/* S_TANH.C

  * 

  * Portions Copyright (c) 1993-1999 Nokia Corporation and/or its subsidiary(-ies).

  * All rights reserved.

  */

 /* @(#)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.

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

  */

 /*

 FUNCTION

         <<tanh>>, <<tanhf>>---hyperbolic tangent

 INDEX

 tanh

 INDEX

 tanhf

 ANSI_SYNOPSIS

         #include <math.h>

         double tanh(double <[x]>);

         float tanhf(float <[x]>);

 TRAD_SYNOPSIS

         #include <math.h>

         double tanh(<[x]>)

         double <[x]>;

         float tanhf(<[x]>)

         float <[x]>;

 DESCRIPTION

 <<tanh>> computes the hyperbolic tangent of

 the argument <[x]>.  Angles are specified in radians.  

 <<tanh(<[x]>)>> is defined as 

 . sinh(<[x]>)/cosh(<[x]>)

 <<tanhf>> is identical, save that it takes and returns <<float>> values.

 RETURNS

 The hyperbolic tangent of <[x]> is returned.

 PORTABILITY

 <<tanh>> is ANSI C.  <<tanhf>> is an extension.

 */

 /* 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 "FDLIBM.H"

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

 /**

 Calculate hyperbolic tangent.

 @return hyperbolic tangent of x.

 @param x Angle expressed in radians (180 degrees = PI radians).

 */	

 EXPORT_C double tanh(double x) __SOFTFP

 {

 	double t,z;

 	__int32_t jx,ix;

     /* High word of |x|. */

 	GET_HIGH_WORD(jx,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<0x3c800000) 		/* |x|<2**-55 */

 		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;

 }