1/* mpfr_asin -- arc-sinus of a floating-point number 2 3Copyright 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013 Free Software Foundation, Inc. 4Contributed by the AriC and Caramel projects, INRIA. 5 6This file is part of the GNU MPFR Library. 7 8The GNU MPFR Library is free software; you can redistribute it and/or modify 9it under the terms of the GNU Lesser General Public License as published by 10the Free Software Foundation; either version 3 of the License, or (at your 11option) any later version. 12 13The GNU MPFR Library is distributed in the hope that it will be useful, but 14WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY 15or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public 16License for more details. 17 18You should have received a copy of the GNU Lesser General Public License 19along with the GNU MPFR Library; see the file COPYING.LESSER. If not, see 20http://www.gnu.org/licenses/ or write to the Free Software Foundation, Inc., 2151 Franklin St, Fifth Floor, Boston, MA 02110-1301, USA. */ 22 23#include "mpfr-impl.h" 24 25int 26mpfr_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} 126