newlib-cygwin/winsup/mingw/mingwex/math/acoshl.c

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#include <math.h>
#include <errno.h>
#include "fastmath.h"
/* acosh(x) = log (x + sqrt(x * x - 1)) */
long double acoshl (long double x)
{
if (isnan (x))
return x;
if (x < 1.0L)
{
errno = EDOM;
return nanl("");
}
if (x > 0x1p32L)
/* Avoid overflow (and unnecessary calculation when
sqrt (x * x - 1) == x).
The M_LN2 define doesn't have enough precison for
long double so use this one. GCC optimizes by replacing
the const with a fldln2 insn. */
return __fast_logl (x) + 6.9314718055994530941723E-1L;
/* Since x >= 1, the arg to log will always be greater than
the fyl2xp1 limit (approx 0.29) so just use logl. */
return __fast_logl (x + __fast_sqrtl((x + 1.0L) * (x - 1.0L)));
}