* 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) 1999-2003 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
#include "times.h"
-unsigned Gammaseries(unsigned order)
+unsigned tgammaseries(unsigned order)
{
- 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;
+ 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 = 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;
+ ++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);
-
- 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;
+ 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 += 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 << 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;
}