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 union { 14 float f; 15 uint32_t i; 16 } u = {x}; 17 uint32_t a = u.i & 0x7fffffff; 18 19 if (a < 0x3f800000 + (1 << 23)) /* |x| < 2, invalid if x < 1 or nan */ 20 /* up to 2ulp error in [1,1.125] */ 21 return log1pf(x - 1 + sqrtf((x - 1) * (x - 1) + 2 * (x - 1))); 22 if (a < 0x3f800000 + (12 << 23)) /* |x| < 0x1p12 */ 23 return logf(2 * x - 1 / (x + sqrtf(x * x - 1))); 24 /* x >= 0x1p12 */ 25 return logf(x) + 0.693147180559945309417232121458176568f; 26} 27