long double
__ieee754_gammal_r (long double x, int *signgamp)
{
/* We don't have a real gamma implementation now. We'll use lgamma
and the exp function. But due to the required boundary
conditions we must check some values separately. */
int64_t hx;
u_int64_t lx;
GET_LDOUBLE_WORDS64 (hx, lx, x);
if (((hx | lx) & 0x7fffffffffffffffLL) == 0)
{
/* Return value for x == 0 is Inf with divide by zero exception. */
*signgamp = 0;
return 1.0 / x;
}
if (hx < 0 && (u_int64_t) hx < 0xfff0000000000000ULL && __rintl (x) == x)
{
/* Return value for integer x < 0 is NaN with invalid exception. */
*signgamp = 0;
return (x - x) / (x - x);
}
if (hx == 0xfff0000000000000ULL)
{
/* x == -Inf. According to ISO this is NaN. */
*signgamp = 0;
return x - x;
}
/* XXX FIXME. */
return __ieee754_expl (__ieee754_lgammal_r (x, signgamp));
}
long double
__ieee754_gammal_r (long double x, int *signgamp)
{
/* We don't have a real gamma implementation now. We'll use lgamma
and the exp function. But due to the required boundary
conditions we must check some values separately. */
u_int32_t es, hx, lx;
GET_LDOUBLE_WORDS (es, hx, lx, x);
if (((es & 0x7fff) | hx | lx) == 0)
{
/* Return value for x == 0 is NaN with invalid exception. */
*signgamp = 0;
return x / x;
}
if (es == 0xffffffff && ((hx & 0x7fffffff) | lx) == 0)
{
/* x == -Inf. According to ISO this is NaN. */
*signgamp = 0;
return x - x;
}
if ((es & 0x7fff) == 0x7fff && ((hx & 0x7fffffff) | lx) != 0)
/* NaN, return it. */
return x;
if ((es & 0x8000) != 0 && x < 0xffffffff && __rintl (x) == x)
{
/* Return value for integer x < 0 is NaN with invalid exception. */
*signgamp = 0;
return (x - x) / (x - x);
}
/* XXX FIXME. */
return __ieee754_expl (__ieee754_lgammal_r (x, signgamp));
}
long double
__lgammal_r(long double x, int *signgamp)
{
long double y = __ieee754_lgammal_r(x,signgamp);
if(__builtin_expect(!isfinite(y), 0)
&& isfinite(x) && _LIB_VERSION != _IEEE_)
return __kernel_standard(x, x,
floorl(x)==x&&x<=0.0
? 215 /* lgamma pole */
: 214); /* lgamma overflow */
return y;
}
long double
__lgammal(long double x)
{
int local_signgam = 0;
long double y = __ieee754_lgammal_r(x,
_LIB_VERSION != _ISOC_
/* ISO C99 does not define the
global variable. */
? &signgam
: &local_signgam);
if(__builtin_expect(!__finitel(y), 0)
&& __finitel(x) && _LIB_VERSION != _IEEE_)
return __kernel_standard_l(x, x,
__floorl(x)==x&&x<=0.0L
? 215 /* lgamma pole */
: 214); /* lgamma overflow */
return y;
}
long double
__ieee754_lgammal_r (long double x, int *signgamp)
{
long double p, q, w, z, nx;
int i, nn;
*signgamp = 1;
if (! __finitel (x))
return x * x;
if (x == 0.0L)
{
if (__signbitl (x))
*signgamp = -1;
}
if (x < 0.0L)
{
q = -x;
p = __floorl (q);
if (p == q)
return (one / (p - p));
i = p;
if ((i & 1) == 0)
*signgamp = -1;
else
*signgamp = 1;
if (q < 0x1p-120L)
return -__logl (q);
z = q - p;
if (z > 0.5L)
{
p += 1.0L;
z = p - q;
}
z = q * __sinl (PIL * z);
w = __ieee754_lgammal_r (q, &i);
z = __logl (PIL / z) - w;
return (z);
}
if (x < 13.5L)
{
p = 0.0L;
nx = __floorl (x + 0.5L);
nn = nx;
switch (nn)
{
case 0:
/* log gamma (x + 1) = log(x) + log gamma(x) */
if (x < 0x1p-120L)
return -__logl (x);
else if (x <= 0.125)
{
p = x * neval (x, RN1, NRN1) / deval (x, RD1, NRD1);
}
else if (x <= 0.375)
{
z = x - 0.25L;
p = z * neval (z, RN1r25, NRN1r25) / deval (z, RD1r25, NRD1r25);
p += lgam1r25b;
p += lgam1r25a;
}
else if (x <= 0.625)
{
z = x + (1.0L - x0a);
z = z - x0b;
p = neval (z, RN1r5, NRN1r5) / deval (z, RD1r5, NRD1r5);
p = p * z * z;
p = p + y0b;
p = p + y0a;
}
else if (x <= 0.875)
{
z = x - 0.75L;
p = z * neval (z, RN1r75, NRN1r75) / deval (z, RD1r75, NRD1r75);
p += lgam1r75b;
p += lgam1r75a;
}
else
{
z = x - 1.0L;
p = z * neval (z, RN2, NRN2) / deval (z, RD2, NRD2);
}
p = p - __logl (x);
break;
case 1:
if (x < 0.875L)
{
if (x <= 0.625)
{
z = x + (1.0L - x0a);
z = z - x0b;
p = neval (z, RN1r5, NRN1r5) / deval (z, RD1r5, NRD1r5);
p = p * z * z;
p = p + y0b;
p = p + y0a;
}
else if (x <= 0.875)
{
z = x - 0.75L;
p = z * neval (z, RN1r75, NRN1r75)
/ deval (z, RD1r75, NRD1r75);
p += lgam1r75b;
p += lgam1r75a;
}
else
{
z = x - 1.0L;
p = z * neval (z, RN2, NRN2) / deval (z, RD2, NRD2);
}
p = p - __logl (x);
}
else if (x < 1.0L)
{
z = x - 1.0L;
p = z * neval (z, RNr9, NRNr9) / deval (z, RDr9, NRDr9);
}
else if (x == 1.0L)
p = 0.0L;
else if (x <= 1.125L)
{
z = x - 1.0L;
p = z * neval (z, RN1, NRN1) / deval (z, RD1, NRD1);
}
else if (x <= 1.375)
{
z = x - 1.25L;
p = z * neval (z, RN1r25, NRN1r25) / deval (z, RD1r25, NRD1r25);
p += lgam1r25b;
p += lgam1r25a;
}
else
{
/* 1.375 <= x+x0 <= 1.625 */
z = x - x0a;
z = z - x0b;
p = neval (z, RN1r5, NRN1r5) / deval (z, RD1r5, NRD1r5);
p = p * z * z;
p = p + y0b;
p = p + y0a;
}
break;
case 2:
if (x < 1.625L)
{
z = x - x0a;
z = z - x0b;
p = neval (z, RN1r5, NRN1r5) / deval (z, RD1r5, NRD1r5);
p = p * z * z;
p = p + y0b;
p = p + y0a;
}
else if (x < 1.875L)
{
z = x - 1.75L;
p = z * neval (z, RN1r75, NRN1r75) / deval (z, RD1r75, NRD1r75);
p += lgam1r75b;
p += lgam1r75a;
}
else if (x == 2.0L)
p = 0.0L;
else if (x < 2.375L)
{
z = x - 2.0L;
p = z * neval (z, RN2, NRN2) / deval (z, RD2, NRD2);
}
else
{
z = x - 2.5L;
p = z * neval (z, RN2r5, NRN2r5) / deval (z, RD2r5, NRD2r5);
p += lgam2r5b;
p += lgam2r5a;
}
break;
case 3:
if (x < 2.75)
{
z = x - 2.5L;
p = z * neval (z, RN2r5, NRN2r5) / deval (z, RD2r5, NRD2r5);
p += lgam2r5b;
p += lgam2r5a;
}
else
{
z = x - 3.0L;
p = z * neval (z, RN3, NRN3) / deval (z, RD3, NRD3);
p += lgam3b;
p += lgam3a;
}
break;
case 4:
z = x - 4.0L;
p = z * neval (z, RN4, NRN4) / deval (z, RD4, NRD4);
p += lgam4b;
p += lgam4a;
break;
case 5:
z = x - 5.0L;
p = z * neval (z, RN5, NRN5) / deval (z, RD5, NRD5);
p += lgam5b;
p += lgam5a;
break;
case 6:
z = x - 6.0L;
p = z * neval (z, RN6, NRN6) / deval (z, RD6, NRD6);
p += lgam6b;
p += lgam6a;
break;
case 7:
z = x - 7.0L;
p = z * neval (z, RN7, NRN7) / deval (z, RD7, NRD7);
p += lgam7b;
p += lgam7a;
break;
case 8:
z = x - 8.0L;
p = z * neval (z, RN8, NRN8) / deval (z, RD8, NRD8);
p += lgam8b;
p += lgam8a;
break;
case 9:
z = x - 9.0L;
p = z * neval (z, RN9, NRN9) / deval (z, RD9, NRD9);
p += lgam9b;
p += lgam9a;
break;
case 10:
z = x - 10.0L;
p = z * neval (z, RN10, NRN10) / deval (z, RD10, NRD10);
p += lgam10b;
p += lgam10a;
break;
case 11:
z = x - 11.0L;
p = z * neval (z, RN11, NRN11) / deval (z, RD11, NRD11);
p += lgam11b;
p += lgam11a;
break;
case 12:
z = x - 12.0L;
p = z * neval (z, RN12, NRN12) / deval (z, RD12, NRD12);
p += lgam12b;
p += lgam12a;
break;
case 13:
z = x - 13.0L;
p = z * neval (z, RN13, NRN13) / deval (z, RD13, NRD13);
p += lgam13b;
p += lgam13a;
break;
}
return p;
}
if (x > MAXLGM)
return (*signgamp * huge * huge);
q = ls2pi - x;
q = (x - 0.5L) * __logl (x) + q;
if (x > 1.0e18L)
return (q);
p = 1.0L / (x * x);
q += neval (p, RASY, NRASY) / x;
return (q);
}
static long double
gammal_positive (long double x, int *exp2_adj)
{
int local_signgam;
if (x < 0.5L)
{
*exp2_adj = 0;
return __ieee754_expl (__ieee754_lgammal_r (x + 1, &local_signgam)) / x;
}
else if (x <= 1.5L)
{
*exp2_adj = 0;
return __ieee754_expl (__ieee754_lgammal_r (x, &local_signgam));
}
else if (x < 12.5L)
{
/* Adjust into the range for using exp (lgamma). */
*exp2_adj = 0;
long double n = __ceill (x - 1.5L);
long double x_adj = x - n;
long double eps;
long double prod = __gamma_productl (x_adj, 0, n, &eps);
return (__ieee754_expl (__ieee754_lgammal_r (x_adj, &local_signgam))
* prod * (1.0L + eps));
}
else
{
long double eps = 0;
long double x_eps = 0;
long double x_adj = x;
long double prod = 1;
if (x < 24.0L)
{
/* Adjust into the range for applying Stirling's
approximation. */
long double n = __ceill (24.0L - x);
x_adj = x + n;
x_eps = (x - (x_adj - n));
prod = __gamma_productl (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. */
long double exp_adj = -eps;
long double x_adj_int = __roundl (x_adj);
long double x_adj_frac = x_adj - x_adj_int;
int x_adj_log2;
long double x_adj_mant = __frexpl (x_adj, &x_adj_log2);
if (x_adj_mant < M_SQRT1_2l)
{
x_adj_log2--;
x_adj_mant *= 2.0L;
}
*exp2_adj = x_adj_log2 * (int) x_adj_int;
long double ret = (__ieee754_powl (x_adj_mant, x_adj)
* __ieee754_exp2l (x_adj_log2 * x_adj_frac)
* __ieee754_expl (-x_adj)
* __ieee754_sqrtl (2 * M_PIl / x_adj)
/ prod);
exp_adj += x_eps * __ieee754_logl (x_adj);
long double bsum = gamma_coeff[NCOEFF - 1];
long 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 * __expm1l (exp_adj);
}
}