js/src/fdlibm/e_atanh.c

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  15  *
  16  * The Original Code is Mozilla Communicator client code, released
  17  * March 31, 1998.
  18  *
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  20  * Sun Microsystems, Inc.
  21  * Portions created by the Initial Developer are Copyright (C) 1998
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  39
  40 /* @(#)e_atanh.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
  53 /* __ieee754_atanh(x)
  54  * Method :
  55  *    1.Reduced x to positive by atanh(-x) = -atanh(x)
  56  *    2.For x>=0.5
  57  *                  1              2x                          x
  58  *      atanh(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------)
  59  *                  2             1 - x                      1 - x
  60  *
  61  *      For x<0.5
  62  *      atanh(x) = 0.5*log1p(2x+2x*x/(1-x))
  63  *
  64  * Special cases:
  65  *      atanh(x) is NaN if |x| > 1 with signal;
  66  *      atanh(NaN) is that NaN with no signal;
  67  *      atanh(+-1) is +-INF with signal.
  68  *
  69  */
  70
  71 #include "fdlibm.h"
  72
  73 #ifdef __STDC__
  74 static const double one = 1.0, really_big = 1e300;
  75 #else
  76 static double one = 1.0, really_big = 1e300;
  77 #endif
  78
  79 static double zero = 0.0;
  80
  81 #ifdef __STDC__
  82         double __ieee754_atanh(double x)
  83 #else
  84         double __ieee754_atanh(x)
  85         double x;
  86 #endif
  87 {
  88         double t;
  89         int hx,ix;
  90         unsigned lx;
  91         fd_twoints u;
  92         u.d = x;
  93         hx = __HI(u);           /* high word */
  94         lx = __LO(u);           /* low word */
  95         ix = hx&0x7fffffff;
  96         if ((ix|((lx|(-(int)lx))>>31))>0x3ff00000) /* |x|>1 */
  97             return (x-x)/(x-x);
  98         if(ix==0x3ff00000)
  99             return x/zero;
 100         if(ix<0x3e300000&&(really_big+x)>zero) return x;        /* x<2**-28 */
 101         u.d = x;
 102         __HI(u) = ix;           /* x <- |x| */
 103         x = u.d;
 104         if(ix<0x3fe00000) {             /* x < 0.5 */
 105             t = x+x;
 106             t = 0.5*fd_log1p(t+t*x/(one-x));
 107         } else
 108             t = 0.5*fd_log1p((x+x)/(one-x));
 109         if(hx>=0) return t; else return -t;
 110 }