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// Ceres Solver - A fast non-linear least squares minimizer
// Copyright 2022 Google Inc. All rights reserved.
// http://ceres-solver.org/
//
// 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 Google Inc. 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 AND CONTRIBUTORS "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.
//
// Author: yangfan34@lenovo.com (Lenovo Research Device+ Lab - Shanghai)
//
// Optimization for simple blas functions used in the Schur Eliminator.
// These are fairly basic implementations which already yield a significant
// speedup in the eliminator performance.
#ifndef CERES_INTERNAL_SMALL_BLAS_GENERIC_H_
#define CERES_INTERNAL_SMALL_BLAS_GENERIC_H_
namespace ceres {
namespace internal {
// The following macros are used to share code
#define CERES_GEMM_OPT_NAIVE_HEADER \
double c0 = 0.0; \
double c1 = 0.0; \
double c2 = 0.0; \
double c3 = 0.0; \
const double* pa = a; \
const double* pb = b; \
const int span = 4; \
int col_r = col_a & (span - 1); \
int col_m = col_a - col_r;
#define CERES_GEMM_OPT_STORE_MAT1X4 \
if (kOperation > 0) { \
*c++ += c0; \
*c++ += c1; \
*c++ += c2; \
*c++ += c3; \
} else if (kOperation < 0) { \
*c++ -= c0; \
*c++ -= c1; \
*c++ -= c2; \
*c++ -= c3; \
} else { \
*c++ = c0; \
*c++ = c1; \
*c++ = c2; \
*c++ = c3; \
}
// Matrix-Matrix Multiplication
// Figure out 1x4 of Matrix C in one batch
//
// c op a * B;
// where op can be +=, -=, or =, indicated by kOperation.
//
// Matrix C Matrix A Matrix B
//
// C0, C1, C2, C3 op A0, A1, A2, A3, ... * B0, B1, B2, B3
// B4, B5, B6, B7
// B8, B9, Ba, Bb
// Bc, Bd, Be, Bf
// . , . , . , .
// . , . , . , .
// . , . , . , .
//
// unroll for loops
// utilize the data resided in cache
// NOTE: col_a means the columns of A
static inline void MMM_mat1x4(const int col_a,
const double* a,
const double* b,
const int col_stride_b,
double* c,
const int kOperation) {
CERES_GEMM_OPT_NAIVE_HEADER
double av = 0.0;
int bi = 0;
#define CERES_GEMM_OPT_MMM_MAT1X4_MUL \
av = pa[k]; \
pb = b + bi; \
c0 += av * pb[0]; \
c1 += av * pb[1]; \
c2 += av * pb[2]; \
c3 += av * pb[3]; \
pb += 4; \
bi += col_stride_b; \
k++;
for (int k = 0; k < col_m;) {
CERES_GEMM_OPT_MMM_MAT1X4_MUL
CERES_GEMM_OPT_MMM_MAT1X4_MUL
CERES_GEMM_OPT_MMM_MAT1X4_MUL
CERES_GEMM_OPT_MMM_MAT1X4_MUL
}
for (int k = col_m; k < col_a;) {
CERES_GEMM_OPT_MMM_MAT1X4_MUL
}
CERES_GEMM_OPT_STORE_MAT1X4
#undef CERES_GEMM_OPT_MMM_MAT1X4_MUL
}
// Matrix Transpose-Matrix multiplication
// Figure out 1x4 of Matrix C in one batch
//
// c op a' * B;
// where op can be +=, -=, or = indicated by kOperation.
//
// Matrix A
//
// A0
// A1
// A2
// A3
// .
// .
// .
//
// Matrix C Matrix A' Matrix B
//
// C0, C1, C2, C3 op A0, A1, A2, A3, ... * B0, B1, B2, B3
// B4, B5, B6, B7
// B8, B9, Ba, Bb
// Bc, Bd, Be, Bf
// . , . , . , .
// . , . , . , .
// . , . , . , .
//
// unroll for loops
// utilize the data resided in cache
// NOTE: col_a means the columns of A'
static inline void MTM_mat1x4(const int col_a,
const double* a,
const int col_stride_a,
const double* b,
const int col_stride_b,
double* c,
const int kOperation) {
CERES_GEMM_OPT_NAIVE_HEADER
double av = 0.0;
int ai = 0;
int bi = 0;
#define CERES_GEMM_OPT_MTM_MAT1X4_MUL \
av = pa[ai]; \
pb = b + bi; \
c0 += av * pb[0]; \
c1 += av * pb[1]; \
c2 += av * pb[2]; \
c3 += av * pb[3]; \
pb += 4; \
ai += col_stride_a; \
bi += col_stride_b;
for (int k = 0; k < col_m; k += span) {
CERES_GEMM_OPT_MTM_MAT1X4_MUL
CERES_GEMM_OPT_MTM_MAT1X4_MUL
CERES_GEMM_OPT_MTM_MAT1X4_MUL
CERES_GEMM_OPT_MTM_MAT1X4_MUL
}
for (int k = col_m; k < col_a; k++) {
CERES_GEMM_OPT_MTM_MAT1X4_MUL
}
CERES_GEMM_OPT_STORE_MAT1X4
#undef CERES_GEMM_OPT_MTM_MAT1X4_MUL
}
// Matrix-Vector Multiplication
// Figure out 4x1 of vector c in one batch
//
// c op A * b;
// where op can be +=, -=, or =, indicated by kOperation.
//
// Vector c Matrix A Vector b
//
// C0 op A0, A1, A2, A3, ... * B0
// C1 A4, A5, A6, A7, ... B1
// C2 A8, A9, Aa, Ab, ... B2
// C3 Ac, Ad, Ae, Af, ... B3
// .
// .
// .
//
// unroll for loops
// utilize the data resided in cache
// NOTE: col_a means the columns of A
static inline void MVM_mat4x1(const int col_a,
const double* a,
const int col_stride_a,
const double* b,
double* c,
const int kOperation) {
CERES_GEMM_OPT_NAIVE_HEADER
double bv = 0.0;
// clang-format off
#define CERES_GEMM_OPT_MVM_MAT4X1_MUL \
bv = *pb; \
c0 += *(pa ) * bv; \
c1 += *(pa + col_stride_a ) * bv; \
c2 += *(pa + col_stride_a * 2) * bv; \
c3 += *(pa + col_stride_a * 3) * bv; \
pa++; \
pb++;
// clang-format on
for (int k = 0; k < col_m; k += span) {
CERES_GEMM_OPT_MVM_MAT4X1_MUL
CERES_GEMM_OPT_MVM_MAT4X1_MUL
CERES_GEMM_OPT_MVM_MAT4X1_MUL
CERES_GEMM_OPT_MVM_MAT4X1_MUL
}
for (int k = col_m; k < col_a; k++) {
CERES_GEMM_OPT_MVM_MAT4X1_MUL
}
CERES_GEMM_OPT_STORE_MAT1X4
#undef CERES_GEMM_OPT_MVM_MAT4X1_MUL
}
// Matrix Transpose-Vector multiplication
// Figure out 4x1 of vector c in one batch
//
// c op A' * b;
// where op can be +=, -=, or =, indicated by kOperation.
//
// Matrix A
//
// A0, A4, A8, Ac
// A1, A5, A9, Ad
// A2, A6, Aa, Ae
// A3, A7, Ab, Af
// . , . , . , .
// . , . , . , .
// . , . , . , .
//
// Vector c Matrix A' Vector b
//
// C0 op A0, A1, A2, A3, ... * B0
// C1 A4, A5, A6, A7, ... B1
// C2 A8, A9, Aa, Ab, ... B2
// C3 Ac, Ad, Ae, Af, ... B3
// .
// .
// .
//
// unroll for loops
// utilize the data resided in cache
// NOTE: col_a means the columns of A'
static inline void MTV_mat4x1(const int col_a,
const double* a,
const int col_stride_a,
const double* b,
double* c,
const int kOperation) {
CERES_GEMM_OPT_NAIVE_HEADER
double bv = 0.0;
// clang-format off
#define CERES_GEMM_OPT_MTV_MAT4X1_MUL \
bv = *pb; \
c0 += *(pa ) * bv; \
c1 += *(pa + 1) * bv; \
c2 += *(pa + 2) * bv; \
c3 += *(pa + 3) * bv; \
pa += col_stride_a; \
pb++;
// clang-format on
for (int k = 0; k < col_m; k += span) {
CERES_GEMM_OPT_MTV_MAT4X1_MUL
CERES_GEMM_OPT_MTV_MAT4X1_MUL
CERES_GEMM_OPT_MTV_MAT4X1_MUL
CERES_GEMM_OPT_MTV_MAT4X1_MUL
}
for (int k = col_m; k < col_a; k++) {
CERES_GEMM_OPT_MTV_MAT4X1_MUL
}
CERES_GEMM_OPT_STORE_MAT1X4
#undef CERES_GEMM_OPT_MTV_MAT4X1_MUL
}
#undef CERES_GEMM_OPT_NAIVE_HEADER
#undef CERES_GEMM_OPT_STORE_MAT1X4
} // namespace internal
} // namespace ceres
#endif // CERES_INTERNAL_SMALL_BLAS_GENERIC_H_
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