| #include "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; |
| } |
