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)) */ acoshf(float x)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 */ 19 /* up to 2ulp error in [1,1.125] */ 20 return log1pf(x-1 + sqrtf((x-1)*(x-1)+2*(x-1))); 21 if (u.i < 0x3f800000+(12<<23)) 22 /* 2 <= x < 0x1p12 */ 23 return logf(2*x - 1/(x+sqrtf(x*x-1))); 24 /* x >= 0x1p12 or x <= -2 or nan */ 25 return logf(x) + 0.693147180559945309417232121458176568f; 26 } 27