math.hh

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// -*- tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 2 -*-
// vi: set et ts=4 sw=2 sts=2:
#ifndef DUNE_MATH_HH
#define DUNE_MATH_HH
 
#include <cmath>
#include <complex>
#include <limits>
#include <type_traits>
 
#include <dune/common/typeutilities.hh>
 
namespace Dune
{
 
  template< class T >
  struct StandardMathematicalConstants
  {
    static const T e ()
    {
      using std::exp;
      static const T e = exp( T( 1 ) );
      return e;
    }
 
    static const T pi ()
    {
      using std::acos;
      static const T pi = acos( T( -1 ) );
      return pi;
    }
  };
 
 
  template< class Field >
  struct MathematicalConstants
    : public StandardMathematicalConstants<Field>
  {};
 
 
  template <class Mantissa, class Exponent>
  constexpr Mantissa power(Mantissa m, Exponent p)
  {
    static_assert(std::numeric_limits<Exponent>::is_integer, "Exponent must be an integer type!");
 
    auto result = Mantissa(1);
    auto absp = (p<0) ? -p : p;   // This is simply abs, but std::abs is not constexpr
    for (Exponent i = Exponent(0); i<absp; i++)
      result *= m;
 
    if (p<0)
      result = Mantissa(1)/result;
 
    return result;
  }
 
  template <int m>
  struct Factorial
  {
    enum { factorial = m * Factorial<m-1>::factorial };
  };
 
  template <>
  struct Factorial<0>
  {
    // 0! = 1
    enum { factorial = 1 };
  };
 
 
  // T has to be an integral type
  template<class T>
  constexpr inline static T factorial(const T& n) noexcept
  {
    static_assert(std::numeric_limits<T>::is_integer, "`factorial(n)` has to be called with an integer type.");
    T fac = 1;
    for(T k = 0; k < n; ++k)
      fac *= k+1;
    return fac;
  }
 
  template<class T, T n>
  constexpr inline static auto factorial (std::integral_constant<T, n>) noexcept
  {
    return std::integral_constant<T, factorial(n)>{};
  }
 
 
  // T has to be an integral type
  template<class T>
  constexpr inline static T binomial (const T& n, const T& k) noexcept
  {
    static_assert(std::numeric_limits<T>::is_integer, "`binomial(n, k)` has to be called with an integer type.");
 
    if( k < 0 || k > n )
      return 0;
 
    if (2*k > n)
      return binomial(n, n-k);
 
    T bin = 1;
    for(auto i = n-k; i < n; ++i)
      bin *= i+1;
    return bin / factorial(k);
  }
 
  template<class T, T n, T k>
  constexpr inline static auto binomial (std::integral_constant<T, n>, std::integral_constant<T, k>) noexcept
  {
    return std::integral_constant<T, binomial(n, k)>{};
  }
 
  template<class T, T n>
  constexpr inline static auto binomial (std::integral_constant<T, n>, std::integral_constant<T, n>) noexcept
  {
    return std::integral_constant<T, (n >= 0 ? 1 : 0)>{};
  }
 
 
  // conjugate complex does nothing for non-complex types
  template<class K>
  inline K conjugateComplex (const K& x)
  {
    return x;
  }
 
#ifndef DOXYGEN
  // specialization for complex
  template<class K>
  inline std::complex<K> conjugateComplex (const std::complex<K>& c)
  {
    return std::complex<K>(c.real(),-c.imag());
  }
#endif
 
  template <class T>
  int sign(const T& val)
  {
    return (val < 0 ? -1 : 1);
  }
 
 
  namespace Impl {
    // Returns whether a given type behaves like std::complex<>, i.e. whether
    // real() and imag() are defined
    template<class T>
    struct isComplexLike {
      private:
        template<class U>
        static auto test(U* u) -> decltype(u->real(), u->imag(), std::true_type());
 
        template<class U>
        static auto test(...) -> decltype(std::false_type());
 
      public:
        static const bool value = decltype(test<T>(0))::value;
    };
  } // namespace Impl
 
 
  namespace MathOverloads {
 
    struct ADLTag {};
 
#define DUNE_COMMON_MATH_ISFUNCTION(function, stdfunction)         \
    template<class T>                                              \
    auto function(const T &t, PriorityTag<1>, ADLTag)              \
                  -> decltype(function(t)) {                       \
      return function(t);                                          \
    }                                                              \
    template<class T>                                              \
    auto function(const T &t, PriorityTag<0>, ADLTag) {            \
      using std::stdfunction;                                      \
      return stdfunction(t);                                       \
    }                                                              \
    static_assert(true, "Require semicolon to unconfuse editors")
 
    DUNE_COMMON_MATH_ISFUNCTION(isNaN,isnan);
    DUNE_COMMON_MATH_ISFUNCTION(isInf,isinf);
    DUNE_COMMON_MATH_ISFUNCTION(isFinite,isfinite);
#undef DUNE_COMMON_MATH_ISFUNCTION
 
    template<class T>
    auto isUnordered(const T &t1, const T &t2, PriorityTag<1>, ADLTag)
                  -> decltype(isUnordered(t1, t2)) {
      return isUnordered(t1, t2);
    }
 
    template<class T>
    auto isUnordered(const T &t1, const T &t2, PriorityTag<0>, ADLTag) {
      using std::isunordered;
      return isunordered(t1, t2);
    }
  }
 
  namespace MathImpl {
 
    // NOTE: it is important that these functors have names different from the
    // names of the functions they are forwarding to.  Otherwise the
    // unqualified call would find the functor type, not a function, and ADL
    // would never be attempted.
#define DUNE_COMMON_MATH_ISFUNCTION_FUNCTOR(function)                    \
    struct function##Impl {                                              \
      template<class T>                                                  \
      constexpr auto operator()(const T &t) const {                      \
        return function(t, PriorityTag<10>{}, MathOverloads::ADLTag{});  \
      }                                                                  \
    };                                                                   \
    static_assert(true, "Require semicolon to unconfuse editors")
 
    DUNE_COMMON_MATH_ISFUNCTION_FUNCTOR(isNaN);
    DUNE_COMMON_MATH_ISFUNCTION_FUNCTOR(isInf);
    DUNE_COMMON_MATH_ISFUNCTION_FUNCTOR(isFinite);
#undef DUNE_COMMON_MATH_ISFUNCTION_FUNCTOR
 
    struct isUnorderedImpl {
      template<class T>
      constexpr auto operator()(const T &t1, const T &t2) const {
        return isUnordered(t1, t2, PriorityTag<10>{}, MathOverloads::ADLTag{});
      }
    };
 
  } //MathImpl
 
 
  namespace Impl {
    /* This helper has a math functor as a static constexpr member.  Doing
       this as a static member of a template struct means we can do this
       without violating the ODR or putting the definition into a seperate
       compilation unit, while still still ensuring the functor is the same
       lvalue across all compilation units.
     */
    template<class T>
    struct MathDummy
    {
      static constexpr T value{};
    };
 
    template<class T>
    constexpr T MathDummy<T>::value;
 
  } //namespace Impl
 
  namespace {
    /* Provide the math functors directly in the `Dune` namespace.
 
       This actually declares a different name in each translation unit, but
       they all resolve to the same lvalue.
    */
 
 
    constexpr auto const &isNaN = Impl::MathDummy<MathImpl::isNaNImpl>::value;
 
 
    constexpr auto const &isInf = Impl::MathDummy<MathImpl::isInfImpl>::value;
 
 
    constexpr auto const &isFinite = Impl::MathDummy<MathImpl::isFiniteImpl>::value;
 
 
    constexpr auto const &isUnordered = Impl::MathDummy<MathImpl::isUnorderedImpl>::value;
  }
 
  namespace MathOverloads {
    /*Overloads for complex types*/
    template<class T, class = std::enable_if_t<Impl::isComplexLike<T>::value> >
    auto isNaN(const T &t, PriorityTag<2>, ADLTag) {
      return Dune::isNaN(real(t)) || Dune::isNaN(imag(t));
    }
 
    template<class T, class = std::enable_if_t<Impl::isComplexLike<T>::value> >
    auto isInf(const T &t, PriorityTag<2>, ADLTag) {
      return Dune::isInf(real(t)) || Dune::isInf(imag(t));
    }
 
    template<class T, class = std::enable_if_t<Impl::isComplexLike<T>::value> >
    auto isFinite(const T &t, PriorityTag<2>, ADLTag) {
      return Dune::isFinite(real(t)) && Dune::isFinite(imag(t));
    }
  } //MathOverloads
}
 
#endif // #ifndef DUNE_MATH_HH