_count_oracle0 = 0
_count_oracle1 = 0
_count_oracle2 = 0


def sigmoid(w):
    res = scipy.special.expit(w)
    return res

def predict(w):
    return sigmoid(X @ w)

def oracle0(w):
    p = X @ (w)
    res = -np.mean(y*p - np.logaddexp(0, p))
    global _count_oracle0
    _count_oracle0 += 1
    return res

def oracle1(w):
    global _count_oracle1
    _count_oracle1 += 1
    return X.T @ (predict(w) - y) / X.shape[0]

def oracle2(w, d):
    global _count_oracle2
    _count_oracle2 += 1
    res = X @ d
    res = (predict(w) * (1 - predict(w))) * res
    res = X.T @ res
    return res / X.shape[0]