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      1 
      2 /* @(#)s_tanh.c 1.3 95/01/18 */
      3 /*
      4  * ====================================================
      5  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
      6  *
      7  * Developed at SunSoft, a Sun Microsystems, Inc. business.
      8  * Permission to use, copy, modify, and distribute this
      9  * software is freely granted, provided that this notice
     10  * is preserved.
     11  * ====================================================
     12  */
     13 
     14 /* Tanh(x)
     15  * Return the Hyperbolic Tangent of x
     16  *
     17  * Method :
     18  *				       x    -x
     19  *				      e  - e
     20  *	0. ieee_tanh(x) is defined to be -----------
     21  *				       x    -x
     22  *				      e  + e
     23  *	1. reduce x to non-negative by ieee_tanh(-x) = -ieee_tanh(x).
     24  *	2.  0      <= x <= 2**-55 : ieee_tanh(x) := x*(one+x)
     25  *					        -t
     26  *	    2**-55 <  x <=  1     : ieee_tanh(x) := -----; t = ieee_expm1(-2x)
     27  *					       t + 2
     28  *						     2
     29  *	    1      <= x <=  22.0  : ieee_tanh(x) := 1-  ----- ; t=ieee_expm1(2x)
     30  *						   t + 2
     31  *	    22.0   <  x <= INF    : ieee_tanh(x) := 1.
     32  *
     33  * Special cases:
     34  *	tanh(NaN) is NaN;
     35  *	only ieee_tanh(0)=0 is exact for finite argument.
     36  */
     37 
     38 #include "fdlibm.h"
     39 
     40 #ifdef __STDC__
     41 static const double one=1.0, two=2.0, tiny = 1.0e-300;
     42 #else
     43 static double one=1.0, two=2.0, tiny = 1.0e-300;
     44 #endif
     45 
     46 #ifdef __STDC__
     47 	double ieee_tanh(double x)
     48 #else
     49 	double ieee_tanh(x)
     50 	double x;
     51 #endif
     52 {
     53 	double t,z;
     54 	int jx,ix;
     55 
     56     /* High word of |x|. */
     57 	jx = __HI(x);
     58 	ix = jx&0x7fffffff;
     59 
     60     /* x is INF or NaN */
     61 	if(ix>=0x7ff00000) {
     62 	    if (jx>=0) return one/x+one;    /* ieee_tanh(+-inf)=+-1 */
     63 	    else       return one/x-one;    /* ieee_tanh(NaN) = NaN */
     64 	}
     65 
     66     /* |x| < 22 */
     67 	if (ix < 0x40360000) {		/* |x|<22 */
     68 	    if (ix<0x3c800000) 		/* |x|<2**-55 */
     69 		return x*(one+x);    	/* ieee_tanh(small) = small */
     70 	    if (ix>=0x3ff00000) {	/* |x|>=1  */
     71 		t = ieee_expm1(two*ieee_fabs(x));
     72 		z = one - two/(t+two);
     73 	    } else {
     74 	        t = ieee_expm1(-two*ieee_fabs(x));
     75 	        z= -t/(t+two);
     76 	    }
     77     /* |x| > 22, return +-1 */
     78 	} else {
     79 	    z = one - tiny;		/* raised inexact flag */
     80 	}
     81 	return (jx>=0)? z: -z;
     82 }
     83