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 /*
  27  * Copyright 2006 Sun Microsystems, Inc.  All rights reserved.
  28  * Use is subject to license terms.
  29  */
  30 
  31 #pragma weak __acosh = acosh
  32 
  33 
  34 /*
  35  * acosh(x)
  36  * Method :
  37  *      Based on
  38  *              acosh(x) = log [ x + sqrt(x*x-1) ]
  39  *      we have
  40  *              acosh(x) := log(x)+ln2, if x is large; else
  41  *              acosh(x) := log(2x-1/(sqrt(x*x-1)+x)) if x > 2; else
  42  *              acosh(x) := log1p(t+sqrt(2.0*t+t*t)); where t = x-1.
  43  *
  44  * Special cases:
  45  *      acosh(x) is NaN with signal if x < 1.
  46  *      acosh(NaN) is NaN without signal.
  47  */
  48 
  49 #include "libm_protos.h"                /* _SVID_libm_error */
  50 #include "libm_macros.h"
  51 #include <math.h>
  52 
  53 static const double one = 1.0,
  54         ln2 = 6.93147180559945286227e-01;       /* 3FE62E42, FEFA39EF */
  55 
  56 double
  57 acosh(double x)
  58 {
  59         double t;
  60         int hx;
  61 
  62         hx = ((int *)&x)[HIWORD];
  63 
  64         if (hx < 0x3ff00000) {               /* x < 1 */
  65                 if (isnan(x))
  66 #if defined(FPADD_TRAPS_INCOMPLETE_ON_NAN)
  67                         return (hx >= 0xfff80000 ? x : (x - x) / (x - x));
  68 
  69                 /* assumes sparc-like QNaN */
  70 #else
  71                         return ((x - x) / (x - x));
  72 #endif
  73                 else
  74                         return (_SVID_libm_err(x, x, 29));
  75         } else if (hx >= 0x41b00000) {
  76                 /* x > 2**28 */
  77                 if (hx >= 0x7ff00000) {      /* x is inf of NaN */
  78 #if defined(FPADD_TRAPS_INCOMPLETE_ON_NAN)
  79                         return (hx >= 0x7ff80000 ? x : x + x);
  80                         /* assumes sparc-like QNaN */
  81 #else
  82                         return (x + x);
  83 #endif
  84                 } else { /* acosh(huge)=log(2x) */
  85                         return (log(x) + ln2);
  86                 }
  87         } else if (((hx - 0x3ff00000) | ((int *)&x)[LOWORD]) == 0) {
  88                 return (0.0);           /* acosh(1) = 0 */
  89         } else if (hx > 0x40000000) {
  90                 /* 2**28 > x > 2 */
  91                 t = x * x;
  92                 return (log(2.0 * x - one / (x + sqrt(t - one))));
  93         } else {
  94                 /* 1 < x < 2 */
  95                 t = x - one;
  96                 return (log1p(t + sqrt(2.0 * t + t * t)));
  97         }
  98 }