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
  13 #include <sys/cdefs.h>
  14 #if defined(LIBM_SCCS) && !defined(lint)
  15 __RCSID("$NetBSD: e_sinh.c,v 1.11 2002/05/26 22:01:52 wiz Exp $");
  16 #endif
  17
  18 /* __ieee754_sinh(x)
  19  * Method :
  20  * mathematically sinh(x) if defined to be (exp(x)-exp(-x))/2
  21  *      1. Replace x by |x| (sinh(-x) = -sinh(x)).
  22  *      2.
  23  *                                                  E + E/(E+1)
  24  *          0        <= x <= 22     :  sinh(x) := --------------, E=expm1(x)
  25  *                                                      2
  26  *
  27  *          22       <= x <= lnovft :  sinh(x) := exp(x)/2
  28  *          lnovft   <= x <= ln2ovft:  sinh(x) := exp(x/2)/2 * exp(x/2)
  29  *          ln2ovft  <  x           :  sinh(x) := x*shuge (overflow)
  30  *
  31  * Special cases:
  32  *      sinh(x) is |x| if x is +INF, -INF, or NaN.
  33  *      only sinh(0)=0 is exact for finite x.
  34  */
  35
  36 #include "math.h"
  37 #include "math_private.h"
  38
  39 static const double one = 1.0, shuge = 1.0e307;
  40
  41 double
  42 __ieee754_sinh(double x)
  43 {
  44         double t,w,h;
  45         int32_t ix,jx;
  46         u_int32_t lx;
  47
  48     /* High word of |x|. */
  49         GET_HIGH_WORD(jx,x);
  50         ix = jx&0x7fffffff;
  51
  52     /* x is INF or NaN */
  53         if(ix>=0x7ff00000) return x+x;
  54
  55         h = 0.5;
  56         if (jx<0) h = -h;
  57     /* |x| in [0,22], return sign(x)*0.5*(E+E/(E+1))) */
  58         if (ix < 0x40360000) {          /* |x|<22 */
  59             if (ix<0x3e300000)          /* |x|<2**-28 */
  60                 if(shuge+x>one) return x;/* sinh(tiny) = tiny with inexact */
  61             t = expm1(fabs(x));
  62             if(ix<0x3ff00000) return h*(2.0*t-t*t/(t+one));
  63             return h*(t+t/(t+one));
  64         }
  65
  66     /* |x| in [22, log(maxdouble)] return 0.5*exp(|x|) */
  67         if (ix < 0x40862E42)  return h*__ieee754_exp(fabs(x));
  68
  69     /* |x| in [log(maxdouble), overflowthresold] */
  70         GET_LOW_WORD(lx,x);
  71         if (ix<0x408633CE || ((ix==0x408633ce)&&(lx<=(u_int32_t)0x8fb9f87d))) {
  72             w = __ieee754_exp(0.5*fabs(x));
  73             t = h*w;
  74             return t*w;
  75         }
  76
  77     /* |x| > overflowthresold, sinh(x) overflow */
  78         return x*shuge;
  79 }