long double
__roundl (long double x)
{
double xh, xl, hi, lo;
ldbl_unpack (x, &xh, &xl);
/* Return Inf, Nan, +/-0 unchanged. */
if (__builtin_expect (xh != 0.0
&& __builtin_isless (__builtin_fabs (xh),
__builtin_inf ()), 1))
{
hi = __round (xh);
if (hi != xh)
{
/* The high part is not an integer; the low part only
affects the result if the high part is exactly half way
between two integers and the low part is nonzero with the
opposite sign. */
if (fabs (hi - xh) == 0.5)
{
if (xh > 0 && xl < 0)
xh = hi - 1;
else if (xh < 0 && xl > 0)
xh = hi + 1;
else
xh = hi;
}
else
xh = hi;
xl = 0;
}
else
{
/* The high part is a nonzero integer. */
lo = __round (xl);
if (fabs (lo - xl) == 0.5)
{
if (xh > 0 && xl < 0)
xl = lo + 1;
else if (xh < 0 && lo > 0)
xl = lo - 1;
else
xl = lo;
}
else
xl = lo;
xh = hi;
ldbl_canonicalize_int (&xh, &xl);
}
}
else
/* Quiet signaling NaN arguments. */
xh += xh;
return ldbl_pack (xh, xl);
}
Err mathlib_round(UInt16 refnum, double x, double *result) {
#pragma unused(refnum)
*result = __round(x);
return mlErrNone;
}
static double
gamma_positive (double x, int *exp2_adj)
{
int local_signgam;
if (x < 0.5)
{
*exp2_adj = 0;
return __ieee754_exp (__ieee754_lgamma_r (x + 1, &local_signgam)) / x;
}
else if (x <= 1.5)
{
*exp2_adj = 0;
return __ieee754_exp (__ieee754_lgamma_r (x, &local_signgam));
}
else if (x < 6.5)
{
/* Adjust into the range for using exp (lgamma). */
*exp2_adj = 0;
double n = __ceil (x - 1.5);
double x_adj = x - n;
double eps;
double prod = __gamma_product (x_adj, 0, n, &eps);
return (__ieee754_exp (__ieee754_lgamma_r (x_adj, &local_signgam))
* prod * (1.0 + eps));
}
else
{
double eps = 0;
double x_eps = 0;
double x_adj = x;
double prod = 1;
if (x < 12.0)
{
/* Adjust into the range for applying Stirling's
approximation. */
double n = __ceil (12.0 - x);
#if FLT_EVAL_METHOD != 0
volatile
#endif
double x_tmp = x + n;
x_adj = x_tmp;
x_eps = (x - (x_adj - n));
prod = __gamma_product (x_adj - n, x_eps, n, &eps);
}
/* The result is now gamma (X_ADJ + X_EPS) / (PROD * (1 + EPS)).
Compute gamma (X_ADJ + X_EPS) using Stirling's approximation,
starting by computing pow (X_ADJ, X_ADJ) with a power of 2
factored out. */
double exp_adj = -eps;
double x_adj_int = __round (x_adj);
double x_adj_frac = x_adj - x_adj_int;
int x_adj_log2;
double x_adj_mant = __frexp (x_adj, &x_adj_log2);
if (x_adj_mant < M_SQRT1_2)
{
x_adj_log2--;
x_adj_mant *= 2.0;
}
*exp2_adj = x_adj_log2 * (int) x_adj_int;
double ret = (__ieee754_pow (x_adj_mant, x_adj)
* __ieee754_exp2 (x_adj_log2 * x_adj_frac)
* __ieee754_exp (-x_adj)
* __ieee754_sqrt (2 * M_PI / x_adj)
/ prod);
exp_adj += x_eps * __ieee754_log (x);
double bsum = gamma_coeff[NCOEFF - 1];
double x_adj2 = x_adj * x_adj;
for (size_t i = 1; i <= NCOEFF - 1; i++)
bsum = bsum / x_adj2 + gamma_coeff[NCOEFF - 1 - i];
exp_adj += bsum / x_adj;
return ret + ret * __expm1 (exp_adj);
}
}
