e_sinh.c revision 141296 
1141296Sdas
2141296Sdas/* @(#)e_sinh.c 1.3 95/01/18 */
32116Sjkh/*
42116Sjkh * ====================================================
52116Sjkh * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
62116Sjkh *
7141296Sdas * Developed at SunSoft, a Sun Microsystems, Inc. business.
82116Sjkh * Permission to use, copy, modify, and distribute this
9141296Sdas * software is freely granted, provided that this notice
102116Sjkh * is preserved.
112116Sjkh * ====================================================
122116Sjkh */
132116Sjkh
142116Sjkh#ifndef lint
1550476Speterstatic char rcsid[] = "$FreeBSD: head/lib/msun/src/e_sinh.c 141296 2005-02-04 18:26:06Z das $";
162116Sjkh#endif
172116Sjkh
182116Sjkh/* __ieee754_sinh(x)
19141296Sdas * Method :
202116Sjkh * mathematically sinh(x) if defined to be (exp(x)-exp(-x))/2
21141296Sdas *	1. Replace x by |x| (sinh(-x) = -sinh(x)).
22141296Sdas *	2.
232116Sjkh *		                                    E + E/(E+1)
242116Sjkh *	    0        <= x <= 22     :  sinh(x) := --------------, E=expm1(x)
252116Sjkh *			       			        2
262116Sjkh *
27141296Sdas *	    22       <= x <= lnovft :  sinh(x) := exp(x)/2
282116Sjkh *	    lnovft   <= x <= ln2ovft:  sinh(x) := exp(x/2)/2 * exp(x/2)
292116Sjkh *	    ln2ovft  <  x	    :  sinh(x) := x*shuge (overflow)
302116Sjkh *
312116Sjkh * Special cases:
322116Sjkh *	sinh(x) is |x| if x is +INF, -INF, or NaN.
332116Sjkh *	only sinh(0)=0 is exact for finite x.
342116Sjkh */
352116Sjkh
362116Sjkh#include "math.h"
372116Sjkh#include "math_private.h"
382116Sjkh
392116Sjkhstatic const double one = 1.0, shuge = 1.0e307;
402116Sjkh
4197413Salfreddouble
4297413Salfred__ieee754_sinh(double x)
438870Srgrimes{
442116Sjkh	double t,w,h;
452116Sjkh	int32_t ix,jx;
462116Sjkh	u_int32_t lx;
472116Sjkh
482116Sjkh    /* High word of |x|. */
492116Sjkh	GET_HIGH_WORD(jx,x);
502116Sjkh	ix = jx&0x7fffffff;
512116Sjkh
522116Sjkh    /* x is INF or NaN */
53141296Sdas	if(ix>=0x7ff00000) return x+x;
542116Sjkh
552116Sjkh	h = 0.5;
562116Sjkh	if (jx<0) h = -h;
572116Sjkh    /* |x| in [0,22], return sign(x)*0.5*(E+E/(E+1))) */
582116Sjkh	if (ix < 0x40360000) {		/* |x|<22 */
592116Sjkh	    if (ix<0x3e300000) 		/* |x|<2**-28 */
602116Sjkh		if(shuge+x>one) return x;/* sinh(tiny) = tiny with inexact */
612116Sjkh	    t = expm1(fabs(x));
622116Sjkh	    if(ix<0x3ff00000) return h*(2.0*t-t*t/(t+one));
632116Sjkh	    return h*(t+t/(t+one));
642116Sjkh	}
652116Sjkh
662116Sjkh    /* |x| in [22, log(maxdouble)] return 0.5*exp(|x|) */
672116Sjkh	if (ix < 0x40862E42)  return h*__ieee754_exp(fabs(x));
682116Sjkh
692116Sjkh    /* |x| in [log(maxdouble), overflowthresold] */
702116Sjkh	GET_LOW_WORD(lx,x);
7117141Sjkh	if (ix<0x408633CE || ((ix==0x408633ce)&&(lx<=(u_int32_t)0x8fb9f87d))) {
722116Sjkh	    w = __ieee754_exp(0.5*fabs(x));
732116Sjkh	    t = h*w;
742116Sjkh	    return t*w;
752116Sjkh	}
762116Sjkh
772116Sjkh    /* |x| > overflowthresold, sinh(x) overflow */
782116Sjkh	return x*shuge;
792116Sjkh}
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