toolchain/gcc/newlib/libm/math/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 /* __ieee754_atanh(x)
  16  * Method :
  17  *    1.Reduced x to positive by atanh(-x) = -atanh(x)
  18  *    2.For x>=0.5
  19  *                  1              2x                          x
  20  *      atanh(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------)
  21  *                  2             1 - x                      1 - x
  22  *
  23  *      For x<0.5
  24  *      atanh(x) = 0.5*log1p(2x+2x*x/(1-x))
  25  *
  26  * Special cases:
  27  *      atanh(x) is NaN if |x| > 1 with signal;
  28  *      atanh(NaN) is that NaN with no signal;
  29  *      atanh(+-1) is +-INF with signal.
  30  *
  31  */
  32
  33 #include "fdlibm.h"
  34
  35 #ifndef _DOUBLE_IS_32BITS
  36
  37 #ifdef __STDC__
  38 static const double one = 1.0, huge = 1e300;
  39 #else
  40 static double one = 1.0, huge = 1e300;
  41 #endif
  42
  43 #ifdef __STDC__
  44 static const double zero = 0.0;
  45 #else
  46 static double zero = 0.0;
  47 #endif
  48
  49 #ifdef __STDC__
  50         double __ieee754_atanh(double x)
  51 #else
  52         double __ieee754_atanh(x)
  53         double x;
  54 #endif
  55 {
  56         double t;
  57         __int32_t hx,ix;
  58         __uint32_t lx;
  59         EXTRACT_WORDS(hx,lx,x);
  60         ix = hx&0x7fffffff;
  61         if ((ix|((lx|(-lx))>>31))>0x3ff00000) /* |x|>1 */
  62             return (x-x)/(x-x);
  63         if(ix==0x3ff00000)
  64             return x/zero;
  65         if(ix<0x3e300000&&(huge+x)>zero) return x;      /* x<2**-28 */
  66         SET_HIGH_WORD(x,ix);
  67         if(ix<0x3fe00000) {             /* x < 0.5 */
  68             t = x+x;
  69             t = 0.5*log1p(t+t*x/(one-x));
  70         } else
  71             t = 0.5*log1p((x+x)/(one-x));
  72         if(hx>=0) return t; else return -t;
  73 }
  74
  75 #endif /* defined(_DOUBLE_IS_32BITS) */