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@@ -0,0 +1,2956 @@
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+// Copyright 2013-2014 The Rust Project Developers. See the COPYRIGHT
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+// file at the top-level directory of this distribution and at
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+// http://rust-lang.org/COPYRIGHT.
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+//
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+// Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or
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+// http://www.apache.org/licenses/LICENSE-2.0> or the MIT license
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+// <LICENSE-MIT or http://opensource.org/licenses/MIT>, at your
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+// option. This file may not be copied, modified, or distributed
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+// except according to those terms.
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+
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+//! A Big integer (signed version: `BigInt`, unsigned version: `BigUint`).
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+//!
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+//! A `BigUint` is represented as an array of `BigDigit`s.
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+//! A `BigInt` is a combination of `BigUint` and `Sign`.
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+//!
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+//! Common numerical operations are overloaded, so we can treat them
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+//! the same way we treat other numbers.
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+//!
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+//! ## Example
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+//!
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+//! ```rust
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+//! use num::bigint::BigUint;
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+//! use std::num::{Zero, One};
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+//! use std::mem::replace;
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+//!
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+//! // Calculate large fibonacci numbers.
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+//! fn fib(n: uint) -> BigUint {
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+//! let mut f0: BigUint = Zero::zero();
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+//! let mut f1: BigUint = One::one();
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+//! for _ in range(0, n) {
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+//! let f2 = f0 + f1;
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+//! // This is a low cost way of swapping f0 with f1 and f1 with f2.
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+//! f0 = replace(&mut f1, f2);
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+//! }
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+//! f0
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+//! }
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+//!
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+//! // This is a very large number.
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+//! println!("fib(1000) = {}", fib(1000));
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+//! ```
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+//!
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+//! It's easy to generate large random numbers:
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+//!
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+//! ```rust
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+//! use num::bigint::{ToBigInt, RandBigInt};
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+//! use std::rand;
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+//!
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+//! let mut rng = rand::task_rng();
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+//! let a = rng.gen_bigint(1000u);
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+//!
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+//! let low = -10000i.to_bigint().unwrap();
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+//! let high = 10000i.to_bigint().unwrap();
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+//! let b = rng.gen_bigint_range(&low, &high);
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+//!
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+//! // Probably an even larger number.
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+//! println!("{}", a * b);
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+//! ```
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+
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+use Integer;
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+use rand::Rng;
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+
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+use std::{cmp, fmt, hash};
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+use std::default::Default;
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+use std::from_str::FromStr;
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+use std::num::CheckedDiv;
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+use std::num::{ToPrimitive, FromPrimitive};
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+use std::num::{Zero, One, ToStrRadix, FromStrRadix};
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+use std::string::String;
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+use std::{uint, i64, u64};
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+
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+/// A `BigDigit` is a `BigUint`'s composing element.
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+pub type BigDigit = u32;
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+
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+/// A `DoubleBigDigit` is the internal type used to do the computations. Its
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+/// size is the double of the size of `BigDigit`.
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+pub type DoubleBigDigit = u64;
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+
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+pub static ZERO_BIG_DIGIT: BigDigit = 0;
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+static ZERO_VEC: [BigDigit, ..1] = [ZERO_BIG_DIGIT];
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+
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+#[allow(non_snake_case)]
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+pub mod BigDigit {
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+ use super::BigDigit;
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+ use super::DoubleBigDigit;
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+
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+ // `DoubleBigDigit` size dependent
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+ pub static bits: uint = 32;
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+
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+ pub static base: DoubleBigDigit = 1 << bits;
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+ static lo_mask: DoubleBigDigit = (-1 as DoubleBigDigit) >> bits;
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+
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+ #[inline]
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+ fn get_hi(n: DoubleBigDigit) -> BigDigit { (n >> bits) as BigDigit }
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+ #[inline]
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+ fn get_lo(n: DoubleBigDigit) -> BigDigit { (n & lo_mask) as BigDigit }
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+
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+ /// Split one `DoubleBigDigit` into two `BigDigit`s.
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+ #[inline]
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+ pub fn from_doublebigdigit(n: DoubleBigDigit) -> (BigDigit, BigDigit) {
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+ (get_hi(n), get_lo(n))
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+ }
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+
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+ /// Join two `BigDigit`s into one `DoubleBigDigit`
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+ #[inline]
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+ pub fn to_doublebigdigit(hi: BigDigit, lo: BigDigit) -> DoubleBigDigit {
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+ (lo as DoubleBigDigit) | ((hi as DoubleBigDigit) << bits)
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+ }
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+}
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+
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+/// A big unsigned integer type.
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+///
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+/// A `BigUint`-typed value `BigUint { data: vec!(a, b, c) }` represents a number
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+/// `(a + b * BigDigit::base + c * BigDigit::base^2)`.
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+#[deriving(Clone)]
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+pub struct BigUint {
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+ data: Vec<BigDigit>
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+}
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+
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+impl PartialEq for BigUint {
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+ #[inline]
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+ fn eq(&self, other: &BigUint) -> bool {
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+ match self.cmp(other) { Equal => true, _ => false }
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+ }
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+}
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+impl Eq for BigUint {}
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+
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+impl PartialOrd for BigUint {
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+ #[inline]
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+ fn partial_cmp(&self, other: &BigUint) -> Option<Ordering> {
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+ Some(self.cmp(other))
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+ }
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+}
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+
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+impl Ord for BigUint {
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+ #[inline]
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+ fn cmp(&self, other: &BigUint) -> Ordering {
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+ let (s_len, o_len) = (self.data.len(), other.data.len());
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+ if s_len < o_len { return Less; }
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+ if s_len > o_len { return Greater; }
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+
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+ for (&self_i, &other_i) in self.data.iter().rev().zip(other.data.iter().rev()) {
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+ if self_i < other_i { return Less; }
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+ if self_i > other_i { return Greater; }
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+ }
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+ return Equal;
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+ }
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+}
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+
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+impl Default for BigUint {
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+ #[inline]
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+ fn default() -> BigUint { Zero::zero() }
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+}
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+
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+impl<S: hash::Writer> hash::Hash<S> for BigUint {
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+ fn hash(&self, state: &mut S) {
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+ // hash 0 in case it's all 0's
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+ 0u32.hash(state);
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+
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+ let mut found_first_value = false;
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+ for elem in self.data.iter().rev() {
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+ // don't hash any leading 0's, they shouldn't affect the hash
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+ if found_first_value || *elem != 0 {
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+ found_first_value = true;
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+ elem.hash(state);
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+ }
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+ }
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+ }
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+}
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+
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+impl fmt::Show for BigUint {
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+ fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
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+ write!(f, "{}", self.to_str_radix(10))
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+ }
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+}
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+
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+impl FromStr for BigUint {
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+ #[inline]
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+ fn from_str(s: &str) -> Option<BigUint> {
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+ FromStrRadix::from_str_radix(s, 10)
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+ }
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+}
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+
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+impl Num for BigUint {}
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+
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+impl BitAnd<BigUint, BigUint> for BigUint {
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+ fn bitand(&self, other: &BigUint) -> BigUint {
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+ BigUint::new(self.data.iter().zip(other.data.iter()).map(|(ai, bi)| *ai & *bi).collect())
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+ }
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+}
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+
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+impl BitOr<BigUint, BigUint> for BigUint {
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+ fn bitor(&self, other: &BigUint) -> BigUint {
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+ let zeros = ZERO_VEC.iter().cycle();
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+ let (a, b) = if self.data.len() > other.data.len() { (self, other) } else { (other, self) };
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+ let ored = a.data.iter().zip(b.data.iter().chain(zeros)).map(
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+ |(ai, bi)| *ai | *bi
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+ ).collect();
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+ return BigUint::new(ored);
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+ }
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+}
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+
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+impl BitXor<BigUint, BigUint> for BigUint {
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+ fn bitxor(&self, other: &BigUint) -> BigUint {
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+ let zeros = ZERO_VEC.iter().cycle();
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+ let (a, b) = if self.data.len() > other.data.len() { (self, other) } else { (other, self) };
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+ let xored = a.data.iter().zip(b.data.iter().chain(zeros)).map(
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+ |(ai, bi)| *ai ^ *bi
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+ ).collect();
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+ return BigUint::new(xored);
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+ }
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+}
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+
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+impl Shl<uint, BigUint> for BigUint {
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+ #[inline]
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+ fn shl(&self, rhs: &uint) -> BigUint {
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+ let n_unit = *rhs / BigDigit::bits;
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+ let n_bits = *rhs % BigDigit::bits;
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+ return self.shl_unit(n_unit).shl_bits(n_bits);
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+ }
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+}
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+
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+impl Shr<uint, BigUint> for BigUint {
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+ #[inline]
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+ fn shr(&self, rhs: &uint) -> BigUint {
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+ let n_unit = *rhs / BigDigit::bits;
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+ let n_bits = *rhs % BigDigit::bits;
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+ return self.shr_unit(n_unit).shr_bits(n_bits);
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+ }
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+}
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+
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+impl Zero for BigUint {
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+ #[inline]
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+ fn zero() -> BigUint { BigUint::new(Vec::new()) }
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+
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+ #[inline]
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+ fn is_zero(&self) -> bool { self.data.is_empty() }
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+}
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+
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+impl One for BigUint {
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+ #[inline]
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+ fn one() -> BigUint { BigUint::new(vec!(1)) }
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+}
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+
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+impl Unsigned for BigUint {}
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+
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+impl Add<BigUint, BigUint> for BigUint {
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+ fn add(&self, other: &BigUint) -> BigUint {
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+ let zeros = ZERO_VEC.iter().cycle();
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+ let (a, b) = if self.data.len() > other.data.len() { (self, other) } else { (other, self) };
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+
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+ let mut carry = 0;
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+ let mut sum: Vec<BigDigit> = a.data.iter().zip(b.data.iter().chain(zeros)).map(|(ai, bi)| {
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+ let (hi, lo) = BigDigit::from_doublebigdigit(
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+ (*ai as DoubleBigDigit) + (*bi as DoubleBigDigit) + (carry as DoubleBigDigit));
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+ carry = hi;
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+ lo
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+ }).collect();
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+ if carry != 0 { sum.push(carry); }
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+ return BigUint::new(sum);
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+ }
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+}
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+
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+impl Sub<BigUint, BigUint> for BigUint {
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+ fn sub(&self, other: &BigUint) -> BigUint {
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+ let new_len = cmp::max(self.data.len(), other.data.len());
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+ let zeros = ZERO_VEC.iter().cycle();
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+ let (a, b) = (self.data.iter().chain(zeros.clone()), other.data.iter().chain(zeros));
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+
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+ let mut borrow = 0i;
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+ let diff: Vec<BigDigit> = a.take(new_len).zip(b).map(|(ai, bi)| {
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+ let (hi, lo) = BigDigit::from_doublebigdigit(
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+ BigDigit::base
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+ + (*ai as DoubleBigDigit)
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+ - (*bi as DoubleBigDigit)
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+ - (borrow as DoubleBigDigit)
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+ );
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+ /*
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+ hi * (base) + lo == 1*(base) + ai - bi - borrow
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+ => ai - bi - borrow < 0 <=> hi == 0
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+ */
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+ borrow = if hi == 0 { 1 } else { 0 };
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+ lo
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+ }).collect();
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+
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+ assert!(borrow == 0,
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+ "Cannot subtract other from self because other is larger than self.");
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+ return BigUint::new(diff);
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+ }
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+}
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+
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+impl Mul<BigUint, BigUint> for BigUint {
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+ fn mul(&self, other: &BigUint) -> BigUint {
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+ if self.is_zero() || other.is_zero() { return Zero::zero(); }
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+
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+ let (s_len, o_len) = (self.data.len(), other.data.len());
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+ if s_len == 1 { return mul_digit(other, self.data.as_slice()[0]); }
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+ if o_len == 1 { return mul_digit(self, other.data.as_slice()[0]); }
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+
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+ // Using Karatsuba multiplication
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+ // (a1 * base + a0) * (b1 * base + b0)
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+ // = a1*b1 * base^2 +
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+ // (a1*b1 + a0*b0 - (a1-b0)*(b1-a0)) * base +
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+ // a0*b0
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+ let half_len = cmp::max(s_len, o_len) / 2;
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+ let (s_hi, s_lo) = cut_at(self, half_len);
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+ let (o_hi, o_lo) = cut_at(other, half_len);
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+
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+ let ll = s_lo * o_lo;
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+ let hh = s_hi * o_hi;
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+ let mm = {
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+ let (s1, n1) = sub_sign(s_hi, s_lo);
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+ let (s2, n2) = sub_sign(o_hi, o_lo);
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+ match (s1, s2) {
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+ (Equal, _) | (_, Equal) => hh + ll,
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+ (Less, Greater) | (Greater, Less) => hh + ll + (n1 * n2),
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+ (Less, Less) | (Greater, Greater) => hh + ll - (n1 * n2)
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+ }
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+ };
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+
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+ return ll + mm.shl_unit(half_len) + hh.shl_unit(half_len * 2);
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+
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+
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+ fn mul_digit(a: &BigUint, n: BigDigit) -> BigUint {
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+ if n == 0 { return Zero::zero(); }
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+ if n == 1 { return (*a).clone(); }
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+
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+ let mut carry = 0;
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+ let mut prod: Vec<BigDigit> = a.data.iter().map(|ai| {
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+ let (hi, lo) = BigDigit::from_doublebigdigit(
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+ (*ai as DoubleBigDigit) * (n as DoubleBigDigit) + (carry as DoubleBigDigit)
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+ );
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+ carry = hi;
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+ lo
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+ }).collect();
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+ if carry != 0 { prod.push(carry); }
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+ return BigUint::new(prod);
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+ }
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+
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+ #[inline]
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+ fn cut_at(a: &BigUint, n: uint) -> (BigUint, BigUint) {
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+ let mid = cmp::min(a.data.len(), n);
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+ return (BigUint::from_slice(a.data.slice(mid, a.data.len())),
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+ BigUint::from_slice(a.data.slice(0, mid)));
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+ }
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+
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+ #[inline]
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+ fn sub_sign(a: BigUint, b: BigUint) -> (Ordering, BigUint) {
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+ match a.cmp(&b) {
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+ Less => (Less, b - a),
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+ Greater => (Greater, a - b),
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+ _ => (Equal, Zero::zero())
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+ }
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+ }
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+ }
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+}
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+
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+impl Div<BigUint, BigUint> for BigUint {
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+ #[inline]
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+ fn div(&self, other: &BigUint) -> BigUint {
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+ let (q, _) = self.div_rem(other);
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+ return q;
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+ }
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+}
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+
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+impl Rem<BigUint, BigUint> for BigUint {
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+ #[inline]
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+ fn rem(&self, other: &BigUint) -> BigUint {
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+ let (_, r) = self.div_rem(other);
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+ return r;
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+ }
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+}
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+
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+impl Neg<BigUint> for BigUint {
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+ #[inline]
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+ fn neg(&self) -> BigUint { fail!() }
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+}
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+
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+impl CheckedAdd for BigUint {
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+ #[inline]
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+ fn checked_add(&self, v: &BigUint) -> Option<BigUint> {
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+ return Some(self.add(v));
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+ }
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+}
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+
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+impl CheckedSub for BigUint {
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+ #[inline]
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+ fn checked_sub(&self, v: &BigUint) -> Option<BigUint> {
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|
|
+ 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(÷r);
|
|
|
+ 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);
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|
|
+ 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;
|
|
|
+ }
|
|
|
+ })
|
|
|
+ }
|
|
|
+}
|
Aaron Turon
10 年 前