| #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; |
| } |
