lib/libm/atanhf.c


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#include "libm.h"

/* atanh(x) = log((1+x)/(1-x))/2 = log1p(2x/(1-x))/2 ~= x + x^3/3 + o(x^5) */
float atanhf(float x)
{
	union {
		float f;
		uint32_t i;
	} u = { .f = x };
	unsigned s = u.i >> 31;
	float_t y;

	/* |x| */
	u.i &= 0x7fffffff;
	y = u.f;

	if (u.i < 0x3f800000 - (1 << 23)) {
		if (u.i < 0x3f800000 - (32 << 23)) {
			/* handle underflow */
			if (u.i < (1 << 23))
				FORCE_EVAL((float)(y * y));
		} else {
			/* |x| < 0.5, up to 1.7ulp error */
			y = 0.5f * log1pf(2 * y + 2 * y * y / (1 - y));
		}
	} else {
		/* avoid overflow */
		y = 0.5f * log1pf(2 * (y / (1 - y)));
	}
	return s ? -y : y;
}