path: root/src/math/asinhl.c

#include "libm.h"

#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
long double asinhl(long double x)
{
	return asinh(x);
}
#elif LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384
/* asinh(x) = sign(x)*log(|x|+sqrt(x*x+1)) ~= x - x^3/6 + o(x^5) */
long double asinhl(long double x)
{
	union {
		long double f;
		struct{uint64_t m; uint16_t se; uint16_t pad;} i;
	} u = {.f = x};
	unsigned e = u.i.se & 0x7fff;
	unsigned s = u.i.se >> 15;

	/* |x| */
	u.i.se = e;
	x = u.f;

	if (e >= 0x3fff + 32) {
		/* |x| >= 0x1p32 or inf or nan */
		x = logl(x) + 0.693147180559945309417232121458176568L;
	} else if (e >= 0x3fff + 1) {
		/* |x| >= 2 */
		x = logl(2*x + 1/(sqrtl(x*x+1)+x));
	} else if (e >= 0x3fff - 32) {
		/* |x| >= 0x1p-32 */
		x = log1pl(x + x*x/(sqrtl(x*x+1)+1));
	} else {
		/* |x| < 0x1p-32, raise inexact if x!=0 */
		FORCE_EVAL(x + 0x1p120f);
	}
	return s ? -x : x;
}
#endif