1 /*
   2  * CDDL HEADER START
   3  *
   4  * The contents of this file are subject to the terms of the
   5  * Common Development and Distribution License (the "License").
   6  * You may not use this file except in compliance with the License.
   7  *
   8  * You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE
   9  * or http://www.opensolaris.org/os/licensing.
  10  * See the License for the specific language governing permissions
  11  * and limitations under the License.
  12  *
  13  * When distributing Covered Code, include this CDDL HEADER in each
  14  * file and include the License file at usr/src/OPENSOLARIS.LICENSE.
  15  * If applicable, add the following below this CDDL HEADER, with the
  16  * fields enclosed by brackets "[]" replaced with your own identifying
  17  * information: Portions Copyright [yyyy] [name of copyright owner]
  18  *
  19  * CDDL HEADER END
  20  */
  21 
  22 /*
  23  * Copyright 2011 Nexenta Systems, Inc.  All rights reserved.
  24  */
  25 /*
  26  * Copyright 2006 Sun Microsystems, Inc.  All rights reserved.
  27  * Use is subject to license terms.
  28  */
  29 
  30 #if defined(ELFOBJ)
  31 #pragma weak asinl = __asinl
  32 #endif
  33 
  34 /*
  35  *      asinl(x) = atan2l(x,sqrt(1-x*x));
  36  *
  37  * For better accuracy, 1-x*x is computed as follows
  38  *      1-x*x                     if x <  0.5,
  39  *      2*(1-|x|)-(1-|x|)*(1-|x|) if x >= 0.5.
  40  *
  41  * Special cases:
  42  *      if x is NaN, return x itself;
  43  *      if |x|>1, return NaN with invalid signal.
  44  */
  45 
  46 #include "libm.h"
  47 
  48 static const long double zero = 0.0L, small = 1.0e-20L, half = 0.5L, one = 1.0L;
  49 #ifndef lint
  50 static const long double big = 1.0e+20L;
  51 #endif
  52 
  53 long double
  54 asinl(long double x) {
  55         long double t, w;
  56 
  57         w = fabsl(x);
  58         if (isnanl(x))
  59                 return (x + x);
  60         else if (w <= half) {
  61                 if (w < small) {
  62 #ifndef lint
  63                         volatile long double dummy = w + big;
  64                                                         /* inexact if w != 0 */
  65 #endif
  66                         return (x);
  67                 } else
  68                         return (atanl(x / sqrtl(one - x * x)));
  69         } else if (w < one) {
  70                 t = one - w;
  71                 w = t + t;
  72                 return (atanl(x / sqrtl(w - t * t)));
  73         } else if (w == one)
  74                 return (atan2l(x, zero));       /* asin(+-1) =  +- PI/2 */
  75         else
  76                 return (zero / zero);           /* |x| > 1: invalid */
  77 }