libstd: move bigint to dedicated num directory

1 files changed, 1647 insertions, 0 deletions

diff --git a/src/libstd/num/bigint.rs b/src/libstd/num/bigint.rs
new file mode 100644
index 00000000000..35b1a28a465
--- /dev/null
+++ b/src/libstd/num/bigint.rs
@@ -0,0 +1,1647 @@
+// Copyright 2013 The Rust Project Developers. See the COPYRIGHT
+// file at the top-level directory of this distribution and at
+// http://rust-lang.org/COPYRIGHT.
+//
+// Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or
+// http://www.apache.org/licenses/LICENSE-2.0> or the MIT license
+// <LICENSE-MIT or http://opensource.org/licenses/MIT>, at your
+// option. This file may not be copied, modified, or distributed
+// except according to those terms.
+
+/*!
+
+A Big integer (signed version: BigInt, unsigned version: BigUint).
+
+A BigUint is represented as an array of BigDigits.
+A BigInt is a combination of BigUint and Sign.
+*/
+
+use core::cmp::{Eq, Ord};
+use core::num::{IntConvertible, Zero, One};
+use core::*;
+
+/**
+A BigDigit is a BigUint's composing element.
+
+A BigDigit is half the size of machine word size.
+*/
+#[cfg(target_arch = "x86")]
+#[cfg(target_arch = "arm")]
+#[cfg(target_arch = "mips")]
+pub type BigDigit = u16;
+
+/**
+A BigDigit is a BigUint's composing element.
+
+A BigDigit is half the size of machine word size.
+*/
+#[cfg(target_arch = "x86_64")]
+pub type BigDigit = u32;
+
+pub mod BigDigit {
+    use bigint::BigDigit;
+
+    #[cfg(target_arch = "x86")]
+    #[cfg(target_arch = "arm")]
+    #[cfg(target_arch = "mips")]
+    pub static bits: uint = 16;
+
+    #[cfg(target_arch = "x86_64")]
+    pub static bits: uint = 32;
+
+    pub static base: uint = 1 << bits;
+    priv static hi_mask: uint = (-1 as uint) << bits;
+    priv static lo_mask: uint = (-1 as uint) >> bits;
+
+    priv fn get_hi(n: uint) -> BigDigit { (n >> bits) as BigDigit }
+    priv fn get_lo(n: uint) -> BigDigit { (n & lo_mask) as BigDigit }
+
+    /// Split one machine sized unsigned integer into two BigDigits.
+    pub fn from_uint(n: uint) -> (BigDigit, BigDigit) {
+        (get_hi(n), get_lo(n))
+    }
+
+    /// Join two BigDigits into one machine sized unsigned integer
+    pub fn to_uint(hi: BigDigit, lo: BigDigit) -> uint {
+        (lo as uint) | ((hi as uint) << bits)
+    }
+}
+
+/**
+A big unsigned integer type.
+
+A BigUint-typed value BigUint { data: @[a, b, c] } represents a number
+(a + b * BigDigit::base + c * BigDigit::base^2).
+*/
+pub struct BigUint {
+    priv data: ~[BigDigit]
+}
+
+impl Eq for BigUint {
+    fn eq(&self, other: &BigUint) -> bool { self.cmp(other) == 0 }
+    fn ne(&self, other: &BigUint) -> bool { self.cmp(other) != 0 }
+}
+
+impl Ord for BigUint {
+    fn lt(&self, other: &BigUint) -> bool { self.cmp(other) <  0 }
+    fn le(&self, other: &BigUint) -> bool { self.cmp(other) <= 0 }
+    fn ge(&self, other: &BigUint) -> bool { self.cmp(other) >= 0 }
+    fn gt(&self, other: &BigUint) -> bool { self.cmp(other) >  0 }
+}
+
+impl ToStr for BigUint {
+    fn to_str(&self) -> ~str { self.to_str_radix(10) }
+}
+
+impl from_str::FromStr for BigUint {
+    fn from_str(s: &str) -> Option<BigUint> {
+        BigUint::from_str_radix(s, 10)
+    }
+}
+
+impl Shl<uint, BigUint> for BigUint {
+    fn shl(&self, rhs: &uint) -> BigUint {
+        let n_unit = *rhs / BigDigit::bits;
+        let n_bits = *rhs % BigDigit::bits;
+        return self.shl_unit(n_unit).shl_bits(n_bits);
+    }
+}
+
+impl Shr<uint, BigUint> for BigUint {
+    fn shr(&self, rhs: &uint) -> BigUint {
+        let n_unit = *rhs / BigDigit::bits;
+        let n_bits = *rhs % BigDigit::bits;
+        return self.shr_unit(n_unit).shr_bits(n_bits);
+    }
+}
+
+impl Zero for BigUint {
+    fn zero() -> BigUint { BigUint::new(~[]) }
+}
+
+impl One for BigUint {
+    pub fn one() -> BigUint { BigUint::new(~[1]) }
+}
+
+impl Add<BigUint, BigUint> for BigUint {
+    fn add(&self, other: &BigUint) -> BigUint {
+        let new_len = uint::max(self.data.len(), other.data.len());
+
+        let mut carry = 0;
+        let sum = do vec::from_fn(new_len) |i| {
+            let ai = if i < self.data.len()  { self.data[i]  } else { 0 };
+            let bi = if i < other.data.len() { other.data[i] } else { 0 };
+            let (hi, lo) = BigDigit::from_uint(
+                (ai as uint) + (bi as uint) + (carry as uint)
+            );
+            carry = hi;
+            lo
+        };
+        if carry == 0 { return BigUint::new(sum) };
+        return BigUint::new(sum + [carry]);
+    }
+}
+
+impl Sub<BigUint, BigUint> for BigUint {
+    fn sub(&self, other: &BigUint) -> BigUint {
+        let new_len = uint::max(self.data.len(), other.data.len());
+
+        let mut borrow = 0;
+        let diff = do vec::from_fn(new_len) |i| {
+            let ai = if i < self.data.len()  { self.data[i]  } else { 0 };
+            let bi = if i < other.data.len() { other.data[i] } else { 0 };
+            let (hi, lo) = BigDigit::from_uint(
+                (BigDigit::base) +
+                (ai as uint) - (bi as uint) - (borrow as uint)
+            );
+            /*
+            hi * (base) + lo == 1*(base) + ai - bi - borrow
+            => ai - bi - borrow < 0 <=> hi == 0
+            */
+            borrow = if hi == 0 { 1 } else { 0 };
+            lo
+        };
+
+        assert!(borrow == 0);     // <=> assert!((self >= other));
+        return BigUint::new(diff);
+    }
+}
+
+impl Mul<BigUint, BigUint> for BigUint {
+    fn mul(&self, other: &BigUint) -> BigUint {
+        if self.is_zero() || other.is_zero() { return Zero::zero(); }
+
+        let s_len = self.data.len(), o_len = other.data.len();
+        if s_len == 1 { return mul_digit(other, self.data[0]);  }
+        if o_len == 1 { return mul_digit(self,  other.data[0]); }
+
+        // Using Karatsuba multiplication
+        // (a1 * base + a0) * (b1 * base + b0)
+        // = a1*b1 * base^2 +
+        //   (a1*b1 + a0*b0 - (a1-b0)*(b1-a0)) * base +
+        //   a0*b0
+        let half_len = uint::max(s_len, o_len) / 2;
+        let (sHi, sLo) = cut_at(self,  half_len);
+        let (oHi, oLo) = cut_at(other, half_len);
+
+        let ll = sLo * oLo;
+        let hh = sHi * oHi;
+        let mm = {
+            let (s1, n1) = sub_sign(sHi, sLo);
+            let (s2, n2) = sub_sign(oHi, oLo);
+            if s1 * s2 < 0 {
+                hh + ll + (n1 * n2)
+            } else if s1 * s2 > 0 {
+                hh + ll - (n1 * n2)
+            } else {
+                hh + ll
+            }
+        };
+
+        return ll + mm.shl_unit(half_len) + hh.shl_unit(half_len * 2);
+
+        fn mul_digit(a: &BigUint, n: BigDigit) -> BigUint {
+            if n == 0 { return Zero::zero(); }
+            if n == 1 { return copy *a; }
+
+            let mut carry = 0;
+            let prod = do vec::map(a.data) |ai| {
+                let (hi, lo) = BigDigit::from_uint(
+                    (*ai as uint) * (n as uint) + (carry as uint)
+                );
+                carry = hi;
+                lo
+            };
+            if carry == 0 { return BigUint::new(prod) };
+            return BigUint::new(prod + [carry]);
+        }
+
+        fn cut_at(a: &BigUint, n: uint) -> (BigUint, BigUint) {
+            let mid = uint::min(a.data.len(), n);
+            return (BigUint::from_slice(vec::slice(a.data, mid,
+                                                   a.data.len())),
+                    BigUint::from_slice(vec::slice(a.data, 0, mid)));
+        }
+
+        fn sub_sign(a: BigUint, b: BigUint) -> (int, BigUint) {
+            match a.cmp(&b) {
+                s if s < 0 => (s, b - a),
+                s if s > 0 => (s, a - b),
+                _          => (0, Zero::zero())
+            }
+        }
+    }
+}
+
+impl Div<BigUint, BigUint> for BigUint {
+    fn div(&self, other: &BigUint) -> BigUint {
+        let (d, _) = self.divmod(other);
+        return d;
+    }
+}
+
+impl Modulo<BigUint, BigUint> for BigUint {
+    fn modulo(&self, other: &BigUint) -> BigUint {
+        let (_, m) = self.divmod(other);
+        return m;
+    }
+}
+
+impl Neg<BigUint> for BigUint {
+    fn neg(&self) -> BigUint { fail!() }
+}
+
+impl IntConvertible for BigUint {
+    fn to_int(&self) -> int {
+        uint::min(self.to_uint(), int::max_value as uint) as int
+    }
+
+    fn from_int(n: int) -> BigUint {
+        if (n < 0) { Zero::zero() } else { BigUint::from_uint(n as uint) }
+    }
+}
+
+pub impl BigUint {
+    /// Creates and initializes an BigUint.
+    pub fn new(v: ~[BigDigit]) -> BigUint {
+        // omit trailing zeros
+        let new_len = v.rposition(|n| *n != 0).map_default(0, |p| *p + 1);
+
+        if new_len == v.len() { return BigUint { data: v }; }
+        let mut v = v;
+        unsafe { v.truncate(new_len); }
+        return BigUint { data: v };
+    }
+
+    /// Creates and initializes an BigUint.
+    pub fn from_uint(n: uint) -> BigUint {
+        match BigDigit::from_uint(n) {
+            (0,  0)  => Zero::zero(),
+            (0,  n0) => BigUint::new(~[n0]),
+            (n1, n0) => BigUint::new(~[n0, n1])
+        }
+    }
+
+    /// Creates and initializes an BigUint.
+    pub fn from_slice(slice: &[BigDigit]) -> BigUint {
+        return BigUint::new(vec::from_slice(slice));
+    }
+
+    /// Creates and initializes an BigUint.
+    pub fn from_str_radix(s: &str, radix: uint)
+        -> Option<BigUint> {
+        BigUint::parse_bytes(str::to_bytes(s), radix)
+    }
+
+    /// Creates and initializes an BigUint.
+    pub fn parse_bytes(buf: &[u8], radix: uint)
+        -> Option<BigUint> {
+        let (base, unit_len) = get_radix_base(radix);
+        let base_num: BigUint = BigUint::from_uint(base);
+
+        let mut end             = buf.len();
+        let mut n: BigUint      = Zero::zero();
+        let mut power: BigUint  = One::one();
+        loop {
+            let start = uint::max(end, unit_len) - unit_len;
+            match uint::parse_bytes(vec::slice(buf, start, end), radix) {
+                Some(d) => n += BigUint::from_uint(d) * power,
+                None    => return None
+            }
+            if end <= unit_len {
+                return Some(n);
+            }
+            end -= unit_len;
+            power *= base_num;
+        }
+    }
+
+    fn abs(&self) -> BigUint { copy *self }
+
+    /// Compare two BigUint value.
+    fn cmp(&self, other: &BigUint) -> int {
+        let s_len = self.data.len(), o_len = other.data.len();
+        if s_len < o_len { return -1; }
+        if s_len > o_len { return  1;  }
+
+        for self.data.eachi_reverse |i, elm| {
+            match (*elm, other.data[i]) {
+                (l, r) if l < r => return -1,
+                (l, r) if l > r => return  1,
+                _               => loop
+            };
+        }
+        return 0;
+    }
+
+    fn divmod(&self, other: &BigUint) -> (BigUint, BigUint) {
+        if other.is_zero() { fail!() }
+        if self.is_zero() { return (Zero::zero(), Zero::zero()); }
+        if *other == One::one() { return (copy *self, Zero::zero()); }
+
+        match self.cmp(other) {
+            s if s < 0 => return (Zero::zero(), copy *self),
+            0          => return (One::one(), Zero::zero()),
+            _          => {} // Do nothing
+        }
+
+        let mut shift = 0;
+        let mut n = *other.data.last();
+        while n < (1 << BigDigit::bits - 2) {
+            n <<= 1;
+            shift += 1;
+        }
+        assert!(shift < BigDigit::bits);
+        let (d, m) = divmod_inner(self << shift, other << shift);
+        return (d, m >> shift);
+
+        fn divmod_inner(a: BigUint, b: BigUint) -> (BigUint, BigUint) {
+            let mut r = a;
+            let mut d = Zero::zero::<BigUint>();
+            let mut n = 1;
+            while r >= b {
+                let mut (d0, d_unit, b_unit) = div_estimate(&r, &b, n);
+                let mut prod = b * d0;
+                while prod > r {
+                    d0   -= d_unit;
+                    prod -= b_unit;
+                }
+                if d0.is_zero() {
+                    n = 2;
+                    loop;
+                }
+                n = 1;
+                d += d0;
+                r -= prod;
+            }
+            return (d, r);
+        }
+
+        fn div_estimate(a: &BigUint, b: &BigUint, n: uint)
+            -> (BigUint, BigUint, BigUint) {
+            if a.data.len() < n {
+                return (Zero::zero(), Zero::zero(), copy *a);
+            }
+
+            let an = vec::slice(a.data, a.data.len() - n, a.data.len());
+            let bn = *b.data.last();
+            let mut d = ~[];
+            let mut carry = 0;
+            for an.each_reverse |elt| {
+                let ai = BigDigit::to_uint(carry, *elt);
+                let di = ai / (bn as uint);
+                assert!(di < BigDigit::base);
+                carry = (ai % (bn as uint)) as BigDigit;
+                d = ~[di as BigDigit] + d;
+            }
+
+            let shift = (a.data.len() - an.len()) - (b.data.len() - 1);
+            if shift == 0 {
+                return (BigUint::new(d), One::one(), copy *b);
+            }
+            return (BigUint::from_slice(d).shl_unit(shift),
+                    One::one::<BigUint>().shl_unit(shift),
+                    b.shl_unit(shift));
+        }
+    }
+
+    fn quot(&self, other: &BigUint) -> BigUint {
+        let (q, _) = self.quotrem(other);
+        return q;
+    }
+    fn rem(&self, other: &BigUint) -> BigUint {
+        let (_, r) = self.quotrem(other);
+        return r;
+    }
+    fn quotrem(&self, other: &BigUint) -> (BigUint, BigUint) {
+        self.divmod(other)
+    }
+
+    fn is_zero(&self) -> bool { self.data.is_empty() }
+    fn is_not_zero(&self) -> bool { !self.data.is_empty() }
+    fn is_positive(&self) -> bool { self.is_not_zero() }
+    fn is_negative(&self) -> bool { false }
+    fn is_nonpositive(&self) -> bool { self.is_zero() }
+    fn is_nonnegative(&self) -> bool { true }
+
+    fn to_uint(&self) -> uint {
+        match self.data.len() {
+            0 => 0,
+            1 => self.data[0] as uint,
+            2 => BigDigit::to_uint(self.data[1], self.data[0]),
+            _ => uint::max_value
+        }
+    }
+
+    fn to_str_radix(&self, radix: uint) -> ~str {
+        assert!(1 < radix && radix <= 16);
+        let (base, max_len) = get_radix_base(radix);
+        if base == BigDigit::base {
+            return fill_concat(self.data, radix, max_len)
+        }
+        return fill_concat(convert_base(copy *self, base), radix, max_len);
+
+        fn convert_base(n: BigUint, base: uint) -> ~[BigDigit] {
+            let divider    = BigUint::from_uint(base);
+            let mut result = ~[];
+            let mut r      = n;
+            while r > divider {
+                let (d, r0) = r.divmod(&divider);
+                result += [r0.to_uint() as BigDigit];
+                r = d;
+            }
+            if r.is_not_zero() {
+                result += [r.to_uint() as BigDigit];
+            }
+            return result;
+        }
+
+        fn fill_concat(v: &[BigDigit], radix: uint, l: uint) -> ~str {
+            if v.is_empty() { return ~"0" }
+            let s = str::concat(vec::reversed(v).map(|n| {
+                let s = uint::to_str_radix(*n as uint, radix);
+                str::from_chars(vec::from_elem(l - s.len(), '0')) + s
+            }));
+            str::trim_left_chars(s, ['0']).to_owned()
+        }
+    }
+
+    priv fn shl_unit(self, n_unit: uint) -> BigUint {
+        if n_unit == 0 || self.is_zero() { return self; }
+
+        return BigUint::new(vec::from_elem(n_unit, 0) + self.data);
+    }
+
+    priv fn shl_bits(self, n_bits: uint) -> BigUint {
+        if n_bits == 0 || self.is_zero() { return self; }
+
+        let mut carry = 0;
+        let shifted = do vec::map(self.data) |elem| {
+            let (hi, lo) = BigDigit::from_uint(
+                (*elem as uint) << n_bits | (carry as uint)
+            );
+            carry = hi;
+            lo
+        };
+        if carry == 0 { return BigUint::new(shifted); }
+        return BigUint::new(shifted + [carry]);
+    }
+
+    priv fn shr_unit(self, n_unit: uint) -> BigUint {
+        if n_unit == 0 { return self; }
+        if self.data.len() < n_unit { return Zero::zero(); }
+        return BigUint::from_slice(
+            vec::slice(self.data, n_unit, self.data.len())
+        );
+    }
+
+    priv fn shr_bits(self, n_bits: uint) -> BigUint {
+        if n_bits == 0 || self.data.is_empty() { return self; }
+
+        let mut borrow = 0;
+        let mut shifted = ~[];
+        for self.data.each_reverse |elem| {
+            shifted = ~[(*elem >> n_bits) | borrow] + shifted;
+            borrow = *elem << (uint::bits - n_bits);
+        }
+        return BigUint::new(shifted);
+    }
+}
+
+#[cfg(target_arch = "x86_64")]
+priv fn get_radix_base(radix: uint) -> (uint, uint) {
+    assert!(1 < radix && radix <= 16);
+    match radix {
+        2  => (4294967296, 32),
+        3  => (3486784401, 20),
+        4  => (4294967296, 16),
+        5  => (1220703125, 13),
+        6  => (2176782336, 12),
+        7  => (1977326743, 11),
+        8  => (1073741824, 10),
+        9  => (3486784401, 10),
+        10 => (1000000000, 9),
+        11 => (2357947691, 9),
+        12 => (429981696,  8),
+        13 => (815730721,  8),
+        14 => (1475789056, 8),
+        15 => (2562890625, 8),
+        16 => (4294967296, 8),
+        _  => fail!()
+    }
+}
+
+#[cfg(target_arch = "arm")]
+#[cfg(target_arch = "x86")]
+#[cfg(target_arch = "mips")]
+priv fn get_radix_base(radix: uint) -> (uint, uint) {
+    assert!(1 < radix && radix <= 16);
+    match radix {
+        2  => (65536, 16),
+        3  => (59049, 10),
+        4  => (65536, 8),
+        5  => (15625, 6),
+        6  => (46656, 6),
+        7  => (16807, 5),
+        8  => (32768, 5),
+        9  => (59049, 5),
+        10 => (10000, 4),
+        11 => (14641, 4),
+        12 => (20736, 4),
+        13 => (28561, 4),
+        14 => (38416, 4),
+        15 => (50625, 4),
+        16 => (65536, 4),
+        _  => fail!()
+    }
+}
+
+/// A Sign is a BigInt's composing element.
+#[deriving(Eq)]
+pub enum Sign { Minus, Zero, Plus }
+
+impl Ord for Sign {
+    fn lt(&self, other: &Sign) -> bool { self.cmp(other) <  0 }
+    fn le(&self, other: &Sign) -> bool { self.cmp(other) <= 0 }
+    fn ge(&self, other: &Sign) -> bool { self.cmp(other) >= 0 }
+    fn gt(&self, other: &Sign) -> bool { self.cmp(other) >  0 }
+}
+
+pub impl Sign {
+    /// Compare two Sign.
+    fn cmp(&self, other: &Sign) -> int {
+        match (*self, *other) {
+          (Minus, Minus) | (Zero,  Zero) | (Plus, Plus) =>  0,
+          (Minus, Zero)  | (Minus, Plus) | (Zero, Plus) => -1,
+          _                                             =>  1
+        }
+    }
+
+    /// Negate Sign value.
+    fn neg(&self) -> Sign {
+        match *self {
+          Minus => Plus,
+          Zero  => Zero,
+          Plus  => Minus
+        }
+    }
+}
+
+/// A big signed integer type.
+pub struct BigInt {
+    priv sign: Sign,
+    priv data: BigUint
+}
+
+impl Eq for BigInt {
+    fn eq(&self, other: &BigInt) -> bool { self.cmp(other) == 0 }
+    fn ne(&self, other: &BigInt) -> bool { self.cmp(other) != 0 }
+}
+
+impl Ord for BigInt {
+    fn lt(&self, other: &BigInt) -> bool { self.cmp(other) <  0 }
+    fn le(&self, other: &BigInt) -> bool { self.cmp(other) <= 0 }
+    fn ge(&self, other: &BigInt) -> bool { self.cmp(other) >= 0 }
+    fn gt(&self, other: &BigInt) -> bool { self.cmp(other) >  0 }
+}
+
+impl ToStr for BigInt {
+    fn to_str(&self) -> ~str { self.to_str_radix(10) }
+}
+
+impl from_str::FromStr for BigInt {
+    fn from_str(s: &str) -> Option<BigInt> {
+        BigInt::from_str_radix(s, 10)
+    }
+}
+
+impl Shl<uint, BigInt> for BigInt {
+    fn shl(&self, rhs: &uint) -> BigInt {
+        BigInt::from_biguint(self.sign, self.data << *rhs)
+    }
+}
+
+impl Shr<uint, BigInt> for BigInt {
+    fn shr(&self, rhs: &uint) -> BigInt {
+        BigInt::from_biguint(self.sign, self.data >> *rhs)
+    }
+}
+
+impl Zero for BigInt {
+    pub fn zero() -> BigInt {
+        BigInt::from_biguint(Zero, Zero::zero())
+    }
+}
+
+impl One for BigInt {
+    pub fn one() -> BigInt {
+        BigInt::from_biguint(Plus, One::one())
+    }
+}
+
+impl Add<BigInt, BigInt> for BigInt {
+    fn add(&self, other: &BigInt) -> BigInt {
+        match (self.sign, other.sign) {
+            (Zero, _)      => copy *other,
+            (_,    Zero)   => copy *self,
+            (Plus, Plus)   => BigInt::from_biguint(Plus,
+                                                   self.data + other.data),
+            (Plus, Minus)  => self - (-*other),
+            (Minus, Plus)  => other - (-*self),
+            (Minus, Minus) => -((-self) + (-*other))
+        }
+    }
+}
+
+impl Sub<BigInt, BigInt> for BigInt {
+    fn sub(&self, other: &BigInt) -> BigInt {
+        match (self.sign, other.sign) {
+            (Zero, _)    => -other,
+            (_,    Zero) => copy *self,
+            (Plus, Plus) => match self.data.cmp(&other.data) {
+                s if s < 0 =>
+                    BigInt::from_biguint(Minus, other.data - self.data),
+                s if s > 0 =>
+                    BigInt::from_biguint(Plus, self.data - other.data),
+                _ =>
+                    Zero::zero()
+            },
+            (Plus, Minus) => self + (-*other),
+            (Minus, Plus) => -((-self) + *other),
+            (Minus, Minus) => (-other) - (-*self)
+        }
+    }
+}
+
+impl Mul<BigInt, BigInt> for BigInt {
+    fn mul(&self, other: &BigInt) -> BigInt {
+        match (self.sign, other.sign) {
+            (Zero, _)     | (_,     Zero)  => Zero::zero(),
+            (Plus, Plus)  | (Minus, Minus) => {
+                BigInt::from_biguint(Plus, self.data * other.data)
+            },
+            (Plus, Minus) | (Minus, Plus) => {
+                BigInt::from_biguint(Minus, self.data * other.data)
+            }
+        }
+    }
+}
+
+impl Div<BigInt, BigInt> for BigInt {
+    fn div(&self, other: &BigInt) -> BigInt {
+        let (d, _) = self.divmod(other);
+        return d;
+    }
+}
+
+impl Modulo<BigInt, BigInt> for BigInt {
+    fn modulo(&self, other: &BigInt) -> BigInt {
+        let (_, m) = self.divmod(other);
+        return m;
+    }
+}
+
+impl Neg<BigInt> for BigInt {
+    fn neg(&self) -> BigInt {
+        BigInt::from_biguint(self.sign.neg(), copy self.data)
+    }
+}
+
+impl IntConvertible for BigInt {
+    fn to_int(&self) -> int {
+        match self.sign {
+            Plus  => uint::min(self.to_uint(), int::max_value as uint) as int,
+            Zero  => 0,
+            Minus => uint::min((-self).to_uint(),
+                               (int::max_value as uint) + 1) as int
+        }
+    }
+
+    fn from_int(n: int) -> BigInt {
+        if n > 0 {
+           return BigInt::from_biguint(Plus,  BigUint::from_uint(n as uint));
+        }
+        if n < 0 {
+            return BigInt::from_biguint(
+                Minus, BigUint::from_uint(uint::max_value - (n as uint) + 1)
+            );
+        }
+        return Zero::zero();
+    }
+}
+
+pub impl BigInt {
+    /// Creates and initializes an BigInt.
+    pub fn new(sign: Sign, v: ~[BigDigit]) -> BigInt {
+        BigInt::from_biguint(sign, BigUint::new(v))
+    }
+
+    /// Creates and initializes an BigInt.
+    pub fn from_biguint(sign: Sign, data: BigUint) -> BigInt {
+        if sign == Zero || data.is_zero() {
+            return BigInt { sign: Zero, data: Zero::zero() };
+        }
+        return BigInt { sign: sign, data: data };
+    }
+
+    /// Creates and initializes an BigInt.
+    pub fn from_uint(n: uint) -> BigInt {
+        if n == 0 { return Zero::zero(); }
+        return BigInt::from_biguint(Plus, BigUint::from_uint(n));
+    }
+
+    /// Creates and initializes an BigInt.
+    pub fn from_slice(sign: Sign, slice: &[BigDigit]) -> BigInt {
+        BigInt::from_biguint(sign, BigUint::from_slice(slice))
+    }
+
+    /// Creates and initializes an BigInt.
+    pub fn from_str_radix(s: &str, radix: uint)
+        -> Option<BigInt> {
+        BigInt::parse_bytes(str::to_bytes(s), radix)
+    }
+
+    /// Creates and initializes an BigInt.
+    pub fn parse_bytes(buf: &[u8], radix: uint)
+        -> Option<BigInt> {
+        if buf.is_empty() { return None; }
+        let mut sign  = Plus;
+        let mut start = 0;
+        if buf[0] == ('-' as u8) {
+            sign  = Minus;
+            start = 1;
+        }
+        return BigUint::parse_bytes(vec::slice(buf, start, buf.len()), radix)
+            .map(|bu| BigInt::from_biguint(sign, *bu));
+    }
+
+    fn abs(&self) -> BigInt {
+        BigInt::from_biguint(Plus, copy self.data)
+    }
+
+    fn cmp(&self, other: &BigInt) -> int {
+        let ss = self.sign, os = other.sign;
+        if ss < os { return -1; }
+        if ss > os { return  1; }
+
+        assert!(ss == os);
+        match ss {
+            Zero  => 0,
+            Plus  => self.data.cmp(&other.data),
+            Minus => self.data.cmp(&other.data).neg(),
+        }
+    }
+
+    fn divmod(&self, other: &BigInt) -> (BigInt, BigInt) {
+        // m.sign == other.sign
+        let (d_ui, m_ui) = self.data.divmod(&other.data);
+        let d = BigInt::from_biguint(Plus, d_ui),
+            m = BigInt::from_biguint(Plus, m_ui);
+        match (self.sign, other.sign) {
+            (_,    Zero)   => fail!(),
+            (Plus, Plus)  | (Zero, Plus)  => (d, m),
+            (Plus, Minus) | (Zero, Minus) => if m.is_zero() {
+                (-d, Zero::zero())
+            } else {
+                (-d - One::one(), m + *other)
+            },
+            (Minus, Plus) => if m.is_zero() {
+                (-d, Zero::zero())
+            } else {
+                (-d - One::one(), other - m)
+            },
+            (Minus, Minus) => (d, -m)
+        }
+    }
+
+    fn quot(&self, other: &BigInt) -> BigInt {
+        let (q, _) = self.quotrem(other);
+        return q;
+    }
+    fn rem(&self, other: &BigInt) -> BigInt {
+        let (_, r) = self.quotrem(other);
+        return r;
+    }
+
+    fn quotrem(&self, other: &BigInt) -> (BigInt, BigInt) {
+        // r.sign == self.sign
+        let (q_ui, r_ui) = self.data.quotrem(&other.data);
+        let q = BigInt::from_biguint(Plus, q_ui);
+        let r = BigInt::from_biguint(Plus, r_ui);
+        match (self.sign, other.sign) {
+            (_,    Zero)   => fail!(),
+            (Plus, Plus)  | (Zero, Plus)  => ( q,  r),
+            (Plus, Minus) | (Zero, Minus) => (-q,  r),
+            (Minus, Plus)                 => (-q, -r),
+            (Minus, Minus)                => ( q, -r)
+        }
+    }
+
+    fn is_zero(&self) -> bool { self.sign == Zero }
+    fn is_not_zero(&self) -> bool { self.sign != Zero }
+    fn is_positive(&self) -> bool { self.sign == Plus }
+    fn is_negative(&self) -> bool { self.sign == Minus }
+    fn is_nonpositive(&self) -> bool { self.sign != Plus }
+    fn is_nonnegative(&self) -> bool { self.sign != Minus }
+
+    fn to_uint(&self) -> uint {
+        match self.sign {
+            Plus  => self.data.to_uint(),
+            Zero  => 0,
+            Minus => 0
+        }
+    }
+
+    fn to_str_radix(&self, radix: uint) -> ~str {
+        match self.sign {
+            Plus  => self.data.to_str_radix(radix),
+            Zero  => ~"0",
+            Minus => ~"-" + self.data.to_str_radix(radix)
+        }
+    }
+}
+
+#[cfg(test)]
+mod biguint_tests {
+
+    use core::*;
+    use core::num::{IntConvertible, Zero, One};
+    use super::{BigUint, BigDigit};
+
+    #[test]
+    fn test_from_slice() {
+        fn check(slice: &[BigDigit], data: &[BigDigit]) {
+            assert!(data == BigUint::from_slice(slice).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(~[-1], ~[-1]);
+    }
+
+    #[test]
+    fn test_cmp() {
+        let data = [ &[], &[1], &[2], &[-1], &[0, 1], &[2, 1], &[1, 1, 1]  ]
+            .map(|v| BigUint::from_slice(*v));
+        for data.eachi |i, ni| {
+            for vec::slice(data, i, data.len()).eachi |j0, nj| {
+                let j = j0 + i;
+                if i == j {
+                    assert!(ni.cmp(nj) == 0);
+                    assert!(nj.cmp(ni) == 0);
+                    assert!(ni == nj);
+                    assert!(!(ni != nj));
+                    assert!(ni <= nj);
+                    assert!(ni >= nj);
+                    assert!(!(ni < nj));
+                    assert!(!(ni > nj));
+                } else {
+                    assert!(ni.cmp(nj) < 0);
+                    assert!(nj.cmp(ni) > 0);
+
+                    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_shl() {
+        fn check(v: ~[BigDigit], shift: uint, ans: ~[BigDigit]) {
+            assert!(BigUint::new(v) << shift == BigUint::new(ans));
+        }
+
+        check(~[], 3, ~[]);
+        check(~[1, 1, 1], 3, ~[1 << 3, 1 << 3, 1 << 3]);
+        check(~[1 << (BigDigit::bits - 2)], 2, ~[0, 1]);
+        check(~[1 << (BigDigit::bits - 2)], 3, ~[0, 2]);
+        check(~[1 << (BigDigit::bits - 2)], 3 + BigDigit::bits, ~[0, 0, 2]);
+
+        test_shl_bits();
+
+        #[cfg(target_arch = "x86_64")]
+        fn test_shl_bits() {
+            check(~[0x7654_3210, 0xfedc_ba98,
+                    0x7654_3210, 0xfedc_ba98], 4,
+                  ~[0x6543_2100, 0xedcb_a987,
+                    0x6543_210f, 0xedcb_a987, 0xf]);
+            check(~[0x2222_1111, 0x4444_3333,
+                    0x6666_5555, 0x8888_7777], 16,
+                  ~[0x1111_0000, 0x3333_2222,
+                    0x5555_4444, 0x7777_6666, 0x8888]);
+        }
+
+        #[cfg(target_arch = "arm")]
+        #[cfg(target_arch = "x86")]
+        #[cfg(target_arch = "mips")]
+        fn test_shl_bits() {
+            check(~[0x3210, 0x7654, 0xba98, 0xfedc,
+                    0x3210, 0x7654, 0xba98, 0xfedc], 4,
+                  ~[0x2100, 0x6543, 0xa987, 0xedcb,
+                    0x210f, 0x6543, 0xa987, 0xedcb, 0xf]);
+            check(~[0x1111, 0x2222, 0x3333, 0x4444,
+                    0x5555, 0x6666, 0x7777, 0x8888], 16,
+                  ~[0x0000, 0x1111, 0x2222, 0x3333,
+                    0x4444, 0x5555, 0x6666, 0x7777, 0x8888]);
+        }
+
+    }
+
+    #[test]
+    #[ignore(cfg(target_arch = "x86"))]
+    #[ignore(cfg(target_arch = "arm"))]
+    #[ignore(cfg(target_arch = "mips"))]
+    fn test_shr() {
+        fn check(v: ~[BigDigit], shift: uint, ans: ~[BigDigit]) {
+            assert!(BigUint::new(v) >> shift == BigUint::new(ans));
+        }
+
+        check(~[], 3, ~[]);
+        check(~[1, 1, 1], 3,
+              ~[1 << (BigDigit::bits - 3), 1 << (BigDigit::bits - 3)]);
+        check(~[1 << 2], 2, ~[1]);
+        check(~[1, 2], 3, ~[1 << (BigDigit::bits - 2)]);
+        check(~[1, 1, 2], 3 + BigDigit::bits, ~[1 << (BigDigit::bits - 2)]);
+        test_shr_bits();
+
+        #[cfg(target_arch = "x86_64")]
+        fn test_shr_bits() {
+            check(~[0x6543_2100, 0xedcb_a987,
+                    0x6543_210f, 0xedcb_a987, 0xf], 4,
+                  ~[0x7654_3210, 0xfedc_ba98,
+                    0x7654_3210, 0xfedc_ba98]);
+            check(~[0x1111_0000, 0x3333_2222,
+                    0x5555_4444, 0x7777_6666, 0x8888], 16,
+                  ~[0x2222_1111, 0x4444_3333,
+                    0x6666_5555, 0x8888_7777]);
+        }
+
+        #[cfg(target_arch = "arm")]
+        #[cfg(target_arch = "x86")]
+        #[cfg(target_arch = "mips")]
+        fn test_shr_bits() {
+            check(~[0x2100, 0x6543, 0xa987, 0xedcb,
+                    0x210f, 0x6543, 0xa987, 0xedcb, 0xf], 4,
+                  ~[0x3210, 0x7654, 0xba98, 0xfedc,
+                    0x3210, 0x7654, 0xba98, 0xfedc]);
+            check(~[0x0000, 0x1111, 0x2222, 0x3333,
+                    0x4444, 0x5555, 0x6666, 0x7777, 0x8888], 16,
+                  ~[0x1111, 0x2222, 0x3333, 0x4444,
+                    0x5555, 0x6666, 0x7777, 0x8888]);
+        }
+    }
+
+    #[test]
+    fn test_convert_int() {
+        fn check(v: ~[BigDigit], i: int) {
+            let b = BigUint::new(v);
+            assert!(b == IntConvertible::from_int(i));
+            assert!(b.to_int() == i);
+        }
+
+        check(~[], 0);
+        check(~[1], 1);
+        check(~[-1], (uint::max_value >> BigDigit::bits) as int);
+        check(~[ 0,  1], ((uint::max_value >> BigDigit::bits) + 1) as int);
+        check(~[-1, -1 >> 1], int::max_value);
+
+        assert!(BigUint::new(~[0, -1]).to_int() == int::max_value);
+        assert!(BigUint::new(~[0, 0, 1]).to_int() == int::max_value);
+        assert!(BigUint::new(~[0, 0, -1]).to_int() == int::max_value);
+    }
+
+    #[test]
+    fn test_convert_uint() {
+        fn check(v: ~[BigDigit], u: uint) {
+            let b = BigUint::new(v);
+            assert!(b == BigUint::from_uint(u));
+            assert!(b.to_uint() == u);
+        }
+
+        check(~[], 0);
+        check(~[ 1], 1);
+        check(~[-1], uint::max_value >> BigDigit::bits);
+        check(~[ 0,  1], (uint::max_value >> BigDigit::bits) + 1);
+        check(~[ 0, -1], uint::max_value << BigDigit::bits);
+        check(~[-1, -1], uint::max_value);
+
+        assert!(BigUint::new(~[0, 0, 1]).to_uint()  == uint::max_value);
+        assert!(BigUint::new(~[0, 0, -1]).to_uint() == uint::max_value);
+    }
+
+    static sum_triples: &'static [(&'static [BigDigit],
+                                   &'static [BigDigit],
+                                   &'static [BigDigit])] = &[
+        (&[],          &[],       &[]),
+        (&[],          &[ 1],     &[ 1]),
+        (&[ 1],        &[ 1],     &[ 2]),
+        (&[ 1],        &[ 1,  1], &[ 2,  1]),
+        (&[ 1],        &[-1],     &[ 0,  1]),
+        (&[ 1],        &[-1, -1], &[ 0,  0, 1]),
+        (&[-1, -1],    &[-1, -1], &[-2, -1, 1]),
+        (&[ 1,  1, 1], &[-1, -1], &[ 0,  1, 2]),
+        (&[ 2,  2, 1], &[-1, -2], &[ 1,  1, 2])
+    ];
+
+    #[test]
+    fn test_add() {
+        for sum_triples.each |elm| {
+            let (aVec, bVec, cVec) = *elm;
+            let a = BigUint::from_slice(aVec);
+            let b = BigUint::from_slice(bVec);
+            let c = BigUint::from_slice(cVec);
+
+            assert!(a + b == c);
+            assert!(b + a == c);
+        }
+    }
+
+    #[test]
+    fn test_sub() {
+        for sum_triples.each |elm| {
+            let (aVec, bVec, cVec) = *elm;
+            let a = BigUint::from_slice(aVec);
+            let b = BigUint::from_slice(bVec);
+            let c = BigUint::from_slice(cVec);
+
+            assert!(c - a == b);
+            assert!(c - b == a);
+        }
+    }
+
+    static mul_triples: &'static [(&'static [BigDigit],
+                                   &'static [BigDigit],
+                                   &'static [BigDigit])] = &[
+        (&[],               &[],               &[]),
+        (&[],               &[ 1],             &[]),
+        (&[ 2],             &[],               &[]),
+        (&[ 1],             &[ 1],             &[1]),
+        (&[ 2],             &[ 3],             &[ 6]),
+        (&[ 1],             &[ 1,  1,  1],     &[1, 1,  1]),
+        (&[ 1,  2,  3],     &[ 3],             &[ 3,  6,  9]),
+        (&[ 1,  1,  1],     &[-1],             &[-1, -1, -1]),
+        (&[ 1,  2,  3],     &[-1],             &[-1, -2, -2, 2]),
+        (&[ 1,  2,  3,  4], &[-1],             &[-1, -2, -2, -2, 3]),
+        (&[-1],             &[-1],             &[ 1, -2]),
+        (&[-1, -1],         &[-1],             &[ 1, -1, -2]),
+        (&[-1, -1, -1],     &[-1],             &[ 1, -1, -1, -2]),
+        (&[-1, -1, -1, -1], &[-1],             &[ 1, -1, -1, -1, -2]),
+        (&[-1/2 + 1],       &[ 2],             &[ 0,  1]),
+        (&[0, -1/2 + 1],    &[ 2],             &[ 0,  0,  1]),
+        (&[ 1,  2],         &[ 1,  2,  3],     &[1, 4,  7,  6]),
+        (&[-1, -1],         &[-1, -1, -1],     &[1, 0, -1, -2, -1]),
+        (&[-1, -1, -1],     &[-1, -1, -1, -1], &[1, 0,  0, -1, -2, -1, -1]),
+        (&[ 0,  0,  1],     &[ 1,  2,  3],     &[0, 0,  1,  2,  3]),
+        (&[ 0,  0,  1],     &[ 0,  0,  0,  1], &[0, 0,  0,  0,  0,  1])
+    ];
+
+    static divmod_quadruples: &'static [(&'static [BigDigit],
+                                         &'static [BigDigit],
+                                         &'static [BigDigit],
+                                         &'static [BigDigit])]
+        = &[
+            (&[ 1],        &[ 2], &[],               &[1]),
+            (&[ 1,  1],    &[ 2], &[-1/2+1],         &[1]),
+            (&[ 1,  1, 1], &[ 2], &[-1/2+1, -1/2+1], &[1]),
+            (&[ 0,  1],    &[-1], &[1],              &[1]),
+            (&[-1, -1],    &[-2], &[2, 1],           &[3])
+        ];
+
+    #[test]
+    fn test_mul() {
+        for mul_triples.each |elm| {
+            let (aVec, bVec, cVec) = *elm;
+            let a = BigUint::from_slice(aVec);
+            let b = BigUint::from_slice(bVec);
+            let c = BigUint::from_slice(cVec);
+
+            assert!(a * b == c);
+            assert!(b * a == c);
+        }
+
+        for divmod_quadruples.each |elm| {
+            let (aVec, bVec, cVec, dVec) = *elm;
+            let a = BigUint::from_slice(aVec);
+            let b = BigUint::from_slice(bVec);
+            let c = BigUint::from_slice(cVec);
+            let d = BigUint::from_slice(dVec);
+
+            assert!(a == b * c + d);
+            assert!(a == c * b + d);
+        }
+    }
+
+    #[test]
+    fn test_divmod() {
+        for mul_triples.each |elm| {
+            let (aVec, bVec, cVec) = *elm;
+            let a = BigUint::from_slice(aVec);
+            let b = BigUint::from_slice(bVec);
+            let c = BigUint::from_slice(cVec);
+
+            if a.is_not_zero() {
+                assert!(c.divmod(&a) == (b, Zero::zero()));
+            }
+            if b.is_not_zero() {
+                assert!(c.divmod(&b) == (a, Zero::zero()));
+            }
+        }
+
+        for divmod_quadruples.each |elm| {
+            let (aVec, bVec, cVec, dVec) = *elm;
+            let a = BigUint::from_slice(aVec);
+            let b = BigUint::from_slice(bVec);
+            let c = BigUint::from_slice(cVec);
+            let d = BigUint::from_slice(dVec);
+
+            if b.is_not_zero() { assert!(a.divmod(&b) == (c, d)); }
+        }
+    }
+
+    fn to_str_pairs() -> ~[ (BigUint, ~[(uint, ~str)]) ] {
+        let bits = BigDigit::bits;
+        ~[( Zero::zero(), ~[
+            (2, ~"0"), (3, ~"0")
+        ]), ( BigUint::from_slice([ 0xff ]), ~[
+            (2,  ~"11111111"),
+            (3,  ~"100110"),
+            (4,  ~"3333"),
+            (5,  ~"2010"),
+            (6,  ~"1103"),
+            (7,  ~"513"),
+            (8,  ~"377"),
+            (9,  ~"313"),
+            (10, ~"255"),
+            (11, ~"212"),
+            (12, ~"193"),
+            (13, ~"168"),
+            (14, ~"143"),
+            (15, ~"120"),
+            (16, ~"ff")
+        ]), ( BigUint::from_slice([ 0xfff ]), ~[
+            (2,  ~"111111111111"),
+            (4,  ~"333333"),
+            (16, ~"fff")
+        ]), ( BigUint::from_slice([ 1, 2 ]), ~[
+            (2,
+             ~"10" +
+             str::from_chars(vec::from_elem(bits - 1, '0')) + "1"),
+            (4,
+             ~"2" +
+             str::from_chars(vec::from_elem(bits / 2 - 1, '0')) + "1"),
+            (10, match bits {
+                32 => ~"8589934593", 16 => ~"131073", _ => fail!()
+            }),
+            (16,
+             ~"2" +
+             str::from_chars(vec::from_elem(bits / 4 - 1, '0')) + "1")
+        ]), ( BigUint::from_slice([ 1, 2, 3 ]), ~[
+            (2,
+             ~"11" +
+             str::from_chars(vec::from_elem(bits - 2, '0')) + "10" +
+             str::from_chars(vec::from_elem(bits - 1, '0')) + "1"),
+            (4,
+             ~"3" +
+             str::from_chars(vec::from_elem(bits / 2 - 1, '0')) + "2" +
+             str::from_chars(vec::from_elem(bits / 2 - 1, '0')) + "1"),
+            (10, match bits {
+                32 => ~"55340232229718589441",
+                16 => ~"12885032961",
+                _ => fail!()
+            }),
+            (16, ~"3" +
+             str::from_chars(vec::from_elem(bits / 4 - 1, '0')) + "2" +
+             str::from_chars(vec::from_elem(bits / 4 - 1, '0')) + "1")
+        ]) ]
+    }
+
+    #[test]
+    fn test_to_str_radix() {
+        for to_str_pairs().each |num_pair| {
+            let &(n, rs) = num_pair;
+            for rs.each |str_pair| {
+                let &(radix, str) = str_pair;
+                assert!(n.to_str_radix(radix) == str);
+            }
+        }
+    }
+
+    #[test]
+    fn test_from_str_radix() {
+        for to_str_pairs().each |num_pair| {
+            let &(n, rs) = num_pair;
+            for rs.each |str_pair| {
+                let &(radix, str) = str_pair;
+                assert!(Some(n) == BigUint::from_str_radix(str, radix));
+            }
+        }
+
+        assert!(BigUint::from_str_radix(~"Z", 10) == None);
+        assert!(BigUint::from_str_radix(~"_", 2) == None);
+        assert!(BigUint::from_str_radix(~"-1", 10) == None);
+    }
+
+    #[test]
+    fn test_factor() {
+        fn factor(n: uint) -> BigUint {
+            let mut f= One::one::<BigUint>();
+            for uint::range(2, n + 1) |i| {
+                f *= BigUint::from_uint(i);
+            }
+            return f;
+        }
+
+        fn check(n: uint, s: &str) {
+            let n = factor(n);
+            let ans = match BigUint::from_str_radix(s, 10) {
+                Some(x) => x, None => fail!()
+            };
+            assert!(n == ans);
+        }
+
+        check(3, "6");
+        check(10, "3628800");
+        check(20, "2432902008176640000");
+        check(30, "265252859812191058636308480000000");
+    }
+}
+
+#[cfg(test)]
+mod bigint_tests {
+    use super::{BigInt, BigUint, BigDigit, Sign, Minus, Zero, Plus};
+
+    use core::*;
+    use core::num::{IntConvertible, Zero, One};
+
+    #[test]
+    fn test_from_biguint() {
+        fn check(inp_s: Sign, inp_n: uint, ans_s: Sign, ans_n: uint) {
+            let inp = BigInt::from_biguint(inp_s, BigUint::from_uint(inp_n));
+            let ans = BigInt { sign: ans_s, data: BigUint::from_uint(ans_n)};
+            assert!(inp == ans);
+        }
+        check(Plus, 1, Plus, 1);
+        check(Plus, 0, Zero, 0);
+        check(Minus, 1, Minus, 1);
+        check(Zero, 1, Zero, 0);
+    }
+
+    #[test]
+    fn test_cmp() {
+        let vs = [ &[2], &[1, 1], &[2, 1], &[1, 1, 1] ];
+        let mut nums = vec::reversed(vs)
+            .map(|s| BigInt::from_slice(Minus, *s));
+        nums.push(Zero::zero());
+        nums.push_all_move(vs.map(|s| BigInt::from_slice(Plus, *s)));
+
+        for nums.eachi |i, ni| {
+            for vec::slice(nums, i, nums.len()).eachi |j0, nj| {
+                let j = i + j0;
+                if i == j {
+                    assert!(ni.cmp(nj) == 0);
+                    assert!(nj.cmp(ni) == 0);
+                    assert!(ni == nj);
+                    assert!(!(ni != nj));
+                    assert!(ni <= nj);
+                    assert!(ni >= nj);
+                    assert!(!(ni < nj));
+                    assert!(!(ni > nj));
+                } else {
+                    assert!(ni.cmp(nj) < 0);
+                    assert!(nj.cmp(ni) > 0);
+
+                    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_convert_int() {
+        fn check(b: BigInt, i: int) {
+            assert!(b == IntConvertible::from_int(i));
+            assert!(b.to_int() == i);
+        }
+
+        check(Zero::zero(), 0);
+        check(One::one(), 1);
+        check(BigInt::from_biguint(
+            Plus, BigUint::from_uint(int::max_value as uint)
+        ), int::max_value);
+
+        assert!(BigInt::from_biguint(
+            Plus, BigUint::from_uint(int::max_value as uint + 1)
+        ).to_int() == int::max_value);
+        assert!(BigInt::from_biguint(
+            Plus, BigUint::new(~[1, 2, 3])
+        ).to_int() == int::max_value);
+
+        check(BigInt::from_biguint(
+            Minus, BigUint::from_uint(-int::min_value as uint)
+        ), int::min_value);
+        assert!(BigInt::from_biguint(
+            Minus, BigUint::from_uint(-int::min_value as uint + 1)
+        ).to_int() == int::min_value);
+        assert!(BigInt::from_biguint(
+            Minus, BigUint::new(~[1, 2, 3])
+        ).to_int() == int::min_value);
+    }
+
+    #[test]
+    fn test_convert_uint() {
+        fn check(b: BigInt, u: uint) {
+            assert!(b == BigInt::from_uint(u));
+            assert!(b.to_uint() == u);
+        }
+
+        check(Zero::zero(), 0);
+        check(One::one(), 1);
+
+        check(
+            BigInt::from_biguint(Plus, BigUint::from_uint(uint::max_value)),
+            uint::max_value);
+        assert!(BigInt::from_biguint(
+            Plus, BigUint::new(~[1, 2, 3])
+        ).to_uint() == uint::max_value);
+
+        assert!(BigInt::from_biguint(
+            Minus, BigUint::from_uint(uint::max_value)
+        ).to_uint() == 0);
+        assert!(BigInt::from_biguint(
+            Minus, BigUint::new(~[1, 2, 3])
+        ).to_uint() == 0);
+    }
+
+    static sum_triples: &'static [(&'static [BigDigit],
+                                   &'static [BigDigit],
+                                   &'static [BigDigit])] = &[
+        (&[],          &[],       &[]),
+        (&[],          &[ 1],     &[ 1]),
+        (&[ 1],        &[ 1],     &[ 2]),
+        (&[ 1],        &[ 1,  1], &[ 2,  1]),
+        (&[ 1],        &[-1],     &[ 0,  1]),
+        (&[ 1],        &[-1, -1], &[ 0,  0, 1]),
+        (&[-1, -1],    &[-1, -1], &[-2, -1, 1]),
+        (&[ 1,  1, 1], &[-1, -1], &[ 0,  1, 2]),
+        (&[ 2,  2, 1], &[-1, -2], &[ 1,  1, 2])
+    ];
+
+    #[test]
+    fn test_add() {
+        for sum_triples.each |elm| {
+            let (aVec, bVec, cVec) = *elm;
+            let a = BigInt::from_slice(Plus, aVec);
+            let b = BigInt::from_slice(Plus, bVec);
+            let c = BigInt::from_slice(Plus, cVec);
+
+            assert!(a + b == c);
+            assert!(b + a == c);
+            assert!(c + (-a) == b);
+            assert!(c + (-b) == a);
+            assert!(a + (-c) == (-b));
+            assert!(b + (-c) == (-a));
+            assert!((-a) + (-b) == (-c));
+            assert!(a + (-a) == Zero::zero());
+        }
+    }
+
+    #[test]
+    fn test_sub() {
+        for sum_triples.each |elm| {
+            let (aVec, bVec, cVec) = *elm;
+            let a = BigInt::from_slice(Plus, aVec);
+            let b = BigInt::from_slice(Plus, bVec);
+            let c = BigInt::from_slice(Plus, cVec);
+
+            assert!(c - a == b);
+            assert!(c - b == a);
+            assert!((-b) - a == (-c));
+            assert!((-a) - b == (-c));
+            assert!(b - (-a) == c);
+            assert!(a - (-b) == c);
+            assert!((-c) - (-a) == (-b));
+            assert!(a - a == Zero::zero());
+        }
+    }
+
+    static mul_triples: &'static [(&'static [BigDigit],
+                                   &'static [BigDigit],
+                                   &'static [BigDigit])] = &[
+        (&[],               &[],               &[]),
+        (&[],               &[ 1],             &[]),
+        (&[ 2],             &[],               &[]),
+        (&[ 1],             &[ 1],             &[1]),
+        (&[ 2],             &[ 3],             &[ 6]),
+        (&[ 1],             &[ 1,  1,  1],     &[1, 1,  1]),
+        (&[ 1,  2,  3],     &[ 3],             &[ 3,  6,  9]),
+        (&[ 1,  1,  1],     &[-1],             &[-1, -1, -1]),
+        (&[ 1,  2,  3],     &[-1],             &[-1, -2, -2, 2]),
+        (&[ 1,  2,  3,  4], &[-1],             &[-1, -2, -2, -2, 3]),
+        (&[-1],             &[-1],             &[ 1, -2]),
+        (&[-1, -1],         &[-1],             &[ 1, -1, -2]),
+        (&[-1, -1, -1],     &[-1],             &[ 1, -1, -1, -2]),
+        (&[-1, -1, -1, -1], &[-1],             &[ 1, -1, -1, -1, -2]),
+        (&[-1/2 + 1],       &[ 2],             &[ 0,  1]),
+        (&[0, -1/2 + 1],    &[ 2],             &[ 0,  0,  1]),
+        (&[ 1,  2],         &[ 1,  2,  3],     &[1, 4,  7,  6]),
+        (&[-1, -1],         &[-1, -1, -1],     &[1, 0, -1, -2, -1]),
+        (&[-1, -1, -1],     &[-1, -1, -1, -1], &[1, 0,  0, -1, -2, -1, -1]),
+        (&[ 0,  0,  1],     &[ 1,  2,  3],     &[0, 0,  1,  2,  3]),
+        (&[ 0,  0,  1],     &[ 0,  0,  0,  1], &[0, 0,  0,  0,  0,  1])
+    ];
+
+    static divmod_quadruples: &'static [(&'static [BigDigit],
+                                         &'static [BigDigit],
+                                         &'static [BigDigit],
+                                         &'static [BigDigit])]
+        = &[
+            (&[ 1],        &[ 2], &[],               &[1]),
+            (&[ 1,  1],    &[ 2], &[-1/2+1],         &[1]),
+            (&[ 1,  1, 1], &[ 2], &[-1/2+1, -1/2+1], &[1]),
+            (&[ 0,  1],    &[-1], &[1],              &[1]),
+            (&[-1, -1],    &[-2], &[2, 1],           &[3])
+        ];
+
+    #[test]
+    fn test_mul() {
+        for mul_triples.each |elm| {
+            let (aVec, bVec, cVec) = *elm;
+            let a = BigInt::from_slice(Plus, aVec);
+            let b = BigInt::from_slice(Plus, bVec);
+            let c = BigInt::from_slice(Plus, cVec);
+
+            assert!(a * b == c);
+            assert!(b * a == c);
+
+            assert!((-a) * b == -c);
+            assert!((-b) * a == -c);
+        }
+
+        for divmod_quadruples.each |elm| {
+            let (aVec, bVec, cVec, dVec) = *elm;
+            let a = BigInt::from_slice(Plus, aVec);
+            let b = BigInt::from_slice(Plus, bVec);
+            let c = BigInt::from_slice(Plus, cVec);
+            let d = BigInt::from_slice(Plus, dVec);
+
+            assert!(a == b * c + d);
+            assert!(a == c * b + d);
+        }
+    }
+
+    #[test]
+    fn test_divmod() {
+        fn check_sub(a: &BigInt, b: &BigInt, ans_d: &BigInt, ans_m: &BigInt) {
+            let (d, m) = a.divmod(b);
+            if m.is_not_zero() {
+                assert!(m.sign == b.sign);
+            }
+            assert!(m.abs() <= b.abs());
+            assert!(*a == b * d + m);
+            assert!(d == *ans_d);
+            assert!(m == *ans_m);
+        }
+
+        fn check(a: &BigInt, b: &BigInt, d: &BigInt, m: &BigInt) {
+            if m.is_zero() {
+                check_sub(a, b, d, m);
+                check_sub(a, &b.neg(), &d.neg(), m);
+                check_sub(&a.neg(), b, &d.neg(), m);
+                check_sub(&a.neg(), &b.neg(), d, m);
+            } else {
+                check_sub(a, b, d, m);
+                check_sub(a, &b.neg(), &(d.neg() - One::one()), &(m - *b));
+                check_sub(&a.neg(), b, &(d.neg() - One::one()), &(b - *m));
+                check_sub(&a.neg(), &b.neg(), d, &m.neg());
+            }
+        }
+
+        for mul_triples.each |elm| {
+            let (aVec, bVec, cVec) = *elm;
+            let a = BigInt::from_slice(Plus, aVec);
+            let b = BigInt::from_slice(Plus, bVec);
+            let c = BigInt::from_slice(Plus, cVec);
+
+            if a.is_not_zero() { check(&c, &a, &b, &Zero::zero()); }
+            if b.is_not_zero() { check(&c, &b, &a, &Zero::zero()); }
+        }
+
+        for divmod_quadruples.each |elm| {
+            let (aVec, bVec, cVec, dVec) = *elm;
+            let a = BigInt::from_slice(Plus, aVec);
+            let b = BigInt::from_slice(Plus, bVec);
+            let c = BigInt::from_slice(Plus, cVec);
+            let d = BigInt::from_slice(Plus, dVec);
+
+            if b.is_not_zero() {
+                check(&a, &b, &c, &d);
+            }
+        }
+    }
+
+
+    #[test]
+    fn test_quotrem() {
+        fn check_sub(a: &BigInt, b: &BigInt, ans_q: &BigInt, ans_r: &BigInt) {
+            let (q, r) = a.quotrem(b);
+            if r.is_not_zero() {
+                assert!(r.sign == a.sign);
+            }
+            assert!(r.abs() <= b.abs());
+            assert!(*a == b * q + r);
+            assert!(q == *ans_q);
+            assert!(r == *ans_r);
+        }
+
+        fn check(a: &BigInt, b: &BigInt, q: &BigInt, r: &BigInt) {
+            check_sub(a, b, q, r);
+            check_sub(a, &b.neg(), &q.neg(), r);
+            check_sub(&a.neg(), b, &q.neg(), &r.neg());
+            check_sub(&a.neg(), &b.neg(), q, &r.neg());
+        }
+        for mul_triples.each |elm| {
+            let (aVec, bVec, cVec) = *elm;
+            let a = BigInt::from_slice(Plus, aVec);
+            let b = BigInt::from_slice(Plus, bVec);
+            let c = BigInt::from_slice(Plus, cVec);
+
+            if a.is_not_zero() { check(&c, &a, &b, &Zero::zero()); }
+            if b.is_not_zero() { check(&c, &b, &a, &Zero::zero()); }
+        }
+
+        for divmod_quadruples.each |elm| {
+            let (aVec, bVec, cVec, dVec) = *elm;
+            let a = BigInt::from_slice(Plus, aVec);
+            let b = BigInt::from_slice(Plus, bVec);
+            let c = BigInt::from_slice(Plus, cVec);
+            let d = BigInt::from_slice(Plus, dVec);
+
+            if b.is_not_zero() {
+                check(&a, &b, &c, &d);
+            }
+        }
+    }
+
+    #[test]
+    fn test_to_str_radix() {
+        fn check(n: int, ans: &str) {
+            assert!(ans == IntConvertible::from_int::<BigInt>(
+                n).to_str_radix(10));
+        }
+        check(10, "10");
+        check(1, "1");
+        check(0, "0");
+        check(-1, "-1");
+        check(-10, "-10");
+    }
+
+
+    #[test]
+    fn test_from_str_radix() {
+        fn check(s: &str, ans: Option<int>) {
+            let ans = ans.map(|&n| IntConvertible::from_int(n));
+            assert!(BigInt::from_str_radix(s, 10) == ans);
+        }
+        check("10", Some(10));
+        check("1", Some(1));
+        check("0", Some(0));
+        check("-1", Some(-1));
+        check("-10", Some(-10));
+        check("Z", None);
+        check("_", None);
+    }
+
+    #[test]
+    fn test_neg() {
+        assert!(-BigInt::new(Plus,  ~[1, 1, 1]) ==
+            BigInt::new(Minus, ~[1, 1, 1]));
+        assert!(-BigInt::new(Minus, ~[1, 1, 1]) ==
+            BigInt::new(Plus,  ~[1, 1, 1]));
+        assert!(-Zero::zero::<BigInt>() == Zero::zero::<BigInt>());
+    }
+}
+