/* Simple tests on the Psi-function (aka polygamma-function). We stuff in
arguments where the result exists in closed form and check if it's ok. */
static unsigned inifcns_consist_psi()
{
using GiNaC::log;
using GiNaC::tgamma;
unsigned result = 0;
symbol x;
ex e, f;
// We check psi(1) and psi(1/2) implicitly by calculating the curious
// little identity tgamma(1)'/tgamma(1) - tgamma(1/2)'/tgamma(1/2) == 2*log(2).
e += (tgamma(x).diff(x)/tgamma(x)).subs(x==numeric(1));
e -= (tgamma(x).diff(x)/tgamma(x)).subs(x==numeric(1,2));
if (e!=2*log(2)) {
clog << "tgamma(1)'/tgamma(1) - tgamma(1/2)'/tgamma(1/2) erroneously returned "
<< e << " instead of 2*log(2)" << endl;
++result;
}
return result;
}
/* Simple tests on the tgamma function. We stuff in arguments where the results
* exists in closed form and check if it's ok. */
static unsigned inifcns_consist_gamma()
{
using GiNaC::tgamma;
unsigned result = 0;
ex e;
e = tgamma(1);
for (int i=2; i<8; ++i)
e += tgamma(ex(i));
if (e != numeric(874)) {
clog << "tgamma(1)+...+tgamma(7) erroneously returned "
<< e << " instead of 874" << endl;
++result;
}
e = tgamma(1);
for (int i=2; i<8; ++i)
e *= tgamma(ex(i));
if (e != numeric(24883200)) {
clog << "tgamma(1)*...*tgamma(7) erroneously returned "
<< e << " instead of 24883200" << endl;
++result;
}
e = tgamma(ex(numeric(5, 2)))*tgamma(ex(numeric(9, 2)))*64;
if (e != 315*Pi) {
clog << "64*tgamma(5/2)*tgamma(9/2) erroneously returned "
<< e << " instead of 315*Pi" << endl;
++result;
}
e = tgamma(ex(numeric(-13, 2)));
for (int i=-13; i<7; i=i+2)
e += tgamma(ex(numeric(i, 2)));
e = (e*tgamma(ex(numeric(15, 2)))*numeric(512));
if (e != numeric(633935)*Pi) {
clog << "512*(tgamma(-13/2)+...+tgamma(5/2))*tgamma(15/2) erroneously returned "
<< e << " instead of 633935*Pi" << endl;
++result;
}
return result;
}
/* F_ab(a, i, b, j, "x") is a common pattern in all vertex evaluators. */
static ex F_ab(int a, int i, int b, int j, const symbol &x)
{
using GiNaC::tgamma;
if ((i==0 && a<=0) || (j==0 && b<=0))
return 0;
else
return (tgamma(2-a-(i+1)*x)*
tgamma(2-b-(1+j)*x)*
tgamma(a+b-2+(1+i+j)*x)/
tgamma(a+i*x)/
tgamma(b+j*x)/tgamma(4-a-b-(2+i+j)*x));
}
