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#include "libm.h"
/* asinh(x) = sign(x)*log(|x|+sqrt(x*x+1)) ~= x - x^3/6 + o(x^5) */
float asinhf(float x)
{
union {
float f;
uint32_t i;
} u = { .f = x };
uint32_t i = u.i & 0x7fffffff;
unsigned s = u.i >> 31;
/* |x| */
u.i = i;
x = u.f;
if (i >= 0x3f800000 + (12 << 23)) {
/* |x| >= 0x1p12 or inf or nan */
x = logf(x) + 0.693147180559945309417232121458176568f;
} else if (i >= 0x3f800000 + (1 << 23)) {
/* |x| >= 2 */
x = logf(2 * x + 1 / (sqrtf(x * x + 1) + x));
} else if (i >= 0x3f800000 - (12 << 23)) {
/* |x| >= 0x1p-12, up to 1.6ulp error in [0.125,0.5] */
x = log1pf(x + x * x / (sqrtf(x * x + 1) + 1));
} else {
/* |x| < 0x1p-12, raise inexact if x!=0 */
FORCE_EVAL(x + 0x1p120f);
}
return s ? -x : x;
}
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