diff --git a/src/libstd/bigint.rs b/src/libstd/bigint.rs new file mode 100644 index 000000000000..b66b7c61900a --- /dev/null +++ b/src/libstd/bigint.rs @@ -0,0 +1,663 @@ +/*! + +A Big signed integer. + +A BigInt is a combination of BigUint and Sign. +*/ + +use core::cmp::{Eq, Ord}; + +use biguint::{BigDigit, BigUint}; + +/// A Sign is a BigInt's composing element. +pub enum Sign { Minus, Zero, Plus } + +impl Sign : Eq { + pure fn eq(&self, other: &Sign) -> bool { self.cmp(other) == 0 } + pure fn ne(&self, other: &Sign) -> bool { self.cmp(other) != 0 } +} + +impl Sign : Ord { + pure fn lt(&self, other: &Sign) -> bool { self.cmp(other) < 0 } + pure fn le(&self, other: &Sign) -> bool { self.cmp(other) <= 0 } + pure fn ge(&self, other: &Sign) -> bool { self.cmp(other) >= 0 } + pure fn gt(&self, other: &Sign) -> bool { self.cmp(other) > 0 } +} + +pub impl Sign { + /// Compare two Sign. + pure fn cmp(other: &Sign) -> int { + match (self, *other) { + (Minus, Minus) | (Zero, Zero) | (Plus, Plus) => 0, + (Minus, Zero) | (Minus, Plus) | (Zero, Plus) => -1, + _ => 1 + } + } + + /// Negate Sign value. + pure fn neg() -> Sign { + match(self) { + Minus => Plus, + Zero => Zero, + Plus => Minus + } + } +} + +/// A big signed integer type. +pub struct BigInt { + priv sign: Sign, + priv data: BigUint +} + +impl BigInt : Eq { + pure fn eq(&self, other: &BigInt) -> bool { self.cmp(other) == 0 } + pure fn ne(&self, other: &BigInt) -> bool { self.cmp(other) != 0 } +} + +impl BigInt : Ord { + pure fn lt(&self, other: &BigInt) -> bool { self.cmp(other) < 0 } + pure fn le(&self, other: &BigInt) -> bool { self.cmp(other) <= 0 } + pure fn ge(&self, other: &BigInt) -> bool { self.cmp(other) >= 0 } + pure fn gt(&self, other: &BigInt) -> bool { self.cmp(other) > 0 } +} + +impl BigInt : ToStr { + pure fn to_str() -> ~str { self.to_str_radix(10) } +} + +impl BigInt : from_str::FromStr { + static pure fn from_str(s: &str) -> Option { + BigInt::from_str_radix(s, 10) + } +} + +impl BigInt : Shl { + pure fn shl(&self, rhs: &uint) -> BigInt { + BigInt::from_biguint(self.sign, self.data << *rhs) + } +} + +impl BigInt : Shr { + pure fn shr(&self, rhs: &uint) -> BigInt { + BigInt::from_biguint(self.sign, self.data >> *rhs) + } +} + +impl BigInt : Num { + pure fn add(&self, other: &BigInt) -> BigInt { + match (self.sign, other.sign) { + (Zero, _) => *other, + (_, Zero) => *self, + (Plus, Plus) => BigInt::from_biguint(Plus, + self.data + other.data), + (Plus, Minus) => self - (-*other), + (Minus, Plus) => other - (-*self), + (Minus, Minus) => -((-self) + (-*other)) + } + } + pure fn sub(&self, other: &BigInt) -> BigInt { + match (self.sign, other.sign) { + (Zero, _) => -other, + (_, Zero) => *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), + _ => + BigInt::zero() + }, + (Plus, Minus) => self + (-*other), + (Minus, Plus) => -((-self) + *other), + (Minus, Minus) => (-other) - (-*self) + } + } + pure fn mul(&self, other: &BigInt) -> BigInt { + match (self.sign, other.sign) { + (Zero, _) | (_, Zero) => BigInt::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) + } + } + } + pure fn div(&self, other: &BigInt) -> BigInt { + self.divmod(other).first() + } + pure fn modulo(&self, other: &BigInt) -> BigInt { + self.divmod(other).second() + } + pure fn neg(&self) -> BigInt { + BigInt::from_biguint(self.sign.neg(), self.data) + } + + pure 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 + } + } + + static pure 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 BigInt::zero(); + } +} + +pub impl BigInt { + /// Creates and initializes an BigInt. + static pub pure fn from_biguint(sign: Sign, data: BigUint) -> BigInt { + if sign == Zero || data.is_zero() { + return BigInt { sign: Zero, data: BigUint::zero() }; + } + return BigInt { sign: sign, data: data }; + } + + /// Creates and initializes an BigInt. + static pub pure fn from_uint(n: uint) -> BigInt { + if n == 0 { return BigInt::zero(); } + return BigInt::from_biguint(Plus, BigUint::from_uint(n)); + } + + /// Creates and initializes an BigInt. + static pub pure fn from_slice(sign: Sign, slice: &[BigDigit]) -> BigInt { + BigInt::from_biguint(sign, BigUint::from_slice(slice)) + } + + /// Creates and initializes an BigInt. + static pub pure fn from_at_vec(sign: Sign, at_vec: @[BigDigit]) + -> BigInt { + BigInt::from_biguint(sign, BigUint::from_at_vec(at_vec)) + } + + /// Creates and initializes an BigInt. + static pub pure fn from_str_radix(s: &str, radix: uint) + -> Option { + BigInt::parse_bytes(str::to_bytes(s), radix) + } + + /// Creates and initializes an BigInt. + static pub pure fn parse_bytes(buf: &[u8], radix: uint) + -> Option { + 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::view(buf, start, buf.len()), radix) + .map(|bu| BigInt::from_biguint(sign, *bu)); + } + + static pub pure fn zero() -> BigInt { + BigInt::from_biguint(Zero, BigUint::zero()) + } + static pub pure fn one() -> BigInt { + BigInt::from_biguint(Plus, BigUint::one()) + } + + pure fn abs() -> BigInt { BigInt::from_biguint(Plus, self.data) } + + pure fn cmp(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(), + } + } + + pure fn divmod(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, BigInt::zero()) + } else { + (-d - BigInt::one(), m + *other) + }, + (Minus, Plus) => if m.is_zero() { + (-d, BigInt::zero()) + } else { + (-d - BigInt::one(), other - m) + }, + (Minus, Minus) => (d, -m) + } + } + + pure fn quot(other: &BigInt) -> BigInt { self.quotrem(other).first() } + pure fn rem(other: &BigInt) -> BigInt { self.quotrem(other).second() } + + pure fn quotrem(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) + } + } + + pure fn is_zero() -> bool { self.sign == Zero } + pure fn is_not_zero() -> bool { self.sign != Zero } + pure fn is_positive() -> bool { self.sign == Plus } + pure fn is_negative() -> bool { self.sign == Minus } + pure fn is_nonpositive() -> bool { self.sign != Plus } + pure fn is_nonnegative() -> bool { self.sign != Minus } + + pure fn to_uint() -> uint { + match self.sign { + Plus => self.data.to_uint(), + Zero => 0, + Minus => 0 + } + } + + pure fn to_str_radix(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 tests { + #[test] + fn test_from_biguint() { + assert BigInt::from_biguint(Plus, BigUint::from_uint(1)) == + BigInt { sign: Plus, data: BigUint::from_uint(1) }; + assert BigInt::from_biguint(Plus, BigUint::zero()) == + BigInt { sign: Zero, data: BigUint::zero() }; + assert BigInt::from_biguint(Minus, BigUint::from_uint(1)) == + BigInt { sign: Minus, data: BigUint::from_uint(1) }; + assert BigInt::from_biguint(Zero, BigUint::from_uint(1)) == + BigInt { sign: Zero, data: BigUint::zero() }; + } + + #[test] + fn test_cmp() { + let uints = [ &[2], &[1, 1], &[2, 1], &[1, 1, 1] ] + .map(|data| BigUint::from_slice(*data)); + let nums: ~[BigInt] + = vec::reversed(uints).map(|bu| BigInt::from_biguint(Minus, *bu)) + + [ BigInt::zero() ] + + uints.map(|bu| BigInt::from_biguint(Plus, *bu)); + + for nums.eachi |i, ni| { + for vec::view(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_conv(b: BigInt, i: int) { + assert b == num::from_int(i); + assert b.to_int() == i; + } + + check_conv(BigInt::zero(), 0); + check_conv(BigInt::one(), 1); + check_conv( + 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::from_at_vec(@[1, 2, 3]) + ).to_int() == int::max_value; + + check_conv( + 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::from_at_vec(@[1, 2, 3]) + ).to_int() == int::min_value; + } + + #[test] + fn test_convert_uint() { + fn check_conv(b: BigInt, u: uint) { + assert b == BigInt::from_uint(u); + assert b.to_uint() == u; + } + + check_conv(BigInt::zero(), 0); + check_conv(BigInt::one(), 1); + + check_conv( + BigInt::from_biguint(Plus, BigUint::from_uint(uint::max_value)), + uint::max_value); + assert BigInt::from_biguint( + Plus, BigUint::from_at_vec(@[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::from_at_vec(@[1, 2, 3]) + ).to_uint() == 0; + } + + const sum_triples: &[(&[BigDigit], &[BigDigit], &[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) == BigInt::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 == BigInt::zero(); + } + } + + const mul_triples: &[(&[BigDigit], &[BigDigit], &[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]) + ]; + + const divmod_quadruples: &[(&[BigDigit], &[BigDigit], + &[BigDigit], &[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_divmod_sub(a: BigInt, b: 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; + } + fn check_divmod(a: BigInt, b: BigInt, c: BigInt, d: BigInt) { + check_divmod_sub(a, b); + check_divmod_sub(a, -b); + check_divmod_sub(-a, b); + check_divmod_sub(-a, -b); + + if d.is_zero() { + assert a.divmod(&b) == (c, BigInt::zero()); + assert (-a).divmod(&b) == (-c, BigInt::zero()); + assert (a).divmod(&-b) == (-c, BigInt::zero()); + assert (-a).divmod(&-b) == (c, BigInt::zero()); + } else { + // a == bc + d + assert a.divmod(&b) == (c, d); + // a == (-b)(-c - 1) + (d - b) + assert a.divmod(&-b) == (-c - BigInt::one(), d - b); + // (-a) == b (-c - 1) + (b - d) + assert (-a).divmod(&b) == (-c - BigInt::one(), b - d); + // (-a) == (-b)(c) - d + assert (-a).divmod(&-b) == (c, -d); + } + } + 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_divmod(c, a, b, BigInt::zero()); } + if b.is_not_zero() { check_divmod(c, b, a, BigInt::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_divmod(a, b, c, d); + } + } + } + + + #[test] + fn test_quotrem() { + fn check_quotrem_sub(a: BigInt, b: 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; + } + fn check_quotrem(a: BigInt, b: BigInt, c: BigInt, d: BigInt) { + check_quotrem_sub(a, b); + check_quotrem_sub(a, -b); + check_quotrem_sub(-a, b); + check_quotrem_sub(-a, -b); + + if d.is_zero() { + assert a.quotrem(&b) == (c, BigInt::zero()); + assert (-a).quotrem(&b) == (-c, BigInt::zero()); + assert (a).quotrem(&-b) == (-c, BigInt::zero()); + assert (-a).quotrem(&-b) == (c, BigInt::zero()); + } else { + // a == bc + d + assert a.quotrem(&b) == (c, d); + // a == (-b)(-c) + d + assert a.quotrem(&-b) == (-c, d); + // (-a) == b (-c) + (-d) + assert (-a).quotrem(&b) == (-c, -d); + // (-a) == (-b)(c) - d + assert (-a).quotrem(&-b) == (c, -d); + } + } + 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_quotrem(c, a, b, BigInt::zero()); } + if b.is_not_zero() { check_quotrem(c, b, a, BigInt::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_quotrem(a, b, c, d); + } + } + } + + #[test] + fn test_to_str_radix() { + assert BigInt::from_biguint(Plus, BigUint::from_uint(10)) + .to_str_radix(10) == ~"10"; + assert BigInt::one().to_str_radix(10) == ~"1"; + assert BigInt::zero().to_str_radix(10) == ~"0"; + assert (-BigInt::one()).to_str_radix(10) == ~"-1"; + assert BigInt::from_biguint(Minus, BigUint::from_uint(10)) + .to_str_radix(10) == ~"-10"; + } + + + #[test] + fn test_from_str_radix() { + assert BigInt::from_biguint(Plus, BigUint::from_uint(10)) == + BigInt::from_str_radix(~"10", 10).get(); + assert BigInt::one()== BigInt::from_str_radix(~"1", 10).get(); + assert BigInt::zero() == BigInt::from_str_radix(~"0", 10).get(); + assert (-BigInt::one()) == BigInt::from_str_radix(~"-1", 10).get(); + assert BigInt::from_biguint(Minus, BigUint::from_uint(10)) == + BigInt::from_str_radix(~"-10", 10).get(); + + assert BigInt::from_str_radix(~"Z", 10) == None; + assert BigInt::from_str_radix(~"_", 2) == None; + assert BigInt::from_str_radix(~"-1", 10) == + Some(BigInt::from_biguint(Minus, BigUint::one())); + } + + #[test] + fn test_neg() { + assert -BigInt::from_at_vec(Plus, @[1, 1, 1]) == + BigInt::from_at_vec(Minus, @[1, 1, 1]); + assert -BigInt::from_at_vec(Minus, @[1, 1, 1]) == + BigInt::from_at_vec(Plus, @[1, 1, 1]); + assert -BigInt::zero() == BigInt::zero(); + } +} + diff --git a/src/libstd/biguint.rs b/src/libstd/biguint.rs new file mode 100644 index 000000000000..63cedbc1369d --- /dev/null +++ b/src/libstd/biguint.rs @@ -0,0 +1,840 @@ +/*! + +A Big unsigned integer. + +A BigUint is represented as an array of BigDigits. +*/ + +use core::cmp::{Eq, Ord}; + +/** +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")] +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 { + #[cfg(target_arch = "x86")] + #[cfg(target_arch = "arm")] + pub const bits: uint = 16; + + #[cfg(target_arch = "x86_64")] + pub const bits: uint = 32; + + pub const base: uint = 1 << bits; + priv const hi_mask: uint = (-1 as uint) << bits; + priv const lo_mask: uint = (-1 as uint) >> bits; + + priv pure fn get_hi(n: uint) -> BigDigit { (n >> bits) as BigDigit } + priv pure fn get_lo(n: uint) -> BigDigit { (n & lo_mask) as BigDigit } + + /// Split one machine sized unsigned integer into two BigDigits. + pub pure fn from_uint(n: uint) -> (BigDigit, BigDigit) { + (get_hi(n), get_lo(n)) + } + + /// Join two BigDigits into one machine sized unsigned integer + pub pure 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 BigUint : Eq { + pure fn eq(&self, other: &BigUint) -> bool { self.cmp(other) == 0 } + pure fn ne(&self, other: &BigUint) -> bool { self.cmp(other) != 0 } +} + +impl BigUint : Ord { + pure fn lt(&self, other: &BigUint) -> bool { self.cmp(other) < 0 } + pure fn le(&self, other: &BigUint) -> bool { self.cmp(other) <= 0 } + pure fn ge(&self, other: &BigUint) -> bool { self.cmp(other) >= 0 } + pure fn gt(&self, other: &BigUint) -> bool { self.cmp(other) > 0 } +} + +impl BigUint : ToStr { + pure fn to_str() -> ~str { self.to_str_radix(10) } +} + +impl BigUint : from_str::FromStr { + static pure fn from_str(s: &str) -> Option { + BigUint::from_str_radix(s, 10) + } +} + +impl BigUint : Shl { + pure 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 BigUint : Shr { + pure 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 BigUint : Num { + pure fn add(&self, other: &BigUint) -> BigUint { + let new_len = uint::max(self.data.len(), other.data.len()); + + let mut carry = 0; + let sum = do at_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::from_at_vec(sum) }; + return BigUint::from_at_vec(sum + [carry]); + } + + pure fn sub(&self, other: &BigUint) -> BigUint { + let new_len = uint::max(self.data.len(), other.data.len()); + + let mut borrow = 0; + let diff = do at_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::from_at_vec(diff); + } + + pure fn mul(&self, other: &BigUint) -> BigUint { + if self.is_zero() || other.is_zero() { return BigUint::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 = match (sub_sign(sHi, sLo), sub_sign(oHi, oLo)) { + ((s1, n1), (s2, n2)) if s1 * s2 < 0 => hh + ll + (n1 * n2), + ((s1, n1), (s2, n2)) if s1 * s2 > 0 => hh + ll - (n1 * n2), + _ => hh + ll, + }; + + return ll + mm.shl_unit(half_len) + hh.shl_unit(half_len * 2); + + pure fn mul_digit(a: &BigUint, n: BigDigit) -> BigUint { + if n == 0 { return BigUint::zero(); } + if n == 1 { return *a; } + + let mut carry = 0; + let prod = do at_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::from_at_vec(prod) }; + return BigUint::from_at_vec(prod + [carry]); + } + + pure fn cut_at(a: &BigUint, n: uint) -> (BigUint, BigUint) { + let mid = uint::min(a.data.len(), n); + return (BigUint::from_slice(vec::view(a.data, mid, a.data.len())), + BigUint::from_slice(vec::view(a.data, 0, mid))); + } + + pure 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, BigUint::zero()) + } + } + } + + pure fn div(&self, other: &BigUint) -> BigUint{ + self.divmod(other).first() + } + pure fn modulo(&self, other: &BigUint) -> BigUint { + self.divmod(other).second() + } + + pure fn neg(&self) -> BigUint { fail } + + pure fn to_int(&self) -> int { + uint::min(self.to_uint(), int::max_value as uint) as int + } + + static pure fn from_int(n: int) -> BigUint { + if (n < 0) { BigUint::zero() } else { BigUint::from_uint(n as uint) } + } +} + +pub impl BigUint { + /// Creates and initializes an BigUint. + static pub pure fn from_uint(n: uint) -> BigUint { + match BigDigit::from_uint(n) { + (0, 0) => BigUint::zero(), + (0, n0) => BigUint::from_at_vec(@[n0]), + (n1, n0) => BigUint::from_at_vec(@[n0, n1]) + } + } + + /// Creates and initializes an BigUint. + static pub pure fn from_slice(slice: &[BigDigit]) -> BigUint { + // omit trailing zeros + let new_len = slice.rposition(|n| *n != 0) + .map_default(0, |p| *p + 1); + + return BigUint { data: at_vec::from_fn(new_len, |i| slice[i]) }; + } + + /// Creates and initializes an BigUint. + static pub pure fn from_at_vec(at_vec: @[BigDigit]) -> BigUint { + // omit trailing zeros + let new_len = at_vec.rposition(|n| *n != 0) + .map_default(0, |p| *p + 1); + + if new_len == at_vec.len() { return BigUint { data: at_vec }; } + return BigUint { data: at_vec::from_fn(new_len, |i| at_vec[i]) }; + } + + /// Creates and initializes an BigUint. + static pub pure fn from_str_radix(s: &str, radix: uint) + -> Option { + BigUint::parse_bytes(str::to_bytes(s), radix) + } + + /// Creates and initializes an BigUint. + static pub pure fn parse_bytes(buf: &[u8], radix: uint) + -> Option { + 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 = BigUint::zero(); + let mut power: BigUint = BigUint::one(); + loop { + let start = uint::max(end, unit_len) - unit_len; + match uint::parse_bytes(vec::view(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; + } + } + + static pub pure fn zero() -> BigUint { BigUint::from_at_vec(@[]) } + static pub pure fn one() -> BigUint { BigUint::from_at_vec(@[1]) } + + pure fn abs() -> BigUint { self } + + /// Compare two BigUint value. + pure fn cmp(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 vec::rev_eachi(self.data) |i, elm| { + match (*elm, other.data[i]) { + (l, r) if l < r => return -1, + (l, r) if l > r => return 1, + _ => loop + }; + } + return 0; + } + + pure fn divmod(other: &BigUint) -> (BigUint, BigUint) { + if other.is_zero() { fail } + if self.is_zero() { return (BigUint::zero(), BigUint::zero()); } + if *other == BigUint::one() { return (self, BigUint::zero()); } + + match self.cmp(other) { + s if s < 0 => return (BigUint::zero(), self), + 0 => return (BigUint::one(), BigUint::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); + + + pure fn divmod_inner(a: BigUint, b: BigUint) -> (BigUint, BigUint) { + let mut r = a; + let mut d = BigUint::zero(); + 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); + } + + pure fn div_estimate(a: BigUint, b: BigUint, n: uint) + -> (BigUint, BigUint, BigUint) { + if a.data.len() < n { + return (BigUint::zero(), BigUint::zero(), a); + } + + let an = vec::view(a.data, a.data.len() - n, a.data.len()); + let bn = b.data.last(); + let mut d = ~[]; + let mut carry = 0; + for vec::rev_each(an) |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); + return (BigUint::from_slice(d).shl_unit(shift), + BigUint::one().shl_unit(shift), + b.shl_unit(shift)); + } + } + + pure fn quot(other: &BigUint) -> BigUint { self.quotrem(other).first() } + pure fn rem(other: &BigUint) -> BigUint { self.quotrem(other).second() } + pure fn quotrem(other: &BigUint) -> (BigUint, BigUint) { + self.divmod(other) + } + + pure fn is_zero() -> bool { self.data.is_empty() } + pure fn is_not_zero() -> bool { self.data.is_not_empty() } + pure fn is_positive() -> bool { self.is_not_zero() } + pure fn is_negative() -> bool { false } + pure fn is_nonpositive() -> bool { self.is_zero() } + pure fn is_nonnegative() -> bool { true } + + pure fn to_uint() -> 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 + } + } + + pure fn to_str_radix(radix: uint) -> ~str { + assert 1 < radix && radix <= 16; + + pure fn convert_base(n: BigUint, base: uint) -> @[BigDigit] { + if base == BigDigit::base { return n.data; } + let divider = BigUint::from_uint(base); + let mut result = @[]; + let mut r = n; + while r > divider { + let (d, r0) = r.divmod(÷r); + result += [r0.to_uint() as BigDigit]; + r = d; + } + if r.is_not_zero() { + result += [r.to_uint() as BigDigit]; + } + return result; + } + + pure fn fill_concat(v: &[BigDigit], radix: uint, l: uint) -> ~str { + if v.is_empty() { return ~"0" } + str::trim_left_chars(str::concat(vec::reversed(v).map(|n| { + let s = uint::to_str(*n as uint, radix); + str::from_chars(vec::from_elem(l - s.len(), '0')) + s + })), ['0']) + } + + let (base, max_len) = get_radix_base(radix); + return fill_concat(convert_base(self, base), radix, max_len); + } + + priv pure fn shl_unit(n_unit: uint) -> BigUint { + if n_unit == 0 || self.is_zero() { return self; } + + return BigUint::from_at_vec(at_vec::from_elem(n_unit, 0) + self.data); + } + + priv pure fn shl_bits(n_bits: uint) -> BigUint { + if n_bits == 0 || self.is_zero() { return self; } + + let mut carry = 0; + let shifted = do at_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::from_at_vec(shifted); } + return BigUint::from_at_vec(shifted + [carry]); + } + + priv pure fn shr_unit(n_unit: uint) -> BigUint { + if n_unit == 0 { return self; } + if self.data.len() < n_unit { return BigUint::zero(); } + return BigUint::from_slice( + vec::view(self.data, n_unit, self.data.len()) + ); + } + + priv pure fn shr_bits(n_bits: uint) -> BigUint { + if n_bits == 0 || self.data.is_empty() { return self; } + + let mut borrow = 0; + let mut shifted = @[]; + for vec::rev_each(self.data) |elem| { + // internal compiler error: no enclosing scope with id 10671 + // shifted = @[(*elem >> n_bits) | borrow] + shifted; + shifted = at_vec::append(@[(*elem >> n_bits) | borrow], shifted); + borrow = *elem << (uint::bits - n_bits); + } + return BigUint::from_at_vec(shifted); + } +} + +priv pure 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(test)] +mod tests { + #[test] + fn test_from_slice() { + let pairs = [ + (&[1], &[1]), + (&[0, 0], &[]), + (&[1, 2, 0, 0], &[1, 2]), + (&[0, 0, 1, 2, 0, 0], &[0, 0, 1, 2]), + (&[-1], &[-1]) + ]; + for pairs.each |p| { + assert p.second() == BigUint::from_slice(p.first()).data; + } + } + + #[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::view(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() { + assert BigUint::from_at_vec(@[]) << 3 == BigUint::from_at_vec(@[]); + assert BigUint::from_at_vec(@[1, 1, 1]) << 3 == + BigUint::from_at_vec(@[1 << 3, 1 << 3, 1 << 3]); + + assert BigUint::from_at_vec(@[1 << (BigDigit::bits - 2)]) << 2 == + BigUint::from_at_vec(@[0, 1]); + assert BigUint::from_at_vec(@[1 << (BigDigit::bits - 2)]) << 3 == + BigUint::from_at_vec(@[0, 2]); + assert (BigUint::from_at_vec(@[1 << (BigDigit::bits - 2)]) + << (3 + BigDigit::bits)) == + BigUint::from_at_vec(@[0, 0, 2]); + + assert BigUint::from_at_vec( + @[0x7654_3210, 0xfedc_ba98, 0x7654_3210, 0xfedc_ba98] + ) << 4 == BigUint::from_at_vec( + @[0x6543_2100, 0xedcb_a987, 0x6543_210f, 0xedcb_a987, 0xf] + ); + assert BigUint::from_at_vec( + @[0x2222_1111, 0x4444_3333, 0x6666_5555, 0x8888_7777] + ) << 16 == BigUint::from_at_vec( + @[0x1111_0000, 0x3333_2222, 0x5555_4444, 0x7777_6666, 0x8888] + ); + } + + #[test] + fn test_shr() { + assert BigUint::from_at_vec(@[]) >> 3 == BigUint::from_at_vec(@[]); + assert BigUint::from_at_vec(@[1, 1, 1]) >> 3 == BigUint::from_at_vec( + @[1 << (BigDigit::bits - 3), 1 << (BigDigit::bits - 3)] + ); + + assert BigUint::from_at_vec(@[1 << 2]) >> 2 == + BigUint::from_at_vec(@[1]); + assert BigUint::from_at_vec(@[1, 2]) >> 3 == + BigUint::from_at_vec(@[1 << (BigDigit::bits - 2)]); + assert BigUint::from_at_vec(@[1, 1, 2]) >> (3 + BigDigit::bits) == + BigUint::from_at_vec(@[1 << (BigDigit::bits - 2)]); + + assert BigUint::from_at_vec( + @[0x6543_2100, 0xedcb_a987, 0x6543_210f, 0xedcb_a987, 0xf] + ) >> 4 == BigUint::from_at_vec( + @[0x7654_3210, 0xfedc_ba98, 0x7654_3210, 0xfedc_ba98] + ); + + assert BigUint::from_at_vec( + @[0x1111_0000, 0x3333_2222, 0x5555_4444, 0x7777_6666, 0x8888] + ) >> 16 == BigUint::from_at_vec( + @[0x2222_1111, 0x4444_3333, 0x6666_5555, 0x8888_7777] + ); + } + + #[test] + fn test_convert_int() { + fn check_conv(b: BigUint, i: int) { + assert b == num::from_int(i); + assert b.to_int() == i; + } + + check_conv(BigUint::zero(), 0); + check_conv(BigUint::from_at_vec(@[1]), 1); + + check_conv(BigUint::from_at_vec(@[-1]), + (uint::max_value >> BigDigit::bits) as int); + check_conv(BigUint::from_at_vec(@[ 0, 1]), + ((uint::max_value >> BigDigit::bits) + 1) as int); + check_conv(BigUint::from_at_vec(@[-1, -1 >> 1]), + int::max_value); + + assert BigUint::from_at_vec(@[0, -1]).to_int() == int::max_value; + assert BigUint::from_at_vec(@[0, 0, 1]).to_int() == int::max_value; + assert BigUint::from_at_vec(@[0, 0, -1]).to_int() == int::max_value; + } + + #[test] + fn test_convert_uint() { + fn check_conv(b: BigUint, u: uint) { + assert b == BigUint::from_uint(u); + assert b.to_uint() == u; + } + + check_conv(BigUint::zero(), 0); + check_conv(BigUint::from_at_vec(@[ 1]), 1); + check_conv(BigUint::from_at_vec(@[-1]), + uint::max_value >> BigDigit::bits); + check_conv(BigUint::from_at_vec(@[ 0, 1]), + (uint::max_value >> BigDigit::bits) + 1); + check_conv(BigUint::from_at_vec(@[ 0, -1]), + uint::max_value << BigDigit::bits); + check_conv(BigUint::from_at_vec(@[-1, -1]), + uint::max_value); + + assert BigUint::from_at_vec(@[0, 0, 1]).to_uint() == uint::max_value; + assert BigUint::from_at_vec(@[0, 0, -1]).to_uint() == uint::max_value; + } + + const sum_triples: &[(&[BigDigit], &[BigDigit], &[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; + } + } + + const mul_triples: &[(&[BigDigit], &[BigDigit], &[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]) + ]; + + const divmod_quadruples: &[(&[BigDigit], &[BigDigit], + &[BigDigit], &[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, BigUint::zero()); + } + if b.is_not_zero() { + assert c.divmod(&b) == (a, BigUint::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)]) ] { + ~[( BigUint::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(31, '0')) + "1"), + (4, ~"2" + str::from_chars(vec::from_elem(15, '0')) + "1"), + (10, ~"8589934593"), + (16, ~"2" + str::from_chars(vec::from_elem(7, '0')) + "1") + ]), (BigUint::from_slice([ 1, 2, 3 ]), ~[ + (2, ~"11" + str::from_chars(vec::from_elem(30, '0')) + "10" + + str::from_chars(vec::from_elem(31, '0')) + "1"), + (4, ~"3" + str::from_chars(vec::from_elem(15, '0')) + "2" + + str::from_chars(vec::from_elem(15, '0')) + "1"), + (10, ~"55340232229718589441"), + (16, ~"3" + str::from_chars(vec::from_elem(7, '0')) + "2" + + str::from_chars(vec::from_elem(7, '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= BigUint::one(); + for uint::range(2, n + 1) |i| { + f *= BigUint::from_uint(i); + } + return f; + } + + assert factor(3) == BigUint::from_str_radix(~"6", 10).get(); + assert factor(10) == BigUint::from_str_radix(~"3628800", 10).get(); + assert factor(20) == BigUint::from_str_radix( + ~"2432902008176640000", 10).get(); + assert factor(30) == BigUint::from_str_radix( + ~"265252859812191058636308480000000", 10).get(); + } +} diff --git a/src/libstd/std.rc b/src/libstd/std.rc index eb3a74108280..4820068098f1 100644 --- a/src/libstd/std.rc +++ b/src/libstd/std.rc @@ -98,6 +98,8 @@ pub mod cmp; pub mod base64; pub mod rl; pub mod workcache; +pub mod bigint; +pub mod biguint; #[cfg(unicode)] mod unicode;