newlib/libm/math/e_cosh.c

   1
   2 /* @(#)e_cosh.c 5.1 93/09/24 */
   3 /*
   4  * ====================================================
   5  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
   6  *
   7  * Developed at SunPro, 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 /* __ieee754_cosh(x)
  15  * Method :
  16  * mathematically cosh(x) if defined to be (exp(x)+exp(-x))/2
  17  *      1. Replace x by |x| (cosh(x) = cosh(-x)).
  18  *      2.
  19  *                                                      [ exp(x) - 1 ]^2
  20  *          0        <= x <= ln2/2  :  cosh(x) := 1 + -------------------
  21  *                                                         2*exp(x)
  22  *
  23  *                                                exp(x) +  1/exp(x)
  24  *          ln2/2    <= x <= 22     :  cosh(x) := -------------------
  25  *                                                        2
  26  *          22       <= x <= lnovft :  cosh(x) := exp(x)/2
  27  *          lnovft   <= x <= ln2ovft:  cosh(x) := exp(x/2)/2 * exp(x/2)
  28  *          ln2ovft  <  x           :  cosh(x) := overflow
  29  *
  30  * Special cases:
  31  *      cosh(x) is |x| if x is +INF, -INF, or NaN.
  32  *      only cosh(0)=1 is exact for finite x.
  33  */
  34
  35 #include "fdlibm.h"
  36 #include "math_config.h"
  37
  38 #ifndef _DOUBLE_IS_32BITS
  39
  40 #ifdef __STDC__
  41 static const double one = 1.0, half=0.5;
  42 #else
  43 static double one = 1.0, half=0.5;
  44 #endif
  45
  46 #ifdef __STDC__
  47         double __ieee754_cosh(double x)
  48 #else
  49         double __ieee754_cosh(x)
  50         double x;
  51 #endif
  52 {
  53         double t,w;
  54         __int32_t ix;
  55         __uint32_t lx;
  56
  57     /* High word of |x|. */
  58         GET_HIGH_WORD(ix,x);
  59         ix &= 0x7fffffff;
  60
  61     /* x is INF or NaN */
  62         if(ix>=0x7ff00000) return x*x;
  63
  64     /* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */
  65         if(ix<0x3fd62e43) {
  66             t = expm1(fabs(x));
  67             w = one+t;
  68             if (ix<0x3c800000) return w;        /* cosh(tiny) = 1 */
  69             return one+(t*t)/(w+w);
  70         }
  71
  72     /* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */
  73         if (ix < 0x40360000) {
  74                 t = __ieee754_exp(fabs(x));
  75                 return half*t+half/t;
  76         }
  77
  78     /* |x| in [22, log(maxdouble)] return half*exp(|x|) */
  79         if (ix < 0x40862E42)  return half*__ieee754_exp(fabs(x));
  80
  81     /* |x| in [log(maxdouble), overflowthresold] */
  82         GET_LOW_WORD(lx,x);
  83         if (ix<0x408633CE ||
  84              (ix==0x408633ce && lx<=(__uint32_t)0x8fb9f87d)) {
  85             w = __ieee754_exp(half*fabs(x));
  86             t = half*w;
  87             return t*w;
  88         }
  89
  90     /* |x| > overflowthresold, cosh(x) overflow */
  91         return __math_oflow(0);
  92 }
  93
  94 #endif /* defined(_DOUBLE_IS_32BITS) */