1203 lines
33 KiB
Rust
1203 lines
33 KiB
Rust
use std::borrow::Cow;
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use std::default::Default;
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use std::iter::repeat;
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use std::ops::{Add, BitAnd, BitOr, BitXor, Div, Mul, Neg, Rem, Shl, Shr, Sub};
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use std::str::{self, FromStr};
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use std::fmt;
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use std::cmp;
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use std::cmp::Ordering::{self, Less, Greater, Equal};
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use std::{f32, f64};
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use std::{u8, u64};
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use std::ascii::AsciiExt;
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#[cfg(feature = "serde")]
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use serde;
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use integer::Integer;
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use traits::{ToPrimitive, FromPrimitive, Float, Num, Unsigned, CheckedAdd, CheckedSub, CheckedMul,
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CheckedDiv, Zero, One};
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#[path = "algorithms.rs"]
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mod algorithms;
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pub use self::algorithms::big_digit;
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pub use self::big_digit::{BigDigit, DoubleBigDigit, ZERO_BIG_DIGIT};
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use self::algorithms::{mac_with_carry, mul3, div_rem, div_rem_digit};
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use self::algorithms::{__add2, add2, sub2, sub2rev};
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use self::algorithms::{biguint_shl, biguint_shr};
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use self::algorithms::{cmp_slice, fls, ilog2};
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use ParseBigIntError;
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#[cfg(test)]
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#[path = "tests/biguint.rs"]
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mod biguint_tests;
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/// A big unsigned integer type.
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///
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/// A `BigUint`-typed value `BigUint { data: vec!(a, b, c) }` represents a number
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/// `(a + b * big_digit::BASE + c * big_digit::BASE^2)`.
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#[derive(Clone, Debug, Hash)]
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#[cfg_attr(feature = "rustc-serialize", derive(RustcEncodable, RustcDecodable))]
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pub struct BigUint {
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data: Vec<BigDigit>,
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}
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impl PartialEq for BigUint {
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#[inline]
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fn eq(&self, other: &BigUint) -> bool {
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match self.cmp(other) {
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Equal => true,
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_ => false,
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}
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}
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}
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impl Eq for BigUint {}
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impl PartialOrd for BigUint {
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#[inline]
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fn partial_cmp(&self, other: &BigUint) -> Option<Ordering> {
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Some(self.cmp(other))
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}
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}
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impl Ord for BigUint {
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#[inline]
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fn cmp(&self, other: &BigUint) -> Ordering {
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cmp_slice(&self.data[..], &other.data[..])
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}
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}
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impl Default for BigUint {
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#[inline]
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fn default() -> BigUint {
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Zero::zero()
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}
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}
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impl fmt::Display for BigUint {
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fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
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f.pad_integral(true, "", &self.to_str_radix(10))
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}
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}
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impl fmt::LowerHex for BigUint {
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fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
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f.pad_integral(true, "0x", &self.to_str_radix(16))
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}
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}
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impl fmt::UpperHex for BigUint {
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fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
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f.pad_integral(true, "0x", &self.to_str_radix(16).to_ascii_uppercase())
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}
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}
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impl fmt::Binary for BigUint {
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fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
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f.pad_integral(true, "0b", &self.to_str_radix(2))
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}
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}
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impl fmt::Octal for BigUint {
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fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
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f.pad_integral(true, "0o", &self.to_str_radix(8))
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}
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}
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impl FromStr for BigUint {
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type Err = ParseBigIntError;
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#[inline]
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fn from_str(s: &str) -> Result<BigUint, ParseBigIntError> {
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BigUint::from_str_radix(s, 10)
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}
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}
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// Convert from a power of two radix (bits == ilog2(radix)) where bits evenly divides
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// BigDigit::BITS
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fn from_bitwise_digits_le(v: &[u8], bits: usize) -> BigUint {
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debug_assert!(!v.is_empty() && bits <= 8 && big_digit::BITS % bits == 0);
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debug_assert!(v.iter().all(|&c| (c as BigDigit) < (1 << bits)));
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let digits_per_big_digit = big_digit::BITS / bits;
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let data = v.chunks(digits_per_big_digit)
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.map(|chunk| {
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chunk.iter().rev().fold(0, |acc, &c| (acc << bits) | c as BigDigit)
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})
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.collect();
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BigUint::new(data)
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}
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// Convert from a power of two radix (bits == ilog2(radix)) where bits doesn't evenly divide
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// BigDigit::BITS
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fn from_inexact_bitwise_digits_le(v: &[u8], bits: usize) -> BigUint {
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debug_assert!(!v.is_empty() && bits <= 8 && big_digit::BITS % bits != 0);
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debug_assert!(v.iter().all(|&c| (c as BigDigit) < (1 << bits)));
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let big_digits = (v.len() * bits + big_digit::BITS - 1) / big_digit::BITS;
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let mut data = Vec::with_capacity(big_digits);
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let mut d = 0;
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let mut dbits = 0; // number of bits we currently have in d
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// walk v accumululating bits in d; whenever we accumulate big_digit::BITS in d, spit out a
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// big_digit:
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for &c in v {
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d |= (c as BigDigit) << dbits;
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dbits += bits;
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if dbits >= big_digit::BITS {
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data.push(d);
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dbits -= big_digit::BITS;
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// if dbits was > big_digit::BITS, we dropped some of the bits in c (they couldn't fit
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// in d) - grab the bits we lost here:
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d = (c as BigDigit) >> (bits - dbits);
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}
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}
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if dbits > 0 {
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debug_assert!(dbits < big_digit::BITS);
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data.push(d as BigDigit);
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}
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BigUint::new(data)
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}
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// Read little-endian radix digits
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fn from_radix_digits_be(v: &[u8], radix: u32) -> BigUint {
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debug_assert!(!v.is_empty() && !radix.is_power_of_two());
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debug_assert!(v.iter().all(|&c| (c as u32) < radix));
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// Estimate how big the result will be, so we can pre-allocate it.
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let bits = (radix as f64).log2() * v.len() as f64;
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let big_digits = (bits / big_digit::BITS as f64).ceil();
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let mut data = Vec::with_capacity(big_digits as usize);
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let (base, power) = get_radix_base(radix);
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let radix = radix as BigDigit;
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let r = v.len() % power;
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let i = if r == 0 {
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power
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} else {
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r
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};
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let (head, tail) = v.split_at(i);
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let first = head.iter().fold(0, |acc, &d| acc * radix + d as BigDigit);
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data.push(first);
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debug_assert!(tail.len() % power == 0);
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for chunk in tail.chunks(power) {
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if data.last() != Some(&0) {
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data.push(0);
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}
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let mut carry = 0;
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for d in data.iter_mut() {
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*d = mac_with_carry(0, *d, base, &mut carry);
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}
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debug_assert!(carry == 0);
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let n = chunk.iter().fold(0, |acc, &d| acc * radix + d as BigDigit);
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add2(&mut data, &[n]);
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}
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BigUint::new(data)
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}
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impl Num for BigUint {
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type FromStrRadixErr = ParseBigIntError;
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/// Creates and initializes a `BigUint`.
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fn from_str_radix(s: &str, radix: u32) -> Result<BigUint, ParseBigIntError> {
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assert!(2 <= radix && radix <= 36, "The radix must be within 2...36");
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let mut s = s;
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if s.starts_with('+') {
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let tail = &s[1..];
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if !tail.starts_with('+') {
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s = tail
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}
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}
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if s.is_empty() {
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// create ParseIntError::Empty
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let e = u64::from_str_radix(s, radix).unwrap_err();
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return Err(e.into());
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}
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// First normalize all characters to plain digit values
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let mut v = Vec::with_capacity(s.len());
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for b in s.bytes() {
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let d = match b {
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b'0'...b'9' => b - b'0',
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b'a'...b'z' => b - b'a' + 10,
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b'A'...b'Z' => b - b'A' + 10,
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_ => u8::MAX,
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};
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if d < radix as u8 {
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v.push(d);
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} else {
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// create ParseIntError::InvalidDigit
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// Include the previous character for context.
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let i = cmp::max(v.len(), 1) - 1;
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let e = u64::from_str_radix(&s[i..], radix).unwrap_err();
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return Err(e.into());
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}
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}
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let res = if radix.is_power_of_two() {
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// Powers of two can use bitwise masks and shifting instead of multiplication
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let bits = ilog2(radix);
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v.reverse();
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if big_digit::BITS % bits == 0 {
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from_bitwise_digits_le(&v, bits)
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} else {
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from_inexact_bitwise_digits_le(&v, bits)
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}
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} else {
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from_radix_digits_be(&v, radix)
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};
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Ok(res)
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}
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}
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forward_all_binop_to_val_ref_commutative!(impl BitAnd for BigUint, bitand);
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impl<'a> BitAnd<&'a BigUint> for BigUint {
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type Output = BigUint;
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#[inline]
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fn bitand(self, other: &BigUint) -> BigUint {
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let mut data = self.data;
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for (ai, &bi) in data.iter_mut().zip(other.data.iter()) {
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*ai &= bi;
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}
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data.truncate(other.data.len());
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BigUint::new(data)
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}
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}
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forward_all_binop_to_val_ref_commutative!(impl BitOr for BigUint, bitor);
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impl<'a> BitOr<&'a BigUint> for BigUint {
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type Output = BigUint;
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fn bitor(self, other: &BigUint) -> BigUint {
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let mut data = self.data;
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for (ai, &bi) in data.iter_mut().zip(other.data.iter()) {
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*ai |= bi;
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}
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if other.data.len() > data.len() {
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let extra = &other.data[data.len()..];
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data.extend(extra.iter().cloned());
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}
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BigUint::new(data)
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}
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}
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forward_all_binop_to_val_ref_commutative!(impl BitXor for BigUint, bitxor);
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impl<'a> BitXor<&'a BigUint> for BigUint {
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type Output = BigUint;
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fn bitxor(self, other: &BigUint) -> BigUint {
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let mut data = self.data;
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for (ai, &bi) in data.iter_mut().zip(other.data.iter()) {
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*ai ^= bi;
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}
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if other.data.len() > data.len() {
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let extra = &other.data[data.len()..];
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data.extend(extra.iter().cloned());
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}
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BigUint::new(data)
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}
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}
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impl Shl<usize> for BigUint {
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type Output = BigUint;
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#[inline]
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fn shl(self, rhs: usize) -> BigUint {
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biguint_shl(Cow::Owned(self), rhs)
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}
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}
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impl<'a> Shl<usize> for &'a BigUint {
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type Output = BigUint;
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#[inline]
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fn shl(self, rhs: usize) -> BigUint {
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biguint_shl(Cow::Borrowed(self), rhs)
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}
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}
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impl Shr<usize> for BigUint {
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type Output = BigUint;
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#[inline]
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fn shr(self, rhs: usize) -> BigUint {
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biguint_shr(Cow::Owned(self), rhs)
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}
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}
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impl<'a> Shr<usize> for &'a BigUint {
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type Output = BigUint;
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#[inline]
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fn shr(self, rhs: usize) -> BigUint {
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biguint_shr(Cow::Borrowed(self), rhs)
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}
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}
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impl Zero for BigUint {
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#[inline]
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fn zero() -> BigUint {
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BigUint::new(Vec::new())
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}
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#[inline]
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fn is_zero(&self) -> bool {
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self.data.is_empty()
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}
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}
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impl One for BigUint {
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#[inline]
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fn one() -> BigUint {
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BigUint::new(vec![1])
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}
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}
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impl Unsigned for BigUint {}
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forward_all_binop_to_val_ref_commutative!(impl Add for BigUint, add);
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impl<'a> Add<&'a BigUint> for BigUint {
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type Output = BigUint;
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fn add(mut self, other: &BigUint) -> BigUint {
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if self.data.len() < other.data.len() {
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let extra = other.data.len() - self.data.len();
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self.data.extend(repeat(0).take(extra));
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}
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let carry = __add2(&mut self.data[..], &other.data[..]);
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if carry != 0 {
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self.data.push(carry);
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}
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self
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}
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}
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forward_val_val_binop!(impl Sub for BigUint, sub);
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forward_ref_ref_binop!(impl Sub for BigUint, sub);
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impl<'a> Sub<&'a BigUint> for BigUint {
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type Output = BigUint;
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fn sub(mut self, other: &BigUint) -> BigUint {
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sub2(&mut self.data[..], &other.data[..]);
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self.normalize()
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}
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}
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impl<'a> Sub<BigUint> for &'a BigUint {
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type Output = BigUint;
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fn sub(self, mut other: BigUint) -> BigUint {
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if other.data.len() < self.data.len() {
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let extra = self.data.len() - other.data.len();
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other.data.extend(repeat(0).take(extra));
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}
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sub2rev(&self.data[..], &mut other.data[..]);
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other.normalize()
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}
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}
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forward_all_binop_to_ref_ref!(impl Mul for BigUint, mul);
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impl<'a, 'b> Mul<&'b BigUint> for &'a BigUint {
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type Output = BigUint;
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#[inline]
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fn mul(self, other: &BigUint) -> BigUint {
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mul3(&self.data[..], &other.data[..])
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}
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}
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forward_all_binop_to_ref_ref!(impl Div for BigUint, div);
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impl<'a, 'b> Div<&'b BigUint> for &'a BigUint {
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type Output = BigUint;
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#[inline]
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fn div(self, other: &BigUint) -> BigUint {
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let (q, _) = self.div_rem(other);
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return q;
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}
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}
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forward_all_binop_to_ref_ref!(impl Rem for BigUint, rem);
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impl<'a, 'b> Rem<&'b BigUint> for &'a BigUint {
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type Output = BigUint;
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#[inline]
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fn rem(self, other: &BigUint) -> BigUint {
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let (_, r) = self.div_rem(other);
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return r;
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}
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}
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impl Neg for BigUint {
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type Output = BigUint;
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#[inline]
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fn neg(self) -> BigUint {
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panic!()
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}
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}
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impl<'a> Neg for &'a BigUint {
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type Output = BigUint;
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#[inline]
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fn neg(self) -> BigUint {
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panic!()
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}
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}
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impl CheckedAdd for BigUint {
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#[inline]
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fn checked_add(&self, v: &BigUint) -> Option<BigUint> {
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return Some(self.add(v));
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}
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}
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impl CheckedSub for BigUint {
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#[inline]
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fn checked_sub(&self, v: &BigUint) -> Option<BigUint> {
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match self.cmp(v) {
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Less => None,
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Equal => Some(Zero::zero()),
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Greater => Some(self.sub(v)),
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}
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}
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}
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impl CheckedMul for BigUint {
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#[inline]
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fn checked_mul(&self, v: &BigUint) -> Option<BigUint> {
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return Some(self.mul(v));
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}
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}
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impl CheckedDiv for BigUint {
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#[inline]
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fn checked_div(&self, v: &BigUint) -> Option<BigUint> {
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if v.is_zero() {
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return None;
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}
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return Some(self.div(v));
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}
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}
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impl Integer for BigUint {
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#[inline]
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fn div_rem(&self, other: &BigUint) -> (BigUint, BigUint) {
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div_rem(self, other)
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}
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#[inline]
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fn div_floor(&self, other: &BigUint) -> BigUint {
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let (d, _) = div_rem(self, other);
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d
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}
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#[inline]
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fn mod_floor(&self, other: &BigUint) -> BigUint {
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let (_, m) = div_rem(self, other);
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m
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}
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#[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: &BigUint) -> BigUint {
|
|
// Use Euclid's algorithm
|
|
let mut m = (*self).clone();
|
|
let mut n = (*other).clone();
|
|
while !m.is_zero() {
|
|
let temp = m;
|
|
m = n % &temp;
|
|
n = temp;
|
|
}
|
|
return n;
|
|
}
|
|
|
|
/// Calculates the Lowest Common Multiple (LCM) of the number and `other`.
|
|
#[inline]
|
|
fn lcm(&self, other: &BigUint) -> BigUint {
|
|
((self * other) / self.gcd(other))
|
|
}
|
|
|
|
/// Deprecated, use `is_multiple_of` instead.
|
|
#[inline]
|
|
fn divides(&self, other: &BigUint) -> bool {
|
|
self.is_multiple_of(other)
|
|
}
|
|
|
|
/// Returns `true` if the number is a multiple of `other`.
|
|
#[inline]
|
|
fn is_multiple_of(&self, other: &BigUint) -> bool {
|
|
(self % other).is_zero()
|
|
}
|
|
|
|
/// Returns `true` if the number is divisible by `2`.
|
|
#[inline]
|
|
fn is_even(&self) -> bool {
|
|
// Considering only the last digit.
|
|
match self.data.first() {
|
|
Some(x) => x.is_even(),
|
|
None => true,
|
|
}
|
|
}
|
|
|
|
/// Returns `true` if the number is not divisible by `2`.
|
|
#[inline]
|
|
fn is_odd(&self) -> bool {
|
|
!self.is_even()
|
|
}
|
|
}
|
|
|
|
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().and_then(|n| {
|
|
// If top bit of u64 is set, it's too large to convert to i64.
|
|
if n >> 63 == 0 {
|
|
Some(n as i64)
|
|
} else {
|
|
None
|
|
}
|
|
})
|
|
}
|
|
|
|
#[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]
|
|
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]
|
|
fn from_u64(n: u64) -> Option<BigUint> {
|
|
Some(BigUint::from(n))
|
|
}
|
|
|
|
#[inline]
|
|
fn from_f64(mut n: f64) -> Option<BigUint> {
|
|
// handle NAN, INFINITY, NEG_INFINITY
|
|
if !n.is_finite() {
|
|
return None;
|
|
}
|
|
|
|
// match the rounding of casting from float to int
|
|
n = n.trunc();
|
|
|
|
// handle 0.x, -0.x
|
|
if n.is_zero() {
|
|
return Some(BigUint::zero());
|
|
}
|
|
|
|
let (mantissa, exponent, sign) = Float::integer_decode(n);
|
|
|
|
if sign == -1 {
|
|
return None;
|
|
}
|
|
|
|
let mut ret = BigUint::from(mantissa);
|
|
if exponent > 0 {
|
|
ret = ret << exponent as usize;
|
|
} else if exponent < 0 {
|
|
ret = ret >> (-exponent) as usize;
|
|
}
|
|
Some(ret)
|
|
}
|
|
}
|
|
|
|
impl From<u64> for BigUint {
|
|
#[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
|
|
}
|
|
}
|
|
|
|
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);
|
|
impl_to_biguint!(usize, FromPrimitive::from_usize);
|
|
impl_to_biguint!(u8, FromPrimitive::from_u8);
|
|
impl_to_biguint!(u16, FromPrimitive::from_u16);
|
|
impl_to_biguint!(u32, FromPrimitive::from_u32);
|
|
impl_to_biguint!(u64, FromPrimitive::from_u64);
|
|
impl_to_biguint!(f32, FromPrimitive::from_f32);
|
|
impl_to_biguint!(f64, FromPrimitive::from_f64);
|
|
|
|
// Extract bitwise digits that evenly divide BigDigit
|
|
fn to_bitwise_digits_le(u: &BigUint, bits: usize) -> Vec<u8> {
|
|
debug_assert!(!u.is_zero() && bits <= 8 && big_digit::BITS % bits == 0);
|
|
|
|
let last_i = u.data.len() - 1;
|
|
let mask: BigDigit = (1 << bits) - 1;
|
|
let digits_per_big_digit = big_digit::BITS / bits;
|
|
let digits = (u.bits() + bits - 1) / bits;
|
|
let mut res = Vec::with_capacity(digits);
|
|
|
|
for mut r in u.data[..last_i].iter().cloned() {
|
|
for _ in 0..digits_per_big_digit {
|
|
res.push((r & mask) as u8);
|
|
r >>= bits;
|
|
}
|
|
}
|
|
|
|
let mut r = u.data[last_i];
|
|
while r != 0 {
|
|
res.push((r & mask) as u8);
|
|
r >>= bits;
|
|
}
|
|
|
|
res
|
|
}
|
|
|
|
// Extract bitwise digits that don't evenly divide BigDigit
|
|
fn to_inexact_bitwise_digits_le(u: &BigUint, bits: usize) -> Vec<u8> {
|
|
debug_assert!(!u.is_zero() && bits <= 8 && big_digit::BITS % bits != 0);
|
|
|
|
let 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_str_radix_reversed(u: &BigUint, radix: u32) -> Vec<u8> {
|
|
assert!(2 <= radix && radix <= 36, "The radix must be within 2...36");
|
|
|
|
if u.is_zero() {
|
|
return vec![b'0'];
|
|
}
|
|
|
|
let mut res = if radix.is_power_of_two() {
|
|
// Powers of two can use bitwise masks and shifting instead of division
|
|
let bits = 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)
|
|
};
|
|
|
|
// Now convert everything to ASCII digits.
|
|
for r in &mut res {
|
|
debug_assert!((*r as u32) < radix);
|
|
if *r < 10 {
|
|
*r += b'0';
|
|
} else {
|
|
*r += b'a' - 10;
|
|
}
|
|
}
|
|
res
|
|
}
|
|
|
|
impl BigUint {
|
|
/// Creates and initializes a `BigUint`.
|
|
///
|
|
/// The digits are in little-endian base 2^32.
|
|
#[inline]
|
|
pub fn new(digits: Vec<BigDigit>) -> BigUint {
|
|
BigUint { data: digits }.normalize()
|
|
}
|
|
|
|
/// Creates and initializes a `BigUint`.
|
|
///
|
|
/// The digits are in little-endian base 2^32.
|
|
#[inline]
|
|
pub fn from_slice(slice: &[BigDigit]) -> BigUint {
|
|
BigUint::new(slice.to_vec())
|
|
}
|
|
|
|
/// Creates and initializes a `BigUint`.
|
|
///
|
|
/// The bytes are in big-endian byte order.
|
|
///
|
|
/// # Examples
|
|
///
|
|
/// ```
|
|
/// use num_bigint::BigUint;
|
|
///
|
|
/// assert_eq!(BigUint::from_bytes_be(b"A"),
|
|
/// BigUint::parse_bytes(b"65", 10).unwrap());
|
|
/// assert_eq!(BigUint::from_bytes_be(b"AA"),
|
|
/// BigUint::parse_bytes(b"16705", 10).unwrap());
|
|
/// assert_eq!(BigUint::from_bytes_be(b"AB"),
|
|
/// BigUint::parse_bytes(b"16706", 10).unwrap());
|
|
/// assert_eq!(BigUint::from_bytes_be(b"Hello world!"),
|
|
/// BigUint::parse_bytes(b"22405534230753963835153736737", 10).unwrap());
|
|
/// ```
|
|
#[inline]
|
|
pub fn from_bytes_be(bytes: &[u8]) -> BigUint {
|
|
if bytes.is_empty() {
|
|
Zero::zero()
|
|
} else {
|
|
let mut v = bytes.to_vec();
|
|
v.reverse();
|
|
BigUint::from_bytes_le(&*v)
|
|
}
|
|
}
|
|
|
|
/// Creates and initializes a `BigUint`.
|
|
///
|
|
/// The bytes are in little-endian byte order.
|
|
#[inline]
|
|
pub fn from_bytes_le(bytes: &[u8]) -> BigUint {
|
|
if bytes.is_empty() {
|
|
Zero::zero()
|
|
} else {
|
|
from_bitwise_digits_le(bytes, 8)
|
|
}
|
|
}
|
|
|
|
/// Returns the byte representation of the `BigUint` in little-endian byte order.
|
|
///
|
|
/// # Examples
|
|
///
|
|
/// ```
|
|
/// use num_bigint::BigUint;
|
|
///
|
|
/// let i = BigUint::parse_bytes(b"1125", 10).unwrap();
|
|
/// assert_eq!(i.to_bytes_le(), vec![101, 4]);
|
|
/// ```
|
|
#[inline]
|
|
pub fn to_bytes_le(&self) -> Vec<u8> {
|
|
if self.is_zero() {
|
|
vec![0]
|
|
} else {
|
|
to_bitwise_digits_le(self, 8)
|
|
}
|
|
}
|
|
|
|
/// Returns the byte representation of the `BigUint` in big-endian byte order.
|
|
///
|
|
/// # Examples
|
|
///
|
|
/// ```
|
|
/// use num_bigint::BigUint;
|
|
///
|
|
/// let i = BigUint::parse_bytes(b"1125", 10).unwrap();
|
|
/// assert_eq!(i.to_bytes_be(), vec![4, 101]);
|
|
/// ```
|
|
#[inline]
|
|
pub fn to_bytes_be(&self) -> Vec<u8> {
|
|
let mut v = self.to_bytes_le();
|
|
v.reverse();
|
|
v
|
|
}
|
|
|
|
/// Returns the integer formatted as a string in the given radix.
|
|
/// `radix` must be in the range `[2, 36]`.
|
|
///
|
|
/// # Examples
|
|
///
|
|
/// ```
|
|
/// use num_bigint::BigUint;
|
|
///
|
|
/// let i = BigUint::parse_bytes(b"ff", 16).unwrap();
|
|
/// assert_eq!(i.to_str_radix(16), "ff");
|
|
/// ```
|
|
#[inline]
|
|
pub fn to_str_radix(&self, radix: u32) -> String {
|
|
let mut v = to_str_radix_reversed(self, radix);
|
|
v.reverse();
|
|
unsafe { String::from_utf8_unchecked(v) }
|
|
}
|
|
|
|
/// Creates and initializes a `BigUint`.
|
|
///
|
|
/// # Examples
|
|
///
|
|
/// ```
|
|
/// use num_bigint::{BigUint, ToBigUint};
|
|
///
|
|
/// assert_eq!(BigUint::parse_bytes(b"1234", 10), ToBigUint::to_biguint(&1234));
|
|
/// assert_eq!(BigUint::parse_bytes(b"ABCD", 16), ToBigUint::to_biguint(&0xABCD));
|
|
/// assert_eq!(BigUint::parse_bytes(b"G", 16), None);
|
|
/// ```
|
|
#[inline]
|
|
pub fn parse_bytes(buf: &[u8], radix: u32) -> Option<BigUint> {
|
|
str::from_utf8(buf).ok().and_then(|s| BigUint::from_str_radix(s, radix).ok())
|
|
}
|
|
|
|
/// Determines the fewest bits necessary to express the `BigUint`.
|
|
#[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) -> BigUint {
|
|
while let Some(&0) = self.data.last() {
|
|
self.data.pop();
|
|
}
|
|
self
|
|
}
|
|
}
|
|
|
|
#[cfg(feature = "serde")]
|
|
impl serde::Serialize for BigUint {
|
|
fn serialize<S>(&self, serializer: &mut S) -> Result<(), S::Error>
|
|
where S: serde::Serializer
|
|
{
|
|
self.data.serialize(serializer)
|
|
}
|
|
}
|
|
|
|
#[cfg(feature = "serde")]
|
|
impl serde::Deserialize for BigUint {
|
|
fn deserialize<D>(deserializer: &mut D) -> Result<Self, D::Error>
|
|
where D: serde::Deserializer
|
|
{
|
|
let data = try!(Vec::deserialize(deserializer));
|
|
Ok(BigUint { data: data })
|
|
}
|
|
}
|
|
|
|
/// Returns the greatest power of the radix <= big_digit::BASE
|
|
#[inline]
|
|
fn get_radix_base(radix: u32) -> (BigDigit, usize) {
|
|
debug_assert!(2 <= radix && radix <= 36, "The radix must be within 2...36");
|
|
debug_assert!(!radix.is_power_of_two());
|
|
|
|
// To generate this table:
|
|
// for radix in 2u64..37 {
|
|
// 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);
|
|
// }
|
|
|
|
match big_digit::BITS {
|
|
32 => {
|
|
const BASES: [(u32, usize); 37] = [(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
|
|
];
|
|
|
|
let (base, power) = BASES[radix as usize];
|
|
(base as BigDigit, power)
|
|
}
|
|
64 => {
|
|
const BASES: [(u64, usize); 37] = [(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
|
|
];
|
|
|
|
let (base, power) = BASES[radix as usize];
|
|
(base as BigDigit, power)
|
|
}
|
|
_ => panic!("Invalid bigdigit size")
|
|
}
|
|
}
|