int main(int argc, char** argv) {
arg_size = 1024;
if(argc > 1) arg_size = atoi(argv[1]);
arg_cutoff_value = 64;
if(argc > 2) arg_cutoff_value = atoi(argv[2]);
if((arg_size & (arg_size - 1)) != 0 || (arg_size % 16) != 0) inncabs::error("Error: matrix size must be a power of 2 and a multiple of 16\n");
REAL *A = alloc_matrix(arg_size);
REAL *B = alloc_matrix(arg_size);
REAL *C = alloc_matrix(arg_size);
REAL *D = alloc_matrix(arg_size);
std::stringstream ss;
ss << "Strassen Algorithm (" << arg_size << " x " << arg_size
<< " matrix with cutoff " << arg_cutoff_value << ") ";
init_matrix(arg_size, A, arg_size);
init_matrix(arg_size, B, arg_size);
OptimizedStrassenMultiply_seq(D, A, B, arg_size, arg_size, arg_size, arg_size, 1);
inncabs::run_all(
[&](const std::launch l) {
OptimizedStrassenMultiply_par(l, C, A, B, arg_size, arg_size, arg_size, arg_size, 1);
return 1;
},
[&](int result) {
return compare_matrix(arg_size, C, arg_size, D, arg_size);
},
ss.str()
);
}
/*****************************************************************************
**
** OptimizedStrassenMultiply
**
** For large matrices A, B, and C of size MatrixSize * MatrixSize this
** function performs the operation C = A x B efficiently.
**
** INPUT:
** C = (*C WRITE) Address of top left element of matrix C.
** A = (*A IS READ ONLY) Address of top left element of matrix A.
** B = (*B IS READ ONLY) Address of top left element of matrix B.
** MatrixSize = Size of matrices (for n*n matrix, MatrixSize = n)
** RowWidthA = Number of elements in memory between A[x,y] and A[x,y+1]
** RowWidthB = Number of elements in memory between B[x,y] and B[x,y+1]
** RowWidthC = Number of elements in memory between C[x,y] and C[x,y+1]
**
** OUTPUT:
** C = (*C WRITE) Matrix C contains A x B. (Initial value of *C undefined.)
**
*****************************************************************************/
void OptimizedStrassenMultiply_seq(REAL *C, REAL *A, REAL *B, unsigned MatrixSize,
unsigned RowWidthC, unsigned RowWidthA, unsigned RowWidthB, int Depth)
{
unsigned QuadrantSize = MatrixSize >> 1; /* MatixSize / 2 */
unsigned QuadrantSizeInBytes = sizeof(REAL) * QuadrantSize * QuadrantSize
+ 32;
unsigned Column, Row;
/************************************************************************
** For each matrix A, B, and C, we'll want pointers to each quandrant
** in the matrix. These quandrants will be addressed as follows:
** -- --
** | A11 A12 |
** | |
** | A21 A22 |
** -- --
************************************************************************/
REAL /* *A11, *B11, *C11, */ *A12, *B12, *C12,
*A21, *B21, *C21, *A22, *B22, *C22;
REAL *S1,*S2,*S3,*S4,*S5,*S6,*S7,*S8,*M2,*M5,*T1sMULT;
#define T2sMULT C22
#define NumberOfVariables 11
PTR TempMatrixOffset = 0;
PTR MatrixOffsetA = 0;
PTR MatrixOffsetB = 0;
char *Heap;
void *StartHeap;
/* Distance between the end of a matrix row and the start of the next row */
PTR RowIncrementA = ( RowWidthA - QuadrantSize ) << 3;
PTR RowIncrementB = ( RowWidthB - QuadrantSize ) << 3;
PTR RowIncrementC = ( RowWidthC - QuadrantSize ) << 3;
if (MatrixSize <= bots_app_cutoff_value) {
MultiplyByDivideAndConquer(C, A, B, MatrixSize, RowWidthC, RowWidthA, RowWidthB, 0);
return;
}
/* Initialize quandrant matrices */
#define A11 A
#define B11 B
#define C11 C
A12 = A11 + QuadrantSize;
B12 = B11 + QuadrantSize;
C12 = C11 + QuadrantSize;
A21 = A + (RowWidthA * QuadrantSize);
B21 = B + (RowWidthB * QuadrantSize);
C21 = C + (RowWidthC * QuadrantSize);
A22 = A21 + QuadrantSize;
B22 = B21 + QuadrantSize;
C22 = C21 + QuadrantSize;
/* Allocate Heap Space Here */
StartHeap = Heap = malloc(QuadrantSizeInBytes * NumberOfVariables);
/* ensure that heap is on cache boundary */
if ( ((PTR) Heap) & 31)
Heap = (char*) ( ((PTR) Heap) + 32 - ( ((PTR) Heap) & 31) );
/* Distribute the heap space over the variables */
S1 = (REAL*) Heap; Heap += QuadrantSizeInBytes;
S2 = (REAL*) Heap; Heap += QuadrantSizeInBytes;
S3 = (REAL*) Heap; Heap += QuadrantSizeInBytes;
S4 = (REAL*) Heap; Heap += QuadrantSizeInBytes;
S5 = (REAL*) Heap; Heap += QuadrantSizeInBytes;
S6 = (REAL*) Heap; Heap += QuadrantSizeInBytes;
S7 = (REAL*) Heap; Heap += QuadrantSizeInBytes;
S8 = (REAL*) Heap; Heap += QuadrantSizeInBytes;
M2 = (REAL*) Heap; Heap += QuadrantSizeInBytes;
M5 = (REAL*) Heap; Heap += QuadrantSizeInBytes;
T1sMULT = (REAL*) Heap; Heap += QuadrantSizeInBytes;
/***************************************************************************
** Step through all columns row by row (vertically)
** (jumps in memory by RowWidth => bad locality)
** (but we want the best locality on the innermost loop)
***************************************************************************/
for (Row = 0; Row < QuadrantSize; Row++) {
/*************************************************************************
** Step through each row horizontally (addressing elements in each column)
** (jumps linearly througn memory => good locality)
*************************************************************************/
for (Column = 0; Column < QuadrantSize; Column++) {
/***********************************************************
** Within this loop, the following holds for MatrixOffset:
** MatrixOffset = (Row * RowWidth) + Column
** (note: that the unit of the offset is number of reals)
***********************************************************/
/* Element of Global Matrix, such as A, B, C */
#define E(Matrix) (* (REAL*) ( ((PTR) Matrix) + TempMatrixOffset ) )
#define EA(Matrix) (* (REAL*) ( ((PTR) Matrix) + MatrixOffsetA ) )
#define EB(Matrix) (* (REAL*) ( ((PTR) Matrix) + MatrixOffsetB ) )
/* FIXME - may pay to expand these out - got higher speed-ups below */
/* S4 = A12 - ( S2 = ( S1 = A21 + A22 ) - A11 ) */
E(S4) = EA(A12) - ( E(S2) = ( E(S1) = EA(A21) + EA(A22) ) - EA(A11) );
/* S8 = (S6 = B22 - ( S5 = B12 - B11 ) ) - B21 */
E(S8) = ( E(S6) = EB(B22) - ( E(S5) = EB(B12) - EB(B11) ) ) - EB(B21);
/* S3 = A11 - A21 */
E(S3) = EA(A11) - EA(A21);
/* S7 = B22 - B12 */
E(S7) = EB(B22) - EB(B12);
TempMatrixOffset += sizeof(REAL);
MatrixOffsetA += sizeof(REAL);
MatrixOffsetB += sizeof(REAL);
} /* end row loop*/
MatrixOffsetA += RowIncrementA;
MatrixOffsetB += RowIncrementB;
} /* end column loop */
/* M2 = A11 x B11 */
OptimizedStrassenMultiply_seq(M2, A11, B11, QuadrantSize, QuadrantSize, RowWidthA, RowWidthB, Depth+1);
/* M5 = S1 * S5 */
OptimizedStrassenMultiply_seq(M5, S1, S5, QuadrantSize, QuadrantSize, QuadrantSize, QuadrantSize, Depth+1);
/* Step 1 of T1 = S2 x S6 + M2 */
OptimizedStrassenMultiply_seq(T1sMULT, S2, S6, QuadrantSize, QuadrantSize, QuadrantSize, QuadrantSize, Depth+1);
/* Step 1 of T2 = T1 + S3 x S7 */
OptimizedStrassenMultiply_seq(C22, S3, S7, QuadrantSize, RowWidthC /*FIXME*/, QuadrantSize, QuadrantSize, Depth+1);
/* Step 1 of C11 = M2 + A12 * B21 */
OptimizedStrassenMultiply_seq(C11, A12, B21, QuadrantSize, RowWidthC, RowWidthA, RowWidthB, Depth+1);
/* Step 1 of C12 = S4 x B22 + T1 + M5 */
OptimizedStrassenMultiply_seq(C12, S4, B22, QuadrantSize, RowWidthC, QuadrantSize, RowWidthB, Depth+1);
/* Step 1 of C21 = T2 - A22 * S8 */
OptimizedStrassenMultiply_seq(C21, A22, S8, QuadrantSize, RowWidthC, RowWidthA, QuadrantSize, Depth+1);
/***************************************************************************
** Step through all columns row by row (vertically)
** (jumps in memory by RowWidth => bad locality)
** (but we want the best locality on the innermost loop)
***************************************************************************/
for (Row = 0; Row < QuadrantSize; Row++) {
/*************************************************************************
** Step through each row horizontally (addressing elements in each column)
** (jumps linearly througn memory => good locality)
*************************************************************************/
for (Column = 0; Column < QuadrantSize; Column += 4) {
REAL LocalM5_0 = *(M5);
REAL LocalM5_1 = *(M5+1);
REAL LocalM5_2 = *(M5+2);
REAL LocalM5_3 = *(M5+3);
REAL LocalM2_0 = *(M2);
REAL LocalM2_1 = *(M2+1);
REAL LocalM2_2 = *(M2+2);
REAL LocalM2_3 = *(M2+3);
REAL T1_0 = *(T1sMULT) + LocalM2_0;
REAL T1_1 = *(T1sMULT+1) + LocalM2_1;
REAL T1_2 = *(T1sMULT+2) + LocalM2_2;
REAL T1_3 = *(T1sMULT+3) + LocalM2_3;
REAL T2_0 = *(C22) + T1_0;
REAL T2_1 = *(C22+1) + T1_1;
REAL T2_2 = *(C22+2) + T1_2;
REAL T2_3 = *(C22+3) + T1_3;
(*(C11)) += LocalM2_0;
(*(C11+1)) += LocalM2_1;
(*(C11+2)) += LocalM2_2;
(*(C11+3)) += LocalM2_3;
(*(C12)) += LocalM5_0 + T1_0;
(*(C12+1)) += LocalM5_1 + T1_1;
(*(C12+2)) += LocalM5_2 + T1_2;
(*(C12+3)) += LocalM5_3 + T1_3;
(*(C22)) = LocalM5_0 + T2_0;
(*(C22+1)) = LocalM5_1 + T2_1;
(*(C22+2)) = LocalM5_2 + T2_2;
(*(C22+3)) = LocalM5_3 + T2_3;
(*(C21 )) = (- *(C21 )) + T2_0;
(*(C21+1)) = (- *(C21+1)) + T2_1;
(*(C21+2)) = (- *(C21+2)) + T2_2;
(*(C21+3)) = (- *(C21+3)) + T2_3;
M5 += 4;
M2 += 4;
T1sMULT += 4;
C11 += 4;
C12 += 4;
C21 += 4;
C22 += 4;
}
C11 = (REAL*) ( ((PTR) C11 ) + RowIncrementC);
C12 = (REAL*) ( ((PTR) C12 ) + RowIncrementC);
C21 = (REAL*) ( ((PTR) C21 ) + RowIncrementC);
C22 = (REAL*) ( ((PTR) C22 ) + RowIncrementC);
}
free(StartHeap);
}
void strassen_main_seq(REAL *A, REAL *B, REAL *C, int n)
{
bots_message("Computing sequential Strassen algorithm (n=%d) ", n);
OptimizedStrassenMultiply_seq(C, A, B, n, n, n, n, 1);
bots_message(" completed!\n");
}
