1 /* 2 * Experimental data distribution table generator 3 * Taken from the uncopyrighted NISTnet code (public domain). 4 * 5 * Read in a series of "random" data values, either 6 * experimentally or generated from some probability distribution. 7 * From this, create the inverse distribution table used to approximate 8 * the distribution. 9 */ 10 #include <stdio.h> 11 #include <stdlib.h> 12 #include <math.h> 13 #include <malloc.h> 14 #include <string.h> 15 #include <sys/types.h> 16 #include <sys/stat.h> 17 18 19 double * 20 readdoubles(FILE *fp, int *number) 21 { 22 struct stat info; 23 double *x; 24 int limit; 25 int n=0, i; 26 27 fstat(fileno(fp), &info); 28 if (info.st_size > 0) { 29 limit = 2*info.st_size/sizeof(double); /* @@ approximate */ 30 } else { 31 limit = 10000; 32 } 33 34 x = calloc(limit, sizeof(double)); 35 if (!x) { 36 perror("double alloc"); 37 exit(3); 38 } 39 40 for (i=0; i<limit; ++i){ 41 fscanf(fp, "%lf", &x[i]); 42 if (feof(fp)) 43 break; 44 ++n; 45 } 46 *number = n; 47 return x; 48 } 49 50 void 51 arraystats(double *x, int limit, double *mu, double *sigma, double *rho) 52 { 53 int n=0, i; 54 double sumsquare=0.0, sum=0.0, top=0.0; 55 double sigma2=0.0; 56 57 for (i=0; i<limit; ++i){ 58 sumsquare += x[i]*x[i]; 59 sum += x[i]; 60 ++n; 61 } 62 *mu = sum/(double)n; 63 *sigma = sqrt((sumsquare - (double)n*(*mu)*(*mu))/(double)(n-1)); 64 65 for (i=1; i < n; ++i){ 66 top += ((double)x[i]- *mu)*((double)x[i-1]- *mu); 67 sigma2 += ((double)x[i-1] - *mu)*((double)x[i-1] - *mu); 68 69 } 70 *rho = top/sigma2; 71 } 72 73 /* Create a (normalized) distribution table from a set of observed 74 * values. The table is fixed to run from (as it happens) -4 to +4, 75 * with granularity .00002. 76 */ 77 78 #define TABLESIZE 16384/4 79 #define TABLEFACTOR 8192 80 #ifndef MINSHORT 81 #define MINSHORT -32768 82 #define MAXSHORT 32767 83 #endif 84 85 /* Since entries in the inverse are scaled by TABLEFACTOR, and can't be bigger 86 * than MAXSHORT, we don't bother looking at a larger domain than this: 87 */ 88 #define DISTTABLEDOMAIN ((MAXSHORT/TABLEFACTOR)+1) 89 #define DISTTABLEGRANULARITY 50000 90 #define DISTTABLESIZE (DISTTABLEDOMAIN*DISTTABLEGRANULARITY*2) 91 92 static int * 93 makedist(double *x, int limit, double mu, double sigma) 94 { 95 int *table; 96 int i, index, first=DISTTABLESIZE, last=0; 97 double input; 98 99 table = calloc(DISTTABLESIZE, sizeof(int)); 100 if (!table) { 101 perror("table alloc"); 102 exit(3); 103 } 104 105 for (i=0; i < limit; ++i) { 106 /* Normalize value */ 107 input = (x[i]-mu)/sigma; 108 109 index = (int)rint((input+DISTTABLEDOMAIN)*DISTTABLEGRANULARITY); 110 if (index < 0) index = 0; 111 if (index >= DISTTABLESIZE) index = DISTTABLESIZE-1; 112 ++table[index]; 113 if (index > last) 114 last = index +1; 115 if (index < first) 116 first = index; 117 } 118 return table; 119 } 120 121 /* replace an array by its cumulative distribution */ 122 static void 123 cumulativedist(int *table, int limit, int *total) 124 { 125 int accum=0; 126 127 while (--limit >= 0) { 128 accum += *table; 129 *table++ = accum; 130 } 131 *total = accum; 132 } 133 134 static short * 135 inverttable(int *table, int inversesize, int tablesize, int cumulative) 136 { 137 int i, inverseindex, inversevalue; 138 short *inverse; 139 double findex, fvalue; 140 141 inverse = (short *)malloc(inversesize*sizeof(short)); 142 for (i=0; i < inversesize; ++i) { 143 inverse[i] = MINSHORT; 144 } 145 for (i=0; i < tablesize; ++i) { 146 findex = ((double)i/(double)DISTTABLEGRANULARITY) - DISTTABLEDOMAIN; 147 fvalue = (double)table[i]/(double)cumulative; 148 inverseindex = (int)rint(fvalue*inversesize); 149 inversevalue = (int)rint(findex*TABLEFACTOR); 150 if (inversevalue <= MINSHORT) inversevalue = MINSHORT+1; 151 if (inversevalue > MAXSHORT) inversevalue = MAXSHORT; 152 inverse[inverseindex] = inversevalue; 153 } 154 return inverse; 155 156 } 157 158 /* Run simple linear interpolation over the table to fill in missing entries */ 159 static void 160 interpolatetable(short *table, int limit) 161 { 162 int i, j, last, lasti = -1; 163 164 last = MINSHORT; 165 for (i=0; i < limit; ++i) { 166 if (table[i] == MINSHORT) { 167 for (j=i; j < limit; ++j) 168 if (table[j] != MINSHORT) 169 break; 170 if (j < limit) { 171 table[i] = last + (i-lasti)*(table[j]-last)/(j-lasti); 172 } else { 173 table[i] = last + (i-lasti)*(MAXSHORT-last)/(limit-lasti); 174 } 175 } else { 176 last = table[i]; 177 lasti = i; 178 } 179 } 180 } 181 182 static void 183 printtable(const short *table, int limit) 184 { 185 int i; 186 187 printf("# This is the distribution table for the experimental distribution.\n"); 188 189 for (i=0 ; i < limit; ++i) { 190 printf("%d%c", table[i], 191 (i % 8) == 7 ? '\n' : ' '); 192 } 193 } 194 195 int 196 main(int argc, char **argv) 197 { 198 FILE *fp; 199 double *x; 200 double mu, sigma, rho; 201 int limit; 202 int *table; 203 short *inverse; 204 int total; 205 206 if (argc > 1) { 207 if (!(fp = fopen(argv[1], "r"))) { 208 perror(argv[1]); 209 exit(1); 210 } 211 } else { 212 fp = stdin; 213 } 214 x = readdoubles(fp, &limit); 215 if (limit <= 0) { 216 fprintf(stderr, "Nothing much read!\n"); 217 exit(2); 218 } 219 arraystats(x, limit, &mu, &sigma, &rho); 220 #ifdef DEBUG 221 fprintf(stderr, "%d values, mu %10.4f, sigma %10.4f, rho %10.4f\n", 222 limit, mu, sigma, rho); 223 #endif 224 225 table = makedist(x, limit, mu, sigma); 226 free((void *) x); 227 cumulativedist(table, DISTTABLESIZE, &total); 228 inverse = inverttable(table, TABLESIZE, DISTTABLESIZE, total); 229 interpolatetable(inverse, TABLESIZE); 230 printtable(inverse, TABLESIZE); 231 return 0; 232 } 233
