diff --git a/Cargo.toml b/Cargo.toml index 37edb98..378484a 100644 --- a/Cargo.toml +++ b/Cargo.toml @@ -1,44 +1,52 @@ [package] - -name = "num" -version = "0.1.31" authors = ["The Rust Project Developers"] -license = "MIT/Apache-2.0" -homepage = "https://github.com/rust-num/num" -repository = "https://github.com/rust-num/num" +description = "A collection of numeric types and traits for Rust, including bigint,\ncomplex, rational, range iterators, generic integers, and more!\n" documentation = "http://rust-num.github.io/num" +homepage = "https://github.com/rust-num/num" keywords = ["mathematics", "numerics"] -description = """ -A collection of numeric types and traits for Rust, including bigint, -complex, rational, range iterators, generic integers, and more! -""" - -[dependencies] -rand = { version = "0.3.8", optional = true } -rustc-serialize = { version = "0.3.13", optional = true } -serde = { version = "^0.7.0", optional = true } - -[dependencies.num-traits] -path = "./traits" - -[dependencies.num-integer] -path = "./integer" - -[dev-dependencies] -# Some tests of non-rand functionality still use rand because the tests -# themselves are randomized. -rand = { version = "0.3.8" } - -[features] - -complex = [] -rational = [] -bigint = [] -default = ["bigint", "complex", "rand", "rational", "rustc-serialize"] +license = "MIT/Apache-2.0" +name = "num" +repository = "https://github.com/rust-num/num" +version = "0.1.31" [[bench]] name = "bigint" [[bench]] -name = "shootout-pidigits" harness = false +name = "shootout-pidigits" + +[dependencies] + +[dependencies.num-bigint] +optional = false +path = "bigint" + +[dependencies.num-integer] +path = "./integer" + +[dependencies.num-traits] +path = "./traits" + +[dependencies.rand] +optional = true +version = "0.3.8" + +[dependencies.rustc-serialize] +optional = true +version = "0.3.13" + +[dependencies.serde] +optional = true +version = "^0.7.0" + +[dev-dependencies] + +[dev-dependencies.rand] +version = "0.3.8" + +[features] +bigint = [] +complex = [] +default = ["bigint", "complex", "rand", "rational", "rustc-serialize"] +rational = [] diff --git a/bigint/Cargo.toml b/bigint/Cargo.toml new file mode 100644 index 0000000..729e5cc --- /dev/null +++ b/bigint/Cargo.toml @@ -0,0 +1,22 @@ +[package] +authors = ["Łukasz Jan Niemier "] +name = "num-bigint" +version = "0.1.0" + +[dependencies] + +[dependencies.num-integer] +optional = false +path = "../integer" + +[dependencies.num-traits] +optional = false +path = "../traits" + +[dependencies.rand] +optional = true +version = "0.3.14" + +[dependencies.serde] +optional = true +version = "0.7.0" diff --git a/bigint/src/lib.rs b/bigint/src/lib.rs new file mode 100644 index 0000000..7bb3cc5 --- /dev/null +++ b/bigint/src/lib.rs @@ -0,0 +1,5129 @@ +// 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() { +//! # } +//! ``` + +extern crate num_integer as integer; +extern crate num_traits as traits; + +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 integer::Integer; +use traits::{ToPrimitive, FromPrimitive, Float, 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 FromStrRadixErr = 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 FromStrRadixErr = 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()) + } + + + /// 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/integer/src/lib.rs b/integer/src/lib.rs index 94d5f82..6059133 100644 --- a/integer/src/lib.rs +++ b/integer/src/lib.rs @@ -14,11 +14,7 @@ extern crate num_traits as traits; use traits::{Num, Signed}; -pub trait Integer - : Sized - + Num - + PartialOrd + Ord + Eq -{ +pub trait Integer: Sized + Num + PartialOrd + Ord + Eq { /// Floored integer division. /// /// # Examples @@ -162,19 +158,37 @@ pub trait Integer } /// Simultaneous integer division and modulus -#[inline] pub fn div_rem(x: T, y: T) -> (T, T) { x.div_rem(&y) } +#[inline] +pub fn div_rem(x: T, y: T) -> (T, T) { + x.div_rem(&y) +} /// Floored integer division -#[inline] pub fn div_floor(x: T, y: T) -> T { x.div_floor(&y) } +#[inline] +pub fn div_floor(x: T, y: T) -> T { + x.div_floor(&y) +} /// Floored integer modulus -#[inline] pub fn mod_floor(x: T, y: T) -> T { x.mod_floor(&y) } +#[inline] +pub fn mod_floor(x: T, y: T) -> T { + x.mod_floor(&y) +} /// Simultaneous floored integer division and modulus -#[inline] pub fn div_mod_floor(x: T, y: T) -> (T, T) { x.div_mod_floor(&y) } +#[inline] +pub fn div_mod_floor(x: T, y: T) -> (T, T) { + x.div_mod_floor(&y) +} /// Calculates the Greatest Common Divisor (GCD) of the number and `other`. The /// result is always positive. -#[inline(always)] pub fn gcd(x: T, y: T) -> T { x.gcd(&y) } +#[inline(always)] +pub fn gcd(x: T, y: T) -> T { + x.gcd(&y) +} /// Calculates the Lowest Common Multiple (LCM) of the number and `other`. -#[inline(always)] pub fn lcm(x: T, y: T) -> T { x.lcm(&y) } +#[inline(always)] +pub fn lcm(x: T, y: T) -> T { + x.lcm(&y) +} macro_rules! impl_integer_for_isize { ($T:ty, $test_mod:ident) => ( @@ -470,11 +484,11 @@ macro_rules! impl_integer_for_isize { ) } -impl_integer_for_isize!(i8, test_integer_i8); -impl_integer_for_isize!(i16, test_integer_i16); -impl_integer_for_isize!(i32, test_integer_i32); -impl_integer_for_isize!(i64, test_integer_i64); -impl_integer_for_isize!(isize, test_integer_isize); +impl_integer_for_isize!(i8, test_integer_i8); +impl_integer_for_isize!(i16, test_integer_i16); +impl_integer_for_isize!(i32, test_integer_i32); +impl_integer_for_isize!(i64, test_integer_i64); +impl_integer_for_isize!(isize, test_integer_isize); macro_rules! impl_integer_for_usize { ($T:ty, $test_mod:ident) => ( @@ -641,8 +655,8 @@ macro_rules! impl_integer_for_usize { ) } -impl_integer_for_usize!(u8, test_integer_u8); -impl_integer_for_usize!(u16, test_integer_u16); -impl_integer_for_usize!(u32, test_integer_u32); -impl_integer_for_usize!(u64, test_integer_u64); +impl_integer_for_usize!(u8, test_integer_u8); +impl_integer_for_usize!(u16, test_integer_u16); +impl_integer_for_usize!(u32, test_integer_u32); +impl_integer_for_usize!(u64, test_integer_u64); impl_integer_for_usize!(usize, test_integer_usize); diff --git a/src/lib.rs b/src/lib.rs index 46e0adb..a44bb9b 100644 --- a/src/lib.rs +++ b/src/lib.rs @@ -59,6 +59,7 @@ extern crate num_traits; extern crate num_integer; +extern crate num_bigint; #[cfg(feature = "rustc-serialize")] extern crate rustc_serialize; @@ -91,7 +92,7 @@ pub use traits::{Num, Zero, One, Signed, Unsigned, Bounded, use std::ops::{Mul}; #[cfg(feature = "bigint")] -pub mod bigint; +pub mod bigint { pub use num_bigint::*; } pub mod complex; pub mod integer { pub use num_integer::*; } pub mod iter; diff --git a/traits/src/lib.rs b/traits/src/lib.rs index 9665094..c0dce24 100644 --- a/traits/src/lib.rs +++ b/traits/src/lib.rs @@ -34,16 +34,16 @@ pub trait Num: PartialEq + Zero + One + Add + Sub + Mul + Div + Rem { - type Error; + type FromStrRadixErr; /// Convert from a string and radix <= 36. - fn from_str_radix(str: &str, radix: u32) -> Result; + fn from_str_radix(str: &str, radix: u32) -> Result; } macro_rules! int_trait_impl { ($name:ident for $($t:ty)*) => ($( impl $name for $t { - type Error = ::std::num::ParseIntError; + type FromStrRadixErr = ::std::num::ParseIntError; fn from_str_radix(s: &str, radix: u32) -> Result { @@ -65,10 +65,10 @@ pub struct ParseFloatError { macro_rules! float_trait_impl { ($name:ident for $($t:ty)*) => ($( impl $name for $t { - type Error = ParseFloatError; + type FromStrRadixErr = ParseFloatError; fn from_str_radix(src: &str, radix: u32) - -> Result + -> Result { use self::FloatErrorKind::*; use self::ParseFloatError as PFE;