/*- * SPDX-License-Identifier: BSD-3-Clause * * Copyright (c) 1983, 1993 * The Regents of the University of California. All rights reserved. * * Redistribution and use in source and binary forms, with or without * modification, are permitted provided that the following conditions * are met: * 1. Redistributions of source code must retain the above copyright * notice, this list of conditions and the following disclaimer. * 2. Redistributions in binary form must reproduce the above copyright * notice, this list of conditions and the following disclaimer in the * documentation and/or other materials provided with the distribution. * 3. Neither the name of the University nor the names of its contributors * may be used to endorse or promote products derived from this software * without specific prior written permission. * * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF * SUCH DAMAGE. */ #include <stdint.h> #include <stdlib.h> /* * random.c: * * 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() routine 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 uint32_t's; 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 ints 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 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. * * Modified 28 December 1994 by Jacob S. Rosenberg. * The following changes have been made: * All references to the type u_int have been changed to unsigned long. * All references to type int have been changed to type long. Other * cleanups have been made as well. A warning for both initstate and * setstate has been inserted to the effect that on Sparc platforms * the 'arg_state' variable must be forced to begin on word boundaries. * This can be easily done by casting a long integer array to char *. * The overall logic has been left STRICTLY alone. This software was * tested on both a VAX and Sun SpacsStation with exactly the same * results. The new version and the original give IDENTICAL results. * The new version is somewhat faster than the original. As the * documentation says: "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." For a buffer of * 128 bytes, this new version runs about 19 percent faster and for a 16 * byte buffer it is about 5 percent faster. */ /* * For each of the currently supported random number generators, we have a * break value on the amount of state information (you need at least this * many 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 * the separation between the two lower order coefficients of the trinomial. */ #define TYPE_0 0 /* linear congruential */ #define BREAK_0 8 #define DEG_0 0 #define SEP_0 0 #define TYPE_1 1 /* x**7 + x**3 + 1 */ #define BREAK_1 32 #define DEG_1 7 #define SEP_1 3 #define TYPE_2 2 /* x**15 + x + 1 */ #define BREAK_2 64 #define DEG_2 15 #define SEP_2 1 #define TYPE_3 3 /* x**31 + x**3 + 1 */ #define BREAK_3 128 #define DEG_3 31 #define SEP_3 3 #define TYPE_4 4 /* x**63 + x + 1 */ #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 */ #define NSHUFF 50 /* to drop some "seed -> 1st value" linearity */ static const int degrees[MAX_TYPES] = { DEG_0, DEG_1, DEG_2, DEG_3, DEG_4 }; static const 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 uint32_t randtbl[DEG_3 + 1] = { TYPE_3, 0x2cf41758, 0x27bb3711, 0x4916d4d1, 0x7b02f59f, 0x9b8e28eb, 0xc0e80269, 0x696f5c16, 0x878f1ff5, 0x52d9c07f, 0x916a06cd, 0xb50b3a20, 0x2776970a, 0xee4eb2a6, 0xe94640ec, 0xb1d65612, 0x9d1ed968, 0x1043f6b7, 0xa3432a76, 0x17eacbb9, 0x3c09e2eb, 0x4f8c2b3, 0x708a1f57, 0xee341814, 0x95d0e4d2, 0xb06f216c, 0x8bd2e72e, 0x8f7c38d7, 0xcfc6a8fc, 0x2a59495, 0xa20d2a69, 0xe29d12d1 }; /* * 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 cyclically 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 uint32_t *fptr = &randtbl[SEP_3 + 1]; static uint32_t *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 uint32_t *state = &randtbl[1]; static int rand_type = TYPE_3; static int rand_deg = DEG_3; static int rand_sep = SEP_3; static uint32_t *end_ptr = &randtbl[DEG_3 + 1]; static inline uint32_t good_rand(uint32_t ctx) { /* * Compute x = (7^5 * x) mod (2^31 - 1) * wihout overflowing 31 bits: * (2^31 - 1) = 127773 * (7^5) + 2836 * From "Random number generators: good ones are hard to find", * Park and Miller, Communications of the ACM, vol. 31, no. 10, * October 1988, p. 1195. */ int32_t hi, lo, x; /* Transform to [1, 0x7ffffffe] range. */ x = (ctx % 0x7ffffffe) + 1; hi = x / 127773; lo = x % 127773; x = 16807 * lo - 2836 * hi; if (x < 0) x += 0x7fffffff; /* Transform to [0, 0x7ffffffd] range. */ return (x - 1); } /* * srandom: * * 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(unsigned int x) { int i, lim; state[0] = (uint32_t)x; if (rand_type == TYPE_0) lim = NSHUFF; else { for (i = 1; i < rand_deg; i++) state[i] = good_rand(state[i - 1]); fptr = &state[rand_sep]; rptr = &state[0]; lim = 10 * rand_deg; } for (i = 0; i < lim; i++) (void)random(); } /* * srandomdev: * * Many programs choose the seed value in a totally predictable manner. * This often causes problems. We seed the generator using pseudo-random * data from the kernel. * * Note that this particular seeding procedure can generate states * which are impossible to reproduce by calling srandom() with any * value, since the succeeding terms in the state buffer are no longer * derived from the LC algorithm applied to a fixed seed. */ #if 0 void srandomdev(void) { int mib[2]; size_t expected, len; if (rand_type == TYPE_0) expected = len = sizeof(state[0]); else expected = len = rand_deg * sizeof(state[0]); mib[0] = CTL_KERN; mib[1] = KERN_ARND; if (sysctl(mib, 2, state, &len, NULL, 0) == -1 || len != expected) { /* * The sysctl cannot fail. If it does fail on some FreeBSD * derivative or after some future change, just abort so that * the problem will be found and fixed. abort is not normally * suitable for a library but makes sense here. */ abort(); } if (rand_type != TYPE_0) { fptr = &state[rand_sep]; rptr = &state[0]; } } #endif /* * initstate: * * 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. * * Note: The Sparc platform requires that arg_state begin on an int * word boundary; otherwise a bus error will occur. Even so, lint will * complain about mis-alignment, but you should disregard these messages. */ char * initstate(unsigned int seed, char *arg_state, size_t n) { char *ostate = (char *)(&state[-1]); uint32_t *int_arg_state = (uint32_t *)arg_state; if (n < BREAK_0) return (NULL); if (rand_type == TYPE_0) state[-1] = rand_type; else state[-1] = MAX_TYPES * (rptr - state) + rand_type; if (n < BREAK_1) { 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 = int_arg_state + 1; /* first location */ end_ptr = &state[rand_deg]; /* must set end_ptr before srandom */ srandom(seed); if (rand_type == TYPE_0) int_arg_state[0] = rand_type; else int_arg_state[0] = MAX_TYPES * (rptr - state) + rand_type; return (ostate); } /* * setstate: * * 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. * * Note: The Sparc platform requires that arg_state begin on an int * word boundary; otherwise a bus error will occur. Even so, lint will * complain about mis-alignment, but you should disregard these messages. */ char * setstate(char *arg_state) { uint32_t *new_state = (uint32_t *)arg_state; uint32_t type = new_state[0] % MAX_TYPES; uint32_t rear = new_state[0] / MAX_TYPES; char *ostate = (char *)(&state[-1]); if (type != TYPE_0 && rear >= (uint32_t)degrees[type]) return (NULL); if (rand_type == TYPE_0) state[-1] = rand_type; else state[-1] = MAX_TYPES * (rptr - state) + rand_type; rand_type = type; rand_deg = degrees[type]; rand_sep = seps[type]; state = new_state + 1; if (rand_type != TYPE_0) { rptr = &state[rear]; fptr = &state[(rear + rand_sep) % rand_deg]; } end_ptr = &state[rand_deg]; /* set end_ptr too */ return (ostate); } /* * random: * * 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 the 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. */ int random(void) { uint32_t i; uint32_t *f, *r; if (rand_type == TYPE_0) { i = state[0]; state[0] = i = good_rand(i); } else { /* * Use local variables rather than static variables for speed. */ f = fptr; r = rptr; *f += *r; i = *f >> 1; /* chucking least random bit */ if (++f >= end_ptr) { f = state; ++r; } else if (++r >= end_ptr) { r = state; } fptr = f; rptr = r; } return ((long)i); }
