libm/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 #if defined(LIBM_SCCS) && !defined(lint)
  14 static char rcsid[] = "$NetBSD: e_sinh.c,v 1.7 1995/05/10 20:46:13 jtc 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
  39 #ifdef __STDC__
  40 static const double one = 1.0, shuge = 1.0e307;
  41 #else
  42 static double one = 1.0, shuge = 1.0e307;
  43 #endif
  44
  45 #ifdef __STDC__
  46         double attribute_hidden __ieee754_sinh(double x)
  47 #else
  48         double attribute_hidden __ieee754_sinh(x)
  49         double x;
  50 #endif
  51 {
  52         double t,w,h;
  53         int32_t ix,jx;
  54         u_int32_t lx;
  55
  56     /* High word of |x|. */
  57         GET_HIGH_WORD(jx,x);
  58         ix = jx&0x7fffffff;
  59
  60     /* x is INF or NaN */
  61         if(ix>=0x7ff00000) return x+x;
  62
  63         h = 0.5;
  64         if (jx<0) h = -h;
  65     /* |x| in [0,22], return sign(x)*0.5*(E+E/(E+1))) */
  66         if (ix < 0x40360000) {          /* |x|<22 */
  67             if (ix<0x3e300000)          /* |x|<2**-28 */
  68                 if(shuge+x>one) return x;/* sinh(tiny) = tiny with inexact */
  69             t = expm1(fabs(x));
  70             if(ix<0x3ff00000) return h*(2.0*t-t*t/(t+one));
  71             return h*(t+t/(t+one));
  72         }
  73
  74     /* |x| in [22, log(maxdouble)] return 0.5*exp(|x|) */
  75         if (ix < 0x40862E42)  return h*__ieee754_exp(fabs(x));
  76
  77     /* |x| in [log(maxdouble), overflowthresold] */
  78         GET_LOW_WORD(lx,x);
  79         if (ix<0x408633CE || ((ix==0x408633ce)&&(lx<=(u_int32_t)0x8fb9f87d))) {
  80             w = __ieee754_exp(0.5*fabs(x));
  81             t = h*w;
  82             return t*w;
  83         }
  84
  85     /* |x| > overflowthresold, sinh(x) overflow */
  86         return x*shuge;
  87 }