/* E_COSH.C

  * 

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

  * All rights reserved.

  */

 /* @(#)e_cosh.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.

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

  */

 /* __ieee754_cosh(x)

  * Method : 

  * mathematically cosh(x) if defined to be (exp(x)+exp(-x))/2

  *	1. Replace x by |x| (cosh(x) = cosh(-x)). 

  *	2. 

  *		                                        [ exp(x) - 1 ]^2 

  *	    0        <= x <= ln2/2  :  cosh(x) := 1 + -------------------

  *			       			           2*exp(x)

  *

  *		                                  exp(x) +  1/exp(x)

  *	    ln2/2    <= x <= 22     :  cosh(x) := -------------------

  *			       			          2

  *	    22       <= x <= lnovft :  cosh(x) := exp(x)/2 

  *	    lnovft   <= x <= ln2ovft:  cosh(x) := exp(x/2)/2 * exp(x/2)

  *	    ln2ovft  <  x	    :  cosh(x) := huge*huge (overflow)

  *

  * Special cases:

  *	cosh(x) is |x| if x is +INF, -INF, or NaN.

  *	only cosh(0)=1 is exact for finite x.

  */

 #include "FDLIBM.H"

 static const double one = 1.0, half=0.5, huge = 1.0e300;

 EXPORT_C double __ieee754_cosh(double x) __SOFTFP

 {	

 	double t,w;

 	__int32_t ix;

 	__uint32_t lx;

     /* High word of |x|. */

 	GET_HIGH_WORD(ix,x);

 	ix &= 0x7fffffff;

     /* x is INF or NaN */

 	if(ix>=0x7ff00000) return x*x;	

     /* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */

 	if(ix<0x3fd62e43) {

 	    t = expm1(fabs(x));

 	    w = one+t;

 	    if (ix<0x3c800000) return w;	/* cosh(tiny) = 1 */

 	    return one+(t*t)/(w+w);

 	}

     /* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */

 	if (ix < 0x40360000) {

 		t = __ieee754_exp(fabs(x));

 		return half*t+half/t;

 	}

     /* |x| in [22, log(maxdouble)] return half*exp(|x|) */

 	if (ix < 0x40862E42)  return half*__ieee754_exp(fabs(x));

     /* |x| in [log(maxdouble), overflowthresold] */

 	GET_LOW_WORD(lx,x);

 	if (ix<0x408633CE || 

 	      ((ix==0x408633ce)&&(lx<=(__uint32_t)0x8fb9f87d))) {

 	    w = __ieee754_exp(half*fabs(x));

 	    t = half*w;

 	    return t*w;

 	}

     /* |x| > overflowthresold, cosh(x) overflow */

 	return huge*huge;

 }