itkNumericTraits.h

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/*=========================================================================
 *
 *  Copyright NumFOCUS
 *
 *  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;
 
template <typename T>
class NumericTraits : public std::numeric_limits<T>
{
public:
  using TraitsType = std::numeric_limits<T>;
 
  using ValueType = T;
 
  using PrintType = T;
 
  using AbsType = T;
 
  using AccumulateType = double;
 
  using MeasurementVectorType = FixedArray<ValueType, 1>;
 
  using FloatType = float;
 
  using RealType = double;
 
  using ScalarRealType = RealType;
 
  static const T ITKCommon_EXPORT Zero;
 
  static const T ITKCommon_EXPORT One;
 
  static constexpr T
  NonpositiveMin()
  {
    return TraitsType::lowest();
  }
 
  static bool
  IsPositive(T val)
  {
    return val > Zero;
  }
 
  static bool
  IsNonpositive(T val)
  {
    return val <= Zero;
  }
 
  static bool
  IsNegative(T val)
  {
    return val < Zero;
  }
 
  static bool
  IsNonnegative(T val)
  {
    return val >= Zero;
  }
 
  static constexpr bool IsSigned = false;
 
  static constexpr bool IsInteger = false;
 
  static constexpr bool IsComplex = false;
 
  static T
  ZeroValue()
  {
    return Zero;
  }
 
  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();
  }
 
  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();
  }
 
  static unsigned int
  GetLength(const T &)
  {
    return GetLength();
  }
 
  static unsigned int
  GetLength()
  {
    return 1;
  }
 
  static T
  NonpositiveMin(const T &)
  {
    return NonpositiveMin();
  }
 
  static T
  ZeroValue(const T &)
  {
    return ZeroValue();
  }
 
  static T
  OneValue(const T &)
  {
    return OneValue();
  }
 
  template <typename TArray>
  static void
  AssignToArray(const T & v, TArray & mv)
  {
    mv[0] = v;
  }
};
 
 
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();
  }
};
 
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();
  }
};
 
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();
  }
};
 
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();
  }
};
 
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();
  }
};
 
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();
  }
};
 
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();
  }
};
 
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();
  }
};
 
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();
  }
};
 
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();
  }
};
 
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();
  }
};
 
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();
  }
};
 
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();
  }
};
 
 
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();
  }
};
 
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();
  }
};
 
 
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