import numpy as np

def is_equal(x, y):
    """Test whether two complex numbers are equal with special consideration for NaNs.

    Parameters
    ----------
    x : complex
        First input number.
    y : complex
        Second input number.

    Returns
    -------
    bool
        Boolean indicating whether two complex numbers are equal.

    Examples
    --------
    >>> import numpy as np
    >>> is_equal(complex(np.nan, np.nan), complex(np.nan, np.nan))
    True
    """
    re1 = y.real
    im1 = y.imag

    re2 = x.real
    im2 = x.imag
    if re1 == re1:
        if im1 == im1:
            # Second value has non-NaN real and imaginary components, so test for component equality:
            return (re1 == re2) and (im1 == im2)
        
        if im2 == im2:
            # Second value has a NaN imaginary component, but first value does not:
            return False
        
        # Both values have NaN imaginary components:
        return True

    if im1 == im1:
        # Second value has a NaN real component, but a non-NaN imaginary component...
        if re2 == re2:
            # First value has a non-NaN real component:
            return False
        
        # Both values have NaN real components, so test for imaginary component equality:
        return (im1 == im2)

    if re2 == re2 or im2 == im2:
        # Second value has real and imaginary components which are NaN, but first value does not:
        return False

    # Both values have real and imaginary components which are NaN:
    return True

def compare(v, e):
    actual = np.expm1(v) 
    print('Value: {value}'.format(value=str(v)))
    print('Actual: {actual}'.format(actual=str(actual)))
    print('Expected: {expected}'.format(expected=str(e)))
    print('Equal: {is_equal}'.format(is_equal=str(is_equal(actual, e))))
    print('\n')

# Case 1
v = complex(np.inf, 0.0)
e = complex(np.inf, 0.0)
compare(v, e) # np.exmp1 returns (inf+nanj), vs np.exp(complex(np.inf, 0.0))-1.0 == (inf+0j)

# Case 2
v = complex(-np.inf, np.inf)
e = complex(-1.0, 0.0)
compare(v, e) # np.exmp1 returns (nan+nanj), vs np.exp(complex(-np.inf, np.inf))-1.0 == (-1+0j)

# Case 3
v = complex(-np.inf, np.nan)
e = complex(-1.0, 0.0)
compare(v, e) # np.exmp1 returns (nan+nanj), vs np.exp(complex(-np.inf, np.nan))-1.0 == (-1+0j)

# Case 4
v = complex(np.nan, 0.0)
e = complex(np.nan, 0.0)
compare(v, e) # np.exmp1 returns (nan+nanj), vs np.exp(complex(np.nan, 0.0))-1.0 == (nan+0j)