// the _3 prefix has to match the id of the form you have created
add_action( "gform_after_submission_20", "login_form_after_submission_20", 10, 2 );
function login_form_after_submission_20($entry, $form) {
    // get the username and pass
    $username = $entry[1];
    $pass = $entry[2];
    $creds = array();
    // create the credentials array
    $creds['user_login'] = $username;
    $creds['user_password'] = $pass;
    // sign in the user and set him as the logged in user
    $sign = wp_signon( $creds );
    wp_set_current_user( $sign->ID );
}


// the _3 prefix has to match the id of the form you have created
add_filter( "gform_field_validation_20", "login_validate_field_20", 10, 4 );
function login_validate_field_20($result, $value, $form, $field) {
    // make sure this variable is global
    // this function is fired via recurrence for each field, s
    global $user;
    // validate username
    if ( $field['cssClass'] === 'username' ) {
        $user = get_user_by( 'login', $value );
        if ( empty( $user->user_login ) ) {
            $result["is_valid"] = false;
            $result["message"] = "Invalid username provided.";
        }
    }
    // validate pass
    if ( $field['cssClass'] === 'password' ) {
        if ( !$user or !wp_check_password( $value, $user->data->user_pass, $user->ID ) ) {
            $result["is_valid"] = false;
            $result["message"] = "Invalid password provided.";
        }
    }
    return $result;
}