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/* generic file for evaluation of hypergeometric series using binary splitting
Copyright (C) 1999-2001 Free Software Foundation.
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., 59 Temple Place - Suite 330, Boston,
MA 02111-1307, 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, int r, int m)
{
int n,i,k,j,l;
int is_p_one = 0;
mpz_t* P,*S;
#ifdef A
mpz_t *T;
#endif
mpz_t* ptoj;
#ifdef R_IS_RATIONAL
mpz_t* qtoj;
mpfr_t tmp;
#endif
int diff, expo;
int precy = MPFR_PREC(y);
TMP_DECL(marker);
TMP_MARK(marker);
MPFR_CLEAR_FLAGS(y);
n = 1 << m;
P = (mpz_t*) TMP_ALLOC ((m+1) * sizeof(mpz_t));
S = (mpz_t*) TMP_ALLOC ((m+1) * sizeof(mpz_t));
ptoj = (mpz_t*) TMP_ALLOC ((m+1) * sizeof(mpz_t)); /* ptoj[i] = mantissa^(2^i) */
#ifdef A
T = (mpz_t*) TMP_ALLOC ((m+1) * sizeof(mpz_t));
#endif
#ifdef R_IS_RATIONAL
qtoj = (mpz_t*) 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_si(ptoj[0], 1);
#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
j=i+1; l=0; while ((j & 1) == 0) {
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
l++; j>>=1; k--;
}
}
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_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_2exp(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
}
TMP_FREE(marker);
return 0;
}
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