125 lines
4.2 KiB
C
125 lines
4.2 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 "mpn_extras.h"
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#include "arith.h"
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#if FLINT64
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#define FLINT_HARMONIC_MAX_TINY 46
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#else
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#define FLINT_HARMONIC_MAX_TINY 24
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#endif
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const mp_limb_t FLINT_HARMONIC_TINY_P[] =
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{
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UWORD(0), UWORD(1), UWORD(3), UWORD(11), UWORD(25), UWORD(137), UWORD(49), UWORD(363), UWORD(761), UWORD(7129), UWORD(7381),
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UWORD(83711), UWORD(86021), UWORD(1145993), UWORD(1171733), UWORD(1195757), UWORD(2436559), UWORD(42142223),
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UWORD(14274301), UWORD(275295799), UWORD(55835135), UWORD(18858053), UWORD(19093197), UWORD(444316699),
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UWORD(1347822955),
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#if FLINT64
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UWORD(34052522467), UWORD(34395742267), UWORD(312536252003), UWORD(315404588903),
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UWORD(9227046511387), UWORD(9304682830147), UWORD(290774257297357), UWORD(586061125622639),
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UWORD(53676090078349), UWORD(54062195834749), UWORD(54437269998109), UWORD(54801925434709),
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UWORD(2040798836801833), UWORD(2053580969474233), UWORD(2066035355155033),
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UWORD(2078178381193813), UWORD(85691034670497533), UWORD(12309312989335019),
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UWORD(532145396070491417), UWORD(5884182435213075787), UWORD(5914085889685464427),
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UWORD(5943339269060627227),
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#endif
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};
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const mp_limb_t FLINT_HARMONIC_TINY_Q[] =
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{
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UWORD(1), UWORD(1), UWORD(2), UWORD(6), UWORD(12), UWORD(60), UWORD(20), UWORD(140), UWORD(280), UWORD(2520), UWORD(2520),
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UWORD(27720), UWORD(27720), UWORD(360360), UWORD(360360), UWORD(360360), UWORD(720720), UWORD(12252240),
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UWORD(4084080), UWORD(77597520), UWORD(15519504), UWORD(5173168), UWORD(5173168), UWORD(118982864),
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UWORD(356948592),
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#if FLINT64
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UWORD(8923714800), UWORD(8923714800), UWORD(80313433200), UWORD(80313433200), UWORD(2329089562800),
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UWORD(2329089562800), UWORD(72201776446800), UWORD(144403552893600), UWORD(13127595717600),
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UWORD(13127595717600), UWORD(13127595717600), UWORD(13127595717600), UWORD(485721041551200),
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UWORD(485721041551200), UWORD(485721041551200), UWORD(485721041551200),
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UWORD(19914562703599200), UWORD(2844937529085600), UWORD(122332313750680800),
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UWORD(1345655451257488800), UWORD(1345655451257488800), UWORD(1345655451257488800),
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#endif
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};
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static void
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_mpq_harmonic_odd_balanced(fmpz_t num, fmpz_t den, slong n)
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{
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mpz_t p, q;
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mp_ptr t, v;
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mp_size_t ts, vs;
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slong size;
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if (n <= 0)
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{
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fmpz_zero(num);
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fmpz_one(den);
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return;
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}
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/* TODO: we could avoid the copying/allocation overhead when there
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is guaranteed to be sufficient space in res already */
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size = FLINT_BIT_COUNT(n) * (n+2) + 2*FLINT_BITS;
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mpz_init2(p, size);
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mpz_init2(q, size);
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t = p->_mp_d;
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v = q->_mp_d;
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flint_mpn_harmonic_odd_balanced(t, &ts, v, &vs, 1, n+1, n, 1);
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p->_mp_size = ts;
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q->_mp_size = vs;
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fmpz_set_mpz(num, p);
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fmpz_set_mpz(den, q);
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mpz_clear(p);
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mpz_clear(q);
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_fmpq_canonicalise(num, den);
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}
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void _arith_harmonic_number(fmpz_t num, fmpz_t den, slong n)
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{
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n = FLINT_MAX(n, 0);
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if (n <= FLINT_HARMONIC_MAX_TINY)
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{
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fmpz_set_ui(num, FLINT_HARMONIC_TINY_P[n]);
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fmpz_set_ui(den, FLINT_HARMONIC_TINY_Q[n]);
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}
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else
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{
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_mpq_harmonic_odd_balanced(num, den, n);
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}
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}
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void arith_harmonic_number(fmpq_t x, slong n)
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{
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_arith_harmonic_number(fmpq_numref(x), fmpq_denref(x), n);
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}
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