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/* mpfr_asin -- arc-sinus of a floating-point number
Copyright (C) 2001 Free Software Foundation.
This file is part of the MPFR Library, and was contributed by Mathieu Dutour.
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., 59 Temple Place - Suite 330, Boston,
MA 02111-1307, USA. */
#include <stdio.h>
#include <stdlib.h>
#include "gmp.h"
#include "gmp-impl.h"
#include "mpfr.h"
#include "mpfr-impl.h"
int
mpfr_asin (mpfr_ptr asin, mpfr_srcptr x, mp_rnd_t rnd_mode)
{
mpfr_t xp;
mpfr_t arcs;
int signe, suplement;
mpfr_t tmp;
int Prec;
int prec_asin;
int good = 0;
int realprec;
int estimated_delta;
int compared;
/* Trivial cases */
if (MPFR_IS_NAN(x) || MPFR_IS_INF(x))
{
MPFR_SET_NAN(asin);
MPFR_RET_NAN;
}
/* Set x_p=|x| */
signe = MPFR_SIGN(x);
mpfr_init2 (xp, MPFR_PREC(x));
mpfr_set (xp, x, rnd_mode);
if (signe == -1)
MPFR_CHANGE_SIGN(xp);
compared = mpfr_cmp_ui (xp, 1);
if (compared > 0) /* asin(x) = NaN for |x| > 1 */
{
MPFR_SET_NAN(asin);
mpfr_clear(xp);
MPFR_RET_NAN;
}
if (compared == 0) /* x = 1 or x = -1 */
{
if (signe > 0) /* asin(+1) = Pi/2 */
mpfr_const_pi (asin, rnd_mode);
else /* asin(-1) = -Pi/2 */
{
if (rnd_mode == GMP_RNDU)
rnd_mode = GMP_RNDD;
else if (rnd_mode == GMP_RNDD)
rnd_mode = GMP_RNDU;
mpfr_const_pi (asin, rnd_mode);
}
MPFR_EXP(asin)--;
mpfr_clear(xp);
return 1; /* inexact */
}
if (MPFR_IS_ZERO(x)) /* x = 0 */
{
mpfr_set_ui (asin, 0, GMP_RNDN);
mpfr_clear(xp);
return 0; /* exact result */
}
prec_asin = MPFR_PREC(asin);
mpfr_ui_sub (xp, 1, xp, GMP_RNDD);
suplement = 2 - MPFR_EXP(xp);
#ifdef DEBUG
printf("suplement=%d\n", suplement);
#endif
realprec = prec_asin + 10;
while (!good)
{
estimated_delta = 1 + suplement;
Prec = realprec+estimated_delta;
/* Initialisation */
mpfr_init2 (tmp, Prec);
mpfr_init2 (arcs, Prec);
#ifdef DEBUG
printf("Prec=%d\n", Prec);
printf(" x=");
mpfr_out_str (stdout, 2, 0, x, GMP_RNDN);
printf ("\n");
#endif
mpfr_mul (tmp, x, x, GMP_RNDN);
#ifdef DEBUG
printf(" x^2=");
mpfr_out_str (stdout, 2, 0, tmp, GMP_RNDN);
printf ("\n");
#endif
mpfr_ui_sub (tmp, 1, tmp, GMP_RNDN);
#ifdef DEBUG
printf(" 1-x^2=");
mpfr_out_str (stdout, 2, 0, tmp, GMP_RNDN);
printf ("\n");
printf("10: 1-x^2=");
mpfr_out_str (stdout, 10, 0, tmp, GMP_RNDN);
printf ("\n");
#endif
mpfr_sqrt (tmp, tmp, GMP_RNDN);
#ifdef DEBUG
printf(" sqrt(1-x^2)=");
mpfr_out_str (stdout, 2, 0, tmp, GMP_RNDN);
printf ("\n");
printf("10: sqrt(1-x^2)=");
mpfr_out_str (stdout, 10, 0, tmp, GMP_RNDN);
printf ("\n");
#endif
mpfr_div (tmp, x, tmp, GMP_RNDN);
#ifdef DEBUG
printf("x/sqrt(1-x^2)=");
mpfr_out_str (stdout, 2, 0, tmp, GMP_RNDN);
printf ("\n");
#endif
mpfr_atan (arcs, tmp, GMP_RNDN);
#ifdef DEBUG
printf("atan(x/..x^2)=");
mpfr_out_str (stdout, 2, 0, arcs, GMP_RNDN);
printf ("\n");
#endif
if (mpfr_can_round (arcs, realprec, GMP_RNDN, rnd_mode, MPFR_PREC(asin)))
{
mpfr_set (asin, arcs, rnd_mode);
#ifdef DEBUG
printf("asin =");
mpfr_out_str (stdout, 2, prec_asin, asin, GMP_RNDN);
printf ("\n");
#endif
good = 1;
}
else
{
realprec += _mpfr_ceil_log2 ((double) realprec);
#ifdef DEBUG
printf("RETRY\n");
#endif
}
mpfr_clear (tmp);
mpfr_clear (arcs);
}
mpfr_clear (xp);
return 1; /* inexact result */
}
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