lib/libm/src/e_cosh.c

   1
   2 /* @(#)e_cosh.c 1.3 95/01/18 */
   3 /* $FreeBSD: head/lib/msun/src/e_cosh.c 226598 2011-10-21 06:28:47Z das $ */
   4 /*
   5  * ====================================================
   6  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
   7  *
   8  * Developed at SunSoft, a Sun Microsystems, Inc. business.
   9  * Permission to use, copy, modify, and distribute this
  10  * software is freely granted, provided that this notice
  11  * is preserved.
  12  * ====================================================
  13  */
  14
  15 /* __ieee754_cosh(x)
  16  * Method :
  17  * mathematically cosh(x) if defined to be (exp(x)+exp(-x))/2
  18  *      1. Replace x by |x| (cosh(x) = cosh(-x)).
  19  *      2.
  20  *                                                      [ exp(x) - 1 ]^2
  21  *          0        <= x <= ln2/2  :  cosh(x) := 1 + -------------------
  22  *                                                         2*exp(x)
  23  *
  24  *                                                exp(x) +  1/exp(x)
  25  *          ln2/2    <= x <= 22     :  cosh(x) := -------------------
  26  *                                                        2
  27  *          22       <= x <= lnovft :  cosh(x) := exp(x)/2
  28  *          lnovft   <= x <= ln2ovft:  cosh(x) := exp(x/2)/2 * exp(x/2)
  29  *          ln2ovft  <  x           :  cosh(x) := huge*huge (overflow)
  30  *
  31  * Special cases:
  32  *      cosh(x) is |x| if x is +INF, -INF, or NaN.
  33  *      only cosh(0)=1 is exact for finite x.
  34  */
  35
  36 #include "math.h"
  37 #include "math_private.h"
  38
  39 static const double one = 1.0, half=0.5, huge = 1.0e300;
  40
  41 double
  42 __ieee754_cosh(double x)
  43 {
  44         double t,w;
  45         int32_t ix;
  46
  47     /* High word of |x|. */
  48         GET_HIGH_WORD(ix,x);
  49         ix &= 0x7fffffff;
  50
  51     /* x is INF or NaN */
  52         if(ix>=0x7ff00000) return x*x;
  53
  54     /* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */
  55         if(ix<0x3fd62e43) {
  56             t = expm1(fabs(x));
  57             w = one+t;
  58             if (ix<0x3c800000) return w;        /* cosh(tiny) = 1 */
  59             return one+(t*t)/(w+w);
  60         }
  61
  62     /* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */
  63         if (ix < 0x40360000) {
  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)  return half*__ieee754_exp(fabs(x));
  70
  71     /* |x| in [log(maxdouble), overflowthresold] */
  72         if (ix<=0x408633CE)
  73             return __ldexp_exp(fabs(x), -1);
  74
  75     /* |x| > overflowthresold, cosh(x) overflow */
  76         return huge*huge;
  77 }