/*************************************************************************/ /* */ /* Copyright (c) 1994 Stanford University */ /* */ /* All rights reserved. */ /* */ /* Permission is given to use, copy, and modify this software for any */ /* non-commercial purpose as long as this copyright notice is not */ /* removed. All other uses, including redistribution in whole or in */ /* part, are forbidden without prior written permission. */ /* */ /* This software is provided with absolutely no warranty and no */ /* support. */ /* */ /*************************************************************************/ /////////////////////////////////////////////////////////////////////////// // This port of the SPLASH FFT benchmark on the ALMOS-MKH OS has been // done by Alain Greiner (august 2018). // // This application performs the 1D fast Fourier transfom for an array // of N complex points, using the Cooley-Tuckey FFT method. // The N data points are seen as a 2D array (rootN rows * rootN columns). // Each thread handle (rootN / nthreads) rows. The N input data points // be initialised in three different modes: // - CONSTANT : all data points have the same [1,0] value // - COSIN : data point n has [cos(n/N) , sin(n/N)] values // - RANDOM : data points have pseudo random values // // This application uses 4 shared data arrays, that are distributed // in all clusters (one sub-buffer per cluster): // - data[N] contains N input data points, with 2 double per point. // - trans[N] contains N intermediate data points, 2 double per point. // - umain[rootN] contains rootN coefs required for a rootN points FFT. // - twid[N] contains N coefs : exp(2*pi*i*j/N) / i and j in [0,rootN-1]. // For data, trans, twid, each sub-buffer contains (N/nclusters) points. // For umain, each sub-buffer contains (rootN/nclusters) points. // // The main parameters for this generic application are the following: // - M : N = 2**M = number of data points / M must be an even number. // - T : nthreads = ncores defined by the hardware / must be power of 2. // // There is one thread per core. // The max number of clusters is defined by (X_MAX * Y_MAX). // The max number of cores per cluster is defined by CORES_MAX. // // Several configuration parameters can be defined below: // - VERBOSE : Print out complex data points arrays. // - CHECK : Perform both FFT and inverse FFT to check output/input. // - DEBUG : Display intermediate results // // Regarding final instrumentation: // - the sequencial initialisation time (init_time) is computed // by the main thread in the main() function. // - The parallel execution time (parallel_time[i]) is computed by each // thread(i) in the slave() function. // - The synchronisation time related to the barriers (sync_time[i]) // is computed by each thread(i) in the slave() function. // The results are displayed on the TXT terminal, and registered on disk. /////////////////////////////////////////////////////////////////////////// #include #include #include #include #include #include #include #include // constants #define PI 3.14159265359 #define PAGE_SIZE 4096 #define X_MAX 16 // max number of clusters in a row #define Y_MAX 16 // max number of clusters in a column #define CORES_MAX 4 // max number of cores in a cluster #define CLUSTERS_MAX X_MAX * Y_MAX #define THREADS_MAX CLUSTERS_MAX * CORES_MAX #define RANDOM 0 #define COSIN 1 #define CONSTANT 2 // parameters #define DEFAULT_M 6 #define VERBOSE 0 #define CHECK 0 #define DEBUG_MAIN 1 #define DEBUG_FFT1D 0 #define DEBUG_ONCE 0 #define MODE COSIN // macro to swap two variables #define SWAP(a,b) { double tmp; tmp = a; a = b; b = tmp; } ///////////////////////////////////////////////////////////////////////////////// // global variables ///////////////////////////////////////////////////////////////////////////////// unsigned int x_size; // number of clusters per row in the mesh unsigned int y_size; // number of clusters per column in the mesh unsigned int ncores; // number of cores per cluster long nthreads; // total number of threads (one thread per core) long nclusters; // total number of clusters long M = DEFAULT_M; // log2(number of points) long N; // number of points (N = 2^M) long rootN; // rootN = 2^M/2 long rows_per_thread; // number of data "rows" handled by a single thread long points_per_cluster; // number of data points per cluster // arrays of pointers on distributed buffers (one sub-buffer per cluster) double * data[CLUSTERS_MAX]; // original time-domain data double * trans[CLUSTERS_MAX]; // used as auxiliary space for transpose double * bloup[CLUSTERS_MAX]; // used as auxiliary space for DFT double * umain[CLUSTERS_MAX]; // roots of unity used fo rootN points FFT double * twid[CLUSTERS_MAX]; // twiddle factor : exp(-2iPI*k*n/N) // instrumentation counters long parallel_time[THREADS_MAX]; // total computation time (per thread) long sync_time[THREADS_MAX]; // cumulative waiting time in barriers (per thread) long init_time; // initialisation time (in main) // synchronisation barrier (all threads) pthread_barrier_t barrier; pthread_barrierattr_t barrierattr; // threads identifiers, attributes, and arguments pthread_t trdid[THREADS_MAX]; // kernel threads identifiers pthread_attr_t attr[THREADS_MAX]; // POSIX thread attributes long args[THREADS_MAX]; // slave function arguments ///////////////////////////////////////////////////////////////////////////////// // functions declaration ///////////////////////////////////////////////////////////////////////////////// void slave(); double CheckSum(double ** x); void InitX(double ** x , unsigned int mode); void InitU(double ** u); void InitT(double ** u); long BitReverse( long k ); void FFT1D( long direction , double ** x , double ** tmp , double * upriv, double ** twid , long MyNum , long MyFirst , long MyLast ); void TwiddleOneCol(long direction, long j, double ** u, double ** x, long offset_x ); void Scale( double **x, long offset_x ); void Transpose( double ** src, double ** dest, long MyFirst, long MyLast ); void Copy( double ** src, double ** dest, long MyFirst , long MyLast ); void Reverse( double ** x, long offset_x ); void FFT1DOnce( long direction , double * u , double ** x , long offset_x ); void PrintArray( double ** x , long size ); void SimpleDft( long direction , long size , double ** src , long src_offset , double ** dst , long dst_offset ); /////////////////////////////////////////////////////////////////// // This main() function execute the sequencial initialisation // launch the parallel execution, and makes the instrumentation. /////////////////////////////////////////////////////////////////// void main() { unsigned int main_cxy; // main thread cluster unsigned int main_x; // main thread X coordinate unsigned int main_y; // main thread y coordinate unsigned int main_lid; // main thread local core index unsigned int main_tid; // main thread continuous index unsigned int x; // current index for cluster X coordinate unsigned int y; // current index for cluster Y coordinate unsigned int lid; // current index for core in a cluster unsigned int ci; // continuous cluster index (from x,y) unsigned int cxy; // hardware specific cluster identifier unsigned int tid; // continuous thread index unsigned long long start_init_cycle; unsigned long long start_exec_cycle; unsigned long long end_exec_cycle; #if CHECK double ck1; // for input/output checking double ck3; // for input/output checking #endif // get FFT application start cycle if( get_cycle( &start_init_cycle ) ) { printf("[FFT ERROR] cannot get start cycle\n"); } // get platform parameters to compute nthreads & nclusters if( get_config( &x_size , &y_size , &ncores ) ) { printf("\n[FFT ERROR] cannot get hardware configuration\n"); exit( 0 ); } // check ncores if( (ncores != 1) && (ncores != 2) && (ncores != 4) ) { printf("\n[FFT ERROR] number of cores per cluster must be 1/2/4\n"); exit( 0 ); } // check x_size if( (x_size != 1) && (x_size != 2) && (x_size != 4) && (x_size != 8) && (x_size != 16) ) { printf("\n[FFT ERROR] x_size must be 1/2/4/8/16\n"); exit( 0 ); } // check y_size if( (y_size != 1) && (y_size != 2) && (y_size != 4) && (y_size != 8) && (y_size != 16) ) { printf("\n[FFT ERROR] y_size must be 1/2/4/8/16\n"); exit( 0 ); } nthreads = x_size * y_size * ncores; nclusters = x_size * y_size; // compute various constants depending on N and T N = 1 << M; rootN = 1 << (M / 2); rows_per_thread = rootN / nthreads; points_per_cluster = N / nclusters; // check N versus T if( rootN < nthreads ) { printf("\n[FFT ERROR] sqrt(N) must be larger than T\n"); exit( 0 ); } // get main thread coordinates (main_x, main_y, main_lid) get_core( &main_cxy , &main_lid ); main_x = HAL_X_FROM_CXY( main_cxy ); main_y = HAL_Y_FROM_CXY( main_cxy ); main_tid = (((main_x * y_size) + main_y) * ncores) + main_lid; printf("\n[FFT] main starts on core[%x,%d] / %d complex points / %d thread(s)\n", main_cxy, main_lid, N, nthreads ); // allocate memory for the distributed data[i], trans[i], umain[i], twid[i] buffers // the index (i) is a continuous cluster index long data_size = (N / nclusters) * 2 * sizeof(double); long coefs_size = (rootN / nclusters) * 2 * sizeof(double); for (x = 0 ; x < x_size ; x++) { for (y = 0 ; y < y_size ; y++) { ci = x * y_size + y; cxy = HAL_CXY_FROM_XY( x , y ); data[ci] = (double *)remote_malloc( data_size , cxy ); trans[ci] = (double *)remote_malloc( data_size , cxy ); bloup[ci] = (double *)remote_malloc( data_size , cxy ); umain[ci] = (double *)remote_malloc( coefs_size , cxy ); twid[ci] = (double *)remote_malloc( data_size , cxy ); } } // arrays initialisation InitX( data , MODE ); InitU( umain ); InitT( twid ); #if CHECK ck1 = CheckSum( data ); #endif #if VERBOSE printf("\nData values / base = %x\n", &data[0][0] ); PrintArray( data , N ); printf("\nTwiddle values / base = %x\n", &twid[0][0] ); PrintArray( twid , N ); SimpleDft( 1 , N , data , 0 , bloup , 0 ); printf("\nExpected results / base = %x\n", &bloup[0][0] ); PrintArray( bloup , N ); #endif // initialise distributed barrier barrierattr.x_size = x_size; barrierattr.y_size = y_size; barrierattr.nthreads = ncores; pthread_barrier_init( &barrier, &barrierattr , nthreads); // launch other threads to execute the slave() function // on cores other than the core running the main thread for (x = 0 ; x < x_size ; x++) { for (y = 0 ; y < y_size ; y++) { for ( lid = 0 ; lid < ncores ; lid++ ) { // compute thread continuous index tid = (((x * y_size) + y) * ncores) + lid; // set thread attributes attr[tid].attributes = PT_ATTR_CLUSTER_DEFINED | PT_ATTR_CORE_DEFINED; attr[tid].cxy = HAL_CXY_FROM_XY( x , y ); attr[tid].lid = lid; // set slave function argument args[tid] = tid; // create thread if( tid != main_tid ) { if ( pthread_create( &trdid[tid], // pointer on kernel identifier &attr[tid], // pointer on thread attributes &slave, // pointer on function &args[tid]) ) // pointer on function arguments { printf("\n[FFT ERROR] creating thread %x\n", trdid[tid] ); exit( 0 ); } #if DEBUG_MAIN printf("\n[FFT] thread %x created\n", trdid[tid] ); #endif } } } } // register sequencial initalisation completion cycle get_cycle( &start_exec_cycle ); init_time = (long)(start_exec_cycle - start_init_cycle); printf("\n[FFT] enter parallel execution / cycle %d\n", (long)start_exec_cycle ); // main execute itself the slave() function slave( &args[main_tid] ); // wait other threads completion for (x = 0 ; x < x_size ; x++) { for (y = 0 ; y < y_size ; y++) { for ( lid = 0 ; lid < ncores ; lid++ ) { // compute thread continuous index long tid = (((x * y_size) + y) * ncores) + lid; if( tid != main_tid ) { #if DEBUG_MAIN printf("\n[FFT] before join for thread %x\n", trdid[tid] ); #endif if( pthread_join( trdid[tid] , NULL ) ) { printf("\n[FFT ERROR] joining thread %x\n", trdid[tid] ); exit( 0 ); } #if DEBUG_MAIN printf("\n[FFT] after join for thread %x\n", trdid[tid] ); #endif } } } } // register parallel execution completion cycle get_cycle( &end_exec_cycle ); printf("\n[FFT] complete parallel execution / cycle %d\n", (long)end_exec_cycle ); #if VERBOSE printf("\nData values after FFT:\n"); PrintArray( data , N ); #endif #if CHECK ck3 = CheckSum( data ); printf("\n*** Results ***\n"); printf("Checksum difference is %f (%f, %f)\n", ck1 - ck3, ck1, ck3); if (fabs(ck1 - ck3) < 0.001) printf("Results OK\n"); else printf("Results KO\n"); #endif // instrumentation char string[256]; snprintf( string , 256 , "/home/fft_%d_%d_%d_%d", x_size , y_size , ncores , N ); // open instrumentation file FILE * f = fopen( string , NULL ); if ( f == NULL ) { printf("\n[FFT ERROR] cannot open instrumentation file %s\n", string ); exit( 0 ); } snprintf( string , 256 , "\n[FFT] instrumentation : (%dx%dx%d) threads / %d points\n", x_size, y_size, ncores , N ); // display on terminal, and save to instrumentation file printf( "%s" , string ); fprintf( f , string ); long min_para = parallel_time[0]; long max_para = parallel_time[0]; long min_sync = sync_time[0]; long max_sync = sync_time[0]; for (tid = 1 ; tid < nthreads ; tid++) { if (parallel_time[tid] > max_para) max_para = parallel_time[tid]; if (parallel_time[tid] < min_para) min_para = parallel_time[tid]; if (sync_time[tid] > max_sync) max_sync = sync_time[tid]; if (sync_time[tid] < min_sync) min_sync = sync_time[tid]; } snprintf( string , 256 , "\n Init Parallel Barrier\n" "MIN : %d | %d | %d (cycles)\n" "MAX : %d | %d | %d (cycles)\n", (int)init_time, (int)min_para, (int)min_sync, (int)init_time, (int)max_para, (int)max_sync ); // display on terminal, and save to instrumentation file printf("%s" , string ); fprintf( f , string ); // close instrumentation file and exit fclose( f ); exit( 0 ); } // end main() /////////////////////////////////////////////////////////////// // This function is executed in parallel by all threads. /////////////////////////////////////////////////////////////// void slave( long * tid ) { long i; long MyNum; // continuous thread index long MyFirst; // index first row allocated to thread long MyLast; // index last row allocated to thread double * upriv; long c_id; long c_offset; unsigned long long parallel_start; unsigned long long parallel_stop; unsigned long long barrier_start; unsigned long long barrier_stop; MyNum = *tid; // get // initialise instrumentation get_cycle( ¶llel_start ); // allocate and initialise local array upriv[] // that is a local copy of the rootN coefs defined in umain[] upriv = (double *)malloc(2 * (rootN - 1) * sizeof(double)); for ( i = 0 ; i < (rootN - 1) ; i++) { c_id = i / (rootN / nclusters); c_offset = i % (rootN / nclusters); upriv[2*i] = umain[c_id][2*c_offset]; upriv[2*i+1] = umain[c_id][2*c_offset+1]; } // compute first and last rows handled by the thread MyFirst = rootN * MyNum / nthreads; MyLast = rootN * (MyNum + 1) / nthreads; // perform forward FFT FFT1D( 1 , data , trans , upriv , twid , MyNum , MyFirst , MyLast ); // BARRIER get_cycle( &barrier_start ); pthread_barrier_wait( &barrier ); get_cycle( &barrier_stop ); sync_time[MyNum] = (long)(barrier_stop - barrier_start); #if CHECK get_cycle( &barrier_start ); pthread_barrier_wait( &barrier ); get_cycle( &barrier_stop ); sync_time[MyNum] += (long)(barrier_stop - barrier_start); FFT1D( -1 , data , trans , upriv , twid , MyNum , MyFirst , MyLast ); #endif // register computation time get_cycle( ¶llel_stop ); parallel_time[MyNum] = (long)(parallel_stop - parallel_start); // exit if MyNum != 0 if( MyNum ) exit( 0 ); } // end slave() //////////////////////////////////////////////////////////////////////////////////////// // This function makes the DFT from the src[nclusters][points_per_cluster] distributed // buffer, to the dst[nclusters][points_per_cluster] distributed buffer. //////////////////////////////////////////////////////////////////////////////////////// void SimpleDft( long direction, long size, // number of points double ** src, // source distributed buffer long src_offset, // offset in source array double ** dst, // destination distributed buffer long dst_offset ) // offset in destination array { long n , k; double phi; // 2*PI*n*k/N double u_r; // cos( phi ) double u_c; // sin( phi ) double d_r; // Re(data[n]) double d_c; // Im(data[n]) double accu_r; // Re(accu) double accu_c; // Im(accu) long c_id; // distributed buffer cluster index long c_offset; // offset in distributed buffer for ( k = 0 ; k < size ; k++ ) // loop on the output data points { // initialise accu accu_r = 0; accu_c = 0; for ( n = 0 ; n < size ; n++ ) // loop on the input data points { // compute coef phi = (double)(2*PI*n*k) / size; u_r = cos( phi ); u_c = -sin( phi ) * direction; // get input data point c_id = (src_offset + n) / (points_per_cluster); c_offset = (src_offset + n) % (points_per_cluster); d_r = data[c_id][2*c_offset]; d_c = data[c_id][2*c_offset+1]; // increment accu accu_r += ((u_r*d_r) - (u_c*d_c)); accu_c += ((u_r*d_c) + (u_c*d_r)); } // scale for inverse DFT if ( direction == -1 ) { accu_r /= size; accu_c /= size; } // set output data point c_id = (dst_offset + k) / (points_per_cluster); c_offset = (dst_offset + k) % (points_per_cluster); dst[c_id][2*c_offset] = accu_r; dst[c_id][2*c_offset+1] = accu_c; } } // end SimpleDft() //////////////////////////// double CheckSum(double ** x) { long i , j; double cks; long c_id; long c_offset; cks = 0.0; for (j = 0; j < rootN ; j++) { for (i = 0; i < rootN ; i++) { c_id = (rootN * j + i) / (points_per_cluster); c_offset = (rootN * j + i) % (points_per_cluster); cks += data[c_id][2*c_offset] + data[c_id][2*c_offset+1]; } } return(cks); } //////////////////////////// void InitX(double ** x, unsigned int mode ) { long i , j; long c_id; long c_offset; long index; for ( j = 0 ; j < rootN ; j++ ) // loop on row index { for ( i = 0 ; i < rootN ; i++ ) // loop on point in a row { index = j * rootN + i; c_id = index / (points_per_cluster); c_offset = index % (points_per_cluster); // complex input signal is random if ( mode == RANDOM ) { data[c_id][2*c_offset] = ( (double)rand() ) / 65536; data[c_id][2*c_offset+1] = ( (double)rand() ) / 65536; } // complex input signal is cos(n/N) / sin(n/N) if ( mode == COSIN ) { double phi = (double)( 2 * PI * index) / N; data[c_id][2*c_offset] = cos( phi ); data[c_id][2*c_offset+1] = sin( phi ); } // complex input signal is constant if ( mode == CONSTANT ) { data[c_id][2*c_offset] = 1.0; data[c_id][2*c_offset+1] = 0.0; } } } } ///////////////////////// void InitU( double ** u ) { long q; long j; long base; long n1; long c_id; long c_offset; double phi; long stop = 0; for (q = 0 ; ((1 << q) < N) && (stop == 0) ; q++) { n1 = 1 << q; base = n1 - 1; for (j = 0; (j < n1) && (stop == 0) ; j++) { if (base + j > rootN - 1) return; c_id = (base + j) / (rootN / nclusters); c_offset = (base + j) % (rootN / nclusters); phi = (double)(2.0 * PI * j) / (2 * n1); u[c_id][2*c_offset] = cos( phi ); u[c_id][2*c_offset+1] = -sin( phi ); } } } ////////////////////////// void InitT( double ** u ) { long i, j; long index; long c_id; long c_offset; double phi; for ( j = 0 ; j < rootN ; j++ ) // loop on row index { for ( i = 0 ; i < rootN ; i++ ) // loop on points in a row { index = j * rootN + i; c_id = index / (points_per_cluster); c_offset = index % (points_per_cluster); phi = (double)(2.0 * PI * i * j) / N; u[c_id][2*c_offset] = cos( phi ); u[c_id][2*c_offset+1] = -sin( phi ); } } } //////////////////////////////////////////////////////////////////////////////////////// // This function returns an index value that is the bit reverse of the input value. //////////////////////////////////////////////////////////////////////////////////////// long BitReverse( long k ) { long i; long j; long tmp; j = 0; tmp = k; for (i = 0; i < M/2 ; i++) { j = 2 * j + (tmp & 0x1); tmp = tmp >> 1; } return j; } //////////////////////////////////////////////////////////////////////////////////////// // This function perform the in place (direct or inverse) FFT on the N data points // contained in the distributed buffers x[nclusters][points_per_cluster]. // It handles the (N) points 1D array as a (rootN*rootN) points 2D array. // 1) it transpose (rootN/nthreads ) rows from x to tmp. // 2) it make (rootN/nthreads) FFT on the tmp rows and apply the twiddle factor. // 3) it transpose (rootN/nthreads) columns from tmp to x. // 4) it make (rootN/nthreads) FFT on the x rows. // It calls the FFT1DOnce() 2*(rootN/nthreads) times to perform the in place FFT // on the rootN points contained in a row. //////////////////////////////////////////////////////////////////////////////////////// void FFT1D( long direction, // direct : 1 / inverse : -1 double ** x, // input & output distributed data points array double ** tmp, // auxiliary distributed data points array double * upriv, // local array containing coefs for rootN FFT double ** twid, // distributed arrays containing N twiddle factors long MyNum, long MyFirst, long MyLast ) { long j; unsigned long long barrier_start; unsigned long long barrier_stop; // transpose (rootN/nthreads) rows from x to tmp Transpose( x , tmp , MyFirst , MyLast ); #if DEBUG_FFT1D printf("\n@@@ tmp after first transpose\n"); PrintArray( tmp , N ); #endif // BARRIER get_cycle( &barrier_start ); pthread_barrier_wait( &barrier ); get_cycle( &barrier_stop ); sync_time[MyNum] = (long)(barrier_stop - barrier_start); // do FFTs on rows of tmp (i.e. columns of x) and apply twiddle factor for (j = MyFirst; j < MyLast; j++) { FFT1DOnce( direction , upriv , tmp , j * rootN ); TwiddleOneCol( direction , j , twid , tmp , j * rootN ); } #if DEBUG_FFT1D printf("\n@@@ tmp after columns FFT + twiddle \n"); PrintArray( tmp , N ); #endif // BARRIER get_cycle( &barrier_start ); pthread_barrier_wait( &barrier ); get_cycle( &barrier_stop ); sync_time[MyNum] += (long)(barrier_stop - barrier_start); // transpose tmp to x Transpose( tmp , x , MyFirst , MyLast ); #if DEBUG_FFT1D printf("\n@@@ x after second transpose \n"); PrintArray( x , N ); #endif // BARRIER get_cycle( &barrier_start ); pthread_barrier_wait( &barrier ); get_cycle( &barrier_stop ); sync_time[MyNum] += (long)(barrier_stop - barrier_start); // do FFTs on rows of x and apply the scaling factor for (j = MyFirst; j < MyLast; j++) { FFT1DOnce( direction , upriv , x , j * rootN ); if (direction == -1) Scale( x , j * rootN ); } #if DEBUG_FFT1D printf("\n@@@ x after rows FFT + scaling \n"); PrintArray( x , N ); #endif // BARRIER get_cycle( &barrier_start ); pthread_barrier_wait( &barrier ); get_cycle( &barrier_stop ); sync_time[MyNum] += (long)(barrier_stop - barrier_start); // transpose x to tmp Transpose( x , tmp , MyFirst , MyLast ); #if DEBUG_FFT1D printf("\n@@@ tmp after third transpose \n"); PrintArray( tmp , N ); #endif // BARRIER get_cycle( &barrier_start ); pthread_barrier_wait( &barrier ); get_cycle( &barrier_stop ); sync_time[MyNum] += (long)(barrier_stop - barrier_start); // copy tmp to x Copy( tmp , x , MyFirst , MyLast ); #if DEBUG_FFT1D printf("\n@@@ x after final copy \n"); PrintArray( x , N ); #endif } // end FFT1D() ///////////////////////////////////////////////////////////////////////////////////// // This function multiply all points contained in a row (rootN points) of the // x[] array by the corresponding twiddle factor, contained in the u[] array. ///////////////////////////////////////////////////////////////////////////////////// void TwiddleOneCol( long direction, long j, // y coordinate in 2D view of coef array double ** u, // coef array base address double ** x, // data array base address long offset_x ) // first point in N points data array { long i; double omega_r; double omega_c; double x_r; double x_c; long c_id; long c_offset; for (i = 0; i < rootN ; i++) // loop on the rootN points { // get coef c_id = (j * rootN + i) / (points_per_cluster); c_offset = (j * rootN + i) % (points_per_cluster); omega_r = u[c_id][2*c_offset]; omega_c = direction * u[c_id][2*c_offset+1]; // access data c_id = (offset_x + i) / (points_per_cluster); c_offset = (offset_x + i) % (points_per_cluster); x_r = x[c_id][2*c_offset]; x_c = x[c_id][2*c_offset+1]; x[c_id][2*c_offset] = omega_r*x_r - omega_c * x_c; x[c_id][2*c_offset+1] = omega_r*x_c + omega_c * x_r; } } // end TwiddleOneCol() //////////////////////// void Scale( double ** x, // data array base address long offset_x ) // first point of the row to be scaled { long i; long c_id; long c_offset; for (i = 0; i < rootN ; i++) { c_id = (offset_x + i) / (points_per_cluster); c_offset = (offset_x + i) % (points_per_cluster); data[c_id][2*c_offset] /= N; data[c_id][2*c_offset + 1] /= N; } } //////////////////////////// void Transpose( double ** src, // source buffer (array of pointers) double ** dest, // destination buffer (array of pointers) long MyFirst, // first row allocated to the thread long MyLast ) // last row allocated to the thread { long row; // row index long point; // data point index in a row long index_src; // absolute index in the source N points array long c_id_src; // cluster for the source buffer long c_offset_src; // offset in the source buffer long index_dst; // absolute index in the dest N points array long c_id_dst; // cluster for the dest buffer long c_offset_dst; // offset in the dest buffer // scan all data points allocated to the thread // (between MyFirst row and MyLast row) from the source buffer // and write these points to the destination buffer for ( row = MyFirst ; row < MyLast ; row++ ) // loop on the rows { for ( point = 0 ; point < rootN ; point++ ) // loop on points in row { index_src = row * rootN + point; c_id_src = index_src / (points_per_cluster); c_offset_src = index_src % (points_per_cluster); index_dst = point * rootN + row; c_id_dst = index_dst / (points_per_cluster); c_offset_dst = index_dst % (points_per_cluster); dest[c_id_dst][2*c_offset_dst] = src[c_id_src][2*c_offset_src]; dest[c_id_dst][2*c_offset_dst+1] = src[c_id_src][2*c_offset_src+1]; } } } // end Transpose() ///////////////////////// void Copy( double ** src, // source buffer (array of pointers) double ** dest, // destination buffer (array of pointers) long MyFirst, // first row allocated to the thread long MyLast ) // last row allocated to the thread { long row; // row index long point; // data point index in a row long index; // absolute index in the N points array long c_id; // cluster index long c_offset; // offset in local buffer // scan all data points allocated to the thread for ( row = MyFirst ; row < MyLast ; row++ ) // loop on the rows { for ( point = 0 ; point < rootN ; point++ ) // loop on points in row { index = row * rootN + point; c_id = index / (points_per_cluster); c_offset = index % (points_per_cluster); dest[c_id][2*c_offset] = src[c_id][2*c_offset]; dest[c_id][2*c_offset+1] = src[c_id][2*c_offset+1]; } } } // end Copy() ////////////////////////// void Reverse( double ** x, long offset_x ) { long j, k; long c_id_j; long c_offset_j; long c_id_k; long c_offset_k; for (k = 0 ; k < rootN ; k++) { j = BitReverse( k ); if (j > k) { c_id_j = (offset_x + j) / (points_per_cluster); c_offset_j = (offset_x + j) % (points_per_cluster); c_id_k = (offset_x + k) / (points_per_cluster); c_offset_k = (offset_x + k) % (points_per_cluster); SWAP(x[c_id_j][2*c_offset_j] , x[c_id_k][2*c_offset_k]); SWAP(x[c_id_j][2*c_offset_j+1], x[c_id_k][2*c_offset_k+1]); } } } ///////////////////////////////////////////////////////////////////////////// // This function makes the in-place FFT on all points contained in a row // (i.e. rootN points) of the x[nclusters][points_per_cluster] array. ///////////////////////////////////////////////////////////////////////////// void FFT1DOnce( long direction, // direct / inverse double * u, // private coefs array double ** x, // array of pointers on distributed buffers long offset_x ) // absolute offset in the x array { long j; long k; long q; long L; long r; long Lstar; double * u1; long offset_x1; // index first butterfly input long offset_x2; // index second butterfly output double omega_r; // real part butterfy coef double omega_c; // complex part butterfly coef double tau_r; double tau_c; double d1_r; // real part first butterfly input double d1_c; // imag part first butterfly input double d2_r; // real part second butterfly input double d2_c; // imag part second butterfly input long c_id_1; // cluster index for first butterfly input long c_offset_1; // offset for first butterfly input long c_id_2; // cluster index for second butterfly input long c_offset_2; // offset for second butterfly input #if DEBUG_ONCE unsigned int p; printf("\n@@@ FFT ROW data in / %d points / offset = %d\n", rootN , offset_x ); for ( p = 0 ; p < rootN ; p++ ) { long index = offset_x + p; long c_id = index / (points_per_cluster); long c_offset = index % (points_per_cluster); printf("%f , %f | ", x[c_id][2*c_offset] , x[c_id][2*c_offset+1] ); } printf("\n"); #endif // This makes the rootN input points reordering Reverse( x , offset_x ); #if DEBUG_ONCE printf("\n@@@ FFT ROW data after reverse\n"); for ( p = 0 ; p < rootN ; p++ ) { long index = offset_x + p; long c_id = index / (points_per_cluster); long c_offset = index % (points_per_cluster); printf("%f , %f | ", x[c_id][2*c_offset] , x[c_id][2*c_offset+1] ); } printf("\n"); #endif // This implements the multi-stages, in place Butterfly network for (q = 1; q <= M/2 ; q++) // loop on stages { L = 1 << q; // number of points per subset for current stage r = rootN / L; // number of subsets Lstar = L / 2; u1 = &u[2 * (Lstar - 1)]; for (k = 0; k < r; k++) // loop on the subsets { offset_x1 = offset_x + (k * L); // index first point offset_x2 = offset_x + (k * L + Lstar); // index second point #if DEBUG_ONCE printf("\n ### q = %d / k = %d / x1 = %d / x2 = %d\n", q , k , offset_x1 , offset_x2 ); #endif // makes all in-place butterfly(s) for subset for (j = 0; j < Lstar; j++) { // get coef omega_r = u1[2*j]; omega_c = direction * u1[2*j+1]; // get d[x1] address and value c_id_1 = (offset_x1 + j) / (points_per_cluster); c_offset_1 = (offset_x1 + j) % (points_per_cluster); d1_r = x[c_id_1][2*c_offset_1]; d1_c = x[c_id_1][2*c_offset_1+1]; // get d[x2] address and value c_id_2 = (offset_x2 + j) / (points_per_cluster); c_offset_2 = (offset_x2 + j) % (points_per_cluster); d2_r = x[c_id_2][2*c_offset_2]; d2_c = x[c_id_2][2*c_offset_2+1]; #if DEBUG_ONCE printf("\n ### d1_in = (%f , %f) / d2_in = (%f , %f) / coef = (%f , %f)\n", d1_r , d1_c , d2_r , d2_c , omega_r , omega_c); #endif // tau = omega * d[x2] tau_r = omega_r * d2_r - omega_c * d2_c; tau_c = omega_r * d2_c + omega_c * d2_r; // set new value for d[x1] = d[x1] + omega * d[x2] x[c_id_1][2*c_offset_1] = d1_r + tau_r; x[c_id_1][2*c_offset_1+1] = d1_c + tau_c; // set new value for d[x2] = d[x1] - omega * d[x2] x[c_id_2][2*c_offset_2] = d1_r - tau_r; x[c_id_2][2*c_offset_2+1] = d1_c - tau_c; #if DEBUG_ONCE printf("\n ### d1_out = (%f , %f) / d2_out = (%f , %f)\n", d1_r + tau_r , d1_c + tau_c , d2_r - tau_r , d2_c - tau_c ); #endif } } } #if DEBUG_ONCE printf("\n@@@ FFT ROW data out\n"); for ( p = 0 ; p < rootN ; p++ ) { long index = offset_x + p; long c_id = index / (points_per_cluster); long c_offset = index % (points_per_cluster); printf("%f , %f | ", x[c_id][2*c_offset] , x[c_id][2*c_offset+1] ); } printf("\n"); #endif } // end FFT1DOnce() ////////////////////////////////// void PrintArray( double ** array, long size ) { long i; long c_id; long c_offset; // float display for (i = 0; i < size ; i++) { c_id = i / (points_per_cluster); c_offset = i % (points_per_cluster); printf(" %f %f |", array[c_id][2*c_offset], array[c_id][2*c_offset+1]); if ( (i+1) % 4 == 0) printf("\n"); } printf("\n"); } // Local Variables: // tab-width: 4 // c-basic-offset: 4 // c-file-offsets:((innamespace . 0)(inline-open . 0)) // indent-tabs-mode: nil // End: // vim: filetype=cpp:expandtab:shiftwidth=4:tabstop=4:softtabstop=4