js/src/fdlibm/s_asinh.c

   1 /* -*- Mode: C; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 4 -*-
   2  *
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   5  *
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   7  * 1.1 (the "License"); you may not use this file except in compliance with
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  12  * WITHOUT WARRANTY OF ANY KIND, either express or implied. See the License
  13  * for the specific language governing rights and limitations under the
  14  * License.
  15  *
  16  * The Original Code is Mozilla Communicator client code, released
  17  * March 31, 1998.
  18  *
  19  * The Initial Developer of the Original Code is
  20  * Sun Microsystems, Inc.
  21  * Portions created by the Initial Developer are Copyright (C) 1998
  22  * the Initial Developer. All Rights Reserved.
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  39
  40 /* @(#)s_asinh.c 1.3 95/01/18 */
  41 /*
  42  * ====================================================
  43  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
  44  *
  45  * Developed at SunSoft, a Sun Microsystems, Inc. business.
  46  * Permission to use, copy, modify, and distribute this
  47  * software is freely granted, provided that this notice
  48  * is preserved.
  49  * ====================================================
  50  */
  51
  52 /* asinh(x)
  53  * Method :
  54  *      Based on
  55  *              asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ]
  56  *      we have
  57  *      asinh(x) := x  if  1+x*x=1,
  58  *               := sign(x)*(log(x)+ln2)) for large |x|, else
  59  *               := sign(x)*log(2|x|+1/(|x|+sqrt(x*x+1))) if|x|>2, else
  60  *               := sign(x)*log1p(|x| + x^2/(1 + sqrt(1+x^2)))
  61  */
  62
  63 #include "fdlibm.h"
  64
  65 #ifdef __STDC__
  66 static const double
  67 #else
  68 static double
  69 #endif
  70 one =  1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
  71 ln2 =  6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */
  72 really_big=  1.00000000000000000000e+300;
  73
  74 #ifdef __STDC__
  75         double fd_asinh(double x)
  76 #else
  77         double fd_asinh(x)
  78         double x;
  79 #endif
  80 {
  81         fd_twoints u;
  82         double t,w;
  83         int hx,ix;
  84         u.d = x;
  85         hx = __HI(u);
  86         ix = hx&0x7fffffff;
  87         if(ix>=0x7ff00000) return x+x;  /* x is inf or NaN */
  88         if(ix< 0x3e300000) {    /* |x|<2**-28 */
  89             if(really_big+x>one) return x;      /* return x inexact except 0 */
  90         }
  91         if(ix>0x41b00000) {     /* |x| > 2**28 */
  92             w = __ieee754_log(fd_fabs(x))+ln2;
  93         } else if (ix>0x40000000) {     /* 2**28 > |x| > 2.0 */
  94             t = fd_fabs(x);
  95             w = __ieee754_log(2.0*t+one/(fd_sqrt(x*x+one)+t));
  96         } else {                /* 2.0 > |x| > 2**-28 */
  97             t = x*x;
  98             w =fd_log1p(fd_fabs(x)+t/(one+fd_sqrt(one+t)));
  99         }
 100         if(hx>0) return w; else return -w;
 101 }