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  1. /* Copyright (C) 1995 DJ Delorie, see COPYING.DJ for details */
  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. #if defined(LIBM_SCCS) && !defined(lint)
  15. static char rcsid[] = "$Id: e_cosh.c,v 1.5 1994/08/18 23:05:15 jtc Exp $";
  16. #endif
  17.  
  18. /* __ieee754_cosh(x)
  19.  * Method :
  20.  * mathematically cosh(x) if defined to be (exp(x)+exp(-x))/2
  21.  *      1. Replace x by |x| (cosh(x) = cosh(-x)).
  22.  *      2.
  23.  *                                                      [ exp(x) - 1 ]^2
  24.  *          0        <= x <= ln2/2  :  cosh(x) := 1 + -------------------
  25.  *                                                         2*exp(x)
  26.  *
  27.  *                                                exp(x) +  1/exp(x)
  28.  *          ln2/2    <= x <= 22     :  cosh(x) := -------------------
  29.  *                                                        2
  30.  *          22       <= x <= lnovft :  cosh(x) := exp(x)/2
  31.  *          lnovft   <= x <= ln2ovft:  cosh(x) := exp(x/2)/2 * exp(x/2)
  32.  *          ln2ovft  <  x           :  cosh(x) := huge*huge (overflow)
  33.  *
  34.  * Special cases:
  35.  *      cosh(x) is |x| if x is +INF, -INF, or NaN.
  36.  *      only cosh(0)=1 is exact for finite x.
  37.  */
  38.  
  39. #include "math.h"
  40. #include "math_private.h"
  41.  
  42. #ifdef __STDC__
  43. static const double one = 1.0, half=0.5, huge = 1.0e300;
  44. #else
  45. static double one = 1.0, half=0.5, huge = 1.0e300;
  46. #endif
  47.  
  48. #ifdef __STDC__
  49.         double __ieee754_cosh(double x)
  50. #else
  51.         double __ieee754_cosh(x)
  52.         double x;
  53. #endif
  54. {      
  55.         double t,w;
  56.         int32_t ix;
  57.         u_int32_t lx;
  58.  
  59.     /* High word of |x|. */
  60.         GET_HIGH_WORD(ix,x);
  61.         ix &= 0x7fffffff;
  62.  
  63.     /* x is INF or NaN */
  64.         if(ix>=0x7ff00000) return x*x; 
  65.  
  66.     /* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */
  67.         if(ix<0x3fd62e43) {
  68.             t = expm1(fabs(x));
  69.             w = one+t;
  70.             if (ix<0x3c800000) return w;        /* cosh(tiny) = 1 */
  71.             return one+(t*t)/(w+w);
  72.         }
  73.  
  74.     /* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */
  75.         if (ix < 0x40360000) {
  76.                 t = __ieee754_exp(fabs(x));
  77.                 return half*t+half/t;
  78.         }
  79.  
  80.     /* |x| in [22, log(maxdouble)] return half*exp(|x|) */
  81.         if (ix < 0x40862E42)  return half*__ieee754_exp(fabs(x));
  82.  
  83.     /* |x| in [log(maxdouble), overflowthresold] */
  84.         GET_LOW_WORD(lx,x);
  85.         if (ix<0x408633CE ||
  86.               ((ix==0x408633ce)&&(lx<=(u_int32_t)0x8fb9f87dU))) {
  87.             w = __ieee754_exp(half*fabs(x));
  88.             t = half*w;
  89.             return t*w;
  90.         }
  91.  
  92.     /* |x| > overflowthresold, cosh(x) overflow */
  93.         return huge*huge;
  94. }
  95.