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  1.  
  2. /* @(#)e_sinh.c 5.1 93/09/24 */
  3. /*
  4.  * ====================================================
  5.  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
  6.  *
  7.  * Developed at SunPro, a Sun Microsystems, Inc. business.
  8.  * Permission to use, copy, modify, and distribute this
  9.  * software is freely granted, provided that this notice
  10.  * is preserved.
  11.  * ====================================================
  12.  */
  13.  
  14. /* __ieee754_sinh(x)
  15.  * Method :
  16.  * mathematically sinh(x) if defined to be (exp(x)-exp(-x))/2
  17.  *      1. Replace x by |x| (sinh(-x) = -sinh(x)).
  18.  *      2.
  19.  *                                                  E + E/(E+1)
  20.  *          0        <= x <= 22     :  sinh(x) := --------------, E=expm1(x)
  21.  *                                                      2
  22.  *
  23.  *          22       <= x <= lnovft :  sinh(x) := exp(x)/2
  24.  *          lnovft   <= x <= ln2ovft:  sinh(x) := exp(x/2)/2 * exp(x/2)
  25.  *          ln2ovft  <  x           :  sinh(x) := x*shuge (overflow)
  26.  *
  27.  * Special cases:
  28.  *      sinh(x) is |x| if x is +INF, -INF, or NaN.
  29.  *      only sinh(0)=0 is exact for finite x.
  30.  */
  31.  
  32. #include "fdlibm.h"
  33.  
  34. #ifdef __STDC__
  35. static const double one = 1.0, shuge = 1.0e307;
  36. #else
  37. static double one = 1.0, shuge = 1.0e307;
  38. #endif
  39.  
  40. #ifdef __STDC__
  41.         double sinh(double x)
  42. #else
  43.         double sinh(x)
  44.         double x;
  45. #endif
  46. {      
  47.         double t,w,h;
  48.         __int32_t ix,jx;
  49.         __uint32_t lx;
  50.  
  51.     /* High word of |x|. */
  52.         GET_HIGH_WORD(jx,x);
  53.         ix = jx&0x7fffffff;
  54.  
  55.     /* x is INF or NaN */
  56.         if(ix>=0x7ff00000) return x+x; 
  57.  
  58.         h = 0.5;
  59.         if (jx<0) h = -h;
  60.     /* |x| in [0,22], return sign(x)*0.5*(E+E/(E+1))) */
  61.         if (ix < 0x40360000) {          /* |x|<22 */
  62.             if (ix<0x3e300000)          /* |x|<2**-28 */
  63.                 if(shuge+x>one) return x;/* sinh(tiny) = tiny with inexact */
  64.             t = expm1(fabs(x));
  65.             if(ix<0x3ff00000) return h*(2.0*t-t*t/(t+one));
  66.             return h*(t+t/(t+one));
  67.         }
  68.  
  69.     /* |x| in [22, log(maxdouble)] return 0.5*exp(|x|) */
  70.         if (ix < 0x40862E42)  return h * exp(fabs(x));
  71.  
  72.     /* |x| in [log(maxdouble), overflowthresold] */
  73.         GET_LOW_WORD(lx,x);
  74.        if (ix<0x408633CE || (ix==0x408633ce && lx<=(__uint32_t)0x8fb9f87d)) {
  75.             w = exp(0.5*fabs(x));
  76.             t = h*w;
  77.             return t*w;
  78.         }
  79.  
  80.     /* |x| > overflowthresold, sinh(x) overflow */
  81.         return x*shuge;
  82. }
  83.  
  84.