/* @(#)s_tanh.c 5.1 93/09/24 */

/*

 * ====================================================

 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.

 *

 * Developed at SunPro, a Sun Microsystems, Inc. business.

 * Permission to use, copy, modify, and distribute this

 * software is freely granted, provided that this notice

 * is preserved.

 * ====================================================

 */

#if defined(LIBM_SCCS) && !defined(lint)

static char rcsid[] = "$NetBSD: s_tanh.c,v 1.7 1995/05/10 20:48:22 jtc Exp $";

#endif

/* Tanh(x)

 * Return the Hyperbolic Tangent of x

 *

 * Method :

 *				       x    -x

 *				      e  - e

 *	0. tanh(x) is defined to be -----------

 *				       x    -x

 *				      e  + e

 *	1. reduce x to non-negative by tanh(-x) = -tanh(x).

 *	2.  0      <= x <= 2**-55 : tanh(x) := x*(one+x)

 *					        -t

 *	    2**-55 <  x <=  1     : tanh(x) := -----; t = expm1(-2x)

 *					       t + 2

 *						     2

 *	    1      <= x <=  22.0  : tanh(x) := 1-  ----- ; t=expm1(2x)

 *						   t + 2

 *	    22.0   <  x <= INF    : tanh(x) := 1.

 *

 * Special cases:

 *	tanh(NaN) is NaN;

 *	only tanh(0)=0 is exact for finite argument.

 */

#include <float.h>

#include <math.h>

#include <math_private.h>

#include <math-underflow.h>

#include <libm-alias-double.h>

static const double one = 1.0, two = 2.0, tiny = 1.0e-300;

double

__tanh (double x)

{

  double t, z;

  int32_t jx, ix, lx;

  /* High word of |x|. */

  EXTRACT_WORDS (jx, lx, x);

  ix = jx & 0x7fffffff;

  /* x is INF or NaN */

  if (ix >= 0x7ff00000)

    {

      if (jx >= 0)

	return one / x + one;               /* tanh(+-inf)=+-1 */

      else

	return one / x - one;               /* tanh(NaN) = NaN */

    }

  /* |x| < 22 */

  if (ix < 0x40360000)                  /* |x|<22 */

    {

      if ((ix | lx) == 0)

	return x;                       /* x == +-0 */

      if (ix < 0x3c800000)              /* |x|<2**-55 */

	{

	  math_check_force_underflow (x);

	  return x * (one + x);           /* tanh(small) = small */

	}

      if (ix >= 0x3ff00000)             /* |x|>=1  */

	{

	  t = __expm1 (two * fabs (x));

	  z = one - two / (t + two);

	}

      else

	{

	  t = __expm1 (-two * fabs (x));

	  z = -t / (t + two);

	}

      /* |x| > 22, return +-1 */

    }

  else

    {

      z = one - tiny;                   /* raised inexact flag */

    }

  return (jx >= 0) ? z : -z;

}

libm_alias_double (__tanh, tanh)