use std::borrow::Cow;
use std::default::Default;
use std::iter::repeat;
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(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};
#[path = "algorithms.rs"]
mod algorithms;
#[path = "monty.rs"]
mod monty;
pub use self::algorithms::big_digit;
pub use self::big_digit::{BigDigit, DoubleBigDigit, ZERO_BIG_DIGIT};
use self::algorithms::{mac_with_carry, mul3, scalar_mul, div_rem, div_rem_digit};
use self::algorithms::{__add2, 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;
#[cfg(test)]
#[path = "tests/biguint.rs"]
mod biguint_tests;
#[derive(Clone, Debug, Hash)]
#[cfg_attr(has_derive_rustc_serialize, derive(RustcEncodable, RustcDecodable))]
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 {
f.pad_integral(true, "0x", &self.to_str_radix(16).to_ascii_uppercase())
}
}
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)
}
}
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)
}
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; for &c in v {
d |= (c as BigDigit) << dbits;
dbits += bits;
if dbits >= big_digit::BITS {
data.push(d);
dbits -= big_digit::BITS;
d = (c as BigDigit) >> (bits - dbits);
}
}
if dbits > 0 {
debug_assert!(dbits < big_digit::BITS);
data.push(d as BigDigit);
}
BigUint::new(data)
}
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));
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;
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() {
let e = u64::from_str_radix(s, radix).unwrap_err();
return Err(e.into());
}
if s.starts_with('_') {
let e = u64::from_str_radix(s, radix).unwrap_err();
return Err(e.into());
}
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 {
let i = cmp::max(v.len(), 1) - 1;
let e = u64::from_str_radix(&s[i..], radix).unwrap_err();
return Err(e.into());
}
}
let res = if radix.is_power_of_two() {
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_all_binop_to_val_ref_commutative!(impl BitAnd for BigUint, bitand);
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) {
*self = biguint_shl(Cow::Borrowed(&*self), 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])
}
}
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) {
if self.data.len() < other.data.len() {
let extra = other.data.len() - self.data.len();
self.data.extend(repeat(0).take(extra));
}
let carry = __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 {
if other.data.len() < self.data.len() {
let extra = self.data.len() - other.data.len();
other.data.extend(repeat(0).take(extra));
}
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(0);
}
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
};
}
}
}
}
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)
}
#[inline]
fn gcd(&self, other: &Self) -> Self {
if self.is_zero() {
return other.clone();
}
if other.is_zero() {
return self.clone();
}
let mut m = self.clone();
let mut n = other.clone();
let shift = cmp::min(
n.trailing_zeros(),
m.trailing_zeros()
);
n >>= n.trailing_zeros();
while !m.is_zero() {
m >>= m.trailing_zeros();
if n > m { mem::swap(&mut n, &mut m) }
m -= &n;
}
n << shift
}
#[inline]
fn lcm(&self, other: &BigUint) -> BigUint {
self / self.gcd(other) * other
}
#[inline]
fn divides(&self, other: &BigUint) -> bool {
self.is_multiple_of(other)
}
#[inline]
fn is_multiple_of(&self, other: &BigUint) -> bool {
(self % other).is_zero()
}
#[inline]
fn is_even(&self) -> bool {
match self.data.first() {
Some(x) => x.is_even(),
None => true,
}
}
#[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 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> {
if !n.is_finite() {
return None;
}
n = n.trunc();
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);
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: $T) -> Self {
BigUint::from(n as u64)
}
}
}
}
impl_biguint_from_uint!(u8);
impl_biguint_from_uint!(u16);
impl_biguint_from_uint!(u32);
impl_biguint_from_uint!(usize);
pub trait ToBigUint {
fn to_biguint(&self) -> Option<BigUint>;
}
impl ToBigUint for BigUint {
#[inline]
fn to_biguint(&self) -> Option<BigUint> {
Some(self.clone())
}
}
macro_rules! impl_to_biguint {
($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);
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
}
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;
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
}
#[inline(always)] fn to_radix_digits_le(u: &BigUint, radix: u32) -> Vec<u8> {
debug_assert!(!u.is_zero() && !radix.is_power_of_two());
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() {
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 {
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);
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 {
#[inline]
pub fn new(digits: Vec<BigDigit>) -> BigUint {
BigUint { data: digits }.normalized()
}
#[inline]
pub fn from_slice(slice: &[BigDigit]) -> BigUint {
BigUint::new(slice.to_vec())
}
#[inline]
pub fn assign_from_slice(&mut self, slice: &[BigDigit]) {
self.data.resize(slice.len(), 0);
self.data.clone_from_slice(slice);
self.normalize();
}
#[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)
}
}
#[inline]
pub fn from_bytes_le(bytes: &[u8]) -> BigUint {
if bytes.is_empty() {
Zero::zero()
} else {
from_bitwise_digits_le(bytes, 8)
}
}
#[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())
}
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() {
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)
}
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() {
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)
}
#[inline]
pub fn to_bytes_be(&self) -> Vec<u8> {
let mut v = self.to_bytes_le();
v.reverse();
v
}
#[inline]
pub fn to_bytes_le(&self) -> Vec<u8> {
if self.is_zero() {
vec![0]
} else {
to_bitwise_digits_le(self, 8)
}
}
#[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) }
}
#[inline]
pub fn to_radix_be(&self, radix: u32) -> Vec<u8> {
let mut v = to_radix_le(self, radix);
v.reverse();
v
}
#[inline]
pub fn to_radix_le(&self, radix: u32) -> Vec<u8> {
to_radix_le(self, radix)
}
#[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;
}
fn trailing_zeros(&self) -> usize {
self.data
.iter()
.enumerate()
.find(|&(_, &digit)| digit != 0)
.map(|(i, digit)| i * big_digit::BITS + digit.trailing_zeros() as usize)
.unwrap_or(0)
}
#[inline]
fn normalize(&mut self) {
while let Some(&0) = self.data.last() {
self.data.pop();
}
}
#[inline]
fn normalized(mut self) -> BigUint {
self.normalize();
self
}
pub fn modpow(&self, exponent: &Self, modulus: &Self) -> Self {
assert!(!modulus.is_zero(), "divide by zero!");
if modulus.is_odd() {
return monty_modpow(self, exponent, 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
}
}
#[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 })
}
}
#[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());
match big_digit::BITS {
32 => {
const BASES: [(u32, usize); 257] = [
( 0, 0),
( 0, 0),
( 0, 0), (3486784401, 20), ( 0, 0), (1220703125, 13), (2176782336, 12), (1977326743, 11), ( 0, 0), (3486784401, 10), (1000000000, 9), (2357947691, 9), ( 429981696, 8), ( 815730721, 8), (1475789056, 8), (2562890625, 8), ( 0, 0), ( 410338673, 7), ( 612220032, 7), ( 893871739, 7), (1280000000, 7), (1801088541, 7), (2494357888, 7), (3404825447, 7), ( 191102976, 6), ( 244140625, 6), ( 308915776, 6), ( 387420489, 6), ( 481890304, 6), ( 594823321, 6), ( 729000000, 6), ( 887503681, 6), ( 0, 0), (1291467969, 6), (1544804416, 6), (1838265625, 6), (2176782336, 6), (2565726409, 6), (3010936384, 6), (3518743761, 6), (4096000000, 6), ( 115856201, 5), ( 130691232, 5), ( 147008443, 5), ( 164916224, 5), ( 184528125, 5), ( 205962976, 5), ( 229345007, 5), ( 254803968, 5), ( 282475249, 5), ( 312500000, 5), ( 345025251, 5), ( 380204032, 5), ( 418195493, 5), ( 459165024, 5), ( 503284375, 5), ( 550731776, 5), ( 601692057, 5), ( 656356768, 5), ( 714924299, 5), ( 777600000, 5), ( 844596301, 5), ( 916132832, 5), ( 992436543, 5), ( 0, 0), (1160290625, 5), (1252332576, 5), (1350125107, 5), (1453933568, 5), (1564031349, 5), (1680700000, 5), (1804229351, 5), (1934917632, 5), (2073071593, 5), (2219006624, 5), (2373046875, 5), (2535525376, 5), (2706784157, 5), (2887174368, 5), (3077056399, 5), (3276800000, 5), (3486784401, 5), (3707398432, 5), (3939040643, 5), (4182119424, 5), ( 52200625, 4), ( 54700816, 4), ( 57289761, 4), ( 59969536, 4), ( 62742241, 4), ( 65610000, 4), ( 68574961, 4), ( 71639296, 4), ( 74805201, 4), ( 78074896, 4), ( 81450625, 4), ( 84934656, 4), ( 88529281, 4), ( 92236816, 4), ( 96059601, 4), ( 100000000, 4), ( 104060401, 4), ( 108243216, 4), ( 112550881, 4), ( 116985856, 4), ( 121550625, 4), ( 126247696, 4), ( 131079601, 4), ( 136048896, 4), ( 141158161, 4), ( 146410000, 4), ( 151807041, 4), ( 157351936, 4), ( 163047361, 4), ( 168896016, 4), ( 174900625, 4), ( 181063936, 4), ( 187388721, 4), ( 193877776, 4), ( 200533921, 4), ( 207360000, 4), ( 214358881, 4), ( 221533456, 4), ( 228886641, 4), ( 236421376, 4), ( 244140625, 4), ( 252047376, 4), ( 260144641, 4), ( 0, 0), ( 276922881, 4), ( 285610000, 4), ( 294499921, 4), ( 303595776, 4), ( 312900721, 4), ( 322417936, 4), ( 332150625, 4), ( 342102016, 4), ( 352275361, 4), ( 362673936, 4), ( 373301041, 4), ( 384160000, 4), ( 395254161, 4), ( 406586896, 4), ( 418161601, 4), ( 429981696, 4), ( 442050625, 4), ( 454371856, 4), ( 466948881, 4), ( 479785216, 4), ( 492884401, 4), ( 506250000, 4), ( 519885601, 4), ( 533794816, 4), ( 547981281, 4), ( 562448656, 4), ( 577200625, 4), ( 592240896, 4), ( 607573201, 4), ( 623201296, 4), ( 639128961, 4), ( 655360000, 4), ( 671898241, 4), ( 688747536, 4), ( 705911761, 4), ( 723394816, 4), ( 741200625, 4), ( 759333136, 4), ( 777796321, 4), ( 796594176, 4), ( 815730721, 4), ( 835210000, 4), ( 855036081, 4), ( 875213056, 4), ( 895745041, 4), ( 916636176, 4), ( 937890625, 4), ( 959512576, 4), ( 981506241, 4), (1003875856, 4), (1026625681, 4), (1049760000, 4), (1073283121, 4), (1097199376, 4), (1121513121, 4), (1146228736, 4), (1171350625, 4), (1196883216, 4), (1222830961, 4), (1249198336, 4), (1275989841, 4), (1303210000, 4), (1330863361, 4), (1358954496, 4), (1387488001, 4), (1416468496, 4), (1445900625, 4), (1475789056, 4), (1506138481, 4), (1536953616, 4), (1568239201, 4), (1600000000, 4), (1632240801, 4), (1664966416, 4), (1698181681, 4), (1731891456, 4), (1766100625, 4), (1800814096, 4), (1836036801, 4), (1871773696, 4), (1908029761, 4), (1944810000, 4), (1982119441, 4), (2019963136, 4), (2058346161, 4), (2097273616, 4), (2136750625, 4), (2176782336, 4), (2217373921, 4), (2258530576, 4), (2300257521, 4), (2342560000, 4), (2385443281, 4), (2428912656, 4), (2472973441, 4), (2517630976, 4), (2562890625, 4), (2608757776, 4), (2655237841, 4), (2702336256, 4), (2750058481, 4), (2798410000, 4), (2847396321, 4), (2897022976, 4), (2947295521, 4), (2998219536, 4), (3049800625, 4), (3102044416, 4), (3154956561, 4), (3208542736, 4), (3262808641, 4), (3317760000, 4), (3373402561, 4), (3429742096, 4), (3486784401, 4), (3544535296, 4), (3603000625, 4), (3662186256, 4), (3722098081, 4), (3782742016, 4), (3844124001, 4), (3906250000, 4), (3969126001, 4), (4032758016, 4), (4097152081, 4), (4162314256, 4), (4228250625, 4), ( 0, 0), ];
let (base, power) = BASES[radix as usize];
(base as BigDigit, power)
}
64 => {
const BASES: [(u64, usize); 257] = [
( 0, 0),
( 0, 0),
( 9223372036854775808, 63), (12157665459056928801, 40), ( 4611686018427387904, 31), ( 7450580596923828125, 27), ( 4738381338321616896, 24), ( 3909821048582988049, 22), ( 9223372036854775808, 21), (12157665459056928801, 20), (10000000000000000000, 19), ( 5559917313492231481, 18), ( 2218611106740436992, 17), ( 8650415919381337933, 17), ( 2177953337809371136, 16), ( 6568408355712890625, 16), ( 1152921504606846976, 15), ( 2862423051509815793, 15), ( 6746640616477458432, 15), (15181127029874798299, 15), ( 1638400000000000000, 14), ( 3243919932521508681, 14), ( 6221821273427820544, 14), (11592836324538749809, 14), ( 876488338465357824, 13), ( 1490116119384765625, 13), ( 2481152873203736576, 13), ( 4052555153018976267, 13), ( 6502111422497947648, 13), (10260628712958602189, 13), (15943230000000000000, 13), ( 787662783788549761, 12), ( 1152921504606846976, 12), ( 1667889514952984961, 12), ( 2386420683693101056, 12), ( 3379220508056640625, 12), ( 4738381338321616896, 12), ( 6582952005840035281, 12), ( 9065737908494995456, 12), (12381557655576425121, 12), (16777216000000000000, 12), ( 550329031716248441, 11), ( 717368321110468608, 11), ( 929293739471222707, 11), ( 1196683881290399744, 11), ( 1532278301220703125, 11), ( 1951354384207722496, 11), ( 2472159215084012303, 11), ( 3116402981210161152, 11), ( 3909821048582988049, 11), ( 4882812500000000000, 11), ( 6071163615208263051, 11), ( 7516865509350965248, 11), ( 9269035929372191597, 11), (11384956040305711104, 11), (13931233916552734375, 11), (16985107389382393856, 11), ( 362033331456891249, 10), ( 430804206899405824, 10), ( 511116753300641401, 10), ( 604661760000000000, 10), ( 713342911662882601, 10), ( 839299365868340224, 10), ( 984930291881790849, 10), ( 1152921504606846976, 10), ( 1346274334462890625, 10), ( 1568336880910795776, 10), ( 1822837804551761449, 10), ( 2113922820157210624, 10), ( 2446194060654759801, 10), ( 2824752490000000000, 10), ( 3255243551009881201, 10), ( 3743906242624487424, 10), ( 4297625829703557649, 10), ( 4923990397355877376, 10), ( 5631351470947265625, 10), ( 6428888932339941376, 10), ( 7326680472586200649, 10), ( 8335775831236199424, 10), ( 9468276082626847201, 10), (10737418240000000000, 10), (12157665459056928801, 10), (13744803133596058624, 10), (15516041187205853449, 10), (17490122876598091776, 10), ( 231616946283203125, 9), ( 257327417311663616, 9), ( 285544154243029527, 9), ( 316478381828866048, 9), ( 350356403707485209, 9), ( 387420489000000000, 9), ( 427929800129788411, 9), ( 472161363286556672, 9), ( 520411082988487293, 9), ( 572994802228616704, 9), ( 630249409724609375, 9), ( 692533995824480256, 9), ( 760231058654565217, 9), ( 833747762130149888, 9), ( 913517247483640899, 9), ( 1000000000000000000, 9), ( 1093685272684360901, 9), ( 1195092568622310912, 9), ( 1304773183829244583, 9), ( 1423311812421484544, 9), ( 1551328215978515625, 9), ( 1689478959002692096, 9), ( 1838459212420154507, 9), ( 1999004627104432128, 9), ( 2171893279442309389, 9), ( 2357947691000000000, 9), ( 2558036924386500591, 9), ( 2773078757450186752, 9), ( 3004041937984268273, 9), ( 3251948521156637184, 9), ( 3517876291919921875, 9), ( 3802961274698203136, 9), ( 4108400332687853397, 9), ( 4435453859151328768, 9), ( 4785448563124474679, 9), ( 5159780352000000000, 9), ( 5559917313492231481, 9), ( 5987402799531080192, 9), ( 6443858614676334363, 9), ( 6930988311686938624, 9), ( 7450580596923828125, 9), ( 8004512848309157376, 9), ( 8594754748609397887, 9), ( 9223372036854775808, 9), ( 9892530380752880769, 9), (10604499373000000000, 9), (11361656654439817571, 9), (12166492167065567232, 9), (13021612539908538853, 9), (13929745610903012864, 9), (14893745087865234375, 9), (15916595351771938816, 9), (17001416405572203977, 9), (18151468971815029248, 9), ( 139353667211683681, 8), ( 147578905600000000, 8), ( 156225851787813921, 8), ( 165312903998914816, 8), ( 174859124550883201, 8), ( 184884258895036416, 8), ( 195408755062890625, 8), ( 206453783524884736, 8), ( 218041257467152161, 8), ( 230193853492166656, 8), ( 242935032749128801, 8), ( 256289062500000000, 8), ( 270281038127131201, 8), ( 284936905588473856, 8), ( 300283484326400961, 8), ( 316348490636206336, 8), ( 333160561500390625, 8), ( 350749278894882816, 8), ( 369145194573386401, 8), ( 388379855336079616, 8), ( 408485828788939521, 8), ( 429496729600000000, 8), ( 451447246258894081, 8), ( 474373168346071296, 8), ( 498311414318121121, 8), ( 523300059815673856, 8), ( 549378366500390625, 8), ( 576586811427594496, 8), ( 604967116961135041, 8), ( 634562281237118976, 8), ( 665416609183179841, 8), ( 697575744100000000, 8), ( 731086699811838561, 8), ( 765997893392859136, 8), ( 802359178476091681, 8), ( 840221879151902976, 8), ( 879638824462890625, 8), ( 920664383502155776, 8), ( 963354501121950081, 8), ( 1007766734259732736, 8), ( 1053960288888713761, 8), ( 1101996057600000000, 8), ( 1151936657823500641, 8), ( 1203846470694789376, 8), ( 1257791680575160641, 8), ( 1313840315232157696, 8), ( 1372062286687890625, 8), ( 1432529432742502656, 8), ( 1495315559180183521, 8), ( 1560496482665168896, 8), ( 1628150074335205281, 8), ( 1698356304100000000, 8), ( 1771197285652216321, 8), ( 1846757322198614016, 8), ( 1925122952918976001, 8), ( 2006383000160502016, 8), ( 2090628617375390625, 8), ( 2177953337809371136, 8), ( 2268453123948987361, 8), ( 2362226417735475456, 8), ( 2459374191553118401, 8), ( 2560000000000000000, 8), ( 2664210032449121601, 8), ( 2772113166407885056, 8), ( 2883821021683985761, 8), ( 2999448015365799936, 8), ( 3119111417625390625, 8), ( 3242931408352297216, 8), ( 3371031134626313601, 8), ( 3503536769037500416, 8), ( 3640577568861717121, 8), ( 3782285936100000000, 8), ( 3928797478390152481, 8), ( 4080251070798954496, 8), ( 4236788918503437921, 8), ( 4398556620369715456, 8), ( 4565703233437890625, 8), ( 4738381338321616896, 8), ( 4916747105530914241, 8), ( 5100960362726891776, 8), ( 5291184662917065441, 8), ( 5487587353600000000, 8), ( 5690339646868044961, 8), ( 5899616690476974336, 8), ( 6115597639891380481, 8), ( 6338465731314712576, 8), ( 6568408355712890625, 8), ( 6805617133840466176, 8), ( 7050287992278341281, 8), ( 7302621240492097536, 8), ( 7562821648920027361, 8), ( 7831098528100000000, 8), ( 8107665808844335041, 8), ( 8392742123471896576, 8), ( 8686550888106661441, 8), ( 8989320386052055296, 8), ( 9301283852250390625, 8), ( 9622679558836781056, 8), ( 9953750901796946721, 8), (10294746488738365696, 8), (10645920227784266881, 8), (11007531417600000000, 8), (11379844838561358721, 8), (11763130845074473216, 8), (12157665459056928801, 8), (12563730464589807616, 8), (12981613503750390625, 8), (13411608173635297536, 8), (13854014124583882561, 8), (14309137159611744256, 8), (14777289335064248001, 8), (15258789062500000000, 8), (15753961211814252001, 8), (16263137215612256256, 8), (16786655174842630561, 8), (17324859965700833536, 8), (17878103347812890625, 8), ( 72057594037927936, 7), ];
let (base, power) = BASES[radix as usize];
(base as BigDigit, power)
}
_ => panic!("Invalid bigdigit size")
}
}