#include "strassen.hpp" #include "tbb/task_scheduler_init.h" #include "tbb/task.h" class StrassenTBB: public tbb::task { REAL *C; REAL *A; REAL *B; unsigned MatrixSize; unsigned RowWidthC; unsigned RowWidthA; unsigned RowWidthB; int Depth; public: StrassenTBB(REAL *C, REAL *A, REAL *B, unsigned MatrixSize, unsigned RowWidthC, unsigned RowWidthA, unsigned RowWidthB, int Depth): C(C), A(A), B(B), MatrixSize(MatrixSize), RowWidthC(RowWidthC), RowWidthA(RowWidthA), RowWidthB(RowWidthB), Depth(Depth) {} task* execute() { 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 <= CUTOFF_SIZE) { MultiplyByDivideAndConquer(C, A, B, MatrixSize, RowWidthC, RowWidthA, RowWidthB, 0); return nullptr; } /* 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 */ Heap = static_cast(malloc(QuadrantSizeInBytes * NumberOfVariables)); StartHeap = Heap; /* 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 */ tbb::task_list list; /* M2 = A11 x B11 */ list.push_back( *new(allocate_child()) StrassenTBB(M2, A11, B11, QuadrantSize, QuadrantSize, RowWidthA, RowWidthB, Depth+1) ); /* M5 = S1 * S5 */ list.push_back( *new(allocate_child()) StrassenTBB(M5, S1, S5, QuadrantSize, QuadrantSize, QuadrantSize, QuadrantSize, Depth+1) ); /* Step 1 of T1 = S2 x S6 + M2 */ list.push_back( *new(allocate_child()) StrassenTBB(T1sMULT, S2, S6, QuadrantSize, QuadrantSize, QuadrantSize, QuadrantSize, Depth+1) ); /* Step 1 of T2 = T1 + S3 x S7 */ list.push_back( *new(allocate_child()) StrassenTBB(C22, S3, S7, QuadrantSize, RowWidthC /*FIXME*/, QuadrantSize, QuadrantSize, Depth+1) ); /* Step 1 of C11 = M2 + A12 * B21 */ list.push_back( *new(allocate_child()) StrassenTBB(C11, A12, B21, QuadrantSize, RowWidthC, RowWidthA, RowWidthB, Depth+1) ); /* Step 1 of C12 = S4 x B22 + T1 + M5 */ list.push_back( *new(allocate_child()) StrassenTBB(C12, S4, B22, QuadrantSize, RowWidthC, QuadrantSize, RowWidthB, Depth+1) ); /* Step 1 of C21 = T2 - A22 * S8 */ list.push_back( *new(allocate_child()) StrassenTBB(C21, A22, S8, QuadrantSize, RowWidthC, RowWidthA, QuadrantSize, Depth+1) ); set_ref_count(8); spawn_and_wait_for_all(list); /********************************************** ** Synchronization Point **********************************************/ /*************************************************************************** ** 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); return nullptr; } // End of execute() }; void strassen_tbb(unsigned num_threads, REAL *A, REAL *B, REAL *C, int n) { tbb::task_scheduler_init init(num_threads); auto& root = *new(tbb::task::allocate_root()) StrassenTBB(C, A, B, n, n, n, n, 1); tbb::task::spawn_root_and_wait(root); } std::chrono::microseconds measure_time_tbb(unsigned num_threads, REAL *A, REAL *B, REAL *C, int n) { auto beg = std::chrono::high_resolution_clock::now(); strassen_tbb(num_threads, A, B, C, n); auto end = std::chrono::high_resolution_clock::now(); return std::chrono::duration_cast(end - beg); }