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105 lines
2.7 KiB
Plaintext
105 lines
2.7 KiB
Plaintext
/*
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* constants - implementation of different constants to arbitrary precision
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*
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* Copyright (C) 2013 Christoph Zurnieden
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*
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* constants 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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* constants 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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* @(#) $Revision: 30.3 $
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* @(#) $Id: constants.cal,v 30.3 2013/08/11 08:41:38 chongo Exp $
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* @(#) $Source: /usr/local/src/bin/calc/cal/RCS/constants.cal,v $
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*
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* Under source code control: 2013/08/11 01:31:28
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* File existed as early as: 2013
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*/
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static resource_debug_level;
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resource_debug_level = config("resource_debug", 0);
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static __CZ__euler_mascheroni = 0;
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static __CZ__euler_mascheroni_prec = 0;
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define e(){
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local k temp1 temp2 ret eps factor upperlimit prec;
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prec = digits(1/epsilon());
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if(__CZ__euler_mascheroni != 0 && __CZ__euler_mascheroni_prec >= prec)
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return __CZ__euler_mascheroni;
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if(prec<=20) return 2.718281828459045235360287471;
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if(prec<=1800){
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__CZ__euler_mascheroni = exp(1);
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__CZ__euler_mascheroni_prec = prec;
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}
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eps=epsilon(1e-20);
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factor = 1;
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k = 0;
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upperlimit = prec * ln(10);
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while(k<upperlimit){
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k += ln(factor);
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factor++;
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}
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epsilon(eps);
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temp1 = 0;
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ret = 1;
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for(k=3;k<=factor;k++){
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temp2 = temp1;
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temp1 = ret;
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ret = (k-1) *(temp1 + temp2);
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}
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ret = inverse( ret * inverse(factorial(factor) ) ) ;
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__CZ__euler_mascheroni = ret;
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__CZ__euler_mascheroni_prec = prec;
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return ret;
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}
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/* Lupas' series */
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static __CZ__catalan = 0;
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static __CZ__catalan_prec = 0;
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define G(){
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local eps a s t n;
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eps = epsilon(epsilon()*1e-10);
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if(__CZ__catalan != 0 && __CZ__catalan >= log(1/eps))
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return __CZ__catalan;
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a = 1;
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s = 0;
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t = 1;
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n = 1;
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while(abs(t)> eps){
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a *= 32 * n^3 * (2*n-1);
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a /=((3-16*n+16*n^2)^2);
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t = a * (-1)^(n-1) * (40*n^2-24*n+3) / (n^3 * (2*n-1));
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s += t;
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n += 1;
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}
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s = s/64;
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__CZ__catalan = s;
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__CZ__catalan_prec = log(1/eps);
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epsilon(eps);
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return s;
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}
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config("resource_debug", resource_debug_level),;
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if (config("resource_debug") & 3) {
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print "e()";
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print "G()";
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}
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