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jeremybenn |
// 2007-02-04 Edward Smith-Rowland <3dw4rd@verizon.net>
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//
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// Copyright (C) 2007, 2009 Free Software Foundation, Inc.
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//
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// This file is part of the GNU ISO C++ Library. This library is free
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// software; you can redistribute it and/or modify it under the
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// terms of the GNU General Public License as published by the
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// Free Software Foundation; either version 3, or (at your option)
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// any later version.
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//
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// This library is distributed in the hope that it will be useful,
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// but WITHOUT ANY WARRANTY; without even the implied warranty of
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// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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// GNU General Public License for more details.
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//
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// You should have received a copy of the GNU General Public License along
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// with this library; see the file COPYING3. If not see
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// <http://www.gnu.org/licenses/>.
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// legendre
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// Compare against values generated by the GNU Scientific Library.
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// The GSL can be found on the web: http://www.gnu.org/software/gsl/
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#include <tr1/cmath>
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#if defined(__TEST_DEBUG)
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#include <iostream>
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#define VERIFY(A) \
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if (!(A)) \
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{ \
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std::cout << "line " << __LINE__ \
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<< " max_abs_frac = " << max_abs_frac \
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<< std::endl; \
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}
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#else
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#include <testsuite_hooks.h>
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#endif
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#include "../testcase.h"
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// Test data for l=0.
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testcase_legendre<double> data001[] = {
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{ 1.0000000000000000, 0, -1.0000000000000000 },
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{ 1.0000000000000000, 0, -0.90000000000000002 },
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{ 1.0000000000000000, 0, -0.80000000000000004 },
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{ 1.0000000000000000, 0, -0.69999999999999996 },
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{ 1.0000000000000000, 0, -0.59999999999999998 },
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{ 1.0000000000000000, 0, -0.50000000000000000 },
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{ 1.0000000000000000, 0, -0.40000000000000002 },
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{ 1.0000000000000000, 0, -0.30000000000000004 },
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{ 1.0000000000000000, 0, -0.19999999999999996 },
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{ 1.0000000000000000, 0, -0.099999999999999978 },
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{ 1.0000000000000000, 0, 0.0000000000000000 },
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{ 1.0000000000000000, 0, 0.10000000000000009 },
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{ 1.0000000000000000, 0, 0.19999999999999996 },
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{ 1.0000000000000000, 0, 0.30000000000000004 },
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{ 1.0000000000000000, 0, 0.39999999999999991 },
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{ 1.0000000000000000, 0, 0.50000000000000000 },
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{ 1.0000000000000000, 0, 0.60000000000000009 },
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{ 1.0000000000000000, 0, 0.69999999999999996 },
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{ 1.0000000000000000, 0, 0.80000000000000004 },
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{ 1.0000000000000000, 0, 0.89999999999999991 },
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{ 1.0000000000000000, 0, 1.0000000000000000 },
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};
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// Test function for l=0.
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template <typename Tp>
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void test001()
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{
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const Tp eps = std::numeric_limits<Tp>::epsilon();
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Tp max_abs_diff = -Tp(1);
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Tp max_abs_frac = -Tp(1);
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unsigned int num_datum = sizeof(data001)
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/ sizeof(testcase_legendre<double>);
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for (unsigned int i = 0; i < num_datum; ++i)
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{
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const Tp f = std::tr1::legendre(Tp(data001[i].l), Tp(data001[i].x));
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const Tp f0 = data001[i].f0;
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const Tp diff = f - f0;
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if (std::abs(diff) > max_abs_diff)
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max_abs_diff = std::abs(diff);
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if (std::abs(f0) > Tp(10) * eps
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&& std::abs(f) > Tp(10) * eps)
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{
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const Tp frac = diff / f0;
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if (std::abs(frac) > max_abs_frac)
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max_abs_frac = std::abs(frac);
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}
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}
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VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
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}
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// Test data for l=1.
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testcase_legendre<double> data002[] = {
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{ -1.0000000000000000, 1, -1.0000000000000000 },
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{ -0.90000000000000002, 1, -0.90000000000000002 },
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{ -0.80000000000000004, 1, -0.80000000000000004 },
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{ -0.69999999999999996, 1, -0.69999999999999996 },
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{ -0.59999999999999998, 1, -0.59999999999999998 },
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{ -0.50000000000000000, 1, -0.50000000000000000 },
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{ -0.40000000000000002, 1, -0.40000000000000002 },
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{ -0.30000000000000004, 1, -0.30000000000000004 },
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{ -0.19999999999999996, 1, -0.19999999999999996 },
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{ -0.099999999999999978, 1, -0.099999999999999978 },
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{ 0.0000000000000000, 1, 0.0000000000000000 },
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{ 0.10000000000000009, 1, 0.10000000000000009 },
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{ 0.19999999999999996, 1, 0.19999999999999996 },
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{ 0.30000000000000004, 1, 0.30000000000000004 },
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{ 0.39999999999999991, 1, 0.39999999999999991 },
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{ 0.50000000000000000, 1, 0.50000000000000000 },
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{ 0.60000000000000009, 1, 0.60000000000000009 },
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{ 0.69999999999999996, 1, 0.69999999999999996 },
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{ 0.80000000000000004, 1, 0.80000000000000004 },
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{ 0.89999999999999991, 1, 0.89999999999999991 },
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{ 1.0000000000000000, 1, 1.0000000000000000 },
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};
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// Test function for l=1.
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template <typename Tp>
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void test002()
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{
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const Tp eps = std::numeric_limits<Tp>::epsilon();
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Tp max_abs_diff = -Tp(1);
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Tp max_abs_frac = -Tp(1);
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unsigned int num_datum = sizeof(data002)
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/ sizeof(testcase_legendre<double>);
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for (unsigned int i = 0; i < num_datum; ++i)
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{
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const Tp f = std::tr1::legendre(Tp(data002[i].l), Tp(data002[i].x));
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const Tp f0 = data002[i].f0;
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const Tp diff = f - f0;
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if (std::abs(diff) > max_abs_diff)
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max_abs_diff = std::abs(diff);
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if (std::abs(f0) > Tp(10) * eps
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&& std::abs(f) > Tp(10) * eps)
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{
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const Tp frac = diff / f0;
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if (std::abs(frac) > max_abs_frac)
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max_abs_frac = std::abs(frac);
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}
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}
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VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
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}
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// Test data for l=2.
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testcase_legendre<double> data003[] = {
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{ 1.0000000000000000, 2, -1.0000000000000000 },
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{ 0.71500000000000008, 2, -0.90000000000000002 },
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{ 0.46000000000000019, 2, -0.80000000000000004 },
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{ 0.23499999999999988, 2, -0.69999999999999996 },
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{ 0.039999999999999925, 2, -0.59999999999999998 },
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{ -0.12500000000000000, 2, -0.50000000000000000 },
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{ -0.25999999999999995, 2, -0.40000000000000002 },
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{ -0.36499999999999999, 2, -0.30000000000000004 },
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{ -0.44000000000000006, 2, -0.19999999999999996 },
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{ -0.48499999999999999, 2, -0.099999999999999978 },
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{ -0.50000000000000000, 2, 0.0000000000000000 },
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{ -0.48499999999999999, 2, 0.10000000000000009 },
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{ -0.44000000000000006, 2, 0.19999999999999996 },
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{ -0.36499999999999999, 2, 0.30000000000000004 },
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{ -0.26000000000000012, 2, 0.39999999999999991 },
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{ -0.12500000000000000, 2, 0.50000000000000000 },
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{ 0.040000000000000147, 2, 0.60000000000000009 },
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{ 0.23499999999999988, 2, 0.69999999999999996 },
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{ 0.46000000000000019, 2, 0.80000000000000004 },
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{ 0.71499999999999986, 2, 0.89999999999999991 },
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{ 1.0000000000000000, 2, 1.0000000000000000 },
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};
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// Test function for l=2.
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template <typename Tp>
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void test003()
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{
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const Tp eps = std::numeric_limits<Tp>::epsilon();
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Tp max_abs_diff = -Tp(1);
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Tp max_abs_frac = -Tp(1);
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unsigned int num_datum = sizeof(data003)
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/ sizeof(testcase_legendre<double>);
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for (unsigned int i = 0; i < num_datum; ++i)
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{
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const Tp f = std::tr1::legendre(Tp(data003[i].l), Tp(data003[i].x));
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const Tp f0 = data003[i].f0;
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const Tp diff = f - f0;
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if (std::abs(diff) > max_abs_diff)
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max_abs_diff = std::abs(diff);
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if (std::abs(f0) > Tp(10) * eps
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&& std::abs(f) > Tp(10) * eps)
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{
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const Tp frac = diff / f0;
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if (std::abs(frac) > max_abs_frac)
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max_abs_frac = std::abs(frac);
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}
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}
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VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
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}
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// Test data for l=5.
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testcase_legendre<double> data004[] = {
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{ -1.0000000000000000, 5, -1.0000000000000000 },
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{ 0.041141249999999997, 5, -0.90000000000000002 },
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{ 0.39951999999999993, 5, -0.80000000000000004 },
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{ 0.36519874999999991, 5, -0.69999999999999996 },
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{ 0.15263999999999994, 5, -0.59999999999999998 },
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{ -0.089843750000000000, 5, -0.50000000000000000 },
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{ -0.27063999999999988, 5, -0.40000000000000002 },
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{ -0.34538624999999995, 5, -0.30000000000000004 },
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{ -0.30751999999999996, 5, -0.19999999999999996 },
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{ -0.17882874999999995, 5, -0.099999999999999978 },
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{ 0.0000000000000000, 5, 0.0000000000000000 },
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{ 0.17882875000000015, 5, 0.10000000000000009 },
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{ 0.30751999999999996, 5, 0.19999999999999996 },
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{ 0.34538624999999995, 5, 0.30000000000000004 },
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{ 0.27064000000000010, 5, 0.39999999999999991 },
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{ 0.089843750000000000, 5, 0.50000000000000000 },
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{ -0.15264000000000022, 5, 0.60000000000000009 },
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{ -0.36519874999999991, 5, 0.69999999999999996 },
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{ -0.39951999999999993, 5, 0.80000000000000004 },
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{ -0.041141250000000407, 5, 0.89999999999999991 },
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{ 1.0000000000000000, 5, 1.0000000000000000 },
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};
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// Test function for l=5.
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template <typename Tp>
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void test004()
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{
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const Tp eps = std::numeric_limits<Tp>::epsilon();
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Tp max_abs_diff = -Tp(1);
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Tp max_abs_frac = -Tp(1);
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unsigned int num_datum = sizeof(data004)
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/ sizeof(testcase_legendre<double>);
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for (unsigned int i = 0; i < num_datum; ++i)
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{
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const Tp f = std::tr1::legendre(Tp(data004[i].l), Tp(data004[i].x));
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const Tp f0 = data004[i].f0;
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const Tp diff = f - f0;
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if (std::abs(diff) > max_abs_diff)
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max_abs_diff = std::abs(diff);
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if (std::abs(f0) > Tp(10) * eps
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&& std::abs(f) > Tp(10) * eps)
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{
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const Tp frac = diff / f0;
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if (std::abs(frac) > max_abs_frac)
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max_abs_frac = std::abs(frac);
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}
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}
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VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
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}
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// Test data for l=10.
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testcase_legendre<double> data005[] = {
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{ 1.0000000000000000, 10, -1.0000000000000000 },
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{ -0.26314561785585977, 10, -0.90000000000000002 },
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{ 0.30052979559999998, 10, -0.80000000000000004 },
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{ 0.085805795531640333, 10, -0.69999999999999996 },
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{ -0.24366274560000006, 10, -0.59999999999999998 },
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{ -0.18822860717773438, 10, -0.50000000000000000 },
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{ 0.096839064399999869, 10, -0.40000000000000002 },
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{ 0.25147634951601561, 10, -0.30000000000000004 },
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{ 0.12907202559999989, 10, -0.19999999999999996 },
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{ -0.12212499738710947, 10, -0.099999999999999978 },
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{ -0.24609375000000000, 10, 0.0000000000000000 },
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{ -0.12212499738710922, 10, 0.10000000000000009 },
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{ 0.12907202559999989, 10, 0.19999999999999996 },
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{ 0.25147634951601561, 10, 0.30000000000000004 },
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{ 0.096839064400000258, 10, 0.39999999999999991 },
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{ -0.18822860717773438, 10, 0.50000000000000000 },
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{ -0.24366274559999987, 10, 0.60000000000000009 },
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{ 0.085805795531640333, 10, 0.69999999999999996 },
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{ 0.30052979559999998, 10, 0.80000000000000004 },
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{ -0.26314561785585888, 10, 0.89999999999999991 },
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{ 1.0000000000000000, 10, 1.0000000000000000 },
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};
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// Test function for l=10.
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template <typename Tp>
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void test005()
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{
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const Tp eps = std::numeric_limits<Tp>::epsilon();
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Tp max_abs_diff = -Tp(1);
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Tp max_abs_frac = -Tp(1);
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unsigned int num_datum = sizeof(data005)
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/ sizeof(testcase_legendre<double>);
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for (unsigned int i = 0; i < num_datum; ++i)
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{
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const Tp f = std::tr1::legendre(Tp(data005[i].l), Tp(data005[i].x));
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const Tp f0 = data005[i].f0;
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const Tp diff = f - f0;
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if (std::abs(diff) > max_abs_diff)
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max_abs_diff = std::abs(diff);
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if (std::abs(f0) > Tp(10) * eps
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&& std::abs(f) > Tp(10) * eps)
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{
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const Tp frac = diff / f0;
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if (std::abs(frac) > max_abs_frac)
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max_abs_frac = std::abs(frac);
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}
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}
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VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
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}
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// Test data for l=20.
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303 |
|
|
testcase_legendre<double> data006[] = {
|
304 |
|
|
{ 1.0000000000000000, 20, -1.0000000000000000 },
|
305 |
|
|
{ -0.14930823530984821, 20, -0.90000000000000002 },
|
306 |
|
|
{ 0.22420460541741344, 20, -0.80000000000000004 },
|
307 |
|
|
{ -0.20457394463834172, 20, -0.69999999999999996 },
|
308 |
|
|
{ 0.15916752910098114, 20, -0.59999999999999998 },
|
309 |
|
|
{ -0.048358381067373557, 20, -0.50000000000000000 },
|
310 |
|
|
{ -0.10159261558628156, 20, -0.40000000000000002 },
|
311 |
|
|
{ 0.18028715947998047, 20, -0.30000000000000004 },
|
312 |
|
|
{ -0.098042194344594741, 20, -0.19999999999999996 },
|
313 |
|
|
{ -0.082077130944527649, 20, -0.099999999999999978 },
|
314 |
|
|
{ 0.17619705200195312, 20, 0.0000000000000000 },
|
315 |
|
|
{ -0.082077130944528037, 20, 0.10000000000000009 },
|
316 |
|
|
{ -0.098042194344594741, 20, 0.19999999999999996 },
|
317 |
|
|
{ 0.18028715947998047, 20, 0.30000000000000004 },
|
318 |
|
|
{ -0.10159261558628112, 20, 0.39999999999999991 },
|
319 |
|
|
{ -0.048358381067373557, 20, 0.50000000000000000 },
|
320 |
|
|
{ 0.15916752910098084, 20, 0.60000000000000009 },
|
321 |
|
|
{ -0.20457394463834172, 20, 0.69999999999999996 },
|
322 |
|
|
{ 0.22420460541741344, 20, 0.80000000000000004 },
|
323 |
|
|
{ -0.14930823530984949, 20, 0.89999999999999991 },
|
324 |
|
|
{ 1.0000000000000000, 20, 1.0000000000000000 },
|
325 |
|
|
};
|
326 |
|
|
|
327 |
|
|
// Test function for l=20.
|
328 |
|
|
template <typename Tp>
|
329 |
|
|
void test006()
|
330 |
|
|
{
|
331 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
332 |
|
|
Tp max_abs_diff = -Tp(1);
|
333 |
|
|
Tp max_abs_frac = -Tp(1);
|
334 |
|
|
unsigned int num_datum = sizeof(data006)
|
335 |
|
|
/ sizeof(testcase_legendre<double>);
|
336 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
337 |
|
|
{
|
338 |
|
|
const Tp f = std::tr1::legendre(Tp(data006[i].l), Tp(data006[i].x));
|
339 |
|
|
const Tp f0 = data006[i].f0;
|
340 |
|
|
const Tp diff = f - f0;
|
341 |
|
|
if (std::abs(diff) > max_abs_diff)
|
342 |
|
|
max_abs_diff = std::abs(diff);
|
343 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
344 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
345 |
|
|
{
|
346 |
|
|
const Tp frac = diff / f0;
|
347 |
|
|
if (std::abs(frac) > max_abs_frac)
|
348 |
|
|
max_abs_frac = std::abs(frac);
|
349 |
|
|
}
|
350 |
|
|
}
|
351 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
352 |
|
|
}
|
353 |
|
|
|
354 |
|
|
// Test data for l=50.
|
355 |
|
|
testcase_legendre<double> data007[] = {
|
356 |
|
|
{ 1.0000000000000000, 50, -1.0000000000000000 },
|
357 |
|
|
{ -0.17003765994383685, 50, -0.90000000000000002 },
|
358 |
|
|
{ 0.13879737345093118, 50, -0.80000000000000004 },
|
359 |
|
|
{ -0.014572731645892805, 50, -0.69999999999999996 },
|
360 |
|
|
{ -0.058860798844002173, 50, -0.59999999999999998 },
|
361 |
|
|
{ -0.031059099239609828, 50, -0.50000000000000000 },
|
362 |
|
|
{ 0.041569033381825368, 50, -0.40000000000000002 },
|
363 |
|
|
{ 0.10911051574714808, 50, -0.30000000000000004 },
|
364 |
|
|
{ 0.083432272204197466, 50, -0.19999999999999996 },
|
365 |
|
|
{ -0.038205812661313579, 50, -0.099999999999999978 },
|
366 |
|
|
{ -0.11227517265921705, 50, 0.0000000000000000 },
|
367 |
|
|
{ -0.038205812661314169, 50, 0.10000000000000009 },
|
368 |
|
|
{ 0.083432272204197466, 50, 0.19999999999999996 },
|
369 |
|
|
{ 0.10911051574714808, 50, 0.30000000000000004 },
|
370 |
|
|
{ 0.041569033381824647, 50, 0.39999999999999991 },
|
371 |
|
|
{ -0.031059099239609828, 50, 0.50000000000000000 },
|
372 |
|
|
{ -0.058860798844001430, 50, 0.60000000000000009 },
|
373 |
|
|
{ -0.014572731645892805, 50, 0.69999999999999996 },
|
374 |
|
|
{ 0.13879737345093118, 50, 0.80000000000000004 },
|
375 |
|
|
{ -0.17003765994383663, 50, 0.89999999999999991 },
|
376 |
|
|
{ 1.0000000000000000, 50, 1.0000000000000000 },
|
377 |
|
|
};
|
378 |
|
|
|
379 |
|
|
// Test function for l=50.
|
380 |
|
|
template <typename Tp>
|
381 |
|
|
void test007()
|
382 |
|
|
{
|
383 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
384 |
|
|
Tp max_abs_diff = -Tp(1);
|
385 |
|
|
Tp max_abs_frac = -Tp(1);
|
386 |
|
|
unsigned int num_datum = sizeof(data007)
|
387 |
|
|
/ sizeof(testcase_legendre<double>);
|
388 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
389 |
|
|
{
|
390 |
|
|
const Tp f = std::tr1::legendre(Tp(data007[i].l), Tp(data007[i].x));
|
391 |
|
|
const Tp f0 = data007[i].f0;
|
392 |
|
|
const Tp diff = f - f0;
|
393 |
|
|
if (std::abs(diff) > max_abs_diff)
|
394 |
|
|
max_abs_diff = std::abs(diff);
|
395 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
396 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
397 |
|
|
{
|
398 |
|
|
const Tp frac = diff / f0;
|
399 |
|
|
if (std::abs(frac) > max_abs_frac)
|
400 |
|
|
max_abs_frac = std::abs(frac);
|
401 |
|
|
}
|
402 |
|
|
}
|
403 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
404 |
|
|
}
|
405 |
|
|
|
406 |
|
|
// Test data for l=100.
|
407 |
|
|
testcase_legendre<double> data008[] = {
|
408 |
|
|
{ 1.0000000000000000, 100, -1.0000000000000000 },
|
409 |
|
|
{ 0.10226582055871908, 100, -0.90000000000000002 },
|
410 |
|
|
{ 0.050861167913584124, 100, -0.80000000000000004 },
|
411 |
|
|
{ -0.077132507199778780, 100, -0.69999999999999996 },
|
412 |
|
|
{ -0.023747023905133110, 100, -0.59999999999999998 },
|
413 |
|
|
{ -0.060518025961861198, 100, -0.50000000000000000 },
|
414 |
|
|
{ -0.072258202125684429, 100, -0.40000000000000002 },
|
415 |
|
|
{ 0.057127392202801719, 100, -0.30000000000000004 },
|
416 |
|
|
{ 0.014681835355659636, 100, -0.19999999999999996 },
|
417 |
|
|
{ -0.063895098434750303, 100, -0.099999999999999978 },
|
418 |
|
|
{ 0.079589237387178727, 100, 0.0000000000000000 },
|
419 |
|
|
{ -0.063895098434749775, 100, 0.10000000000000009 },
|
420 |
|
|
{ 0.014681835355659636, 100, 0.19999999999999996 },
|
421 |
|
|
{ 0.057127392202801719, 100, 0.30000000000000004 },
|
422 |
|
|
{ -0.072258202125685012, 100, 0.39999999999999991 },
|
423 |
|
|
{ -0.060518025961861198, 100, 0.50000000000000000 },
|
424 |
|
|
{ -0.023747023905134217, 100, 0.60000000000000009 },
|
425 |
|
|
{ -0.077132507199778780, 100, 0.69999999999999996 },
|
426 |
|
|
{ 0.050861167913584124, 100, 0.80000000000000004 },
|
427 |
|
|
{ 0.10226582055871723, 100, 0.89999999999999991 },
|
428 |
|
|
{ 1.0000000000000000, 100, 1.0000000000000000 },
|
429 |
|
|
};
|
430 |
|
|
|
431 |
|
|
// Test function for l=100.
|
432 |
|
|
template <typename Tp>
|
433 |
|
|
void test008()
|
434 |
|
|
{
|
435 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
436 |
|
|
Tp max_abs_diff = -Tp(1);
|
437 |
|
|
Tp max_abs_frac = -Tp(1);
|
438 |
|
|
unsigned int num_datum = sizeof(data008)
|
439 |
|
|
/ sizeof(testcase_legendre<double>);
|
440 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
441 |
|
|
{
|
442 |
|
|
const Tp f = std::tr1::legendre(Tp(data008[i].l), Tp(data008[i].x));
|
443 |
|
|
const Tp f0 = data008[i].f0;
|
444 |
|
|
const Tp diff = f - f0;
|
445 |
|
|
if (std::abs(diff) > max_abs_diff)
|
446 |
|
|
max_abs_diff = std::abs(diff);
|
447 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
448 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
449 |
|
|
{
|
450 |
|
|
const Tp frac = diff / f0;
|
451 |
|
|
if (std::abs(frac) > max_abs_frac)
|
452 |
|
|
max_abs_frac = std::abs(frac);
|
453 |
|
|
}
|
454 |
|
|
}
|
455 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
456 |
|
|
}
|
457 |
|
|
|
458 |
|
|
int main(int, char**)
|
459 |
|
|
{
|
460 |
|
|
test001<double>();
|
461 |
|
|
test002<double>();
|
462 |
|
|
test003<double>();
|
463 |
|
|
test004<double>();
|
464 |
|
|
test005<double>();
|
465 |
|
|
test006<double>();
|
466 |
|
|
test007<double>();
|
467 |
|
|
test008<double>();
|
468 |
|
|
return 0;
|
469 |
|
|
}
|