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/* mpfr_erfc -- The Complementary Error Function of a floating-point number
Copyright 2005, 2006 Free Software Foundation, Inc.
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 MPFR 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. */
#include <stdlib.h>
#define MPFR_NEED_LONGLONG_H
#include "mpfr-impl.h"
/* erfc(x) = 1 - erf(x) */
int
mpfr_erfc (mpfr_ptr y, mpfr_srcptr x, mp_rnd_t rnd)
{
int inex;
mpfr_t tmp;
mp_exp_t te, err;
mp_prec_t prec;
MPFR_SAVE_EXPO_DECL (expo);
MPFR_ZIV_DECL (loop);
MPFR_LOG_FUNC (("x[%#R]=%R rnd=%d", x, x, rnd),
("y[%#R]=%R inexact=%d", y, y, inex));
if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (x)))
{
if (MPFR_IS_NAN (x))
{
MPFR_SET_NAN (y);
MPFR_RET_NAN;
}
/* erfc(+inf) = 0+, erfc(-inf) = 2 erfc (0) = 1 */
else if (MPFR_IS_INF (x))
return mpfr_set_ui (y, MPFR_IS_POS (x) ? 0 : 2, rnd);
else
return mpfr_set_ui (y, 1, rnd);
}
if (MPFR_SIGN (x) > 0)
{
/* for x >= 38582, erfc(x) < 2^(-2^31) */
if (mpfr_cmp_ui (x, 38582) >= 0)
return mpfr_underflow (y, (rnd == GMP_RNDN) ? GMP_RNDZ : rnd, 1);
if (MPFR_GET_EXP (x) >= 12)
{
/* FIXME: Improve the algorithm to be able to compute the actual
value. For the time being, we regard this as a range error,
so that the caller can cleanly deal with the problem. */
fprintf (stderr, "MPFR: Error, too large input in mpfr_erfc\n");
MPFR_SET_ERANGE ();
MPFR_SET_NAN (y);
MPFR_RET_NAN;
}
}
/* for x < 0, erfc(x) tends to 2 by below */
if (MPFR_SIGN (x) < 0)
{
if ((MPFR_PREC(y) <= 8 && mpfr_cmp_si (x, -2)) ||
(MPFR_PREC(y) <= 26 && mpfr_cmp_si (x, -4)) ||
(MPFR_PREC(y) <= 97 && mpfr_cmp_si (x, -9)))
{
mpfr_set_ui (y, 2, GMP_RNDN);
mpfr_set_inexflag ();
if (rnd == GMP_RNDZ || rnd == GMP_RNDD)
{
mpfr_nextbelow (y);
return -1;
}
else
return 1;
}
}
/* Init stuff */
MPFR_SAVE_EXPO_MARK (expo);
prec = MPFR_PREC (y) + MPFR_INT_CEIL_LOG2 (MPFR_PREC (y)) + 3;
mpfr_init2 (tmp, prec);
MPFR_ZIV_INIT (loop, prec); /* Initialize the ZivLoop controler */
for (;;) /* Infinite loop */
{
mpfr_erf (tmp, x, GMP_RNDN);
MPFR_ASSERTD (!MPFR_IS_SINGULAR (tmp)); /* FIXME: 0 only for x=0 ? */
te = MPFR_GET_EXP (tmp);
mpfr_ui_sub (tmp, 1, tmp, GMP_RNDN);
/* See error analysis of expm1 for details */
if (MPFR_IS_ZERO (tmp))
prec *=2;
else
{
err = prec - (MAX (te - MPFR_GET_EXP (tmp), 0) + 1);
if (MPFR_LIKELY (MPFR_CAN_ROUND (tmp, err, MPFR_PREC (y), rnd)))
break;
}
MPFR_ZIV_NEXT (loop, prec); /* Increase used precision */
mpfr_set_prec (tmp, prec);
}
MPFR_ZIV_FREE (loop); /* Free the ZivLoop Controler */
inex = mpfr_set (y, tmp, rnd); /* Set y to the computed value */
mpfr_clear (tmp);
MPFR_SAVE_EXPO_FREE (expo);
return mpfr_check_range (y, inex, rnd);
}
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