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glibc  2.9
e_sinh.c
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00001 /* @(#)e_sinh.c 5.1 93/09/24 */
00002 /*
00003  * ====================================================
00004  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
00005  *
00006  * Developed at SunPro, a Sun Microsystems, Inc. business.
00007  * Permission to use, copy, modify, and distribute this
00008  * software is freely granted, provided that this notice 
00009  * is preserved.
00010  * ====================================================
00011  */
00012 
00013 #if defined(LIBM_SCCS) && !defined(lint)
00014 static char rcsid[] = "$NetBSD: e_sinh.c,v 1.7 1995/05/10 20:46:13 jtc Exp $";
00015 #endif
00016 
00017 /* __ieee754_sinh(x)
00018  * Method : 
00019  * mathematically sinh(x) if defined to be (exp(x)-exp(-x))/2
00020  *     1. Replace x by |x| (sinh(-x) = -sinh(x)). 
00021  *     2. 
00022  *                                                E + E/(E+1)
00023  *         0        <= x <= 22     :  sinh(x) := --------------, E=expm1(x)
00024  *                                                       2
00025  *
00026  *         22       <= x <= lnovft :  sinh(x) := exp(x)/2 
00027  *         lnovft   <= x <= ln2ovft:  sinh(x) := exp(x/2)/2 * exp(x/2)
00028  *         ln2ovft  <  x        :  sinh(x) := x*shuge (overflow)
00029  *
00030  * Special cases:
00031  *     sinh(x) is |x| if x is +INF, -INF, or NaN.
00032  *     only sinh(0)=0 is exact for finite x.
00033  */
00034 
00035 #include "math.h"
00036 #include "math_private.h"
00037 
00038 #ifdef __STDC__
00039 static const double one = 1.0, shuge = 1.0e307;
00040 #else
00041 static double one = 1.0, shuge = 1.0e307;
00042 #endif
00043 
00044 #ifdef __STDC__
00045        double __ieee754_sinh(double x)
00046 #else
00047        double __ieee754_sinh(x)
00048        double x;
00049 #endif
00050 {      
00051        double t,w,h;
00052        int32_t ix,jx;
00053        u_int32_t lx;
00054 
00055     /* High word of |x|. */
00056        GET_HIGH_WORD(jx,x);
00057        ix = jx&0x7fffffff;
00058 
00059     /* x is INF or NaN */
00060        if(ix>=0x7ff00000) return x+x;     
00061 
00062        h = 0.5;
00063        if (jx<0) h = -h;
00064     /* |x| in [0,22], return sign(x)*0.5*(E+E/(E+1))) */
00065        if (ix < 0x40360000) {             /* |x|<22 */
00066            if (ix<0x3e300000)             /* |x|<2**-28 */
00067               if(shuge+x>one) return x;/* sinh(tiny) = tiny with inexact */
00068            t = __expm1(fabs(x));
00069            if(ix<0x3ff00000) return h*(2.0*t-t*t/(t+one));
00070            return h*(t+t/(t+one));
00071        }
00072 
00073     /* |x| in [22, log(maxdouble)] return 0.5*exp(|x|) */
00074        if (ix < 0x40862e42)  return h*__ieee754_exp(fabs(x));
00075 
00076     /* |x| in [log(maxdouble), overflowthresold] */
00077        GET_LOW_WORD(lx,x);
00078        if (ix<0x408633ce || ((ix==0x408633ce)&&(lx<=(u_int32_t)0x8fb9f87d))) {
00079            w = __ieee754_exp(0.5*fabs(x));
00080            t = h*w;
00081            return t*w;
00082        }
00083 
00084     /* |x| > overflowthresold, sinh(x) overflow */
00085        return x*shuge;
00086 }