124 lines
3.8 KiB
C
124 lines
3.8 KiB
C
/* mpfr_asin -- arc-sinus of a floating-point number
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Copyright 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010, 2011 Free Software Foundation, Inc.
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Contributed by the Arenaire and Cacao projects, INRIA.
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This file is part of the GNU MPFR Library, and was contributed by Mathieu Dutour.
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The GNU MPFR Library is free software; you can redistribute it and/or modify
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it under the terms of the GNU Lesser General Public License as published by
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the Free Software Foundation; either version 3 of the License, or (at your
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option) any later version.
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The GNU MPFR Library is distributed in the hope that it will be useful, but
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WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
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or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public
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License for more details.
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You should have received a copy of the GNU Lesser General Public License
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along with the GNU MPFR Library; see the file COPYING.LESSER. If not, see
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http://www.gnu.org/licenses/ or write to the Free Software Foundation, Inc.,
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51 Franklin St, Fifth Floor, Boston, MA 02110-1301, USA. */
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#include "mpfr-impl.h"
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int
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mpfr_asin (mpfr_ptr asin, mpfr_srcptr x, mpfr_rnd_t rnd_mode)
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{
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mpfr_t xp;
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int compared, inexact;
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mpfr_prec_t prec;
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mpfr_exp_t xp_exp;
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MPFR_SAVE_EXPO_DECL (expo);
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MPFR_ZIV_DECL (loop);
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MPFR_LOG_FUNC (("x[%#R]=%R rnd=%d", x, x, rnd_mode),
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("asin[%#R]=%R inexact=%d", asin, asin, inexact));
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/* Special cases */
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if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (x)))
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{
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if (MPFR_IS_NAN (x) || MPFR_IS_INF (x))
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{
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MPFR_SET_NAN (asin);
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MPFR_RET_NAN;
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}
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else /* x = 0 */
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{
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MPFR_ASSERTD (MPFR_IS_ZERO (x));
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MPFR_SET_ZERO (asin);
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MPFR_SET_SAME_SIGN (asin, x);
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MPFR_RET (0); /* exact result */
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}
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}
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/* asin(x) = x + x^3/6 + ... so the error is < 2^(3*EXP(x)-2) */
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MPFR_FAST_COMPUTE_IF_SMALL_INPUT (asin, x, -2 * MPFR_GET_EXP (x), 2, 1,
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rnd_mode, {});
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/* Set x_p=|x| (x is a normal number) */
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mpfr_init2 (xp, MPFR_PREC (x));
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inexact = mpfr_abs (xp, x, MPFR_RNDN);
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MPFR_ASSERTD (inexact == 0);
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compared = mpfr_cmp_ui (xp, 1);
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MPFR_SAVE_EXPO_MARK (expo);
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if (MPFR_UNLIKELY (compared >= 0))
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{
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mpfr_clear (xp);
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if (compared > 0) /* asin(x) = NaN for |x| > 1 */
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{
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MPFR_SAVE_EXPO_FREE (expo);
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MPFR_SET_NAN (asin);
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MPFR_RET_NAN;
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}
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else /* x = 1 or x = -1 */
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{
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if (MPFR_IS_POS (x)) /* asin(+1) = Pi/2 */
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inexact = mpfr_const_pi (asin, rnd_mode);
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else /* asin(-1) = -Pi/2 */
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{
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inexact = -mpfr_const_pi (asin, MPFR_INVERT_RND(rnd_mode));
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MPFR_CHANGE_SIGN (asin);
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}
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mpfr_div_2ui (asin, asin, 1, rnd_mode);
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}
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}
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else
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{
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/* Compute exponent of 1 - ABS(x) */
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mpfr_ui_sub (xp, 1, xp, MPFR_RNDD);
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MPFR_ASSERTD (MPFR_GET_EXP (xp) <= 0);
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MPFR_ASSERTD (MPFR_GET_EXP (x) <= 0);
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xp_exp = 2 - MPFR_GET_EXP (xp);
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/* Set up initial prec */
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prec = MPFR_PREC (asin) + 10 + xp_exp;
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/* use asin(x) = atan(x/sqrt(1-x^2)) */
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MPFR_ZIV_INIT (loop, prec);
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for (;;)
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{
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mpfr_set_prec (xp, prec);
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mpfr_sqr (xp, x, MPFR_RNDN);
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mpfr_ui_sub (xp, 1, xp, MPFR_RNDN);
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mpfr_sqrt (xp, xp, MPFR_RNDN);
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mpfr_div (xp, x, xp, MPFR_RNDN);
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mpfr_atan (xp, xp, MPFR_RNDN);
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if (MPFR_LIKELY (MPFR_CAN_ROUND (xp, prec - xp_exp,
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MPFR_PREC (asin), rnd_mode)))
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break;
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MPFR_ZIV_NEXT (loop, prec);
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}
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MPFR_ZIV_FREE (loop);
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inexact = mpfr_set (asin, xp, rnd_mode);
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mpfr_clear (xp);
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}
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MPFR_SAVE_EXPO_FREE (expo);
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return mpfr_check_range (asin, inexact, rnd_mode);
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}
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