Issue with atan2 at 0

[artivis]

Hi,

The following snippet does not run successfully whereas I would expect it to,

bool atan2_at_zero() {

    using CppAD::AD;
    using CppAD::NearEqual;

    bool ok = true;
    double eps99 = 99.0 * std::numeric_limits<double>::epsilon();

    CPPAD_TESTVECTOR(AD<double>) v(2);
    v[0] = 1; // real: cos(0)
    v[1] = 0; // imag: sin(0)

    Independent(v);

    CPPAD_TESTVECTOR(AD<double>) t(1);
    t[0] = atan2(v[1], v[0]);

    CppAD::ADFun<double> f(v, t);

    CPPAD_TESTVECTOR(double) vv(2);
    vv[0] = CppAD::Value(v[0]);
    vv[1] = CppAD::Value(v[1]);

    auto grad = f.Jacobian(vv);

    ok   &= NearEqual(t[0], 0., eps99, eps99);       // ok
    ok   &= NearEqual(grad[0], 1., eps99, eps99);    // fails
    ok   &= NearEqual(grad[1], 0., eps99, eps99);    // ok

    return ok;
}

Being new to CppAD, I'm not sure if I'm doing it wrong or if this is an actual bug.

[bradbell]

This seems to be a bug. The following code passes (fails) its test when y is VALUE_OF_Y_OK (VALUE_OF_Y_FAILS):

# include <cppad/cppad.hpp>

# define VALUE_OF_Y_FAILS 0.0
# define VALUE_OF_Y_OK    1e-200
int main ()
{   using CppAD::AD;
    using CppAD::NearEqual;
    //
    bool ok      = true;
    double eps99 = 99.0 * std::numeric_limits<double>::epsilon();
    double x     = 1.0;                    // r*cos(0)
    double y     = VALUE_OF_Y_FAILS;       // r*sin(0)
    double r     = std::sqrt( x*x + y*y ); // r
    //
    CppAD::vector< AD<double> > av(2);
    av[0] = x; 
    av[1] = y;
    Independent(av);
    //
    CppAD::vector< AD<double> > at(1);
    at[0] = atan2(av[1], av[0]);
    CppAD::ADFun<double> f(av, at);
    //
    CppAD::vector<double> v(2);
    v[0] = x;
    v[1] = y;
    CppAD::vector<double>  grad = f.Jacobian(v);
    std::cout << "grad  = " << grad << "\n";
    //
    // see https://en.wikipedia.org/wiki/Atan2#Derivative
    ok   &= NearEqual( CppAD::Value(at[0]), 0., eps99, eps99);       // atan2
    ok   &= NearEqual(grad[0], -y / r, eps99, eps99);                // fails
    ok   &= NearEqual(grad[1],  x / r, eps99, eps99);                // ok
    //
    std::cout << "ok = " << ok << "\n";
    //
    return int( ! ok );
}

[bradbell]

@artivis
I think this has been fixed by the change to atan2.hpp in
a1d19b7

Please close this bug If you are satisfied with this correction.

[artivis]

@bradbell, Thanks for the quick fix 👍 .
I'll give it a try asap.

[artivis]

I can confirm that the issue is fixed. Thanks again @bradbell.