@njit
def get_grid_nodes(grid):
    """
    Get the actual grid points from a grid tuple.
    """
    x_min, x_max, x_num = grid
    return np.linspace(x_min, x_max, x_num)

@njit
def linear_interp_1d_scalar(x_min, x_max, x_num, y_values, x_val):
    """Helper function for scalar interpolation"""
    x_nodes = np.linspace(x_min, x_max, x_num)

    # Extrapolation with linear extension
    if x_val <= x_nodes[0]:
        # Linear extrapolation using first two points
        if x_num >= 2:
            slope = (y_values[1] - y_values[0]) / (x_nodes[1] - x_nodes[0])
            return y_values[0] + slope * (x_val - x_nodes[0])
        else:
            return y_values[0]

    if x_val >= x_nodes[-1]:
        # Linear extrapolation using last two points
        if x_num >= 2:
            slope = (y_values[-1] - y_values[-2]) / (x_nodes[-1] - x_nodes[-2])
            return y_values[-1] + slope * (x_val - x_nodes[-1])
        else:
            return y_values[-1]

    # Binary search for the right interval
    left = 0
    right = x_num - 1
    while right - left > 1:
        mid = (left + right) // 2
        if x_nodes[mid] <= x_val:
            left = mid
        else:
            right = mid

    # Linear interpolation
    x_left = x_nodes[left]
    x_right = x_nodes[right]
    y_left = y_values[left]
    y_right = y_values[right]

    weight = (x_val - x_left) / (x_right - x_left)
    return y_left * (1 - weight) + y_right * weight

@njit
def linear_interp_1d(x_grid, y_values, x_query):
    """
    Perform 1D linear interpolation.
    """
    x_min, x_max, x_num = x_grid
    return linear_interp_1d_scalar(x_min, x_max, x_num, y_values, x_query[0])