/** @file time_gammaseries.cpp * * Some timings on series expansion of the Gamma function around a pole. */ /* * GiNaC Copyright (C) 1999-2004 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 * the Free Software Foundation; either version 2 of the License, or * (at your option) any later version. * * This program is distributed in the hope that it will be useful, * but WITHOUT ANY WARRANTY; without even the implied warranty of * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the * GNU General Public License for more details. * * 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 */ #include "times.h" 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 = 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() { unsigned result = 0; cout << "timing Laurent series expansion of Gamma function" << flush; clog << "-------Laurent series expansion of Gamma function:" << endl; vector sizes; vector times; timer omega; sizes.push_back(10); sizes.push_back(15); sizes.push_back(20); sizes.push_back(25); for (vector::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::iterator i=sizes.begin(); i!=sizes.end(); ++i) cout << '\t' << (*i); cout << endl << " time/s:"; for (vector::iterator i=times.begin(); i!=times.end(); ++i) cout << '\t' << int(1000*(*i))*0.001; cout << endl; return result; }