ceph/src/boost/libs/math/test/test_lambert_w_integrals_quad.cpp

   1 // Copyright Paul A. Bristow 2016, 2017, 2018.
   2 // Copyright John Maddock 2016.
   3
   4 // Use, modification and distribution are subject to the
   5 // Boost Software License, Version 1.0.
   6 // (See accompanying file LICENSE_1_0.txt
   7 // or copy at http://www.boost.org/LICENSE_1_0.txt)
   8
   9 // test_lambert_w_integrals.cpp
  10 //! \brief quadrature tests that cover the whole range of the Lambert W0 function.
  11
  12 #include <boost/config.hpp>   // for BOOST_MSVC definition etc.
  13 #include <boost/version.hpp>   // for BOOST_MSVC versions.
  14
  15 // Boost macros
  16 #define BOOST_TEST_MAIN
  17 #define BOOST_LIB_DIAGNOSTIC "on" // Report library file details.
  18 #include <boost/test/included/unit_test.hpp> // Boost.Test
  19 // #include <boost/test/unit_test.hpp> // Boost.Test
  20 #include <boost/test/tools/floating_point_comparison.hpp>
  21
  22 #include <boost/array.hpp>
  23 #include <boost/type_traits/is_constructible.hpp>
  24 #include <boost/multiprecision/cpp_bin_float.hpp>
  25 using boost::multiprecision::cpp_bin_float_quad;
  26
  27 #include <boost/math/special_functions/fpclassify.hpp> // isnan, isfinite.
  28 #include <boost/math/special_functions/next.hpp> // float_next, float_prior
  29 using boost::math::float_next;
  30 using boost::math::float_prior;
  31 #include <boost/math/special_functions/ulp.hpp>  // ulp
  32
  33 #include <boost/math/tools/test_value.hpp>  // for create_test_value and macro BOOST_MATH_TEST_VALUE.
  34 #include <boost/math/policies/policy.hpp>
  35 using boost::math::policies::digits2;
  36 using boost::math::policies::digits10;
  37 #include <boost/math/special_functions/lambert_w.hpp> // For Lambert W lambert_w function.
  38 using boost::math::lambert_wm1;
  39 using boost::math::lambert_w0;
  40
  41 #include <limits>
  42 #include <cmath>
  43 #include <typeinfo>
  44 #include <iostream>
  45 #include <type_traits>
  46 #include <exception>
  47
  48 std::string show_versions(void);
  49
  50 // Added code and test for Integral of the Lambert W function: by Nick Thompson.
  51 // https://en.wikipedia.org/wiki/Lambert_W_function#Definite_integrals
  52
  53 #include <boost/math/constants/constants.hpp> // for integral tests.
  54 #include <boost/math/quadrature/tanh_sinh.hpp> // for integral tests.
  55 #include <boost/math/quadrature/exp_sinh.hpp> // for integral tests.
  56
  57   using boost::math::policies::policy;
  58   using boost::math::policies::make_policy;
  59
  60 // using statements needed for changing error handling policy.
  61 using boost::math::policies::evaluation_error;
  62 using boost::math::policies::domain_error;
  63 using boost::math::policies::overflow_error;
  64 using boost::math::policies::ignore_error;
  65 using boost::math::policies::throw_on_error;
  66
  67 typedef policy<
  68   domain_error<throw_on_error>,
  69   overflow_error<ignore_error>
  70 > no_throw_policy;
  71
  72 // Assumes that function has a throw policy, for example:
  73 //    NOT lambert_w0<T>(1 / (x * x), no_throw_policy());
  74 // Error in function boost::math::quadrature::exp_sinh<double>::integrate:
  75 // The exp_sinh quadrature evaluated your function at a singular point and resulted in inf.
  76 // Please ensure your function evaluates to a finite number of its entire domain.
  77 template <typename T>
  78 T debug_integration_proc(T x)
  79 {
  80    T result; // warning C4701: potentially uninitialized local variable 'result' used
  81   // T result = 0 ; // But result may not be assigned below?
  82   try
  83   {
  84    // Assign function call to result in here...
  85     if (x <= sqrt(boost::math::tools::min_value<T>()) )
  86     {
  87       result = 0;
  88     }
  89     else
  90     {
  91       result = lambert_w0<T>(1 / (x * x));
  92     }
  93    // result = lambert_w0<T>(1 / (x * x), no_throw_policy());  // Bad idea, less helpful diagnostic message is:
  94     // Error in function boost::math::quadrature::exp_sinh<double>::integrate:
  95     // The exp_sinh quadrature evaluated your function at a singular point and resulted in inf.
  96     // Please ensure your function evaluates to a finite number of its entire domain.
  97
  98   } // try
  99   catch (const std::exception& e)
 100   {
 101     std::cout << "Exception " << e.what() << std::endl;
 102     // set breakpoint here:
 103     std::cout << "Unexpected exception thrown in integration code at abscissa (x): " << x << "." << std::endl;
 104     if (!std::isfinite(result))
 105     {
 106       // set breakpoint here:
 107       std::cout << "Unexpected non-finite result in integration code at abscissa (x): " << x << "." << std::endl;
 108     }
 109     if (std::isnan(result))
 110     {
 111       // set breakpoint here:
 112       std::cout << "Unexpected non-finite result in integration code at abscissa (x): " << x << "." << std::endl;
 113     }
 114   } // catch
 115   return result;
 116 } // T debug_integration_proc(T x)
 117
 118 template<class Real>
 119 void test_integrals()
 120 {
 121   // Integral of the Lambert W function:
 122   // https://en.wikipedia.org/wiki/Lambert_W_function
 123   using boost::math::quadrature::tanh_sinh;
 124   using boost::math::quadrature::exp_sinh;
 125   // file:///I:/modular-boost/libs/math/doc/html/math_toolkit/quadrature/double_exponential/de_tanh_sinh.html
 126   using std::sqrt;
 127
 128   std::cout << "Integration of type " << typeid(Real).name()  << std::endl;
 129
 130   Real tol = std::numeric_limits<Real>::epsilon();
 131   { //  // Integrate for function lambert_W0(z);
 132     tanh_sinh<Real> ts;
 133     Real a = 0;
 134     Real b = boost::math::constants::e<Real>();
 135     auto f = [](Real z)->Real
 136     {
 137       return lambert_w0<Real>(z);
 138     };
 139     Real z = ts.integrate(f, a, b); // OK without any decltype(f)
 140     BOOST_CHECK_CLOSE_FRACTION(z, boost::math::constants::e<Real>() - 1, tol);
 141   }
 142   {
 143     // Integrate for function lambert_W0(z/(z sqrt(z)).
 144     exp_sinh<Real> es;
 145     auto f = [](Real z)->Real
 146     {
 147       return lambert_w0<Real>(z)/(z * sqrt(z));
 148     };
 149     Real z = es.integrate(f); // OK
 150     BOOST_CHECK_CLOSE_FRACTION(z, 2 * boost::math::constants::root_two_pi<Real>(), tol);
 151   }
 152   {
 153     // Integrate for function lambert_W0(1/z^2).
 154     exp_sinh<Real> es;
 155     //const Real sqrt_min = sqrt(boost::math::tools::min_value<Real>()); // 1.08420217e-19 fo 32-bit float.
 156     // error C3493: 'sqrt_min' cannot be implicitly captured because no default capture mode has been specified
 157     auto f = [](Real z)->Real
 158     {
 159       if (z <= sqrt(boost::math::tools::min_value<Real>()) )
 160       { // Too small would underflow z * z and divide by zero to overflow 1/z^2 for lambert_w0 z parameter.
 161         return static_cast<Real>(0);
 162       }
 163       else
 164       {
 165         return lambert_w0<Real>(1 / (z * z)); // warning C4756: overflow in constant arithmetic, even though cannot happen.
 166       }
 167     };
 168     Real z = es.integrate(f);
 169     BOOST_CHECK_CLOSE_FRACTION(z, boost::math::constants::root_two_pi<Real>(), tol);
 170   }
 171 } // template<class Real> void test_integrals()
 172
 173
 174 BOOST_AUTO_TEST_CASE( integrals )
 175 {
 176   std::cout << "Macro BOOST_MATH_LAMBERT_W0_INTEGRALS is defined." << std::endl;
 177   BOOST_TEST_MESSAGE("\nTest Lambert W0 integrals.");
 178   try
 179   {
 180   // using statements needed to change precision policy.
 181   using boost::math::policies::policy;
 182   using boost::math::policies::make_policy;
 183   using boost::math::policies::precision;
 184   using boost::math::policies::digits2;
 185   using boost::math::policies::digits10;
 186
 187   // using statements needed for changing error handling policy.
 188   using boost::math::policies::evaluation_error;
 189   using boost::math::policies::domain_error;
 190   using boost::math::policies::overflow_error;
 191   using boost::math::policies::ignore_error;
 192   using boost::math::policies::throw_on_error;
 193
 194   /*
 195   typedef policy<
 196     domain_error<throw_on_error>,
 197     overflow_error<ignore_error>
 198   > no_throw_policy;
 199
 200   // Experiment with better diagnostics.
 201   typedef float Real;
 202
 203   Real inf = std::numeric_limits<Real>::infinity();
 204   Real max = (std::numeric_limits<Real>::max)();
 205   std::cout.precision(std::numeric_limits<Real>::max_digits10);
 206   //std::cout << "lambert_w0(inf) = " << lambert_w0(inf) << std::endl; // lambert_w0(inf) = 1.79769e+308
 207   std::cout << "lambert_w0(inf, throw_policy()) = " << lambert_w0(inf, no_throw_policy()) << std::endl; // inf
 208   std::cout << "lambert_w0(max) = " << lambert_w0(max) << std::endl; // lambert_w0(max) = 703.227
 209   //std::cout << lambert_w0(inf) << std::endl; // inf - will throw.
 210   std::cout << "lambert_w0(0) = " << lambert_w0(0.) << std::endl; // 0
 211   std::cout << "lambert_w0(std::numeric_limits<Real>::denorm_min()) = " << lambert_w0(std::numeric_limits<Real>::denorm_min()) << std::endl; // 4.94066e-324
 212   std::cout << "lambert_w0(std::numeric_limits<Real>::min()) = " << lambert_w0((std::numeric_limits<Real>::min)()) << std::endl; // 2.22507e-308
 213
 214   // Approximate the largest lambert_w you can get for type T?
 215   float max_w_f = boost::math::lambert_w_detail::lambert_w0_approx((std::numeric_limits<float>::max)()); // Corless equation 4.19, page 349, and Chapeau-Blondeau equation 20, page 2162.
 216   std::cout << "w max_f " << max_w_f << std::endl; // 84.2879
 217   Real max_w = boost::math::lambert_w_detail::lambert_w0_approx((std::numeric_limits<Real>::max)()); // Corless equation 4.19, page 349, and Chapeau-Blondeau equation 20, page 2162.
 218   std::cout << "w max " << max_w << std::endl; // 703.227
 219
 220   std::cout << "lambert_w0(7.2416706213544837e-163) = " << lambert_w0(7.2416706213544837e-163) << std::endl; //
 221   std::cout << "test integral 1/z^2" << std::endl;
 222   std::cout << "ULP = " << boost::math::ulp(1., policy<digits2<> >()) << std::endl; // ULP = 2.2204460492503131e-16
 223   std::cout << "ULP = " << boost::math::ulp(1e-10, policy<digits2<> >()) << std::endl; // ULP = 2.2204460492503131e-16
 224   std::cout << "ULP = " << boost::math::ulp(1., policy<digits2<11> >()) << std::endl; // ULP = 2.2204460492503131e-16
 225   std::cout << "epsilon =  " << std::numeric_limits<Real>::epsilon() << std::endl; //
 226   std::cout << "sqrt(max) =  " << sqrt(boost::math::tools::max_value<float>() ) << std::endl; // sqrt(max) =  1.8446742974197924e+19
 227   std::cout << "sqrt(min) =  " << sqrt(boost::math::tools::min_value<float>() ) << std::endl; // sqrt(min) =  1.0842021724855044e-19
 228
 229
 230
 231 // Demo debug version.
 232 Real tol = std::numeric_limits<Real>::epsilon();
 233 Real x;
 234 {
 235   using boost::math::quadrature::exp_sinh;
 236   exp_sinh<Real> es;
 237   // Function to be integrated, lambert_w0(1/z^2).
 238
 239     //auto f = [](Real z)->Real
 240     //{ // Naive - no protection against underflow and subsequent divide by zero.
 241     //  return lambert_w0<Real>(1 / (z * z));
 242     //};
 243     // Diagnostic is:
 244     // Error in function boost::math::lambert_w0<Real>: Expected a finite value but got inf
 245
 246     auto f = [](Real z)->Real
 247     { // Debug with diagnostics for underflow and subsequent divide by zero and other bad things.
 248       return debug_integration_proc(z);
 249     };
 250     // Exception Error in function boost::math::lambert_w0<double>: Expected a finite value but got inf.
 251
 252     // Unexpected exception thrown in integration code at abscissa: 7.2416706213544837e-163.
 253     // Unexpected exception thrown in integration code at abscissa (x): 3.478765835953569e-23.
 254     x = es.integrate(f);
 255     std::cout << "es.integrate(f) = " << x << std::endl;
 256     BOOST_CHECK_CLOSE_FRACTION(x, boost::math::constants::root_two_pi<Real>(), tol);
 257     // root_two_pi<double = 2.506628274631000502
 258   }
 259     */
 260
 261   test_integrals<cpp_bin_float_quad>();
 262   }
 263   catch (std::exception& ex)
 264   {
 265     std::cout << ex.what() << std::endl;
 266   }
 267 }
 268