108 lines
2.8 KiB
C
108 lines
2.8 KiB
C
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/*=============================================================================
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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) 2011 Fredrik Johansson
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******************************************************************************/
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#include <math.h>
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#include "arith.h"
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void mpfr_zeta_inv_euler_product(mpfr_t res, ulong s, int char_4)
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{
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mpz_t z, x, y, r;
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mp_limb_t p;
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slong prec, powprec, yexp, shift;
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mpz_init(x);
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mpz_init(y);
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mpz_init(z);
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mpz_init(r);
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prec = mpfr_get_prec(res) + 32 + 2*FLINT_BIT_COUNT(s);
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flint_mpz_set_ui(z, UWORD(1));
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mpz_mul_2exp(z, z, prec);
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if (!char_4)
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{
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flint_mpz_set_ui(r, UWORD(1));
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mpz_mul_2exp(r, r, prec - s);
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mpz_sub(z, z, r);
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}
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p = UWORD(3);
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while (1)
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{
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slong i;
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powprec = prec - s*log(p)*1.4426950408889634 + 1;
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/* flint_printf("prime %wu, powprec %wd\n", p, powprec); */
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if (powprec < 5)
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break;
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flint_mpz_set_ui(x, p);
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flint_mpz_set_ui(y, UWORD(1));
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yexp = 0;
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/* Slow equivalent: flint_mpz_pow_ui(y, x, s) */
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flint_mpz_set_ui(y, p);
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for (i = FLINT_BIT_COUNT(s) - 2; i >= 0; i--)
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{
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mpz_mul(y, y, y);
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yexp += yexp;
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shift = mpz_sizeinbase(y, 2) - powprec - 4;
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if (shift >= 0)
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{
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mpz_tdiv_q_2exp(y, y, shift);
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yexp += shift;
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}
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if (s & (UWORD(1)<<i))
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flint_mpz_mul_ui(y, y, p);
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}
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shift = yexp;
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if (shift >= 0)
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mpz_tdiv_q_2exp(r, z, shift);
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else
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mpz_mul_2exp(r, z, -shift);
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mpz_tdiv_q(r, r, y);
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if (char_4 && (p % 4 == 3))
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mpz_add(z, z, r);
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else
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mpz_sub(z, z, r);
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p = n_nextprime(p, 0);
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}
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mpfr_set_z_2exp(res, z, -prec, GMP_RNDN);
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mpz_clear(x);
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mpz_clear(y);
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mpz_clear(z);
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mpz_clear(r);
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}
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