[469] | 1 | /*************************************************************************/ |
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| 2 | /* */ |
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| 3 | /* Copyright (c) 1994 Stanford University */ |
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| 4 | /* */ |
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| 5 | /* All rights reserved. */ |
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| 6 | /* */ |
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| 7 | /* Permission is given to use, copy, and modify this software for any */ |
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| 8 | /* non-commercial purpose as long as this copyright notice is not */ |
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| 9 | /* removed. All other uses, including redistribution in whole or in */ |
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| 10 | /* part, are forbidden without prior written permission. */ |
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| 11 | /* */ |
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| 12 | /* This software is provided with absolutely no warranty and no */ |
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| 13 | /* support. */ |
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| 14 | /* */ |
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| 15 | /*************************************************************************/ |
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| 16 | |
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| 17 | /////////////////////////////////////////////////////////////////////////// |
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| 18 | // This port of the SPLASH FFT benchmark on the ALMOS-MKH OS has been |
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| 19 | // done by Alain Greiner (august 2018). |
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| 20 | // |
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| 21 | // This application performs the 1D fast Fourier transfom for an array |
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| 22 | // of N complex points, using the Cooley-Tuckey FFT method. |
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| 23 | // The N data points are seen as a 2D array (rootN rows * rootN columns). |
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| 24 | // Each thread handle (rootN / nthreads) rows. The N input data points |
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| 25 | // be initialised in three different modes: |
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| 26 | // - CONSTANT : all data points have the same [1,0] value |
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| 27 | // - COSIN : data point n has [cos(n/N) , sin(n/N)] values |
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| 28 | // - RANDOM : data points have pseudo random values |
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| 29 | // |
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| 30 | // This application uses 4 shared data arrays, that are distributed |
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| 31 | // in all clusters (one sub-buffer per cluster): |
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| 32 | // - data[N] contains N input data points, with 2 double per point. |
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| 33 | // - trans[N] contains N intermediate data points, 2 double per point. |
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| 34 | // - umain[rootN] contains rootN coefs required for a rootN points FFT. |
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| 35 | // - twid[N] contains N coefs : exp(2*pi*i*j/N) / i and j in [0,rootN-1]. |
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| 36 | // For data, trans, twid, each sub-buffer contains (N/nclusters) points. |
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| 37 | // For umain, each sub-buffer contains (rootN/nclusters) points. |
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| 38 | // |
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| 39 | // The main parameters for this generic application are the following: |
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| 40 | // - M : N = 2**M = number of data points / M must be an even number. |
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| 41 | // - T : nthreads = ncores defined by the hardware / must be power of 2. |
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| 42 | // |
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| 43 | // There is one thread per core. |
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| 44 | // The max number of clusters is defined by (X_MAX * Y_MAX). |
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| 45 | // The max number of cores per cluster is defined by CORES_MAX. |
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| 46 | // |
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| 47 | // Several configuration parameters can be defined below: |
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| 48 | // - VERBOSE : Print out complex data points arrays. |
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| 49 | // - CHECK : Perform both FFT and inverse FFT to check output/input. |
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| 50 | // - DEBUG : Display intermediate results |
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| 51 | // |
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| 52 | // Regarding final instrumentation: |
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| 53 | // - the sequencial initialisation time (init_time) is computed |
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| 54 | // by the main thread in the main() function. |
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| 55 | // - The parallel execution time (parallel_time[i]) is computed by each |
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| 56 | // thread(i) in the slave() function. |
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| 57 | // - The synchronisation time related to the barriers (sync_time[i]) |
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| 58 | // is computed by each thread(i) in the slave() function. |
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| 59 | // The results are displayed on the TXT terminal, and registered on disk. |
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| 60 | /////////////////////////////////////////////////////////////////////////// |
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| 61 | |
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| 62 | #include <math.h> |
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| 63 | #include <stdio.h> |
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| 64 | #include <stdlib.h> |
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| 65 | #include <fcntl.h> |
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| 66 | #include <unistd.h> |
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| 67 | #include <pthread.h> |
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| 68 | #include <almosmkh.h> |
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| 69 | #include <hal_macros.h> |
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| 70 | |
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| 71 | // constants |
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| 72 | |
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| 73 | #define PI 3.14159265359 |
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| 74 | #define PAGE_SIZE 4096 |
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| 75 | #define X_MAX 16 // max number of clusters in a row |
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| 76 | #define Y_MAX 16 // max number of clusters in a column |
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| 77 | #define CORES_MAX 4 // max number of cores in a cluster |
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| 78 | #define CLUSTERS_MAX X_MAX * Y_MAX |
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| 79 | #define THREADS_MAX CLUSTERS_MAX * CORES_MAX |
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| 80 | #define RANDOM 0 |
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| 81 | #define COSIN 1 |
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| 82 | #define CONSTANT 2 |
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| 83 | |
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| 84 | // parameters |
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| 85 | |
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| 86 | #define DEFAULT_M 6 |
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| 87 | #define VERBOSE 0 |
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| 88 | #define CHECK 0 |
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| 89 | #define DEBUG_MAIN 1 |
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| 90 | #define DEBUG_FFT1D 0 |
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| 91 | #define DEBUG_ONCE 0 |
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| 92 | #define MODE COSIN |
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| 93 | |
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| 94 | // macro to swap two variables |
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| 95 | #define SWAP(a,b) { double tmp; tmp = a; a = b; b = tmp; } |
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| 96 | |
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| 97 | ///////////////////////////////////////////////////////////////////////////////// |
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| 98 | // global variables |
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| 99 | ///////////////////////////////////////////////////////////////////////////////// |
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| 100 | |
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| 101 | unsigned int x_size; // number of clusters per row in the mesh |
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| 102 | unsigned int y_size; // number of clusters per column in the mesh |
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| 103 | unsigned int ncores; // number of cores per cluster |
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| 104 | long nthreads; // total number of threads (one thread per core) |
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| 105 | long nclusters; // total number of clusters |
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| 106 | long M = DEFAULT_M; // log2(number of points) |
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| 107 | long N; // number of points (N = 2^M) |
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| 108 | long rootN; // rootN = 2^M/2 |
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| 109 | long rows_per_thread; // number of data "rows" handled by a single thread |
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| 110 | long points_per_cluster; // number of data points per cluster |
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| 111 | |
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| 112 | // arrays of pointers on distributed buffers (one sub-buffer per cluster) |
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| 113 | double * data[CLUSTERS_MAX]; // original time-domain data |
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| 114 | double * trans[CLUSTERS_MAX]; // used as auxiliary space for transpose |
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| 115 | double * bloup[CLUSTERS_MAX]; // used as auxiliary space for DFT |
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| 116 | double * umain[CLUSTERS_MAX]; // roots of unity used fo rootN points FFT |
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| 117 | double * twid[CLUSTERS_MAX]; // twiddle factor : exp(-2iPI*k*n/N) |
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| 118 | |
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| 119 | // instrumentation counters |
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| 120 | long parallel_time[THREADS_MAX]; // total computation time (per thread) |
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| 121 | long sync_time[THREADS_MAX]; // cumulative waiting time in barriers (per thread) |
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| 122 | long init_time; // initialisation time (in main) |
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| 123 | |
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| 124 | // synchronisation barrier (all threads) |
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| 125 | pthread_barrier_t barrier; |
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| 126 | pthread_barrierattr_t barrierattr; |
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| 127 | |
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| 128 | // threads identifiers, attributes, and arguments |
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| 129 | pthread_t trdid[THREADS_MAX]; // kernel threads identifiers |
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| 130 | pthread_attr_t attr[THREADS_MAX]; // POSIX thread attributes |
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| 131 | long args[THREADS_MAX]; // slave function arguments |
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| 132 | |
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| 133 | ///////////////////////////////////////////////////////////////////////////////// |
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| 134 | // functions declaration |
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| 135 | ///////////////////////////////////////////////////////////////////////////////// |
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| 136 | |
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| 137 | void slave(); |
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| 138 | |
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| 139 | double CheckSum(double ** x); |
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| 140 | |
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| 141 | void InitX(double ** x , unsigned int mode); |
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| 142 | |
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| 143 | void InitU(double ** u); |
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| 144 | |
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| 145 | void InitT(double ** u); |
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| 146 | |
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| 147 | long BitReverse( long k ); |
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| 148 | |
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| 149 | void FFT1D( long direction , double ** x , double ** tmp , double * upriv, |
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| 150 | double ** twid , long MyNum , long MyFirst , long MyLast ); |
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| 151 | |
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| 152 | void TwiddleOneCol(long direction, long j, double ** u, double ** x, long offset_x ); |
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| 153 | |
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| 154 | void Scale( double **x, long offset_x ); |
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| 155 | |
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| 156 | void Transpose( double ** src, double ** dest, long MyFirst, long MyLast ); |
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| 157 | |
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| 158 | void Copy( double ** src, double ** dest, long MyFirst , long MyLast ); |
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| 159 | |
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| 160 | void Reverse( double ** x, long offset_x ); |
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| 161 | |
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| 162 | void FFT1DOnce( long direction , double * u , double ** x , long offset_x ); |
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| 163 | |
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| 164 | void PrintArray( double ** x , long size ); |
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| 165 | |
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| 166 | void SimpleDft( long direction , long size , double ** src , long src_offset , |
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| 167 | double ** dst , long dst_offset ); |
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| 168 | |
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| 169 | /////////////////////////////////////////////////////////////////// |
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| 170 | // This main() function execute the sequencial initialisation |
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| 171 | // launch the parallel execution, and makes the instrumentation. |
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| 172 | /////////////////////////////////////////////////////////////////// |
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| 173 | void main() |
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| 174 | { |
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| 175 | unsigned int main_cxy; // main thread cluster |
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| 176 | unsigned int main_x; // main thread X coordinate |
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| 177 | unsigned int main_y; // main thread y coordinate |
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| 178 | unsigned int main_lid; // main thread local core index |
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| 179 | unsigned int main_tid; // main thread continuous index |
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| 180 | |
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| 181 | unsigned int x; // current index for cluster X coordinate |
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| 182 | unsigned int y; // current index for cluster Y coordinate |
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| 183 | unsigned int lid; // current index for core in a cluster |
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| 184 | unsigned int ci; // continuous cluster index (from x,y) |
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| 185 | unsigned int cxy; // hardware specific cluster identifier |
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| 186 | unsigned int tid; // continuous thread index |
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| 187 | |
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| 188 | unsigned long long start_init_cycle; |
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| 189 | unsigned long long start_exec_cycle; |
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| 190 | unsigned long long end_exec_cycle; |
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| 191 | |
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| 192 | #if CHECK |
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| 193 | double ck1; // for input/output checking |
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| 194 | double ck3; // for input/output checking |
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| 195 | #endif |
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| 196 | |
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| 197 | // get FFT application start cycle |
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| 198 | if( get_cycle( &start_init_cycle ) ) |
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| 199 | { |
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| 200 | printf("[FFT ERROR] cannot get start cycle\n"); |
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| 201 | } |
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| 202 | |
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| 203 | // get platform parameters to compute nthreads & nclusters |
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| 204 | if( get_config( &x_size , &y_size , &ncores ) ) |
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| 205 | { |
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| 206 | printf("\n[FFT ERROR] cannot get hardware configuration\n"); |
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| 207 | exit( 0 ); |
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| 208 | } |
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| 209 | |
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| 210 | // check ncores |
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| 211 | if( (ncores != 1) && (ncores != 2) && (ncores != 4) ) |
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| 212 | { |
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| 213 | printf("\n[FFT ERROR] number of cores per cluster must be 1/2/4\n"); |
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| 214 | exit( 0 ); |
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| 215 | } |
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| 216 | |
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| 217 | // check x_size |
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| 218 | if( (x_size != 1) && (x_size != 2) && (x_size != 4) && (x_size != 8) && (x_size != 16) ) |
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| 219 | { |
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| 220 | printf("\n[FFT ERROR] x_size must be 1/2/4/8/16\n"); |
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| 221 | exit( 0 ); |
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| 222 | } |
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| 223 | |
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| 224 | // check y_size |
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| 225 | if( (y_size != 1) && (y_size != 2) && (y_size != 4) && (y_size != 8) && (y_size != 16) ) |
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| 226 | { |
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| 227 | printf("\n[FFT ERROR] y_size must be 1/2/4/8/16\n"); |
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| 228 | exit( 0 ); |
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| 229 | } |
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| 230 | |
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| 231 | nthreads = x_size * y_size * ncores; |
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| 232 | nclusters = x_size * y_size; |
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| 233 | |
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| 234 | // compute various constants depending on N and T |
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| 235 | N = 1 << M; |
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| 236 | rootN = 1 << (M / 2); |
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| 237 | rows_per_thread = rootN / nthreads; |
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| 238 | points_per_cluster = N / nclusters; |
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| 239 | |
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| 240 | // check N versus T |
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| 241 | if( rootN < nthreads ) |
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| 242 | { |
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| 243 | printf("\n[FFT ERROR] sqrt(N) must be larger than T\n"); |
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| 244 | exit( 0 ); |
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| 245 | } |
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| 246 | |
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| 247 | // get main thread coordinates (main_x, main_y, main_lid) |
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| 248 | get_core( &main_cxy , &main_lid ); |
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| 249 | main_x = HAL_X_FROM_CXY( main_cxy ); |
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| 250 | main_y = HAL_Y_FROM_CXY( main_cxy ); |
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| 251 | main_tid = (((main_x * y_size) + main_y) * ncores) + main_lid; |
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| 252 | |
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| 253 | printf("\n[FFT] main starts on core[%x,%d] / %d complex points / %d thread(s)\n", |
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| 254 | main_cxy, main_lid, N, nthreads ); |
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| 255 | |
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| 256 | // allocate memory for the distributed data[i], trans[i], umain[i], twid[i] buffers |
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| 257 | // the index (i) is a continuous cluster index |
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| 258 | long data_size = (N / nclusters) * 2 * sizeof(double); |
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| 259 | long coefs_size = (rootN / nclusters) * 2 * sizeof(double); |
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| 260 | for (x = 0 ; x < x_size ; x++) |
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| 261 | { |
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| 262 | for (y = 0 ; y < y_size ; y++) |
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| 263 | { |
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| 264 | ci = x * y_size + y; |
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| 265 | cxy = HAL_CXY_FROM_XY( x , y ); |
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| 266 | data[ci] = (double *)remote_malloc( data_size , cxy ); |
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| 267 | trans[ci] = (double *)remote_malloc( data_size , cxy ); |
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| 268 | bloup[ci] = (double *)remote_malloc( data_size , cxy ); |
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| 269 | umain[ci] = (double *)remote_malloc( coefs_size , cxy ); |
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| 270 | twid[ci] = (double *)remote_malloc( data_size , cxy ); |
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| 271 | } |
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| 272 | } |
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| 273 | |
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| 274 | // arrays initialisation |
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| 275 | InitX( data , MODE ); |
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| 276 | InitU( umain ); |
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| 277 | InitT( twid ); |
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| 278 | |
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| 279 | #if CHECK |
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| 280 | ck1 = CheckSum( data ); |
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| 281 | #endif |
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| 282 | |
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| 283 | #if VERBOSE |
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| 284 | printf("\nData values / base = %x\n", &data[0][0] ); |
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| 285 | PrintArray( data , N ); |
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| 286 | |
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| 287 | printf("\nTwiddle values / base = %x\n", &twid[0][0] ); |
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| 288 | PrintArray( twid , N ); |
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| 289 | |
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| 290 | SimpleDft( 1 , N , data , 0 , bloup , 0 ); |
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| 291 | |
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| 292 | printf("\nExpected results / base = %x\n", &bloup[0][0] ); |
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| 293 | PrintArray( bloup , N ); |
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| 294 | #endif |
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| 295 | |
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| 296 | // initialise distributed barrier |
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| 297 | barrierattr.x_size = x_size; |
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| 298 | barrierattr.y_size = y_size; |
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| 299 | barrierattr.nthreads = ncores; |
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| 300 | pthread_barrier_init( &barrier, &barrierattr , nthreads); |
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| 301 | |
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| 302 | // launch other threads to execute the slave() function |
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| 303 | // on cores other than the core running the main thread |
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| 304 | for (x = 0 ; x < x_size ; x++) |
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| 305 | { |
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| 306 | for (y = 0 ; y < y_size ; y++) |
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| 307 | { |
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| 308 | for ( lid = 0 ; lid < ncores ; lid++ ) |
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| 309 | { |
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| 310 | // compute thread continuous index |
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| 311 | tid = (((x * y_size) + y) * ncores) + lid; |
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| 312 | |
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| 313 | // set thread attributes |
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| 314 | attr[tid].attributes = PT_ATTR_CLUSTER_DEFINED | PT_ATTR_CORE_DEFINED; |
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| 315 | attr[tid].cxy = HAL_CXY_FROM_XY( x , y ); |
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| 316 | attr[tid].lid = lid; |
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| 317 | |
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| 318 | // set slave function argument |
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| 319 | args[tid] = tid; |
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| 320 | |
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| 321 | // create thread |
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| 322 | if( tid != main_tid ) |
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| 323 | { |
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| 324 | if ( pthread_create( &trdid[tid], // pointer on kernel identifier |
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| 325 | &attr[tid], // pointer on thread attributes |
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| 326 | &slave, // pointer on function |
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| 327 | &args[tid]) ) // pointer on function arguments |
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| 328 | { |
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| 329 | printf("\n[FFT ERROR] creating thread %x\n", trdid[tid] ); |
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| 330 | exit( 0 ); |
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| 331 | } |
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| 332 | #if DEBUG_MAIN |
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| 333 | printf("\n[FFT] thread %x created\n", trdid[tid] ); |
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| 334 | #endif |
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| 335 | } |
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| 336 | } |
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| 337 | } |
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| 338 | } |
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| 339 | |
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| 340 | // register sequencial initalisation completion cycle |
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| 341 | get_cycle( &start_exec_cycle ); |
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| 342 | init_time = (long)(start_exec_cycle - start_init_cycle); |
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| 343 | printf("\n[FFT] enter parallel execution / cycle %d\n", (long)start_exec_cycle ); |
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| 344 | |
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| 345 | // main execute itself the slave() function |
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| 346 | slave( &args[main_tid] ); |
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| 347 | |
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| 348 | // wait other threads completion |
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| 349 | for (x = 0 ; x < x_size ; x++) |
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| 350 | { |
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| 351 | for (y = 0 ; y < y_size ; y++) |
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| 352 | { |
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| 353 | for ( lid = 0 ; lid < ncores ; lid++ ) |
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| 354 | { |
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| 355 | // compute thread continuous index |
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| 356 | long tid = (((x * y_size) + y) * ncores) + lid; |
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| 357 | |
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| 358 | if( tid != main_tid ) |
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| 359 | { |
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| 360 | #if DEBUG_MAIN |
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| 361 | printf("\n[FFT] before join for thread %x\n", trdid[tid] ); |
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| 362 | #endif |
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| 363 | |
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| 364 | if( pthread_join( trdid[tid] , NULL ) ) |
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| 365 | { |
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| 366 | printf("\n[FFT ERROR] joining thread %x\n", trdid[tid] ); |
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| 367 | exit( 0 ); |
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| 368 | } |
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| 369 | |
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| 370 | #if DEBUG_MAIN |
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| 371 | printf("\n[FFT] after join for thread %x\n", trdid[tid] ); |
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| 372 | #endif |
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| 373 | } |
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| 374 | } |
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| 375 | } |
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| 376 | } |
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| 377 | |
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| 378 | // register parallel execution completion cycle |
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| 379 | get_cycle( &end_exec_cycle ); |
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| 380 | printf("\n[FFT] complete parallel execution / cycle %d\n", (long)end_exec_cycle ); |
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| 381 | |
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| 382 | #if VERBOSE |
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| 383 | printf("\nData values after FFT:\n"); |
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| 384 | PrintArray( data , N ); |
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| 385 | #endif |
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| 386 | |
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| 387 | #if CHECK |
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| 388 | ck3 = CheckSum( data ); |
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| 389 | printf("\n*** Results ***\n"); |
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| 390 | printf("Checksum difference is %f (%f, %f)\n", ck1 - ck3, ck1, ck3); |
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| 391 | if (fabs(ck1 - ck3) < 0.001) printf("Results OK\n"); |
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| 392 | else printf("Results KO\n"); |
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| 393 | #endif |
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| 394 | |
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| 395 | // instrumentation |
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| 396 | char string[256]; |
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| 397 | |
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| 398 | snprintf( string , 256 , "/home/fft_%d_%d_%d_%d", x_size , y_size , ncores , N ); |
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| 399 | |
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| 400 | // open instrumentation file |
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| 401 | FILE * f = fopen( string , NULL ); |
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| 402 | if ( f == NULL ) |
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| 403 | { |
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| 404 | printf("\n[FFT ERROR] cannot open instrumentation file %s\n", string ); |
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| 405 | exit( 0 ); |
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| 406 | } |
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| 407 | |
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| 408 | snprintf( string , 256 , "\n[FFT] instrumentation : (%dx%dx%d) threads / %d points\n", |
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| 409 | x_size, y_size, ncores , N ); |
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| 410 | |
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| 411 | // display on terminal, and save to instrumentation file |
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| 412 | printf( "%s" , string ); |
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| 413 | fprintf( f , string ); |
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| 414 | |
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| 415 | long min_para = parallel_time[0]; |
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| 416 | long max_para = parallel_time[0]; |
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| 417 | long min_sync = sync_time[0]; |
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| 418 | long max_sync = sync_time[0]; |
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| 419 | |
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| 420 | for (tid = 1 ; tid < nthreads ; tid++) |
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| 421 | { |
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| 422 | if (parallel_time[tid] > max_para) max_para = parallel_time[tid]; |
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| 423 | if (parallel_time[tid] < min_para) min_para = parallel_time[tid]; |
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| 424 | if (sync_time[tid] > max_sync) max_sync = sync_time[tid]; |
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| 425 | if (sync_time[tid] < min_sync) min_sync = sync_time[tid]; |
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| 426 | } |
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| 427 | |
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| 428 | snprintf( string , 256 , "\n Init Parallel Barrier\n" |
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| 429 | "MIN : %d | %d | %d (cycles)\n" |
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| 430 | "MAX : %d | %d | %d (cycles)\n", |
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| 431 | (int)init_time, (int)min_para, (int)min_sync, |
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| 432 | (int)init_time, (int)max_para, (int)max_sync ); |
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| 433 | |
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| 434 | // display on terminal, and save to instrumentation file |
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| 435 | printf("%s" , string ); |
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| 436 | fprintf( f , string ); |
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| 437 | |
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| 438 | // close instrumentation file and exit |
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| 439 | fclose( f ); |
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| 440 | |
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| 441 | exit( 0 ); |
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| 442 | |
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| 443 | } // end main() |
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| 444 | |
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| 445 | /////////////////////////////////////////////////////////////// |
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| 446 | // This function is executed in parallel by all threads. |
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| 447 | /////////////////////////////////////////////////////////////// |
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| 448 | void slave( long * tid ) |
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| 449 | { |
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| 450 | long i; |
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| 451 | long MyNum; // continuous thread index |
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| 452 | long MyFirst; // index first row allocated to thread |
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| 453 | long MyLast; // index last row allocated to thread |
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| 454 | double * upriv; |
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| 455 | long c_id; |
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| 456 | long c_offset; |
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| 457 | |
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| 458 | unsigned long long parallel_start; |
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| 459 | unsigned long long parallel_stop; |
---|
| 460 | unsigned long long barrier_start; |
---|
| 461 | unsigned long long barrier_stop; |
---|
| 462 | |
---|
| 463 | MyNum = *tid; |
---|
| 464 | |
---|
| 465 | // get |
---|
| 466 | // initialise instrumentation |
---|
| 467 | get_cycle( ¶llel_start ); |
---|
| 468 | |
---|
| 469 | // allocate and initialise local array upriv[] |
---|
| 470 | // that is a local copy of the rootN coefs defined in umain[] |
---|
| 471 | upriv = (double *)malloc(2 * (rootN - 1) * sizeof(double)); |
---|
| 472 | for ( i = 0 ; i < (rootN - 1) ; i++) |
---|
| 473 | { |
---|
| 474 | c_id = i / (rootN / nclusters); |
---|
| 475 | c_offset = i % (rootN / nclusters); |
---|
| 476 | upriv[2*i] = umain[c_id][2*c_offset]; |
---|
| 477 | upriv[2*i+1] = umain[c_id][2*c_offset+1]; |
---|
| 478 | } |
---|
| 479 | |
---|
| 480 | // compute first and last rows handled by the thread |
---|
| 481 | MyFirst = rootN * MyNum / nthreads; |
---|
| 482 | MyLast = rootN * (MyNum + 1) / nthreads; |
---|
| 483 | |
---|
| 484 | // perform forward FFT |
---|
| 485 | FFT1D( 1 , data , trans , upriv , twid , MyNum , MyFirst , MyLast ); |
---|
| 486 | |
---|
| 487 | // BARRIER |
---|
| 488 | get_cycle( &barrier_start ); |
---|
| 489 | pthread_barrier_wait( &barrier ); |
---|
| 490 | get_cycle( &barrier_stop ); |
---|
| 491 | |
---|
| 492 | sync_time[MyNum] = (long)(barrier_stop - barrier_start); |
---|
| 493 | |
---|
| 494 | #if CHECK |
---|
| 495 | |
---|
| 496 | get_cycle( &barrier_start ); |
---|
| 497 | pthread_barrier_wait( &barrier ); |
---|
| 498 | get_cycle( &barrier_stop ); |
---|
| 499 | |
---|
| 500 | sync_time[MyNum] += (long)(barrier_stop - barrier_start); |
---|
| 501 | |
---|
| 502 | FFT1D( -1 , data , trans , upriv , twid , MyNum , MyFirst , MyLast ); |
---|
| 503 | |
---|
| 504 | #endif |
---|
| 505 | |
---|
| 506 | // register computation time |
---|
| 507 | get_cycle( ¶llel_stop ); |
---|
| 508 | parallel_time[MyNum] = (long)(parallel_stop - parallel_start); |
---|
| 509 | |
---|
| 510 | // exit if MyNum != 0 |
---|
| 511 | if( MyNum ) exit( 0 ); |
---|
| 512 | |
---|
| 513 | } // end slave() |
---|
| 514 | |
---|
| 515 | //////////////////////////////////////////////////////////////////////////////////////// |
---|
| 516 | // This function makes the DFT from the src[nclusters][points_per_cluster] distributed |
---|
| 517 | // buffer, to the dst[nclusters][points_per_cluster] distributed buffer. |
---|
| 518 | //////////////////////////////////////////////////////////////////////////////////////// |
---|
| 519 | void SimpleDft( long direction, |
---|
| 520 | long size, // number of points |
---|
| 521 | double ** src, // source distributed buffer |
---|
| 522 | long src_offset, // offset in source array |
---|
| 523 | double ** dst, // destination distributed buffer |
---|
| 524 | long dst_offset ) // offset in destination array |
---|
| 525 | { |
---|
| 526 | long n , k; |
---|
| 527 | double phi; // 2*PI*n*k/N |
---|
| 528 | double u_r; // cos( phi ) |
---|
| 529 | double u_c; // sin( phi ) |
---|
| 530 | double d_r; // Re(data[n]) |
---|
| 531 | double d_c; // Im(data[n]) |
---|
| 532 | double accu_r; // Re(accu) |
---|
| 533 | double accu_c; // Im(accu) |
---|
| 534 | long c_id; // distributed buffer cluster index |
---|
| 535 | long c_offset; // offset in distributed buffer |
---|
| 536 | |
---|
| 537 | for ( k = 0 ; k < size ; k++ ) // loop on the output data points |
---|
| 538 | { |
---|
| 539 | // initialise accu |
---|
| 540 | accu_r = 0; |
---|
| 541 | accu_c = 0; |
---|
| 542 | |
---|
| 543 | for ( n = 0 ; n < size ; n++ ) // loop on the input data points |
---|
| 544 | { |
---|
| 545 | // compute coef |
---|
| 546 | phi = (double)(2*PI*n*k) / size; |
---|
| 547 | u_r = cos( phi ); |
---|
| 548 | u_c = -sin( phi ) * direction; |
---|
| 549 | |
---|
| 550 | // get input data point |
---|
| 551 | c_id = (src_offset + n) / (points_per_cluster); |
---|
| 552 | c_offset = (src_offset + n) % (points_per_cluster); |
---|
| 553 | d_r = data[c_id][2*c_offset]; |
---|
| 554 | d_c = data[c_id][2*c_offset+1]; |
---|
| 555 | |
---|
| 556 | // increment accu |
---|
| 557 | accu_r += ((u_r*d_r) - (u_c*d_c)); |
---|
| 558 | accu_c += ((u_r*d_c) + (u_c*d_r)); |
---|
| 559 | } |
---|
| 560 | |
---|
| 561 | // scale for inverse DFT |
---|
| 562 | if ( direction == -1 ) |
---|
| 563 | { |
---|
| 564 | accu_r /= size; |
---|
| 565 | accu_c /= size; |
---|
| 566 | } |
---|
| 567 | |
---|
| 568 | // set output data point |
---|
| 569 | c_id = (dst_offset + k) / (points_per_cluster); |
---|
| 570 | c_offset = (dst_offset + k) % (points_per_cluster); |
---|
| 571 | dst[c_id][2*c_offset] = accu_r; |
---|
| 572 | dst[c_id][2*c_offset+1] = accu_c; |
---|
| 573 | } |
---|
| 574 | |
---|
| 575 | } // end SimpleDft() |
---|
| 576 | |
---|
| 577 | //////////////////////////// |
---|
| 578 | double CheckSum(double ** x) |
---|
| 579 | { |
---|
| 580 | long i , j; |
---|
| 581 | double cks; |
---|
| 582 | long c_id; |
---|
| 583 | long c_offset; |
---|
| 584 | |
---|
| 585 | cks = 0.0; |
---|
| 586 | for (j = 0; j < rootN ; j++) |
---|
| 587 | { |
---|
| 588 | for (i = 0; i < rootN ; i++) |
---|
| 589 | { |
---|
| 590 | c_id = (rootN * j + i) / (points_per_cluster); |
---|
| 591 | c_offset = (rootN * j + i) % (points_per_cluster); |
---|
| 592 | |
---|
| 593 | cks += data[c_id][2*c_offset] + data[c_id][2*c_offset+1]; |
---|
| 594 | } |
---|
| 595 | } |
---|
| 596 | return(cks); |
---|
| 597 | } |
---|
| 598 | |
---|
| 599 | |
---|
| 600 | //////////////////////////// |
---|
| 601 | void InitX(double ** x, |
---|
| 602 | unsigned int mode ) |
---|
| 603 | { |
---|
| 604 | long i , j; |
---|
| 605 | long c_id; |
---|
| 606 | long c_offset; |
---|
| 607 | long index; |
---|
| 608 | |
---|
| 609 | for ( j = 0 ; j < rootN ; j++ ) // loop on row index |
---|
| 610 | { |
---|
| 611 | for ( i = 0 ; i < rootN ; i++ ) // loop on point in a row |
---|
| 612 | { |
---|
| 613 | index = j * rootN + i; |
---|
| 614 | c_id = index / (points_per_cluster); |
---|
| 615 | c_offset = index % (points_per_cluster); |
---|
| 616 | |
---|
| 617 | // complex input signal is random |
---|
| 618 | if ( mode == RANDOM ) |
---|
| 619 | { |
---|
| 620 | data[c_id][2*c_offset] = ( (double)rand() ) / 65536; |
---|
| 621 | data[c_id][2*c_offset+1] = ( (double)rand() ) / 65536; |
---|
| 622 | } |
---|
| 623 | |
---|
| 624 | |
---|
| 625 | // complex input signal is cos(n/N) / sin(n/N) |
---|
| 626 | if ( mode == COSIN ) |
---|
| 627 | { |
---|
| 628 | double phi = (double)( 2 * PI * index) / N; |
---|
| 629 | data[c_id][2*c_offset] = cos( phi ); |
---|
| 630 | data[c_id][2*c_offset+1] = sin( phi ); |
---|
| 631 | } |
---|
| 632 | |
---|
| 633 | // complex input signal is constant |
---|
| 634 | if ( mode == CONSTANT ) |
---|
| 635 | { |
---|
| 636 | data[c_id][2*c_offset] = 1.0; |
---|
| 637 | data[c_id][2*c_offset+1] = 0.0; |
---|
| 638 | } |
---|
| 639 | } |
---|
| 640 | } |
---|
| 641 | } |
---|
| 642 | |
---|
| 643 | ///////////////////////// |
---|
| 644 | void InitU( double ** u ) |
---|
| 645 | { |
---|
| 646 | long q; |
---|
| 647 | long j; |
---|
| 648 | long base; |
---|
| 649 | long n1; |
---|
| 650 | long c_id; |
---|
| 651 | long c_offset; |
---|
| 652 | double phi; |
---|
| 653 | long stop = 0; |
---|
| 654 | |
---|
| 655 | for (q = 0 ; ((1 << q) < N) && (stop == 0) ; q++) |
---|
| 656 | { |
---|
| 657 | n1 = 1 << q; |
---|
| 658 | base = n1 - 1; |
---|
| 659 | for (j = 0; (j < n1) && (stop == 0) ; j++) |
---|
| 660 | { |
---|
| 661 | if (base + j > rootN - 1) return; |
---|
| 662 | |
---|
| 663 | c_id = (base + j) / (rootN / nclusters); |
---|
| 664 | c_offset = (base + j) % (rootN / nclusters); |
---|
| 665 | phi = (double)(2.0 * PI * j) / (2 * n1); |
---|
| 666 | u[c_id][2*c_offset] = cos( phi ); |
---|
| 667 | u[c_id][2*c_offset+1] = -sin( phi ); |
---|
| 668 | } |
---|
| 669 | } |
---|
| 670 | } |
---|
| 671 | |
---|
| 672 | ////////////////////////// |
---|
| 673 | void InitT( double ** u ) |
---|
| 674 | { |
---|
| 675 | long i, j; |
---|
| 676 | long index; |
---|
| 677 | long c_id; |
---|
| 678 | long c_offset; |
---|
| 679 | double phi; |
---|
| 680 | |
---|
| 681 | for ( j = 0 ; j < rootN ; j++ ) // loop on row index |
---|
| 682 | { |
---|
| 683 | for ( i = 0 ; i < rootN ; i++ ) // loop on points in a row |
---|
| 684 | { |
---|
| 685 | index = j * rootN + i; |
---|
| 686 | c_id = index / (points_per_cluster); |
---|
| 687 | c_offset = index % (points_per_cluster); |
---|
| 688 | |
---|
| 689 | phi = (double)(2.0 * PI * i * j) / N; |
---|
| 690 | u[c_id][2*c_offset] = cos( phi ); |
---|
| 691 | u[c_id][2*c_offset+1] = -sin( phi ); |
---|
| 692 | } |
---|
| 693 | } |
---|
| 694 | } |
---|
| 695 | |
---|
| 696 | //////////////////////////////////////////////////////////////////////////////////////// |
---|
| 697 | // This function returns an index value that is the bit reverse of the input value. |
---|
| 698 | //////////////////////////////////////////////////////////////////////////////////////// |
---|
| 699 | long BitReverse( long k ) |
---|
| 700 | { |
---|
| 701 | long i; |
---|
| 702 | long j; |
---|
| 703 | long tmp; |
---|
| 704 | |
---|
| 705 | j = 0; |
---|
| 706 | tmp = k; |
---|
| 707 | for (i = 0; i < M/2 ; i++) |
---|
| 708 | { |
---|
| 709 | j = 2 * j + (tmp & 0x1); |
---|
| 710 | tmp = tmp >> 1; |
---|
| 711 | } |
---|
| 712 | return j; |
---|
| 713 | } |
---|
| 714 | |
---|
| 715 | //////////////////////////////////////////////////////////////////////////////////////// |
---|
| 716 | // This function perform the in place (direct or inverse) FFT on the N data points |
---|
| 717 | // contained in the distributed buffers x[nclusters][points_per_cluster]. |
---|
| 718 | // It handles the (N) points 1D array as a (rootN*rootN) points 2D array. |
---|
| 719 | // 1) it transpose (rootN/nthreads ) rows from x to tmp. |
---|
| 720 | // 2) it make (rootN/nthreads) FFT on the tmp rows and apply the twiddle factor. |
---|
| 721 | // 3) it transpose (rootN/nthreads) columns from tmp to x. |
---|
| 722 | // 4) it make (rootN/nthreads) FFT on the x rows. |
---|
| 723 | // It calls the FFT1DOnce() 2*(rootN/nthreads) times to perform the in place FFT |
---|
| 724 | // on the rootN points contained in a row. |
---|
| 725 | //////////////////////////////////////////////////////////////////////////////////////// |
---|
| 726 | void FFT1D( long direction, // direct : 1 / inverse : -1 |
---|
| 727 | double ** x, // input & output distributed data points array |
---|
| 728 | double ** tmp, // auxiliary distributed data points array |
---|
| 729 | double * upriv, // local array containing coefs for rootN FFT |
---|
| 730 | double ** twid, // distributed arrays containing N twiddle factors |
---|
| 731 | long MyNum, |
---|
| 732 | long MyFirst, |
---|
| 733 | long MyLast ) |
---|
| 734 | { |
---|
| 735 | long j; |
---|
| 736 | unsigned long long barrier_start; |
---|
| 737 | unsigned long long barrier_stop; |
---|
| 738 | |
---|
| 739 | // transpose (rootN/nthreads) rows from x to tmp |
---|
| 740 | Transpose( x , tmp , MyFirst , MyLast ); |
---|
| 741 | |
---|
| 742 | #if DEBUG_FFT1D |
---|
| 743 | printf("\n@@@ tmp after first transpose\n"); |
---|
| 744 | PrintArray( tmp , N ); |
---|
| 745 | #endif |
---|
| 746 | |
---|
| 747 | // BARRIER |
---|
| 748 | get_cycle( &barrier_start ); |
---|
| 749 | pthread_barrier_wait( &barrier ); |
---|
| 750 | get_cycle( &barrier_stop ); |
---|
| 751 | |
---|
| 752 | sync_time[MyNum] = (long)(barrier_stop - barrier_start); |
---|
| 753 | |
---|
| 754 | // do FFTs on rows of tmp (i.e. columns of x) and apply twiddle factor |
---|
| 755 | for (j = MyFirst; j < MyLast; j++) |
---|
| 756 | { |
---|
| 757 | FFT1DOnce( direction , upriv , tmp , j * rootN ); |
---|
| 758 | TwiddleOneCol( direction , j , twid , tmp , j * rootN ); |
---|
| 759 | } |
---|
| 760 | |
---|
| 761 | #if DEBUG_FFT1D |
---|
| 762 | printf("\n@@@ tmp after columns FFT + twiddle \n"); |
---|
| 763 | PrintArray( tmp , N ); |
---|
| 764 | #endif |
---|
| 765 | |
---|
| 766 | // BARRIER |
---|
| 767 | get_cycle( &barrier_start ); |
---|
| 768 | pthread_barrier_wait( &barrier ); |
---|
| 769 | get_cycle( &barrier_stop ); |
---|
| 770 | |
---|
| 771 | sync_time[MyNum] += (long)(barrier_stop - barrier_start); |
---|
| 772 | |
---|
| 773 | // transpose tmp to x |
---|
| 774 | Transpose( tmp , x , MyFirst , MyLast ); |
---|
| 775 | |
---|
| 776 | #if DEBUG_FFT1D |
---|
| 777 | printf("\n@@@ x after second transpose \n"); |
---|
| 778 | PrintArray( x , N ); |
---|
| 779 | #endif |
---|
| 780 | |
---|
| 781 | // BARRIER |
---|
| 782 | get_cycle( &barrier_start ); |
---|
| 783 | pthread_barrier_wait( &barrier ); |
---|
| 784 | get_cycle( &barrier_stop ); |
---|
| 785 | |
---|
| 786 | sync_time[MyNum] += (long)(barrier_stop - barrier_start); |
---|
| 787 | |
---|
| 788 | // do FFTs on rows of x and apply the scaling factor |
---|
| 789 | for (j = MyFirst; j < MyLast; j++) |
---|
| 790 | { |
---|
| 791 | FFT1DOnce( direction , upriv , x , j * rootN ); |
---|
| 792 | if (direction == -1) Scale( x , j * rootN ); |
---|
| 793 | } |
---|
| 794 | |
---|
| 795 | #if DEBUG_FFT1D |
---|
| 796 | printf("\n@@@ x after rows FFT + scaling \n"); |
---|
| 797 | PrintArray( x , N ); |
---|
| 798 | #endif |
---|
| 799 | |
---|
| 800 | // BARRIER |
---|
| 801 | get_cycle( &barrier_start ); |
---|
| 802 | pthread_barrier_wait( &barrier ); |
---|
| 803 | get_cycle( &barrier_stop ); |
---|
| 804 | |
---|
| 805 | sync_time[MyNum] += (long)(barrier_stop - barrier_start); |
---|
| 806 | |
---|
| 807 | // transpose x to tmp |
---|
| 808 | Transpose( x , tmp , MyFirst , MyLast ); |
---|
| 809 | |
---|
| 810 | #if DEBUG_FFT1D |
---|
| 811 | printf("\n@@@ tmp after third transpose \n"); |
---|
| 812 | PrintArray( tmp , N ); |
---|
| 813 | #endif |
---|
| 814 | |
---|
| 815 | // BARRIER |
---|
| 816 | get_cycle( &barrier_start ); |
---|
| 817 | pthread_barrier_wait( &barrier ); |
---|
| 818 | get_cycle( &barrier_stop ); |
---|
| 819 | |
---|
| 820 | sync_time[MyNum] += (long)(barrier_stop - barrier_start); |
---|
| 821 | |
---|
| 822 | // copy tmp to x |
---|
| 823 | Copy( tmp , x , MyFirst , MyLast ); |
---|
| 824 | |
---|
| 825 | #if DEBUG_FFT1D |
---|
| 826 | printf("\n@@@ x after final copy \n"); |
---|
| 827 | PrintArray( x , N ); |
---|
| 828 | #endif |
---|
| 829 | |
---|
| 830 | |
---|
| 831 | } // end FFT1D() |
---|
| 832 | |
---|
| 833 | ///////////////////////////////////////////////////////////////////////////////////// |
---|
| 834 | // This function multiply all points contained in a row (rootN points) of the |
---|
| 835 | // x[] array by the corresponding twiddle factor, contained in the u[] array. |
---|
| 836 | ///////////////////////////////////////////////////////////////////////////////////// |
---|
| 837 | void TwiddleOneCol( long direction, |
---|
| 838 | long j, // y coordinate in 2D view of coef array |
---|
| 839 | double ** u, // coef array base address |
---|
| 840 | double ** x, // data array base address |
---|
| 841 | long offset_x ) // first point in N points data array |
---|
| 842 | { |
---|
| 843 | long i; |
---|
| 844 | double omega_r; |
---|
| 845 | double omega_c; |
---|
| 846 | double x_r; |
---|
| 847 | double x_c; |
---|
| 848 | long c_id; |
---|
| 849 | long c_offset; |
---|
| 850 | |
---|
| 851 | for (i = 0; i < rootN ; i++) // loop on the rootN points |
---|
| 852 | { |
---|
| 853 | // get coef |
---|
| 854 | c_id = (j * rootN + i) / (points_per_cluster); |
---|
| 855 | c_offset = (j * rootN + i) % (points_per_cluster); |
---|
| 856 | omega_r = u[c_id][2*c_offset]; |
---|
| 857 | omega_c = direction * u[c_id][2*c_offset+1]; |
---|
| 858 | |
---|
| 859 | // access data |
---|
| 860 | c_id = (offset_x + i) / (points_per_cluster); |
---|
| 861 | c_offset = (offset_x + i) % (points_per_cluster); |
---|
| 862 | x_r = x[c_id][2*c_offset]; |
---|
| 863 | x_c = x[c_id][2*c_offset+1]; |
---|
| 864 | |
---|
| 865 | x[c_id][2*c_offset] = omega_r*x_r - omega_c * x_c; |
---|
| 866 | x[c_id][2*c_offset+1] = omega_r*x_c + omega_c * x_r; |
---|
| 867 | } |
---|
| 868 | } // end TwiddleOneCol() |
---|
| 869 | |
---|
| 870 | //////////////////////// |
---|
| 871 | void Scale( double ** x, // data array base address |
---|
| 872 | long offset_x ) // first point of the row to be scaled |
---|
| 873 | { |
---|
| 874 | long i; |
---|
| 875 | long c_id; |
---|
| 876 | long c_offset; |
---|
| 877 | |
---|
| 878 | for (i = 0; i < rootN ; i++) |
---|
| 879 | { |
---|
| 880 | c_id = (offset_x + i) / (points_per_cluster); |
---|
| 881 | c_offset = (offset_x + i) % (points_per_cluster); |
---|
| 882 | data[c_id][2*c_offset] /= N; |
---|
| 883 | data[c_id][2*c_offset + 1] /= N; |
---|
| 884 | } |
---|
| 885 | } |
---|
| 886 | |
---|
| 887 | //////////////////////////// |
---|
| 888 | void Transpose( double ** src, // source buffer (array of pointers) |
---|
| 889 | double ** dest, // destination buffer (array of pointers) |
---|
| 890 | long MyFirst, // first row allocated to the thread |
---|
| 891 | long MyLast ) // last row allocated to the thread |
---|
| 892 | { |
---|
| 893 | long row; // row index |
---|
| 894 | long point; // data point index in a row |
---|
| 895 | |
---|
| 896 | long index_src; // absolute index in the source N points array |
---|
| 897 | long c_id_src; // cluster for the source buffer |
---|
| 898 | long c_offset_src; // offset in the source buffer |
---|
| 899 | |
---|
| 900 | long index_dst; // absolute index in the dest N points array |
---|
| 901 | long c_id_dst; // cluster for the dest buffer |
---|
| 902 | long c_offset_dst; // offset in the dest buffer |
---|
| 903 | |
---|
| 904 | |
---|
| 905 | // scan all data points allocated to the thread |
---|
| 906 | // (between MyFirst row and MyLast row) from the source buffer |
---|
| 907 | // and write these points to the destination buffer |
---|
| 908 | for ( row = MyFirst ; row < MyLast ; row++ ) // loop on the rows |
---|
| 909 | { |
---|
| 910 | for ( point = 0 ; point < rootN ; point++ ) // loop on points in row |
---|
| 911 | { |
---|
| 912 | index_src = row * rootN + point; |
---|
| 913 | c_id_src = index_src / (points_per_cluster); |
---|
| 914 | c_offset_src = index_src % (points_per_cluster); |
---|
| 915 | |
---|
| 916 | index_dst = point * rootN + row; |
---|
| 917 | c_id_dst = index_dst / (points_per_cluster); |
---|
| 918 | c_offset_dst = index_dst % (points_per_cluster); |
---|
| 919 | |
---|
| 920 | dest[c_id_dst][2*c_offset_dst] = src[c_id_src][2*c_offset_src]; |
---|
| 921 | dest[c_id_dst][2*c_offset_dst+1] = src[c_id_src][2*c_offset_src+1]; |
---|
| 922 | } |
---|
| 923 | } |
---|
| 924 | } // end Transpose() |
---|
| 925 | |
---|
| 926 | ///////////////////////// |
---|
| 927 | void Copy( double ** src, // source buffer (array of pointers) |
---|
| 928 | double ** dest, // destination buffer (array of pointers) |
---|
| 929 | long MyFirst, // first row allocated to the thread |
---|
| 930 | long MyLast ) // last row allocated to the thread |
---|
| 931 | { |
---|
| 932 | long row; // row index |
---|
| 933 | long point; // data point index in a row |
---|
| 934 | |
---|
| 935 | long index; // absolute index in the N points array |
---|
| 936 | long c_id; // cluster index |
---|
| 937 | long c_offset; // offset in local buffer |
---|
| 938 | |
---|
| 939 | // scan all data points allocated to the thread |
---|
| 940 | for ( row = MyFirst ; row < MyLast ; row++ ) // loop on the rows |
---|
| 941 | { |
---|
| 942 | for ( point = 0 ; point < rootN ; point++ ) // loop on points in row |
---|
| 943 | { |
---|
| 944 | index = row * rootN + point; |
---|
| 945 | c_id = index / (points_per_cluster); |
---|
| 946 | c_offset = index % (points_per_cluster); |
---|
| 947 | |
---|
| 948 | dest[c_id][2*c_offset] = src[c_id][2*c_offset]; |
---|
| 949 | dest[c_id][2*c_offset+1] = src[c_id][2*c_offset+1]; |
---|
| 950 | } |
---|
| 951 | } |
---|
| 952 | } // end Copy() |
---|
| 953 | |
---|
| 954 | ////////////////////////// |
---|
| 955 | void Reverse( double ** x, |
---|
| 956 | long offset_x ) |
---|
| 957 | { |
---|
| 958 | long j, k; |
---|
| 959 | long c_id_j; |
---|
| 960 | long c_offset_j; |
---|
| 961 | long c_id_k; |
---|
| 962 | long c_offset_k; |
---|
| 963 | |
---|
| 964 | for (k = 0 ; k < rootN ; k++) |
---|
| 965 | { |
---|
| 966 | j = BitReverse( k ); |
---|
| 967 | if (j > k) |
---|
| 968 | { |
---|
| 969 | c_id_j = (offset_x + j) / (points_per_cluster); |
---|
| 970 | c_offset_j = (offset_x + j) % (points_per_cluster); |
---|
| 971 | c_id_k = (offset_x + k) / (points_per_cluster); |
---|
| 972 | c_offset_k = (offset_x + k) % (points_per_cluster); |
---|
| 973 | |
---|
| 974 | SWAP(x[c_id_j][2*c_offset_j] , x[c_id_k][2*c_offset_k]); |
---|
| 975 | SWAP(x[c_id_j][2*c_offset_j+1], x[c_id_k][2*c_offset_k+1]); |
---|
| 976 | } |
---|
| 977 | } |
---|
| 978 | } |
---|
| 979 | |
---|
| 980 | ///////////////////////////////////////////////////////////////////////////// |
---|
| 981 | // This function makes the in-place FFT on all points contained in a row |
---|
| 982 | // (i.e. rootN points) of the x[nclusters][points_per_cluster] array. |
---|
| 983 | ///////////////////////////////////////////////////////////////////////////// |
---|
| 984 | void FFT1DOnce( long direction, // direct / inverse |
---|
| 985 | double * u, // private coefs array |
---|
| 986 | double ** x, // array of pointers on distributed buffers |
---|
| 987 | long offset_x ) // absolute offset in the x array |
---|
| 988 | { |
---|
| 989 | long j; |
---|
| 990 | long k; |
---|
| 991 | long q; |
---|
| 992 | long L; |
---|
| 993 | long r; |
---|
| 994 | long Lstar; |
---|
| 995 | double * u1; |
---|
| 996 | |
---|
| 997 | long offset_x1; // index first butterfly input |
---|
| 998 | long offset_x2; // index second butterfly output |
---|
| 999 | |
---|
| 1000 | double omega_r; // real part butterfy coef |
---|
| 1001 | double omega_c; // complex part butterfly coef |
---|
| 1002 | |
---|
| 1003 | double tau_r; |
---|
| 1004 | double tau_c; |
---|
| 1005 | |
---|
| 1006 | double d1_r; // real part first butterfly input |
---|
| 1007 | double d1_c; // imag part first butterfly input |
---|
| 1008 | double d2_r; // real part second butterfly input |
---|
| 1009 | double d2_c; // imag part second butterfly input |
---|
| 1010 | |
---|
| 1011 | long c_id_1; // cluster index for first butterfly input |
---|
| 1012 | long c_offset_1; // offset for first butterfly input |
---|
| 1013 | long c_id_2; // cluster index for second butterfly input |
---|
| 1014 | long c_offset_2; // offset for second butterfly input |
---|
| 1015 | |
---|
| 1016 | #if DEBUG_ONCE |
---|
| 1017 | unsigned int p; |
---|
| 1018 | printf("\n@@@ FFT ROW data in / %d points / offset = %d\n", |
---|
| 1019 | rootN , offset_x ); |
---|
| 1020 | for ( p = 0 ; p < rootN ; p++ ) |
---|
| 1021 | { |
---|
| 1022 | long index = offset_x + p; |
---|
| 1023 | long c_id = index / (points_per_cluster); |
---|
| 1024 | long c_offset = index % (points_per_cluster); |
---|
| 1025 | printf("%f , %f | ", x[c_id][2*c_offset] , x[c_id][2*c_offset+1] ); |
---|
| 1026 | } |
---|
| 1027 | printf("\n"); |
---|
| 1028 | #endif |
---|
| 1029 | |
---|
| 1030 | // This makes the rootN input points reordering |
---|
| 1031 | Reverse( x , offset_x ); |
---|
| 1032 | |
---|
| 1033 | #if DEBUG_ONCE |
---|
| 1034 | printf("\n@@@ FFT ROW data after reverse\n"); |
---|
| 1035 | for ( p = 0 ; p < rootN ; p++ ) |
---|
| 1036 | { |
---|
| 1037 | long index = offset_x + p; |
---|
| 1038 | long c_id = index / (points_per_cluster); |
---|
| 1039 | long c_offset = index % (points_per_cluster); |
---|
| 1040 | printf("%f , %f | ", x[c_id][2*c_offset] , x[c_id][2*c_offset+1] ); |
---|
| 1041 | } |
---|
| 1042 | printf("\n"); |
---|
| 1043 | #endif |
---|
| 1044 | |
---|
| 1045 | // This implements the multi-stages, in place Butterfly network |
---|
| 1046 | for (q = 1; q <= M/2 ; q++) // loop on stages |
---|
| 1047 | { |
---|
| 1048 | L = 1 << q; // number of points per subset for current stage |
---|
| 1049 | r = rootN / L; // number of subsets |
---|
| 1050 | Lstar = L / 2; |
---|
| 1051 | u1 = &u[2 * (Lstar - 1)]; |
---|
| 1052 | for (k = 0; k < r; k++) // loop on the subsets |
---|
| 1053 | { |
---|
| 1054 | offset_x1 = offset_x + (k * L); // index first point |
---|
| 1055 | offset_x2 = offset_x + (k * L + Lstar); // index second point |
---|
| 1056 | |
---|
| 1057 | #if DEBUG_ONCE |
---|
| 1058 | printf("\n ### q = %d / k = %d / x1 = %d / x2 = %d\n", |
---|
| 1059 | q , k , offset_x1 , offset_x2 ); |
---|
| 1060 | #endif |
---|
| 1061 | // makes all in-place butterfly(s) for subset |
---|
| 1062 | for (j = 0; j < Lstar; j++) |
---|
| 1063 | { |
---|
| 1064 | // get coef |
---|
| 1065 | omega_r = u1[2*j]; |
---|
| 1066 | omega_c = direction * u1[2*j+1]; |
---|
| 1067 | |
---|
| 1068 | // get d[x1] address and value |
---|
| 1069 | c_id_1 = (offset_x1 + j) / (points_per_cluster); |
---|
| 1070 | c_offset_1 = (offset_x1 + j) % (points_per_cluster); |
---|
| 1071 | d1_r = x[c_id_1][2*c_offset_1]; |
---|
| 1072 | d1_c = x[c_id_1][2*c_offset_1+1]; |
---|
| 1073 | |
---|
| 1074 | // get d[x2] address and value |
---|
| 1075 | c_id_2 = (offset_x2 + j) / (points_per_cluster); |
---|
| 1076 | c_offset_2 = (offset_x2 + j) % (points_per_cluster); |
---|
| 1077 | d2_r = x[c_id_2][2*c_offset_2]; |
---|
| 1078 | d2_c = x[c_id_2][2*c_offset_2+1]; |
---|
| 1079 | |
---|
| 1080 | #if DEBUG_ONCE |
---|
| 1081 | printf("\n ### d1_in = (%f , %f) / d2_in = (%f , %f) / coef = (%f , %f)\n", |
---|
| 1082 | d1_r , d1_c , d2_r , d2_c , omega_r , omega_c); |
---|
| 1083 | #endif |
---|
| 1084 | // tau = omega * d[x2] |
---|
| 1085 | tau_r = omega_r * d2_r - omega_c * d2_c; |
---|
| 1086 | tau_c = omega_r * d2_c + omega_c * d2_r; |
---|
| 1087 | |
---|
| 1088 | // set new value for d[x1] = d[x1] + omega * d[x2] |
---|
| 1089 | x[c_id_1][2*c_offset_1] = d1_r + tau_r; |
---|
| 1090 | x[c_id_1][2*c_offset_1+1] = d1_c + tau_c; |
---|
| 1091 | |
---|
| 1092 | // set new value for d[x2] = d[x1] - omega * d[x2] |
---|
| 1093 | x[c_id_2][2*c_offset_2] = d1_r - tau_r; |
---|
| 1094 | x[c_id_2][2*c_offset_2+1] = d1_c - tau_c; |
---|
| 1095 | |
---|
| 1096 | #if DEBUG_ONCE |
---|
| 1097 | printf("\n ### d1_out = (%f , %f) / d2_out = (%f , %f)\n", |
---|
| 1098 | d1_r + tau_r , d1_c + tau_c , d2_r - tau_r , d2_c - tau_c ); |
---|
| 1099 | #endif |
---|
| 1100 | } |
---|
| 1101 | } |
---|
| 1102 | } |
---|
| 1103 | |
---|
| 1104 | #if DEBUG_ONCE |
---|
| 1105 | printf("\n@@@ FFT ROW data out\n"); |
---|
| 1106 | for ( p = 0 ; p < rootN ; p++ ) |
---|
| 1107 | { |
---|
| 1108 | long index = offset_x + p; |
---|
| 1109 | long c_id = index / (points_per_cluster); |
---|
| 1110 | long c_offset = index % (points_per_cluster); |
---|
| 1111 | printf("%f , %f | ", x[c_id][2*c_offset] , x[c_id][2*c_offset+1] ); |
---|
| 1112 | } |
---|
| 1113 | printf("\n"); |
---|
| 1114 | #endif |
---|
| 1115 | |
---|
| 1116 | } // end FFT1DOnce() |
---|
| 1117 | |
---|
| 1118 | ////////////////////////////////// |
---|
| 1119 | void PrintArray( double ** array, |
---|
| 1120 | long size ) |
---|
| 1121 | { |
---|
| 1122 | long i; |
---|
| 1123 | long c_id; |
---|
| 1124 | long c_offset; |
---|
| 1125 | |
---|
| 1126 | // float display |
---|
| 1127 | for (i = 0; i < size ; i++) |
---|
| 1128 | { |
---|
| 1129 | c_id = i / (points_per_cluster); |
---|
| 1130 | c_offset = i % (points_per_cluster); |
---|
| 1131 | |
---|
| 1132 | printf(" %f %f |", array[c_id][2*c_offset], array[c_id][2*c_offset+1]); |
---|
| 1133 | |
---|
| 1134 | if ( (i+1) % 4 == 0) printf("\n"); |
---|
| 1135 | } |
---|
| 1136 | printf("\n"); |
---|
| 1137 | } |
---|
| 1138 | |
---|
| 1139 | |
---|
| 1140 | // Local Variables: |
---|
| 1141 | // tab-width: 4 |
---|
| 1142 | // c-basic-offset: 4 |
---|
| 1143 | // c-file-offsets:((innamespace . 0)(inline-open . 0)) |
---|
| 1144 | // indent-tabs-mode: nil |
---|
| 1145 | // End: |
---|
| 1146 | |
---|
| 1147 | // vim: filetype=cpp:expandtab:shiftwidth=4:tabstop=4:softtabstop=4 |
---|
| 1148 | |
---|