118 lines
3.5 KiB
C
118 lines
3.5 KiB
C
/*=============================================================================
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This file is part of FLINT.
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FLINT is free software; you can redistribute it and/or modify
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it under the terms of the GNU General Public License as published by
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the Free Software Foundation; either version 2 of the License, or
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(at your option) any later version.
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FLINT is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with FLINT; if not, write to the Free Software
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Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
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=============================================================================*/
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/******************************************************************************
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Copyright (C) 2010 Fredrik Johansson
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******************************************************************************/
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#include "flint.h"
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#include "ulong_extras.h"
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#define FLINT_MU_LOOKUP_CUTOFF 1024
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#if FLINT64
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const mp_limb_t FLINT_MOEBIUS_ODD[] =
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{
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UWORD(0x4289108a05208102), UWORD(0x19988004a8a12422), UWORD(0x1a8245028906a062),
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UWORD(0x229428012aa26a00), UWORD(0x8422a98980440a18), 0x224925084068929aUL,
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UWORD(0xa1200942a8980a84), UWORD(0x8622622216a00428), UWORD(0x6060829286a590a9),
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UWORD(0x5a2190081420a1a8), UWORD(0x8a92a284a8018200), UWORD(0x980a2602491a2248),
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UWORD(0x8106a08982a26848), UWORD(0xa60085a6004a5919), UWORD(0x88a188245a221228),
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UWORD(0x0108884a22186025)
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};
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#else
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const mp_limb_t FLINT_MOEBIUS_ODD[] =
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{
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UWORD(0x05208102), 0x4289108aUL, UWORD(0xa8a12422), UWORD(0x19988004), UWORD(0x8906a062),
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UWORD(0x1a824502), UWORD(0x2aa26a00), UWORD(0x22942801), UWORD(0x80440a18), UWORD(0x8422a989),
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0x4068929aUL, UWORD(0x22492508), UWORD(0xa8980a84), UWORD(0xa1200942), UWORD(0x16a00428),
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UWORD(0x86226222), UWORD(0x86a590a9), UWORD(0x60608292), UWORD(0x1420a1a8), UWORD(0x5a219008),
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UWORD(0xa8018200), UWORD(0x8a92a284), UWORD(0x491a2248), UWORD(0x980a2602), UWORD(0x82a26848),
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UWORD(0x8106a089), UWORD(0x004a5919), UWORD(0xa60085a6), UWORD(0x5a221228), UWORD(0x88a18824),
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UWORD(0x22186025), 0x0108884aUL
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};
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#endif
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void n_moebius_mu_vec(int * mu, ulong len)
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{
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slong k;
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ulong pi;
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const mp_limb_t * primes;
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mp_limb_t p, q;
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pi = n_prime_pi(len);
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primes = n_primes_arr_readonly(pi);
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if (len)
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mu[0] = 0;
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for (k = 1; k < len; k++)
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mu[k] = 1;
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for (k = 0; k < pi; k++)
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{
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p = primes[k];
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for (q = p; q < len; q += p)
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mu[q] = -mu[q];
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p = p * p;
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for (q = p; q < len; q += p)
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mu[q] = 0;
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}
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}
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int n_moebius_mu(mp_limb_t n)
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{
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int i;
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n_factor_t fac;
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if (n % 2 == 0)
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{
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if (n % 4 == 0)
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return 0;
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return -n_moebius_mu(n / 2);
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}
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if (n < FLINT_MU_LOOKUP_CUTOFF)
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{
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mp_limb_t m;
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n -= 1;
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m = FLINT_MOEBIUS_ODD[n / FLINT_BITS];
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m &= (UWORD(3) << (n % FLINT_BITS));
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m >>= (n % FLINT_BITS);
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return ((int) m) - 1;
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}
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/* Weed out just a few more common squares first */
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if (n % 9 == 0 || n % 25 == 0)
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return 0;
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n_factor_init(&fac);
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n_factor(&fac, n, 1);
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for (i = 0; i < fac.num; i++)
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{
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if (fac.exp[i] != 1)
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return 0;
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}
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if (fac.num % 2)
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return -1;
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else
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return 1;
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}
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