1#include "libm.h" 2 3#if FLT_EVAL_METHOD==2 4#undef sqrtf 5#define sqrtf sqrtl 6#elif FLT_EVAL_METHOD==1 7#undef sqrtf 8#define sqrtf sqrt 9#endif 10 11/* acosh(x) = log(x + sqrt(x*x-1)) */ 12float acoshf(float x) 13{ 14 union {float f; uint32_t i;} u = {x}; 15 uint32_t a = u.i & 0x7fffffff; 16 17 if (a < 0x3f800000+(1<<23)) 18 /* |x| < 2, invalid if x < 1 or nan */ 19 /* up to 2ulp error in [1,1.125] */ 20 return log1pf(x-1 + sqrtf((x-1)*(x-1)+2*(x-1))); 21 if (a < 0x3f800000+(12<<23)) 22 /* |x| < 0x1p12 */ 23 return logf(2*x - 1/(x+sqrtf(x*x-1))); 24 /* x >= 0x1p12 */ 25 return logf(x) + 0.693147180559945309417232121458176568f; 26} 27