filter.cpp

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/*
Copyright 2012. All rights reserved.
Institute of Measurement and Control Systems
Karlsruhe Institute of Technology, Germany

This file is part of libelas.
Authors: Julius Ziegler, Andreas Geiger

libelas is free software; you can redistribute it and/or modify it under the
terms of the GNU General Public License as published by the Free Software
Foundation; either version 3 of the License, or any later version.

libelas 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 General Public License for more details.

You should have received a copy of the GNU General Public License along with
libelas; if not, write to the Free Software Foundation, Inc., 51 Franklin
Street, Fifth Floor, Boston, MA 02110-1301, USA
*/

#include <stdio.h>
#include <iostream>
#include <string.h>
#include <cassert>

#include "filter.h"

// define fixed-width datatypes for Visual Studio projects
// Linux env has the stdint.h
#ifndef _MSC_VER
  #include <stdint.h>
#else
  typedef __int8            int8_t;
  typedef __int16           int16_t;
  typedef __int32           int32_t;
  typedef __int64           int64_t;
  typedef unsigned __int8   uint8_t;
  typedef unsigned __int16  uint16_t;
  typedef unsigned __int32  uint32_t;
  typedef unsigned __int64  uint64_t;
#endif

// fast filters: implements 3x3 and 5x5 sobel filters and
//               5x5 blob and corner filters based on SSE2/3 instructions
namespace filter {

  // private namespace, public user functions at the bottom of this file
  namespace detail {
      //图像积分
    void integral_image( const uint8_t* in, int32_t* out, int w, int h ) {
      int32_t* out_top = out;
      const uint8_t* line_end = in + w;
      const uint8_t* in_end   = in + w*h;
      int32_t line_sum = 0;
      for( ; in != line_end; in++, out++ ) {
        line_sum += *in;
        *out = line_sum;
      }
      for( ; in != in_end; ) {
        int32_t line_sum = 0;
        const uint8_t* line_end = in + w;
        for( ; in != line_end; in++, out++, out_top++ ) {
          line_sum += *in;
          *out = *out_top + line_sum;
        }
      }
    }

    void unpack_8bit_to_16bit( const __m128i a, __m128i& b0, __m128i& b1 ) {
      __m128i zero = _mm_setzero_si128();
      //b0:0,a0
      b0 = _mm_unpacklo_epi8( a, zero );
      //b1:0,a1
      b1 = _mm_unpackhi_epi8( a, zero );
    }

    void pack_16bit_to_8bit_saturate( const __m128i a0, const __m128i a1, __m128i& b ) {
      b = _mm_packus_epi16( a0, a1 );
    }

    // convolve image with a (1,4,6,4,1) row vector. Result is accumulated into output.
    // output is scaled by 1/128, then clamped to [-128,128], and finally shifted to [0,255].
    void convolve_14641_row_5x5_16bit( const int16_t* in, uint8_t* out, int w, int h ) {
      assert( w % 16 == 0 && "width must be multiple of 16!" );
      const __m128i* i0 = (const __m128i*)(in);
      const int16_t* i1 = in+1;
      const int16_t* i2 = in+2;
      const int16_t* i3 = in+3;
      const int16_t* i4 = in+4;
      uint8_t* result   = out + 2;
      const int16_t* const end_input = in + w*h;
      __m128i offs = _mm_set1_epi16( 128 );
      for( ; i4 < end_input; i0 += 1, i1 += 8, i2 += 8, i3 += 8, i4 += 8, result += 16 ) {
        __m128i result_register_lo;
        __m128i result_register_hi;
        for( int i=0; i<2; i++ ) {
          __m128i* result_register;
          if( i==0 ) result_register = &result_register_lo;
          else       result_register = &result_register_hi;
          __m128i i0_register = *i0;
          __m128i i1_register = _mm_loadu_si128( (__m128i*)( i1 ) );
          __m128i i2_register = _mm_loadu_si128( (__m128i*)( i2 ) );
          __m128i i3_register = _mm_loadu_si128( (__m128i*)( i3 ) );
          __m128i i4_register = _mm_loadu_si128( (__m128i*)( i4 ) );
          *result_register = _mm_setzero_si128();
          *result_register = _mm_add_epi16( i0_register, *result_register );
          i1_register      = _mm_add_epi16( i1_register, i1_register  );
          i1_register      = _mm_add_epi16( i1_register, i1_register  );
          *result_register = _mm_add_epi16( i1_register, *result_register );
          i2_register      = _mm_add_epi16( i2_register, i2_register  );
          *result_register = _mm_add_epi16( i2_register, *result_register );
          i2_register      = _mm_add_epi16( i2_register, i2_register  );
          *result_register = _mm_add_epi16( i2_register, *result_register );
          i3_register      = _mm_add_epi16( i3_register, i3_register  );
          i3_register      = _mm_add_epi16( i3_register, i3_register  );
          *result_register = _mm_add_epi16( i3_register, *result_register );
          *result_register = _mm_add_epi16( i4_register, *result_register );
          //右移命令,1/128
          *result_register = _mm_srai_epi16( *result_register, 7 );
          *result_register = _mm_add_epi16( *result_register, offs );
          if( i==0 ) {
            i0 += 1;
            i1 += 8;
            i2 += 8;
            i3 += 8;
            i4 += 8;
          }
        }
        pack_16bit_to_8bit_saturate( result_register_lo, result_register_hi, result_register_lo );
        _mm_storeu_si128( ((__m128i*)( result )), result_register_lo );
      }
    }

    // convolve image with a (1,2,0,-2,-1) row vector. Result is accumulated into output.
    // This one works on 16bit input and 8bit output.
    // output is scaled by 1/128, then clamped to [-128,128], and finally shifted to [0,255].
    void convolve_12021_row_5x5_16bit( const int16_t* in, uint8_t* out, int w, int h ) {
      assert( w % 16 == 0 && "width must be multiple of 16!" );
      const __m128i*  i0 = (const __m128i*)(in);
      const int16_t*    i1 = in+1;
      const int16_t*    i3 = in+3;
      const int16_t*    i4 = in+4;
      uint8_t* result    = out + 2;
      const int16_t* const end_input = in + w*h;
      __m128i offs = _mm_set1_epi16( 128 );
      for( ; i4 < end_input; i0 += 1, i1 += 8, i3 += 8, i4 += 8, result += 16 ) {
        __m128i result_register_lo;
        __m128i result_register_hi;
        for( int i=0; i<2; i++ ) {
          __m128i* result_register;
          if( i==0 ) result_register = &result_register_lo;
          else       result_register = &result_register_hi;
          __m128i i0_register = *i0;
          __m128i i1_register = _mm_loadu_si128( (__m128i*)( i1 ) );
          __m128i i3_register = _mm_loadu_si128( (__m128i*)( i3 ) );
          __m128i i4_register = _mm_loadu_si128( (__m128i*)( i4 ) );
          *result_register = _mm_setzero_si128();
          *result_register = _mm_add_epi16( i0_register,   *result_register );
          i1_register      = _mm_add_epi16( i1_register, i1_register  );
          *result_register = _mm_add_epi16( i1_register,   *result_register );
          i3_register      = _mm_add_epi16( i3_register, i3_register  );
          *result_register = _mm_sub_epi16( *result_register, i3_register );
          *result_register = _mm_sub_epi16( *result_register, i4_register );
          *result_register = _mm_srai_epi16( *result_register, 7 );
          *result_register = _mm_add_epi16( *result_register, offs );
          if( i==0 ) {
            i0 += 1;
            i1 += 8;
            i3 += 8;
            i4 += 8;
          }
        }
        pack_16bit_to_8bit_saturate( result_register_lo, result_register_hi, result_register_lo );
        _mm_storeu_si128( ((__m128i*)( result )), result_register_lo );
      }
    }

    // convolve image with a (1,2,1) row vector. Result is accumulated into output.
    // This one works on 16bit input and 8bit output.
    // output is scaled by 1/4, then clamped to [-128,128], and finally shifted to [0,255].
    void convolve_121_row_3x3_16bit( const int16_t* in, uint8_t* out, int w, int h ) {
      assert( w % 16 == 0 && "width must be multiple of 16!" );
      const __m128i* i0 = (const __m128i*)(in);
      const int16_t* i1 = in+1;
      const int16_t* i2 = in+2;
      uint8_t* result   = out + 1;
      const int16_t* const end_input = in + w*h;
      const size_t blocked_loops = (w*h-2)/16;
      __m128i offs = _mm_set1_epi16( 128 );
      for( size_t i=0; i != blocked_loops; i++ ) {
        __m128i result_register_lo;
        __m128i result_register_hi;
        __m128i i1_register;
        __m128i i2_register;

        i1_register        = _mm_loadu_si128( (__m128i*)( i1 ) );
        i2_register        = _mm_loadu_si128( (__m128i*)( i2 ) );
        result_register_lo = *i0;
        /*result_register_lo = _mm_loadu_si128(i0);*/
        //i1*2
        i1_register        = _mm_add_epi16( i1_register, i1_register );
        //i0+2*i1;
        result_register_lo = _mm_add_epi16( i1_register, result_register_lo );
        //i0+2*i1+i2;
        result_register_lo = _mm_add_epi16( i2_register, result_register_lo );
        //1/4
        result_register_lo = _mm_srai_epi16( result_register_lo, 2 );
        //+=128
        result_register_lo = _mm_add_epi16( result_register_lo, offs );

        i0++;
        i1+=8;
        i2+=8;

        i1_register        = _mm_loadu_si128( (__m128i*)( i1 ) );
        i2_register        = _mm_loadu_si128( (__m128i*)( i2 ) );
        result_register_hi = *i0;
        i1_register        = _mm_add_epi16( i1_register, i1_register );
        result_register_hi = _mm_add_epi16( i1_register, result_register_hi );
        result_register_hi = _mm_add_epi16( i2_register, result_register_hi );
        result_register_hi = _mm_srai_epi16( result_register_hi, 2 );
        result_register_hi = _mm_add_epi16( result_register_hi, offs );

        i0++;
        i1+=8;
        i2+=8;

        pack_16bit_to_8bit_saturate( result_register_lo, result_register_hi, result_register_lo );
        _mm_storeu_si128( ((__m128i*)( result )), result_register_lo );

        result += 16;
      }
    }

    // convolve image with a (1,0,-1) row vector. Result is accumulated into output.
    // This one works on 16bit input and 8bit output.
    // output is scaled by 1/4, then clamped to [-128,128], and finally shifted to [0,255].
    void convolve_101_row_3x3_16bit( const int16_t* in, uint8_t* out, int w, int h ) {
      assert( w % 16 == 0 && "width must be multiple of 16!" );
      const __m128i*  i0 = (const __m128i*)(in);
      const int16_t*    i2 = in+2;
      uint8_t* result    = out + 1;
      const int16_t* const end_input = in + w*h;
      const size_t blocked_loops = (w*h-2)/16;
      __m128i offs = _mm_set1_epi16( 128 );
      for( size_t i=0; i != blocked_loops; i++ ) {
        __m128i result_register_lo;
        __m128i result_register_hi;
        __m128i i2_register;

        i2_register = _mm_loadu_si128( (__m128i*)( i2 ) );
        result_register_lo  = *i0;
        result_register_lo  = _mm_sub_epi16( result_register_lo, i2_register );
        result_register_lo  = _mm_srai_epi16( result_register_lo, 2 );
        result_register_lo  = _mm_add_epi16( result_register_lo, offs );

        i0 += 1;
        i2 += 8;

        i2_register = _mm_loadu_si128( (__m128i*)( i2 ) );
        result_register_hi  = *i0;
        result_register_hi  = _mm_sub_epi16( result_register_hi, i2_register );
        result_register_hi  = _mm_srai_epi16( result_register_hi, 2 );
        result_register_hi  = _mm_add_epi16( result_register_hi, offs );

        i0 += 1;
        i2 += 8;

        pack_16bit_to_8bit_saturate( result_register_lo, result_register_hi, result_register_lo );
        _mm_storeu_si128( ((__m128i*)( result )), result_register_lo );

        result += 16;
      }

      for( ; i2 < end_input; i2++, result++) {
        *result = ((*(i2-2) - *i2)>>2)+128;
      }
    }

    void convolve_cols_5x5( const unsigned char* in, int16_t* out_v, int16_t* out_h, int w, int h ) {
      using namespace std;
      memset( out_h, 0, w*h*sizeof(int16_t) );
      memset( out_v, 0, w*h*sizeof(int16_t) );
      assert( w % 16 == 0 && "width must be multiple of 16!" );
      //std::cout<<"w="<<w<<"h="<<h<<std::endl;
      //w=512,w_chunk=32
      //一行有多少个__m128i
      const int w_chunk  = w/16;
      __m128i*  i0       = (__m128i*)( in );
      __m128i*  i1       = (__m128i*)( in ) + w_chunk*1;
      __m128i*  i2       = (__m128i*)( in ) + w_chunk*2;
      __m128i*  i3       = (__m128i*)( in ) + w_chunk*3;
      __m128i*  i4       = (__m128i*)( in ) + w_chunk*4;
      //水平方向,从第三行开始
      __m128i* result_h  = (__m128i*)( out_h ) + 4*w_chunk;
      //竖直方向
      __m128i* result_v  = (__m128i*)( out_v ) + 4*w_chunk;
      __m128i* end_input = (__m128i*)( in ) + w_chunk*h;
      //八个数全是6
      __m128i sixes      = _mm_set1_epi16( 6 );
      __m128i fours      = _mm_set1_epi16( 4 );
      for( ; i4 != end_input; i0++, i1++, i2++, i3++, i4++, result_v+=2, result_h+=2 ) {
        __m128i ilo, ihi;
        //扩展成16bits
        unpack_8bit_to_16bit( *i0, ihi, ilo );
        //高八位数字与地八位数字
        *result_h     = _mm_add_epi16( ihi, *result_h );
        *(result_h+1) = _mm_add_epi16( ilo, *(result_h+1) );
        //高低八位数字
        *result_v     = _mm_add_epi16( *result_v, ihi );
        *(result_v+1) = _mm_add_epi16( *(result_v+1), ilo );

        //ihi,ilo已经被清空,重新装入i1的数据
        unpack_8bit_to_16bit( *i1, ihi, ilo );
        //i0+2i1
        *result_h     = _mm_add_epi16( ihi, *result_h );
        *result_h     = _mm_add_epi16( ihi, *result_h );
        *(result_h+1) = _mm_add_epi16( ilo, *(result_h+1) );
        *(result_h+1) = _mm_add_epi16( ilo, *(result_h+1) );
        ihi = _mm_mullo_epi16( ihi, fours );
        ilo = _mm_mullo_epi16( ilo, fours );
        //4倍高低八位
        //i0+4i1
        *result_v     = _mm_add_epi16( *result_v, ihi );
        *(result_v+1) = _mm_add_epi16( *(result_v+1), ilo );

        unpack_8bit_to_16bit( *i2, ihi, ilo );
        //i0+2i1+0i2
        ihi = _mm_mullo_epi16( ihi, sixes );
        ilo = _mm_mullo_epi16( ilo, sixes );
        //6倍高低八位
        //i0+4i1+6i2
        *result_v     = _mm_add_epi16( *result_v, ihi );
        *(result_v+1) = _mm_add_epi16( *(result_v+1), ilo );

        unpack_8bit_to_16bit( *i3, ihi, ilo );
        //i0+2i1+0i2-2i1
        *result_h     = _mm_sub_epi16( *result_h, ihi );
        *result_h     = _mm_sub_epi16( *result_h, ihi );
        *(result_h+1) = _mm_sub_epi16( *(result_h+1), ilo );
        *(result_h+1) = _mm_sub_epi16( *(result_h+1), ilo );
        ihi = _mm_mullo_epi16( ihi, fours );
        ilo = _mm_mullo_epi16( ilo, fours );
        //i0+4i1+6i2+4i3
        *result_v     = _mm_add_epi16( *result_v, ihi );
        *(result_v+1) = _mm_add_epi16( *(result_v+1), ilo );

        unpack_8bit_to_16bit( *i4, ihi, ilo );
        //i0+2i1+0i2-2i3-i4
        *result_h     = _mm_sub_epi16( *result_h, ihi );
        *(result_h+1) = _mm_sub_epi16( *(result_h+1), ilo );
        //i0+4i1+6i2+4i3+i4
        *result_v     = _mm_add_epi16( *result_v, ihi );
        *(result_v+1) = _mm_add_epi16( *(result_v+1), ilo );
      }
    }

    void convolve_col_p1p1p0m1m1_5x5( const unsigned char* in, int16_t* out, int w, int h ) {
      memset( out, 0, w*h*sizeof(int16_t) );
      using namespace std;
      assert( w % 16 == 0 && "width must be multiple of 16!" );
      const int w_chunk  = w/16;
      __m128i*  i0       = (__m128i*)( in );
      __m128i*  i1       = (__m128i*)( in ) + w_chunk*1;
      __m128i*  i3       = (__m128i*)( in ) + w_chunk*3;
      __m128i*  i4       = (__m128i*)( in ) + w_chunk*4;
      __m128i* result    = (__m128i*)( out ) + 4*w_chunk;
      __m128i* end_input = (__m128i*)( in ) + w_chunk*h;
      for( ; i4 != end_input; i0++, i1++, i3++, i4++, result+=2 ) {
        __m128i ilo0, ihi0;
        unpack_8bit_to_16bit( *i0, ihi0, ilo0 );
        __m128i ilo1, ihi1;
        unpack_8bit_to_16bit( *i1, ihi1, ilo1 );
        *result     = _mm_add_epi16( ihi0, ihi1 );
        *(result+1) = _mm_add_epi16( ilo0, ilo1 );
        __m128i ilo, ihi;
        unpack_8bit_to_16bit( *i3, ihi, ilo );
        *result     = _mm_sub_epi16( *result, ihi );
        *(result+1) = _mm_sub_epi16( *(result+1), ilo );
        unpack_8bit_to_16bit( *i4, ihi, ilo );
        *result     = _mm_sub_epi16( *result, ihi );
        *(result+1) = _mm_sub_epi16( *(result+1), ilo );
      }
    }

    void convolve_row_p1p1p0m1m1_5x5( const int16_t* in, int16_t* out, int w, int h ) {
      assert( w % 16 == 0 && "width must be multiple of 16!" );
      const __m128i*  i0 = (const __m128i*)(in);
      const int16_t*    i1 = in+1;
      const int16_t*    i3 = in+3;
      const int16_t*    i4 = in+4;
      int16_t* result    = out + 2;
      const int16_t* const end_input = in + w*h;
      for( ; i4+8 < end_input; i0 += 1, i1 += 8, i3 += 8, i4 += 8, result += 8 ) {
        __m128i result_register;
        __m128i i0_register = *i0;
        __m128i i1_register = _mm_loadu_si128( (__m128i*)( i1 ) );
        __m128i i3_register = _mm_loadu_si128( (__m128i*)( i3 ) );
        __m128i i4_register = _mm_loadu_si128( (__m128i*)( i4 ) );
        result_register     = _mm_add_epi16( i0_register,     i1_register );
        result_register     = _mm_sub_epi16( result_register, i3_register );
        result_register     = _mm_sub_epi16( result_register, i4_register );
        _mm_storeu_si128( ((__m128i*)( result )), result_register );
      }
    }

    void convolve_cols_3x3( const unsigned char* in, int16_t* out_v, int16_t* out_h, int w, int h ) {
      using namespace std;
      assert( w % 16 == 0 && "width must be multiple of 16!" );
      const int w_chunk  = w/16;
      __m128i*  i0       = (__m128i*)( in );
      __m128i*  i1       = (__m128i*)( in ) + w_chunk*1;
      __m128i*  i2       = (__m128i*)( in ) + w_chunk*2;
      __m128i* result_h  = (__m128i*)( out_h ) + 2*w_chunk;
      __m128i* result_v  = (__m128i*)( out_v ) + 2*w_chunk;
      __m128i* end_input = (__m128i*)( in ) + w_chunk*h;
      for( ; i2 != end_input; i0++, i1++, i2++, result_v+=2, result_h+=2 ) {
        *result_h     = _mm_setzero_si128();
        *(result_h+1) = _mm_setzero_si128();
        *result_v     = _mm_setzero_si128();
        *(result_v+1) = _mm_setzero_si128();
        __m128i ilo, ihi;
        unpack_8bit_to_16bit( *i0, ihi, ilo );
        unpack_8bit_to_16bit( *i0, ihi, ilo );
        *result_h     = _mm_add_epi16( ihi, *result_h );
        *(result_h+1) = _mm_add_epi16( ilo, *(result_h+1) );
        *result_v     = _mm_add_epi16( *result_v, ihi );
        *(result_v+1) = _mm_add_epi16( *(result_v+1), ilo );
        unpack_8bit_to_16bit( *i1, ihi, ilo );
        *result_v     = _mm_add_epi16( *result_v, ihi );
        *(result_v+1) = _mm_add_epi16( *(result_v+1), ilo );
        *result_v     = _mm_add_epi16( *result_v, ihi );
        *(result_v+1) = _mm_add_epi16( *(result_v+1), ilo );
        unpack_8bit_to_16bit( *i2, ihi, ilo );
        *result_h     = _mm_sub_epi16( *result_h, ihi );
        *(result_h+1) = _mm_sub_epi16( *(result_h+1), ilo );
        *result_v     = _mm_add_epi16( *result_v, ihi );
        *(result_v+1) = _mm_add_epi16( *(result_v+1), ilo );
      }
    }
  };

  void sobel3x3( const uint8_t* in, uint8_t* out_v, uint8_t* out_h, int w, int h ) {
    int16_t* temp_h = (int16_t*)( _mm_malloc( w*h*sizeof( int16_t ), 16 ) );
    int16_t* temp_v = (int16_t*)( _mm_malloc( w*h*sizeof( int16_t ), 16 ) );
    detail::convolve_cols_3x3( in, temp_v, temp_h, w, h );
    detail::convolve_101_row_3x3_16bit( temp_v, out_v, w, h );
    detail::convolve_121_row_3x3_16bit( temp_h, out_h, w, h );
    _mm_free( temp_h );
    _mm_free( temp_v );
  }

  //小核对噪声更加敏感,大核在更多像素上计算拟合
  void sobel5x5( const uint8_t* in, uint8_t* out_v, uint8_t* out_h, int w, int h ) {
    int16_t* temp_h = (int16_t*)( _mm_malloc( w*h*sizeof( int16_t ), 16 ) );
    int16_t* temp_v = (int16_t*)( _mm_malloc( w*h*sizeof( int16_t ), 16 ) );
    detail::convolve_cols_5x5( in, temp_v, temp_h, w, h );
    detail::convolve_12021_row_5x5_16bit( temp_v, out_v, w, h );
    detail::convolve_14641_row_5x5_16bit( temp_h, out_h, w, h );
    _mm_free( temp_h );
    _mm_free( temp_v );
  }

  // -1 -1  0  1  1
  // -1 -1  0  1  1
  //  0  0  0  0  0
  //  1  1  0 -1 -1
  //  1  1  0 -1 -1
  void checkerboard5x5( const uint8_t* in, int16_t* out, int w, int h ) {
    int16_t* temp = (int16_t*)( _mm_malloc( w*h*sizeof( int16_t ), 16 ) );
    detail::convolve_col_p1p1p0m1m1_5x5( in, temp, w, h );
    detail::convolve_row_p1p1p0m1m1_5x5( temp, out, w, h );
    _mm_free( temp );
  }

  // -1 -1 -1 -1 -1
  // -1  1  1  1 -1
  // -1  1  8  1 -1
  // -1  1  1  1 -1
  // -1 -1 -1 -1 -1
  void blob5x5( const uint8_t* in, int16_t* out, int w, int h ) {
    int32_t* integral = (int32_t*)( _mm_malloc( w*h*sizeof( int32_t ), 16 ) );
    detail::integral_image( in, integral, w, h );
    int16_t* out_ptr   = out + 3 + 3*w;
    int16_t* out_end   = out + w * h - 2 - 2*w;
    const int32_t* i00 = integral;
    const int32_t* i50 = integral + 5;
    const int32_t* i05 = integral + 5*w;
    const int32_t* i55 = integral + 5 + 5*w;
    const int32_t* i11 = integral + 1 + 1*w;
    const int32_t* i41 = integral + 4 + 1*w;
    const int32_t* i14 = integral + 1 + 4*w;
    const int32_t* i44 = integral + 4 + 4*w;
    const uint8_t* im22 = in + 3 + 3*w;
    for( ; out_ptr != out_end; out_ptr++, i00++, i50++, i05++, i55++, i11++, i41++, i14++, i44++, im22++ ) {
      int32_t result = 0;
      result = -( *i55 - *i50 - *i05 + *i00 );
      result += 2*( *i44 - *i41 - *i14 + *i11 );
      result += 7* *im22;
      *out_ptr = result;
    }
    _mm_free( integral );
  }
};