lib/msun/src/e_cosh.c

   1
   2 /* @(#)e_cosh.c 1.3 95/01/18 */
   3 /*
   4  * ====================================================
   5  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
   6  *
   7  * Developed at SunSoft, 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 #ifndef lint
  15 static char rcsid[] = "$FreeBSD$";
  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 static const double one = 1.0, half=0.5, huge = 1.0e300;
  43
  44 double
  45 __ieee754_cosh(double x)
  46 {
  47         double t,w;
  48         int32_t ix;
  49         u_int32_t lx;
  50
  51     /* High word of |x|. */
  52         GET_HIGH_WORD(ix,x);
  53         ix &= 0x7fffffff;
  54
  55     /* x is INF or NaN */
  56         if(ix>=0x7ff00000) return x*x;
  57
  58     /* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */
  59         if(ix<0x3fd62e43) {
  60             t = expm1(fabs(x));
  61             w = one+t;
  62             if (ix<0x3c800000) return w;        /* cosh(tiny) = 1 */
  63             return one+(t*t)/(w+w);
  64         }
  65
  66     /* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */
  67         if (ix < 0x40360000) {
  68                 t = __ieee754_exp(fabs(x));
  69                 return half*t+half/t;
  70         }
  71
  72     /* |x| in [22, log(maxdouble)] return half*exp(|x|) */
  73         if (ix < 0x40862E42)  return half*__ieee754_exp(fabs(x));
  74
  75     /* |x| in [log(maxdouble), overflowthresold] */
  76         GET_LOW_WORD(lx,x);
  77         if (ix<0x408633CE ||
  78               ((ix==0x408633ce)&&(lx<=(u_int32_t)0x8fb9f87d))) {
  79             w = __ieee754_exp(half*fabs(x));
  80             t = half*w;
  81             return t*w;
  82         }
  83
  84     /* |x| > overflowthresold, cosh(x) overflow */
  85         return huge*huge;
  86 }