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a31078bbec
Some folks might think: “you still use RCS”?!? And we will say, hey, at least we switched from SCCS to RCS back in … I think it was around 1994 ... at least we are keeping up! :-) :-) :-) Logs say that SCCS version 18 became RCS version 19 on 1994 March 18. RCS served us well. But now it is time to move on. And so we are switching to git. Calc releases produce a lot of file changes. In the 125 releases of calc since 1996, when I started managing calc releases, there have been 15473 file mods!
71 lines
1.7 KiB
Plaintext
71 lines
1.7 KiB
Plaintext
/*
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* psqrt - calculate square roots modulo a prime
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*
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* Copyright (C) 1999 David I. Bell
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*
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* Calc is open software; you can redistribute it and/or modify it under
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* the terms of the version 2.1 of the GNU Lesser General Public License
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* as published by the Free Software Foundation.
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*
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* Calc is distributed in the hope that it will be useful, but WITHOUT
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* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
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* or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General
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* Public License for more details.
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*
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* A copy of version 2.1 of the GNU Lesser General Public License is
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* distributed with calc under the filename COPYING-LGPL. You should have
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* received a copy with calc; if not, write to Free Software Foundation, Inc.
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* 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
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*
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* Under source code control: 1990/02/15 01:50:35
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* File existed as early as: before 1990
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*
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* Share and enjoy! :-) http://www.isthe.com/chongo/tech/comp/calc/
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*/
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/*
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* Returns null if number is not prime or if there is no square root.
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* The smaller square root is always returned.
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*/
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define psqrt(u, p)
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{
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local p1, q, n, y, r, v, w, t, k;
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p1 = p - 1;
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r = lowbit(p1);
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q = p >> r;
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t = 1 << (r - 1);
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for (n = 2; ; n++) {
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if (ptest(n, 1) == 0)
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continue;
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y = pmod(n, q, p);
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k = pmod(y, t, p);
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if (k == 1)
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continue;
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if (k != p1)
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return;
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break;
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}
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t = pmod(u, (q - 1) / 2, p);
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v = (t * u) % p;
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w = (t^2 * u) % p;
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while (w != 1) {
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k = 0;
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t = w;
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do {
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k++;
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t = t^2 % p;
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} while (t != 1);
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if (k == r)
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return;
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t = pmod(y, 1 << (r - k - 1), p);
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y = t^2 % p;
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v = (v * t) % p;
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w = (w * y) % p;
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r = k;
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}
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return min(v, p - v);
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}
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