Yiming Jing | cf21fc4 | 2021-07-16 13:23:26 -0700 | [diff] [blame] | 1 | use super::monty::monty_modpow; |
| 2 | use super::BigUint; |
| 3 | |
| 4 | use crate::big_digit::{self, BigDigit}; |
| 5 | |
| 6 | use num_integer::Integer; |
| 7 | use num_traits::{One, Pow, ToPrimitive, Zero}; |
| 8 | |
| 9 | impl<'b> Pow<&'b BigUint> for BigUint { |
| 10 | type Output = BigUint; |
| 11 | |
| 12 | #[inline] |
| 13 | fn pow(self, exp: &BigUint) -> BigUint { |
| 14 | if self.is_one() || exp.is_zero() { |
| 15 | BigUint::one() |
| 16 | } else if self.is_zero() { |
| 17 | BigUint::zero() |
| 18 | } else if let Some(exp) = exp.to_u64() { |
| 19 | self.pow(exp) |
| 20 | } else if let Some(exp) = exp.to_u128() { |
| 21 | self.pow(exp) |
| 22 | } else { |
| 23 | // At this point, `self >= 2` and `exp >= 2¹²⁸`. The smallest possible result given |
| 24 | // `2.pow(2¹²⁸)` would require far more memory than 64-bit targets can address! |
| 25 | panic!("memory overflow") |
| 26 | } |
| 27 | } |
| 28 | } |
| 29 | |
| 30 | impl Pow<BigUint> for BigUint { |
| 31 | type Output = BigUint; |
| 32 | |
| 33 | #[inline] |
| 34 | fn pow(self, exp: BigUint) -> BigUint { |
| 35 | Pow::pow(self, &exp) |
| 36 | } |
| 37 | } |
| 38 | |
| 39 | impl<'a, 'b> Pow<&'b BigUint> for &'a BigUint { |
| 40 | type Output = BigUint; |
| 41 | |
| 42 | #[inline] |
| 43 | fn pow(self, exp: &BigUint) -> BigUint { |
| 44 | if self.is_one() || exp.is_zero() { |
| 45 | BigUint::one() |
| 46 | } else if self.is_zero() { |
| 47 | BigUint::zero() |
| 48 | } else { |
| 49 | self.clone().pow(exp) |
| 50 | } |
| 51 | } |
| 52 | } |
| 53 | |
| 54 | impl<'a> Pow<BigUint> for &'a BigUint { |
| 55 | type Output = BigUint; |
| 56 | |
| 57 | #[inline] |
| 58 | fn pow(self, exp: BigUint) -> BigUint { |
| 59 | Pow::pow(self, &exp) |
| 60 | } |
| 61 | } |
| 62 | |
| 63 | macro_rules! pow_impl { |
| 64 | ($T:ty) => { |
| 65 | impl Pow<$T> for BigUint { |
| 66 | type Output = BigUint; |
| 67 | |
| 68 | fn pow(self, mut exp: $T) -> BigUint { |
| 69 | if exp == 0 { |
| 70 | return BigUint::one(); |
| 71 | } |
| 72 | let mut base = self; |
| 73 | |
| 74 | while exp & 1 == 0 { |
| 75 | base = &base * &base; |
| 76 | exp >>= 1; |
| 77 | } |
| 78 | |
| 79 | if exp == 1 { |
| 80 | return base; |
| 81 | } |
| 82 | |
| 83 | let mut acc = base.clone(); |
| 84 | while exp > 1 { |
| 85 | exp >>= 1; |
| 86 | base = &base * &base; |
| 87 | if exp & 1 == 1 { |
Joel Galenson | 7bace41 | 2021-09-22 14:05:35 -0700 | [diff] [blame^] | 88 | acc *= &base; |
Yiming Jing | cf21fc4 | 2021-07-16 13:23:26 -0700 | [diff] [blame] | 89 | } |
| 90 | } |
| 91 | acc |
| 92 | } |
| 93 | } |
| 94 | |
| 95 | impl<'b> Pow<&'b $T> for BigUint { |
| 96 | type Output = BigUint; |
| 97 | |
| 98 | #[inline] |
| 99 | fn pow(self, exp: &$T) -> BigUint { |
| 100 | Pow::pow(self, *exp) |
| 101 | } |
| 102 | } |
| 103 | |
| 104 | impl<'a> Pow<$T> for &'a BigUint { |
| 105 | type Output = BigUint; |
| 106 | |
| 107 | #[inline] |
| 108 | fn pow(self, exp: $T) -> BigUint { |
| 109 | if exp == 0 { |
| 110 | return BigUint::one(); |
| 111 | } |
| 112 | Pow::pow(self.clone(), exp) |
| 113 | } |
| 114 | } |
| 115 | |
| 116 | impl<'a, 'b> Pow<&'b $T> for &'a BigUint { |
| 117 | type Output = BigUint; |
| 118 | |
| 119 | #[inline] |
| 120 | fn pow(self, exp: &$T) -> BigUint { |
| 121 | Pow::pow(self, *exp) |
| 122 | } |
| 123 | } |
| 124 | }; |
| 125 | } |
| 126 | |
| 127 | pow_impl!(u8); |
| 128 | pow_impl!(u16); |
| 129 | pow_impl!(u32); |
| 130 | pow_impl!(u64); |
| 131 | pow_impl!(usize); |
| 132 | pow_impl!(u128); |
| 133 | |
| 134 | pub(super) fn modpow(x: &BigUint, exponent: &BigUint, modulus: &BigUint) -> BigUint { |
| 135 | assert!( |
| 136 | !modulus.is_zero(), |
| 137 | "attempt to calculate with zero modulus!" |
| 138 | ); |
| 139 | |
| 140 | if modulus.is_odd() { |
| 141 | // For an odd modulus, we can use Montgomery multiplication in base 2^32. |
| 142 | monty_modpow(x, exponent, modulus) |
| 143 | } else { |
| 144 | // Otherwise do basically the same as `num::pow`, but with a modulus. |
| 145 | plain_modpow(x, &exponent.data, modulus) |
| 146 | } |
| 147 | } |
| 148 | |
| 149 | fn plain_modpow(base: &BigUint, exp_data: &[BigDigit], modulus: &BigUint) -> BigUint { |
| 150 | assert!( |
| 151 | !modulus.is_zero(), |
| 152 | "attempt to calculate with zero modulus!" |
| 153 | ); |
| 154 | |
| 155 | let i = match exp_data.iter().position(|&r| r != 0) { |
| 156 | None => return BigUint::one(), |
| 157 | Some(i) => i, |
| 158 | }; |
| 159 | |
| 160 | let mut base = base % modulus; |
| 161 | for _ in 0..i { |
| 162 | for _ in 0..big_digit::BITS { |
| 163 | base = &base * &base % modulus; |
| 164 | } |
| 165 | } |
| 166 | |
| 167 | let mut r = exp_data[i]; |
| 168 | let mut b = 0u8; |
| 169 | while r.is_even() { |
| 170 | base = &base * &base % modulus; |
| 171 | r >>= 1; |
| 172 | b += 1; |
| 173 | } |
| 174 | |
| 175 | let mut exp_iter = exp_data[i + 1..].iter(); |
| 176 | if exp_iter.len() == 0 && r.is_one() { |
| 177 | return base; |
| 178 | } |
| 179 | |
| 180 | let mut acc = base.clone(); |
| 181 | r >>= 1; |
| 182 | b += 1; |
| 183 | |
| 184 | { |
| 185 | let mut unit = |exp_is_odd| { |
| 186 | base = &base * &base % modulus; |
| 187 | if exp_is_odd { |
Joel Galenson | 7bace41 | 2021-09-22 14:05:35 -0700 | [diff] [blame^] | 188 | acc *= &base; |
| 189 | acc %= modulus; |
Yiming Jing | cf21fc4 | 2021-07-16 13:23:26 -0700 | [diff] [blame] | 190 | } |
| 191 | }; |
| 192 | |
| 193 | if let Some(&last) = exp_iter.next_back() { |
| 194 | // consume exp_data[i] |
| 195 | for _ in b..big_digit::BITS { |
| 196 | unit(r.is_odd()); |
| 197 | r >>= 1; |
| 198 | } |
| 199 | |
| 200 | // consume all other digits before the last |
| 201 | for &r in exp_iter { |
| 202 | let mut r = r; |
| 203 | for _ in 0..big_digit::BITS { |
| 204 | unit(r.is_odd()); |
| 205 | r >>= 1; |
| 206 | } |
| 207 | } |
| 208 | r = last; |
| 209 | } |
| 210 | |
| 211 | debug_assert_ne!(r, 0); |
| 212 | while !r.is_zero() { |
| 213 | unit(r.is_odd()); |
| 214 | r >>= 1; |
| 215 | } |
| 216 | } |
| 217 | acc |
| 218 | } |
| 219 | |
| 220 | #[test] |
| 221 | fn test_plain_modpow() { |
| 222 | let two = &BigUint::from(2u32); |
| 223 | let modulus = BigUint::from(0x1100u32); |
| 224 | |
| 225 | let exp = vec![0, 0b1]; |
| 226 | assert_eq!( |
| 227 | two.pow(0b1_00000000_u32) % &modulus, |
| 228 | plain_modpow(&two, &exp, &modulus) |
| 229 | ); |
| 230 | let exp = vec![0, 0b10]; |
| 231 | assert_eq!( |
| 232 | two.pow(0b10_00000000_u32) % &modulus, |
| 233 | plain_modpow(&two, &exp, &modulus) |
| 234 | ); |
| 235 | let exp = vec![0, 0b110010]; |
| 236 | assert_eq!( |
| 237 | two.pow(0b110010_00000000_u32) % &modulus, |
| 238 | plain_modpow(&two, &exp, &modulus) |
| 239 | ); |
| 240 | let exp = vec![0b1, 0b1]; |
| 241 | assert_eq!( |
| 242 | two.pow(0b1_00000001_u32) % &modulus, |
| 243 | plain_modpow(&two, &exp, &modulus) |
| 244 | ); |
| 245 | let exp = vec![0b1100, 0, 0b1]; |
| 246 | assert_eq!( |
| 247 | two.pow(0b1_00000000_00001100_u32) % &modulus, |
| 248 | plain_modpow(&two, &exp, &modulus) |
| 249 | ); |
| 250 | } |
| 251 | |
| 252 | #[test] |
| 253 | fn test_pow_biguint() { |
| 254 | let base = BigUint::from(5u8); |
| 255 | let exponent = BigUint::from(3u8); |
| 256 | |
| 257 | assert_eq!(BigUint::from(125u8), base.pow(exponent)); |
| 258 | } |