[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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[574] | 48 | // - PRINT_ARRAY : 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_MAIN : Display intermediate results in main() |
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| 51 | // - DEBUG_FFT1D : Display intermediate results in FFT1D() |
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| 52 | // - DEBUG_ROW : |
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[469] | 53 | // |
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| 54 | // Regarding final instrumentation: |
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| 55 | // - the sequencial initialisation time (init_time) is computed |
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| 56 | // by the main thread in the main() function. |
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| 57 | // - The parallel execution time (parallel_time[i]) is computed by each |
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| 58 | // thread(i) in the slave() function. |
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| 59 | // - The synchronisation time related to the barriers (sync_time[i]) |
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| 60 | // is computed by each thread(i) in the slave() function. |
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| 61 | // The results are displayed on the TXT terminal, and registered on disk. |
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| 62 | /////////////////////////////////////////////////////////////////////////// |
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| 63 | |
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| 64 | #include <math.h> |
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| 65 | #include <stdio.h> |
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| 66 | #include <stdlib.h> |
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| 67 | #include <fcntl.h> |
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| 68 | #include <unistd.h> |
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| 69 | #include <pthread.h> |
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| 70 | #include <almosmkh.h> |
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| 71 | #include <hal_macros.h> |
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| 72 | |
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| 73 | // constants |
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| 74 | |
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| 75 | #define PI 3.14159265359 |
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| 76 | #define PAGE_SIZE 4096 |
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| 77 | #define X_MAX 16 // max number of clusters in a row |
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| 78 | #define Y_MAX 16 // max number of clusters in a column |
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| 79 | #define CORES_MAX 4 // max number of cores in a cluster |
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| 80 | #define CLUSTERS_MAX X_MAX * Y_MAX |
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| 81 | #define THREADS_MAX CLUSTERS_MAX * CORES_MAX |
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| 82 | #define RANDOM 0 |
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| 83 | #define COSIN 1 |
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| 84 | #define CONSTANT 2 |
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| 85 | |
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| 86 | // parameters |
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| 87 | |
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| 88 | #define DEFAULT_M 6 |
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[574] | 89 | #define MODE COSIN |
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[469] | 90 | #define CHECK 0 |
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[574] | 91 | #define DEBUG_MAIN 0 // trace main() function (detailed if odd) |
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| 92 | #define DEBUG_FFT1D 0 // trace FFT1D() function (detailed if odd) |
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| 93 | #define DEBUG_ROW 0 // trace FFTRow() function (detailed if odd) |
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| 94 | #define PRINT_ARRAY 0 |
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[469] | 95 | |
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| 96 | // macro to swap two variables |
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| 97 | #define SWAP(a,b) { double tmp; tmp = a; a = b; b = tmp; } |
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| 98 | |
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| 99 | ///////////////////////////////////////////////////////////////////////////////// |
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| 100 | // global variables |
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| 101 | ///////////////////////////////////////////////////////////////////////////////// |
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| 102 | |
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| 103 | unsigned int x_size; // number of clusters per row in the mesh |
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| 104 | unsigned int y_size; // number of clusters per column in the mesh |
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| 105 | unsigned int ncores; // number of cores per cluster |
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[473] | 106 | unsigned int nthreads; // total number of threads (one thread per core) |
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| 107 | unsigned int nclusters; // total number of clusters |
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| 108 | unsigned int M = DEFAULT_M; // log2(number of points) |
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| 109 | unsigned int N; // number of points (N = 2^M) |
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| 110 | unsigned int rootN; // rootN = 2^M/2 |
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| 111 | unsigned int rows_per_thread; // number of data "rows" handled by a single thread |
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| 112 | unsigned int points_per_cluster; // number of data points per cluster |
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[469] | 113 | |
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| 114 | // arrays of pointers on distributed buffers (one sub-buffer per cluster) |
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| 115 | double * data[CLUSTERS_MAX]; // original time-domain data |
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| 116 | double * trans[CLUSTERS_MAX]; // used as auxiliary space for transpose |
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| 117 | double * bloup[CLUSTERS_MAX]; // used as auxiliary space for DFT |
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| 118 | double * umain[CLUSTERS_MAX]; // roots of unity used fo rootN points FFT |
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| 119 | double * twid[CLUSTERS_MAX]; // twiddle factor : exp(-2iPI*k*n/N) |
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| 120 | |
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| 121 | // instrumentation counters |
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| 122 | long parallel_time[THREADS_MAX]; // total computation time (per thread) |
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| 123 | long sync_time[THREADS_MAX]; // cumulative waiting time in barriers (per thread) |
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| 124 | long init_time; // initialisation time (in main) |
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| 125 | |
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| 126 | // synchronisation barrier (all threads) |
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| 127 | pthread_barrier_t barrier; |
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| 128 | pthread_barrierattr_t barrierattr; |
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| 129 | |
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| 130 | // threads identifiers, attributes, and arguments |
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| 131 | pthread_t trdid[THREADS_MAX]; // kernel threads identifiers |
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| 132 | pthread_attr_t attr[THREADS_MAX]; // POSIX thread attributes |
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[473] | 133 | unsigned int args[THREADS_MAX]; // slave function arguments |
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[469] | 134 | |
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| 135 | ///////////////////////////////////////////////////////////////////////////////// |
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| 136 | // functions declaration |
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| 137 | ///////////////////////////////////////////////////////////////////////////////// |
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| 138 | |
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[503] | 139 | void slave( unsigned int * tid ); |
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[469] | 140 | |
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[503] | 141 | double CheckSum( void ); |
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[469] | 142 | |
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| 143 | void InitX(double ** x , unsigned int mode); |
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| 144 | |
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| 145 | void InitU(double ** u); |
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| 146 | |
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| 147 | void InitT(double ** u); |
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| 148 | |
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[473] | 149 | unsigned int BitReverse( unsigned int k ); |
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[469] | 150 | |
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[473] | 151 | void FFT1D( int direction, |
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| 152 | double ** x, |
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| 153 | double ** tmp, |
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| 154 | double * upriv, |
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| 155 | double ** twid, |
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| 156 | unsigned int MyNum, |
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| 157 | unsigned int MyFirst, |
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| 158 | unsigned int MyLast ); |
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[469] | 159 | |
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[473] | 160 | void TwiddleOneCol( int direction, |
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| 161 | unsigned int j, |
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| 162 | double ** u, |
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| 163 | double ** x, |
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| 164 | unsigned int offset_x ); |
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[469] | 165 | |
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[473] | 166 | void Scale( double ** x, |
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| 167 | unsigned int offset_x ); |
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[469] | 168 | |
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[473] | 169 | void Transpose( double ** src, |
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| 170 | double ** dest, |
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| 171 | unsigned int MyFirst, |
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| 172 | unsigned int MyLast ); |
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[469] | 173 | |
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[473] | 174 | void Copy( double ** src, |
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| 175 | double ** dest, |
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| 176 | unsigned int MyFirst, |
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| 177 | unsigned int MyLast ); |
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[469] | 178 | |
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[473] | 179 | void Reverse( double ** x, |
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| 180 | unsigned int offset_x ); |
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[469] | 181 | |
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[574] | 182 | void FFTRow( int direction, |
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[473] | 183 | double * u, |
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| 184 | double ** x, |
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| 185 | unsigned int offset_x ); |
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[469] | 186 | |
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[473] | 187 | void PrintArray( double ** x, |
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| 188 | unsigned int size ); |
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[469] | 189 | |
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[473] | 190 | void SimpleDft( int direction, |
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| 191 | unsigned int size, |
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| 192 | double ** src, |
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| 193 | unsigned int src_offset, |
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| 194 | double ** dst, |
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| 195 | unsigned int dst_offset ); |
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[469] | 196 | |
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| 197 | /////////////////////////////////////////////////////////////////// |
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| 198 | // This main() function execute the sequencial initialisation |
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| 199 | // launch the parallel execution, and makes the instrumentation. |
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| 200 | /////////////////////////////////////////////////////////////////// |
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[503] | 201 | void main ( void ) |
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[469] | 202 | { |
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| 203 | unsigned int main_cxy; // main thread cluster |
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| 204 | unsigned int main_x; // main thread X coordinate |
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| 205 | unsigned int main_y; // main thread y coordinate |
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| 206 | unsigned int main_lid; // main thread local core index |
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| 207 | unsigned int main_tid; // main thread continuous index |
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| 208 | |
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| 209 | unsigned int x; // current index for cluster X coordinate |
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| 210 | unsigned int y; // current index for cluster Y coordinate |
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| 211 | unsigned int lid; // current index for core in a cluster |
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| 212 | unsigned int ci; // continuous cluster index (from x,y) |
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| 213 | unsigned int cxy; // hardware specific cluster identifier |
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| 214 | unsigned int tid; // continuous thread index |
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| 215 | |
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| 216 | unsigned long long start_init_cycle; |
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| 217 | unsigned long long start_exec_cycle; |
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| 218 | unsigned long long end_exec_cycle; |
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| 219 | |
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| 220 | #if CHECK |
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| 221 | double ck1; // for input/output checking |
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| 222 | double ck3; // for input/output checking |
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| 223 | #endif |
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| 224 | |
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| 225 | // get FFT application start cycle |
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| 226 | if( get_cycle( &start_init_cycle ) ) |
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| 227 | { |
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| 228 | printf("[FFT ERROR] cannot get start cycle\n"); |
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| 229 | } |
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| 230 | |
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| 231 | // get platform parameters to compute nthreads & nclusters |
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| 232 | if( get_config( &x_size , &y_size , &ncores ) ) |
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| 233 | { |
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| 234 | printf("\n[FFT ERROR] cannot get hardware configuration\n"); |
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| 235 | exit( 0 ); |
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| 236 | } |
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| 237 | |
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| 238 | // check ncores |
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| 239 | if( (ncores != 1) && (ncores != 2) && (ncores != 4) ) |
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| 240 | { |
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| 241 | printf("\n[FFT ERROR] number of cores per cluster must be 1/2/4\n"); |
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| 242 | exit( 0 ); |
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| 243 | } |
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| 244 | |
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| 245 | // check x_size |
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| 246 | if( (x_size != 1) && (x_size != 2) && (x_size != 4) && (x_size != 8) && (x_size != 16) ) |
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| 247 | { |
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| 248 | printf("\n[FFT ERROR] x_size must be 1/2/4/8/16\n"); |
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| 249 | exit( 0 ); |
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| 250 | } |
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| 251 | |
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| 252 | // check y_size |
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| 253 | if( (y_size != 1) && (y_size != 2) && (y_size != 4) && (y_size != 8) && (y_size != 16) ) |
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| 254 | { |
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| 255 | printf("\n[FFT ERROR] y_size must be 1/2/4/8/16\n"); |
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| 256 | exit( 0 ); |
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| 257 | } |
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| 258 | |
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| 259 | nthreads = x_size * y_size * ncores; |
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| 260 | nclusters = x_size * y_size; |
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| 261 | |
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| 262 | // compute various constants depending on N and T |
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| 263 | N = 1 << M; |
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| 264 | rootN = 1 << (M / 2); |
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| 265 | rows_per_thread = rootN / nthreads; |
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| 266 | points_per_cluster = N / nclusters; |
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| 267 | |
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| 268 | // check N versus T |
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| 269 | if( rootN < nthreads ) |
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| 270 | { |
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| 271 | printf("\n[FFT ERROR] sqrt(N) must be larger than T\n"); |
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| 272 | exit( 0 ); |
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| 273 | } |
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| 274 | |
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| 275 | // get main thread coordinates (main_x, main_y, main_lid) |
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| 276 | get_core( &main_cxy , &main_lid ); |
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| 277 | main_x = HAL_X_FROM_CXY( main_cxy ); |
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| 278 | main_y = HAL_Y_FROM_CXY( main_cxy ); |
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| 279 | main_tid = (((main_x * y_size) + main_y) * ncores) + main_lid; |
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| 280 | |
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| 281 | printf("\n[FFT] main starts on core[%x,%d] / %d complex points / %d thread(s)\n", |
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| 282 | main_cxy, main_lid, N, nthreads ); |
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| 283 | |
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| 284 | // allocate memory for the distributed data[i], trans[i], umain[i], twid[i] buffers |
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| 285 | // the index (i) is a continuous cluster index |
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[473] | 286 | unsigned int data_size = (N / nclusters) * 2 * sizeof(double); |
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| 287 | unsigned int coefs_size = (rootN / nclusters) * 2 * sizeof(double); |
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[469] | 288 | for (x = 0 ; x < x_size ; x++) |
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| 289 | { |
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| 290 | for (y = 0 ; y < y_size ; y++) |
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| 291 | { |
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| 292 | ci = x * y_size + y; |
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| 293 | cxy = HAL_CXY_FROM_XY( x , y ); |
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| 294 | data[ci] = (double *)remote_malloc( data_size , cxy ); |
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| 295 | trans[ci] = (double *)remote_malloc( data_size , cxy ); |
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| 296 | bloup[ci] = (double *)remote_malloc( data_size , cxy ); |
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| 297 | umain[ci] = (double *)remote_malloc( coefs_size , cxy ); |
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| 298 | twid[ci] = (double *)remote_malloc( data_size , cxy ); |
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| 299 | } |
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| 300 | } |
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| 301 | |
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[574] | 302 | printf("\n[FFT] complete remote_malloc\n"); |
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| 303 | |
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[469] | 304 | // arrays initialisation |
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| 305 | InitX( data , MODE ); |
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| 306 | InitU( umain ); |
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| 307 | InitT( twid ); |
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| 308 | |
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[574] | 309 | printf("\n[FFT] complete init arrays\n"); |
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| 310 | |
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[469] | 311 | #if CHECK |
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[473] | 312 | ck1 = CheckSum(); |
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[469] | 313 | #endif |
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| 314 | |
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[574] | 315 | #if PRINT_ARRAY |
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[469] | 316 | printf("\nData values / base = %x\n", &data[0][0] ); |
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| 317 | PrintArray( data , N ); |
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| 318 | |
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| 319 | printf("\nTwiddle values / base = %x\n", &twid[0][0] ); |
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| 320 | PrintArray( twid , N ); |
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| 321 | |
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| 322 | SimpleDft( 1 , N , data , 0 , bloup , 0 ); |
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| 323 | |
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| 324 | printf("\nExpected results / base = %x\n", &bloup[0][0] ); |
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| 325 | PrintArray( bloup , N ); |
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| 326 | #endif |
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| 327 | |
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| 328 | // initialise distributed barrier |
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| 329 | barrierattr.x_size = x_size; |
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| 330 | barrierattr.y_size = y_size; |
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| 331 | barrierattr.nthreads = ncores; |
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[473] | 332 | if( pthread_barrier_init( &barrier, &barrierattr , nthreads) ) |
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| 333 | { |
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| 334 | printf("\n[FFT ERROR] cannot initialize barrier\n"); |
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| 335 | exit( 0 ); |
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| 336 | } |
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[469] | 337 | |
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[473] | 338 | printf("\n[FFT] main completes barrier init\n"); |
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| 339 | |
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[469] | 340 | // launch other threads to execute the slave() function |
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| 341 | // on cores other than the core running the main thread |
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| 342 | for (x = 0 ; x < x_size ; x++) |
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| 343 | { |
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| 344 | for (y = 0 ; y < y_size ; y++) |
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| 345 | { |
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| 346 | for ( lid = 0 ; lid < ncores ; lid++ ) |
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| 347 | { |
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| 348 | // compute thread continuous index |
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| 349 | tid = (((x * y_size) + y) * ncores) + lid; |
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| 350 | |
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| 351 | // set thread attributes |
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| 352 | attr[tid].attributes = PT_ATTR_CLUSTER_DEFINED | PT_ATTR_CORE_DEFINED; |
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| 353 | attr[tid].cxy = HAL_CXY_FROM_XY( x , y ); |
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| 354 | attr[tid].lid = lid; |
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| 355 | |
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| 356 | // set slave function argument |
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| 357 | args[tid] = tid; |
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| 358 | |
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| 359 | // create thread |
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| 360 | if( tid != main_tid ) |
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| 361 | { |
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| 362 | if ( pthread_create( &trdid[tid], // pointer on kernel identifier |
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| 363 | &attr[tid], // pointer on thread attributes |
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| 364 | &slave, // pointer on function |
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| 365 | &args[tid]) ) // pointer on function arguments |
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| 366 | { |
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| 367 | printf("\n[FFT ERROR] creating thread %x\n", trdid[tid] ); |
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| 368 | exit( 0 ); |
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| 369 | } |
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| 370 | #if DEBUG_MAIN |
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[473] | 371 | printf("\n[FFT] main created thread %x\n", trdid[tid] ); |
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[469] | 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 sequencial initalisation completion cycle |
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| 379 | get_cycle( &start_exec_cycle ); |
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| 380 | init_time = (long)(start_exec_cycle - start_init_cycle); |
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[574] | 381 | printf("\n[FFT] main enter parallel execution\n"); |
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[469] | 382 | |
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| 383 | // main execute itself the slave() function |
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| 384 | slave( &args[main_tid] ); |
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| 385 | |
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| 386 | // wait other threads completion |
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| 387 | for (x = 0 ; x < x_size ; x++) |
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| 388 | { |
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| 389 | for (y = 0 ; y < y_size ; y++) |
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| 390 | { |
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| 391 | for ( lid = 0 ; lid < ncores ; lid++ ) |
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| 392 | { |
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| 393 | // compute thread continuous index |
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[473] | 394 | tid = (((x * y_size) + y) * ncores) + lid; |
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[469] | 395 | |
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| 396 | if( tid != main_tid ) |
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| 397 | { |
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| 398 | #if DEBUG_MAIN |
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[574] | 399 | printf("\n[FFT] main join thread %x\n", trdid[tid] ); |
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[469] | 400 | #endif |
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| 401 | if( pthread_join( trdid[tid] , NULL ) ) |
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| 402 | { |
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| 403 | printf("\n[FFT ERROR] joining thread %x\n", trdid[tid] ); |
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| 404 | exit( 0 ); |
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| 405 | } |
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| 406 | |
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| 407 | } |
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| 408 | } |
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| 409 | } |
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| 410 | } |
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| 411 | |
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| 412 | // register parallel execution completion cycle |
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| 413 | get_cycle( &end_exec_cycle ); |
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| 414 | printf("\n[FFT] complete parallel execution / cycle %d\n", (long)end_exec_cycle ); |
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| 415 | |
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[574] | 416 | #if PRINT_ARRAY |
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[469] | 417 | printf("\nData values after FFT:\n"); |
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| 418 | PrintArray( data , N ); |
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| 419 | #endif |
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| 420 | |
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| 421 | #if CHECK |
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[473] | 422 | ck3 = CheckSum(); |
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[469] | 423 | printf("\n*** Results ***\n"); |
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| 424 | printf("Checksum difference is %f (%f, %f)\n", ck1 - ck3, ck1, ck3); |
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| 425 | if (fabs(ck1 - ck3) < 0.001) printf("Results OK\n"); |
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| 426 | else printf("Results KO\n"); |
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| 427 | #endif |
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| 428 | |
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| 429 | // instrumentation |
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| 430 | char string[256]; |
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| 431 | |
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| 432 | snprintf( string , 256 , "/home/fft_%d_%d_%d_%d", x_size , y_size , ncores , N ); |
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| 433 | |
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| 434 | // open instrumentation file |
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| 435 | FILE * f = fopen( string , NULL ); |
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| 436 | if ( f == NULL ) |
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| 437 | { |
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| 438 | printf("\n[FFT ERROR] cannot open instrumentation file %s\n", string ); |
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| 439 | exit( 0 ); |
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| 440 | } |
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| 441 | |
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| 442 | snprintf( string , 256 , "\n[FFT] instrumentation : (%dx%dx%d) threads / %d points\n", |
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| 443 | x_size, y_size, ncores , N ); |
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| 444 | |
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| 445 | // display on terminal, and save to instrumentation file |
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| 446 | printf( "%s" , string ); |
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| 447 | fprintf( f , string ); |
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| 448 | |
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| 449 | long min_para = parallel_time[0]; |
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| 450 | long max_para = parallel_time[0]; |
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| 451 | long min_sync = sync_time[0]; |
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| 452 | long max_sync = sync_time[0]; |
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| 453 | |
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| 454 | for (tid = 1 ; tid < nthreads ; tid++) |
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| 455 | { |
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| 456 | if (parallel_time[tid] > max_para) max_para = parallel_time[tid]; |
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| 457 | if (parallel_time[tid] < min_para) min_para = parallel_time[tid]; |
---|
| 458 | if (sync_time[tid] > max_sync) max_sync = sync_time[tid]; |
---|
| 459 | if (sync_time[tid] < min_sync) min_sync = sync_time[tid]; |
---|
| 460 | } |
---|
| 461 | |
---|
| 462 | snprintf( string , 256 , "\n Init Parallel Barrier\n" |
---|
| 463 | "MIN : %d | %d | %d (cycles)\n" |
---|
| 464 | "MAX : %d | %d | %d (cycles)\n", |
---|
| 465 | (int)init_time, (int)min_para, (int)min_sync, |
---|
| 466 | (int)init_time, (int)max_para, (int)max_sync ); |
---|
| 467 | |
---|
| 468 | // display on terminal, and save to instrumentation file |
---|
| 469 | printf("%s" , string ); |
---|
| 470 | fprintf( f , string ); |
---|
| 471 | |
---|
| 472 | // close instrumentation file and exit |
---|
| 473 | fclose( f ); |
---|
| 474 | |
---|
| 475 | exit( 0 ); |
---|
| 476 | |
---|
| 477 | } // end main() |
---|
| 478 | |
---|
| 479 | /////////////////////////////////////////////////////////////// |
---|
| 480 | // This function is executed in parallel by all threads. |
---|
| 481 | /////////////////////////////////////////////////////////////// |
---|
[473] | 482 | void slave( unsigned int * tid ) |
---|
[469] | 483 | { |
---|
[473] | 484 | unsigned int i; |
---|
| 485 | unsigned int MyNum; // continuous thread index |
---|
| 486 | unsigned int MyFirst; // index first row allocated to thread |
---|
| 487 | unsigned int MyLast; // index last row allocated to thread |
---|
| 488 | double * upriv; |
---|
| 489 | unsigned int c_id; |
---|
| 490 | unsigned int c_offset; |
---|
[469] | 491 | |
---|
| 492 | unsigned long long parallel_start; |
---|
| 493 | unsigned long long parallel_stop; |
---|
| 494 | unsigned long long barrier_start; |
---|
| 495 | unsigned long long barrier_stop; |
---|
| 496 | |
---|
| 497 | MyNum = *tid; |
---|
| 498 | |
---|
| 499 | // get |
---|
| 500 | // initialise instrumentation |
---|
| 501 | get_cycle( ¶llel_start ); |
---|
| 502 | |
---|
| 503 | // allocate and initialise local array upriv[] |
---|
| 504 | // that is a local copy of the rootN coefs defined in umain[] |
---|
| 505 | upriv = (double *)malloc(2 * (rootN - 1) * sizeof(double)); |
---|
| 506 | for ( i = 0 ; i < (rootN - 1) ; i++) |
---|
| 507 | { |
---|
| 508 | c_id = i / (rootN / nclusters); |
---|
| 509 | c_offset = i % (rootN / nclusters); |
---|
| 510 | upriv[2*i] = umain[c_id][2*c_offset]; |
---|
| 511 | upriv[2*i+1] = umain[c_id][2*c_offset+1]; |
---|
| 512 | } |
---|
| 513 | |
---|
| 514 | // compute first and last rows handled by the thread |
---|
| 515 | MyFirst = rootN * MyNum / nthreads; |
---|
| 516 | MyLast = rootN * (MyNum + 1) / nthreads; |
---|
| 517 | |
---|
| 518 | // perform forward FFT |
---|
| 519 | FFT1D( 1 , data , trans , upriv , twid , MyNum , MyFirst , MyLast ); |
---|
| 520 | |
---|
| 521 | // BARRIER |
---|
| 522 | get_cycle( &barrier_start ); |
---|
| 523 | pthread_barrier_wait( &barrier ); |
---|
| 524 | get_cycle( &barrier_stop ); |
---|
| 525 | |
---|
| 526 | sync_time[MyNum] = (long)(barrier_stop - barrier_start); |
---|
| 527 | |
---|
| 528 | #if CHECK |
---|
| 529 | get_cycle( &barrier_start ); |
---|
| 530 | pthread_barrier_wait( &barrier ); |
---|
| 531 | get_cycle( &barrier_stop ); |
---|
| 532 | |
---|
| 533 | sync_time[MyNum] += (long)(barrier_stop - barrier_start); |
---|
| 534 | |
---|
| 535 | FFT1D( -1 , data , trans , upriv , twid , MyNum , MyFirst , MyLast ); |
---|
| 536 | #endif |
---|
| 537 | |
---|
| 538 | // register computation time |
---|
| 539 | get_cycle( ¶llel_stop ); |
---|
| 540 | parallel_time[MyNum] = (long)(parallel_stop - parallel_start); |
---|
| 541 | |
---|
| 542 | // exit if MyNum != 0 |
---|
[574] | 543 | if( MyNum ) pthread_exit( 0 ); |
---|
[469] | 544 | |
---|
| 545 | } // end slave() |
---|
| 546 | |
---|
| 547 | //////////////////////////////////////////////////////////////////////////////////////// |
---|
| 548 | // This function makes the DFT from the src[nclusters][points_per_cluster] distributed |
---|
| 549 | // buffer, to the dst[nclusters][points_per_cluster] distributed buffer. |
---|
| 550 | //////////////////////////////////////////////////////////////////////////////////////// |
---|
[473] | 551 | void SimpleDft( int direction, // 1 direct / -1 reverse |
---|
| 552 | unsigned int size, // number of points |
---|
| 553 | double ** src, // source distributed buffer |
---|
| 554 | unsigned int src_offset, // offset in source array |
---|
| 555 | double ** dst, // destination distributed buffer |
---|
| 556 | unsigned int dst_offset ) // offset in destination array |
---|
[469] | 557 | { |
---|
[473] | 558 | unsigned int n , k; |
---|
| 559 | double phi; // 2*PI*n*k/N |
---|
| 560 | double u_r; // cos( phi ) |
---|
| 561 | double u_c; // sin( phi ) |
---|
| 562 | double d_r; // Re(data[n]) |
---|
| 563 | double d_c; // Im(data[n]) |
---|
| 564 | double accu_r; // Re(accu) |
---|
| 565 | double accu_c; // Im(accu) |
---|
| 566 | unsigned int c_id; // distributed buffer cluster index |
---|
| 567 | unsigned int c_offset; // offset in distributed buffer |
---|
[469] | 568 | |
---|
| 569 | for ( k = 0 ; k < size ; k++ ) // loop on the output data points |
---|
| 570 | { |
---|
| 571 | // initialise accu |
---|
| 572 | accu_r = 0; |
---|
| 573 | accu_c = 0; |
---|
| 574 | |
---|
| 575 | for ( n = 0 ; n < size ; n++ ) // loop on the input data points |
---|
| 576 | { |
---|
| 577 | // compute coef |
---|
| 578 | phi = (double)(2*PI*n*k) / size; |
---|
| 579 | u_r = cos( phi ); |
---|
| 580 | u_c = -sin( phi ) * direction; |
---|
| 581 | |
---|
| 582 | // get input data point |
---|
| 583 | c_id = (src_offset + n) / (points_per_cluster); |
---|
| 584 | c_offset = (src_offset + n) % (points_per_cluster); |
---|
[473] | 585 | d_r = src[c_id][2*c_offset]; |
---|
| 586 | d_c = src[c_id][2*c_offset+1]; |
---|
[469] | 587 | |
---|
| 588 | // increment accu |
---|
| 589 | accu_r += ((u_r*d_r) - (u_c*d_c)); |
---|
| 590 | accu_c += ((u_r*d_c) + (u_c*d_r)); |
---|
| 591 | } |
---|
| 592 | |
---|
| 593 | // scale for inverse DFT |
---|
| 594 | if ( direction == -1 ) |
---|
| 595 | { |
---|
| 596 | accu_r /= size; |
---|
| 597 | accu_c /= size; |
---|
| 598 | } |
---|
| 599 | |
---|
| 600 | // set output data point |
---|
| 601 | c_id = (dst_offset + k) / (points_per_cluster); |
---|
| 602 | c_offset = (dst_offset + k) % (points_per_cluster); |
---|
| 603 | dst[c_id][2*c_offset] = accu_r; |
---|
| 604 | dst[c_id][2*c_offset+1] = accu_c; |
---|
| 605 | } |
---|
| 606 | |
---|
| 607 | } // end SimpleDft() |
---|
| 608 | |
---|
[473] | 609 | ///////////////// |
---|
[503] | 610 | double CheckSum( void ) |
---|
[469] | 611 | { |
---|
[473] | 612 | unsigned int i , j; |
---|
[469] | 613 | double cks; |
---|
[473] | 614 | unsigned int c_id; |
---|
| 615 | unsigned int c_offset; |
---|
[469] | 616 | |
---|
| 617 | cks = 0.0; |
---|
| 618 | for (j = 0; j < rootN ; j++) |
---|
| 619 | { |
---|
| 620 | for (i = 0; i < rootN ; i++) |
---|
| 621 | { |
---|
| 622 | c_id = (rootN * j + i) / (points_per_cluster); |
---|
| 623 | c_offset = (rootN * j + i) % (points_per_cluster); |
---|
| 624 | |
---|
| 625 | cks += data[c_id][2*c_offset] + data[c_id][2*c_offset+1]; |
---|
| 626 | } |
---|
| 627 | } |
---|
| 628 | return(cks); |
---|
| 629 | } |
---|
| 630 | |
---|
| 631 | |
---|
| 632 | //////////////////////////// |
---|
| 633 | void InitX(double ** x, |
---|
| 634 | unsigned int mode ) |
---|
| 635 | { |
---|
[473] | 636 | unsigned int i , j; |
---|
| 637 | unsigned int c_id; |
---|
| 638 | unsigned int c_offset; |
---|
| 639 | unsigned int index; |
---|
[469] | 640 | |
---|
| 641 | for ( j = 0 ; j < rootN ; j++ ) // loop on row index |
---|
| 642 | { |
---|
| 643 | for ( i = 0 ; i < rootN ; i++ ) // loop on point in a row |
---|
| 644 | { |
---|
| 645 | index = j * rootN + i; |
---|
| 646 | c_id = index / (points_per_cluster); |
---|
| 647 | c_offset = index % (points_per_cluster); |
---|
| 648 | |
---|
| 649 | // complex input signal is random |
---|
| 650 | if ( mode == RANDOM ) |
---|
| 651 | { |
---|
[473] | 652 | x[c_id][2*c_offset] = ( (double)rand() ) / 65536; |
---|
| 653 | x[c_id][2*c_offset+1] = ( (double)rand() ) / 65536; |
---|
[469] | 654 | } |
---|
| 655 | |
---|
| 656 | |
---|
| 657 | // complex input signal is cos(n/N) / sin(n/N) |
---|
| 658 | if ( mode == COSIN ) |
---|
| 659 | { |
---|
| 660 | double phi = (double)( 2 * PI * index) / N; |
---|
[473] | 661 | x[c_id][2*c_offset] = cos( phi ); |
---|
| 662 | x[c_id][2*c_offset+1] = sin( phi ); |
---|
[469] | 663 | } |
---|
| 664 | |
---|
| 665 | // complex input signal is constant |
---|
| 666 | if ( mode == CONSTANT ) |
---|
| 667 | { |
---|
[473] | 668 | x[c_id][2*c_offset] = 1.0; |
---|
| 669 | x[c_id][2*c_offset+1] = 0.0; |
---|
[469] | 670 | } |
---|
| 671 | } |
---|
| 672 | } |
---|
| 673 | } |
---|
| 674 | |
---|
| 675 | ///////////////////////// |
---|
| 676 | void InitU( double ** u ) |
---|
| 677 | { |
---|
[473] | 678 | unsigned int q; |
---|
| 679 | unsigned int j; |
---|
| 680 | unsigned int base; |
---|
| 681 | unsigned int n1; |
---|
| 682 | unsigned int c_id; |
---|
| 683 | unsigned int c_offset; |
---|
[469] | 684 | double phi; |
---|
[473] | 685 | unsigned int stop = 0; |
---|
[469] | 686 | |
---|
[473] | 687 | for (q = 0 ; ((unsigned int)(1 << q) < N) && (stop == 0) ; q++) |
---|
[469] | 688 | { |
---|
| 689 | n1 = 1 << q; |
---|
| 690 | base = n1 - 1; |
---|
| 691 | for (j = 0; (j < n1) && (stop == 0) ; j++) |
---|
| 692 | { |
---|
| 693 | if (base + j > rootN - 1) return; |
---|
| 694 | |
---|
| 695 | c_id = (base + j) / (rootN / nclusters); |
---|
| 696 | c_offset = (base + j) % (rootN / nclusters); |
---|
| 697 | phi = (double)(2.0 * PI * j) / (2 * n1); |
---|
| 698 | u[c_id][2*c_offset] = cos( phi ); |
---|
| 699 | u[c_id][2*c_offset+1] = -sin( phi ); |
---|
| 700 | } |
---|
| 701 | } |
---|
| 702 | } |
---|
| 703 | |
---|
| 704 | ////////////////////////// |
---|
| 705 | void InitT( double ** u ) |
---|
| 706 | { |
---|
[473] | 707 | unsigned int i, j; |
---|
| 708 | unsigned int index; |
---|
| 709 | unsigned int c_id; |
---|
| 710 | unsigned int c_offset; |
---|
[469] | 711 | double phi; |
---|
| 712 | |
---|
| 713 | for ( j = 0 ; j < rootN ; j++ ) // loop on row index |
---|
| 714 | { |
---|
| 715 | for ( i = 0 ; i < rootN ; i++ ) // loop on points in a row |
---|
| 716 | { |
---|
| 717 | index = j * rootN + i; |
---|
| 718 | c_id = index / (points_per_cluster); |
---|
| 719 | c_offset = index % (points_per_cluster); |
---|
| 720 | |
---|
| 721 | phi = (double)(2.0 * PI * i * j) / N; |
---|
| 722 | u[c_id][2*c_offset] = cos( phi ); |
---|
| 723 | u[c_id][2*c_offset+1] = -sin( phi ); |
---|
| 724 | } |
---|
| 725 | } |
---|
| 726 | } |
---|
| 727 | |
---|
| 728 | //////////////////////////////////////////////////////////////////////////////////////// |
---|
| 729 | // This function returns an index value that is the bit reverse of the input value. |
---|
| 730 | //////////////////////////////////////////////////////////////////////////////////////// |
---|
[473] | 731 | unsigned int BitReverse( unsigned int k ) |
---|
[469] | 732 | { |
---|
[473] | 733 | unsigned int i; |
---|
| 734 | unsigned int j; |
---|
| 735 | unsigned int tmp; |
---|
[469] | 736 | |
---|
| 737 | j = 0; |
---|
| 738 | tmp = k; |
---|
| 739 | for (i = 0; i < M/2 ; i++) |
---|
| 740 | { |
---|
| 741 | j = 2 * j + (tmp & 0x1); |
---|
| 742 | tmp = tmp >> 1; |
---|
| 743 | } |
---|
| 744 | return j; |
---|
| 745 | } |
---|
| 746 | |
---|
| 747 | //////////////////////////////////////////////////////////////////////////////////////// |
---|
| 748 | // This function perform the in place (direct or inverse) FFT on the N data points |
---|
| 749 | // contained in the distributed buffers x[nclusters][points_per_cluster]. |
---|
| 750 | // It handles the (N) points 1D array as a (rootN*rootN) points 2D array. |
---|
| 751 | // 1) it transpose (rootN/nthreads ) rows from x to tmp. |
---|
| 752 | // 2) it make (rootN/nthreads) FFT on the tmp rows and apply the twiddle factor. |
---|
| 753 | // 3) it transpose (rootN/nthreads) columns from tmp to x. |
---|
| 754 | // 4) it make (rootN/nthreads) FFT on the x rows. |
---|
[574] | 755 | // It calls the FFTRow() 2*(rootN/nthreads) times to perform the in place FFT |
---|
[469] | 756 | // on the rootN points contained in a row. |
---|
| 757 | //////////////////////////////////////////////////////////////////////////////////////// |
---|
[473] | 758 | void FFT1D( int direction, // direct 1 / inverse -1 |
---|
| 759 | double ** x, // input & output distributed data points array |
---|
| 760 | double ** tmp, // auxiliary distributed data points array |
---|
| 761 | double * upriv, // local array containing coefs for rootN FFT |
---|
| 762 | double ** twid, // distributed arrays containing N twiddle factors |
---|
| 763 | unsigned int MyNum, // thread continuous index |
---|
| 764 | unsigned int MyFirst, |
---|
| 765 | unsigned int MyLast ) |
---|
[469] | 766 | { |
---|
[473] | 767 | unsigned int j; |
---|
[469] | 768 | unsigned long long barrier_start; |
---|
| 769 | unsigned long long barrier_stop; |
---|
| 770 | |
---|
[574] | 771 | #if DEBUG_FFT1D |
---|
| 772 | printf("\n[FFT] %s : thread %x enter / first %d / last %d\n", |
---|
| 773 | __FUNCTION__, MyNum, MyFirst, MyLast ); |
---|
| 774 | #endif |
---|
| 775 | |
---|
[469] | 776 | // transpose (rootN/nthreads) rows from x to tmp |
---|
| 777 | Transpose( x , tmp , MyFirst , MyLast ); |
---|
| 778 | |
---|
[574] | 779 | #if( DEBUG_FFT1D & 1 ) |
---|
| 780 | unsigned long long cycle; |
---|
| 781 | get_cycle( &cycle ); |
---|
| 782 | printf("\n[FFT] %s : thread %x after first transpose / cycle %d\n", |
---|
| 783 | __FUNCTION__, MyNum, (unsigned int)cycle ); |
---|
| 784 | if( PRINT_ARRAY ) PrintArray( tmp , N ); |
---|
[469] | 785 | #endif |
---|
| 786 | |
---|
| 787 | // BARRIER |
---|
| 788 | get_cycle( &barrier_start ); |
---|
| 789 | pthread_barrier_wait( &barrier ); |
---|
| 790 | get_cycle( &barrier_stop ); |
---|
| 791 | sync_time[MyNum] = (long)(barrier_stop - barrier_start); |
---|
| 792 | |
---|
[574] | 793 | #if( DEBUG_FFT1D & 1 ) |
---|
| 794 | get_cycle( &cycle ); |
---|
| 795 | printf("\n[FFT] %s : thread %x exit barrier after first transpose / cycle %d\n", |
---|
| 796 | __FUNCTION__, MyNum, (unsigned int)cycle ); |
---|
| 797 | #endif |
---|
| 798 | |
---|
[469] | 799 | // do FFTs on rows of tmp (i.e. columns of x) and apply twiddle factor |
---|
| 800 | for (j = MyFirst; j < MyLast; j++) |
---|
| 801 | { |
---|
[574] | 802 | FFTRow( direction , upriv , tmp , j * rootN ); |
---|
| 803 | |
---|
[469] | 804 | TwiddleOneCol( direction , j , twid , tmp , j * rootN ); |
---|
| 805 | } |
---|
| 806 | |
---|
[574] | 807 | #if( DEBUG_FFT1D & 1 ) |
---|
[473] | 808 | printf("\n[FFT] %s : thread %x after first twiddle\n", __FUNCTION__, MyNum); |
---|
[574] | 809 | if( PRINT_ARRAY ) PrintArray( tmp , N ); |
---|
[469] | 810 | #endif |
---|
| 811 | |
---|
| 812 | // BARRIER |
---|
| 813 | get_cycle( &barrier_start ); |
---|
| 814 | pthread_barrier_wait( &barrier ); |
---|
| 815 | get_cycle( &barrier_stop ); |
---|
| 816 | |
---|
[574] | 817 | #if( DEBUG_FFT1D & 1 ) |
---|
| 818 | printf("\n[FFT] %s : thread %x exit barrier after first twiddle\n", __FUNCTION__, MyNum); |
---|
| 819 | #endif |
---|
| 820 | |
---|
[469] | 821 | sync_time[MyNum] += (long)(barrier_stop - barrier_start); |
---|
| 822 | |
---|
| 823 | // transpose tmp to x |
---|
| 824 | Transpose( tmp , x , MyFirst , MyLast ); |
---|
| 825 | |
---|
[574] | 826 | #if( DEBUG_FFT1D & 1 ) |
---|
[473] | 827 | printf("\n[FFT] %s : thread %x after second transpose\n", __FUNCTION__, MyNum); |
---|
[574] | 828 | if( PRINT_ARRAY ) PrintArray( x , N ); |
---|
[469] | 829 | #endif |
---|
| 830 | |
---|
| 831 | // BARRIER |
---|
| 832 | get_cycle( &barrier_start ); |
---|
| 833 | pthread_barrier_wait( &barrier ); |
---|
| 834 | get_cycle( &barrier_stop ); |
---|
| 835 | |
---|
[574] | 836 | #if( DEBUG_FFT1D & 1 ) |
---|
| 837 | printf("\n[FFT] %s : thread %x exit barrier after second transpose\n", __FUNCTION__, MyNum); |
---|
| 838 | #endif |
---|
| 839 | |
---|
[469] | 840 | sync_time[MyNum] += (long)(barrier_stop - barrier_start); |
---|
| 841 | |
---|
| 842 | // do FFTs on rows of x and apply the scaling factor |
---|
| 843 | for (j = MyFirst; j < MyLast; j++) |
---|
| 844 | { |
---|
[574] | 845 | FFTRow( direction , upriv , x , j * rootN ); |
---|
[469] | 846 | if (direction == -1) Scale( x , j * rootN ); |
---|
| 847 | } |
---|
| 848 | |
---|
[574] | 849 | #if( DEBUG_FFT1D & 1 ) |
---|
[473] | 850 | printf("\n[FFT] %s : thread %x after FFT on rows\n", __FUNCTION__, MyNum); |
---|
[574] | 851 | if( PRINT_ARRAY ) PrintArray( x , N ); |
---|
[469] | 852 | #endif |
---|
| 853 | |
---|
| 854 | // BARRIER |
---|
| 855 | get_cycle( &barrier_start ); |
---|
| 856 | pthread_barrier_wait( &barrier ); |
---|
| 857 | get_cycle( &barrier_stop ); |
---|
| 858 | |
---|
[574] | 859 | #if( DEBUG_FFT1D & 1 ) |
---|
| 860 | printf("\n[FFT] %s : thread %x exit barrier after FFT on rows\n", __FUNCTION__, MyNum); |
---|
| 861 | #endif |
---|
[469] | 862 | sync_time[MyNum] += (long)(barrier_stop - barrier_start); |
---|
| 863 | |
---|
| 864 | // transpose x to tmp |
---|
| 865 | Transpose( x , tmp , MyFirst , MyLast ); |
---|
| 866 | |
---|
[574] | 867 | #if( DEBUG_FFT1D & 1 ) |
---|
[473] | 868 | printf("\n[FFT] %s : thread %x after third transpose\n", __FUNCTION__, MyNum); |
---|
[574] | 869 | if( PRINT_ARRAY ) PrintArray( x , N ); |
---|
[469] | 870 | #endif |
---|
| 871 | |
---|
| 872 | // BARRIER |
---|
| 873 | get_cycle( &barrier_start ); |
---|
| 874 | pthread_barrier_wait( &barrier ); |
---|
| 875 | get_cycle( &barrier_stop ); |
---|
| 876 | |
---|
[574] | 877 | #if( DEBUG_FFT1D & 1 ) |
---|
| 878 | printf("\n[FFT] %s : thread %x exit barrier after third transpose\n", __FUNCTION__, MyNum); |
---|
| 879 | #endif |
---|
| 880 | |
---|
[469] | 881 | sync_time[MyNum] += (long)(barrier_stop - barrier_start); |
---|
[574] | 882 | sync_time[MyNum] += (long)(barrier_stop - barrier_start); |
---|
[469] | 883 | |
---|
| 884 | // copy tmp to x |
---|
| 885 | Copy( tmp , x , MyFirst , MyLast ); |
---|
| 886 | |
---|
| 887 | #if DEBUG_FFT1D |
---|
[574] | 888 | printf("\n[FFT] %s : thread %x completed\n", __FUNCTION__, MyNum); |
---|
| 889 | if( PRINT_ARRAY ) PrintArray( x , N ); |
---|
[469] | 890 | #endif |
---|
| 891 | |
---|
| 892 | |
---|
| 893 | } // end FFT1D() |
---|
| 894 | |
---|
| 895 | ///////////////////////////////////////////////////////////////////////////////////// |
---|
| 896 | // This function multiply all points contained in a row (rootN points) of the |
---|
| 897 | // x[] array by the corresponding twiddle factor, contained in the u[] array. |
---|
| 898 | ///////////////////////////////////////////////////////////////////////////////////// |
---|
[473] | 899 | void TwiddleOneCol( int direction, |
---|
| 900 | unsigned int j, // y coordinate in 2D view of coef array |
---|
| 901 | double ** u, // coef array base address |
---|
| 902 | double ** x, // data array base address |
---|
| 903 | unsigned int offset_x ) // first point in N points data array |
---|
[469] | 904 | { |
---|
[473] | 905 | unsigned int i; |
---|
[469] | 906 | double omega_r; |
---|
| 907 | double omega_c; |
---|
| 908 | double x_r; |
---|
| 909 | double x_c; |
---|
[473] | 910 | unsigned int c_id; |
---|
| 911 | unsigned int c_offset; |
---|
[469] | 912 | |
---|
| 913 | for (i = 0; i < rootN ; i++) // loop on the rootN points |
---|
| 914 | { |
---|
| 915 | // get coef |
---|
| 916 | c_id = (j * rootN + i) / (points_per_cluster); |
---|
| 917 | c_offset = (j * rootN + i) % (points_per_cluster); |
---|
| 918 | omega_r = u[c_id][2*c_offset]; |
---|
| 919 | omega_c = direction * u[c_id][2*c_offset+1]; |
---|
| 920 | |
---|
| 921 | // access data |
---|
| 922 | c_id = (offset_x + i) / (points_per_cluster); |
---|
| 923 | c_offset = (offset_x + i) % (points_per_cluster); |
---|
| 924 | x_r = x[c_id][2*c_offset]; |
---|
| 925 | x_c = x[c_id][2*c_offset+1]; |
---|
| 926 | |
---|
| 927 | x[c_id][2*c_offset] = omega_r*x_r - omega_c * x_c; |
---|
| 928 | x[c_id][2*c_offset+1] = omega_r*x_c + omega_c * x_r; |
---|
| 929 | } |
---|
| 930 | } // end TwiddleOneCol() |
---|
| 931 | |
---|
[473] | 932 | //////////////////////////// |
---|
| 933 | void Scale( double ** x, // data array base address |
---|
| 934 | unsigned int offset_x ) // first point of the row to be scaled |
---|
[469] | 935 | { |
---|
[473] | 936 | unsigned int i; |
---|
| 937 | unsigned int c_id; |
---|
| 938 | unsigned int c_offset; |
---|
[469] | 939 | |
---|
| 940 | for (i = 0; i < rootN ; i++) |
---|
| 941 | { |
---|
| 942 | c_id = (offset_x + i) / (points_per_cluster); |
---|
| 943 | c_offset = (offset_x + i) % (points_per_cluster); |
---|
[473] | 944 | x[c_id][2*c_offset] /= N; |
---|
| 945 | x[c_id][2*c_offset + 1] /= N; |
---|
[469] | 946 | } |
---|
| 947 | } |
---|
| 948 | |
---|
[473] | 949 | /////////////////////////////////// |
---|
| 950 | void Transpose( double ** src, // source buffer (array of pointers) |
---|
| 951 | double ** dest, // destination buffer (array of pointers) |
---|
| 952 | unsigned int MyFirst, // first row allocated to the thread |
---|
| 953 | unsigned int MyLast ) // last row allocated to the thread |
---|
[469] | 954 | { |
---|
[473] | 955 | unsigned int row; // row index |
---|
| 956 | unsigned int point; // data point index in a row |
---|
[469] | 957 | |
---|
[473] | 958 | unsigned int index_src; // absolute index in the source N points array |
---|
| 959 | unsigned int c_id_src; // cluster for the source buffer |
---|
| 960 | unsigned int c_offset_src; // offset in the source buffer |
---|
[469] | 961 | |
---|
[473] | 962 | unsigned int index_dst; // absolute index in the dest N points array |
---|
| 963 | unsigned int c_id_dst; // cluster for the dest buffer |
---|
| 964 | unsigned int c_offset_dst; // offset in the dest buffer |
---|
[469] | 965 | |
---|
| 966 | |
---|
| 967 | // scan all data points allocated to the thread |
---|
| 968 | // (between MyFirst row and MyLast row) from the source buffer |
---|
| 969 | // and write these points to the destination buffer |
---|
| 970 | for ( row = MyFirst ; row < MyLast ; row++ ) // loop on the rows |
---|
| 971 | { |
---|
| 972 | for ( point = 0 ; point < rootN ; point++ ) // loop on points in row |
---|
| 973 | { |
---|
| 974 | index_src = row * rootN + point; |
---|
| 975 | c_id_src = index_src / (points_per_cluster); |
---|
| 976 | c_offset_src = index_src % (points_per_cluster); |
---|
| 977 | |
---|
| 978 | index_dst = point * rootN + row; |
---|
| 979 | c_id_dst = index_dst / (points_per_cluster); |
---|
| 980 | c_offset_dst = index_dst % (points_per_cluster); |
---|
| 981 | |
---|
| 982 | dest[c_id_dst][2*c_offset_dst] = src[c_id_src][2*c_offset_src]; |
---|
| 983 | dest[c_id_dst][2*c_offset_dst+1] = src[c_id_src][2*c_offset_src+1]; |
---|
| 984 | } |
---|
| 985 | } |
---|
| 986 | } // end Transpose() |
---|
| 987 | |
---|
[473] | 988 | ////////////////////////////// |
---|
| 989 | void Copy( double ** src, // source buffer (array of pointers) |
---|
| 990 | double ** dest, // destination buffer (array of pointers) |
---|
| 991 | unsigned int MyFirst, // first row allocated to the thread |
---|
| 992 | unsigned int MyLast ) // last row allocated to the thread |
---|
[469] | 993 | { |
---|
[473] | 994 | unsigned int row; // row index |
---|
| 995 | unsigned int point; // data point index in a row |
---|
[469] | 996 | |
---|
[473] | 997 | unsigned int index; // absolute index in the N points array |
---|
| 998 | unsigned int c_id; // cluster index |
---|
| 999 | unsigned int c_offset; // offset in local buffer |
---|
[469] | 1000 | |
---|
| 1001 | // scan all data points allocated to the thread |
---|
| 1002 | for ( row = MyFirst ; row < MyLast ; row++ ) // loop on the rows |
---|
| 1003 | { |
---|
| 1004 | for ( point = 0 ; point < rootN ; point++ ) // loop on points in row |
---|
| 1005 | { |
---|
| 1006 | index = row * rootN + point; |
---|
| 1007 | c_id = index / (points_per_cluster); |
---|
| 1008 | c_offset = index % (points_per_cluster); |
---|
| 1009 | |
---|
| 1010 | dest[c_id][2*c_offset] = src[c_id][2*c_offset]; |
---|
| 1011 | dest[c_id][2*c_offset+1] = src[c_id][2*c_offset+1]; |
---|
| 1012 | } |
---|
| 1013 | } |
---|
| 1014 | } // end Copy() |
---|
| 1015 | |
---|
[473] | 1016 | /////////////////////////////// |
---|
| 1017 | void Reverse( double ** x, |
---|
| 1018 | unsigned int offset_x ) |
---|
[469] | 1019 | { |
---|
[473] | 1020 | unsigned int j, k; |
---|
| 1021 | unsigned int c_id_j; |
---|
| 1022 | unsigned int c_offset_j; |
---|
| 1023 | unsigned int c_id_k; |
---|
| 1024 | unsigned int c_offset_k; |
---|
[469] | 1025 | |
---|
| 1026 | for (k = 0 ; k < rootN ; k++) |
---|
| 1027 | { |
---|
| 1028 | j = BitReverse( k ); |
---|
| 1029 | if (j > k) |
---|
| 1030 | { |
---|
| 1031 | c_id_j = (offset_x + j) / (points_per_cluster); |
---|
| 1032 | c_offset_j = (offset_x + j) % (points_per_cluster); |
---|
| 1033 | c_id_k = (offset_x + k) / (points_per_cluster); |
---|
| 1034 | c_offset_k = (offset_x + k) % (points_per_cluster); |
---|
| 1035 | |
---|
| 1036 | SWAP(x[c_id_j][2*c_offset_j] , x[c_id_k][2*c_offset_k]); |
---|
| 1037 | SWAP(x[c_id_j][2*c_offset_j+1], x[c_id_k][2*c_offset_k+1]); |
---|
| 1038 | } |
---|
| 1039 | } |
---|
| 1040 | } |
---|
| 1041 | |
---|
| 1042 | ///////////////////////////////////////////////////////////////////////////// |
---|
| 1043 | // This function makes the in-place FFT on all points contained in a row |
---|
| 1044 | // (i.e. rootN points) of the x[nclusters][points_per_cluster] array. |
---|
| 1045 | ///////////////////////////////////////////////////////////////////////////// |
---|
[574] | 1046 | void FFTRow( int direction, // 1 direct / -1 inverse |
---|
[473] | 1047 | double * u, // private coefs array |
---|
| 1048 | double ** x, // array of pointers on distributed buffers |
---|
| 1049 | unsigned int offset_x ) // absolute offset in the x array |
---|
[469] | 1050 | { |
---|
[473] | 1051 | unsigned int j; |
---|
| 1052 | unsigned int k; |
---|
| 1053 | unsigned int q; |
---|
| 1054 | unsigned int L; |
---|
| 1055 | unsigned int r; |
---|
| 1056 | unsigned int Lstar; |
---|
[469] | 1057 | double * u1; |
---|
| 1058 | |
---|
[473] | 1059 | unsigned int offset_x1; // index first butterfly input |
---|
| 1060 | unsigned int offset_x2; // index second butterfly output |
---|
[469] | 1061 | |
---|
[473] | 1062 | double omega_r; // real part butterfy coef |
---|
| 1063 | double omega_c; // complex part butterfly coef |
---|
[469] | 1064 | |
---|
[473] | 1065 | double tau_r; |
---|
| 1066 | double tau_c; |
---|
[469] | 1067 | |
---|
[473] | 1068 | double d1_r; // real part first butterfly input |
---|
| 1069 | double d1_c; // imag part first butterfly input |
---|
| 1070 | double d2_r; // real part second butterfly input |
---|
| 1071 | double d2_c; // imag part second butterfly input |
---|
[469] | 1072 | |
---|
[473] | 1073 | unsigned int c_id_1; // cluster index for first butterfly input |
---|
| 1074 | unsigned int c_offset_1; // offset for first butterfly input |
---|
| 1075 | unsigned int c_id_2; // cluster index for second butterfly input |
---|
| 1076 | unsigned int c_offset_2; // offset for second butterfly input |
---|
[469] | 1077 | |
---|
[574] | 1078 | #if DEBUG_ROW |
---|
[469] | 1079 | unsigned int p; |
---|
[574] | 1080 | printf("\n[FFT] ROW data in / %d points / offset = %d\n", rootN , offset_x ); |
---|
| 1081 | |
---|
[469] | 1082 | for ( p = 0 ; p < rootN ; p++ ) |
---|
| 1083 | { |
---|
[473] | 1084 | unsigned int index = offset_x + p; |
---|
| 1085 | unsigned int c_id = index / (points_per_cluster); |
---|
| 1086 | unsigned int c_offset = index % (points_per_cluster); |
---|
[469] | 1087 | printf("%f , %f | ", x[c_id][2*c_offset] , x[c_id][2*c_offset+1] ); |
---|
| 1088 | } |
---|
| 1089 | printf("\n"); |
---|
| 1090 | #endif |
---|
| 1091 | |
---|
| 1092 | // This makes the rootN input points reordering |
---|
| 1093 | Reverse( x , offset_x ); |
---|
| 1094 | |
---|
[574] | 1095 | #if DEBUG_ROW |
---|
| 1096 | printf("\n[FFT] ROW data after reverse / %d points / offset = %d\n", rootN , offset_x ); |
---|
| 1097 | |
---|
[469] | 1098 | for ( p = 0 ; p < rootN ; p++ ) |
---|
| 1099 | { |
---|
[473] | 1100 | unsigned int index = offset_x + p; |
---|
| 1101 | unsigned int c_id = index / (points_per_cluster); |
---|
| 1102 | unsigned int c_offset = index % (points_per_cluster); |
---|
[469] | 1103 | printf("%f , %f | ", x[c_id][2*c_offset] , x[c_id][2*c_offset+1] ); |
---|
| 1104 | } |
---|
| 1105 | printf("\n"); |
---|
| 1106 | #endif |
---|
| 1107 | |
---|
| 1108 | // This implements the multi-stages, in place Butterfly network |
---|
| 1109 | for (q = 1; q <= M/2 ; q++) // loop on stages |
---|
| 1110 | { |
---|
| 1111 | L = 1 << q; // number of points per subset for current stage |
---|
| 1112 | r = rootN / L; // number of subsets |
---|
| 1113 | Lstar = L / 2; |
---|
| 1114 | u1 = &u[2 * (Lstar - 1)]; |
---|
| 1115 | for (k = 0; k < r; k++) // loop on the subsets |
---|
| 1116 | { |
---|
| 1117 | offset_x1 = offset_x + (k * L); // index first point |
---|
| 1118 | offset_x2 = offset_x + (k * L + Lstar); // index second point |
---|
| 1119 | |
---|
[574] | 1120 | #if (DEBUG_ROW & 1) |
---|
| 1121 | printf("\n ### q = %d / k = %d / x1 = %d / x2 = %d\n", q , k , offset_x1 , offset_x2 ); |
---|
[469] | 1122 | #endif |
---|
| 1123 | // makes all in-place butterfly(s) for subset |
---|
| 1124 | for (j = 0; j < Lstar; j++) |
---|
| 1125 | { |
---|
| 1126 | // get coef |
---|
| 1127 | omega_r = u1[2*j]; |
---|
| 1128 | omega_c = direction * u1[2*j+1]; |
---|
| 1129 | |
---|
| 1130 | // get d[x1] address and value |
---|
| 1131 | c_id_1 = (offset_x1 + j) / (points_per_cluster); |
---|
| 1132 | c_offset_1 = (offset_x1 + j) % (points_per_cluster); |
---|
| 1133 | d1_r = x[c_id_1][2*c_offset_1]; |
---|
| 1134 | d1_c = x[c_id_1][2*c_offset_1+1]; |
---|
| 1135 | |
---|
| 1136 | // get d[x2] address and value |
---|
| 1137 | c_id_2 = (offset_x2 + j) / (points_per_cluster); |
---|
| 1138 | c_offset_2 = (offset_x2 + j) % (points_per_cluster); |
---|
| 1139 | d2_r = x[c_id_2][2*c_offset_2]; |
---|
| 1140 | d2_c = x[c_id_2][2*c_offset_2+1]; |
---|
| 1141 | |
---|
[574] | 1142 | #if (DEBUG_ROW & 1) |
---|
[469] | 1143 | printf("\n ### d1_in = (%f , %f) / d2_in = (%f , %f) / coef = (%f , %f)\n", |
---|
| 1144 | d1_r , d1_c , d2_r , d2_c , omega_r , omega_c); |
---|
| 1145 | #endif |
---|
| 1146 | // tau = omega * d[x2] |
---|
| 1147 | tau_r = omega_r * d2_r - omega_c * d2_c; |
---|
| 1148 | tau_c = omega_r * d2_c + omega_c * d2_r; |
---|
| 1149 | |
---|
| 1150 | // set new value for d[x1] = d[x1] + omega * d[x2] |
---|
| 1151 | x[c_id_1][2*c_offset_1] = d1_r + tau_r; |
---|
| 1152 | x[c_id_1][2*c_offset_1+1] = d1_c + tau_c; |
---|
| 1153 | |
---|
| 1154 | // set new value for d[x2] = d[x1] - omega * d[x2] |
---|
| 1155 | x[c_id_2][2*c_offset_2] = d1_r - tau_r; |
---|
| 1156 | x[c_id_2][2*c_offset_2+1] = d1_c - tau_c; |
---|
| 1157 | |
---|
[574] | 1158 | #if (DEBUG_ROW & 1) |
---|
[469] | 1159 | printf("\n ### d1_out = (%f , %f) / d2_out = (%f , %f)\n", |
---|
| 1160 | d1_r + tau_r , d1_c + tau_c , d2_r - tau_r , d2_c - tau_c ); |
---|
| 1161 | #endif |
---|
| 1162 | } |
---|
| 1163 | } |
---|
| 1164 | } |
---|
| 1165 | |
---|
[574] | 1166 | #if DEBUG_ROW |
---|
| 1167 | printf("\n[FFT] ROW data out / %d points / offset = %d\n", rootN , offset_x ); |
---|
[469] | 1168 | for ( p = 0 ; p < rootN ; p++ ) |
---|
| 1169 | { |
---|
[473] | 1170 | unsigned int index = offset_x + p; |
---|
| 1171 | unsigned int c_id = index / (points_per_cluster); |
---|
| 1172 | unsigned int c_offset = index % (points_per_cluster); |
---|
[469] | 1173 | printf("%f , %f | ", x[c_id][2*c_offset] , x[c_id][2*c_offset+1] ); |
---|
| 1174 | } |
---|
| 1175 | printf("\n"); |
---|
| 1176 | #endif |
---|
| 1177 | |
---|
[574] | 1178 | } // end FFTRow() |
---|
[469] | 1179 | |
---|
[473] | 1180 | /////////////////////////////////////// |
---|
| 1181 | void PrintArray( double ** array, |
---|
| 1182 | unsigned int size ) |
---|
[469] | 1183 | { |
---|
[473] | 1184 | unsigned int i; |
---|
| 1185 | unsigned int c_id; |
---|
| 1186 | unsigned int c_offset; |
---|
[469] | 1187 | |
---|
| 1188 | // float display |
---|
| 1189 | for (i = 0; i < size ; i++) |
---|
| 1190 | { |
---|
| 1191 | c_id = i / (points_per_cluster); |
---|
| 1192 | c_offset = i % (points_per_cluster); |
---|
| 1193 | |
---|
| 1194 | printf(" %f %f |", array[c_id][2*c_offset], array[c_id][2*c_offset+1]); |
---|
| 1195 | |
---|
| 1196 | if ( (i+1) % 4 == 0) printf("\n"); |
---|
| 1197 | } |
---|
| 1198 | printf("\n"); |
---|
| 1199 | } |
---|
| 1200 | |
---|
| 1201 | |
---|
| 1202 | // Local Variables: |
---|
| 1203 | // tab-width: 4 |
---|
| 1204 | // c-basic-offset: 4 |
---|
| 1205 | // c-file-offsets:((innamespace . 0)(inline-open . 0)) |
---|
| 1206 | // indent-tabs-mode: nil |
---|
| 1207 | // End: |
---|
| 1208 | |
---|
| 1209 | // vim: filetype=cpp:expandtab:shiftwidth=4:tabstop=4:softtabstop=4 |
---|
| 1210 | |
---|