source/libs/mpfr/mpfr-3.1.3/src/acos.c

   1 /* mpfr_acos -- arc-cosinus of a floating-point number
   2
   3 Copyright 2001-2015 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 #define MPFR_NEED_LONGLONG_H
  24 #include "mpfr-impl.h"
  25
  26 int
  27 mpfr_acos (mpfr_ptr acos, mpfr_srcptr x, mpfr_rnd_t rnd_mode)
  28 {
  29   mpfr_t xp, arcc, tmp;
  30   mpfr_exp_t supplement;
  31   mpfr_prec_t prec;
  32   int sign, compared, inexact;
  33   MPFR_SAVE_EXPO_DECL (expo);
  34   MPFR_ZIV_DECL (loop);
  35
  36   MPFR_LOG_FUNC
  37     (("x[%Pu]=%.*Rg rnd=%d", mpfr_get_prec(x), mpfr_log_prec, x, rnd_mode),
  38      ("acos[%Pu]=%.*Rg inexact=%d",
  39       mpfr_get_prec(acos), mpfr_log_prec, acos, inexact));
  40
  41   /* Singular cases */
  42   if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (x)))
  43     {
  44       if (MPFR_IS_NAN (x) || MPFR_IS_INF (x))
  45         {
  46           MPFR_SET_NAN (acos);
  47           MPFR_RET_NAN;
  48         }
  49       else /* necessarily x=0 */
  50         {
  51           MPFR_ASSERTD(MPFR_IS_ZERO(x));
  52           /* acos(0)=Pi/2 */
  53           MPFR_SAVE_EXPO_MARK (expo);
  54           inexact = mpfr_const_pi (acos, rnd_mode);
  55           mpfr_div_2ui (acos, acos, 1, rnd_mode); /* exact */
  56           MPFR_SAVE_EXPO_FREE (expo);
  57           return mpfr_check_range (acos, inexact, rnd_mode);
  58         }
  59     }
  60
  61   /* Set x_p=|x| */
  62   sign = MPFR_SIGN (x);
  63   mpfr_init2 (xp, MPFR_PREC (x));
  64   mpfr_abs (xp, x, MPFR_RNDN); /* Exact */
  65
  66   compared = mpfr_cmp_ui (xp, 1);
  67
  68   if (MPFR_UNLIKELY (compared >= 0))
  69     {
  70       mpfr_clear (xp);
  71       if (compared > 0) /* acos(x) = NaN for x > 1 */
  72         {
  73           MPFR_SET_NAN(acos);
  74           MPFR_RET_NAN;
  75         }
  76       else
  77         {
  78           if (MPFR_IS_POS_SIGN (sign)) /* acos(+1) = 0 */
  79             return mpfr_set_ui (acos, 0, rnd_mode);
  80           else /* acos(-1) = Pi */
  81             return mpfr_const_pi (acos, rnd_mode);
  82         }
  83     }
  84
  85   MPFR_SAVE_EXPO_MARK (expo);
  86
  87   /* Compute the supplement */
  88   mpfr_ui_sub (xp, 1, xp, MPFR_RNDD);
  89   if (MPFR_IS_POS_SIGN (sign))
  90     supplement = 2 - 2 * MPFR_GET_EXP (xp);
  91   else
  92     supplement = 2 - MPFR_GET_EXP (xp);
  93   mpfr_clear (xp);
  94
  95   prec = MPFR_PREC (acos);
  96   prec += MPFR_INT_CEIL_LOG2(prec) + 10 + supplement;
  97
  98   /* VL: The following change concerning prec comes from r3145
  99      "Optimize mpfr_acos by choosing a better initial precision."
 100      but it doesn't seem to be correct and leads to problems (assertion
 101      failure or very important inefficiency) with tiny arguments.
 102      Therefore, I've disabled it. */
 103   /* If x ~ 2^-N, acos(x) ~ PI/2 - x - x^3/6
 104      If Prec < 2*N, we can't round since x^3/6 won't be counted. */
 105 #if 0
 106   if (MPFR_PREC (acos) >= MPFR_PREC (x) && MPFR_GET_EXP (x) < 0)
 107     {
 108       mpfr_uexp_t pmin = (mpfr_uexp_t) (-2 * MPFR_GET_EXP (x)) + 5;
 109       MPFR_ASSERTN (pmin <= MPFR_PREC_MAX);
 110       if (prec < pmin)
 111         prec = pmin;
 112     }
 113 #endif
 114
 115   mpfr_init2 (tmp, prec);
 116   mpfr_init2 (arcc, prec);
 117
 118   MPFR_ZIV_INIT (loop, prec);
 119   for (;;)
 120     {
 121       /* acos(x) = Pi/2 - asin(x) = Pi/2 - atan(x/sqrt(1-x^2)) */
 122       mpfr_sqr (tmp, x, MPFR_RNDN);
 123       mpfr_ui_sub (tmp, 1, tmp, MPFR_RNDN);
 124       mpfr_sqrt (tmp, tmp, MPFR_RNDN);
 125       mpfr_div (tmp, x, tmp, MPFR_RNDN);
 126       mpfr_atan (arcc, tmp, MPFR_RNDN);
 127       mpfr_const_pi (tmp, MPFR_RNDN);
 128       mpfr_div_2ui (tmp, tmp, 1, MPFR_RNDN);
 129       mpfr_sub (arcc, tmp, arcc, MPFR_RNDN);
 130
 131       if (MPFR_LIKELY (MPFR_CAN_ROUND (arcc, prec - supplement,
 132                                        MPFR_PREC (acos), rnd_mode)))
 133         break;
 134       MPFR_ZIV_NEXT (loop, prec);
 135       mpfr_set_prec (tmp, prec);
 136       mpfr_set_prec (arcc, prec);
 137     }
 138   MPFR_ZIV_FREE (loop);
 139
 140   inexact = mpfr_set (acos, arcc, rnd_mode);
 141   mpfr_clear (tmp);
 142   mpfr_clear (arcc);
 143
 144   MPFR_SAVE_EXPO_FREE (expo);
 145   return mpfr_check_range (acos, inexact, rnd_mode);
 146 }