BUG#27927:Partition pruning not optimal with TO_DAYS and YEAR functions

- Introduced val_int_endpoint() function which converts between func 
  argument intervals and func value intervals for monotonic functions.
- Made partition interval analyzer use part_expr->val_int_endpoint()
  to check if the edge values should be included.

mysql-test/r/partition_pruning.result

@@ -911,3 +911,31 @@ explain partitions select * from t1 where a>-2 and a <=0;
 id	select_type	table	partitions	type	possible_keys	key	key_len	ref	rows	Extra
 1	SIMPLE	t1	p3	ALL	NULL	NULL	NULL	NULL	4	Using where
 drop table t1;
+CREATE TABLE t1 ( recdate  DATETIME NOT NULL )
+PARTITION BY RANGE( TO_DAYS(recdate) ) (
+PARTITION p0 VALUES LESS THAN ( TO_DAYS('2007-03-08') ),
+PARTITION p1 VALUES LESS THAN ( TO_DAYS('2007-04-01') )
+);
+INSERT INTO t1 VALUES ('2007-03-01 12:00:00');
+INSERT INTO t1 VALUES ('2007-03-07 12:00:00');
+INSERT INTO t1 VALUES ('2007-03-08 12:00:00');
+INSERT INTO t1 VALUES ('2007-03-15 12:00:00');
+must use p0 only:
+explain partitions select * from t1 where recdate < '2007-03-08 00:00:00';
+id	select_type	table	partitions	type	possible_keys	key	key_len	ref	rows	Extra
+1	SIMPLE	t1	p0	ALL	NULL	NULL	NULL	NULL	2	Using where
+drop table t1;
+CREATE TABLE t1 ( recdate  DATETIME NOT NULL )
+PARTITION BY RANGE( YEAR(recdate) ) (
+PARTITION p0 VALUES LESS THAN (2006),
+PARTITION p1 VALUES LESS THAN (2007)
+);
+INSERT INTO t1 VALUES ('2005-03-01 12:00:00');
+INSERT INTO t1 VALUES ('2005-03-01 12:00:00');
+INSERT INTO t1 VALUES ('2006-03-01 12:00:00');
+INSERT INTO t1 VALUES ('2006-03-01 12:00:00');
+must use p0 only:
+explain partitions select * from t1 where recdate < '2006-01-01 00:00:00';
+id	select_type	table	partitions	type	possible_keys	key	key_len	ref	rows	Extra
+1	SIMPLE	t1	p0	ALL	NULL	NULL	NULL	NULL	2	Using where
+drop table t1;

mysql-test/t/partition_pruning.test

@@ -761,3 +761,34 @@ insert into t1 values (-15),(-5),(5),(15),(-15),(-5),(5),(15);
 explain partitions select * from t1 where a>-2 and a <=0;
 drop table t1;
 
+
+#
+# BUG#27927 Partition pruning not optimal with TO_DAYS function
+# 
+
+CREATE TABLE t1 ( recdate  DATETIME NOT NULL )
+PARTITION BY RANGE( TO_DAYS(recdate) ) (
+  PARTITION p0 VALUES LESS THAN ( TO_DAYS('2007-03-08') ),
+  PARTITION p1 VALUES LESS THAN ( TO_DAYS('2007-04-01') )
+);
+INSERT INTO t1 VALUES ('2007-03-01 12:00:00');
+INSERT INTO t1 VALUES ('2007-03-07 12:00:00');
+INSERT INTO t1 VALUES ('2007-03-08 12:00:00');
+INSERT INTO t1 VALUES ('2007-03-15 12:00:00');
+-- echo must use p0 only:
+explain partitions select * from t1 where recdate < '2007-03-08 00:00:00';
+
+drop table t1;
+CREATE TABLE t1 ( recdate  DATETIME NOT NULL )
+PARTITION BY RANGE( YEAR(recdate) ) (
+  PARTITION p0 VALUES LESS THAN (2006),
+  PARTITION p1 VALUES LESS THAN (2007)
+);
+INSERT INTO t1 VALUES ('2005-03-01 12:00:00');
+INSERT INTO t1 VALUES ('2005-03-01 12:00:00');
+INSERT INTO t1 VALUES ('2006-03-01 12:00:00');
+INSERT INTO t1 VALUES ('2006-03-01 12:00:00');
+
+-- echo must use p0 only:
+explain partitions select * from t1 where recdate < '2006-01-01 00:00:00';
+drop table t1;

sql/item.cc

@@ -2069,6 +2069,11 @@ Item *Item_field::get_tmp_table_item(THD *thd)
   return new_item;
 }
 
+longlong Item_field::val_int_endpoint(bool left_endp, bool *incl_endp)
+{
+  longlong res= val_int();
+  return null_value? LONGLONG_MIN : res;
+}
 
 /*
   Create an item from a string we KNOW points to a valid longlong

sql/item.h

@@ -569,6 +569,43 @@ class Item {
   virtual enum_monotonicity_info get_monotonicity_info() const
   { return NON_MONOTONIC; }
 
+  /*
+    Convert "func_arg $CMP$ const" half-interval into "FUNC(func_arg) $CMP2$ const2"
+
+    SYNOPSIS
+      val_int_endpoint()
+        left_endp  FALSE  <=> The interval is "x < const" or "x <= const"
+                   TRUE   <=> The interval is "x > const" or "x >= const"
+
+        incl_endp  IN   TRUE <=> the comparison is '<' or '>'
+                        FALSE <=> the comparison is '<=' or '>='
+                   OUT  The same but for the "F(x) $CMP$ F(const)" comparison
+
+    DESCRIPTION
+      This function is defined only for unary monotonic functions. The caller
+      supplies the source half-interval
+
+         x $CMP$ const
+
+      The value of const is supplied implicitly as the value this item's
+      argument, the form of $CMP$ comparison is specified through the
+      function's arguments. The calle returns the result interval
+         
+         F(x) $CMP2$ F(const)
+      
+      passing back F(const) as the return value, and the form of $CMP2$ 
+      through the out parameter. NULL values are assumed to be comparable and
+      be less than any non-NULL values.
+
+    RETURN
+      The output range bound, which equal to the value of val_int()
+        - If the value of the function is NULL then the bound is the 
+          smallest possible value of LONGLONG_MIN 
+  */
+  virtual longlong val_int_endpoint(bool left_endp, bool *incl_endp)
+  { DBUG_ASSERT(0); }
+
+
   /* valXXX methods must return NULL or 0 or 0.0 if null_value is set. */
   /*
     Return double precision floating point representation of item.
@@ -1401,6 +1438,7 @@ class Item_field :public Item_ident
   {
     return MONOTONIC_STRICT_INCREASING;
   }
+  longlong val_int_endpoint(bool left_endp, bool *incl_endp);
   Field *get_tmp_table_field() { return result_field; }
   Field *tmp_table_field(TABLE *t_arg) { return result_field; }
   bool get_date(MYSQL_TIME *ltime,uint fuzzydate);

sql/item_timefunc.cc

@@ -962,6 +962,44 @@ enum_monotonicity_info Item_func_to_days::get_monotonicity_info() const
 }
 
 
+longlong Item_func_to_days::val_int_endpoint(bool left_endp, bool *incl_endp)
+{
+  DBUG_ASSERT(fixed == 1);
+  MYSQL_TIME ltime;
+  longlong res;
+  if (get_arg0_date(&ltime, TIME_NO_ZERO_DATE))
+  {
+    /* got NULL, leave the incl_endp intact */
+    return LONGLONG_MIN;
+  }
+  res=(longlong) calc_daynr(ltime.year,ltime.month,ltime.day);
+  
+  if (args[0]->field_type() == MYSQL_TYPE_DATE)
+  {
+    // TO_DAYS() is strictly monotonic for dates, leave incl_endp intact
+    return res;
+  }
+ 
+  /*
+    Handle the special but practically useful case of datetime values that
+    point to day bound ("strictly less" comparison stays intact):
+
+      col < '2007-09-15 00:00:00'  -> TO_DAYS(col) <  TO_DAYS('2007-09-15')
+
+    which is different from the general case ("strictly less" changes to
+    "less or equal"):
+
+      col < '2007-09-15 12:34:56'  -> TO_DAYS(col) <= TO_DAYS('2007-09-15')
+  */
+  if (!left_endp && !(ltime.hour || ltime.minute || ltime.second ||
+                      ltime.second_part))
+    ; /* do nothing */
+  else
+    *incl_endp= TRUE;
+  return res;
+}
+
+
 longlong Item_func_dayofyear::val_int()
 {
   DBUG_ASSERT(fixed == 1);
@@ -1152,7 +1190,7 @@ longlong Item_func_year::val_int()
   Get information about this Item tree monotonicity
 
   SYNOPSIS
-    Item_func_to_days::get_monotonicity_info()
+    Item_func_year::get_monotonicity_info()
 
   DESCRIPTION
   Get information about monotonicity of the function represented by this item
@@ -1171,6 +1209,37 @@ enum_monotonicity_info Item_func_year::get_monotonicity_info() const
   return NON_MONOTONIC;
 }
 
+
+longlong Item_func_year::val_int_endpoint(bool left_endp, bool *incl_endp)
+{
+  DBUG_ASSERT(fixed == 1);
+  MYSQL_TIME ltime;
+  if (get_arg0_date(&ltime, TIME_FUZZY_DATE))
+  {
+    /* got NULL, leave the incl_endp intact */
+    return LONGLONG_MIN;
+  }
+
+  /*
+    Handle the special but practically useful case of datetime values that
+    point to year bound ("strictly less" comparison stays intact) :
+
+      col < '2007-01-01 00:00:00'  -> YEAR(col) <  2007
+
+    which is different from the general case ("strictly less" changes to
+    "less or equal"):
+
+      col < '2007-09-15 23:00:00'  -> YEAR(col) <= 2007
+  */
+  if (!left_endp && ltime.day == 1 && ltime.month == 1 && 
+      !(ltime.hour || ltime.minute || ltime.second || ltime.second_part))
+    ; /* do nothing */
+  else
+    *incl_endp= TRUE;
+  return ltime.year;
+}
+
+
 longlong Item_func_unix_timestamp::val_int()
 {
   MYSQL_TIME ltime;

sql/item_timefunc.h

@@ -68,6 +68,7 @@ class Item_func_to_days :public Item_int_func
     maybe_null=1; 
   }
   enum_monotonicity_info get_monotonicity_info() const;
+  longlong val_int_endpoint(bool left_endp, bool *incl_endp);
   bool check_partition_func_processor(uchar *int_arg) {return FALSE;}
 };
 
@@ -248,6 +249,7 @@ class Item_func_year :public Item_int_func
   longlong val_int();
   const char *func_name() const { return "year"; }
   enum_monotonicity_info get_monotonicity_info() const;
+  longlong val_int_endpoint(bool left_endp, bool *incl_endp);
   void fix_length_and_dec()
   { 
     decimals=0;

sql/partition_info.h

@@ -139,20 +139,6 @@ class partition_info : public Sql_alloc
   */
   get_partitions_in_range_iter get_subpart_iter_for_interval;
   
-  /*
-    Valid iff
-    get_part_iter_for_interval=get_part_iter_for_interval_via_walking:
-      controls how we'll process "field < C" and "field > C" intervals.
-      If the partitioning function F is strictly increasing, then for any x, y
-      "x < y" => "F(x) < F(y)" (*), i.e. when we get interval "field < C" 
-      we can perform partition pruning on the equivalent "F(field) < F(C)".
-
-      If the partitioning function not strictly increasing (it is simply
-      increasing), then instead of (*) we get "x < y" => "F(x) <= F(y)"
-      i.e. for interval "field < C" we can perform partition pruning for
-      "F(field) <= F(C)".
-  */
-  bool range_analysis_include_bounds;
   /********************************************
    * INTERVAL ANALYSIS ENDS 
    ********************************************/

sql/sql_partition.cc

@@ -2743,7 +2743,8 @@ uint32 get_list_array_idx_for_endpoint(partition_info *part_info,
   uint min_list_index= 0, max_list_index= part_info->no_list_values - 1;
   longlong list_value;
   /* Get the partitioning function value for the endpoint */
-  longlong part_func_value= part_val_int(part_info->part_expr);
+  longlong part_func_value= 
+    part_info->part_expr->val_int_endpoint(left_endpoint, &include_endpoint);
   bool unsigned_flag= part_info->part_expr->unsigned_flag;
   DBUG_ENTER("get_list_array_idx_for_endpoint");
 
@@ -2887,7 +2888,9 @@ uint32 get_partition_id_range_for_endpoint(partition_info *part_info,
   uint max_partition= part_info->no_parts - 1;
   uint min_part_id= 0, max_part_id= max_partition, loc_part_id;
   /* Get the partitioning function value for the endpoint */
-  longlong part_func_value= part_val_int(part_info->part_expr);
+  longlong part_func_value= 
+    part_info->part_expr->val_int_endpoint(left_endpoint, &include_endpoint);
+
   bool unsigned_flag= part_info->part_expr->unsigned_flag;
   DBUG_ENTER("get_partition_id_range_for_endpoint");
 
@@ -6590,8 +6593,6 @@ void make_used_partitions_str(partition_info *part_info, String *parts_str)
 #ifdef WITH_PARTITION_STORAGE_ENGINE
 static void set_up_range_analysis_info(partition_info *part_info)
 {
-  enum_monotonicity_info minfo;
-
   /* Set the catch-all default */
   part_info->get_part_iter_for_interval= NULL;
   part_info->get_subpart_iter_for_interval= NULL;
@@ -6603,11 +6604,8 @@ static void set_up_range_analysis_info(partition_info *part_info)
   switch (part_info->part_type) {
   case RANGE_PARTITION:
   case LIST_PARTITION:
-    minfo= part_info->part_expr->get_monotonicity_info();
-    if (minfo != NON_MONOTONIC)
+    if (part_info->part_expr->get_monotonicity_info() != NON_MONOTONIC)
     {
-      part_info->range_analysis_include_bounds=
-        test(minfo == MONOTONIC_INCREASING);
       part_info->get_part_iter_for_interval=
         get_part_iter_for_interval_via_mapping;
       goto setup_subparts;
@@ -6775,8 +6773,7 @@ int get_part_iter_for_interval_via_mapping(partition_info *part_info,
         index-in-ordered-array-of-list-constants (for LIST) space.
       */
       store_key_image_to_rec(field, min_value, field_len);
-      bool include_endp= part_info->range_analysis_include_bounds ||
-                         !test(flags & NEAR_MIN);
+      bool include_endp= !test(flags & NEAR_MIN);
       part_iter->part_nums.start= get_endpoint(part_info, 1, include_endp);
       part_iter->part_nums.cur= part_iter->part_nums.start;
       if (part_iter->part_nums.start == max_endpoint_val)
@@ -6790,8 +6787,7 @@ int get_part_iter_for_interval_via_mapping(partition_info *part_info,
   else
   {
     store_key_image_to_rec(field, max_value, field_len);
-    bool include_endp= part_info->range_analysis_include_bounds ||
-                       !test(flags & NEAR_MAX);
+    bool include_endp= !test(flags & NEAR_MAX);
     part_iter->part_nums.end= get_endpoint(part_info, 0, include_endp);
     if (part_iter->part_nums.start == part_iter->part_nums.end &&
         !part_iter->ret_null_part)