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#include <float.h> // for FLT_EVAL_METHOD
#include <math.h> // for log, sqrt, acosh, log1p
#include <stdint.h> // for uint64_t
#if FLT_EVAL_METHOD == 2
#undef sqrt
#define sqrt sqrtl
#endif
/* acosh(x) = log(x + sqrt(x*x-1)) */
double acosh(double x)
{
union {
double f;
uint64_t i;
} u = { .f = x };
unsigned e = u.i >> 52 & 0x7ff;
/* x < 1 domain error is handled in the called functions */
if (e < 0x3ff + 1)
/* |x| < 2, up to 2ulp error in [1,1.125] */
return log1p(x - 1 + sqrt((x - 1) * (x - 1) + 2 * (x - 1)));
if (e < 0x3ff + 26)
/* |x| < 0x1p26 */
return log(2 * x - 1 / (x + sqrt(x * x - 1)));
/* |x| >= 0x1p26 or nan */
return log(x) + 0.693147180559945309417232121458176568;
}
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