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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. #ifndef _DOUBLE_IS_32BITS
  38.  
  39. #ifdef __STDC__
  40. static const double one = 1.0, half=0.5, huge = 1.0e300;
  41. #else
  42. static double one = 1.0, half=0.5, huge = 1.0e300;
  43. #endif
  44.  
  45. #ifdef __STDC__
  46.         double __ieee754_cosh(double x)
  47. #else
  48.         double __ieee754_cosh(x)
  49.         double x;
  50. #endif
  51. {      
  52.         double t,w;
  53.         __int32_t ix;
  54.         __uint32_t lx;
  55.  
  56.     /* High word of |x|. */
  57.         GET_HIGH_WORD(ix,x);
  58.         ix &= 0x7fffffff;
  59.  
  60.     /* x is INF or NaN */
  61.         if(ix>=0x7ff00000) return x*x; 
  62.  
  63.     /* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */
  64.         if(ix<0x3fd62e43) {
  65.             t = expm1(fabs(x));
  66.             w = one+t;
  67.             if (ix<0x3c800000) return w;        /* cosh(tiny) = 1 */
  68.             return one+(t*t)/(w+w);
  69.         }
  70.  
  71.     /* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */
  72.         if (ix < 0x40360000) {
  73.                 t = __ieee754_exp(fabs(x));
  74.                 return half*t+half/t;
  75.         }
  76.  
  77.     /* |x| in [22, log(maxdouble)] return half*exp(|x|) */
  78.         if (ix < 0x40862E42)  return half*__ieee754_exp(fabs(x));
  79.  
  80.     /* |x| in [log(maxdouble), overflowthresold] */
  81.         GET_LOW_WORD(lx,x);
  82.         if (ix<0x408633CE ||
  83.              (ix==0x408633ce && lx<=(__uint32_t)0x8fb9f87d)) {
  84.             w = __ieee754_exp(half*fabs(x));
  85.             t = half*w;
  86.             return t*w;
  87.         }
  88.  
  89.     /* |x| > overflowthresold, cosh(x) overflow */
  90.         return huge*huge;
  91. }
  92.  
  93. #endif /* defined(_DOUBLE_IS_32BITS) */
  94.