usr/src/lib/libm/common/C/asinh.c

   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 __asinh = asinh
  31
  32 /* INDENT OFF */
  33 /*
  34  * asinh(x)
  35  * Method :
  36  *      Based on
  37  *              asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ]
  38  *      we have
  39  *      asinh(x) := x  if  1+x*x == 1,
  40  *               := sign(x)*(log(x)+ln2)) for large |x|, else
  41  *               := sign(x)*log(2|x|+1/(|x|+sqrt(x*x+1))) if|x| > 2, else
  42  *               := sign(x)*log1p(|x|+x^2/(1+sqrt(1+x^2)))
  43  */
  44 /* INDENT ON */
  45
  46 #include "libm_macros.h"
  47 #include <math.h>
  48
  49 static const double xxx[] = {
  50 /* one */       1.00000000000000000000e+00,     /* 3FF00000, 00000000 */
  51 /* ln2 */       6.93147180559945286227e-01,     /* 3FE62E42, FEFA39EF */
  52 /* huge */      1.00000000000000000000e+300
  53 };
  54 #define one     xxx[0]
  55 #define ln2     xxx[1]
  56 #define huge    xxx[2]
  57
  58 double
  59 asinh(double x) {
  60         double t, w;
  61         int hx, ix;
  62
  63         hx = ((int *) &x)[HIWORD];
  64         ix = hx & 0x7fffffff;
  65         if (ix >= 0x7ff00000)
  66 #if defined(FPADD_TRAPS_INCOMPLETE_ON_NAN)
  67                 return (ix >= 0x7ff80000 ? x : x + x);
  68                 /* assumes sparc-like QNaN */
  69 #else
  70                 return (x + x); /* x is inf or NaN */
  71 #endif
  72         if (ix < 0x3e300000) {  /* |x|<2**-28 */
  73                 if (huge + x > one)
  74                         return (x);     /* return x inexact except 0 */
  75         }
  76         if (ix > 0x41b00000) {  /* |x| > 2**28 */
  77                 w = log(fabs(x)) + ln2;
  78         } else if (ix > 0x40000000) {
  79                 /* 2**28 > |x| > 2.0 */
  80                 t = fabs(x);
  81                 w = log(2.0 * t + one / (sqrt(x * x + one) + t));
  82         } else {
  83                 /* 2.0 > |x| > 2**-28 */
  84                 t = x * x;
  85                 w = log1p(fabs(x) + t / (one + sqrt(one + t)));
  86         }
  87         return (hx > 0 ? w : -w);
  88 }