1 #include "libm.h" 2 3 #if FLT_EVAL_METHOD==2 4 #undef sqrt 5 #define sqrt sqrtl 6 #endif 7 8 /* acosh(x) = log(x + sqrt(x*x-1)) */ acosh(double x)9double acosh(double x) 10 { 11 union {double f; uint64_t i;} u = {.f = x}; 12 unsigned e = u.i >> 52 & 0x7ff; 13 14 /* x < 1 domain error is handled in the called functions */ 15 16 if (e < 0x3ff + 1) 17 /* |x| < 2, up to 2ulp error in [1,1.125] */ 18 return log1p(x-1 + sqrt((x-1)*(x-1)+2*(x-1))); 19 if (e < 0x3ff + 26) 20 /* |x| < 0x1p26 */ 21 return log(2*x - 1/(x+sqrt(x*x-1))); 22 /* |x| >= 0x1p26 or nan */ 23 return log(x) + 0.693147180559945309417232121458176568; 24 } 25