pub fn check_primitive_root(
g: u64,
phi: u64,
br: &BarrettReduction<u128>,
pf: &[(u64, u32)],
) -> boolExamples found in repository?
crates/competitive/src/math/primitive_root.rs (line 11)
3pub fn primitive_root(p: u64) -> u64 {
4 if p == 2 {
5 return 1;
6 }
7 let phi = p - 1;
8 let pf = prime_factors(phi);
9 let br = BarrettReduction::<u128>::new(p as _);
10 for g in 2..=3.min(p - 1) {
11 if check_primitive_root(g, phi, &br, &pf) {
12 return g;
13 }
14 }
15 let mut rng = Xorshift::default();
16 loop {
17 let g = ((rng.rand64() as u128 * (p - 2) as u128) >> 64) as u64 + 2;
18 if check_primitive_root(g, phi, &br, &pf) {
19 return g;
20 }
21 }
22}More examples
crates/competitive/src/math/discrete_logarithm.rs (line 436)
381fn discrete_logarithm_prime_power(a: u64, b: u64, p: u64, e: u32) -> Option<(u64, u64)> {
382 assert_ne!(p, 0);
383 assert_ne!(e, 0);
384 let n = p.pow(e);
385 assert!(a < n);
386 assert!(b < n);
387 assert_eq!(gcd(a, p), 1);
388 if p == 1 {
389 return Some((0, 1));
390 }
391 if a == 0 {
392 return if b == 0 { Some((1, 1)) } else { None };
393 }
394 if b == 0 {
395 return None;
396 }
397 if e == 1 {
398 return IC.with(|ic| unsafe { &mut *ic.get() }.discrete_logarithm(a, b, p));
399 }
400 let br = BarrettReduction::<u128>::new(n as _);
401 if p == 2 {
402 if e >= 3 {
403 if a % 4 == 1 && b % 4 != 1 {
404 return None;
405 }
406 let aa = if a % 4 == 1 { a } else { n - a };
407 let bb = if b % 4 == 1 { b } else { n - b };
408 let g = 5;
409 let ord = n / 4;
410 let x = pohlig_hellman_prime_power_order(g, aa, n, p, e - 2)?;
411 let y = pohlig_hellman_prime_power_order(g, bb, n, p, e - 2)?;
412 let t = solve_linear_congruence(x, y, ord)?;
413 match (a % 4 == 1, b % 4 == 1) {
414 (true, true) => Some(t),
415 (false, true) if t.0 % 2 == 0 => Some((t.0, lcm(t.1, 2))),
416 (false, false) if t.0 % 2 == 1 => Some((t.0, lcm(t.1, 2))),
417 (false, false) if a == b => Some((1, lcm(t.1, 2))),
418 _ => None,
419 }
420 } else if a == 1 {
421 if b == 1 { Some((0, 1)) } else { None }
422 } else {
423 assert_eq!(a, 3);
424 if b == 1 {
425 Some((0, 2))
426 } else if b == 3 {
427 Some((1, 2))
428 } else {
429 None
430 }
431 }
432 } else {
433 let ord = n - n / p;
434 let pf_ord = prime_factors(ord);
435 let g = (2..)
436 .find(|&g| check_primitive_root(g, ord, &br, &pf_ord))
437 .unwrap();
438 let mut pf_p = prime_factors(p - 1);
439 pf_p.push((p, e - 1));
440 let mut abm = vec![];
441 for (q, c) in pf_p {
442 let m = q.pow(c);
443 let d = ord / m;
444 let gg = pow(g, d, &br);
445 let aa = pow(a, d, &br);
446 let bb = pow(b, d, &br);
447 let x = pohlig_hellman_prime_power_order(gg, aa, n, q, c)?;
448 let y = pohlig_hellman_prime_power_order(gg, bb, n, q, c)?;
449 abm.push((x, y, m));
450 }
451 solve_linear_congruences(abm)
452 }
453}