29 lines
707 B
C
29 lines
707 B
C
#include "libc/math/libm.h"
|
|
|
|
/* asinh(x) = sign(x)*log(|x|+sqrt(x*x+1)) ~= x - x^3/6 + o(x^5) */
|
|
double asinh(double x)
|
|
{
|
|
union {double f; uint64_t i;} u = {.f = x};
|
|
unsigned e = u.i >> 52 & 0x7ff;
|
|
unsigned s = u.i >> 63;
|
|
|
|
/* |x| */
|
|
u.i &= (uint64_t)-1/2;
|
|
x = u.f;
|
|
|
|
if (e >= 0x3ff + 26) {
|
|
/* |x| >= 0x1p26 or inf or nan */
|
|
x = log(x) + 0.693147180559945309417232121458176568;
|
|
} else if (e >= 0x3ff + 1) {
|
|
/* |x| >= 2 */
|
|
x = log(2*x + 1/(sqrt(x*x+1)+x));
|
|
} else if (e >= 0x3ff - 26) {
|
|
/* |x| >= 0x1p-26, up to 1.6ulp error in [0.125,0.5] */
|
|
x = log1p(x + x*x/(sqrt(x*x+1)+1));
|
|
} else {
|
|
/* |x| < 0x1p-26, raise inexact if x != 0 */
|
|
FORCE_EVAL(x + 0x1p120f);
|
|
}
|
|
return s ? -x : x;
|
|
}
|