/usr/share/calc/pi.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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 | /*
* pi - various routines to calculate pi
*
* Copyright (C) 1999-2004 David I. Bell
*
* 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: pi.cal,v 30.1 2007/03/16 11:09:54 chongo Exp $
* @(#) $Source: /usr/local/src/cmd/calc/cal/RCS/pi.cal,v $
*
* Under source code control: 1991/05/22 21:56:37
* File existed as early as: 1991
*
* Share and enjoy! :-) http://www.isthe.com/chongo/tech/comp/calc/
*/
/*
* Calculate pi within the specified epsilon using the quartic convergence
* iteration.
*/
define qpi(epsilon)
{
local niter, yn, ym, tm, an, am, t, tn, sqrt2, epsilon2, count, digits;
local bits, bits2;
if (isnull(epsilon))
epsilon = epsilon();
digits = digits(1/epsilon);
if (digits <= 8) { niter = 1; epsilon = 1e-8; }
else if (digits <= 40) { niter = 2; epsilon = 1e-40; }
else if (digits <= 170) { niter = 3; epsilon = 1e-170; }
else if (digits <= 693) { niter = 4; epsilon = 1e-693; }
else {
niter = 4;
t = 693;
while (t < digits) {
++niter;
t *= 4;
}
}
epsilon2 = epsilon/(digits/10 + 1);
digits = digits(1/epsilon2);
sqrt2 = sqrt(2, epsilon2);
bits = abs(ilog2(epsilon)) + 1;
bits2 = abs(ilog2(epsilon2)) + 1;
yn = sqrt2 - 1;
an = 6 - 4 * sqrt2;
tn = 2;
for (count = 0; count < niter; ++count) {
ym = yn;
am = an;
tn *= 4;
t = sqrt(sqrt(1-ym^4, epsilon2), epsilon2);
yn = (1-t)/(1+t);
an = (1+yn)^4*am-tn*yn*(1+yn+yn^2);
yn = bround(yn, bits2);
an = bround(an, bits2);
}
return (bround(1/an, bits));
}
/*
* Print digits of PI forever, neatly formatted, using calc.
*
* Written by Klaus Alexander Seistrup <klaus@seistrup.dk>
* on a dull Friday evening in November 1999.
*
* Inspired by an algorithm conceived by Lambert Meertens.
*
* See also the ABC Programmer's Handbook, by Geurts, Meertens & Pemberton,
* published by Prentice-Hall (UK) Ltd., 1990.
*
*/
define piforever()
{
local k = 2;
local a = 4;
local b = 1;
local a1 = 12;
local b1 = 4;
local a2, b2, p, q, d, d1;
local stdout = files(1);
local first = 1, row = -1, col = 0;
while (1) {
/*
* Next approximation
*/
p = k * k;
q = k + ++k;
a2 = a;
b2 = b;
a = a1;
a1 = p * a2 + q * a1;
b = b1;
b1 = p * b2 + q * b1;
/*
* Print common digits
*/
d = a // b;
d1 = a1 // b1;
while (d == d1) {
if (first) {
printf("%d.", d);
first = 0;
} else {
if (!(col % 50)) {
printf("\n");
col = 0;
if (!(++row % 20)) {
printf("\n");
row = 0;
}
}
printf("%d", d);
if (!(++col % 10))
printf(" ");
}
a = 10 * (a % b);
a1 = 10 * (a1 % b1);
d = a // b;
d1 = a1 // b1;
}
fflush(stdout);
}
}
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