sysdeps/ieee754/dbl-64/e_cosh.c

   1 /* Optimized by Ulrich Drepper <drepper@gmail.com>, 2011 */
   2 /*
   3  * ====================================================
   4  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
   5  *
   6  * Developed at SunPro, a Sun Microsystems, Inc. business.
   7  * Permission to use, copy, modify, and distribute this
   8  * software is freely granted, provided that this notice
   9  * is preserved.
  10  * ====================================================
  11  */
  12
  13 /* __ieee754_cosh(x)
  14  * Method :
  15  * mathematically cosh(x) if defined to be (exp(x)+exp(-x))/2
  16  *      1. Replace x by |x| (cosh(x) = cosh(-x)).
  17  *      2.
  18  *                                                      [ exp(x) - 1 ]^2
  19  *          0        <= x <= ln2/2  :  cosh(x) := 1 + -------------------
  20  *                                                         2*exp(x)
  21  *
  22  *                                                exp(x) +  1/exp(x)
  23  *          ln2/2    <= x <= 22     :  cosh(x) := -------------------
  24  *                                                        2
  25  *          22       <= x <= lnovft :  cosh(x) := exp(x)/2
  26  *          lnovft   <= x <= ln2ovft:  cosh(x) := exp(x/2)/2 * exp(x/2)
  27  *          ln2ovft  <  x           :  cosh(x) := huge*huge (overflow)
  28  *
  29  * Special cases:
  30  *      cosh(x) is |x| if x is +INF, -INF, or NaN.
  31  *      only cosh(0)=1 is exact for finite x.
  32  */
  33
  34 #include <math.h>
  35 #include <math_private.h>
  36
  37 static const double one = 1.0, half=0.5, huge = 1.0e300;
  38
  39 double
  40 __ieee754_cosh (double x)
  41 {
  42         double t,w;
  43         int32_t ix;
  44         u_int32_t lx;
  45
  46     /* High word of |x|. */
  47         GET_HIGH_WORD(ix,x);
  48         ix &= 0x7fffffff;
  49
  50     /* |x| in [0,22] */
  51         if (ix < 0x40360000) {
  52             /* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */
  53                 if(ix<0x3fd62e43) {
  54                     t = __expm1(fabs(x));
  55                     w = one+t;
  56                     if (ix<0x3c800000) return w;        /* cosh(tiny) = 1 */
  57                     return one+(t*t)/(w+w);
  58                 }
  59
  60             /* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */
  61                 t = __ieee754_exp(fabs(x));
  62                 return half*t+half/t;
  63         }
  64
  65     /* |x| in [22, log(maxdouble)] return half*exp(|x|) */
  66         if (ix < 0x40862e42)  return half*__ieee754_exp(fabs(x));
  67
  68     /* |x| in [log(maxdouble), overflowthresold] */
  69         GET_LOW_WORD(lx,x);
  70         if (ix<0x408633ce || ((ix==0x408633ce)&&(lx<=(u_int32_t)0x8fb9f87d))) {
  71             w = __ieee754_exp(half*fabs(x));
  72             t = half*w;
  73             return t*w;
  74         }
  75
  76     /* x is INF or NaN */
  77         if(ix>=0x7ff00000) return x*x;
  78
  79     /* |x| > overflowthresold, cosh(x) overflow */
  80         return huge*huge;
  81 }
  82 strong_alias (__ieee754_cosh, __cosh_finite)