1 /** @file exam_inifcns_nstdsums.cpp
3 * This test routine applies assorted tests on initially known higher level
7 * GiNaC Copyright (C) 1999-2020 Johannes Gutenberg University Mainz, Germany
9 * This program is free software; you can redistribute it and/or modify
10 * it under the terms of the GNU General Public License as published by
11 * the Free Software Foundation; either version 2 of the License, or
12 * (at your option) any later version.
14 * This program is distributed in the hope that it will be useful,
15 * but WITHOUT ANY WARRANTY; without even the implied warranty of
16 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
17 * GNU General Public License for more details.
19 * You should have received a copy of the GNU General Public License
20 * along with this program; if not, write to the Free Software
21 * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
25 using namespace GiNaC;
32 ////////////////////////////////////////////////////////////////////////////////
33 ////////////////////////////////////////////////////////////////////////////////
35 ////////////////////////////////////////////////////////////////////////////////
36 ////////////////////////////////////////////////////////////////////////////////
40 * The data in the following include file has been produced by the following
41 * Mathematica (V4.1) script:
44 * x={2/10,1,14/10,30/10}
46 * st = OpenAppend["exam_inifcns_nstdsums_data.raw"]
47 * $NumberMarks = False
50 * Do[Write[st, i]; Write[st,j]; Write[st,x[[k]]+I*y[[l]]];
51 * Write[st,Chop[N[PolyLog[i,j,x[[k]]+I*y[[l]]],25]]],{i,3},{j,3}], {k,4}],{l,3}]
54 * Do[Write[st, i]; Write[st,j]; Write[st,-x[[k]]+I*y[[l]]];
55 * Write[st,Chop[N[PolyLog[i,j,-x[[k]]+I*y[[l]]],25]]],{i,3},{j,3}], {k,4}], {l,3}]
59 * and postprocessed by the following shell script
64 * cat exam_inifcns_nstdsums_data.raw | sed -e 's/\*\^/E/g' > exam_inifcns_nstdsums_data.raw2
65 * echo 'constexpr string polylogdata[] = {' > exam_inifcns_nstdsums.h
66 * for i in `cat exam_inifcns_nstdsums_data.raw2`; do echo \"$i\",; done >> exam_inifcns_nstdsums.h
67 * echo '"-999"};' >> exam_inifcns_nstdsums.h
71 #include "exam_inifcns_nstdsums.h"
74 // signals end of data
75 const int ENDMARK = -999;
78 static unsigned inifcns_test_S()
80 int digitsbuf = Digits;
83 ex prec = 5 * pow(10, -(ex)Digits);
89 ex n(polylogdata[i++],symbol());
93 ex p(polylogdata[i++],symbol());
94 ex x(polylogdata[i++],symbol());
95 ex res(polylogdata[i++],symbol());
96 ex res2 = S(n, p, x).evalf();
97 if (abs(res-res2) > prec) {
98 clog << "S(" << n << "," << p << "," << x << ") seems to be wrong:" << endl;
99 clog << "GiNaC : " << res2 << endl;
100 clog << "Reference : " << res << endl;
101 clog << "Abs. Difference : " << res2-res << endl;
103 ex reldiff = abs((res2-res)/res2);
104 clog << "Rel. Difference : " << reldiff << endl;
109 cout << "." << flush;
119 ////////////////////////////////////////////////////////////////////////////////
120 ////////////////////////////////////////////////////////////////////////////////
122 ////////////////////////////////////////////////////////////////////////////////
123 ////////////////////////////////////////////////////////////////////////////////
126 static unsigned inifcns_test_HLi()
129 int digitsbuf = Digits;
131 ex prec = 5 * pow(10, -(ex)Digits);
132 numeric almostone("0.999999999999999999");
137 res.append(H(lst{2,1},numeric(1)/2).hold() - (zeta(3)/8 - pow(log(2),3)/6));
138 res.append(H(lst{2,1,3},numeric(1)/3).hold() - Li(lst{2,1,3},lst{numeric(1)/3,1,1}).hold());
139 res.append(H(lst{2,1,3},numeric(98)/100).hold() - Li(lst{2,1,3},lst{numeric(98)/100,1,1}).hold());
140 res.append(H(lst{2,1,3},numeric(245)/100).hold() - Li(lst{2,1,3},lst{numeric(245)/100,1,1}).hold());
141 res.append(H(lst{4,1,1,1},numeric(1)/3).hold() - S(3,4,numeric(1)/3).hold());
142 res.append(H(lst{4,1,1,1},numeric(98)/100).hold() - S(3,4,numeric(98)/100).hold());
143 res.append(H(lst{4,1,1,1},numeric(245)/100).hold() - S(3,4,numeric(245)/100).hold());
144 res.append(H(lst{2,2,3},almostone).hold() - zeta(lst{2,2,3}));
145 res.append(H(lst{-3,-1,2,1},almostone).hold() - zeta(lst{3,1,2,1},lst{-1,1,-1,1}));
146 res.append(H(lst{-2,1,3},numeric(1)/3).hold() - -Li(lst{2,1,3},lst{-numeric(1)/3,-1,1}).hold());
147 res.append(H(lst{-2,1,3},numeric(98)/100).hold() - -Li(lst{2,1,3},lst{-numeric(98)/100,-1,1}).hold());
148 res.append(H(lst{-2,1,3},numeric(245)/100).hold() - -Li(lst{2,1,3},lst{-numeric(245)/100,-1,1}).hold());
149 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));
151 for (lst::const_iterator it = res.begin(); it != res.end(); it++) {
152 ex diff = abs((*it).evalf());
154 clog << *it << " seems to be wrong: " << diff << endl;
157 cout << "." << flush;
163 numeric cdif = ex_to<numeric>(H(lst{2,2,1},5.0-5.0*I) - H(lst{2,2,1},5.0+5.0*I));
164 numeric cadd = ex_to<numeric>(H(lst{2,2,1},5.0-5.0*I) + H(lst{2,2,1},5.0+5.0*I));
165 if ((cdif.real() > prec) || (cadd.imag() > prec)) {
166 clog << "complex conjugation test of H({2,2,1},5.0-5.0*I) seems to be wrong: " << cdif << " " << cadd << endl;
174 ////////////////////////////////////////////////////////////////////////////////
175 ////////////////////////////////////////////////////////////////////////////////
177 ////////////////////////////////////////////////////////////////////////////////
178 ////////////////////////////////////////////////////////////////////////////////
181 static unsigned inifcns_test_zeta()
183 int digitsbuf = Digits;
189 res.append(zeta(lst{2,1}) - zeta(3));
190 res.append(zeta(lst{2,1,1,1,1}) - zeta(6));
191 res.append(zeta(lst{6,3}) - (zeta(9)*83/2 - zeta(2)*zeta(7)*21 - zeta(2)*zeta(2)*zeta(5)*12/5));
192 res.append(zeta(lst{4,2,3}) - (-zeta(9)*59 + zeta(2)*zeta(7)*28 + pow(zeta(2),2)*zeta(5)*4 -
193 pow(zeta(3),3)/3 + pow(zeta(2),3)*zeta(3)*8/21));
194 res.append(zeta(lst{3,1,3,1,3,1,3,1}) - (2*pow(Pi,16)/factorial(18)));
195 res.append(zeta(lst{2},lst{-1}) - -zeta(2)/2);
196 res.append(zeta(lst{1,2},lst{-1,1}) - (-zeta(3)/4 - zeta(lst{1},lst{-1})*zeta(2)/2));
197 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
198 - zeta(lst{3,1},lst{-1,1})*3/2 - zeta(lst{1},lst{-1})*zeta(3)*21/8));
200 for (lst::const_iterator it = res.begin(); it != res.end(); it++) {
202 ex prec = 5 * pow(10, -(ex)Digits);
203 ex diff = abs((*it).evalf());
205 clog << *it << " seems to be wrong: " << diff << endl;
206 clog << "Digits: " << Digits << endl;
209 cout << "." << flush;
211 prec = 5 * pow(10, -(ex)Digits);
212 diff = abs((*it).evalf());
214 clog << *it << " seems to be wrong: " << diff << endl;
215 clog << "Digits: " << Digits << endl;
218 cout << "." << flush;
227 ////////////////////////////////////////////////////////////////////////////////
228 ////////////////////////////////////////////////////////////////////////////////
230 ////////////////////////////////////////////////////////////////////////////////
231 ////////////////////////////////////////////////////////////////////////////////
234 static unsigned inifcns_test_LiG()
236 int digitsbuf = Digits;
238 ex prec = 5 * pow(10, -(ex)Digits);
239 numeric almostone("0.99999999999999999999");
244 res.append(Li(lst{4}, lst{6}).hold() - Li(4, 6.0));
245 res.append(G(lst{0,0,5.0,0,2.0,0,0,0,3.0},0.5).hold()
246 + Li(lst{3,2,4}, lst{numeric(1,10), numeric(5,2), numeric(2,3)}));
247 res.append(Li(lst{2,1,1}, lst{almostone, almostone, almostone}) - zeta(lst{2,1,1}));
249 // check Li_{1,1} against known expression
250 symbol x("x"), y("y");
252 ex s1 = Li(lst{1,1},lst{x,y});
253 ex s2 = log(1-1/x/y-eps)*log((1-1/x-eps)/(1/x/y-1/x)) + Li(2,(1-1/x/y-eps)/(1/x-1/x/y))
254 - log(-1/x/y-eps)*log((-1/x-eps)/(1/x/y-1/x)) - Li(2,(-1/x/y-eps)/(1/x-1/x/y))
255 - log(-1/x/y-eps)*log(1-1/x-eps) + log(-1/x/y-eps)*log(-1/x-eps);
256 res.append(s1.subs(lst{x==numeric(1)/2, y==3}) - s2.subs(lst{x==numeric(1)/2, y==3}));
257 res.append(s1.subs(lst{x==numeric(3)/2, y==numeric(1)/2}) - s2.subs(lst{x==numeric(3)/2, y==numeric(1)/2}));
258 res.append(s1.subs(lst{x==2, y==numeric(4)/5}) - s2.subs(lst{x==2, y==numeric(4)/5}));
260 // shuffle and quasi-shuffle identities
261 res.append(G(lst{0,0.2},1).hold() * G(lst{0.5},1).hold() - G(lst{0.5,0,0.2},1).hold()
262 - G(lst{0,0.5,0.2},1).hold() - G(lst{0,0.2,0.5},1).hold());
263 res.append(G(lst{0,0.5},1).hold() * G(lst{0.6},1).hold() - G(lst{0,0.5,0.5*0.6},1).hold()
264 - G(lst{0.6,0,0.5*0.6},1).hold() + G(lst{0,0,0.5*0.6},1).hold());
265 res.append(Li(lst{2},lst{numeric(1,5)}).hold() * Li(lst{3},lst{7}).hold() - Li(lst{2,3},lst{numeric(1,5),7}).hold()
266 - Li(lst{3,2},lst{7,numeric(1,5)}).hold() - Li(lst{5},lst{numeric(7,5)}).hold());
267 symbol a1, a2, a3, a4;
268 res.append((G(lst{a1,a2},1) * G(lst{a3,a4},1) - G(lst{a1,a2,a3,a4},1)
269 - G(lst{a1,a3,a2,a4},1) - G(lst{a3,a1,a2,a4},1)
270 - G(lst{a1,a3,a4,a2},1) - G(lst{a3,a1,a4,a2},1) - G(lst{a3,a4,a1,a2},1))
271 .subs(lst{a1==numeric(1)/10, a2==numeric(3)/10, a3==numeric(7)/10, a4==5}));
272 res.append(G(lst{-0.009},1).hold() * G(lst{-8,1.4999},1).hold() - G(lst{-0.009,-8,1.4999},1).hold()
273 - G(lst{-8,-0.009,1.4999},1).hold() - G(lst{-8,1.4999,-0.009},1).hold());
274 res.append(G(lst{sqrt(numeric(1)/2)+I*sqrt(numeric(1)/2)},1).hold() * G(lst{1.51,-0.999},1).hold()
275 - G(lst{sqrt(numeric(1)/2)+I*sqrt(numeric(1)/2),1.51,-0.999},1).hold()
276 - G(lst{1.51,sqrt(numeric(1)/2)+I*sqrt(numeric(1)/2),-0.999},1).hold()
277 - G(lst{1.51,-0.999,sqrt(numeric(1)/2)+I*sqrt(numeric(1)/2)},1).hold());
278 // checks for hoelder convolution which is used if one argument has a distance to one smaller than 0.01
279 res.append(G(lst{0, 1.2, 1, 1.01}, 1).hold() - G(lst{0, 1.2, 1, numeric("1.009999999999999999")}, 1).hold());
281 for (lst::const_iterator it = res.begin(); it != res.end(); it++) {
282 ex diff = abs((*it).evalf());
284 clog << *it << " seems to be wrong: " << diff << endl;
287 cout << "." << flush;
296 ////////////////////////////////////////////////////////////////////////////////
297 ////////////////////////////////////////////////////////////////////////////////
298 // legacy exam - checking for historical bugs
299 ////////////////////////////////////////////////////////////////////////////////
300 ////////////////////////////////////////////////////////////////////////////////
303 static unsigned inifcns_test_legacy()
305 int digitsbuf = Digits;
307 ex prec = 5 * pow(10, -(ex)Digits);
311 ex r1 = zeta(lst{1,1,1,1,1,1}, lst{-1,-1,-1,1,1,1});
312 if ((r1.evalf() - numeric("-0.0012588769028204890704")) > prec) {
313 clog << "zeta({1,1,1,1,1,1},{-1,-1,-1,1,1,1}) seems to be wrong." << endl;
317 ex x1 = exp(2*Pi*I/13).evalf();
318 ex x2 = exp(24*Pi*I/13).evalf();
319 ex r2 = Li(lst{2},lst{x1}).hold().evalf();
320 ex r3 = Li(lst{2},lst{x2}).hold().evalf();
321 if ( abs(r2-conjugate(r3)) > prec ) {
322 clog << "Legacy test 2 seems to be wrong." << endl;
326 ex x3 = exp(5*Pi*I/3).evalf();
327 ex r4 = Li(lst{3},lst{x3}).hold().evalf();
328 if ( abs(r4 - numeric("0.40068563438653142847-0.95698384815740185713*I")) > prec ) {
329 clog << "Legacy test 3 seems to be wrong." << endl;
334 prec = 5 * pow(10, -(ex)Digits);
336 x1 = exp(Pi*I/3).evalf();
337 x2 = exp(2*Pi*I/3).evalf();
339 ex x4 = exp(4*Pi*I/3).evalf();
340 ex x5 = exp(5*Pi*I/3).evalf();
342 ex r5 = Li(lst{1,1,1,1},lst{x2,x4,x3,x0}).hold().evalf();
343 ex r6 = Li(lst{1,1,1,1},lst{x4,x2,x3,x0}).hold().evalf();
344 if ( abs(r5-conjugate(r6)) > prec ) {
345 clog << "Legacy test 4 seems to be wrong." << endl;
349 ex r7 = Li(lst{1,2,1},lst{x3,x2,x4}).hold().evalf()
350 +Li(lst{1,1,2},lst{x3,x2,x4}).hold().evalf()
351 +Li(lst{1,1,1,1},lst{x3,x0,x2,x4}).hold().evalf()
352 +Li(lst{1,1,1,1},lst{x3,x2,x0,x4}).hold().evalf()
353 +Li(lst{1,1,1,1},lst{x3,x2,x4,x0}).hold().evalf()
354 +Li(lst{1,2,1},lst{x2,x1,x0}).hold().evalf()
355 +Li(lst{1,1,2},lst{x2,x3,x4}).hold().evalf()
356 +Li(lst{1,1,1,1},lst{x2,x4,x3,x0}).hold().evalf()
357 +Li(lst{1,1,1,1},lst{x2,x3,x4,x0}).hold().evalf()
358 +Li(lst{1,1,1,1},lst{x2,x3,x0,x4}).hold().evalf()
359 +Li(lst{2,2},lst{x5,x4}).hold().evalf()
360 +Li(lst{2,1,1},lst{x5,x0,x4}).hold().evalf()
361 +Li(lst{2,1,1},lst{x5,x4,x0}).hold().evalf()
362 -Li(lst{1,1},lst{x3,x0}).hold().evalf()*Li(lst{1,1},lst{x2,x4}).hold().evalf();
363 if ( abs(r7) > prec ) {
364 clog << "Legacy test 5 seems to be wrong." << endl;
373 static unsigned check_G_y_one_bug()
376 exprs.push_back(G(lst{-1,-1, 1,-1, 0}, 1));
377 exprs.push_back(G(lst{-1, 0, 1,-1, 0}, 1));
378 exprs.push_back(G(lst{-1, 1,-1,-1, 0}, 1));
379 exprs.push_back(G(lst{-1, 1,-1, 0, 0}, 1));
380 exprs.push_back(G(lst{-1, 1,-1, 1, 0}, 1));
381 exprs.push_back(G(lst{-1, 1, 0,-1, 0}, 1));
382 exprs.push_back(G(lst{-1, 1, 1,-1, 0}, 1));
383 exprs.push_back(G(lst{ 0,-1, 1,-1, 0}, 1));
384 exprs.push_back(G(lst{ 0, 1, 1,-1, 0}, 1));
386 for (exvector::const_iterator ep = exprs.begin(); ep != exprs.end(); ++ep) {
388 ex val = ep->evalf();
389 if (!is_a<numeric>(val)) {
390 clog << "evalf(" << *ep << ") is not a number: " << val << endl;
393 } catch (std::exception& oops) {
394 clog << "evalf(" << *ep << "): got an exception" << oops.what() << endl;
401 unsigned exam_inifcns_nstdsums(void)
405 cout << "examining consistency of nestedsums functions" << flush;
407 result += inifcns_test_zeta();
408 result += inifcns_test_S();
409 result += inifcns_test_HLi();
410 result += inifcns_test_LiG();
411 result += inifcns_test_legacy();
412 result += check_G_y_one_bug();
417 int main(int argc, char** argv)
419 return exam_inifcns_nstdsums();