Extract bigint

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!
-"""
+license = "MIT/Apache-2.0"
+name = "num"
+repository = "https://github.com/rust-num/num"
+version = "0.1.31"
+
+[[bench]]
+name = "bigint"
+
+[[bench]]
+harness = false
+name = "shootout-pidigits"
 
 [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-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]
-# Some tests of non-rand functionality still use rand because the tests
-# themselves are randomized.
-rand = { version = "0.3.8" }
 
-[features]
+[dev-dependencies.rand]
+version = "0.3.8"
 
-complex = []
-rational = []
+[features]
 bigint = []
+complex = []
 default = ["bigint", "complex", "rand", "rational", "rustc-serialize"]
-
-[[bench]]
-name = "bigint"
-
-[[bench]]
-name = "shootout-pidigits"
-harness = false
+rational = []

bigint/Cargo.toml

@@ -0,0 +1,22 @@
+[package]
+authors = ["Łukasz Jan Niemier <[email protected]>"]
+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"

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 <LICENSE-APACHE or
+// http://www.apache.org/licenses/LICENSE-2.0> or the MIT license
+// <LICENSE-MIT or http://opensource.org/licenses/MIT>, at your
+// option. This file may not be copied, modified, or distributed
+// except according to those terms.
+
+//! A Big integer (signed version: `BigInt`, unsigned version: `BigUint`).
+//!
+//! A `BigUint` is represented as 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<BigDigit>,
+}
+
+impl PartialEq for BigUint {
+    #[inline]
+    fn eq(&self, other: &BigUint) -> bool {
+        match self.cmp(other) {
+            Equal => true,
+            _ => false,
+        }
+    }
+}
+impl Eq for BigUint {}
+
+impl PartialOrd for BigUint {
+    #[inline]
+    fn partial_cmp(&self, other: &BigUint) -> Option<Ordering> {
+        Some(self.cmp(other))
+    }
+}
+
+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, ParseBigIntError> {
+        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<BigUint, ParseBigIntError> {
+        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<BigUint>, 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<usize> for BigUint {
+    type Output = BigUint;
+
+    #[inline]
+    fn shl(self, rhs: usize) -> BigUint {
+        biguint_shl(Cow::Owned(self), rhs)
+    }
+}
+
+impl<'a> Shl<usize> 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<BigUint>, 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<usize> for BigUint {
+    type Output = BigUint;
+
+    #[inline]
+    fn shr(self, rhs: usize) -> BigUint {
+        biguint_shr(Cow::Owned(self), rhs)
+    }
+}
+
+impl<'a> Shr<usize> 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<BigUint> {
+        return Some(self.add(v));
+    }
+}
+
+impl CheckedSub for BigUint {
+    #[inline]
+    fn checked_sub(&self, v: &BigUint) -> Option<BigUint> {
+        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<BigUint> {
+        return Some(self.mul(v));
+    }
+}
+
+impl CheckedDiv for BigUint {
+    #[inline]
+    fn checked_div(&self, v: &BigUint) -> Option<BigUint> {
+        if v.is_zero() {
+            return None;
+        }
+        return Some(self.div(v));
+    }
+}
+
+impl Integer for BigUint {
+    #[inline]
+    fn div_rem(&self, other: &BigUint) -> (BigUint, BigUint) {
+        self.div_mod_floor(other)
+    }
+
+    #[inline]
+    fn div_floor(&self, other: &BigUint) -> BigUint {
+        let (d, _) = self.div_mod_floor(other);
+        return d;
+    }
+
+    #[inline]
+    fn mod_floor(&self, other: &BigUint) -> BigUint {
+        let (_, m) = self.div_mod_floor(other);
+        return m;
+    }
+
+    fn div_mod_floor(&self, other: &BigUint) -> (BigUint, BigUint) {
+        if other.is_zero() {
+            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<i64> {
+        self.to_u64().and_then(|n| {
+            // If top bit of u64 is set, it's too large to convert to i64.
+            if n >> 63 == 0 {
+                Some(n as i64)
+            } else {
+                None
+            }
+        })
+    }
+
+    // `DoubleBigDigit` size dependent
+    #[inline]
+    fn to_u64(&self) -> Option<u64> {
+        match self.data.len() {
+            0 => Some(0),
+            1 => Some(self.data[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<f32> {
+        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<f64> {
+        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<BigUint> {
+        if n >= 0 {
+            Some(BigUint::from(n as u64))
+        } else {
+            None
+        }
+    }
+
+    #[inline]
+    fn from_u64(n: u64) -> Option<BigUint> {
+        Some(BigUint::from(n))
+    }
+
+    #[inline]
+    fn from_f64(mut n: f64) -> Option<BigUint> {
+        // 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<u64> 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: $T) -> Self {
+                BigUint::from(n as u64)
+            }
+        }
+    }
+}
+
+impl_biguint_from_uint!(u8);
+impl_biguint_from_uint!(u16);
+impl_biguint_from_uint!(u32);
+impl_biguint_from_uint!(usize);
+
+/// A generic trait for converting a value to a `BigUint`.
+pub trait ToBigUint {
+    /// Converts the value of `self` to a `BigUint`.
+    fn to_biguint(&self) -> Option<BigUint>;
+}
+
+impl ToBigUint for BigInt {
+    #[inline]
+    fn to_biguint(&self) -> Option<BigUint> {
+        if self.sign == Plus {
+            Some(self.data.clone())
+        } else if self.sign == NoSign {
+            Some(Zero::zero())
+        } else {
+            None
+        }
+    }
+}
+
+impl ToBigUint for BigUint {
+    #[inline]
+    fn to_biguint(&self) -> Option<BigUint> {
+        Some(self.clone())
+    }
+}
+
+macro_rules! impl_to_biguint {
+    ($T:ty, $from_ty:path) => {
+        impl ToBigUint for $T {
+            #[inline]
+            fn to_biguint(&self) -> Option<BigUint> {
+                $from_ty(*self)
+            }
+        }
+    }
+}
+
+impl_to_biguint!(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<u8> {
+    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<u8> {
+    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<u8> {
+    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<u8> {
+    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<BigDigit>) -> 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<u8> {
+        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<u8> {
+        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<BigUint> {
+        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<S>(&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<D>(deserializer: &mut D) -> Result<Self, D::Error>
+        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<Sign> 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<S>(&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<D>(deserializer: &mut D) -> Result<Self, D::Error>
+        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<Ordering> {
+        Some(self.cmp(other))
+    }
+}
+
+impl Ord for BigInt {
+    #[inline]
+    fn cmp(&self, other: &BigInt) -> Ordering {
+        let scmp = self.sign.cmp(&other.sign);
+        if scmp != Equal {
+            return scmp;
+        }
+
+        match self.sign {
+            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, ParseBigIntError> {
+        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<BigInt, ParseBigIntError> {
+        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<usize> for BigInt {
+    type Output = BigInt;
+
+    #[inline]
+    fn shl(self, rhs: usize) -> BigInt {
+        (&self) << rhs
+    }
+}
+
+impl<'a> Shl<usize> for &'a BigInt {
+    type Output = BigInt;
+
+    #[inline]
+    fn shl(self, rhs: usize) -> BigInt {
+        BigInt::from_biguint(self.sign, &self.data << rhs)
+    }
+}
+
+impl Shr<usize> for BigInt {
+    type Output = BigInt;
+
+    #[inline]
+    fn shr(self, rhs: usize) -> BigInt {
+        BigInt::from_biguint(self.sign, self.data >> rhs)
+    }
+}
+
+impl<'a> Shr<usize> 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 - $b_data),
+                    Equal => Zero::zero(),
+                },
+        }
+    };
+}
+
+impl<'a, 'b> Add<&'b BigInt> for &'a BigInt {
+    type Output = BigInt;
+
+    #[inline]
+    fn add(self, other: &BigInt) -> BigInt {
+        bigint_add!(self,
+                    self.clone(),
+                    &self.data,
+                    other,
+                    other.clone(),
+                    &other.data)
+    }
+}
+
+impl<'a> Add<BigInt> for &'a BigInt {
+    type Output = BigInt;
+
+    #[inline]
+    fn add(self, other: BigInt) -> BigInt {
+        bigint_add!(self, self.clone(), &self.data, other, other, other.data)
+    }
+}
+
+impl<'a> Add<&'a BigInt> for BigInt {
+    type Output = BigInt;
+
+    #[inline]
+    fn add(self, other: &BigInt) -> BigInt {
+        bigint_add!(self, self, self.data, other, other.clone(), &other.data)
+    }
+}
+
+impl Add<BigInt> for BigInt {
+    type Output = BigInt;
+
+    #[inline]
+    fn add(self, other: BigInt) -> BigInt {
+        bigint_add!(self, self, self.data, other, other, other.data)
+    }
+}
+
+// We want to forward to BigUint::sub, but it's not clear how that will go until
+// we compare both sign and magnitude.  So we duplicate this body for every
+// val/ref combination, deferring that decision to BigUint's own forwarding.
+macro_rules! bigint_sub {
+    ($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<BigInt> 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<BigInt> 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<BigInt> {
+        return Some(self.add(v));
+    }
+}
+
+impl CheckedSub for BigInt {
+    #[inline]
+    fn checked_sub(&self, v: &BigInt) -> Option<BigInt> {
+        return Some(self.sub(v));
+    }
+}
+
+impl CheckedMul for BigInt {
+    #[inline]
+    fn checked_mul(&self, v: &BigInt) -> Option<BigInt> {
+        return Some(self.mul(v));
+    }
+}
+
+impl CheckedDiv for BigInt {
+    #[inline]
+    fn checked_div(&self, v: &BigInt) -> Option<BigInt> {
+        if v.is_zero() {
+            return None;
+        }
+        return Some(self.div(v));
+    }
+}
+
+impl Integer for BigInt {
+    #[inline]
+    fn div_rem(&self, other: &BigInt) -> (BigInt, BigInt) {
+        // r.sign == self.sign
+        let (d_ui, r_ui) = self.data.div_mod_floor(&other.data);
+        let d = BigInt::from_biguint(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<i64> {
+        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<u64> {
+        match self.sign {
+            Plus => self.data.to_u64(),
+            NoSign => Some(0),
+            Minus => None,
+        }
+    }
+
+    #[inline]
+    fn to_f32(&self) -> Option<f32> {
+        self.data.to_f32().map(|n| {
+            if self.sign == Minus {
+                -n
+            } else {
+                n
+            }
+        })
+    }
+
+    #[inline]
+    fn to_f64(&self) -> Option<f64> {
+        self.data.to_f64().map(|n| {
+            if self.sign == Minus {
+                -n
+            } else {
+                n
+            }
+        })
+    }
+}
+
+impl FromPrimitive for BigInt {
+    #[inline]
+    fn from_i64(n: i64) -> Option<BigInt> {
+        Some(BigInt::from(n))
+    }
+
+    #[inline]
+    fn from_u64(n: u64) -> Option<BigInt> {
+        Some(BigInt::from(n))
+    }
+
+    #[inline]
+    fn from_f64(n: f64) -> Option<BigInt> {
+        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<i64> 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: $T) -> Self {
+                BigInt::from(n as i64)
+            }
+        }
+    }
+}
+
+impl_bigint_from_int!(i8);
+impl_bigint_from_int!(i16);
+impl_bigint_from_int!(i32);
+impl_bigint_from_int!(isize);
+
+impl From<u64> for BigInt {
+    #[inline]
+    fn from(n: u64) -> Self {
+        if n > 0 {
+            BigInt {
+                sign: Plus,
+                data: BigUint::from(n),
+            }
+        } else {
+            BigInt::zero()
+        }
+    }
+}
+
+macro_rules! impl_bigint_from_uint {
+    ($T:ty) => {
+        impl From<$T> for BigInt {
+            #[inline]
+            fn from(n: $T) -> Self {
+                BigInt::from(n as u64)
+            }
+        }
+    }
+}
+
+impl_bigint_from_uint!(u8);
+impl_bigint_from_uint!(u16);
+impl_bigint_from_uint!(u32);
+impl_bigint_from_uint!(usize);
+
+impl From<BigUint> for BigInt {
+    #[inline]
+    fn from(n: BigUint) -> Self {
+        if n.is_zero() {
+            BigInt::zero()
+        } else {
+            BigInt {
+                sign: Plus,
+                data: n,
+            }
+        }
+    }
+}
+
+#[cfg(feature = "serde")]
+impl serde::Serialize for BigInt {
+    fn serialize<S>(&self, serializer: &mut S) -> Result<(), S::Error>
+        where S: serde::Serializer
+    {
+        (self.sign, &self.data).serialize(serializer)
+    }
+}
+
+#[cfg(feature = "serde")]
+impl serde::Deserialize for BigInt {
+    fn deserialize<D>(deserializer: &mut D) -> Result<Self, D::Error>
+        where D: serde::Deserializer
+    {
+        let (sign, data) = try!(serde::Deserialize::deserialize(deserializer));
+        Ok(BigInt {
+            sign: sign,
+            data: data,
+        })
+    }
+}
+
+/// A generic trait for converting a value to a `BigInt`.
+pub trait ToBigInt {
+    /// Converts the value of `self` to a `BigInt`.
+    fn to_bigint(&self) -> Option<BigInt>;
+}
+
+impl ToBigInt for BigInt {
+    #[inline]
+    fn to_bigint(&self) -> Option<BigInt> {
+        Some(self.clone())
+    }
+}
+
+impl ToBigInt for BigUint {
+    #[inline]
+    fn to_bigint(&self) -> Option<BigInt> {
+        if self.is_zero() {
+            Some(Zero::zero())
+        } else {
+            Some(BigInt {
+                sign: Plus,
+                data: self.clone(),
+            })
+        }
+    }
+}
+
+macro_rules! impl_to_bigint {
+    ($T:ty, $from_ty:path) => {
+        impl ToBigInt for $T {
+            #[inline]
+            fn to_bigint(&self) -> Option<BigInt> {
+                $from_ty(*self)
+            }
+        }
+    }
+}
+
+impl_to_bigint!(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<R: Rng> 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<BigDigit>) -> 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<u8>) {
+        (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<u8>) {
+        (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<BigInt> {
+        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<BigUint> {
+        match self.sign {
+            Plus => Some(self.data.clone()),
+            NoSign => Some(Zero::zero()),
+            Minus => None,
+        }
+    }
+
+    #[inline]
+    pub fn checked_add(&self, v: &BigInt) -> Option<BigInt> {
+        return Some(self.add(v));
+    }
+
+    #[inline]
+    pub fn checked_sub(&self, v: &BigInt) -> Option<BigInt> {
+        return Some(self.sub(v));
+    }
+
+    #[inline]
+    pub fn checked_mul(&self, v: &BigInt) -> Option<BigInt> {
+        return Some(self.mul(v));
+    }
+
+    #[inline]
+    pub fn checked_div(&self, v: &BigInt) -> Option<BigInt> {
+        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<ParseIntError> 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<BigUint> = 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::<String>())),
+                   (4,
+                    format!("2{}1", repeat("0").take(bits / 2 - 1).collect::<String>())),
+                   (10,
+                    match bits {
+                       32 => "8589934593".to_string(),
+                       16 => "131073".to_string(),
+                       _ => panic!(),
+                   }),
+                   (16,
+                    format!("2{}1", repeat("0").take(bits / 4 - 1).collect::<String>()))]),
+             (BigUint::from_slice(&[1, 2, 3]),
+              vec![(2,
+                    format!("11{}10{}1",
+                            repeat("0").take(bits - 2).collect::<String>(),
+                            repeat("0").take(bits - 1).collect::<String>())),
+                   (4,
+                    format!("3{}2{}1",
+                            repeat("0").take(bits / 2 - 1).collect::<String>(),
+                            repeat("0").take(bits / 2 - 1).collect::<String>())),
+                   (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::<String>(),
+                            repeat("0").take(bits / 4 - 1).collect::<String>()))])]
+    }
+
+    #[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<isize>) {
+            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::<String>()).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);
+    }
+}

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<T: Integer>(x: T, y: T) -> (T, T) { x.div_rem(&y) }
+#[inline]
+pub fn div_rem<T: Integer>(x: T, y: T) -> (T, T) {
+    x.div_rem(&y)
+}
 /// Floored integer division
-#[inline] pub fn div_floor<T: Integer>(x: T, y: T) -> T { x.div_floor(&y) }
+#[inline]
+pub fn div_floor<T: Integer>(x: T, y: T) -> T {
+    x.div_floor(&y)
+}
 /// Floored integer modulus
-#[inline] pub fn mod_floor<T: Integer>(x: T, y: T) -> T { x.mod_floor(&y) }
+#[inline]
+pub fn mod_floor<T: Integer>(x: T, y: T) -> T {
+    x.mod_floor(&y)
+}
 /// Simultaneous floored integer division and modulus
-#[inline] pub fn div_mod_floor<T: Integer>(x: T, y: T) -> (T, T) { x.div_mod_floor(&y) }
+#[inline]
+pub fn div_mod_floor<T: Integer>(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<T: Integer>(x: T, y: T) -> T { x.gcd(&y) }
+#[inline(always)]
+pub fn gcd<T: Integer>(x: T, y: T) -> T {
+    x.gcd(&y)
+}
 /// Calculates the Lowest Common Multiple (LCM) of the number and `other`.
-#[inline(always)] pub fn lcm<T: Integer>(x: T, y: T) -> T { x.lcm(&y) }
+#[inline(always)]
+pub fn lcm<T: Integer>(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);

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;

traits/src/lib.rs

@@ -34,16 +34,16 @@ pub trait Num: PartialEq + Zero + One
     + Add<Output = Self> + Sub<Output = Self>
     + Mul<Output = Self> + Div<Output = Self> + Rem<Output = Self>
 {
-    type Error;
+    type FromStrRadixErr;
 
     /// Convert from a string and radix <= 36.
-    fn from_str_radix(str: &str, radix: u32) -> Result<Self, Self::Error>;
+    fn from_str_radix(str: &str, radix: u32) -> Result<Self, Self::FromStrRadixErr>;
 }
 
 macro_rules! int_trait_impl {
     ($name:ident for $($t:ty)*) => ($(
         impl $name for $t {
-            type Error = ::std::num::ParseIntError;
+            type FromStrRadixErr = ::std::num::ParseIntError;
             fn from_str_radix(s: &str, radix: u32)
                               -> Result<Self, ::std::num::ParseIntError>
             {
@@ -65,10 +65,10 @@ pub struct ParseFloatError {
 macro_rules! float_trait_impl {
     ($name:ident for $($t:ty)*) => ($(
         impl $name for $t {
-            type Error = ParseFloatError;
+            type FromStrRadixErr = ParseFloatError;
 
             fn from_str_radix(src: &str, radix: u32)
-                              -> Result<Self, Self::Error>
+                              -> Result<Self, Self::FromStrRadixErr>
             {
                 use self::FloatErrorKind::*;
                 use self::ParseFloatError as PFE;