4.3BSD - /usr/src/lib/libc/gen/random.c

   1: /*
   2:  * Copyright (c) 1983 Regents of the University of California.
   3:  * All rights reserved.  The Berkeley software License Agreement
   4:  * specifies the terms and conditions for redistribution.
   5:  */
   6: 
   7: #if defined(LIBC_SCCS) && !defined(lint)
   8: static char sccsid[] = "@(#)random.c	5.2 (Berkeley) 3/9/86";
   9: #endif LIBC_SCCS and not lint
  10: 
  11: #include    <stdio.h>
  12: 
  13: /*
  14:  * random.c:
  15:  * An improved random number generation package.  In addition to the standard
  16:  * rand()/srand() like interface, this package also has a special state info
  17:  * interface.  The initstate() routine is called with a seed, an array of
  18:  * bytes, and a count of how many bytes are being passed in; this array is then
  19:  * initialized to contain information for random number generation with that
  20:  * much state information.  Good sizes for the amount of state information are
  21:  * 32, 64, 128, and 256 bytes.  The state can be switched by calling the
  22:  * setstate() routine with the same array as was initiallized with initstate().
  23:  * By default, the package runs with 128 bytes of state information and
  24:  * generates far better random numbers than a linear congruential generator.
  25:  * If the amount of state information is less than 32 bytes, a simple linear
  26:  * congruential R.N.G. is used.
  27:  * Internally, the state information is treated as an array of longs; the
  28:  * zeroeth element of the array is the type of R.N.G. being used (small
  29:  * integer); the remainder of the array is the state information for the
  30:  * R.N.G.  Thus, 32 bytes of state information will give 7 longs worth of
  31:  * state information, which will allow a degree seven polynomial.  (Note: the
  32:  * zeroeth word of state information also has some other information stored
  33:  * in it -- see setstate() for details).
  34:  * The random number generation technique is a linear feedback shift register
  35:  * approach, employing trinomials (since there are fewer terms to sum up that
  36:  * way).  In this approach, the least significant bit of all the numbers in
  37:  * the state table will act as a linear feedback shift register, and will have
  38:  * period 2^deg - 1 (where deg is the degree of the polynomial being used,
  39:  * assuming that the polynomial is irreducible and primitive).  The higher
  40:  * order bits will have longer periods, since their values are also influenced
  41:  * by pseudo-random carries out of the lower bits.  The total period of the
  42:  * generator is approximately deg*(2**deg - 1); thus doubling the amount of
  43:  * state information has a vast influence on the period of the generator.
  44:  * Note: the deg*(2**deg - 1) is an approximation only good for large deg,
  45:  * when the period of the shift register is the dominant factor.  With deg
  46:  * equal to seven, the period is actually much longer than the 7*(2**7 - 1)
  47:  * predicted by this formula.
  48:  */
  49: 
  50: 
  51: 
  52: /*
  53:  * For each of the currently supported random number generators, we have a
  54:  * break value on the amount of state information (you need at least this
  55:  * many bytes of state info to support this random number generator), a degree
  56:  * for the polynomial (actually a trinomial) that the R.N.G. is based on, and
  57:  * the separation between the two lower order coefficients of the trinomial.
  58:  */
  59: 
  60: #define     TYPE_0      0       /* linear congruential */
  61: #define     BREAK_0     8
  62: #define     DEG_0       0
  63: #define     SEP_0       0
  64: 
  65: #define     TYPE_1      1       /* x**7 + x**3 + 1 */
  66: #define     BREAK_1     32
  67: #define     DEG_1       7
  68: #define     SEP_1       3
  69: 
  70: #define     TYPE_2      2       /* x**15 + x + 1 */
  71: #define     BREAK_2     64
  72: #define     DEG_2       15
  73: #define     SEP_2       1
  74: 
  75: #define     TYPE_3      3       /* x**31 + x**3 + 1 */
  76: #define     BREAK_3     128
  77: #define     DEG_3       31
  78: #define     SEP_3       3
  79: 
  80: #define     TYPE_4      4       /* x**63 + x + 1 */
  81: #define     BREAK_4     256
  82: #define     DEG_4       63
  83: #define     SEP_4       1
  84: 
  85: 
  86: /*
  87:  * Array versions of the above information to make code run faster -- relies
  88:  * on fact that TYPE_i == i.
  89:  */
  90: 
  91: #define     MAX_TYPES   5       /* max number of types above */
  92: 
  93: static  int     degrees[ MAX_TYPES ]    = { DEG_0, DEG_1, DEG_2,
  94:                                 DEG_3, DEG_4 };
  95: 
  96: static  int     seps[ MAX_TYPES ]   = { SEP_0, SEP_1, SEP_2,
  97:                                 SEP_3, SEP_4 };
  98: 
  99: 
 100: 
 101: /*
 102:  * Initially, everything is set up as if from :
 103:  *		initstate( 1, &randtbl, 128 );
 104:  * Note that this initialization takes advantage of the fact that srandom()
 105:  * advances the front and rear pointers 10*rand_deg times, and hence the
 106:  * rear pointer which starts at 0 will also end up at zero; thus the zeroeth
 107:  * element of the state information, which contains info about the current
 108:  * position of the rear pointer is just
 109:  *	MAX_TYPES*(rptr - state) + TYPE_3 == TYPE_3.
 110:  */
 111: 
 112: static  long        randtbl[ DEG_3 + 1 ]    = { TYPE_3,
 113:                 0x9a319039, 0x32d9c024, 0x9b663182, 0x5da1f342,
 114:                 0xde3b81e0, 0xdf0a6fb5, 0xf103bc02, 0x48f340fb,
 115:                 0x7449e56b, 0xbeb1dbb0, 0xab5c5918, 0x946554fd,
 116:                 0x8c2e680f, 0xeb3d799f, 0xb11ee0b7, 0x2d436b86,
 117:                 0xda672e2a, 0x1588ca88, 0xe369735d, 0x904f35f7,
 118:                 0xd7158fd6, 0x6fa6f051, 0x616e6b96, 0xac94efdc,
 119:                 0x36413f93, 0xc622c298, 0xf5a42ab8, 0x8a88d77b,
 120:                     0xf5ad9d0e, 0x8999220b, 0x27fb47b9 };
 121: 
 122: /*
 123:  * fptr and rptr are two pointers into the state info, a front and a rear
 124:  * pointer.  These two pointers are always rand_sep places aparts, as they cycle
 125:  * cyclically through the state information.  (Yes, this does mean we could get
 126:  * away with just one pointer, but the code for random() is more efficient this
 127:  * way).  The pointers are left positioned as they would be from the call
 128:  *			initstate( 1, randtbl, 128 )
 129:  * (The position of the rear pointer, rptr, is really 0 (as explained above
 130:  * in the initialization of randtbl) because the state table pointer is set
 131:  * to point to randtbl[1] (as explained below).
 132:  */
 133: 
 134: static  long        *fptr           = &randtbl[ SEP_3 + 1 ];
 135: static  long        *rptr           = &randtbl[ 1 ];
 136: 
 137: 
 138: 
 139: /*
 140:  * The following things are the pointer to the state information table,
 141:  * the type of the current generator, the degree of the current polynomial
 142:  * being used, and the separation between the two pointers.
 143:  * Note that for efficiency of random(), we remember the first location of
 144:  * the state information, not the zeroeth.  Hence it is valid to access
 145:  * state[-1], which is used to store the type of the R.N.G.
 146:  * Also, we remember the last location, since this is more efficient than
 147:  * indexing every time to find the address of the last element to see if
 148:  * the front and rear pointers have wrapped.
 149:  */
 150: 
 151: static  long        *state          = &randtbl[ 1 ];
 152: 
 153: static  int     rand_type       = TYPE_3;
 154: static  int     rand_deg        = DEG_3;
 155: static  int     rand_sep        = SEP_3;
 156: 
 157: static  long        *end_ptr        = &randtbl[ DEG_3 + 1 ];
 158: 
 159: 
 160: 
 161: /*
 162:  * srandom:
 163:  * Initialize the random number generator based on the given seed.  If the
 164:  * type is the trivial no-state-information type, just remember the seed.
 165:  * Otherwise, initializes state[] based on the given "seed" via a linear
 166:  * congruential generator.  Then, the pointers are set to known locations
 167:  * that are exactly rand_sep places apart.  Lastly, it cycles the state
 168:  * information a given number of times to get rid of any initial dependencies
 169:  * introduced by the L.C.R.N.G.
 170:  * Note that the initialization of randtbl[] for default usage relies on
 171:  * values produced by this routine.
 172:  */
 173: 
 174: srandom( x )
 175: 
 176:     unsigned        x;
 177: {
 178:         register  int       i, j;
 179: 
 180:     if(  rand_type  ==  TYPE_0  )  {
 181:         state[ 0 ] = x;
 182:     }
 183:     else  {
 184:         j = 1;
 185:         state[ 0 ] = x;
 186:         for( i = 1; i < rand_deg; i++ )  {
 187:         state[i] = 1103515245*state[i - 1] + 12345;
 188:         }
 189:         fptr = &state[ rand_sep ];
 190:         rptr = &state[ 0 ];
 191:         for( i = 0; i < 10*rand_deg; i++ )  random();
 192:     }
 193: }
 194: 
 195: 
 196: 
 197: /*
 198:  * initstate:
 199:  * Initialize the state information in the given array of n bytes for
 200:  * future random number generation.  Based on the number of bytes we
 201:  * are given, and the break values for the different R.N.G.'s, we choose
 202:  * the best (largest) one we can and set things up for it.  srandom() is
 203:  * then called to initialize the state information.
 204:  * Note that on return from srandom(), we set state[-1] to be the type
 205:  * multiplexed with the current value of the rear pointer; this is so
 206:  * successive calls to initstate() won't lose this information and will
 207:  * be able to restart with setstate().
 208:  * Note: the first thing we do is save the current state, if any, just like
 209:  * setstate() so that it doesn't matter when initstate is called.
 210:  * Returns a pointer to the old state.
 211:  */
 212: 
 213: char  *
 214: initstate( seed, arg_state, n )
 215: 
 216:     unsigned        seed;           /* seed for R. N. G. */
 217:     char        *arg_state;     /* pointer to state array */
 218:     int         n;          /* # bytes of state info */
 219: {
 220:     register  char      *ostate     = (char *)( &state[ -1 ] );
 221: 
 222:     if(  rand_type  ==  TYPE_0  )  state[ -1 ] = rand_type;
 223:     else  state[ -1 ] = MAX_TYPES*(rptr - state) + rand_type;
 224:     if(  n  <  BREAK_1  )  {
 225:         if(  n  <  BREAK_0  )  {
 226:         fprintf( stderr, "initstate: not enough state (%d bytes) with which to do jack; ignored.\n" );
 227:         return;
 228:         }
 229:         rand_type = TYPE_0;
 230:         rand_deg = DEG_0;
 231:         rand_sep = SEP_0;
 232:     }
 233:     else  {
 234:         if(  n  <  BREAK_2  )  {
 235:         rand_type = TYPE_1;
 236:         rand_deg = DEG_1;
 237:         rand_sep = SEP_1;
 238:         }
 239:         else  {
 240:         if(  n  <  BREAK_3  )  {
 241:             rand_type = TYPE_2;
 242:             rand_deg = DEG_2;
 243:             rand_sep = SEP_2;
 244:         }
 245:         else  {
 246:             if(  n  <  BREAK_4  )  {
 247:             rand_type = TYPE_3;
 248:             rand_deg = DEG_3;
 249:             rand_sep = SEP_3;
 250:             }
 251:             else  {
 252:             rand_type = TYPE_4;
 253:             rand_deg = DEG_4;
 254:             rand_sep = SEP_4;
 255:             }
 256:         }
 257:         }
 258:     }
 259:     state = &(  ( (long *)arg_state )[1]  );    /* first location */
 260:     end_ptr = &state[ rand_deg ];   /* must set end_ptr before srandom */
 261:     srandom( seed );
 262:     if(  rand_type  ==  TYPE_0  )  state[ -1 ] = rand_type;
 263:     else  state[ -1 ] = MAX_TYPES*(rptr - state) + rand_type;
 264:     return( ostate );
 265: }
 266: 
 267: 
 268: 
 269: /*
 270:  * setstate:
 271:  * Restore the state from the given state array.
 272:  * Note: it is important that we also remember the locations of the pointers
 273:  * in the current state information, and restore the locations of the pointers
 274:  * from the old state information.  This is done by multiplexing the pointer
 275:  * location into the zeroeth word of the state information.
 276:  * Note that due to the order in which things are done, it is OK to call
 277:  * setstate() with the same state as the current state.
 278:  * Returns a pointer to the old state information.
 279:  */
 280: 
 281: char  *
 282: setstate( arg_state )
 283: 
 284:     char        *arg_state;
 285: {
 286:     register  long      *new_state  = (long *)arg_state;
 287:     register  int       type        = new_state[0]%MAX_TYPES;
 288:     register  int       rear        = new_state[0]/MAX_TYPES;
 289:     char            *ostate     = (char *)( &state[ -1 ] );
 290: 
 291:     if(  rand_type  ==  TYPE_0  )  state[ -1 ] = rand_type;
 292:     else  state[ -1 ] = MAX_TYPES*(rptr - state) + rand_type;
 293:     switch(  type  )  {
 294:         case  TYPE_0:
 295:         case  TYPE_1:
 296:         case  TYPE_2:
 297:         case  TYPE_3:
 298:         case  TYPE_4:
 299:         rand_type = type;
 300:         rand_deg = degrees[ type ];
 301:         rand_sep = seps[ type ];
 302:         break;
 303: 
 304:         default:
 305:         fprintf( stderr, "setstate: state info has been munged; not changed.\n" );
 306:     }
 307:     state = &new_state[ 1 ];
 308:     if(  rand_type  !=  TYPE_0  )  {
 309:         rptr = &state[ rear ];
 310:         fptr = &state[ (rear + rand_sep)%rand_deg ];
 311:     }
 312:     end_ptr = &state[ rand_deg ];       /* set end_ptr too */
 313:     return( ostate );
 314: }
 315: 
 316: 
 317: 
 318: /*
 319:  * random:
 320:  * If we are using the trivial TYPE_0 R.N.G., just do the old linear
 321:  * congruential bit.  Otherwise, we do our fancy trinomial stuff, which is the
 322:  * same in all ther other cases due to all the global variables that have been
 323:  * set up.  The basic operation is to add the number at the rear pointer into
 324:  * the one at the front pointer.  Then both pointers are advanced to the next
 325:  * location cyclically in the table.  The value returned is the sum generated,
 326:  * reduced to 31 bits by throwing away the "least random" low bit.
 327:  * Note: the code takes advantage of the fact that both the front and
 328:  * rear pointers can't wrap on the same call by not testing the rear
 329:  * pointer if the front one has wrapped.
 330:  * Returns a 31-bit random number.
 331:  */
 332: 
 333: long
 334: random()
 335: {
 336:     long        i;
 337: 
 338:     if(  rand_type  ==  TYPE_0  )  {
 339:         i = state[0] = ( state[0]*1103515245 + 12345 )&0x7fffffff;
 340:     }
 341:     else  {
 342:         *fptr += *rptr;
 343:         i = (*fptr >> 1)&0x7fffffff;    /* chucking least random bit */
 344:         if(  ++fptr  >=  end_ptr  )  {
 345:         fptr = state;
 346:         ++rptr;
 347:         }
 348:         else  {
 349:         if(  ++rptr  >=  end_ptr  )  rptr = state;
 350:         }
 351:     }
 352:     return( i );
 353: }

Defined functions

Defined variables

Defined macros