Common/include/itkNumericTraits.h

/*=========================================================================
 *
 *  Copyright Insight Software Consortium
 *
 *  Licensed under the Apache License, Version 2.0 (the "License");
 *  you may not use this file except in compliance with the License.
 *  You may obtain a copy of the License at
 *
 *         http://www.apache.org/licenses/LICENSE-2.0.txt
 *
 *  Unless required by applicable law or agreed to in writing, software
 *  distributed under the License is distributed on an "AS IS" BASIS,
 *  WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 *  See the License for the specific language governing permissions and
 *  limitations under the License.
 *
 *=========================================================================*/
#ifndef itkNumericTraits_h
#define itkNumericTraits_h

#include "itkMacro.h"

#undef min
#undef max

#define itkNUMERIC_TRAITS_MIN_MAX_MACRO()          \
  static constexpr ValueType min(ValueType)         \
    {                                              \
    return std::numeric_limits< ValueType >::min(); \
    }                                              \
  static constexpr ValueType max(ValueType)         \
    {                                              \
    return std::numeric_limits< ValueType >::max(); \
    }                                              \
  static constexpr ValueType min()                  \
    {                                              \
    return std::numeric_limits< ValueType >::min(); \
    }                                              \
  static constexpr ValueType max()                  \
    {                                              \
    return std::numeric_limits< ValueType >::max(); \
    }

#include <limits> // for std::numeric_limits
#include <complex>

namespace itk
{

// forward decare to avoid circular dependencies
template< typename TValue, unsigned int VLength>  class FixedArray;

/** \class NumericTraits
 * \brief Define additional traits for native types such as int or float.
 *
 * NumericTraits is used to extend the traits associated with native types
 * such as float, char, int, and so on. These traits are extensions of the
 * standard numeric_limits defined by the C++ compilers. Some of the added
 * traits include minimum and maximum value; accumulation type; etc.
 *
 * \ingroup DataRepresentation
 * \ingroup ITKCommon
 *
 * \wiki
 * \wikiexample{SimpleOperations/NumericTraits,Get some basic information about a type}
 * \endwiki
 */
template< typename T >
class NumericTraits:public std::numeric_limits< T >
{
public:
  /** The type of this limits trait object. */
  using TraitsType = std::numeric_limits< T >;

  /** Return the type of this native type. */
  using ValueType = T;

  /** Return the type that can be printed. */
  using PrintType = T;

  /** Return value of std::abs(). */
  using AbsType = T;

  /** Accumulation of addition and multiplication. */
  using AccumulateType = double;

  /** Measurement vector type */
  using MeasurementVectorType = FixedArray<ValueType, 1>;

  /** Typedef for operations that use floating point instead of real precision
   *  to save memory */
  using FloatType = float;

  /** Type for real-valued scalar operations. */
  using RealType = double;

  /** Type for real-valued scalar operations. */
  using ScalarRealType = RealType;

  /** Additive identity. */
  static const T ITKCommon_EXPORT Zero;

  /** Multiplicative identity. */
  static const T ITKCommon_EXPORT One;

  /** Smallest (most nonpositive) value */
  static constexpr T NonpositiveMin() { return TraitsType::lowest(); }

  /** Is a given value positive? */
  static bool IsPositive(T val) { return val > Zero; }

  /** Is a given value nonpositive? */
  static bool IsNonpositive(T val) { return val <= Zero; }

  /** Is a given value negative? */
  static bool IsNegative(T val) { return val < Zero; }

  /** Is a given value nonnegative? */
  static bool IsNonnegative(T val) { return val >= Zero; }

  /** Is a given type signed? -- default is no.
      For uniform array data types in ITK, the value of IsSigned
      is determined by the component elements of the array.*/
  static constexpr bool IsSigned = false;

  /** Is a given type an integer? -- default is no.
      For uniform array data types in ITK, the value of IsInteger
      is determined by the component elements of the array.*/
  static constexpr bool IsInteger = false;

  /** Is a given type complex? -- default is no.
      For uniform array data types in ITK, the value of IsComplex
      is determined by the component elements of the array.*/
  static constexpr bool IsComplex = false;

  /** Return zero value. This function should be used to support
   *  RGBPixel type and standard types (not vectors) */
  static T ZeroValue() { return Zero; }

  /** Return one value. This function should be used to support
   *  RGBPixel type and standard types (not vectors) */
  static T OneValue() { return One; }

  /* Provide a default implementation of the max() method with
   * argument. This API is needed for VariableLengthVector because
   * its length is only known at run-time. Specializations of the
   * VariableLengthVector will provide a different implementation
   * where a vector of the correct size is built. */
  static constexpr T max(const T &) { return TraitsType::max(); }
  static constexpr T min(const T &) { return TraitsType::min(); }

  /** Scalars cannot be resized, so an exception will
   * be thrown if the input size is not 1.  If the size is valid
   * the will be zeros. This API is needed for VariableLengthVector because
   * its length is only known at run-time. Specializations of the
   * VariableLengthVector will provide a different implementation
   * where a vector of the correct size is built.
   */
  static void SetLength(T & m, const unsigned int s)
  {
    if ( s != 1 )
      {
      itkGenericExceptionMacro(<< "Cannot set the size of a scalar to " << s);
      }
    m = NumericTraits< ValueType >::ZeroValue();
  }
  /** Return the length of the scalar. This API is needed for
   * VariableLengthVector because
   * its length is only known at run-time. Specializations of the
   * VariableLengthVector will provide a different implementation
   * where a vector of the correct size is built.
   */
  static unsigned int GetLength(const T &)
  {
    return GetLength();
  }

  /** Return the length of the scalar: 1. Array types can return a different value */
  static unsigned int GetLength()
  {
    return 1;
  }

  /** Smallest (most nonpositive) value. This API is needed for
   * VariableLengthVector because its length is only known at run-time.
   */
  static T NonpositiveMin(const T &)
  {
    return NonpositiveMin();
  }

  /** Zero value. This API is needed for
   * VariableLengthVector because its length is only known at run-time.
   */
  static T ZeroValue(const T &)
  {
    return ZeroValue();
  }

  /** One value. This API is needed for
   * VariableLengthVector because its length is only known at run-time.
   */
  static T OneValue(const T &)
  {
    return OneValue();
  }

  /** assign the value to an array */
  template<typename TArray>
  static void AssignToArray( const T & v, TArray & mv )
  {
    mv[0] = v;
  }

};

/// \cond HIDE_SPECIALIZATION_DOCUMENTATION

/** \class NumericTraits<bool>
 * \brief Define traits for type bool.
 *
 * \ingroup DataRepresentation
 * \ingroup ITKCommon
 */

template< >
class NumericTraits< bool > :public std::numeric_limits< bool >
{
public:
  using ValueType = bool;
  using PrintType = bool;
  using AbsType = unsigned char;
  using AccumulateType = unsigned char;
  using RealType = double;
  using ScalarRealType = RealType;
  using FloatType = float;
  using MeasurementVectorType = FixedArray<ValueType, 1>;

  static constexpr bool ITKCommon_EXPORT Zero = false;
  static constexpr bool ITKCommon_EXPORT One = true;

  static constexpr bool min() { return false; }
  static constexpr bool max() { return true; }
  static constexpr bool min(bool) { return min(); }
  static constexpr bool max(bool) { return max(); }
  static constexpr bool NonpositiveMin() { return false; }
  static constexpr bool IsPositive(bool val) { return val; }
  static constexpr bool IsNonpositive(bool val) { return !val; }
  static constexpr bool IsNegative(bool val) { return val ? false : false; }
  static constexpr bool IsNonnegative(bool val) { return val ? true : true; }
  static constexpr bool IsSigned = false;
  static constexpr bool IsInteger = true;
  static constexpr bool IsComplex = false;
  static constexpr bool ZeroValue() { return Zero; }
  static constexpr bool OneValue() { return One; }
  static constexpr unsigned int GetLength(const ValueType &) { return 1; }
  static constexpr unsigned int GetLength() { return 1; }
  static constexpr ValueType NonpositiveMin(const ValueType &) { return NonpositiveMin(); }
  static constexpr ValueType ZeroValue(const ValueType &) { return ZeroValue(); }
  static constexpr ValueType OneValue(const ValueType &) { return OneValue(); }

  template<typename TArray>
  static void AssignToArray( const ValueType & v, TArray & mv )
  {
    mv[0] = v;
  }
  static void SetLength(ValueType & m, const unsigned int s)
  {
    if ( s != 1 )
      {
      itkGenericExceptionMacro(<< "Cannot set the size of a scalar to " << s);
      }
    m = NumericTraits< ValueType >::ZeroValue();
  }

};

/** \class NumericTraits<char>
 * \brief Define traits for type char.
 * NOTE: char is not guaranteed to be signed. On SGI computers, the default is unsigned
 * \ingroup ITKCommon
 */
template< >
class NumericTraits< char > :public std::numeric_limits< char >
{
public:
  using ValueType = char;
  using PrintType = int;
  using AbsType = unsigned char;
  using AccumulateType = short;
  using RealType = double;
  using ScalarRealType = RealType;
  using FloatType = float;
  using MeasurementVectorType = FixedArray<ValueType, 1>;

  static constexpr char ITKCommon_EXPORT Zero = 0;
  static constexpr char ITKCommon_EXPORT One = 1;

  itkNUMERIC_TRAITS_MIN_MAX_MACRO();

  static constexpr char NonpositiveMin() { return lowest(); }
  static constexpr bool IsPositive(char val) { return val > Zero; }
  static constexpr bool IsNonpositive(char val) { return val <= Zero; }

  static constexpr bool IsNegative(char) { return false; }
  static constexpr bool IsNonnegative(char) { return true; }
  static constexpr bool IsSigned = std::numeric_limits<char>::is_signed;

  static constexpr bool IsInteger = std::numeric_limits<char>::is_integer;
  static constexpr bool IsComplex = false;
  static constexpr char ZeroValue() { return Zero; }
  static constexpr char OneValue() { return One; }
  static constexpr unsigned int GetLength(const ValueType &) { return 1; }
  static constexpr unsigned int GetLength() { return 1; }
  static constexpr ValueType NonpositiveMin(const ValueType &) { return NonpositiveMin(); }
  static constexpr ValueType ZeroValue(const ValueType &) { return ZeroValue(); }
  static constexpr ValueType OneValue(const ValueType &) { return OneValue(); }

  template<typename TArray>
  static void AssignToArray( const ValueType & v, TArray & mv )
  {
    mv[0] = v;
  }
  static void SetLength(ValueType & m, const unsigned int s)
  {
    if ( s != 1 )
      {
      itkGenericExceptionMacro(<< "Cannot set the size of a scalar to " << s);
      }
    m = NumericTraits< ValueType >::ZeroValue();
  }
};

/** \class NumericTraits<char>
 * \brief Define traits for type char.
 * NOTE: char is not guaranteed to be signed. On SGI computers, the default is unsigned
 * \ingroup ITKCommon
 */
template< >
class NumericTraits< signed char > :public std::numeric_limits< signed char >
{
public:
  using ValueType = signed char;
  using PrintType = int;
  using AbsType = unsigned char;
  using AccumulateType = short;
  using RealType = double;
  using ScalarRealType = RealType;
  using FloatType = float;
  using MeasurementVectorType = FixedArray<ValueType, 1>;

  static constexpr signed char ITKCommon_EXPORT Zero = 0;
  static constexpr signed char ITKCommon_EXPORT One = 1;

  static constexpr signed char min() { return -128; }
  static constexpr signed char max() { return 127; }
  static constexpr signed char min(signed char) { return min(); }
  static constexpr signed char max(signed char) { return max(); }
  static constexpr signed char NonpositiveMin() { return lowest(); }
  static constexpr bool IsPositive(signed char val) { return val > Zero; }
  static constexpr bool IsNonpositive(signed char val) { return val <= Zero; }
  static constexpr bool IsNegative(signed char val) { return val < Zero; }
  static constexpr bool IsNonnegative(signed char val) { return val >= Zero; }
  static constexpr bool IsSigned = true;
  static constexpr bool IsInteger = true;
  static constexpr bool IsComplex = false;
  static constexpr signed char  ZeroValue() { return Zero; }
  static constexpr signed char OneValue() { return One; }
  static constexpr unsigned int GetLength(const ValueType &) { return 1; }
  static constexpr unsigned int GetLength() { return 1; }
  static constexpr ValueType NonpositiveMin(const ValueType &) { return NonpositiveMin(); }
  static constexpr ValueType ZeroValue(const ValueType &) { return ZeroValue(); }
  static constexpr ValueType OneValue(const ValueType &) { return OneValue(); }

  template<typename TArray>
  static void AssignToArray( const ValueType & v, TArray & mv )
  {
    mv[0] = v;
  }
  static void SetLength(ValueType & m, const unsigned int s)
  {
    if ( s != 1 )
      {
      itkGenericExceptionMacro(<< "Cannot set the size of a scalar to " << s);
      }
    m = NumericTraits< ValueType >::ZeroValue();
  }
};

/** \class NumericTraits<unsigned char>
 * \brief Define traits for type unsigned char.
 * \ingroup DataRepresentation
 * \ingroup ITKCommon
 */
template< >
class NumericTraits< unsigned char > :public std::numeric_limits< unsigned char >
{
public:
  using ValueType = unsigned char;
  using PrintType = int;
  using AbsType = unsigned char;
  using AccumulateType = unsigned short;
  using RealType = double;
  using ScalarRealType = RealType;
  using FloatType = float;
  using MeasurementVectorType = FixedArray<ValueType, 1>;

  static constexpr unsigned char ITKCommon_EXPORT Zero = 0;
  static constexpr unsigned char ITKCommon_EXPORT One = 1;

  itkNUMERIC_TRAITS_MIN_MAX_MACRO();

  static constexpr unsigned char NonpositiveMin() { return std::numeric_limits< ValueType >::lowest(); }
  static constexpr bool IsPositive(unsigned char val) { return val != Zero; }
  static constexpr bool IsNonpositive(unsigned char val) { return val == Zero; }
  static constexpr bool IsNegative(unsigned char val) { return val ? false : false; }
  static constexpr bool IsNonnegative(unsigned char val) { return val ? true : true; }
  static constexpr bool IsSigned = false;
  static constexpr bool IsInteger = true;
  static constexpr bool IsComplex = false;
  static constexpr unsigned char  ZeroValue() { return Zero; }
  static constexpr unsigned char OneValue() { return One; }
  static constexpr unsigned int GetLength(const ValueType &) { return 1; }
  static constexpr unsigned int GetLength() { return 1; }
  static constexpr ValueType NonpositiveMin(const ValueType &) { return NonpositiveMin(); }
  static constexpr ValueType ZeroValue(const ValueType &) { return ZeroValue(); }
  static constexpr ValueType OneValue(const ValueType &) { return OneValue(); }

  template<typename TArray>
  static void AssignToArray( const ValueType & v, TArray & mv )
  {
    mv[0] = v;
  }
  static void SetLength(ValueType & m, const unsigned int s)
  {
    if ( s != 1 )
      {
      itkGenericExceptionMacro(<< "Cannot set the size of a scalar to " << s);
      }
    m = NumericTraits< ValueType >::ZeroValue();
  }
};

/** \class NumericTraits<short>
 * \brief Define traits for type short.
 * \ingroup ITKCommon
 */
template< >
class NumericTraits< short > :public std::numeric_limits< short >
{
public:
  using ValueType = short;
  using PrintType = short;
  using AbsType = unsigned short;
  using AccumulateType = int;
  using RealType = double;
  using ScalarRealType = RealType;
  using FloatType = float;
  using MeasurementVectorType = FixedArray<ValueType, 1>;

  static constexpr short ITKCommon_EXPORT Zero = 0;
  static constexpr short ITKCommon_EXPORT One = 1;

  itkNUMERIC_TRAITS_MIN_MAX_MACRO();
  static constexpr short NonpositiveMin() { return std::numeric_limits< ValueType >::lowest(); }
  static constexpr bool IsPositive(short val) { return val > Zero; }
  static constexpr bool IsNonpositive(short val) { return val <= Zero; }
  static constexpr bool IsNegative(short val) { return val < Zero; }
  static constexpr bool IsNonnegative(short val) { return val >= Zero; }
  static constexpr bool IsSigned = true;
  static constexpr bool IsInteger = true;
  static constexpr bool IsComplex = false;
  static constexpr short  ZeroValue() { return Zero; }
  static constexpr short OneValue() { return One; }
  static constexpr unsigned int GetLength(const ValueType &) { return 1; }
  static constexpr unsigned int GetLength() { return 1; }
  static constexpr ValueType NonpositiveMin(const ValueType &) { return NonpositiveMin(); }
  static constexpr ValueType ZeroValue(const ValueType &) { return ZeroValue(); }
  static constexpr ValueType OneValue(const ValueType &) { return OneValue(); }

  template<typename TArray>
  static void AssignToArray( const ValueType & v, TArray & mv )
  {
    mv[0] = v;
  }
  static void SetLength(ValueType & m, const unsigned int s)
  {
    if ( s != 1 )
      {
      itkGenericExceptionMacro(<< "Cannot set the size of a scalar to " << s);
      }
    m = NumericTraits< ValueType >::ZeroValue();
  }
};

/** \class NumericTraits<unsigned short>
 * \brief Define traits for type unsigned short.
 * \ingroup DataRepresentation
 * \ingroup ITKCommon
 */
template< >
class NumericTraits< unsigned short > :public std::numeric_limits< unsigned short >
{
public:
  using ValueType = unsigned short;
  using PrintType = unsigned short;
  using AbsType = unsigned short;
  using AccumulateType = unsigned int;
  using RealType = double;
  using ScalarRealType = RealType;
  using FloatType = float;
  using MeasurementVectorType = FixedArray<ValueType, 1>;

  static constexpr unsigned short ITKCommon_EXPORT Zero = 0;
  static constexpr unsigned short ITKCommon_EXPORT One = 1;

  itkNUMERIC_TRAITS_MIN_MAX_MACRO();
  static constexpr unsigned short NonpositiveMin() { return std::numeric_limits< ValueType >::lowest(); }
  static constexpr bool IsPositive(unsigned short val) { return val != Zero; }
  static constexpr bool IsNonpositive(unsigned short val) { return val == Zero; }
  static constexpr bool IsNegative(unsigned short val) { return val ? false : false; }
  static constexpr bool IsNonnegative(unsigned short val) { return val ? true : true; }
  static constexpr bool IsSigned = false;
  static constexpr bool IsInteger = true;
  static constexpr bool IsComplex = false;
  static constexpr unsigned short ZeroValue() { return Zero; }
  static constexpr unsigned short OneValue() { return One; }
  static constexpr unsigned int GetLength(const ValueType &) { return 1; }
  static constexpr unsigned int GetLength() { return 1; }
  static constexpr ValueType NonpositiveMin(const ValueType &) { return NonpositiveMin(); }
  static constexpr ValueType ZeroValue(const ValueType &) { return ZeroValue(); }
  static constexpr ValueType OneValue(const ValueType &) { return OneValue(); }

  template<typename TArray>
  static void AssignToArray( const ValueType & v, TArray & mv )
  {
    mv[0] = v;
  }
  static void SetLength(ValueType & m, const unsigned int s)
  {
    if ( s != 1 )
      {
      itkGenericExceptionMacro(<< "Cannot set the size of a scalar to " << s);
      }
    m = NumericTraits< ValueType >::ZeroValue();
  }
};

/** \class NumericTraits<int>
 * \brief Define traits for type int.
 * \ingroup ITKCommon
 */
template< >
class NumericTraits< int > :public std::numeric_limits< int >
{
public:
  using ValueType = int;
  using PrintType = int;
  using AbsType = unsigned int;
  using AccumulateType = long;
  using RealType = double;
  using ScalarRealType = RealType;
  using FloatType = float;
  using MeasurementVectorType = FixedArray<ValueType, 1>;

  static constexpr int ITKCommon_EXPORT Zero = 0;
  static constexpr int ITKCommon_EXPORT One = 1;

  itkNUMERIC_TRAITS_MIN_MAX_MACRO();
  static constexpr int NonpositiveMin() { return std::numeric_limits< ValueType >::lowest(); }
  static constexpr bool IsPositive(int val) { return val > Zero; }
  static constexpr bool IsNonpositive(int val) { return val <= Zero; }
  static constexpr bool IsNegative(int val) { return val < Zero; }
  static constexpr bool IsNonnegative(int val) { return val >= Zero; }
  static constexpr bool IsSigned = true;
  static constexpr bool IsInteger = true;
  static constexpr bool IsComplex = false;
  static constexpr int  ZeroValue() { return Zero; }
  static constexpr int OneValue() { return One; }
  static constexpr unsigned int GetLength(const ValueType &) { return 1; }
  static constexpr unsigned int GetLength() { return 1; }
  static constexpr ValueType NonpositiveMin(const ValueType &) { return NonpositiveMin(); }
  static constexpr ValueType ZeroValue(const ValueType &) { return ZeroValue(); }
  static constexpr ValueType OneValue(const ValueType &) { return OneValue(); }

  template<typename TArray>
  static void AssignToArray( const ValueType & v, TArray & mv )
  {
    mv[0] = v;
  }
  static void SetLength(ValueType & m, const unsigned int s)
  {
    if ( s != 1 )
      {
      itkGenericExceptionMacro(<< "Cannot set the size of a scalar to " << s);
      }
    m = NumericTraits< ValueType >::ZeroValue();
  }
};

/** \class NumericTraits<unsigned int>
 * \brief Define traits for type unsigned int.
 * \ingroup DataRepresentation
 * \ingroup ITKCommon
 */
template< >
class NumericTraits< unsigned int > :public std::numeric_limits< unsigned int >
{
public:
  using ValueType = unsigned int;
  using PrintType = unsigned int;
  using AbsType = unsigned int;
  using AccumulateType = unsigned int;
  using RealType = double;
  using ScalarRealType = RealType;
  using FloatType = float;
  using MeasurementVectorType = FixedArray<ValueType, 1>;

  static constexpr unsigned int ITKCommon_EXPORT Zero = 0;
  static constexpr unsigned int ITKCommon_EXPORT One = 1;

  static constexpr unsigned int min() { return 0; }
  static constexpr unsigned int max() { return static_cast< unsigned int >( -1 ); }
  static constexpr unsigned int min(unsigned int) { return std::numeric_limits< ValueType >::min(); }
  static constexpr unsigned int max(unsigned int) { return std::numeric_limits< ValueType >::max(); }
  static constexpr unsigned int NonpositiveMin() { return 0; }
  static constexpr bool IsPositive(unsigned int val) { return val != Zero; }
  static constexpr bool IsNonpositive(unsigned int val) { return val == Zero; }
  static constexpr bool IsNegative(unsigned int val) { return val ? false : false; }
  static constexpr bool IsNonnegative(unsigned int val) { return val ? true : true; }
  static constexpr bool IsSigned = false;
  static constexpr bool IsInteger = true;
  static constexpr bool IsComplex = false;
  static constexpr unsigned int  ZeroValue() { return Zero; }
  static constexpr unsigned int OneValue() { return One; }
  static constexpr unsigned int GetLength(const ValueType &) { return 1; }
  static constexpr unsigned int GetLength() { return 1; }
  static constexpr ValueType NonpositiveMin(const ValueType &) { return NonpositiveMin(); }
  static constexpr ValueType ZeroValue(const ValueType &) { return ZeroValue(); }
  static constexpr ValueType OneValue(const ValueType &) { return OneValue(); }

  template<typename TArray>
  static void AssignToArray( const ValueType & v, TArray & mv )
  {
    mv[0] = v;
  }
  static void SetLength(ValueType & m, const unsigned int s)
  {
    if ( s != 1 )
      {
      itkGenericExceptionMacro(<< "Cannot set the size of a scalar to " << s);
      }
    m = NumericTraits< ValueType >::ZeroValue();
  }
};

/** \class NumericTraits<long>
 * \brief Define traits for type long.
 * \ingroup DataRepresentation
 * \ingroup ITKCommon
 */
template< >
class NumericTraits< long > :public std::numeric_limits< long >
{
public:
  using ValueType = long;
  using PrintType = long;
  using AbsType = unsigned long;
  using AccumulateType = long;
  using RealType = double;
  using ScalarRealType = RealType;
  using FloatType = float;
  using MeasurementVectorType = FixedArray<ValueType, 1>;

  static constexpr long ITKCommon_EXPORT Zero = 0L;
  static constexpr long ITKCommon_EXPORT One = 1L;

  itkNUMERIC_TRAITS_MIN_MAX_MACRO();
  static constexpr long NonpositiveMin() { return std::numeric_limits< ValueType >::lowest(); }
  static constexpr bool IsPositive(long val) { return val > Zero; }
  static constexpr bool IsNonpositive(long val) { return val <= Zero; }
  static constexpr bool IsNegative(long val) { return val < Zero; }
  static constexpr bool IsNonnegative(long val) { return val >= Zero; }
  static constexpr bool IsSigned = true;
  static constexpr bool IsInteger = true;
  static constexpr bool IsComplex = false;
  static constexpr long  ZeroValue() { return Zero; }
  static constexpr long OneValue() { return One; }
  static constexpr unsigned int GetLength(const ValueType &) { return 1; }
  static constexpr unsigned int GetLength() { return 1; }
  static constexpr ValueType NonpositiveMin(const ValueType &) { return NonpositiveMin(); }
  static constexpr ValueType ZeroValue(const ValueType &) { return ZeroValue(); }
  static constexpr ValueType OneValue(const ValueType &) { return OneValue(); }

  template<typename TArray>
  static void AssignToArray( const ValueType & v, TArray & mv )
  {
    mv[0] = v;
  }
  static void SetLength(ValueType & m, const unsigned int s)
  {
    if ( s != 1 )
      {
      itkGenericExceptionMacro(<< "Cannot set the size of a scalar to " << s);
      }
    m = NumericTraits< ValueType >::ZeroValue();
  }
};

/** \class NumericTraits<unsigned long>
 * \brief Define traits for type unsigned long.
 * \ingroup DataRepresentation
 * \ingroup ITKCommon
 */
template< >
class NumericTraits< unsigned long > :public std::numeric_limits< unsigned long >
{
public:
  using ValueType = unsigned long;
  using PrintType = unsigned long;
  using AbsType = unsigned long;
  using AccumulateType = unsigned long;
  using RealType = double;
  using ScalarRealType = RealType;
  using FloatType = float;
  using MeasurementVectorType = FixedArray<ValueType, 1>;

  static constexpr unsigned long ITKCommon_EXPORT Zero = 0UL;
  static constexpr unsigned long ITKCommon_EXPORT One = 1UL;

  itkNUMERIC_TRAITS_MIN_MAX_MACRO();
  static constexpr unsigned long NonpositiveMin() { return std::numeric_limits< ValueType >::lowest(); }
  static constexpr bool IsPositive(unsigned long val) { return val != Zero; }
  static constexpr bool IsNonpositive(unsigned long val) { return val == Zero; }
  static constexpr bool IsNegative(unsigned long) { return false; }
  static constexpr bool IsNonnegative(unsigned long) { return true; }
  static constexpr bool IsSigned = false;
  static constexpr bool IsInteger = true;
  static constexpr bool IsComplex = false;
  static constexpr unsigned long  ZeroValue() { return Zero; }
  static constexpr unsigned long  OneValue() { return One; }
  static constexpr unsigned int GetLength(const ValueType &) { return 1; }
  static constexpr unsigned int GetLength() { return 1; }
  static constexpr ValueType NonpositiveMin(const ValueType &) { return NonpositiveMin(); }
  static constexpr ValueType ZeroValue(const ValueType &) { return ZeroValue(); }
  static constexpr ValueType OneValue(const ValueType &) { return OneValue(); }

  template<typename TArray>
  static void AssignToArray( const ValueType & v, TArray & mv )
  {
    mv[0] = v;
  }
  static void SetLength(ValueType & m, const unsigned int s)
  {
    if ( s != 1 )
      {
      itkGenericExceptionMacro(<< "Cannot set the size of a scalar to " << s);
      }
    m = NumericTraits< ValueType >::ZeroValue();
  }
};

/** \class NumericTraits<float>
 * \brief Define traits for type float.
 * \ingroup DataRepresentation
 * \ingroup ITKCommon
 */
template< >
class NumericTraits< float > :public std::numeric_limits< float >
{
public:
  using ValueType = float;
  using PrintType = float;
  using AbsType = float;
  using AccumulateType = double;
  using RealType = double;
  using ScalarRealType = RealType;
  using FloatType = float;
  using MeasurementVectorType = FixedArray<ValueType, 1>;


  static constexpr float ITKCommon_EXPORT Zero =0.0f;
  static constexpr float ITKCommon_EXPORT One =1.0f;

  itkNUMERIC_TRAITS_MIN_MAX_MACRO();
  static constexpr float NonpositiveMin() { return std::numeric_limits< ValueType >::lowest(); }
  static constexpr bool IsPositive(float val) { return val > Zero; }
  static constexpr bool IsNonpositive(float val) { return val <= Zero; }
  static constexpr bool IsNegative(float val) { return val < Zero; }
  static constexpr bool IsNonnegative(float val) { return val >= Zero; }
  static constexpr bool IsSigned = true;
  static constexpr bool IsInteger = false;
  static constexpr bool IsComplex = false;
  static constexpr float  ZeroValue() { return Zero; }
  static constexpr float  OneValue() { return One; }
  static constexpr unsigned int GetLength(const ValueType &) { return 1; }
  static constexpr unsigned int GetLength() { return 1; }
  static constexpr ValueType NonpositiveMin(const ValueType &) { return NonpositiveMin(); }
  static constexpr ValueType ZeroValue(const ValueType &) { return ZeroValue(); }
  static constexpr ValueType OneValue(const ValueType &) { return OneValue(); }

  template<typename TArray>
  static void AssignToArray( const ValueType & v, TArray & mv )
  {
    mv[0] = v;
  }
  static void SetLength(ValueType & m, const unsigned int s)
  {
    if ( s != 1 )
      {
      itkGenericExceptionMacro(<< "Cannot set the size of a scalar to " << s);
      }
    m = NumericTraits< ValueType >::ZeroValue();
  }
};

/** \class NumericTraits<double>
 * \brief Define traits for type double.
 * \ingroup DataRepresentation
 * \ingroup ITKCommon
 */
template< >
class NumericTraits< double > :public std::numeric_limits< double >
{
public:
  using ValueType = double;
  using PrintType = double;
  using AbsType = double;
  using AccumulateType = double;
  using RealType = double;
  using ScalarRealType = RealType;
  using FloatType = float;
  using MeasurementVectorType = FixedArray<ValueType, 1>;

  static constexpr double ITKCommon_EXPORT Zero = 0.0;
  static constexpr double ITKCommon_EXPORT One  = 1.0;

  itkNUMERIC_TRAITS_MIN_MAX_MACRO();
  static constexpr double NonpositiveMin() { return std::numeric_limits< ValueType >::lowest(); }
  static constexpr bool IsPositive(double val) { return val > Zero; }
  static constexpr bool IsNonpositive(double val) { return val <= Zero; }
  static constexpr bool IsNegative(double val) { return val < Zero; }
  static constexpr bool IsNonnegative(double val) { return val >= Zero; }
  static constexpr bool IsSigned = true;
  static constexpr bool IsInteger = false;
  static constexpr bool IsComplex = false;
  static constexpr double  ZeroValue() { return Zero; }
  static constexpr double  OneValue() { return One; }
  static constexpr unsigned int GetLength(const ValueType &) { return 1; }
  static constexpr unsigned int GetLength() { return 1; }
  static constexpr ValueType NonpositiveMin(const ValueType &) { return NonpositiveMin(); }
  static constexpr ValueType ZeroValue(const ValueType &) { return ZeroValue(); }
  static constexpr ValueType OneValue(const ValueType &) { return OneValue(); }

  template<typename TArray>
  static void AssignToArray( const ValueType & v, TArray & mv )
  {
    mv[0] = v;
  }
  static void SetLength(ValueType & m, const unsigned int s)
  {
    if ( s != 1 )
      {
      itkGenericExceptionMacro(<< "Cannot set the size of a scalar to " << s);
      }
    m = NumericTraits< ValueType >::ZeroValue();
  }
};

/** \class NumericTraits<long double>
 * \brief Define traits for type long double.
 * \ingroup DataRepresentation
 * \ingroup ITKCommon
 */
template< >
class NumericTraits< long double > :public std::numeric_limits< long double >
{
public:
  using ValueType = long double;
#if defined( __SUNPRO_CC ) && defined( _ILP32 )
  // sun studio in 32 bit mode is unable to print long double values: it
  // segfaults.
  // conversion to double will give usable results if the value is in the double
  // range - better than nothing.
  using PrintType = double;
#else
  using PrintType = long double;
#endif
  using AbsType = long double;
  using AccumulateType = long double;
  using RealType = long double;
  using ScalarRealType = RealType;
  using FloatType = float;
  using MeasurementVectorType = FixedArray<ValueType, 1>;

  static constexpr long double ITKCommon_EXPORT Zero = 0.0;
  static constexpr long double ITKCommon_EXPORT One = 1.0;

  itkNUMERIC_TRAITS_MIN_MAX_MACRO();
  static constexpr long double NonpositiveMin() { return std::numeric_limits< ValueType >::lowest(); }
  static constexpr bool IsPositive(long double val) { return val > Zero; }
  static constexpr bool IsNonpositive(long double val) { return val <= Zero; }
  static constexpr bool IsNegative(long double val) { return val < Zero; }
  static constexpr bool IsNonnegative(long double val) { return val >= Zero; }
  static constexpr bool IsSigned = true;
  static constexpr bool IsInteger = false;
  static constexpr bool IsComplex = false;
  static constexpr long double ZeroValue() { return Zero; }
  static constexpr long double OneValue() { return One; }
  static constexpr unsigned int GetLength(const ValueType &) { return 1; }
  static constexpr unsigned int GetLength() { return 1; }
  static constexpr ValueType NonpositiveMin(const ValueType &) { return NonpositiveMin(); }
  static constexpr ValueType ZeroValue(const ValueType &) { return ZeroValue(); }
  static constexpr ValueType OneValue(const ValueType &) { return OneValue(); }

  template<typename TArray>
  static void AssignToArray( const ValueType & v, TArray & mv )
  {
    mv[0] = v;
  }
  static void SetLength(ValueType & m, const unsigned int s)
  {
    if ( s != 1 )
      {
      itkGenericExceptionMacro(<< "Cannot set the size of a scalar to " << s);
      }
    m = NumericTraits< ValueType >::ZeroValue();
  }
};


/** \class NumericTraits<long long>
 * \brief Define traits for type long long.
 * \ingroup DataRepresentation
 * \ingroup ITKCommon
 */
template< >
class NumericTraits< long long > :
  public std::numeric_limits< long long >
{
public:
  using ValueType = long long;
  using PrintType = long long;
  using AbsType = long long;
  using AccumulateType = long long;
  using RealType = double;
  using ScalarRealType = RealType;
  using FloatType = float;
  using MeasurementVectorType = FixedArray<ValueType, 1>;

  static constexpr ValueType ITKCommon_EXPORT Zero = 0LL;
  static constexpr ValueType ITKCommon_EXPORT One = 1LL;

  itkNUMERIC_TRAITS_MIN_MAX_MACRO();
  static constexpr ValueType NonpositiveMin() { return std::numeric_limits< ValueType >::lowest(); }
  static constexpr bool IsPositive(ValueType val) { return val > Zero; }
  static constexpr bool IsNonpositive(ValueType val) { return val <= Zero; }
  static constexpr bool IsNegative(ValueType val) { return val < Zero; }
  static constexpr bool IsNonnegative(ValueType val) { return val >= Zero; }
  static constexpr bool IsSigned = true;
  static constexpr bool IsInteger = true;
  static constexpr bool IsComplex = false;
  static constexpr ValueType  ZeroValue() { return Zero; }
  static constexpr ValueType  OneValue() { return One; }
  static constexpr unsigned int GetLength(const ValueType &) { return 1; }
  static constexpr unsigned int GetLength() { return 1; }
  static constexpr ValueType NonpositiveMin(const ValueType &) { return NonpositiveMin(); }
  static constexpr ValueType ZeroValue(const ValueType &) { return ZeroValue(); }
  static constexpr ValueType OneValue(const ValueType &) { return OneValue(); }

  template<typename TArray>
  static void AssignToArray( const ValueType & v, TArray & mv )
  {
    mv[0] = v;
  }
  static void SetLength(ValueType & m, const unsigned int s)
  {
    if ( s != 1 )
      {
      itkGenericExceptionMacro(<< "Cannot set the size of a scalar to " << s);
      }
    m = NumericTraits< ValueType >::ZeroValue();
  }
};

/** \class NumericTraits<unsigned long long>
 * \brief Define traits for type unsigned long long.
 * \ingroup DataRepresentation
 * \ingroup ITKCommon
 */
template< >
class NumericTraits< unsigned long long > :
  public std::numeric_limits< unsigned long long >
{
public:
  using ValueType = unsigned long long;
  using PrintType = unsigned long long;
  using AbsType = unsigned long long;
  using AccumulateType = unsigned long long;
  using RealType = double;
  using ScalarRealType = RealType;
  using FloatType = float;
  using MeasurementVectorType = FixedArray<ValueType, 1>;

  static constexpr ValueType ITKCommon_EXPORT Zero = 0ULL;
  static constexpr ValueType ITKCommon_EXPORT One = 1ULL;

  itkNUMERIC_TRAITS_MIN_MAX_MACRO();
  static constexpr ValueType NonpositiveMin() { return std::numeric_limits< ValueType >::lowest(); }
  static constexpr bool IsPositive(ValueType val) { return val != Zero; }
  static constexpr bool IsNonpositive(ValueType val) { return val == Zero; }
  static constexpr bool IsNegative(ValueType) { return false; }
  static constexpr bool IsNonnegative(ValueType) { return true; }
  static constexpr bool IsSigned = false;
  static constexpr bool IsInteger = true;
  static constexpr bool IsComplex = false;
  static constexpr ValueType ZeroValue() { return Zero; }
  static constexpr ValueType OneValue() { return One; }
  static constexpr unsigned int GetLength(const ValueType &) { return 1; }
  static constexpr unsigned int GetLength() { return 1; }
  static constexpr ValueType NonpositiveMin(const ValueType &) { return NonpositiveMin(); }
  static constexpr ValueType ZeroValue(const ValueType &) { return ZeroValue(); }
  static constexpr ValueType OneValue(const ValueType &) { return OneValue(); }

  template<typename TArray>
  static void AssignToArray( const ValueType & v, TArray & mv )
  {
    mv[0] = v;
  }
  static void SetLength(ValueType & m, const unsigned int s)
  {
    if ( s != 1 )
      {
      itkGenericExceptionMacro(<< "Cannot set the size of a scalar to " << s);
      }
    m = NumericTraits< ValueType >::ZeroValue();
  }
};


/** \class NumericTraits< std::complex<TComponent> >
 * \brief Define traits for type std::complex<TComponent>.
 * \ingroup DataRepresentation
 * \ingroup ITKCommon
 */
template<typename TComponent>
class NumericTraits< std::complex< TComponent > >
{
public:
  using Self = std::complex< TComponent >;
  // for backward compatibility
  using TheType = Self;
  using ValueType = TComponent;
  using PrintType = Self;
  using AbsType = double;
  using AccumulateType = Self;
  using RealType = std::complex< double >;
  using ScalarRealType = double;
  using FloatType = std::complex< float >;
  using MeasurementVectorType = FixedArray<ValueType, 2>;

  static const Self ITKCommon_EXPORT Zero;
  static const Self ITKCommon_EXPORT One;

  static constexpr Self min() { return std::numeric_limits< ValueType >::min(); }
  static constexpr Self max() { return std::numeric_limits< ValueType >::max(); }
  static constexpr Self min(Self) { return min(); }
  static constexpr Self max(Self) { return max(); }
  static constexpr ValueType epsilon() { return std::numeric_limits<ValueType>::epsilon(); }
  static constexpr Self NonpositiveMin()
  {
    return Self(NumericTraits< ValueType >::NonpositiveMin(), 0);
  }

  static constexpr bool IsPositive(Self val) { return val.real() > 0; }
  static constexpr bool IsNonpositive(Self val) { return val.real() <= 0; }
  static constexpr bool IsNegative(Self val) { return val.real() < 0; }
  static constexpr bool IsNonnegative(Self val) { return val.real() >= 0; }

  static constexpr bool IsSigned = NumericTraits< ValueType >::IsSigned;
  static constexpr bool IsInteger = false;
  static constexpr bool IsComplex = true;
  static Self ZeroValue() { return Self(0, 0); }
  static Self OneValue() { return Self(1, 0); }
  static constexpr unsigned int GetLength(const Self &) { return 2; }
  static constexpr unsigned int GetLength() { return 2; }
  static constexpr Self NonpositiveMin(const Self &) { return NonpositiveMin(); }
  static Self ZeroValue(const Self &) { return ZeroValue(); }
  static Self OneValue(const Self &) { return OneValue(); }

  template<typename TArray>
  static void AssignToArray( const Self & v, TArray & mv )
  {
    mv[0] = v.real();
    mv[1] = v.imag();
  }
  static void SetLength(Self & m, const unsigned int s)
  {
    if ( s != 2 )
      {
      itkGenericExceptionMacro(<< "Cannot set the size of a complex to " << s);
      }
    m = NumericTraits< ValueType >::ZeroValue();
  }
};
} // end namespace itk

#include "itkFixedArray.h"

#endif // itkNumericTraits_h