1 /* mpfr_acos -- arc-cosinus of a floating-point number
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.
6 This file is part of the GNU MPFR Library.
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.
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.
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. */
23 #define MPFR_NEED_LONGLONG_H
24 #include "mpfr-impl.h"
27 mpfr_acos (mpfr_ptr acos
, mpfr_srcptr x
, mpfr_rnd_t rnd_mode
)
30 mpfr_exp_t supplement
;
32 int sign
, compared
, inexact
;
33 MPFR_SAVE_EXPO_DECL (expo
);
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
));
42 if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (x
)))
44 if (MPFR_IS_NAN (x
) || MPFR_IS_INF (x
))
49 else /* necessarily x=0 */
51 MPFR_ASSERTD(MPFR_IS_ZERO(x
));
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
);
63 mpfr_init2 (xp
, MPFR_PREC (x
));
64 mpfr_abs (xp
, x
, MPFR_RNDN
); /* Exact */
66 compared
= mpfr_cmp_ui (xp
, 1);
68 if (MPFR_UNLIKELY (compared
>= 0))
71 if (compared
> 0) /* acos(x) = NaN for x > 1 */
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
);
85 MPFR_SAVE_EXPO_MARK (expo
);
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
);
92 supplement
= 2 - MPFR_GET_EXP (xp
);
95 prec
= MPFR_PREC (acos
);
96 prec
+= MPFR_INT_CEIL_LOG2(prec
) + 10 + supplement
;
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. */
106 if (MPFR_PREC (acos
) >= MPFR_PREC (x
) && MPFR_GET_EXP (x
) < 0)
108 mpfr_uexp_t pmin
= (mpfr_uexp_t
) (-2 * MPFR_GET_EXP (x
)) + 5;
109 MPFR_ASSERTN (pmin
<= MPFR_PREC_MAX
);
115 mpfr_init2 (tmp
, prec
);
116 mpfr_init2 (arcc
, prec
);
118 MPFR_ZIV_INIT (loop
, prec
);
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
);
131 if (MPFR_LIKELY (MPFR_CAN_ROUND (arcc
, prec
- supplement
,
132 MPFR_PREC (acos
), rnd_mode
)))
134 MPFR_ZIV_NEXT (loop
, prec
);
135 mpfr_set_prec (tmp
, prec
);
136 mpfr_set_prec (arcc
, prec
);
138 MPFR_ZIV_FREE (loop
);
140 inexact
= mpfr_set (acos
, arcc
, rnd_mode
);
144 MPFR_SAVE_EXPO_FREE (expo
);
145 return mpfr_check_range (acos
, inexact
, rnd_mode
);