/*--------------------------------------------------------------------*/
/*     Copyright (C) 2004-2016  Serge Iovleff

    This program is free software; you can 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 of the
    License, or (at your option) any later version.

    This program is distributed in the hope that it will be useful,
    but WITHOUT ANY WARRANTY; without even the implied warranty of
    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
    GNU Lesser General Public License for more details.

    You should have received a copy of the GNU Lesser General Public
    License along with this program; if not, write to the
    Free Software Foundation, Inc.,
    59 Temple Place,
    Suite 330,
    Boston, MA 02111-1307
    USA

    Contact : S..._Dot_I..._At_stkpp_Dot_org (see copyright for ...)
*/

/*
 * Project:  STKernel::Arithmetic
 * Purpose:  DSefine template arithmetic for handling special values (NA).
 * Author:   Serge Iovleff, S..._Dot_I..._At_stkpp_Dot_org (see copyright for ...)
 **/

/** @file STK_Arithmetic.h
 *  @brief In this file we define for the template class Arithmetic for
 *  handling the greatest, lowest, NA,... values of all types.
 **/

#ifndef STK_ARITHMETIC_H
#define STK_ARITHMETIC_H

#include <climits>

namespace STK
{
/** @ingroup Arithmetic
  *  @brief Arithmetic properties of STK fundamental types.
  *
  *  This class allows a program to obtain information about the
  *  representation of a STK fundamental type on a given platform. For
  *  non-fundamental STK types, the functions will return 0 and the data
  *  members will all be @c false.
  *
  *  -# A NA (Not Available) type is defined. If the fundamental
  *  type have a quiet_NaN, a NA is a quiet_NaN and
  *  the quiet_NaN is no more available.
  *  -# If the fundamental type does not have a NaN, the greatest value
  *  is used.
  *  -# If the fundamental type is an Integral type (@c union), a NA is
  *  the value (if any) defined in the declaration.
  *
  *  The class arithmetic<Type> inherit from @c std::numeric_limits<Type>
  *  whom which we give hereafter the definition.
    @code
    template<typename _Tp>
    struct numeric_limits
    {
      // This will be true for all fundamental types (which have
      // specializations), and false for everything else.
      static const bool is_specialized = false;

      // The number of @c radix digits that be represented without change:  for
      // integer types, the number of non-sign bits in the mantissa; for
      // floating types, the number of @c radix digits in the mantissa.
      static const int digits = 0;

      // The number of base 10 digits that can be represented without change.
      static const int digits10 = 0;

      // True if the type is signed.
      static const bool is_signed = false;

      // True if the type is integer.
      static const bool is_integer = false;

      // True if the type uses an exact representation.  "All integer types are
      //  exact, but not all exact types are integer.  For example, rational and
      //  fixed-exponent representations are exact but not integer."
      //  [18.2.1.2]/15
      static const bool is_exact = false;

      // For integer types, specifies the base of the representation.  For
      // floating types, specifies the base of the exponent representation.
      static const int radix = 0;

      // The minimum negative integer such that @c radix raised to the power of
      // (one less than that integer) is a normalized floating point number.
      static const int min_exponent = 0;

      // The minimum negative integer such that 10 raised to that power is in
      // the range of normalized floating point numbers.
      static const int min_exponent10 = 0;

      // The maximum positive integer such that @c radix raised to the power of
      // (one less than that integer) is a representable finite floating point
      // number.
      static const int max_exponent = 0;

      // The maximum positive integer such that 10 raised to that power is in
      //    the range of representable finite floating point numbers.
      static const int max_exponent10 = 0;

      // True if the type has a representation for positive infinity.
      static const bool has_infinity = false;

      // True if the type has a representation for a quiet (non-signaling)
      // "Not a Number."
      static const bool has_quiet_NaN = false;

      // True if the type has a representation for a signaling
      //    "Not a Number."
      static const bool has_signaling_NaN = false;

      // See std::float_denorm_style for more information.
      static const float_denorm_style has_denorm = denorm_absent;

      // "True if loss of accuracy is detected as a denormalization loss,
      //    rather than as an inexact result." [18.2.1.2]/42
      static const bool has_denorm_loss = false;

      // True if-and-only-if the type adheres to the IEC 559 standard, also
      // known as IEEE 754.  (Only makes sense for floating point types.)
      static const bool is_iec559 = false;

      // "True if the set of values representable by the type is finite. All
      // built-in types are bounded, this member would be false for arbitrary
      // precision types." [18.2.1.2]/54
      static const bool is_bounded = false;

      // True if the type is @e modulo, that is, if it is possible to add two
      // positive numbers and have a result that wraps around to a third number
      // that is less.  Typically false for floating types, true for unsigned
      // integers, and true for signed integers.
      static const bool is_modulo = false;

      // True if trapping is implemented for this type.
      static const bool traps = false;

      /// True if tinyness is detected before rounding.  (see IEC 559)
      static const bool tinyness_before = false;

      // See std::float_round_style for more information.  This is only
      // meaningful for floating types; integer types will all be
      // round_toward_zero.
      static const float_round_style round_style = round_toward_zero;

      // The minimum finite value, or for floating types with
      // denormalization, the minimum positive normalized value.
      static _Tp min() throw() { return static_cast<_Tp>(0); }

      // The maximum finite value.
      static _Tp max() throw() { return static_cast<_Tp>(0); }

      // The @e machine @e epsilon:  the difference between 1 and the least
      //value greater than 1 that is representable.
      static _Tp epsilon() throw() { return static_cast<_Tp>(0); }

      // The maximum rounding error measurement (see LIA-1).
      static _Tp round_error() throw() { return static_cast<_Tp>(0); }

      // The representation of positive infinity, if @c has_infinity.
      static _Tp infinity() throw()  { return static_cast<_Tp>(0); }

      // The representation of a quiet "Not a Number," if @c has_quiet_NaN.
      static _Tp quiet_NaN() throw() { return static_cast<_Tp>(0); }

      // The representation of a signaling "Not a Number," if
      // @c has_signaling_NaN.
      static _Tp signaling_NaN() throw() { return static_cast<_Tp>(0); }

      // The minimum positive denormalized value.  For types where
      // @c has_denorm is false, this is the minimum positive normalized
      //  value.
      static _Tp denorm_min() throw() { return static_cast<_Tp>(0); }
  };
  @endcode
  *
  **/
template<class Type>
struct Arithmetic: public std::numeric_limits<Type>
{
  /** True if the type has a representation for a "Not Available."    */
  static const bool hasNA = false;
  /** Adding a Non Available (NA) special number
   * @return the NA value of the type @c Type
   **/
  static inline Type NA() throw() { return static_cast<Type>(0);}
  /** @param x the value to test.
   *  @return @c true if the parameter @c x is a NA value, @c false otherwise
   **/
  static inline bool isNA(Type const& x) throw() { return false;}
  /** @param x the value to test.
   *  @return @c true if the parameter @c x is an infinite value, @c false
   *  otherwise
   **/
  static inline bool isInfinite(Type const& x) throw() { return false; }
  /** @param x the value to test.
   *  @return @c true if the parameter @c x is a finite value, @c false
   *  otherwise
   **/
  static inline bool isFinite(Type const& x) throw() { return (!isNA(x) && !isInfinite(x));}
};

/** @ingroup Arithmetic
 *  @brief utility method allowing to know if a value is a NA (Not Available) value */
template<class Type>
bool isNA(Type const& x) { return Arithmetic<Type>::isNA(x);}

/** @ingroup Arithmetic
 *  @brief utility method allowing to know if a value is a finite value */
template<class Type>
bool isFinite(Type const& x) { return Arithmetic<Type>::isFinite(x);}

/** @ingroup Arithmetic
 *  @brief utility method allowing to know if a value is an infinite value */
template<class Type>
bool isInfinite(Type const& x) { return Arithmetic<Type>::isInfinite(x);}

} // namespace STK

#endif /* STK_ARITHMETIC_H */
