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glibc-2.31
stdlib/random.c
300 строк
12 KB
Joseph Myers
Update copyright dates with scripts/update-copyrights.
01 янв 2020, 03:14
01 янв 2020, 03:14
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/* Copyright (C) 1995-2020 Free Software Foundation, Inc. The GNU C Library is free software; you can redistribute it and/or modify it under the terms of the GNU Lesser General Public License as published by the Free Software Foundation; either version 2.1 of the License, or (at your option) any later version. The GNU C Library is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more details. You should have received a copy of the GNU Lesser General Public License along with the GNU C Library; if not, see <https://www.gnu.org/licenses/>. */ /* * 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. * Rewritten to use reentrant functions by Ulrich Drepper, 1995. */ /* Copyright (C) 1983 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. 4. 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 <libc-lock.h> #include <limits.h> #include <stddef.h> #include <stdlib.h> /* 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 initialized 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 zeroth 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 zeroth 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 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 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. */ /* 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 zeroth 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 int32_t randtbl[DEG_3 + 1] = { TYPE_3, -1726662223, 379960547, 1735697613, 1040273694, 1313901226, 1627687941, -179304937, -2073333483, 1780058412, -1989503057, -615974602, 344556628, 939512070, -1249116260, 1507946756, -812545463, 154635395, 1388815473, -1926676823, 525320961, -1009028674, 968117788, -123449607, 1284210865, 435012392, -2017506339, -911064859, -370259173, 1132637927, 1398500161, -205601318, }; static struct random_data unsafe_state = { /* FPTR and RPTR are two pointers into the state info, a front and a rear pointer. These two pointers are always rand_sep places apart, 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).) */ .fptr = &randtbl[SEP_3 + 1], .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 zeroth. 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. */ .state = &randtbl[1], .rand_type = TYPE_3, .rand_deg = DEG_3, .rand_sep = SEP_3, .end_ptr = &randtbl[sizeof (randtbl) / sizeof (randtbl[0])] }; /* POSIX.1c requires that there is mutual exclusion for the `rand' and `srand' functions to prevent concurrent calls from modifying common data. */ __libc_lock_define_initialized (static, lock) /* 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) { __libc_lock_lock (lock); (void) __srandom_r (x, &unsafe_state); __libc_lock_unlock (lock); } weak_alias (__srandom, srandom) weak_alias (__srandom, srand) /* 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. */ char * __initstate (unsigned int seed, char *arg_state, size_t n) { int32_t *ostate; int ret; __libc_lock_lock (lock); ostate = &unsafe_state.state[-1]; ret = __initstate_r (seed, arg_state, n, &unsafe_state); __libc_lock_unlock (lock); return ret == -1 ? NULL : (char *) ostate; } weak_alias (__initstate, initstate) /* 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 zeroth 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. */ char * __setstate (char *arg_state) { int32_t *ostate; __libc_lock_lock (lock); ostate = &unsafe_state.state[-1]; if (__setstate_r (arg_state, &unsafe_state) < 0) ostate = NULL; __libc_lock_unlock (lock); return (char *) ostate; } weak_alias (__setstate, setstate) /* 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. */ long int __random (void) { int32_t retval; __libc_lock_lock (lock); (void) __random_r (&unsafe_state, &retval); __libc_lock_unlock (lock); return retval; } weak_alias (__random, random)