double cosh(double x)
{
double t, w;
int32_t ix;
GET_HIGH_WORD(ix, x);
ix &= 0x7fffffff;
/* x is INF or NaN */
if (ix >= 0x7ff00000)
return x*x;
/* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */
if (ix < 0x3fd62e43) {
t = expm1(fabs(x));
w = 1.0+t;
if (ix < 0x3c800000)
return w; /* cosh(tiny) = 1 */
return 1.0 + (t*t)/(w+w);
}
/* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|))/2; */
if (ix < 0x40360000) {
t = exp(fabs(x));
return 0.5*t + 0.5/t;
}
/* |x| in [22, log(maxdouble)] return 0.5*exp(|x|) */
if (ix < 0x40862E42)
return 0.5*exp(fabs(x));
/* |x| in [log(maxdouble), overflowthresold] */
if (ix <= 0x408633CE)
return __expo2(fabs(x));
/* |x| > overflowthresold, cosh(x) overflow */
return huge*huge;
}
double sinh(double x)
{
double t, h;
int32_t ix, jx;
/* High word of |x|. */
GET_HIGH_WORD(jx, x);
ix = jx & 0x7fffffff;
/* x is INF or NaN */
if (ix >= 0x7ff00000)
return x + x;
h = 0.5;
if (jx < 0) h = -h;
/* |x| in [0,22], return sign(x)*0.5*(E+E/(E+1))) */
if (ix < 0x40360000) { /* |x|<22 */
if (ix < 0x3e300000) /* |x|<2**-28 */
/* raise inexact, return x */
if (huge+x > 1.0)
return x;
t = expm1(fabs(x));
if (ix < 0x3ff00000)
return h*(2.0*t - t*t/(t+1.0));
return h*(t + t/(t+1.0));
}
/* |x| in [22, log(maxdouble)] return 0.5*exp(|x|) */
if (ix < 0x40862E42)
return h*exp(fabs(x));
/* |x| in [log(maxdouble), overflowthresold] */
if (ix <= 0x408633CE)
return h * 2.0 * __expo2(fabs(x)); /* h is for sign only */
/* |x| > overflowthresold, sinh(x) overflow */
return x*huge;
}
