/** @file time_gammaseries.cpp
*
- * Some timings on series expansion of the gamma function around a pole. */
+ * 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) 1999-2015 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 "ginac.h"
+#include "timer.h"
+using namespace GiNaC;
-unsigned gammaseries(unsigned order)
+#include <iostream>
+#include <vector>
+using namespace std;
+
+unsigned tgammaseries(unsigned order)
+{
+ unsigned result = 0;
+ symbol x;
+
+ ex myseries = series(GiNaC::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 = exp(-.57721566490153286*(order-1))/(order-1);
+ if (abs((last_coeff-pow(-1,ex(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;
+ ++result;
+ }
+
+ return result;
+}
+
+unsigned time_gammaseries()
{
- unsigned result = 0;
- symbol x;
-
- ex myseries = series(gamma(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)) {
- clog << "The " << order-1
- << "th order coefficient in the power series expansion of gamma(0) was erroneously found to be "
- << last_coeff << ", violating a simple estimate." << endl;
- ++result;
- }
-
- return result;
+ unsigned result = 0;
+
+ cout << "timing Laurent series expansion of Gamma function" << flush;
+
+ vector<unsigned> sizes;
+ vector<double> times;
+ timer omega;
+
+ 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;
+ }
+
+ // print the report:
+ cout << endl << " order: ";
+ for (vector<unsigned>::iterator i=sizes.begin(); i!=sizes.end(); ++i)
+ cout << '\t' << *i;
+ cout << endl << " time/s:";
+ for (vector<double>::iterator i=times.begin(); i!=times.end(); ++i)
+ cout << '\t' << *i;
+ cout << endl;
+
+ return result;
}
-unsigned time_gammaseries(void)
+extern void randomify_symbol_serials();
+
+int main(int argc, char** argv)
{
- 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);
-
- for (vector<unsigned>::iterator i=sizes.begin(); i!=sizes.end(); ++i) {
- omega.start();
- result += gammaseries(*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 << endl << " time/s:";
- for (vector<double>::iterator i=times.begin(); i!=times.end(); ++i)
- cout << '\t' << int(1000*(*i))*0.001;
- cout << endl;
-
- return result;
+ randomify_symbol_serials();
+ cout << setprecision(2) << showpoint;
+ return time_gammaseries();
}