blob: 5d4aaf8939c234bffed114f59367affb7f5976dd [file] [log] [blame]
use std::borrow::Cow;
use std::default::Default;
use std::iter::{Product, Sum};
use std::ops::{Add, BitAnd, BitOr, BitXor, Div, Mul, Neg, Rem, Shl, Shr, Sub,
AddAssign, BitAndAssign, BitOrAssign, BitXorAssign, DivAssign,
MulAssign, RemAssign, ShlAssign, ShrAssign, SubAssign};
use std::str::{self, FromStr};
use std::fmt;
use std::cmp;
use std::mem;
use std::cmp::Ordering::{self, Less, Greater, Equal};
use std::{f32, f64};
use std::{u8, u64};
#[allow(deprecated, unused_imports)]
use std::ascii::AsciiExt;
#[cfg(feature = "serde")]
use serde;
use integer::Integer;
use traits::{ToPrimitive, FromPrimitive, Float, Num, Unsigned, CheckedAdd, CheckedSub, CheckedMul,
CheckedDiv, Zero, One};
use big_digit::{self, BigDigit, DoubleBigDigit};
#[path = "algorithms.rs"]
mod algorithms;
#[path = "monty.rs"]
mod monty;
use self::algorithms::{mac_with_carry, mul3, scalar_mul, div_rem, div_rem_digit};
use self::algorithms::{__add2, __sub2rev, add2, sub2, sub2rev};
use self::algorithms::{biguint_shl, biguint_shr};
use self::algorithms::{cmp_slice, fls, ilog2};
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 {}
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<BigDigit> for BigUint, add);
forward_all_scalar_binop_to_val_val_commutative!(impl Add<DoubleBigDigit> for BigUint, add);
impl Add<BigDigit> for BigUint {
type Output = BigUint;
#[inline]
fn add(mut self, other: BigDigit) -> BigUint {
self += other;
self
}
}
impl AddAssign<BigDigit> for BigUint {
#[inline]
fn add_assign(&mut self, other: BigDigit) {
if other != 0 {
if self.data.len() == 0 {
self.data.push(0);
}
let carry = __add2(&mut self.data, &[other]);
if carry != 0 {
self.data.push(carry);
}
}
}
}
impl Add<DoubleBigDigit> for BigUint {
type Output = BigUint;
#[inline]
fn add(mut self, other: DoubleBigDigit) -> BigUint {
self += other;
self
}
}
impl AddAssign<DoubleBigDigit> for BigUint {
#[inline]
fn add_assign(&mut self, other: DoubleBigDigit) {
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);
}
}
}
}
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<BigDigit> for BigUint, sub);
forward_all_scalar_binop_to_val_val!(impl Sub<DoubleBigDigit> for BigUint, sub);
impl Sub<BigDigit> for BigUint {
type Output = BigUint;
#[inline]
fn sub(mut self, other: BigDigit) -> BigUint {
self -= other;
self
}
}
impl SubAssign<BigDigit> for BigUint {
fn sub_assign(&mut self, other: BigDigit) {
sub2(&mut self.data[..], &[other]);
self.normalize();
}
}
impl Sub<BigUint> for BigDigit {
type Output = BigUint;
#[inline]
fn sub(self, mut other: BigUint) -> BigUint {
if other.data.len() == 0 {
other.data.push(self);
} else {
sub2rev(&[self], &mut other.data[..]);
}
other.normalized()
}
}
impl Sub<DoubleBigDigit> for BigUint {
type Output = BigUint;
#[inline]
fn sub(mut self, other: DoubleBigDigit) -> BigUint {
self -= other;
self
}
}
impl SubAssign<DoubleBigDigit> for BigUint {
fn sub_assign(&mut self, other: DoubleBigDigit) {
let (hi, lo) = big_digit::from_doublebigdigit(other);
sub2(&mut self.data[..], &[lo, hi]);
self.normalize();
}
}
impl Sub<BigUint> for DoubleBigDigit {
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()
}
}
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<BigDigit> for BigUint, mul);
forward_all_scalar_binop_to_val_val_commutative!(impl Mul<DoubleBigDigit> for BigUint, mul);
impl Mul<BigDigit> for BigUint {
type Output = BigUint;
#[inline]
fn mul(mut self, other: BigDigit) -> BigUint {
self *= other;
self
}
}
impl MulAssign<BigDigit> for BigUint {
#[inline]
fn mul_assign(&mut self, other: BigDigit) {
if other == 0 {
self.data.clear();
} else {
let carry = scalar_mul(&mut self.data[..], other);
if carry != 0 {
self.data.push(carry);
}
}
}
}
impl Mul<DoubleBigDigit> for BigUint {
type Output = BigUint;
#[inline]
fn mul(mut self, other: DoubleBigDigit) -> BigUint {
self *= other;
self
}
}
impl MulAssign<DoubleBigDigit> for BigUint {
#[inline]
fn mul_assign(&mut self, other: DoubleBigDigit) {
if other == 0 {
self.data.clear();
} else if other <= BigDigit::max_value() as DoubleBigDigit {
*self *= other as BigDigit
} else {
let (hi, lo) = big_digit::from_doublebigdigit(other);
*self = mul3(&self.data[..], &[lo, hi])
}
}
}
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<BigDigit> for BigUint, div);
forward_all_scalar_binop_to_val_val!(impl Div<DoubleBigDigit> for BigUint, div);
impl Div<BigDigit> for BigUint {
type Output = BigUint;
#[inline]
fn div(self, other: BigDigit) -> BigUint {
let (q, _) = div_rem_digit(self, other);
q
}
}
impl DivAssign<BigDigit> for BigUint {
#[inline]
fn div_assign(&mut self, other: BigDigit) {
*self = &*self / other;
}
}
impl Div<BigUint> for BigDigit {
type Output = BigUint;
#[inline]
fn div(self, other: BigUint) -> BigUint {
match other.data.len() {
0 => panic!(),
1 => From::from(self / other.data[0]),
_ => Zero::zero(),
}
}
}
impl Div<DoubleBigDigit> for BigUint {
type Output = BigUint;
#[inline]
fn div(self, other: DoubleBigDigit) -> BigUint {
let (q, _) = self.div_rem(&From::from(other));
q
}
}
impl DivAssign<DoubleBigDigit> for BigUint {
#[inline]
fn div_assign(&mut self, other: DoubleBigDigit) {
*self = &*self / other;
}
}
impl Div<BigUint> for DoubleBigDigit {
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(),
}
}
}
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<BigDigit> for BigUint, rem);
forward_all_scalar_binop_to_val_val!(impl Rem<DoubleBigDigit> for BigUint, rem);
impl Rem<BigDigit> for BigUint {
type Output = BigUint;
#[inline]
fn rem(self, other: BigDigit) -> BigUint {
let (_, r) = div_rem_digit(self, other);
From::from(r)
}
}
impl RemAssign<BigDigit> for BigUint {
#[inline]
fn rem_assign(&mut self, other: BigDigit) {
*self = &*self % other;
}
}
impl Rem<BigUint> for BigDigit {
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
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);
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<DoubleBigDigit> for BigUint {
type Output = BigUint;
#[inline]
fn rem(self, other: DoubleBigDigit) -> BigUint {
let (_, r) = self.div_rem(&From::from(other));
r
}
}
impl RemAssign<DoubleBigDigit> for BigUint {
#[inline]
fn rem_assign(&mut self, other: DoubleBigDigit) {
*self = &*self % other;
}
}
impl Rem<BigUint> for DoubleBigDigit {
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()
}
}
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 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()
}
}
#[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]);