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/* generic file for evaluation of hypergeometric series using binary splitting
Copyright 1999, 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007 Free Software Foundation, Inc.
Contributed by the Arenaire and Cacao projects, INRIA.
This file is part of the MPFR Library.
The MPFR 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 MPdFR 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 MPFR Library; see the file COPYING.LIB. If not, write to
the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston,
MA 02110-1301, USA. */
#ifndef GENERIC
# error You should specify a name
#endif
#ifdef B
# ifndef A
# error B cannot be used without A
# endif
#endif
/* Compute the first 2^m terms from the hypergeometric series
with x = p / 2^r */
static int
GENERIC (mpfr_ptr y, mpz_srcptr p, long r, int m)
{
unsigned long n,i,k,j,l;
int is_p_one;
mpz_t* P,*S;
#ifdef A
mpz_t *T;
#endif
mpz_t* ptoj;
#ifdef R_IS_RATIONAL
mpz_t* qtoj;
mpfr_t tmp;
#endif
mp_exp_t diff, expo;
mp_prec_t precy = MPFR_PREC(y);
MPFR_TMP_DECL(marker);
MPFR_TMP_MARK(marker);
MPFR_CLEAR_FLAGS(y);
n = 1UL << m;
P = (mpz_t*) MPFR_TMP_ALLOC ((m+1) * sizeof(mpz_t));
S = (mpz_t*) MPFR_TMP_ALLOC ((m+1) * sizeof(mpz_t));
ptoj = (mpz_t*) MPFR_TMP_ALLOC ((m+1) * sizeof(mpz_t)); /* ptoj[i] = mantissa^(2^i) */
#ifdef A
T = (mpz_t*) MPFR_TMP_ALLOC ((m+1) * sizeof(mpz_t));
#endif
#ifdef R_IS_RATIONAL
qtoj = (mpz_t*) MPFR_TMP_ALLOC ((m+1) * sizeof(mpz_t));
#endif
for (i = 0 ; i <= m ; i++)
{
mpz_init (P[i]);
mpz_init (S[i]);
mpz_init (ptoj[i]);
#ifdef R_IS_RATIONAL
mpz_init (qtoj[i]);
#endif
#ifdef A
mpz_init (T[i]);
#endif
}
mpz_set (ptoj[0], p);
#ifdef C
# if C2 != 1
mpz_mul_ui (ptoj[0], ptoj[0], C2);
# endif
#endif
is_p_one = mpz_cmp_ui(ptoj[0], 1) == 0;
#ifdef A
# ifdef B
mpz_set_ui (T[0], A1 * B1);
# else
mpz_set_ui (T[0], A1);
# endif
#endif
if (!is_p_one)
for (i = 1 ; i < m ; i++)
mpz_mul (ptoj[i], ptoj[i-1], ptoj[i-1]);
#ifdef R_IS_RATIONAL
mpz_set_si (qtoj[0], r);
for (i = 1 ; i <= m ; i++)
mpz_mul(qtoj[i], qtoj[i-1], qtoj[i-1]);
#endif
mpz_set_ui (P[0], 1);
mpz_set_ui (S[0], 1);
k = 0;
for (i = 1 ; i < n ; i++) {
k++;
#ifdef A
# ifdef B
mpz_set_ui (T[k], (A1 + A2*i)*(B1+B2*i));
# else
mpz_set_ui (T[k], A1 + A2*i);
# endif
#endif
#ifdef C
# ifdef NO_FACTORIAL
mpz_set_ui (P[k], (C1 + C2 * (i-1)));
mpz_set_ui (S[k], 1);
# else
mpz_set_ui (P[k], (i+1) * (C1 + C2 * (i-1)));
mpz_set_ui (S[k], i+1);
# endif
#else
# ifdef NO_FACTORIAL
mpz_set_ui (P[k], 1);
# else
mpz_set_ui (P[k], i+1);
# endif
mpz_set (S[k], P[k]);
#endif
for (j = i+1, l = 0 ; (j & 1) == 0 ; l++, j>>=1, k--) {
if (!is_p_one)
mpz_mul (S[k], S[k], ptoj[l]);
#ifdef A
# ifdef B
# if (A2*B2) != 1
mpz_mul_ui (P[k], P[k], A2*B2);
# endif
# else
# if A2 != 1
mpz_mul_ui (P[k], P[k], A2);
# endif
#endif
mpz_mul (S[k], S[k], T[k-1]);
#endif
mpz_mul (S[k-1], S[k-1], P[k]);
#ifdef R_IS_RATIONAL
mpz_mul (S[k-1], S[k-1], qtoj[l]);
#else
mpz_mul_2exp (S[k-1], S[k-1], r*(1<<l));
#endif
mpz_add (S[k-1], S[k-1], S[k]);
mpz_mul (P[k-1], P[k-1], P[k]);
#ifdef A
mpz_mul (T[k-1], T[k-1], T[k]);
#endif
}
}
diff = mpz_sizeinbase(S[0],2) - 2*precy;
expo = diff;
if (diff >= 0)
mpz_div_2exp(S[0],S[0],diff);
else
mpz_mul_2exp(S[0],S[0],-diff);
diff = mpz_sizeinbase(P[0],2) - precy;
expo -= diff;
if (diff >=0)
mpz_div_2exp(P[0],P[0],diff);
else
mpz_mul_2exp(P[0],P[0],-diff);
mpz_tdiv_q(S[0], S[0], P[0]);
mpfr_set_z(y, S[0], GMP_RNDD);
MPFR_SET_EXP (y, MPFR_GET_EXP (y) + expo);
#ifdef R_IS_RATIONAL
/* exact division */
mpz_div_ui (qtoj[m], qtoj[m], r);
mpfr_init2 (tmp, MPFR_PREC(y));
mpfr_set_z (tmp, qtoj[m] , GMP_RNDD);
mpfr_div (y, y, tmp, GMP_RNDD);
mpfr_clear (tmp);
#else
mpfr_div_2ui(y, y, r*(i-1), GMP_RNDN);
#endif
for (i = 0 ; i <= m ; i++)
{
mpz_clear (P[i]);
mpz_clear (S[i]);
mpz_clear (ptoj[i]);
#ifdef R_IS_RATIONAL
mpz_clear (qtoj[i]);
#endif
#ifdef A
mpz_clear (T[i]);
#endif
}
MPFR_TMP_FREE (marker);
return 0;
}
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