sl@0: /* S_TANH.C
sl@0:  * 
sl@0:  * Portions Copyright (c) 1993-1999 Nokia Corporation and/or its subsidiary(-ies).
sl@0:  * All rights reserved.
sl@0:  */
sl@0: 
sl@0: 
sl@0: /* @(#)s_tanh.c 5.1 93/09/24 */
sl@0: /*
sl@0:  * ====================================================
sl@0:  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
sl@0:  *
sl@0:  * Developed at SunPro, a Sun Microsystems, Inc. business.
sl@0:  * Permission to use, copy, modify, and distribute this
sl@0:  * software is freely granted, provided that this notice 
sl@0:  * is preserved.
sl@0:  * ====================================================
sl@0:  */
sl@0: 
sl@0: /*
sl@0: 
sl@0: FUNCTION
sl@0:         <<tanh>>, <<tanhf>>---hyperbolic tangent
sl@0: 
sl@0: INDEX
sl@0: tanh
sl@0: INDEX
sl@0: tanhf
sl@0: 
sl@0: ANSI_SYNOPSIS
sl@0:         #include <math.h>
sl@0:         double tanh(double <[x]>);
sl@0:         float tanhf(float <[x]>);
sl@0: 
sl@0: TRAD_SYNOPSIS
sl@0:         #include <math.h>
sl@0:         double tanh(<[x]>)
sl@0:         double <[x]>;
sl@0: 
sl@0:         float tanhf(<[x]>)
sl@0:         float <[x]>;
sl@0: 
sl@0: 
sl@0: DESCRIPTION
sl@0: 
sl@0: <<tanh>> computes the hyperbolic tangent of
sl@0: the argument <[x]>.  Angles are specified in radians.  
sl@0: 
sl@0: <<tanh(<[x]>)>> is defined as 
sl@0: . sinh(<[x]>)/cosh(<[x]>)
sl@0: 	
sl@0: <<tanhf>> is identical, save that it takes and returns <<float>> values.
sl@0: 
sl@0: RETURNS
sl@0: The hyperbolic tangent of <[x]> is returned.
sl@0: 
sl@0: PORTABILITY
sl@0: <<tanh>> is ANSI C.  <<tanhf>> is an extension.
sl@0: 
sl@0: */
sl@0: 
sl@0: /* Tanh(x)
sl@0:  * Return the Hyperbolic Tangent of x
sl@0:  *
sl@0:  * Method :
sl@0:  *				       x    -x
sl@0:  *				      e  - e
sl@0:  *	0. tanh(x) is defined to be -----------
sl@0:  *				       x    -x
sl@0:  *				      e  + e
sl@0:  *	1. reduce x to non-negative by tanh(-x) = -tanh(x).
sl@0:  *	2.  0      <= x <= 2**-55 : tanh(x) := x*(one+x)
sl@0:  *					        -t
sl@0:  *	    2**-55 <  x <=  1     : tanh(x) := -----; t = expm1(-2x)
sl@0:  *					       t + 2
sl@0:  *						     2
sl@0:  *	    1      <= x <=  22.0  : tanh(x) := 1-  ----- ; t=expm1(2x)
sl@0:  *						   t + 2
sl@0:  *	    22.0   <  x <= INF    : tanh(x) := 1.
sl@0:  *
sl@0:  * Special cases:
sl@0:  *	tanh(NaN) is NaN;
sl@0:  *	only tanh(0)=0 is exact for finite argument.
sl@0:  */
sl@0: 
sl@0: #include "FDLIBM.H"
sl@0: 
sl@0: static const double one=1.0, two=2.0, tiny = 1.0e-300;
sl@0: 
sl@0: /**
sl@0: Calculate hyperbolic tangent.
sl@0: @return hyperbolic tangent of x.
sl@0: @param x Angle expressed in radians (180 degrees = PI radians).
sl@0: */	
sl@0: EXPORT_C double tanh(double x) __SOFTFP
sl@0: {
sl@0: 	double t,z;
sl@0: 	__int32_t jx,ix;
sl@0: 
sl@0:     /* High word of |x|. */
sl@0: 	GET_HIGH_WORD(jx,x);
sl@0: 	ix = jx&0x7fffffff;
sl@0: 
sl@0:     /* x is INF or NaN */
sl@0: 	if(ix>=0x7ff00000) { 
sl@0: 	    if (jx>=0) return one/x+one;    /* tanh(+-inf)=+-1 */
sl@0: 	    else       return one/x-one;    /* tanh(NaN) = NaN */
sl@0: 	}
sl@0: 
sl@0:     /* |x| < 22 */
sl@0: 	if (ix < 0x40360000) {		/* |x|<22 */
sl@0: 	    if (ix<0x3c800000) 		/* |x|<2**-55 */
sl@0: 		return x*(one+x);    	/* tanh(small) = small */
sl@0: 	    if (ix>=0x3ff00000) {	/* |x|>=1  */
sl@0: 		t = expm1(two*fabs(x));
sl@0: 		z = one - two/(t+two);
sl@0: 	    } else {
sl@0: 	        t = expm1(-two*fabs(x));
sl@0: 	        z= -t/(t+two);
sl@0: 	    }
sl@0:     /* |x| > 22, return +-1 */
sl@0: 	} else {
sl@0: 	    z = one - tiny;		/* raised inexact flag */
sl@0: 	}
sl@0: 	return (jx>=0)? z: -z;
sl@0: }