2 * Copyright (c) 1983 Regents of the University of California.
5 * Redistribution and use in source and binary forms, with or without
6 * modification, are permitted provided that the following conditions
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 [rescinded 22 July 1999]
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15 * may be used to endorse or promote products derived from this software
16 * without specific prior written permission.
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
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.
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}, void *@var{arg_state}, unsigned long @var{n})
42 @deftypefnx Supplement void* setstate (void *@var{arg_state})
44 Random number functions. @code{random} returns a random number in the
45 range 0 to @code{LONG_MAX}. @code{srandom} initializes the random
46 number generator to some starting point determined by @var{seed}
47 (else, the values returned by @code{random} are always the same for each
48 run of the program). @code{initstate} and @code{setstate} allow fine-grained
49 control over the state of the random number generator.
66 #define ULONG_MAX ((unsigned long)(~0L)) /* 0xFFFFFFFF for 32-bits */
67 #define LONG_MAX ((long)(ULONG_MAX >> 1)) /* 0x7FFFFFFF for 32-bits*/
72 # define NULL (void *) 0
77 # define NULL (void *) 0
85 /* An improved random number generation package. In addition to the standard
86 rand()/srand() like interface, this package also has a special state info
87 interface. The initstate() routine is called with a seed, an array of
88 bytes, and a count of how many bytes are being passed in; this array is
89 then initialized to contain information for random number generation with
90 that much state information. Good sizes for the amount of state
91 information are 32, 64, 128, and 256 bytes. The state can be switched by
92 calling the setstate() function with the same array as was initiallized
93 with initstate(). By default, the package runs with 128 bytes of state
94 information and generates far better random numbers than a linear
95 congruential generator. If the amount of state information is less than
96 32 bytes, a simple linear congruential R.N.G. is used. Internally, the
97 state information is treated as an array of longs; the zeroeth element of
98 the array is the type of R.N.G. being used (small integer); the remainder
99 of the array is the state information for the R.N.G. Thus, 32 bytes of
100 state information will give 7 longs worth of state information, which will
101 allow a degree seven polynomial. (Note: The zeroeth word of state
102 information also has some other information stored in it; see setstate
103 for details). The random number generation technique is a linear feedback
104 shift register approach, employing trinomials (since there are fewer terms
105 to sum up that way). In this approach, the least significant bit of all
106 the numbers in the state table will act as a linear feedback shift register,
107 and will have period 2^deg - 1 (where deg is the degree of the polynomial
108 being used, assuming that the polynomial is irreducible and primitive).
109 The higher order bits will have longer periods, since their values are
110 also influenced by pseudo-random carries out of the lower bits. The
111 total period of the generator is approximately deg*(2**deg - 1); thus
112 doubling the amount of state information has a vast influence on the
113 period of the generator. Note: The deg*(2**deg - 1) is an approximation
114 only good for large deg, when the period of the shift register is the
115 dominant factor. With deg equal to seven, the period is actually much
116 longer than the 7*(2**7 - 1) predicted by this formula. */
120 /* For each of the currently supported random number generators, we have a
121 break value on the amount of state information (you need at least thi
122 bytes of state info to support this random number generator), a degree for
123 the polynomial (actually a trinomial) that the R.N.G. is based on, and
124 separation between the two lower order coefficients of the trinomial. */
126 /* Linear congruential. */
132 /* x**7 + x**3 + 1. */
144 /* x**31 + x**3 + 1. */
157 /* Array versions of the above information to make code run faster.
158 Relies on fact that TYPE_i == i. */
160 #define MAX_TYPES 5 /* Max number of types above. */
162 static int degrees
[MAX_TYPES
] = { DEG_0
, DEG_1
, DEG_2
, DEG_3
, DEG_4
};
163 static int seps
[MAX_TYPES
] = { SEP_0
, SEP_1
, SEP_2
, SEP_3
, SEP_4
};
167 /* Initially, everything is set up as if from:
168 initstate(1, randtbl, 128);
169 Note that this initialization takes advantage of the fact that srandom
170 advances the front and rear pointers 10*rand_deg times, and hence the
171 rear pointer which starts at 0 will also end up at zero; thus the zeroeth
172 element of the state information, which contains info about the current
173 position of the rear pointer is just
174 (MAX_TYPES * (rptr - state)) + TYPE_3 == TYPE_3. */
176 static long int randtbl
[DEG_3
+ 1] =
178 0x9a319039, 0x32d9c024, 0x9b663182, 0x5da1f342,
179 0xde3b81e0, 0xdf0a6fb5, 0xf103bc02, 0x48f340fb,
180 0x7449e56b, 0xbeb1dbb0, 0xab5c5918, 0x946554fd,
181 0x8c2e680f, 0xeb3d799f, 0xb11ee0b7, 0x2d436b86,
182 0xda672e2a, 0x1588ca88, 0xe369735d, 0x904f35f7,
183 0xd7158fd6, 0x6fa6f051, 0x616e6b96, 0xac94efdc,
184 0x36413f93, 0xc622c298, 0xf5a42ab8, 0x8a88d77b,
185 0xf5ad9d0e, 0x8999220b, 0x27fb47b9
188 /* FPTR and RPTR are two pointers into the state info, a front and a rear
189 pointer. These two pointers are always rand_sep places aparts, as they
190 cycle through the state information. (Yes, this does mean we could get
191 away with just one pointer, but the code for random is more efficient
192 this way). The pointers are left positioned as they would be from the call:
193 initstate(1, randtbl, 128);
194 (The position of the rear pointer, rptr, is really 0 (as explained above
195 in the initialization of randtbl) because the state table pointer is set
196 to point to randtbl[1] (as explained below).) */
198 static long int *fptr
= &randtbl
[SEP_3
+ 1];
199 static long int *rptr
= &randtbl
[1];
203 /* The following things are the pointer to the state information table,
204 the type of the current generator, the degree of the current polynomial
205 being used, and the separation between the two pointers.
206 Note that for efficiency of random, we remember the first location of
207 the state information, not the zeroeth. Hence it is valid to access
208 state[-1], which is used to store the type of the R.N.G.
209 Also, we remember the last location, since this is more efficient than
210 indexing every time to find the address of the last element to see if
211 the front and rear pointers have wrapped. */
213 static long int *state
= &randtbl
[1];
215 static int rand_type
= TYPE_3
;
216 static int rand_deg
= DEG_3
;
217 static int rand_sep
= SEP_3
;
219 static long int *end_ptr
= &randtbl
[sizeof(randtbl
) / sizeof(randtbl
[0])];
221 /* Initialize the random number generator based on the given seed. If the
222 type is the trivial no-state-information type, just remember the seed.
223 Otherwise, initializes state[] based on the given "seed" via a linear
224 congruential generator. Then, the pointers are set to known locations
225 that are exactly rand_sep places apart. Lastly, it cycles the state
226 information a given number of times to get rid of any initial dependencies
227 introduced by the L.C.R.N.G. Note that the initialization of randtbl[]
228 for default usage relies on values produced by this routine. */
234 if (rand_type
!= TYPE_0
)
237 for (i
= 1; i
< rand_deg
; ++i
)
238 state
[i
] = (1103515145 * state
[i
- 1]) + 12345;
239 fptr
= &state
[rand_sep
];
241 for (i
= 0; i
< 10 * rand_deg
; ++i
)
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. */
258 initstate (seed
, arg_state
, n
)
263 PTR ostate
= (PTR
) &state
[-1];
265 if (rand_type
== TYPE_0
)
266 state
[-1] = rand_type
;
268 state
[-1] = (MAX_TYPES
* (rptr
- state
)) + rand_type
;
280 else if (n
< BREAK_2
)
286 else if (n
< BREAK_3
)
292 else if (n
< BREAK_4
)
305 state
= &((long int *) arg_state
)[1]; /* First location. */
306 /* Must set END_PTR before srandom. */
307 end_ptr
= &state
[rand_deg
];
309 if (rand_type
== TYPE_0
)
310 state
[-1] = rand_type
;
312 state
[-1] = (MAX_TYPES
* (rptr
- state
)) + rand_type
;
317 /* Restore the state from the given state array.
318 Note: It is important that we also remember the locations of the pointers
319 in the current state information, and restore the locations of the pointers
320 from the old state information. This is done by multiplexing the pointer
321 location into the zeroeth word of the state information. Note that due
322 to the order in which things are done, it is OK to call setstate with the
323 same state as the current state
324 Returns a pointer to the old state information. */
330 register long int *new_state
= (long int *) arg_state
;
331 register int type
= new_state
[0] % MAX_TYPES
;
332 register int rear
= new_state
[0] / MAX_TYPES
;
333 PTR ostate
= (PTR
) &state
[-1];
335 if (rand_type
== TYPE_0
)
336 state
[-1] = rand_type
;
338 state
[-1] = (MAX_TYPES
* (rptr
- state
)) + rand_type
;
348 rand_deg
= degrees
[type
];
349 rand_sep
= seps
[type
];
352 /* State info munged. */
357 state
= &new_state
[1];
358 if (rand_type
!= TYPE_0
)
361 fptr
= &state
[(rear
+ rand_sep
) % rand_deg
];
363 /* Set end_ptr too. */
364 end_ptr
= &state
[rand_deg
];
369 /* If we are using the trivial TYPE_0 R.N.G., just do the old linear
370 congruential bit. Otherwise, we do our fancy trinomial stuff, which is the
371 same in all ther other cases due to all the global variables that have been
372 set up. The basic operation is to add the number at the rear pointer into
373 the one at the front pointer. Then both pointers are advanced to the next
374 location cyclically in the table. The value returned is the sum generated,
375 reduced to 31 bits by throwing away the "least random" low bit.
376 Note: The code takes advantage of the fact that both the front and
377 rear pointers can't wrap on the same call by not testing the rear
378 pointer if the front one has wrapped. Returns a 31-bit random number. */
383 if (rand_type
== TYPE_0
)
385 state
[0] = ((state
[0] * 1103515245) + 12345) & LONG_MAX
;
392 /* Chucking least random bit. */
393 i
= (*fptr
>> 1) & LONG_MAX
;
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