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#include <float.h> // for FLT_EVAL_METHOD
#include <math.h> // for logf, sqrtf, acoshf, log1pf
#include <stdint.h> // for uint32_t
#if FLT_EVAL_METHOD == 2
#undef sqrtf
#define sqrtf sqrtl
#elif FLT_EVAL_METHOD == 1
#undef sqrtf
#define sqrtf sqrt
#endif
/* acosh(x) = log(x + sqrt(x*x-1)) */
float acoshf(float x)
{
union {
float f;
uint32_t i;
} u = { x };
uint32_t a = u.i & 0x7fffffff;
if (a < 0x3f800000 + (1 << 23))
/* |x| < 2, invalid if x < 1 */
/* up to 2ulp error in [1,1.125] */
return log1pf(x - 1 + sqrtf((x - 1) * (x - 1) + 2 * (x - 1)));
if (u.i < 0x3f800000 + (12 << 23))
/* 2 <= x < 0x1p12 */
return logf(2 * x - 1 / (x + sqrtf(x * x - 1)));
/* x >= 0x1p12 or x <= -2 or nan */
return logf(x) + 0.693147180559945309417232121458176568f;
}
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