29 lines
727 B
C
29 lines
727 B
C
#include "libc/math/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;
|
|
}
|