# random.c之随机数字生成C语言源代码欣赏

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/*
* Copyright (c) 1983 Regents of the University of California.
*
* Redistribution and use in source and binary forms are permitted
* provided that the above copyright notice and this paragraph are
* duplicated in all such forms and that any documentation,
* advertising materials, and other materials related to such
* distribution and use acknowledge that the software was developed
* by the University of California, Berkeley.  The name of the
* University may not be used to endorse or promote products derived
* from this software without specific prior written permission.
* THIS SOFTWARE IS PROVIDED AS IS'' AND WITHOUT ANY EXPRESS OR
* IMPLIED WARRANTIES, INCLUDING, WITHOUT LIMITATION, THE IMPLIED
* WARRANTIES OF MERCHANTIBILITY AND FITNESS FOR A PARTICULAR PURPOSE.
*/

/*
* 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.
*/

#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 ();

/* 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 };

/* 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,
};

/* 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];

/* 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 (x)
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
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 (seed, arg_state, n)
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 (arg_state)
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 ()
{
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;
}
}


posted on 2011-02-03 14:46 cnmaizi 阅读(...) 评论(...) 编辑 收藏