/* 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;
}
int main(int argc, char *argv[])
{
int N;
if (argc == 2) {
N = std::atoi(argv[1]);
} else {
N = 100;
}
ex e, f, s, a0, a1;
a0 = symbol("a0");
a1 = symbol("a1");
e = a0 + a1;
f = 0;
for (long long i = 2; i < N; i++) {
std::ostringstream o;
o << "a" << i;
s = symbol(o.str());
e = e + sin(s);
f = f + sin(s);
}
f = -f;
auto t1 = std::chrono::high_resolution_clock::now();
e = expand(pow(e, 2));
e = e.subs(a0 == f);
e = expand(e);
auto t2 = std::chrono::high_resolution_clock::now();
std::cout << std::chrono::duration_cast<std::chrono::milliseconds>(t2 - t1)
.count()
<< "ms" << std::endl;
std::cout << e << std::endl;
return 0;
}
/* 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));
}
/* Assorted tests on other transcendental functions. */
static unsigned inifcns_consist_trans()
{
using GiNaC::asin; using GiNaC::acos;
using GiNaC::asinh; using GiNaC::acosh; using GiNaC::atanh;
unsigned result = 0;
symbol x("x");
ex chk;
chk = asin(1)-acos(0);
if (!chk.is_zero()) {
clog << "asin(1)-acos(0) erroneously returned " << chk
<< " instead of 0" << endl;
++result;
}
// arbitrary check of type sin(f(x)):
chk = pow(sin(acos(x)),2) + pow(sin(asin(x)),2)
- (1+pow(x,2))*pow(sin(atan(x)),2);
if (chk != 1-pow(x,2)) {
clog << "sin(acos(x))^2 + sin(asin(x))^2 - (1+x^2)*sin(atan(x))^2 "
<< "erroneously returned " << chk << " instead of 1-x^2" << endl;
++result;
}
// arbitrary check of type cos(f(x)):
chk = pow(cos(acos(x)),2) + pow(cos(asin(x)),2)
- (1+pow(x,2))*pow(cos(atan(x)),2);
if (!chk.is_zero()) {
clog << "cos(acos(x))^2 + cos(asin(x))^2 - (1+x^2)*cos(atan(x))^2 "
<< "erroneously returned " << chk << " instead of 0" << endl;
++result;
}
// arbitrary check of type tan(f(x)):
chk = tan(acos(x))*tan(asin(x)) - tan(atan(x));
if (chk != 1-x) {
clog << "tan(acos(x))*tan(asin(x)) - tan(atan(x)) "
<< "erroneously returned " << chk << " instead of -x+1" << endl;
++result;
}
// arbitrary check of type sinh(f(x)):
chk = -pow(sinh(acosh(x)),2).expand()*pow(sinh(atanh(x)),2)
- pow(sinh(asinh(x)),2);
if (!chk.is_zero()) {
clog << "expand(-(sinh(acosh(x)))^2)*(sinh(atanh(x))^2) - sinh(asinh(x))^2 "
<< "erroneously returned " << chk << " instead of 0" << endl;
++result;
}
// arbitrary check of type cosh(f(x)):
chk = (pow(cosh(asinh(x)),2) - 2*pow(cosh(acosh(x)),2))
* pow(cosh(atanh(x)),2);
if (chk != 1) {
clog << "(cosh(asinh(x))^2 - 2*cosh(acosh(x))^2) * cosh(atanh(x))^2 "
<< "erroneously returned " << chk << " instead of 1" << endl;
++result;
}
// arbitrary check of type tanh(f(x)):
chk = (pow(tanh(asinh(x)),-2) - pow(tanh(acosh(x)),2)).expand()
* pow(tanh(atanh(x)),2);
if (chk != 2) {
clog << "expand(tanh(acosh(x))^2 - tanh(asinh(x))^(-2)) * tanh(atanh(x))^2 "
<< "erroneously returned " << chk << " instead of 2" << endl;
++result;
}
// check consistency of log and eta phases:
for (int r1=-1; r1<=1; ++r1) {
for (int i1=-1; i1<=1; ++i1) {
ex x1 = r1+I*i1;
if (x1.is_zero())
continue;
for (int r2=-1; r2<=1; ++r2) {
for (int i2=-1; i2<=1; ++i2) {
ex x2 = r2+I*i2;
if (x2.is_zero())
continue;
if (abs(evalf(eta(x1,x2)-log(x1*x2)+log(x1)+log(x2)))>.1e-12) {
clog << "either eta(x,y), log(x), log(y) or log(x*y) is wrong"
<< " at x==" << x1 << ", y==" << x2 << endl;
++result;
}
}
}
}
}
return result;
}
static unsigned inifcns_consist_log()
{
unsigned result = 0;
symbol z("a"), w("b");
realsymbol a("a"), b("b");
possymbol p("p"), q("q");
// do not expand
if (!log(z*w).expand(expand_options::expand_transcendental).is_equal(log(z*w)))
++result;
// do not expand
if (!log(a*b).expand(expand_options::expand_transcendental).is_equal(log(a*b)))
++result;
// shall expand
if (!log(p*q).expand(expand_options::expand_transcendental).is_equal(log(p) + log(q)))
++result;
// a bit more complicated
ex e1 = log(-7*p*pow(q,3)*a*pow(b,2)*z*w).expand(expand_options::expand_transcendental);
ex e2 = log(7)+log(p)+log(pow(q,3))+log(-z*a*w*pow(b,2));
if (!e1.is_equal(e2))
++result;
// shall not do for non-real powers
if (ex(log(pow(p,z))).is_equal(z*log(p)))
++result;
// shall not do for non-positive basis
if (ex(log(pow(a,b))).is_equal(b*log(a)))
++result;
return result;
}
