/* acosh(x) = log (x + sqrt(x * x - 1)) */ long double acoshl (long double x) { if (isnan (x)) return x; if (x < 1.0L) { errno = EDOM; return nanl(""); } if (x > 0x1p32L) /* Avoid overflow (and unnecessary calculation when sqrt (x * x - 1) == x). The M_LN2 define doesn't have enough precison for long double so use this one. GCC optimizes by replacing the const with a fldln2 insn. */ return __fast_logl (x) + 6.9314718055994530941723E-1L; /* Since x >= 1, the arg to log will always be greater than the fyl2xp1 limit (approx 0.29) so just use logl. */ return __fast_logl (x + __fast_sqrtl((x + 1.0L) * (x - 1.0L))); }
/* asinh(x) = copysign(log(fabs(x) + sqrt(x * x + 1.0)), x) */ long double asinhl(long double x) { long double z; if (!isfinite (x)) return x; z = fabsl (x); /* Avoid setting FPU underflow exception flag in x * x. */ #if 0 if ( z < 0x1p-32) return x; #endif /* Use log1p to avoid cancellation with small x. Put x * x in denom, so overflow is harmless. asinh(x) = log1p (x + sqrt (x * x + 1.0) - 1.0) = log1p (x + x * x / (sqrt (x * x + 1.0) + 1.0)) */ z = __fast_log1pl (z + z * z / (__fast_sqrtl (z * z + 1.0L) + 1.0L)); return ( x > 0.0 ? z : -z); }