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 [rescinded 22 July 1999]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 #  ifndef NULL
  72 #    define NULL (void *) 0
  73 #  endif
  74 #else
  75 #  ifndef NULL
  76 #    define NULL (void *) 0
  77 #  endif
  78 #endif
  79
  80 #endif
  81
  82 long int random (void);
  83
  84 /* An improved random number generation package.  In addition to the standard
  85    rand()/srand() like interface, this package also has a special state info
  86    interface.  The initstate() routine is called with a seed, an array of
  87    bytes, and a count of how many bytes are being passed in; this array is
  88    then initialized to contain information for random number generation with
  89    that much state information.  Good sizes for the amount of state
  90    information are 32, 64, 128, and 256 bytes.  The state can be switched by
  91    calling the setstate() function with the same array as was initiallized
  92    with initstate().  By default, the package runs with 128 bytes of state
  93    information and generates far better random numbers than a linear
  94    congruential generator.  If the amount of state information is less than
  95    32 bytes, a simple linear congruential R.N.G. is used.  Internally, the
  96    state information is treated as an array of longs; the zeroeth element of
  97    the array is the type of R.N.G. being used (small integer); the remainder
  98    of the array is the state information for the R.N.G.  Thus, 32 bytes of
  99    state information will give 7 longs worth of state information, which will
 100    allow a degree seven polynomial.  (Note: The zeroeth word of state
 101    information also has some other information stored in it; see setstate
 102    for details).  The random number generation technique is a linear feedback
 103    shift register approach, employing trinomials (since there are fewer terms
 104    to sum up that way).  In this approach, the least significant bit of all
 105    the numbers in the state table will act as a linear feedback shift register,
 106    and will have period 2^deg - 1 (where deg is the degree of the polynomial
 107    being used, assuming that the polynomial is irreducible and primitive).
 108    The higher order bits will have longer periods, since their values are
 109    also influenced by pseudo-random carries out of the lower bits.  The
 110    total period of the generator is approximately deg*(2**deg - 1); thus
 111    doubling the amount of state information has a vast influence on the
 112    period of the generator.  Note: The deg*(2**deg - 1) is an approximation
 113    only good for large deg, when the period of the shift register is the
 114    dominant factor.  With deg equal to seven, the period is actually much
 115    longer than the 7*(2**7 - 1) predicted by this formula.  */
 116
 117
 118
 119 /* For each of the currently supported random number generators, we have a
 120    break value on the amount of state information (you need at least thi
 121    bytes of state info to support this random number generator), a degree for
 122    the polynomial (actually a trinomial) that the R.N.G. is based on, and
 123    separation between the two lower order coefficients of the trinomial.  */
 124
 125 /* Linear congruential.  */
 126 #define TYPE_0          0
 127 #define BREAK_0         8
 128 #define DEG_0           0
 129 #define SEP_0           0
 130
 131 /* x**7 + x**3 + 1.  */
 132 #define TYPE_1          1
 133 #define BREAK_1         32
 134 #define DEG_1           7
 135 #define SEP_1           3
 136
 137 /* x**15 + x + 1.  */
 138 #define TYPE_2          2
 139 #define BREAK_2         64
 140 #define DEG_2           15
 141 #define SEP_2           1
 142
 143 /* x**31 + x**3 + 1.  */
 144 #define TYPE_3          3
 145 #define BREAK_3         128
 146 #define DEG_3           31
 147 #define SEP_3           3
 148
 149 /* x**63 + x + 1.  */
 150 #define TYPE_4          4
 151 #define BREAK_4         256
 152 #define DEG_4           63
 153 #define SEP_4           1
 154
 155
 156 /* Array versions of the above information to make code run faster.
 157    Relies on fact that TYPE_i == i.  */
 158
 159 #define MAX_TYPES       5       /* Max number of types above.  */
 160
 161 static int degrees[MAX_TYPES] = { DEG_0, DEG_1, DEG_2, DEG_3, DEG_4 };
 162 static int seps[MAX_TYPES] = { SEP_0, SEP_1, SEP_2, SEP_3, SEP_4 };
 163
 164
 165
 166 /* Initially, everything is set up as if from:
 167         initstate(1, randtbl, 128);
 168    Note that this initialization takes advantage of the fact that srandom
 169    advances the front and rear pointers 10*rand_deg times, and hence the
 170    rear pointer which starts at 0 will also end up at zero; thus the zeroeth
 171    element of the state information, which contains info about the current
 172    position of the rear pointer is just
 173         (MAX_TYPES * (rptr - state)) + TYPE_3 == TYPE_3.  */
 174
 175 static long int randtbl[DEG_3 + 1] =
 176   { TYPE_3,
 177       0x9a319039, 0x32d9c024, 0x9b663182, 0x5da1f342,
 178       0xde3b81e0, 0xdf0a6fb5, 0xf103bc02, 0x48f340fb,
 179       0x7449e56b, 0xbeb1dbb0, 0xab5c5918, 0x946554fd,
 180       0x8c2e680f, 0xeb3d799f, 0xb11ee0b7, 0x2d436b86,
 181       0xda672e2a, 0x1588ca88, 0xe369735d, 0x904f35f7,
 182       0xd7158fd6, 0x6fa6f051, 0x616e6b96, 0xac94efdc,
 183       0x36413f93, 0xc622c298, 0xf5a42ab8, 0x8a88d77b,
 184       0xf5ad9d0e, 0x8999220b, 0x27fb47b9
 185     };
 186
 187 /* FPTR and RPTR are two pointers into the state info, a front and a rear
 188    pointer.  These two pointers are always rand_sep places aparts, as they
 189    cycle through the state information.  (Yes, this does mean we could get
 190    away with just one pointer, but the code for random is more efficient
 191    this way).  The pointers are left positioned as they would be from the call:
 192         initstate(1, randtbl, 128);
 193    (The position of the rear pointer, rptr, is really 0 (as explained above
 194    in the initialization of randtbl) because the state table pointer is set
 195    to point to randtbl[1] (as explained below).)  */
 196
 197 static long int *fptr = &randtbl[SEP_3 + 1];
 198 static long int *rptr = &randtbl[1];
 199
 200
 201
 202 /* The following things are the pointer to the state information table,
 203    the type of the current generator, the degree of the current polynomial
 204    being used, and the separation between the two pointers.
 205    Note that for efficiency of random, we remember the first location of
 206    the state information, not the zeroeth.  Hence it is valid to access
 207    state[-1], which is used to store the type of the R.N.G.
 208    Also, we remember the last location, since this is more efficient than
 209    indexing every time to find the address of the last element to see if
 210    the front and rear pointers have wrapped.  */
 211
 212 static long int *state = &randtbl[1];
 213
 214 static int rand_type = TYPE_3;
 215 static int rand_deg = DEG_3;
 216 static int rand_sep = SEP_3;
 217
 218 static long int *end_ptr = &randtbl[sizeof(randtbl) / sizeof(randtbl[0])];
 219 \f
 220 /* Initialize the random number generator based on the given seed.  If the
 221    type is the trivial no-state-information type, just remember the seed.
 222    Otherwise, initializes state[] based on the given "seed" via a linear
 223    congruential generator.  Then, the pointers are set to known locations
 224    that are exactly rand_sep places apart.  Lastly, it cycles the state
 225    information a given number of times to get rid of any initial dependencies
 226    introduced by the L.C.R.N.G.  Note that the initialization of randtbl[]
 227    for default usage relies on values produced by this routine.  */
 228 void
 229 srandom (unsigned int x)
 230 {
 231   state[0] = x;
 232   if (rand_type != TYPE_0)
 233     {
 234       register long int i;
 235       for (i = 1; i < rand_deg; ++i)
 236         state[i] = (1103515145 * state[i - 1]) + 12345;
 237       fptr = &state[rand_sep];
 238       rptr = &state[0];
 239       for (i = 0; i < 10 * rand_deg; ++i)
 240         random();
 241     }
 242 }
 243 \f
 244 /* Initialize the state information in the given array of N bytes for
 245    future random number generation.  Based on the number of bytes we
 246    are given, and the break values for the different R.N.G.'s, we choose
 247    the best (largest) one we can and set things up for it.  srandom is
 248    then called to initialize the state information.  Note that on return
 249    from srandom, we set state[-1] to be the type multiplexed with the current
 250    value of the rear pointer; this is so successive calls to initstate won't
 251    lose this information and will be able to restart with setstate.
 252    Note: The first thing we do is save the current state, if any, just like
 253    setstate so that it doesn't matter when initstate is called.
 254    Returns a pointer to the old state.  */
 255 void *
 256 initstate (unsigned int seed, void *arg_state, unsigned long n)
 257 {
 258   void *ostate = (void *) &state[-1];
 259
 260   if (rand_type == TYPE_0)
 261     state[-1] = rand_type;
 262   else
 263     state[-1] = (MAX_TYPES * (rptr - state)) + rand_type;
 264   if (n < BREAK_1)
 265     {
 266       if (n < BREAK_0)
 267         {
 268           errno = EINVAL;
 269           return NULL;
 270         }
 271       rand_type = TYPE_0;
 272       rand_deg = DEG_0;
 273       rand_sep = SEP_0;
 274     }
 275   else if (n < BREAK_2)
 276     {
 277       rand_type = TYPE_1;
 278       rand_deg = DEG_1;
 279       rand_sep = SEP_1;
 280     }
 281   else if (n < BREAK_3)
 282     {
 283       rand_type = TYPE_2;
 284       rand_deg = DEG_2;
 285       rand_sep = SEP_2;
 286     }
 287   else if (n < BREAK_4)
 288     {
 289       rand_type = TYPE_3;
 290       rand_deg = DEG_3;
 291       rand_sep = SEP_3;
 292     }
 293   else
 294     {
 295       rand_type = TYPE_4;
 296       rand_deg = DEG_4;
 297       rand_sep = SEP_4;
 298     }
 299
 300   state = &((long int *) arg_state)[1]; /* First location.  */
 301   /* Must set END_PTR before srandom.  */
 302   end_ptr = &state[rand_deg];
 303   srandom(seed);
 304   if (rand_type == TYPE_0)
 305     state[-1] = rand_type;
 306   else
 307     state[-1] = (MAX_TYPES * (rptr - state)) + rand_type;
 308
 309   return ostate;
 310 }
 311 \f
 312 /* Restore the state from the given state array.
 313    Note: It is important that we also remember the locations of the pointers
 314    in the current state information, and restore the locations of the pointers
 315    from the old state information.  This is done by multiplexing the pointer
 316    location into the zeroeth word of the state information. Note that due
 317    to the order in which things are done, it is OK to call setstate with the
 318    same state as the current state
 319    Returns a pointer to the old state information.  */
 320
 321 void *
 322 setstate (void *arg_state)
 323 {
 324   register long int *new_state = (long int *) arg_state;
 325   register int type = new_state[0] % MAX_TYPES;
 326   register int rear = new_state[0] / MAX_TYPES;
 327   void *ostate = (void *) &state[-1];
 328
 329   if (rand_type == TYPE_0)
 330     state[-1] = rand_type;
 331   else
 332     state[-1] = (MAX_TYPES * (rptr - state)) + rand_type;
 333
 334   switch (type)
 335     {
 336     case TYPE_0:
 337     case TYPE_1:
 338     case TYPE_2:
 339     case TYPE_3:
 340     case TYPE_4:
 341       rand_type = type;
 342       rand_deg = degrees[type];
 343       rand_sep = seps[type];
 344       break;
 345     default:
 346       /* State info munged.  */
 347       errno = EINVAL;
 348       return NULL;
 349     }
 350
 351   state = &new_state[1];
 352   if (rand_type != TYPE_0)
 353     {
 354       rptr = &state[rear];
 355       fptr = &state[(rear + rand_sep) % rand_deg];
 356     }
 357   /* Set end_ptr too.  */
 358   end_ptr = &state[rand_deg];
 359
 360   return ostate;
 361 }
 362 \f
 363 /* If we are using the trivial TYPE_0 R.N.G., just do the old linear
 364    congruential bit.  Otherwise, we do our fancy trinomial stuff, which is the
 365    same in all ther other cases due to all the global variables that have been
 366    set up.  The basic operation is to add the number at the rear pointer into
 367    the one at the front pointer.  Then both pointers are advanced to the next
 368    location cyclically in the table.  The value returned is the sum generated,
 369    reduced to 31 bits by throwing away the "least random" low bit.
 370    Note: The code takes advantage of the fact that both the front and
 371    rear pointers can't wrap on the same call by not testing the rear
 372    pointer if the front one has wrapped.  Returns a 31-bit random number.  */
 373
 374 long int
 375 random (void)
 376 {
 377   if (rand_type == TYPE_0)
 378     {
 379       state[0] = ((state[0] * 1103515245) + 12345) & LONG_MAX;
 380       return state[0];
 381     }
 382   else
 383     {
 384       long int i;
 385       *fptr += *rptr;
 386       /* Chucking least random bit.  */
 387       i = (*fptr >> 1) & LONG_MAX;
 388       ++fptr;
 389       if (fptr >= end_ptr)
 390         {
 391           fptr = state;
 392           ++rptr;
 393         }
 394       else
 395         {
 396           ++rptr;
 397           if (rptr >= end_ptr)
 398             rptr = state;
 399         }
 400       return i;
 401     }
 402 }