numbers.h

// ---------------------------------------------------------------------
//
// Copyright (C) 2006 - 2018 by the deal.II authors
//
// This file is part of the deal.II library.
//
// The deal.II library is free software; you can use it, redistribute
// it, and/or modify it under the terms of the GNU Lesser General
// Public License as published by the Free Software Foundation; either
// version 2.1 of the License, or (at your option) any later version.
// The full text of the license can be found in the file LICENSE at
// the top level of the deal.II distribution.
//
// ---------------------------------------------------------------------

#ifndef dealii_numbers_h
#define dealii_numbers_h


#include <deal.II/base/config.h>
#include <deal.II/base/types.h>

#include <cmath>
#include <cstdlib>
#include <complex>

#ifdef DEAL_II_WITH_CUDA
#  include <cuda_runtime_api.h>
#  define DEAL_II_CUDA_HOST_DEV __host__ __device__
#else
#  define DEAL_II_CUDA_HOST_DEV
#endif

DEAL_II_NAMESPACE_OPEN

// forward declarations to support abs or sqrt operations on VectorizedArray
template <typename Number> class VectorizedArray;
template <typename T> struct EnableIfScalar;

DEAL_II_NAMESPACE_CLOSE

// Declare / Import auto-differentiable math functions in(to) standard
// namespace before numbers::NumberTraits is defined
#ifdef DEAL_II_WITH_ADOLC
#include <adolc/adouble.h> // Taped double
#include <deal.II/differentiation/ad/adolc_math.h>
#endif
// Ideally we'd like to #include <deal.II/differentiation/ad/sacado_math.h>
// but header indirectly references numbers.h. We therefore simply
// import the whole Sacado header at this point to get the math
// functions imported into the standard namespace.
#ifdef DEAL_II_WITH_TRILINOS
#include <Sacado.hpp>
#endif

namespace std
{
  template <typename Number> DEAL_II_ALWAYS_INLINE ::VectorizedArray<Number>
  sqrt(const ::VectorizedArray<Number> &);
  template <typename Number> DEAL_II_ALWAYS_INLINE ::VectorizedArray<Number>
  abs(const ::VectorizedArray<Number> &);
  template <typename Number> DEAL_II_ALWAYS_INLINE ::VectorizedArray<Number>
  max(const ::VectorizedArray<Number> &, const ::VectorizedArray<Number> &);
  template <typename Number> DEAL_II_ALWAYS_INLINE ::VectorizedArray<Number>
  min (const ::VectorizedArray<Number> &, const ::VectorizedArray<Number> &);
  template <typename Number> ::VectorizedArray<Number>
  pow(const ::VectorizedArray<Number> &, const Number p);
  template <typename Number> ::VectorizedArray<Number>
  sin(const ::VectorizedArray<Number> &);
  template <typename Number> ::VectorizedArray<Number>
  cos(const ::VectorizedArray<Number> &);
  template <typename Number> ::VectorizedArray<Number>
  tan(const ::VectorizedArray<Number> &);
  template <typename Number> ::VectorizedArray<Number>
  exp(const ::VectorizedArray<Number> &);
  template <typename Number> ::VectorizedArray<Number>
  log(const ::VectorizedArray<Number> &);
}

DEAL_II_NAMESPACE_OPEN

namespace numbers
{
  static const double  E       = 2.7182818284590452354;

  static const double  LOG2E   = 1.4426950408889634074;

  static const double  LOG10E  = 0.43429448190325182765;

  static const double  LN2     = 0.69314718055994530942;

  static const double  LN10    = 2.30258509299404568402;

  static const double  PI      = 3.14159265358979323846;

  static const double  PI_2    = 1.57079632679489661923;

  static const double  PI_4    = 0.78539816339744830962;

  static const double  SQRT2   = 1.41421356237309504880;

  static const double  SQRT1_2 = 0.70710678118654752440;

  DEAL_II_DEPRECATED
  bool is_nan (const double x);

  bool is_finite (const double x);

  bool is_finite (const std::complex<double> &x);

  bool is_finite (const std::complex<float> &x);

  bool is_finite (const std::complex<long double> &x);

  template <typename Number1,typename Number2>
  bool
  values_are_equal (const Number1 &value_1, const Number2 &value_2);

  template <typename Number1,typename Number2>
  bool
  values_are_not_equal (const Number1 &value_1, const Number2 &value_2);

  template <typename Number>
  bool
  value_is_zero (const Number &value);

  template <typename Number1,typename Number2>
  bool
  value_is_less_than (const Number1 &value_1, const Number2 &value_2);

  template <typename Number1,typename Number2>
  bool
  value_is_less_than_or_equal_to (const Number1 &value_1, const Number2 &value_2);



  template <typename Number1,typename Number2>
  bool
  value_is_greater_than (const Number1 &value_1, const Number2 &value_2);

  template <typename Number1,typename Number2>
  bool
  value_is_greater_than_or_equal_to (const Number1 &value_1, const Number2 &value_2);

  template <typename number>
  struct NumberTraits
  {
    static const bool is_complex = false;

    typedef number real_type;

    static
    DEAL_II_CUDA_HOST_DEV
    const number &conjugate (const number &x);

    static
    DEAL_II_CUDA_HOST_DEV
    real_type abs_square (const number &x);

    static
    real_type abs (const number &x);
  };


  template <typename number>
  struct NumberTraits<std::complex<number> >
  {
    static const bool is_complex = true;

    typedef number real_type;

    static
    std::complex<number> conjugate (const std::complex<number> &x);

    static
    real_type abs_square (const std::complex<number> &x);


    static
    real_type abs (const std::complex<number> &x);
  };

  // --------------- inline and template functions ---------------- //

  inline bool is_nan (const double x)
  {
    return std::isnan(x);
  }

  inline bool is_finite (const double x)
  {
    return std::isfinite(x);
  }



  inline bool is_finite (const std::complex<double> &x)
  {
    // Check complex numbers for infinity
    // by testing real and imaginary part
    return ( is_finite (x.real())
             &&
             is_finite (x.imag()) );
  }



  inline bool is_finite (const std::complex<float> &x)
  {
    // Check complex numbers for infinity
    // by testing real and imaginary part
    return ( is_finite (x.real())
             &&
             is_finite (x.imag()) );
  }



  inline bool is_finite (const std::complex<long double> &x)
  {
    // Same for std::complex<long double>
    return ( is_finite (x.real())
             &&
             is_finite (x.imag()) );
  }


  template <typename number>
  DEAL_II_CUDA_HOST_DEV
  const number &
  NumberTraits<number>::conjugate (const number &x)
  {
    return x;
  }



  template <typename number>
  DEAL_II_CUDA_HOST_DEV
  typename NumberTraits<number>::real_type
  NumberTraits<number>::abs_square (const number &x)
  {
    return x * x;
  }



  template <typename number>
  typename NumberTraits<number>::real_type
  NumberTraits<number>::abs (const number &x)
  {
    return std::abs(x);
  }



  template <typename number>
  std::complex<number>
  NumberTraits<std::complex<number> >::conjugate (const std::complex<number> &x)
  {
    return std::conj(x);
  }



  template <typename number>
  typename NumberTraits<std::complex<number> >::real_type
  NumberTraits<std::complex<number> >::abs (const std::complex<number> &x)
  {
    return std::abs(x);
  }



  template <typename number>
  typename NumberTraits<std::complex<number> >::real_type
  NumberTraits<std::complex<number> >::abs_square (const std::complex<number> &x)
  {
    return std::norm (x);
  }

}


// Forward declarations
namespace Differentiation
{
  namespace AD
  {

    namespace internal
    {
      // Defined in differentiation/ad/ad_number_traits.h
      template <typename T>
      struct NumberType;
    }

    // Defined in differentiation/ad/ad_number_traits.h
    template <typename NumberType>
    struct is_ad_number;
  }
}


namespace internal
{
  template<typename From, typename To>
  struct is_explicitly_convertible
  {
    // Source: https://stackoverflow.com/a/16944130
  private:
    template<typename T>
    static void f(T);

    template<typename F, typename T>
    static constexpr auto test(int) ->
    decltype(f(static_cast<T>(std::declval<F>())),true)
    {
      return true;
    }

    template<typename F, typename T>
    static constexpr auto test(...) -> bool
    {
      return false;
    }

  public:

    static bool const value = test<From,To>(0);
  };

  template <typename T>
  struct NumberType
  {
    static DEAL_II_CUDA_HOST_DEV const T &value (const T &t)
    {
      return t;
    }

    // Below are generic functions that allows an overload for any
    // type U that is transformable to type T. This is particularly
    // useful when needing to cast exotic number types
    // (e.g. auto-differentiable or symbolic numbers) to a floating
    // point one, such as might  happen when converting between tensor
    // types.

    // Type T is constructible from F.
    template<typename F>
    static T
    value (const F &f,
           typename std::enable_if<
           !std::is_same<typename std::decay<T>::type,typename std::decay<F>::type>::value &&
           std::is_constructible<T,F>::value
           >::type * = nullptr)
    {
      return T(f);
    }

    // Type T is explicitly convertible (but not constructible) from F.
    template<typename F>
    static T
    value (const F &f,
           typename std::enable_if<
           !std::is_same<typename std::decay<T>::type,typename std::decay<F>::type>::value &&
           !std::is_constructible<T,F>::value &&
           is_explicitly_convertible<const F,T>::value
           >::type * = nullptr)
    {
      return static_cast<T>(f);
    }

    // Sacado doesn't provide any conversion operators, so we have
    // to extract the value and perform further conversions from there.
    // To be safe, we extend this to other possible AD numbers that
    // might fall into the same category.
    template<typename F>
    static T
    value (const F &f,
           typename std::enable_if<
           !std::is_same<typename std::decay<T>::type,typename std::decay<F>::type>::value &&
           !std::is_constructible<T,F>::value &&
           !is_explicitly_convertible<const F,T>::value &&
           Differentiation::AD::is_ad_number<F>::value
           >::type * = nullptr)
    {
      return Differentiation::AD::internal::NumberType<T>::value(f);
    }

  };

  template <typename T>
  struct NumberType<std::complex<T> >
  {
    static const std::complex<T> &value (const std::complex<T> &t)
    {
      return t;
    }

    static std::complex<T> value (const T &t)
    {
      return std::complex<T>(t);
    }

    // Facilitate cast from complex<double> to complex<float>
    template <typename U>
    static std::complex<T> value (const std::complex<U> &t)
    {
      return std::complex<T>(
               NumberType<T>::value(t.real()),
               NumberType<T>::value(t.imag()));
    }
  };
}

namespace numbers
{

#ifdef DEAL_II_ADOLC_WITH_ADVANCED_BRANCHING

  // Defined in differentiation/ad/adolc_number_types.cc
  bool
  values_are_equal (const adouble &value_1,
                    const adouble &value_2);


  template <typename Number>
  bool
  values_are_equal (const adouble &value_1,
                    const Number  &value_2)
  {
    // Use the specialized definition for two Adol-C taped types
    return values_are_equal(value_1, internal::NumberType<adouble>::value(value_2));
  }


  template <typename Number>
  bool
  values_are_equal (const Number  &value_1,
                    const adouble &value_2)
  {
    // Use the above definition
    return values_are_equal(value_2, value_1);
  }

  // Defined in differentiation/ad/adolc_number_types.cc
  bool
  value_is_less_than (const adouble &value_1,
                      const adouble &value_2);


  template <typename Number>
  bool
  value_is_less_than (const adouble &value_1,
                      const Number  &value_2)
  {
    // Use the specialized definition for two Adol-C taped types
    return value_is_less_than(value_1, internal::NumberType<adouble>::value(value_2));
  }


  template <typename Number>
  bool
  value_is_less_than (const Number  &value_1,
                      const adouble &value_2)
  {
    // Use the specialized definition for two Adol-C taped types
    return value_is_less_than(internal::NumberType<adouble>::value(value_1), value_2);
  }

#endif


  template <typename Number1,typename Number2>
  inline bool
  values_are_equal (const Number1 &value_1, const Number2 &value_2)
  {
    return (value_1 == internal::NumberType<Number1>::value(value_2));
  }


  template <typename Number1,typename Number2>
  inline bool
  values_are_not_equal (const Number1 &value_1, const Number2 &value_2)
  {
    return !(values_are_equal(value_1,value_2));
  }


  template <typename Number>
  inline bool
  value_is_zero (const Number &value)
  {
    return values_are_equal(value, 0.0);
  }


  template <typename Number1,typename Number2>
  inline bool
  value_is_less_than (const Number1 &value_1, const Number2 &value_2)
  {
    return (value_1 < internal::NumberType<Number1>::value(value_2));
  }


  template <typename Number1,typename Number2>
  inline bool
  value_is_less_than_or_equal_to (const Number1 &value_1, const Number2 &value_2)
  {
    return (value_is_less_than(value_1,value_2) || values_are_equal(value_1,value_2));
  }


  template <typename Number1,typename Number2>
  bool
  value_is_greater_than (const Number1 &value_1, const Number2 &value_2)
  {
    return !(value_is_less_than_or_equal_to(value_1,value_2));
  }


  template <typename Number1,typename Number2>
  inline bool
  value_is_greater_than_or_equal_to (const Number1 &value_1, const Number2 &value_2)
  {
    return !(value_is_less_than(value_1,value_2));
  }
}

DEAL_II_NAMESPACE_CLOSE

#endif