sysdeps/ieee754/dbl-64/s_tanh.c

   1 /* @(#)s_tanh.c 5.1 93/09/24 */
   2 /*
   3  * ====================================================
   4  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
   5  *
   6  * Developed at SunPro, a Sun Microsystems, Inc. business.
   7  * Permission to use, copy, modify, and distribute this
   8  * software is freely granted, provided that this notice
   9  * is preserved.
  10  * ====================================================
  11  */
  12
  13 #if defined(LIBM_SCCS) && !defined(lint)
  14 static char rcsid[] = "$NetBSD: s_tanh.c,v 1.7 1995/05/10 20:48:22 jtc Exp $";
  15 #endif
  16
  17 /* Tanh(x)
  18  * Return the Hyperbolic Tangent of x
  19  *
  20  * Method :
  21  *                                     x    -x
  22  *                                    e  - e
  23  *      0. tanh(x) is defined to be -----------
  24  *                                     x    -x
  25  *                                    e  + e
  26  *      1. reduce x to non-negative by tanh(-x) = -tanh(x).
  27  *      2.  0      <= x <= 2**-55 : tanh(x) := x*(one+x)
  28  *                                              -t
  29  *          2**-55 <  x <=  1     : tanh(x) := -----; t = expm1(-2x)
  30  *                                             t + 2
  31  *                                                   2
  32  *          1      <= x <=  22.0  : tanh(x) := 1-  ----- ; t=expm1(2x)
  33  *                                                 t + 2
  34  *          22.0   <  x <= INF    : tanh(x) := 1.
  35  *
  36  * Special cases:
  37  *      tanh(NaN) is NaN;
  38  *      only tanh(0)=0 is exact for finite argument.
  39  */
  40
  41 #include <math.h>
  42 #include <math_private.h>
  43
  44 static const double one = 1.0, two = 2.0, tiny = 1.0e-300;
  45
  46 double
  47 __tanh (double x)
  48 {
  49   double t, z;
  50   int32_t jx, ix, lx;
  51
  52   /* High word of |x|. */
  53   EXTRACT_WORDS (jx, lx, x);
  54   ix = jx & 0x7fffffff;
  55
  56   /* x is INF or NaN */
  57   if (ix >= 0x7ff00000)
  58     {
  59       if (jx >= 0)
  60         return one / x + one;               /* tanh(+-inf)=+-1 */
  61       else
  62         return one / x - one;               /* tanh(NaN) = NaN */
  63     }
  64
  65   /* |x| < 22 */
  66   if (ix < 0x40360000)                  /* |x|<22 */
  67     {
  68       if ((ix | lx) == 0)
  69         return x;                       /* x == +-0 */
  70       if (ix < 0x3c800000)              /* |x|<2**-55 */
  71         return x * (one + x);           /* tanh(small) = small */
  72       if (ix >= 0x3ff00000)             /* |x|>=1  */
  73         {
  74           t = __expm1 (two * fabs (x));
  75           z = one - two / (t + two);
  76         }
  77       else
  78         {
  79           t = __expm1 (-two * fabs (x));
  80           z = -t / (t + two);
  81         }
  82       /* |x| > 22, return +-1 */
  83     }
  84   else
  85     {
  86       z = one - tiny;                   /* raised inexact flag */
  87     }
  88   return (jx >= 0) ? z : -z;
  89 }
  90 weak_alias (__tanh, tanh)
  91 #ifdef NO_LONG_DOUBLE
  92 strong_alias (__tanh, __tanhl)
  93 weak_alias (__tanh, tanhl)
  94 #endif