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e_cosh.c (2378B)

      1 /* @(#)e_cosh.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 #ifndef lint
     14 static char rcsid[] = "$FreeBSD: src/lib/msun/src/e_cosh.c,v 1.7 2002/05/28 17:03:12 alfred Exp $";
     15 #endif
     16 
     17 /* __ieee754_cosh(x)
     18  * Method :
     19  * mathematically cosh(x) if defined to be (exp(x)+exp(-x))/2
     20  *	1. Replace x by |x| (cosh(x) = cosh(-x)).
     21  *	2.
     22  *		                                        [ exp(x) - 1 ]^2
     23  *	    0        <= x <= ln2/2  :  cosh(x) := 1 + -------------------
     24  *			       			           2*exp(x)
     25  *
     26  *		                                  exp(x) +  1/exp(x)
     27  *	    ln2/2    <= x <= 22     :  cosh(x) := -------------------
     28  *			       			          2
     29  *	    22       <= x <= lnovft :  cosh(x) := exp(x)/2
     30  *	    lnovft   <= x <= ln2ovft:  cosh(x) := exp(x/2)/2 * exp(x/2)
     31  *	    ln2ovft  <  x	    :  cosh(x) := huge*huge (overflow)
     32  *
     33  * Special cases:
     34  *	cosh(x) is |x| if x is +INF, -INF, or NaN.
     35  *	only cosh(0)=1 is exact for finite x.
     36  */
     37 
     38 #include "math.h"
     39 #include "math_private.h"
     40 
     41 static const double one = 1.0, half=0.5, huge = 1.0e300;
     42 
     43 double
     44 __ieee754_cosh(double x)
     45 {
     46 	double t,w;
     47 	int32_t ix;
     48 	u_int32_t lx;
     49 
     50     /* High word of |x|. */
     51 	GET_HIGH_WORD(ix,x);
     52 	ix &= 0x7fffffff;
     53 
     54     /* x is INF or NaN */
     55 	if(ix>=0x7ff00000) return x*x;
     56 
     57     /* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */
     58 	if(ix<0x3fd62e43) {
     59 	    t = expm1(fabs(x));
     60 	    w = one+t;
     61 	    if (ix<0x3c800000) return w;	/* cosh(tiny) = 1 */
     62 	    return one+(t*t)/(w+w);
     63 	}
     64 
     65     /* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */
     66 	if (ix < 0x40360000) {
     67 		t = __ieee754_exp(fabs(x));
     68 		return half*t+half/t;
     69 	}
     70 
     71     /* |x| in [22, log(maxdouble)] return half*exp(|x|) */
     72 	if (ix < 0x40862E42)  return half*__ieee754_exp(fabs(x));
     73 
     74     /* |x| in [log(maxdouble), overflowthresold] */
     75 	GET_LOW_WORD(lx,x);
     76 	if (ix<0x408633CE ||
     77 	      ((ix==0x408633ce)&&(lx<=(u_int32_t)0x8fb9f87d))) {
     78 	    w = __ieee754_exp(half*fabs(x));
     79 	    t = half*w;
     80 	    return t*w;
     81 	}
     82 
     83     /* |x| > overflowthresold, cosh(x) overflow */
     84 	return huge*huge;
     85 }