| /* |
| * 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. |
| * 3. [rescinded 22 July 1999] |
| * 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. |
| */ |
| |
| /* |
| * 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. |
| */ |
| |
| /* |
| |
| @deftypefn Supplement {long int} random (void) |
| @deftypefnx Supplement void srandom (unsigned int @var{seed}) |
| @deftypefnx Supplement void* initstate (unsigned int @var{seed}, void *@var{arg_state}, unsigned long @var{n}) |
| @deftypefnx Supplement void* setstate (void *@var{arg_state}) |
| |
| Random number functions. @code{random} returns a random number in the |
| range 0 to @code{LONG_MAX}. @code{srandom} initializes the random |
| number generator to some starting point determined by @var{seed} |
| (else, the values returned by @code{random} are always the same for each |
| run of the program). @code{initstate} and @code{setstate} allow fine-grained |
| control over the state of the random number generator. |
| |
| @end deftypefn |
| |
| */ |
| |
| #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; |
| } |
| } |