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
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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 [rescinded 22 July 1999]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}, @
42 void *@var{arg_state}, unsigned long @var{n})
43 @deftypefnx Supplement void* setstate (void *@var{arg_state})
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.
67 #define ULONG_MAX ((unsigned long)(~0L)) /* 0xFFFFFFFF for 32-bits */
68 #define LONG_MAX ((long)(ULONG_MAX >> 1)) /* 0x7FFFFFFF for 32-bits*/
73 # define NULL (void *) 0
78 # define NULL (void *) 0
84 long int random (void);
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. */
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. */
127 /* Linear congruential. */
133 /* x**7 + x**3 + 1. */
145 /* x**31 + x**3 + 1. */
158 /* Array versions of the above information to make code run faster.
159 Relies on fact that TYPE_i == i. */
161 #define MAX_TYPES 5 /* Max number of types above. */
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
};
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. */
177 static long int randtbl
[DEG_3
+ 1] =
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
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).) */
199 static long int *fptr
= &randtbl
[SEP_3
+ 1];
200 static long int *rptr
= &randtbl
[1];
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. */
214 static long int *state
= &randtbl
[1];
216 static int rand_type
= TYPE_3
;
217 static int rand_deg
= DEG_3
;
218 static int rand_sep
= SEP_3
;
220 static long int *end_ptr
= &randtbl
[sizeof(randtbl
) / sizeof(randtbl
[0])];
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. */
231 srandom (unsigned int x
)
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 (unsigned int seed
, PTR arg_state
, unsigned long n
)
260 PTR ostate
= (PTR
) &state
[-1];
262 if (rand_type
== TYPE_0
)
263 state
[-1] = rand_type
;
265 state
[-1] = (MAX_TYPES
* (rptr
- state
)) + rand_type
;
277 else if (n
< BREAK_2
)
283 else if (n
< BREAK_3
)
289 else if (n
< BREAK_4
)
302 state
= &((long int *) arg_state
)[1]; /* First location. */
303 /* Must set END_PTR before srandom. */
304 end_ptr
= &state
[rand_deg
];
306 if (rand_type
== TYPE_0
)
307 state
[-1] = rand_type
;
309 state
[-1] = (MAX_TYPES
* (rptr
- state
)) + rand_type
;
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. */
324 setstate (PTR arg_state
)
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];
331 if (rand_type
== TYPE_0
)
332 state
[-1] = rand_type
;
334 state
[-1] = (MAX_TYPES
* (rptr
- state
)) + rand_type
;
344 rand_deg
= degrees
[type
];
345 rand_sep
= seps
[type
];
348 /* State info munged. */
353 state
= &new_state
[1];
354 if (rand_type
!= TYPE_0
)
357 fptr
= &state
[(rear
+ rand_sep
) % rand_deg
];
359 /* Set end_ptr too. */
360 end_ptr
= &state
[rand_deg
];
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. */
379 if (rand_type
== TYPE_0
)
381 state
[0] = ((state
[0] * 1103515245) + 12345) & LONG_MAX
;
388 /* Chucking least random bit. */
389 i
= (*fptr
>> 1) & LONG_MAX
;
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