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 #pragma weak __asinl = asinl
  31 
  32 /*
  33  *      asinl(x) = atan2l(x,sqrt(1-x*x));
  34  *
  35  * For better accuracy, 1-x*x is computed as follows
  36  *      1-x*x                     if x <  0.5,
  37  *      2*(1-|x|)-(1-|x|)*(1-|x|) if x >= 0.5.
  38  *
  39  * Special cases:
  40  *      if x is NaN, return x itself;
  41  *      if |x|>1, return NaN with invalid signal.
  42  */
  43 
  44 #include "libm.h"
  45 
  46 static const long double zero = 0.0L, small = 1.0e-20L, half = 0.5L, one = 1.0L;
  47 #ifndef lint
  48 static const long double big = 1.0e+20L;
  49 #endif
  50 
  51 long double
  52 asinl(long double x) {
  53         long double t, w;
  54 #ifndef lint
  55         volatile long double dummy;
  56 #endif
  57 
  58         w = fabsl(x);
  59         if (isnanl(x))
  60                 return (x + x);
  61         else if (w <= half) {
  62                 if (w < small) {
  63 #ifndef lint
  64                         dummy = w + big;
  65                                                         /* inexact if w != 0 */
  66 #endif
  67                         return (x);
  68                 } else
  69                         return (atanl(x / sqrtl(one - x * x)));
  70         } else if (w < one) {
  71                 t = one - w;
  72                 w = t + t;
  73                 return (atanl(x / sqrtl(w - t * t)));
  74         } else if (w == one)
  75                 return (atan2l(x, zero));       /* asin(+-1) =  +- PI/2 */
  76         else
  77                 return (zero / zero);           /* |x| > 1: invalid */
  78 }