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#include "libm.h" // for FORCE_EVAL
#include <math.h> // for log1p, atanh, double_t
#include <stdint.h> // for uint64_t
/* atanh(x) = log((1+x)/(1-x))/2 = log1p(2x/(1-x))/2 ~= x + x^3/3 + o(x^5) */
double atanh(double x)
{
union {
double f;
uint64_t i;
} u = { .f = x };
unsigned e = u.i >> 52 & 0x7ff;
unsigned s = u.i >> 63;
double_t y;
/* |x| */
u.i &= (uint64_t)-1 / 2;
y = u.f;
if (e < 0x3ff - 1) {
if (e < 0x3ff - 32) {
/* handle underflow */
if (e == 0)
FORCE_EVAL((float)y);
} else {
/* |x| < 0.5, up to 1.7ulp error */
y = 0.5 * log1p(2 * y + 2 * y * y / (1 - y));
}
} else {
/* avoid overflow */
y = 0.5 * log1p(2 * (y / (1 - y)));
}
return s ? -y : y;
}
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