itkMathDetail.h

Go to the documentation of this file.

/*=========================================================================
 *
 *  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.
 *
 *=========================================================================*/
/*=========================================================================
 *
 *  Portions of this file are subject to the VTK Toolkit Version 3 copyright.
 *
 *  Copyright (c) Ken Martin, Will Schroeder, Bill Lorensen
 *
 *  For complete copyright, license and disclaimer of warranty information
 *  please refer to the NOTICE file at the top of the ITK source tree.
 *
 *=========================================================================*/
#ifndef itkMathDetail_h
#define itkMathDetail_h

#include "itkIntTypes.h"
#include "itkNumericTraits.h"

#include <cfenv>

#if defined( ITK_HAVE_EMMINTRIN_H ) && !defined( ITK_WRAPPING_PARSER )
#include <emmintrin.h> // sse 2 intrinsics
#endif /* ITK_HAVE_EMMINTRIN_H && ! ITK_WRAPPING_PARSER */

// assume no SSE2:
#define USE_SSE2_64IMPL 0
#define USE_SSE2_32IMPL 0

// For apple assume sse2 is on for all intel builds, check for 64 and 32
// bit versions
#if defined(__APPLE__) && defined( __SSE2__ ) && !defined( ITK_WRAPPING_PARSER )

#  if defined( __i386__ )
#    undef  USE_SSE2_32IMPL
#    define USE_SSE2_32IMPL 1
#  endif

#  if defined(  __x86_64 )
//   Turn on the 64 bits implementation
#    undef  USE_SSE2_64IMPL
#    define USE_SSE2_64IMPL 1
//   Turn on also the 32 bits implementation
//   since it is available in 64 bits versions.
#    undef  USE_SSE2_32IMPL
#    define USE_SSE2_32IMPL 1
#  endif

#else

// For non-apple (no universal binary possible) just use the
// try-compile set ITK_COMPILER_SUPPORTS_SSE2_32 and
// ITK_COMPILER_SUPPORTS_SSE2_64 to set values:

#  if defined(ITK_COMPILER_SUPPORTS_SSE2_32) && !defined( ITK_WRAPPING_PARSER )
#    undef  USE_SSE2_32IMPL
#    define USE_SSE2_32IMPL 1
#  endif
#  if defined(ITK_COMPILER_SUPPORTS_SSE2_64) && !defined( ITK_WRAPPING_PARSER )
#    undef  USE_SSE2_64IMPL
#    define USE_SSE2_64IMPL 1
#  endif

#endif


// Turn on 32-bit and 64-bit asm impl when using GCC on x86 platform with the
// following exception:
//   GCCXML
#if defined( __GNUC__ ) && ( !defined( ITK_WRAPPING_PARSER ) ) &&  ( defined( __i386__ ) || defined( __i386 ) \
  || defined( __x86_64__ ) || defined( __x86_64 ) )
#define GCC_USE_ASM_32IMPL 1
#define GCC_USE_ASM_64IMPL 1
#else
#define GCC_USE_ASM_32IMPL 0
#define GCC_USE_ASM_64IMPL 0
#endif
// Turn on 32-bit and 64-bit asm impl when using msvc on 32 bits windows
#if defined( VCL_VC ) && ( !defined( ITK_WRAPPING_PARSER ) ) && !defined( _WIN64 )
#define VC_USE_ASM_32IMPL 1
#define VC_USE_ASM_64IMPL 1
#else
#define VC_USE_ASM_32IMPL 0
#define VC_USE_ASM_64IMPL 0
#endif

namespace itk
{
namespace Math
{
namespace Detail
{
// The functions defined in this namespace are not meant to be used directly
// and thus do not adhere to the standard backward-compatibility
// policy of ITK, as any Detail namespace should be considered private.
// Please use the functions from the itk::Math namespace instead

// Base versions

CLANG_PRAGMA_PUSH
CLANG_SUPPRESS_Wfloat_equal

template< typename TReturn, typename TInput >
inline TReturn RoundHalfIntegerToEven_base(TInput x)
{
  if ( NumericTraits< TInput >::IsNonnegative(x) )
    {
    x += static_cast< TInput >( 0.5 );
    }
  else
    {
    x -= static_cast< TInput >( 0.5 );
    }

  const auto r = static_cast< TReturn >( x );
  return ( x != static_cast< TInput >( r ) ) ? r : static_cast< TReturn >( 2 * ( r / 2 ) );
}

template< typename TReturn, typename TInput >
inline TReturn RoundHalfIntegerUp_base(TInput x)
{
  x += static_cast< TInput >( 0.5 );
  const auto r = static_cast< TReturn >( x );
  return ( NumericTraits< TInput >::IsNonnegative(x) ) ?
         r :
         ( x == static_cast< TInput >( r ) ? r : r - static_cast< TReturn >( 1 ) );
}

template< typename TReturn, typename TInput >
inline TReturn Floor_base(TInput x)
{
  const auto r = static_cast< TReturn >( x );

  return ( NumericTraits< TInput >::IsNonnegative(x) ) ?
         r :
         ( x == static_cast< TInput >( r ) ? r : r - static_cast< TReturn >( 1 ) );
}

template< typename TReturn, typename TInput >
inline TReturn Ceil_base(TInput x)
{
  const auto r = static_cast< TReturn >( x );

  return ( NumericTraits< TInput >::IsNegative(x) ) ?
         r :
         ( x == static_cast< TInput >( r ) ? r : r + static_cast< TReturn >( 1 ) );
}

CLANG_PRAGMA_POP

// 32 bits versions

#if USE_SSE2_32IMPL // sse2 implementation

inline int32_t RoundHalfIntegerToEven_32(double x)
{
  #if defined( ITK_CHECK_FPU_ROUNDING_MODE )
  itkAssertInDebugAndIgnoreInReleaseMacro(fegetround() == FE_TONEAREST);
  #endif
  return _mm_cvtsd_si32( _mm_set_sd(x) );
}

inline int32_t RoundHalfIntegerToEven_32(float x)
{
  #if defined( ITK_CHECK_FPU_ROUNDING_MODE )
  itkAssertInDebugAndIgnoreInReleaseMacro(fegetround() == FE_TONEAREST);
  #endif
  return _mm_cvtss_si32( _mm_set_ss(x) );
}

#elif GCC_USE_ASM_32IMPL // gcc asm implementation

inline int32_t RoundHalfIntegerToEven_32(double x)
{
  #if defined( ITK_CHECK_FPU_ROUNDING_MODE )
  itkAssertInDebugAndIgnoreInReleaseMacro(fegetround() == FE_TONEAREST);
  #endif
  int32_t r;
  __asm__ __volatile__ ( "fistpl %0" : "=m" ( r ) : "t" ( x ) : "st" );
  return r;
}

inline int32_t RoundHalfIntegerToEven_32(float x)
{
  #if defined( ITK_CHECK_FPU_ROUNDING_MODE )
  itkAssertInDebugAndIgnoreInReleaseMacro(fegetround() == FE_TONEAREST);
  #endif
  int32_t r;
  __asm__ __volatile__ ( "fistpl %0" : "=m" ( r ) : "t" ( x ) : "st" );
  return r;
}

#elif VC_USE_ASM_32IMPL // msvc asm implementation

inline int32_t RoundHalfIntegerToEven_32(double x)
{
  #if defined( ITK_CHECK_FPU_ROUNDING_MODE )
  itkAssertInDebugAndIgnoreInReleaseMacro(fegetround() == FE_TONEAREST);
  #endif
  int32_t r;
  __asm
    {
    fld x
    fistp r
    }
  return r;
}

inline int32_t RoundHalfIntegerToEven_32(float x)
{
  #if defined( ITK_CHECK_FPU_ROUNDING_MODE )
  itkAssertInDebugAndIgnoreInReleaseMacro(fegetround() == FE_TONEAREST);
  #endif
  int32_t r;
  __asm
    {
    fld x
    fistp r
    }
  return r;
}

#else // Base implementation

inline int32_t RoundHalfIntegerToEven_32(double x) { return RoundHalfIntegerToEven_base< int32_t, double >(x); }
inline int32_t RoundHalfIntegerToEven_32(float x) { return RoundHalfIntegerToEven_base< int32_t, float >(x); }

#endif

#if USE_SSE2_32IMPL || GCC_USE_ASM_32IMPL || VC_USE_ASM_32IMPL

inline int32_t RoundHalfIntegerUp_32(double x) { return RoundHalfIntegerToEven_32(2 * x + 0.5) >> 1; }
inline int32_t RoundHalfIntegerUp_32(float x) { return RoundHalfIntegerToEven_32(2 * x + 0.5f) >> 1; }

inline int32_t Floor_32(double x) { return RoundHalfIntegerToEven_32(2 * x - 0.5) >> 1; }
inline int32_t Floor_32(float x) { return RoundHalfIntegerToEven_32(2 * x - 0.5f) >> 1; }

inline int32_t Ceil_32(double x) { return -( RoundHalfIntegerToEven_32(-0.5 - 2 * x) >> 1 ); }
inline int32_t Ceil_32(float x) { return -( RoundHalfIntegerToEven_32(-0.5f - 2 * x) >> 1 ); }

#else // Base implementation

inline int32_t RoundHalfIntegerUp_32(double x) { return RoundHalfIntegerUp_base< int32_t, double >(x); }
inline int32_t RoundHalfIntegerUp_32(float x) { return RoundHalfIntegerUp_base< int32_t, float >(x); }

inline int32_t Floor_32(double x) { return Floor_base< int32_t, double >(x); }
inline int32_t Floor_32(float x) { return Floor_base< int32_t, float >(x); }

inline int32_t Ceil_32(double x) { return Ceil_base< int32_t, double >(x); }
inline int32_t Ceil_32(float x) { return Ceil_base< int32_t, float >(x); }

#endif // USE_SSE2_32IMPL || GCC_USE_ASM_32IMPL || VC_USE_ASM_32IMPL

// 64 bits versions

#if USE_SSE2_64IMPL // sse2 implementation

inline int64_t RoundHalfIntegerToEven_64(double x)
{
  #if defined( ITK_CHECK_FPU_ROUNDING_MODE )
  itkAssertInDebugAndIgnoreInReleaseMacro(fegetround() == FE_TONEAREST);
  #endif
  return _mm_cvtsd_si64( _mm_set_sd(x) );
}

inline int64_t RoundHalfIntegerToEven_64(float x)
{
  #if defined( ITK_CHECK_FPU_ROUNDING_MODE )
  itkAssertInDebugAndIgnoreInReleaseMacro(fegetround() == FE_TONEAREST);
  #endif
  return _mm_cvtss_si64( _mm_set_ss(x) );
}

#elif GCC_USE_ASM_64IMPL // gcc asm implementation

inline int64_t RoundHalfIntegerToEven_64(double x)
{
  #if defined( ITK_CHECK_FPU_ROUNDING_MODE )
  itkAssertInDebugAndIgnoreInReleaseMacro(fegetround() == FE_TONEAREST);
  #endif
  int64_t r;
  __asm__ __volatile__ ( "fistpll %0" : "=m" ( r ) : "t" ( x ) : "st" );
  return r;
}

inline int64_t RoundHalfIntegerToEven_64(float x)
{
  #if defined( ITK_CHECK_FPU_ROUNDING_MODE )
  itkAssertInDebugAndIgnoreInReleaseMacro(fegetround() == FE_TONEAREST);
  #endif
  int64_t r;
  __asm__ __volatile__ ( "fistpll %0" : "=m" ( r ) : "t" ( x ) : "st" );
  return r;
}

#elif VC_USE_ASM_64IMPL // msvc asm implementation

inline int64_t RoundHalfIntegerToEven_64(double x)
{
  #if defined( ITK_CHECK_FPU_ROUNDING_MODE )
  itkAssertInDebugAndIgnoreInReleaseMacro(fegetround() == FE_TONEAREST);
  #endif
  int64_t r;
  __asm
    {
    fld x
    fistp r
    }
  return r;
}

inline int64_t RoundHalfIntegerToEven_64(float x)
{
  #if defined( ITK_CHECK_FPU_ROUNDING_MODE )
  itkAssertInDebugAndIgnoreInReleaseMacro(fegetround() == FE_TONEAREST);
  #endif
  int64_t r;
  __asm
    {
    fld x
    fistp r
    }
  return r;
}

#else // Base implementation

inline int64_t RoundHalfIntegerToEven_64(double x) { return RoundHalfIntegerToEven_base< int64_t, double >(x); }
inline int64_t RoundHalfIntegerToEven_64(float x) { return RoundHalfIntegerToEven_base< int64_t, float >(x); }

#endif

#if USE_SSE2_64IMPL || GCC_USE_ASM_64IMPL || VC_USE_ASM_64IMPL

inline int64_t RoundHalfIntegerUp_64(double x) { return RoundHalfIntegerToEven_64(2 * x + 0.5) >> 1; }
inline int64_t RoundHalfIntegerUp_64(float x) { return RoundHalfIntegerToEven_64(2 * x + 0.5f) >> 1; }

inline int64_t Floor_64(double x) { return RoundHalfIntegerToEven_64(2 * x - 0.5) >> 1; }
inline int64_t Floor_64(float x) { return RoundHalfIntegerToEven_64(2 * x - 0.5f) >> 1; }

inline int64_t Ceil_64(double x) { return -( RoundHalfIntegerToEven_64(-0.5 - 2 * x) >> 1 ); }
inline int64_t Ceil_64(float x) { return -( RoundHalfIntegerToEven_64(-0.5f - 2 * x) >> 1 ); }

#else // Base implementation

inline int64_t RoundHalfIntegerUp_64(double x) { return RoundHalfIntegerUp_base< int64_t, double >(x); }
inline int64_t RoundHalfIntegerUp_64(float x) { return RoundHalfIntegerUp_base< int64_t, float >(x); }

inline int64_t Floor_64(double x) { return Floor_base< int64_t, double >(x); }
inline int64_t Floor_64(float x) { return Floor_base< int64_t, float >(x); }

inline int64_t Ceil_64(double x) { return Ceil_base< int64_t, double >(x); }
inline int64_t Ceil_64(float x) { return Ceil_base< int64_t, float >(x); }

#endif // USE_SSE2_64IMPL || GCC_USE_ASM_64IMPL || VC_USE_ASM_64IMPL

template <typename T>
struct FloatIEEETraits;

template <>
struct FloatIEEETraits<float>
{
  using IntType = int32_t;
  using UIntType = uint32_t;
};

template <>
struct FloatIEEETraits<double>
{
  using IntType = int64_t;
  using UIntType = uint64_t;
};

template <typename T>
union FloatIEEE
{
  using FloatType = T;
  using IntType = typename FloatIEEETraits<T>::IntType;
  using UIntType = typename FloatIEEETraits<T>::UIntType;

  FloatType asFloat;
  IntType asInt;
  UIntType asUInt;

  FloatIEEE(FloatType f): asFloat(f) {}
  FloatIEEE(IntType i): asInt(i) {}
  bool Sign() const
    {
    return (asUInt >> (sizeof(asUInt)*8-1)) != 0;
    }
  IntType AsULP() const
    {
    return this->Sign()? IntType(~(~UIntType(0) >> 1) - asUInt) : asInt;
    }
};

} // end namespace Detail
} // end namespace Math

// move to itkConceptChecking?
namespace Concept
{
template< typename T >
struct FloatOrDouble;
template< >
struct FloatOrDouble< float > {};
template< >
struct FloatOrDouble< double > {};
} // end namespace Concept
} // end namespace itk

#undef USE_SSE2_32IMPL
#undef GCC_USE_ASM_32IMPL
#undef VC_USE_ASM_32IMPL

#undef USE_SSE2_64IMPL
#undef GCC_USE_ASM_64IMPL
#undef VC_USE_ASM_64IMPL

#endif // end of itkMathDetail.h