stdlib/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 <ansidecl.h>
  25 #include <errno.h>
  26 #include <limits.h>
  27 #include <stddef.h>
  28 #include <stdlib.h>
  29
  30
  31 /* An improved random number generation package.  In addition to the standard
  32    rand()/srand() like interface, this package also has a special state info
  33    interface.  The initstate() routine is called with a seed, an array of
  34    bytes, and a count of how many bytes are being passed in; this array is
  35    then initialized to contain information for random number generation with
  36    that much state information.  Good sizes for the amount of state
  37    information are 32, 64, 128, and 256 bytes.  The state can be switched by
  38    calling the setstate() function with the same array as was initiallized
  39    with initstate().  By default, the package runs with 128 bytes of state
  40    information and generates far better random numbers than a linear
  41    congruential generator.  If the amount of state information is less than
  42    32 bytes, a simple linear congruential R.N.G. is used.  Internally, the
  43    state information is treated as an array of longs; the zeroeth element of
  44    the array is the type of R.N.G. being used (small integer); the remainder
  45    of the array is the state information for the R.N.G.  Thus, 32 bytes of
  46    state information will give 7 longs worth of state information, which will
  47    allow a degree seven polynomial.  (Note: The zeroeth word of state
  48    information also has some other information stored in it; see setstate
  49    for details).  The random number generation technique is a linear feedback
  50    shift register approach, employing trinomials (since there are fewer terms
  51    to sum up that way).  In this approach, the least significant bit of all
  52    the numbers in the state table will act as a linear feedback shift register,
  53    and will have period 2^deg - 1 (where deg is the degree of the polynomial
  54    being used, assuming that the polynomial is irreducible and primitive).
  55    The higher order bits will have longer periods, since their values are
  56    also influenced by pseudo-random carries out of the lower bits.  The
  57    total period of the generator is approximately deg*(2**deg - 1); thus
  58    doubling the amount of state information has a vast influence on the
  59    period of the generator.  Note: The deg*(2**deg - 1) is an approximation
  60    only good for large deg, when the period of the shift register is the
  61    dominant factor.  With deg equal to seven, the period is actually much
  62    longer than the 7*(2**7 - 1) predicted by this formula.  */
  63
  64
  65
  66 /* For each of the currently supported random number generators, we have a
  67    break value on the amount of state information (you need at least thi
  68    bytes of state info to support this random number generator), a degree for
  69    the polynomial (actually a trinomial) that the R.N.G. is based on, and
  70    separation between the two lower order coefficients of the trinomial.  */
  71
  72 /* Linear congruential.  */
  73 #define TYPE_0          0
  74 #define BREAK_0         8
  75 #define DEG_0           0
  76 #define SEP_0           0
  77
  78 /* x**7 + x**3 + 1.  */
  79 #define TYPE_1          1
  80 #define BREAK_1         32
  81 #define DEG_1           7
  82 #define SEP_1           3
  83
  84 /* x**15 + x + 1.  */
  85 #define TYPE_2          2
  86 #define BREAK_2         64
  87 #define DEG_2           15
  88 #define SEP_2           1
  89
  90 /* x**31 + x**3 + 1.  */
  91 #define TYPE_3          3
  92 #define BREAK_3         128
  93 #define DEG_3           31
  94 #define SEP_3           3
  95
  96 /* x**63 + x + 1.  */
  97 #define TYPE_4          4
  98 #define BREAK_4         256
  99 #define DEG_4           63
 100 #define SEP_4           1
 101
 102
 103 /* Array versions of the above information to make code run faster.
 104    Relies on fact that TYPE_i == i.  */
 105
 106 #define MAX_TYPES       5       /* Max number of types above.  */
 107
 108 static int degrees[MAX_TYPES] = { DEG_0, DEG_1, DEG_2, DEG_3, DEG_4 };
 109 static int seps[MAX_TYPES] = { SEP_0, SEP_1, SEP_2, SEP_3, SEP_4 };
 110
 111
 112
 113 /* Initially, everything is set up as if from:
 114         initstate(1, randtbl, 128);
 115    Note that this initialization takes advantage of the fact that srandom
 116    advances the front and rear pointers 10*rand_deg times, and hence the
 117    rear pointer which starts at 0 will also end up at zero; thus the zeroeth
 118    element of the state information, which contains info about the current
 119    position of the rear pointer is just
 120         (MAX_TYPES * (rptr - state)) + TYPE_3 == TYPE_3.  */
 121
 122 static long int randtbl[DEG_3 + 1] =
 123   {
 124     TYPE_3,
 125
 126     -1726662223, 379960547, 1735697613, 1040273694, 1313901226,
 127     1627687941, -179304937, -2073333483, 1780058412, -1989503057,
 128     -615974602, 344556628, 939512070, -1249116260, 1507946756,
 129     -812545463, 154635395, 1388815473, -1926676823, 525320961,
 130     -1009028674, 968117788, -123449607, 1284210865, 435012392,
 131     -2017506339, -911064859, -370259173, 1132637927, 1398500161,
 132     -205601318,
 133   };
 134
 135 /* FPTR and RPTR are two pointers into the state info, a front and a rear
 136    pointer.  These two pointers are always rand_sep places aparts, as they
 137    cycle through the state information.  (Yes, this does mean we could get
 138    away with just one pointer, but the code for random is more efficient
 139    this way).  The pointers are left positioned as they would be from the call:
 140         initstate(1, randtbl, 128);
 141    (The position of the rear pointer, rptr, is really 0 (as explained above
 142    in the initialization of randtbl) because the state table pointer is set
 143    to point to randtbl[1] (as explained below).)  */
 144
 145 static long int *fptr = &randtbl[SEP_3 + 1];
 146 static long int *rptr = &randtbl[1];
 147
 148
 149
 150 /* The following things are the pointer to the state information table,
 151    the type of the current generator, the degree of the current polynomial
 152    being used, and the separation between the two pointers.
 153    Note that for efficiency of random, we remember the first location of
 154    the state information, not the zeroeth.  Hence it is valid to access
 155    state[-1], which is used to store the type of the R.N.G.
 156    Also, we remember the last location, since this is more efficient than
 157    indexing every time to find the address of the last element to see if
 158    the front and rear pointers have wrapped.  */
 159
 160 static long int *state = &randtbl[1];
 161
 162 static int rand_type = TYPE_3;
 163 static int rand_deg = DEG_3;
 164 static int rand_sep = SEP_3;
 165
 166 static long int *end_ptr = &randtbl[sizeof(randtbl) / sizeof(randtbl[0])];
 167 \f
 168 /* Initialize the random number generator based on the given seed.  If the
 169    type is the trivial no-state-information type, just remember the seed.
 170    Otherwise, initializes state[] based on the given "seed" via a linear
 171    congruential generator.  Then, the pointers are set to known locations
 172    that are exactly rand_sep places apart.  Lastly, it cycles the state
 173    information a given number of times to get rid of any initial dependencies
 174    introduced by the L.C.R.N.G.  Note that the initialization of randtbl[]
 175    for default usage relies on values produced by this routine.  */
 176 void
 177 DEFUN(__srandom, (x), unsigned int x)
 178 {
 179   state[0] = x;
 180   if (rand_type != TYPE_0)
 181     {
 182       register long int i;
 183       for (i = 1; i < rand_deg; ++i)
 184         {
 185           /* This does:
 186                state[i] = (16807 * state[i - 1]) % 2147483647;
 187              but avoids overflowing 31 bits.  */
 188           long int hi = state[i - 1] / 127773;
 189           long int lo = state[i - 1] % 127773;
 190           long int test = 16807 * lo - 2836 * hi;
 191           state[i] = test + (test < 0 ? 2147483647 : 0);
 192         }
 193       fptr = &state[rand_sep];
 194       rptr = &state[0];
 195       for (i = 0; i < 10 * rand_deg; ++i)
 196         (void) __random ();
 197     }
 198 }
 199
 200 weak_alias (__srandom, srandom)
 201 weak_alias (__srandom, srand)
 202 \f
 203 /* Initialize the state information in the given array of N bytes for
 204    future random number generation.  Based on the number of bytes we
 205    are given, and the break values for the different R.N.G.'s, we choose
 206    the best (largest) one we can and set things up for it.  srandom is
 207    then called to initialize the state information.  Note that on return
 208    from srandom, we set state[-1] to be the type multiplexed with the current
 209    value of the rear pointer; this is so successive calls to initstate won't
 210    lose this information and will be able to restart with setstate.
 211    Note: The first thing we do is save the current state, if any, just like
 212    setstate so that it doesn't matter when initstate is called.
 213    Returns a pointer to the old state.  */
 214 PTR
 215 DEFUN(__initstate, (seed, arg_state, n),
 216       unsigned int seed AND PTR arg_state AND size_t n)
 217 {
 218   PTR ostate = (PTR) &state[-1];
 219
 220   if (rand_type == TYPE_0)
 221     state[-1] = rand_type;
 222   else
 223     state[-1] = (MAX_TYPES * (rptr - state)) + rand_type;
 224   if (n < BREAK_1)
 225     {
 226       if (n < BREAK_0)
 227         {
 228           errno = EINVAL;
 229           return NULL;
 230         }
 231       rand_type = TYPE_0;
 232       rand_deg = DEG_0;
 233       rand_sep = SEP_0;
 234     }
 235   else if (n < BREAK_2)
 236     {
 237       rand_type = TYPE_1;
 238       rand_deg = DEG_1;
 239       rand_sep = SEP_1;
 240     }
 241   else if (n < BREAK_3)
 242     {
 243       rand_type = TYPE_2;
 244       rand_deg = DEG_2;
 245       rand_sep = SEP_2;
 246     }
 247   else if (n < BREAK_4)
 248     {
 249       rand_type = TYPE_3;
 250       rand_deg = DEG_3;
 251       rand_sep = SEP_3;
 252     }
 253   else
 254     {
 255       rand_type = TYPE_4;
 256       rand_deg = DEG_4;
 257       rand_sep = SEP_4;
 258     }
 259
 260   state = &((long int *) arg_state)[1]; /* First location.  */
 261   /* Must set END_PTR before srandom.  */
 262   end_ptr = &state[rand_deg];
 263   __srandom(seed);
 264   if (rand_type == TYPE_0)
 265     state[-1] = rand_type;
 266   else
 267     state[-1] = (MAX_TYPES * (rptr - state)) + rand_type;
 268
 269   return ostate;
 270 }
 271
 272 weak_alias (__initstate, initstate)
 273 \f
 274 /* Restore the state from the given state array.
 275    Note: It is important that we also remember the locations of the pointers
 276    in the current state information, and restore the locations of the pointers
 277    from the old state information.  This is done by multiplexing the pointer
 278    location into the zeroeth word of the state information. Note that due
 279    to the order in which things are done, it is OK to call setstate with the
 280    same state as the current state
 281    Returns a pointer to the old state information.  */
 282 PTR
 283 DEFUN(__setstate, (arg_state), PTR arg_state)
 284 {
 285   register long int *new_state = (long int *) arg_state;
 286   register int type = new_state[0] % MAX_TYPES;
 287   register int rear = new_state[0] / MAX_TYPES;
 288   PTR ostate = (PTR) &state[-1];
 289
 290   if (rand_type == TYPE_0)
 291     state[-1] = rand_type;
 292   else
 293     state[-1] = (MAX_TYPES * (rptr - state)) + rand_type;
 294
 295   switch (type)
 296     {
 297     case TYPE_0:
 298     case TYPE_1:
 299     case TYPE_2:
 300     case TYPE_3:
 301     case TYPE_4:
 302       rand_type = type;
 303       rand_deg = degrees[type];
 304       rand_sep = seps[type];
 305       break;
 306     default:
 307       /* State info munged.  */
 308       errno = EINVAL;
 309       return NULL;
 310     }
 311
 312   state = &new_state[1];
 313   if (rand_type != TYPE_0)
 314     {
 315       rptr = &state[rear];
 316       fptr = &state[(rear + rand_sep) % rand_deg];
 317     }
 318   /* Set end_ptr too.  */
 319   end_ptr = &state[rand_deg];
 320
 321   return ostate;
 322 }
 323
 324 weak_alias (__setstate, setstate)
 325 \f
 326 /* If we are using the trivial TYPE_0 R.N.G., just do the old linear
 327    congruential bit.  Otherwise, we do our fancy trinomial stuff, which is the
 328    same in all ther other cases due to all the global variables that have been
 329    set up.  The basic operation is to add the number at the rear pointer into
 330    the one at the front pointer.  Then both pointers are advanced to the next
 331    location cyclically in the table.  The value returned is the sum generated,
 332    reduced to 31 bits by throwing away the "least random" low bit.
 333    Note: The code takes advantage of the fact that both the front and
 334    rear pointers can't wrap on the same call by not testing the rear
 335    pointer if the front one has wrapped.  Returns a 31-bit random number.  */
 336
 337 long int
 338 DEFUN_VOID(__random)
 339 {
 340   if (rand_type == TYPE_0)
 341     {
 342       state[0] = ((state[0] * 1103515245) + 12345) & LONG_MAX;
 343       return state[0];
 344     }
 345   else
 346     {
 347       long int i;
 348       *fptr += *rptr;
 349       /* Chucking least random bit.  */
 350       i = (*fptr >> 1) & LONG_MAX;
 351       ++fptr;
 352       if (fptr >= end_ptr)
 353         {
 354           fptr = state;
 355           ++rptr;
 356         }
 357       else
 358         {
 359           ++rptr;
 360           if (rptr >= end_ptr)
 361             rptr = state;
 362         }
 363       return i;
 364     }
 365 }
 366
 367 weak_alias (__random, random)