/* | |

* 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 [rescinded 22 July 1999] | |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. | |

*/ | |

/* | |

@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__ | |

# ifndef NULL | |

# define NULL (void *) 0 | |

# endif | |

#else | |

# 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 }; | |

/* 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]; | |

/* 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. */ | |

void * | |

initstate (unsigned int seed, void *arg_state, unsigned long n) | |

{ | |

void *ostate = (void *) &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. */ | |

void * | |

setstate (void *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; | |

void *ostate = (void *) &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; | |

} | |

} |