/** @file exam_inifcns_nstdsums.cpp * * This test routine applies assorted tests on initially known higher level * functions. */ /* * GiNaC Copyright (C) 1999-2003 Johannes Gutenberg University Mainz, Germany * * This program is free software; you can redistribute it and/or modify * it under the terms of the GNU General Public License as published by * the Free Software Foundation; either version 2 of the License, or * (at your option) any later version. * * This program 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 General Public License for more details. * * You should have received a copy of the GNU General Public License * along with this program; if not, write to the Free Software * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA */ #include "exams.h" #include //////////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////////// // S exam //////////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////////// /* * The data in the following include file has been produced by the following * Mathematica (V4.1) script: * * * x={2/10,1,14/10,30/10} * y={0,3/10,-14/10} * st = OpenAppend["exam_inifcns_nstdsums_data.raw"] * \$NumberMarks = False * Do[ * Do[ * Do[Write[st, i]; Write[st,j]; Write[st,x[[k]]+I*y[[l]]]; * Write[st,Chop[N[PolyLog[i,j,x[[k]]+I*y[[l]]],25]]],{i,3},{j,3}], {k,4}],{l,3}] * Do[ * Do[ * Do[Write[st, i]; Write[st,j]; Write[st,-x[[k]]+I*y[[l]]]; * Write[st,Chop[N[PolyLog[i,j,-x[[k]]+I*y[[l]]],25]]],{i,3},{j,3}], {k,4}], {l,3}] * Close[st] * * * and postprocessed by the following shell script * * * #/bin/sh * IFS=\$'\n' * cat exam_inifcns_nstdsums_data.raw | sed -e 's/\*\^/E/g' > exam_inifcns_nstdsums_data.raw2 * echo 'const char *data[] = {' > exam_inifcns_nstdsums_data.raw3 * for i in `cat exam_inifcns_nstdsums_data.raw2`; do echo \"\$i\",; done >> exam_inifcns_nstdsums_data.raw3 * echo '"-999"};' >> exam_inifcns_nstdsums.h * * */ #include "exam_inifcns_nstdsums.h" // signals end of data const int ENDMARK = -999; static unsigned inifcns_test_S() { int digitsbuf = Digits; // precision of data Digits = 22; ex prec = 5 * pow(10, -(int)Digits); unsigned result = 0; int i = 0; while (true) { ex n(data[i++],symbol()); if (n == ENDMARK) { break; } ex p(data[i++],symbol()); ex x(data[i++],symbol()); ex res(data[i++],symbol()); ex res2 = S(n, p, x).evalf(); if (abs(res-res2) > prec) { clog << "S(" << n << "," << p << "," << x << ") seems to be wrong:" << endl; clog << "GiNaC : " << res2 << endl; clog << "Reference : " << res << endl; clog << "Abs. Difference : " << res2-res << endl; if (res2 != 0) { ex reldiff = abs((res2-res)/res2); clog << "Rel. Difference : " << reldiff << endl; } result++; } if (i % 80) { cout << "." << flush; } } Digits = digitsbuf; return result; } //////////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////////// // H/Li exam //////////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////////// static unsigned inifcns_test_HLi() { int digitsbuf = Digits; Digits = 17; ex prec = 5 * pow(10, -(int)Digits); numeric almostone("0.999999999999999999"); unsigned result = 0; lst res; res.append(H(lst(2,1),numeric(1)/2).hold() - (zeta(3)/8 - pow(log(2),3)/6)); res.append(H(lst(2,1,3),numeric(1)/3).hold() - Li(lst(2,1,3),lst(numeric(1)/3,1,1)).hold()); res.append(H(lst(2,1,3),numeric(98)/100).hold() - Li(lst(2,1,3),lst(numeric(98)/100,1,1)).hold()); res.append(H(lst(2,1,3),numeric(245)/100).hold() - Li(lst(2,1,3),lst(numeric(245)/100,1,1)).hold()); res.append(H(lst(4,1,1,1),numeric(1)/3).hold() - S(3,4,numeric(1)/3).hold()); res.append(H(lst(4,1,1,1),numeric(98)/100).hold() - S(3,4,numeric(98)/100).hold()); res.append(H(lst(4,1,1,1),numeric(245)/100).hold() - S(3,4,numeric(245)/100).hold()); res.append(H(lst(2,2,3),almostone).hold() - zeta(lst(2,2,3))); res.append(H(lst(-3,-1,2,1),almostone).hold() - zeta(lst(3,1,2,1),lst(-1,1,-1,1))); res.append(H(lst(-2,1,3),numeric(1)/3).hold() - -Li(lst(2,1,3),lst(-numeric(1)/3,-1,1)).hold()); res.append(H(lst(-2,1,3),numeric(98)/100).hold() - -Li(lst(2,1,3),lst(-numeric(98)/100,-1,1)).hold()); res.append(H(lst(-2,1,3),numeric(245)/100).hold() - -Li(lst(2,1,3),lst(-numeric(245)/100,-1,1)).hold()); res.append(H(lst(-3,1,-2,0,0),numeric(3)/10).hold() - convert_H_to_Li(lst(-3,1,-2,0,0),numeric(3)/10).eval()); for (lst::const_iterator it = res.begin(); it != res.end(); it++) { ex diff = abs((*it).evalf()); if (diff > prec) { clog << *it << " seems to be wrong: " << diff << endl; result++; } cout << "." << flush; } Digits = digitsbuf; return result; } //////////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////////// // zeta exam //////////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////////// static unsigned inifcns_test_zeta() { int digitsbuf = Digits; unsigned result = 0; lst res; res.append(zeta(lst(2,1)) - zeta(3)); res.append(zeta(lst(2,1,1,1,1)) - zeta(6)); res.append(zeta(lst(6,3)) - (zeta(9)*83/2 - zeta(2)*zeta(7)*21 - zeta(2)*zeta(2)*zeta(5)*12/5)); res.append(zeta(lst(4,2,3)) - (-zeta(9)*59 + zeta(2)*zeta(7)*28 + pow(zeta(2),2)*zeta(5)*4 - pow(zeta(3),3)/3 + pow(zeta(2),3)*zeta(3)*8/21)); res.append(zeta(lst(3,1,3,1,3,1,3,1)) - (2*pow(Pi,16)/factorial(18))); res.append(zeta(lst(2),lst(-1)) - -zeta(2)/2); res.append(zeta(lst(1,2),lst(-1,1)) - (-zeta(3)/4 - zeta(lst(1),lst(-1))*zeta(2)/2)); res.append(zeta(lst(2,1,1),lst(-1,-1,1)) - (-pow(zeta(2),2)*23/40 - pow(zeta(lst(1),lst(-1)),2)*zeta(2)*3/4 - zeta(lst(3,1),lst(-1,1))*3/2 - zeta(lst(1),lst(-1))*zeta(3)*21/8)); for (lst::const_iterator it = res.begin(); it != res.end(); it++) { Digits = 17; ex prec = 5 * pow(10, -(int)Digits); ex diff = abs((*it).evalf()); if (diff > prec) { clog << *it << " seems to be wrong: " << diff << endl; clog << "Digits: " << Digits << endl; result++; } cout << "." << flush; Digits = 40; prec = 5 * pow(10, -(int)Digits); diff = abs((*it).evalf()); if (diff > prec) { clog << *it << " seems to be wrong: " << diff << endl; clog << "Digits: " << Digits << endl; result++; } cout << "." << flush; } Digits = digitsbuf; return result; } unsigned exam_inifcns_nstdsums(void) { unsigned result = 0; cout << "examining consistency of nestedsums functions" << flush; clog << "----------consistency of nestedsums functions:" << endl; result += inifcns_test_zeta(); result += inifcns_test_S(); result += inifcns_test_HLi(); if (!result) { cout << " passed " << endl; clog << "(no output)" << endl; } else { cout << " failed " << endl; } return result; }