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      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 #include  <LibConfig.h>
     13 #include  <sys/EfiCdefs.h>
     14 #if defined(LIBM_SCCS) && !defined(lint)
     15 __RCSID("$NetBSD: e_cosh.c,v 1.11 2002/05/26 22:01:49 wiz Exp $");
     16 #endif
     17 
     18 #if defined(_MSC_VER)           /* Handle Microsoft VC++ compiler specifics. */
     19   // C4756: overflow in constant arithmetic
     20   #pragma warning ( disable : 4756 )
     21 #endif
     22 
     23 /* __ieee754_cosh(x)
     24  * Method :
     25  * mathematically cosh(x) if defined to be (exp(x)+exp(-x))/2
     26  *  1. Replace x by |x| (cosh(x) = cosh(-x)).
     27  *  2.
     28  *                                            [ exp(x) - 1 ]^2
     29  *      0        <= x <= ln2/2  :  cosh(x) := 1 + -------------------
     30  *                             2*exp(x)
     31  *
     32  *                                      exp(x) +  1/exp(x)
     33  *      ln2/2    <= x <= 22     :  cosh(x) := -------------------
     34  *                            2
     35  *      22       <= x <= lnovft :  cosh(x) := exp(x)/2
     36  *      lnovft   <= x <= ln2ovft:  cosh(x) := exp(x/2)/2 * exp(x/2)
     37  *      ln2ovft  <  x     :  cosh(x) := huge*huge (overflow)
     38  *
     39  * Special cases:
     40  *  cosh(x) is |x| if x is +INF, -INF, or NaN.
     41  *  only cosh(0)=1 is exact for finite x.
     42  */
     43 
     44 #include "math.h"
     45 #include "math_private.h"
     46 
     47 static const double one = 1.0, half=0.5, huge = 1.0e300;
     48 
     49 double
     50 __ieee754_cosh(double x)
     51 {
     52   double t,w;
     53   int32_t ix;
     54   u_int32_t lx;
     55 
     56     /* High word of |x|. */
     57   GET_HIGH_WORD(ix,x);
     58   ix &= 0x7fffffff;
     59 
     60     /* x is INF or NaN */
     61   if(ix>=0x7ff00000) return x*x;
     62 
     63     /* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */
     64   if(ix<0x3fd62e43) {
     65       t = expm1(fabs(x));
     66       w = one+t;
     67       if (ix<0x3c800000) return w;  /* cosh(tiny) = 1 */
     68       return one+(t*t)/(w+w);
     69   }
     70 
     71     /* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */
     72   if (ix < 0x40360000) {
     73     t = __ieee754_exp(fabs(x));
     74     return half*t+half/t;
     75   }
     76 
     77     /* |x| in [22, log(maxdouble)] return half*exp(|x|) */
     78   if (ix < 0x40862E42)  return half*__ieee754_exp(fabs(x));
     79 
     80     /* |x| in [log(maxdouble), overflowthresold] */
     81   GET_LOW_WORD(lx,x);
     82   if (ix<0x408633CE ||
     83         ((ix==0x408633ce)&&(lx<=(u_int32_t)0x8fb9f87d))) {
     84       w = __ieee754_exp(half*fabs(x));
     85       t = half*w;
     86       return t*w;
     87   }
     88 
     89     /* |x| > overflowthresold, cosh(x) overflow */
     90   return huge*huge;
     91 }
     92