vx32

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e_sinh.c (2176B)

      1 /* @(#)e_sinh.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_sinh.c,v 1.8 2002/05/28 18:15:04 alfred Exp $";
     15 #endif
     16 
     17 /* __ieee754_sinh(x)
     18  * Method :
     19  * mathematically sinh(x) if defined to be (exp(x)-exp(-x))/2
     20  *	1. Replace x by |x| (sinh(-x) = -sinh(x)).
     21  *	2.
     22  *		                                    E + E/(E+1)
     23  *	    0        <= x <= 22     :  sinh(x) := --------------, E=expm1(x)
     24  *			       			        2
     25  *
     26  *	    22       <= x <= lnovft :  sinh(x) := exp(x)/2
     27  *	    lnovft   <= x <= ln2ovft:  sinh(x) := exp(x/2)/2 * exp(x/2)
     28  *	    ln2ovft  <  x	    :  sinh(x) := x*shuge (overflow)
     29  *
     30  * Special cases:
     31  *	sinh(x) is |x| if x is +INF, -INF, or NaN.
     32  *	only sinh(0)=0 is exact for finite x.
     33  */
     34 
     35 #include "math.h"
     36 #include "math_private.h"
     37 
     38 static const double one = 1.0, shuge = 1.0e307;
     39 
     40 double
     41 __ieee754_sinh(double x)
     42 {
     43 	double t,w,h;
     44 	int32_t ix,jx;
     45 	u_int32_t lx;
     46 
     47     /* High word of |x|. */
     48 	GET_HIGH_WORD(jx,x);
     49 	ix = jx&0x7fffffff;
     50 
     51     /* x is INF or NaN */
     52 	if(ix>=0x7ff00000) return x+x;
     53 
     54 	h = 0.5;
     55 	if (jx<0) h = -h;
     56     /* |x| in [0,22], return sign(x)*0.5*(E+E/(E+1))) */
     57 	if (ix < 0x40360000) {		/* |x|<22 */
     58 	    if (ix<0x3e300000) 		/* |x|<2**-28 */
     59 		if(shuge+x>one) return x;/* sinh(tiny) = tiny with inexact */
     60 	    t = expm1(fabs(x));
     61 	    if(ix<0x3ff00000) return h*(2.0*t-t*t/(t+one));
     62 	    return h*(t+t/(t+one));
     63 	}
     64 
     65     /* |x| in [22, log(maxdouble)] return 0.5*exp(|x|) */
     66 	if (ix < 0x40862E42)  return h*__ieee754_exp(fabs(x));
     67 
     68     /* |x| in [log(maxdouble), overflowthresold] */
     69 	GET_LOW_WORD(lx,x);
     70 	if (ix<0x408633CE || ((ix==0x408633ce)&&(lx<=(u_int32_t)0x8fb9f87d))) {
     71 	    w = __ieee754_exp(0.5*fabs(x));
     72 	    t = h*w;
     73 	    return t*w;
     74 	}
     75 
     76     /* |x| > overflowthresold, sinh(x) overflow */
     77 	return x*shuge;
     78 }