mirror of
https://github.com/lcn2/calc.git
synced 2025-08-16 01:03:29 +03:00
51 lines
923 B
Plaintext
51 lines
923 B
Plaintext
/*
|
|
* Copyright (c) 1995 David I. Bell
|
|
* Permission is granted to use, distribute, or modify this source,
|
|
* provided that this copyright notice remains intact.
|
|
*
|
|
* Calculate square roots modulo a prime.
|
|
*
|
|
* Returns null if number is not prime or if there is no square root.
|
|
* The smaller square root is always returned.
|
|
*/
|
|
|
|
define psqrt(u, p)
|
|
{
|
|
local p1, q, n, y, r, v, w, t, k;
|
|
|
|
p1 = p - 1;
|
|
r = lowbit(p1);
|
|
q = p >> r;
|
|
t = 1 << (r - 1);
|
|
for (n = 2; ; n++) {
|
|
if (ptest(n, 1) == 0)
|
|
continue;
|
|
y = pmod(n, q, p);
|
|
k = pmod(y, t, p);
|
|
if (k == 1)
|
|
continue;
|
|
if (k != p1)
|
|
return;
|
|
break;
|
|
}
|
|
t = pmod(u, (q - 1) / 2, p);
|
|
v = (t * u) % p;
|
|
w = (t^2 * u) % p;
|
|
while (w != 1) {
|
|
k = 0;
|
|
t = w;
|
|
do {
|
|
k++;
|
|
t = t^2 % p;
|
|
} while (t != 1);
|
|
if (k == r)
|
|
return;
|
|
t = pmod(y, 1 << (r - k - 1), p);
|
|
y = t^2 % p;
|
|
v = (v * t) % p;
|
|
w = (w * y) % p;
|
|
r = k;
|
|
}
|
|
return min(v, p - v);
|
|
}
|