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Some folks might think: “you still use RCS”?!? And we will say, hey, at least we switched from SCCS to RCS back in … I think it was around 1994 ... at least we are keeping up! :-) :-) :-) Logs say that SCCS version 18 became RCS version 19 on 1994 March 18. RCS served us well. But now it is time to move on. And so we are switching to git. Calc releases produce a lot of file changes. In the 125 releases of calc since 1996, when I started managing calc releases, there have been 15473 file mods!
94 lines
2.4 KiB
Plaintext
94 lines
2.4 KiB
Plaintext
/*
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* bernoulli - clculate the Nth Bernoulli number B(n)
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*
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* Copyright (C) 2000 David I. Bell and Landon Curt Noll
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*
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* Calc is open software; you can redistribute it and/or modify it under
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* the terms of the version 2.1 of the GNU Lesser General Public License
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* as published by the Free Software Foundation.
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*
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* Calc is distributed in the hope that it will be useful, but WITHOUT
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* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
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* or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General
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* Public License for more details.
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*
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* A copy of version 2.1 of the GNU Lesser General Public License is
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* distributed with calc under the filename COPYING-LGPL. You should have
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* received a copy with calc; if not, write to Free Software Foundation, Inc.
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* 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
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*
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* Under source code control: 1991/09/30 11:18:41
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* File existed as early as: 1991
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*
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* Share and enjoy! :-) http://www.isthe.com/chongo/tech/comp/calc/
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*/
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/*
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* Calculate the Nth Bernoulli number B(n).
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*
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* NOTE: This is now a bulitin function.
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*
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* The non-buildin code used the following symbolic formula to calculate B(n):
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*
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* (b+1)^(n+1) - b^(n+1) = 0
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*
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* where b is a dummy value, and each power b^i gets replaced by B(i).
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* For example, for n = 3:
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*
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* (b+1)^4 - b^4 = 0
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* b^4 + 4*b^3 + 6*b^2 + 4*b + 1 - b^4 = 0
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* 4*b^3 + 6*b^2 + 4*b + 1 = 0
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* 4*B(3) + 6*B(2) + 4*B(1) + 1 = 0
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* B(3) = -(6*B(2) + 4*B(1) + 1) / 4
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*
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* The combinatorial factors in the expansion of the above formula are
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* calculated interatively, and we use the fact that B(2i+1) = 0 if i > 0.
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* Since all previous B(n)'s are needed to calculate a particular B(n), all
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* values obtained are saved in an array for ease in repeated calculations.
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*/
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/*
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static Bnmax;
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static mat Bn[1001];
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*/
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define B(n)
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{
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/*
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local nn, np1, i, sum, mulval, divval, combval;
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if (!isint(n) || (n < 0))
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quit "Non-negative integer required for Bernoulli";
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if (n == 0)
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return 1;
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if (n == 1)
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return -1/2;
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if (isodd(n))
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return 0;
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if (n > 1000)
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quit "Very large Bernoulli";
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if (n <= Bnmax)
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return Bn[n];
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for (nn = Bnmax + 2; nn <= n; nn+=2) {
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np1 = nn + 1;
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mulval = np1;
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divval = 1;
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combval = 1;
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sum = 1 - np1 / 2;
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for (i = 2; i < np1; i+=2) {
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combval = combval * mulval-- / divval++;
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combval = combval * mulval-- / divval++;
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sum += combval * Bn[i];
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}
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Bn[nn] = -sum / np1;
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}
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Bnmax = n;
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return Bn[n];
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*/
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return bernoulli(n);
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}
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