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  1. /* Copyright (C) 1994 DJ Delorie, see COPYING.DJ for details */
  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. #if defined(LIBM_SCCS) && !defined(lint)
  15. static char rcsid[] = "$Id: e_sinh.c,v 1.5 1994/08/18 23:06:03 jtc 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. #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 __ieee754_sinh(double x)
  47. #else
  48.         double __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. }
  88.