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      1 
      2 /* @(#)e_cosh.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 #ifndef lint
     15 static char rcsid[] = "$FreeBSD: src/lib/msun/src/e_cosh.c,v 1.8 2005/02/04 18:26:05 das Exp $";
     16 #endif
     17 
     18 /* __ieee754_cosh(x)
     19  * Method :
     20  * mathematically cosh(x) if defined to be (exp(x)+exp(-x))/2
     21  *	1. Replace x by |x| (cosh(x) = cosh(-x)).
     22  *	2.
     23  *		                                        [ exp(x) - 1 ]^2
     24  *	    0        <= x <= ln2/2  :  cosh(x) := 1 + -------------------
     25  *			       			           2*exp(x)
     26  *
     27  *		                                  exp(x) +  1/exp(x)
     28  *	    ln2/2    <= x <= 22     :  cosh(x) := -------------------
     29  *			       			          2
     30  *	    22       <= x <= lnovft :  cosh(x) := exp(x)/2
     31  *	    lnovft   <= x <= ln2ovft:  cosh(x) := exp(x/2)/2 * exp(x/2)
     32  *	    ln2ovft  <  x	    :  cosh(x) := huge*huge (overflow)
     33  *
     34  * Special cases:
     35  *	cosh(x) is |x| if x is +INF, -INF, or NaN.
     36  *	only cosh(0)=1 is exact for finite x.
     37  */
     38 
     39 #include "math.h"
     40 #include "math_private.h"
     41 
     42 static const double one = 1.0, half=0.5, huge = 1.0e300;
     43 
     44 double
     45 __ieee754_cosh(double x)
     46 {
     47 	double t,w;
     48 	int32_t ix;
     49 	u_int32_t lx;
     50 
     51     /* High word of |x|. */
     52 	GET_HIGH_WORD(ix,x);
     53 	ix &= 0x7fffffff;
     54 
     55     /* x is INF or NaN */
     56 	if(ix>=0x7ff00000) return x*x;
     57 
     58     /* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */
     59 	if(ix<0x3fd62e43) {
     60 	    t = expm1(fabs(x));
     61 	    w = one+t;
     62 	    if (ix<0x3c800000) return w;	/* cosh(tiny) = 1 */
     63 	    return one+(t*t)/(w+w);
     64 	}
     65 
     66     /* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */
     67 	if (ix < 0x40360000) {
     68 		t = __ieee754_exp(fabs(x));
     69 		return half*t+half/t;
     70 	}
     71 
     72     /* |x| in [22, log(maxdouble)] return half*exp(|x|) */
     73 	if (ix < 0x40862E42)  return half*__ieee754_exp(fabs(x));
     74 
     75     /* |x| in [log(maxdouble), overflowthresold] */
     76 	GET_LOW_WORD(lx,x);
     77 	if (ix<0x408633CE ||
     78 	      ((ix==0x408633ce)&&(lx<=(u_int32_t)0x8fb9f87d))) {
     79 	    w = __ieee754_exp(half*fabs(x));
     80 	    t = half*w;
     81 	    return t*w;
     82 	}
     83 
     84     /* |x| > overflowthresold, cosh(x) overflow */
     85 	return huge*huge;
     86 }
     87