30 lines
577 B
C
30 lines
577 B
C
|
#include "libm.h"
|
||
|
|
|
||
|
|
/* 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;
|
||
|
|
}
|