/* asinh(x) = copysign(log(fabs(x) + sqrt(x * x + 1.0)), x) */
long double asinhl(long double x)
{
long double z;
if (!isfinite (x))
return x;
z = fabsl (x);
/* Avoid setting FPU underflow exception flag in x * x. */
#if 0
if ( z < 0x1p-32)
return x;
#endif
/* Use log1p to avoid cancellation with small x. Put
x * x in denom, so overflow is harmless.
asinh(x) = log1p (x + sqrt (x * x + 1.0) - 1.0)
= log1p (x + x * x / (sqrt (x * x + 1.0) + 1.0)) */
z = __fast_log1pl (z + z * z / (__fast_sqrtl (z * z + 1.0L) + 1.0L));
return ( x > 0.0 ? z : -z);
}
/* atanh (x) = 0.5 * log ((1.0 + x)/(1.0 - x)) */
long double atanhl (long double x)
{
long double z;
if (isnan (x))
return x;
z = fabsl (x);
if (z == 1.0L)
{
errno = ERANGE;
return (x > 0 ? INFINITY : -INFINITY);
}
if ( z > 1.0L)
{
errno = EDOM;
return nanl("");
}
/* Rearrange formula to avoid precision loss for small x.
atanh(x) = 0.5 * log ((1.0 + x)/(1.0 - x))
= 0.5 * log1p ((1.0 + x)/(1.0 - x) - 1.0)
= 0.5 * log1p ((1.0 + x - 1.0 + x) /(1.0 - x))
= 0.5 * log1p ((2.0 * x ) / (1.0 - x)) */
z = 0.5L * __fast_log1pl ((z + z) / (1.0L - z));
return x >= 0 ? z : -z;
}
