cuda-samples/Samples/5_Domain_Specific/dxtc/CudaMath.h

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// Math functions and operators to be used with vector types.

#ifndef CUDAMATH_H
#define CUDAMATH_H

#include <cooperative_groups.h>

namespace cg = cooperative_groups;

// Use power method to find the first eigenvector.
// https://en.wikipedia.org/wiki/Power_iteration
inline __device__ __host__ float3 firstEigenVector(float matrix[6]) {
  // 8 iterations seems to be more than enough.

  float3 v = make_float3(1.0f, 1.0f, 1.0f);

  for (int i = 0; i < 8; i++) {
    float x = v.x * matrix[0] + v.y * matrix[1] + v.z * matrix[2];
    float y = v.x * matrix[1] + v.y * matrix[3] + v.z * matrix[4];
    float z = v.x * matrix[2] + v.y * matrix[4] + v.z * matrix[5];
    float m = max(max(x, y), z);
    float iv = 1.0f / m;
    v = make_float3(x * iv, y * iv, z * iv);
  }

  return v;
}

inline __device__ void colorSums(const float3 *colors, float3 *sums,
                                 cg::thread_group tile) {
  const int idx = threadIdx.x;

  sums[idx] = colors[idx];
  cg::sync(tile);
  sums[idx] += sums[idx ^ 8];
  cg::sync(tile);
  sums[idx] += sums[idx ^ 4];
  cg::sync(tile);
  sums[idx] += sums[idx ^ 2];
  cg::sync(tile);
  sums[idx] += sums[idx ^ 1];
}

inline __device__ float3 bestFitLine(const float3 *colors, float3 color_sum,
                                     cg::thread_group tile) {
  // Compute covariance matrix of the given colors.
  const int idx = threadIdx.x;

  float3 diff = colors[idx] - color_sum * (1.0f / 16.0f);

  // @@ Eliminate two-way bank conflicts here.
  // @@ It seems that doing that and unrolling the reduction doesn't help...
  __shared__ float covariance[16 * 6];

  covariance[6 * idx + 0] = diff.x * diff.x;  // 0, 6, 12, 2, 8, 14, 4, 10, 0
  covariance[6 * idx + 1] = diff.x * diff.y;
  covariance[6 * idx + 2] = diff.x * diff.z;
  covariance[6 * idx + 3] = diff.y * diff.y;
  covariance[6 * idx + 4] = diff.y * diff.z;
  covariance[6 * idx + 5] = diff.z * diff.z;

  cg::sync(tile);
  for (int d = 8; d > 0; d >>= 1) {
    if (idx < d) {
      covariance[6 * idx + 0] += covariance[6 * (idx + d) + 0];
      covariance[6 * idx + 1] += covariance[6 * (idx + d) + 1];
      covariance[6 * idx + 2] += covariance[6 * (idx + d) + 2];
      covariance[6 * idx + 3] += covariance[6 * (idx + d) + 3];
      covariance[6 * idx + 4] += covariance[6 * (idx + d) + 4];
      covariance[6 * idx + 5] += covariance[6 * (idx + d) + 5];
    }
    cg::sync(tile);
  }

  // Compute first eigen vector.
  return firstEigenVector(covariance);
}

#endif  // CUDAMATH_H