint(237).unwrap()),
FromPrimitive::from_uint(236).unwrap());
}
let l = FromPrimitive::from_uint(403469000 + 2352).unwrap();
let u = FromPrimitive::from_uint(403469000 + 3513).unwrap();
for _ in range(0u, 1000) {
let n: BigUint = rng.gen_biguint_below(&u);
assert!(n < u);
let n: BigUint = rng.gen_biguint_range(&l, &u);
assert!(n >= l);
assert!(n < u);
}
}
#[test]
#[should_fail]
fn test_zero_rand_range() {
task_rng().gen_biguint_range(&FromPrimitive::from_uint(54).unwrap(),
&FromPrimitive::from_uint(54).unwrap());
}
#[test]
#[should_fail]
fn test_negative_rand_range() {
let mut rng = task_rng();
let l = FromPrimitive::from_uint(2352).unwrap();
let u = FromPrimitive::from_uint(3513).unwrap();
// Switching u and l should fail:
let _n: BigUint = rng.gen_biguint_range(&u, &l);
}
}
#[cfg(test)]
mod bigint_tests {
use Integer;
use super::{BigDigit, BigUint, ToBigUint};
use super::{Sign, Minus, Zero, Plus, BigInt, RandBigInt, ToBigInt};
use std::cmp::{Less, Equal, Greater};
use std::i64;
use std::num::CheckedDiv;
use std::num::{Zero, One, FromStrRadix, ToStrRadix};
use std::num::{ToPrimitive, FromPrimitive};
use std::rand::task_rng;
use std::u64;
use std::hash::hash;
#[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, FromPrimitive::from_uint(inp_n).unwrap());
let ans = BigInt { sign: ans_s, data: FromPrimitive::from_uint(ans_n).unwrap()};
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: [&[BigDigit], ..4] = [ &[2 as BigDigit], &[1, 1], &[2, 1], &[1, 1, 1] ];
let mut nums = Vec::new();
for s in vs.iter().rev() {
nums.push(BigInt::from_slice(Minus, *s));
}
nums.push(Zero::zero());
nums.extend(vs.iter().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_hash() {
let a = BigInt::new(Zero, vec!());
let b = BigInt::new(Zero, vec!(0));
let c = BigInt::new(Plus, vec!(1));
let d = BigInt::new(Plus, vec!(1,0,0,0,0,0));
let e = BigInt::new(Plus, vec!(0,0,0,0,0,1));
let f = BigInt::new(Minus, vec!(1));
assert!(hash(&a) == hash(&b));
assert!(hash(&b) != hash(&c));
assert!(hash(&c) == hash(&d));
assert!(hash(&d) != hash(&e));
assert!(hash(&c) != hash(&f));
}
#[test]
fn test_convert_i64() {
fn check(b1: BigInt, i: i64) {
let b2: BigInt = FromPrimitive::from_i64(i).unwrap();
assert!(b1 == b2);
assert!(b1.to_i64().unwrap() == i);
}
check(Zero::zero(), 0);
check(One::one(), 1);
check(i64::MIN.to_bigint().unwrap(), i64::MIN);
check(i64::MAX.to_bigint().unwrap(), i64::MAX);
assert_eq!(
(i64::MAX as u64 + 1).to_bigint().unwrap().to_i64(),
None);
assert_eq!(
BigInt::from_biguint(Plus, BigUint::new(vec!(1, 2, 3, 4, 5))).to_i64(),
None);
assert_eq!(
BigInt::from_biguint(Minus, BigUint::new(vec!(1,0,0,1<<(BigDigit::bits-1)))).to_i64(),
None);
assert_eq!(
BigInt::from_biguint(Minus, BigUint::new(vec!(1, 2, 3, 4, 5))).to_i64(),
None);
}
#[test]
fn test_convert_u64() {
fn check(b1: BigInt, u: u64) {
let b2: BigInt = FromPrimitive::from_u64(u).unwrap();
assert!(b1 == b2);
assert!(b1.to_u64().unwrap() == u);
}
check(Zero::zero(), 0);
check(One::one(), 1);
check(u64::MIN.to_bigint().unwrap(), u64::MIN);
check(u64::MAX.to_bigint().unwrap(), u64::MAX);
assert_eq!(
BigInt::from_biguint(Plus, BigUint::new(vec!(1, 2, 3, 4, 5))).to_u64(),
None);
let max_value: BigUint = FromPrimitive::from_u64(u64::MAX).unwrap();
assert_eq!(BigInt::from_biguint(Minus, max_value).to_u64(), None);
assert_eq!(BigInt::from_biguint(Minus, BigUint::new(vec!(1, 2, 3, 4, 5))).to_u64(), None);
}
#[test]
fn test_convert_to_biguint() {
fn check(n: BigInt, ans_1: BigUint) {
assert_eq!(n.to_biguint().unwrap(), ans_1);
assert_eq!(n.to_biguint().unwrap().to_bigint().unwrap(), n);
}
let zero: BigInt = Zero::zero();
let unsigned_zero: BigUint = Zero::zero();
let positive = BigInt::from_biguint(
Plus, BigUint::new(vec!(1,2,3)));
let negative = -positive;
check(zero, unsigned_zero);
check(positive, BigUint::new(vec!(1,2,3)));
assert_eq!(negative.to_biguint(), None);
}
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 (a_vec, b_vec, c_vec) = *elm;
let a = BigInt::from_slice(Plus, a_vec);
let b = BigInt::from_slice(Plus, b_vec);
let c = BigInt::from_slice(Plus, c_vec);
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 (a_vec, b_vec, c_vec) = *elm;
let a = BigInt::from_slice(Plus, a_vec);
let b = BigInt::from_slice(Plus, b_vec);
let c = BigInt::from_slice(Plus, c_vec);
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 (a_vec, b_vec, c_vec) = *elm;
let a = BigInt::from_slice(Plus, a_vec);
let b = BigInt::from_slice(Plus, b_vec);
let c = BigInt::from_slice(Plus, c_vec);
assert!(a * b == c);
assert!(b * a == c);
assert!((-a) * b == -c);
assert!((-b) * a == -c);
}
for elm in div_rem_quadruples.iter() {
let (a_vec, b_vec, c_vec, d_vec) = *elm;
let a = BigInt::from_slice(Plus, a_vec);
let b = BigInt::from_slice(Plus, b_vec);
let c = BigInt::from_slice(Plus, c_vec);
let d = BigInt::from_slice(Plus, d_vec);
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 (a_vec, b_vec, c_vec) = *elm;
let a = BigInt::from_slice(Plus, a_vec);
let b = BigInt::from_slice(Plus, b_vec);
let c = BigInt::from_slice(Plus, c_vec);
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 (a_vec, b_vec, c_vec, d_vec) = *elm;
let a = BigInt::from_slice(Plus, a_vec);
let b = BigInt::from_slice(Plus, b_vec);
let c = BigInt::from_slice(Plus, c_vec);
let d = BigInt::from_slice(Plus, d_vec);
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 (a_vec, b_vec, c_vec) = *elm;
let a = BigInt::from_slice(Plus, a_vec);
let b = BigInt::from_slice(Plus, b_vec);
let c = BigInt::from_slice(Plus, c_vec);
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 (a_vec, b_vec, c_vec, d_vec) = *elm;
let a = BigInt::from_slice(Plus, a_vec);
let b = BigInt::from_slice(Plus, b_vec);
let c = BigInt::from_slice(Plus, c_vec);
let d = BigInt::from_slice(Plus, d_vec);
if !b.is_zero() {
check(&a, &b, &c, &d);
}
}
}
#[test]
fn test_checked_add() {
for elm in sum_triples.iter() {
let (a_vec, b_vec, c_vec) = *elm;
let a = BigInt::from_slice(Plus, a_vec);
let b = BigInt::from_slice(Plus, b_vec);
let c = BigInt::from_slice(Plus, c_vec);
assert!(a.checked_add(&b).unwrap() == c);
assert!(b.checked_add(&a).unwrap() == c);
assert!(c.checked_add(&(-a)).unwrap() == b);
assert!(c.checked_add(&(-b)).unwrap() == a);
assert!(a.checked_add(&(-c)).unwrap() == (-b));
assert!(b.checked_add(&(-c)).unwrap() == (-a));
assert!((-a).checked_add(&(-b)).unwrap() == (-c))
assert!(a.checked_add(&(-a)).unwrap() == Zero::zero());
}
}
#[test]
fn test_checked_sub() {
for elm in sum_triples.iter() {
let (a_vec, b_vec, c_vec) = *elm;
let a = BigInt::from_slice(Plus, a_vec);
let b = BigInt::from_slice(Plus, b_vec);
let c = BigInt::from_slice(Plus, c_vec);
assert!(c.checked_sub(&a).unwrap() == b);
assert!(c.checked_sub(&b).unwrap() == a);
assert!((-b).checked_sub(&a).unwrap() == (-c))
assert!((-a).checked_sub(&b).unwrap() == (-c))
assert!(b.checked_sub(&(-a)).unwrap() == c);
assert!(a.checked_sub(&(-b)).unwrap() == c);
assert!((-c).checked_sub(&(-a)).unwrap() == (-b));
assert!(a.checked_sub(&a).unwrap() == Zero::zero());
}
}
#[test]
fn test_checked_mul() {
for elm in mul_triples.iter() {
let (a_vec, b_vec, c_vec) = *elm;
let a = BigInt::from_slice(Plus, a_vec);
let b = BigInt::from_slice(Plus, b_vec);
let c = BigInt::from_slice(Plus, c_vec);
assert!(a.checked_mul(&b).unwrap() == c);
assert!(b.checked_mul(&a).unwrap() == c);
assert!((-a).checked_mul(&b).unwrap() == -c);
assert!((-b).checked_mul(&a).unwrap() == -c);
}
for elm in div_rem_quadruples.iter() {
let (a_vec, b_vec, c_vec, d_vec) = *elm;
let a = BigInt::from_slice(Plus, a_vec);
let b = BigInt::from_slice(Plus, b_vec);
let c = BigInt::from_slice(Plus, c_vec);
let d = BigInt::from_slice(Plus, d_vec);
assert!(a == b.checked_mul(&c).unwrap() + d);
assert!(a == c.checked_mul(&b).unwrap() + d);
}
}
#[test]
fn test_checked_div() {
for elm in mul_triples.iter() {
let (a_vec, b_vec, c_vec) = *elm;
let a = BigInt::from_slice(Plus, a_vec);
let b = BigInt::from_slice(Plus, b_vec);
let c = BigInt::from_slice(Plus, c_vec);
if !a.is_zero() {
assert!(c.checked_div(&a).unwrap() == b);
assert!((-c).checked_div(&(-a)).unwrap() == b);
assert!((-c).checked_div(&a).unwrap() == -b);
}
if !b.is_zero() {
assert!(c.checked_div(&b).unwrap() == a);
assert!((-c).checked_div(&(-b)).unwrap() == a);
assert!((-c).checked_div(&b).unwrap() == -a);
}
assert!(c.checked_div(&Zero::zero()).is_none());
assert!((-c).checked_div(&Zero::zero()).is_none());
}
}
#[test]
fn test_gcd() {
fn check(a: int, b: int, c: int) {
let big_a: BigInt = FromPrimitive::from_int(a).unwrap();
let big_b: BigInt = FromPrimitive::from_int(b).unwrap();
let big_c: BigInt = FromPrimitive::from_int(c).unwrap();
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 = FromPrimitive::from_int(a).unwrap();
let big_b: BigInt = FromPrimitive::from_int(b).unwrap();
let big_c: BigInt = FromPrimitive::from_int(c).unwrap();
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() {
let zero: BigInt = Zero::zero();
let one: BigInt = One::one();
assert_eq!((-one).abs_sub(&one), zero);
let one: BigInt = One::one();
let zero: BigInt = Zero::zero();
assert_eq!(one.abs_sub(&one), zero);
let one: BigInt = One::one();
let zero: BigInt = Zero::zero();
assert_eq!(one.abs_sub(&zero), one);
let one: BigInt = One::one();
let two: BigInt = FromPrimitive::from_int(2).unwrap();
assert_eq!(one.abs_sub(&-one), two);
}
#[test]
fn test_to_str_radix() {
fn check(n: int, ans: &str) {
let n: BigInt = FromPrimitive::from_int(n).unwrap();
assert!(ans == n.to_str_radix(10).as_slice());
}
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| {
let x: BigInt = FromPrimitive::from_int(n).unwrap();
x
});
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);
// issue 10522, this hit an edge case that caused it to
// attempt to allocate a vector of size (-1u) == huge.
let x: BigInt =
from_str(format!("1{}", "0".repeat(36)).as_slice()).unwrap();
let _y = x.to_string();
}
#[test]
fn test_neg() {
assert!(-BigInt::new(Plus, vec!(1, 1, 1)) ==
BigInt::new(Minus, vec!(1, 1, 1)));
assert!(-BigInt::new(Minus, vec!(1, 1, 1)) ==
BigInt::new(Plus, vec!(1, 1, 1)));
let zero: BigInt = Zero::zero();
assert_eq!(-zero, zero);
}
#[test]
fn test_rand() {
let mut rng = task_rng();
let _n: BigInt = rng.gen_bigint(137);
assert!(rng.gen_bigint(0).is_zero());
}
#[test]
fn test_rand_range() {
let mut rng = task_rng();
for _ in range(0u, 10) {
assert_eq!(rng.gen_bigint_range(&FromPrimitive::from_uint(236).unwrap(),
&FromPrimitive::from_uint(237).unwrap()),
FromPrimitive::from_uint(236).unwrap());
}
fn check(l: BigInt, u: BigInt) {
let mut rng = task_rng();
for _ in range(0u, 1000) {
let n: BigInt = rng.gen_bigint_range(&l, &u);
assert!(n >= l);
assert!(n < u);
}
}
let l: BigInt = FromPrimitive::from_uint(403469000 + 2352).unwrap();
let u: BigInt = FromPrimitive::from_uint(403469000 + 3513).unwrap();
check( l.clone(), u.clone());
check(-l.clone(), u.clone());
check(-u.clone(), -l.clone());
}
#[test]
#[should_fail]
fn test_zero_rand_range() {
task_rng().gen_bigint_range(&FromPrimitive::from_int(54).unwrap(),
&FromPrimitive::from_int(54).unwrap());
}
#[test]
#[should_fail]
fn test_negative_rand_range() {
let mut rng = task_rng();
let l = FromPrimitive::from_uint(2352).unwrap();
let u = FromPrimitive::from_uint(3513).unwrap();
// Switching u and l should fail:
let _n: BigInt = rng.gen_bigint_range(&u, &l);
}
}
#[cfg(test)]
mod bench {
extern crate test;
use self::test::Bencher;
use super::BigUint;
use std::iter;
use std::mem::replace;
use std::num::{FromPrimitive, Zero, One};
fn factorial(n: uint) -> BigUint {
let mut f: BigUint = One::one();
for i in iter::range_inclusive(1, n) {
f = f * FromPrimitive::from_uint(i).unwrap();
}
f
}
fn fib(n: uint) -> BigUint {
let mut f0: BigUint = Zero::zero();
let mut f1: BigUint = One::one();
for _ in range(0, n) {
let f2 = f0 + f1;
f0 = replace(&mut f1, f2);
}
f0
}
#[bench]
fn factorial_100(b: &mut Bencher) {
b.iter(|| {
factorial(100);
});
}
#[bench]
fn fib_100(b: &mut Bencher) {
b.iter(|| {
fib(100);
});
}
#[bench]
fn to_string(b: &mut Bencher) {
let fac = factorial(100);
let fib = fib(100);
b.iter(|| {
fac.to_string();
});
b.iter(|| {
fib.to_string();
});
}
#[bench]
fn shr(b: &mut Bencher) {
let n = { let one : BigUint = One::one(); one << 1000 };
b.iter(|| {
let mut m = n.clone();
for _ in range(0u, 10) {
m = m >> 1;
}
})
}
}
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