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, with or without
   6  * modification, are permitted provided that the following conditions
   7  * are met:
   8  * 1. Redistributions of source code must retain the above copyright
   9  *    notice, this list of conditions and the following disclaimer.
  10  * 2. Redistributions in binary form must reproduce the above copyright
  11  *    notice, this list of conditions and the following disclaimer in the
  12  *    documentation and/or other materials provided with the distribution.
  13  * 3. [rescinded 22 July 1999]
  14  * 4. Neither the name of the University nor the names of its contributors
  15  *    may be used to endorse or promote products derived from this software
  16  *    without specific prior written permission.
  17  *
  18  * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
  19  * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
  20  * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
  21  * ARE DISCLAIMED.  IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
  22  * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
  23  * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
  24  * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
  25  * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
  26  * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
  27  * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
  28  * SUCH DAMAGE.
  29  */
  30
  31 /*
  32  * This is derived from the Berkeley source:
  33  *      @(#)random.c    5.5 (Berkeley) 7/6/88
  34  * It was reworked for the GNU C Library by Roland McGrath.
  35  */
  36
  37 /*
  38
  39 @deftypefn Supplement {long int} random (void)
  40 @deftypefnx Supplement void srandom (unsigned int @var{seed})
  41 @deftypefnx Supplement void* initstate (unsigned int @var{seed}, void *@var{arg_state}, unsigned long @var{n})
  42 @deftypefnx Supplement void* setstate (void *@var{arg_state})
  43
  44 Random number functions.  @code{random} returns a random number in the
  45 range 0 to @code{LONG_MAX}.  @code{srandom} initializes the random
  46 number generator to some starting point determined by @var{seed}
  47 (else, the values returned by @code{random} are always the same for each
  48 run of the program).  @code{initstate} and @code{setstate} allow fine-grained
  49 control over the state of the random number generator.
  50
  51 @end deftypefn
  52
  53 */
  54
  55 #include <errno.h>
  56
  57 #if 0
  58
  59 #include <ansidecl.h>
  60 #include <limits.h>
  61 #include <stddef.h>
  62 #include <stdlib.h>
  63
  64 #else
  65
  66 #define ULONG_MAX  ((unsigned long)(~0L))     /* 0xFFFFFFFF for 32-bits */
  67 #define LONG_MAX   ((long)(ULONG_MAX >> 1))   /* 0x7FFFFFFF for 32-bits*/
  68
  69 #ifdef __STDC__
  70 #  define PTR void *
  71 #  ifndef NULL
  72 #    define NULL (void *) 0
  73 #  endif
  74 #else
  75 #  define PTR char *
  76 #  ifndef NULL
  77 #    define NULL (void *) 0
  78 #  endif
  79 #endif
  80
  81 #endif
  82
  83 long int random ();
  84
  85 /* An improved random number generation package.  In addition to the standard
  86    rand()/srand() like interface, this package also has a special state info
  87    interface.  The initstate() routine is called with a seed, an array of
  88    bytes, and a count of how many bytes are being passed in; this array is
  89    then initialized to contain information for random number generation with
  90    that much state information.  Good sizes for the amount of state
  91    information are 32, 64, 128, and 256 bytes.  The state can be switched by
  92    calling the setstate() function with the same array as was initiallized
  93    with initstate().  By default, the package runs with 128 bytes of state
  94    information and generates far better random numbers than a linear
  95    congruential generator.  If the amount of state information is less than
  96    32 bytes, a simple linear congruential R.N.G. is used.  Internally, the
  97    state information is treated as an array of longs; the zeroeth element of
  98    the array is the type of R.N.G. being used (small integer); the remainder
  99    of the array is the state information for the R.N.G.  Thus, 32 bytes of
 100    state information will give 7 longs worth of state information, which will
 101    allow a degree seven polynomial.  (Note: The zeroeth word of state
 102    information also has some other information stored in it; see setstate
 103    for details).  The random number generation technique is a linear feedback
 104    shift register approach, employing trinomials (since there are fewer terms
 105    to sum up that way).  In this approach, the least significant bit of all
 106    the numbers in the state table will act as a linear feedback shift register,
 107    and will have period 2^deg - 1 (where deg is the degree of the polynomial
 108    being used, assuming that the polynomial is irreducible and primitive).
 109    The higher order bits will have longer periods, since their values are
 110    also influenced by pseudo-random carries out of the lower bits.  The
 111    total period of the generator is approximately deg*(2**deg - 1); thus
 112    doubling the amount of state information has a vast influence on the
 113    period of the generator.  Note: The deg*(2**deg - 1) is an approximation
 114    only good for large deg, when the period of the shift register is the
 115    dominant factor.  With deg equal to seven, the period is actually much
 116    longer than the 7*(2**7 - 1) predicted by this formula.  */
 117
 118
 119
 120 /* For each of the currently supported random number generators, we have a
 121    break value on the amount of state information (you need at least thi
 122    bytes of state info to support this random number generator), a degree for
 123    the polynomial (actually a trinomial) that the R.N.G. is based on, and
 124    separation between the two lower order coefficients of the trinomial.  */
 125
 126 /* Linear congruential.  */
 127 #define TYPE_0          0
 128 #define BREAK_0         8
 129 #define DEG_0           0
 130 #define SEP_0           0
 131
 132 /* x**7 + x**3 + 1.  */
 133 #define TYPE_1          1
 134 #define BREAK_1         32
 135 #define DEG_1           7
 136 #define SEP_1           3
 137
 138 /* x**15 + x + 1.  */
 139 #define TYPE_2          2
 140 #define BREAK_2         64
 141 #define DEG_2           15
 142 #define SEP_2           1
 143
 144 /* x**31 + x**3 + 1.  */
 145 #define TYPE_3          3
 146 #define BREAK_3         128
 147 #define DEG_3           31
 148 #define SEP_3           3
 149
 150 /* x**63 + x + 1.  */
 151 #define TYPE_4          4
 152 #define BREAK_4         256
 153 #define DEG_4           63
 154 #define SEP_4           1
 155
 156
 157 /* Array versions of the above information to make code run faster.
 158    Relies on fact that TYPE_i == i.  */
 159
 160 #define MAX_TYPES       5       /* Max number of types above.  */
 161
 162 static int degrees[MAX_TYPES] = { DEG_0, DEG_1, DEG_2, DEG_3, DEG_4 };
 163 static int seps[MAX_TYPES] = { SEP_0, SEP_1, SEP_2, SEP_3, SEP_4 };
 164
 165
 166
 167 /* Initially, everything is set up as if from:
 168         initstate(1, randtbl, 128);
 169    Note that this initialization takes advantage of the fact that srandom
 170    advances the front and rear pointers 10*rand_deg times, and hence the
 171    rear pointer which starts at 0 will also end up at zero; thus the zeroeth
 172    element of the state information, which contains info about the current
 173    position of the rear pointer is just
 174         (MAX_TYPES * (rptr - state)) + TYPE_3 == TYPE_3.  */
 175
 176 static long int randtbl[DEG_3 + 1] =
 177   { TYPE_3,
 178       0x9a319039, 0x32d9c024, 0x9b663182, 0x5da1f342,
 179       0xde3b81e0, 0xdf0a6fb5, 0xf103bc02, 0x48f340fb,
 180       0x7449e56b, 0xbeb1dbb0, 0xab5c5918, 0x946554fd,
 181       0x8c2e680f, 0xeb3d799f, 0xb11ee0b7, 0x2d436b86,
 182       0xda672e2a, 0x1588ca88, 0xe369735d, 0x904f35f7,
 183       0xd7158fd6, 0x6fa6f051, 0x616e6b96, 0xac94efdc,
 184       0x36413f93, 0xc622c298, 0xf5a42ab8, 0x8a88d77b,
 185       0xf5ad9d0e, 0x8999220b, 0x27fb47b9
 186     };
 187
 188 /* FPTR and RPTR are two pointers into the state info, a front and a rear
 189    pointer.  These two pointers are always rand_sep places aparts, as they
 190    cycle through the state information.  (Yes, this does mean we could get
 191    away with just one pointer, but the code for random is more efficient
 192    this way).  The pointers are left positioned as they would be from the call:
 193         initstate(1, randtbl, 128);
 194    (The position of the rear pointer, rptr, is really 0 (as explained above
 195    in the initialization of randtbl) because the state table pointer is set
 196    to point to randtbl[1] (as explained below).)  */
 197
 198 static long int *fptr = &randtbl[SEP_3 + 1];
 199 static long int *rptr = &randtbl[1];
 200
 201
 202
 203 /* The following things are the pointer to the state information table,
 204    the type of the current generator, the degree of the current polynomial
 205    being used, and the separation between the two pointers.
 206    Note that for efficiency of random, we remember the first location of
 207    the state information, not the zeroeth.  Hence it is valid to access
 208    state[-1], which is used to store the type of the R.N.G.
 209    Also, we remember the last location, since this is more efficient than
 210    indexing every time to find the address of the last element to see if
 211    the front and rear pointers have wrapped.  */
 212
 213 static long int *state = &randtbl[1];
 214
 215 static int rand_type = TYPE_3;
 216 static int rand_deg = DEG_3;
 217 static int rand_sep = SEP_3;
 218
 219 static long int *end_ptr = &randtbl[sizeof(randtbl) / sizeof(randtbl[0])];
 220 \f
 221 /* Initialize the random number generator based on the given seed.  If the
 222    type is the trivial no-state-information type, just remember the seed.
 223    Otherwise, initializes state[] based on the given "seed" via a linear
 224    congruential generator.  Then, the pointers are set to known locations
 225    that are exactly rand_sep places apart.  Lastly, it cycles the state
 226    information a given number of times to get rid of any initial dependencies
 227    introduced by the L.C.R.N.G.  Note that the initialization of randtbl[]
 228    for default usage relies on values produced by this routine.  */
 229 void
 230 srandom (x)
 231   unsigned int x;
 232 {
 233   state[0] = x;
 234   if (rand_type != TYPE_0)
 235     {
 236       register long int i;
 237       for (i = 1; i < rand_deg; ++i)
 238         state[i] = (1103515145 * state[i - 1]) + 12345;
 239       fptr = &state[rand_sep];
 240       rptr = &state[0];
 241       for (i = 0; i < 10 * rand_deg; ++i)
 242         random();
 243     }
 244 }
 245 \f
 246 /* Initialize the state information in the given array of N bytes for
 247    future random number generation.  Based on the number of bytes we
 248    are given, and the break values for the different R.N.G.'s, we choose
 249    the best (largest) one we can and set things up for it.  srandom is
 250    then called to initialize the state information.  Note that on return
 251    from srandom, we set state[-1] to be the type multiplexed with the current
 252    value of the rear pointer; this is so successive calls to initstate won't
 253    lose this information and will be able to restart with setstate.
 254    Note: The first thing we do is save the current state, if any, just like
 255    setstate so that it doesn't matter when initstate is called.
 256    Returns a pointer to the old state.  */
 257 PTR
 258 initstate (seed, arg_state, n)
 259   unsigned int seed;
 260   PTR arg_state;
 261   unsigned long n;
 262 {
 263   PTR ostate = (PTR) &state[-1];
 264
 265   if (rand_type == TYPE_0)
 266     state[-1] = rand_type;
 267   else
 268     state[-1] = (MAX_TYPES * (rptr - state)) + rand_type;
 269   if (n < BREAK_1)
 270     {
 271       if (n < BREAK_0)
 272         {
 273           errno = EINVAL;
 274           return NULL;
 275         }
 276       rand_type = TYPE_0;
 277       rand_deg = DEG_0;
 278       rand_sep = SEP_0;
 279     }
 280   else if (n < BREAK_2)
 281     {
 282       rand_type = TYPE_1;
 283       rand_deg = DEG_1;
 284       rand_sep = SEP_1;
 285     }
 286   else if (n < BREAK_3)
 287     {
 288       rand_type = TYPE_2;
 289       rand_deg = DEG_2;
 290       rand_sep = SEP_2;
 291     }
 292   else if (n < BREAK_4)
 293     {
 294       rand_type = TYPE_3;
 295       rand_deg = DEG_3;
 296       rand_sep = SEP_3;
 297     }
 298   else
 299     {
 300       rand_type = TYPE_4;
 301       rand_deg = DEG_4;
 302       rand_sep = SEP_4;
 303     }
 304
 305   state = &((long int *) arg_state)[1]; /* First location.  */
 306   /* Must set END_PTR before srandom.  */
 307   end_ptr = &state[rand_deg];
 308   srandom(seed);
 309   if (rand_type == TYPE_0)
 310     state[-1] = rand_type;
 311   else
 312     state[-1] = (MAX_TYPES * (rptr - state)) + rand_type;
 313
 314   return ostate;
 315 }
 316 \f
 317 /* Restore the state from the given state array.
 318    Note: It is important that we also remember the locations of the pointers
 319    in the current state information, and restore the locations of the pointers
 320    from the old state information.  This is done by multiplexing the pointer
 321    location into the zeroeth word of the state information. Note that due
 322    to the order in which things are done, it is OK to call setstate with the
 323    same state as the current state
 324    Returns a pointer to the old state information.  */
 325
 326 PTR
 327 setstate (arg_state)
 328   PTR arg_state;
 329 {
 330   register long int *new_state = (long int *) arg_state;
 331   register int type = new_state[0] % MAX_TYPES;
 332   register int rear = new_state[0] / MAX_TYPES;
 333   PTR ostate = (PTR) &state[-1];
 334
 335   if (rand_type == TYPE_0)
 336     state[-1] = rand_type;
 337   else
 338     state[-1] = (MAX_TYPES * (rptr - state)) + rand_type;
 339
 340   switch (type)
 341     {
 342     case TYPE_0:
 343     case TYPE_1:
 344     case TYPE_2:
 345     case TYPE_3:
 346     case TYPE_4:
 347       rand_type = type;
 348       rand_deg = degrees[type];
 349       rand_sep = seps[type];
 350       break;
 351     default:
 352       /* State info munged.  */
 353       errno = EINVAL;
 354       return NULL;
 355     }
 356
 357   state = &new_state[1];
 358   if (rand_type != TYPE_0)
 359     {
 360       rptr = &state[rear];
 361       fptr = &state[(rear + rand_sep) % rand_deg];
 362     }
 363   /* Set end_ptr too.  */
 364   end_ptr = &state[rand_deg];
 365
 366   return ostate;
 367 }
 368 \f
 369 /* If we are using the trivial TYPE_0 R.N.G., just do the old linear
 370    congruential bit.  Otherwise, we do our fancy trinomial stuff, which is the
 371    same in all ther other cases due to all the global variables that have been
 372    set up.  The basic operation is to add the number at the rear pointer into
 373    the one at the front pointer.  Then both pointers are advanced to the next
 374    location cyclically in the table.  The value returned is the sum generated,
 375    reduced to 31 bits by throwing away the "least random" low bit.
 376    Note: The code takes advantage of the fact that both the front and
 377    rear pointers can't wrap on the same call by not testing the rear
 378    pointer if the front one has wrapped.  Returns a 31-bit random number.  */
 379
 380 long int
 381 random ()
 382 {
 383   if (rand_type == TYPE_0)
 384     {
 385       state[0] = ((state[0] * 1103515245) + 12345) & LONG_MAX;
 386       return state[0];
 387     }
 388   else
 389     {
 390       long int i;
 391       *fptr += *rptr;
 392       /* Chucking least random bit.  */
 393       i = (*fptr >> 1) & LONG_MAX;
 394       ++fptr;
 395       if (fptr >= end_ptr)
 396         {
 397           fptr = state;
 398           ++rptr;
 399         }
 400       else
 401         {
 402           ++rptr;
 403           if (rptr >= end_ptr)
 404             rptr = state;
 405         }
 406       return i;
 407     }
 408 }