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 [rescinded 22 July 1999]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 /*
38 
39 @deftypefn Supplement {long int} random (void)
40 @deftypefnx Supplement void srandom (unsigned int @var{seed})
41 @deftypefnx Supplement void* initstate (unsigned int @var{seed}, @
42   void *@var{arg_state}, unsigned long @var{n})
43 @deftypefnx Supplement void* setstate (void *@var{arg_state})
44 
45 Random number functions.  @code{random} returns a random number in the
46 range 0 to @code{LONG_MAX}.  @code{srandom} initializes the random
47 number generator to some starting point determined by @var{seed}
48 (else, the values returned by @code{random} are always the same for each
49 run of the program).  @code{initstate} and @code{setstate} allow fine-grained
50 control over the state of the random number generator.
51 
52 @end deftypefn
53 
54 */
55 
56 #include <errno.h>
57 
58 #if 0
59 
60 #include <ansidecl.h>
61 #include <limits.h>
62 #include <stddef.h>
63 #include <stdlib.h>
64 
65 #else
66 
67 #define	ULONG_MAX  ((unsigned long)(~0L))     /* 0xFFFFFFFF for 32-bits */
68 #define	LONG_MAX   ((long)(ULONG_MAX >> 1))   /* 0x7FFFFFFF for 32-bits*/
69 
70 #ifdef __STDC__
71 #  define PTR void *
72 #  ifndef NULL
73 #    define NULL (void *) 0
74 #  endif
75 #else
76 #  define PTR char *
77 #  ifndef NULL
78 #    define NULL (void *) 0
79 #  endif
80 #endif
81 
82 #endif
83 
84 long int random (void);
85 
86 /* An improved random number generation package.  In addition to the standard
87    rand()/srand() like interface, this package also has a special state info
88    interface.  The initstate() routine is called with a seed, an array of
89    bytes, and a count of how many bytes are being passed in; this array is
90    then initialized to contain information for random number generation with
91    that much state information.  Good sizes for the amount of state
92    information are 32, 64, 128, and 256 bytes.  The state can be switched by
93    calling the setstate() function with the same array as was initiallized
94    with initstate().  By default, the package runs with 128 bytes of state
95    information and generates far better random numbers than a linear
96    congruential generator.  If the amount of state information is less than
97    32 bytes, a simple linear congruential R.N.G. is used.  Internally, the
98    state information is treated as an array of longs; the zeroeth element of
99    the array is the type of R.N.G. being used (small integer); the remainder
100    of the array is the state information for the R.N.G.  Thus, 32 bytes of
101    state information will give 7 longs worth of state information, which will
102    allow a degree seven polynomial.  (Note: The zeroeth word of state
103    information also has some other information stored in it; see setstate
104    for details).  The random number generation technique is a linear feedback
105    shift register approach, employing trinomials (since there are fewer terms
106    to sum up that way).  In this approach, the least significant bit of all
107    the numbers in the state table will act as a linear feedback shift register,
108    and will have period 2^deg - 1 (where deg is the degree of the polynomial
109    being used, assuming that the polynomial is irreducible and primitive).
110    The higher order bits will have longer periods, since their values are
111    also influenced by pseudo-random carries out of the lower bits.  The
112    total period of the generator is approximately deg*(2**deg - 1); thus
113    doubling the amount of state information has a vast influence on the
114    period of the generator.  Note: The deg*(2**deg - 1) is an approximation
115    only good for large deg, when the period of the shift register is the
116    dominant factor.  With deg equal to seven, the period is actually much
117    longer than the 7*(2**7 - 1) predicted by this formula.  */
118 
119 
120 
121 /* For each of the currently supported random number generators, we have a
122    break value on the amount of state information (you need at least thi
123    bytes of state info to support this random number generator), a degree for
124    the polynomial (actually a trinomial) that the R.N.G. is based on, and
125    separation between the two lower order coefficients of the trinomial.  */
126 
127 /* Linear congruential.  */
128 #define	TYPE_0		0
129 #define	BREAK_0		8
130 #define	DEG_0		0
131 #define	SEP_0		0
132 
133 /* x**7 + x**3 + 1.  */
134 #define	TYPE_1		1
135 #define	BREAK_1		32
136 #define	DEG_1		7
137 #define	SEP_1		3
138 
139 /* x**15 + x + 1.  */
140 #define	TYPE_2		2
141 #define	BREAK_2		64
142 #define	DEG_2		15
143 #define	SEP_2		1
144 
145 /* x**31 + x**3 + 1.  */
146 #define	TYPE_3		3
147 #define	BREAK_3		128
148 #define	DEG_3		31
149 #define	SEP_3		3
150 
151 /* x**63 + x + 1.  */
152 #define	TYPE_4		4
153 #define	BREAK_4		256
154 #define	DEG_4		63
155 #define	SEP_4		1
156 
157 
158 /* Array versions of the above information to make code run faster.
159    Relies on fact that TYPE_i == i.  */
160 
161 #define	MAX_TYPES	5	/* Max number of types above.  */
162 
163 static int degrees[MAX_TYPES] = { DEG_0, DEG_1, DEG_2, DEG_3, DEG_4 };
164 static int seps[MAX_TYPES] = { SEP_0, SEP_1, SEP_2, SEP_3, SEP_4 };
165 
166 
167 
168 /* Initially, everything is set up as if from:
169 	initstate(1, randtbl, 128);
170    Note that this initialization takes advantage of the fact that srandom
171    advances the front and rear pointers 10*rand_deg times, and hence the
172    rear pointer which starts at 0 will also end up at zero; thus the zeroeth
173    element of the state information, which contains info about the current
174    position of the rear pointer is just
175 	(MAX_TYPES * (rptr - state)) + TYPE_3 == TYPE_3.  */
176 
177 static long int randtbl[DEG_3 + 1] =
178   { TYPE_3,
179       0x9a319039, 0x32d9c024, 0x9b663182, 0x5da1f342,
180       0xde3b81e0, 0xdf0a6fb5, 0xf103bc02, 0x48f340fb,
181       0x7449e56b, 0xbeb1dbb0, 0xab5c5918, 0x946554fd,
182       0x8c2e680f, 0xeb3d799f, 0xb11ee0b7, 0x2d436b86,
183       0xda672e2a, 0x1588ca88, 0xe369735d, 0x904f35f7,
184       0xd7158fd6, 0x6fa6f051, 0x616e6b96, 0xac94efdc,
185       0x36413f93, 0xc622c298, 0xf5a42ab8, 0x8a88d77b,
186       0xf5ad9d0e, 0x8999220b, 0x27fb47b9
187     };
188 
189 /* FPTR and RPTR are two pointers into the state info, a front and a rear
190    pointer.  These two pointers are always rand_sep places aparts, as they
191    cycle through the state information.  (Yes, this does mean we could get
192    away with just one pointer, but the code for random is more efficient
193    this way).  The pointers are left positioned as they would be from the call:
194 	initstate(1, randtbl, 128);
195    (The position of the rear pointer, rptr, is really 0 (as explained above
196    in the initialization of randtbl) because the state table pointer is set
197    to point to randtbl[1] (as explained below).)  */
198 
199 static long int *fptr = &randtbl[SEP_3 + 1];
200 static long int *rptr = &randtbl[1];
201 
202 
203 
204 /* The following things are the pointer to the state information table,
205    the type of the current generator, the degree of the current polynomial
206    being used, and the separation between the two pointers.
207    Note that for efficiency of random, we remember the first location of
208    the state information, not the zeroeth.  Hence it is valid to access
209    state[-1], which is used to store the type of the R.N.G.
210    Also, we remember the last location, since this is more efficient than
211    indexing every time to find the address of the last element to see if
212    the front and rear pointers have wrapped.  */
213 
214 static long int *state = &randtbl[1];
215 
216 static int rand_type = TYPE_3;
217 static int rand_deg = DEG_3;
218 static int rand_sep = SEP_3;
219 
220 static long int *end_ptr = &randtbl[sizeof(randtbl) / sizeof(randtbl[0])];
221 
222 /* Initialize the random number generator based on the given seed.  If the
223    type is the trivial no-state-information type, just remember the seed.
224    Otherwise, initializes state[] based on the given "seed" via a linear
225    congruential generator.  Then, the pointers are set to known locations
226    that are exactly rand_sep places apart.  Lastly, it cycles the state
227    information a given number of times to get rid of any initial dependencies
228    introduced by the L.C.R.N.G.  Note that the initialization of randtbl[]
229    for default usage relies on values produced by this routine.  */
230 void
srandom(unsigned int x)231 srandom (unsigned int x)
232 {
233   state[0] = x;
234   if (rand_type != TYPE_0)
235     {
236       register long int i;
237       for (i = 1; i < rand_deg; ++i)
238 	state[i] = (1103515145 * state[i - 1]) + 12345;
239       fptr = &state[rand_sep];
240       rptr = &state[0];
241       for (i = 0; i < 10 * rand_deg; ++i)
242 	random();
243     }
244 }
245 
246 /* Initialize the state information in the given array of N bytes for
247    future random number generation.  Based on the number of bytes we
248    are given, and the break values for the different R.N.G.'s, we choose
249    the best (largest) one we can and set things up for it.  srandom is
250    then called to initialize the state information.  Note that on return
251    from srandom, we set state[-1] to be the type multiplexed with the current
252    value of the rear pointer; this is so successive calls to initstate won't
253    lose this information and will be able to restart with setstate.
254    Note: The first thing we do is save the current state, if any, just like
255    setstate so that it doesn't matter when initstate is called.
256    Returns a pointer to the old state.  */
257 PTR
initstate(unsigned int seed,PTR arg_state,unsigned long n)258 initstate (unsigned int seed, PTR arg_state, unsigned long n)
259 {
260   PTR ostate = (PTR) &state[-1];
261 
262   if (rand_type == TYPE_0)
263     state[-1] = rand_type;
264   else
265     state[-1] = (MAX_TYPES * (rptr - state)) + rand_type;
266   if (n < BREAK_1)
267     {
268       if (n < BREAK_0)
269 	{
270 	  errno = EINVAL;
271 	  return NULL;
272 	}
273       rand_type = TYPE_0;
274       rand_deg = DEG_0;
275       rand_sep = SEP_0;
276     }
277   else if (n < BREAK_2)
278     {
279       rand_type = TYPE_1;
280       rand_deg = DEG_1;
281       rand_sep = SEP_1;
282     }
283   else if (n < BREAK_3)
284     {
285       rand_type = TYPE_2;
286       rand_deg = DEG_2;
287       rand_sep = SEP_2;
288     }
289   else if (n < BREAK_4)
290     {
291       rand_type = TYPE_3;
292       rand_deg = DEG_3;
293       rand_sep = SEP_3;
294     }
295   else
296     {
297       rand_type = TYPE_4;
298       rand_deg = DEG_4;
299       rand_sep = SEP_4;
300     }
301 
302   state = &((long int *) arg_state)[1];	/* First location.  */
303   /* Must set END_PTR before srandom.  */
304   end_ptr = &state[rand_deg];
305   srandom(seed);
306   if (rand_type == TYPE_0)
307     state[-1] = rand_type;
308   else
309     state[-1] = (MAX_TYPES * (rptr - state)) + rand_type;
310 
311   return ostate;
312 }
313 
314 /* Restore the state from the given state array.
315    Note: It is important that we also remember the locations of the pointers
316    in the current state information, and restore the locations of the pointers
317    from the old state information.  This is done by multiplexing the pointer
318    location into the zeroeth word of the state information. Note that due
319    to the order in which things are done, it is OK to call setstate with the
320    same state as the current state
321    Returns a pointer to the old state information.  */
322 
323 PTR
setstate(PTR arg_state)324 setstate (PTR arg_state)
325 {
326   register long int *new_state = (long int *) arg_state;
327   register int type = new_state[0] % MAX_TYPES;
328   register int rear = new_state[0] / MAX_TYPES;
329   PTR ostate = (PTR) &state[-1];
330 
331   if (rand_type == TYPE_0)
332     state[-1] = rand_type;
333   else
334     state[-1] = (MAX_TYPES * (rptr - state)) + rand_type;
335 
336   switch (type)
337     {
338     case TYPE_0:
339     case TYPE_1:
340     case TYPE_2:
341     case TYPE_3:
342     case TYPE_4:
343       rand_type = type;
344       rand_deg = degrees[type];
345       rand_sep = seps[type];
346       break;
347     default:
348       /* State info munged.  */
349       errno = EINVAL;
350       return NULL;
351     }
352 
353   state = &new_state[1];
354   if (rand_type != TYPE_0)
355     {
356       rptr = &state[rear];
357       fptr = &state[(rear + rand_sep) % rand_deg];
358     }
359   /* Set end_ptr too.  */
360   end_ptr = &state[rand_deg];
361 
362   return ostate;
363 }
364 
365 /* If we are using the trivial TYPE_0 R.N.G., just do the old linear
366    congruential bit.  Otherwise, we do our fancy trinomial stuff, which is the
367    same in all ther other cases due to all the global variables that have been
368    set up.  The basic operation is to add the number at the rear pointer into
369    the one at the front pointer.  Then both pointers are advanced to the next
370    location cyclically in the table.  The value returned is the sum generated,
371    reduced to 31 bits by throwing away the "least random" low bit.
372    Note: The code takes advantage of the fact that both the front and
373    rear pointers can't wrap on the same call by not testing the rear
374    pointer if the front one has wrapped.  Returns a 31-bit random number.  */
375 
376 long int
random(void)377 random (void)
378 {
379   if (rand_type == TYPE_0)
380     {
381       state[0] = ((state[0] * 1103515245) + 12345) & LONG_MAX;
382       return state[0];
383     }
384   else
385     {
386       long int i;
387       *fptr += *rptr;
388       /* Chucking least random bit.  */
389       i = (*fptr >> 1) & LONG_MAX;
390       ++fptr;
391       if (fptr >= end_ptr)
392 	{
393 	  fptr = state;
394 	  ++rptr;
395 	}
396       else
397 	{
398 	  ++rptr;
399 	  if (rptr >= end_ptr)
400 	    rptr = state;
401 	}
402       return i;
403     }
404 }
405