src/math/acosh.c

   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)) */
   9 double 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 }