lib/libm/src/e_sinh.c

   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  * $NetBSD: e_sinh.c,v 1.11 2002/05/26 22:01:52 wiz Exp $
  13  * $DragonFly: src/lib/libm/src/e_sinh.c,v 1.1 2005/07/26 21:15:20 joerg Exp $
  14  */
  15
  16 /* sinh(x)
  17  * Method :
  18  * mathematically sinh(x) if defined to be (exp(x)-exp(-x))/2
  19  *      1. Replace x by |x| (sinh(-x) = -sinh(x)).
  20  *      2.
  21  *                                                  E + E/(E+1)
  22  *          0        <= x <= 22     :  sinh(x) := --------------, E=expm1(x)
  23  *                                                      2
  24  *
  25  *          22       <= x <= lnovft :  sinh(x) := exp(x)/2
  26  *          lnovft   <= x <= ln2ovft:  sinh(x) := exp(x/2)/2 * exp(x/2)
  27  *          ln2ovft  <  x           :  sinh(x) := x*shuge (overflow)
  28  *
  29  * Special cases:
  30  *      sinh(x) is |x| if x is +INF, -INF, or NaN.
  31  *      only sinh(0)=0 is exact for finite x.
  32  */
  33
  34 #include <math.h>
  35 #include "math_private.h"
  36
  37 static const double one = 1.0, shuge = 1.0e307;
  38
  39 double
  40 sinh(double x)
  41 {
  42         double t,w,h;
  43         int32_t ix,jx;
  44         u_int32_t lx;
  45
  46     /* High word of |x|. */
  47         GET_HIGH_WORD(jx,x);
  48         ix = jx&0x7fffffff;
  49
  50     /* x is INF or NaN */
  51         if(ix>=0x7ff00000) return x+x;
  52
  53         h = 0.5;
  54         if (jx<0) h = -h;
  55     /* |x| in [0,22], return sign(x)*0.5*(E+E/(E+1))) */
  56         if (ix < 0x40360000) {          /* |x|<22 */
  57             if (ix<0x3e300000)          /* |x|<2**-28 */
  58                 if(shuge+x>one) return x;/* sinh(tiny) = tiny with inexact */
  59             t = expm1(fabs(x));
  60             if(ix<0x3ff00000) return h*(2.0*t-t*t/(t+one));
  61             return h*(t+t/(t+one));
  62         }
  63
  64     /* |x| in [22, log(maxdouble)] return 0.5*exp(|x|) */
  65         if (ix < 0x40862E42)  return h*exp(fabs(x));
  66
  67     /* |x| in [log(maxdouble), overflowthresold] */
  68         GET_LOW_WORD(lx,x);
  69         if (ix<0x408633CE || ((ix==0x408633ce)&&(lx<=(u_int32_t)0x8fb9f87d))) {
  70             w = exp(0.5*fabs(x));
  71             t = h*w;
  72             return t*w;
  73         }
  74
  75     /* |x| > overflowthresold, sinh(x) overflow */
  76         return x*shuge;
  77 }