lib/libm/src/e_cosh.c

   1 /* @(#)e_cosh.c 5.1 93/09/24 */
   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 /* 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 <float.h>
  35 #include <math.h>
  36
  37 #include "math_private.h"
  38
  39 static const double one = 1.0, half=0.5, huge = 1.0e300;
  40
  41 double
  42 cosh(double x)
  43 {
  44         double t,w;
  45         int32_t ix;
  46         u_int32_t lx;
  47
  48     /* High word of |x|. */
  49         GET_HIGH_WORD(ix,x);
  50         ix &= 0x7fffffff;
  51
  52     /* x is INF or NaN */
  53         if(ix>=0x7ff00000) return x*x;
  54
  55     /* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */
  56         if(ix<0x3fd62e43) {
  57             t = expm1(fabs(x));
  58             w = one+t;
  59             if (ix<0x3c800000) return w;        /* cosh(tiny) = 1 */
  60             return one+(t*t)/(w+w);
  61         }
  62
  63     /* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */
  64         if (ix < 0x40360000) {
  65                 t = exp(fabs(x));
  66                 return half*t+half/t;
  67         }
  68
  69     /* |x| in [22, log(maxdouble)] return half*exp(|x|) */
  70         if (ix < 0x40862E42)  return half*exp(fabs(x));
  71
  72     /* |x| in [log(maxdouble), overflowthresold] */
  73         GET_LOW_WORD(lx,x);
  74         if (ix<0x408633CE ||
  75               ((ix==0x408633ce)&&(lx<=(u_int32_t)0x8fb9f87d))) {
  76             w = exp(half*fabs(x));
  77             t = half*w;
  78             return t*w;
  79         }
  80
  81     /* |x| > overflowthresold, cosh(x) overflow */
  82         return huge*huge;
  83 }
  84
  85 #if     LDBL_MANT_DIG == 53
  86 __strong_alias(coshl, cosh);
  87 #endif  /* LDBL_MANT_DIG == 53 */