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 [rescinded 22 July 1999]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