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a31078bbec
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!
113 lines
3.3 KiB
Plaintext
113 lines
3.3 KiB
Plaintext
/*
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* zeta2 - Hurwitz Zeta function
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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: 2013/08/11 01:31:28
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* File existed as early as: 2013
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*/
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/*
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* hide internal function from resource debugging
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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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define hurwitzzeta(s,a){
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local realpart_a imagpart_s tmp tmp1 tmp2 tmp3;
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local sum1 sum2 sum3 i k n precision result limit;
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local limit_function offset offset_squared rest_sum eps;
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/*
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According to Linas Vepstas' "An efficient algorithm for accelerating
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the convergence of oscillatory series, useful for computing the
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polylogarithm and Hurwitz zeta functions" the Euler-Maclaurin series
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is the fastest in most cases.
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With a lot of help of the PARI/GP implementation by Prof. Henri Cohen,
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hence the different license.
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*/
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eps=epsilon( epsilon() * 1e-3);
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realpart_a=re(a);
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if(realpart_a>1.5){
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tmp=floor(realpart_a-0.5);
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sum1 = 0;
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for( i = 1 ; i <= tmp ; i++){
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sum1 += ( a - i )^( -s );
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}
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epsilon(eps);
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return (hurwitzzeta(s,a-tmp)-sum1);
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}
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if(realpart_a<=0){
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tmp=ceil(-realpart_a+0.5);
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for( i = 0 ; i <= tmp-1 ; i++){
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sum2 += ( a + i )^( -s );
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}
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epsilon(eps);
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return (hurwitzzeta(s,a+tmp)+sum2);
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}
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precision=digits(1/epsilon());
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realpart_a=re(s);
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imagpart_s=im(s);
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epsilon(1e-9);
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result=s-1.;
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if(abs(result)<0.1){
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result=-1;
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}
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else
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result=ln(result);
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limit=(precision*ln(10)-re((s-.5)*result)+(1.*realpart_a)*ln(2.*pi()))/2;
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limit=max(2,ceil(max(limit,abs(s*1.)/2)));
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limit_function=ceil(sqrt((limit+realpart_a/2-.25)^2+(imagpart_s*1.)^2/4)/
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pi());
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if (config("user_debug") > 0) {
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print "limit_function = " limit_function;
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print "limit = " limit;
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print "prec = " precision;
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}
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/* Full precison plus 5 digits angstzuschlag*/
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epsilon( (10^(-precision)) * 1e-5);
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tmp3=(a+limit_function+0.)^(-s);
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sum3 = tmp3/2;
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for(n=0;n<=limit_function-1;n++){
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sum3 += (a+n)^(-s);
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}
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result=sum3;
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offset=a+limit_function;
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offset_squared=1./(offset*offset);
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tmp1=2*s-1;
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tmp2=s*(s-1);
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rest_sum=bernoulli(2*limit);
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for(k=2*limit-2;k>=2;k-=2){
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rest_sum=bernoulli(k)+offset_squared*
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(k*k+tmp1*k+tmp2)*rest_sum/((k+1)*(k+2));
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}
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rest_sum=offset*(1+offset_squared*tmp2*rest_sum/2);
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result+=rest_sum*tmp3/(s-1);
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epsilon(eps);
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return result;
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}
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/*
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* restore internal function from resource debugging
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* report important interface functions
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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 "hurwitzzeta(s,a)";
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}
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