float
__exp2f (float x)
{
float z = __ieee754_exp2f (x);
if (__builtin_expect (!isfinite (z) || z == 0, 0)
&& isfinite (x) && _LIB_VERSION != _IEEE_)
/* exp2 overflow: 144, exp2 underflow: 145 */
return __kernel_standard_f (x, x, 144 + !!signbit (x));
return z;
}
float
__exp2f (float x) /* wrapper exp2f */
{
#ifdef _IEEE_LIBM
return __ieee754_exp2f (x);
#else
float z;
z = __ieee754_exp2f (x);
if (_LIB_VERSION != _IEEE_ && __finitef (x))
{
if (x > o_threshold)
/* exp2 overflow */
return (float) __kernel_standard ((double) x, (double) x, 144);
else if (x <= u_threshold)
/* exp2 underflow */
return (float) __kernel_standard ((double) x, (double) x, 145);
}
return z;
#endif
}
static float
gammaf_positive (float x, int *exp2_adj)
{
int local_signgam;
if (x < 0.5f)
{
*exp2_adj = 0;
return __ieee754_expf (__ieee754_lgammaf_r (x + 1, &local_signgam)) / x;
}
else if (x <= 1.5f)
{
*exp2_adj = 0;
return __ieee754_expf (__ieee754_lgammaf_r (x, &local_signgam));
}
else if (x < 2.5f)
{
*exp2_adj = 0;
float x_adj = x - 1;
return (__ieee754_expf (__ieee754_lgammaf_r (x_adj, &local_signgam))
* x_adj);
}
else
{
float eps = 0;
float x_eps = 0;
float x_adj = x;
float prod = 1;
if (x < 4.0f)
{
/* Adjust into the range for applying Stirling's
approximation. */
float n = __ceilf (4.0f - x);
x_adj = math_narrow_eval (x + n);
x_eps = (x - (x_adj - n));
prod = __gamma_productf (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. */
float exp_adj = -eps;
float x_adj_int = __roundf (x_adj);
float x_adj_frac = x_adj - x_adj_int;
int x_adj_log2;
float x_adj_mant = __frexpf (x_adj, &x_adj_log2);
if (x_adj_mant < (float) M_SQRT1_2)
{
x_adj_log2--;
x_adj_mant *= 2.0f;
}
*exp2_adj = x_adj_log2 * (int) x_adj_int;
float ret = (__ieee754_powf (x_adj_mant, x_adj)
* __ieee754_exp2f (x_adj_log2 * x_adj_frac)
* __ieee754_expf (-x_adj)
* __ieee754_sqrtf (2 * (float) M_PI / x_adj)
/ prod);
exp_adj += x_eps * __ieee754_logf (x_adj);
float bsum = gamma_coeff[NCOEFF - 1];
float 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 * __expm1f (exp_adj);
}
}
