0,0 → 1,404 |
/* |
* Copyright (c) 1983 Regents of the University of California. |
* All rights reserved. |
* |
* Redistribution and use in source and binary forms, with or without |
* modification, are permitted provided that the following conditions |
* are met: |
* 1. Redistributions of source code must retain the above copyright |
* notice, this list of conditions and the following disclaimer. |
* 2. Redistributions in binary form must reproduce the above copyright |
* notice, this list of conditions and the following disclaimer in the |
* documentation and/or other materials provided with the distribution. |
* 3. [rescinded 22 July 1999] |
* 4. Neither the name of the University nor the names of its contributors |
* may be used to endorse or promote products derived from this software |
* without specific prior written permission. |
* |
* THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND |
* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE |
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE |
* ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE |
* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL |
* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS |
* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) |
* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT |
* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY |
* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF |
* SUCH DAMAGE. |
*/ |
|
/* |
* This is derived from the Berkeley source: |
* @(#)random.c 5.5 (Berkeley) 7/6/88 |
* It was reworked for the GNU C Library by Roland McGrath. |
*/ |
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/* |
|
@deftypefn Supplement {long int} random (void) |
@deftypefnx Supplement void srandom (unsigned int @var{seed}) |
@deftypefnx Supplement void* initstate (unsigned int @var{seed}, @ |
void *@var{arg_state}, unsigned long @var{n}) |
@deftypefnx Supplement void* setstate (void *@var{arg_state}) |
|
Random number functions. @code{random} returns a random number in the |
range 0 to @code{LONG_MAX}. @code{srandom} initializes the random |
number generator to some starting point determined by @var{seed} |
(else, the values returned by @code{random} are always the same for each |
run of the program). @code{initstate} and @code{setstate} allow fine-grained |
control over the state of the random number generator. |
|
@end deftypefn |
|
*/ |
|
#include <errno.h> |
|
#if 0 |
|
#include <ansidecl.h> |
#include <limits.h> |
#include <stddef.h> |
#include <stdlib.h> |
|
#else |
|
#define ULONG_MAX ((unsigned long)(~0L)) /* 0xFFFFFFFF for 32-bits */ |
#define LONG_MAX ((long)(ULONG_MAX >> 1)) /* 0x7FFFFFFF for 32-bits*/ |
|
#ifdef __STDC__ |
# define PTR void * |
# ifndef NULL |
# define NULL (void *) 0 |
# endif |
#else |
# define PTR char * |
# ifndef NULL |
# define NULL (void *) 0 |
# endif |
#endif |
|
#endif |
|
long int random (void); |
|
/* An improved random number generation package. In addition to the standard |
rand()/srand() like interface, this package also has a special state info |
interface. The initstate() routine is called with a seed, an array of |
bytes, and a count of how many bytes are being passed in; this array is |
then initialized to contain information for random number generation with |
that much state information. Good sizes for the amount of state |
information are 32, 64, 128, and 256 bytes. The state can be switched by |
calling the setstate() function with the same array as was initiallized |
with initstate(). By default, the package runs with 128 bytes of state |
information and generates far better random numbers than a linear |
congruential generator. If the amount of state information is less than |
32 bytes, a simple linear congruential R.N.G. is used. Internally, the |
state information is treated as an array of longs; the zeroeth element of |
the array is the type of R.N.G. being used (small integer); the remainder |
of the array is the state information for the R.N.G. Thus, 32 bytes of |
state information will give 7 longs worth of state information, which will |
allow a degree seven polynomial. (Note: The zeroeth word of state |
information also has some other information stored in it; see setstate |
for details). The random number generation technique is a linear feedback |
shift register approach, employing trinomials (since there are fewer terms |
to sum up that way). In this approach, the least significant bit of all |
the numbers in the state table will act as a linear feedback shift register, |
and will have period 2^deg - 1 (where deg is the degree of the polynomial |
being used, assuming that the polynomial is irreducible and primitive). |
The higher order bits will have longer periods, since their values are |
also influenced by pseudo-random carries out of the lower bits. The |
total period of the generator is approximately deg*(2**deg - 1); thus |
doubling the amount of state information has a vast influence on the |
period of the generator. Note: The deg*(2**deg - 1) is an approximation |
only good for large deg, when the period of the shift register is the |
dominant factor. With deg equal to seven, the period is actually much |
longer than the 7*(2**7 - 1) predicted by this formula. */ |
|
|
|
/* For each of the currently supported random number generators, we have a |
break value on the amount of state information (you need at least thi |
bytes of state info to support this random number generator), a degree for |
the polynomial (actually a trinomial) that the R.N.G. is based on, and |
separation between the two lower order coefficients of the trinomial. */ |
|
/* Linear congruential. */ |
#define TYPE_0 0 |
#define BREAK_0 8 |
#define DEG_0 0 |
#define SEP_0 0 |
|
/* x**7 + x**3 + 1. */ |
#define TYPE_1 1 |
#define BREAK_1 32 |
#define DEG_1 7 |
#define SEP_1 3 |
|
/* x**15 + x + 1. */ |
#define TYPE_2 2 |
#define BREAK_2 64 |
#define DEG_2 15 |
#define SEP_2 1 |
|
/* x**31 + x**3 + 1. */ |
#define TYPE_3 3 |
#define BREAK_3 128 |
#define DEG_3 31 |
#define SEP_3 3 |
|
/* x**63 + x + 1. */ |
#define TYPE_4 4 |
#define BREAK_4 256 |
#define DEG_4 63 |
#define SEP_4 1 |
|
|
/* Array versions of the above information to make code run faster. |
Relies on fact that TYPE_i == i. */ |
|
#define MAX_TYPES 5 /* Max number of types above. */ |
|
static int degrees[MAX_TYPES] = { DEG_0, DEG_1, DEG_2, DEG_3, DEG_4 }; |
static int seps[MAX_TYPES] = { SEP_0, SEP_1, SEP_2, SEP_3, SEP_4 }; |
|
|
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/* Initially, everything is set up as if from: |
initstate(1, randtbl, 128); |
Note that this initialization takes advantage of the fact that srandom |
advances the front and rear pointers 10*rand_deg times, and hence the |
rear pointer which starts at 0 will also end up at zero; thus the zeroeth |
element of the state information, which contains info about the current |
position of the rear pointer is just |
(MAX_TYPES * (rptr - state)) + TYPE_3 == TYPE_3. */ |
|
static long int randtbl[DEG_3 + 1] = |
{ TYPE_3, |
0x9a319039, 0x32d9c024, 0x9b663182, 0x5da1f342, |
0xde3b81e0, 0xdf0a6fb5, 0xf103bc02, 0x48f340fb, |
0x7449e56b, 0xbeb1dbb0, 0xab5c5918, 0x946554fd, |
0x8c2e680f, 0xeb3d799f, 0xb11ee0b7, 0x2d436b86, |
0xda672e2a, 0x1588ca88, 0xe369735d, 0x904f35f7, |
0xd7158fd6, 0x6fa6f051, 0x616e6b96, 0xac94efdc, |
0x36413f93, 0xc622c298, 0xf5a42ab8, 0x8a88d77b, |
0xf5ad9d0e, 0x8999220b, 0x27fb47b9 |
}; |
|
/* FPTR and RPTR are two pointers into the state info, a front and a rear |
pointer. These two pointers are always rand_sep places aparts, as they |
cycle through the state information. (Yes, this does mean we could get |
away with just one pointer, but the code for random is more efficient |
this way). The pointers are left positioned as they would be from the call: |
initstate(1, randtbl, 128); |
(The position of the rear pointer, rptr, is really 0 (as explained above |
in the initialization of randtbl) because the state table pointer is set |
to point to randtbl[1] (as explained below).) */ |
|
static long int *fptr = &randtbl[SEP_3 + 1]; |
static long int *rptr = &randtbl[1]; |
|
|
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/* The following things are the pointer to the state information table, |
the type of the current generator, the degree of the current polynomial |
being used, and the separation between the two pointers. |
Note that for efficiency of random, we remember the first location of |
the state information, not the zeroeth. Hence it is valid to access |
state[-1], which is used to store the type of the R.N.G. |
Also, we remember the last location, since this is more efficient than |
indexing every time to find the address of the last element to see if |
the front and rear pointers have wrapped. */ |
|
static long int *state = &randtbl[1]; |
|
static int rand_type = TYPE_3; |
static int rand_deg = DEG_3; |
static int rand_sep = SEP_3; |
|
static long int *end_ptr = &randtbl[sizeof(randtbl) / sizeof(randtbl[0])]; |
|
/* Initialize the random number generator based on the given seed. If the |
type is the trivial no-state-information type, just remember the seed. |
Otherwise, initializes state[] based on the given "seed" via a linear |
congruential generator. Then, the pointers are set to known locations |
that are exactly rand_sep places apart. Lastly, it cycles the state |
information a given number of times to get rid of any initial dependencies |
introduced by the L.C.R.N.G. Note that the initialization of randtbl[] |
for default usage relies on values produced by this routine. */ |
void |
srandom (unsigned int x) |
{ |
state[0] = x; |
if (rand_type != TYPE_0) |
{ |
register long int i; |
for (i = 1; i < rand_deg; ++i) |
state[i] = (1103515145 * state[i - 1]) + 12345; |
fptr = &state[rand_sep]; |
rptr = &state[0]; |
for (i = 0; i < 10 * rand_deg; ++i) |
random(); |
} |
} |
|
/* Initialize the state information in the given array of N bytes for |
future random number generation. Based on the number of bytes we |
are given, and the break values for the different R.N.G.'s, we choose |
the best (largest) one we can and set things up for it. srandom is |
then called to initialize the state information. Note that on return |
from srandom, we set state[-1] to be the type multiplexed with the current |
value of the rear pointer; this is so successive calls to initstate won't |
lose this information and will be able to restart with setstate. |
Note: The first thing we do is save the current state, if any, just like |
setstate so that it doesn't matter when initstate is called. |
Returns a pointer to the old state. */ |
PTR |
initstate (unsigned int seed, PTR arg_state, unsigned long n) |
{ |
PTR ostate = (PTR) &state[-1]; |
|
if (rand_type == TYPE_0) |
state[-1] = rand_type; |
else |
state[-1] = (MAX_TYPES * (rptr - state)) + rand_type; |
if (n < BREAK_1) |
{ |
if (n < BREAK_0) |
{ |
errno = EINVAL; |
return NULL; |
} |
rand_type = TYPE_0; |
rand_deg = DEG_0; |
rand_sep = SEP_0; |
} |
else if (n < BREAK_2) |
{ |
rand_type = TYPE_1; |
rand_deg = DEG_1; |
rand_sep = SEP_1; |
} |
else if (n < BREAK_3) |
{ |
rand_type = TYPE_2; |
rand_deg = DEG_2; |
rand_sep = SEP_2; |
} |
else if (n < BREAK_4) |
{ |
rand_type = TYPE_3; |
rand_deg = DEG_3; |
rand_sep = SEP_3; |
} |
else |
{ |
rand_type = TYPE_4; |
rand_deg = DEG_4; |
rand_sep = SEP_4; |
} |
|
state = &((long int *) arg_state)[1]; /* First location. */ |
/* Must set END_PTR before srandom. */ |
end_ptr = &state[rand_deg]; |
srandom(seed); |
if (rand_type == TYPE_0) |
state[-1] = rand_type; |
else |
state[-1] = (MAX_TYPES * (rptr - state)) + rand_type; |
|
return ostate; |
} |
|
/* Restore the state from the given state array. |
Note: It is important that we also remember the locations of the pointers |
in the current state information, and restore the locations of the pointers |
from the old state information. This is done by multiplexing the pointer |
location into the zeroeth word of the state information. Note that due |
to the order in which things are done, it is OK to call setstate with the |
same state as the current state |
Returns a pointer to the old state information. */ |
|
PTR |
setstate (PTR arg_state) |
{ |
register long int *new_state = (long int *) arg_state; |
register int type = new_state[0] % MAX_TYPES; |
register int rear = new_state[0] / MAX_TYPES; |
PTR ostate = (PTR) &state[-1]; |
|
if (rand_type == TYPE_0) |
state[-1] = rand_type; |
else |
state[-1] = (MAX_TYPES * (rptr - state)) + rand_type; |
|
switch (type) |
{ |
case TYPE_0: |
case TYPE_1: |
case TYPE_2: |
case TYPE_3: |
case TYPE_4: |
rand_type = type; |
rand_deg = degrees[type]; |
rand_sep = seps[type]; |
break; |
default: |
/* State info munged. */ |
errno = EINVAL; |
return NULL; |
} |
|
state = &new_state[1]; |
if (rand_type != TYPE_0) |
{ |
rptr = &state[rear]; |
fptr = &state[(rear + rand_sep) % rand_deg]; |
} |
/* Set end_ptr too. */ |
end_ptr = &state[rand_deg]; |
|
return ostate; |
} |
|
/* If we are using the trivial TYPE_0 R.N.G., just do the old linear |
congruential bit. Otherwise, we do our fancy trinomial stuff, which is the |
same in all ther other cases due to all the global variables that have been |
set up. The basic operation is to add the number at the rear pointer into |
the one at the front pointer. Then both pointers are advanced to the next |
location cyclically in the table. The value returned is the sum generated, |
reduced to 31 bits by throwing away the "least random" low bit. |
Note: The code takes advantage of the fact that both the front and |
rear pointers can't wrap on the same call by not testing the rear |
pointer if the front one has wrapped. Returns a 31-bit random number. */ |
|
long int |
random (void) |
{ |
if (rand_type == TYPE_0) |
{ |
state[0] = ((state[0] * 1103515245) + 12345) & LONG_MAX; |
return state[0]; |
} |
else |
{ |
long int i; |
*fptr += *rptr; |
/* Chucking least random bit. */ |
i = (*fptr >> 1) & LONG_MAX; |
++fptr; |
if (fptr >= end_ptr) |
{ |
fptr = state; |
++rptr; |
} |
else |
{ |
++rptr; |
if (rptr >= end_ptr) |
rptr = state; |
} |
return i; |
} |
} |