stdlib/random.c

   1 /* Copyright (C) 1995-2015 Free Software Foundation, Inc.
   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, see
  15    <http://www.gnu.org/licenses/>.  */
  16
  17 /*
  18  * This is derived from the Berkeley source:
  19  *      @(#)random.c    5.5 (Berkeley) 7/6/88
  20  * It was reworked for the GNU C Library by Roland McGrath.
  21  * Rewritten to use reentrant functions by Ulrich Drepper, 1995.
  22  */
  23
  24 /*
  25    Copyright (C) 1983 Regents of the University of California.
  26    All rights reserved.
  27
  28    Redistribution and use in source and binary forms, with or without
  29    modification, are permitted provided that the following conditions
  30    are met:
  31
  32    1. Redistributions of source code must retain the above copyright
  33       notice, this list of conditions and the following disclaimer.
  34    2. Redistributions in binary form must reproduce the above copyright
  35       notice, this list of conditions and the following disclaimer in the
  36       documentation and/or other materials provided with the distribution.
  37    4. Neither the name of the University nor the names of its contributors
  38       may be used to endorse or promote products derived from this software
  39       without specific prior written permission.
  40
  41    THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
  42    ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
  43    IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
  44    ARE DISCLAIMED.  IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
  45    FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
  46    DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
  47    OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
  48    HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
  49    LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
  50    OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
  51    SUCH DAMAGE.*/
  52
  53 #include <bits/libc-lock.h>
  54 #include <limits.h>
  55 #include <stddef.h>
  56 #include <stdlib.h>
  57
  58
  59 /* An improved random number generation package.  In addition to the standard
  60    rand()/srand() like interface, this package also has a special state info
  61    interface.  The initstate() routine is called with a seed, an array of
  62    bytes, and a count of how many bytes are being passed in; this array is
  63    then initialized to contain information for random number generation with
  64    that much state information.  Good sizes for the amount of state
  65    information are 32, 64, 128, and 256 bytes.  The state can be switched by
  66    calling the setstate() function with the same array as was initialized
  67    with initstate().  By default, the package runs with 128 bytes of state
  68    information and generates far better random numbers than a linear
  69    congruential generator.  If the amount of state information is less than
  70    32 bytes, a simple linear congruential R.N.G. is used.  Internally, the
  71    state information is treated as an array of longs; the zeroth element of
  72    the array is the type of R.N.G. being used (small integer); the remainder
  73    of the array is the state information for the R.N.G.  Thus, 32 bytes of
  74    state information will give 7 longs worth of state information, which will
  75    allow a degree seven polynomial.  (Note: The zeroth word of state
  76    information also has some other information stored in it; see setstate
  77    for details).  The random number generation technique is a linear feedback
  78    shift register approach, employing trinomials (since there are fewer terms
  79    to sum up that way).  In this approach, the least significant bit of all
  80    the numbers in the state table will act as a linear feedback shift register,
  81    and will have period 2^deg - 1 (where deg is the degree of the polynomial
  82    being used, assuming that the polynomial is irreducible and primitive).
  83    The higher order bits will have longer periods, since their values are
  84    also influenced by pseudo-random carries out of the lower bits.  The
  85    total period of the generator is approximately deg*(2**deg - 1); thus
  86    doubling the amount of state information has a vast influence on the
  87    period of the generator.  Note: The deg*(2**deg - 1) is an approximation
  88    only good for large deg, when the period of the shift register is the
  89    dominant factor.  With deg equal to seven, the period is actually much
  90    longer than the 7*(2**7 - 1) predicted by this formula.  */
  91
  92
  93
  94 /* For each of the currently supported random number generators, we have a
  95    break value on the amount of state information (you need at least this many
  96    bytes of state info to support this random number generator), a degree for
  97    the polynomial (actually a trinomial) that the R.N.G. is based on, and
  98    separation between the two lower order coefficients of the trinomial.  */
  99
 100 /* Linear congruential.  */
 101 #define TYPE_0          0
 102 #define BREAK_0         8
 103 #define DEG_0           0
 104 #define SEP_0           0
 105
 106 /* x**7 + x**3 + 1.  */
 107 #define TYPE_1          1
 108 #define BREAK_1         32
 109 #define DEG_1           7
 110 #define SEP_1           3
 111
 112 /* x**15 + x + 1.  */
 113 #define TYPE_2          2
 114 #define BREAK_2         64
 115 #define DEG_2           15
 116 #define SEP_2           1
 117
 118 /* x**31 + x**3 + 1.  */
 119 #define TYPE_3          3
 120 #define BREAK_3         128
 121 #define DEG_3           31
 122 #define SEP_3           3
 123
 124 /* x**63 + x + 1.  */
 125 #define TYPE_4          4
 126 #define BREAK_4         256
 127 #define DEG_4           63
 128 #define SEP_4           1
 129
 130
 131 /* Array versions of the above information to make code run faster.
 132    Relies on fact that TYPE_i == i.  */
 133
 134 #define MAX_TYPES       5       /* Max number of types above.  */
 135
 136
 137 /* Initially, everything is set up as if from:
 138         initstate(1, randtbl, 128);
 139    Note that this initialization takes advantage of the fact that srandom
 140    advances the front and rear pointers 10*rand_deg times, and hence the
 141    rear pointer which starts at 0 will also end up at zero; thus the zeroth
 142    element of the state information, which contains info about the current
 143    position of the rear pointer is just
 144         (MAX_TYPES * (rptr - state)) + TYPE_3 == TYPE_3.  */
 145
 146 static int32_t randtbl[DEG_3 + 1] =
 147   {
 148     TYPE_3,
 149
 150     -1726662223, 379960547, 1735697613, 1040273694, 1313901226,
 151     1627687941, -179304937, -2073333483, 1780058412, -1989503057,
 152     -615974602, 344556628, 939512070, -1249116260, 1507946756,
 153     -812545463, 154635395, 1388815473, -1926676823, 525320961,
 154     -1009028674, 968117788, -123449607, 1284210865, 435012392,
 155     -2017506339, -911064859, -370259173, 1132637927, 1398500161,
 156     -205601318,
 157   };
 158
 159
 160 static struct random_data unsafe_state =
 161   {
 162 /* FPTR and RPTR are two pointers into the state info, a front and a rear
 163    pointer.  These two pointers are always rand_sep places apart, as they
 164    cycle through the state information.  (Yes, this does mean we could get
 165    away with just one pointer, but the code for random is more efficient
 166    this way).  The pointers are left positioned as they would be from the call:
 167         initstate(1, randtbl, 128);
 168    (The position of the rear pointer, rptr, is really 0 (as explained above
 169    in the initialization of randtbl) because the state table pointer is set
 170    to point to randtbl[1] (as explained below).)  */
 171
 172     .fptr = &randtbl[SEP_3 + 1],
 173     .rptr = &randtbl[1],
 174
 175 /* The following things are the pointer to the state information table,
 176    the type of the current generator, the degree of the current polynomial
 177    being used, and the separation between the two pointers.
 178    Note that for efficiency of random, we remember the first location of
 179    the state information, not the zeroth.  Hence it is valid to access
 180    state[-1], which is used to store the type of the R.N.G.
 181    Also, we remember the last location, since this is more efficient than
 182    indexing every time to find the address of the last element to see if
 183    the front and rear pointers have wrapped.  */
 184
 185     .state = &randtbl[1],
 186
 187     .rand_type = TYPE_3,
 188     .rand_deg = DEG_3,
 189     .rand_sep = SEP_3,
 190
 191     .end_ptr = &randtbl[sizeof (randtbl) / sizeof (randtbl[0])]
 192 };
 193 \f
 194 /* POSIX.1c requires that there is mutual exclusion for the `rand' and
 195    `srand' functions to prevent concurrent calls from modifying common
 196    data.  */
 197 __libc_lock_define_initialized (static, lock)
 198 \f
 199 /* Initialize the random number generator based on the given seed.  If the
 200    type is the trivial no-state-information type, just remember the seed.
 201    Otherwise, initializes state[] based on the given "seed" via a linear
 202    congruential generator.  Then, the pointers are set to known locations
 203    that are exactly rand_sep places apart.  Lastly, it cycles the state
 204    information a given number of times to get rid of any initial dependencies
 205    introduced by the L.C.R.N.G.  Note that the initialization of randtbl[]
 206    for default usage relies on values produced by this routine.  */
 207 void
 208 __srandom (x)
 209      unsigned int x;
 210 {
 211   __libc_lock_lock (lock);
 212   (void) __srandom_r (x, &unsafe_state);
 213   __libc_lock_unlock (lock);
 214 }
 215
 216 weak_alias (__srandom, srandom)
 217 weak_alias (__srandom, srand)
 218 \f
 219 /* Initialize the state information in the given array of N bytes for
 220    future random number generation.  Based on the number of bytes we
 221    are given, and the break values for the different R.N.G.'s, we choose
 222    the best (largest) one we can and set things up for it.  srandom is
 223    then called to initialize the state information.  Note that on return
 224    from srandom, we set state[-1] to be the type multiplexed with the current
 225    value of the rear pointer; this is so successive calls to initstate won't
 226    lose this information and will be able to restart with setstate.
 227    Note: The first thing we do is save the current state, if any, just like
 228    setstate so that it doesn't matter when initstate is called.
 229    Returns a pointer to the old state.  */
 230 char *
 231 __initstate (seed, arg_state, n)
 232      unsigned int seed;
 233      char *arg_state;
 234      size_t n;
 235 {
 236   int32_t *ostate;
 237   int ret;
 238
 239   __libc_lock_lock (lock);
 240
 241   ostate = &unsafe_state.state[-1];
 242
 243   ret = __initstate_r (seed, arg_state, n, &unsafe_state);
 244
 245   __libc_lock_unlock (lock);
 246
 247   return ret == -1 ? NULL : (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 (void)
 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)