struct read_ref_at_cb {
        const char *refname;
-       unsigned long at_time;
+       timestamp_t at_time;
        int cnt;
        int reccnt;
        unsigned char *sha1;
        unsigned char osha1[20];
        unsigned char nsha1[20];
        int tz;
-       unsigned long date;
+       timestamp_t date;
        char **msg;
-       unsigned long *cutoff_time;
+       timestamp_t *cutoff_time;
        int *cutoff_tz;
        int *cutoff_cnt;
 };
 
 static int read_ref_at_ent(struct object_id *ooid, struct object_id *noid,
-               const char *email, unsigned long timestamp, int tz,
+               const char *email, timestamp_t timestamp, int tz,
                const char *message, void *cb_data)
 {
        struct read_ref_at_cb *cb = cb_data;
 }
 
 static int read_ref_at_ent_oldest(struct object_id *ooid, struct object_id *noid,
-                                 const char *email, unsigned long timestamp,
+                                 const char *email, timestamp_t timestamp,
                                  int tz, const char *message, void *cb_data)
 {
        struct read_ref_at_cb *cb = cb_data;
        return 1;
 }
 
-int read_ref_at(const char *refname, unsigned int flags, unsigned long at_time, int cnt,
+int read_ref_at(const char *refname, unsigned int flags, timestamp_t at_time, int cnt,
                unsigned char *sha1, char **msg,
-               unsigned long *cutoff_time, int *cutoff_tz, int *cutoff_cnt)
+               timestamp_t *cutoff_time, int *cutoff_tz, int *cutoff_cnt)
 {
        struct read_ref_at_cb cb;