source/libs/mpfr/mpfr-3.1.2/src/asin.c

   1 /* mpfr_asin -- arc-sinus of a floating-point number
   2
   3 Copyright 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013 Free Software Foundation, Inc.
   4 Contributed by the AriC and Caramel projects, INRIA.
   5
   6 This file is part of the GNU MPFR Library.
   7
   8 The GNU MPFR Library is free software; you can redistribute it and/or modify
   9 it under the terms of the GNU Lesser General Public License as published by
  10 the Free Software Foundation; either version 3 of the License, or (at your
  11 option) any later version.
  12
  13 The GNU MPFR Library is distributed in the hope that it will be useful, but
  14 WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
  15 or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General Public
  16 License for more details.
  17
  18 You should have received a copy of the GNU Lesser General Public License
  19 along with the GNU MPFR Library; see the file COPYING.LESSER.  If not, see
  20 http://www.gnu.org/licenses/ or write to the Free Software Foundation, Inc.,
  21 51 Franklin St, Fifth Floor, Boston, MA 02110-1301, USA. */
  22
  23 #include "mpfr-impl.h"
  24
  25 int
  26 mpfr_asin (mpfr_ptr asin, mpfr_srcptr x, mpfr_rnd_t rnd_mode)
  27 {
  28   mpfr_t xp;
  29   int compared, inexact;
  30   mpfr_prec_t prec;
  31   mpfr_exp_t xp_exp;
  32   MPFR_SAVE_EXPO_DECL (expo);
  33   MPFR_ZIV_DECL (loop);
  34
  35   MPFR_LOG_FUNC (
  36     ("x[%Pu]=%.*Rg rnd=%d", mpfr_get_prec (x), mpfr_log_prec, x, rnd_mode),
  37     ("asin[%Pu]=%.*Rg inexact=%d", mpfr_get_prec (asin), mpfr_log_prec, asin,
  38      inexact));
  39
  40   /* Special cases */
  41   if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (x)))
  42     {
  43       if (MPFR_IS_NAN (x) || MPFR_IS_INF (x))
  44         {
  45           MPFR_SET_NAN (asin);
  46           MPFR_RET_NAN;
  47         }
  48       else /* x = 0 */
  49         {
  50           MPFR_ASSERTD (MPFR_IS_ZERO (x));
  51           MPFR_SET_ZERO (asin);
  52           MPFR_SET_SAME_SIGN (asin, x);
  53           MPFR_RET (0); /* exact result */
  54         }
  55     }
  56
  57   /* asin(x) = x + x^3/6 + ... so the error is < 2^(3*EXP(x)-2) */
  58   MPFR_FAST_COMPUTE_IF_SMALL_INPUT (asin, x, -2 * MPFR_GET_EXP (x), 2, 1,
  59                                     rnd_mode, {});
  60
  61   /* Set x_p=|x| (x is a normal number) */
  62   mpfr_init2 (xp, MPFR_PREC (x));
  63   inexact = mpfr_abs (xp, x, MPFR_RNDN);
  64   MPFR_ASSERTD (inexact == 0);
  65
  66   compared = mpfr_cmp_ui (xp, 1);
  67
  68   MPFR_SAVE_EXPO_MARK (expo);
  69
  70   if (MPFR_UNLIKELY (compared >= 0))
  71     {
  72       mpfr_clear (xp);
  73       if (compared > 0)                  /* asin(x) = NaN for |x| > 1 */
  74         {
  75           MPFR_SAVE_EXPO_FREE (expo);
  76           MPFR_SET_NAN (asin);
  77           MPFR_RET_NAN;
  78         }
  79       else                              /* x = 1 or x = -1 */
  80         {
  81           if (MPFR_IS_POS (x)) /* asin(+1) = Pi/2 */
  82             inexact = mpfr_const_pi (asin, rnd_mode);
  83           else /* asin(-1) = -Pi/2 */
  84             {
  85               inexact = -mpfr_const_pi (asin, MPFR_INVERT_RND(rnd_mode));
  86               MPFR_CHANGE_SIGN (asin);
  87             }
  88           mpfr_div_2ui (asin, asin, 1, rnd_mode);
  89         }
  90     }
  91   else
  92     {
  93       /* Compute exponent of 1 - ABS(x) */
  94       mpfr_ui_sub (xp, 1, xp, MPFR_RNDD);
  95       MPFR_ASSERTD (MPFR_GET_EXP (xp) <= 0);
  96       MPFR_ASSERTD (MPFR_GET_EXP (x) <= 0);
  97       xp_exp = 2 - MPFR_GET_EXP (xp);
  98
  99       /* Set up initial prec */
 100       prec = MPFR_PREC (asin) + 10 + xp_exp;
 101
 102       /* use asin(x) = atan(x/sqrt(1-x^2)) */
 103       MPFR_ZIV_INIT (loop, prec);
 104       for (;;)
 105         {
 106           mpfr_set_prec (xp, prec);
 107           mpfr_sqr (xp, x, MPFR_RNDN);
 108           mpfr_ui_sub (xp, 1, xp, MPFR_RNDN);
 109           mpfr_sqrt (xp, xp, MPFR_RNDN);
 110           mpfr_div (xp, x, xp, MPFR_RNDN);
 111           mpfr_atan (xp, xp, MPFR_RNDN);
 112           if (MPFR_LIKELY (MPFR_CAN_ROUND (xp, prec - xp_exp,
 113                                            MPFR_PREC (asin), rnd_mode)))
 114             break;
 115           MPFR_ZIV_NEXT (loop, prec);
 116         }
 117       MPFR_ZIV_FREE (loop);
 118       inexact = mpfr_set (asin, xp, rnd_mode);
 119
 120       mpfr_clear (xp);
 121     }
 122
 123   MPFR_SAVE_EXPO_FREE (expo);
 124   return mpfr_check_range (asin, inexact, rnd_mode);
 125 }