* Some timings on series expansion of the Gamma function around a pole. */
/*
- * GiNaC Copyright (C) 1999-2000 Johannes Gutenberg University Mainz, Germany
+ * GiNaC Copyright (C) 1999-2008 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 "times.h"
+#include <iostream>
+#include <vector>
+#include "ginac.h"
+#include "timer.h"
+using namespace std;
+using namespace GiNaC;
unsigned tgammaseries(unsigned order)
{
unsigned result = 0;
symbol x;
-
+
ex myseries = series(tgamma(x),x==0,order);
// compute the last coefficient numerically:
ex last_coeff = myseries.coeff(x,order-1).evalf();
// compute a bound for that coefficient using a variation of the leading
// term in Stirling's formula:
- ex bound = evalf(exp(ex(-.57721566490153286*(order-1)))/(order-1));
- if (evalf(abs((last_coeff-pow(-1,order))/bound)) > numeric(1)) {
+ ex bound = exp(-.57721566490153286*(order-1))/(order-1);
+ if (abs((last_coeff-pow(-1,order))/bound) > 1) {
clog << "The " << order-1
- << "th order coefficient in the power series expansion of tgamma(0) was erroneously found to be "
- << last_coeff << ", violating a simple estimate." << endl;
+ << "th order coefficient in the power series expansion of tgamma(0) was erroneously found to be "
+ << last_coeff << ", violating a simple estimate." << endl;
++result;
}
-
+
return result;
}
-unsigned time_gammaseries(void)
+unsigned time_gammaseries()
{
unsigned result = 0;
-
+
cout << "timing Laurent series expansion of Gamma function" << flush;
- clog << "-------Laurent series expansion of Gamma function:" << endl;
-
+
vector<unsigned> sizes;
vector<double> times;
timer omega;
-
- sizes.push_back(10);
- sizes.push_back(15);
+
sizes.push_back(20);
sizes.push_back(25);
-
+ sizes.push_back(30);
+ sizes.push_back(35);
+
for (vector<unsigned>::iterator i=sizes.begin(); i!=sizes.end(); ++i) {
omega.start();
result += tgammaseries(*i);
times.push_back(omega.read());
cout << '.' << flush;
}
-
- if (!result) {
- cout << " passed ";
- clog << "(no output)" << endl;
- } else {
- cout << " failed ";
- }
+
// print the report:
cout << endl << " order: ";
for (vector<unsigned>::iterator i=sizes.begin(); i!=sizes.end(); ++i)
- cout << '\t' << (*i);
+ cout << '\t' << *i;
cout << endl << " time/s:";
for (vector<double>::iterator i=times.begin(); i!=times.end(); ++i)
- cout << '\t' << int(1000*(*i))*0.001;
+ cout << '\t' << *i;
cout << endl;
return result;
}
+
+extern void randomify_symbol_serials();
+
+int main(int argc, char** argv)
+{
+ randomify_symbol_serials();
+ cout << setprecision(2) << showpoint;
+ return time_gammaseries();
+}