1 /* mpfr_asin -- arc-sinus of a floating-point number 2 3 Copyright 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010, 2011 Free Software Foundation, Inc. 4 Contributed by the Arenaire 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 } 126