diff --git a/include/crm/common/util.h b/include/crm/common/util.h
index 686ca35cd3..e276123fa4 100644
--- a/include/crm/common/util.h
+++ b/include/crm/common/util.h
@@ -1,272 +1,274 @@
 /*
  * Copyright 2004-2020 the Pacemaker project contributors
  *
  * The version control history for this file may have further details.
  *
  * This source code is licensed under the GNU Lesser General Public License
  * version 2.1 or later (LGPLv2.1+) WITHOUT ANY WARRANTY.
  */
 
 #ifndef CRM_COMMON_UTIL__H
 #  define CRM_COMMON_UTIL__H
 
 #ifdef __cplusplus
 extern "C" {
 #endif
 
 /**
  * \file
  * \brief Utility functions
  * \ingroup core
  */
 
 #  include <sys/types.h>    // gid_t, mode_t, size_t, time_t, uid_t
 #  include <stdlib.h>
 #  include <stdbool.h>
 #  include <stdint.h>       // uint32_t
 #  include <limits.h>
 #  include <signal.h>
 #  include <glib.h>
 
 #  include <libxml/tree.h>
 
 #  include <crm/lrmd.h>
 #  include <crm/common/acl.h>
 #  include <crm/common/results.h>
 
 #  define ONLINESTATUS  "online"  // Status of an online client
 #  define OFFLINESTATUS "offline" // Status of an offline client
 
 // public name/value pair functions (from nvpair.c)
 int pcmk_scan_nvpair(const char *input, char **name, char **value);
 char *pcmk_format_nvpair(const char *name, const char *value, const char *units);
 char *pcmk_format_named_time(const char *name, time_t epoch_time);
 
 /* public Pacemaker Remote functions (from remote.c) */
 int crm_default_remote_port(void);
 
 /* public string functions (from strings.c) */
 char *crm_itoa_stack(int an_int, char *buf, size_t len);
 gboolean crm_is_true(const char *s);
 int crm_str_to_boolean(const char *s, int *ret);
 long long crm_parse_ll(const char *text, const char *default_text);
 int crm_parse_int(const char *text, const char *default_text);
 long long crm_get_msec(const char *input);
 char * crm_strip_trailing_newline(char *str);
 gboolean crm_strcase_equal(gconstpointer a, gconstpointer b);
 guint crm_strcase_hash(gconstpointer v);
 guint g_str_hash_traditional(gconstpointer v);
 char *crm_strdup_printf(char const *format, ...) __attribute__ ((__format__ (__printf__, 1, 2)));
 int pcmk_numeric_strcasecmp(const char *s1, const char *s2);
 
 #  define crm_str_hash g_str_hash_traditional
 
 static inline char *
 crm_itoa(int an_int)
 {
     return crm_strdup_printf("%d", an_int);
 }
 
 static inline char *
 crm_ftoa(double a_float)
 {
     return crm_strdup_printf("%f", a_float);
 }
 
 static inline char *
 crm_ttoa(time_t epoch_time)
 {
     return crm_strdup_printf("%lld", (long long) epoch_time);
 }
 
 /*!
  * \brief Create hash table with dynamically allocated string keys/values
  *
  * \return Newly allocated hash table
  * \note It is the caller's responsibility to free the result, using
  *       g_hash_table_destroy().
  */
 static inline GHashTable *
 crm_str_table_new(void)
 {
     return g_hash_table_new_full(crm_str_hash, g_str_equal, free, free);
 }
 
 /*!
  * \brief Create hash table with case-insensitive dynamically allocated string keys/values
  *
  * \return Newly allocated hash table
  * \note It is the caller's responsibility to free the result, using
  *       g_hash_table_destroy().
  */
 static inline GHashTable *
 crm_strcase_table_new(void)
 {
     return g_hash_table_new_full(crm_strcase_hash, crm_strcase_equal, free, free);
 }
 
 GHashTable *crm_str_table_dup(GHashTable *old_table);
 
 #  define crm_atoi(text, default_text) crm_parse_int(text, default_text)
 
 /* public I/O functions (from io.c) */
 void crm_build_path(const char *path_c, mode_t mode);
 
 guint crm_parse_interval_spec(const char *input);
 int char2score(const char *score);
 char *score2char(int score);
 char *score2char_stack(int score, char *buf, size_t len);
 
 /* public operation functions (from operations.c) */
 gboolean parse_op_key(const char *key, char **rsc_id, char **op_type,
                       guint *interval_ms);
 gboolean decode_transition_key(const char *key, char **uuid, int *transition_id,
                                int *action_id, int *target_rc);
 gboolean decode_transition_magic(const char *magic, char **uuid,
                                  int *transition_id, int *action_id,
                                  int *op_status, int *op_rc, int *target_rc);
 int rsc_op_expected_rc(lrmd_event_data_t *event);
 gboolean did_rsc_op_fail(lrmd_event_data_t *event, int target_rc);
 bool crm_op_needs_metadata(const char *rsc_class, const char *op);
 xmlNode *crm_create_op_xml(xmlNode *parent, const char *prefix,
                            const char *task, const char *interval_spec,
                            const char *timeout);
 #define CRM_DEFAULT_OP_TIMEOUT_S "20s"
 
 // Public resource agent functions (from agents.c)
 
 // Capabilities supported by a resource agent standard
 enum pcmk_ra_caps {
     pcmk_ra_cap_none         = 0,
     pcmk_ra_cap_provider     = (1 << 0), // Requires provider
     pcmk_ra_cap_status       = (1 << 1), // Supports status instead of monitor
     pcmk_ra_cap_params       = (1 << 2), // Supports parameters
     pcmk_ra_cap_unique       = (1 << 3), // Supports unique clones
     pcmk_ra_cap_promotable   = (1 << 4), // Supports promotable clones
     pcmk_ra_cap_stdin        = (1 << 5), // Reads from standard input
     pcmk_ra_cap_fence_params = (1 << 6), // Supports pcmk_monitor_timeout, etc.
 };
 
 uint32_t pcmk_get_ra_caps(const char *standard);
 char *crm_generate_ra_key(const char *standard, const char *provider,
                           const char *type);
 int crm_parse_agent_spec(const char *spec, char **standard, char **provider,
                          char **type);
 
 
 int compare_version(const char *version1, const char *version2);
 
 /* coverity[+kill] */
 void crm_abort(const char *file, const char *function, int line,
                const char *condition, gboolean do_core, gboolean do_fork);
 
 /*!
  * \brief Check whether any of specified flags are set in a flag group
  *
  * \param[in] flag_group        The flag group being examined
  * \param[in] flags_to_check    Which flags in flag_group should be checked
  *
- * \return true if any of flags_to_check are set in flag_group
+ * \return true if \p flags_to_check is nonzero and any of its flags are set in
+ *         \p flag_group, or false otherwise
  */
 static inline bool
 pcmk_any_flags_set(uint64_t flag_group, uint64_t flags_to_check)
 {
     return (flag_group & flags_to_check) != 0;
 }
 
 /*!
  * \brief Check whether all of specified flags are set in a flag group
  *
  * \param[in] flag_group        The flag group being examined
  * \param[in] flags_to_check    Which flags in flag_group should be checked
  *
- * \return true if all of flags_to_check are set in flag_group
+ * \return true if \p flags_to_check is zero or all of its flags are set in
+ *         \p flag_group, or false otherwise
  */
 static inline bool
 pcmk_all_flags_set(uint64_t flag_group, uint64_t flags_to_check)
 {
     return (flag_group & flags_to_check) == flags_to_check;
 }
 
 /*!
  * \brief Convenience alias for pcmk_all_flags_set(), to check single flag
  */
 #define pcmk_is_set(g, f)   pcmk_all_flags_set((g), (f))
 
 static inline guint
 crm_hash_table_size(GHashTable * hashtable)
 {
     if (hashtable == NULL) {
         return 0;
     }
     return g_hash_table_size(hashtable);
 }
 
 char *crm_meta_name(const char *field);
 const char *crm_meta_value(GHashTable * hash, const char *field);
 
 char *crm_md5sum(const char *buffer);
 
 char *crm_generate_uuid(void);
 bool crm_is_daemon_name(const char *name);
 
 int crm_user_lookup(const char *name, uid_t * uid, gid_t * gid);
 int pcmk_daemon_user(uid_t *uid, gid_t *gid);
 
 #ifdef HAVE_GNUTLS_GNUTLS_H
 void crm_gnutls_global_init(void);
 #endif
 
 char *pcmk_hostname(void);
 
 bool pcmk_str_is_infinity(const char *s);
 bool pcmk_str_is_minus_infinity(const char *s);
 
 #ifndef PCMK__NO_COMPAT
 /* Everything here is deprecated and kept only for public API backward
  * compatibility. It will be moved to compatibility.h in a future release.
  */
 
 //! \deprecated Use crm_parse_interval_spec() instead
 #define crm_get_interval crm_parse_interval_spec
 
 //! \deprecated Use !pcmk_is_set() or !pcmk_all_flags_set() instead
 static inline gboolean
 is_not_set(long long word, long long bit)
 {
     return ((word & bit) == 0);
 }
 
 //! \deprecated Use pcmk_is_set() or pcmk_all_flags_set() instead
 static inline gboolean
 is_set(long long word, long long bit)
 {
     return ((word & bit) == bit);
 }
 
 //! \deprecated Use pcmk_any_flags_set() instead
 static inline gboolean
 is_set_any(long long word, long long bit)
 {
     return ((word & bit) != 0);
 }
 
 //! \deprecated Use pcmk_get_ra_caps() instead
 bool crm_provider_required(const char *standard);
 
 //! \deprecated Use strcmp or strcasecmp instead
 gboolean crm_str_eq(const char *a, const char *b, gboolean use_case);
 
 //! \deprecated Use strcmp instead
 gboolean safe_str_neq(const char *a, const char *b);
 
 //! \deprecated Use strcasecmp instead
 #define safe_str_eq(a, b) crm_str_eq(a, b, FALSE)
 
 #endif // PCMK__NO_COMPAT
 
 #ifdef __cplusplus
 }
 #endif
 
 #endif
diff --git a/lib/common/tests/flags/pcmk_all_flags_set.c b/lib/common/tests/flags/pcmk_all_flags_set.c
index 6251d5f387..222ed10d88 100644
--- a/lib/common/tests/flags/pcmk_all_flags_set.c
+++ b/lib/common/tests/flags/pcmk_all_flags_set.c
@@ -1,35 +1,37 @@
 /*
  * Copyright 2020 the Pacemaker project contributors
  *
  * The version control history for this file may have further details.
  *
  * This source code is licensed under the GNU Lesser General Public License
  * version 2.1 or later (LGPLv2.1+) WITHOUT ANY WARRANTY.
  */
 
 #include <crm_internal.h>
 
 static void
 all_set(void) {
     g_assert(pcmk_all_flags_set(0x000, 0x003) == false);
     g_assert(pcmk_all_flags_set(0x00f, 0x003) == true);
     g_assert(pcmk_all_flags_set(0x00f, 0x010) == false);
     g_assert(pcmk_all_flags_set(0x00f, 0x011) == false);
+    g_assert(pcmk_all_flags_set(0x000, 0x000) == true);
+    g_assert(pcmk_all_flags_set(0x00f, 0x000) == true);
 }
 
 static void
 one_is_set(void) {
     // pcmk_is_set() is a simple macro alias for pcmk_all_flags_set()
     g_assert(pcmk_is_set(0x00f, 0x001) == true);
     g_assert(pcmk_is_set(0x00f, 0x010) == false);
 }
 
 int
 main(int argc, char **argv)
 {
     g_test_init(&argc, &argv, NULL);
 
     g_test_add_func("/common/flags/all_set/all_set", all_set);
     g_test_add_func("/common/flags/all_set/is_set", one_is_set);
     return g_test_run();
 }
diff --git a/lib/common/tests/flags/pcmk_any_flags_set.c b/lib/common/tests/flags/pcmk_any_flags_set.c
index 190750b936..f2f468c147 100644
--- a/lib/common/tests/flags/pcmk_any_flags_set.c
+++ b/lib/common/tests/flags/pcmk_any_flags_set.c
@@ -1,28 +1,30 @@
 /*
  * Copyright 2020 the Pacemaker project contributors
  *
  * The version control history for this file may have further details.
  *
  * This source code is licensed under the GNU Lesser General Public License
  * version 2.1 or later (LGPLv2.1+) WITHOUT ANY WARRANTY.
  */
 
 #include <crm_internal.h>
 
 static void
 any_set(void) {
     g_assert(pcmk_any_flags_set(0x000, 0x000) == false);
     g_assert(pcmk_any_flags_set(0x000, 0x001) == false);
     g_assert(pcmk_any_flags_set(0x00f, 0x001) == true);
     g_assert(pcmk_any_flags_set(0x00f, 0x010) == false);
     g_assert(pcmk_any_flags_set(0x00f, 0x011) == true);
+    g_assert(pcmk_any_flags_set(0x000, 0x000) == false);
+    g_assert(pcmk_any_flags_set(0x00f, 0x000) == false);
 }
 
 int
 main(int argc, char **argv)
 {
     g_test_init(&argc, &argv, NULL);
 
     g_test_add_func("/common/flags/any_set/any_set", any_set);
     return g_test_run();
 }