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     {
  53       /* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */
  54       if (ix < 0x3fd62e43)
  55         {
  56           if (ix < 0x3c800000)
  57             return one;                                   /* cosh(tiny) = 1 */
  58           t = __expm1 (fabs (x));
  59           w = one + t;
  60           return one + (t * t) / (w + w);
  61         }
  62
  63       /* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */
  64       t = __ieee754_exp (fabs (x));
  65       return half * t + half / t;
  66     }
  67
  68   /* |x| in [22, log(maxdouble)] return half*exp(|x|) */
  69   if (ix < 0x40862e42)
  70     return half * __ieee754_exp (fabs (x));
  71
  72   /* |x| in [log(maxdouble), overflowthresold] */
  73   GET_LOW_WORD (lx, x);
  74   if (ix < 0x408633ce || ((ix == 0x408633ce) && (lx <= (u_int32_t) 0x8fb9f87d)))
  75     {
  76       w = __ieee754_exp (half * fabs (x));
  77       t = half * w;
  78       return t * w;
  79     }
  80
  81   /* x is INF or NaN */
  82   if (ix >= 0x7ff00000)
  83     return x * x;
  84
  85   /* |x| > overflowthresold, cosh(x) overflow */
  86   return huge * huge;
  87 }
  88 strong_alias (__ieee754_cosh, __cosh_finite)