/usr/share/calc/randmprime.cal is in apcalc-common 2.12.4.4-2.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 | /*
* 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.
*
* @(#) $Revision: 30.1 $
* @(#) $Id: randmprime.cal,v 30.1 2007/03/16 11:09:54 chongo Exp $
* @(#) $Source: /usr/local/src/cmd/calc/cal/RCS/randmprime.cal,v $
*
* 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;
}
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