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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 }