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/* Mersenne Twister pseudo-random number generator functions.
Copyright 2002, 2003 Free Software Foundation, Inc.
This file is part of the GNU MP Library.
The GNU MP 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 3 of the License, or (at your
option) any later version.
The GNU MP 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 MP Library. If not, see */
#include "gmp.h"
#include "gmp-impl.h"
#include "randmt.h"
/* Calculate (b^e) mod (2^n-k) for e=1074888996, n=19937 and k=20023,
needed by the seeding function below. */
static void
mangle_seed (mpz_ptr r, mpz_srcptr b_orig)
mpz_t t, b;
unsigned long e = 0x40118124;
unsigned long bit = 0x20000000;
mpz_init (t);
mpz_init_set (b, b_orig); /* in case r==b_orig */
mpz_set (r, b);
mpz_mul (r, r, r);
for (;;)
mpz_tdiv_q_2exp (t, r, 19937L);
if (mpz_sgn (t) == 0)
mpz_tdiv_r_2exp (r, r, 19937L);
mpz_addmul_ui (r, t, 20023L);
if ((e & bit) != 0)
e &= ~bit;
mpz_mul (r, r, b);
goto reduce;
bit >>= 1;
while (bit != 0);
mpz_clear (t);
mpz_clear (b);
/* Seeding function. Uses powering modulo a non-Mersenne prime to obtain
a permutation of the input seed space. The modulus is 2^19937-20023,
which is probably prime. The power is 1074888996. In order to avoid
seeds 0 and 1 generating invalid or strange output, the input seed is
first manipulated as follows:
seed1 = seed mod (2^19937-20027) + 2
so that seed1 lies between 2 and 2^19937-20026 inclusive. Then the
powering is performed as follows:
seed2 = (seed1^1074888996) mod (2^19937-20023)
and then seed2 is used to bootstrap the buffer.
This method aims to give guarantees that:
a) seed2 will never be zero,
b) seed2 will very seldom have a very low population of ones in its
binary representation, and
c) every seed between 0 and 2^19937-20028 (inclusive) will yield a
different sequence.
The period of the seeding function is 2^19937-20027. This means that
with seeds 2^19937-20027, 2^19937-20026, ... the exact same sequences
are obtained as with seeds 0, 1, etc.; it also means that seed -1
produces the same sequence as seed 2^19937-20028, etc.
static void
randseed_mt (gmp_randstate_t rstate, mpz_srcptr seed)
int i;
size_t cnt;
gmp_rand_mt_struct *p;
mpz_t mod; /* Modulus. */
mpz_t seed1; /* Intermediate result. */
p = (gmp_rand_mt_struct *) RNG_STATE (rstate);
mpz_init (mod);
mpz_init (seed1);
mpz_set_ui (mod, 0L);
mpz_setbit (mod, 19937L);
mpz_sub_ui (mod, mod, 20027L);
mpz_mod (seed1, seed, mod); /* Reduce `seed' modulo `mod'. */
mpz_add_ui (seed1, seed1, 2L); /* seed1 is now ready. */
mangle_seed (seed1, seed1); /* Perform the mangling by powering. */
/* Copy the last bit into bit 31 of mt[0] and clear it. */
p->mt[0] = (mpz_tstbit (seed1, 19936L) != 0) ? 0x80000000 : 0;
mpz_clrbit (seed1, 19936L);
/* Split seed1 into N-1 32-bit chunks. */
mpz_export (&p->mt[1], &cnt, -1, sizeof (p->mt[1]), 0,
8 * sizeof (p->mt[1]) - 32, seed1);
ASSERT (cnt <= N);
while (cnt < N)
p->mt[cnt++] = 0;
mpz_clear (mod);
mpz_clear (seed1);
/* Warm the generator up if necessary. */
if (WARM_UP != 0)
for (i = 0; i < WARM_UP / N; i++)
__gmp_mt_recalc_buffer (p->mt);
p->mti = WARM_UP % N;
static const gmp_randfnptr_t Mersenne_Twister_Generator = {
/* Initialize MT-specific data. */
gmp_randinit_mt (gmp_randstate_t rstate)
__gmp_randinit_mt_noseed (rstate);
RNG_FNPTR (rstate) = (void *) &Mersenne_Twister_Generator;