diff --git a/src/bigint.rs b/src/bigint.rs deleted file mode 100644 index a98752d..0000000 --- a/src/bigint.rs +++ /dev/null @@ -1,4987 +0,0 @@ -// Copyright 2013-2014 The Rust Project Developers. See the COPYRIGHT -// file at the top-level directory of this distribution and at -// http://rust-lang.org/COPYRIGHT. -// -// Licensed under the Apache License, Version 2.0 or the MIT license -// , at your -// option. This file may not be copied, modified, or distributed -// except according to those terms. - -//! A Big integer (signed version: `BigInt`, unsigned version: `BigUint`). -//! -//! A `BigUint` is represented as a vector of `BigDigit`s. -//! A `BigInt` is a combination of `BigUint` and `Sign`. -//! -//! Common numerical operations are overloaded, so we can treat them -//! the same way we treat other numbers. -//! -//! ## Example -//! -//! ```rust -//! use num::{BigUint, Zero, One}; -//! use std::mem::replace; -//! -//! // Calculate large fibonacci numbers. -//! fn fib(n: usize) -> BigUint { -//! let mut f0: BigUint = Zero::zero(); -//! let mut f1: BigUint = One::one(); -//! for _ in 0..n { -//! let f2 = f0 + &f1; -//! // This is a low cost way of swapping f0 with f1 and f1 with f2. -//! f0 = replace(&mut f1, f2); -//! } -//! f0 -//! } -//! -//! // This is a very large number. -//! println!("fib(1000) = {}", fib(1000)); -//! ``` -//! -//! It's easy to generate large random numbers: -//! -//! ```rust -//! extern crate rand; -//! extern crate num; -//! -//! # #[cfg(feature = "rand")] -//! # fn main() { -//! use num::bigint::{ToBigInt, RandBigInt}; -//! -//! let mut rng = rand::thread_rng(); -//! let a = rng.gen_bigint(1000); -//! -//! let low = -10000.to_bigint().unwrap(); -//! let high = 10000.to_bigint().unwrap(); -//! let b = rng.gen_bigint_range(&low, &high); -//! -//! // Probably an even larger number. -//! println!("{}", a * b); -//! # } -//! -//! # #[cfg(not(feature = "rand"))] -//! # fn main() { -//! # } -//! ``` - -use Integer; - -use std::borrow::Cow; -use std::default::Default; -use std::error::Error; -use std::iter::repeat; -use std::num::ParseIntError; -use std::ops::{Add, BitAnd, BitOr, BitXor, Div, Mul, Neg, Rem, Shl, Shr, Sub}; -use std::str::{self, FromStr}; -use std::fmt; -use std::cmp::Ordering::{self, Less, Greater, Equal}; -use std::{f32, f64}; -use std::{u8, i64, u64}; -use std::ascii::AsciiExt; - -#[cfg(feature = "serde")] -use serde; - -// Some of the tests of non-RNG-based functionality are randomized using the -// RNG-based functionality, so the RNG-based functionality needs to be enabled -// for tests. -#[cfg(any(feature = "rand", test))] -use rand::Rng; - -use traits::{ToPrimitive, FromPrimitive, Float}; - -use {Num, Unsigned, CheckedAdd, CheckedSub, CheckedMul, CheckedDiv, Signed, Zero, One}; -use self::Sign::{Minus, NoSign, Plus}; - -/// A `BigDigit` is a `BigUint`'s composing element. -pub type BigDigit = u32; - -/// A `DoubleBigDigit` is the internal type used to do the computations. Its -/// size is the double of the size of `BigDigit`. -pub type DoubleBigDigit = u64; - -pub const ZERO_BIG_DIGIT: BigDigit = 0; - -#[allow(non_snake_case)] -pub mod big_digit { - use super::BigDigit; - use super::DoubleBigDigit; - - // `DoubleBigDigit` size dependent - pub const BITS: usize = 32; - - pub const BASE: DoubleBigDigit = 1 << BITS; - const LO_MASK: DoubleBigDigit = (-1i32 as DoubleBigDigit) >> BITS; - - #[inline] - fn get_hi(n: DoubleBigDigit) -> BigDigit { (n >> BITS) as BigDigit } - #[inline] - fn get_lo(n: DoubleBigDigit) -> BigDigit { (n & LO_MASK) as BigDigit } - - /// Split one `DoubleBigDigit` into two `BigDigit`s. - #[inline] - pub fn from_doublebigdigit(n: DoubleBigDigit) -> (BigDigit, BigDigit) { - (get_hi(n), get_lo(n)) - } - - /// Join two `BigDigit`s into one `DoubleBigDigit` - #[inline] - pub fn to_doublebigdigit(hi: BigDigit, lo: BigDigit) -> DoubleBigDigit { - (lo as DoubleBigDigit) | ((hi as DoubleBigDigit) << BITS) - } -} - -/* - * Generic functions for add/subtract/multiply with carry/borrow: - */ - -// Add with carry: -#[inline] -fn adc(a: BigDigit, b: BigDigit, carry: &mut BigDigit) -> BigDigit { - let (hi, lo) = big_digit::from_doublebigdigit( - (a as DoubleBigDigit) + - (b as DoubleBigDigit) + - (*carry as DoubleBigDigit)); - - *carry = hi; - lo -} - -// Subtract with borrow: -#[inline] -fn sbb(a: BigDigit, b: BigDigit, borrow: &mut BigDigit) -> BigDigit { - let (hi, lo) = big_digit::from_doublebigdigit( - big_digit::BASE - + (a as DoubleBigDigit) - - (b as DoubleBigDigit) - - (*borrow as DoubleBigDigit)); - /* - hi * (base) + lo == 1*(base) + ai - bi - borrow - => ai - bi - borrow < 0 <=> hi == 0 - */ - *borrow = if hi == 0 { 1 } else { 0 }; - lo -} - -#[inline] -fn mac_with_carry(a: BigDigit, b: BigDigit, c: BigDigit, carry: &mut BigDigit) -> BigDigit { - let (hi, lo) = big_digit::from_doublebigdigit( - (a as DoubleBigDigit) + - (b as DoubleBigDigit) * (c as DoubleBigDigit) + - (*carry as DoubleBigDigit)); - *carry = hi; - lo -} - -/// Divide a two digit numerator by a one digit divisor, returns quotient and remainder: -/// -/// Note: the caller must ensure that both the quotient and remainder will fit into a single digit. -/// This is _not_ true for an arbitrary numerator/denominator. -/// -/// (This function also matches what the x86 divide instruction does). -#[inline] -fn div_wide(hi: BigDigit, lo: BigDigit, divisor: BigDigit) -> (BigDigit, BigDigit) { - debug_assert!(hi < divisor); - - let lhs = big_digit::to_doublebigdigit(hi, lo); - let rhs = divisor as DoubleBigDigit; - ((lhs / rhs) as BigDigit, (lhs % rhs) as BigDigit) -} - -/// A big unsigned integer type. -/// -/// A `BigUint`-typed value `BigUint { data: vec!(a, b, c) }` represents a number -/// `(a + b * big_digit::BASE + c * big_digit::BASE^2)`. -#[derive(Clone, Debug, Hash)] -#[cfg_attr(feature = "rustc-serialize", derive(RustcEncodable, RustcDecodable))] -pub struct BigUint { - data: Vec -} - -impl PartialEq for BigUint { - #[inline] - fn eq(&self, other: &BigUint) -> bool { - match self.cmp(other) { Equal => true, _ => false } - } -} -impl Eq for BigUint {} - -impl PartialOrd for BigUint { - #[inline] - fn partial_cmp(&self, other: &BigUint) -> Option { - Some(self.cmp(other)) - } -} - -fn cmp_slice(a: &[BigDigit], b: &[BigDigit]) -> Ordering { - debug_assert!(a.last() != Some(&0)); - debug_assert!(b.last() != Some(&0)); - - let (a_len, b_len) = (a.len(), b.len()); - if a_len < b_len { return Less; } - if a_len > b_len { return Greater; } - - for (&ai, &bi) in a.iter().rev().zip(b.iter().rev()) { - if ai < bi { return Less; } - if ai > bi { return Greater; } - } - return Equal; -} - -impl Ord for BigUint { - #[inline] - fn cmp(&self, other: &BigUint) -> Ordering { - cmp_slice(&self.data[..], &other.data[..]) - } -} - -impl Default for BigUint { - #[inline] - fn default() -> BigUint { Zero::zero() } -} - -impl fmt::Display for BigUint { - fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result { - f.pad_integral(true, "", &self.to_str_radix(10)) - } -} - -impl fmt::LowerHex for BigUint { - fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result { - f.pad_integral(true, "0x", &self.to_str_radix(16)) - } -} - -impl fmt::UpperHex for BigUint { - fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result { - f.pad_integral(true, "0x", &self.to_str_radix(16).to_ascii_uppercase()) - } -} - -impl fmt::Binary for BigUint { - fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result { - f.pad_integral(true, "0b", &self.to_str_radix(2)) - } -} - -impl fmt::Octal for BigUint { - fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result { - f.pad_integral(true, "0o", &self.to_str_radix(8)) - } -} - -impl FromStr for BigUint { - type Err = ParseBigIntError; - - #[inline] - fn from_str(s: &str) -> Result { - BigUint::from_str_radix(s, 10) - } -} - -// Read bitwise digits that evenly divide BigDigit -fn from_bitwise_digits_le(v: &[u8], bits: usize) -> BigUint { - debug_assert!(!v.is_empty() && bits <= 8 && big_digit::BITS % bits == 0); - debug_assert!(v.iter().all(|&c| (c as BigDigit) < (1 << bits))); - - let digits_per_big_digit = big_digit::BITS / bits; - - let data = v.chunks(digits_per_big_digit).map(|chunk| { - chunk.iter().rev().fold(0u32, |acc, &c| (acc << bits) | c as BigDigit) - }).collect(); - - BigUint::new(data) -} - -// Read bitwise digits that don't evenly divide BigDigit -fn from_inexact_bitwise_digits_le(v: &[u8], bits: usize) -> BigUint { - debug_assert!(!v.is_empty() && bits <= 8 && big_digit::BITS % bits != 0); - debug_assert!(v.iter().all(|&c| (c as BigDigit) < (1 << bits))); - - let big_digits = (v.len() * bits + big_digit::BITS - 1) / big_digit::BITS; - let mut data = Vec::with_capacity(big_digits); - - let mut d = 0; - let mut dbits = 0; - for &c in v { - d |= (c as DoubleBigDigit) << dbits; - dbits += bits; - if dbits >= big_digit::BITS { - let (hi, lo) = big_digit::from_doublebigdigit(d); - data.push(lo); - d = hi as DoubleBigDigit; - dbits -= big_digit::BITS; - } - } - - if dbits > 0 { - debug_assert!(dbits < big_digit::BITS); - data.push(d as BigDigit); - } - - BigUint::new(data) -} - -// Read little-endian radix digits -fn from_radix_digits_be(v: &[u8], radix: u32) -> BigUint { - debug_assert!(!v.is_empty() && !radix.is_power_of_two()); - debug_assert!(v.iter().all(|&c| (c as u32) < radix)); - - // Estimate how big the result will be, so we can pre-allocate it. - let bits = (radix as f64).log2() * v.len() as f64; - let big_digits = (bits / big_digit::BITS as f64).ceil(); - let mut data = Vec::with_capacity(big_digits as usize); - - let (base, power) = get_radix_base(radix); - debug_assert!(base < (1 << 32)); - let base = base as BigDigit; - - let r = v.len() % power; - let i = if r == 0 { power } else { r }; - let (head, tail) = v.split_at(i); - - let first = head.iter().fold(0, |acc, &d| acc * radix + d as BigDigit); - data.push(first); - - debug_assert!(tail.len() % power == 0); - for chunk in tail.chunks(power) { - if data.last() != Some(&0) { - data.push(0); - } - - let mut carry = 0; - for d in data.iter_mut() { - *d = mac_with_carry(0, *d, base, &mut carry); - } - debug_assert!(carry == 0); - - let n = chunk.iter().fold(0, |acc, &d| acc * radix + d as BigDigit); - add2(&mut data, &[n]); - } - - BigUint::new(data) -} - -impl Num for BigUint { - type Error = ParseBigIntError; - - /// Creates and initializes a `BigUint`. - fn from_str_radix(s: &str, radix: u32) -> Result { - assert!(2 <= radix && radix <= 36, "The radix must be within 2...36"); - let mut s = s; - if s.starts_with('+') { - let tail = &s[1..]; - if !tail.starts_with('+') { s = tail } - } - - if s.is_empty() { - // create ParseIntError::Empty - let e = u64::from_str_radix(s, radix).unwrap_err(); - return Err(e.into()); - } - - // First normalize all characters to plain digit values - let mut v = Vec::with_capacity(s.len()); - for b in s.bytes() { - let d = match b { - b'0' ... b'9' => b - b'0', - b'a' ... b'z' => b - b'a' + 10, - b'A' ... b'Z' => b - b'A' + 10, - _ => u8::MAX, - }; - if d < radix as u8 { - v.push(d); - } else { - // create ParseIntError::InvalidDigit - let e = u64::from_str_radix(&s[v.len()..], radix).unwrap_err(); - return Err(e.into()); - } - } - - let res = if radix.is_power_of_two() { - // Powers of two can use bitwise masks and shifting instead of multiplication - let bits = radix.trailing_zeros() as usize; - v.reverse(); - if big_digit::BITS % bits == 0 { - from_bitwise_digits_le(&v, bits) - } else { - from_inexact_bitwise_digits_le(&v, bits) - } - } else { - from_radix_digits_be(&v, radix) - }; - Ok(res) - } -} - -macro_rules! forward_val_val_binop { - (impl $imp:ident for $res:ty, $method:ident) => { - impl $imp<$res> for $res { - type Output = $res; - - #[inline] - fn $method(self, other: $res) -> $res { - // forward to val-ref - $imp::$method(self, &other) - } - } - } -} - -macro_rules! forward_val_val_binop_commutative { - (impl $imp:ident for $res:ty, $method:ident) => { - impl $imp<$res> for $res { - type Output = $res; - - #[inline] - fn $method(self, other: $res) -> $res { - // forward to val-ref, with the larger capacity as val - if self.data.capacity() >= other.data.capacity() { - $imp::$method(self, &other) - } else { - $imp::$method(other, &self) - } - } - } - } -} - -macro_rules! forward_ref_val_binop { - (impl $imp:ident for $res:ty, $method:ident) => { - impl<'a> $imp<$res> for &'a $res { - type Output = $res; - - #[inline] - fn $method(self, other: $res) -> $res { - // forward to ref-ref - $imp::$method(self, &other) - } - } - } -} - -macro_rules! forward_ref_val_binop_commutative { - (impl $imp:ident for $res:ty, $method:ident) => { - impl<'a> $imp<$res> for &'a $res { - type Output = $res; - - #[inline] - fn $method(self, other: $res) -> $res { - // reverse, forward to val-ref - $imp::$method(other, self) - } - } - } -} - -macro_rules! forward_val_ref_binop { - (impl $imp:ident for $res:ty, $method:ident) => { - impl<'a> $imp<&'a $res> for $res { - type Output = $res; - - #[inline] - fn $method(self, other: &$res) -> $res { - // forward to ref-ref - $imp::$method(&self, other) - } - } - } -} - -macro_rules! forward_ref_ref_binop { - (impl $imp:ident for $res:ty, $method:ident) => { - impl<'a, 'b> $imp<&'b $res> for &'a $res { - type Output = $res; - - #[inline] - fn $method(self, other: &$res) -> $res { - // forward to val-ref - $imp::$method(self.clone(), other) - } - } - } -} - -macro_rules! forward_ref_ref_binop_commutative { - (impl $imp:ident for $res:ty, $method:ident) => { - impl<'a, 'b> $imp<&'b $res> for &'a $res { - type Output = $res; - - #[inline] - fn $method(self, other: &$res) -> $res { - // forward to val-ref, choosing the larger to clone - if self.data.len() >= other.data.len() { - $imp::$method(self.clone(), other) - } else { - $imp::$method(other.clone(), self) - } - } - } - } -} - -// Forward everything to ref-ref, when reusing storage is not helpful -macro_rules! forward_all_binop_to_ref_ref { - (impl $imp:ident for $res:ty, $method:ident) => { - forward_val_val_binop!(impl $imp for $res, $method); - forward_val_ref_binop!(impl $imp for $res, $method); - forward_ref_val_binop!(impl $imp for $res, $method); - }; -} - -// Forward everything to val-ref, so LHS storage can be reused -macro_rules! forward_all_binop_to_val_ref { - (impl $imp:ident for $res:ty, $method:ident) => { - forward_val_val_binop!(impl $imp for $res, $method); - forward_ref_val_binop!(impl $imp for $res, $method); - forward_ref_ref_binop!(impl $imp for $res, $method); - }; -} - -// Forward everything to val-ref, commutatively, so either LHS or RHS storage can be reused -macro_rules! forward_all_binop_to_val_ref_commutative { - (impl $imp:ident for $res:ty, $method:ident) => { - forward_val_val_binop_commutative!(impl $imp for $res, $method); - forward_ref_val_binop_commutative!(impl $imp for $res, $method); - forward_ref_ref_binop_commutative!(impl $imp for $res, $method); - }; -} - -forward_all_binop_to_val_ref_commutative!(impl BitAnd for BigUint, bitand); - -impl<'a> BitAnd<&'a BigUint> for BigUint { - type Output = BigUint; - - #[inline] - fn bitand(self, other: &BigUint) -> BigUint { - let mut data = self.data; - for (ai, &bi) in data.iter_mut().zip(other.data.iter()) { - *ai &= bi; - } - data.truncate(other.data.len()); - BigUint::new(data) - } -} - -forward_all_binop_to_val_ref_commutative!(impl BitOr for BigUint, bitor); - -impl<'a> BitOr<&'a BigUint> for BigUint { - type Output = BigUint; - - fn bitor(self, other: &BigUint) -> BigUint { - let mut data = self.data; - for (ai, &bi) in data.iter_mut().zip(other.data.iter()) { - *ai |= bi; - } - if other.data.len() > data.len() { - let extra = &other.data[data.len()..]; - data.extend(extra.iter().cloned()); - } - BigUint::new(data) - } -} - -forward_all_binop_to_val_ref_commutative!(impl BitXor for BigUint, bitxor); - -impl<'a> BitXor<&'a BigUint> for BigUint { - type Output = BigUint; - - fn bitxor(self, other: &BigUint) -> BigUint { - let mut data = self.data; - for (ai, &bi) in data.iter_mut().zip(other.data.iter()) { - *ai ^= bi; - } - if other.data.len() > data.len() { - let extra = &other.data[data.len()..]; - data.extend(extra.iter().cloned()); - } - BigUint::new(data) - } -} - -#[inline] -fn biguint_shl(n: Cow, bits: usize) -> BigUint { - let n_unit = bits / big_digit::BITS; - let mut data = match n_unit { - 0 => n.into_owned().data, - _ => { - let len = n_unit + n.data.len() + 1; - let mut data = Vec::with_capacity(len); - data.extend(repeat(0).take(n_unit)); - data.extend(n.data.iter().cloned()); - data - }, - }; - - let n_bits = bits % big_digit::BITS; - if n_bits > 0 { - let mut carry = 0; - for elem in data[n_unit..].iter_mut() { - let new_carry = *elem >> (big_digit::BITS - n_bits); - *elem = (*elem << n_bits) | carry; - carry = new_carry; - } - if carry != 0 { - data.push(carry); - } - } - - BigUint::new(data) -} - -impl Shl for BigUint { - type Output = BigUint; - - #[inline] - fn shl(self, rhs: usize) -> BigUint { - biguint_shl(Cow::Owned(self), rhs) - } -} - -impl<'a> Shl for &'a BigUint { - type Output = BigUint; - - #[inline] - fn shl(self, rhs: usize) -> BigUint { - biguint_shl(Cow::Borrowed(self), rhs) - } -} - -#[inline] -fn biguint_shr(n: Cow, bits: usize) -> BigUint { - let n_unit = bits / big_digit::BITS; - if n_unit >= n.data.len() { return Zero::zero(); } - let mut data = match n_unit { - 0 => n.into_owned().data, - _ => n.data[n_unit..].to_vec(), - }; - - let n_bits = bits % big_digit::BITS; - if n_bits > 0 { - let mut borrow = 0; - for elem in data.iter_mut().rev() { - let new_borrow = *elem << (big_digit::BITS - n_bits); - *elem = (*elem >> n_bits) | borrow; - borrow = new_borrow; - } - } - - BigUint::new(data) -} - -impl Shr for BigUint { - type Output = BigUint; - - #[inline] - fn shr(self, rhs: usize) -> BigUint { - biguint_shr(Cow::Owned(self), rhs) - } -} - -impl<'a> Shr for &'a BigUint { - type Output = BigUint; - - #[inline] - fn shr(self, rhs: usize) -> BigUint { - biguint_shr(Cow::Borrowed(self), rhs) - } -} - -impl Zero for BigUint { - #[inline] - fn zero() -> BigUint { BigUint::new(Vec::new()) } - - #[inline] - fn is_zero(&self) -> bool { self.data.is_empty() } -} - -impl One for BigUint { - #[inline] - fn one() -> BigUint { BigUint::new(vec!(1)) } -} - -impl Unsigned for BigUint {} - -forward_all_binop_to_val_ref_commutative!(impl Add for BigUint, add); - -// Only for the Add impl: -#[must_use] -#[inline] -fn __add2(a: &mut [BigDigit], b: &[BigDigit]) -> BigDigit { - let mut b_iter = b.iter(); - let mut carry = 0; - - for ai in a.iter_mut() { - if let Some(bi) = b_iter.next() { - *ai = adc(*ai, *bi, &mut carry); - } else if carry != 0 { - *ai = adc(*ai, 0, &mut carry); - } else { - break; - } - } - - debug_assert!(b_iter.next() == None); - carry -} - -/// /Two argument addition of raw slices: -/// a += b -/// -/// The caller _must_ ensure that a is big enough to store the result - typically this means -/// resizing a to max(a.len(), b.len()) + 1, to fit a possible carry. -fn add2(a: &mut [BigDigit], b: &[BigDigit]) { - let carry = __add2(a, b); - - debug_assert!(carry == 0); -} - -/* - * We'd really prefer to avoid using add2/sub2 directly as much as possible - since they make the - * caller entirely responsible for ensuring a's vector is big enough, and that the result is - * normalized, they're rather error prone and verbose: - * - * We could implement the Add and Sub traits for BigUint + BigDigit slices, like below - this works - * great, except that then it becomes the module's public interface, which we probably don't want: - * - * I'm keeping the code commented out, because I think this is worth revisiting: - -impl<'a> Add<&'a [BigDigit]> for BigUint { - type Output = BigUint; - - fn add(mut self, other: &[BigDigit]) -> BigUint { - if self.data.len() < other.len() { - let extra = other.len() - self.data.len(); - self.data.extend(repeat(0).take(extra)); - } - - let carry = __add2(&mut self.data[..], other); - if carry != 0 { - self.data.push(carry); - } - - self - } -} - */ - -impl<'a> Add<&'a BigUint> for BigUint { - type Output = BigUint; - - fn add(mut self, other: &BigUint) -> BigUint { - if self.data.len() < other.data.len() { - let extra = other.data.len() - self.data.len(); - self.data.extend(repeat(0).take(extra)); - } - - let carry = __add2(&mut self.data[..], &other.data[..]); - if carry != 0 { - self.data.push(carry); - } - - self - } -} - -forward_all_binop_to_val_ref!(impl Sub for BigUint, sub); - -fn sub2(a: &mut [BigDigit], b: &[BigDigit]) { - let mut b_iter = b.iter(); - let mut borrow = 0; - - for ai in a.iter_mut() { - if let Some(bi) = b_iter.next() { - *ai = sbb(*ai, *bi, &mut borrow); - } else if borrow != 0 { - *ai = sbb(*ai, 0, &mut borrow); - } else { - break; - } - } - - /* note: we're _required_ to fail on underflow */ - assert!(borrow == 0 && b_iter.all(|x| *x == 0), - "Cannot subtract b from a because b is larger than a."); -} - -impl<'a> Sub<&'a BigUint> for BigUint { - type Output = BigUint; - - fn sub(mut self, other: &BigUint) -> BigUint { - sub2(&mut self.data[..], &other.data[..]); - self.normalize() - } -} - -fn sub_sign(a: &[BigDigit], b: &[BigDigit]) -> BigInt { - // Normalize: - let a = &a[..a.iter().rposition(|&x| x != 0).map_or(0, |i| i + 1)]; - let b = &b[..b.iter().rposition(|&x| x != 0).map_or(0, |i| i + 1)]; - - match cmp_slice(a, b) { - Greater => { - let mut ret = BigUint::from_slice(a); - sub2(&mut ret.data[..], b); - BigInt::from_biguint(Plus, ret.normalize()) - }, - Less => { - let mut ret = BigUint::from_slice(b); - sub2(&mut ret.data[..], a); - BigInt::from_biguint(Minus, ret.normalize()) - }, - _ => Zero::zero(), - } -} - -forward_all_binop_to_ref_ref!(impl Mul for BigUint, mul); - -/// Three argument multiply accumulate: -/// acc += b * c -fn mac_digit(acc: &mut [BigDigit], b: &[BigDigit], c: BigDigit) { - if c == 0 { return; } - - let mut b_iter = b.iter(); - let mut carry = 0; - - for ai in acc.iter_mut() { - if let Some(bi) = b_iter.next() { - *ai = mac_with_carry(*ai, *bi, c, &mut carry); - } else if carry != 0 { - *ai = mac_with_carry(*ai, 0, c, &mut carry); - } else { - break; - } - } - - assert!(carry == 0); -} - -/// Three argument multiply accumulate: -/// acc += b * c -fn mac3(acc: &mut [BigDigit], b: &[BigDigit], c: &[BigDigit]) { - let (x, y) = if b.len() < c.len() { (b, c) } else { (c, b) }; - - /* - * Karatsuba multiplication is slower than long multiplication for small x and y: - */ - if x.len() <= 4 { - for (i, xi) in x.iter().enumerate() { - mac_digit(&mut acc[i..], y, *xi); - } - } else { - /* - * Karatsuba multiplication: - * - * The idea is that we break x and y up into two smaller numbers that each have about half - * as many digits, like so (note that multiplying by b is just a shift): - * - * x = x0 + x1 * b - * y = y0 + y1 * b - * - * With some algebra, we can compute x * y with three smaller products, where the inputs to - * each of the smaller products have only about half as many digits as x and y: - * - * x * y = (x0 + x1 * b) * (y0 + y1 * b) - * - * x * y = x0 * y0 - * + x0 * y1 * b - * + x1 * y0 * b - * + x1 * y1 * b^2 - * - * Let p0 = x0 * y0 and p2 = x1 * y1: - * - * x * y = p0 - * + (x0 * y1 + x1 * p0) * b - * + p2 * b^2 - * - * The real trick is that middle term: - * - * x0 * y1 + x1 * y0 - * - * = x0 * y1 + x1 * y0 - p0 + p0 - p2 + p2 - * - * = x0 * y1 + x1 * y0 - x0 * y0 - x1 * y1 + p0 + p2 - * - * Now we complete the square: - * - * = -(x0 * y0 - x0 * y1 - x1 * y0 + x1 * y1) + p0 + p2 - * - * = -((x1 - x0) * (y1 - y0)) + p0 + p2 - * - * Let p1 = (x1 - x0) * (y1 - y0), and substitute back into our original formula: - * - * x * y = p0 - * + (p0 + p2 - p1) * b - * + p2 * b^2 - * - * Where the three intermediate products are: - * - * p0 = x0 * y0 - * p1 = (x1 - x0) * (y1 - y0) - * p2 = x1 * y1 - * - * In doing the computation, we take great care to avoid unnecessary temporary variables - * (since creating a BigUint requires a heap allocation): thus, we rearrange the formula a - * bit so we can use the same temporary variable for all the intermediate products: - * - * x * y = p2 * b^2 + p2 * b - * + p0 * b + p0 - * - p1 * b - * - * The other trick we use is instead of doing explicit shifts, we slice acc at the - * appropriate offset when doing the add. - */ - - /* - * When x is smaller than y, it's significantly faster to pick b such that x is split in - * half, not y: - */ - let b = x.len() / 2; - let (x0, x1) = x.split_at(b); - let (y0, y1) = y.split_at(b); - - /* We reuse the same BigUint for all the intermediate multiplies: */ - - let len = y.len() + 1; - let mut p = BigUint { data: vec![0; len] }; - - // p2 = x1 * y1 - mac3(&mut p.data[..], x1, y1); - - // Not required, but the adds go faster if we drop any unneeded 0s from the end: - p = p.normalize(); - - add2(&mut acc[b..], &p.data[..]); - add2(&mut acc[b * 2..], &p.data[..]); - - // Zero out p before the next multiply: - p.data.truncate(0); - p.data.extend(repeat(0).take(len)); - - // p0 = x0 * y0 - mac3(&mut p.data[..], x0, y0); - p = p.normalize(); - - add2(&mut acc[..], &p.data[..]); - add2(&mut acc[b..], &p.data[..]); - - // p1 = (x1 - x0) * (y1 - y0) - // We do this one last, since it may be negative and acc can't ever be negative: - let j0 = sub_sign(x1, x0); - let j1 = sub_sign(y1, y0); - - match j0.sign * j1.sign { - Plus => { - p.data.truncate(0); - p.data.extend(repeat(0).take(len)); - - mac3(&mut p.data[..], &j0.data.data[..], &j1.data.data[..]); - p = p.normalize(); - - sub2(&mut acc[b..], &p.data[..]); - }, - Minus => { - mac3(&mut acc[b..], &j0.data.data[..], &j1.data.data[..]); - }, - NoSign => (), - } - } -} - -fn mul3(x: &[BigDigit], y: &[BigDigit]) -> BigUint { - let len = x.len() + y.len() + 1; - let mut prod = BigUint { data: vec![0; len] }; - - mac3(&mut prod.data[..], x, y); - prod.normalize() -} - -impl<'a, 'b> Mul<&'b BigUint> for &'a BigUint { - type Output = BigUint; - - #[inline] - fn mul(self, other: &BigUint) -> BigUint { - mul3(&self.data[..], &other.data[..]) - } -} - -fn div_rem_digit(mut a: BigUint, b: BigDigit) -> (BigUint, BigDigit) { - let mut rem = 0; - - for d in a.data.iter_mut().rev() { - let (q, r) = div_wide(rem, *d, b); - *d = q; - rem = r; - } - - (a.normalize(), rem) -} - -forward_all_binop_to_ref_ref!(impl Div for BigUint, div); - -impl<'a, 'b> Div<&'b BigUint> for &'a BigUint { - type Output = BigUint; - - #[inline] - fn div(self, other: &BigUint) -> BigUint { - let (q, _) = self.div_rem(other); - return q; - } -} - -forward_all_binop_to_ref_ref!(impl Rem for BigUint, rem); - -impl<'a, 'b> Rem<&'b BigUint> for &'a BigUint { - type Output = BigUint; - - #[inline] - fn rem(self, other: &BigUint) -> BigUint { - let (_, r) = self.div_rem(other); - return r; - } -} - -impl Neg for BigUint { - type Output = BigUint; - - #[inline] - fn neg(self) -> BigUint { panic!() } -} - -impl<'a> Neg for &'a BigUint { - type Output = BigUint; - - #[inline] - fn neg(self) -> BigUint { panic!() } -} - -impl CheckedAdd for BigUint { - #[inline] - fn checked_add(&self, v: &BigUint) -> Option { - return Some(self.add(v)); - } -} - -impl CheckedSub for BigUint { - #[inline] - fn checked_sub(&self, v: &BigUint) -> Option { - match self.cmp(v) { - Less => None, - Equal => Some(Zero::zero()), - Greater => Some(self.sub(v)), - } - } -} - -impl CheckedMul for BigUint { - #[inline] - fn checked_mul(&self, v: &BigUint) -> Option { - return Some(self.mul(v)); - } -} - -impl CheckedDiv for BigUint { - #[inline] - fn checked_div(&self, v: &BigUint) -> Option { - 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() { panic!() } - if self.is_zero() { return (Zero::zero(), Zero::zero()); } - if *other == One::one() { return (self.clone(), Zero::zero()); } - - /* Required or the q_len calculation below can underflow: */ - match self.cmp(other) { - Less => return (Zero::zero(), self.clone()), - Equal => return (One::one(), Zero::zero()), - Greater => {} // Do nothing - } - - /* - * This algorithm is from Knuth, TAOCP vol 2 section 4.3, algorithm D: - * - * First, normalize the arguments so the highest bit in the highest digit of the divisor is - * set: the main loop uses the highest digit of the divisor for generating guesses, so we - * want it to be the largest number we can efficiently divide by. - */ - let shift = other.data.last().unwrap().leading_zeros() as usize; - let mut a = self << shift; - let b = other << shift; - - /* - * The algorithm works by incrementally calculating "guesses", q0, for part of the - * remainder. Once we have any number q0 such that q0 * b <= a, we can set - * - * q += q0 - * a -= q0 * b - * - * and then iterate until a < b. Then, (q, a) will be our desired quotient and remainder. - * - * q0, our guess, is calculated by dividing the last few digits of a by the last digit of b - * - this should give us a guess that is "close" to the actual quotient, but is possibly - * greater than the actual quotient. If q0 * b > a, we simply use iterated subtraction - * until we have a guess such that q0 & b <= a. - */ - - let bn = *b.data.last().unwrap(); - let q_len = a.data.len() - b.data.len() + 1; - let mut q = BigUint { data: vec![0; q_len] }; - - /* - * We reuse the same temporary to avoid hitting the allocator in our inner loop - this is - * sized to hold a0 (in the common case; if a particular digit of the quotient is zero a0 - * can be bigger). - */ - let mut tmp = BigUint { data: Vec::with_capacity(2) }; - - for j in (0..q_len).rev() { - /* - * When calculating our next guess q0, we don't need to consider the digits below j - * + b.data.len() - 1: we're guessing digit j of the quotient (i.e. q0 << j) from - * digit bn of the divisor (i.e. bn << (b.data.len() - 1) - so the product of those - * two numbers will be zero in all digits up to (j + b.data.len() - 1). - */ - let offset = j + b.data.len() - 1; - if offset >= a.data.len() { - continue; - } - - /* just avoiding a heap allocation: */ - let mut a0 = tmp; - a0.data.truncate(0); - a0.data.extend(a.data[offset..].iter().cloned()); - - /* - * q0 << j * big_digit::BITS is our actual quotient estimate - we do the shifts - * implicitly at the end, when adding and subtracting to a and q. Not only do we - * save the cost of the shifts, the rest of the arithmetic gets to work with - * smaller numbers. - */ - let (mut q0, _) = div_rem_digit(a0, bn); - let mut prod = &b * &q0; - - while cmp_slice(&prod.data[..], &a.data[j..]) == Greater { - let one: BigUint = One::one(); - q0 = q0 - one; - prod = prod - &b; - } - - add2(&mut q.data[j..], &q0.data[..]); - sub2(&mut a.data[j..], &prod.data[..]); - a = a.normalize(); - - tmp = q0; - } - - debug_assert!(a < b); - - (q.normalize(), a >> 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. - #[inline] - fn divides(&self, other: &BigUint) -> bool { 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.first() { - 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 { - 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 { - match self.data.len() { - 0 => Some(0), - 1 => Some(self.data[0] as u64), - 2 => Some(big_digit::to_doublebigdigit(self.data[1], self.data[0]) - as u64), - _ => None - } - } - - // `DoubleBigDigit` size dependent - #[inline] - fn to_f32(&self) -> Option { - match self.data.len() { - 0 => Some(f32::zero()), - 1 => Some(self.data[0] as f32), - len => { - // this will prevent any overflow of exponent - if len > (f32::MAX_EXP as usize) / big_digit::BITS { - None - } else { - let exponent = (len - 2) * big_digit::BITS; - // we need 25 significant digits, 24 to be stored and 1 for rounding - // this gives at least 33 significant digits - let mantissa = big_digit::to_doublebigdigit(self.data[len - 1], self.data[len - 2]); - // this cast handles rounding - let ret = (mantissa as f32) * 2.0.powi(exponent as i32); - if ret.is_infinite() { - None - } else { - Some(ret) - } - } - } - } - } - - // `DoubleBigDigit` size dependent - #[inline] - fn to_f64(&self) -> Option { - match self.data.len() { - 0 => Some(f64::zero()), - 1 => Some(self.data[0] as f64), - 2 => Some(big_digit::to_doublebigdigit(self.data[1], self.data[0]) as f64), - len => { - // this will prevent any overflow of exponent - if len > (f64::MAX_EXP as usize) / big_digit::BITS { - None - } else { - let mut exponent = (len - 2) * big_digit::BITS; - let mut mantissa = big_digit::to_doublebigdigit(self.data[len - 1], self.data[len - 2]); - // we need at least 54 significant bit digits, 53 to be stored and 1 for rounding - // so we take enough from the next BigDigit to make it up to 64 - let shift = mantissa.leading_zeros() as usize; - if shift > 0 { - mantissa <<= shift; - mantissa |= self.data[len - 3] as u64 >> (big_digit::BITS - shift); - exponent -= shift; - } - // this cast handles rounding - let ret = (mantissa as f64) * 2.0.powi(exponent as i32); - if ret.is_infinite() { - None - } else { - Some(ret) - } - } - } - } - } -} - -impl FromPrimitive for BigUint { - #[inline] - fn from_i64(n: i64) -> Option { - if n >= 0 { - Some(BigUint::from(n as u64)) - } else { - None - } - } - - #[inline] - fn from_u64(n: u64) -> Option { - Some(BigUint::from(n)) - } - - #[inline] - fn from_f64(mut n: f64) -> Option { - // handle NAN, INFINITY, NEG_INFINITY - if !n.is_finite() { - return None; - } - - // match the rounding of casting from float to int - n = n.trunc(); - - // handle 0.x, -0.x - if n.is_zero() { - return Some(BigUint::zero()); - } - - let (mantissa, exponent, sign) = Float::integer_decode(n); - - if sign == -1 { - return None; - } - - let mut ret = BigUint::from(mantissa); - if exponent > 0 { - ret = ret << exponent as usize; - } else if exponent < 0 { - ret = ret >> (-exponent) as usize; - } - Some(ret) - } -} - -impl From for BigUint { - // `DoubleBigDigit` size dependent - #[inline] - fn from(n: u64) -> Self { - match big_digit::from_doublebigdigit(n) { - (0, 0) => BigUint::zero(), - (0, n0) => BigUint { data: vec![n0] }, - (n1, n0) => BigUint { data: vec![n0, n1] }, - } - } -} - -macro_rules! impl_biguint_from_uint { - ($T:ty) => { - impl From<$T> for BigUint { - #[inline] - fn from(n: $T) -> Self { - BigUint::from(n as u64) - } - } - } -} - -impl_biguint_from_uint!(u8); -impl_biguint_from_uint!(u16); -impl_biguint_from_uint!(u32); -impl_biguint_from_uint!(usize); - -/// A generic trait for converting a value to a `BigUint`. -pub trait ToBigUint { - /// Converts the value of `self` to a `BigUint`. - fn to_biguint(&self) -> Option; -} - -impl ToBigUint for BigInt { - #[inline] - fn to_biguint(&self) -> Option { - if self.sign == Plus { - Some(self.data.clone()) - } else if self.sign == NoSign { - Some(Zero::zero()) - } else { - None - } - } -} - -impl ToBigUint for BigUint { - #[inline] - fn to_biguint(&self) -> Option { - Some(self.clone()) - } -} - -macro_rules! impl_to_biguint { - ($T:ty, $from_ty:path) => { - impl ToBigUint for $T { - #[inline] - fn to_biguint(&self) -> Option { - $from_ty(*self) - } - } - } -} - -impl_to_biguint!(isize, FromPrimitive::from_isize); -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!(usize, FromPrimitive::from_usize); -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_to_biguint!(f32, FromPrimitive::from_f32); -impl_to_biguint!(f64, FromPrimitive::from_f64); - -// Extract bitwise digits that evenly divide BigDigit -fn to_bitwise_digits_le(u: &BigUint, bits: usize) -> Vec { - debug_assert!(!u.is_zero() && bits <= 8 && big_digit::BITS % bits == 0); - - let last_i = u.data.len() - 1; - let mask: BigDigit = (1 << bits) - 1; - let digits_per_big_digit = big_digit::BITS / bits; - let digits = (u.bits() + bits - 1) / bits; - let mut res = Vec::with_capacity(digits); - - for mut r in u.data[..last_i].iter().cloned() { - for _ in 0..digits_per_big_digit { - res.push((r & mask) as u8); - r >>= bits; - } - } - - let mut r = u.data[last_i]; - while r != 0 { - res.push((r & mask) as u8); - r >>= bits; - } - - res -} - -// Extract bitwise digits that don't evenly divide BigDigit -fn to_inexact_bitwise_digits_le(u: &BigUint, bits: usize) -> Vec { - debug_assert!(!u.is_zero() && bits <= 8 && big_digit::BITS % bits != 0); - - let last_i = u.data.len() - 1; - let mask: DoubleBigDigit = (1 << bits) - 1; - let digits = (u.bits() + bits - 1) / bits; - let mut res = Vec::with_capacity(digits); - - let mut r = 0; - let mut rbits = 0; - for hi in u.data[..last_i].iter().cloned() { - r |= (hi as DoubleBigDigit) << rbits; - rbits += big_digit::BITS; - - while rbits >= bits { - res.push((r & mask) as u8); - r >>= bits; - rbits -= bits; - } - } - - r |= (u.data[last_i] as DoubleBigDigit) << rbits; - while r != 0 { - res.push((r & mask) as u8); - r >>= bits; - } - - res -} - -// Extract little-endian radix digits -#[inline(always)] // forced inline to get const-prop for radix=10 -fn to_radix_digits_le(u: &BigUint, radix: u32) -> Vec { - debug_assert!(!u.is_zero() && !radix.is_power_of_two()); - - // Estimate how big the result will be, so we can pre-allocate it. - let radix_digits = ((u.bits() as f64) / (radix as f64).log2()).ceil(); - let mut res = Vec::with_capacity(radix_digits as usize); - let mut digits = u.clone(); - - let (base, power) = get_radix_base(radix); - debug_assert!(base < (1 << 32)); - let base = base as BigDigit; - - while digits.data.len() > 1 { - let (q, mut r) = div_rem_digit(digits, base); - for _ in 0..power { - res.push((r % radix) as u8); - r /= radix; - } - digits = q; - } - - let mut r = digits.data[0]; - while r != 0 { - res.push((r % radix) as u8); - r /= radix; - } - - res -} - -fn to_str_radix_reversed(u: &BigUint, radix: u32) -> Vec { - assert!(2 <= radix && radix <= 36, "The radix must be within 2...36"); - - if u.is_zero() { - return vec![b'0'] - } - - let mut res = if radix.is_power_of_two() { - // Powers of two can use bitwise masks and shifting instead of division - let bits = radix.trailing_zeros() as usize; - if big_digit::BITS % bits == 0 { - to_bitwise_digits_le(u, bits) - } else { - to_inexact_bitwise_digits_le(u, bits) - } - } else if radix == 10 { - // 10 is so common that it's worth separating out for const-propagation. - // Optimizers can often turn constant division into a faster multiplication. - to_radix_digits_le(u, 10) - } else { - to_radix_digits_le(u, radix) - }; - - // Now convert everything to ASCII digits. - for r in &mut res { - debug_assert!((*r as u32) < radix); - if *r < 10 { - *r += b'0'; - } else { - *r += b'a' - 10; - } - } - res -} - -impl BigUint { - /// Creates and initializes a `BigUint`. - /// - /// The digits are in little-endian base 2^32. - #[inline] - pub fn new(digits: Vec) -> BigUint { - BigUint { data: digits }.normalize() - } - - /// Creates and initializes a `BigUint`. - /// - /// The digits are in little-endian base 2^32. - #[inline] - pub fn from_slice(slice: &[BigDigit]) -> BigUint { - BigUint::new(slice.to_vec()) - } - - /// Creates and initializes a `BigUint`. - /// - /// The bytes are in big-endian byte order. - /// - /// # Examples - /// - /// ``` - /// use num::bigint::BigUint; - /// - /// assert_eq!(BigUint::from_bytes_be(b"A"), - /// BigUint::parse_bytes(b"65", 10).unwrap()); - /// assert_eq!(BigUint::from_bytes_be(b"AA"), - /// BigUint::parse_bytes(b"16705", 10).unwrap()); - /// assert_eq!(BigUint::from_bytes_be(b"AB"), - /// BigUint::parse_bytes(b"16706", 10).unwrap()); - /// assert_eq!(BigUint::from_bytes_be(b"Hello world!"), - /// BigUint::parse_bytes(b"22405534230753963835153736737", 10).unwrap()); - /// ``` - #[inline] - pub fn from_bytes_be(bytes: &[u8]) -> BigUint { - if bytes.is_empty() { - Zero::zero() - } else { - let mut v = bytes.to_vec(); - v.reverse(); - BigUint::from_bytes_le(&*v) - } - } - - /// Creates and initializes a `BigUint`. - /// - /// The bytes are in little-endian byte order. - #[inline] - pub fn from_bytes_le(bytes: &[u8]) -> BigUint { - if bytes.is_empty() { - Zero::zero() - } else { - from_bitwise_digits_le(bytes, 8) - } - } - - /// Returns the byte representation of the `BigUint` in little-endian byte order. - /// - /// # Examples - /// - /// ``` - /// use num::bigint::BigUint; - /// - /// let i = BigUint::parse_bytes(b"1125", 10).unwrap(); - /// assert_eq!(i.to_bytes_le(), vec![101, 4]); - /// ``` - #[inline] - pub fn to_bytes_le(&self) -> Vec { - if self.is_zero() { - vec![0] - } else { - to_bitwise_digits_le(self, 8) - } - } - - /// Returns the byte representation of the `BigUint` in big-endian byte order. - /// - /// # Examples - /// - /// ``` - /// use num::bigint::BigUint; - /// - /// let i = BigUint::parse_bytes(b"1125", 10).unwrap(); - /// assert_eq!(i.to_bytes_be(), vec![4, 101]); - /// ``` - #[inline] - pub fn to_bytes_be(&self) -> Vec { - let mut v = self.to_bytes_le(); - v.reverse(); - v - } - - /// Returns the integer formatted as a string in the given radix. - /// `radix` must be in the range `[2, 36]`. - /// - /// # Examples - /// - /// ``` - /// use num::bigint::BigUint; - /// - /// let i = BigUint::parse_bytes(b"ff", 16).unwrap(); - /// assert_eq!(i.to_str_radix(16), "ff"); - /// ``` - #[inline] - pub fn to_str_radix(&self, radix: u32) -> String { - let mut v = to_str_radix_reversed(self, radix); - v.reverse(); - unsafe { String::from_utf8_unchecked(v) } - } - - /// Creates and initializes a `BigUint`. - /// - /// # Examples - /// - /// ``` - /// use num::bigint::{BigUint, ToBigUint}; - /// - /// assert_eq!(BigUint::parse_bytes(b"1234", 10), ToBigUint::to_biguint(&1234)); - /// assert_eq!(BigUint::parse_bytes(b"ABCD", 16), ToBigUint::to_biguint(&0xABCD)); - /// assert_eq!(BigUint::parse_bytes(b"G", 16), None); - /// ``` - #[inline] - pub fn parse_bytes(buf: &[u8], radix: u32) -> Option { - str::from_utf8(buf).ok().and_then(|s| BigUint::from_str_radix(s, radix).ok()) - } - - /// Determines the fewest bits necessary to express the `BigUint`. - pub fn bits(&self) -> usize { - if self.is_zero() { return 0; } - let zeros = self.data.last().unwrap().leading_zeros(); - return self.data.len()*big_digit::BITS - zeros as usize; - } - - /// Strips off trailing zero bigdigits - comparisons require the last element in the vector to - /// be nonzero. - #[inline] - fn normalize(mut self) -> BigUint { - while let Some(&0) = self.data.last() { - self.data.pop(); - } - self - } -} - -#[cfg(feature = "serde")] -impl serde::Serialize for BigUint { - fn serialize(&self, serializer: &mut S) -> Result<(), S::Error> where - S: serde::Serializer - { - self.data.serialize(serializer) - } -} - -#[cfg(feature = "serde")] -impl serde::Deserialize for BigUint { - fn deserialize(deserializer: &mut D) -> Result where - D: serde::Deserializer, - { - let data = try!(Vec::deserialize(deserializer)); - Ok(BigUint { - data: data, - }) - } -} - -// `DoubleBigDigit` size dependent -/// Returns the greatest power of the radix <= big_digit::BASE -#[inline] -fn get_radix_base(radix: u32) -> (DoubleBigDigit, usize) { - // To generate this table: - // let target = std::u32::max as u64 + 1; - // for radix in 2u64..37 { - // let power = (target as f64).log(radix as f64) as u32; - // let base = radix.pow(power); - // println!("({:10}, {:2}), // {:2}", base, power, radix); - // } - const BASES: [(DoubleBigDigit, usize); 37] = [ - (0, 0), (0, 0), - (4294967296, 32), // 2 - (3486784401, 20), // 3 - (4294967296, 16), // 4 - (1220703125, 13), // 5 - (2176782336, 12), // 6 - (1977326743, 11), // 7 - (1073741824, 10), // 8 - (3486784401, 10), // 9 - (1000000000, 9), // 10 - (2357947691, 9), // 11 - ( 429981696, 8), // 12 - ( 815730721, 8), // 13 - (1475789056, 8), // 14 - (2562890625, 8), // 15 - (4294967296, 8), // 16 - ( 410338673, 7), // 17 - ( 612220032, 7), // 18 - ( 893871739, 7), // 19 - (1280000000, 7), // 20 - (1801088541, 7), // 21 - (2494357888, 7), // 22 - (3404825447, 7), // 23 - ( 191102976, 6), // 24 - ( 244140625, 6), // 25 - ( 308915776, 6), // 26 - ( 387420489, 6), // 27 - ( 481890304, 6), // 28 - ( 594823321, 6), // 29 - ( 729000000, 6), // 30 - ( 887503681, 6), // 31 - (1073741824, 6), // 32 - (1291467969, 6), // 33 - (1544804416, 6), // 34 - (1838265625, 6), // 35 - (2176782336, 6), // 36 - ]; - - assert!(2 <= radix && radix <= 36, "The radix must be within 2...36"); - BASES[radix as usize] -} - -/// A Sign is a `BigInt`'s composing element. -#[derive(PartialEq, PartialOrd, Eq, Ord, Copy, Clone, Debug, Hash)] -#[cfg_attr(feature = "rustc-serialize", derive(RustcEncodable, RustcDecodable))] -pub enum Sign { Minus, NoSign, Plus } - -impl Neg for Sign { - type Output = Sign; - - /// Negate Sign value. - #[inline] - fn neg(self) -> Sign { - match self { - Minus => Plus, - NoSign => NoSign, - Plus => Minus - } - } -} - -impl Mul for Sign { - type Output = Sign; - - #[inline] - fn mul(self, other: Sign) -> Sign { - match (self, other) { - (NoSign, _) | (_, NoSign) => NoSign, - (Plus, Plus) | (Minus, Minus) => Plus, - (Plus, Minus) | (Minus, Plus) => Minus, - } - } -} - -#[cfg(feature = "serde")] -impl serde::Serialize for Sign { - fn serialize(&self, serializer: &mut S) -> Result<(), S::Error> where - S: serde::Serializer - { - match *self { - Sign::Minus => (-1i8).serialize(serializer), - Sign::NoSign => 0i8.serialize(serializer), - Sign::Plus => 1i8.serialize(serializer), - } - } -} - -#[cfg(feature = "serde")] -impl serde::Deserialize for Sign { - fn deserialize(deserializer: &mut D) -> Result where - D: serde::Deserializer, - { - use serde::de::Error; - - let sign: i8 = try!(serde::Deserialize::deserialize(deserializer)); - match sign { - -1 => Ok(Sign::Minus), - 0 => Ok(Sign::NoSign), - 1 => Ok(Sign::Plus), - _ => Err(D::Error::invalid_value("sign must be -1, 0, or 1")), - } - } -} - -/// A big signed integer type. -#[derive(Clone, Debug, Hash)] -#[cfg_attr(feature = "rustc-serialize", derive(RustcEncodable, RustcDecodable))] -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 { - 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 { - NoSign => 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::Display for BigInt { - fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result { - f.pad_integral(!self.is_negative(), "", &self.data.to_str_radix(10)) - } -} - -impl fmt::Binary for BigInt { - fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result { - f.pad_integral(!self.is_negative(), "0b", &self.data.to_str_radix(2)) - } -} - -impl fmt::Octal for BigInt { - fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result { - f.pad_integral(!self.is_negative(), "0o", &self.data.to_str_radix(8)) - } -} - -impl fmt::LowerHex for BigInt { - fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result { - f.pad_integral(!self.is_negative(), "0x", &self.data.to_str_radix(16)) - } -} - -impl fmt::UpperHex for BigInt { - fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result { - f.pad_integral(!self.is_negative(), "0x", &self.data.to_str_radix(16).to_ascii_uppercase()) - } -} - -impl FromStr for BigInt { - type Err = ParseBigIntError; - - #[inline] - fn from_str(s: &str) -> Result { - BigInt::from_str_radix(s, 10) - } -} - -impl Num for BigInt { - type Error = ParseBigIntError; - - /// Creates and initializes a BigInt. - #[inline] - fn from_str_radix(mut s: &str, radix: u32) -> Result { - let sign = if s.starts_with('-') { - let tail = &s[1..]; - if !tail.starts_with('+') { s = tail } - Minus - } else { Plus }; - let bu = try!(BigUint::from_str_radix(s, radix)); - Ok(BigInt::from_biguint(sign, bu)) - } -} - -impl Shl for BigInt { - type Output = BigInt; - - #[inline] - fn shl(self, rhs: usize) -> BigInt { (&self) << rhs } -} - -impl<'a> Shl for &'a BigInt { - type Output = BigInt; - - #[inline] - fn shl(self, rhs: usize) -> BigInt { - BigInt::from_biguint(self.sign, &self.data << rhs) - } -} - -impl Shr for BigInt { - type Output = BigInt; - - #[inline] - fn shr(self, rhs: usize) -> BigInt { - BigInt::from_biguint(self.sign, self.data >> rhs) - } -} - -impl<'a> Shr for &'a BigInt { - type Output = BigInt; - - #[inline] - fn shr(self, rhs: usize) -> BigInt { - BigInt::from_biguint(self.sign, &self.data >> rhs) - } -} - -impl Zero for BigInt { - #[inline] - fn zero() -> BigInt { - BigInt::from_biguint(NoSign, Zero::zero()) - } - - #[inline] - fn is_zero(&self) -> bool { self.sign == NoSign } -} - -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 | NoSign => 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()), - NoSign => Zero::zero(), - } - } - - #[inline] - fn is_positive(&self) -> bool { self.sign == Plus } - - #[inline] - fn is_negative(&self) -> bool { self.sign == Minus } -} - -// We want to forward to BigUint::add, but it's not clear how that will go until -// we compare both sign and magnitude. So we duplicate this body for every -// val/ref combination, deferring that decision to BigUint's own forwarding. -macro_rules! bigint_add { - ($a:expr, $a_owned:expr, $a_data:expr, $b:expr, $b_owned:expr, $b_data:expr) => { - match ($a.sign, $b.sign) { - (_, NoSign) => $a_owned, - (NoSign, _) => $b_owned, - // same sign => keep the sign with the sum of magnitudes - (Plus, Plus) | (Minus, Minus) => - BigInt::from_biguint($a.sign, $a_data + $b_data), - // opposite signs => keep the sign of the larger with the difference of magnitudes - (Plus, Minus) | (Minus, Plus) => - match $a.data.cmp(&$b.data) { - Less => BigInt::from_biguint($b.sign, $b_data - $a_data), - Greater => BigInt::from_biguint($a.sign, $a_data - $b_data), - Equal => Zero::zero(), - }, - } - }; -} - -impl<'a, 'b> Add<&'b BigInt> for &'a BigInt { - type Output = BigInt; - - #[inline] - fn add(self, other: &BigInt) -> BigInt { - bigint_add!(self, self.clone(), &self.data, other, other.clone(), &other.data) - } -} - -impl<'a> Add for &'a BigInt { - type Output = BigInt; - - #[inline] - fn add(self, other: BigInt) -> BigInt { - bigint_add!(self, self.clone(), &self.data, other, other, other.data) - } -} - -impl<'a> Add<&'a BigInt> for BigInt { - type Output = BigInt; - - #[inline] - fn add(self, other: &BigInt) -> BigInt { - bigint_add!(self, self, self.data, other, other.clone(), &other.data) - } -} - -impl Add for BigInt { - type Output = BigInt; - - #[inline] - fn add(self, other: BigInt) -> BigInt { - bigint_add!(self, self, self.data, other, other, other.data) - } -} - -// We want to forward to BigUint::sub, but it's not clear how that will go until -// we compare both sign and magnitude. So we duplicate this body for every -// val/ref combination, deferring that decision to BigUint's own forwarding. -macro_rules! bigint_sub { - ($a:expr, $a_owned:expr, $a_data:expr, $b:expr, $b_owned:expr, $b_data:expr) => { - match ($a.sign, $b.sign) { - (_, NoSign) => $a_owned, - (NoSign, _) => -$b_owned, - // opposite signs => keep the sign of the left with the sum of magnitudes - (Plus, Minus) | (Minus, Plus) => - BigInt::from_biguint($a.sign, $a_data + $b_data), - // same sign => keep or toggle the sign of the left with the difference of magnitudes - (Plus, Plus) | (Minus, Minus) => - match $a.data.cmp(&$b.data) { - Less => BigInt::from_biguint(-$a.sign, $b_data - $a_data), - Greater => BigInt::from_biguint($a.sign, $a_data - $b_data), - Equal => Zero::zero(), - }, - } - }; -} - -impl<'a, 'b> Sub<&'b BigInt> for &'a BigInt { - type Output = BigInt; - - #[inline] - fn sub(self, other: &BigInt) -> BigInt { - bigint_sub!(self, self.clone(), &self.data, other, other.clone(), &other.data) - } -} - -impl<'a> Sub for &'a BigInt { - type Output = BigInt; - - #[inline] - fn sub(self, other: BigInt) -> BigInt { - bigint_sub!(self, self.clone(), &self.data, other, other, other.data) - } -} - -impl<'a> Sub<&'a BigInt> for BigInt { - type Output = BigInt; - - #[inline] - fn sub(self, other: &BigInt) -> BigInt { - bigint_sub!(self, self, self.data, other, other.clone(), &other.data) - } -} - -impl Sub for BigInt { - type Output = BigInt; - - #[inline] - fn sub(self, other: BigInt) -> BigInt { - bigint_sub!(self, self, self.data, other, other, other.data) - } -} - -forward_all_binop_to_ref_ref!(impl Mul for BigInt, mul); - -impl<'a, 'b> Mul<&'b BigInt> for &'a BigInt { - type Output = BigInt; - - #[inline] - fn mul(self, other: &BigInt) -> BigInt { - BigInt::from_biguint(self.sign * other.sign, - &self.data * &other.data) - } -} - -forward_all_binop_to_ref_ref!(impl Div for BigInt, div); - -impl<'a, 'b> Div<&'b BigInt> for &'a BigInt { - type Output = BigInt; - - #[inline] - fn div(self, other: &BigInt) -> BigInt { - let (q, _) = self.div_rem(other); - q - } -} - -forward_all_binop_to_ref_ref!(impl Rem for BigInt, rem); - -impl<'a, 'b> Rem<&'b BigInt> for &'a BigInt { - type Output = BigInt; - - #[inline] - fn rem(self, other: &BigInt) -> BigInt { - let (_, r) = self.div_rem(other); - r - } -} - -impl Neg for BigInt { - type Output = BigInt; - - #[inline] - fn neg(mut self) -> BigInt { - self.sign = -self.sign; - self - } -} - -impl<'a> Neg for &'a BigInt { - type Output = BigInt; - - #[inline] - fn neg(self) -> BigInt { - -self.clone() - } -} - -impl CheckedAdd for BigInt { - #[inline] - fn checked_add(&self, v: &BigInt) -> Option { - return Some(self.add(v)); - } -} - -impl CheckedSub for BigInt { - #[inline] - fn checked_sub(&self, v: &BigInt) -> Option { - return Some(self.sub(v)); - } -} - -impl CheckedMul for BigInt { - #[inline] - fn checked_mul(&self, v: &BigInt) -> Option { - return Some(self.mul(v)); - } -} - -impl CheckedDiv for BigInt { - #[inline] - fn checked_div(&self, v: &BigInt) -> Option { - 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(self.sign, d_ui); - let r = BigInt::from_biguint(self.sign, r_ui); - if other.is_negative() { (-d, r) } else { (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); - let one: BigInt = One::one(); - match (self.sign, other.sign) { - (_, NoSign) => panic!(), - (Plus, Plus) | (NoSign, Plus) => (d, m), - (Plus, Minus) | (NoSign, Minus) => { - if m.is_zero() { - (-d, Zero::zero()) - } else { - (-d - one, m + other) - } - }, - (Minus, Plus) => { - if m.is_zero() { - (-d, Zero::zero()) - } else { - (-d - 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. - #[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 { - match self.sign { - Plus => self.data.to_i64(), - NoSign => 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 { - match self.sign { - Plus => self.data.to_u64(), - NoSign => Some(0), - Minus => None - } - } - - #[inline] - fn to_f32(&self) -> Option { - self.data.to_f32().map(|n| if self.sign == Minus { -n } else { n }) - } - - #[inline] - fn to_f64(&self) -> Option { - self.data.to_f64().map(|n| if self.sign == Minus { -n } else { n }) - } -} - -impl FromPrimitive for BigInt { - #[inline] - fn from_i64(n: i64) -> Option { - Some(BigInt::from(n)) - } - - #[inline] - fn from_u64(n: u64) -> Option { - Some(BigInt::from(n)) - } - - #[inline] - fn from_f64(n: f64) -> Option { - if n >= 0.0 { - BigUint::from_f64(n).map(|x| BigInt::from_biguint(Plus, x)) - } else { - BigUint::from_f64(-n).map(|x| BigInt::from_biguint(Minus, x)) - } - } -} - -impl From for BigInt { - #[inline] - fn from(n: i64) -> Self { - if n >= 0 { - BigInt::from(n as u64) - } else { - let u = u64::MAX - (n as u64) + 1; - BigInt { sign: Minus, data: BigUint::from(u) } - } - } -} - -macro_rules! impl_bigint_from_int { - ($T:ty) => { - impl From<$T> for BigInt { - #[inline] - fn from(n: $T) -> Self { - BigInt::from(n as i64) - } - } - } -} - -impl_bigint_from_int!(i8); -impl_bigint_from_int!(i16); -impl_bigint_from_int!(i32); -impl_bigint_from_int!(isize); - -impl From for BigInt { - #[inline] - fn from(n: u64) -> Self { - if n > 0 { - BigInt { sign: Plus, data: BigUint::from(n) } - } else { - BigInt::zero() - } - } -} - -macro_rules! impl_bigint_from_uint { - ($T:ty) => { - impl From<$T> for BigInt { - #[inline] - fn from(n: $T) -> Self { - BigInt::from(n as u64) - } - } - } -} - -impl_bigint_from_uint!(u8); -impl_bigint_from_uint!(u16); -impl_bigint_from_uint!(u32); -impl_bigint_from_uint!(usize); - -impl From for BigInt { - #[inline] - fn from(n: BigUint) -> Self { - if n.is_zero() { - BigInt::zero() - } else { - BigInt { sign: Plus, data: n } - } - } -} - -#[cfg(feature = "serde")] -impl serde::Serialize for BigInt { - fn serialize(&self, serializer: &mut S) -> Result<(), S::Error> where - S: serde::Serializer - { - (self.sign, &self.data).serialize(serializer) - } -} - -#[cfg(feature = "serde")] -impl serde::Deserialize for BigInt { - fn deserialize(deserializer: &mut D) -> Result where - D: serde::Deserializer, - { - let (sign, data) = try!(serde::Deserialize::deserialize(deserializer)); - Ok(BigInt { - sign: sign, - data: data, - }) - } -} - -/// A generic trait for converting a value to a `BigInt`. -pub trait ToBigInt { - /// Converts the value of `self` to a `BigInt`. - fn to_bigint(&self) -> Option; -} - -impl ToBigInt for BigInt { - #[inline] - fn to_bigint(&self) -> Option { - Some(self.clone()) - } -} - -impl ToBigInt for BigUint { - #[inline] - fn to_bigint(&self) -> Option { - if self.is_zero() { - Some(Zero::zero()) - } else { - Some(BigInt { sign: Plus, data: self.clone() }) - } - } -} - -macro_rules! impl_to_bigint { - ($T:ty, $from_ty:path) => { - impl ToBigInt for $T { - #[inline] - fn to_bigint(&self) -> Option { - $from_ty(*self) - } - } - } -} - -impl_to_bigint!(isize, FromPrimitive::from_isize); -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!(usize, FromPrimitive::from_usize); -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_to_bigint!(f32, FromPrimitive::from_f32); -impl_to_bigint!(f64, FromPrimitive::from_f64); - -pub trait RandBigInt { - /// Generate a random `BigUint` of the given bit size. - fn gen_biguint(&mut self, bit_size: usize) -> BigUint; - - /// Generate a random BigInt of the given bit size. - fn gen_bigint(&mut self, bit_size: usize) -> 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; -} - -#[cfg(any(feature = "rand", test))] -impl RandBigInt for R { - fn gen_biguint(&mut self, bit_size: usize) -> BigUint { - let (digits, rem) = bit_size.div_rem(&big_digit::BITS); - let mut data = Vec::with_capacity(digits+1); - for _ in 0 .. digits { - data.push(self.gen()); - } - if rem > 0 { - let final_digit: BigDigit = self.gen(); - data.push(final_digit >> (big_digit::BITS - rem)); - } - BigUint::new(data) - } - - fn gen_bigint(&mut self, bit_size: usize) -> 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 { - NoSign - } - } 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 in little-endian base 2^32. - #[inline] - pub fn new(sign: Sign, digits: Vec) -> BigInt { - BigInt::from_biguint(sign, BigUint::new(digits)) - } - - /// Creates and initializes a `BigInt`. - /// - /// The digits are in little-endian base 2^32. - #[inline] - pub fn from_biguint(sign: Sign, data: BigUint) -> BigInt { - if sign == NoSign || data.is_zero() { - return BigInt { sign: NoSign, 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`. - /// - /// The bytes are in big-endian byte order. - /// - /// # Examples - /// - /// ``` - /// use num::bigint::{BigInt, Sign}; - /// - /// assert_eq!(BigInt::from_bytes_be(Sign::Plus, b"A"), - /// BigInt::parse_bytes(b"65", 10).unwrap()); - /// assert_eq!(BigInt::from_bytes_be(Sign::Plus, b"AA"), - /// BigInt::parse_bytes(b"16705", 10).unwrap()); - /// assert_eq!(BigInt::from_bytes_be(Sign::Plus, b"AB"), - /// BigInt::parse_bytes(b"16706", 10).unwrap()); - /// assert_eq!(BigInt::from_bytes_be(Sign::Plus, b"Hello world!"), - /// BigInt::parse_bytes(b"22405534230753963835153736737", 10).unwrap()); - /// ``` - #[inline] - pub fn from_bytes_be(sign: Sign, bytes: &[u8]) -> BigInt { - BigInt::from_biguint(sign, BigUint::from_bytes_be(bytes)) - } - - /// Creates and initializes a `BigInt`. - /// - /// The bytes are in little-endian byte order. - #[inline] - pub fn from_bytes_le(sign: Sign, bytes: &[u8]) -> BigInt { - BigInt::from_biguint(sign, BigUint::from_bytes_le(bytes)) - } - - /// Returns the sign and the byte representation of the `BigInt` in little-endian byte order. - /// - /// # Examples - /// - /// ``` - /// use num::bigint::{ToBigInt, Sign}; - /// - /// let i = -1125.to_bigint().unwrap(); - /// assert_eq!(i.to_bytes_le(), (Sign::Minus, vec![101, 4])); - /// ``` - #[inline] - pub fn to_bytes_le(&self) -> (Sign, Vec) { - (self.sign, self.data.to_bytes_le()) - } - - /// Returns the sign and the byte representation of the `BigInt` in big-endian byte order. - /// - /// # Examples - /// - /// ``` - /// use num::bigint::{ToBigInt, Sign}; - /// - /// let i = -1125.to_bigint().unwrap(); - /// assert_eq!(i.to_bytes_be(), (Sign::Minus, vec![4, 101])); - /// ``` - #[inline] - pub fn to_bytes_be(&self) -> (Sign, Vec) { - (self.sign, self.data.to_bytes_be()) - } - - /// Returns the integer formatted as a string in the given radix. - /// `radix` must be in the range `[2, 36]`. - /// - /// # Examples - /// - /// ``` - /// use num::bigint::BigInt; - /// - /// let i = BigInt::parse_bytes(b"ff", 16).unwrap(); - /// assert_eq!(i.to_str_radix(16), "ff"); - /// ``` - #[inline] - pub fn to_str_radix(&self, radix: u32) -> String { - let mut v = to_str_radix_reversed(&self.data, radix); - - if self.is_negative() { - v.push(b'-'); - } - - v.reverse(); - unsafe { String::from_utf8_unchecked(v) } - } - - /// Returns the sign of the `BigInt` as a `Sign`. - /// - /// # Examples - /// - /// ``` - /// use num::bigint::{ToBigInt, Sign}; - /// - /// assert_eq!(ToBigInt::to_bigint(&1234).unwrap().sign(), Sign::Plus); - /// assert_eq!(ToBigInt::to_bigint(&-4321).unwrap().sign(), Sign::Minus); - /// assert_eq!(ToBigInt::to_bigint(&0).unwrap().sign(), Sign::NoSign); - /// ``` - #[inline] - pub fn sign(&self) -> Sign { - self.sign - } - - /// Creates and initializes a `BigInt`. - /// - /// # Examples - /// - /// ``` - /// use num::bigint::{BigInt, ToBigInt}; - /// - /// assert_eq!(BigInt::parse_bytes(b"1234", 10), ToBigInt::to_bigint(&1234)); - /// assert_eq!(BigInt::parse_bytes(b"ABCD", 16), ToBigInt::to_bigint(&0xABCD)); - /// assert_eq!(BigInt::parse_bytes(b"G", 16), None); - /// ``` - #[inline] - pub fn parse_bytes(buf: &[u8], radix: u32) -> Option { - str::from_utf8(buf).ok().and_then(|s| BigInt::from_str_radix(s, radix).ok()) - } - - /// Determines the fewest bits necessary to express the `BigInt`, - /// not including the sign. - pub fn bits(&self) -> usize { - self.data.bits() - } - - /// Converts this `BigInt` into a `BigUint`, if it's not negative. - #[inline] - pub fn to_biguint(&self) -> Option { - match self.sign { - Plus => Some(self.data.clone()), - NoSign => Some(Zero::zero()), - Minus => None - } - } - - #[inline] - pub fn checked_add(&self, v: &BigInt) -> Option { - return Some(self.add(v)); - } - - #[inline] - pub fn checked_sub(&self, v: &BigInt) -> Option { - return Some(self.sub(v)); - } - - #[inline] - pub fn checked_mul(&self, v: &BigInt) -> Option { - return Some(self.mul(v)); - } - - #[inline] - pub fn checked_div(&self, v: &BigInt) -> Option { - if v.is_zero() { - return None; - } - return Some(self.div(v)); - } -} - -#[derive(Debug, PartialEq)] -pub enum ParseBigIntError { - ParseInt(ParseIntError), - Other, -} - -impl fmt::Display for ParseBigIntError { - fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result { - match self { - &ParseBigIntError::ParseInt(ref e) => e.fmt(f), - &ParseBigIntError::Other => "failed to parse provided string".fmt(f) - } - } -} - -impl Error for ParseBigIntError { - fn description(&self) -> &str { "failed to parse bigint/biguint" } -} - -impl From for ParseBigIntError { - fn from(err: ParseIntError) -> ParseBigIntError { - ParseBigIntError::ParseInt(err) - } -} - -#[cfg(test)] -mod biguint_tests { - use Integer; - use super::{BigDigit, BigUint, ToBigUint, big_digit}; - use super::{BigInt, RandBigInt, ToBigInt}; - use super::Sign::Plus; - - use std::cmp::Ordering::{Less, Equal, Greater}; - use std::{f32, f64}; - use std::i64; - use std::iter::repeat; - use std::str::FromStr; - use std::{u8, u16, u32, u64, usize}; - - use rand::thread_rng; - use {Num, Zero, One, CheckedAdd, CheckedSub, CheckedMul, CheckedDiv}; - use {ToPrimitive, FromPrimitive}; - use Float; - - /// Assert that an op works for all val/ref combinations - macro_rules! assert_op { - ($left:ident $op:tt $right:ident == $expected:expr) => { - assert_eq!((&$left) $op (&$right), $expected); - assert_eq!((&$left) $op $right.clone(), $expected); - assert_eq!($left.clone() $op (&$right), $expected); - assert_eq!($left.clone() $op $right.clone(), $expected); - }; - } - - #[test] - fn test_from_slice() { - fn check(slice: &[BigDigit], data: &[BigDigit]) { - assert!(BigUint::from_slice(slice).data == data); - } - check(&[1], &[1]); - check(&[0, 0, 0], &[]); - check(&[1, 2, 0, 0], &[1, 2]); - check(&[0, 0, 1, 2], &[0, 0, 1, 2]); - check(&[0, 0, 1, 2, 0, 0], &[0, 0, 1, 2]); - check(&[-1i32 as BigDigit], &[-1i32 as BigDigit]); - } - - #[test] - fn test_from_bytes_be() { - fn check(s: &str, result: &str) { - assert_eq!(BigUint::from_bytes_be(s.as_bytes()), - BigUint::parse_bytes(result.as_bytes(), 10).unwrap()); - } - check("A", "65"); - check("AA", "16705"); - check("AB", "16706"); - check("Hello world!", "22405534230753963835153736737"); - assert_eq!(BigUint::from_bytes_be(&[]), Zero::zero()); - } - - #[test] - fn test_to_bytes_be() { - fn check(s: &str, result: &str) { - let b = BigUint::parse_bytes(result.as_bytes(), 10).unwrap(); - assert_eq!(b.to_bytes_be(), s.as_bytes()); - } - check("A", "65"); - check("AA", "16705"); - check("AB", "16706"); - check("Hello world!", "22405534230753963835153736737"); - let b: BigUint = Zero::zero(); - assert_eq!(b.to_bytes_be(), [0]); - - // Test with leading/trailing zero bytes and a full BigDigit of value 0 - let b = BigUint::from_str_radix("00010000000000000200", 16).unwrap(); - assert_eq!(b.to_bytes_be(), [1, 0, 0, 0, 0, 0, 0, 2, 0]); - } - - #[test] - fn test_from_bytes_le() { - fn check(s: &str, result: &str) { - assert_eq!(BigUint::from_bytes_le(s.as_bytes()), - BigUint::parse_bytes(result.as_bytes(), 10).unwrap()); - } - check("A", "65"); - check("AA", "16705"); - check("BA", "16706"); - check("!dlrow olleH", "22405534230753963835153736737"); - assert_eq!(BigUint::from_bytes_le(&[]), Zero::zero()); - } - - #[test] - fn test_to_bytes_le() { - fn check(s: &str, result: &str) { - let b = BigUint::parse_bytes(result.as_bytes(), 10).unwrap(); - assert_eq!(b.to_bytes_le(), s.as_bytes()); - } - check("A", "65"); - check("AA", "16705"); - check("BA", "16706"); - check("!dlrow olleH", "22405534230753963835153736737"); - let b: BigUint = Zero::zero(); - assert_eq!(b.to_bytes_le(), [0]); - - // Test with leading/trailing zero bytes and a full BigDigit of value 0 - let b = BigUint::from_str_radix("00010000000000000200", 16).unwrap(); - assert_eq!(b.to_bytes_le(), [0, 2, 0, 0, 0, 0, 0, 0, 1]); - } - - #[test] - fn test_cmp() { - let data: [&[_]; 7] = [ &[], &[1], &[2], &[!0], &[0, 1], &[2, 1], &[1, 1, 1] ]; - let data: Vec = data.iter().map(|v| BigUint::from_slice(*v)).collect(); - for (i, ni) in data.iter().enumerate() { - for (j0, nj) in data[i..].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)); - } - - const BIT_TESTS: &'static [(&'static [BigDigit], - &'static [BigDigit], - &'static [BigDigit], - &'static [BigDigit], - &'static [BigDigit])] = &[ - // LEFT RIGHT AND OR XOR - ( &[], &[], &[], &[], &[] ), - ( &[268, 482, 17], &[964, 54], &[260, 34], &[972, 502, 17], &[712, 468, 17] ), - ]; - - #[test] - fn test_bitand() { - for elm in BIT_TESTS { - 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_op!(a & b == c); - assert_op!(b & a == c); - } - } - - #[test] - fn test_bitor() { - for elm in BIT_TESTS { - 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_op!(a | b == c); - assert_op!(b | a == c); - } - } - - #[test] - fn test_bitxor() { - for elm in BIT_TESTS { - 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_op!(a ^ b == c); - assert_op!(b ^ a == c); - assert_op!(a ^ c == b); - assert_op!(c ^ a == b); - assert_op!(b ^ c == a); - assert_op!(c ^ b == a); - } - } - - #[test] - fn test_shl() { - fn check(s: &str, shift: usize, ans: &str) { - let opt_biguint = BigUint::from_str_radix(s, 16).ok(); - let bu = (opt_biguint.unwrap() << shift).to_str_radix(16); - assert_eq!(bu, 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: usize, ans: &str) { - let opt_biguint = BigUint::from_str_radix(s, 16).ok(); - let bu = (opt_biguint.unwrap() >> shift).to_str_radix(16); - assert_eq!(bu, 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"); - } - - const N1: BigDigit = -1i32 as BigDigit; - const N2: BigDigit = -2i32 as BigDigit; - - // `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*big_digit::BITS))); - check(BigUint::new(vec!(N1 )), (1 << (1*big_digit::BITS)) - 1); - check(BigUint::new(vec!( 0, 1 )), (1 << (1*big_digit::BITS))); - check(BigUint::new(vec!(N1, N1 >> 1)), i64::MAX); - - assert_eq!(i64::MIN.to_biguint(), None); - assert_eq!(BigUint::new(vec!(N1, N1 )).to_i64(), None); - assert_eq!(BigUint::new(vec!( 0, 0, 1)).to_i64(), None); - assert_eq!(BigUint::new(vec!(N1, N1, N1)).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*big_digit::BITS))); - check(BigUint::new(vec!(N1 )), (1 << (1*big_digit::BITS)) - 1); - check(BigUint::new(vec!( 0, 1)), (1 << (1*big_digit::BITS))); - check(BigUint::new(vec!(N1, N1)), u64::MAX); - - assert_eq!(BigUint::new(vec!( 0, 0, 1)).to_u64(), None); - assert_eq!(BigUint::new(vec!(N1, N1, N1)).to_u64(), None); - } - - #[test] - fn test_convert_f32() { - fn check(b1: &BigUint, f: f32) { - let b2 = BigUint::from_f32(f).unwrap(); - assert_eq!(b1, &b2); - assert_eq!(b1.to_f32().unwrap(), f); - } - - check(&BigUint::zero(), 0.0); - check(&BigUint::one(), 1.0); - check(&BigUint::from(u16::MAX), 2.0.powi(16) - 1.0); - check(&BigUint::from(1u64 << 32), 2.0.powi(32)); - check(&BigUint::from_slice(&[0, 0, 1]), 2.0.powi(64)); - check(&((BigUint::one() << 100) + (BigUint::one() << 123)), 2.0.powi(100) + 2.0.powi(123)); - check(&(BigUint::one() << 127), 2.0.powi(127)); - check(&(BigUint::from((1u64 << 24) - 1) << (128 - 24)), f32::MAX); - - // keeping all 24 digits with the bits at different offsets to the BigDigits - let x: u32 = 0b00000000101111011111011011011101; - let mut f = x as f32; - let mut b = BigUint::from(x); - for _ in 0..64 { - check(&b, f); - f *= 2.0; - b = b << 1; - } - - // this number when rounded to f64 then f32 isn't the same as when rounded straight to f32 - let n: u64 = 0b0000000000111111111111111111111111011111111111111111111111111111; - assert!((n as f64) as f32 != n as f32); - assert_eq!(BigUint::from(n).to_f32(), Some(n as f32)); - - // test rounding up with the bits at different offsets to the BigDigits - let mut f = ((1u64 << 25) - 1) as f32; - let mut b = BigUint::from(1u64 << 25); - for _ in 0..64 { - assert_eq!(b.to_f32(), Some(f)); - f *= 2.0; - b = b << 1; - } - - // rounding - assert_eq!(BigUint::from_f32(-1.0), None); - assert_eq!(BigUint::from_f32(-0.99999), Some(BigUint::zero())); - assert_eq!(BigUint::from_f32(-0.5), Some(BigUint::zero())); - assert_eq!(BigUint::from_f32(-0.0), Some(BigUint::zero())); - assert_eq!(BigUint::from_f32(f32::MIN_POSITIVE / 2.0), Some(BigUint::zero())); - assert_eq!(BigUint::from_f32(f32::MIN_POSITIVE), Some(BigUint::zero())); - assert_eq!(BigUint::from_f32(0.5), Some(BigUint::zero())); - assert_eq!(BigUint::from_f32(0.99999), Some(BigUint::zero())); - assert_eq!(BigUint::from_f32(f32::consts::E), Some(BigUint::from(2u32))); - assert_eq!(BigUint::from_f32(f32::consts::PI), Some(BigUint::from(3u32))); - - // special float values - assert_eq!(BigUint::from_f32(f32::NAN), None); - assert_eq!(BigUint::from_f32(f32::INFINITY), None); - assert_eq!(BigUint::from_f32(f32::NEG_INFINITY), None); - assert_eq!(BigUint::from_f32(f32::MIN), None); - - // largest BigUint that will round to a finite f32 value - let big_num = (BigUint::one() << 128) - BigUint::one() - (BigUint::one() << (128 - 25)); - assert_eq!(big_num.to_f32(), Some(f32::MAX)); - assert_eq!((big_num + BigUint::one()).to_f32(), None); - - assert_eq!(((BigUint::one() << 128) - BigUint::one()).to_f32(), None); - assert_eq!((BigUint::one() << 128).to_f32(), None); - } - - #[test] - fn test_convert_f64() { - fn check(b1: &BigUint, f: f64) { - let b2 = BigUint::from_f64(f).unwrap(); - assert_eq!(b1, &b2); - assert_eq!(b1.to_f64().unwrap(), f); - } - - check(&BigUint::zero(), 0.0); - check(&BigUint::one(), 1.0); - check(&BigUint::from(u32::MAX), 2.0.powi(32) - 1.0); - check(&BigUint::from(1u64 << 32), 2.0.powi(32)); - check(&BigUint::from_slice(&[0, 0, 1]), 2.0.powi(64)); - check(&((BigUint::one() << 100) + (BigUint::one() << 152)), 2.0.powi(100) + 2.0.powi(152)); - check(&(BigUint::one() << 1023), 2.0.powi(1023)); - check(&(BigUint::from((1u64 << 53) - 1) << (1024 - 53)), f64::MAX); - - // keeping all 53 digits with the bits at different offsets to the BigDigits - let x: u64 = 0b0000000000011110111110110111111101110111101111011111011011011101; - let mut f = x as f64; - let mut b = BigUint::from(x); - for _ in 0..128 { - check(&b, f); - f *= 2.0; - b = b << 1; - } - - // test rounding up with the bits at different offsets to the BigDigits - let mut f = ((1u64 << 54) - 1) as f64; - let mut b = BigUint::from(1u64 << 54); - for _ in 0..128 { - assert_eq!(b.to_f64(), Some(f)); - f *= 2.0; - b = b << 1; - } - - // rounding - assert_eq!(BigUint::from_f64(-1.0), None); - assert_eq!(BigUint::from_f64(-0.99999), Some(BigUint::zero())); - assert_eq!(BigUint::from_f64(-0.5), Some(BigUint::zero())); - assert_eq!(BigUint::from_f64(-0.0), Some(BigUint::zero())); - assert_eq!(BigUint::from_f64(f64::MIN_POSITIVE / 2.0), Some(BigUint::zero())); - assert_eq!(BigUint::from_f64(f64::MIN_POSITIVE), Some(BigUint::zero())); - assert_eq!(BigUint::from_f64(0.5), Some(BigUint::zero())); - assert_eq!(BigUint::from_f64(0.99999), Some(BigUint::zero())); - assert_eq!(BigUint::from_f64(f64::consts::E), Some(BigUint::from(2u32))); - assert_eq!(BigUint::from_f64(f64::consts::PI), Some(BigUint::from(3u32))); - - // special float values - assert_eq!(BigUint::from_f64(f64::NAN), None); - assert_eq!(BigUint::from_f64(f64::INFINITY), None); - assert_eq!(BigUint::from_f64(f64::NEG_INFINITY), None); - assert_eq!(BigUint::from_f64(f64::MIN), None); - - // largest BigUint that will round to a finite f64 value - let big_num = (BigUint::one() << 1024) - BigUint::one() - (BigUint::one() << (1024 - 54)); - assert_eq!(big_num.to_f64(), Some(f64::MAX)); - assert_eq!((big_num + BigUint::one()).to_f64(), None); - - assert_eq!(((BigInt::one() << 1024) - BigInt::one()).to_f64(), None); - assert_eq!((BigUint::one() << 1024).to_f64(), 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)))); - } - - #[test] - fn test_convert_from_uint() { - macro_rules! check { - ($ty:ident, $max:expr) => { - assert_eq!(BigUint::from($ty::zero()), BigUint::zero()); - assert_eq!(BigUint::from($ty::one()), BigUint::one()); - assert_eq!(BigUint::from($ty::MAX - $ty::one()), $max - BigUint::one()); - assert_eq!(BigUint::from($ty::MAX), $max); - } - } - - check!(u8, BigUint::from_slice(&[u8::MAX as BigDigit])); - check!(u16, BigUint::from_slice(&[u16::MAX as BigDigit])); - check!(u32, BigUint::from_slice(&[u32::MAX])); - check!(u64, BigUint::from_slice(&[u32::MAX, u32::MAX])); - check!(usize, BigUint::from(usize::MAX as u64)); - } - - const SUM_TRIPLES: &'static [(&'static [BigDigit], - &'static [BigDigit], - &'static [BigDigit])] = &[ - (&[], &[], &[]), - (&[], &[ 1], &[ 1]), - (&[ 1], &[ 1], &[ 2]), - (&[ 1], &[ 1, 1], &[ 2, 1]), - (&[ 1], &[N1], &[ 0, 1]), - (&[ 1], &[N1, N1], &[ 0, 0, 1]), - (&[N1, N1], &[N1, N1], &[N2, N1, 1]), - (&[ 1, 1, 1], &[N1, N1], &[ 0, 1, 2]), - (&[ 2, 2, 1], &[N1, N2], &[ 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_op!(a + b == c); - assert_op!(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_op!(c - a == b); - assert_op!(c - b == a); - } - } - - #[test] - #[should_panic] - fn test_sub_fail_on_underflow() { - let (a, b) : (BigUint, BigUint) = (Zero::zero(), One::one()); - a - b; - } - - const M: u32 = ::std::u32::MAX; - const 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], &[N1], &[N1, N1, N1]), - (&[ 1, 2, 3], &[N1], &[N1, N2, N2, 2]), - (&[ 1, 2, 3, 4], &[N1], &[N1, N2, N2, N2, 3]), - (&[N1], &[N1], &[ 1, N2]), - (&[N1, N1], &[N1], &[ 1, N1, N2]), - (&[N1, N1, N1], &[N1], &[ 1, N1, N1, N2]), - (&[N1, N1, N1, N1], &[N1], &[ 1, N1, N1, N1, N2]), - (&[ M/2 + 1], &[ 2], &[ 0, 1]), - (&[0, M/2 + 1], &[ 2], &[ 0, 0, 1]), - (&[ 1, 2], &[ 1, 2, 3], &[1, 4, 7, 6]), - (&[N1, N1], &[N1, N1, N1], &[1, 0, N1, N2, N1]), - (&[N1, N1, N1], &[N1, N1, N1, N1], &[1, 0, 0, N1, N2, N1, N1]), - (&[ 0, 0, 1], &[ 1, 2, 3], &[0, 0, 1, 2, 3]), - (&[ 0, 0, 1], &[ 0, 0, 0, 1], &[0, 0, 0, 0, 0, 1]) - ]; - - const DIV_REM_QUADRUPLES: &'static [(&'static [BigDigit], - &'static [BigDigit], - &'static [BigDigit], - &'static [BigDigit])] - = &[ - (&[ 1], &[ 2], &[], &[1]), - (&[ 1, 1], &[ 2], &[ M/2+1], &[1]), - (&[ 1, 1, 1], &[ 2], &[ M/2+1, M/2+1], &[1]), - (&[ 0, 1], &[N1], &[1], &[1]), - (&[N1, N1], &[N2], &[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_op!(a * b == c); - assert_op!(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_op!(c / a == b); - assert_op!(c % a == Zero::zero()); - assert_eq!(c.div_rem(&a), (b.clone(), Zero::zero())); - } - if !b.is_zero() { - assert_op!(c / b == a); - assert_op!(c % b == Zero::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_op!(a / b == c); - assert_op!(a % b == d); - 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: usize, b: usize, c: usize) { - let big_a: BigUint = FromPrimitive::from_usize(a).unwrap(); - let big_b: BigUint = FromPrimitive::from_usize(b).unwrap(); - let big_c: BigUint = FromPrimitive::from_usize(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: usize, b: usize, c: usize) { - let big_a: BigUint = FromPrimitive::from_usize(a).unwrap(); - let big_b: BigUint = FromPrimitive::from_usize(b).unwrap(); - let big_c: BigUint = FromPrimitive::from_usize(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<(u32, String)>)> { - let bits = big_digit::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", repeat("0").take(bits - 1).collect::())), - (4, - format!("2{}1", repeat("0").take(bits / 2 - 1).collect::())), - (10, match bits { - 32 => "8589934593".to_string(), - 16 => "131073".to_string(), - _ => panic!() - }), - (16, - format!("2{}1", repeat("0").take(bits / 4 - 1).collect::())) - )), ( BigUint::from_slice(&[ 1, 2, 3 ]), vec!( - (2, - format!("11{}10{}1", - repeat("0").take(bits - 2).collect::(), - repeat("0").take(bits - 1).collect::())), - (4, - format!("3{}2{}1", - repeat("0").take(bits / 2 - 1).collect::(), - repeat("0").take(bits / 2 - 1).collect::())), - (8, match bits { - 32 => "6000000000100000000001".to_string(), - 16 => "140000400001".to_string(), - _ => panic!() - }), - (10, match bits { - 32 => "55340232229718589441".to_string(), - 16 => "12885032961".to_string(), - _ => panic!() - }), - (16, - format!("3{}2{}1", - repeat("0").take(bits / 4 - 1).collect::(), - repeat("0").take(bits / 4 - 1).collect::())) - )) ) - } - - #[test] - fn test_to_str_radix() { - let r = to_str_pairs(); - for num_pair in r.iter() { - let &(ref n, ref rs) = num_pair; - for str_pair in rs.iter() { - let &(ref radix, ref str) = str_pair; - assert_eq!(n.to_str_radix(*radix), *str); - } - } - } - - #[test] - fn test_from_str_radix() { - let r = to_str_pairs(); - for num_pair in r.iter() { - let &(ref n, ref rs) = num_pair; - for str_pair in rs.iter() { - let &(ref radix, ref str) = str_pair; - assert_eq!(n, - &BigUint::from_str_radix(str, *radix).unwrap()); - } - } - - let zed = BigUint::from_str_radix("Z", 10).ok(); - assert_eq!(zed, None); - let blank = BigUint::from_str_radix("_", 2).ok(); - assert_eq!(blank, None); - let plus_one = BigUint::from_str_radix("+1", 10).ok(); - assert_eq!(plus_one, Some(BigUint::from_slice(&[1]))); - let plus_plus_one = BigUint::from_str_radix("++1", 10).ok(); - assert_eq!(plus_plus_one, None); - let minus_one = BigUint::from_str_radix("-1", 10).ok(); - assert_eq!(minus_one, None); - } - - #[test] - fn test_all_str_radix() { - use std::ascii::AsciiExt; - - let n = BigUint::new((0..10).collect()); - for radix in 2..37 { - let s = n.to_str_radix(radix); - let x = BigUint::from_str_radix(&s, radix); - assert_eq!(x.unwrap(), n); - - let s = s.to_ascii_uppercase(); - let x = BigUint::from_str_radix(&s, radix); - assert_eq!(x.unwrap(), n); - } - } - - #[test] - fn test_lower_hex() { - let a = BigUint::parse_bytes(b"A", 16).unwrap(); - let hello = BigUint::parse_bytes("22405534230753963835153736737".as_bytes(), 10).unwrap(); - - assert_eq!(format!("{:x}", a), "a"); - assert_eq!(format!("{:x}", hello), "48656c6c6f20776f726c6421"); - assert_eq!(format!("{:♥>+#8x}", a), "♥♥♥♥+0xa"); - } - - #[test] - fn test_upper_hex() { - let a = BigUint::parse_bytes(b"A", 16).unwrap(); - let hello = BigUint::parse_bytes("22405534230753963835153736737".as_bytes(), 10).unwrap(); - - assert_eq!(format!("{:X}", a), "A"); - assert_eq!(format!("{:X}", hello), "48656C6C6F20776F726C6421"); - assert_eq!(format!("{:♥>+#8X}", a), "♥♥♥♥+0xA"); - } - - #[test] - fn test_binary() { - let a = BigUint::parse_bytes(b"A", 16).unwrap(); - let hello = BigUint::parse_bytes("224055342307539".as_bytes(), 10).unwrap(); - - assert_eq!(format!("{:b}", a), "1010"); - assert_eq!(format!("{:b}", hello), "110010111100011011110011000101101001100011010011"); - assert_eq!(format!("{:♥>+#8b}", a), "♥+0b1010"); - } - - #[test] - fn test_octal() { - let a = BigUint::parse_bytes(b"A", 16).unwrap(); - let hello = BigUint::parse_bytes("22405534230753963835153736737".as_bytes(), 10).unwrap(); - - assert_eq!(format!("{:o}", a), "12"); - assert_eq!(format!("{:o}", hello), "22062554330674403566756233062041"); - assert_eq!(format!("{:♥>+#8o}", a), "♥♥♥+0o12"); - } - - #[test] - fn test_display() { - let a = BigUint::parse_bytes(b"A", 16).unwrap(); - let hello = BigUint::parse_bytes("22405534230753963835153736737".as_bytes(), 10).unwrap(); - - assert_eq!(format!("{}", a), "10"); - assert_eq!(format!("{}", hello), "22405534230753963835153736737"); - assert_eq!(format!("{:♥>+#8}", a), "♥♥♥♥♥+10"); - } - - #[test] - fn test_factor() { - fn factor(n: usize) -> BigUint { - let mut f: BigUint = One::one(); - for i in 2..n + 1 { - // FIXME(#5992): assignment operator overloads - // f *= FromPrimitive::from_usize(i); - let bu: BigUint = FromPrimitive::from_usize(i).unwrap(); - f = f * bu; - } - return f; - } - - fn check(n: usize, s: &str) { - let n = factor(n); - let ans = match BigUint::from_str_radix(s, 10) { - Ok(x) => x, Err(_) => panic!() - }; - 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_usize(0).unwrap(); - assert_eq!(n.bits(), 0); - let n: BigUint = FromPrimitive::from_usize(1).unwrap(); - assert_eq!(n.bits(), 1); - let n: BigUint = FromPrimitive::from_usize(3).unwrap(); - assert_eq!(n.bits(), 2); - let n: BigUint = BigUint::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 = thread_rng(); - let _n: BigUint = rng.gen_biguint(137); - assert!(rng.gen_biguint(0).is_zero()); - } - - #[test] - fn test_rand_range() { - let mut rng = thread_rng(); - - for _ in 0..10 { - assert_eq!(rng.gen_bigint_range(&FromPrimitive::from_usize(236).unwrap(), - &FromPrimitive::from_usize(237).unwrap()), - FromPrimitive::from_usize(236).unwrap()); - } - - let l = FromPrimitive::from_usize(403469000 + 2352).unwrap(); - let u = FromPrimitive::from_usize(403469000 + 3513).unwrap(); - for _ in 0..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_panic] - fn test_zero_rand_range() { - thread_rng().gen_biguint_range(&FromPrimitive::from_usize(54).unwrap(), - &FromPrimitive::from_usize(54).unwrap()); - } - - #[test] - #[should_panic] - fn test_negative_rand_range() { - let mut rng = thread_rng(); - let l = FromPrimitive::from_usize(2352).unwrap(); - let u = FromPrimitive::from_usize(3513).unwrap(); - // Switching u and l should fail: - let _n: BigUint = rng.gen_biguint_range(&u, &l); - } - - #[test] - fn test_sub_sign() { - use super::sub_sign; - let a = BigInt::from_str_radix("265252859812191058636308480000000", 10).unwrap(); - let b = BigInt::from_str_radix("26525285981219105863630848000000", 10).unwrap(); - - assert_eq!(sub_sign(&a.data.data[..], &b.data.data[..]), &a - &b); - assert_eq!(sub_sign(&b.data.data[..], &a.data.data[..]), &b - &a); - } - - fn test_mul_divide_torture_count(count: usize) { - use rand::{SeedableRng, StdRng, Rng}; - - let bits_max = 1 << 12; - let seed: &[_] = &[1, 2, 3, 4]; - let mut rng: StdRng = SeedableRng::from_seed(seed); - - for _ in 0..count { - /* Test with numbers of random sizes: */ - let xbits = rng.gen_range(0, bits_max); - let ybits = rng.gen_range(0, bits_max); - - let x = rng.gen_biguint(xbits); - let y = rng.gen_biguint(ybits); - - if x.is_zero() || y.is_zero() { - continue; - } - - let prod = &x * &y; - assert_eq!(&prod / &x, y); - assert_eq!(&prod / &y, x); - } - } - - #[test] - fn test_mul_divide_torture() { - test_mul_divide_torture_count(1000); - } - - #[test] - #[ignore] - fn test_mul_divide_torture_long() { - test_mul_divide_torture_count(1000000); - } -} - -#[cfg(test)] -mod bigint_tests { - use Integer; - use super::{BigDigit, BigUint, ToBigUint}; - use super::{Sign, BigInt, RandBigInt, ToBigInt, big_digit}; - use super::Sign::{Minus, NoSign, Plus}; - - use std::cmp::Ordering::{Less, Equal, Greater}; - use std::{f32, f64}; - use std::{i8, i16, i32, i64, isize}; - use std::iter::repeat; - use std::{u8, u16, u32, u64, usize}; - use std::ops::{Neg}; - - use rand::thread_rng; - - use {Zero, One, Signed, ToPrimitive, FromPrimitive, Num}; - use Float; - - /// Assert that an op works for all val/ref combinations - macro_rules! assert_op { - ($left:ident $op:tt $right:ident == $expected:expr) => { - assert_eq!((&$left) $op (&$right), $expected); - assert_eq!((&$left) $op $right.clone(), $expected); - assert_eq!($left.clone() $op (&$right), $expected); - assert_eq!($left.clone() $op $right.clone(), $expected); - }; - } - - #[test] - fn test_from_biguint() { - fn check(inp_s: Sign, inp_n: usize, ans_s: Sign, ans_n: usize) { - let inp = BigInt::from_biguint(inp_s, FromPrimitive::from_usize(inp_n).unwrap()); - let ans = BigInt { sign: ans_s, data: FromPrimitive::from_usize(ans_n).unwrap()}; - assert_eq!(inp, ans); - } - check(Plus, 1, Plus, 1); - check(Plus, 0, NoSign, 0); - check(Minus, 1, Minus, 1); - check(NoSign, 1, NoSign, 0); - } - - #[test] - fn test_from_bytes_be() { - fn check(s: &str, result: &str) { - assert_eq!(BigInt::from_bytes_be(Plus, s.as_bytes()), - BigInt::parse_bytes(result.as_bytes(), 10).unwrap()); - } - check("A", "65"); - check("AA", "16705"); - check("AB", "16706"); - check("Hello world!", "22405534230753963835153736737"); - assert_eq!(BigInt::from_bytes_be(Plus, &[]), Zero::zero()); - assert_eq!(BigInt::from_bytes_be(Minus, &[]), Zero::zero()); - } - - #[test] - fn test_to_bytes_be() { - fn check(s: &str, result: &str) { - let b = BigInt::parse_bytes(result.as_bytes(), 10).unwrap(); - let (sign, v) = b.to_bytes_be(); - assert_eq!((Plus, s.as_bytes()), (sign, &*v)); - } - check("A", "65"); - check("AA", "16705"); - check("AB", "16706"); - check("Hello world!", "22405534230753963835153736737"); - let b: BigInt = Zero::zero(); - assert_eq!(b.to_bytes_be(), (NoSign, vec![0])); - - // Test with leading/trailing zero bytes and a full BigDigit of value 0 - let b = BigInt::from_str_radix("00010000000000000200", 16).unwrap(); - assert_eq!(b.to_bytes_be(), (Plus, vec![1, 0, 0, 0, 0, 0, 0, 2, 0])); - } - - #[test] - fn test_from_bytes_le() { - fn check(s: &str, result: &str) { - assert_eq!(BigInt::from_bytes_le(Plus, s.as_bytes()), - BigInt::parse_bytes(result.as_bytes(), 10).unwrap()); - } - check("A", "65"); - check("AA", "16705"); - check("BA", "16706"); - check("!dlrow olleH", "22405534230753963835153736737"); - assert_eq!(BigInt::from_bytes_le(Plus, &[]), Zero::zero()); - assert_eq!(BigInt::from_bytes_le(Minus, &[]), Zero::zero()); - } - - #[test] - fn test_to_bytes_le() { - fn check(s: &str, result: &str) { - let b = BigInt::parse_bytes(result.as_bytes(), 10).unwrap(); - let (sign, v) = b.to_bytes_le(); - assert_eq!((Plus, s.as_bytes()), (sign, &*v)); - } - check("A", "65"); - check("AA", "16705"); - check("BA", "16706"); - check("!dlrow olleH", "22405534230753963835153736737"); - let b: BigInt = Zero::zero(); - assert_eq!(b.to_bytes_le(), (NoSign, vec![0])); - - // Test with leading/trailing zero bytes and a full BigDigit of value 0 - let b = BigInt::from_str_radix("00010000000000000200", 16).unwrap(); - assert_eq!(b.to_bytes_le(), (Plus, vec![0, 2, 0, 0, 0, 0, 0, 0, 1])); - } - - #[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[i..].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(NoSign, vec!()); - let b = BigInt::new(NoSign, 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<<(big_digit::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_f32() { - fn check(b1: &BigInt, f: f32) { - let b2 = BigInt::from_f32(f).unwrap(); - assert_eq!(b1, &b2); - assert_eq!(b1.to_f32().unwrap(), f); - let neg_b1 = -b1; - let neg_b2 = BigInt::from_f32(-f).unwrap(); - assert_eq!(neg_b1, neg_b2); - assert_eq!(neg_b1.to_f32().unwrap(), -f); - } - - check(&BigInt::zero(), 0.0); - check(&BigInt::one(), 1.0); - check(&BigInt::from(u16::MAX), 2.0.powi(16) - 1.0); - check(&BigInt::from(1u64 << 32), 2.0.powi(32)); - check(&BigInt::from_slice(Plus, &[0, 0, 1]), 2.0.powi(64)); - check(&((BigInt::one() << 100) + (BigInt::one() << 123)), 2.0.powi(100) + 2.0.powi(123)); - check(&(BigInt::one() << 127), 2.0.powi(127)); - check(&(BigInt::from((1u64 << 24) - 1) << (128 - 24)), f32::MAX); - - // keeping all 24 digits with the bits at different offsets to the BigDigits - let x: u32 = 0b00000000101111011111011011011101; - let mut f = x as f32; - let mut b = BigInt::from(x); - for _ in 0..64 { - check(&b, f); - f *= 2.0; - b = b << 1; - } - - // this number when rounded to f64 then f32 isn't the same as when rounded straight to f32 - let mut n: i64 = 0b0000000000111111111111111111111111011111111111111111111111111111; - assert!((n as f64) as f32 != n as f32); - assert_eq!(BigInt::from(n).to_f32(), Some(n as f32)); - n = -n; - assert!((n as f64) as f32 != n as f32); - assert_eq!(BigInt::from(n).to_f32(), Some(n as f32)); - - // test rounding up with the bits at different offsets to the BigDigits - let mut f = ((1u64 << 25) - 1) as f32; - let mut b = BigInt::from(1u64 << 25); - for _ in 0..64 { - assert_eq!(b.to_f32(), Some(f)); - f *= 2.0; - b = b << 1; - } - - // rounding - assert_eq!(BigInt::from_f32(-f32::consts::PI), Some(BigInt::from(-3i32))); - assert_eq!(BigInt::from_f32(-f32::consts::E), Some(BigInt::from(-2i32))); - assert_eq!(BigInt::from_f32(-0.99999), Some(BigInt::zero())); - assert_eq!(BigInt::from_f32(-0.5), Some(BigInt::zero())); - assert_eq!(BigInt::from_f32(-0.0), Some(BigInt::zero())); - assert_eq!(BigInt::from_f32(f32::MIN_POSITIVE / 2.0), Some(BigInt::zero())); - assert_eq!(BigInt::from_f32(f32::MIN_POSITIVE), Some(BigInt::zero())); - assert_eq!(BigInt::from_f32(0.5), Some(BigInt::zero())); - assert_eq!(BigInt::from_f32(0.99999), Some(BigInt::zero())); - assert_eq!(BigInt::from_f32(f32::consts::E), Some(BigInt::from(2u32))); - assert_eq!(BigInt::from_f32(f32::consts::PI), Some(BigInt::from(3u32))); - - // special float values - assert_eq!(BigInt::from_f32(f32::NAN), None); - assert_eq!(BigInt::from_f32(f32::INFINITY), None); - assert_eq!(BigInt::from_f32(f32::NEG_INFINITY), None); - - // largest BigInt that will round to a finite f32 value - let big_num = (BigInt::one() << 128) - BigInt::one() - (BigInt::one() << (128 - 25)); - assert_eq!(big_num.to_f32(), Some(f32::MAX)); - assert_eq!((&big_num + BigInt::one()).to_f32(), None); - assert_eq!((-&big_num).to_f32(), Some(f32::MIN)); - assert_eq!(((-&big_num) - BigInt::one()).to_f32(), None); - - assert_eq!(((BigInt::one() << 128) - BigInt::one()).to_f32(), None); - assert_eq!((BigInt::one() << 128).to_f32(), None); - assert_eq!((-((BigInt::one() << 128) - BigInt::one())).to_f32(), None); - assert_eq!((-(BigInt::one() << 128)).to_f32(), None); - } - - #[test] - fn test_convert_f64() { - fn check(b1: &BigInt, f: f64) { - let b2 = BigInt::from_f64(f).unwrap(); - assert_eq!(b1, &b2); - assert_eq!(b1.to_f64().unwrap(), f); - let neg_b1 = -b1; - let neg_b2 = BigInt::from_f64(-f).unwrap(); - assert_eq!(neg_b1, neg_b2); - assert_eq!(neg_b1.to_f64().unwrap(), -f); - } - - check(&BigInt::zero(), 0.0); - check(&BigInt::one(), 1.0); - check(&BigInt::from(u32::MAX), 2.0.powi(32) - 1.0); - check(&BigInt::from(1u64 << 32), 2.0.powi(32)); - check(&BigInt::from_slice(Plus, &[0, 0, 1]), 2.0.powi(64)); - check(&((BigInt::one() << 100) + (BigInt::one() << 152)), 2.0.powi(100) + 2.0.powi(152)); - check(&(BigInt::one() << 1023), 2.0.powi(1023)); - check(&(BigInt::from((1u64 << 53) - 1) << (1024 - 53)), f64::MAX); - - // keeping all 53 digits with the bits at different offsets to the BigDigits - let x: u64 = 0b0000000000011110111110110111111101110111101111011111011011011101; - let mut f = x as f64; - let mut b = BigInt::from(x); - for _ in 0..128 { - check(&b, f); - f *= 2.0; - b = b << 1; - } - - // test rounding up with the bits at different offsets to the BigDigits - let mut f = ((1u64 << 54) - 1) as f64; - let mut b = BigInt::from(1u64 << 54); - for _ in 0..128 { - assert_eq!(b.to_f64(), Some(f)); - f *= 2.0; - b = b << 1; - } - - // rounding - assert_eq!(BigInt::from_f64(-f64::consts::PI), Some(BigInt::from(-3i32))); - assert_eq!(BigInt::from_f64(-f64::consts::E), Some(BigInt::from(-2i32))); - assert_eq!(BigInt::from_f64(-0.99999), Some(BigInt::zero())); - assert_eq!(BigInt::from_f64(-0.5), Some(BigInt::zero())); - assert_eq!(BigInt::from_f64(-0.0), Some(BigInt::zero())); - assert_eq!(BigInt::from_f64(f64::MIN_POSITIVE / 2.0), Some(BigInt::zero())); - assert_eq!(BigInt::from_f64(f64::MIN_POSITIVE), Some(BigInt::zero())); - assert_eq!(BigInt::from_f64(0.5), Some(BigInt::zero())); - assert_eq!(BigInt::from_f64(0.99999), Some(BigInt::zero())); - assert_eq!(BigInt::from_f64(f64::consts::E), Some(BigInt::from(2u32))); - assert_eq!(BigInt::from_f64(f64::consts::PI), Some(BigInt::from(3u32))); - - // special float values - assert_eq!(BigInt::from_f64(f64::NAN), None); - assert_eq!(BigInt::from_f64(f64::INFINITY), None); - assert_eq!(BigInt::from_f64(f64::NEG_INFINITY), None); - - // largest BigInt that will round to a finite f64 value - let big_num = (BigInt::one() << 1024) - BigInt::one() - (BigInt::one() << (1024 - 54)); - assert_eq!(big_num.to_f64(), Some(f64::MAX)); - assert_eq!((&big_num + BigInt::one()).to_f64(), None); - assert_eq!((-&big_num).to_f64(), Some(f64::MIN)); - assert_eq!(((-&big_num) - BigInt::one()).to_f64(), None); - - assert_eq!(((BigInt::one() << 1024) - BigInt::one()).to_f64(), None); - assert_eq!((BigInt::one() << 1024).to_f64(), None); - assert_eq!((-((BigInt::one() << 1024) - BigInt::one())).to_f64(), None); - assert_eq!((-(BigInt::one() << 1024)).to_f64(), 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); - } - - #[test] - fn test_convert_from_uint() { - macro_rules! check { - ($ty:ident, $max:expr) => { - assert_eq!(BigInt::from($ty::zero()), BigInt::zero()); - assert_eq!(BigInt::from($ty::one()), BigInt::one()); - assert_eq!(BigInt::from($ty::MAX - $ty::one()), $max - BigInt::one()); - assert_eq!(BigInt::from($ty::MAX), $max); - } - } - - check!(u8, BigInt::from_slice(Plus, &[u8::MAX as BigDigit])); - check!(u16, BigInt::from_slice(Plus, &[u16::MAX as BigDigit])); - check!(u32, BigInt::from_slice(Plus, &[u32::MAX as BigDigit])); - check!(u64, BigInt::from_slice(Plus, &[u32::MAX as BigDigit, u32::MAX as BigDigit])); - check!(usize, BigInt::from(usize::MAX as u64)); - } - - #[test] - fn test_convert_from_int() { - macro_rules! check { - ($ty:ident, $min:expr, $max:expr) => { - assert_eq!(BigInt::from($ty::MIN), $min); - assert_eq!(BigInt::from($ty::MIN + $ty::one()), $min + BigInt::one()); - assert_eq!(BigInt::from(-$ty::one()), -BigInt::one()); - assert_eq!(BigInt::from($ty::zero()), BigInt::zero()); - assert_eq!(BigInt::from($ty::one()), BigInt::one()); - assert_eq!(BigInt::from($ty::MAX - $ty::one()), $max - BigInt::one()); - assert_eq!(BigInt::from($ty::MAX), $max); - } - } - - check!(i8, BigInt::from_slice(Minus, &[1 << 7]), - BigInt::from_slice(Plus, &[i8::MAX as BigDigit])); - check!(i16, BigInt::from_slice(Minus, &[1 << 15]), - BigInt::from_slice(Plus, &[i16::MAX as BigDigit])); - check!(i32, BigInt::from_slice(Minus, &[1 << 31]), - BigInt::from_slice(Plus, &[i32::MAX as BigDigit])); - check!(i64, BigInt::from_slice(Minus, &[0, 1 << 31]), - BigInt::from_slice(Plus, &[u32::MAX as BigDigit, i32::MAX as BigDigit])); - check!(isize, BigInt::from(isize::MIN as i64), - BigInt::from(isize::MAX as i64)); - } - - #[test] - fn test_convert_from_biguint() { - assert_eq!(BigInt::from(BigUint::zero()), BigInt::zero()); - assert_eq!(BigInt::from(BigUint::one()), BigInt::one()); - assert_eq!(BigInt::from(BigUint::from_slice(&[1, 2, 3])), BigInt::from_slice(Plus, &[1, 2, 3])); - } - - const N1: BigDigit = -1i32 as BigDigit; - const N2: BigDigit = -2i32 as BigDigit; - - const SUM_TRIPLES: &'static [(&'static [BigDigit], - &'static [BigDigit], - &'static [BigDigit])] = &[ - (&[], &[], &[]), - (&[], &[ 1], &[ 1]), - (&[ 1], &[ 1], &[ 2]), - (&[ 1], &[ 1, 1], &[ 2, 1]), - (&[ 1], &[N1], &[ 0, 1]), - (&[ 1], &[N1, N1], &[ 0, 0, 1]), - (&[N1, N1], &[N1, N1], &[N2, N1, 1]), - (&[ 1, 1, 1], &[N1, N1], &[ 0, 1, 2]), - (&[ 2, 2, 1], &[N1, N2], &[ 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); - let (na, nb, nc) = (-&a, -&b, -&c); - - assert_op!(a + b == c); - assert_op!(b + a == c); - assert_op!(c + na == b); - assert_op!(c + nb == a); - assert_op!(a + nc == nb); - assert_op!(b + nc == na); - assert_op!(na + nb == nc); - assert_op!(a + na == 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); - let (na, nb, nc) = (-&a, -&b, -&c); - - assert_op!(c - a == b); - assert_op!(c - b == a); - assert_op!(nb - a == nc); - assert_op!(na - b == nc); - assert_op!(b - na == c); - assert_op!(a - nb == c); - assert_op!(nc - na == nb); - assert_op!(a - a == Zero::zero()); - } - } - - const M: u32 = ::std::u32::MAX; - 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], &[N1], &[N1, N1, N1]), - (&[ 1, 2, 3], &[N1], &[N1, N2, N2, 2]), - (&[ 1, 2, 3, 4], &[N1], &[N1, N2, N2, N2, 3]), - (&[N1], &[N1], &[ 1, N2]), - (&[N1, N1], &[N1], &[ 1, N1, N2]), - (&[N1, N1, N1], &[N1], &[ 1, N1, N1, N2]), - (&[N1, N1, N1, N1], &[N1], &[ 1, N1, N1, N1, N2]), - (&[ M/2 + 1], &[ 2], &[ 0, 1]), - (&[0, M/2 + 1], &[ 2], &[ 0, 0, 1]), - (&[ 1, 2], &[ 1, 2, 3], &[1, 4, 7, 6]), - (&[N1, N1], &[N1, N1, N1], &[1, 0, N1, N2, N1]), - (&[N1, N1, N1], &[N1, N1, N1, N1], &[1, 0, 0, N1, N2, N1, N1]), - (&[ 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], &[ M/2+1], &[1]), - (&[ 1, 1, 1], &[ 2], &[ M/2+1, M/2+1], &[1]), - (&[ 0, 1], &[N1], &[1], &[1]), - (&[N1, N1], &[N2], &[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); - let (na, nb, nc) = (-&a, -&b, -&c); - - assert_op!(a * b == c); - assert_op!(b * a == c); - assert_op!(na * nb == c); - - assert_op!(na * b == nc); - assert_op!(nb * a == nc); - } - - 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 { - let one: BigInt = One::one(); - check_sub(a, b, d, m); - check_sub(a, &b.neg(), &(d.neg() - &one), &(m - b)); - check_sub(&a.neg(), b, &(d.neg() - &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); - - let (a, b, ans_q, ans_r) = (a.clone(), b.clone(), ans_q.clone(), ans_r.clone()); - assert_op!(a / b == ans_q); - assert_op!(a % b == 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: isize, b: isize, c: isize) { - let big_a: BigInt = FromPrimitive::from_isize(a).unwrap(); - let big_b: BigInt = FromPrimitive::from_isize(b).unwrap(); - let big_c: BigInt = FromPrimitive::from_isize(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: isize, b: isize, c: isize) { - let big_a: BigInt = FromPrimitive::from_isize(a).unwrap(); - let big_b: BigInt = FromPrimitive::from_isize(b).unwrap(); - let big_c: BigInt = FromPrimitive::from_isize(c).unwrap(); - - assert_eq!(big_a.lcm(&big_b), big_c); - } - - check(1, 0, 0); - check(0, 1, 0); - check(1, 1, 1); - check(-1, 1, 1); - check(1, -1, 1); - check(-1, -1, 1); - check(8, 9, 72); - check(11, 5, 55); - } - - #[test] - fn test_abs_sub() { - let zero: BigInt = Zero::zero(); - let one: BigInt = One::one(); - assert_eq!((-&one).abs_sub(&one), zero); - let one: BigInt = One::one(); - let zero: BigInt = Zero::zero(); - assert_eq!(one.abs_sub(&one), zero); - let one: BigInt = One::one(); - let zero: BigInt = Zero::zero(); - assert_eq!(one.abs_sub(&zero), one); - let one: BigInt = One::one(); - let two: BigInt = FromPrimitive::from_isize(2).unwrap(); - assert_eq!(one.abs_sub(&-&one), two); - } - - #[test] - fn test_from_str_radix() { - fn check(s: &str, ans: Option) { - let ans = ans.map(|n| { - let x: BigInt = FromPrimitive::from_isize(n).unwrap(); - x - }); - assert_eq!(BigInt::from_str_radix(s, 10).ok(), ans); - } - check("10", Some(10)); - check("1", Some(1)); - check("0", Some(0)); - check("-1", Some(-1)); - check("-10", Some(-10)); - check("+10", Some(10)); - check("--7", None); - check("++5", None); - check("+-9", None); - check("-+3", None); - 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 = - format!("1{}", repeat("0").take(36).collect::()).parse().unwrap(); - let _y = x.to_string(); - } - - #[test] - fn test_lower_hex() { - let a = BigInt::parse_bytes(b"A", 16).unwrap(); - let hello = BigInt::parse_bytes("-22405534230753963835153736737".as_bytes(), 10).unwrap(); - - assert_eq!(format!("{:x}", a), "a"); - assert_eq!(format!("{:x}", hello), "-48656c6c6f20776f726c6421"); - assert_eq!(format!("{:♥>+#8x}", a), "♥♥♥♥+0xa"); - } - - #[test] - fn test_upper_hex() { - let a = BigInt::parse_bytes(b"A", 16).unwrap(); - let hello = BigInt::parse_bytes("-22405534230753963835153736737".as_bytes(), 10).unwrap(); - - assert_eq!(format!("{:X}", a), "A"); - assert_eq!(format!("{:X}", hello), "-48656C6C6F20776F726C6421"); - assert_eq!(format!("{:♥>+#8X}", a), "♥♥♥♥+0xA"); - } - - #[test] - fn test_binary() { - let a = BigInt::parse_bytes(b"A", 16).unwrap(); - let hello = BigInt::parse_bytes("-224055342307539".as_bytes(), 10).unwrap(); - - assert_eq!(format!("{:b}", a), "1010"); - assert_eq!(format!("{:b}", hello), "-110010111100011011110011000101101001100011010011"); - assert_eq!(format!("{:♥>+#8b}", a), "♥+0b1010"); - } - - #[test] - fn test_octal() { - let a = BigInt::parse_bytes(b"A", 16).unwrap(); - let hello = BigInt::parse_bytes("-22405534230753963835153736737".as_bytes(), 10).unwrap(); - - assert_eq!(format!("{:o}", a), "12"); - assert_eq!(format!("{:o}", hello), "-22062554330674403566756233062041"); - assert_eq!(format!("{:♥>+#8o}", a), "♥♥♥+0o12"); - } - - #[test] - fn test_display() { - let a = BigInt::parse_bytes(b"A", 16).unwrap(); - let hello = BigInt::parse_bytes("-22405534230753963835153736737".as_bytes(), 10).unwrap(); - - assert_eq!(format!("{}", a), "10"); - assert_eq!(format!("{}", hello), "-22405534230753963835153736737"); - assert_eq!(format!("{:♥>+#8}", a), "♥♥♥♥♥+10"); - } - - #[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 = thread_rng(); - let _n: BigInt = rng.gen_bigint(137); - assert!(rng.gen_bigint(0).is_zero()); - } - - #[test] - fn test_rand_range() { - let mut rng = thread_rng(); - - for _ in 0..10 { - assert_eq!(rng.gen_bigint_range(&FromPrimitive::from_usize(236).unwrap(), - &FromPrimitive::from_usize(237).unwrap()), - FromPrimitive::from_usize(236).unwrap()); - } - - fn check(l: BigInt, u: BigInt) { - let mut rng = thread_rng(); - for _ in 0..1000 { - let n: BigInt = rng.gen_bigint_range(&l, &u); - assert!(n >= l); - assert!(n < u); - } - } - let l: BigInt = FromPrimitive::from_usize(403469000 + 2352).unwrap(); - let u: BigInt = FromPrimitive::from_usize(403469000 + 3513).unwrap(); - check( l.clone(), u.clone()); - check(-l.clone(), u.clone()); - check(-u.clone(), -l.clone()); - } - - #[test] - #[should_panic] - fn test_zero_rand_range() { - thread_rng().gen_bigint_range(&FromPrimitive::from_isize(54).unwrap(), - &FromPrimitive::from_isize(54).unwrap()); - } - - #[test] - #[should_panic] - fn test_negative_rand_range() { - let mut rng = thread_rng(); - let l = FromPrimitive::from_usize(2352).unwrap(); - let u = FromPrimitive::from_usize(3513).unwrap(); - // Switching u and l should fail: - let _n: BigInt = rng.gen_bigint_range(&u, &l); - } -} diff --git a/src/iter.rs b/src/iter.rs deleted file mode 100644 index 33bc267..0000000 --- a/src/iter.rs +++ /dev/null @@ -1,372 +0,0 @@ -// Copyright 2013-2014 The Rust Project Developers. See the COPYRIGHT -// file at the top-level directory of this distribution and at -// http://rust-lang.org/COPYRIGHT. -// -// Licensed under the Apache License, Version 2.0 or the MIT license -// , at your -// option. This file may not be copied, modified, or distributed -// except according to those terms. - -//! External iterators for generic mathematics - -use {Integer, Zero, One, CheckedAdd, ToPrimitive}; -use std::ops::{Add, Sub}; - -/// An iterator over the range [start, stop) -#[derive(Clone)] -pub struct Range { - state: A, - stop: A, - one: A -} - -/// Returns an iterator over the given range [start, stop) (that is, starting -/// at start (inclusive), and ending at stop (exclusive)). -/// -/// # Example -/// -/// ```rust -/// use num::iter; -/// -/// let array = [0, 1, 2, 3, 4]; -/// -/// for i in iter::range(0, 5) { -/// println!("{}", i); -/// assert_eq!(i, array[i]); -/// } -/// ``` -#[inline] -pub fn range(start: A, stop: A) -> Range - where A: Add + PartialOrd + Clone + One -{ - Range{state: start, stop: stop, one: One::one()} -} - -// FIXME: rust-lang/rust#10414: Unfortunate type bound -impl Iterator for Range - where A: Add + PartialOrd + Clone + ToPrimitive -{ - type Item = A; - - #[inline] - fn next(&mut self) -> Option { - if self.state < self.stop { - let result = self.state.clone(); - self.state = self.state.clone() + self.one.clone(); - Some(result) - } else { - None - } - } - - #[inline] - fn size_hint(&self) -> (usize, Option) { - // This first checks if the elements are representable as i64. If they aren't, try u64 (to - // handle cases like range(huge, huger)). We don't use usize/int because the difference of - // the i64/u64 might lie within their range. - let bound = match self.state.to_i64() { - Some(a) => { - let sz = self.stop.to_i64().map(|b| b.checked_sub(a)); - match sz { - Some(Some(bound)) => bound.to_usize(), - _ => None, - } - }, - None => match self.state.to_u64() { - Some(a) => { - let sz = self.stop.to_u64().map(|b| b.checked_sub(a)); - match sz { - Some(Some(bound)) => bound.to_usize(), - _ => None - } - }, - None => None - } - }; - - match bound { - Some(b) => (b, Some(b)), - // Standard fallback for unbounded/unrepresentable bounds - None => (0, None) - } - } -} - -/// `Integer` is required to ensure the range will be the same regardless of -/// the direction it is consumed. -impl DoubleEndedIterator for Range - where A: Integer + Clone + ToPrimitive -{ - #[inline] - fn next_back(&mut self) -> Option { - if self.stop > self.state { - self.stop = self.stop.clone() - self.one.clone(); - Some(self.stop.clone()) - } else { - None - } - } -} - -/// An iterator over the range [start, stop] -#[derive(Clone)] -pub struct RangeInclusive { - range: Range, - done: bool, -} - -/// Return an iterator over the range [start, stop] -#[inline] -pub fn range_inclusive(start: A, stop: A) -> RangeInclusive - where A: Add + PartialOrd + Clone + One -{ - RangeInclusive{range: range(start, stop), done: false} -} - -impl Iterator for RangeInclusive - where A: Add + PartialOrd + Clone + ToPrimitive -{ - type Item = A; - - #[inline] - fn next(&mut self) -> Option { - match self.range.next() { - Some(x) => Some(x), - None => { - if !self.done && self.range.state == self.range.stop { - self.done = true; - Some(self.range.stop.clone()) - } else { - None - } - } - } - } - - #[inline] - fn size_hint(&self) -> (usize, Option) { - let (lo, hi) = self.range.size_hint(); - if self.done { - (lo, hi) - } else { - let lo = lo.saturating_add(1); - let hi = match hi { - Some(x) => x.checked_add(1), - None => None - }; - (lo, hi) - } - } -} - -impl DoubleEndedIterator for RangeInclusive - where A: Sub + Integer + Clone + ToPrimitive -{ - #[inline] - fn next_back(&mut self) -> Option { - if self.range.stop > self.range.state { - let result = self.range.stop.clone(); - self.range.stop = self.range.stop.clone() - self.range.one.clone(); - Some(result) - } else if !self.done && self.range.state == self.range.stop { - self.done = true; - Some(self.range.stop.clone()) - } else { - None - } - } -} - -/// An iterator over the range [start, stop) by `step`. It handles overflow by stopping. -#[derive(Clone)] -pub struct RangeStep { - state: A, - stop: A, - step: A, - rev: bool, -} - -/// Return an iterator over the range [start, stop) by `step`. It handles overflow by stopping. -#[inline] -pub fn range_step(start: A, stop: A, step: A) -> RangeStep - where A: CheckedAdd + PartialOrd + Clone + Zero -{ - let rev = step < Zero::zero(); - RangeStep{state: start, stop: stop, step: step, rev: rev} -} - -impl Iterator for RangeStep - where A: CheckedAdd + PartialOrd + Clone -{ - type Item = A; - - #[inline] - fn next(&mut self) -> Option { - if (self.rev && self.state > self.stop) || (!self.rev && self.state < self.stop) { - let result = self.state.clone(); - match self.state.checked_add(&self.step) { - Some(x) => self.state = x, - None => self.state = self.stop.clone() - } - Some(result) - } else { - None - } - } -} - -/// An iterator over the range [start, stop] by `step`. It handles overflow by stopping. -#[derive(Clone)] -pub struct RangeStepInclusive { - state: A, - stop: A, - step: A, - rev: bool, - done: bool, -} - -/// Return an iterator over the range [start, stop] by `step`. It handles overflow by stopping. -#[inline] -pub fn range_step_inclusive(start: A, stop: A, step: A) -> RangeStepInclusive - where A: CheckedAdd + PartialOrd + Clone + Zero -{ - let rev = step < Zero::zero(); - RangeStepInclusive{state: start, stop: stop, step: step, rev: rev, done: false} -} - -impl Iterator for RangeStepInclusive - where A: CheckedAdd + PartialOrd + Clone + PartialEq -{ - type Item = A; - - #[inline] - fn next(&mut self) -> Option { - if !self.done && ((self.rev && self.state >= self.stop) || - (!self.rev && self.state <= self.stop)) { - let result = self.state.clone(); - match self.state.checked_add(&self.step) { - Some(x) => self.state = x, - None => self.done = true - } - Some(result) - } else { - None - } - } -} - -#[cfg(test)] -mod tests { - use std::usize; - use std::ops::{Add, Mul}; - use std::cmp::Ordering; - use {One, ToPrimitive}; - - #[test] - fn test_range() { - /// A mock type to check Range when ToPrimitive returns None - struct Foo; - - impl ToPrimitive for Foo { - fn to_i64(&self) -> Option { None } - fn to_u64(&self) -> Option { None } - } - - impl Add for Foo { - type Output = Foo; - - fn add(self, _: Foo) -> Foo { - Foo - } - } - - impl PartialEq for Foo { - fn eq(&self, _: &Foo) -> bool { - true - } - } - - impl PartialOrd for Foo { - fn partial_cmp(&self, _: &Foo) -> Option { - None - } - } - - impl Clone for Foo { - fn clone(&self) -> Foo { - Foo - } - } - - impl Mul for Foo { - type Output = Foo; - - fn mul(self, _: Foo) -> Foo { - Foo - } - } - - impl One for Foo { - fn one() -> Foo { - Foo - } - } - - assert!(super::range(0, 5).collect::>() == vec![0, 1, 2, 3, 4]); - assert!(super::range(-10, -1).collect::>() == - vec![-10, -9, -8, -7, -6, -5, -4, -3, -2]); - assert!(super::range(0, 5).rev().collect::>() == vec![4, 3, 2, 1, 0]); - assert_eq!(super::range(200, -5).count(), 0); - assert_eq!(super::range(200, -5).rev().count(), 0); - assert_eq!(super::range(200, 200).count(), 0); - assert_eq!(super::range(200, 200).rev().count(), 0); - - assert_eq!(super::range(0, 100).size_hint(), (100, Some(100))); - // this test is only meaningful when sizeof usize < sizeof u64 - assert_eq!(super::range(usize::MAX - 1, usize::MAX).size_hint(), (1, Some(1))); - assert_eq!(super::range(-10, -1).size_hint(), (9, Some(9))); - } - - #[test] - fn test_range_inclusive() { - assert!(super::range_inclusive(0, 5).collect::>() == - vec![0, 1, 2, 3, 4, 5]); - assert!(super::range_inclusive(0, 5).rev().collect::>() == - vec![5, 4, 3, 2, 1, 0]); - assert_eq!(super::range_inclusive(200, -5).count(), 0); - assert_eq!(super::range_inclusive(200, -5).rev().count(), 0); - assert!(super::range_inclusive(200, 200).collect::>() == vec![200]); - assert!(super::range_inclusive(200, 200).rev().collect::>() == vec![200]); - } - - #[test] - fn test_range_step() { - assert!(super::range_step(0, 20, 5).collect::>() == - vec![0, 5, 10, 15]); - assert!(super::range_step(20, 0, -5).collect::>() == - vec![20, 15, 10, 5]); - assert!(super::range_step(20, 0, -6).collect::>() == - vec![20, 14, 8, 2]); - assert!(super::range_step(200u8, 255, 50).collect::>() == - vec![200u8, 250]); - assert!(super::range_step(200, -5, 1).collect::>() == vec![]); - assert!(super::range_step(200, 200, 1).collect::>() == vec![]); - } - - #[test] - fn test_range_step_inclusive() { - assert!(super::range_step_inclusive(0, 20, 5).collect::>() == - vec![0, 5, 10, 15, 20]); - assert!(super::range_step_inclusive(20, 0, -5).collect::>() == - vec![20, 15, 10, 5, 0]); - assert!(super::range_step_inclusive(20, 0, -6).collect::>() == - vec![20, 14, 8, 2]); - assert!(super::range_step_inclusive(200u8, 255, 50).collect::>() == - vec![200u8, 250]); - assert!(super::range_step_inclusive(200, -5, 1).collect::>() == - vec![]); - assert!(super::range_step_inclusive(200, 200, 1).collect::>() == - vec![200]); - } -}