3 /* acosh(x) = log(x + sqrt(x*x-1)) */
6 union {float f; uint32_t i;} u = {x};
7 uint32_t a = u.i & 0x7fffffff;
9 if (a < 0x3f800000+(1<<23))
10 /* |x| < 2, invalid if x < 1 or nan */
11 /* up to 2ulp error in [1,1.125] */
12 return log1pf(x-1 + sqrtf((x-1)*(x-1)+2*(x-1)));
13 if (a < 0x3f800000+(12<<23))
15 return logf(2*x - 1/(x+sqrtf(x*x-1)));
17 return logf(x) + 0.693147180559945309417232121458176568f;