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  1.  
  2. /* @(#)e_cosh.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_cosh(x)
  15.  * Method :
  16.  * mathematically cosh(x) if defined to be (exp(x)+exp(-x))/2
  17.  *      1. Replace x by |x| (cosh(x) = cosh(-x)).
  18.  *      2.
  19.  *                                                      [ exp(x) - 1 ]^2
  20.  *          0        <= x <= ln2/2  :  cosh(x) := 1 + -------------------
  21.  *                                                         2*exp(x)
  22.  *
  23.  *                                                exp(x) +  1/exp(x)
  24.  *          ln2/2    <= x <= 22     :  cosh(x) := -------------------
  25.  *                                                        2
  26.  *          22       <= x <= lnovft :  cosh(x) := exp(x)/2
  27.  *          lnovft   <= x <= ln2ovft:  cosh(x) := exp(x/2)/2 * exp(x/2)
  28.  *          ln2ovft  <  x           :  cosh(x) := huge*huge (overflow)
  29.  *
  30.  * Special cases:
  31.  *      cosh(x) is |x| if x is +INF, -INF, or NaN.
  32.  *      only cosh(0)=1 is exact for finite x.
  33.  */
  34.  
  35. #include "fdlibm.h"
  36.  
  37. #ifdef __STDC__
  38. static const double one = 1.0, half=0.5, huge = 1.0e300;
  39. #else
  40. static double one = 1.0, half=0.5, huge = 1.0e300;
  41. #endif
  42.  
  43. #ifdef __STDC__
  44.         double cosh(double x)
  45. #else
  46.         double cosh(x)
  47.         double x;
  48. #endif
  49. {      
  50.         double t,w;
  51.         __int32_t ix;
  52.         __uint32_t lx;
  53.  
  54.     /* High word of |x|. */
  55.         GET_HIGH_WORD(ix,x);
  56.         ix &= 0x7fffffff;
  57.  
  58.     /* x is INF or NaN */
  59.         if(ix>=0x7ff00000) return x*x; 
  60.  
  61.     /* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */
  62.         if(ix<0x3fd62e43) {
  63.             t = expm1(fabs(x));
  64.             w = one+t;
  65.             if (ix<0x3c800000) return w;        /* cosh(tiny) = 1 */
  66.             return one+(t*t)/(w+w);
  67.         }
  68.  
  69.     /* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */
  70.         if (ix < 0x40360000) {
  71.                 t = exp(fabs(x));
  72.                 return half*t+half/t;
  73.         }
  74.  
  75.     /* |x| in [22, log(maxdouble)] return half*exp(|x|) */
  76.         if (ix < 0x40862E42)  return half*exp(fabs(x));
  77.  
  78.     /* |x| in [log(maxdouble), overflowthresold] */
  79.         GET_LOW_WORD(lx,x);
  80.         if (ix<0x408633CE ||
  81.              (ix==0x408633ce && lx<=(__uint32_t)0x8fb9f87d)) {
  82.             w = exp(half*fabs(x));
  83.             t = half*w;
  84.             return t*w;
  85.         }
  86.  
  87.     /* |x| > overflowthresold, cosh(x) overflow */
  88.         return huge*huge;
  89. }
  90.  
  91.