libm/e_cosh.c

   1 /*
   2  * ====================================================
   3  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
   4  *
   5  * Developed at SunPro, a Sun Microsystems, Inc. business.
   6  * Permission to use, copy, modify, and distribute this
   7  * software is freely granted, provided that this notice
   8  * is preserved.
   9  * ====================================================
  10  */
  11
  12 /* __ieee754_cosh(x)
  13  * Method :
  14  * mathematically cosh(x) if defined to be (exp(x)+exp(-x))/2
  15  *      1. Replace x by |x| (cosh(x) = cosh(-x)).
  16  *      2.
  17  *                                                      [ exp(x) - 1 ]^2
  18  *          0        <= x <= ln2/2  :  cosh(x) := 1 + -------------------
  19  *                                                         2*exp(x)
  20  *
  21  *                                                exp(x) +  1/exp(x)
  22  *          ln2/2    <= x <= 22     :  cosh(x) := -------------------
  23  *                                                        2
  24  *          22       <= x <= lnovft :  cosh(x) := exp(x)/2
  25  *          lnovft   <= x <= ln2ovft:  cosh(x) := exp(x/2)/2 * exp(x/2)
  26  *          ln2ovft  <  x           :  cosh(x) := huge*huge (overflow)
  27  *
  28  * Special cases:
  29  *      cosh(x) is |x| if x is +INF, -INF, or NaN.
  30  *      only cosh(0)=1 is exact for finite x.
  31  */
  32
  33 #include "math.h"
  34 #include "math_private.h"
  35
  36 static const double one = 1.0, half=0.5, huge = 1.0e300;
  37
  38 double __ieee754_cosh(double x)
  39 {
  40         double t,w;
  41         int32_t ix;
  42         u_int32_t lx;
  43
  44     /* High word of |x|. */
  45         GET_HIGH_WORD(ix,x);
  46         ix &= 0x7fffffff;
  47
  48     /* x is INF or NaN */
  49         if(ix>=0x7ff00000) return x*x;
  50
  51     /* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */
  52         if(ix<0x3fd62e43) {
  53             t = expm1(fabs(x));
  54             w = one+t;
  55             if (ix<0x3c800000) return w;        /* cosh(tiny) = 1 */
  56             return one+(t*t)/(w+w);
  57         }
  58
  59     /* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */
  60         if (ix < 0x40360000) {
  61                 t = __ieee754_exp(fabs(x));
  62                 return half*t+half/t;
  63         }
  64
  65     /* |x| in [22, log(maxdouble)] return half*exp(|x|) */
  66         if (ix < 0x40862E42)  return half*__ieee754_exp(fabs(x));
  67
  68     /* |x| in [log(maxdouble), overflowthresold] */
  69         GET_LOW_WORD(lx,x);
  70         if (ix<0x408633CE ||
  71               ((ix==0x408633ce)&&(lx<=(u_int32_t)0x8fb9f87d))) {
  72             w = __ieee754_exp(half*fabs(x));
  73             t = half*w;
  74             return t*w;
  75         }
  76
  77     /* |x| > overflowthresold, cosh(x) overflow */
  78         return huge*huge;
  79 }
  80
  81 /*
  82  * wrapper cosh(x)
  83  */
  84 #ifndef _IEEE_LIBM
  85 double cosh(double x)
  86 {
  87         double z = __ieee754_cosh(x);
  88         if (_LIB_VERSION == _IEEE_ || isnan(x))
  89                 return z;
  90         if (fabs(x) > 7.10475860073943863426e+02)
  91                 return __kernel_standard(x, x, 5); /* cosh overflow */
  92         return z;
  93 }
  94 #else
  95 strong_alias(__ieee754_cosh, cosh)
  96 #endif
  97 libm_hidden_def(cosh)