| #[allow(deprecated, unused_imports)] |
| use std::ascii::AsciiExt; |
| use std::borrow::Cow; |
| use std::cmp; |
| use std::cmp::Ordering::{self, Equal, Greater, Less}; |
| use std::default::Default; |
| use std::fmt; |
| use std::iter::{Product, Sum}; |
| use std::mem; |
| use std::ops::{ |
| Add, AddAssign, BitAnd, BitAndAssign, BitOr, BitOrAssign, BitXor, BitXorAssign, Div, DivAssign, |
| Mul, MulAssign, Neg, Rem, RemAssign, Shl, ShlAssign, Shr, ShrAssign, Sub, SubAssign, |
| }; |
| use std::str::{self, FromStr}; |
| use std::{f32, f64}; |
| use std::{u64, u8}; |
| |
| #[cfg(feature = "serde")] |
| use serde; |
| |
| use integer::{Integer, Roots}; |
| use traits::{ |
| CheckedAdd, CheckedDiv, CheckedMul, CheckedSub, Float, FromPrimitive, Num, One, Pow, |
| ToPrimitive, Unsigned, Zero, |
| }; |
| |
| use big_digit::{self, BigDigit}; |
| |
| #[path = "algorithms.rs"] |
| mod algorithms; |
| #[path = "monty.rs"] |
| mod monty; |
| |
| use self::algorithms::{__add2, __sub2rev, add2, sub2, sub2rev}; |
| use self::algorithms::{biguint_shl, biguint_shr}; |
| use self::algorithms::{cmp_slice, fls, ilog2}; |
| use self::algorithms::{div_rem, div_rem_digit, mac_with_carry, mul3, scalar_mul}; |
| use self::monty::monty_modpow; |
| |
| use UsizePromotion; |
| |
| use ParseBigIntError; |
| |
| /// A big unsigned integer type. |
| #[derive(Clone, Debug, Hash)] |
| pub struct BigUint { |
| data: Vec<BigDigit>, |
| } |
| |
| impl PartialEq for BigUint { |
| #[inline] |
| fn eq(&self, other: &BigUint) -> bool { |
| match self.cmp(other) { |
| Equal => true, |
| _ => false, |
| } |
| } |
| } |
| impl Eq for BigUint {} |
| |
| impl PartialOrd for BigUint { |
| #[inline] |
| fn partial_cmp(&self, other: &BigUint) -> Option<Ordering> { |
| Some(self.cmp(other)) |
| } |
| } |
| |
| impl Ord for BigUint { |
| #[inline] |
| fn cmp(&self, other: &BigUint) -> Ordering { |
| cmp_slice(&self.data[..], &other.data[..]) |
| } |
| } |
| |
| impl Default for BigUint { |
| #[inline] |
| fn default() -> BigUint { |
| Zero::zero() |
| } |
| } |
| |
| impl fmt::Display for BigUint { |
| fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result { |
| f.pad_integral(true, "", &self.to_str_radix(10)) |
| } |
| } |
| |
| impl fmt::LowerHex for BigUint { |
| fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result { |
| f.pad_integral(true, "0x", &self.to_str_radix(16)) |
| } |
| } |
| |
| impl fmt::UpperHex for BigUint { |
| fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result { |
| let mut s = self.to_str_radix(16); |
| s.make_ascii_uppercase(); |
| f.pad_integral(true, "0x", &s) |
| } |
| } |
| |
| impl fmt::Binary for BigUint { |
| fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result { |
| f.pad_integral(true, "0b", &self.to_str_radix(2)) |
| } |
| } |
| |
| impl fmt::Octal for BigUint { |
| fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result { |
| f.pad_integral(true, "0o", &self.to_str_radix(8)) |
| } |
| } |
| |
| impl FromStr for BigUint { |
| type Err = ParseBigIntError; |
| |
| #[inline] |
| fn from_str(s: &str) -> Result<BigUint, ParseBigIntError> { |
| BigUint::from_str_radix(s, 10) |
| } |
| } |
| |
| // Convert from a power of two radix (bits == ilog2(radix)) where bits evenly divides |
| // BigDigit::BITS |
| fn from_bitwise_digits_le(v: &[u8], bits: usize) -> BigUint { |
| debug_assert!(!v.is_empty() && bits <= 8 && big_digit::BITS % bits == 0); |
| debug_assert!(v.iter().all(|&c| (c as BigDigit) < (1 << bits))); |
| |
| let digits_per_big_digit = big_digit::BITS / bits; |
| |
| let data = v |
| .chunks(digits_per_big_digit) |
| .map(|chunk| { |
| chunk |
| .iter() |
| .rev() |
| .fold(0, |acc, &c| (acc << bits) | c as BigDigit) |
| }) |
| .collect(); |
| |
| BigUint::new(data) |
| } |
| |
| // Convert from a power of two radix (bits == ilog2(radix)) where bits doesn't evenly divide |
| // BigDigit::BITS |
| fn from_inexact_bitwise_digits_le(v: &[u8], bits: usize) -> BigUint { |
| debug_assert!(!v.is_empty() && bits <= 8 && big_digit::BITS % bits != 0); |
| debug_assert!(v.iter().all(|&c| (c as BigDigit) < (1 << bits))); |
| |
| let big_digits = (v.len() * bits + big_digit::BITS - 1) / big_digit::BITS; |
| let mut data = Vec::with_capacity(big_digits); |
| |
| let mut d = 0; |
| let mut dbits = 0; // number of bits we currently have in d |
| |
| // walk v accumululating bits in d; whenever we accumulate big_digit::BITS in d, spit out a |
| // big_digit: |
| for &c in v { |
| d |= (c as BigDigit) << dbits; |
| dbits += bits; |
| |
| if dbits >= big_digit::BITS { |
| data.push(d); |
| dbits -= big_digit::BITS; |
| // if dbits was > big_digit::BITS, we dropped some of the bits in c (they couldn't fit |
| // in d) - grab the bits we lost here: |
| d = (c as BigDigit) >> (bits - dbits); |
| } |
| } |
| |
| if dbits > 0 { |
| debug_assert!(dbits < big_digit::BITS); |
| data.push(d as BigDigit); |
| } |
| |
| BigUint::new(data) |
| } |
| |
| // Read little-endian radix digits |
| fn from_radix_digits_be(v: &[u8], radix: u32) -> BigUint { |
| debug_assert!(!v.is_empty() && !radix.is_power_of_two()); |
| debug_assert!(v.iter().all(|&c| (c as u32) < radix)); |
| |
| // Estimate how big the result will be, so we can pre-allocate it. |
| let bits = (radix as f64).log2() * v.len() as f64; |
| let big_digits = (bits / big_digit::BITS as f64).ceil(); |
| let mut data = Vec::with_capacity(big_digits as usize); |
| |
| let (base, power) = get_radix_base(radix); |
| let radix = radix as BigDigit; |
| |
| let r = v.len() % power; |
| let i = if r == 0 { power } else { r }; |
| let (head, tail) = v.split_at(i); |
| |
| let first = head.iter().fold(0, |acc, &d| acc * radix + d as BigDigit); |
| data.push(first); |
| |
| debug_assert!(tail.len() % power == 0); |
| for chunk in tail.chunks(power) { |
| if data.last() != Some(&0) { |
| data.push(0); |
| } |
| |
| let mut carry = 0; |
| for d in data.iter_mut() { |
| *d = mac_with_carry(0, *d, base, &mut carry); |
| } |
| debug_assert!(carry == 0); |
| |
| let n = chunk.iter().fold(0, |acc, &d| acc * radix + d as BigDigit); |
| add2(&mut data, &[n]); |
| } |
| |
| BigUint::new(data) |
| } |
| |
| impl Num for BigUint { |
| type FromStrRadixErr = ParseBigIntError; |
| |
| /// Creates and initializes a `BigUint`. |
| fn from_str_radix(s: &str, radix: u32) -> Result<BigUint, ParseBigIntError> { |
| assert!(2 <= radix && radix <= 36, "The radix must be within 2...36"); |
| let mut s = s; |
| if s.starts_with('+') { |
| let tail = &s[1..]; |
| if !tail.starts_with('+') { |
| s = tail |
| } |
| } |
| |
| if s.is_empty() { |
| return Err(ParseBigIntError::empty()); |
| } |
| |
| if s.starts_with('_') { |
| // Must lead with a real digit! |
| return Err(ParseBigIntError::invalid()); |
| } |
| |
| // First normalize all characters to plain digit values |
| let mut v = Vec::with_capacity(s.len()); |
| for b in s.bytes() { |
| let d = match b { |
| b'0'...b'9' => b - b'0', |
| b'a'...b'z' => b - b'a' + 10, |
| b'A'...b'Z' => b - b'A' + 10, |
| b'_' => continue, |
| _ => u8::MAX, |
| }; |
| if d < radix as u8 { |
| v.push(d); |
| } else { |
| return Err(ParseBigIntError::invalid()); |
| } |
| } |
| |
| let res = if radix.is_power_of_two() { |
| // Powers of two can use bitwise masks and shifting instead of multiplication |
| let bits = ilog2(radix); |
| v.reverse(); |
| if big_digit::BITS % bits == 0 { |
| from_bitwise_digits_le(&v, bits) |
| } else { |
| from_inexact_bitwise_digits_le(&v, bits) |
| } |
| } else { |
| from_radix_digits_be(&v, radix) |
| }; |
| Ok(res) |
| } |
| } |
| |
| forward_val_val_binop!(impl BitAnd for BigUint, bitand); |
| forward_ref_val_binop!(impl BitAnd for BigUint, bitand); |
| |
| // do not use forward_ref_ref_binop_commutative! for bitand so that we can |
| // clone the smaller value rather than the larger, avoiding over-allocation |
| impl<'a, 'b> BitAnd<&'b BigUint> for &'a BigUint { |
| type Output = BigUint; |
| |
| #[inline] |
| fn bitand(self, other: &BigUint) -> BigUint { |
| // forward to val-ref, choosing the smaller to clone |
| if self.data.len() <= other.data.len() { |
| self.clone() & other |
| } else { |
| other.clone() & self |
| } |
| } |
| } |
| |
| forward_val_assign!(impl BitAndAssign for BigUint, bitand_assign); |
| |
| impl<'a> BitAnd<&'a BigUint> for BigUint { |
| type Output = BigUint; |
| |
| #[inline] |
| fn bitand(mut self, other: &BigUint) -> BigUint { |
| self &= other; |
| self |
| } |
| } |
| impl<'a> BitAndAssign<&'a BigUint> for BigUint { |
| #[inline] |
| fn bitand_assign(&mut self, other: &BigUint) { |
| for (ai, &bi) in self.data.iter_mut().zip(other.data.iter()) { |
| *ai &= bi; |
| } |
| self.data.truncate(other.data.len()); |
| self.normalize(); |
| } |
| } |
| |
| forward_all_binop_to_val_ref_commutative!(impl BitOr for BigUint, bitor); |
| forward_val_assign!(impl BitOrAssign for BigUint, bitor_assign); |
| |
| impl<'a> BitOr<&'a BigUint> for BigUint { |
| type Output = BigUint; |
| |
| fn bitor(mut self, other: &BigUint) -> BigUint { |
| self |= other; |
| self |
| } |
| } |
| impl<'a> BitOrAssign<&'a BigUint> for BigUint { |
| #[inline] |
| fn bitor_assign(&mut self, other: &BigUint) { |
| for (ai, &bi) in self.data.iter_mut().zip(other.data.iter()) { |
| *ai |= bi; |
| } |
| if other.data.len() > self.data.len() { |
| let extra = &other.data[self.data.len()..]; |
| self.data.extend(extra.iter().cloned()); |
| } |
| } |
| } |
| |
| forward_all_binop_to_val_ref_commutative!(impl BitXor for BigUint, bitxor); |
| forward_val_assign!(impl BitXorAssign for BigUint, bitxor_assign); |
| |
| impl<'a> BitXor<&'a BigUint> for BigUint { |
| type Output = BigUint; |
| |
| fn bitxor(mut self, other: &BigUint) -> BigUint { |
| self ^= other; |
| self |
| } |
| } |
| impl<'a> BitXorAssign<&'a BigUint> for BigUint { |
| #[inline] |
| fn bitxor_assign(&mut self, other: &BigUint) { |
| for (ai, &bi) in self.data.iter_mut().zip(other.data.iter()) { |
| *ai ^= bi; |
| } |
| if other.data.len() > self.data.len() { |
| let extra = &other.data[self.data.len()..]; |
| self.data.extend(extra.iter().cloned()); |
| } |
| self.normalize(); |
| } |
| } |
| |
| impl Shl<usize> for BigUint { |
| type Output = BigUint; |
| |
| #[inline] |
| fn shl(self, rhs: usize) -> BigUint { |
| biguint_shl(Cow::Owned(self), rhs) |
| } |
| } |
| impl<'a> Shl<usize> for &'a BigUint { |
| type Output = BigUint; |
| |
| #[inline] |
| fn shl(self, rhs: usize) -> BigUint { |
| biguint_shl(Cow::Borrowed(self), rhs) |
| } |
| } |
| |
| impl ShlAssign<usize> for BigUint { |
| #[inline] |
| fn shl_assign(&mut self, rhs: usize) { |
| let n = mem::replace(self, BigUint::zero()); |
| *self = n << rhs; |
| } |
| } |
| |
| impl Shr<usize> for BigUint { |
| type Output = BigUint; |
| |
| #[inline] |
| fn shr(self, rhs: usize) -> BigUint { |
| biguint_shr(Cow::Owned(self), rhs) |
| } |
| } |
| impl<'a> Shr<usize> for &'a BigUint { |
| type Output = BigUint; |
| |
| #[inline] |
| fn shr(self, rhs: usize) -> BigUint { |
| biguint_shr(Cow::Borrowed(self), rhs) |
| } |
| } |
| |
| impl ShrAssign<usize> for BigUint { |
| #[inline] |
| fn shr_assign(&mut self, rhs: usize) { |
| let n = mem::replace(self, BigUint::zero()); |
| *self = n >> rhs; |
| } |
| } |
| |
| impl Zero for BigUint { |
| #[inline] |
| fn zero() -> BigUint { |
| BigUint::new(Vec::new()) |
| } |
| |
| #[inline] |
| fn is_zero(&self) -> bool { |
| self.data.is_empty() |
| } |
| } |
| |
| impl One for BigUint { |
| #[inline] |
| fn one() -> BigUint { |
| BigUint::new(vec![1]) |
| } |
| |
| #[inline] |
| fn is_one(&self) -> bool { |
| self.data[..] == [1] |
| } |
| } |
| |
| impl Unsigned for BigUint {} |
| |
| macro_rules! pow_impl { |
| ($T:ty) => { |
| impl<'a> Pow<$T> for &'a BigUint { |
| type Output = BigUint; |
| |
| #[inline] |
| fn pow(self, mut exp: $T) -> Self::Output { |
| if exp == 0 { |
| return BigUint::one(); |
| } |
| let mut base = self.clone(); |
| |
| while exp & 1 == 0 { |
| base = &base * &base; |
| exp >>= 1; |
| } |
| |
| if exp == 1 { |
| return base; |
| } |
| |
| let mut acc = base.clone(); |
| while exp > 1 { |
| exp >>= 1; |
| base = &base * &base; |
| if exp & 1 == 1 { |
| acc = &acc * &base; |
| } |
| } |
| acc |
| } |
| } |
| |
| impl<'a, 'b> Pow<&'b $T> for &'a BigUint { |
| type Output = BigUint; |
| |
| #[inline] |
| fn pow(self, exp: &$T) -> Self::Output { |
| self.pow(*exp) |
| } |
| } |
| }; |
| } |
| |
| pow_impl!(u8); |
| pow_impl!(u16); |
| pow_impl!(u32); |
| pow_impl!(u64); |
| pow_impl!(usize); |
| #[cfg(has_i128)] |
| pow_impl!(u128); |
| |
| forward_all_binop_to_val_ref_commutative!(impl Add for BigUint, add); |
| forward_val_assign!(impl AddAssign for BigUint, add_assign); |
| |
| impl<'a> Add<&'a BigUint> for BigUint { |
| type Output = BigUint; |
| |
| fn add(mut self, other: &BigUint) -> BigUint { |
| self += other; |
| self |
| } |
| } |
| impl<'a> AddAssign<&'a BigUint> for BigUint { |
| #[inline] |
| fn add_assign(&mut self, other: &BigUint) { |
| let self_len = self.data.len(); |
| let carry = if self_len < other.data.len() { |
| let lo_carry = __add2(&mut self.data[..], &other.data[..self_len]); |
| self.data.extend_from_slice(&other.data[self_len..]); |
| __add2(&mut self.data[self_len..], &[lo_carry]) |
| } else { |
| __add2(&mut self.data[..], &other.data[..]) |
| }; |
| if carry != 0 { |
| self.data.push(carry); |
| } |
| } |
| } |
| |
| promote_unsigned_scalars!(impl Add for BigUint, add); |
| promote_unsigned_scalars_assign!(impl AddAssign for BigUint, add_assign); |
| forward_all_scalar_binop_to_val_val_commutative!(impl Add<u32> for BigUint, add); |
| forward_all_scalar_binop_to_val_val_commutative!(impl Add<u64> for BigUint, add); |
| #[cfg(has_i128)] |
| forward_all_scalar_binop_to_val_val_commutative!(impl Add<u128> for BigUint, add); |
| |
| impl Add<u32> for BigUint { |
| type Output = BigUint; |
| |
| #[inline] |
| fn add(mut self, other: u32) -> BigUint { |
| self += other; |
| self |
| } |
| } |
| |
| impl AddAssign<u32> for BigUint { |
| #[inline] |
| fn add_assign(&mut self, other: u32) { |
| if other != 0 { |
| if self.data.len() == 0 { |
| self.data.push(0); |
| } |
| |
| let carry = __add2(&mut self.data, &[other as BigDigit]); |
| if carry != 0 { |
| self.data.push(carry); |
| } |
| } |
| } |
| } |
| |
| impl Add<u64> for BigUint { |
| type Output = BigUint; |
| |
| #[inline] |
| fn add(mut self, other: u64) -> BigUint { |
| self += other; |
| self |
| } |
| } |
| |
| impl AddAssign<u64> for BigUint { |
| #[inline] |
| fn add_assign(&mut self, other: u64) { |
| let (hi, lo) = big_digit::from_doublebigdigit(other); |
| if hi == 0 { |
| *self += lo; |
| } else { |
| while self.data.len() < 2 { |
| self.data.push(0); |
| } |
| |
| let carry = __add2(&mut self.data, &[lo, hi]); |
| if carry != 0 { |
| self.data.push(carry); |
| } |
| } |
| } |
| } |
| |
| #[cfg(has_i128)] |
| impl Add<u128> for BigUint { |
| type Output = BigUint; |
| |
| #[inline] |
| fn add(mut self, other: u128) -> BigUint { |
| self += other; |
| self |
| } |
| } |
| |
| #[cfg(has_i128)] |
| impl AddAssign<u128> for BigUint { |
| #[inline] |
| fn add_assign(&mut self, other: u128) { |
| if other <= u64::max_value() as u128 { |
| *self += other as u64 |
| } else { |
| let (a, b, c, d) = u32_from_u128(other); |
| let carry = if a > 0 { |
| while self.data.len() < 4 { |
| self.data.push(0); |
| } |
| __add2(&mut self.data, &[d, c, b, a]) |
| } else { |
| debug_assert!(b > 0); |
| while self.data.len() < 3 { |
| self.data.push(0); |
| } |
| __add2(&mut self.data, &[d, c, b]) |
| }; |
| |
| if carry != 0 { |
| self.data.push(carry); |
| } |
| } |
| } |
| } |
| |
| forward_val_val_binop!(impl Sub for BigUint, sub); |
| forward_ref_ref_binop!(impl Sub for BigUint, sub); |
| forward_val_assign!(impl SubAssign for BigUint, sub_assign); |
| |
| impl<'a> Sub<&'a BigUint> for BigUint { |
| type Output = BigUint; |
| |
| fn sub(mut self, other: &BigUint) -> BigUint { |
| self -= other; |
| self |
| } |
| } |
| impl<'a> SubAssign<&'a BigUint> for BigUint { |
| fn sub_assign(&mut self, other: &'a BigUint) { |
| sub2(&mut self.data[..], &other.data[..]); |
| self.normalize(); |
| } |
| } |
| |
| impl<'a> Sub<BigUint> for &'a BigUint { |
| type Output = BigUint; |
| |
| fn sub(self, mut other: BigUint) -> BigUint { |
| let other_len = other.data.len(); |
| if other_len < self.data.len() { |
| let lo_borrow = __sub2rev(&self.data[..other_len], &mut other.data); |
| other.data.extend_from_slice(&self.data[other_len..]); |
| if lo_borrow != 0 { |
| sub2(&mut other.data[other_len..], &[1]) |
| } |
| } else { |
| sub2rev(&self.data[..], &mut other.data[..]); |
| } |
| other.normalized() |
| } |
| } |
| |
| promote_unsigned_scalars!(impl Sub for BigUint, sub); |
| promote_unsigned_scalars_assign!(impl SubAssign for BigUint, sub_assign); |
| forward_all_scalar_binop_to_val_val!(impl Sub<u32> for BigUint, sub); |
| forward_all_scalar_binop_to_val_val!(impl Sub<u64> for BigUint, sub); |
| #[cfg(has_i128)] |
| forward_all_scalar_binop_to_val_val!(impl Sub<u128> for BigUint, sub); |
| |
| impl Sub<u32> for BigUint { |
| type Output = BigUint; |
| |
| #[inline] |
| fn sub(mut self, other: u32) -> BigUint { |
| self -= other; |
| self |
| } |
| } |
| impl SubAssign<u32> for BigUint { |
| fn sub_assign(&mut self, other: u32) { |
| sub2(&mut self.data[..], &[other as BigDigit]); |
| self.normalize(); |
| } |
| } |
| |
| impl Sub<BigUint> for u32 { |
| type Output = BigUint; |
| |
| #[inline] |
| fn sub(self, mut other: BigUint) -> BigUint { |
| if other.data.len() == 0 { |
| other.data.push(self as BigDigit); |
| } else { |
| sub2rev(&[self as BigDigit], &mut other.data[..]); |
| } |
| other.normalized() |
| } |
| } |
| |
| impl Sub<u64> for BigUint { |
| type Output = BigUint; |
| |
| #[inline] |
| fn sub(mut self, other: u64) -> BigUint { |
| self -= other; |
| self |
| } |
| } |
| |
| impl SubAssign<u64> for BigUint { |
| #[inline] |
| fn sub_assign(&mut self, other: u64) { |
| let (hi, lo) = big_digit::from_doublebigdigit(other); |
| sub2(&mut self.data[..], &[lo, hi]); |
| self.normalize(); |
| } |
| } |
| |
| impl Sub<BigUint> for u64 { |
| type Output = BigUint; |
| |
| #[inline] |
| fn sub(self, mut other: BigUint) -> BigUint { |
| while other.data.len() < 2 { |
| other.data.push(0); |
| } |
| |
| let (hi, lo) = big_digit::from_doublebigdigit(self); |
| sub2rev(&[lo, hi], &mut other.data[..]); |
| other.normalized() |
| } |
| } |
| |
| #[cfg(has_i128)] |
| impl Sub<u128> for BigUint { |
| type Output = BigUint; |
| |
| #[inline] |
| fn sub(mut self, other: u128) -> BigUint { |
| self -= other; |
| self |
| } |
| } |
| #[cfg(has_i128)] |
| impl SubAssign<u128> for BigUint { |
| fn sub_assign(&mut self, other: u128) { |
| let (a, b, c, d) = u32_from_u128(other); |
| sub2(&mut self.data[..], &[d, c, b, a]); |
| self.normalize(); |
| } |
| } |
| |
| #[cfg(has_i128)] |
| impl Sub<BigUint> for u128 { |
| type Output = BigUint; |
| |
| #[inline] |
| fn sub(self, mut other: BigUint) -> BigUint { |
| while other.data.len() < 4 { |
| other.data.push(0); |
| } |
| |
| let (a, b, c, d) = u32_from_u128(self); |
| sub2rev(&[d, c, b, a], &mut other.data[..]); |
| other.normalized() |
| } |
| } |
| |
| forward_all_binop_to_ref_ref!(impl Mul for BigUint, mul); |
| forward_val_assign!(impl MulAssign for BigUint, mul_assign); |
| |
| impl<'a, 'b> Mul<&'b BigUint> for &'a BigUint { |
| type Output = BigUint; |
| |
| #[inline] |
| fn mul(self, other: &BigUint) -> BigUint { |
| mul3(&self.data[..], &other.data[..]) |
| } |
| } |
| impl<'a> MulAssign<&'a BigUint> for BigUint { |
| #[inline] |
| fn mul_assign(&mut self, other: &'a BigUint) { |
| *self = &*self * other |
| } |
| } |
| |
| promote_unsigned_scalars!(impl Mul for BigUint, mul); |
| promote_unsigned_scalars_assign!(impl MulAssign for BigUint, mul_assign); |
| forward_all_scalar_binop_to_val_val_commutative!(impl Mul<u32> for BigUint, mul); |
| forward_all_scalar_binop_to_val_val_commutative!(impl Mul<u64> for BigUint, mul); |
| #[cfg(has_i128)] |
| forward_all_scalar_binop_to_val_val_commutative!(impl Mul<u128> for BigUint, mul); |
| |
| impl Mul<u32> for BigUint { |
| type Output = BigUint; |
| |
| #[inline] |
| fn mul(mut self, other: u32) -> BigUint { |
| self *= other; |
| self |
| } |
| } |
| impl MulAssign<u32> for BigUint { |
| #[inline] |
| fn mul_assign(&mut self, other: u32) { |
| if other == 0 { |
| self.data.clear(); |
| } else { |
| let carry = scalar_mul(&mut self.data[..], other as BigDigit); |
| if carry != 0 { |
| self.data.push(carry); |
| } |
| } |
| } |
| } |
| |
| impl Mul<u64> for BigUint { |
| type Output = BigUint; |
| |
| #[inline] |
| fn mul(mut self, other: u64) -> BigUint { |
| self *= other; |
| self |
| } |
| } |
| impl MulAssign<u64> for BigUint { |
| #[inline] |
| fn mul_assign(&mut self, other: u64) { |
| if other == 0 { |
| self.data.clear(); |
| } else if other <= BigDigit::max_value() as u64 { |
| *self *= other as BigDigit |
| } else { |
| let (hi, lo) = big_digit::from_doublebigdigit(other); |
| *self = mul3(&self.data[..], &[lo, hi]) |
| } |
| } |
| } |
| |
| #[cfg(has_i128)] |
| impl Mul<u128> for BigUint { |
| type Output = BigUint; |
| |
| #[inline] |
| fn mul(mut self, other: u128) -> BigUint { |
| self *= other; |
| self |
| } |
| } |
| #[cfg(has_i128)] |
| impl MulAssign<u128> for BigUint { |
| #[inline] |
| fn mul_assign(&mut self, other: u128) { |
| if other == 0 { |
| self.data.clear(); |
| } else if other <= BigDigit::max_value() as u128 { |
| *self *= other as BigDigit |
| } else { |
| let (a, b, c, d) = u32_from_u128(other); |
| *self = mul3(&self.data[..], &[d, c, b, a]) |
| } |
| } |
| } |
| |
| forward_all_binop_to_ref_ref!(impl Div for BigUint, div); |
| forward_val_assign!(impl DivAssign for BigUint, div_assign); |
| |
| impl<'a, 'b> Div<&'b BigUint> for &'a BigUint { |
| type Output = BigUint; |
| |
| #[inline] |
| fn div(self, other: &BigUint) -> BigUint { |
| let (q, _) = self.div_rem(other); |
| q |
| } |
| } |
| impl<'a> DivAssign<&'a BigUint> for BigUint { |
| #[inline] |
| fn div_assign(&mut self, other: &'a BigUint) { |
| *self = &*self / other; |
| } |
| } |
| |
| promote_unsigned_scalars!(impl Div for BigUint, div); |
| promote_unsigned_scalars_assign!(impl DivAssign for BigUint, div_assign); |
| forward_all_scalar_binop_to_val_val!(impl Div<u32> for BigUint, div); |
| forward_all_scalar_binop_to_val_val!(impl Div<u64> for BigUint, div); |
| #[cfg(has_i128)] |
| forward_all_scalar_binop_to_val_val!(impl Div<u128> for BigUint, div); |
| |
| impl Div<u32> for BigUint { |
| type Output = BigUint; |
| |
| #[inline] |
| fn div(self, other: u32) -> BigUint { |
| let (q, _) = div_rem_digit(self, other as BigDigit); |
| q |
| } |
| } |
| impl DivAssign<u32> for BigUint { |
| #[inline] |
| fn div_assign(&mut self, other: u32) { |
| *self = &*self / other; |
| } |
| } |
| |
| impl Div<BigUint> for u32 { |
| type Output = BigUint; |
| |
| #[inline] |
| fn div(self, other: BigUint) -> BigUint { |
| match other.data.len() { |
| 0 => panic!(), |
| 1 => From::from(self as BigDigit / other.data[0]), |
| _ => Zero::zero(), |
| } |
| } |
| } |
| |
| impl Div<u64> for BigUint { |
| type Output = BigUint; |
| |
| #[inline] |
| fn div(self, other: u64) -> BigUint { |
| let (q, _) = self.div_rem(&From::from(other)); |
| q |
| } |
| } |
| impl DivAssign<u64> for BigUint { |
| #[inline] |
| fn div_assign(&mut self, other: u64) { |
| *self = &*self / other; |
| } |
| } |
| |
| impl Div<BigUint> for u64 { |
| type Output = BigUint; |
| |
| #[inline] |
| fn div(self, other: BigUint) -> BigUint { |
| match other.data.len() { |
| 0 => panic!(), |
| 1 => From::from(self / other.data[0] as u64), |
| 2 => From::from(self / big_digit::to_doublebigdigit(other.data[1], other.data[0])), |
| _ => Zero::zero(), |
| } |
| } |
| } |
| |
| #[cfg(has_i128)] |
| impl Div<u128> for BigUint { |
| type Output = BigUint; |
| |
| #[inline] |
| fn div(self, other: u128) -> BigUint { |
| let (q, _) = self.div_rem(&From::from(other)); |
| q |
| } |
| } |
| #[cfg(has_i128)] |
| impl DivAssign<u128> for BigUint { |
| #[inline] |
| fn div_assign(&mut self, other: u128) { |
| *self = &*self / other; |
| } |
| } |
| |
| #[cfg(has_i128)] |
| impl Div<BigUint> for u128 { |
| type Output = BigUint; |
| |
| #[inline] |
| fn div(self, other: BigUint) -> BigUint { |
| match other.data.len() { |
| 0 => panic!(), |
| 1 => From::from(self / other.data[0] as u128), |
| 2 => From::from( |
| self / big_digit::to_doublebigdigit(other.data[1], other.data[0]) as u128, |
| ), |
| 3 => From::from(self / u32_to_u128(0, other.data[2], other.data[1], other.data[0])), |
| 4 => From::from( |
| self / u32_to_u128(other.data[3], other.data[2], other.data[1], other.data[0]), |
| ), |
| _ => Zero::zero(), |
| } |
| } |
| } |
| |
| forward_all_binop_to_ref_ref!(impl Rem for BigUint, rem); |
| forward_val_assign!(impl RemAssign for BigUint, rem_assign); |
| |
| impl<'a, 'b> Rem<&'b BigUint> for &'a BigUint { |
| type Output = BigUint; |
| |
| #[inline] |
| fn rem(self, other: &BigUint) -> BigUint { |
| let (_, r) = self.div_rem(other); |
| r |
| } |
| } |
| impl<'a> RemAssign<&'a BigUint> for BigUint { |
| #[inline] |
| fn rem_assign(&mut self, other: &BigUint) { |
| *self = &*self % other; |
| } |
| } |
| |
| promote_unsigned_scalars!(impl Rem for BigUint, rem); |
| promote_unsigned_scalars_assign!(impl RemAssign for BigUint, rem_assign); |
| forward_all_scalar_binop_to_val_val!(impl Rem<u32> for BigUint, rem); |
| forward_all_scalar_binop_to_val_val!(impl Rem<u64> for BigUint, rem); |
| #[cfg(has_i128)] |
| forward_all_scalar_binop_to_val_val!(impl Rem<u128> for BigUint, rem); |
| |
| impl Rem<u32> for BigUint { |
| type Output = BigUint; |
| |
| #[inline] |
| fn rem(self, other: u32) -> BigUint { |
| let (_, r) = div_rem_digit(self, other as BigDigit); |
| From::from(r) |
| } |
| } |
| impl RemAssign<u32> for BigUint { |
| #[inline] |
| fn rem_assign(&mut self, other: u32) { |
| *self = &*self % other; |
| } |
| } |
| |
| impl Rem<BigUint> for u32 { |
| type Output = BigUint; |
| |
| #[inline] |
| fn rem(mut self, other: BigUint) -> BigUint { |
| self %= other; |
| From::from(self) |
| } |
| } |
| |
| macro_rules! impl_rem_assign_scalar { |
| ($scalar:ty, $to_scalar:ident) => { |
| forward_val_assign_scalar!(impl RemAssign for BigUint, $scalar, rem_assign); |
| impl<'a> RemAssign<&'a BigUint> for $scalar { |
| #[inline] |
| fn rem_assign(&mut self, other: &BigUint) { |
| *self = match other.$to_scalar() { |
| None => *self, |
| Some(0) => panic!(), |
| Some(v) => *self % v |
| }; |
| } |
| } |
| } |
| } |
| // we can scalar %= BigUint for any scalar, including signed types |
| #[cfg(has_i128)] |
| impl_rem_assign_scalar!(u128, to_u128); |
| impl_rem_assign_scalar!(usize, to_usize); |
| impl_rem_assign_scalar!(u64, to_u64); |
| impl_rem_assign_scalar!(u32, to_u32); |
| impl_rem_assign_scalar!(u16, to_u16); |
| impl_rem_assign_scalar!(u8, to_u8); |
| #[cfg(has_i128)] |
| impl_rem_assign_scalar!(i128, to_i128); |
| impl_rem_assign_scalar!(isize, to_isize); |
| impl_rem_assign_scalar!(i64, to_i64); |
| impl_rem_assign_scalar!(i32, to_i32); |
| impl_rem_assign_scalar!(i16, to_i16); |
| impl_rem_assign_scalar!(i8, to_i8); |
| |
| impl Rem<u64> for BigUint { |
| type Output = BigUint; |
| |
| #[inline] |
| fn rem(self, other: u64) -> BigUint { |
| let (_, r) = self.div_rem(&From::from(other)); |
| r |
| } |
| } |
| impl RemAssign<u64> for BigUint { |
| #[inline] |
| fn rem_assign(&mut self, other: u64) { |
| *self = &*self % other; |
| } |
| } |
| |
| impl Rem<BigUint> for u64 { |
| type Output = BigUint; |
| |
| #[inline] |
| fn rem(mut self, other: BigUint) -> BigUint { |
| self %= other; |
| From::from(self) |
| } |
| } |
| |
| #[cfg(has_i128)] |
| impl Rem<u128> for BigUint { |
| type Output = BigUint; |
| |
| #[inline] |
| fn rem(self, other: u128) -> BigUint { |
| let (_, r) = self.div_rem(&From::from(other)); |
| r |
| } |
| } |
| #[cfg(has_i128)] |
| impl RemAssign<u128> for BigUint { |
| #[inline] |
| fn rem_assign(&mut self, other: u128) { |
| *self = &*self % other; |
| } |
| } |
| |
| #[cfg(has_i128)] |
| impl Rem<BigUint> for u128 { |
| type Output = BigUint; |
| |
| #[inline] |
| fn rem(mut self, other: BigUint) -> BigUint { |
| self %= other; |
| From::from(self) |
| } |
| } |
| |
| impl Neg for BigUint { |
| type Output = BigUint; |
| |
| #[inline] |
| fn neg(self) -> BigUint { |
| panic!() |
| } |
| } |
| |
| impl<'a> Neg for &'a BigUint { |
| type Output = BigUint; |
| |
| #[inline] |
| fn neg(self) -> BigUint { |
| panic!() |
| } |
| } |
| |
| impl CheckedAdd for BigUint { |
| #[inline] |
| fn checked_add(&self, v: &BigUint) -> Option<BigUint> { |
| return Some(self.add(v)); |
| } |
| } |
| |
| impl CheckedSub for BigUint { |
| #[inline] |
| fn checked_sub(&self, v: &BigUint) -> Option<BigUint> { |
| match self.cmp(v) { |
| Less => None, |
| Equal => Some(Zero::zero()), |
| Greater => Some(self.sub(v)), |
| } |
| } |
| } |
| |
| impl CheckedMul for BigUint { |
| #[inline] |
| fn checked_mul(&self, v: &BigUint) -> Option<BigUint> { |
| return Some(self.mul(v)); |
| } |
| } |
| |
| impl CheckedDiv for BigUint { |
| #[inline] |
| fn checked_div(&self, v: &BigUint) -> Option<BigUint> { |
| if v.is_zero() { |
| return None; |
| } |
| return Some(self.div(v)); |
| } |
| } |
| |
| impl Integer for BigUint { |
| #[inline] |
| fn div_rem(&self, other: &BigUint) -> (BigUint, BigUint) { |
| div_rem(self, other) |
| } |
| |
| #[inline] |
| fn div_floor(&self, other: &BigUint) -> BigUint { |
| let (d, _) = div_rem(self, other); |
| d |
| } |
| |
| #[inline] |
| fn mod_floor(&self, other: &BigUint) -> BigUint { |
| let (_, m) = div_rem(self, other); |
| m |
| } |
| |
| #[inline] |
| fn div_mod_floor(&self, other: &BigUint) -> (BigUint, BigUint) { |
| div_rem(self, other) |
| } |
| |
| /// Calculates the Greatest Common Divisor (GCD) of the number and `other`. |
| /// |
| /// The result is always positive. |
| #[inline] |
| fn gcd(&self, other: &Self) -> Self { |
| #[inline] |
| fn twos(x: &BigUint) -> usize { |
| trailing_zeros(x).unwrap_or(0) |
| } |
| |
| // Stein's algorithm |
| if self.is_zero() { |
| return other.clone(); |
| } |
| if other.is_zero() { |
| return self.clone(); |
| } |
| let mut m = self.clone(); |
| let mut n = other.clone(); |
| |
| // find common factors of 2 |
| let shift = cmp::min(twos(&n), twos(&m)); |
| |
| // divide m and n by 2 until odd |
| // m inside loop |
| n >>= twos(&n); |
| |
| while !m.is_zero() { |
| m >>= twos(&m); |
| if n > m { |
| mem::swap(&mut n, &mut m) |
| } |
| m -= &n; |
| } |
| |
| n << shift |
| } |
| |
| /// Calculates the Lowest Common Multiple (LCM) of the number and `other`. |
| #[inline] |
| fn lcm(&self, other: &BigUint) -> BigUint { |
| self / self.gcd(other) * other |
| } |
| |
| /// Deprecated, use `is_multiple_of` instead. |
| #[inline] |
| fn divides(&self, other: &BigUint) -> bool { |
| self.is_multiple_of(other) |
| } |
| |
| /// Returns `true` if the number is a multiple of `other`. |
| #[inline] |
| fn is_multiple_of(&self, other: &BigUint) -> bool { |
| (self % other).is_zero() |
| } |
| |
| /// Returns `true` if the number is divisible by `2`. |
| #[inline] |
| fn is_even(&self) -> bool { |
| // Considering only the last digit. |
| match self.data.first() { |
| Some(x) => x.is_even(), |
| None => true, |
| } |
| } |
| |
| /// Returns `true` if the number is not divisible by `2`. |
| #[inline] |
| fn is_odd(&self) -> bool { |
| !self.is_even() |
| } |
| } |
| |
| #[inline] |
| fn fixpoint<F>(mut x: BigUint, max_bits: usize, f: F) -> BigUint |
| where |
| F: Fn(&BigUint) -> BigUint, |
| { |
| let mut xn = f(&x); |
| |
| // If the value increased, then the initial guess must have been low. |
| // Repeat until we reverse course. |
| while x < xn { |
| // Sometimes an increase will go way too far, especially with large |
| // powers, and then take a long time to walk back. We know an upper |
| // bound based on bit size, so saturate on that. |
| x = if xn.bits() > max_bits { |
| BigUint::one() << max_bits |
| } else { |
| xn |
| }; |
| xn = f(&x); |
| } |
| |
| // Now keep repeating while the estimate is decreasing. |
| while x > xn { |
| x = xn; |
| xn = f(&x); |
| } |
| x |
| } |
| |
| impl Roots for BigUint { |
| // nth_root, sqrt and cbrt use Newton's method to compute |
| // principal root of a given degree for a given integer. |
| |
| // Reference: |
| // Brent & Zimmermann, Modern Computer Arithmetic, v0.5.9, Algorithm 1.14 |
| fn nth_root(&self, n: u32) -> Self { |
| assert!(n > 0, "root degree n must be at least 1"); |
| |
| if self.is_zero() || self.is_one() { |
| return self.clone(); |
| } |
| |
| match n { |
| // Optimize for small n |
| 1 => return self.clone(), |
| 2 => return self.sqrt(), |
| 3 => return self.cbrt(), |
| _ => (), |
| } |
| |
| // The root of non-zero values less than 2ⁿ can only be 1. |
| let bits = self.bits(); |
| if bits <= n as usize { |
| return BigUint::one() |
| } |
| |
| // If we fit in `u64`, compute the root that way. |
| if let Some(x) = self.to_u64() { |
| return x.nth_root(n).into(); |
| } |
| |
| let max_bits = bits / n as usize + 1; |
| |
| let guess = if let Some(f) = self.to_f64() { |
| // We fit in `f64` (lossy), so get a better initial guess from that. |
| BigUint::from_f64((f.ln() / f64::from(n)).exp()).unwrap() |
| } else { |
| // Try to guess by scaling down such that it does fit in `f64`. |
| // With some (x * 2ⁿᵏ), its nth root ≈ (ⁿ√x * 2ᵏ) |
| let nsz = n as usize; |
| let extra_bits = bits - (f64::MAX_EXP as usize - 1); |
| let root_scale = (extra_bits + (nsz - 1)) / nsz; |
| let scale = root_scale * nsz; |
| if scale < bits && bits - scale > nsz { |
| (self >> scale).nth_root(n) << root_scale |
| } else { |
| BigUint::one() << max_bits |
| } |
| }; |
| |
| let n_min_1 = n - 1; |
| fixpoint(guess, max_bits, move |s| { |
| let q = self / s.pow(n_min_1); |
| let t = n_min_1 * s + q; |
| t / n |
| }) |
| } |
| |
| // Reference: |
| // Brent & Zimmermann, Modern Computer Arithmetic, v0.5.9, Algorithm 1.13 |
| fn sqrt(&self) -> Self { |
| if self.is_zero() || self.is_one() { |
| return self.clone(); |
| } |
| |
| // If we fit in `u64`, compute the root that way. |
| if let Some(x) = self.to_u64() { |
| return x.sqrt().into(); |
| } |
| |
| let bits = self.bits(); |
| let max_bits = bits / 2 as usize + 1; |
| |
| let guess = if let Some(f) = self.to_f64() { |
| // We fit in `f64` (lossy), so get a better initial guess from that. |
| BigUint::from_f64(f.sqrt()).unwrap() |
| } else { |
| // Try to guess by scaling down such that it does fit in `f64`. |
| // With some (x * 2²ᵏ), its sqrt ≈ (√x * 2ᵏ) |
| let extra_bits = bits - (f64::MAX_EXP as usize - 1); |
| let root_scale = (extra_bits + 1) / 2; |
| let scale = root_scale * 2; |
| (self >> scale).sqrt() << root_scale |
| }; |
| |
| fixpoint(guess, max_bits, move |s| { |
| let q = self / s; |
| let t = s + q; |
| t >> 1 |
| }) |
| } |
| |
| fn cbrt(&self) -> Self { |
| if self.is_zero() || self.is_one() { |
| return self.clone(); |
| } |
| |
| // If we fit in `u64`, compute the root that way. |
| if let Some(x) = self.to_u64() { |
| return x.cbrt().into(); |
| } |
| |
| let bits = self.bits(); |
| let max_bits = bits / 3 as usize + 1; |
| |
| let guess = if let Some(f) = self.to_f64() { |
| // We fit in `f64` (lossy), so get a better initial guess from that. |
| BigUint::from_f64(f.cbrt()).unwrap() |
| } else { |
| // Try to guess by scaling down such that it does fit in `f64`. |
| // With some (x * 2³ᵏ), its cbrt ≈ (∛x * 2ᵏ) |
| let extra_bits = bits - (f64::MAX_EXP as usize - 1); |
| let root_scale = (extra_bits + 2) / 3; |
| let scale = root_scale * 3; |
| (self >> scale).cbrt() << root_scale |
| }; |
| |
| |
| fixpoint(guess, max_bits, move |s| { |
| let q = self / (s * s); |
| let t = (s << 1) + q; |
| t / 3u32 |
| }) |
| } |
| } |
| |
| fn high_bits_to_u64(v: &BigUint) -> u64 { |
| match v.data.len() { |
| 0 => 0, |
| 1 => v.data[0] as u64, |
| _ => { |
| let mut bits = v.bits(); |
| let mut ret = 0u64; |
| let mut ret_bits = 0; |
| |
| for d in v.data.iter().rev() { |
| let digit_bits = (bits - 1) % big_digit::BITS + 1; |
| let bits_want = cmp::min(64 - ret_bits, digit_bits); |
| |
| if bits_want != 64 { |
| ret <<= bits_want; |
| } |
| ret |= *d as u64 >> (digit_bits - bits_want); |
| ret_bits += bits_want; |
| bits -= bits_want; |
| |
| if ret_bits == 64 { |
| break; |
| } |
| } |
| |
| ret |
| } |
| } |
| } |
| |
| impl ToPrimitive for BigUint { |
| #[inline] |
| fn to_i64(&self) -> Option<i64> { |
| self.to_u64().as_ref().and_then(u64::to_i64) |
| } |
| |
| #[inline] |
| #[cfg(has_i128)] |
| fn to_i128(&self) -> Option<i128> { |
| self.to_u128().as_ref().and_then(u128::to_i128) |
| } |
| |
| #[inline] |
| fn to_u64(&self) -> Option<u64> { |
| let mut ret: u64 = 0; |
| let mut bits = 0; |
| |
| for i in self.data.iter() { |
| if bits >= 64 { |
| return None; |
| } |
| |
| ret += (*i as u64) << bits; |
| bits += big_digit::BITS; |
| } |
| |
| Some(ret) |
| } |
| |
| #[inline] |
| #[cfg(has_i128)] |
| fn to_u128(&self) -> Option<u128> { |
| let mut ret: u128 = 0; |
| let mut bits = 0; |
| |
| for i in self.data.iter() { |
| if bits >= 128 { |
| return None; |
| } |
| |
| ret |= (*i as u128) << bits; |
| bits += big_digit::BITS; |
| } |
| |
| Some(ret) |
| } |
| |
| #[inline] |
| fn to_f32(&self) -> Option<f32> { |
| let mantissa = high_bits_to_u64(self); |
| let exponent = self.bits() - fls(mantissa); |
| |
| if exponent > f32::MAX_EXP as usize { |
| None |
| } else { |
| let ret = (mantissa as f32) * 2.0f32.powi(exponent as i32); |
| if ret.is_infinite() { |
| None |
| } else { |
| Some(ret) |
| } |
| } |
| } |
| |
| #[inline] |
| fn to_f64(&self) -> Option<f64> { |
| let mantissa = high_bits_to_u64(self); |
| let exponent = self.bits() - fls(mantissa); |
| |
| if exponent > f64::MAX_EXP as usize { |
| None |
| } else { |
| let ret = (mantissa as f64) * 2.0f64.powi(exponent as i32); |
| if ret.is_infinite() { |
| None |
| } else { |
| Some(ret) |
| } |
| } |
| } |
| } |
| |
| impl FromPrimitive for BigUint { |
| #[inline] |
| fn from_i64(n: i64) -> Option<BigUint> { |
| if n >= 0 { |
| Some(BigUint::from(n as u64)) |
| } else { |
| None |
| } |
| } |
| |
| #[inline] |
| #[cfg(has_i128)] |
| fn from_i128(n: i128) -> Option<BigUint> { |
| if n >= 0 { |
| Some(BigUint::from(n as u128)) |
| } else { |
| None |
| } |
| } |
| |
| #[inline] |
| fn from_u64(n: u64) -> Option<BigUint> { |
| Some(BigUint::from(n)) |
| } |
| |
| #[inline] |
| #[cfg(has_i128)] |
| fn from_u128(n: u128) -> Option<BigUint> { |
| Some(BigUint::from(n)) |
| } |
| |
| #[inline] |
| fn from_f64(mut n: f64) -> Option<BigUint> { |
| // handle NAN, INFINITY, NEG_INFINITY |
| if !n.is_finite() { |
| return None; |
| } |
| |
| // match the rounding of casting from float to int |
| n = n.trunc(); |
| |
| // handle 0.x, -0.x |
| if n.is_zero() { |
| return Some(BigUint::zero()); |
| } |
| |
| let (mantissa, exponent, sign) = Float::integer_decode(n); |
| |
| if sign == -1 { |
| return None; |
| } |
| |
| let mut ret = BigUint::from(mantissa); |
| if exponent > 0 { |
| ret = ret << exponent as usize; |
| } else if exponent < 0 { |
| ret = ret >> (-exponent) as usize; |
| } |
| Some(ret) |
| } |
| } |
| |
| impl From<u64> for BigUint { |
| #[inline] |
| fn from(mut n: u64) -> Self { |
| let mut ret: BigUint = Zero::zero(); |
| |
| while n != 0 { |
| ret.data.push(n as BigDigit); |
| // don't overflow if BITS is 64: |
| n = (n >> 1) >> (big_digit::BITS - 1); |
| } |
| |
| ret |
| } |
| } |
| |
| #[cfg(has_i128)] |
| impl From<u128> for BigUint { |
| #[inline] |
| fn from(mut n: u128) -> Self { |
| let mut ret: BigUint = Zero::zero(); |
| |
| while n != 0 { |
| ret.data.push(n as BigDigit); |
| n >>= big_digit::BITS; |
| } |
| |
| ret |
| } |
| } |
| |
| macro_rules! impl_biguint_from_uint { |
| ($T:ty) => { |
| impl From<$T> for BigUint { |
| #[inline] |
| fn from(n: $T) -> Self { |
| BigUint::from(n as u64) |
| } |
| } |
| }; |
| } |
| |
| impl_biguint_from_uint!(u8); |
| impl_biguint_from_uint!(u16); |
| impl_biguint_from_uint!(u32); |
| impl_biguint_from_uint!(usize); |
| |
| /// A generic trait for converting a value to a `BigUint`. |
| pub trait ToBigUint { |
| /// Converts the value of `self` to a `BigUint`. |
| fn to_biguint(&self) -> Option<BigUint>; |
| } |
| |
| impl ToBigUint for BigUint { |
| #[inline] |
| fn to_biguint(&self) -> Option<BigUint> { |
| Some(self.clone()) |
| } |
| } |
| |
| macro_rules! impl_to_biguint { |
| ($T:ty, $from_ty:path) => { |
| impl ToBigUint for $T { |
| #[inline] |
| fn to_biguint(&self) -> Option<BigUint> { |
| $from_ty(*self) |
| } |
| } |
| }; |
| } |
| |
| impl_to_biguint!(isize, FromPrimitive::from_isize); |
| impl_to_biguint!(i8, FromPrimitive::from_i8); |
| impl_to_biguint!(i16, FromPrimitive::from_i16); |
| impl_to_biguint!(i32, FromPrimitive::from_i32); |
| impl_to_biguint!(i64, FromPrimitive::from_i64); |
| #[cfg(has_i128)] |
| impl_to_biguint!(i128, FromPrimitive::from_i128); |
| |
| impl_to_biguint!(usize, FromPrimitive::from_usize); |
| impl_to_biguint!(u8, FromPrimitive::from_u8); |
| impl_to_biguint!(u16, FromPrimitive::from_u16); |
| impl_to_biguint!(u32, FromPrimitive::from_u32); |
| impl_to_biguint!(u64, FromPrimitive::from_u64); |
| #[cfg(has_i128)] |
| impl_to_biguint!(u128, FromPrimitive::from_u128); |
| |
| impl_to_biguint!(f32, FromPrimitive::from_f32); |
| impl_to_biguint!(f64, FromPrimitive::from_f64); |
| |
| // Extract bitwise digits that evenly divide BigDigit |
| fn to_bitwise_digits_le(u: &BigUint, bits: usize) -> Vec<u8> { |
| debug_assert!(!u.is_zero() && bits <= 8 && big_digit::BITS % bits == 0); |
| |
| let last_i = u.data.len() - 1; |
| let mask: BigDigit = (1 << bits) - 1; |
| let digits_per_big_digit = big_digit::BITS / bits; |
| let digits = (u.bits() + bits - 1) / bits; |
| let mut res = Vec::with_capacity(digits); |
| |
| for mut r in u.data[..last_i].iter().cloned() { |
| for _ in 0..digits_per_big_digit { |
| res.push((r & mask) as u8); |
| r >>= bits; |
| } |
| } |
| |
| let mut r = u.data[last_i]; |
| while r != 0 { |
| res.push((r & mask) as u8); |
| r >>= bits; |
| } |
| |
| res |
| } |
| |
| // Extract bitwise digits that don't evenly divide BigDigit |
| fn to_inexact_bitwise_digits_le(u: &BigUint, bits: usize) -> Vec<u8> { |
| debug_assert!(!u.is_zero() && bits <= 8 && big_digit::BITS % bits != 0); |
| |
| let mask: BigDigit = (1 << bits) - 1; |
| let digits = (u.bits() + bits - 1) / bits; |
| let mut res = Vec::with_capacity(digits); |
| |
| let mut r = 0; |
| let mut rbits = 0; |
| |
| for c in &u.data { |
| r |= *c << rbits; |
| rbits += big_digit::BITS; |
| |
| while rbits >= bits { |
| res.push((r & mask) as u8); |
| r >>= bits; |
| |
| // r had more bits than it could fit - grab the bits we lost |
| if rbits > big_digit::BITS { |
| r = *c >> (big_digit::BITS - (rbits - bits)); |
| } |
| |
| rbits -= bits; |
| } |
| } |
| |
| if rbits != 0 { |
| res.push(r as u8); |
| } |
| |
| while let Some(&0) = res.last() { |
| res.pop(); |
| } |
| |
| res |
| } |
| |
| // Extract little-endian radix digits |
| #[inline(always)] // forced inline to get const-prop for radix=10 |
| fn to_radix_digits_le(u: &BigUint, radix: u32) -> Vec<u8> { |
| debug_assert!(!u.is_zero() && !radix.is_power_of_two()); |
| |
| // Estimate how big the result will be, so we can pre-allocate it. |
| let radix_digits = ((u.bits() as f64) / (radix as f64).log2()).ceil(); |
| let mut res = Vec::with_capacity(radix_digits as usize); |
| let mut digits = u.clone(); |
| |
| let (base, power) = get_radix_base(radix); |
| let radix = radix as BigDigit; |
| |
| while digits.data.len() > 1 { |
| let (q, mut r) = div_rem_digit(digits, base); |
| for _ in 0..power { |
| res.push((r % radix) as u8); |
| r /= radix; |
| } |
| digits = q; |
| } |
| |
| let mut r = digits.data[0]; |
| while r != 0 { |
| res.push((r % radix) as u8); |
| r /= radix; |
| } |
| |
| res |
| } |
| |
| pub fn to_radix_le(u: &BigUint, radix: u32) -> Vec<u8> { |
| if u.is_zero() { |
| vec![0] |
| } else if radix.is_power_of_two() { |
| // Powers of two can use bitwise masks and shifting instead of division |
| let bits = ilog2(radix); |
| if big_digit::BITS % bits == 0 { |
| to_bitwise_digits_le(u, bits) |
| } else { |
| to_inexact_bitwise_digits_le(u, bits) |
| } |
| } else if radix == 10 { |
| // 10 is so common that it's worth separating out for const-propagation. |
| // Optimizers can often turn constant division into a faster multiplication. |
| to_radix_digits_le(u, 10) |
| } else { |
| to_radix_digits_le(u, radix) |
| } |
| } |
| |
| pub fn to_str_radix_reversed(u: &BigUint, radix: u32) -> Vec<u8> { |
| assert!(2 <= radix && radix <= 36, "The radix must be within 2...36"); |
| |
| if u.is_zero() { |
| return vec![b'0']; |
| } |
| |
| let mut res = to_radix_le(u, radix); |
| |
| // Now convert everything to ASCII digits. |
| for r in &mut res { |
| debug_assert!((*r as u32) < radix); |
| if *r < 10 { |
| *r += b'0'; |
| } else { |
| *r += b'a' - 10; |
| } |
| } |
| res |
| } |
| |
| impl BigUint { |
| /// Creates and initializes a `BigUint`. |
| /// |
| /// The digits are in little-endian base 2<sup>32</sup>. |
| #[inline] |
| pub fn new(digits: Vec<u32>) -> BigUint { |
| BigUint { data: digits }.normalized() |
| } |
| |
| /// Creates and initializes a `BigUint`. |
| /// |
| /// The digits are in little-endian base 2<sup>32</sup>. |
| #[inline] |
| pub fn from_slice(slice: &[u32]) -> BigUint { |
| BigUint::new(slice.to_vec()) |
| } |
| |
| /// Assign a value to a `BigUint`. |
| /// |
| /// The digits are in little-endian base 2<sup>32</sup>. |
| #[inline] |
| pub fn assign_from_slice(&mut self, slice: &[u32]) { |
| self.data.resize(slice.len(), 0); |
| self.data.clone_from_slice(slice); |
| self.normalize(); |
| } |
| |
| /// Creates and initializes a `BigUint`. |
| /// |
| /// The bytes are in big-endian byte order. |
| /// |
| /// # Examples |
| /// |
| /// ``` |
| /// use num_bigint::BigUint; |
| /// |
| /// assert_eq!(BigUint::from_bytes_be(b"A"), |
| /// BigUint::parse_bytes(b"65", 10).unwrap()); |
| /// assert_eq!(BigUint::from_bytes_be(b"AA"), |
| /// BigUint::parse_bytes(b"16705", 10).unwrap()); |
| /// assert_eq!(BigUint::from_bytes_be(b"AB"), |
| /// BigUint::parse_bytes(b"16706", 10).unwrap()); |
| /// assert_eq!(BigUint::from_bytes_be(b"Hello world!"), |
| /// BigUint::parse_bytes(b"22405534230753963835153736737", 10).unwrap()); |
| /// ``` |
| #[inline] |
| pub fn from_bytes_be(bytes: &[u8]) -> BigUint { |
| if bytes.is_empty() { |
| Zero::zero() |
| } else { |
| let mut v = bytes.to_vec(); |
| v.reverse(); |
| BigUint::from_bytes_le(&*v) |
| } |
| } |
| |
| /// Creates and initializes a `BigUint`. |
| /// |
| /// The bytes are in little-endian byte order. |
| #[inline] |
| pub fn from_bytes_le(bytes: &[u8]) -> BigUint { |
| if bytes.is_empty() { |
| Zero::zero() |
| } else { |
| from_bitwise_digits_le(bytes, 8) |
| } |
| } |
| |
| /// Creates and initializes a `BigUint`. The input slice must contain |
| /// ascii/utf8 characters in [0-9a-zA-Z]. |
| /// `radix` must be in the range `2...36`. |
| /// |
| /// The function `from_str_radix` from the `Num` trait provides the same logic |
| /// for `&str` buffers. |
| /// |
| /// # Examples |
| /// |
| /// ``` |
| /// use num_bigint::{BigUint, ToBigUint}; |
| /// |
| /// assert_eq!(BigUint::parse_bytes(b"1234", 10), ToBigUint::to_biguint(&1234)); |
| /// assert_eq!(BigUint::parse_bytes(b"ABCD", 16), ToBigUint::to_biguint(&0xABCD)); |
| /// assert_eq!(BigUint::parse_bytes(b"G", 16), None); |
| /// ``` |
| #[inline] |
| pub fn parse_bytes(buf: &[u8], radix: u32) -> Option<BigUint> { |
| str::from_utf8(buf) |
| .ok() |
| .and_then(|s| BigUint::from_str_radix(s, radix).ok()) |
| } |
| |
| /// Creates and initializes a `BigUint`. Each u8 of the input slice is |
| /// interpreted as one digit of the number |
| /// and must therefore be less than `radix`. |
| /// |
| /// The bytes are in big-endian byte order. |
| /// `radix` must be in the range `2...256`. |
| /// |
| /// # Examples |
| /// |
| /// ``` |
| /// use num_bigint::{BigUint}; |
| /// |
| /// let inbase190 = &[15, 33, 125, 12, 14]; |
| /// let a = BigUint::from_radix_be(inbase190, 190).unwrap(); |
| /// assert_eq!(a.to_radix_be(190), inbase190); |
| /// ``` |
| pub fn from_radix_be(buf: &[u8], radix: u32) -> Option<BigUint> { |
| assert!( |
| 2 <= radix && radix <= 256, |
| "The radix must be within 2...256" |
| ); |
| |
| if radix != 256 && buf.iter().any(|&b| b >= radix as u8) { |
| return None; |
| } |
| |
| let res = if radix.is_power_of_two() { |
| // Powers of two can use bitwise masks and shifting instead of multiplication |
| let bits = ilog2(radix); |
| let mut v = Vec::from(buf); |
| v.reverse(); |
| if big_digit::BITS % bits == 0 { |
| from_bitwise_digits_le(&v, bits) |
| } else { |
| from_inexact_bitwise_digits_le(&v, bits) |
| } |
| } else { |
| from_radix_digits_be(buf, radix) |
| }; |
| |
| Some(res) |
| } |
| |
| /// Creates and initializes a `BigUint`. Each u8 of the input slice is |
| /// interpreted as one digit of the number |
| /// and must therefore be less than `radix`. |
| /// |
| /// The bytes are in little-endian byte order. |
| /// `radix` must be in the range `2...256`. |
| /// |
| /// # Examples |
| /// |
| /// ``` |
| /// use num_bigint::{BigUint}; |
| /// |
| /// let inbase190 = &[14, 12, 125, 33, 15]; |
| /// let a = BigUint::from_radix_be(inbase190, 190).unwrap(); |
| /// assert_eq!(a.to_radix_be(190), inbase190); |
| /// ``` |
| pub fn from_radix_le(buf: &[u8], radix: u32) -> Option<BigUint> { |
| assert!( |
| 2 <= radix && radix <= 256, |
| "The radix must be within 2...256" |
| ); |
| |
| if radix != 256 && buf.iter().any(|&b| b >= radix as u8) { |
| return None; |
| } |
| |
| let res = if radix.is_power_of_two() { |
| // Powers of two can use bitwise masks and shifting instead of multiplication |
| let bits = ilog2(radix); |
| if big_digit::BITS % bits == 0 { |
| from_bitwise_digits_le(buf, bits) |
| } else { |
| from_inexact_bitwise_digits_le(buf, bits) |
| } |
| } else { |
| let mut v = Vec::from(buf); |
| v.reverse(); |
| from_radix_digits_be(&v, radix) |
| }; |
| |
| Some(res) |
| } |
| |
| /// Returns the byte representation of the `BigUint` in big-endian byte order. |
| /// |
| /// # Examples |
| /// |
| /// ``` |
| /// use num_bigint::BigUint; |
| /// |
| /// let i = BigUint::parse_bytes(b"1125", 10).unwrap(); |
| /// assert_eq!(i.to_bytes_be(), vec![4, 101]); |
| /// ``` |
| #[inline] |
| pub fn to_bytes_be(&self) -> Vec<u8> { |
| let mut v = self.to_bytes_le(); |
| v.reverse(); |
| v |
| } |
| |
| /// Returns the byte representation of the `BigUint` in little-endian byte order. |
| /// |
| /// # Examples |
| /// |
| /// ``` |
| /// use num_bigint::BigUint; |
| /// |
| /// let i = BigUint::parse_bytes(b"1125", 10).unwrap(); |
| /// assert_eq!(i.to_bytes_le(), vec![101, 4]); |
| /// ``` |
| #[inline] |
| pub fn to_bytes_le(&self) -> Vec<u8> { |
| if self.is_zero() { |
| vec![0] |
| } else { |
| to_bitwise_digits_le(self, 8) |
| } |
| } |
| |
| /// Returns the integer formatted as a string in the given radix. |
| /// `radix` must be in the range `2...36`. |
| /// |
| /// # Examples |
| /// |
| /// ``` |
| /// use num_bigint::BigUint; |
| /// |
| /// let i = BigUint::parse_bytes(b"ff", 16).unwrap(); |
| /// assert_eq!(i.to_str_radix(16), "ff"); |
| /// ``` |
| #[inline] |
| pub fn to_str_radix(&self, radix: u32) -> String { |
| let mut v = to_str_radix_reversed(self, radix); |
| v.reverse(); |
| unsafe { String::from_utf8_unchecked(v) } |
| } |
| |
| /// Returns the integer in the requested base in big-endian digit order. |
| /// The output is not given in a human readable alphabet but as a zero |
| /// based u8 number. |
| /// `radix` must be in the range `2...256`. |
| /// |
| /// # Examples |
| /// |
| /// ``` |
| /// use num_bigint::BigUint; |
| /// |
| /// assert_eq!(BigUint::from(0xFFFFu64).to_radix_be(159), |
| /// vec![2, 94, 27]); |
| /// // 0xFFFF = 65535 = 2*(159^2) + 94*159 + 27 |
| /// ``` |
| #[inline] |
| pub fn to_radix_be(&self, radix: u32) -> Vec<u8> { |
| let mut v = to_radix_le(self, radix); |
| v.reverse(); |
| v |
| } |
| |
| /// Returns the integer in the requested base in little-endian digit order. |
| /// The output is not given in a human readable alphabet but as a zero |
| /// based u8 number. |
| /// `radix` must be in the range `2...256`. |
| /// |
| /// # Examples |
| /// |
| /// ``` |
| /// use num_bigint::BigUint; |
| /// |
| /// assert_eq!(BigUint::from(0xFFFFu64).to_radix_le(159), |
| /// vec![27, 94, 2]); |
| /// // 0xFFFF = 65535 = 27 + 94*159 + 2*(159^2) |
| /// ``` |
| #[inline] |
| pub fn to_radix_le(&self, radix: u32) -> Vec<u8> { |
| to_radix_le(self, radix) |
| } |
| |
| /// Determines the fewest bits necessary to express the `BigUint`. |
| #[inline] |
| pub fn bits(&self) -> usize { |
| if self.is_zero() { |
| return 0; |
| } |
| let zeros = self.data.last().unwrap().leading_zeros(); |
| return self.data.len() * big_digit::BITS - zeros as usize; |
| } |
| |
| /// Strips off trailing zero bigdigits - comparisons require the last element in the vector to |
| /// be nonzero. |
| #[inline] |
| fn normalize(&mut self) { |
| while let Some(&0) = self.data.last() { |
| self.data.pop(); |
| } |
| } |
| |
| /// Returns a normalized `BigUint`. |
| #[inline] |
| fn normalized(mut self) -> BigUint { |
| self.normalize(); |
| self |
| } |
| |
| /// Returns `(self ^ exponent) % modulus`. |
| /// |
| /// Panics if the modulus is zero. |
| pub fn modpow(&self, exponent: &Self, modulus: &Self) -> Self { |
| assert!(!modulus.is_zero(), "divide by zero!"); |
| |
| // For an odd modulus, we can use Montgomery multiplication in base 2^32. |
| if modulus.is_odd() { |
| return monty_modpow(self, exponent, modulus); |
| } |
| |
| // Otherwise do basically the same as `num::pow`, but with a modulus. |
| let one = BigUint::one(); |
| if exponent.is_zero() { |
| return one; |
| } |
| |
| let mut base = self % modulus; |
| let mut exp = exponent.clone(); |
| while exp.is_even() { |
| base = &base * &base % modulus; |
| exp >>= 1; |
| } |
| if exp == one { |
| return base; |
| } |
| |
| let mut acc = base.clone(); |
| while exp > one { |
| exp >>= 1; |
| base = &base * &base % modulus; |
| if exp.is_odd() { |
| acc = acc * &base % modulus; |
| } |
| } |
| acc |
| } |
| |
| /// Returns the truncated principal square root of `self` -- |
| /// see [Roots::sqrt](https://docs.rs/num-integer/0.1/num_integer/trait.Roots.html#method.sqrt) |
| pub fn sqrt(&self) -> Self { |
| Roots::sqrt(self) |
| } |
| |
| /// Returns the truncated principal cube root of `self` -- |
| /// see [Roots::cbrt](https://docs.rs/num-integer/0.1/num_integer/trait.Roots.html#method.cbrt). |
| pub fn cbrt(&self) -> Self { |
| Roots::cbrt(self) |
| } |
| |
| /// Returns the truncated principal `n`th root of `self` -- |
| /// see [Roots::nth_root](https://docs.rs/num-integer/0.1/num_integer/trait.Roots.html#tymethod.nth_root). |
| pub fn nth_root(&self, n: u32) -> Self { |
| Roots::nth_root(self, n) |
| } |
| } |
| |
| /// Returns the number of least-significant bits that are zero, |
| /// or `None` if the entire number is zero. |
| pub fn trailing_zeros(u: &BigUint) -> Option<usize> { |
| u.data |
| .iter() |
| .enumerate() |
| .find(|&(_, &digit)| digit != 0) |
| .map(|(i, digit)| i * big_digit::BITS + digit.trailing_zeros() as usize) |
| } |
| |
| impl_sum_iter_type!(BigUint); |
| impl_product_iter_type!(BigUint); |
| |
| pub trait IntDigits { |
| fn digits(&self) -> &[BigDigit]; |
| fn digits_mut(&mut self) -> &mut Vec<BigDigit>; |
| fn normalize(&mut self); |
| fn capacity(&self) -> usize; |
| fn len(&self) -> usize; |
| } |
| |
| impl IntDigits for BigUint { |
| #[inline] |
| fn digits(&self) -> &[BigDigit] { |
| &self.data |
| } |
| #[inline] |
| fn digits_mut(&mut self) -> &mut Vec<BigDigit> { |
| &mut self.data |
| } |
| #[inline] |
| fn normalize(&mut self) { |
| self.normalize(); |
| } |
| #[inline] |
| fn capacity(&self) -> usize { |
| self.data.capacity() |
| } |
| #[inline] |
| fn len(&self) -> usize { |
| self.data.len() |
| } |
| } |
| |
| /// Combine four `u32`s into a single `u128`. |
| #[cfg(has_i128)] |
| #[inline] |
| fn u32_to_u128(a: u32, b: u32, c: u32, d: u32) -> u128 { |
| u128::from(d) | (u128::from(c) << 32) | (u128::from(b) << 64) | (u128::from(a) << 96) |
| } |
| |
| /// Split a single `u128` into four `u32`. |
| #[cfg(has_i128)] |
| #[inline] |
| fn u32_from_u128(n: u128) -> (u32, u32, u32, u32) { |
| ( |
| (n >> 96) as u32, |
| (n >> 64) as u32, |
| (n >> 32) as u32, |
| n as u32, |
| ) |
| } |
| |
| #[cfg(feature = "serde")] |
| impl serde::Serialize for BigUint { |
| fn serialize<S>(&self, serializer: S) -> Result<S::Ok, S::Error> |
| where |
| S: serde::Serializer, |
| { |
| // Note: do not change the serialization format, or it may break forward |
| // and backward compatibility of serialized data! If we ever change the |
| // internal representation, we should still serialize in base-`u32`. |
| let data: &Vec<u32> = &self.data; |
| data.serialize(serializer) |
| } |
| } |
| |
| #[cfg(feature = "serde")] |
| impl<'de> serde::Deserialize<'de> for BigUint { |
| fn deserialize<D>(deserializer: D) -> Result<Self, D::Error> |
| where |
| D: serde::Deserializer<'de>, |
| { |
| let data: Vec<u32> = try!(Vec::deserialize(deserializer)); |
| Ok(BigUint::new(data)) |
| } |
| } |
| |
| /// Returns the greatest power of the radix <= big_digit::BASE |
| #[inline] |
| fn get_radix_base(radix: u32) -> (BigDigit, usize) { |
| debug_assert!( |
| 2 <= radix && radix <= 256, |
| "The radix must be within 2...256" |
| ); |
| debug_assert!(!radix.is_power_of_two()); |
| |
| // To generate this table: |
| // for radix in 2u64..257 { |
| // let mut power = big_digit::BITS / fls(radix as u64); |
| // let mut base = radix.pow(power as u32); |
| // |
| // while let Some(b) = base.checked_mul(radix) { |
| // if b > big_digit::MAX { |
| // break; |
| // } |
| // base = b; |
| // power += 1; |
| // } |
| // |
| // println!("({:10}, {:2}), // {:2}", base, power, radix); |
| // } |
| // and |
| // for radix in 2u64..257 { |
| // let mut power = 64 / fls(radix as u64); |
| // let mut base = radix.pow(power as u32); |
| // |
| // while let Some(b) = base.checked_mul(radix) { |
| // base = b; |
| // power += 1; |
| // } |
| // |
| // println!("({:20}, {:2}), // {:2}", base, power, radix); |
| // } |
| match big_digit::BITS { |
| 32 => { |
| const BASES: [(u32, usize); 257] = [ |
| (0, 0), |
| (0, 0), |
| (0, 0), // 2 |
| (3486784401, 20), // 3 |
| (0, 0), // 4 |
| (1220703125, 13), // 5 |
| (2176782336, 12), // 6 |
| (1977326743, 11), // 7 |
| (0, 0), // 8 |
| (3486784401, 10), // 9 |
| (1000000000, 9), // 10 |
| (2357947691, 9), // 11 |
| (429981696, 8), // 12 |
| (815730721, 8), // 13 |
| (1475789056, 8), // 14 |
| (2562890625, 8), // 15 |
| (0, 0), // 16 |
| (410338673, 7), // 17 |
| (612220032, 7), // 18 |
| (893871739, 7), // 19 |
| (1280000000, 7), // 20 |
| (1801088541, 7), // 21 |
| (2494357888, 7), // 22 |
| (3404825447, 7), // 23 |
| (191102976, 6), // 24 |
| (244140625, 6), // 25 |
| (308915776, 6), // 26 |
| (387420489, 6), // 27 |
| (481890304, 6), // 28 |
| (594823321, 6), // 29 |
| (729000000, 6), // 30 |
| (887503681, 6), // 31 |
| (0, 0), // 32 |
| (1291467969, 6), // 33 |
| (1544804416, 6), // 34 |
| (1838265625, 6), // 35 |
| (2176782336, 6), // 36 |
| (2565726409, 6), // 37 |
| (3010936384, 6), // 38 |
| (3518743761, 6), // 39 |
| (4096000000, 6), // 40 |
| (115856201, 5), // 41 |
| (130691232, 5), // 42 |
| (147008443, 5), // 43 |
| (164916224, 5), // 44 |
| (184528125, 5), // 45 |
| (205962976, 5), // 46 |
| (229345007, 5), // 47 |
| (254803968, 5), // 48 |
| (282475249, 5), // 49 |
| (312500000, 5), // 50 |
| (345025251, 5), // 51 |
| (380204032, 5), // 52 |
| (418195493, 5), // 53 |
| (459165024, 5), // 54 |
| (503284375, 5), // 55 |
| (550731776, 5), // 56 |
| (601692057, 5), // 57 |
| (656356768, 5), // 58 |
| (714924299, 5), // 59 |
| (777600000, 5), // 60 |
| (844596301, 5), // 61 |
| (916132832, 5), // 62 |
| (992436543, 5), // 63 |
| (0, 0), // 64 |
| (1160290625, 5), // 65 |
| (1252332576, 5), // 66 |
| (1350125107, 5), // 67 |
| (1453933568, 5), // 68 |
| (1564031349, 5), // 69 |
| (1680700000, 5), // 70 |
| (1804229351, 5), // 71 |
| (1934917632, 5), // 72 |
| (2073071593, 5), // 73 |
| (2219006624, 5), // 74 |
| (2373046875, 5), // 75 |
| (2535525376, 5), // 76 |
| (2706784157, 5), // 77 |
| (2887174368, 5), // 78 |
| (3077056399, 5), // 79 |
| (3276800000, 5), // 80 |
| (3486784401, 5), // 81 |
| (3707398432, 5), // 82 |
| (3939040643, 5), // 83 |
| (4182119424, 5), // 84 |
| (52200625, 4), // 85 |
| (54700816, 4), // 86 |
| (57289761, 4), // 87 |
| (59969536, 4), // 88 |
| (62742241, 4), // 89 |
| (65610000, 4), // 90 |
| (68574961, 4), // 91 |
| (71639296, 4), // 92 |
| (74805201, 4), // 93 |
| (78074896, 4), // 94 |
| (81450625, 4), // 95 |
| (84934656, 4), // 96 |
| (88529281, 4), // 97 |
| (92236816, 4), // 98 |
| (96059601, 4), // 99 |
| (100000000, 4), // 100 |
| (104060401, 4), // 101 |
| (108243216, 4), // 102 |
| (112550881, 4), // 103 |
| (116985856, 4), // 104 |
| (121550625, 4), // 105 |
| (126247696, 4), // 106 |
| (131079601, 4), // 107 |
| (136048896, 4), // 108 |
| (141158161, 4), // 109 |
| (146410000, 4), // 110 |
| (151807041, 4), // 111 |
| (157351936, 4), // 112 |
| (163047361, 4), // 113 |
| (168896016, 4), // 114 |
| (174900625, 4), // 115 |
| (181063936, 4), // 116 |
| (187388721, 4), // 117 |
| (193877776, 4), // 118 |
| (200533921, 4), // 119 |
| (207360000, 4), // 120 |
| (214358881, 4), // 121 |
| (221533456, 4), // 122 |
| (228886641, 4), // 123 |
| (236421376, 4), // 124 |
| (244140625, 4), // 125 |
| (252047376, 4), // 126 |
| (260144641, 4), // 127 |
| (0, 0), // 128 |
| (276922881, 4), // 129 |
| (285610000, 4), // 130 |
| (294499921, 4), // 131 |
| (303595776, 4), // 132 |
| (312900721, 4), // 133 |
| (322417936, 4), // 134 |
| (332150625, 4), // 135 |
| (342102016, 4), // 136 |
| (352275361, 4), // 137 |
| (362673936, 4), // 138 |
| (373301041, 4), // 139 |
| (384160000, 4), // 140 |
| (395254161, 4), // 141 |
| (406586896, 4), // 142 |
| (418161601, 4), // 143 |
| (429981696, 4), // 144 |
| (442050625, 4), // 145 |
| (454371856, 4), // 146 |
| (466948881, 4), // 147 |
| (479785216, 4), // 148 |
| (492884401, 4), // 149 |
| (506250000, 4), // 150 |
| (519885601, 4), // 151 |
| (533794816, 4), // 152 |
| (547981281, 4), // 153 |
| (562448656, 4), // 154 |
| (577200625, 4), // 155 |
| (592240896, 4), // 156 |
| (607573201, 4), // 157 |
| (623201296, 4), // 158 |
| (639128961, 4), // 159 |
| (655360000, 4), // 160 |
| (671898241, 4), // 161 |
| (688747536, 4), // 162 |
| (705911761, 4), // 163 |
| (723394816, 4), // 164 |
| (741200625, 4), // 165 |
| (759333136, 4), // 166 |
| (777796321, 4), // 167 |
| (796594176, 4), // 168 |
| (815730721, 4), // 169 |
| (835210000, 4), // 170 |
| (855036081, 4), // 171 |
| (875213056, 4), // 172 |
| (895745041, 4), // 173 |
| (916636176, 4), // 174 |
| (937890625, 4), // 175 |
| (959512576, 4), // 176 |
| (981506241, 4), // 177 |
| (1003875856, 4), // 178 |
| (1026625681, 4), // 179 |
| (1049760000, 4), // 180 |
| (1073283121, 4), // 181 |
| (1097199376, 4), // 182 |
| (1121513121, 4), // 183 |
| (1146228736, 4), // 184 |
| (1171350625, 4), // 185 |
| (1196883216, 4), // 186 |
| (1222830961, 4), // 187 |
| (1249198336, 4), // 188 |
| (1275989841, 4), // 189 |
| (1303210000, 4), // 190 |
| (1330863361, 4), // 191 |
| (1358954496, 4), // 192 |
| (1387488001, 4), // 193 |
| (1416468496, 4), // 194 |
| (1445900625, 4), // 195 |
| (1475789056, 4), // 196 |
| (1506138481, 4), // 197 |
| (1536953616, 4), // 198 |
| (1568239201, 4), // 199 |
| (1600000000, 4), // 200 |
| (1632240801, 4), // 201 |
| (1664966416, 4), // 202 |
| (1698181681, 4), // 203 |
| (1731891456, 4), // 204 |
| (1766100625, 4), // 205 |
| (1800814096, 4), // 206 |
| (1836036801, 4), // 207 |
| (1871773696, 4), // 208 |
| (1908029761, 4), // 209 |
| (1944810000, 4), // 210 |
| (1982119441, 4), // 211 |
| (2019963136, 4), // 212 |
| (2058346161, 4), // 213 |
| (2097273616, 4), // 214 |
| (2136750625, 4), // 215 |
| (2176782336, 4), // 216 |
| (2217373921, 4), // 217 |
| (2258530576, 4), // 218 |
| (2300257521, 4), // 219 |
| (2342560000, 4), // 220 |
| (2385443281, 4), // 221 |
| (2428912656, 4), // 222 |
| (2472973441, 4), // 223 |
| (2517630976, 4), // 224 |
| (2562890625, 4), // 225 |
| (2608757776, 4), // 226 |
| (2655237841, 4), // 227 |
| (2702336256, 4), // 228 |
| (2750058481, 4), // 229 |
| (2798410000, 4), // 230 |
| (2847396321, 4), // 231 |
| (2897022976, 4), // 232 |
| (2947295521, 4), // 233 |
| (2998219536, 4), // 234 |
| (3049800625, 4), // 235 |
| (3102044416, 4), // 236 |
| (3154956561, 4), // 237 |
| (3208542736, 4), // 238 |
| (3262808641, 4), // 239 |
| (3317760000, 4), // 240 |
| (3373402561, 4), // 241 |
| (3429742096, 4), // 242 |
| (3486784401, 4), // 243 |
| (3544535296, 4), // 244 |
| (3603000625, 4), // 245 |
| (3662186256, 4), // 246 |
| (3722098081, 4), // 247 |
| (3782742016, 4), // 248 |
| (3844124001, 4), // 249 |
| (3906250000, 4), // 250 |
| (3969126001, 4), // 251 |
| (4032758016, 4), // 252 |
| (4097152081, 4), // 253 |
| (4162314256, 4), // 254 |
| (4228250625, 4), // 255 |
| (0, 0), // 256 |
| ]; |
| |
| let (base, power) = BASES[radix as usize]; |
| (base as BigDigit, power) |
| } |
| 64 => { |
| const BASES: [(u64, usize); 257] = [ |
| (0, 0), |
| (0, 0), |
| (9223372036854775808, 63), // 2 |
| (12157665459056928801, 40), // 3 |
| (4611686018427387904, 31), // 4 |
| (7450580596923828125, 27), // 5 |
| (4738381338321616896, 24), // 6 |
| (3909821048582988049, 22), // 7 |
| (9223372036854775808, 21), // 8 |
| (12157665459056928801, 20), // 9 |
| (10000000000000000000, 19), // 10 |
| (5559917313492231481, 18), // 11 |
| (2218611106740436992, 17), // 12 |
| (8650415919381337933, 17), // 13 |
| (2177953337809371136, 16), // 14 |
| (6568408355712890625, 16), // 15 |
| (1152921504606846976, 15), // 16 |
| (2862423051509815793, 15), // 17 |
| (6746640616477458432, 15), // 18 |
| (15181127029874798299, 15), // 19 |
| (1638400000000000000, 14), // 20 |
| (3243919932521508681, 14), // 21 |
| (6221821273427820544, 14), // 22 |
| (11592836324538749809, 14), // 23 |
| (876488338465357824, 13), // 24 |
| (1490116119384765625, 13), // 25 |
| (2481152873203736576, 13), // 26 |
| (4052555153018976267, 13), // 27 |
| (6502111422497947648, 13), // 28 |
| (10260628712958602189, 13), // 29 |
| (15943230000000000000, 13), // 30 |
| (787662783788549761, 12), // 31 |
| (1152921504606846976, 12), // 32 |
| (1667889514952984961, 12), // 33 |
| (2386420683693101056, 12), // 34 |
| (3379220508056640625, 12), // 35 |
| (4738381338321616896, 12), // 36 |
| (6582952005840035281, 12), // 37 |
| (9065737908494995456, 12), // 38 |
| (12381557655576425121, 12), // 39 |
| (16777216000000000000, 12), // 40 |
| (550329031716248441, 11), // 41 |
| (717368321110468608, 11), // 42 |
| (929293739471222707, 11), // 43 |
| (1196683881290399744, 11), // 44 |
| (1532278301220703125, 11), // 45 |
| (1951354384207722496, 11), // 46 |
| (2472159215084012303, 11), // 47 |
| (3116402981210161152, 11), // 48 |
| (3909821048582988049, 11), // 49 |
| (4882812500000000000, 11), // 50 |
| (6071163615208263051, 11), // 51 |
| (7516865509350965248, 11), // 52 |
| (9269035929372191597, 11), // 53 |
| (11384956040305711104, 11), // 54 |
| (13931233916552734375, 11), // 55 |
| (16985107389382393856, 11), // 56 |
| (362033331456891249, 10), // 57 |
| (430804206899405824, 10), // 58 |
| (511116753300641401, 10), // 59 |
| (604661760000000000, 10), // 60 |
| (713342911662882601, 10), // 61 |
| (839299365868340224, 10), // 62 |
| (984930291881790849, 10), // 63 |
| (1152921504606846976, 10), // 64 |
| (1346274334462890625, 10), // 65 |
| (1568336880910795776, 10), // 66 |
| (1822837804551761449, 10), // 67 |
| (2113922820157210624, 10), // 68 |
| (2446194060654759801, 10), // 69 |
| (2824752490000000000, 10), // 70 |
| (3255243551009881201, 10), // 71 |
| (3743906242624487424, 10), // 72 |
| (4297625829703557649, 10), // 73 |
| (4923990397355877376, 10), // 74 |
| (5631351470947265625, 10), // 75 |
| (6428888932339941376, 10), // 76 |
| (7326680472586200649, 10), // 77 |
| (8335775831236199424, 10), // 78 |
| (9468276082626847201, 10), // 79 |
| (10737418240000000000, 10), // 80 |
| (12157665459056928801, 10), // 81 |
| (13744803133596058624, 10), // 82 |
| (15516041187205853449, 10), // 83 |
| (17490122876598091776, 10), // 84 |
| (231616946283203125, 9), // 85 |
| (257327417311663616, 9), // 86 |
| (285544154243029527, 9), // 87 |
| (316478381828866048, 9), // 88 |
| (350356403707485209, 9), // 89 |
| (387420489000000000, 9), // 90 |
| (427929800129788411, 9), // 91 |
| (472161363286556672, 9), // 92 |
| (520411082988487293, 9), // 93 |
| (572994802228616704, 9), // 94 |
| (630249409724609375, 9), // 95 |
| (692533995824480256, 9), // 96 |
| (760231058654565217, 9), // 97 |
| (833747762130149888, 9), // 98 |
| (913517247483640899, 9), // 99 |
| (1000000000000000000, 9), // 100 |
| (1093685272684360901, 9), // 101 |
| (1195092568622310912, 9), // 102 |
| (1304773183829244583, 9), // 103 |
| (1423311812421484544, 9), // 104 |
| (1551328215978515625, 9), // 105 |
| (1689478959002692096, 9), // 106 |
| (1838459212420154507, 9), // 107 |
| (1999004627104432128, 9), // 108 |
| (2171893279442309389, 9), // 109 |
| (2357947691000000000, 9), // 110 |
| (2558036924386500591, 9), // 111 |
| (2773078757450186752, 9), // 112 |
| (3004041937984268273, 9), // 113 |
| (3251948521156637184, 9), // 114 |
| (3517876291919921875, 9), // 115 |
| (3802961274698203136, 9), // 116 |
| (4108400332687853397, 9), // 117 |
| (4435453859151328768, 9), // 118 |
| (4785448563124474679, 9), // 119 |
| (5159780352000000000, 9), // 120 |
| (5559917313492231481, 9), // 121 |
| (5987402799531080192, 9), // 122 |
| (6443858614676334363, 9), // 123 |
| (6930988311686938624, 9), // 124 |
| (7450580596923828125, 9), // 125 |
| (8004512848309157376, 9), // 126 |
| (8594754748609397887, 9), // 127 |
| (9223372036854775808, 9), // 128 |
| (9892530380752880769, 9), // 129 |
| (10604499373000000000, 9), // 130 |
| (11361656654439817571, 9), // 131 |
| (12166492167065567232, 9), // 132 |
| (13021612539908538853, 9), // 133 |
| (13929745610903012864, 9), // 134 |
| (14893745087865234375, 9), // 135 |
| (15916595351771938816, 9), // 136 |
| (17001416405572203977, 9), // 137 |
| (18151468971815029248, 9), // 138 |
| (139353667211683681, 8), // 139 |
| (147578905600000000, 8), // 140 |
| (156225851787813921, 8), // 141 |
| (165312903998914816, 8), // 142 |
| (174859124550883201, 8), // 143 |
| (184884258895036416, 8), // 144 |
| (195408755062890625, 8), // 145 |
| (206453783524884736, 8), // 146 |
| (218041257467152161, 8), // 147 |
| (230193853492166656, 8), // 148 |
| (242935032749128801, 8), // 149 |
| (256289062500000000, 8), // 150 |
| (270281038127131201, 8), // 151 |
| (284936905588473856, 8), // 152 |
| (300283484326400961, 8), // 153 |
| (316348490636206336, 8), // 154 |
| (333160561500390625, 8), // 155 |
| (350749278894882816, 8), // 156 |
| (369145194573386401, 8), // 157 |
| (388379855336079616, 8), // 158 |
| (408485828788939521, 8), // 159 |
| (429496729600000000, 8), // 160 |
| (451447246258894081, 8), // 161 |
| (474373168346071296, 8), // 162 |
| (498311414318121121, 8), // 163 |
| (523300059815673856, 8), // 164 |
| (549378366500390625, 8), // 165 |
| (576586811427594496, 8), // 166 |
| (604967116961135041, 8), // 167 |
| (634562281237118976, 8), // 168 |
| (665416609183179841, 8), // 169 |
| (697575744100000000, 8), // 170 |
| (731086699811838561, 8), // 171 |
| (765997893392859136, 8), // 172 |
| (802359178476091681, 8), // 173 |
| (840221879151902976, 8), // 174 |
| (879638824462890625, 8), // 175 |
| (920664383502155776, 8), // 176 |
| (963354501121950081, 8), // 177 |
| (1007766734259732736, 8), // 178 |
| (1053960288888713761, 8), // 179 |
| (1101996057600000000, 8), // 180 |
| (1151936657823500641, 8), // 181 |
| (1203846470694789376, 8), // 182 |
| (1257791680575160641, 8), // 183 |
| (1313840315232157696, 8), // 184 |
| (1372062286687890625, 8), // 185 |
| (1432529432742502656, 8), // 186 |
| (1495315559180183521, 8), // 187 |
| (1560496482665168896, 8), // 188 |
| (1628150074335205281, 8), // 189 |
| (1698356304100000000, 8), // 190 |
| (1771197285652216321, 8), // 191 |
| (1846757322198614016, 8), // 192 |
| (1925122952918976001, 8), // 193 |
| (2006383000160502016, 8), // 194 |
| (2090628617375390625, 8), // 195 |
| (2177953337809371136, 8), // 196 |
| (2268453123948987361, 8), // 197 |
| (2362226417735475456, 8), // 198 |
| (2459374191553118401, 8), // 199 |
| (2560000000000000000, 8), // 200 |
| (2664210032449121601, 8), // 201 |
| (2772113166407885056, 8), // 202 |
| (2883821021683985761, 8), // 203 |
| (2999448015365799936, 8), // 204 |
| (3119111417625390625, 8), // 205 |
| (3242931408352297216, 8), // 206 |
| (3371031134626313601, 8), // 207 |
| (3503536769037500416, 8), // 208 |
| (3640577568861717121, 8), // 209 |
| (3782285936100000000, 8), // 210 |
| (3928797478390152481, 8), // 211 |
| (4080251070798954496, 8), // 212 |
| (4236788918503437921, 8), // 213 |
| (4398556620369715456, 8), // 214 |
| (4565703233437890625, 8), // 215 |
| (4738381338321616896, 8), // 216 |
| (4916747105530914241, 8), // 217 |
| (5100960362726891776, 8), // 218 |
| (5291184662917065441, 8), // 219 |
| (5487587353600000000, 8), // 220 |
| (5690339646868044961, 8), // 221 |
| (5899616690476974336, 8), // 222 |
| (6115597639891380481, 8), // 223 |
| (6338465731314712576, 8), // 224 |
| (6568408355712890625, 8), // 225 |
| (6805617133840466176, 8), // 226 |
| (7050287992278341281, 8), // 227 |
| (7302621240492097536, 8), // 228 |
| (7562821648920027361, 8), // 229 |
| (7831098528100000000, 8), // 230 |
| (8107665808844335041, 8), // 231 |
| (8392742123471896576, 8), // 232 |
| (8686550888106661441, 8), // 233 |
| (8989320386052055296, 8), // 234 |
| (9301283852250390625, 8), // 235 |
| (9622679558836781056, 8), // 236 |
| (9953750901796946721, 8), // 237 |
| (10294746488738365696, 8), // 238 |
| (10645920227784266881, 8), // 239 |
| (11007531417600000000, 8), // 240 |
| (11379844838561358721, 8), // 241 |
| (11763130845074473216, 8), // 242 |
| (12157665459056928801, 8), // 243 |
| (12563730464589807616, 8), // 244 |
| (12981613503750390625, 8), // 245 |
| (13411608173635297536, 8), // 246 |
| (13854014124583882561, 8), // 247 |
| (14309137159611744256, 8), // 248 |
| (14777289335064248001, 8), // 249 |
| (15258789062500000000, 8), // 250 |
| (15753961211814252001, 8), // 251 |
| (16263137215612256256, 8), // 252 |
| (16786655174842630561, 8), // 253 |
| (17324859965700833536, 8), // 254 |
| (17878103347812890625, 8), // 255 |
| (72057594037927936, 7), // 256 |
| ]; |
| |
| let (base, power) = BASES[radix as usize]; |
| (base as BigDigit, power) |
| } |
| _ => panic!("Invalid bigdigit size"), |
| } |
| } |
| |
| #[test] |
| fn test_from_slice() { |
| fn check(slice: &[BigDigit], data: &[BigDigit]) { |
| assert!(BigUint::from_slice(slice).data == data); |
| } |
| check(&[1], &[1]); |
| check(&[0, 0, 0], &[]); |
| check(&[1, 2, 0, 0], &[1, 2]); |
| check(&[0, 0, 1, 2], &[0, 0, 1, 2]); |
| check(&[0, 0, 1, 2, 0, 0], &[0, 0, 1, 2]); |
| check(&[-1i32 as BigDigit], &[-1i32 as BigDigit]); |
| } |
| |
| #[test] |
| fn test_assign_from_slice() { |
| fn check(slice: &[BigDigit], data: &[BigDigit]) { |
| let mut p = BigUint::from_slice(&[2627_u32, 0_u32, 9182_u32, 42_u32]); |
| p.assign_from_slice(slice); |
| assert!(p.data == data); |
| } |
| check(&[1], &[1]); |
| check(&[0, 0, 0], &[]); |
| check(&[1, 2, 0, 0], &[1, 2]); |
| check(&[0, 0, 1, 2], &[0, 0, 1, 2]); |
| check(&[0, 0, 1, 2, 0, 0], &[0, 0, 1, 2]); |
| check(&[-1i32 as BigDigit], &[-1i32 as BigDigit]); |
| } |
| |
| #[cfg(has_i128)] |
| #[test] |
| fn test_u32_u128() { |
| assert_eq!(u32_from_u128(0u128), (0, 0, 0, 0)); |
| assert_eq!( |
| u32_from_u128(u128::max_value()), |
| ( |
| u32::max_value(), |
| u32::max_value(), |
| u32::max_value(), |
| u32::max_value() |
| ) |
| ); |
| |
| assert_eq!( |
| u32_from_u128(u32::max_value() as u128), |
| (0, 0, 0, u32::max_value()) |
| ); |
| |
| assert_eq!( |
| u32_from_u128(u64::max_value() as u128), |
| (0, 0, u32::max_value(), u32::max_value()) |
| ); |
| |
| assert_eq!( |
| u32_from_u128((u64::max_value() as u128) + u32::max_value() as u128), |
| (0, 1, 0, u32::max_value() - 1) |
| ); |
| |
| assert_eq!(u32_from_u128(36_893_488_151_714_070_528), (0, 2, 1, 0)); |
| } |
| |
| #[cfg(has_i128)] |
| #[test] |
| fn test_u128_u32_roundtrip() { |
| // roundtrips |
| let values = vec![ |
| 0u128, |
| 1u128, |
| u64::max_value() as u128 * 3, |
| u32::max_value() as u128, |
| u64::max_value() as u128, |
| (u64::max_value() as u128) + u32::max_value() as u128, |
| u128::max_value(), |
| ]; |
| |
| for val in &values { |
| let (a, b, c, d) = u32_from_u128(*val); |
| assert_eq!(u32_to_u128(a, b, c, d), *val); |
| } |
| } |
