toolchain/gcc/newlib/libm/mathfp/e_atanh.c

   1
   2 /* @(#)e_atanh.c 5.1 93/09/24 */
   3 /*
   4  * ====================================================
   5  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
   6  *
   7  * Developed at SunPro, a Sun Microsystems, Inc. business.
   8  * Permission to use, copy, modify, and distribute this
   9  * software is freely granted, provided that this notice
  10  * is preserved.
  11  * ====================================================
  12  *
  13  */
  14
  15 /*
  16 FUNCTION
  17         <<atanh>>, <<atanhf>>---inverse hyperbolic tangent
  18
  19 INDEX
  20         atanh
  21 INDEX
  22         atanhf
  23
  24 ANSI_SYNOPSIS
  25         #include <math.h>
  26         double atanh(double <[x]>);
  27         float atanhf(float <[x]>);
  28
  29 TRAD_SYNOPSIS
  30         #include <math.h>
  31         double atanh(<[x]>)
  32         double <[x]>;
  33
  34         float atanhf(<[x]>)
  35         float <[x]>;
  36
  37 DESCRIPTION
  38         <<atanh>> calculates the inverse hyperbolic tangent of <[x]>.
  39
  40         <<atanhf>> is identical, other than taking and returning
  41         <<float>> values.
  42
  43 RETURNS
  44         <<atanh>> and <<atanhf>> return the calculated value.
  45
  46         If
  47         @ifnottex
  48         |<[x]>|
  49         @end ifnottex
  50         @tex
  51         $|x|$
  52         @end tex
  53         is greater than 1, the global <<errno>> is set to <<EDOM>> and
  54         the result is a NaN.  A <<DOMAIN error>> is reported.
  55
  56         If
  57         @ifnottex
  58         |<[x]>|
  59         @end ifnottex
  60         @tex
  61         $|x|$
  62         @end tex
  63         is 1, the global <<errno>> is set to <<EDOM>>; and the result is
  64         infinity with the same sign as <<x>>.  A <<SING error>> is reported.
  65
  66         You can modify the error handling for these routines using
  67         <<matherr>>.
  68
  69 PORTABILITY
  70         Neither <<atanh>> nor <<atanhf>> are ANSI C.
  71
  72 QUICKREF
  73         atanh - pure
  74         atanhf - pure
  75
  76
  77 */
  78
  79 /* atanh(x)
  80  * Method :
  81  *    1.Reduced x to positive by atanh(-x) = -atanh(x)
  82  *    2.For x>=0.5
  83  *                  1              2x                          x
  84  *      atanh(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------)
  85  *                  2             1 - x                      1 - x
  86  *
  87  *      For x<0.5
  88  *      atanh(x) = 0.5*log1p(2x+2x*x/(1-x))
  89  *
  90  * Special cases:
  91  *      atanh(x) is NaN if |x| > 1 with signal;
  92  *      atanh(NaN) is that NaN with no signal;
  93  *      atanh(+-1) is +-INF with signal.
  94  *
  95  */
  96
  97 #include "fdlibm.h"
  98
  99 #ifndef _DOUBLE_IS_32BITS
 100
 101 #ifdef __STDC__
 102 static const double one = 1.0, huge = 1e300;
 103 #else
 104 static double one = 1.0, huge = 1e300;
 105 #endif
 106
 107 #ifdef __STDC__
 108 static const double zero = 0.0;
 109 #else
 110 static double zero = 0.0;
 111 #endif
 112
 113 #ifdef __STDC__
 114         double atanh(double x)
 115 #else
 116         double atanh(x)
 117         double x;
 118 #endif
 119 {
 120         double t;
 121         __int32_t hx,ix;
 122         __uint32_t lx;
 123         EXTRACT_WORDS(hx,lx,x);
 124         ix = hx&0x7fffffff;
 125         if ((ix|((lx|(-lx))>>31))>0x3ff00000) /* |x|>1 */
 126             return (x-x)/(x-x);
 127         if(ix==0x3ff00000)
 128             return x/zero;
 129         if(ix<0x3e300000&&(huge+x)>zero) return x;      /* x<2**-28 */
 130         SET_HIGH_WORD(x,ix);
 131         if(ix<0x3fe00000) {             /* x < 0.5 */
 132             t = x+x;
 133             t = 0.5*log1p(t+t*x/(one-x));
 134         } else
 135             t = 0.5*log1p((x+x)/(one-x));
 136         if(hx>=0) return t; else return -t;
 137 }
 138
 139 #endif /* defined(_DOUBLE_IS_32BITS) */