# random.c之随机数字生成C语言源代码欣赏

________________________________________ /* * Copyright (c) 1983 Regents of the University of California. * All rights reserved. * * 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, 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 (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 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. */ 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; } }