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 [rescinded 22 July 1999]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