1 // Copyright John Maddock 2006.
2 // Use, modification and distribution are subject to the
3 // Boost Software License, Version 1.0. (See accompanying file
4 // LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
6 #define BOOST_ENABLE_ASSERT_HANDLER
7 #define BOOST_MATH_MAX_SERIES_ITERATION_POLICY INT_MAX
8 // for consistent behaviour across compilers/platforms:
9 #define BOOST_MATH_PROMOTE_DOUBLE_POLICY false
10 // overflow to infinity is OK, we treat these as zero error as long as the sign is correct!
11 #define BOOST_MATH_OVERFLOW_ERROR_POLICY ignore_error
15 #include <boost/multiprecision/mpfr.hpp>
16 #include <boost/multiprecision/cpp_bin_float.hpp>
17 #include <boost/math/special_functions/hypergeometric_1F1.hpp>
18 #include <boost/math/special_functions/hypergeometric_pFq.hpp>
19 #include <boost/math/special_functions/relative_difference.hpp>
21 #include <boost/random.hpp>
24 #include <boost/iostreams/tee.hpp>
25 #include <boost/iostreams/stream.hpp>
27 using boost::multiprecision::mpfr_float;
31 // We convert assertions into exceptions, so we can log them and continue:
33 void assertion_failed(char const * expr, char const *, char const * file, long line)
35 std::ostringstream oss;
36 oss << file << ":" << line << " Assertion failed: " << expr;
37 throw std::runtime_error(oss.str());
42 typedef boost::multiprecision::cpp_bin_float_quad test_type;
49 test_type a_start, a_end;
50 test_type b_start, b_end;
51 test_type a_mult, b_mult;
53 std::cout << "Enter range for paramater a: ";
54 std::cin >> a_start >> a_end;
55 std::cout << "Enter range for paramater b: ";
56 std::cin >> b_start >> b_end;
57 std::cout << "Enter multiplier for a parameter: ";
59 std::cout << "Enter multiplier for b parameter: ";
62 double error_limit = 200;
63 double time_limit = 10.0;
65 for (test_type a = a_start; a < a_end; a_start < 0 ? a /= a_mult : a *= a_mult)
67 for (test_type b = b_start; b < b_end; b_start < 0 ? b /= b_mult : b *= b_mult)
70 test_type last_good = 0;
73 for (test_type z = 1; z < 1e10; z *= z_mult, z_mult *= 2)
75 // std::cout << "z = " << z << std::endl;
76 boost::uintmax_t max_iter = 1000;
77 test_type calc = boost::math::tools::function_ratio_from_forwards_recurrence(boost::math::detail::hypergeometric_1F1_recurrence_a_and_b_coefficients<test_type>(a, b, z), std::numeric_limits<test_type>::epsilon() * 2, max_iter);
78 test_type reference = (test_type)(boost::math::hypergeometric_pFq_precision({ mpfr_float(a) }, { mpfr_float(b) }, mpfr_float(z), 50, time_limit) / boost::math::hypergeometric_pFq_precision({ mpfr_float(a + 1) }, { mpfr_float(b + 1) }, mpfr_float(z), std::numeric_limits<test_type>::digits10 * 2, time_limit));
79 double err = (double)boost::math::epsilon_difference(reference, calc);
81 if (err < error_limit)
92 catch (const std::exception& e)
94 std::cout << "Unexpected exception: " << e.what() << std::endl;
95 std::cout << "For a = " << a << " b = " << b << " z = " << bad * z_mult / 2 << std::endl;
99 z_limit = 1; // Any z is large enough
100 else if (0 == last_good)
101 z_limit = std::numeric_limits<test_type > ::infinity();
105 // At this stage last_good and bad should bracket the edge of the domain, bisect to narrow things down:
107 z_limit = last_good == 0 ? 0 : boost::math::tools::bisect([&a, b, error_limit, time_limit](test_type z)
109 boost::uintmax_t max_iter = 1000;
110 test_type calc = boost::math::tools::function_ratio_from_forwards_recurrence(boost::math::detail::hypergeometric_1F1_recurrence_a_and_b_coefficients<test_type>(a, b, z), std::numeric_limits<test_type>::epsilon() * 2, max_iter);
111 test_type reference = (test_type)(boost::math::hypergeometric_pFq_precision({ mpfr_float(a) }, { mpfr_float(b) }, mpfr_float(z), 50, time_limit + 20) / boost::math::hypergeometric_pFq_precision({ mpfr_float(a + 1) }, { mpfr_float(b + 1) }, mpfr_float(z), std::numeric_limits<test_type>::digits10 * 2, time_limit + 20));
112 test_type err = boost::math::epsilon_difference(reference, calc);
113 return err < error_limit ? 1 : -1;
114 }, bad, last_good, boost::math::tools::equal_floor()).first;
115 z_limit = floor(z_limit + 2); // Give ourselves some headroom!
117 // std::cout << "z_limit = " << z_limit << std::endl;
119 // Now over again for backwards recurrence domain at the same points:
121 bad = z_limit > 1e10 ? 1e10 : z_limit;
124 for (test_type z = bad; z > 1; z /= z_mult, z_mult *= 2)
126 // std::cout << "z = " << z << std::endl;
128 boost::uintmax_t max_iter = 1000;
129 test_type calc = boost::math::tools::function_ratio_from_backwards_recurrence(boost::math::detail::hypergeometric_1F1_recurrence_a_and_b_coefficients<test_type>(a, b, z), std::numeric_limits<test_type>::epsilon() * 2, max_iter);
130 test_type reference = (test_type)(boost::math::hypergeometric_pFq_precision({ mpfr_float(a) }, { mpfr_float(b) }, mpfr_float(z), 50, time_limit) / boost::math::hypergeometric_pFq_precision({ mpfr_float(a - 1) }, { mpfr_float(b - 1) }, mpfr_float(z), std::numeric_limits<test_type>::digits10 * 2, time_limit));
131 test_type err = boost::math::epsilon_difference(reference, calc);
133 if (err < error_limit)
143 catch (const std::exception& e)
146 std::cout << "Unexpected exception: " << e.what() << std::endl;
147 std::cout << "For a = " << a << " b = " << b << " z = " << z << std::endl;
150 test_type lower_z_limit;
153 else if (last_good >= bad)
155 boost::uintmax_t max_iter = 1000;
157 test_type calc = boost::math::tools::function_ratio_from_forwards_recurrence(boost::math::detail::hypergeometric_1F1_recurrence_a_and_b_coefficients<test_type>(a, b, z), std::numeric_limits<test_type>::epsilon() * 2, max_iter);
158 test_type reference = (test_type)(boost::math::hypergeometric_pFq_precision({ mpfr_float(a) }, { mpfr_float(b) }, mpfr_float(z), 50, time_limit) / boost::math::hypergeometric_pFq_precision({ mpfr_float(a + 1) }, { mpfr_float(b + 1) }, mpfr_float(z), std::numeric_limits<test_type>::digits10 * 2, time_limit));
159 test_type err = boost::math::epsilon_difference(reference, calc);
160 if (err < error_limit)
162 lower_z_limit = bad; // Both forwards and backwards iteration work!!!
165 throw std::runtime_error("Internal logic failed!");
170 // At this stage last_good and bad should bracket the edge of the domain, bisect to narrow things down:
172 lower_z_limit = last_good == 0 ? 0 : boost::math::tools::bisect([&a, b, error_limit, time_limit](test_type z)
174 boost::uintmax_t max_iter = 1000;
175 test_type calc = boost::math::tools::function_ratio_from_backwards_recurrence(boost::math::detail::hypergeometric_1F1_recurrence_a_and_b_coefficients<test_type>(a, b, z), std::numeric_limits<test_type>::epsilon() * 2, max_iter);
176 test_type reference = (test_type)(boost::math::hypergeometric_pFq_precision({ mpfr_float(a) }, { mpfr_float(b) }, mpfr_float(z), 50, time_limit + 20) / boost::math::hypergeometric_pFq_precision({ mpfr_float(a - 1) }, { mpfr_float(b - 1) }, mpfr_float(z), std::numeric_limits<test_type>::digits10 * 2, time_limit + 20));
177 test_type err = boost::math::epsilon_difference(reference, calc);
178 return err < error_limit ? 1 : -1;
179 }, last_good, bad, boost::math::tools::equal_floor()).first;
180 z_limit = ceil(z_limit - 2); // Give ourselves some headroom!
183 std::cout << std::setprecision(std::numeric_limits<test_type>::max_digits10) << "{ " << a << ", " << b << ", " << lower_z_limit << ", " << z_limit << "}," << std::endl;
187 catch (const std::exception& e)
189 std::cout << "Unexpected exception: " << e.what() << std::endl;