libm/e_atanh.c

   1 /*
   2  * ====================================================
   3  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
   4  *
   5  * Developed at SunPro, a Sun Microsystems, Inc. business.
   6  * Permission to use, copy, modify, and distribute this
   7  * software is freely granted, provided that this notice
   8  * is preserved.
   9  * ====================================================
  10  */
  11
  12 /* __ieee754_atanh(x)
  13  * Method :
  14  *    1.Reduced x to positive by atanh(-x) = -atanh(x)
  15  *    2.For x>=0.5
  16  *                  1              2x                          x
  17  *      atanh(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------)
  18  *                  2             1 - x                      1 - x
  19  *
  20  *      For x<0.5
  21  *      atanh(x) = 0.5*log1p(2x+2x*x/(1-x))
  22  *
  23  * Special cases:
  24  *      atanh(x) is NaN if |x| > 1 with signal;
  25  *      atanh(NaN) is that NaN with no signal;
  26  *      atanh(+-1) is +-INF with signal.
  27  *
  28  */
  29
  30 #include "math.h"
  31 #include "math_private.h"
  32
  33 static const double one = 1.0, huge = 1e300;
  34
  35 static const double zero = 0.0;
  36
  37 double attribute_hidden __ieee754_atanh(double x)
  38 {
  39         double t;
  40         int32_t hx,ix;
  41         u_int32_t lx;
  42         EXTRACT_WORDS(hx,lx,x);
  43         ix = hx&0x7fffffff;
  44         if ((ix|((lx|(-lx))>>31))>0x3ff00000) /* |x|>1 */
  45             return (x-x)/(x-x);
  46         if(ix==0x3ff00000)
  47             return x/zero;
  48         if(ix<0x3e300000&&(huge+x)>zero) return x;      /* x<2**-28 */
  49         SET_HIGH_WORD(x,ix);
  50         if(ix<0x3fe00000) {             /* x < 0.5 */
  51             t = x+x;
  52             t = 0.5*log1p(t+t*x/(one-x));
  53         } else
  54             t = 0.5*log1p((x+x)/(one-x));
  55         if(hx>=0) return t; else return -t;
  56 }
  57
  58 /*
  59  * wrapper atanh(x)
  60  */
  61 #ifndef _IEEE_LIBM
  62 double atanh(double x)
  63 {
  64         double z, y;
  65         z = __ieee754_atanh(x);
  66         if (_LIB_VERSION == _IEEE_ || isnan(x))
  67                 return z;
  68         y = fabs(x);
  69         if (y >= 1.0) {
  70                 if (y > 1.0)
  71                         return __kernel_standard(x, x, 30); /* atanh(|x|>1) */
  72                 return __kernel_standard(x, x, 31); /* atanh(|x|==1) */
  73         }
  74         return z;
  75 }
  76 #else
  77 strong_alias(__ieee754_atanh, atanh)
  78 #endif
  79 libm_hidden_def(atanh)