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Release calc version 2.11.0t10.5.1

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Landon Curt Noll
1999-12-14 12:23:24 -08:00
parent 94e35d9b07
commit 0514dc0de9
519 changed files with 4194 additions and 17762 deletions
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cal/bernoulli.cal
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/*
* bernoulli - clculate the Nth Bernoulli number B(n)
*
* Copyright (C) 1999 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.
* 59 Temple Place, Suite 330, Boston, MA 02111-1307, USA.
*
* @(#) $Revision: 29.1 $
* @(#) $Id: bernoulli.cal,v 29.1 1999/12/14 09:15:30 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://reality.sgi.com/chongo/tech/comp/calc/
*/
/*
* Calculate the Nth Bernoulli number B(n).
* This uses 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];
}