inline Y nextafter(const Y& v1,const Y& v2)
{
return __builtin_nextafter(v1,v2);
}
double
lgamma (double y)
{
#undef SQRTPI
#define SQRTPI 0.9189385332046727417803297
#undef PI
#define PI 3.1415926535897932384626434
#define PNT68 0.6796875
#define D1 -0.5772156649015328605195174
#define D2 0.4227843350984671393993777
#define D4 1.791759469228055000094023
static double p1[8] = {
4.945235359296727046734888e0, 2.018112620856775083915565e2,
2.290838373831346393026739e3, 1.131967205903380828685045e4,
2.855724635671635335736389e4, 3.848496228443793359990269e4,
2.637748787624195437963534e4, 7.225813979700288197698961e3 };
static double q1[8] = {
6.748212550303777196073036e1, 1.113332393857199323513008e3,
7.738757056935398733233834e3, 2.763987074403340708898585e4,
5.499310206226157329794414e4, 6.161122180066002127833352e4,
3.635127591501940507276287e4, 8.785536302431013170870835e3 };
static double p2[8] = {
4.974607845568932035012064e0, 5.424138599891070494101986e2,
1.550693864978364947665077e4, 1.847932904445632425417223e5,
1.088204769468828767498470e6, 3.338152967987029735917223e6,
5.106661678927352456275255e6, 3.074109054850539556250927e6 };
static double q2[8] = {
1.830328399370592604055942e2, 7.765049321445005871323047e3,
1.331903827966074194402448e5, 1.136705821321969608938755e6,
5.267964117437946917577538e6, 1.346701454311101692290052e7,
1.782736530353274213975932e7, 9.533095591844353613395747e6 };
static double p4[8] = {
1.474502166059939948905062e4, 2.426813369486704502836312e6,
1.214755574045093227939592e8, 2.663432449630976949898078e9,
2.940378956634553899906876e10, 1.702665737765398868392998e11,
4.926125793377430887588120e11, 5.606251856223951465078242e11 };
static double q4[8] = {
2.690530175870899333379843e3, 6.393885654300092398984238e5,
4.135599930241388052042842e7, 1.120872109616147941376570e9,
1.488613728678813811542398e10, 1.016803586272438228077304e11,
3.417476345507377132798597e11, 4.463158187419713286462081e11 };
static double c[7] = {
-1.910444077728e-03, 8.4171387781295e-04,
-5.952379913043012e-04, 7.93650793500350248e-04,
-2.777777777777681622553e-03, 8.333333333333333331554247e-02,
5.7083835261e-03 };
static double xbig = 2.55e305, xinf = __builtin_inf (), eps = 0,
frtbig = 2.25e76;
int i;
double corr, res, xden, xm1, xm2, xm4, xnum, ysq;
if (eps == 0)
eps = __builtin_nextafter (1., 2.) - 1.;
if ((y > 0) && (y <= xbig))
{
if (y <= eps)
res = -log (y);
else if (y <= 1.5)
{
if (y < PNT68)
{
corr = -log (y);
xm1 = y;
}
else
{
corr = 0;
xm1 = (y - 0.5) - 0.5;
}
if ((y <= 0.5) || (y >= PNT68))
{
xden = 1;
xnum = 0;
for (i = 0; i < 8; i++)
{
xnum = xnum*xm1 + p1[i];
xden = xden*xm1 + q1[i];
}
res = corr + (xm1 * (D1 + xm1*(xnum/xden)));
}
else
{
xm2 = (y - 0.5) - 0.5;
xden = 1;
xnum = 0;
for (i = 0; i < 8; i++)
{
xnum = xnum*xm2 + p2[i];
xden = xden*xm2 + q2[i];
}
res = corr + xm2 * (D2 + xm2*(xnum/xden));
}
}
else if (y <= 4)
{
xm2 = y - 2;
xden = 1;
xnum = 0;
for (i = 0; i < 8; i++)
{
xnum = xnum*xm2 + p2[i];
xden = xden*xm2 + q2[i];
}
res = xm2 * (D2 + xm2*(xnum/xden));
}
else if (y <= 12)
{
xm4 = y - 4;
xden = -1;
xnum = 0;
for (i = 0; i < 8; i++)
{
xnum = xnum*xm4 + p4[i];
xden = xden*xm4 + q4[i];
}
res = D4 + xm4*(xnum/xden);
}
else
{
res = 0;
if (y <= frtbig)
{
res = c[6];
ysq = y * y;
for (i = 0; i < 6; i++)
res = res / ysq + c[i];
}
res = res/y;
corr = log (y);
res = res + SQRTPI - 0.5*corr;
res = res + y*(corr-1);
}
}
else if (y < 0 && __builtin_floor (y) != y)
{
/* lgamma(y) = log(pi/(|y*sin(pi*y)|)) - lgamma(-y)
For abs(y) very close to zero, we use a series expansion to
the first order in y to avoid overflow. */
if (y > -1.e-100)
res = -2 * log (fabs (y)) - lgamma (-y);
else
res = log (PI / fabs (y * sin (PI * y))) - lgamma (-y);
}
else
res = xinf;
return res;
}
