libiberty/random.c

   1 /*
   2  * Copyright (c) 1983 Regents of the University of California.
   3  * All rights reserved.
   4  *
   5  * Redistribution and use in source and binary forms are permitted
   6  * provided that the above copyright notice and this paragraph are
   7  * duplicated in all such forms and that any documentation,
   8  * advertising materials, and other materials related to such
   9  * distribution and use acknowledge that the software was developed
  10  * by the University of California, Berkeley.  The name of the
  11  * University may not be used to endorse or promote products derived
  12  * from this software without specific prior written permission.
  13  * THIS SOFTWARE IS PROVIDED ``AS IS'' AND WITHOUT ANY EXPRESS OR
  14  * IMPLIED WARRANTIES, INCLUDING, WITHOUT LIMITATION, THE IMPLIED
  15  * WARRANTIES OF MERCHANTIBILITY AND FITNESS FOR A PARTICULAR PURPOSE.
  16  */
  17
  18 /*
  19  * This is derived from the Berkeley source:
  20  *      @(#)random.c    5.5 (Berkeley) 7/6/88
  21  * It was reworked for the GNU C Library by Roland McGrath.
  22  */
  23
  24 #include <errno.h>
  25
  26 #if 0
  27
  28 #include <ansidecl.h>
  29 #include <limits.h>
  30 #include <stddef.h>
  31 #include <stdlib.h>
  32
  33 #else
  34
  35 #define ULONG_MAX  ((unsigned long)(~0L))     /* 0xFFFFFFFF for 32-bits */
  36 #define LONG_MAX   ((long)(ULONG_MAX >> 1))   /* 0x7FFFFFFF for 32-bits*/
  37
  38 #ifdef __STDC__
  39 #  define PTR void *
  40 #  define NULL (void *) 0
  41 #else
  42 #  define PTR char *
  43 #  define NULL 0
  44 #endif
  45
  46 #endif
  47
  48 long int random ();
  49
  50 /* An improved random number generation package.  In addition to the standard
  51    rand()/srand() like interface, this package also has a special state info
  52    interface.  The initstate() routine is called with a seed, an array of
  53    bytes, and a count of how many bytes are being passed in; this array is
  54    then initialized to contain information for random number generation with
  55    that much state information.  Good sizes for the amount of state
  56    information are 32, 64, 128, and 256 bytes.  The state can be switched by
  57    calling the setstate() function with the same array as was initiallized
  58    with initstate().  By default, the package runs with 128 bytes of state
  59    information and generates far better random numbers than a linear
  60    congruential generator.  If the amount of state information is less than
  61    32 bytes, a simple linear congruential R.N.G. is used.  Internally, the
  62    state information is treated as an array of longs; the zeroeth element of
  63    the array is the type of R.N.G. being used (small integer); the remainder
  64    of the array is the state information for the R.N.G.  Thus, 32 bytes of
  65    state information will give 7 longs worth of state information, which will
  66    allow a degree seven polynomial.  (Note: The zeroeth word of state
  67    information also has some other information stored in it; see setstate
  68    for details).  The random number generation technique is a linear feedback
  69    shift register approach, employing trinomials (since there are fewer terms
  70    to sum up that way).  In this approach, the least significant bit of all
  71    the numbers in the state table will act as a linear feedback shift register,
  72    and will have period 2^deg - 1 (where deg is the degree of the polynomial
  73    being used, assuming that the polynomial is irreducible and primitive).
  74    The higher order bits will have longer periods, since their values are
  75    also influenced by pseudo-random carries out of the lower bits.  The
  76    total period of the generator is approximately deg*(2**deg - 1); thus
  77    doubling the amount of state information has a vast influence on the
  78    period of the generator.  Note: The deg*(2**deg - 1) is an approximation
  79    only good for large deg, when the period of the shift register is the
  80    dominant factor.  With deg equal to seven, the period is actually much
  81    longer than the 7*(2**7 - 1) predicted by this formula.  */
  82
  83
  84
  85 /* For each of the currently supported random number generators, we have a
  86    break value on the amount of state information (you need at least thi
  87    bytes of state info to support this random number generator), a degree for
  88    the polynomial (actually a trinomial) that the R.N.G. is based on, and
  89    separation between the two lower order coefficients of the trinomial.  */
  90
  91 /* Linear congruential.  */
  92 #define TYPE_0          0
  93 #define BREAK_0         8
  94 #define DEG_0           0
  95 #define SEP_0           0
  96
  97 /* x**7 + x**3 + 1.  */
  98 #define TYPE_1          1
  99 #define BREAK_1         32
 100 #define DEG_1           7
 101 #define SEP_1           3
 102
 103 /* x**15 + x + 1.  */
 104 #define TYPE_2          2
 105 #define BREAK_2         64
 106 #define DEG_2           15
 107 #define SEP_2           1
 108
 109 /* x**31 + x**3 + 1.  */
 110 #define TYPE_3          3
 111 #define BREAK_3         128
 112 #define DEG_3           31
 113 #define SEP_3           3
 114
 115 /* x**63 + x + 1.  */
 116 #define TYPE_4          4
 117 #define BREAK_4         256
 118 #define DEG_4           63
 119 #define SEP_4           1
 120
 121
 122 /* Array versions of the above information to make code run faster.
 123    Relies on fact that TYPE_i == i.  */
 124
 125 #define MAX_TYPES       5       /* Max number of types above.  */
 126
 127 static int degrees[MAX_TYPES] = { DEG_0, DEG_1, DEG_2, DEG_3, DEG_4 };
 128 static int seps[MAX_TYPES] = { SEP_0, SEP_1, SEP_2, SEP_3, SEP_4 };
 129
 130
 131
 132 /* Initially, everything is set up as if from:
 133         initstate(1, randtbl, 128);
 134    Note that this initialization takes advantage of the fact that srandom
 135    advances the front and rear pointers 10*rand_deg times, and hence the
 136    rear pointer which starts at 0 will also end up at zero; thus the zeroeth
 137    element of the state information, which contains info about the current
 138    position of the rear pointer is just
 139         (MAX_TYPES * (rptr - state)) + TYPE_3 == TYPE_3.  */
 140
 141 static long int randtbl[DEG_3 + 1] =
 142   { TYPE_3,
 143       0x9a319039, 0x32d9c024, 0x9b663182, 0x5da1f342,
 144       0xde3b81e0, 0xdf0a6fb5, 0xf103bc02, 0x48f340fb,
 145       0x7449e56b, 0xbeb1dbb0, 0xab5c5918, 0x946554fd,
 146       0x8c2e680f, 0xeb3d799f, 0xb11ee0b7, 0x2d436b86,
 147       0xda672e2a, 0x1588ca88, 0xe369735d, 0x904f35f7,
 148       0xd7158fd6, 0x6fa6f051, 0x616e6b96, 0xac94efdc,
 149       0x36413f93, 0xc622c298, 0xf5a42ab8, 0x8a88d77b,
 150       0xf5ad9d0e, 0x8999220b, 0x27fb47b9
 151     };
 152
 153 /* FPTR and RPTR are two pointers into the state info, a front and a rear
 154    pointer.  These two pointers are always rand_sep places aparts, as they
 155    cycle through the state information.  (Yes, this does mean we could get
 156    away with just one pointer, but the code for random is more efficient
 157    this way).  The pointers are left positioned as they would be from the call:
 158         initstate(1, randtbl, 128);
 159    (The position of the rear pointer, rptr, is really 0 (as explained above
 160    in the initialization of randtbl) because the state table pointer is set
 161    to point to randtbl[1] (as explained below).)  */
 162
 163 static long int *fptr = &randtbl[SEP_3 + 1];
 164 static long int *rptr = &randtbl[1];
 165
 166
 167
 168 /* The following things are the pointer to the state information table,
 169    the type of the current generator, the degree of the current polynomial
 170    being used, and the separation between the two pointers.
 171    Note that for efficiency of random, we remember the first location of
 172    the state information, not the zeroeth.  Hence it is valid to access
 173    state[-1], which is used to store the type of the R.N.G.
 174    Also, we remember the last location, since this is more efficient than
 175    indexing every time to find the address of the last element to see if
 176    the front and rear pointers have wrapped.  */
 177
 178 static long int *state = &randtbl[1];
 179
 180 static int rand_type = TYPE_3;
 181 static int rand_deg = DEG_3;
 182 static int rand_sep = SEP_3;
 183
 184 static long int *end_ptr = &randtbl[sizeof(randtbl) / sizeof(randtbl[0])];
 185 \f
 186 /* Initialize the random number generator based on the given seed.  If the
 187    type is the trivial no-state-information type, just remember the seed.
 188    Otherwise, initializes state[] based on the given "seed" via a linear
 189    congruential generator.  Then, the pointers are set to known locations
 190    that are exactly rand_sep places apart.  Lastly, it cycles the state
 191    information a given number of times to get rid of any initial dependencies
 192    introduced by the L.C.R.N.G.  Note that the initialization of randtbl[]
 193    for default usage relies on values produced by this routine.  */
 194 void
 195 srandom (x)
 196   unsigned int x;
 197 {
 198   state[0] = x;
 199   if (rand_type != TYPE_0)
 200     {
 201       register long int i;
 202       for (i = 1; i < rand_deg; ++i)
 203         state[i] = (1103515145 * state[i - 1]) + 12345;
 204       fptr = &state[rand_sep];
 205       rptr = &state[0];
 206       for (i = 0; i < 10 * rand_deg; ++i)
 207         random();
 208     }
 209 }
 210 \f
 211 /* Initialize the state information in the given array of N bytes for
 212    future random number generation.  Based on the number of bytes we
 213    are given, and the break values for the different R.N.G.'s, we choose
 214    the best (largest) one we can and set things up for it.  srandom is
 215    then called to initialize the state information.  Note that on return
 216    from srandom, we set state[-1] to be the type multiplexed with the current
 217    value of the rear pointer; this is so successive calls to initstate won't
 218    lose this information and will be able to restart with setstate.
 219    Note: The first thing we do is save the current state, if any, just like
 220    setstate so that it doesn't matter when initstate is called.
 221    Returns a pointer to the old state.  */
 222 PTR
 223 initstate (seed, arg_state, n)
 224   unsigned int seed;
 225   PTR arg_state;
 226   unsigned long n;
 227 {
 228   PTR ostate = (PTR) &state[-1];
 229
 230   if (rand_type == TYPE_0)
 231     state[-1] = rand_type;
 232   else
 233     state[-1] = (MAX_TYPES * (rptr - state)) + rand_type;
 234   if (n < BREAK_1)
 235     {
 236       if (n < BREAK_0)
 237         {
 238           errno = EINVAL;
 239           return NULL;
 240         }
 241       rand_type = TYPE_0;
 242       rand_deg = DEG_0;
 243       rand_sep = SEP_0;
 244     }
 245   else if (n < BREAK_2)
 246     {
 247       rand_type = TYPE_1;
 248       rand_deg = DEG_1;
 249       rand_sep = SEP_1;
 250     }
 251   else if (n < BREAK_3)
 252     {
 253       rand_type = TYPE_2;
 254       rand_deg = DEG_2;
 255       rand_sep = SEP_2;
 256     }
 257   else if (n < BREAK_4)
 258     {
 259       rand_type = TYPE_3;
 260       rand_deg = DEG_3;
 261       rand_sep = SEP_3;
 262     }
 263   else
 264     {
 265       rand_type = TYPE_4;
 266       rand_deg = DEG_4;
 267       rand_sep = SEP_4;
 268     }
 269
 270   state = &((long int *) arg_state)[1]; /* First location.  */
 271   /* Must set END_PTR before srandom.  */
 272   end_ptr = &state[rand_deg];
 273   srandom(seed);
 274   if (rand_type == TYPE_0)
 275     state[-1] = rand_type;
 276   else
 277     state[-1] = (MAX_TYPES * (rptr - state)) + rand_type;
 278
 279   return ostate;
 280 }
 281 \f
 282 /* Restore the state from the given state array.
 283    Note: It is important that we also remember the locations of the pointers
 284    in the current state information, and restore the locations of the pointers
 285    from the old state information.  This is done by multiplexing the pointer
 286    location into the zeroeth word of the state information. Note that due
 287    to the order in which things are done, it is OK to call setstate with the
 288    same state as the current state
 289    Returns a pointer to the old state information.  */
 290
 291 PTR
 292 setstate (arg_state)
 293   PTR arg_state;
 294 {
 295   register long int *new_state = (long int *) arg_state;
 296   register int type = new_state[0] % MAX_TYPES;
 297   register int rear = new_state[0] / MAX_TYPES;
 298   PTR ostate = (PTR) &state[-1];
 299
 300   if (rand_type == TYPE_0)
 301     state[-1] = rand_type;
 302   else
 303     state[-1] = (MAX_TYPES * (rptr - state)) + rand_type;
 304
 305   switch (type)
 306     {
 307     case TYPE_0:
 308     case TYPE_1:
 309     case TYPE_2:
 310     case TYPE_3:
 311     case TYPE_4:
 312       rand_type = type;
 313       rand_deg = degrees[type];
 314       rand_sep = seps[type];
 315       break;
 316     default:
 317       /* State info munged.  */
 318       errno = EINVAL;
 319       return NULL;
 320     }
 321
 322   state = &new_state[1];
 323   if (rand_type != TYPE_0)
 324     {
 325       rptr = &state[rear];
 326       fptr = &state[(rear + rand_sep) % rand_deg];
 327     }
 328   /* Set end_ptr too.  */
 329   end_ptr = &state[rand_deg];
 330
 331   return ostate;
 332 }
 333 \f
 334 /* If we are using the trivial TYPE_0 R.N.G., just do the old linear
 335    congruential bit.  Otherwise, we do our fancy trinomial stuff, which is the
 336    same in all ther other cases due to all the global variables that have been
 337    set up.  The basic operation is to add the number at the rear pointer into
 338    the one at the front pointer.  Then both pointers are advanced to the next
 339    location cyclically in the table.  The value returned is the sum generated,
 340    reduced to 31 bits by throwing away the "least random" low bit.
 341    Note: The code takes advantage of the fact that both the front and
 342    rear pointers can't wrap on the same call by not testing the rear
 343    pointer if the front one has wrapped.  Returns a 31-bit random number.  */
 344
 345 long int
 346 random ()
 347 {
 348   if (rand_type == TYPE_0)
 349     {
 350       state[0] = ((state[0] * 1103515245) + 12345) & LONG_MAX;
 351       return state[0];
 352     }
 353   else
 354     {
 355       long int i;
 356       *fptr += *rptr;
 357       /* Chucking least random bit.  */
 358       i = (*fptr >> 1) & LONG_MAX;
 359       ++fptr;
 360       if (fptr >= end_ptr)
 361         {
 362           fptr = state;
 363           ++rptr;
 364         }
 365       else
 366         {
 367           ++rptr;
 368           if (rptr >= end_ptr)
 369             rptr = state;
 370         }
 371       return i;
 372     }
 373 }