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src/boost/math/special_functions/detail/erf_inv.hpp  view on Meta::CPAN

   {
      init()
      {
         do_init();
      }
      static void do_init()
      {
         boost::math::erf_inv(static_cast<T>(0.25), Policy());
         boost::math::erf_inv(static_cast<T>(0.55), Policy());
         boost::math::erf_inv(static_cast<T>(0.95), Policy());
         boost::math::erfc_inv(static_cast<T>(1e-15), Policy());
         if(static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1e-130)) != 0)
            boost::math::erfc_inv(static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1e-130)), Policy());

         // Some compilers choke on constants that would underflow, even in code that isn't instantiated
         // so try and filter these cases out in the preprocessor:
#if LDBL_MAX_10_EXP >= 800
         if(static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1e-800)) != 0)
            boost::math::erfc_inv(static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1e-800)), Policy());
         if(static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1e-900)) != 0)
            boost::math::erfc_inv(static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1e-900)), Policy());
#else
         if(static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 64, 1e-800)) != 0)
            boost::math::erfc_inv(static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 64, 1e-800)), Policy());
         if(static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 64, 1e-900)) != 0)
            boost::math::erfc_inv(static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 64, 1e-900)), Policy());
#endif
      }
      void force_instantiate()const{}
   };
   static const init initializer;
   static void force_instantiate()
   {
      initializer.force_instantiate();
   }
};

template <class T, class Policy>
const typename erf_inv_initializer<T, Policy>::init erf_inv_initializer<T, Policy>::initializer;

} // namespace detail

template <class T, class Policy>
typename tools::promote_args<T>::type erfc_inv(T z, const Policy& pol)
{
   typedef typename tools::promote_args<T>::type result_type;

   //
   // Begin by testing for domain errors, and other special cases:
   //
   static const char* function = "boost::math::erfc_inv<%1%>(%1%, %1%)";
   if((z < 0) || (z > 2))
      policies::raise_domain_error<result_type>(function, "Argument outside range [0,2] in inverse erfc function (got p=%1%).", z, pol);
   if(z == 0)
      return policies::raise_overflow_error<result_type>(function, 0, pol);
   if(z == 2)
      return -policies::raise_overflow_error<result_type>(function, 0, pol);
   //
   // Normalise the input, so it's in the range [0,1], we will
   // negate the result if z is outside that range.  This is a simple
   // application of the erfc reflection formula: erfc(-z) = 2 - erfc(z)
   //
   result_type p, q, s;
   if(z > 1)
   {
      q = 2 - z;
      p = 1 - q;
      s = -1;
   }
   else
   {
      p = 1 - z;
      q = z;
      s = 1;
   }
   //
   // A bit of meta-programming to figure out which implementation
   // to use, based on the number of bits in the mantissa of T:
   //
   typedef typename policies::precision<result_type, Policy>::type precision_type;
   typedef typename mpl::if_<
      mpl::or_<mpl::less_equal<precision_type, mpl::int_<0> >, mpl::greater<precision_type, mpl::int_<64> > >,
      mpl::int_<0>,
      mpl::int_<64>
   >::type tag_type;
   //
   // Likewise use internal promotion, so we evaluate at a higher
   // precision internally if it's appropriate:
   //
   typedef typename policies::evaluation<result_type, Policy>::type eval_type;
   typedef typename policies::normalise<
      Policy, 
      policies::promote_float<false>, 
      policies::promote_double<false>, 
      policies::discrete_quantile<>,
      policies::assert_undefined<> >::type forwarding_policy;

   detail::erf_inv_initializer<eval_type, forwarding_policy>::force_instantiate();

   //
   // And get the result, negating where required:
   //
   return s * policies::checked_narrowing_cast<result_type, forwarding_policy>(
      detail::erf_inv_imp(static_cast<eval_type>(p), static_cast<eval_type>(q), forwarding_policy(), static_cast<tag_type const*>(0)), function);
}

template <class T, class Policy>
typename tools::promote_args<T>::type erf_inv(T z, const Policy& pol)
{
   typedef typename tools::promote_args<T>::type result_type;

   //
   // Begin by testing for domain errors, and other special cases:
   //
   static const char* function = "boost::math::erf_inv<%1%>(%1%, %1%)";
   if((z < -1) || (z > 1))
      policies::raise_domain_error<result_type>(function, "Argument outside range [-1, 1] in inverse erf function (got p=%1%).", z, pol);
   if(z == 1)
      return policies::raise_overflow_error<result_type>(function, 0, pol);
   if(z == -1)
      return -policies::raise_overflow_error<result_type>(function, 0, pol);
   if(z == 0)
      return 0;
   //
   // Normalise the input, so it's in the range [0,1], we will
   // negate the result if z is outside that range.  This is a simple
   // application of the erf reflection formula: erf(-z) = -erf(z)
   //
   result_type p, q, s;
   if(z < 0)
   {
      p = -z;
      q = 1 - p;
      s = -1;
   }
   else
   {
      p = z;
      q = 1 - z;
      s = 1;
   }
   //
   // A bit of meta-programming to figure out which implementation
   // to use, based on the number of bits in the mantissa of T:
   //
   typedef typename policies::precision<result_type, Policy>::type precision_type;
   typedef typename mpl::if_<
      mpl::or_<mpl::less_equal<precision_type, mpl::int_<0> >, mpl::greater<precision_type, mpl::int_<64> > >,
      mpl::int_<0>,
      mpl::int_<64>
   >::type tag_type;
   //
   // Likewise use internal promotion, so we evaluate at a higher
   // precision internally if it's appropriate:
   //
   typedef typename policies::evaluation<result_type, Policy>::type eval_type;
   typedef typename policies::normalise<
      Policy, 
      policies::promote_float<false>, 
      policies::promote_double<false>, 
      policies::discrete_quantile<>,
      policies::assert_undefined<> >::type forwarding_policy;
   //
   // Likewise use internal promotion, so we evaluate at a higher
   // precision internally if it's appropriate:
   //
   typedef typename policies::evaluation<result_type, Policy>::type eval_type;

   detail::erf_inv_initializer<eval_type, forwarding_policy>::force_instantiate();
   //
   // And get the result, negating where required:
   //
   return s * policies::checked_narrowing_cast<result_type, forwarding_policy>(
      detail::erf_inv_imp(static_cast<eval_type>(p), static_cast<eval_type>(q), forwarding_policy(), static_cast<tag_type const*>(0)), function);
}

template <class T>
inline typename tools::promote_args<T>::type erfc_inv(T z)
{
   return erfc_inv(z, policies::policy<>());
}

template <class T>
inline typename tools::promote_args<T>::type erf_inv(T z)
{
   return erf_inv(z, policies::policy<>());
}