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| Current File : //proc/self/root/usr/share/calc/randmprime.cal |
/*
* randmprime - generate a random prime of the form h*2^n-1
*
* Copyright (C) 1999 Landon Curt Noll
*
* Calc is open software; you can redistribute it and/or modify it under
* the terms of the version 2.1 of the GNU Lesser General Public License
* as published by the Free Software Foundation.
*
* Calc is distributed in the hope that it will be useful, but WITHOUT
* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
* or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General
* Public License for more details.
*
* A copy of version 2.1 of the GNU Lesser General Public License is
* distributed with calc under the filename COPYING-LGPL. You should have
* received a copy with calc; if not, write to Free Software Foundation, Inc.
* 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
*
* Under source code control: 1994/03/14 23:11:21
* File existed as early as: 1994
*
* chongo <was here> /\oo/\ http://www.isthe.com/chongo/
* Share and enjoy! :-) http://www.isthe.com/chongo/tech/comp/calc/
*/
/* obtain our required libs */
read -once "lucas.cal"
/*
* randmprime - find a random prime of the form h*2^n-1 of a given size
*
* given:
* bits minimum bits in prime to return
* seed random seed for srandom()
* [dbg] if given, enable debugging
*
* returns:
* a prime of the form h*2^n-1
*/
define
randmprime(bits, seed, dbg)
{
local n; /* n as in h*2^n-1 */
local h; /* h as in h*2^n-1 */
local plush; /* value added to h since the beginning */
local init; /* initial cpu time */
local start; /* cpu time before last test */
local stop; /* cpu time afte last test */
local tmp; /* just a tmp place holder value */
local ret; /* h*2^n-1 that is prime */
/* firewall */
if (param(0) < 2 || param(0) > 3) {
quit "bad usage: rndprime(dig, seed [,dbg])";
}
if (!isint(bits) || bits < 0 || !isint(seed) || seed < 0) {
quit "args must be non-negative integers";
}
if (bits < 1) {
bits = 1;
}
if (param(0) == 2 || dbg < 0) {
dbg = 0;
}
/* seed generator */
tmp = srandom(seed, 13);
/* determine initial h and n values */
n = random(bits>>1, highbit(bits)+bits>>1+1);
h = randombit(n);
h += iseven(h);
while (highbit(h) >= n) {
++n;
}
if (dbg >= 1) {
print "DEBUG3: initial h =", h;
print "DEBUG3: initial n =", n;
}
/*
* loop until we find a prime
*/
if (dbg >= 1) {
start = usertime();
init = usertime();
plush = 0;
print "DEBUG1: testing (h+" : plush : ")*2^" : n : "-1";
}
while (lucas(h,n) == 0) {
/* bump h, and n if needed */
if (dbg >= 2) {
stop = usertime();
print "DEBUG2: last test:", stop-start, " total time:", stop-init;
}
if (dbg >= 1) {
print "DEBUG1: composite: (h+" : plush : ")*2^" : n : "-1";
plush += 2;
}
h += 2;
while (highbit(h) >= n) {
++n;
}
if (dbg >= 1) {
print "DEBUG1: testing (h+" : plush : ")*2^" : n : "-1";
start = stop;
}
}
/* found a prime */
if (dbg >= 2) {
stop = usertime();
print "DEBUG2: last test:", stop-start, " total time:", stop-init;
print "DEBUG3: " : h : "*2^" : n : "-1 is prime";
}
if (dbg >= 1) {
print "DEBUG1: prime: (h+" : plush : ")*2^" : n : "-1";
}
ret = h*2^n-1;
if (dbg >= 3) {
print "DEBUG3: highbit(h):", highbit(h);
print "DEBUG3: digits(h):", digits(h);
print "DEBUG3: highbit(n):", highbit(n);
print "DEBUG3: digits(2^n):", int(n*ln(10)/ln(2)+1);
print "DEBUG3: highbit(h*2^n-1):", highbit(ret);
print "DEBUG3: digits(h*2^n)-1:", digits(ret);
}
return ret;
}