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/* Copyright (c) 2022, NVIDIA CORPORATION. All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
* * Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
* * Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in the
* documentation and/or other materials provided with the distribution.
* * Neither the name of NVIDIA CORPORATION nor the names of its
* contributors may be used to endorse or promote products derived
* from this software without specific prior written permission.
*
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS ``AS IS'' AND ANY
* EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
* PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR
* CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
* EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
* PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
* PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY
* OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
* (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
* OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*/
// 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
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