* functions. */
/*
- * GiNaC Copyright (C) 1999-2003 Johannes Gutenberg University Mainz, Germany
+ * GiNaC Copyright (C) 1999-2019 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
*
* 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
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
*/
-#include "exams.h"
+#include "ginac.h"
+using namespace GiNaC;
+#include <iostream>
#include <fstream>
+using namespace std;
////////////////////////////////////////////////////////////////////////////////
* 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 'constexpr string polylogdata[] = {' > exam_inifcns_nstdsums.h
+ * for i in `cat exam_inifcns_nstdsums_data.raw2`; do echo \"$i\",; done >> exam_inifcns_nstdsums.h
* echo '"-999"};' >> exam_inifcns_nstdsums.h
*
*
int digitsbuf = Digits;
// precision of data
Digits = 22;
- ex prec = 5 * pow(10, -(int)Digits);
+ ex prec = 5 * pow(10, -(ex)Digits);
unsigned result = 0;
int i = 0;
while (true) {
- ex n(data[i++],symbol());
+ ex n(polylogdata[i++],symbol());
if (n == ENDMARK) {
break;
}
- ex p(data[i++],symbol());
- ex x(data[i++],symbol());
- ex res(data[i++],symbol());
+ ex p(polylogdata[i++],symbol());
+ ex x(polylogdata[i++],symbol());
+ ex res(polylogdata[i++],symbol());
ex res2 = S(n, p, x).evalf();
if (abs(res-res2) > prec) {
clog << "S(" << n << "," << p << "," << x << ") seems to be wrong:" << endl;
static unsigned inifcns_test_HLi()
{
+ using GiNaC::log;
int digitsbuf = Digits;
Digits = 17;
- ex prec = 5 * pow(10, -(int)Digits);
+ ex prec = 5 * pow(10, -(ex)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());
+ 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));
for (lst::const_iterator it = res.begin(); it != res.end(); it++) {
ex diff = abs((*it).evalf());
Digits = digitsbuf;
+ // conjugate test
+ 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));
+ 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));
+ if ((cdif.real() > prec) || (cadd.imag() > prec)) {
+ clog << "complex conjugation test of H({2,2,1},5.0-5.0*I) seems to be wrong: " << cdif << " " << cadd << endl;
+ result++;
+ }
+
return result;
}
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 -
+ 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));
+ 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 prec = 5 * pow(10, -(ex)Digits);
ex diff = abs((*it).evalf());
if (diff > prec) {
clog << *it << " seems to be wrong: " << diff << endl;
}
cout << "." << flush;
Digits = 40;
- prec = 5 * pow(10, -(int)Digits);
+ prec = 5 * pow(10, -(ex)Digits);
diff = abs((*it).evalf());
if (diff > prec) {
clog << *it << " seems to be wrong: " << diff << endl;
}
+////////////////////////////////////////////////////////////////////////////////
+////////////////////////////////////////////////////////////////////////////////
+// H/Li exam
+////////////////////////////////////////////////////////////////////////////////
+////////////////////////////////////////////////////////////////////////////////
+
+
+static unsigned inifcns_test_LiG()
+{
+ int digitsbuf = Digits;
+ Digits = 17;
+ ex prec = 5 * pow(10, -(ex)Digits);
+ numeric almostone("0.99999999999999999999");
+ unsigned result = 0;
+
+ lst res;
+
+ res.append(Li(lst{4}, lst{6}).hold() - Li(4, 6.0));
+ res.append(G(lst{0,0,5.0,0,2.0,0,0,0,3.0},0.5).hold()
+ + Li(lst{3,2,4}, lst{numeric(1,10), numeric(5,2), numeric(2,3)}));
+ res.append(Li(lst{2,1,1}, lst{almostone, almostone, almostone}) - zeta(lst{2,1,1}));
+
+ // check Li_{1,1} against known expression
+ symbol x("x"), y("y");
+ ex eps = 1e-30*I;
+ ex s1 = Li(lst{1,1},lst{x,y});
+ 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))
+ - 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))
+ - log(-1/x/y-eps)*log(1-1/x-eps) + log(-1/x/y-eps)*log(-1/x-eps);
+ res.append(s1.subs(lst{x==numeric(1)/2, y==3}) - s2.subs(lst{x==numeric(1)/2, y==3}));
+ res.append(s1.subs(lst{x==numeric(3)/2, y==numeric(1)/2}) - s2.subs(lst{x==numeric(3)/2, y==numeric(1)/2}));
+ res.append(s1.subs(lst{x==2, y==numeric(4)/5}) - s2.subs(lst{x==2, y==numeric(4)/5}));
+
+ // shuffle and quasi-shuffle identities
+ res.append(G(lst{0,0.2},1).hold() * G(lst{0.5},1).hold() - G(lst{0.5,0,0.2},1).hold()
+ - G(lst{0,0.5,0.2},1).hold() - G(lst{0,0.2,0.5},1).hold());
+ 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()
+ - G(lst{0.6,0,0.5*0.6},1).hold() + G(lst{0,0,0.5*0.6},1).hold());
+ 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()
+ - Li(lst{3,2},lst{7,numeric(1,5)}).hold() - Li(lst{5},lst{numeric(7,5)}).hold());
+ symbol a1, a2, a3, a4;
+ res.append((G(lst{a1,a2},1) * G(lst{a3,a4},1) - G(lst{a1,a2,a3,a4},1)
+ - G(lst{a1,a3,a2,a4},1) - G(lst{a3,a1,a2,a4},1)
+ - G(lst{a1,a3,a4,a2},1) - G(lst{a3,a1,a4,a2},1) - G(lst{a3,a4,a1,a2},1))
+ .subs(lst{a1==numeric(1)/10, a2==numeric(3)/10, a3==numeric(7)/10, a4==5}));
+ res.append(G(lst{-0.009},1).hold() * G(lst{-8,1.4999},1).hold() - G(lst{-0.009,-8,1.4999},1).hold()
+ - G(lst{-8,-0.009,1.4999},1).hold() - G(lst{-8,1.4999,-0.009},1).hold());
+ res.append(G(lst{sqrt(numeric(1)/2)+I*sqrt(numeric(1)/2)},1).hold() * G(lst{1.51,-0.999},1).hold()
+ - G(lst{sqrt(numeric(1)/2)+I*sqrt(numeric(1)/2),1.51,-0.999},1).hold()
+ - G(lst{1.51,sqrt(numeric(1)/2)+I*sqrt(numeric(1)/2),-0.999},1).hold()
+ - G(lst{1.51,-0.999,sqrt(numeric(1)/2)+I*sqrt(numeric(1)/2)},1).hold());
+ // checks for hoelder convolution which is used if one argument has a distance to one smaller than 0.01
+ res.append(G(lst{0, 1.2, 1, 1.01}, 1).hold() - G(lst{0, 1.2, 1, numeric("1.009999999999999999")}, 1).hold());
+
+ 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;
+}
+
+
+////////////////////////////////////////////////////////////////////////////////
+////////////////////////////////////////////////////////////////////////////////
+// legacy exam - checking for historical bugs
+////////////////////////////////////////////////////////////////////////////////
+////////////////////////////////////////////////////////////////////////////////
+
+
+static unsigned inifcns_test_legacy()
+{
+ int digitsbuf = Digits;
+ Digits = 17;
+ ex prec = 5 * pow(10, -(ex)Digits);
+
+ unsigned result = 0;
+
+ ex r1 = zeta(lst{1,1,1,1,1,1}, lst{-1,-1,-1,1,1,1});
+ if ((r1.evalf() - numeric("-0.0012588769028204890704")) > prec) {
+ clog << "zeta({1,1,1,1,1,1},{-1,-1,-1,1,1,1}) seems to be wrong." << endl;
+ result++;
+ }
+
+ ex x1 = exp(2*Pi*I/13).evalf();
+ ex x2 = exp(24*Pi*I/13).evalf();
+ ex r2 = Li(lst{2},lst{x1}).hold().evalf();
+ ex r3 = Li(lst{2},lst{x2}).hold().evalf();
+ if ( abs(r2-conjugate(r3)) > prec ) {
+ clog << "Legacy test 2 seems to be wrong." << endl;
+ result++;
+ }
+
+ ex x3 = exp(5*Pi*I/3).evalf();
+ ex r4 = Li(lst{3},lst{x3}).hold().evalf();
+ if ( abs(r4 - numeric("0.40068563438653142847-0.95698384815740185713*I")) > prec ) {
+ clog << "Legacy test 3 seems to be wrong." << endl;
+ result++;
+ }
+
+ Digits = 100;
+ prec = 5 * pow(10, -(ex)Digits);
+ ex x0 = 1.;
+ x1 = exp(Pi*I/3).evalf();
+ x2 = exp(2*Pi*I/3).evalf();
+ x3 = -1.;
+ ex x4 = exp(4*Pi*I/3).evalf();
+ ex x5 = exp(5*Pi*I/3).evalf();
+
+ ex r5 = Li(lst{1,1,1,1},lst{x2,x4,x3,x0}).hold().evalf();
+ ex r6 = Li(lst{1,1,1,1},lst{x4,x2,x3,x0}).hold().evalf();
+ if ( abs(r5-conjugate(r6)) > prec ) {
+ clog << "Legacy test 4 seems to be wrong." << endl;
+ result++;
+ }
+
+ ex r7 = Li(lst{1,2,1},lst{x3,x2,x4}).hold().evalf()
+ +Li(lst{1,1,2},lst{x3,x2,x4}).hold().evalf()
+ +Li(lst{1,1,1,1},lst{x3,x0,x2,x4}).hold().evalf()
+ +Li(lst{1,1,1,1},lst{x3,x2,x0,x4}).hold().evalf()
+ +Li(lst{1,1,1,1},lst{x3,x2,x4,x0}).hold().evalf()
+ +Li(lst{1,2,1},lst{x2,x1,x0}).hold().evalf()
+ +Li(lst{1,1,2},lst{x2,x3,x4}).hold().evalf()
+ +Li(lst{1,1,1,1},lst{x2,x4,x3,x0}).hold().evalf()
+ +Li(lst{1,1,1,1},lst{x2,x3,x4,x0}).hold().evalf()
+ +Li(lst{1,1,1,1},lst{x2,x3,x0,x4}).hold().evalf()
+ +Li(lst{2,2},lst{x5,x4}).hold().evalf()
+ +Li(lst{2,1,1},lst{x5,x0,x4}).hold().evalf()
+ +Li(lst{2,1,1},lst{x5,x4,x0}).hold().evalf()
+ -Li(lst{1,1},lst{x3,x0}).hold().evalf()*Li(lst{1,1},lst{x2,x4}).hold().evalf();
+ if ( abs(r7) > prec ) {
+ clog << "Legacy test 5 seems to be wrong." << endl;
+ result++;
+ }
+
+ Digits = digitsbuf;
+
+ return result;
+}
+
+static unsigned check_G_y_one_bug()
+{
+ exvector exprs;
+ exprs.push_back(G(lst{-1,-1, 1,-1, 0}, 1));
+ exprs.push_back(G(lst{-1, 0, 1,-1, 0}, 1));
+ exprs.push_back(G(lst{-1, 1,-1,-1, 0}, 1));
+ exprs.push_back(G(lst{-1, 1,-1, 0, 0}, 1));
+ exprs.push_back(G(lst{-1, 1,-1, 1, 0}, 1));
+ exprs.push_back(G(lst{-1, 1, 0,-1, 0}, 1));
+ exprs.push_back(G(lst{-1, 1, 1,-1, 0}, 1));
+ exprs.push_back(G(lst{ 0,-1, 1,-1, 0}, 1));
+ exprs.push_back(G(lst{ 0, 1, 1,-1, 0}, 1));
+ unsigned err = 0;
+ for (exvector::const_iterator ep = exprs.begin(); ep != exprs.end(); ++ep) {
+ try {
+ ex val = ep->evalf();
+ if (!is_a<numeric>(val)) {
+ clog << "evalf(" << *ep << ") is not a number: " << val << endl;
+ ++err;
+ }
+ } catch (std::exception& oops) {
+ clog << "evalf(" << *ep << "): got an exception" << oops.what() << endl;
+ ++err;
+ }
+ }
+ return err;
+}
+
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;
- }
+ result += inifcns_test_LiG();
+ result += inifcns_test_legacy();
+ result += check_G_y_one_bug();
return result;
}
+
+int main(int argc, char** argv)
+{
+ return exam_inifcns_nstdsums();
+}
git://www.ginac.de / ginac.git / blobdiff