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  * Rewritten to use reentrant functions by Ulrich Drepper, 1995.
  23  */
  24
  25 #include <bits/libc-lock.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 initialized
  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 zeroth 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 zeroth 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 this many
  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
 109 /* Initially, everything is set up as if from:
 110         initstate(1, randtbl, 128);
 111    Note that this initialization takes advantage of the fact that srandom
 112    advances the front and rear pointers 10*rand_deg times, and hence the
 113    rear pointer which starts at 0 will also end up at zero; thus the zeroth
 114    element of the state information, which contains info about the current
 115    position of the rear pointer is just
 116         (MAX_TYPES * (rptr - state)) + TYPE_3 == TYPE_3.  */
 117
 118 static int32_t randtbl[DEG_3 + 1] =
 119   {
 120     TYPE_3,
 121
 122     -1726662223, 379960547, 1735697613, 1040273694, 1313901226,
 123     1627687941, -179304937, -2073333483, 1780058412, -1989503057,
 124     -615974602, 344556628, 939512070, -1249116260, 1507946756,
 125     -812545463, 154635395, 1388815473, -1926676823, 525320961,
 126     -1009028674, 968117788, -123449607, 1284210865, 435012392,
 127     -2017506339, -911064859, -370259173, 1132637927, 1398500161,
 128     -205601318,
 129   };
 130
 131
 132 static struct random_data unsafe_state =
 133   {
 134 /* FPTR and RPTR are two pointers into the state info, a front and a rear
 135    pointer.  These two pointers are always rand_sep places aparts, as they
 136    cycle through the state information.  (Yes, this does mean we could get
 137    away with just one pointer, but the code for random is more efficient
 138    this way).  The pointers are left positioned as they would be from the call:
 139         initstate(1, randtbl, 128);
 140    (The position of the rear pointer, rptr, is really 0 (as explained above
 141    in the initialization of randtbl) because the state table pointer is set
 142    to point to randtbl[1] (as explained below).)  */
 143
 144     fptr : &randtbl[SEP_3 + 1],
 145     rptr : &randtbl[1],
 146
 147 /* The following things are the pointer to the state information table,
 148    the type of the current generator, the degree of the current polynomial
 149    being used, and the separation between the two pointers.
 150    Note that for efficiency of random, we remember the first location of
 151    the state information, not the zeroth.  Hence it is valid to access
 152    state[-1], which is used to store the type of the R.N.G.
 153    Also, we remember the last location, since this is more efficient than
 154    indexing every time to find the address of the last element to see if
 155    the front and rear pointers have wrapped.  */
 156
 157     state : &randtbl[1],
 158
 159     rand_type : TYPE_3,
 160     rand_deg : DEG_3,
 161     rand_sep : SEP_3,
 162
 163     end_ptr : &randtbl[sizeof (randtbl) / sizeof (randtbl[0])]
 164 };
 165 \f
 166 /* POSIX.1c requires that there is mutual exclusion for the `rand' and
 167    `srand' functions to prevent concurrent calls from modifying common
 168    data.  */
 169 __libc_lock_define_initialized (static, lock)
 170 \f
 171 /* Initialize the random number generator based on the given seed.  If the
 172    type is the trivial no-state-information type, just remember the seed.
 173    Otherwise, initializes state[] based on the given "seed" via a linear
 174    congruential generator.  Then, the pointers are set to known locations
 175    that are exactly rand_sep places apart.  Lastly, it cycles the state
 176    information a given number of times to get rid of any initial dependencies
 177    introduced by the L.C.R.N.G.  Note that the initialization of randtbl[]
 178    for default usage relies on values produced by this routine.  */
 179 void
 180 __srandom (x)
 181      unsigned int x;
 182 {
 183   __libc_lock_lock (lock);
 184   (void) __srandom_r (x, &unsafe_state);
 185   __libc_lock_unlock (lock);
 186 }
 187
 188 weak_alias (__srandom, srandom)
 189 weak_alias (__srandom, srand)
 190 \f
 191 /* Initialize the state information in the given array of N bytes for
 192    future random number generation.  Based on the number of bytes we
 193    are given, and the break values for the different R.N.G.'s, we choose
 194    the best (largest) one we can and set things up for it.  srandom is
 195    then called to initialize the state information.  Note that on return
 196    from srandom, we set state[-1] to be the type multiplexed with the current
 197    value of the rear pointer; this is so successive calls to initstate won't
 198    lose this information and will be able to restart with setstate.
 199    Note: The first thing we do is save the current state, if any, just like
 200    setstate so that it doesn't matter when initstate is called.
 201    Returns a pointer to the old state.  */
 202 char *
 203 __initstate (seed, arg_state, n)
 204      unsigned int seed;
 205      char *arg_state;
 206      size_t n;
 207 {
 208   int32_t *ostate;
 209
 210   __libc_lock_lock (lock);
 211
 212   ostate = &unsafe_state.state[-1];
 213
 214   __initstate_r (seed, arg_state, n, &unsafe_state);
 215
 216   __libc_lock_unlock (lock);
 217
 218   return (char *) ostate;
 219 }
 220
 221 weak_alias (__initstate, initstate)
 222 \f
 223 /* Restore the state from the given state array.
 224    Note: It is important that we also remember the locations of the pointers
 225    in the current state information, and restore the locations of the pointers
 226    from the old state information.  This is done by multiplexing the pointer
 227    location into the zeroth word of the state information. Note that due
 228    to the order in which things are done, it is OK to call setstate with the
 229    same state as the current state
 230    Returns a pointer to the old state information.  */
 231 char *
 232 __setstate (arg_state)
 233      char *arg_state;
 234 {
 235   int32_t *ostate;
 236
 237   __libc_lock_lock (lock);
 238
 239   ostate = &unsafe_state.state[-1];
 240
 241   if (__setstate_r (arg_state, &unsafe_state) < 0)
 242     ostate = NULL;
 243
 244   __libc_lock_unlock (lock);
 245
 246   return (char *) ostate;
 247 }
 248
 249 weak_alias (__setstate, setstate)
 250 \f
 251 /* If we are using the trivial TYPE_0 R.N.G., just do the old linear
 252    congruential bit.  Otherwise, we do our fancy trinomial stuff, which is the
 253    same in all the other cases due to all the global variables that have been
 254    set up.  The basic operation is to add the number at the rear pointer into
 255    the one at the front pointer.  Then both pointers are advanced to the next
 256    location cyclically in the table.  The value returned is the sum generated,
 257    reduced to 31 bits by throwing away the "least random" low bit.
 258    Note: The code takes advantage of the fact that both the front and
 259    rear pointers can't wrap on the same call by not testing the rear
 260    pointer if the front one has wrapped.  Returns a 31-bit random number.  */
 261
 262 long int
 263 __random ()
 264 {
 265   int32_t retval;
 266
 267   __libc_lock_lock (lock);
 268
 269   (void) __random_r (&unsafe_state, &retval);
 270
 271   __libc_lock_unlock (lock);
 272
 273   return retval;
 274 }
 275
 276 weak_alias (__random, random)