Yiming Jing | cf21fc4 | 2021-07-16 13:23:26 -0700 | [diff] [blame] | 1 | use crate::big_digit::{self, BigDigit}; |
| 2 | use crate::std_alloc::{String, Vec}; |
| 3 | |
| 4 | use core::cmp; |
| 5 | use core::cmp::Ordering; |
| 6 | use core::default::Default; |
| 7 | use core::fmt; |
| 8 | use core::hash; |
| 9 | use core::mem; |
| 10 | use core::str; |
| 11 | use core::{u32, u64, u8}; |
| 12 | |
| 13 | use num_integer::{Integer, Roots}; |
| 14 | use num_traits::{Num, One, Pow, ToPrimitive, Unsigned, Zero}; |
| 15 | |
| 16 | mod addition; |
| 17 | mod division; |
| 18 | mod multiplication; |
| 19 | mod subtraction; |
| 20 | |
| 21 | mod bits; |
| 22 | mod convert; |
| 23 | mod iter; |
| 24 | mod monty; |
| 25 | mod power; |
| 26 | mod shift; |
| 27 | |
| 28 | #[cfg(any(feature = "quickcheck", feature = "arbitrary"))] |
| 29 | mod arbitrary; |
| 30 | |
| 31 | #[cfg(feature = "serde")] |
| 32 | mod serde; |
| 33 | |
| 34 | pub(crate) use self::convert::to_str_radix_reversed; |
| 35 | pub use self::iter::{U32Digits, U64Digits}; |
| 36 | |
| 37 | /// A big unsigned integer type. |
| 38 | pub struct BigUint { |
| 39 | data: Vec<BigDigit>, |
| 40 | } |
| 41 | |
| 42 | // Note: derived `Clone` doesn't specialize `clone_from`, |
| 43 | // but we want to keep the allocation in `data`. |
| 44 | impl Clone for BigUint { |
| 45 | #[inline] |
| 46 | fn clone(&self) -> Self { |
| 47 | BigUint { |
| 48 | data: self.data.clone(), |
| 49 | } |
| 50 | } |
| 51 | |
| 52 | #[inline] |
| 53 | fn clone_from(&mut self, other: &Self) { |
| 54 | self.data.clone_from(&other.data); |
| 55 | } |
| 56 | } |
| 57 | |
| 58 | impl hash::Hash for BigUint { |
| 59 | #[inline] |
| 60 | fn hash<H: hash::Hasher>(&self, state: &mut H) { |
| 61 | debug_assert!(self.data.last() != Some(&0)); |
| 62 | self.data.hash(state); |
| 63 | } |
| 64 | } |
| 65 | |
| 66 | impl PartialEq for BigUint { |
| 67 | #[inline] |
| 68 | fn eq(&self, other: &BigUint) -> bool { |
| 69 | debug_assert!(self.data.last() != Some(&0)); |
| 70 | debug_assert!(other.data.last() != Some(&0)); |
| 71 | self.data == other.data |
| 72 | } |
| 73 | } |
| 74 | impl Eq for BigUint {} |
| 75 | |
| 76 | impl PartialOrd for BigUint { |
| 77 | #[inline] |
| 78 | fn partial_cmp(&self, other: &BigUint) -> Option<Ordering> { |
| 79 | Some(self.cmp(other)) |
| 80 | } |
| 81 | } |
| 82 | |
| 83 | impl Ord for BigUint { |
| 84 | #[inline] |
| 85 | fn cmp(&self, other: &BigUint) -> Ordering { |
| 86 | cmp_slice(&self.data[..], &other.data[..]) |
| 87 | } |
| 88 | } |
| 89 | |
| 90 | #[inline] |
| 91 | fn cmp_slice(a: &[BigDigit], b: &[BigDigit]) -> Ordering { |
| 92 | debug_assert!(a.last() != Some(&0)); |
| 93 | debug_assert!(b.last() != Some(&0)); |
| 94 | |
| 95 | match Ord::cmp(&a.len(), &b.len()) { |
| 96 | Ordering::Equal => Iterator::cmp(a.iter().rev(), b.iter().rev()), |
| 97 | other => other, |
| 98 | } |
| 99 | } |
| 100 | |
| 101 | impl Default for BigUint { |
| 102 | #[inline] |
| 103 | fn default() -> BigUint { |
| 104 | Zero::zero() |
| 105 | } |
| 106 | } |
| 107 | |
| 108 | impl fmt::Debug for BigUint { |
| 109 | fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result { |
| 110 | fmt::Display::fmt(self, f) |
| 111 | } |
| 112 | } |
| 113 | |
| 114 | impl fmt::Display for BigUint { |
| 115 | fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result { |
| 116 | f.pad_integral(true, "", &self.to_str_radix(10)) |
| 117 | } |
| 118 | } |
| 119 | |
| 120 | impl fmt::LowerHex for BigUint { |
| 121 | fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result { |
| 122 | f.pad_integral(true, "0x", &self.to_str_radix(16)) |
| 123 | } |
| 124 | } |
| 125 | |
| 126 | impl fmt::UpperHex for BigUint { |
| 127 | fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result { |
| 128 | let mut s = self.to_str_radix(16); |
| 129 | s.make_ascii_uppercase(); |
| 130 | f.pad_integral(true, "0x", &s) |
| 131 | } |
| 132 | } |
| 133 | |
| 134 | impl fmt::Binary for BigUint { |
| 135 | fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result { |
| 136 | f.pad_integral(true, "0b", &self.to_str_radix(2)) |
| 137 | } |
| 138 | } |
| 139 | |
| 140 | impl fmt::Octal for BigUint { |
| 141 | fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result { |
| 142 | f.pad_integral(true, "0o", &self.to_str_radix(8)) |
| 143 | } |
| 144 | } |
| 145 | |
| 146 | impl Zero for BigUint { |
| 147 | #[inline] |
| 148 | fn zero() -> BigUint { |
| 149 | BigUint { data: Vec::new() } |
| 150 | } |
| 151 | |
| 152 | #[inline] |
| 153 | fn set_zero(&mut self) { |
| 154 | self.data.clear(); |
| 155 | } |
| 156 | |
| 157 | #[inline] |
| 158 | fn is_zero(&self) -> bool { |
| 159 | self.data.is_empty() |
| 160 | } |
| 161 | } |
| 162 | |
| 163 | impl One for BigUint { |
| 164 | #[inline] |
| 165 | fn one() -> BigUint { |
| 166 | BigUint { data: vec![1] } |
| 167 | } |
| 168 | |
| 169 | #[inline] |
| 170 | fn set_one(&mut self) { |
| 171 | self.data.clear(); |
| 172 | self.data.push(1); |
| 173 | } |
| 174 | |
| 175 | #[inline] |
| 176 | fn is_one(&self) -> bool { |
| 177 | self.data[..] == [1] |
| 178 | } |
| 179 | } |
| 180 | |
| 181 | impl Unsigned for BigUint {} |
| 182 | |
| 183 | impl Integer for BigUint { |
| 184 | #[inline] |
| 185 | fn div_rem(&self, other: &BigUint) -> (BigUint, BigUint) { |
| 186 | division::div_rem_ref(self, other) |
| 187 | } |
| 188 | |
| 189 | #[inline] |
| 190 | fn div_floor(&self, other: &BigUint) -> BigUint { |
| 191 | let (d, _) = division::div_rem_ref(self, other); |
| 192 | d |
| 193 | } |
| 194 | |
| 195 | #[inline] |
| 196 | fn mod_floor(&self, other: &BigUint) -> BigUint { |
| 197 | let (_, m) = division::div_rem_ref(self, other); |
| 198 | m |
| 199 | } |
| 200 | |
| 201 | #[inline] |
| 202 | fn div_mod_floor(&self, other: &BigUint) -> (BigUint, BigUint) { |
| 203 | division::div_rem_ref(self, other) |
| 204 | } |
| 205 | |
| 206 | #[inline] |
| 207 | fn div_ceil(&self, other: &BigUint) -> BigUint { |
| 208 | let (d, m) = division::div_rem_ref(self, other); |
| 209 | if m.is_zero() { |
| 210 | d |
| 211 | } else { |
| 212 | d + 1u32 |
| 213 | } |
| 214 | } |
| 215 | |
| 216 | /// Calculates the Greatest Common Divisor (GCD) of the number and `other`. |
| 217 | /// |
| 218 | /// The result is always positive. |
| 219 | #[inline] |
| 220 | fn gcd(&self, other: &Self) -> Self { |
| 221 | #[inline] |
| 222 | fn twos(x: &BigUint) -> u64 { |
| 223 | x.trailing_zeros().unwrap_or(0) |
| 224 | } |
| 225 | |
| 226 | // Stein's algorithm |
| 227 | if self.is_zero() { |
| 228 | return other.clone(); |
| 229 | } |
| 230 | if other.is_zero() { |
| 231 | return self.clone(); |
| 232 | } |
| 233 | let mut m = self.clone(); |
| 234 | let mut n = other.clone(); |
| 235 | |
| 236 | // find common factors of 2 |
| 237 | let shift = cmp::min(twos(&n), twos(&m)); |
| 238 | |
| 239 | // divide m and n by 2 until odd |
| 240 | // m inside loop |
| 241 | n >>= twos(&n); |
| 242 | |
| 243 | while !m.is_zero() { |
| 244 | m >>= twos(&m); |
| 245 | if n > m { |
| 246 | mem::swap(&mut n, &mut m) |
| 247 | } |
| 248 | m -= &n; |
| 249 | } |
| 250 | |
| 251 | n << shift |
| 252 | } |
| 253 | |
| 254 | /// Calculates the Lowest Common Multiple (LCM) of the number and `other`. |
| 255 | #[inline] |
| 256 | fn lcm(&self, other: &BigUint) -> BigUint { |
| 257 | if self.is_zero() && other.is_zero() { |
| 258 | Self::zero() |
| 259 | } else { |
| 260 | self / self.gcd(other) * other |
| 261 | } |
| 262 | } |
| 263 | |
| 264 | /// Calculates the Greatest Common Divisor (GCD) and |
| 265 | /// Lowest Common Multiple (LCM) together. |
| 266 | #[inline] |
| 267 | fn gcd_lcm(&self, other: &Self) -> (Self, Self) { |
| 268 | let gcd = self.gcd(other); |
| 269 | let lcm = if gcd.is_zero() { |
| 270 | Self::zero() |
| 271 | } else { |
| 272 | self / &gcd * other |
| 273 | }; |
| 274 | (gcd, lcm) |
| 275 | } |
| 276 | |
| 277 | /// Deprecated, use `is_multiple_of` instead. |
| 278 | #[inline] |
| 279 | fn divides(&self, other: &BigUint) -> bool { |
| 280 | self.is_multiple_of(other) |
| 281 | } |
| 282 | |
| 283 | /// Returns `true` if the number is a multiple of `other`. |
| 284 | #[inline] |
| 285 | fn is_multiple_of(&self, other: &BigUint) -> bool { |
| 286 | (self % other).is_zero() |
| 287 | } |
| 288 | |
| 289 | /// Returns `true` if the number is divisible by `2`. |
| 290 | #[inline] |
| 291 | fn is_even(&self) -> bool { |
| 292 | // Considering only the last digit. |
| 293 | match self.data.first() { |
| 294 | Some(x) => x.is_even(), |
| 295 | None => true, |
| 296 | } |
| 297 | } |
| 298 | |
| 299 | /// Returns `true` if the number is not divisible by `2`. |
| 300 | #[inline] |
| 301 | fn is_odd(&self) -> bool { |
| 302 | !self.is_even() |
| 303 | } |
| 304 | |
| 305 | /// Rounds up to nearest multiple of argument. |
| 306 | #[inline] |
| 307 | fn next_multiple_of(&self, other: &Self) -> Self { |
| 308 | let m = self.mod_floor(other); |
| 309 | if m.is_zero() { |
| 310 | self.clone() |
| 311 | } else { |
| 312 | self + (other - m) |
| 313 | } |
| 314 | } |
| 315 | /// Rounds down to nearest multiple of argument. |
| 316 | #[inline] |
| 317 | fn prev_multiple_of(&self, other: &Self) -> Self { |
| 318 | self - self.mod_floor(other) |
| 319 | } |
| 320 | } |
| 321 | |
| 322 | #[inline] |
| 323 | fn fixpoint<F>(mut x: BigUint, max_bits: u64, f: F) -> BigUint |
| 324 | where |
| 325 | F: Fn(&BigUint) -> BigUint, |
| 326 | { |
| 327 | let mut xn = f(&x); |
| 328 | |
| 329 | // If the value increased, then the initial guess must have been low. |
| 330 | // Repeat until we reverse course. |
| 331 | while x < xn { |
| 332 | // Sometimes an increase will go way too far, especially with large |
| 333 | // powers, and then take a long time to walk back. We know an upper |
| 334 | // bound based on bit size, so saturate on that. |
| 335 | x = if xn.bits() > max_bits { |
| 336 | BigUint::one() << max_bits |
| 337 | } else { |
| 338 | xn |
| 339 | }; |
| 340 | xn = f(&x); |
| 341 | } |
| 342 | |
| 343 | // Now keep repeating while the estimate is decreasing. |
| 344 | while x > xn { |
| 345 | x = xn; |
| 346 | xn = f(&x); |
| 347 | } |
| 348 | x |
| 349 | } |
| 350 | |
| 351 | impl Roots for BigUint { |
| 352 | // nth_root, sqrt and cbrt use Newton's method to compute |
| 353 | // principal root of a given degree for a given integer. |
| 354 | |
| 355 | // Reference: |
| 356 | // Brent & Zimmermann, Modern Computer Arithmetic, v0.5.9, Algorithm 1.14 |
| 357 | fn nth_root(&self, n: u32) -> Self { |
| 358 | assert!(n > 0, "root degree n must be at least 1"); |
| 359 | |
| 360 | if self.is_zero() || self.is_one() { |
| 361 | return self.clone(); |
| 362 | } |
| 363 | |
| 364 | match n { |
| 365 | // Optimize for small n |
| 366 | 1 => return self.clone(), |
| 367 | 2 => return self.sqrt(), |
| 368 | 3 => return self.cbrt(), |
| 369 | _ => (), |
| 370 | } |
| 371 | |
| 372 | // The root of non-zero values less than 2ⁿ can only be 1. |
| 373 | let bits = self.bits(); |
| 374 | let n64 = u64::from(n); |
| 375 | if bits <= n64 { |
| 376 | return BigUint::one(); |
| 377 | } |
| 378 | |
| 379 | // If we fit in `u64`, compute the root that way. |
| 380 | if let Some(x) = self.to_u64() { |
| 381 | return x.nth_root(n).into(); |
| 382 | } |
| 383 | |
| 384 | let max_bits = bits / n64 + 1; |
| 385 | |
| 386 | #[cfg(feature = "std")] |
| 387 | let guess = match self.to_f64() { |
| 388 | Some(f) if f.is_finite() => { |
| 389 | use num_traits::FromPrimitive; |
| 390 | |
| 391 | // We fit in `f64` (lossy), so get a better initial guess from that. |
| 392 | BigUint::from_f64((f.ln() / f64::from(n)).exp()).unwrap() |
| 393 | } |
| 394 | _ => { |
| 395 | // Try to guess by scaling down such that it does fit in `f64`. |
| 396 | // With some (x * 2ⁿᵏ), its nth root ≈ (ⁿ√x * 2ᵏ) |
| 397 | let extra_bits = bits - (core::f64::MAX_EXP as u64 - 1); |
Joel Galenson | 7bace41 | 2021-09-22 14:05:35 -0700 | [diff] [blame] | 398 | let root_scale = Integer::div_ceil(&extra_bits, &n64); |
Yiming Jing | cf21fc4 | 2021-07-16 13:23:26 -0700 | [diff] [blame] | 399 | let scale = root_scale * n64; |
| 400 | if scale < bits && bits - scale > n64 { |
| 401 | (self >> scale).nth_root(n) << root_scale |
| 402 | } else { |
| 403 | BigUint::one() << max_bits |
| 404 | } |
| 405 | } |
| 406 | }; |
| 407 | |
| 408 | #[cfg(not(feature = "std"))] |
| 409 | let guess = BigUint::one() << max_bits; |
| 410 | |
| 411 | let n_min_1 = n - 1; |
| 412 | fixpoint(guess, max_bits, move |s| { |
| 413 | let q = self / s.pow(n_min_1); |
| 414 | let t = n_min_1 * s + q; |
| 415 | t / n |
| 416 | }) |
| 417 | } |
| 418 | |
| 419 | // Reference: |
| 420 | // Brent & Zimmermann, Modern Computer Arithmetic, v0.5.9, Algorithm 1.13 |
| 421 | fn sqrt(&self) -> Self { |
| 422 | if self.is_zero() || self.is_one() { |
| 423 | return self.clone(); |
| 424 | } |
| 425 | |
| 426 | // If we fit in `u64`, compute the root that way. |
| 427 | if let Some(x) = self.to_u64() { |
| 428 | return x.sqrt().into(); |
| 429 | } |
| 430 | |
| 431 | let bits = self.bits(); |
| 432 | let max_bits = bits / 2 + 1; |
| 433 | |
| 434 | #[cfg(feature = "std")] |
| 435 | let guess = match self.to_f64() { |
| 436 | Some(f) if f.is_finite() => { |
| 437 | use num_traits::FromPrimitive; |
| 438 | |
| 439 | // We fit in `f64` (lossy), so get a better initial guess from that. |
| 440 | BigUint::from_f64(f.sqrt()).unwrap() |
| 441 | } |
| 442 | _ => { |
| 443 | // Try to guess by scaling down such that it does fit in `f64`. |
| 444 | // With some (x * 2²ᵏ), its sqrt ≈ (√x * 2ᵏ) |
| 445 | let extra_bits = bits - (core::f64::MAX_EXP as u64 - 1); |
| 446 | let root_scale = (extra_bits + 1) / 2; |
| 447 | let scale = root_scale * 2; |
| 448 | (self >> scale).sqrt() << root_scale |
| 449 | } |
| 450 | }; |
| 451 | |
| 452 | #[cfg(not(feature = "std"))] |
| 453 | let guess = BigUint::one() << max_bits; |
| 454 | |
| 455 | fixpoint(guess, max_bits, move |s| { |
| 456 | let q = self / s; |
| 457 | let t = s + q; |
| 458 | t >> 1 |
| 459 | }) |
| 460 | } |
| 461 | |
| 462 | fn cbrt(&self) -> Self { |
| 463 | if self.is_zero() || self.is_one() { |
| 464 | return self.clone(); |
| 465 | } |
| 466 | |
| 467 | // If we fit in `u64`, compute the root that way. |
| 468 | if let Some(x) = self.to_u64() { |
| 469 | return x.cbrt().into(); |
| 470 | } |
| 471 | |
| 472 | let bits = self.bits(); |
| 473 | let max_bits = bits / 3 + 1; |
| 474 | |
| 475 | #[cfg(feature = "std")] |
| 476 | let guess = match self.to_f64() { |
| 477 | Some(f) if f.is_finite() => { |
| 478 | use num_traits::FromPrimitive; |
| 479 | |
| 480 | // We fit in `f64` (lossy), so get a better initial guess from that. |
| 481 | BigUint::from_f64(f.cbrt()).unwrap() |
| 482 | } |
| 483 | _ => { |
| 484 | // Try to guess by scaling down such that it does fit in `f64`. |
| 485 | // With some (x * 2³ᵏ), its cbrt ≈ (∛x * 2ᵏ) |
| 486 | let extra_bits = bits - (core::f64::MAX_EXP as u64 - 1); |
| 487 | let root_scale = (extra_bits + 2) / 3; |
| 488 | let scale = root_scale * 3; |
| 489 | (self >> scale).cbrt() << root_scale |
| 490 | } |
| 491 | }; |
| 492 | |
| 493 | #[cfg(not(feature = "std"))] |
| 494 | let guess = BigUint::one() << max_bits; |
| 495 | |
| 496 | fixpoint(guess, max_bits, move |s| { |
| 497 | let q = self / (s * s); |
| 498 | let t = (s << 1) + q; |
| 499 | t / 3u32 |
| 500 | }) |
| 501 | } |
| 502 | } |
| 503 | |
| 504 | /// A generic trait for converting a value to a `BigUint`. |
| 505 | pub trait ToBigUint { |
| 506 | /// Converts the value of `self` to a `BigUint`. |
| 507 | fn to_biguint(&self) -> Option<BigUint>; |
| 508 | } |
| 509 | |
| 510 | /// Creates and initializes a `BigUint`. |
| 511 | /// |
| 512 | /// The digits are in little-endian base matching `BigDigit`. |
| 513 | #[inline] |
| 514 | pub(crate) fn biguint_from_vec(digits: Vec<BigDigit>) -> BigUint { |
| 515 | BigUint { data: digits }.normalized() |
| 516 | } |
| 517 | |
| 518 | impl BigUint { |
| 519 | /// Creates and initializes a `BigUint`. |
| 520 | /// |
| 521 | /// The base 2<sup>32</sup> digits are ordered least significant digit first. |
| 522 | #[inline] |
| 523 | pub fn new(digits: Vec<u32>) -> BigUint { |
| 524 | let mut big = BigUint::zero(); |
| 525 | |
| 526 | #[cfg(not(u64_digit))] |
| 527 | { |
| 528 | big.data = digits; |
| 529 | big.normalize(); |
| 530 | } |
| 531 | |
| 532 | #[cfg(u64_digit)] |
| 533 | big.assign_from_slice(&digits); |
| 534 | |
| 535 | big |
| 536 | } |
| 537 | |
| 538 | /// Creates and initializes a `BigUint`. |
| 539 | /// |
| 540 | /// The base 2<sup>32</sup> digits are ordered least significant digit first. |
| 541 | #[inline] |
| 542 | pub fn from_slice(slice: &[u32]) -> BigUint { |
| 543 | let mut big = BigUint::zero(); |
| 544 | big.assign_from_slice(slice); |
| 545 | big |
| 546 | } |
| 547 | |
| 548 | /// Assign a value to a `BigUint`. |
| 549 | /// |
| 550 | /// The base 2<sup>32</sup> digits are ordered least significant digit first. |
| 551 | #[inline] |
| 552 | pub fn assign_from_slice(&mut self, slice: &[u32]) { |
| 553 | self.data.clear(); |
| 554 | |
| 555 | #[cfg(not(u64_digit))] |
| 556 | self.data.extend_from_slice(slice); |
| 557 | |
| 558 | #[cfg(u64_digit)] |
| 559 | self.data.extend(slice.chunks(2).map(u32_chunk_to_u64)); |
| 560 | |
| 561 | self.normalize(); |
| 562 | } |
| 563 | |
| 564 | /// Creates and initializes a `BigUint`. |
| 565 | /// |
| 566 | /// The bytes are in big-endian byte order. |
| 567 | /// |
| 568 | /// # Examples |
| 569 | /// |
| 570 | /// ``` |
| 571 | /// use num_bigint::BigUint; |
| 572 | /// |
| 573 | /// assert_eq!(BigUint::from_bytes_be(b"A"), |
| 574 | /// BigUint::parse_bytes(b"65", 10).unwrap()); |
| 575 | /// assert_eq!(BigUint::from_bytes_be(b"AA"), |
| 576 | /// BigUint::parse_bytes(b"16705", 10).unwrap()); |
| 577 | /// assert_eq!(BigUint::from_bytes_be(b"AB"), |
| 578 | /// BigUint::parse_bytes(b"16706", 10).unwrap()); |
| 579 | /// assert_eq!(BigUint::from_bytes_be(b"Hello world!"), |
| 580 | /// BigUint::parse_bytes(b"22405534230753963835153736737", 10).unwrap()); |
| 581 | /// ``` |
| 582 | #[inline] |
| 583 | pub fn from_bytes_be(bytes: &[u8]) -> BigUint { |
| 584 | if bytes.is_empty() { |
| 585 | Zero::zero() |
| 586 | } else { |
| 587 | let mut v = bytes.to_vec(); |
| 588 | v.reverse(); |
| 589 | BigUint::from_bytes_le(&*v) |
| 590 | } |
| 591 | } |
| 592 | |
| 593 | /// Creates and initializes a `BigUint`. |
| 594 | /// |
| 595 | /// The bytes are in little-endian byte order. |
| 596 | #[inline] |
| 597 | pub fn from_bytes_le(bytes: &[u8]) -> BigUint { |
| 598 | if bytes.is_empty() { |
| 599 | Zero::zero() |
| 600 | } else { |
| 601 | convert::from_bitwise_digits_le(bytes, 8) |
| 602 | } |
| 603 | } |
| 604 | |
| 605 | /// Creates and initializes a `BigUint`. The input slice must contain |
| 606 | /// ascii/utf8 characters in [0-9a-zA-Z]. |
| 607 | /// `radix` must be in the range `2...36`. |
| 608 | /// |
| 609 | /// The function `from_str_radix` from the `Num` trait provides the same logic |
| 610 | /// for `&str` buffers. |
| 611 | /// |
| 612 | /// # Examples |
| 613 | /// |
| 614 | /// ``` |
| 615 | /// use num_bigint::{BigUint, ToBigUint}; |
| 616 | /// |
| 617 | /// assert_eq!(BigUint::parse_bytes(b"1234", 10), ToBigUint::to_biguint(&1234)); |
| 618 | /// assert_eq!(BigUint::parse_bytes(b"ABCD", 16), ToBigUint::to_biguint(&0xABCD)); |
| 619 | /// assert_eq!(BigUint::parse_bytes(b"G", 16), None); |
| 620 | /// ``` |
| 621 | #[inline] |
| 622 | pub fn parse_bytes(buf: &[u8], radix: u32) -> Option<BigUint> { |
| 623 | let s = str::from_utf8(buf).ok()?; |
| 624 | BigUint::from_str_radix(s, radix).ok() |
| 625 | } |
| 626 | |
| 627 | /// Creates and initializes a `BigUint`. Each u8 of the input slice is |
| 628 | /// interpreted as one digit of the number |
| 629 | /// and must therefore be less than `radix`. |
| 630 | /// |
| 631 | /// The bytes are in big-endian byte order. |
| 632 | /// `radix` must be in the range `2...256`. |
| 633 | /// |
| 634 | /// # Examples |
| 635 | /// |
| 636 | /// ``` |
| 637 | /// use num_bigint::{BigUint}; |
| 638 | /// |
| 639 | /// let inbase190 = &[15, 33, 125, 12, 14]; |
| 640 | /// let a = BigUint::from_radix_be(inbase190, 190).unwrap(); |
| 641 | /// assert_eq!(a.to_radix_be(190), inbase190); |
| 642 | /// ``` |
| 643 | pub fn from_radix_be(buf: &[u8], radix: u32) -> Option<BigUint> { |
| 644 | convert::from_radix_be(buf, radix) |
| 645 | } |
| 646 | |
| 647 | /// Creates and initializes a `BigUint`. Each u8 of the input slice is |
| 648 | /// interpreted as one digit of the number |
| 649 | /// and must therefore be less than `radix`. |
| 650 | /// |
| 651 | /// The bytes are in little-endian byte order. |
| 652 | /// `radix` must be in the range `2...256`. |
| 653 | /// |
| 654 | /// # Examples |
| 655 | /// |
| 656 | /// ``` |
| 657 | /// use num_bigint::{BigUint}; |
| 658 | /// |
| 659 | /// let inbase190 = &[14, 12, 125, 33, 15]; |
| 660 | /// let a = BigUint::from_radix_be(inbase190, 190).unwrap(); |
| 661 | /// assert_eq!(a.to_radix_be(190), inbase190); |
| 662 | /// ``` |
| 663 | pub fn from_radix_le(buf: &[u8], radix: u32) -> Option<BigUint> { |
| 664 | convert::from_radix_le(buf, radix) |
| 665 | } |
| 666 | |
| 667 | /// Returns the byte representation of the `BigUint` in big-endian byte order. |
| 668 | /// |
| 669 | /// # Examples |
| 670 | /// |
| 671 | /// ``` |
| 672 | /// use num_bigint::BigUint; |
| 673 | /// |
| 674 | /// let i = BigUint::parse_bytes(b"1125", 10).unwrap(); |
| 675 | /// assert_eq!(i.to_bytes_be(), vec![4, 101]); |
| 676 | /// ``` |
| 677 | #[inline] |
| 678 | pub fn to_bytes_be(&self) -> Vec<u8> { |
| 679 | let mut v = self.to_bytes_le(); |
| 680 | v.reverse(); |
| 681 | v |
| 682 | } |
| 683 | |
| 684 | /// Returns the byte representation of the `BigUint` in little-endian byte order. |
| 685 | /// |
| 686 | /// # Examples |
| 687 | /// |
| 688 | /// ``` |
| 689 | /// use num_bigint::BigUint; |
| 690 | /// |
| 691 | /// let i = BigUint::parse_bytes(b"1125", 10).unwrap(); |
| 692 | /// assert_eq!(i.to_bytes_le(), vec![101, 4]); |
| 693 | /// ``` |
| 694 | #[inline] |
| 695 | pub fn to_bytes_le(&self) -> Vec<u8> { |
| 696 | if self.is_zero() { |
| 697 | vec![0] |
| 698 | } else { |
| 699 | convert::to_bitwise_digits_le(self, 8) |
| 700 | } |
| 701 | } |
| 702 | |
| 703 | /// Returns the `u32` digits representation of the `BigUint` ordered least significant digit |
| 704 | /// first. |
| 705 | /// |
| 706 | /// # Examples |
| 707 | /// |
| 708 | /// ``` |
| 709 | /// use num_bigint::BigUint; |
| 710 | /// |
| 711 | /// assert_eq!(BigUint::from(1125u32).to_u32_digits(), vec![1125]); |
| 712 | /// assert_eq!(BigUint::from(4294967295u32).to_u32_digits(), vec![4294967295]); |
| 713 | /// assert_eq!(BigUint::from(4294967296u64).to_u32_digits(), vec![0, 1]); |
| 714 | /// assert_eq!(BigUint::from(112500000000u64).to_u32_digits(), vec![830850304, 26]); |
| 715 | /// ``` |
| 716 | #[inline] |
| 717 | pub fn to_u32_digits(&self) -> Vec<u32> { |
| 718 | self.iter_u32_digits().collect() |
| 719 | } |
| 720 | |
| 721 | /// Returns the `u64` digits representation of the `BigUint` ordered least significant digit |
| 722 | /// first. |
| 723 | /// |
| 724 | /// # Examples |
| 725 | /// |
| 726 | /// ``` |
| 727 | /// use num_bigint::BigUint; |
| 728 | /// |
| 729 | /// assert_eq!(BigUint::from(1125u32).to_u64_digits(), vec![1125]); |
| 730 | /// assert_eq!(BigUint::from(4294967295u32).to_u64_digits(), vec![4294967295]); |
| 731 | /// assert_eq!(BigUint::from(4294967296u64).to_u64_digits(), vec![4294967296]); |
| 732 | /// assert_eq!(BigUint::from(112500000000u64).to_u64_digits(), vec![112500000000]); |
| 733 | /// assert_eq!(BigUint::from(1u128 << 64).to_u64_digits(), vec![0, 1]); |
| 734 | /// ``` |
| 735 | #[inline] |
| 736 | pub fn to_u64_digits(&self) -> Vec<u64> { |
| 737 | self.iter_u64_digits().collect() |
| 738 | } |
| 739 | |
| 740 | /// Returns an iterator of `u32` digits representation of the `BigUint` ordered least |
| 741 | /// significant digit first. |
| 742 | /// |
| 743 | /// # Examples |
| 744 | /// |
| 745 | /// ``` |
| 746 | /// use num_bigint::BigUint; |
| 747 | /// |
| 748 | /// assert_eq!(BigUint::from(1125u32).iter_u32_digits().collect::<Vec<u32>>(), vec![1125]); |
| 749 | /// assert_eq!(BigUint::from(4294967295u32).iter_u32_digits().collect::<Vec<u32>>(), vec![4294967295]); |
| 750 | /// assert_eq!(BigUint::from(4294967296u64).iter_u32_digits().collect::<Vec<u32>>(), vec![0, 1]); |
| 751 | /// assert_eq!(BigUint::from(112500000000u64).iter_u32_digits().collect::<Vec<u32>>(), vec![830850304, 26]); |
| 752 | /// ``` |
| 753 | #[inline] |
| 754 | pub fn iter_u32_digits(&self) -> U32Digits<'_> { |
| 755 | U32Digits::new(self.data.as_slice()) |
| 756 | } |
| 757 | |
| 758 | /// Returns an iterator of `u64` digits representation of the `BigUint` ordered least |
| 759 | /// significant digit first. |
| 760 | /// |
| 761 | /// # Examples |
| 762 | /// |
| 763 | /// ``` |
| 764 | /// use num_bigint::BigUint; |
| 765 | /// |
| 766 | /// assert_eq!(BigUint::from(1125u32).iter_u64_digits().collect::<Vec<u64>>(), vec![1125]); |
| 767 | /// assert_eq!(BigUint::from(4294967295u32).iter_u64_digits().collect::<Vec<u64>>(), vec![4294967295]); |
| 768 | /// assert_eq!(BigUint::from(4294967296u64).iter_u64_digits().collect::<Vec<u64>>(), vec![4294967296]); |
| 769 | /// assert_eq!(BigUint::from(112500000000u64).iter_u64_digits().collect::<Vec<u64>>(), vec![112500000000]); |
| 770 | /// assert_eq!(BigUint::from(1u128 << 64).iter_u64_digits().collect::<Vec<u64>>(), vec![0, 1]); |
| 771 | /// ``` |
| 772 | #[inline] |
| 773 | pub fn iter_u64_digits(&self) -> U64Digits<'_> { |
| 774 | U64Digits::new(self.data.as_slice()) |
| 775 | } |
| 776 | |
| 777 | /// Returns the integer formatted as a string in the given radix. |
| 778 | /// `radix` must be in the range `2...36`. |
| 779 | /// |
| 780 | /// # Examples |
| 781 | /// |
| 782 | /// ``` |
| 783 | /// use num_bigint::BigUint; |
| 784 | /// |
| 785 | /// let i = BigUint::parse_bytes(b"ff", 16).unwrap(); |
| 786 | /// assert_eq!(i.to_str_radix(16), "ff"); |
| 787 | /// ``` |
| 788 | #[inline] |
| 789 | pub fn to_str_radix(&self, radix: u32) -> String { |
| 790 | let mut v = to_str_radix_reversed(self, radix); |
| 791 | v.reverse(); |
| 792 | unsafe { String::from_utf8_unchecked(v) } |
| 793 | } |
| 794 | |
| 795 | /// Returns the integer in the requested base in big-endian digit order. |
| 796 | /// The output is not given in a human readable alphabet but as a zero |
| 797 | /// based u8 number. |
| 798 | /// `radix` must be in the range `2...256`. |
| 799 | /// |
| 800 | /// # Examples |
| 801 | /// |
| 802 | /// ``` |
| 803 | /// use num_bigint::BigUint; |
| 804 | /// |
| 805 | /// assert_eq!(BigUint::from(0xFFFFu64).to_radix_be(159), |
| 806 | /// vec![2, 94, 27]); |
| 807 | /// // 0xFFFF = 65535 = 2*(159^2) + 94*159 + 27 |
| 808 | /// ``` |
| 809 | #[inline] |
| 810 | pub fn to_radix_be(&self, radix: u32) -> Vec<u8> { |
| 811 | let mut v = convert::to_radix_le(self, radix); |
| 812 | v.reverse(); |
| 813 | v |
| 814 | } |
| 815 | |
| 816 | /// Returns the integer in the requested base in little-endian digit order. |
| 817 | /// The output is not given in a human readable alphabet but as a zero |
| 818 | /// based u8 number. |
| 819 | /// `radix` must be in the range `2...256`. |
| 820 | /// |
| 821 | /// # Examples |
| 822 | /// |
| 823 | /// ``` |
| 824 | /// use num_bigint::BigUint; |
| 825 | /// |
| 826 | /// assert_eq!(BigUint::from(0xFFFFu64).to_radix_le(159), |
| 827 | /// vec![27, 94, 2]); |
| 828 | /// // 0xFFFF = 65535 = 27 + 94*159 + 2*(159^2) |
| 829 | /// ``` |
| 830 | #[inline] |
| 831 | pub fn to_radix_le(&self, radix: u32) -> Vec<u8> { |
| 832 | convert::to_radix_le(self, radix) |
| 833 | } |
| 834 | |
| 835 | /// Determines the fewest bits necessary to express the `BigUint`. |
| 836 | #[inline] |
| 837 | pub fn bits(&self) -> u64 { |
| 838 | if self.is_zero() { |
| 839 | return 0; |
| 840 | } |
| 841 | let zeros: u64 = self.data.last().unwrap().leading_zeros().into(); |
| 842 | self.data.len() as u64 * u64::from(big_digit::BITS) - zeros |
| 843 | } |
| 844 | |
| 845 | /// Strips off trailing zero bigdigits - comparisons require the last element in the vector to |
| 846 | /// be nonzero. |
| 847 | #[inline] |
| 848 | fn normalize(&mut self) { |
Joel Galenson | 7bace41 | 2021-09-22 14:05:35 -0700 | [diff] [blame] | 849 | if let Some(&0) = self.data.last() { |
| 850 | let len = self.data.iter().rposition(|&d| d != 0).map_or(0, |i| i + 1); |
| 851 | self.data.truncate(len); |
Yiming Jing | cf21fc4 | 2021-07-16 13:23:26 -0700 | [diff] [blame] | 852 | } |
| 853 | if self.data.len() < self.data.capacity() / 4 { |
| 854 | self.data.shrink_to_fit(); |
| 855 | } |
| 856 | } |
| 857 | |
| 858 | /// Returns a normalized `BigUint`. |
| 859 | #[inline] |
| 860 | fn normalized(mut self) -> BigUint { |
| 861 | self.normalize(); |
| 862 | self |
| 863 | } |
| 864 | |
| 865 | /// Returns `self ^ exponent`. |
| 866 | pub fn pow(&self, exponent: u32) -> Self { |
| 867 | Pow::pow(self, exponent) |
| 868 | } |
| 869 | |
| 870 | /// Returns `(self ^ exponent) % modulus`. |
| 871 | /// |
| 872 | /// Panics if the modulus is zero. |
| 873 | pub fn modpow(&self, exponent: &Self, modulus: &Self) -> Self { |
| 874 | power::modpow(self, exponent, modulus) |
| 875 | } |
| 876 | |
| 877 | /// Returns the truncated principal square root of `self` -- |
| 878 | /// see [Roots::sqrt](https://docs.rs/num-integer/0.1/num_integer/trait.Roots.html#method.sqrt) |
| 879 | pub fn sqrt(&self) -> Self { |
| 880 | Roots::sqrt(self) |
| 881 | } |
| 882 | |
| 883 | /// Returns the truncated principal cube root of `self` -- |
| 884 | /// see [Roots::cbrt](https://docs.rs/num-integer/0.1/num_integer/trait.Roots.html#method.cbrt). |
| 885 | pub fn cbrt(&self) -> Self { |
| 886 | Roots::cbrt(self) |
| 887 | } |
| 888 | |
| 889 | /// Returns the truncated principal `n`th root of `self` -- |
| 890 | /// see [Roots::nth_root](https://docs.rs/num-integer/0.1/num_integer/trait.Roots.html#tymethod.nth_root). |
| 891 | pub fn nth_root(&self, n: u32) -> Self { |
| 892 | Roots::nth_root(self, n) |
| 893 | } |
| 894 | |
| 895 | /// Returns the number of least-significant bits that are zero, |
| 896 | /// or `None` if the entire number is zero. |
| 897 | pub fn trailing_zeros(&self) -> Option<u64> { |
| 898 | let i = self.data.iter().position(|&digit| digit != 0)?; |
| 899 | let zeros: u64 = self.data[i].trailing_zeros().into(); |
| 900 | Some(i as u64 * u64::from(big_digit::BITS) + zeros) |
| 901 | } |
| 902 | |
| 903 | /// Returns the number of least-significant bits that are ones. |
| 904 | pub fn trailing_ones(&self) -> u64 { |
| 905 | if let Some(i) = self.data.iter().position(|&digit| !digit != 0) { |
| 906 | // XXX u64::trailing_ones() introduced in Rust 1.46, |
| 907 | // but we need to be compatible further back. |
| 908 | // Thanks to cuviper for this workaround. |
| 909 | let ones: u64 = (!self.data[i]).trailing_zeros().into(); |
| 910 | i as u64 * u64::from(big_digit::BITS) + ones |
| 911 | } else { |
| 912 | self.data.len() as u64 * u64::from(big_digit::BITS) |
| 913 | } |
| 914 | } |
| 915 | |
| 916 | /// Returns the number of one bits. |
| 917 | pub fn count_ones(&self) -> u64 { |
| 918 | self.data.iter().map(|&d| u64::from(d.count_ones())).sum() |
| 919 | } |
| 920 | |
| 921 | /// Returns whether the bit in the given position is set |
| 922 | pub fn bit(&self, bit: u64) -> bool { |
| 923 | let bits_per_digit = u64::from(big_digit::BITS); |
| 924 | if let Some(digit_index) = (bit / bits_per_digit).to_usize() { |
| 925 | if let Some(digit) = self.data.get(digit_index) { |
| 926 | let bit_mask = (1 as BigDigit) << (bit % bits_per_digit); |
| 927 | return (digit & bit_mask) != 0; |
| 928 | } |
| 929 | } |
| 930 | false |
| 931 | } |
| 932 | |
| 933 | /// Sets or clears the bit in the given position |
| 934 | /// |
| 935 | /// Note that setting a bit greater than the current bit length, a reallocation may be needed |
| 936 | /// to store the new digits |
| 937 | pub fn set_bit(&mut self, bit: u64, value: bool) { |
| 938 | // Note: we're saturating `digit_index` and `new_len` -- any such case is guaranteed to |
| 939 | // fail allocation, and that's more consistent than adding our own overflow panics. |
| 940 | let bits_per_digit = u64::from(big_digit::BITS); |
| 941 | let digit_index = (bit / bits_per_digit) |
| 942 | .to_usize() |
| 943 | .unwrap_or(core::usize::MAX); |
| 944 | let bit_mask = (1 as BigDigit) << (bit % bits_per_digit); |
| 945 | if value { |
| 946 | if digit_index >= self.data.len() { |
| 947 | let new_len = digit_index.saturating_add(1); |
| 948 | self.data.resize(new_len, 0); |
| 949 | } |
| 950 | self.data[digit_index] |= bit_mask; |
| 951 | } else if digit_index < self.data.len() { |
| 952 | self.data[digit_index] &= !bit_mask; |
| 953 | // the top bit may have been cleared, so normalize |
| 954 | self.normalize(); |
| 955 | } |
| 956 | } |
| 957 | } |
| 958 | |
| 959 | pub(crate) trait IntDigits { |
| 960 | fn digits(&self) -> &[BigDigit]; |
| 961 | fn digits_mut(&mut self) -> &mut Vec<BigDigit>; |
| 962 | fn normalize(&mut self); |
| 963 | fn capacity(&self) -> usize; |
| 964 | fn len(&self) -> usize; |
| 965 | } |
| 966 | |
| 967 | impl IntDigits for BigUint { |
| 968 | #[inline] |
| 969 | fn digits(&self) -> &[BigDigit] { |
| 970 | &self.data |
| 971 | } |
| 972 | #[inline] |
| 973 | fn digits_mut(&mut self) -> &mut Vec<BigDigit> { |
| 974 | &mut self.data |
| 975 | } |
| 976 | #[inline] |
| 977 | fn normalize(&mut self) { |
| 978 | self.normalize(); |
| 979 | } |
| 980 | #[inline] |
| 981 | fn capacity(&self) -> usize { |
| 982 | self.data.capacity() |
| 983 | } |
| 984 | #[inline] |
| 985 | fn len(&self) -> usize { |
| 986 | self.data.len() |
| 987 | } |
| 988 | } |
| 989 | |
| 990 | /// Convert a u32 chunk (len is either 1 or 2) to a single u64 digit |
| 991 | #[inline] |
| 992 | fn u32_chunk_to_u64(chunk: &[u32]) -> u64 { |
| 993 | // raw could have odd length |
| 994 | let mut digit = chunk[0] as u64; |
| 995 | if let Some(&hi) = chunk.get(1) { |
| 996 | digit |= (hi as u64) << 32; |
| 997 | } |
| 998 | digit |
| 999 | } |
| 1000 | |
| 1001 | /// Combine four `u32`s into a single `u128`. |
| 1002 | #[cfg(any(test, not(u64_digit)))] |
| 1003 | #[inline] |
| 1004 | fn u32_to_u128(a: u32, b: u32, c: u32, d: u32) -> u128 { |
| 1005 | u128::from(d) | (u128::from(c) << 32) | (u128::from(b) << 64) | (u128::from(a) << 96) |
| 1006 | } |
| 1007 | |
| 1008 | /// Split a single `u128` into four `u32`. |
| 1009 | #[cfg(any(test, not(u64_digit)))] |
| 1010 | #[inline] |
| 1011 | fn u32_from_u128(n: u128) -> (u32, u32, u32, u32) { |
| 1012 | ( |
| 1013 | (n >> 96) as u32, |
| 1014 | (n >> 64) as u32, |
| 1015 | (n >> 32) as u32, |
| 1016 | n as u32, |
| 1017 | ) |
| 1018 | } |
| 1019 | |
| 1020 | #[cfg(not(u64_digit))] |
| 1021 | #[test] |
| 1022 | fn test_from_slice() { |
| 1023 | fn check(slice: &[u32], data: &[BigDigit]) { |
| 1024 | assert_eq!(BigUint::from_slice(slice).data, data); |
| 1025 | } |
| 1026 | check(&[1], &[1]); |
| 1027 | check(&[0, 0, 0], &[]); |
| 1028 | check(&[1, 2, 0, 0], &[1, 2]); |
| 1029 | check(&[0, 0, 1, 2], &[0, 0, 1, 2]); |
| 1030 | check(&[0, 0, 1, 2, 0, 0], &[0, 0, 1, 2]); |
| 1031 | check(&[-1i32 as u32], &[-1i32 as BigDigit]); |
| 1032 | } |
| 1033 | |
| 1034 | #[cfg(u64_digit)] |
| 1035 | #[test] |
| 1036 | fn test_from_slice() { |
| 1037 | fn check(slice: &[u32], data: &[BigDigit]) { |
| 1038 | assert_eq!( |
| 1039 | BigUint::from_slice(slice).data, |
| 1040 | data, |
| 1041 | "from {:?}, to {:?}", |
| 1042 | slice, |
| 1043 | data |
| 1044 | ); |
| 1045 | } |
| 1046 | check(&[1], &[1]); |
| 1047 | check(&[0, 0, 0], &[]); |
| 1048 | check(&[1, 2], &[8_589_934_593]); |
| 1049 | check(&[1, 2, 0, 0], &[8_589_934_593]); |
| 1050 | check(&[0, 0, 1, 2], &[0, 8_589_934_593]); |
| 1051 | check(&[0, 0, 1, 2, 0, 0], &[0, 8_589_934_593]); |
| 1052 | check(&[-1i32 as u32], &[(-1i32 as u32) as BigDigit]); |
| 1053 | } |
| 1054 | |
| 1055 | #[test] |
| 1056 | fn test_u32_u128() { |
| 1057 | assert_eq!(u32_from_u128(0u128), (0, 0, 0, 0)); |
| 1058 | assert_eq!( |
| 1059 | u32_from_u128(u128::max_value()), |
| 1060 | ( |
| 1061 | u32::max_value(), |
| 1062 | u32::max_value(), |
| 1063 | u32::max_value(), |
| 1064 | u32::max_value() |
| 1065 | ) |
| 1066 | ); |
| 1067 | |
| 1068 | assert_eq!( |
| 1069 | u32_from_u128(u32::max_value() as u128), |
| 1070 | (0, 0, 0, u32::max_value()) |
| 1071 | ); |
| 1072 | |
| 1073 | assert_eq!( |
| 1074 | u32_from_u128(u64::max_value() as u128), |
| 1075 | (0, 0, u32::max_value(), u32::max_value()) |
| 1076 | ); |
| 1077 | |
| 1078 | assert_eq!( |
| 1079 | u32_from_u128((u64::max_value() as u128) + u32::max_value() as u128), |
| 1080 | (0, 1, 0, u32::max_value() - 1) |
| 1081 | ); |
| 1082 | |
| 1083 | assert_eq!(u32_from_u128(36_893_488_151_714_070_528), (0, 2, 1, 0)); |
| 1084 | } |
| 1085 | |
| 1086 | #[test] |
| 1087 | fn test_u128_u32_roundtrip() { |
| 1088 | // roundtrips |
| 1089 | let values = vec![ |
| 1090 | 0u128, |
| 1091 | 1u128, |
| 1092 | u64::max_value() as u128 * 3, |
| 1093 | u32::max_value() as u128, |
| 1094 | u64::max_value() as u128, |
| 1095 | (u64::max_value() as u128) + u32::max_value() as u128, |
| 1096 | u128::max_value(), |
| 1097 | ]; |
| 1098 | |
| 1099 | for val in &values { |
| 1100 | let (a, b, c, d) = u32_from_u128(*val); |
| 1101 | assert_eq!(u32_to_u128(a, b, c, d), *val); |
| 1102 | } |
| 1103 | } |