160 lines
4.5 KiB
C
160 lines
4.5 KiB
C
/* Mersenne Twister pseudo-random number generator functions.
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Copyright 2002, 2003 Free Software Foundation, Inc.
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This file is part of the GNU MP Library.
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The GNU MP Library is free software; you can redistribute it and/or modify
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it under the terms of the GNU Lesser General Public License as published by
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the Free Software Foundation; either version 2.1 of the License, or (at your
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option) any later version.
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The GNU MP Library is distributed in the hope that it will be useful, but
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WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
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or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public
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License for more details.
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You should have received a copy of the GNU Lesser General Public License
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along with the GNU MP Library; see the file COPYING.LIB. If not, write to
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the Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston,
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MA 02110-1301, USA. */
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#include "gmp.h"
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#include "gmp-impl.h"
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#include "randmt.h"
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/* Calculate (b^e) mod (2^n-k) for e=1074888996, n=19937 and k=20023,
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needed by the seeding function below. */
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static void
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mangle_seed (mpz_ptr r, mpz_srcptr b_orig)
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{
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mpz_t t, b;
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unsigned long e = 0x40118124;
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unsigned long bit = 0x20000000;
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mpz_init (t);
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mpz_init_set (b, b_orig); /* in case r==b_orig */
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mpz_set (r, b);
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do
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{
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mpz_mul (r, r, r);
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reduce:
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for (;;)
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{
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mpz_tdiv_q_2exp (t, r, 19937L);
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if (mpz_sgn (t) == 0)
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break;
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mpz_tdiv_r_2exp (r, r, 19937L);
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mpz_addmul_ui (r, t, 20023L);
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}
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if ((e & bit) != 0)
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{
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e &= ~bit;
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mpz_mul (r, r, b);
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goto reduce;
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}
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bit >>= 1;
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}
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while (bit != 0);
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mpz_clear (t);
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mpz_clear (b);
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}
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/* Seeding function. Uses powering modulo a non-Mersenne prime to obtain
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a permutation of the input seed space. The modulus is 2^19937-20023,
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which is probably prime. The power is 1074888996. In order to avoid
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seeds 0 and 1 generating invalid or strange output, the input seed is
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first manipulated as follows:
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seed1 = seed mod (2^19937-20027) + 2
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so that seed1 lies between 2 and 2^19937-20026 inclusive. Then the
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powering is performed as follows:
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seed2 = (seed1^1074888996) mod (2^19937-20023)
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and then seed2 is used to bootstrap the buffer.
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This method aims to give guarantees that:
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a) seed2 will never be zero,
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b) seed2 will very seldom have a very low population of ones in its
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binary representation, and
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c) every seed between 0 and 2^19937-20028 (inclusive) will yield a
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different sequence.
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CAVEATS:
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The period of the seeding function is 2^19937-20027. This means that
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with seeds 2^19937-20027, 2^19937-20026, ... the exact same sequences
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are obtained as with seeds 0, 1, etc.; it also means that seed -1
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produces the same sequence as seed 2^19937-20028, etc.
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*/
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static void
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randseed_mt (gmp_randstate_t rstate, mpz_srcptr seed)
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{
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int i;
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size_t cnt;
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gmp_rand_mt_struct *p;
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mpz_t mod; /* Modulus. */
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mpz_t seed1; /* Intermediate result. */
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p = (gmp_rand_mt_struct *) RNG_STATE (rstate);
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mpz_init (mod);
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mpz_init (seed1);
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mpz_set_ui (mod, 0L);
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mpz_setbit (mod, 19937L);
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mpz_sub_ui (mod, mod, 20027L);
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mpz_mod (seed1, seed, mod); /* Reduce `seed' modulo `mod'. */
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mpz_add_ui (seed1, seed1, 2L); /* seed1 is now ready. */
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mangle_seed (seed1, seed1); /* Perform the mangling by powering. */
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/* Copy the last bit into bit 31 of mt[0] and clear it. */
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p->mt[0] = (mpz_tstbit (seed1, 19936L) != 0) ? 0x80000000 : 0;
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mpz_clrbit (seed1, 19936L);
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/* Split seed1 into N-1 32-bit chunks. */
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mpz_export (&p->mt[1], &cnt, -1, sizeof (p->mt[1]), 0,
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8 * sizeof (p->mt[1]) - 32, seed1);
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cnt++;
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ASSERT (cnt <= N);
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while (cnt < N)
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p->mt[cnt++] = 0;
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mpz_clear (mod);
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mpz_clear (seed1);
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/* Warm the generator up if necessary. */
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if (WARM_UP != 0)
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for (i = 0; i < WARM_UP / N; i++)
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__gmp_mt_recalc_buffer (p->mt);
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p->mti = WARM_UP % N;
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}
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static const gmp_randfnptr_t Mersenne_Twister_Generator = {
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randseed_mt,
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__gmp_randget_mt,
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__gmp_randclear_mt,
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__gmp_randiset_mt
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};
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/* Initialize MT-specific data. */
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void
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gmp_randinit_mt (gmp_randstate_t rstate)
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{
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__gmp_randinit_mt_noseed (rstate);
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RNG_FNPTR (rstate) = (void *) &Mersenne_Twister_Generator;
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}
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