how to add login /pass word on home page ?

I used the below code and works, only problem is it not compatible with W3 total cache. Even though I logged out, home page still shows as logged in, other pages shows as logged out. Any idea how to make it work as needed ?

<?php if ( !is_user_logged_in() ) : ?>

				<form name="login-form" id="login-form" action="<?php echo site_url( 'wp-login.php' ) ?>" method="post">
					<input type="text" name="log" id="user_login" value="<?php echo attribute_escape(stripslashes($user_login)); ?><?php _e( 'Username', 'buddypress' ) ?>" onfocus="if (this.value == '<?php _e( 'Username', 'buddypress' ) ?>') {this.value = '';}" onblur="if (this.value == '') {this.value = '<?php _e( 'Username', 'buddypress' ) ?>';}" />
					<input type="password" name="pwd" id="user_pass" class="input" value="" />

					<input type="checkbox" name="rememberme" id="rememberme" value="forever" title="<?php _e( 'Remember Me', 'buddypress' ) ?>" />

					<input type="submit" name="wp-submit" id="wp-submit" value="<?php _e( 'Log In', 'buddypress' ) ?>"/>		

						<input type="button" name="register" id="register" value="<?php _e( 'Register', 'buddypress' ) ?>" onclick="location.href='<?php echo bp_signup_page() ?>'" />

					<input type="hidden" name="redirect_to" value="<?php echo bp_root_domain() ?>" />
					<input type="hidden" name="testcookie" value="1" />

					<?php do_action( 'bp_login_bar_logged_out' ) ?>
				</form>

			<?php else : ?>

				        <div id="logout-link">
					<?php bp_loggedinuser_link() ?>   / <?php bp_log_out_link() ?>
					</div>
					<?php do_action( 'bp_login_bar_logged_in' ) ?>

			<?php endif; ?>