380 lines
13 KiB
C
380 lines
13 KiB
C
/*
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* Copyright (c) 1983 Regents of the University of California.
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* All rights reserved.
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*
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* Redistribution and use in source and binary forms are permitted
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* provided that the above copyright notice and this paragraph are
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* duplicated in all such forms and that any documentation,
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* advertising materials, and other materials related to such
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* distribution and use acknowledge that the software was developed
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* by the University of California, Berkeley. The name of the
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* University may not be used to endorse or promote products derived
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* from this software without specific prior written permission.
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* THIS SOFTWARE IS PROVIDED ``AS IS'' AND WITHOUT ANY EXPRESS OR
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* IMPLIED WARRANTIES, INCLUDING, WITHOUT LIMITATION, THE IMPLIED
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* WARRANTIES OF MERCHANTIBILITY AND FITNESS FOR A PARTICULAR PURPOSE.
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*/
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#if defined(LIBC_SCCS) && !defined(lint)
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static char sccsid[] = "@(#)random.c 5.5 (Berkeley) 7/6/88";
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#endif /* LIBC_SCCS and not lint */
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#include <stdio.h>
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#include "random.h" /* GAWK ADDITION */
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/*
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* random.c:
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* An improved random number generation package. In addition to the standard
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* rand()/srand() like interface, this package also has a special state info
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* interface. The initstate() routine is called with a seed, an array of
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* bytes, and a count of how many bytes are being passed in; this array is then
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* initialized to contain information for random number generation with that
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* much state information. Good sizes for the amount of state information are
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* 32, 64, 128, and 256 bytes. The state can be switched by calling the
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* setstate() routine with the same array as was initiallized with initstate().
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* By default, the package runs with 128 bytes of state information and
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* generates far better random numbers than a linear congruential generator.
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* If the amount of state information is less than 32 bytes, a simple linear
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* congruential R.N.G. is used.
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* Internally, the state information is treated as an array of longs; the
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* zeroeth element of the array is the type of R.N.G. being used (small
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* integer); the remainder of the array is the state information for the
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* R.N.G. Thus, 32 bytes of state information will give 7 longs worth of
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* state information, which will allow a degree seven polynomial. (Note: the
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* zeroeth word of state information also has some other information stored
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* in it -- see setstate() for details).
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* The random number generation technique is a linear feedback shift register
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* approach, employing trinomials (since there are fewer terms to sum up that
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* way). In this approach, the least significant bit of all the numbers in
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* the state table will act as a linear feedback shift register, and will have
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* period 2^deg - 1 (where deg is the degree of the polynomial being used,
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* assuming that the polynomial is irreducible and primitive). The higher
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* order bits will have longer periods, since their values are also influenced
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* by pseudo-random carries out of the lower bits. The total period of the
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* generator is approximately deg*(2**deg - 1); thus doubling the amount of
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* state information has a vast influence on the period of the generator.
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* Note: the deg*(2**deg - 1) is an approximation only good for large deg,
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* when the period of the shift register is the dominant factor. With deg
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* equal to seven, the period is actually much longer than the 7*(2**7 - 1)
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* predicted by this formula.
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*/
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/*
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* For each of the currently supported random number generators, we have a
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* break value on the amount of state information (you need at least this
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* many bytes of state info to support this random number generator), a degree
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* for the polynomial (actually a trinomial) that the R.N.G. is based on, and
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* the separation between the two lower order coefficients of the trinomial.
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*/
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#define TYPE_0 0 /* linear congruential */
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#define BREAK_0 8
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#define DEG_0 0
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#define SEP_0 0
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#define TYPE_1 1 /* x**7 + x**3 + 1 */
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#define BREAK_1 32
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#define DEG_1 7
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#define SEP_1 3
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#define TYPE_2 2 /* x**15 + x + 1 */
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#define BREAK_2 64
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#define DEG_2 15
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#define SEP_2 1
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#define TYPE_3 3 /* x**31 + x**3 + 1 */
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#define BREAK_3 128
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#define DEG_3 31
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#define SEP_3 3
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#ifdef _CRAY
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#define DEG_3_P1 32 /* bug - do addition here */
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#define SEP_3_P1 4 /* *_3 + 1 = _3_P1 */
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#endif
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#define TYPE_4 4 /* x**63 + x + 1 */
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#define BREAK_4 256
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#define DEG_4 63
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#define SEP_4 1
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/*
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* Array versions of the above information to make code run faster -- relies
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* on fact that TYPE_i == i.
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*/
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#define MAX_TYPES 5 /* max number of types above */
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static int degrees[ MAX_TYPES ] = { DEG_0, DEG_1, DEG_2,
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DEG_3, DEG_4 };
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static int seps[ MAX_TYPES ] = { SEP_0, SEP_1, SEP_2,
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SEP_3, SEP_4 };
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/*
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* Initially, everything is set up as if from :
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* initstate( 1, &randtbl, 128 );
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* Note that this initialization takes advantage of the fact that srandom()
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* advances the front and rear pointers 10*rand_deg times, and hence the
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* rear pointer which starts at 0 will also end up at zero; thus the zeroeth
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* element of the state information, which contains info about the current
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* position of the rear pointer is just
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* MAX_TYPES*(rptr - state) + TYPE_3 == TYPE_3.
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*/
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static long randtbl[ DEG_3 + 1 ] = { TYPE_3,
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0x9a319039, 0x32d9c024, 0x9b663182, 0x5da1f342,
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0xde3b81e0, 0xdf0a6fb5, 0xf103bc02, 0x48f340fb,
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0x7449e56b, 0xbeb1dbb0, 0xab5c5918, 0x946554fd,
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0x8c2e680f, 0xeb3d799f, 0xb11ee0b7, 0x2d436b86,
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0xda672e2a, 0x1588ca88, 0xe369735d, 0x904f35f7,
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0xd7158fd6, 0x6fa6f051, 0x616e6b96, 0xac94efdc,
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0x36413f93, 0xc622c298, 0xf5a42ab8, 0x8a88d77b,
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0xf5ad9d0e, 0x8999220b, 0x27fb47b9 };
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/*
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* fptr and rptr are two pointers into the state info, a front and a rear
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* pointer. These two pointers are always rand_sep places aparts, as they cycle
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* cyclically through the state information. (Yes, this does mean we could get
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* away with just one pointer, but the code for random() is more efficient this
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* way). The pointers are left positioned as they would be from the call
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* initstate( 1, randtbl, 128 )
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* (The position of the rear pointer, rptr, is really 0 (as explained above
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* in the initialization of randtbl) because the state table pointer is set
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* to point to randtbl[1] (as explained below).
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*/
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#ifdef _CRAY
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static long *fptr = &randtbl[ SEP_3_P1 ];
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#else
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static long *fptr = &randtbl[ SEP_3 + 1 ];
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#endif
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static long *rptr = &randtbl[ 1 ];
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/*
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* The following things are the pointer to the state information table,
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* the type of the current generator, the degree of the current polynomial
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* being used, and the separation between the two pointers.
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* Note that for efficiency of random(), we remember the first location of
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* the state information, not the zeroeth. Hence it is valid to access
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* state[-1], which is used to store the type of the R.N.G.
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* Also, we remember the last location, since this is more efficient than
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* indexing every time to find the address of the last element to see if
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* the front and rear pointers have wrapped.
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*/
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static long *state = &randtbl[ 1 ];
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static int rand_type = TYPE_3;
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static int rand_deg = DEG_3;
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static int rand_sep = SEP_3;
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#ifdef _CRAY
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static long *end_ptr = &randtbl[ DEG_3_P1 ];
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#else
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static long *end_ptr = &randtbl[ DEG_3 + 1 ];
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#endif
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/*
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* srandom:
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* Initialize the random number generator based on the given seed. If the
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* type is the trivial no-state-information type, just remember the seed.
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* Otherwise, initializes state[] based on the given "seed" via a linear
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* congruential generator. Then, the pointers are set to known locations
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* that are exactly rand_sep places apart. Lastly, it cycles the state
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* information a given number of times to get rid of any initial dependencies
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* introduced by the L.C.R.N.G.
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* Note that the initialization of randtbl[] for default usage relies on
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* values produced by this routine.
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*/
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void
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srandom( x )
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unsigned x;
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{
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register int i, j;
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long random();
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if( rand_type == TYPE_0 ) {
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state[ 0 ] = x;
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}
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else {
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j = 1;
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state[ 0 ] = x;
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for( i = 1; i < rand_deg; i++ ) {
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state[i] = 1103515245*state[i - 1] + 12345;
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}
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fptr = &state[ rand_sep ];
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rptr = &state[ 0 ];
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for( i = 0; i < 10*rand_deg; i++ ) random();
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}
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}
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/*
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* initstate:
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* Initialize the state information in the given array of n bytes for
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* future random number generation. Based on the number of bytes we
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* are given, and the break values for the different R.N.G.'s, we choose
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* the best (largest) one we can and set things up for it. srandom() is
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* then called to initialize the state information.
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* Note that on return from srandom(), we set state[-1] to be the type
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* multiplexed with the current value of the rear pointer; this is so
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* successive calls to initstate() won't lose this information and will
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* be able to restart with setstate().
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* Note: the first thing we do is save the current state, if any, just like
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* setstate() so that it doesn't matter when initstate is called.
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* Returns a pointer to the old state.
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*/
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char *
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initstate( seed, arg_state, n )
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unsigned seed; /* seed for R. N. G. */
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char *arg_state; /* pointer to state array */
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int n; /* # bytes of state info */
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{
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register char *ostate = (char *)( &state[ -1 ] );
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if( rand_type == TYPE_0 ) state[ -1 ] = rand_type;
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else state[ -1 ] = MAX_TYPES*(rptr - state) + rand_type;
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if( n < BREAK_1 ) {
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if( n < BREAK_0 ) {
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fprintf( stderr, "initstate: not enough state (%d bytes) with which to do jack; ignored.\n", n );
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return 0;
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}
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rand_type = TYPE_0;
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rand_deg = DEG_0;
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rand_sep = SEP_0;
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}
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else {
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if( n < BREAK_2 ) {
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rand_type = TYPE_1;
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rand_deg = DEG_1;
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rand_sep = SEP_1;
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}
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else {
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if( n < BREAK_3 ) {
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rand_type = TYPE_2;
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rand_deg = DEG_2;
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rand_sep = SEP_2;
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}
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else {
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if( n < BREAK_4 ) {
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rand_type = TYPE_3;
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rand_deg = DEG_3;
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rand_sep = SEP_3;
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}
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else {
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rand_type = TYPE_4;
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rand_deg = DEG_4;
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rand_sep = SEP_4;
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}
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}
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}
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}
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state = &( ( (long *)arg_state )[1] ); /* first location */
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end_ptr = &state[ rand_deg ]; /* must set end_ptr before srandom */
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srandom( seed );
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if( rand_type == TYPE_0 ) state[ -1 ] = rand_type;
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else state[ -1 ] = MAX_TYPES*(rptr - state) + rand_type;
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return( ostate );
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}
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/*
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* setstate:
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* Restore the state from the given state array.
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* Note: it is important that we also remember the locations of the pointers
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* in the current state information, and restore the locations of the pointers
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* from the old state information. This is done by multiplexing the pointer
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* location into the zeroeth word of the state information.
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* Note that due to the order in which things are done, it is OK to call
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* setstate() with the same state as the current state.
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* Returns a pointer to the old state information.
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*/
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char *
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setstate( arg_state )
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char *arg_state;
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{
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register long *new_state = (long *)arg_state;
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register int type = new_state[0]%MAX_TYPES;
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register int rear = new_state[0]/MAX_TYPES;
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char *ostate = (char *)( &state[ -1 ] );
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if( rand_type == TYPE_0 ) state[ -1 ] = rand_type;
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else state[ -1 ] = MAX_TYPES*(rptr - state) + rand_type;
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switch( type ) {
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case TYPE_0:
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case TYPE_1:
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case TYPE_2:
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case TYPE_3:
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case TYPE_4:
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rand_type = type;
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rand_deg = degrees[ type ];
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rand_sep = seps[ type ];
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break;
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default:
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fprintf( stderr, "setstate: state info has been munged; not changed.\n" );
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}
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state = &new_state[ 1 ];
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if( rand_type != TYPE_0 ) {
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rptr = &state[ rear ];
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fptr = &state[ (rear + rand_sep)%rand_deg ];
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}
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end_ptr = &state[ rand_deg ]; /* set end_ptr too */
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return( ostate );
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}
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/*
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* random:
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* If we are using the trivial TYPE_0 R.N.G., just do the old linear
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* congruential bit. Otherwise, we do our fancy trinomial stuff, which is the
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* same in all ther other cases due to all the global variables that have been
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* set up. The basic operation is to add the number at the rear pointer into
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* the one at the front pointer. Then both pointers are advanced to the next
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* location cyclically in the table. The value returned is the sum generated,
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* reduced to 31 bits by throwing away the "least random" low bit.
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* Note: the code takes advantage of the fact that both the front and
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* rear pointers can't wrap on the same call by not testing the rear
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* pointer if the front one has wrapped.
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* Returns a 31-bit random number.
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*/
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long
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random()
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{
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long i;
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if( rand_type == TYPE_0 ) {
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i = state[0] = ( state[0]*1103515245 + 12345 )&0x7fffffff;
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}
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else {
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*fptr += *rptr;
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i = (*fptr >> 1)&0x7fffffff; /* chucking least random bit */
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if( ++fptr >= end_ptr ) {
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fptr = state;
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++rptr;
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}
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else {
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if( ++rptr >= end_ptr ) rptr = state;
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}
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}
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return( i );
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}
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