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Annotation of 43BSDTahoe/lib/libc/gen/random.c, revision 1.1

1.1     ! root        1: /*
        !             2:  * Copyright (c) 1983 Regents of the University of California.
        !             3:  * All rights reserved.
        !             4:  *
        !             5:  * Redistribution and use in source and binary forms are permitted
        !             6:  * provided that the above copyright notice and this paragraph are
        !             7:  * duplicated in all such forms and that any documentation,
        !             8:  * advertising materials, and other materials related to such
        !             9:  * distribution and use acknowledge that the software was developed
        !            10:  * by the University of California, Berkeley.  The name of the
        !            11:  * University may not be used to endorse or promote products derived
        !            12:  * from this software without specific prior written permission.
        !            13:  * THIS SOFTWARE IS PROVIDED ``AS IS'' AND WITHOUT ANY EXPRESS OR
        !            14:  * IMPLIED WARRANTIES, INCLUDING, WITHOUT LIMITATION, THE IMPLIED
        !            15:  * WARRANTIES OF MERCHANTIBILITY AND FITNESS FOR A PARTICULAR PURPOSE.
        !            16:  */
        !            17: 
        !            18: #if defined(LIBC_SCCS) && !defined(lint)
        !            19: static char sccsid[] = "@(#)random.c   5.5 (Berkeley) 7/6/88";
        !            20: #endif /* LIBC_SCCS and not lint */
        !            21: 
        !            22: #include <stdio.h>
        !            23: 
        !            24: /*
        !            25:  * random.c:
        !            26:  * An improved random number generation package.  In addition to the standard
        !            27:  * rand()/srand() like interface, this package also has a special state info
        !            28:  * interface.  The initstate() routine is called with a seed, an array of
        !            29:  * bytes, and a count of how many bytes are being passed in; this array is then
        !            30:  * initialized to contain information for random number generation with that
        !            31:  * much state information.  Good sizes for the amount of state information are
        !            32:  * 32, 64, 128, and 256 bytes.  The state can be switched by calling the
        !            33:  * setstate() routine with the same array as was initiallized with initstate().
        !            34:  * By default, the package runs with 128 bytes of state information and
        !            35:  * generates far better random numbers than a linear congruential generator.
        !            36:  * If the amount of state information is less than 32 bytes, a simple linear
        !            37:  * congruential R.N.G. is used.
        !            38:  * Internally, the state information is treated as an array of longs; the
        !            39:  * zeroeth element of the array is the type of R.N.G. being used (small
        !            40:  * integer); the remainder of the array is the state information for the
        !            41:  * R.N.G.  Thus, 32 bytes of state information will give 7 longs worth of
        !            42:  * state information, which will allow a degree seven polynomial.  (Note: the 
        !            43:  * zeroeth word of state information also has some other information stored
        !            44:  * in it -- see setstate() for details).
        !            45:  * The random number generation technique is a linear feedback shift register
        !            46:  * approach, employing trinomials (since there are fewer terms to sum up that
        !            47:  * way).  In this approach, the least significant bit of all the numbers in
        !            48:  * the state table will act as a linear feedback shift register, and will have
        !            49:  * period 2^deg - 1 (where deg is the degree of the polynomial being used,
        !            50:  * assuming that the polynomial is irreducible and primitive).  The higher
        !            51:  * order bits will have longer periods, since their values are also influenced
        !            52:  * by pseudo-random carries out of the lower bits.  The total period of the
        !            53:  * generator is approximately deg*(2**deg - 1); thus doubling the amount of
        !            54:  * state information has a vast influence on the period of the generator.
        !            55:  * Note: the deg*(2**deg - 1) is an approximation only good for large deg,
        !            56:  * when the period of the shift register is the dominant factor.  With deg
        !            57:  * equal to seven, the period is actually much longer than the 7*(2**7 - 1)
        !            58:  * predicted by this formula.
        !            59:  */
        !            60: 
        !            61: 
        !            62: 
        !            63: /*
        !            64:  * For each of the currently supported random number generators, we have a
        !            65:  * break value on the amount of state information (you need at least this
        !            66:  * many bytes of state info to support this random number generator), a degree
        !            67:  * for the polynomial (actually a trinomial) that the R.N.G. is based on, and
        !            68:  * the separation between the two lower order coefficients of the trinomial.
        !            69:  */
        !            70: 
        !            71: #define                TYPE_0          0               /* linear congruential */
        !            72: #define                BREAK_0         8
        !            73: #define                DEG_0           0
        !            74: #define                SEP_0           0
        !            75: 
        !            76: #define                TYPE_1          1               /* x**7 + x**3 + 1 */
        !            77: #define                BREAK_1         32
        !            78: #define                DEG_1           7
        !            79: #define                SEP_1           3
        !            80: 
        !            81: #define                TYPE_2          2               /* x**15 + x + 1 */
        !            82: #define                BREAK_2         64
        !            83: #define                DEG_2           15
        !            84: #define                SEP_2           1
        !            85: 
        !            86: #define                TYPE_3          3               /* x**31 + x**3 + 1 */
        !            87: #define                BREAK_3         128
        !            88: #define                DEG_3           31
        !            89: #define                SEP_3           3
        !            90: 
        !            91: #define                TYPE_4          4               /* x**63 + x + 1 */
        !            92: #define                BREAK_4         256
        !            93: #define                DEG_4           63
        !            94: #define                SEP_4           1
        !            95: 
        !            96: 
        !            97: /*
        !            98:  * Array versions of the above information to make code run faster -- relies
        !            99:  * on fact that TYPE_i == i.
        !           100:  */
        !           101: 
        !           102: #define                MAX_TYPES       5               /* max number of types above */
        !           103: 
        !           104: static  int            degrees[ MAX_TYPES ]    = { DEG_0, DEG_1, DEG_2,
        !           105:                                                                DEG_3, DEG_4 };
        !           106: 
        !           107: static  int            seps[ MAX_TYPES ]       = { SEP_0, SEP_1, SEP_2,
        !           108:                                                                SEP_3, SEP_4 };
        !           109: 
        !           110: 
        !           111: 
        !           112: /*
        !           113:  * Initially, everything is set up as if from :
        !           114:  *             initstate( 1, &randtbl, 128 );
        !           115:  * Note that this initialization takes advantage of the fact that srandom()
        !           116:  * advances the front and rear pointers 10*rand_deg times, and hence the
        !           117:  * rear pointer which starts at 0 will also end up at zero; thus the zeroeth
        !           118:  * element of the state information, which contains info about the current
        !           119:  * position of the rear pointer is just
        !           120:  *     MAX_TYPES*(rptr - state) + TYPE_3 == TYPE_3.
        !           121:  */
        !           122: 
        !           123: static  long           randtbl[ DEG_3 + 1 ]    = { TYPE_3,
        !           124:                            0x9a319039, 0x32d9c024, 0x9b663182, 0x5da1f342, 
        !           125:                            0xde3b81e0, 0xdf0a6fb5, 0xf103bc02, 0x48f340fb, 
        !           126:                            0x7449e56b, 0xbeb1dbb0, 0xab5c5918, 0x946554fd, 
        !           127:                            0x8c2e680f, 0xeb3d799f, 0xb11ee0b7, 0x2d436b86, 
        !           128:                            0xda672e2a, 0x1588ca88, 0xe369735d, 0x904f35f7, 
        !           129:                            0xd7158fd6, 0x6fa6f051, 0x616e6b96, 0xac94efdc, 
        !           130:                            0x36413f93, 0xc622c298, 0xf5a42ab8, 0x8a88d77b, 
        !           131:                                        0xf5ad9d0e, 0x8999220b, 0x27fb47b9 };
        !           132: 
        !           133: /*
        !           134:  * fptr and rptr are two pointers into the state info, a front and a rear
        !           135:  * pointer.  These two pointers are always rand_sep places aparts, as they cycle
        !           136:  * cyclically through the state information.  (Yes, this does mean we could get
        !           137:  * away with just one pointer, but the code for random() is more efficient this
        !           138:  * way).  The pointers are left positioned as they would be from the call
        !           139:  *                     initstate( 1, randtbl, 128 )
        !           140:  * (The position of the rear pointer, rptr, is really 0 (as explained above
        !           141:  * in the initialization of randtbl) because the state table pointer is set
        !           142:  * to point to randtbl[1] (as explained below).
        !           143:  */
        !           144: 
        !           145: static  long           *fptr                   = &randtbl[ SEP_3 + 1 ];
        !           146: static  long           *rptr                   = &randtbl[ 1 ];
        !           147: 
        !           148: 
        !           149: 
        !           150: /*
        !           151:  * The following things are the pointer to the state information table,
        !           152:  * the type of the current generator, the degree of the current polynomial
        !           153:  * being used, and the separation between the two pointers.
        !           154:  * Note that for efficiency of random(), we remember the first location of
        !           155:  * the state information, not the zeroeth.  Hence it is valid to access
        !           156:  * state[-1], which is used to store the type of the R.N.G.
        !           157:  * Also, we remember the last location, since this is more efficient than
        !           158:  * indexing every time to find the address of the last element to see if
        !           159:  * the front and rear pointers have wrapped.
        !           160:  */
        !           161: 
        !           162: static  long           *state                  = &randtbl[ 1 ];
        !           163: 
        !           164: static  int            rand_type               = TYPE_3;
        !           165: static  int            rand_deg                = DEG_3;
        !           166: static  int            rand_sep                = SEP_3;
        !           167: 
        !           168: static  long           *end_ptr                = &randtbl[ DEG_3 + 1 ];
        !           169: 
        !           170: 
        !           171: 
        !           172: /*
        !           173:  * srandom:
        !           174:  * Initialize the random number generator based on the given seed.  If the
        !           175:  * type is the trivial no-state-information type, just remember the seed.
        !           176:  * Otherwise, initializes state[] based on the given "seed" via a linear
        !           177:  * congruential generator.  Then, the pointers are set to known locations
        !           178:  * that are exactly rand_sep places apart.  Lastly, it cycles the state
        !           179:  * information a given number of times to get rid of any initial dependencies
        !           180:  * introduced by the L.C.R.N.G.
        !           181:  * Note that the initialization of randtbl[] for default usage relies on
        !           182:  * values produced by this routine.
        !           183:  */
        !           184: 
        !           185: srandom( x )
        !           186: 
        !           187:     unsigned           x;
        !           188: {
        !           189:        register  int           i, j;
        !           190:        long random();
        !           191: 
        !           192:        if(  rand_type  ==  TYPE_0  )  {
        !           193:            state[ 0 ] = x;
        !           194:        }
        !           195:        else  {
        !           196:            j = 1;
        !           197:            state[ 0 ] = x;
        !           198:            for( i = 1; i < rand_deg; i++ )  {
        !           199:                state[i] = 1103515245*state[i - 1] + 12345;
        !           200:            }
        !           201:            fptr = &state[ rand_sep ];
        !           202:            rptr = &state[ 0 ];
        !           203:            for( i = 0; i < 10*rand_deg; i++ )  random();
        !           204:        }
        !           205: }
        !           206: 
        !           207: 
        !           208: 
        !           209: /*
        !           210:  * initstate:
        !           211:  * Initialize the state information in the given array of n bytes for
        !           212:  * future random number generation.  Based on the number of bytes we
        !           213:  * are given, and the break values for the different R.N.G.'s, we choose
        !           214:  * the best (largest) one we can and set things up for it.  srandom() is
        !           215:  * then called to initialize the state information.
        !           216:  * Note that on return from srandom(), we set state[-1] to be the type
        !           217:  * multiplexed with the current value of the rear pointer; this is so
        !           218:  * successive calls to initstate() won't lose this information and will
        !           219:  * be able to restart with setstate().
        !           220:  * Note: the first thing we do is save the current state, if any, just like
        !           221:  * setstate() so that it doesn't matter when initstate is called.
        !           222:  * Returns a pointer to the old state.
        !           223:  */
        !           224: 
        !           225: char  *
        !           226: initstate( seed, arg_state, n )
        !           227: 
        !           228:     unsigned           seed;                   /* seed for R. N. G. */
        !           229:     char               *arg_state;             /* pointer to state array */
        !           230:     int                        n;                      /* # bytes of state info */
        !           231: {
        !           232:        register  char          *ostate         = (char *)( &state[ -1 ] );
        !           233: 
        !           234:        if(  rand_type  ==  TYPE_0  )  state[ -1 ] = rand_type;
        !           235:        else  state[ -1 ] = MAX_TYPES*(rptr - state) + rand_type;
        !           236:        if(  n  <  BREAK_1  )  {
        !           237:            if(  n  <  BREAK_0  )  {
        !           238:                fprintf( stderr, "initstate: not enough state (%d bytes) with which to do jack; ignored.\n", n );
        !           239:                return;
        !           240:            }
        !           241:            rand_type = TYPE_0;
        !           242:            rand_deg = DEG_0;
        !           243:            rand_sep = SEP_0;
        !           244:        }
        !           245:        else  {
        !           246:            if(  n  <  BREAK_2  )  {
        !           247:                rand_type = TYPE_1;
        !           248:                rand_deg = DEG_1;
        !           249:                rand_sep = SEP_1;
        !           250:            }
        !           251:            else  {
        !           252:                if(  n  <  BREAK_3  )  {
        !           253:                    rand_type = TYPE_2;
        !           254:                    rand_deg = DEG_2;
        !           255:                    rand_sep = SEP_2;
        !           256:                }
        !           257:                else  {
        !           258:                    if(  n  <  BREAK_4  )  {
        !           259:                        rand_type = TYPE_3;
        !           260:                        rand_deg = DEG_3;
        !           261:                        rand_sep = SEP_3;
        !           262:                    }
        !           263:                    else  {
        !           264:                        rand_type = TYPE_4;
        !           265:                        rand_deg = DEG_4;
        !           266:                        rand_sep = SEP_4;
        !           267:                    }
        !           268:                }
        !           269:            }
        !           270:        }
        !           271:        state = &(  ( (long *)arg_state )[1]  );        /* first location */
        !           272:        end_ptr = &state[ rand_deg ];   /* must set end_ptr before srandom */
        !           273:        srandom( seed );
        !           274:        if(  rand_type  ==  TYPE_0  )  state[ -1 ] = rand_type;
        !           275:        else  state[ -1 ] = MAX_TYPES*(rptr - state) + rand_type;
        !           276:        return( ostate );
        !           277: }
        !           278: 
        !           279: 
        !           280: 
        !           281: /*
        !           282:  * setstate:
        !           283:  * Restore the state from the given state array.
        !           284:  * Note: it is important that we also remember the locations of the pointers
        !           285:  * in the current state information, and restore the locations of the pointers
        !           286:  * from the old state information.  This is done by multiplexing the pointer
        !           287:  * location into the zeroeth word of the state information.
        !           288:  * Note that due to the order in which things are done, it is OK to call
        !           289:  * setstate() with the same state as the current state.
        !           290:  * Returns a pointer to the old state information.
        !           291:  */
        !           292: 
        !           293: char  *
        !           294: setstate( arg_state )
        !           295: 
        !           296:     char               *arg_state;
        !           297: {
        !           298:        register  long          *new_state      = (long *)arg_state;
        !           299:        register  int           type            = new_state[0]%MAX_TYPES;
        !           300:        register  int           rear            = new_state[0]/MAX_TYPES;
        !           301:        char                    *ostate         = (char *)( &state[ -1 ] );
        !           302: 
        !           303:        if(  rand_type  ==  TYPE_0  )  state[ -1 ] = rand_type;
        !           304:        else  state[ -1 ] = MAX_TYPES*(rptr - state) + rand_type;
        !           305:        switch(  type  )  {
        !           306:            case  TYPE_0:
        !           307:            case  TYPE_1:
        !           308:            case  TYPE_2:
        !           309:            case  TYPE_3:
        !           310:            case  TYPE_4:
        !           311:                rand_type = type;
        !           312:                rand_deg = degrees[ type ];
        !           313:                rand_sep = seps[ type ];
        !           314:                break;
        !           315: 
        !           316:            default:
        !           317:                fprintf( stderr, "setstate: state info has been munged; not changed.\n" );
        !           318:        }
        !           319:        state = &new_state[ 1 ];
        !           320:        if(  rand_type  !=  TYPE_0  )  {
        !           321:            rptr = &state[ rear ];
        !           322:            fptr = &state[ (rear + rand_sep)%rand_deg ];
        !           323:        }
        !           324:        end_ptr = &state[ rand_deg ];           /* set end_ptr too */
        !           325:        return( ostate );
        !           326: }
        !           327: 
        !           328: 
        !           329: 
        !           330: /*
        !           331:  * random:
        !           332:  * If we are using the trivial TYPE_0 R.N.G., just do the old linear
        !           333:  * congruential bit.  Otherwise, we do our fancy trinomial stuff, which is the
        !           334:  * same in all ther other cases due to all the global variables that have been
        !           335:  * set up.  The basic operation is to add the number at the rear pointer into
        !           336:  * the one at the front pointer.  Then both pointers are advanced to the next
        !           337:  * location cyclically in the table.  The value returned is the sum generated,
        !           338:  * reduced to 31 bits by throwing away the "least random" low bit.
        !           339:  * Note: the code takes advantage of the fact that both the front and
        !           340:  * rear pointers can't wrap on the same call by not testing the rear
        !           341:  * pointer if the front one has wrapped.
        !           342:  * Returns a 31-bit random number.
        !           343:  */
        !           344: 
        !           345: long
        !           346: random()
        !           347: {
        !           348:        long            i;
        !           349:        
        !           350:        if(  rand_type  ==  TYPE_0  )  {
        !           351:            i = state[0] = ( state[0]*1103515245 + 12345 )&0x7fffffff;
        !           352:        }
        !           353:        else  {
        !           354:            *fptr += *rptr;
        !           355:            i = (*fptr >> 1)&0x7fffffff;        /* chucking least random bit */
        !           356:            if(  ++fptr  >=  end_ptr  )  {
        !           357:                fptr = state;
        !           358:                ++rptr;
        !           359:            }
        !           360:            else  {
        !           361:                if(  ++rptr  >=  end_ptr  )  rptr = state;
        !           362:            }
        !           363:        }
        !           364:        return( i );
        !           365: }
        !           366: 

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