diff --git a/core/modules/update/update.module b/core/modules/update/update.module
index d9aa464..6f31c56 100644
--- a/core/modules/update/update.module
+++ b/core/modules/update/update.module
@@ -244,7 +244,7 @@ function update_menu() {
  * It both enforces the 'administer software updates' permission and the global
  * kill switch for the authorize.php script.
  *
- * @return
+ * @return bool
  *   TRUE if the current user can access the updater menu items; FALSE
  *   otherwise.
  *
@@ -372,11 +372,11 @@ function _update_no_data() {
  * update_calculate_project_data() will be wrong and produce confusing, bogus
  * results.
  *
- * @param $refresh
+ * @param bool $refresh
  *   (optional) Boolean to indicate if this method should refresh the cache
  *   automatically if there's no data. Defaults to FALSE.
  *
- * @return
+ * @return array
  *   Array of data about available releases, keyed by project shortname.
  *
  * @see update_refresh()
@@ -436,7 +436,7 @@ function update_get_available($refresh = FALSE) {
 /**
  * Creates a new fetch task after loading the necessary include file.
  *
- * @param $project
+ * @param array $project
  *   Associative array of information about a project. See update_get_projects()
  *   for the keys used.
  *
@@ -470,7 +470,7 @@ function update_fetch_data() {
 /**
  * Returns all currently cached data about available releases for all projects.
  *
- * @return
+ * @return array
  *   Array of data about available releases, keyed by project shortname.
  */
 function _update_get_cached_available_releases() {
@@ -495,11 +495,11 @@ function _update_get_cached_available_releases() {
  *
  * Constructs the e-mail notification message when the site is out of date.
  *
- * @param $key
+ * @param string $key
  *   Unique key to indicate what message to build, always 'status_notify'.
- * @param $message
+ * @param array $message
  *   Reference to the message array being built.
- * @param $params
+ * @param array $params
  *   Array of parameters to indicate what kind of text to include in the message
  *   body. This is a keyed array of message type ('core' or 'contrib') as the
  *   keys, and the status reason constant (UPDATE_NOT_SECURE, etc) for the
@@ -536,18 +536,18 @@ function update_mail($key, &$message, $params) {
  * site-wide status report at admin/reports/status and in the body of the
  * notification e-mail messages generated by update_cron().
  *
- * @param $msg_type
+ * @param string $msg_type
  *   String to indicate what kind of message to generate. Can be either 'core'
  *   or 'contrib'.
- * @param $msg_reason
+ * @param int $msg_reason
  *   Integer constant specifying why message is generated.
- * @param $report_link
+ * @param bool $report_link
  *   (optional) Boolean that controls if a link to the updates report should be
  *   added. Defaults to FALSE.
- * @param $langcode
+ * @param string $langcode
  *   (optional) A language code to use. Defaults to NULL.
  *
- * @return
+ * @return string
  *   The properly translated error message for the given key.
  */
 function _update_message_text($msg_type, $msg_reason, $report_link = FALSE, $langcode = NULL) {
@@ -623,6 +623,17 @@ function _update_message_text($msg_type, $msg_reason, $report_link = FALSE, $lan
  * Orders projects based on their status.
  *
  * Callback for uasort() within update_requirements().
+ *
+ * @param array $a
+ *   Associative array of information about a project. See update_get_projects()
+ *   for the keys used.
+ * @param array $b
+ *   Associative array of information about a project. See update_get_projects()
+ *   for the keys used.
+ *
+ * @return int
+ *
+ * @see update_requirements()
  */
 function _update_project_status_sort($a, $b) {
   // The status constants are numerically in the right order, so we can
@@ -641,10 +652,13 @@ function _update_project_status_sort($a, $b) {
  * provides a "Check manually" link that refreshes the available update and
  * redirects back to the same page.
  *
- * @param $variables
+ * @param array $variables
  *   An associative array containing:
  *   - last: The timestamp when the site last checked for available updates.
  *
+ * @return string
+ *   Rendered HTML for the last time we checked for update data.
+ *
  * @see theme_update_report()
  * @see theme_update_available_updates_form()
  * @ingroup themeable
@@ -748,11 +762,11 @@ function update_verify_update_archive($project, $archive_file, $directory) {
 /**
  * Stores data in the private update status cache table.
  *
- * @param $cid
+ * @param string $cid
  *   The cache ID to save the data with.
- * @param $data
+ * @param mixed $data
  *   The data to store.
- * @param $expire
+ * @param int $expire
  *   One of the following values:
  *   - CacheBackendInterface::CACHE_PERMANENT: Indicates that the item should
  *     never be removed except by explicitly using _update_cache_clear().
@@ -783,10 +797,10 @@ function _update_cache_set($cid, $data, $expire) {
 /**
  * Retrieves data from the private update status cache table.
  *
- * @param $cid
+ * @param string $cid
  *   The cache ID to retrieve.
  *
- * @return
+ * @return array
  *   An array of data for the given cache ID, or NULL if the ID was not found.
  *
  * @see _update_cache_set()
@@ -807,7 +821,7 @@ function _update_cache_get($cid) {
  * @param string $cid_prefix
  *   The cache ID prefix.
  *
- * @return
+ * @return array
  *   Associative array of cache items, keyed by cache ID.
  */
 function _update_get_cache_multiple($cid_prefix) {
@@ -830,11 +844,11 @@ function _update_get_cache_multiple($cid_prefix) {
 /**
  * Invalidates cached data relating to update status.
  *
- * @param $cid
+ * @param string $cid
  *   (optional) Cache ID of the record to clear from the private update module
  *   cache. If empty, all records will be cleared from the table except fetch
  *   tasks. Defaults to NULL.
- * @param $wildcard
+ * @param bool $wildcard
  *   (optional) If TRUE, cache IDs starting with $cid are deleted in addition to
  *   the exact cache ID specified by $cid. Defaults to FALSE.
  */
@@ -886,7 +900,7 @@ function update_cache_flush() {
 /**
  * Returns a short unique identifier for this Drupal installation.
  *
- * @return
+ * @return string
  *   An eight character string uniquely identifying this Drupal installation.
  */
 function _update_manager_unique_identifier() {
@@ -900,11 +914,11 @@ function _update_manager_unique_identifier() {
 /**
  * Returns the directory where update archive files should be extracted.
  *
- * @param $create
+ * @param bool $create
  *   (optional) Whether to attempt to create the directory if it does not
  *   already exist. Defaults to TRUE.
  *
- * @return
+ * @return string
  *   The full path to the temporary directory where update file archives should
  *   be extracted.
  */
@@ -922,11 +936,11 @@ function _update_manager_extract_directory($create = TRUE) {
 /**
  * Returns the directory where update archive files should be cached.
  *
- * @param $create
+ * @param bool $create
  *   (optional) Whether to attempt to create the directory if it does not
  *   already exist. Defaults to TRUE.
  *
- * @return
+ * @return string
  *   The full path to the temporary directory where update file archives should
  *   be cached.
  */
@@ -973,7 +987,7 @@ function update_clear_update_disk_cache() {
  * left alone by tar and correctly set to the time the archive file was
  * unpacked.
  *
- * @param $path
+ * @param string $path
  *   A string containing a file path or (streamwrapper) URI.
  */
 function update_delete_file_if_stale($path) {