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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;
}
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