ceph/src/boost/libs/math/test/test_lambert_w_integrals_float.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/math/special_functions/fpclassify.hpp> // isnan, isfinite.
  25 #include <boost/math/special_functions/next.hpp> // float_next, float_prior
  26 using boost::math::float_next;
  27 using boost::math::float_prior;
  28 #include <boost/math/special_functions/ulp.hpp>  // ulp
  29
  30 #include <boost/math/tools/test_value.hpp>  // for create_test_value and macro BOOST_MATH_TEST_VALUE.
  31 #include <boost/math/policies/policy.hpp>
  32 using boost::math::policies::digits2;
  33 using boost::math::policies::digits10;
  34 #include <boost/math/special_functions/lambert_w.hpp> // For Lambert W lambert_w function.
  35 using boost::math::lambert_wm1;
  36 using boost::math::lambert_w0;
  37
  38 #include <limits>
  39 #include <cmath>
  40 #include <typeinfo>
  41 #include <iostream>
  42 #include <type_traits>
  43 #include <exception>
  44
  45 std::string show_versions(void);
  46
  47 // Added code and test for Integral of the Lambert W function: by Nick Thompson.
  48 // https://en.wikipedia.org/wiki/Lambert_W_function#Definite_integrals
  49
  50 #include <boost/math/constants/constants.hpp> // for integral tests.
  51 #include <boost/math/quadrature/tanh_sinh.hpp> // for integral tests.
  52 #include <boost/math/quadrature/exp_sinh.hpp> // for integral tests.
  53
  54   using boost::math::policies::policy;
  55   using boost::math::policies::make_policy;
  56
  57 // using statements needed for changing error handling policy.
  58 using boost::math::policies::evaluation_error;
  59 using boost::math::policies::domain_error;
  60 using boost::math::policies::overflow_error;
  61 using boost::math::policies::ignore_error;
  62 using boost::math::policies::throw_on_error;
  63
  64 typedef policy<
  65   domain_error<throw_on_error>,
  66   overflow_error<ignore_error>
  67 > no_throw_policy;
  68
  69 // Assumes that function has a throw policy, for example:
  70 //    NOT lambert_w0<T>(1 / (x * x), no_throw_policy());
  71 // Error in function boost::math::quadrature::exp_sinh<double>::integrate:
  72 // The exp_sinh quadrature evaluated your function at a singular point and resulted in inf.
  73 // Please ensure your function evaluates to a finite number of its entire domain.
  74 template <typename T>
  75 T debug_integration_proc(T x)
  76 {
  77    T result; // warning C4701: potentially uninitialized local variable 'result' used
  78   // T result = 0 ; // But result may not be assigned below?
  79   try
  80   {
  81    // Assign function call to result in here...
  82     if (x <= sqrt(boost::math::tools::min_value<T>()) )
  83     {
  84       result = 0;
  85     }
  86     else
  87     {
  88       result = lambert_w0<T>(1 / (x * x));
  89     }
  90    // result = lambert_w0<T>(1 / (x * x), no_throw_policy());  // Bad idea, less helpful diagnostic message is:
  91     // Error in function boost::math::quadrature::exp_sinh<double>::integrate:
  92     // The exp_sinh quadrature evaluated your function at a singular point and resulted in inf.
  93     // Please ensure your function evaluates to a finite number of its entire domain.
  94
  95   } // try
  96   catch (const std::exception& e)
  97   {
  98     std::cout << "Exception " << e.what() << std::endl;
  99     // set breakpoint here:
 100     std::cout << "Unexpected exception thrown in integration code at abscissa (x): " << x << "." << std::endl;
 101     if (!std::isfinite(result))
 102     {
 103       // set breakpoint here:
 104       std::cout << "Unexpected non-finite result in integration code at abscissa (x): " << x << "." << std::endl;
 105     }
 106     if (std::isnan(result))
 107     {
 108       // set breakpoint here:
 109       std::cout << "Unexpected non-finite result in integration code at abscissa (x): " << x << "." << std::endl;
 110     }
 111   } // catch
 112   return result;
 113 } // T debug_integration_proc(T x)
 114
 115 template<class Real>
 116 void test_integrals()
 117 {
 118   // Integral of the Lambert W function:
 119   // https://en.wikipedia.org/wiki/Lambert_W_function
 120   using boost::math::quadrature::tanh_sinh;
 121   using boost::math::quadrature::exp_sinh;
 122   // file:///I:/modular-boost/libs/math/doc/html/math_toolkit/quadrature/double_exponential/de_tanh_sinh.html
 123   using std::sqrt;
 124
 125   std::cout << "Integration of type " << typeid(Real).name()  << std::endl;
 126
 127   Real tol = std::numeric_limits<Real>::epsilon();
 128   { //  // Integrate for function lambert_W0(z);
 129     tanh_sinh<Real> ts;
 130     Real a = 0;
 131     Real b = boost::math::constants::e<Real>();
 132     auto f = [](Real z)->Real
 133     {
 134       return lambert_w0<Real>(z);
 135     };
 136     Real z = ts.integrate(f, a, b); // OK without any decltype(f)
 137     BOOST_CHECK_CLOSE_FRACTION(z, boost::math::constants::e<Real>() - 1, tol * 3);
 138   }
 139   {
 140     // Integrate for function lambert_W0(z/(z sqrt(z)).
 141     exp_sinh<Real> es;
 142     auto f = [](Real z)->Real
 143     {
 144       return lambert_w0<Real>(z)/(z * sqrt(z));
 145     };
 146     Real z = es.integrate(f); // OK
 147     BOOST_CHECK_CLOSE_FRACTION(z, 2 * boost::math::constants::root_two_pi<Real>(), tol);
 148   }
 149   {
 150     // Integrate for function lambert_W0(1/z^2).
 151     exp_sinh<Real> es;
 152     //const Real sqrt_min = sqrt(boost::math::tools::min_value<Real>()); // 1.08420217e-19 fo 32-bit float.
 153     // error C3493: 'sqrt_min' cannot be implicitly captured because no default capture mode has been specified
 154     auto f = [](Real z)->Real
 155     {
 156       if (z <= sqrt(boost::math::tools::min_value<Real>()) )
 157       { // Too small would underflow z * z and divide by zero to overflow 1/z^2 for lambert_w0 z parameter.
 158         return static_cast<Real>(0);
 159       }
 160       else
 161       {
 162         return lambert_w0<Real>(1 / (z * z)); // warning C4756: overflow in constant arithmetic, even though cannot happen.
 163       }
 164     };
 165     Real z = es.integrate(f);
 166     BOOST_CHECK_CLOSE_FRACTION(z, boost::math::constants::root_two_pi<Real>(), tol);
 167   }
 168 } // template<class Real> void test_integrals()
 169
 170
 171 BOOST_AUTO_TEST_CASE( integrals )
 172 {
 173   std::cout << "Macro BOOST_MATH_LAMBERT_W0_INTEGRALS is defined." << std::endl;
 174   BOOST_TEST_MESSAGE("\nTest Lambert W0 integrals.");
 175   try
 176   {
 177   // using statements needed to change precision policy.
 178   using boost::math::policies::policy;
 179   using boost::math::policies::make_policy;
 180   using boost::math::policies::precision;
 181   using boost::math::policies::digits2;
 182   using boost::math::policies::digits10;
 183
 184   // using statements needed for changing error handling policy.
 185   using boost::math::policies::evaluation_error;
 186   using boost::math::policies::domain_error;
 187   using boost::math::policies::overflow_error;
 188   using boost::math::policies::ignore_error;
 189   using boost::math::policies::throw_on_error;
 190
 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<float>();
 260   }
 261   catch (std::exception& ex)
 262   {
 263     std::cout << ex.what() << std::endl;
 264   }
 265 }
 266