matrices.h

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/*
    This file is part of darktable,
    Copyright (C) 2021 darktable developers.
 
    darktable 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
    (at your option) any later version.
 
    darktable 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 darktable.  If not, see <http://www.gnu.org/licenses/>.
*/
 
#pragma once
 
#include "common/math.h"
 
// a 3x3 matrix, padded to permit SSE instructions to be used for multiplication and addition
typedef float DT_ALIGNED_ARRAY dt_colormatrix_t[4][4];
 
static inline int mat3SSEinv(dt_colormatrix_t dst, const dt_colormatrix_t src)
{
#define A(y, x) src[(y - 1)][(x - 1)]
#define B(y, x) dst[(y - 1)][(x - 1)]
 
  const float det = A(1, 1) * (A(3, 3) * A(2, 2) - A(3, 2) * A(2, 3))
                    - A(2, 1) * (A(3, 3) * A(1, 2) - A(3, 2) * A(1, 3))
                    + A(3, 1) * (A(2, 3) * A(1, 2) - A(2, 2) * A(1, 3));
 
  const float epsilon = 1e-7f;
  if(fabsf(det) < epsilon) return 1;
 
  const float invDet = 1.f / det;
 
  B(1, 1) = invDet * (A(3, 3) * A(2, 2) - A(3, 2) * A(2, 3));
  B(1, 2) = -invDet * (A(3, 3) * A(1, 2) - A(3, 2) * A(1, 3));
  B(1, 3) = invDet * (A(2, 3) * A(1, 2) - A(2, 2) * A(1, 3));
 
  B(2, 1) = -invDet * (A(3, 3) * A(2, 1) - A(3, 1) * A(2, 3));
  B(2, 2) = invDet * (A(3, 3) * A(1, 1) - A(3, 1) * A(1, 3));
  B(2, 3) = -invDet * (A(2, 3) * A(1, 1) - A(2, 1) * A(1, 3));
 
  B(3, 1) = invDet * (A(3, 2) * A(2, 1) - A(3, 1) * A(2, 2));
  B(3, 2) = -invDet * (A(3, 2) * A(1, 1) - A(3, 1) * A(1, 2));
  B(3, 3) = invDet * (A(2, 2) * A(1, 1) - A(2, 1) * A(1, 2));
#undef A
#undef B
  return 0;
}
 
 
// transpose a padded 3x3 matrix
static inline void transpose_3xSSE(const dt_colormatrix_t input, dt_colormatrix_t output)
{
  output[0][0] = input[0][0];
  output[0][1] = input[1][0];
  output[0][2] = input[2][0];
  output[0][3] = 0.0f;
 
  output[1][0] = input[0][1];
  output[1][1] = input[1][1];
  output[1][2] = input[2][1];
  output[1][3] = 0.0f;
 
  output[2][0] = input[0][2];
  output[2][1] = input[1][2];
  output[2][2] = input[2][2];
  output[2][3] = 0.0f;
 
  for_four_channels(c, aligned(output))
    output[3][c] = 0.0f;
}
 
 
// transpose and pad a 3x3 matrix into the padded format optimized for vectorization
static inline void transpose_3x3_to_3xSSE(const float input[9], dt_colormatrix_t output)
{
  output[0][0] = input[0];
  output[0][1] = input[3];
  output[0][2] = input[6];
  output[0][3] = 0.0f;
 
  output[1][0] = input[1];
  output[1][1] = input[4];
  output[1][2] = input[7];
  output[1][3] = 0.0f;
 
  output[2][0] = input[2];
  output[2][1] = input[5];
  output[2][2] = input[8];
  output[2][3] = 0.0f;
 
  for_four_channels(c, aligned(output))
    output[3][c] = 0.0f;
}
 
// convert a 3x3 matrix into the padded format optimized for vectorization
static inline void repack_double3x3_to_3xSSE(const double input[9], dt_colormatrix_t output)
{
  output[0][0] = input[0];
  output[0][1] = input[1];
  output[0][2] = input[2];
  output[0][3] = 0.0f;
 
  output[1][0] = input[3];
  output[1][1] = input[4];
  output[1][2] = input[5];
  output[1][3] = 0.0f;
 
  output[2][0] = input[6];
  output[2][1] = input[7];
  output[2][2] = input[8];
  output[2][3] = 0.0f;
 
  for(size_t c = 0; c < 4; c++)
    output[3][c] = 0.0f;
}
 
// convert a 3x3 matrix into the padded format optimized for vectorization
static inline void pack_3xSSE_to_3x3(const dt_colormatrix_t input, float output[9])
{
  output[0] = input[0][0];
  output[1] = input[0][1];
  output[2] = input[0][2];
  output[3] = input[1][0];
  output[4] = input[1][1];
  output[5] = input[1][2];
  output[6] = input[2][0];
  output[7] = input[2][1];
  output[8] = input[2][2];
}
 
// vectorized multiplication of padded 3x3 matrices
static inline void dt_colormatrix_mul(dt_colormatrix_t dst, const dt_colormatrix_t m1, const dt_colormatrix_t m2)
{
  for(int k = 0; k < 3; ++k)
  {
    dt_aligned_pixel_t sum = { 0.0f };
    for_each_channel(i)
    {
      for(int j = 0; j < 3; j++)
        sum[i] += m1[k][j] * m2[j][i];
      dst[k][i] = sum[i];
    }
  }
}
 
// multiply two padded 3x3 matrices
// dest needs to be different from m1 and m2
// dest = m1 * m2 in this order
// TODO: see if that refactors with the previous
#ifdef _OPENMP
#pragma omp declare simd
#endif
static inline void mat3SSEmul(dt_colormatrix_t dest, const dt_colormatrix_t m1, const dt_colormatrix_t m2)
{
  for(int k = 0; k < 3; k++)
  {
    for(int i = 0; i < 3; i++)
    {
      float x = 0.0f;
      for(int j = 0; j < 3; j++)
        x += m1[k][j] * m2[j][i];
      dest[k][i] = x;
    }
  }
}
 
#ifdef _OPENMP
#pragma omp declare simd uniform(M) aligned(M:64) aligned(v_in, v_out:16)
#endif
static inline void dot_product(const dt_aligned_pixel_t v_in, const dt_colormatrix_t M, dt_aligned_pixel_t v_out)
{
  // specialized 3x4 dot products of 4x1 RGB-alpha pixels
  #ifdef _OPENMP
  #pragma omp simd aligned(M:64) aligned(v_in, v_out:16)
  #endif
  for(size_t i = 0; i < 3; ++i) v_out[i] = scalar_product(v_in, M[i]);
}
 
 
 
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