lib/libm/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
  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 <float.h>
  37
  38 #include "math.h"
  39 #include "math_private.h"
  40
  41 static const double one = 1.0, half=0.5, huge = 1.0e300;
  42
  43 double
  44 __ieee754_cosh(double x)
  45 {
  46         double t,w;
  47         int32_t ix;
  48
  49     /* High word of |x|. */
  50         GET_HIGH_WORD(ix,x);
  51         ix &= 0x7fffffff;
  52
  53     /* x is INF or NaN */
  54         if(ix>=0x7ff00000) return x*x;
  55
  56     /* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */
  57         if(ix<0x3fd62e43) {
  58             t = expm1(fabs(x));
  59             w = one+t;
  60             if (ix<0x3c800000) return w;        /* cosh(tiny) = 1 */
  61             return one+(t*t)/(w+w);
  62         }
  63
  64     /* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */
  65         if (ix < 0x40360000) {
  66                 t = __ieee754_exp(fabs(x));
  67                 return half*t+half/t;
  68         }
  69
  70     /* |x| in [22, log(maxdouble)] return half*exp(|x|) */
  71         if (ix < 0x40862E42)  return half*__ieee754_exp(fabs(x));
  72
  73     /* |x| in [log(maxdouble), overflowthresold] */
  74         if (ix<=0x408633CE)
  75             return __ldexp_exp(fabs(x), -1);
  76
  77     /* |x| > overflowthresold, cosh(x) overflow */
  78         return huge*huge;
  79 }
  80
  81 #if (LDBL_MANT_DIG == 53)
  82 __weak_reference(cosh, coshl);
  83 #endif