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- #include <stdio.h>
- #include <stdlib.h>
- /*
- * random.c:
- * 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() routine 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 this
- * many 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
- * the separation between the two lower order coefficients of the trinomial.
- */
- #define TYPE_0 0 /* linear congruential */
- #define BREAK_0 8
- #define DEG_0 0
- #define SEP_0 0
- #define TYPE_1 1 /* x**7 + x**3 + 1 */
- #define BREAK_1 32
- #define DEG_1 7
- #define SEP_1 3
- #define TYPE_2 2 /* x**15 + x + 1 */
- #define BREAK_2 64
- #define DEG_2 15
- #define SEP_2 1
- #define TYPE_3 3 /* x**31 + x**3 + 1 */
- #define BREAK_3 128
- #define DEG_3 31
- #define SEP_3 3
- #define TYPE_4 4 /* x**63 + x + 1 */
- #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 struct _randomjunk {
- int degrees[MAX_TYPES];
- int seps[MAX_TYPES];
- long randtbl[ DEG_3 + 1 ];
- /*
- * 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
- * cyclically 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).
- */
- long *fptr, *rptr;
- /*
- * 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.
- */
- long *state;
- int rand_type, rand_deg, rand_sep;
- long *end_ptr;
- } *__randomjunk, *_randomjunk(void), _randominit = {
- /*
- * 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.
- */
- { DEG_0, DEG_1, DEG_2, DEG_3, DEG_4 },
- { SEP_0, SEP_1, SEP_2, SEP_3, SEP_4 },
- { TYPE_3,
- (long)0x9a319039, (long)0x32d9c024, (long)0x9b663182, (long)0x5da1f342,
- (long)0xde3b81e0, (long)0xdf0a6fb5, (long)0xf103bc02, (long)0x48f340fb,
- (long)0x7449e56b, (long)0xbeb1dbb0, (long)0xab5c5918, (long)0x946554fd,
- (long)0x8c2e680f, (long)0xeb3d799f, (long)0xb11ee0b7, (long)0x2d436b86,
- (long)0xda672e2a, (long)0x1588ca88, (long)0xe369735d, (long)0x904f35f7,
- (long)0xd7158fd6, (long)0x6fa6f051, (long)0x616e6b96, (long)0xac94efdc,
- (long)0x36413f93, (long)0xc622c298, (long)0xf5a42ab8, (long)0x8a88d77b,
- (long)0xf5ad9d0e, (long)0x8999220b, (long)0x27fb47b9 },
- &_randominit.randtbl[ SEP_3 + 1 ],
- &_randominit.randtbl[1],
- &_randominit.randtbl[1],
- TYPE_3, DEG_3, SEP_3,
- &_randominit.randtbl[ DEG_3 + 1]
- };
- long random(void);
- static struct _randomjunk *
- _randomjunk(void)
- {
- struct _randomjunk *rp = __randomjunk;
- if (rp == 0) {
- rp = (struct _randomjunk *)malloc(sizeof (*rp));
- if (rp == 0)
- return (0);
- *rp = _randominit;
- __randomjunk = rp;
- }
- return (rp);
- }
- /*
- * srandom:
- * 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 x)
- {
- struct _randomjunk *rp = _randomjunk();
- int i;
- if (rp == 0)
- return;
- if (rp->rand_type == TYPE_0) {
- rp->state[0] = x;
- } else {
- rp->state[0] = x;
- for (i = 1; i < rp->rand_deg; i++) {
- rp->state[i] = 1103515245*rp->state[i - 1] + 12345;
- }
- rp->fptr = &rp->state[rp->rand_sep];
- rp->rptr = &rp->state[0];
- for (i = 0; i < 10 * rp->rand_deg; i++)
- random();
- }
- }
- /*
- * initstate:
- * 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.
- *
- * Arguments:
- * seed: seed for R. N. G.
- * arg_state: pointer to state array
- * n: # bytes of state info
- */
- char *
- initstate(unsigned seed, char *arg_state, int n)
- {
- struct _randomjunk *rp = _randomjunk();
- char *ostate;
- if (rp == 0)
- return (0);
- ostate = (char *)(&rp->state[-1]);
- if (rp->rand_type == TYPE_0) rp->state[-1] = rp->rand_type;
- else rp->state[-1] =
- MAX_TYPES*(rp->rptr - rp->state) + rp->rand_type;
- if (n < BREAK_0) {
- fprintf(stderr,
- "initstate: state array too small, ignored; minimum size is %d bytes\n",
- BREAK_0);
- return (0);
- } else if (n < BREAK_1) {
- rp->rand_type = TYPE_0;
- rp->rand_deg = DEG_0;
- rp->rand_sep = SEP_0;
- } else if (n < BREAK_2) {
- rp->rand_type = TYPE_1;
- rp->rand_deg = DEG_1;
- rp->rand_sep = SEP_1;
- } else if (n < BREAK_3) {
- rp->rand_type = TYPE_2;
- rp->rand_deg = DEG_2;
- rp->rand_sep = SEP_2;
- } else if (n < BREAK_4) {
- rp->rand_type = TYPE_3;
- rp->rand_deg = DEG_3;
- rp->rand_sep = SEP_3;
- } else {
- rp->rand_type = TYPE_4;
- rp->rand_deg = DEG_4;
- rp->rand_sep = SEP_4;
- }
- rp->state = &((long *)arg_state)[1]; /* first location */
- rp->end_ptr = &rp->state[rp->rand_deg]; /* set end_ptr before srandom */
- srandom(seed);
- rp->state[-1] = (rp->rand_type == TYPE_0) ? rp->rand_type
- : MAX_TYPES * (rp->rptr - rp->state) + rp->rand_type;
- return (ostate);
- }
- /*
- * setstate:
- * 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.
- */
- char *
- setstate(char *arg_state)
- {
- struct _randomjunk *rp = _randomjunk();
- long *new_state;
- int type;
- int rear;
- char *ostate;
- if (rp == 0)
- return (0);
- new_state = (long *)arg_state;
- type = new_state[0] % MAX_TYPES;
- rear = new_state[0] / MAX_TYPES;
- ostate = (char *)(&rp->state[-1]);
- rp->state[-1] = (rp->rand_type == TYPE_0) ? rp->rand_type
- : MAX_TYPES*(rp->rptr - rp->state) + rp->rand_type;
- switch (type) {
- case TYPE_0:
- case TYPE_1:
- case TYPE_2:
- case TYPE_3:
- case TYPE_4:
- rp->rand_type = type;
- rp->rand_deg = rp->degrees[type];
- rp->rand_sep = rp->seps[type];
- break;
- default:
- fprintf(stderr, "setstate: invalid state info; not changed.\n");
- }
- rp->state = &new_state[1];
- if (rp->rand_type != TYPE_0) {
- rp->rptr = &rp->state[rear];
- rp->fptr = &rp->state[(rear + rp->rand_sep) % rp->rand_deg];
- }
- rp->end_ptr = &rp->state[rp->rand_deg]; /* set end_ptr too */
- return (ostate);
- }
- /*
- * random:
- * 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
- random(void)
- {
- struct _randomjunk *rp = _randomjunk();
- long i;
- if (rp == 0)
- return (0);
- if (rp->rand_type == TYPE_0) {
- i = rp->state[0] = (rp->state[0]*1103515245 + 12345)&0x7fffffff;
- } else {
- *rp->fptr += *rp->rptr;
- i = (*rp->fptr >> 1)&0x7fffffff; /* chucking least random bit */
- if (++rp->fptr >= rp->end_ptr) {
- rp->fptr = rp->state;
- ++rp->rptr;
- } else if (++rp->rptr >= rp->end_ptr)
- rp->rptr = rp->state;
- }
- return (i);
- }
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发表于 2006-03-29 17:03
发表于 2006-03-30 14:44
