1 // Copyright John Maddock 2006
2 // Copyright Paul A. Bristow 2007
3 // Use, modification and distribution are subject to the
4 // Boost Software License, Version 1.0. (See accompanying file
5 // LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
6
7 #include <pch.hpp>
8
9 #ifdef _MSC_VER
10 # pragma warning(disable : 4267) // conversion from 'size_t' to 'const unsigned int', possible loss of data
11 # pragma warning(disable : 4180) // qualifier applied to function type has no meaning; ignored
12 # pragma warning(disable : 4224) // nonstandard extension used : formal parameter 'function_ptr' was previously defined as a type
13 # pragma warning(disable : 4100) // unreferenced formal parameter (in ublas/functional)
14 #endif
15
16 #include <boost/math/tools/remez.hpp>
17 #define BOOST_TEST_MAIN
18 #include <boost/test/unit_test.hpp>
19 #include <boost/test/tools/floating_point_comparison.hpp>
20 #include <boost/math/special_functions/expm1.hpp>
21 #include <iostream>
22 #include <iomanip>
23
24
test_polynomial()25 void test_polynomial()
26 {
27 #if defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS)
28 double (*f)(double) = boost::math::expm1<double>;
29 #else
30 double (*f)(double) = boost::math::expm1;
31 #endif
32 std::cout << "Testing expm1 approximation, pinned to origin, absolute error, 6 term polynomial\n";
33 boost::math::tools::remez_minimax<double> approx1(f, 6, 0, -1, 1, true, false);
34 std::cout << "Interpolation Error: " << approx1.max_error() << std::endl;
35 for(unsigned i = 0; i < 7; ++i)
36 {
37 approx1.iterate();
38 std::cout << approx1.error_term() << " " << approx1.max_error() << " " << approx1.max_change() << std::endl;
39 }
40 std::cout << "~~~~~~~~~~~~~~~~~~~~~~~~~" << std::endl;
41 std::cout << "Testing expm1 approximation, pinned to origin, relative error, 6 term polynomial\n";
42 boost::math::tools::remez_minimax<double> approx2(f, 6, 0, -1, 1, true, true);
43 std::cout << "Interpolation Error: " << approx1.max_error() << std::endl;
44 for(unsigned i = 0; i < 7; ++i)
45 {
46 approx2.iterate();
47 std::cout << approx2.error_term() << " " << approx2.max_error() << " " << approx2.max_change() << std::endl;
48 }
49 std::cout << "~~~~~~~~~~~~~~~~~~~~~~~~~" << std::endl;
50
51 f = std::exp;
52 std::cout << "Testing exp approximation, not pinned to origin, absolute error, 6 term polynomial\n";
53 boost::math::tools::remez_minimax<double> approx3(f, 6, 0, -1, 1, false, false);
54 std::cout << "Interpolation Error: " << approx1.max_error() << std::endl;
55 for(unsigned i = 0; i < 7; ++i)
56 {
57 approx3.iterate();
58 std::cout << approx3.error_term() << " " << approx3.max_error() << " " << approx3.max_change() << std::endl;
59 }
60 std::cout << "~~~~~~~~~~~~~~~~~~~~~~~~~" << std::endl;
61 std::cout << "Testing exp approximation, not pinned to origin, relative error, 6 term polynomial\n";
62 boost::math::tools::remez_minimax<double> approx4(f, 6, 0, -1, 1, false, true);
63 std::cout << "Interpolation Error: " << approx1.max_error() << std::endl;
64 for(unsigned i = 0; i < 7; ++i)
65 {
66 approx4.iterate();
67 std::cout << approx4.error_term() << " " << approx4.max_error() << " " << approx4.max_change() << std::endl;
68 }
69 std::cout << "~~~~~~~~~~~~~~~~~~~~~~~~~" << std::endl;
70
71 f = std::cos;
72 std::cout << "Testing cos approximation, not pinned to origin, absolute error, 5 term polynomial\n";
73 boost::math::tools::remez_minimax<double> approx5(f, 5, 0, -1, 1, false, false);
74 std::cout << "Interpolation Error: " << approx1.max_error() << std::endl;
75 for(unsigned i = 0; i < 7; ++i)
76 {
77 approx5.iterate();
78 std::cout << approx5.error_term() << " " << approx5.max_error() << " " << approx5.max_change() << std::endl;
79 }
80 std::cout << "~~~~~~~~~~~~~~~~~~~~~~~~~" << std::endl;
81 std::cout << "Testing cos approximation, not pinned to origin, relative error, 5 term polynomial\n";
82 boost::math::tools::remez_minimax<double> approx6(f, 5, 0, -1, 1, false, true);
83 for(unsigned i = 0; i < 7; ++i)
84 {
85 approx6.iterate();
86 std::cout << approx6.error_term() << " " << approx6.max_error() << " " << approx6.max_change() << std::endl;
87 }
88 std::cout << "~~~~~~~~~~~~~~~~~~~~~~~~~" << std::endl;
89
90 f = std::sin;
91 std::cout << "Testing sin approximation, pinned to origin, absolute error, 4 term polynomial\n";
92 boost::math::tools::remez_minimax<double> approx7(f, 4, 0, 0, 1, true, false);
93 for(unsigned i = 0; i < 7; ++i)
94 {
95 approx7.iterate();
96 std::cout << approx7.error_term() << " " << approx7.max_error() << " " << approx7.max_change() << std::endl;
97 }
98 std::cout << "~~~~~~~~~~~~~~~~~~~~~~~~~" << std::endl;
99 std::cout << "Testing sin approximation, pinned to origin, relative error, 4 term polynomial\n";
100 boost::math::tools::remez_minimax<double> approx8(f, 4, 0, 0, 1, true, true);
101 for(unsigned i = 0; i < 7; ++i)
102 {
103 approx8.iterate();
104 std::cout << approx8.error_term() << " " << approx8.max_error() << " " << approx8.max_change() << std::endl;
105 }
106 std::cout << "~~~~~~~~~~~~~~~~~~~~~~~~~" << std::endl;
107 }
108
test_rational()109 void test_rational()
110 {
111 #if defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS)
112 double (*f)(double) = boost::math::expm1<double>;
113 #else
114 double (*f)(double) = boost::math::expm1;
115 #endif
116 std::cout << "Testing expm1 approximation, pinned to origin, absolute error, 3+3 term rational\n";
117 boost::math::tools::remez_minimax<double> approx1(f, 3, 3, -1, 1, true, false);
118 std::cout << "Interpolation Error: " << approx1.max_error() << std::endl;
119 for(unsigned i = 0; i < 7; ++i)
120 {
121 approx1.iterate();
122 std::cout << approx1.error_term() << " " << approx1.max_error() << " " << approx1.max_change() << std::endl;
123 }
124 std::cout << "~~~~~~~~~~~~~~~~~~~~~~~~~" << std::endl;
125 #if 0
126 //
127 // This one causes UBLAS to fail on some systems, so disabled for now.
128 //
129 std::cout << "Testing expm1 approximation, pinned to origin, relative error, 3+3 term rational\n";
130 boost::math::tools::remez_minimax<double> approx2(f, 3, 3, -1, 1, true, true);
131 std::cout << "Interpolation Error: " << approx1.max_error() << std::endl;
132 for(unsigned i = 0; i < 7; ++i)
133 {
134 approx2.iterate();
135 std::cout << approx2.error_term() << " " << approx2.max_error() << " " << approx2.max_change() << std::endl;
136 }
137 std::cout << "~~~~~~~~~~~~~~~~~~~~~~~~~" << std::endl;
138 #endif
139 f = std::exp;
140 std::cout << "Testing exp approximation, not pinned to origin, absolute error, 3+3 term rational\n";
141 boost::math::tools::remez_minimax<double> approx3(f, 3, 3, -1, 1, false, false);
142 std::cout << "Interpolation Error: " << approx1.max_error() << std::endl;
143 for(unsigned i = 0; i < 7; ++i)
144 {
145 approx3.iterate();
146 std::cout << approx3.error_term() << " " << approx3.max_error() << " " << approx3.max_change() << std::endl;
147 }
148 std::cout << "~~~~~~~~~~~~~~~~~~~~~~~~~" << std::endl;
149 std::cout << "Testing exp approximation, not pinned to origin, relative error, 3+3 term rational\n";
150 boost::math::tools::remez_minimax<double> approx4(f, 3, 3, -1, 1, false, true);
151 std::cout << "Interpolation Error: " << approx1.max_error() << std::endl;
152 for(unsigned i = 0; i < 7; ++i)
153 {
154 approx4.iterate();
155 std::cout << approx4.error_term() << " " << approx4.max_error() << " " << approx4.max_change() << std::endl;
156 }
157 std::cout << "~~~~~~~~~~~~~~~~~~~~~~~~~" << std::endl;
158
159 f = std::cos;
160 std::cout << "Testing cos approximation, not pinned to origin, absolute error, 2+2 term rational\n";
161 boost::math::tools::remez_minimax<double> approx5(f, 2, 2, 0, 1, false, false);
162 std::cout << "Interpolation Error: " << approx1.max_error() << std::endl;
163 for(unsigned i = 0; i < 7; ++i)
164 {
165 approx5.iterate();
166 std::cout << approx5.error_term() << " " << approx5.max_error() << " " << approx5.max_change() << std::endl;
167 }
168 std::cout << "~~~~~~~~~~~~~~~~~~~~~~~~~" << std::endl;
169 std::cout << "Testing cos approximation, not pinned to origin, relative error, 2+2 term rational\n";
170 boost::math::tools::remez_minimax<double> approx6(f, 2, 2, 0, 1, false, true);
171 std::cout << "Interpolation Error: " << approx1.max_error() << std::endl;
172 for(unsigned i = 0; i < 7; ++i)
173 {
174 approx6.iterate();
175 std::cout << approx6.error_term() << " " << approx6.max_error() << " " << approx6.max_change() << std::endl;
176 }
177 std::cout << "~~~~~~~~~~~~~~~~~~~~~~~~~" << std::endl;
178 }
179
BOOST_AUTO_TEST_CASE(test_main)180 BOOST_AUTO_TEST_CASE( test_main )
181 {
182 test_polynomial();
183 test_rational();
184
185 }
186
187
188