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Diffstat (limited to 'randmts.c')
| -rw-r--r-- | randmts.c | 159 |
1 files changed, 159 insertions, 0 deletions
diff --git a/randmts.c b/randmts.c new file mode 100644 index 000000000..2c925ef78 --- /dev/null +++ b/randmts.c @@ -0,0 +1,159 @@ +/* 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 2.1 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; see the file COPYING.LIB. If not, write to +the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston, +MA 02111-1307, USA. */ + +#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); + do + { + mpz_mul (r, r, r); + + reduce: + for (;;) + { + mpz_tdiv_q_2exp (t, r, 19937L); + if (mpz_sgn (t) == 0) + break; + 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. + + CAVEATS: + + 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); + cnt++; + 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 = { + randseed_mt, + __gmp_randget_mt, + __gmp_randclear_mt, + __gmp_randiset_mt +}; + +/* Initialize MT-specific data. */ +void +gmp_randinit_mt (gmp_randstate_t rstate) +{ + __gmp_randinit_mt_noseed (rstate); + RNG_FNPTR (rstate) = (void *) &Mersenne_Twister_Generator; +} |