def gradient_descent(x, y, w_in, b_in, alpha, num_iters, cost_function, gradient_function):
    """
    Performs gradient descent to fit w,b. Updates w,b by taking
    num_iters gradient steps with learning rate alpha

    Args:
        x (ndarray (m,))  : Data, m examples
        y (ndarray (m,))  : target values
        w_in,b_in (scalar): initial values of model parameters
        alpha (float):     Learning rate
        num_iters (int):   number of iterations to run gradient descent
        cost_function:     function to call to produce cost
        gradient_function: function to call to produce gradient

    Returns:
        w (scalar): Updated value of parameter after running gradient descent
        b (scalar): Updated value of parameter after running gradient descent
        J_history (List): History of cost values
        p_history (list): History of parameters [w,b]
        """

    w = copy.deepcopy(w_in) # avoid modifying global w_in
    # An array to store cost J and w's at each iteration primarily for graphing later
    J_history = []
    p_history = []
    b = b_in
    w = w_in

    for i in range(num_iters):
        # Calculate the gradient and update the parameters using gradient_function
        dj_dw, dj_db = gradient_function(x, y, w , b)

        # Update Parameters using equation (3) above
        b = b - alpha * dj_db
        w = w - alpha * dj_dw

        # Save cost J at each iteration
        if i<100000:      # prevent resource exhaustion
            J_history.append( cost_function(x, y, w , b))
            p_history.append([w,b])
        # Print cost every at intervals 10 times or as many iterations if < 10
        if i% math.ceil(num_iters/10) == 0:
            print(f"Iteration {i:4}: Cost {J_history[-1]:0.2e} ",
                    f"dj_dw: {dj_dw: 0.3e}, dj_db: {dj_db: 0.3e}  ",f"w: {w: 0.3e}, b:{b: 0.5e}")

    return w, b, J_history, p_history #return w and J,w history for graphing
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