/* 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;
}
/* 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;
}
