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