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Annotation of 42BSD/lib/libc/gen/random.c, revision 1.1

1.1     ! root        1: #ifndef lint
        !             2: static char sccsid[] = "@(#)random.c   4.2     (Berkeley)      83/01/02";
        !             3: #endif
        !             4: 
        !             5: #include       <stdio.h>
        !             6: 
        !             7: /*
        !             8:  * random.c:
        !             9:  * An improved random number generation package.  In addition to the standard
        !            10:  * rand()/srand() like interface, this package also has a special state info
        !            11:  * interface.  The initstate() routine is called with a seed, an array of
        !            12:  * bytes, and a count of how many bytes are being passed in; this array is then
        !            13:  * initialized to contain information for random number generation with that
        !            14:  * much state information.  Good sizes for the amount of state information are
        !            15:  * 32, 64, 128, and 256 bytes.  The state can be switched by calling the
        !            16:  * setstate() routine with the same array as was initiallized with initstate().
        !            17:  * By default, the package runs with 128 bytes of state information and
        !            18:  * generates far better random numbers than a linear congruential generator.
        !            19:  * If the amount of state information is less than 32 bytes, a simple linear
        !            20:  * congruential R.N.G. is used.
        !            21:  * Internally, the state information is treated as an array of longs; the
        !            22:  * zeroeth element of the array is the type of R.N.G. being used (small
        !            23:  * integer); the remainder of the array is the state information for the
        !            24:  * R.N.G.  Thus, 32 bytes of state information will give 7 longs worth of
        !            25:  * state information, which will allow a degree seven polynomial.  (Note: the 
        !            26:  * zeroeth word of state information also has some other information stored
        !            27:  * in it -- see setstate() for details).
        !            28:  * The random number generation technique is a linear feedback shift register
        !            29:  * approach, employing trinomials (since there are fewer terms to sum up that
        !            30:  * way).  In this approach, the least significant bit of all the numbers in
        !            31:  * the state table will act as a linear feedback shift register, and will have
        !            32:  * period 2^deg - 1 (where deg is the degree of the polynomial being used,
        !            33:  * assuming that the polynomial is irreducible and primitive).  The higher
        !            34:  * order bits will have longer periods, since their values are also influenced
        !            35:  * by pseudo-random carries out of the lower bits.  The total period of the
        !            36:  * generator is approximately deg*(2**deg - 1); thus doubling the amount of
        !            37:  * state information has a vast influence on the period of the generator.
        !            38:  * Note: the deg*(2**deg - 1) is an approximation only good for large deg,
        !            39:  * when the period of the shift register is the dominant factor.  With deg
        !            40:  * equal to seven, the period is actually much longer than the 7*(2**7 - 1)
        !            41:  * predicted by this formula.
        !            42:  */
        !            43: 
        !            44: 
        !            45: 
        !            46: /*
        !            47:  * For each of the currently supported random number generators, we have a
        !            48:  * break value on the amount of state information (you need at least this
        !            49:  * many bytes of state info to support this random number generator), a degree
        !            50:  * for the polynomial (actually a trinomial) that the R.N.G. is based on, and
        !            51:  * the separation between the two lower order coefficients of the trinomial.
        !            52:  */
        !            53: 
        !            54: #define                TYPE_0          0               /* linear congruential */
        !            55: #define                BREAK_0         8
        !            56: #define                DEG_0           0
        !            57: #define                SEP_0           0
        !            58: 
        !            59: #define                TYPE_1          1               /* x**7 + x**3 + 1 */
        !            60: #define                BREAK_1         32
        !            61: #define                DEG_1           7
        !            62: #define                SEP_1           3
        !            63: 
        !            64: #define                TYPE_2          2               /* x**15 + x + 1 */
        !            65: #define                BREAK_2         64
        !            66: #define                DEG_2           15
        !            67: #define                SEP_2           1
        !            68: 
        !            69: #define                TYPE_3          3               /* x**31 + x**3 + 1 */
        !            70: #define                BREAK_3         128
        !            71: #define                DEG_3           31
        !            72: #define                SEP_3           3
        !            73: 
        !            74: #define                TYPE_4          4               /* x**63 + x + 1 */
        !            75: #define                BREAK_4         256
        !            76: #define                DEG_4           63
        !            77: #define                SEP_4           1
        !            78: 
        !            79: 
        !            80: /*
        !            81:  * Array versions of the above information to make code run faster -- relies
        !            82:  * on fact that TYPE_i == i.
        !            83:  */
        !            84: 
        !            85: #define                MAX_TYPES       5               /* max number of types above */
        !            86: 
        !            87: static  int            degrees[ MAX_TYPES ]    = { DEG_0, DEG_1, DEG_2,
        !            88:                                                                DEG_3, DEG_4 };
        !            89: 
        !            90: static  int            seps[ MAX_TYPES ]       = { SEP_0, SEP_1, SEP_2,
        !            91:                                                                SEP_3, SEP_4 };
        !            92: 
        !            93: 
        !            94: 
        !            95: /*
        !            96:  * Initially, everything is set up as if from :
        !            97:  *             initstate( 1, &randtbl, 128 );
        !            98:  * Note that this initialization takes advantage of the fact that srandom()
        !            99:  * advances the front and rear pointers 10*rand_deg times, and hence the
        !           100:  * rear pointer which starts at 0 will also end up at zero; thus the zeroeth
        !           101:  * element of the state information, which contains info about the current
        !           102:  * position of the rear pointer is just
        !           103:  *     MAX_TYPES*(rptr - state) + TYPE_3 == TYPE_3.
        !           104:  */
        !           105: 
        !           106: static  long           randtbl[ DEG_3 + 1 ]    = { TYPE_3,
        !           107:                            0x9a319039, 0x32d9c024, 0x9b663182, 0x5da1f342, 
        !           108:                            0xde3b81e0, 0xdf0a6fb5, 0xf103bc02, 0x48f340fb, 
        !           109:                            0x7449e56b, 0xbeb1dbb0, 0xab5c5918, 0x946554fd, 
        !           110:                            0x8c2e680f, 0xeb3d799f, 0xb11ee0b7, 0x2d436b86, 
        !           111:                            0xda672e2a, 0x1588ca88, 0xe369735d, 0x904f35f7, 
        !           112:                            0xd7158fd6, 0x6fa6f051, 0x616e6b96, 0xac94efdc, 
        !           113:                            0x36413f93, 0xc622c298, 0xf5a42ab8, 0x8a88d77b, 
        !           114:                                        0xf5ad9d0e, 0x8999220b, 0x27fb47b9 };
        !           115: 
        !           116: /*
        !           117:  * fptr and rptr are two pointers into the state info, a front and a rear
        !           118:  * pointer.  These two pointers are always rand_sep places aparts, as they cycle
        !           119:  * cyclically through the state information.  (Yes, this does mean we could get
        !           120:  * away with just one pointer, but the code for random() is more efficient this
        !           121:  * way).  The pointers are left positioned as they would be from the call
        !           122:  *                     initstate( 1, randtbl, 128 )
        !           123:  * (The position of the rear pointer, rptr, is really 0 (as explained above
        !           124:  * in the initialization of randtbl) because the state table pointer is set
        !           125:  * to point to randtbl[1] (as explained below).
        !           126:  */
        !           127: 
        !           128: static  long           *fptr                   = &randtbl[ SEP_3 + 1 ];
        !           129: static  long           *rptr                   = &randtbl[ 1 ];
        !           130: 
        !           131: 
        !           132: 
        !           133: /*
        !           134:  * The following things are the pointer to the state information table,
        !           135:  * the type of the current generator, the degree of the current polynomial
        !           136:  * being used, and the separation between the two pointers.
        !           137:  * Note that for efficiency of random(), we remember the first location of
        !           138:  * the state information, not the zeroeth.  Hence it is valid to access
        !           139:  * state[-1], which is used to store the type of the R.N.G.
        !           140:  * Also, we remember the last location, since this is more efficient than
        !           141:  * indexing every time to find the address of the last element to see if
        !           142:  * the front and rear pointers have wrapped.
        !           143:  */
        !           144: 
        !           145: static  long           *state                  = &randtbl[ -1 ];
        !           146: 
        !           147: static  int            rand_type               = TYPE_3;
        !           148: static  int            rand_deg                = DEG_3;
        !           149: static  int            rand_sep                = SEP_3;
        !           150: 
        !           151: static  long           *end_ptr                = &randtbl[ DEG_3 + 1 ];
        !           152: 
        !           153: 
        !           154: 
        !           155: /*
        !           156:  * srandom:
        !           157:  * Initialize the random number generator based on the given seed.  If the
        !           158:  * type is the trivial no-state-information type, just remember the seed.
        !           159:  * Otherwise, initializes state[] based on the given "seed" via a linear
        !           160:  * congruential generator.  Then, the pointers are set to known locations
        !           161:  * that are exactly rand_sep places apart.  Lastly, it cycles the state
        !           162:  * information a given number of times to get rid of any initial dependencies
        !           163:  * introduced by the L.C.R.N.G.
        !           164:  * Note that the initialization of randtbl[] for default usage relies on
        !           165:  * values produced by this routine.
        !           166:  */
        !           167: 
        !           168: srandom( x )
        !           169: 
        !           170:     unsigned           x;
        !           171: {
        !           172:        register  int           i, j;
        !           173: 
        !           174:        if(  rand_type  ==  TYPE_0  )  {
        !           175:            state[ 0 ] = x;
        !           176:        }
        !           177:        else  {
        !           178:            j = 1;
        !           179:            state[ 0 ] = x;
        !           180:            for( i = 1; i < rand_deg; i++ )  {
        !           181:                state[i] = 1103515245*state[i - 1] + 12345;
        !           182:            }
        !           183:            fptr = &state[ rand_sep ];
        !           184:            rptr = &state[ 0 ];
        !           185:            for( i = 0; i < 10*rand_deg; i++ )  random();
        !           186:        }
        !           187: }
        !           188: 
        !           189: 
        !           190: 
        !           191: /*
        !           192:  * initstate:
        !           193:  * Initialize the state information in the given array of n bytes for
        !           194:  * future random number generation.  Based on the number of bytes we
        !           195:  * are given, and the break values for the different R.N.G.'s, we choose
        !           196:  * the best (largest) one we can and set things up for it.  srandom() is
        !           197:  * then called to initialize the state information.
        !           198:  * Note that on return from srandom(), we set state[-1] to be the type
        !           199:  * multiplexed with the current value of the rear pointer; this is so
        !           200:  * successive calls to initstate() won't lose this information and will
        !           201:  * be able to restart with setstate().
        !           202:  * Note: the first thing we do is save the current state, if any, just like
        !           203:  * setstate() so that it doesn't matter when initstate is called.
        !           204:  * Returns a pointer to the old state.
        !           205:  */
        !           206: 
        !           207: char  *
        !           208: initstate( seed, arg_state, n )
        !           209: 
        !           210:     unsigned           seed;                   /* seed for R. N. G. */
        !           211:     char               *arg_state;             /* pointer to state array */
        !           212:     int                        n;                      /* # bytes of state info */
        !           213: {
        !           214:        register  char          *ostate         = (char *)( &state[ -1 ] );
        !           215: 
        !           216:        if(  rand_type  ==  TYPE_0  )  state[ -1 ] = rand_type;
        !           217:        else  state[ -1 ] = MAX_TYPES*(rptr - state) + rand_type;
        !           218:        if(  n  <  BREAK_1  )  {
        !           219:            if(  n  <  BREAK_0  )  {
        !           220:                fprintf( stderr, "initstate: not enough state (%d bytes) with which to do jack; ignored.\n" );
        !           221:                return;
        !           222:            }
        !           223:            rand_type = TYPE_0;
        !           224:            rand_deg = DEG_0;
        !           225:            rand_sep = SEP_0;
        !           226:        }
        !           227:        else  {
        !           228:            if(  n  <  BREAK_2  )  {
        !           229:                rand_type = TYPE_1;
        !           230:                rand_deg = DEG_1;
        !           231:                rand_sep = SEP_1;
        !           232:            }
        !           233:            else  {
        !           234:                if(  n  <  BREAK_3  )  {
        !           235:                    rand_type = TYPE_2;
        !           236:                    rand_deg = DEG_2;
        !           237:                    rand_sep = SEP_2;
        !           238:                }
        !           239:                else  {
        !           240:                    if(  n  <  BREAK_4  )  {
        !           241:                        rand_type = TYPE_3;
        !           242:                        rand_deg = DEG_3;
        !           243:                        rand_sep = SEP_3;
        !           244:                    }
        !           245:                    else  {
        !           246:                        rand_type = TYPE_4;
        !           247:                        rand_deg = DEG_4;
        !           248:                        rand_sep = SEP_4;
        !           249:                    }
        !           250:                }
        !           251:            }
        !           252:        }
        !           253:        state = &(  ( (long *)arg_state )[1]  );        /* first location */
        !           254:        end_ptr = &state[ rand_deg ];   /* must set end_ptr before srandom */
        !           255:        srandom( seed );
        !           256:        if(  rand_type  ==  TYPE_0  )  state[ -1 ] = rand_type;
        !           257:        else  state[ -1 ] = MAX_TYPES*(rptr - state) + rand_type;
        !           258:        return( ostate );
        !           259: }
        !           260: 
        !           261: 
        !           262: 
        !           263: /*
        !           264:  * setstate:
        !           265:  * Restore the state from the given state array.
        !           266:  * Note: it is important that we also remember the locations of the pointers
        !           267:  * in the current state information, and restore the locations of the pointers
        !           268:  * from the old state information.  This is done by multiplexing the pointer
        !           269:  * location into the zeroeth word of the state information.
        !           270:  * Note that due to the order in which things are done, it is OK to call
        !           271:  * setstate() with the same state as the current state.
        !           272:  * Returns a pointer to the old state information.
        !           273:  */
        !           274: 
        !           275: char  *
        !           276: setstate( arg_state )
        !           277: 
        !           278:     char               *arg_state;
        !           279: {
        !           280:        register  long          *new_state      = (long *)arg_state;
        !           281:        register  int           type            = new_state[0]%MAX_TYPES;
        !           282:        register  int           rear            = new_state[0]/MAX_TYPES;
        !           283:        char                    *ostate         = (char *)( &state[ -1 ] );
        !           284: 
        !           285:        if(  rand_type  ==  TYPE_0  )  state[ -1 ] = rand_type;
        !           286:        else  state[ -1 ] = MAX_TYPES*(rptr - state) + rand_type;
        !           287:        switch(  type  )  {
        !           288:            case  TYPE_0:
        !           289:            case  TYPE_1:
        !           290:            case  TYPE_2:
        !           291:            case  TYPE_3:
        !           292:            case  TYPE_4:
        !           293:                rand_type = type;
        !           294:                rand_deg = degrees[ type ];
        !           295:                rand_sep = seps[ type ];
        !           296:                break;
        !           297: 
        !           298:            default:
        !           299:                fprintf( stderr, "setstate: state info has been munged; not changed.\n" );
        !           300:        }
        !           301:        state = &new_state[ 1 ];
        !           302:        if(  rand_type  !=  TYPE_0  )  {
        !           303:            rptr = &state[ rear ];
        !           304:            fptr = &state[ (rear + rand_sep)%rand_deg ];
        !           305:        }
        !           306:        end_ptr = &state[ rand_deg ];           /* set end_ptr too */
        !           307:        return( ostate );
        !           308: }
        !           309: 
        !           310: 
        !           311: 
        !           312: /*
        !           313:  * random:
        !           314:  * If we are using the trivial TYPE_0 R.N.G., just do the old linear
        !           315:  * congruential bit.  Otherwise, we do our fancy trinomial stuff, which is the
        !           316:  * same in all ther other cases due to all the global variables that have been
        !           317:  * set up.  The basic operation is to add the number at the rear pointer into
        !           318:  * the one at the front pointer.  Then both pointers are advanced to the next
        !           319:  * location cyclically in the table.  The value returned is the sum generated,
        !           320:  * reduced to 31 bits by throwing away the "least random" low bit.
        !           321:  * Note: the code takes advantage of the fact that both the front and
        !           322:  * rear pointers can't wrap on the same call by not testing the rear
        !           323:  * pointer if the front one has wrapped.
        !           324:  * Returns a 31-bit random number.
        !           325:  */
        !           326: 
        !           327: long
        !           328: random()
        !           329: {
        !           330:        long            i;
        !           331:        
        !           332:        if(  rand_type  ==  TYPE_0  )  {
        !           333:            i = state[0] = ( state[0]*1103515245 + 12345 )&0x7fffffff;
        !           334:        }
        !           335:        else  {
        !           336:            *fptr += *rptr;
        !           337:            i = (*fptr >> 1)&0x7fffffff;        /* chucking least random bit */
        !           338:            if(  ++fptr  >=  end_ptr  )  {
        !           339:                fptr = state;
        !           340:                ++rptr;
        !           341:            }
        !           342:            else  {
        !           343:                if(  ++rptr  >=  end_ptr  )  rptr = state;
        !           344:            }
        !           345:        }
        !           346:        return( i );
        !           347: }
        !           348: 

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