/usr/share/calc/bernoulli.cal is in apcalc-common 2.12.4.4-2.
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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 | /*
* bernoulli - clculate the Nth Bernoulli number B(n)
*
* Copyright (C) 2000 David I. Bell and 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: bernoulli.cal,v 30.1 2007/03/16 11:09:54 chongo Exp $
* @(#) $Source: /usr/local/src/cmd/calc/cal/RCS/bernoulli.cal,v $
*
* Under source code control: 1991/09/30 11:18:41
* File existed as early as: 1991
*
* Share and enjoy! :-) http://www.isthe.com/chongo/tech/comp/calc/
*/
/*
* Calculate the Nth Bernoulli number B(n).
*
* NOTE: This is now a bulitin function.
*
* The non-buildin code used the following symbolic formula to calculate B(n):
*
* (b+1)^(n+1) - b^(n+1) = 0
*
* where b is a dummy value, and each power b^i gets replaced by B(i).
* For example, for n = 3:
*
* (b+1)^4 - b^4 = 0
* b^4 + 4*b^3 + 6*b^2 + 4*b + 1 - b^4 = 0
* 4*b^3 + 6*b^2 + 4*b + 1 = 0
* 4*B(3) + 6*B(2) + 4*B(1) + 1 = 0
* B(3) = -(6*B(2) + 4*B(1) + 1) / 4
*
* The combinatorial factors in the expansion of the above formula are
* calculated interatively, and we use the fact that B(2i+1) = 0 if i > 0.
* Since all previous B(n)'s are needed to calculate a particular B(n), all
* values obtained are saved in an array for ease in repeated calculations.
*/
/*
static Bnmax;
static mat Bn[1001];
*/
define B(n)
{
/*
local nn, np1, i, sum, mulval, divval, combval;
if (!isint(n) || (n < 0))
quit "Non-negative integer required for Bernoulli";
if (n == 0)
return 1;
if (n == 1)
return -1/2;
if (isodd(n))
return 0;
if (n > 1000)
quit "Very large Bernoulli";
if (n <= Bnmax)
return Bn[n];
for (nn = Bnmax + 2; nn <= n; nn+=2) {
np1 = nn + 1;
mulval = np1;
divval = 1;
combval = 1;
sum = 1 - np1 / 2;
for (i = 2; i < np1; i+=2) {
combval = combval * mulval-- / divval++;
combval = combval * mulval-- / divval++;
sum += combval * Bn[i];
}
Bn[nn] = -sum / np1;
}
Bnmax = n;
return Bn[n];
*/
return bernoulli(n);
}
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