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 reentrent functions by Ulrich Drepper, 1995.
  23  */
  24
  25 #include <limits.h>
  26 #include <stddef.h>
  27 #include <stdlib.h>
  28
  29
  30 /* An improved random number generation package.  In addition to the standard
  31    rand()/srand() like interface, this package also has a special state info
  32    interface.  The initstate() routine is called with a seed, an array of
  33    bytes, and a count of how many bytes are being passed in; this array is
  34    then initialized to contain information for random number generation with
  35    that much state information.  Good sizes for the amount of state
  36    information are 32, 64, 128, and 256 bytes.  The state can be switched by
  37    calling the setstate() function with the same array as was initiallized
  38    with initstate().  By default, the package runs with 128 bytes of state
  39    information and generates far better random numbers than a linear
  40    congruential generator.  If the amount of state information is less than
  41    32 bytes, a simple linear congruential R.N.G. is used.  Internally, the
  42    state information is treated as an array of longs; the zeroeth element of
  43    the array is the type of R.N.G. being used (small integer); the remainder
  44    of the array is the state information for the R.N.G.  Thus, 32 bytes of
  45    state information will give 7 longs worth of state information, which will
  46    allow a degree seven polynomial.  (Note: The zeroeth word of state
  47    information also has some other information stored in it; see setstate
  48    for details).  The random number generation technique is a linear feedback
  49    shift register approach, employing trinomials (since there are fewer terms
  50    to sum up that way).  In this approach, the least significant bit of all
  51    the numbers in the state table will act as a linear feedback shift register,
  52    and will have period 2^deg - 1 (where deg is the degree of the polynomial
  53    being used, assuming that the polynomial is irreducible and primitive).
  54    The higher order bits will have longer periods, since their values are
  55    also influenced by pseudo-random carries out of the lower bits.  The
  56    total period of the generator is approximately deg*(2**deg - 1); thus
  57    doubling the amount of state information has a vast influence on the
  58    period of the generator.  Note: The deg*(2**deg - 1) is an approximation
  59    only good for large deg, when the period of the shift register is the
  60    dominant factor.  With deg equal to seven, the period is actually much
  61    longer than the 7*(2**7 - 1) predicted by this formula.  */
  62
  63
  64
  65 /* For each of the currently supported random number generators, we have a
  66    break value on the amount of state information (you need at least thi
  67    bytes of state info to support this random number generator), a degree for
  68    the polynomial (actually a trinomial) that the R.N.G. is based on, and
  69    separation between the two lower order coefficients of the trinomial.  */
  70
  71 /* Linear congruential.  */
  72 #define TYPE_0          0
  73 #define BREAK_0         8
  74 #define DEG_0           0
  75 #define SEP_0           0
  76
  77 /* x**7 + x**3 + 1.  */
  78 #define TYPE_1          1
  79 #define BREAK_1         32
  80 #define DEG_1           7
  81 #define SEP_1           3
  82
  83 /* x**15 + x + 1.  */
  84 #define TYPE_2          2
  85 #define BREAK_2         64
  86 #define DEG_2           15
  87 #define SEP_2           1
  88
  89 /* x**31 + x**3 + 1.  */
  90 #define TYPE_3          3
  91 #define BREAK_3         128
  92 #define DEG_3           31
  93 #define SEP_3           3
  94
  95 /* x**63 + x + 1.  */
  96 #define TYPE_4          4
  97 #define BREAK_4         256
  98 #define DEG_4           63
  99 #define SEP_4           1
 100
 101
 102 /* Array versions of the above information to make code run faster.
 103    Relies on fact that TYPE_i == i.  */
 104
 105 #define MAX_TYPES       5       /* Max number of types above.  */
 106
 107
 108 /* Initially, everything is set up as if from:
 109         initstate(1, randtbl, 128);
 110    Note that this initialization takes advantage of the fact that srandom
 111    advances the front and rear pointers 10*rand_deg times, and hence the
 112    rear pointer which starts at 0 will also end up at zero; thus the zeroeth
 113    element of the state information, which contains info about the current
 114    position of the rear pointer is just
 115         (MAX_TYPES * (rptr - state)) + TYPE_3 == TYPE_3.  */
 116
 117 static long int randtbl[DEG_3 + 1] =
 118   {
 119     TYPE_3,
 120
 121     -1726662223, 379960547, 1735697613, 1040273694, 1313901226,
 122     1627687941, -179304937, -2073333483, 1780058412, -1989503057,
 123     -615974602, 344556628, 939512070, -1249116260, 1507946756,
 124     -812545463, 154635395, 1388815473, -1926676823, 525320961,
 125     -1009028674, 968117788, -123449607, 1284210865, 435012392,
 126     -2017506339, -911064859, -370259173, 1132637927, 1398500161,
 127     -205601318,
 128   };
 129
 130
 131 static struct random_data unsafe_state =
 132   {
 133 /* FPTR and RPTR are two pointers into the state info, a front and a rear
 134    pointer.  These two pointers are always rand_sep places aparts, as they
 135    cycle through the state information.  (Yes, this does mean we could get
 136    away with just one pointer, but the code for random is more efficient
 137    this way).  The pointers are left positioned as they would be from the call:
 138         initstate(1, randtbl, 128);
 139    (The position of the rear pointer, rptr, is really 0 (as explained above
 140    in the initialization of randtbl) because the state table pointer is set
 141    to point to randtbl[1] (as explained below).)  */
 142
 143     fptr : &randtbl[SEP_3 + 1],
 144     rptr : &randtbl[1],
 145
 146 /* The following things are the pointer to the state information table,
 147    the type of the current generator, the degree of the current polynomial
 148    being used, and the separation between the two pointers.
 149    Note that for efficiency of random, we remember the first location of
 150    the state information, not the zeroeth.  Hence it is valid to access
 151    state[-1], which is used to store the type of the R.N.G.
 152    Also, we remember the last location, since this is more efficient than
 153    indexing every time to find the address of the last element to see if
 154    the front and rear pointers have wrapped.  */
 155
 156     state : &randtbl[1],
 157
 158     rand_type : TYPE_3,
 159     rand_deg : DEG_3,
 160     rand_sep : SEP_3,
 161
 162     end_ptr : &randtbl[sizeof (randtbl) / sizeof (randtbl[0])]
 163 };
 164 \f
 165 /* Initialize the random number generator based on the given seed.  If the
 166    type is the trivial no-state-information type, just remember the seed.
 167    Otherwise, initializes state[] based on the given "seed" via a linear
 168    congruential generator.  Then, the pointers are set to known locations
 169    that are exactly rand_sep places apart.  Lastly, it cycles the state
 170    information a given number of times to get rid of any initial dependencies
 171    introduced by the L.C.R.N.G.  Note that the initialization of randtbl[]
 172    for default usage relies on values produced by this routine.  */
 173 void
 174 __srandom (x)
 175      unsigned int x;
 176 {
 177   (void) __srandom_r (x, &unsafe_state);
 178 }
 179
 180 weak_alias (__srandom, srandom)
 181 weak_alias (__srandom, srand)
 182 \f
 183 /* Initialize the state information in the given array of N bytes for
 184    future random number generation.  Based on the number of bytes we
 185    are given, and the break values for the different R.N.G.'s, we choose
 186    the best (largest) one we can and set things up for it.  srandom is
 187    then called to initialize the state information.  Note that on return
 188    from srandom, we set state[-1] to be the type multiplexed with the current
 189    value of the rear pointer; this is so successive calls to initstate won't
 190    lose this information and will be able to restart with setstate.
 191    Note: The first thing we do is save the current state, if any, just like
 192    setstate so that it doesn't matter when initstate is called.
 193    Returns a pointer to the old state.  */
 194 void *
 195 __initstate (seed, arg_state, n)
 196      unsigned int seed;
 197      void *arg_state;
 198      size_t n;
 199 {
 200   void *ostate = (void *) &unsafe_state.state[-1];
 201
 202   __initstate_r (seed, arg_state, n, &unsafe_state);
 203
 204   return ostate;
 205 }
 206
 207 weak_alias (__initstate, initstate)
 208 \f
 209 /* Restore the state from the given state array.
 210    Note: It is important that we also remember the locations of the pointers
 211    in the current state information, and restore the locations of the pointers
 212    from the old state information.  This is done by multiplexing the pointer
 213    location into the zeroeth word of the state information. Note that due
 214    to the order in which things are done, it is OK to call setstate with the
 215    same state as the current state
 216    Returns a pointer to the old state information.  */
 217 void *
 218 __setstate (arg_state)
 219      void *arg_state;
 220 {
 221   void *ostate = (void *) &unsafe_state.state[-1];
 222
 223   if (__setstate_r (arg_state, &unsafe_state) < 0)
 224     return NULL;
 225
 226   return ostate;
 227 }
 228
 229 weak_alias (__setstate, setstate)
 230 \f
 231 /* If we are using the trivial TYPE_0 R.N.G., just do the old linear
 232    congruential bit.  Otherwise, we do our fancy trinomial stuff, which is the
 233    same in all ther other cases due to all the global variables that have been
 234    set up.  The basic operation is to add the number at the rear pointer into
 235    the one at the front pointer.  Then both pointers are advanced to the next
 236    location cyclically in the table.  The value returned is the sum generated,
 237    reduced to 31 bits by throwing away the "least random" low bit.
 238    Note: The code takes advantage of the fact that both the front and
 239    rear pointers can't wrap on the same call by not testing the rear
 240    pointer if the front one has wrapped.  Returns a 31-bit random number.  */
 241
 242 long int
 243 __random ()
 244 {
 245   long int retval;
 246
 247   (void) __random_r (&unsafe_state, &retval);
 248
 249   return retval;
 250 }
 251
 252 weak_alias (__random, random)