sl@0: /* sl@0: * Copyright (c) 1983, 1993 sl@0: * The Regents of the University of California. All rights reserved. sl@0: * sl@0: * Redistribution and use in source and binary forms, with or without sl@0: * modification, are permitted provided that the following conditions sl@0: * are met: sl@0: * 1. Redistributions of source code must retain the above copyright sl@0: * notice, this list of conditions and the following disclaimer. sl@0: * 2. Redistributions in binary form must reproduce the above copyright sl@0: * notice, this list of conditions and the following disclaimer in the sl@0: * documentation and/or other materials provided with the distribution. sl@0: * 4. Neither the name of the University nor the names of its contributors sl@0: * may be used to endorse or promote products derived from this software sl@0: * without specific prior written permission. sl@0: * sl@0: * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND sl@0: * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE sl@0: * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE sl@0: * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE sl@0: * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL sl@0: * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS sl@0: * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) sl@0: * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT sl@0: * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY sl@0: * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF sl@0: * SUCH DAMAGE. sl@0: * © Portions copyright (c) 2006 Nokia Corporation. All rights reserved. sl@0: */ sl@0: sl@0: #if defined(LIBC_SCCS) && !defined(lint) sl@0: static char sccsid[] = "@(#)random.c 8.2 (Berkeley) 5/19/95"; sl@0: #endif /* LIBC_SCCS and not lint */ sl@0: #include sl@0: __FBSDID("$FreeBSD: src/lib/libc/stdlib/random.c,v 1.24 2004/01/20 03:02:18 das Exp $"); sl@0: sl@0: #include /* for srandomdev() */ sl@0: #include /* for srandomdev() */ sl@0: #include sl@0: #include sl@0: #include sl@0: #include /* for srandomdev() */ sl@0: sl@0: /* sl@0: * random.c: sl@0: * sl@0: * An improved random number generation package. In addition to the standard sl@0: * rand()/srand() like interface, this package also has a special state info sl@0: * interface. The initstate() routine is called with a seed, an array of sl@0: * bytes, and a count of how many bytes are being passed in; this array is sl@0: * then initialized to contain information for random number generation with sl@0: * that much state information. Good sizes for the amount of state sl@0: * information are 32, 64, 128, and 256 bytes. The state can be switched by sl@0: * calling the setstate() routine with the same array as was initiallized sl@0: * with initstate(). By default, the package runs with 128 bytes of state sl@0: * information and generates far better random numbers than a linear sl@0: * congruential generator. If the amount of state information is less than sl@0: * 32 bytes, a simple linear congruential R.N.G. is used. sl@0: * sl@0: * Internally, the state information is treated as an array of uint32_t's; the sl@0: * zeroeth element of the array is the type of R.N.G. being used (small sl@0: * integer); the remainder of the array is the state information for the sl@0: * R.N.G. Thus, 32 bytes of state information will give 7 ints worth of sl@0: * state information, which will allow a degree seven polynomial. (Note: sl@0: * the zeroeth word of state information also has some other information sl@0: * stored in it -- see setstate() for details). sl@0: * sl@0: * The random number generation technique is a linear feedback shift register sl@0: * approach, employing trinomials (since there are fewer terms to sum up that sl@0: * way). In this approach, the least significant bit of all the numbers in sl@0: * the state table will act as a linear feedback shift register, and will sl@0: * have period 2^deg - 1 (where deg is the degree of the polynomial being sl@0: * used, assuming that the polynomial is irreducible and primitive). The sl@0: * higher order bits will have longer periods, since their values are also sl@0: * influenced by pseudo-random carries out of the lower bits. The total sl@0: * period of the generator is approximately deg*(2**deg - 1); thus doubling sl@0: * the amount of state information has a vast influence on the period of the sl@0: * generator. Note: the deg*(2**deg - 1) is an approximation only good for sl@0: * large deg, when the period of the shift is the dominant factor. sl@0: * With deg equal to seven, the period is actually much longer than the sl@0: * 7*(2**7 - 1) predicted by this formula. sl@0: * sl@0: * Modified 28 December 1994 by Jacob S. Rosenberg. sl@0: * The following changes have been made: sl@0: * All references to the type u_int have been changed to unsigned long. sl@0: * All references to type int have been changed to type long. Other sl@0: * cleanups have been made as well. A warning for both initstate and sl@0: * setstate has been inserted to the effect that on Sparc platforms sl@0: * the 'arg_state' variable must be forced to begin on word boundaries. sl@0: * This can be easily done by casting a long integer array to char *. sl@0: * The overall logic has been left STRICTLY alone. This software was sl@0: * tested on both a VAX and Sun SpacsStation with exactly the same sl@0: * results. The new version and the original give IDENTICAL results. sl@0: * The new version is somewhat faster than the original. As the sl@0: * documentation says: "By default, the package runs with 128 bytes of sl@0: * state information and generates far better random numbers than a linear sl@0: * congruential generator. If the amount of state information is less than sl@0: * 32 bytes, a simple linear congruential R.N.G. is used." For a buffer of sl@0: * 128 bytes, this new version runs about 19 percent faster and for a 16 sl@0: * byte buffer it is about 5 percent faster. sl@0: */ sl@0: sl@0: /* sl@0: * For each of the currently supported random number generators, we have a sl@0: * break value on the amount of state information (you need at least this sl@0: * many bytes of state info to support this random number generator), a degree sl@0: * for the polynomial (actually a trinomial) that the R.N.G. is based on, and sl@0: * the separation between the two lower order coefficients of the trinomial. sl@0: */ sl@0: #define TYPE_0 0 /* linear congruential */ sl@0: #define BREAK_0 8 sl@0: #define DEG_0 0 sl@0: #define SEP_0 0 sl@0: sl@0: #define TYPE_1 1 /* x**7 + x**3 + 1 */ sl@0: #define BREAK_1 32 sl@0: #define DEG_1 7 sl@0: #define SEP_1 3 sl@0: sl@0: #define TYPE_2 2 /* x**15 + x + 1 */ sl@0: #define BREAK_2 64 sl@0: #define DEG_2 15 sl@0: #define SEP_2 1 sl@0: sl@0: #define TYPE_3 3 /* x**31 + x**3 + 1 */ sl@0: #define BREAK_3 128 sl@0: #define DEG_3 31 sl@0: #define SEP_3 3 sl@0: sl@0: #define TYPE_4 4 /* x**63 + x + 1 */ sl@0: #define BREAK_4 256 sl@0: #define DEG_4 63 sl@0: #define SEP_4 1 sl@0: sl@0: /* sl@0: * Array versions of the above information to make code run faster -- sl@0: * relies on fact that TYPE_i == i. sl@0: */ sl@0: #define MAX_TYPES 5 /* max number of types above */ sl@0: sl@0: #ifdef USE_WEAK_SEEDING sl@0: #define NSHUFF 0 sl@0: #else /* !USE_WEAK_SEEDING */ sl@0: #define NSHUFF 50 /* to drop some "seed -> 1st value" linearity */ sl@0: #endif /* !USE_WEAK_SEEDING */ sl@0: sl@0: static const int degrees[MAX_TYPES] = { DEG_0, DEG_1, DEG_2, DEG_3, DEG_4 }; sl@0: static const int seps [MAX_TYPES] = { SEP_0, SEP_1, SEP_2, SEP_3, SEP_4 }; sl@0: sl@0: /* sl@0: * Initially, everything is set up as if from: sl@0: * sl@0: * initstate(1, randtbl, 128); sl@0: * sl@0: * Note that this initialization takes advantage of the fact that srandom() sl@0: * advances the front and rear pointers 10*rand_deg times, and hence the sl@0: * rear pointer which starts at 0 will also end up at zero; thus the zeroeth sl@0: * element of the state information, which contains info about the current sl@0: * position of the rear pointer is just sl@0: * sl@0: * MAX_TYPES * (rptr - state) + TYPE_3 == TYPE_3. sl@0: */ sl@0: sl@0: static uint32_t randtbl[DEG_3 + 1] = { sl@0: TYPE_3, sl@0: #ifdef USE_WEAK_SEEDING sl@0: /* Historic implementation compatibility */ sl@0: /* The random sequences do not vary much with the seed */ sl@0: 0x9a319039, 0x32d9c024, 0x9b663182, 0x5da1f342, 0xde3b81e0, 0xdf0a6fb5, sl@0: 0xf103bc02, 0x48f340fb, 0x7449e56b, 0xbeb1dbb0, 0xab5c5918, 0x946554fd, sl@0: 0x8c2e680f, 0xeb3d799f, 0xb11ee0b7, 0x2d436b86, 0xda672e2a, 0x1588ca88, sl@0: 0xe369735d, 0x904f35f7, 0xd7158fd6, 0x6fa6f051, 0x616e6b96, 0xac94efdc, sl@0: 0x36413f93, 0xc622c298, 0xf5a42ab8, 0x8a88d77b, 0xf5ad9d0e, 0x8999220b, sl@0: 0x27fb47b9, sl@0: #else /* !USE_WEAK_SEEDING */ sl@0: 0x991539b1, 0x16a5bce3, 0x6774a4cd, 0x3e01511e, 0x4e508aaa, 0x61048c05, sl@0: 0xf5500617, 0x846b7115, 0x6a19892c, 0x896a97af, 0xdb48f936, 0x14898454, sl@0: 0x37ffd106, 0xb58bff9c, 0x59e17104, 0xcf918a49, 0x09378c83, 0x52c7a471, sl@0: 0x8d293ea9, 0x1f4fc301, 0xc3db71be, 0x39b44e1c, 0xf8a44ef9, 0x4c8b80b1, sl@0: 0x19edc328, 0x87bf4bdd, 0xc9b240e5, 0xe9ee4b1b, 0x4382aee7, 0x535b6b41, sl@0: 0xf3bec5da sl@0: #endif /* !USE_WEAK_SEEDING */ sl@0: }; sl@0: sl@0: /* sl@0: * fptr and rptr are two pointers into the state info, a front and a rear sl@0: * pointer. These two pointers are always rand_sep places aparts, as they sl@0: * cycle cyclically through the state information. (Yes, this does mean we sl@0: * could get away with just one pointer, but the code for random() is more sl@0: * efficient this way). The pointers are left positioned as they would be sl@0: * from the call sl@0: * sl@0: * initstate(1, randtbl, 128); sl@0: * sl@0: * (The position of the rear pointer, rptr, is really 0 (as explained above sl@0: * in the initialization of randtbl) because the state table pointer is set sl@0: * to point to randtbl[1] (as explained below). sl@0: */ sl@0: static uint32_t *fptr = &randtbl[SEP_3 + 1]; sl@0: static uint32_t *rptr = &randtbl[1]; sl@0: sl@0: /* sl@0: * The following things are the pointer to the state information table, the sl@0: * type of the current generator, the degree of the current polynomial being sl@0: * used, and the separation between the two pointers. Note that for efficiency sl@0: * of random(), we remember the first location of the state information, not sl@0: * the zeroeth. Hence it is valid to access state[-1], which is used to sl@0: * store the type of the R.N.G. Also, we remember the last location, since sl@0: * this is more efficient than indexing every time to find the address of sl@0: * the last element to see if the front and rear pointers have wrapped. sl@0: */ sl@0: static uint32_t *state = &randtbl[1]; sl@0: static int rand_type = TYPE_3; sl@0: static int rand_deg = DEG_3; sl@0: static int rand_sep = SEP_3; sl@0: static uint32_t *end_ptr = &randtbl[DEG_3 + 1]; sl@0: sl@0: static inline uint32_t good_rand(int32_t); sl@0: sl@0: static inline uint32_t good_rand (x) sl@0: int32_t x; sl@0: { sl@0: #ifdef USE_WEAK_SEEDING sl@0: /* sl@0: * Historic implementation compatibility. sl@0: * The random sequences do not vary much with the seed, sl@0: * even with overflowing. sl@0: */ sl@0: return (1103515245 * x + 12345); sl@0: #else /* !USE_WEAK_SEEDING */ sl@0: /* sl@0: * Compute x = (7^5 * x) mod (2^31 - 1) sl@0: * wihout overflowing 31 bits: sl@0: * (2^31 - 1) = 127773 * (7^5) + 2836 sl@0: * From "Random number generators: good ones are hard to find", sl@0: * Park and Miller, Communications of the ACM, vol. 31, no. 10, sl@0: * October 1988, p. 1195. sl@0: */ sl@0: int32_t hi, lo; sl@0: sl@0: /* Can't be initialized with 0, so use another value. */ sl@0: if (x == 0) sl@0: x = 123459876; sl@0: hi = x / 127773; sl@0: lo = x % 127773; sl@0: x = 16807 * lo - 2836 * hi; sl@0: if (x < 0) sl@0: x += 0x7fffffff; sl@0: return (x); sl@0: #endif /* !USE_WEAK_SEEDING */ sl@0: } sl@0: sl@0: /* sl@0: * srandom: sl@0: * sl@0: * Initialize the random number generator based on the given seed. If the sl@0: * type is the trivial no-state-information type, just remember the seed. sl@0: * Otherwise, initializes state[] based on the given "seed" via a linear sl@0: * congruential generator. Then, the pointers are set to known locations sl@0: * that are exactly rand_sep places apart. Lastly, it cycles the state sl@0: * information a given number of times to get rid of any initial dependencies sl@0: * introduced by the L.C.R.N.G. Note that the initialization of randtbl[] sl@0: * for default usage relies on values produced by this routine. sl@0: */ sl@0: sl@0: EXPORT_C sl@0: void sl@0: srandom(x) sl@0: unsigned long x; sl@0: { sl@0: int i, lim; sl@0: sl@0: state[0] = (uint32_t)x; sl@0: if (rand_type == TYPE_0) sl@0: lim = NSHUFF; sl@0: else { sl@0: for (i = 1; i < rand_deg; i++) sl@0: state[i] = good_rand(state[i - 1]); sl@0: fptr = &state[rand_sep]; sl@0: rptr = &state[0]; sl@0: lim = 10 * rand_deg; sl@0: } sl@0: for (i = 0; i < lim; i++) sl@0: (void)random(); sl@0: } sl@0: #ifdef __SYMBIAN_COMPILE_UNUSED__ sl@0: /* sl@0: * srandomdev: sl@0: * sl@0: * Many programs choose the seed value in a totally predictable manner. sl@0: * This often causes problems. We seed the generator using the much more sl@0: * secure random(4) interface. Note that this particular seeding sl@0: * procedure can generate states which are impossible to reproduce by sl@0: * calling srandom() with any value, since the succeeding terms in the sl@0: * state buffer are no longer derived from the LC algorithm applied to sl@0: * a fixed seed. sl@0: */ sl@0: void sl@0: srandomdev() sl@0: { sl@0: int fd, done; sl@0: size_t len; sl@0: sl@0: if (rand_type == TYPE_0) sl@0: len = sizeof state[0]; sl@0: else sl@0: len = rand_deg * sizeof state[0]; sl@0: sl@0: done = 0; sl@0: fd = open("/dev/random", O_RDONLY, 0); sl@0: if (fd >= 0) { sl@0: if (read(fd, (void *) state, len) == (ssize_t) len) sl@0: done = 1; sl@0: close(fd); sl@0: } sl@0: sl@0: if (!done) { sl@0: struct timeval tv; sl@0: unsigned long junk = 0; sl@0: sl@0: gettimeofday(&tv, NULL); sl@0: srandom((getpid() << 16) ^ tv.tv_sec ^ tv.tv_usec ^ junk); sl@0: return; sl@0: } sl@0: sl@0: if (rand_type != TYPE_0) { sl@0: fptr = &state[rand_sep]; sl@0: rptr = &state[0]; sl@0: } sl@0: } sl@0: #endif sl@0: /* sl@0: * initstate: sl@0: * sl@0: * Initialize the state information in the given array of n bytes for future sl@0: * random number generation. Based on the number of bytes we are given, and sl@0: * the break values for the different R.N.G.'s, we choose the best (largest) sl@0: * one we can and set things up for it. srandom() is then called to sl@0: * initialize the state information. sl@0: * sl@0: * Note that on return from srandom(), we set state[-1] to be the type sl@0: * multiplexed with the current value of the rear pointer; this is so sl@0: * successive calls to initstate() won't lose this information and will be sl@0: * able to restart with setstate(). sl@0: * sl@0: * Note: the first thing we do is save the current state, if any, just like sl@0: * setstate() so that it doesn't matter when initstate is called. sl@0: * sl@0: * Returns a pointer to the old state. sl@0: * sl@0: * Note: The Sparc platform requires that arg_state begin on an int sl@0: * word boundary; otherwise a bus error will occur. Even so, lint will sl@0: * complain about mis-alignment, but you should disregard these messages. sl@0: */ sl@0: sl@0: EXPORT_C sl@0: char * sl@0: initstate(seed, arg_state, n) sl@0: unsigned long seed; /* seed for R.N.G. */ sl@0: char *arg_state; /* pointer to state array */ sl@0: long n; /* # bytes of state info */ sl@0: { sl@0: char *ostate = (char *)(&state[-1]); sl@0: uint32_t *int_arg_state = (uint32_t *)arg_state; sl@0: sl@0: if (rand_type == TYPE_0) sl@0: state[-1] = rand_type; sl@0: else sl@0: state[-1] = MAX_TYPES * (rptr - state) + rand_type; sl@0: if (n < BREAK_0) { sl@0: (void)fprintf(stderr, sl@0: "random: not enough state (%ld bytes); ignored.\n", n); sl@0: return(0); sl@0: } sl@0: if (n < BREAK_1) { sl@0: rand_type = TYPE_0; sl@0: rand_deg = DEG_0; sl@0: rand_sep = SEP_0; sl@0: } else if (n < BREAK_2) { sl@0: rand_type = TYPE_1; sl@0: rand_deg = DEG_1; sl@0: rand_sep = SEP_1; sl@0: } else if (n < BREAK_3) { sl@0: rand_type = TYPE_2; sl@0: rand_deg = DEG_2; sl@0: rand_sep = SEP_2; sl@0: } else if (n < BREAK_4) { sl@0: rand_type = TYPE_3; sl@0: rand_deg = DEG_3; sl@0: rand_sep = SEP_3; sl@0: } else { sl@0: rand_type = TYPE_4; sl@0: rand_deg = DEG_4; sl@0: rand_sep = SEP_4; sl@0: } sl@0: state = int_arg_state + 1; /* first location */ sl@0: end_ptr = &state[rand_deg]; /* must set end_ptr before srandom */ sl@0: srandom(seed); sl@0: if (rand_type == TYPE_0) sl@0: int_arg_state[0] = rand_type; sl@0: else sl@0: int_arg_state[0] = MAX_TYPES * (rptr - state) + rand_type; sl@0: return(ostate); sl@0: } sl@0: sl@0: /* sl@0: * setstate: sl@0: * sl@0: * Restore the state from the given state array. sl@0: * sl@0: * Note: it is important that we also remember the locations of the pointers sl@0: * in the current state information, and restore the locations of the pointers sl@0: * from the old state information. This is done by multiplexing the pointer sl@0: * location into the zeroeth word of the state information. sl@0: * sl@0: * Note that due to the order in which things are done, it is OK to call sl@0: * setstate() with the same state as the current state. sl@0: * sl@0: * Returns a pointer to the old state information. sl@0: * sl@0: * Note: The Sparc platform requires that arg_state begin on an int sl@0: * word boundary; otherwise a bus error will occur. Even so, lint will sl@0: * complain about mis-alignment, but you should disregard these messages. sl@0: */ sl@0: sl@0: EXPORT_C sl@0: char * sl@0: setstate(arg_state) sl@0: char *arg_state; /* pointer to state array */ sl@0: { sl@0: uint32_t *new_state = (uint32_t *)arg_state; sl@0: uint32_t type = new_state[0] % MAX_TYPES; sl@0: uint32_t rear = new_state[0] / MAX_TYPES; sl@0: char *ostate = (char *)(&state[-1]); sl@0: sl@0: if (rand_type == TYPE_0) sl@0: state[-1] = rand_type; sl@0: else sl@0: state[-1] = MAX_TYPES * (rptr - state) + rand_type; sl@0: switch(type) { sl@0: case TYPE_0: sl@0: case TYPE_1: sl@0: case TYPE_2: sl@0: case TYPE_3: sl@0: case TYPE_4: sl@0: rand_type = type; sl@0: rand_deg = degrees[type]; sl@0: rand_sep = seps[type]; sl@0: break; sl@0: default: sl@0: (void)fprintf(stderr, sl@0: "random: state info corrupted; not changed.\n"); sl@0: } sl@0: state = new_state + 1; sl@0: if (rand_type != TYPE_0) { sl@0: rptr = &state[rear]; sl@0: fptr = &state[(rear + rand_sep) % rand_deg]; sl@0: } sl@0: end_ptr = &state[rand_deg]; /* set end_ptr too */ sl@0: return(ostate); sl@0: } sl@0: sl@0: /* sl@0: * random: sl@0: * sl@0: * If we are using the trivial TYPE_0 R.N.G., just do the old linear sl@0: * congruential bit. Otherwise, we do our fancy trinomial stuff, which is sl@0: * the same in all the other cases due to all the global variables that have sl@0: * been set up. The basic operation is to add the number at the rear pointer sl@0: * into the one at the front pointer. Then both pointers are advanced to sl@0: * the next location cyclically in the table. The value returned is the sum sl@0: * generated, reduced to 31 bits by throwing away the "least random" low bit. sl@0: * sl@0: * Note: the code takes advantage of the fact that both the front and sl@0: * rear pointers can't wrap on the same call by not testing the rear sl@0: * pointer if the front one has wrapped. sl@0: * sl@0: * Returns a 31-bit random number. sl@0: */ sl@0: sl@0: EXPORT_C sl@0: long sl@0: random() sl@0: { sl@0: uint32_t i; sl@0: uint32_t *f, *r; sl@0: sl@0: if (rand_type == TYPE_0) { sl@0: i = state[0]; sl@0: state[0] = i = (good_rand(i)) & 0x7fffffff; sl@0: } else { sl@0: /* sl@0: * Use local variables rather than static variables for speed. sl@0: */ sl@0: f = fptr; r = rptr; sl@0: *f += *r; sl@0: i = (*f >> 1) & 0x7fffffff; /* chucking least random bit */ sl@0: if (++f >= end_ptr) { sl@0: f = state; sl@0: ++r; sl@0: } sl@0: else if (++r >= end_ptr) { sl@0: r = state; sl@0: } sl@0: sl@0: fptr = f; rptr = r; sl@0: } sl@0: return((long)i); sl@0: }