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      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 #include <sys/cdefs.h>
     14 #if defined(LIBM_SCCS) && !defined(lint)
     15 __RCSID("$NetBSD: s_tanh.c,v 1.10 2002/05/26 22:01:59 wiz Exp $");
     16 #endif
     17 
     18 /* Tanh(x)
     19  * Return the Hyperbolic Tangent of x
     20  *
     21  * Method :
     22  *				       x    -x
     23  *				      e  - e
     24  *	0. tanh(x) is defined to be -----------
     25  *				       x    -x
     26  *				      e  + e
     27  *	1. reduce x to non-negative by tanh(-x) = -tanh(x).
     28  *	2.  0      <= x <= 2**-55 : tanh(x) := x*(one+x)
     29  *					        -t
     30  *	    2**-55 <  x <=  1     : tanh(x) := -----; t = expm1(-2x)
     31  *					       t + 2
     32  *						     2
     33  *	    1      <= x <=  22.0  : tanh(x) := 1-  ----- ; t=expm1(2x)
     34  *						   t + 2
     35  *	    22.0   <  x <= INF    : tanh(x) := 1.
     36  *
     37  * Special cases:
     38  *	tanh(NaN) is NaN;
     39  *	only tanh(0)=0 is exact for finite argument.
     40  */
     41 
     42 #include "math.h"
     43 #include "math_private.h"
     44 
     45 static const double one=1.0, two=2.0, tiny = 1.0e-300;
     46 
     47 double
     48 tanh(double x)
     49 {
     50 	double t,z;
     51 	int32_t jx,ix;
     52 
     53     /* High word of |x|. */
     54 	GET_HIGH_WORD(jx,x);
     55 	ix = jx&0x7fffffff;
     56 
     57     /* x is INF or NaN */
     58 	if(ix>=0x7ff00000) {
     59 	    if (jx>=0) return one/x+one;    /* tanh(+-inf)=+-1 */
     60 	    else       return one/x-one;    /* tanh(NaN) = NaN */
     61 	}
     62 
     63     /* |x| < 22 */
     64 	if (ix < 0x40360000) {		/* |x|<22 */
     65 	    if (ix<0x3c800000) 		/* |x|<2**-55 */
     66 		return x*(one+x);    	/* tanh(small) = small */
     67 	    if (ix>=0x3ff00000) {	/* |x|>=1  */
     68 		t = expm1(two*fabs(x));
     69 		z = one - two/(t+two);
     70 	    } else {
     71 	        t = expm1(-two*fabs(x));
     72 	        z= -t/(t+two);
     73 	    }
     74     /* |x| > 22, return +-1 */
     75 	} else {
     76 	    z = one - tiny;		/* raised inexact flag */
     77 	}
     78 	return (jx>=0)? z: -z;
     79 }
     80