stdlib/random.c

   1 /* Copyright (C) 1995 Free Software Foundation
   2
   3    The GNU C Library is free software; you can redistribute it and/or
   4    modify it under the terms of the GNU Lesser General Public
   5    License as published by the Free Software Foundation; either
   6    version 2.1 of the License, or (at your option) any later version.
   7
   8    The GNU C Library is distributed in the hope that it will be useful,
   9    but WITHOUT ANY WARRANTY; without even the implied warranty of
  10    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
  11    Lesser General Public License for more details.
  12
  13    You should have received a copy of the GNU Lesser General Public
  14    License along with the GNU C Library; if not, write to the Free
  15    Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
  16    02111-1307 USA.  */
  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 /*
  26    Copyright (C) 1983 Regents of the University of California.
  27    All rights reserved.
  28
  29    Redistribution and use in source and binary forms, with or without
  30    modification, are permitted provided that the following conditions
  31    are met:
  32
  33    1. Redistributions of source code must retain the above copyright
  34       notice, this list of conditions and the following disclaimer.
  35    2. Redistributions in binary form must reproduce the above copyright
  36       notice, this list of conditions and the following disclaimer in the
  37       documentation and/or other materials provided with the distribution.
  38    4. Neither the name of the University nor the names of its contributors
  39       may be used to endorse or promote products derived from this software
  40       without specific prior written permission.
  41
  42    THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
  43    ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
  44    IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
  45    ARE DISCLAIMED.  IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
  46    FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
  47    DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
  48    OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
  49    HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
  50    LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
  51    OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
  52    SUCH DAMAGE.*/
  53
  54 #include <bits/libc-lock.h>
  55 #include <limits.h>
  56 #include <stddef.h>
  57 #include <stdlib.h>
  58
  59
  60 /* An improved random number generation package.  In addition to the standard
  61    rand()/srand() like interface, this package also has a special state info
  62    interface.  The initstate() routine is called with a seed, an array of
  63    bytes, and a count of how many bytes are being passed in; this array is
  64    then initialized to contain information for random number generation with
  65    that much state information.  Good sizes for the amount of state
  66    information are 32, 64, 128, and 256 bytes.  The state can be switched by
  67    calling the setstate() function with the same array as was initialized
  68    with initstate().  By default, the package runs with 128 bytes of state
  69    information and generates far better random numbers than a linear
  70    congruential generator.  If the amount of state information is less than
  71    32 bytes, a simple linear congruential R.N.G. is used.  Internally, the
  72    state information is treated as an array of longs; the zeroth element of
  73    the array is the type of R.N.G. being used (small integer); the remainder
  74    of the array is the state information for the R.N.G.  Thus, 32 bytes of
  75    state information will give 7 longs worth of state information, which will
  76    allow a degree seven polynomial.  (Note: The zeroth word of state
  77    information also has some other information stored in it; see setstate
  78    for details).  The random number generation technique is a linear feedback
  79    shift register approach, employing trinomials (since there are fewer terms
  80    to sum up that way).  In this approach, the least significant bit of all
  81    the numbers in the state table will act as a linear feedback shift register,
  82    and will have period 2^deg - 1 (where deg is the degree of the polynomial
  83    being used, assuming that the polynomial is irreducible and primitive).
  84    The higher order bits will have longer periods, since their values are
  85    also influenced by pseudo-random carries out of the lower bits.  The
  86    total period of the generator is approximately deg*(2**deg - 1); thus
  87    doubling the amount of state information has a vast influence on the
  88    period of the generator.  Note: The deg*(2**deg - 1) is an approximation
  89    only good for large deg, when the period of the shift register is the
  90    dominant factor.  With deg equal to seven, the period is actually much
  91    longer than the 7*(2**7 - 1) predicted by this formula.  */
  92
  93
  94
  95 /* For each of the currently supported random number generators, we have a
  96    break value on the amount of state information (you need at least this many
  97    bytes of state info to support this random number generator), a degree for
  98    the polynomial (actually a trinomial) that the R.N.G. is based on, and
  99    separation between the two lower order coefficients of the trinomial.  */
 100
 101 /* Linear congruential.  */
 102 #define TYPE_0          0
 103 #define BREAK_0         8
 104 #define DEG_0           0
 105 #define SEP_0           0
 106
 107 /* x**7 + x**3 + 1.  */
 108 #define TYPE_1          1
 109 #define BREAK_1         32
 110 #define DEG_1           7
 111 #define SEP_1           3
 112
 113 /* x**15 + x + 1.  */
 114 #define TYPE_2          2
 115 #define BREAK_2         64
 116 #define DEG_2           15
 117 #define SEP_2           1
 118
 119 /* x**31 + x**3 + 1.  */
 120 #define TYPE_3          3
 121 #define BREAK_3         128
 122 #define DEG_3           31
 123 #define SEP_3           3
 124
 125 /* x**63 + x + 1.  */
 126 #define TYPE_4          4
 127 #define BREAK_4         256
 128 #define DEG_4           63
 129 #define SEP_4           1
 130
 131
 132 /* Array versions of the above information to make code run faster.
 133    Relies on fact that TYPE_i == i.  */
 134
 135 #define MAX_TYPES       5       /* Max number of types above.  */
 136
 137
 138 /* Initially, everything is set up as if from:
 139         initstate(1, randtbl, 128);
 140    Note that this initialization takes advantage of the fact that srandom
 141    advances the front and rear pointers 10*rand_deg times, and hence the
 142    rear pointer which starts at 0 will also end up at zero; thus the zeroth
 143    element of the state information, which contains info about the current
 144    position of the rear pointer is just
 145         (MAX_TYPES * (rptr - state)) + TYPE_3 == TYPE_3.  */
 146
 147 static int32_t randtbl[DEG_3 + 1] =
 148   {
 149     TYPE_3,
 150
 151     -1726662223, 379960547, 1735697613, 1040273694, 1313901226,
 152     1627687941, -179304937, -2073333483, 1780058412, -1989503057,
 153     -615974602, 344556628, 939512070, -1249116260, 1507946756,
 154     -812545463, 154635395, 1388815473, -1926676823, 525320961,
 155     -1009028674, 968117788, -123449607, 1284210865, 435012392,
 156     -2017506339, -911064859, -370259173, 1132637927, 1398500161,
 157     -205601318,
 158   };
 159
 160
 161 static struct random_data unsafe_state =
 162   {
 163 /* FPTR and RPTR are two pointers into the state info, a front and a rear
 164    pointer.  These two pointers are always rand_sep places aparts, as they
 165    cycle through the state information.  (Yes, this does mean we could get
 166    away with just one pointer, but the code for random is more efficient
 167    this way).  The pointers are left positioned as they would be from the call:
 168         initstate(1, randtbl, 128);
 169    (The position of the rear pointer, rptr, is really 0 (as explained above
 170    in the initialization of randtbl) because the state table pointer is set
 171    to point to randtbl[1] (as explained below).)  */
 172
 173     .fptr = &randtbl[SEP_3 + 1],
 174     .rptr = &randtbl[1],
 175
 176 /* The following things are the pointer to the state information table,
 177    the type of the current generator, the degree of the current polynomial
 178    being used, and the separation between the two pointers.
 179    Note that for efficiency of random, we remember the first location of
 180    the state information, not the zeroth.  Hence it is valid to access
 181    state[-1], which is used to store the type of the R.N.G.
 182    Also, we remember the last location, since this is more efficient than
 183    indexing every time to find the address of the last element to see if
 184    the front and rear pointers have wrapped.  */
 185
 186     .state = &randtbl[1],
 187
 188     .rand_type = TYPE_3,
 189     .rand_deg = DEG_3,
 190     .rand_sep = SEP_3,
 191
 192     .end_ptr = &randtbl[sizeof (randtbl) / sizeof (randtbl[0])]
 193 };
 194 \f
 195 /* POSIX.1c requires that there is mutual exclusion for the `rand' and
 196    `srand' functions to prevent concurrent calls from modifying common
 197    data.  */
 198 __libc_lock_define_initialized (static, lock)
 199 \f
 200 /* Initialize the random number generator based on the given seed.  If the
 201    type is the trivial no-state-information type, just remember the seed.
 202    Otherwise, initializes state[] based on the given "seed" via a linear
 203    congruential generator.  Then, the pointers are set to known locations
 204    that are exactly rand_sep places apart.  Lastly, it cycles the state
 205    information a given number of times to get rid of any initial dependencies
 206    introduced by the L.C.R.N.G.  Note that the initialization of randtbl[]
 207    for default usage relies on values produced by this routine.  */
 208 void
 209 __srandom (x)
 210      unsigned int x;
 211 {
 212   __libc_lock_lock (lock);
 213   (void) __srandom_r (x, &unsafe_state);
 214   __libc_lock_unlock (lock);
 215 }
 216
 217 weak_alias (__srandom, srandom)
 218 weak_alias (__srandom, srand)
 219 \f
 220 /* Initialize the state information in the given array of N bytes for
 221    future random number generation.  Based on the number of bytes we
 222    are given, and the break values for the different R.N.G.'s, we choose
 223    the best (largest) one we can and set things up for it.  srandom is
 224    then called to initialize the state information.  Note that on return
 225    from srandom, we set state[-1] to be the type multiplexed with the current
 226    value of the rear pointer; this is so successive calls to initstate won't
 227    lose this information and will be able to restart with setstate.
 228    Note: The first thing we do is save the current state, if any, just like
 229    setstate so that it doesn't matter when initstate is called.
 230    Returns a pointer to the old state.  */
 231 char *
 232 __initstate (seed, arg_state, n)
 233      unsigned int seed;
 234      char *arg_state;
 235      size_t n;
 236 {
 237   int32_t *ostate;
 238
 239   __libc_lock_lock (lock);
 240
 241   ostate = &unsafe_state.state[-1];
 242
 243   __initstate_r (seed, arg_state, n, &unsafe_state);
 244
 245   __libc_lock_unlock (lock);
 246
 247   return (char *) ostate;
 248 }
 249
 250 weak_alias (__initstate, initstate)
 251 \f
 252 /* Restore the state from the given state array.
 253    Note: It is important that we also remember the locations of the pointers
 254    in the current state information, and restore the locations of the pointers
 255    from the old state information.  This is done by multiplexing the pointer
 256    location into the zeroth word of the state information. Note that due
 257    to the order in which things are done, it is OK to call setstate with the
 258    same state as the current state
 259    Returns a pointer to the old state information.  */
 260 char *
 261 __setstate (arg_state)
 262      char *arg_state;
 263 {
 264   int32_t *ostate;
 265
 266   __libc_lock_lock (lock);
 267
 268   ostate = &unsafe_state.state[-1];
 269
 270   if (__setstate_r (arg_state, &unsafe_state) < 0)
 271     ostate = NULL;
 272
 273   __libc_lock_unlock (lock);
 274
 275   return (char *) ostate;
 276 }
 277
 278 weak_alias (__setstate, setstate)
 279 \f
 280 /* If we are using the trivial TYPE_0 R.N.G., just do the old linear
 281    congruential bit.  Otherwise, we do our fancy trinomial stuff, which is the
 282    same in all the other cases due to all the global variables that have been
 283    set up.  The basic operation is to add the number at the rear pointer into
 284    the one at the front pointer.  Then both pointers are advanced to the next
 285    location cyclically in the table.  The value returned is the sum generated,
 286    reduced to 31 bits by throwing away the "least random" low bit.
 287    Note: The code takes advantage of the fact that both the front and
 288    rear pointers can't wrap on the same call by not testing the rear
 289    pointer if the front one has wrapped.  Returns a 31-bit random number.  */
 290
 291 long int
 292 __random ()
 293 {
 294   int32_t retval;
 295
 296   __libc_lock_lock (lock);
 297
 298   (void) __random_r (&unsafe_state, &retval);
 299
 300   __libc_lock_unlock (lock);
 301
 302   return retval;
 303 }
 304
 305 weak_alias (__random, random)