Yiming Jing | cf21fc4 | 2021-07-16 13:23:26 -0700 | [diff] [blame] | 1 | //! Randomization of big integers |
| 2 | |
| 3 | use rand::distributions::uniform::{SampleBorrow, SampleUniform, UniformSampler}; |
| 4 | use rand::prelude::*; |
| 5 | |
| 6 | use crate::BigInt; |
| 7 | use crate::BigUint; |
| 8 | use crate::Sign::*; |
| 9 | |
| 10 | use crate::biguint::biguint_from_vec; |
| 11 | |
| 12 | use num_integer::Integer; |
| 13 | use num_traits::{ToPrimitive, Zero}; |
| 14 | |
| 15 | /// A trait for sampling random big integers. |
| 16 | /// |
| 17 | /// The `rand` feature must be enabled to use this. See crate-level documentation for details. |
| 18 | pub trait RandBigInt { |
| 19 | /// Generate a random `BigUint` of the given bit size. |
| 20 | fn gen_biguint(&mut self, bit_size: u64) -> BigUint; |
| 21 | |
| 22 | /// Generate a random BigInt of the given bit size. |
| 23 | fn gen_bigint(&mut self, bit_size: u64) -> BigInt; |
| 24 | |
| 25 | /// Generate a random `BigUint` less than the given bound. Fails |
| 26 | /// when the bound is zero. |
| 27 | fn gen_biguint_below(&mut self, bound: &BigUint) -> BigUint; |
| 28 | |
| 29 | /// Generate a random `BigUint` within the given range. The lower |
| 30 | /// bound is inclusive; the upper bound is exclusive. Fails when |
| 31 | /// the upper bound is not greater than the lower bound. |
| 32 | fn gen_biguint_range(&mut self, lbound: &BigUint, ubound: &BigUint) -> BigUint; |
| 33 | |
| 34 | /// Generate a random `BigInt` within the given range. The lower |
| 35 | /// bound is inclusive; the upper bound is exclusive. Fails when |
| 36 | /// the upper bound is not greater than the lower bound. |
| 37 | fn gen_bigint_range(&mut self, lbound: &BigInt, ubound: &BigInt) -> BigInt; |
| 38 | } |
| 39 | |
| 40 | fn gen_bits<R: Rng + ?Sized>(rng: &mut R, data: &mut [u32], rem: u64) { |
| 41 | // `fill` is faster than many `gen::<u32>` calls |
| 42 | rng.fill(data); |
| 43 | if rem > 0 { |
| 44 | let last = data.len() - 1; |
| 45 | data[last] >>= 32 - rem; |
| 46 | } |
| 47 | } |
| 48 | |
| 49 | impl<R: Rng + ?Sized> RandBigInt for R { |
| 50 | #[cfg(not(u64_digit))] |
| 51 | fn gen_biguint(&mut self, bit_size: u64) -> BigUint { |
| 52 | let (digits, rem) = bit_size.div_rem(&32); |
| 53 | let len = (digits + (rem > 0) as u64) |
| 54 | .to_usize() |
| 55 | .expect("capacity overflow"); |
| 56 | let mut data = vec![0u32; len]; |
| 57 | gen_bits(self, &mut data, rem); |
| 58 | biguint_from_vec(data) |
| 59 | } |
| 60 | |
| 61 | #[cfg(u64_digit)] |
| 62 | fn gen_biguint(&mut self, bit_size: u64) -> BigUint { |
| 63 | use core::slice; |
| 64 | |
| 65 | let (digits, rem) = bit_size.div_rem(&32); |
| 66 | let len = (digits + (rem > 0) as u64) |
| 67 | .to_usize() |
| 68 | .expect("capacity overflow"); |
Joel Galenson | 7bace41 | 2021-09-22 14:05:35 -0700 | [diff] [blame] | 69 | let native_digits = Integer::div_ceil(&bit_size, &64); |
Yiming Jing | cf21fc4 | 2021-07-16 13:23:26 -0700 | [diff] [blame] | 70 | let native_len = native_digits.to_usize().expect("capacity overflow"); |
| 71 | let mut data = vec![0u64; native_len]; |
| 72 | unsafe { |
| 73 | // Generate bits in a `&mut [u32]` slice for value stability |
| 74 | let ptr = data.as_mut_ptr() as *mut u32; |
| 75 | debug_assert!(native_len * 2 >= len); |
| 76 | let data = slice::from_raw_parts_mut(ptr, len); |
| 77 | gen_bits(self, data, rem); |
| 78 | } |
| 79 | #[cfg(target_endian = "big")] |
| 80 | for digit in &mut data { |
| 81 | // swap u32 digits into u64 endianness |
| 82 | *digit = (*digit << 32) | (*digit >> 32); |
| 83 | } |
| 84 | biguint_from_vec(data) |
| 85 | } |
| 86 | |
| 87 | fn gen_bigint(&mut self, bit_size: u64) -> BigInt { |
| 88 | loop { |
| 89 | // Generate a random BigUint... |
| 90 | let biguint = self.gen_biguint(bit_size); |
| 91 | // ...and then randomly assign it a Sign... |
| 92 | let sign = if biguint.is_zero() { |
| 93 | // ...except that if the BigUint is zero, we need to try |
| 94 | // again with probability 0.5. This is because otherwise, |
| 95 | // the probability of generating a zero BigInt would be |
| 96 | // double that of any other number. |
| 97 | if self.gen() { |
| 98 | continue; |
| 99 | } else { |
| 100 | NoSign |
| 101 | } |
| 102 | } else if self.gen() { |
| 103 | Plus |
| 104 | } else { |
| 105 | Minus |
| 106 | }; |
| 107 | return BigInt::from_biguint(sign, biguint); |
| 108 | } |
| 109 | } |
| 110 | |
| 111 | fn gen_biguint_below(&mut self, bound: &BigUint) -> BigUint { |
| 112 | assert!(!bound.is_zero()); |
| 113 | let bits = bound.bits(); |
| 114 | loop { |
| 115 | let n = self.gen_biguint(bits); |
| 116 | if n < *bound { |
| 117 | return n; |
| 118 | } |
| 119 | } |
| 120 | } |
| 121 | |
| 122 | fn gen_biguint_range(&mut self, lbound: &BigUint, ubound: &BigUint) -> BigUint { |
| 123 | assert!(*lbound < *ubound); |
| 124 | if lbound.is_zero() { |
| 125 | self.gen_biguint_below(ubound) |
| 126 | } else { |
| 127 | lbound + self.gen_biguint_below(&(ubound - lbound)) |
| 128 | } |
| 129 | } |
| 130 | |
| 131 | fn gen_bigint_range(&mut self, lbound: &BigInt, ubound: &BigInt) -> BigInt { |
| 132 | assert!(*lbound < *ubound); |
| 133 | if lbound.is_zero() { |
| 134 | BigInt::from(self.gen_biguint_below(ubound.magnitude())) |
| 135 | } else if ubound.is_zero() { |
| 136 | lbound + BigInt::from(self.gen_biguint_below(lbound.magnitude())) |
| 137 | } else { |
| 138 | let delta = ubound - lbound; |
| 139 | lbound + BigInt::from(self.gen_biguint_below(delta.magnitude())) |
| 140 | } |
| 141 | } |
| 142 | } |
| 143 | |
| 144 | /// The back-end implementing rand's `UniformSampler` for `BigUint`. |
| 145 | #[derive(Clone, Debug)] |
| 146 | pub struct UniformBigUint { |
| 147 | base: BigUint, |
| 148 | len: BigUint, |
| 149 | } |
| 150 | |
| 151 | impl UniformSampler for UniformBigUint { |
| 152 | type X = BigUint; |
| 153 | |
| 154 | #[inline] |
| 155 | fn new<B1, B2>(low_b: B1, high_b: B2) -> Self |
| 156 | where |
| 157 | B1: SampleBorrow<Self::X> + Sized, |
| 158 | B2: SampleBorrow<Self::X> + Sized, |
| 159 | { |
| 160 | let low = low_b.borrow(); |
| 161 | let high = high_b.borrow(); |
| 162 | assert!(low < high); |
| 163 | UniformBigUint { |
| 164 | len: high - low, |
| 165 | base: low.clone(), |
| 166 | } |
| 167 | } |
| 168 | |
| 169 | #[inline] |
| 170 | fn new_inclusive<B1, B2>(low_b: B1, high_b: B2) -> Self |
| 171 | where |
| 172 | B1: SampleBorrow<Self::X> + Sized, |
| 173 | B2: SampleBorrow<Self::X> + Sized, |
| 174 | { |
| 175 | let low = low_b.borrow(); |
| 176 | let high = high_b.borrow(); |
| 177 | assert!(low <= high); |
| 178 | Self::new(low, high + 1u32) |
| 179 | } |
| 180 | |
| 181 | #[inline] |
| 182 | fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> Self::X { |
| 183 | &self.base + rng.gen_biguint_below(&self.len) |
| 184 | } |
| 185 | |
| 186 | #[inline] |
| 187 | fn sample_single<R: Rng + ?Sized, B1, B2>(low: B1, high: B2, rng: &mut R) -> Self::X |
| 188 | where |
| 189 | B1: SampleBorrow<Self::X> + Sized, |
| 190 | B2: SampleBorrow<Self::X> + Sized, |
| 191 | { |
| 192 | rng.gen_biguint_range(low.borrow(), high.borrow()) |
| 193 | } |
| 194 | } |
| 195 | |
| 196 | impl SampleUniform for BigUint { |
| 197 | type Sampler = UniformBigUint; |
| 198 | } |
| 199 | |
| 200 | /// The back-end implementing rand's `UniformSampler` for `BigInt`. |
| 201 | #[derive(Clone, Debug)] |
| 202 | pub struct UniformBigInt { |
| 203 | base: BigInt, |
| 204 | len: BigUint, |
| 205 | } |
| 206 | |
| 207 | impl UniformSampler for UniformBigInt { |
| 208 | type X = BigInt; |
| 209 | |
| 210 | #[inline] |
| 211 | fn new<B1, B2>(low_b: B1, high_b: B2) -> Self |
| 212 | where |
| 213 | B1: SampleBorrow<Self::X> + Sized, |
| 214 | B2: SampleBorrow<Self::X> + Sized, |
| 215 | { |
| 216 | let low = low_b.borrow(); |
| 217 | let high = high_b.borrow(); |
| 218 | assert!(low < high); |
| 219 | UniformBigInt { |
| 220 | len: (high - low).into_parts().1, |
| 221 | base: low.clone(), |
| 222 | } |
| 223 | } |
| 224 | |
| 225 | #[inline] |
| 226 | fn new_inclusive<B1, B2>(low_b: B1, high_b: B2) -> Self |
| 227 | where |
| 228 | B1: SampleBorrow<Self::X> + Sized, |
| 229 | B2: SampleBorrow<Self::X> + Sized, |
| 230 | { |
| 231 | let low = low_b.borrow(); |
| 232 | let high = high_b.borrow(); |
| 233 | assert!(low <= high); |
| 234 | Self::new(low, high + 1u32) |
| 235 | } |
| 236 | |
| 237 | #[inline] |
| 238 | fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> Self::X { |
| 239 | &self.base + BigInt::from(rng.gen_biguint_below(&self.len)) |
| 240 | } |
| 241 | |
| 242 | #[inline] |
| 243 | fn sample_single<R: Rng + ?Sized, B1, B2>(low: B1, high: B2, rng: &mut R) -> Self::X |
| 244 | where |
| 245 | B1: SampleBorrow<Self::X> + Sized, |
| 246 | B2: SampleBorrow<Self::X> + Sized, |
| 247 | { |
| 248 | rng.gen_bigint_range(low.borrow(), high.borrow()) |
| 249 | } |
| 250 | } |
| 251 | |
| 252 | impl SampleUniform for BigInt { |
| 253 | type Sampler = UniformBigInt; |
| 254 | } |
| 255 | |
| 256 | /// A random distribution for `BigUint` and `BigInt` values of a particular bit size. |
| 257 | /// |
| 258 | /// The `rand` feature must be enabled to use this. See crate-level documentation for details. |
| 259 | #[derive(Clone, Copy, Debug)] |
| 260 | pub struct RandomBits { |
| 261 | bits: u64, |
| 262 | } |
| 263 | |
| 264 | impl RandomBits { |
| 265 | #[inline] |
| 266 | pub fn new(bits: u64) -> RandomBits { |
| 267 | RandomBits { bits } |
| 268 | } |
| 269 | } |
| 270 | |
| 271 | impl Distribution<BigUint> for RandomBits { |
| 272 | #[inline] |
| 273 | fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> BigUint { |
| 274 | rng.gen_biguint(self.bits) |
| 275 | } |
| 276 | } |
| 277 | |
| 278 | impl Distribution<BigInt> for RandomBits { |
| 279 | #[inline] |
| 280 | fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> BigInt { |
| 281 | rng.gen_bigint(self.bits) |
| 282 | } |
| 283 | } |