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532 lines
15 KiB
532 lines
15 KiB
14 years ago
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/* Random objects */
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/* ------------------------------------------------------------------
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The code in this module was based on a download from:
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http://www.math.keio.ac.jp/~matumoto/MT2002/emt19937ar.html
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It was modified in 2002 by Raymond Hettinger as follows:
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* the principal computational lines untouched except for tabbing.
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* renamed genrand_res53() to random_random() and wrapped
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in python calling/return code.
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* genrand_int32() and the helper functions, init_genrand()
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and init_by_array(), were declared static, wrapped in
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Python calling/return code. also, their global data
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references were replaced with structure references.
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* unused functions from the original were deleted.
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new, original C python code was added to implement the
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Random() interface.
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The following are the verbatim comments from the original code:
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A C-program for MT19937, with initialization improved 2002/1/26.
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Coded by Takuji Nishimura and Makoto Matsumoto.
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Before using, initialize the state by using init_genrand(seed)
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or init_by_array(init_key, key_length).
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Copyright (C) 1997 - 2002, Makoto Matsumoto and Takuji Nishimura,
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All rights reserved.
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Redistribution and use in source and binary forms, with or without
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modification, are permitted provided that the following conditions
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are met:
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1. Redistributions of source code must retain the above copyright
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notice, this list of conditions and the following disclaimer.
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2. Redistributions in binary form must reproduce the above copyright
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notice, this list of conditions and the following disclaimer in the
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documentation and/or other materials provided with the distribution.
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3. The names of its contributors may not be used to endorse or promote
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products derived from this software without specific prior written
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permission.
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THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
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"AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
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LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
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A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR
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CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
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EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
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PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
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PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
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LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
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NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
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SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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Any feedback is very welcome.
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http://www.math.keio.ac.jp/matumoto/emt.html
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email: matumoto@math.keio.ac.jp
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*/
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/* ---------------------------------------------------------------*/
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#include "Python.h"
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#include <time.h> /* for seeding to current time */
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/* Period parameters -- These are all magic. Don't change. */
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#define N 624
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#define M 397
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#define MATRIX_A 0x9908b0dfUL /* constant vector a */
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#define UPPER_MASK 0x80000000UL /* most significant w-r bits */
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#define LOWER_MASK 0x7fffffffUL /* least significant r bits */
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typedef struct {
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PyObject_HEAD
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unsigned long state[N];
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int index;
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} RandomObject;
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static PyTypeObject Random_Type;
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#define RandomObject_Check(v) ((v)->ob_type == &Random_Type)
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/* Random methods */
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/* generates a random number on [0,0xffffffff]-interval */
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static unsigned long
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genrand_int32(RandomObject *self)
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{
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unsigned long y;
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static unsigned long mag01[2]={0x0UL, MATRIX_A};
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/* mag01[x] = x * MATRIX_A for x=0,1 */
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unsigned long *mt;
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mt = self->state;
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if (self->index >= N) { /* generate N words at one time */
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int kk;
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for (kk=0;kk<N-M;kk++) {
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y = (mt[kk]&UPPER_MASK)|(mt[kk+1]&LOWER_MASK);
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mt[kk] = mt[kk+M] ^ (y >> 1) ^ mag01[y & 0x1UL];
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}
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for (;kk<N-1;kk++) {
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y = (mt[kk]&UPPER_MASK)|(mt[kk+1]&LOWER_MASK);
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mt[kk] = mt[kk+(M-N)] ^ (y >> 1) ^ mag01[y & 0x1UL];
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}
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y = (mt[N-1]&UPPER_MASK)|(mt[0]&LOWER_MASK);
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mt[N-1] = mt[M-1] ^ (y >> 1) ^ mag01[y & 0x1UL];
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self->index = 0;
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}
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y = mt[self->index++];
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y ^= (y >> 11);
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y ^= (y << 7) & 0x9d2c5680UL;
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y ^= (y << 15) & 0xefc60000UL;
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y ^= (y >> 18);
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return y;
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}
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/* random_random is the function named genrand_res53 in the original code;
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* generates a random number on [0,1) with 53-bit resolution; note that
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* 9007199254740992 == 2**53; I assume they're spelling "/2**53" as
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* multiply-by-reciprocal in the (likely vain) hope that the compiler will
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* optimize the division away at compile-time. 67108864 is 2**26. In
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* effect, a contains 27 random bits shifted left 26, and b fills in the
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* lower 26 bits of the 53-bit numerator.
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* The orginal code credited Isaku Wada for this algorithm, 2002/01/09.
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*/
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static PyObject *
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random_random(RandomObject *self)
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{
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unsigned long a=genrand_int32(self)>>5, b=genrand_int32(self)>>6;
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return PyFloat_FromDouble((a*67108864.0+b)*(1.0/9007199254740992.0));
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}
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/* initializes mt[N] with a seed */
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static void
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init_genrand(RandomObject *self, unsigned long s)
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{
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int mti;
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unsigned long *mt;
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mt = self->state;
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mt[0]= s & 0xffffffffUL;
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for (mti=1; mti<N; mti++) {
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mt[mti] =
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(1812433253UL * (mt[mti-1] ^ (mt[mti-1] >> 30)) + mti);
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/* See Knuth TAOCP Vol2. 3rd Ed. P.106 for multiplier. */
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/* In the previous versions, MSBs of the seed affect */
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/* only MSBs of the array mt[]. */
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/* 2002/01/09 modified by Makoto Matsumoto */
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mt[mti] &= 0xffffffffUL;
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/* for >32 bit machines */
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}
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self->index = mti;
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return;
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}
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/* initialize by an array with array-length */
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/* init_key is the array for initializing keys */
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/* key_length is its length */
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static PyObject *
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init_by_array(RandomObject *self, unsigned long init_key[], unsigned long key_length)
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{
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unsigned int i, j, k; /* was signed in the original code. RDH 12/16/2002 */
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unsigned long *mt;
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mt = self->state;
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init_genrand(self, 19650218UL);
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i=1; j=0;
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k = (N>key_length ? N : key_length);
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for (; k; k--) {
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mt[i] = (mt[i] ^ ((mt[i-1] ^ (mt[i-1] >> 30)) * 1664525UL))
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+ init_key[j] + j; /* non linear */
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mt[i] &= 0xffffffffUL; /* for WORDSIZE > 32 machines */
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i++; j++;
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if (i>=N) { mt[0] = mt[N-1]; i=1; }
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if (j>=key_length) j=0;
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}
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for (k=N-1; k; k--) {
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mt[i] = (mt[i] ^ ((mt[i-1] ^ (mt[i-1] >> 30)) * 1566083941UL))
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- i; /* non linear */
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mt[i] &= 0xffffffffUL; /* for WORDSIZE > 32 machines */
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i++;
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if (i>=N) { mt[0] = mt[N-1]; i=1; }
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}
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mt[0] = 0x80000000UL; /* MSB is 1; assuring non-zero initial array */
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Py_INCREF(Py_None);
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return Py_None;
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}
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/*
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* The rest is Python-specific code, neither part of, nor derived from, the
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* Twister download.
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*/
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static PyObject *
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random_seed(RandomObject *self, PyObject *args)
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{
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PyObject *result = NULL; /* guilty until proved innocent */
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PyObject *masklower = NULL;
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PyObject *thirtytwo = NULL;
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PyObject *n = NULL;
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unsigned long *key = NULL;
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unsigned long keymax; /* # of allocated slots in key */
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unsigned long keyused; /* # of used slots in key */
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int err;
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PyObject *arg = NULL;
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if (!PyArg_UnpackTuple(args, "seed", 0, 1, &arg))
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return NULL;
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if (arg == NULL || arg == Py_None) {
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time_t now;
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time(&now);
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init_genrand(self, (unsigned long)now);
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Py_INCREF(Py_None);
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return Py_None;
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}
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/* If the arg is an int or long, use its absolute value; else use
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* the absolute value of its hash code.
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*/
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if (PyInt_Check(arg) || PyLong_Check(arg))
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n = PyNumber_Absolute(arg);
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else {
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long hash = PyObject_Hash(arg);
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if (hash == -1)
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goto Done;
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n = PyLong_FromUnsignedLong((unsigned long)hash);
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}
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if (n == NULL)
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goto Done;
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/* Now split n into 32-bit chunks, from the right. Each piece is
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* stored into key, which has a capacity of keymax chunks, of which
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* keyused are filled. Alas, the repeated shifting makes this a
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* quadratic-time algorithm; we'd really like to use
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* _PyLong_AsByteArray here, but then we'd have to break into the
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* long representation to figure out how big an array was needed
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* in advance.
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*/
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keymax = 8; /* arbitrary; grows later if needed */
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keyused = 0;
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key = (unsigned long *)PyMem_Malloc(keymax * sizeof(*key));
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if (key == NULL)
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goto Done;
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masklower = PyLong_FromUnsignedLong(0xffffffffU);
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if (masklower == NULL)
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goto Done;
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thirtytwo = PyInt_FromLong(32L);
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if (thirtytwo == NULL)
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goto Done;
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while ((err=PyObject_IsTrue(n))) {
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PyObject *newn;
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PyObject *pychunk;
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unsigned long chunk;
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if (err == -1)
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goto Done;
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pychunk = PyNumber_And(n, masklower);
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if (pychunk == NULL)
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goto Done;
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chunk = PyLong_AsUnsignedLong(pychunk);
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Py_DECREF(pychunk);
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if (chunk == (unsigned long)-1 && PyErr_Occurred())
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goto Done;
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newn = PyNumber_Rshift(n, thirtytwo);
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if (newn == NULL)
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goto Done;
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Py_DECREF(n);
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n = newn;
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if (keyused >= keymax) {
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unsigned long bigger = keymax << 1;
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if ((bigger >> 1) != keymax) {
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PyErr_NoMemory();
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goto Done;
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}
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key = (unsigned long *)PyMem_Realloc(key,
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bigger * sizeof(*key));
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if (key == NULL)
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goto Done;
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keymax = bigger;
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}
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assert(keyused < keymax);
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key[keyused++] = chunk;
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}
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if (keyused == 0)
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key[keyused++] = 0UL;
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result = init_by_array(self, key, keyused);
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Done:
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Py_XDECREF(masklower);
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Py_XDECREF(thirtytwo);
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Py_XDECREF(n);
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PyMem_Free(key);
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return result;
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}
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static PyObject *
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random_getstate(RandomObject *self)
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{
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PyObject *state;
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PyObject *element;
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int i;
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state = PyTuple_New(N+1);
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if (state == NULL)
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return NULL;
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for (i=0; i<N ; i++) {
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element = PyInt_FromLong((long)(self->state[i]));
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if (element == NULL)
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goto Fail;
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PyTuple_SET_ITEM(state, i, element);
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}
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element = PyInt_FromLong((long)(self->index));
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if (element == NULL)
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goto Fail;
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PyTuple_SET_ITEM(state, i, element);
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return state;
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Fail:
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Py_DECREF(state);
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return NULL;
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}
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static PyObject *
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random_setstate(RandomObject *self, PyObject *state)
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{
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int i;
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long element;
|
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|
|
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if (!PyTuple_Check(state)) {
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PyErr_SetString(PyExc_TypeError,
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"state vector must be a tuple");
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return NULL;
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}
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|
if (PyTuple_Size(state) != N+1) {
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PyErr_SetString(PyExc_ValueError,
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"state vector is the wrong size");
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|
return NULL;
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|
}
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for (i=0; i<N ; i++) {
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element = PyInt_AsLong(PyTuple_GET_ITEM(state, i));
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|
if (element == -1 && PyErr_Occurred())
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|
return NULL;
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self->state[i] = (unsigned long)element;
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|
}
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|
|
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|
element = PyInt_AsLong(PyTuple_GET_ITEM(state, i));
|
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|
if (element == -1 && PyErr_Occurred())
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|
return NULL;
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|
self->index = (int)element;
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|
|
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|
Py_INCREF(Py_None);
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return Py_None;
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}
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|
/*
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|
Jumpahead should be a fast way advance the generator n-steps ahead, but
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lacking a formula for that, the next best is to use n and the existing
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state to create a new state far away from the original.
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|
|
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|
The generator uses constant spaced additive feedback, so shuffling the
|
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|
state elements ought to produce a state which would not be encountered
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|
(in the near term) by calls to random(). Shuffling is normally
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|
implemented by swapping the ith element with another element ranging
|
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|
from 0 to i inclusive. That allows the element to have the possibility
|
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|
of not being moved. Since the goal is to produce a new, different
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|
state, the swap element is ranged from 0 to i-1 inclusive. This assures
|
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|
that each element gets moved at least once.
|
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|
|
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|
To make sure that consecutive calls to jumpahead(n) produce different
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|
states (even in the rare case of involutory shuffles), i+1 is added to
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|
each element at position i. Successive calls are then guaranteed to
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|
have changing (growing) values as well as shuffled positions.
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|
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|
Finally, the self->index value is set to N so that the generator itself
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|
kicks in on the next call to random(). This assures that all results
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have been through the generator and do not just reflect alterations to
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the underlying state.
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*/
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|
static PyObject *
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|
random_jumpahead(RandomObject *self, PyObject *n)
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{
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long i, j;
|
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|
PyObject *iobj;
|
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|
PyObject *remobj;
|
||
|
unsigned long *mt, tmp;
|
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|
if (!PyInt_Check(n) && !PyLong_Check(n)) {
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PyErr_Format(PyExc_TypeError, "jumpahead requires an "
|
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|
"integer, not '%s'",
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n->ob_type->tp_name);
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return NULL;
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}
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|
mt = self->state;
|
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for (i = N-1; i > 1; i--) {
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iobj = PyInt_FromLong(i);
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|
if (iobj == NULL)
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|
return NULL;
|
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|
remobj = PyNumber_Remainder(n, iobj);
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|
Py_DECREF(iobj);
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|
if (remobj == NULL)
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|
return NULL;
|
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|
j = PyInt_AsLong(remobj);
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|
Py_DECREF(remobj);
|
||
|
if (j == -1L && PyErr_Occurred())
|
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|
return NULL;
|
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|
tmp = mt[i];
|
||
|
mt[i] = mt[j];
|
||
|
mt[j] = tmp;
|
||
|
}
|
||
|
|
||
|
for (i = 0; i < N; i++)
|
||
|
mt[i] += i+1;
|
||
|
|
||
|
self->index = N;
|
||
|
Py_INCREF(Py_None);
|
||
|
return Py_None;
|
||
|
}
|
||
|
|
||
|
static PyObject *
|
||
|
random_new(PyTypeObject *type, PyObject *args, PyObject *kwds)
|
||
|
{
|
||
|
RandomObject *self;
|
||
|
PyObject *tmp;
|
||
|
|
||
|
self = (RandomObject *)type->tp_alloc(type, 0);
|
||
|
if (self == NULL)
|
||
|
return NULL;
|
||
|
tmp = random_seed(self, args);
|
||
|
if (tmp == NULL) {
|
||
|
Py_DECREF(self);
|
||
|
return NULL;
|
||
|
}
|
||
|
Py_DECREF(tmp);
|
||
|
return (PyObject *)self;
|
||
|
}
|
||
|
|
||
|
static PyMethodDef random_methods[] = {
|
||
|
{"random", (PyCFunction)random_random, METH_NOARGS,
|
||
|
PyDoc_STR("random() -> x in the interval [0, 1).")},
|
||
|
{"seed", (PyCFunction)random_seed, METH_VARARGS,
|
||
|
PyDoc_STR("seed([n]) -> None. Defaults to current time.")},
|
||
|
{"getstate", (PyCFunction)random_getstate, METH_NOARGS,
|
||
|
PyDoc_STR("getstate() -> tuple containing the current state.")},
|
||
|
{"setstate", (PyCFunction)random_setstate, METH_O,
|
||
|
PyDoc_STR("setstate(state) -> None. Restores generator state.")},
|
||
|
{"jumpahead", (PyCFunction)random_jumpahead, METH_O,
|
||
|
PyDoc_STR("jumpahead(int) -> None. Create new state from "
|
||
|
"existing state and integer.")},
|
||
|
{NULL, NULL} /* sentinel */
|
||
|
};
|
||
|
|
||
|
PyDoc_STRVAR(random_doc,
|
||
|
"Random() -> create a random number generator with its own internal state.");
|
||
|
|
||
|
static PyTypeObject Random_Type = {
|
||
|
PyObject_HEAD_INIT(NULL)
|
||
|
0, /*ob_size*/
|
||
|
"_random.Random", /*tp_name*/
|
||
|
sizeof(RandomObject), /*tp_basicsize*/
|
||
|
0, /*tp_itemsize*/
|
||
|
/* methods */
|
||
|
0, /*tp_dealloc*/
|
||
|
0, /*tp_print*/
|
||
|
0, /*tp_getattr*/
|
||
|
0, /*tp_setattr*/
|
||
|
0, /*tp_compare*/
|
||
|
0, /*tp_repr*/
|
||
|
0, /*tp_as_number*/
|
||
|
0, /*tp_as_sequence*/
|
||
|
0, /*tp_as_mapping*/
|
||
|
0, /*tp_hash*/
|
||
|
0, /*tp_call*/
|
||
|
0, /*tp_str*/
|
||
|
PyObject_GenericGetAttr, /*tp_getattro*/
|
||
|
0, /*tp_setattro*/
|
||
|
0, /*tp_as_buffer*/
|
||
|
Py_TPFLAGS_DEFAULT | Py_TPFLAGS_BASETYPE, /*tp_flags*/
|
||
|
random_doc, /*tp_doc*/
|
||
|
0, /*tp_traverse*/
|
||
|
0, /*tp_clear*/
|
||
|
0, /*tp_richcompare*/
|
||
|
0, /*tp_weaklistoffset*/
|
||
|
0, /*tp_iter*/
|
||
|
0, /*tp_iternext*/
|
||
|
random_methods, /*tp_methods*/
|
||
|
0, /*tp_members*/
|
||
|
0, /*tp_getset*/
|
||
|
0, /*tp_base*/
|
||
|
0, /*tp_dict*/
|
||
|
0, /*tp_descr_get*/
|
||
|
0, /*tp_descr_set*/
|
||
|
0, /*tp_dictoffset*/
|
||
|
0, /*tp_init*/
|
||
|
0, /*tp_alloc*/
|
||
|
random_new, /*tp_new*/
|
||
|
_PyObject_Del, /*tp_free*/
|
||
|
0, /*tp_is_gc*/
|
||
|
};
|
||
|
|
||
|
PyDoc_STRVAR(module_doc,
|
||
|
"Module implements the Mersenne Twister random number generator.");
|
||
|
|
||
|
PyMODINIT_FUNC
|
||
|
init_random(void)
|
||
|
{
|
||
|
PyObject *m;
|
||
|
|
||
|
if (PyType_Ready(&Random_Type) < 0)
|
||
|
return;
|
||
|
m = Py_InitModule3("_random", NULL, module_doc);
|
||
|
Py_INCREF(&Random_Type);
|
||
|
PyModule_AddObject(m, "Random", (PyObject *)&Random_Type);
|
||
|
}
|