Commit 34d11713 authored by igor@rurik.mysql.com's avatar igor@rurik.mysql.com

Merge rurik.mysql.com:/home/igor/mysql-5.0-opt

into  rurik.mysql.com:/home/igor/dev-opt/mysql-5.0-opt-bug16081
parents 43e05210 0e96978c
......@@ -1126,7 +1126,7 @@ a b a b
7 8 7 5
EXPLAIN SELECT * FROM t1 LEFT JOIN t2 ON t1.a = t2.a WHERE t1.a = t2.a OR t1.a = t2.b;
id select_type table type possible_keys key key_len ref rows Extra
1 SIMPLE t2 ALL PRIMARY NULL NULL NULL 4 Using where
1 SIMPLE t2 ALL PRIMARY NULL NULL NULL 4
1 SIMPLE t1 eq_ref PRIMARY PRIMARY 4 test.t2.a 1
EXPLAIN SELECT * FROM t1 LEFT JOIN t2 ON t1.a = t2.a WHERE t1.a IN(t2.a, t2.b);
id select_type table type possible_keys key key_len ref rows Extra
......
......@@ -181,3 +181,128 @@ SELECT ROW(1,1,1) = ROW(1,1,1) as `1`, ROW(1,1,1) = ROW(1,2,1) as `0`, ROW(1,NUL
select row(NULL,1)=(2,0);
row(NULL,1)=(2,0)
0
CREATE TABLE t1 (a int, b int, PRIMARY KEY (a,b));
INSERT INTO t1 VALUES (1,1), (2,1), (3,1), (1,2), (3,2), (3,3);
EXPLAIN SELECT * FROM t1 WHERE a=3 AND b=2;
id select_type table type possible_keys key key_len ref rows Extra
1 SIMPLE t1 const PRIMARY PRIMARY 8 const,const 1 Using index
EXPLAIN SELECT * FROM t1 WHERE (a,b)=(3,2);
id select_type table type possible_keys key key_len ref rows Extra
1 SIMPLE t1 const PRIMARY PRIMARY 8 const,const 1 Using index
SELECT * FROM t1 WHERE a=3 and b=2;
a b
3 2
SELECT * FROM t1 WHERE (a,b)=(3,2);
a b
3 2
CREATE TABLE t2 (a int, b int, c int, PRIMARY KEY (a,b,c));
INSERT INTO t2 VALUES
(1,1,2), (3,1,3), (1,2,2), (4,4,2),
(1,1,1), (3,1,1), (1,2,1);
EXPLAIN SELECT * FROM t1,t2 WHERE t1.a=t2.a AND t1.b=t2.b;
id select_type table type possible_keys key key_len ref rows Extra
1 SIMPLE t1 index PRIMARY PRIMARY 8 NULL 6 Using index
1 SIMPLE t2 ref PRIMARY PRIMARY 8 test.t1.a,test.t1.b 1 Using index
EXPLAIN SELECT * FROM t1,t2 WHERE (t1.a,t1.b)=(t2.a,t2.b);
id select_type table type possible_keys key key_len ref rows Extra
1 SIMPLE t1 index PRIMARY PRIMARY 8 NULL 6 Using index
1 SIMPLE t2 ref PRIMARY PRIMARY 8 test.t1.a,test.t1.b 1 Using index
SELECT * FROM t1,t2 WHERE t1.a=t2.a and t1.b=t2.b;
a b a b c
1 1 1 1 1
1 1 1 1 2
1 2 1 2 1
1 2 1 2 2
3 1 3 1 1
3 1 3 1 3
SELECT * FROM t1,t2 WHERE (t1.a,t1.b)=(t2.a,t2.b);
a b a b c
1 1 1 1 1
1 1 1 1 2
1 2 1 2 1
1 2 1 2 2
3 1 3 1 1
3 1 3 1 3
EXPLAIN SELECT * FROM t1,t2 WHERE t1.a=t2.a AND t1.b=2;
id select_type table type possible_keys key key_len ref rows Extra
1 SIMPLE t1 index PRIMARY PRIMARY 8 NULL 5 Using where; Using index
1 SIMPLE t2 ref PRIMARY PRIMARY 4 test.t1.a 1 Using index
EXPLAIN SELECT * FROM t1,t2 WHERE (t1.a,t1.b)=(t2.a,2);
id select_type table type possible_keys key key_len ref rows Extra
1 SIMPLE t1 index PRIMARY PRIMARY 8 NULL 5 Using where; Using index
1 SIMPLE t2 ref PRIMARY PRIMARY 4 test.t1.a 1 Using index
SELECT * FROM t1,t2 WHERE t1.a=1 and t1.b=t2.b;
a b a b c
1 1 1 1 2
1 1 3 1 3
1 2 1 2 2
1 1 1 1 1
1 1 3 1 1
1 2 1 2 1
SELECT * FROM t1,t2 WHERE (t1.a,t1.b)=(t2.a,2);
a b a b c
1 2 1 1 1
1 2 1 1 2
1 2 1 2 1
1 2 1 2 2
3 2 3 1 1
3 2 3 1 3
EXPLAIN EXTENDED SELECT * FROM t1,t2 WHERE (t1.a,t1.b)=(t2.a,t2.b+1);
id select_type table type possible_keys key key_len ref rows Extra
1 SIMPLE t1 index PRIMARY PRIMARY 8 NULL 6 Using index
1 SIMPLE t2 ref PRIMARY PRIMARY 4 test.t1.a 1 Using where; Using index
Warnings:
Note 1003 select `test`.`t1`.`a` AS `a`,`test`.`t1`.`b` AS `b`,`test`.`t2`.`a` AS `a`,`test`.`t2`.`b` AS `b`,`test`.`t2`.`c` AS `c` from `test`.`t1` join `test`.`t2` where ((`test`.`t2`.`a` = `test`.`t1`.`a`) and (`test`.`t1`.`b` = (`test`.`t2`.`b` + 1)))
SELECT * FROM t1,t2 WHERE (t1.a,t1.b)=(t2.a,t2.b+1);
a b a b c
1 2 1 1 1
1 2 1 1 2
3 2 3 1 1
3 2 3 1 3
EXPLAIN EXTENDED SELECT * FROM t1,t2 WHERE (t1.a-1,t1.b)=(t2.a-1,t2.b+1);
id select_type table type possible_keys key key_len ref rows Extra
1 SIMPLE t1 index NULL PRIMARY 8 NULL 6 Using index
1 SIMPLE t2 index NULL PRIMARY 12 NULL 7 Using where; Using index
Warnings:
Note 1003 select `test`.`t1`.`a` AS `a`,`test`.`t1`.`b` AS `b`,`test`.`t2`.`a` AS `a`,`test`.`t2`.`b` AS `b`,`test`.`t2`.`c` AS `c` from `test`.`t1` join `test`.`t2` where (((`test`.`t1`.`a` - 1) = (`test`.`t2`.`a` - 1)) and (`test`.`t1`.`b` = (`test`.`t2`.`b` + 1)))
SELECT * FROM t1,t2 WHERE (t1.a-1,t1.b)=(t2.a-1,t2.b+1);
a b a b c
1 2 1 1 2
3 2 3 1 3
1 2 1 1 1
3 2 3 1 1
EXPLAIN SELECT * FROM t2 WHERE a=3 AND b=2;
id select_type table type possible_keys key key_len ref rows Extra
1 SIMPLE t2 ref PRIMARY PRIMARY 8 const,const 1 Using index
EXPLAIN SELECT * FROM t2 WHERE (a,b)=(3,2);
id select_type table type possible_keys key key_len ref rows Extra
1 SIMPLE t2 ref PRIMARY PRIMARY 8 const,const 1 Using index
SELECT * FROM t2 WHERE a=3 and b=2;
a b c
SELECT * FROM t2 WHERE (a,b)=(3,2);
a b c
EXPLAIN SELECT * FROM t1,t2 WHERE t2.a=t1.a AND t2.b=2 AND t2.c=1;
id select_type table type possible_keys key key_len ref rows Extra
1 SIMPLE t1 index PRIMARY PRIMARY 8 NULL 6 Using index
1 SIMPLE t2 eq_ref PRIMARY PRIMARY 12 test.t1.a,const,const 1 Using index
EXPLAIN EXTENDED SELECT * FROM t1,t2 WHERE (t2.a,(t2.b,t2.c))=(t1.a,(2,1));
id select_type table type possible_keys key key_len ref rows Extra
1 SIMPLE t1 index PRIMARY PRIMARY 8 NULL 6 Using index
1 SIMPLE t2 eq_ref PRIMARY PRIMARY 12 test.t1.a,const,const 1 Using index
Warnings:
Note 1003 select `test`.`t1`.`a` AS `a`,`test`.`t1`.`b` AS `b`,`test`.`t2`.`a` AS `a`,`test`.`t2`.`b` AS `b`,`test`.`t2`.`c` AS `c` from `test`.`t1` join `test`.`t2` where ((`test`.`t2`.`c` = 1) and (`test`.`t2`.`b` = 2) and (`test`.`t2`.`a` = `test`.`t1`.`a`))
SELECT * FROM t1,t2 WHERE (t2.a,(t2.b,t2.c))=(t1.a,(2,1));
a b a b c
1 1 1 2 1
1 2 1 2 1
EXPLAIN EXTENDED SELECT * FROM t1,t2 WHERE t2.a=t1.a AND (t2.b,t2.c)=(2,1);
id select_type table type possible_keys key key_len ref rows Extra
1 SIMPLE t1 index PRIMARY PRIMARY 8 NULL 6 Using index
1 SIMPLE t2 eq_ref PRIMARY PRIMARY 12 test.t1.a,const,const 1 Using index
Warnings:
Note 1003 select `test`.`t1`.`a` AS `a`,`test`.`t1`.`b` AS `b`,`test`.`t2`.`a` AS `a`,`test`.`t2`.`b` AS `b`,`test`.`t2`.`c` AS `c` from `test`.`t1` join `test`.`t2` where ((`test`.`t2`.`c` = 1) and (`test`.`t2`.`b` = 2) and (`test`.`t2`.`a` = `test`.`t1`.`a`))
SELECT * FROM t1,t2 WHERE t2.a=t1.a AND (t2.b,t2.c)=(2,1);
a b a b c
1 1 1 2 1
1 2 1 2 1
DROP TABLE t1,t2;
......@@ -92,3 +92,50 @@ SELECT ROW(NULL,10) <=> ROW(3,NULL);
#
SELECT ROW(1,1,1) = ROW(1,1,1) as `1`, ROW(1,1,1) = ROW(1,2,1) as `0`, ROW(1,NULL,1) = ROW(2,2,1) as `0`, ROW(1,NULL,1) = ROW(1,2,2) as `0`, ROW(1,NULL,1) = ROW(1,2,1) as `null` ;
select row(NULL,1)=(2,0);
#
# Bug #16081: row equalities are to be used for query optimizations
#
CREATE TABLE t1 (a int, b int, PRIMARY KEY (a,b));
INSERT INTO t1 VALUES (1,1), (2,1), (3,1), (1,2), (3,2), (3,3);
EXPLAIN SELECT * FROM t1 WHERE a=3 AND b=2;
EXPLAIN SELECT * FROM t1 WHERE (a,b)=(3,2);
SELECT * FROM t1 WHERE a=3 and b=2;
SELECT * FROM t1 WHERE (a,b)=(3,2);
CREATE TABLE t2 (a int, b int, c int, PRIMARY KEY (a,b,c));
INSERT INTO t2 VALUES
(1,1,2), (3,1,3), (1,2,2), (4,4,2),
(1,1,1), (3,1,1), (1,2,1);
EXPLAIN SELECT * FROM t1,t2 WHERE t1.a=t2.a AND t1.b=t2.b;
EXPLAIN SELECT * FROM t1,t2 WHERE (t1.a,t1.b)=(t2.a,t2.b);
SELECT * FROM t1,t2 WHERE t1.a=t2.a and t1.b=t2.b;
SELECT * FROM t1,t2 WHERE (t1.a,t1.b)=(t2.a,t2.b);
EXPLAIN SELECT * FROM t1,t2 WHERE t1.a=t2.a AND t1.b=2;
EXPLAIN SELECT * FROM t1,t2 WHERE (t1.a,t1.b)=(t2.a,2);
SELECT * FROM t1,t2 WHERE t1.a=1 and t1.b=t2.b;
SELECT * FROM t1,t2 WHERE (t1.a,t1.b)=(t2.a,2);
EXPLAIN EXTENDED SELECT * FROM t1,t2 WHERE (t1.a,t1.b)=(t2.a,t2.b+1);
SELECT * FROM t1,t2 WHERE (t1.a,t1.b)=(t2.a,t2.b+1);
EXPLAIN EXTENDED SELECT * FROM t1,t2 WHERE (t1.a-1,t1.b)=(t2.a-1,t2.b+1);
SELECT * FROM t1,t2 WHERE (t1.a-1,t1.b)=(t2.a-1,t2.b+1);
EXPLAIN SELECT * FROM t2 WHERE a=3 AND b=2;
EXPLAIN SELECT * FROM t2 WHERE (a,b)=(3,2);
SELECT * FROM t2 WHERE a=3 and b=2;
SELECT * FROM t2 WHERE (a,b)=(3,2);
EXPLAIN SELECT * FROM t1,t2 WHERE t2.a=t1.a AND t2.b=2 AND t2.c=1;
EXPLAIN EXTENDED SELECT * FROM t1,t2 WHERE (t2.a,(t2.b,t2.c))=(t1.a,(2,1));
SELECT * FROM t1,t2 WHERE (t2.a,(t2.b,t2.c))=(t1.a,(2,1));
EXPLAIN EXTENDED SELECT * FROM t1,t2 WHERE t2.a=t1.a AND (t2.b,t2.c)=(2,1);
SELECT * FROM t1,t2 WHERE t2.a=t1.a AND (t2.b,t2.c)=(2,1);
DROP TABLE t1,t2;
......@@ -94,9 +94,9 @@ class base_list :public Sql_alloc
inline base_list() { empty(); }
inline base_list(const base_list &tmp) :Sql_alloc()
{
elements=tmp.elements;
first=tmp.first;
last=tmp.last;
elements= tmp.elements;
first= tmp.first;
last= elements ? tmp.last : &first;
}
inline base_list(bool error) { }
inline bool push_back(void *info)
......
......@@ -6351,29 +6351,30 @@ Item_equal *find_item_equal(COND_EQUAL *cond_equal, Field *field,
/*
Check whether an item is a simple equality predicate and if so
create/find a multiple equality for this predicate
Check whether an equality can be used to build multiple equalities
SYNOPSIS
check_equality()
item item to check
cond_equal multiple equalities that must hold together with the predicate
check_simple_equality()
left_item left term of the quality to be checked
right_item right term of the equality to be checked
item equality item if the equality originates from a condition
predicate, 0 if the equality is the result of row elimination
cond_equal multiple equalities that must hold together with the equality
DESCRIPTION
This function first checks whether an item is a simple equality i.e.
the one that equates a field with another field or a constant
(item=constant_item or item=field_item).
If this is the case the function looks a for a multiple equality
This function first checks whether the equality (left_item=right_item)
is a simple equality i.e. the one that equates a field with another field
or a constant (field=field_item or field=const_item).
If this is the case the function looks for a multiple equality
in the lists referenced directly or indirectly by cond_equal inferring
the given simple equality. If it doesn't find any, it builds a multiple
equality that covers the predicate, i.e. the predicate can be inferred
from it.
from this multiple equality.
The built multiple equality could be obtained in such a way:
create a binary multiple equality equivalent to the predicate, then
merge it, if possible, with one of old multiple equalities.
This guarantees that the set of multiple equalities covering equality
predicates will
be minimal.
predicates will be minimal.
EXAMPLE
For the where condition
......@@ -6391,7 +6392,7 @@ Item_equal *find_item_equal(COND_EQUAL *cond_equal, Field *field,
and will transform *cond_equal into (ptr(CE),[Item_equal(f,e)]).
NOTES
Now only fields that have the same type defintions (verified by
Now only fields that have the same type definitions (verified by
the Field::eq_def method) are placed to the same multiple equalities.
Because of this some equality predicates are not eliminated and
can be used in the constant propagation procedure.
......@@ -6424,18 +6425,14 @@ Item_equal *find_item_equal(COND_EQUAL *cond_equal, Field *field,
copying would be much more complicated.
RETURN
TRUE - if the predicate is a simple equality predicate
FALSE - otherwise
TRUE if the predicate is a simple equality predicate to be used
for building multiple equalities
FALSE otherwise
*/
static bool check_equality(Item *item, COND_EQUAL *cond_equal)
static bool check_simple_equality(Item *left_item, Item *right_item,
Item *item, COND_EQUAL *cond_equal)
{
if (item->type() == Item::FUNC_ITEM &&
((Item_func*) item)->functype() == Item_func::EQ_FUNC)
{
Item *left_item= ((Item_func*) item)->arguments()[0];
Item *right_item= ((Item_func*) item)->arguments()[1];
if (left_item->type() == Item::REF_ITEM &&
((Item_ref*)left_item)->ref_type() == Item_ref::VIEW_REF)
{
......@@ -6463,9 +6460,6 @@ static bool check_equality(Item *item, COND_EQUAL *cond_equal)
if (!left_field->eq_def(right_field))
return FALSE;
if (left_field->eq(right_field)) /* f = f */
return TRUE;
/* Search for multiple equalities containing field1 and/or field2 */
bool left_copyfl, right_copyfl;
Item_equal *left_item_equal=
......@@ -6473,6 +6467,10 @@ static bool check_equality(Item *item, COND_EQUAL *cond_equal)
Item_equal *right_item_equal=
find_item_equal(cond_equal, right_field, &right_copyfl);
/* As (NULL=NULL) != TRUE we can't just remove the predicate f=f */
if (left_field->eq(right_field)) /* f = f */
return (!(left_field->maybe_null() && !left_item_equal));
if (left_item_equal && left_item_equal == right_item_equal)
{
/*
......@@ -6555,7 +6553,16 @@ static bool check_equality(Item *item, COND_EQUAL *cond_equal)
if (field_item->result_type() == STRING_RESULT)
{
CHARSET_INFO *cs= ((Field_str*) field_item->field)->charset();
if ((cs != ((Item_cond *) item)->compare_collation()) ||
if (!item)
{
Item_func_eq *eq_item;
if ((eq_item= new Item_func_eq(left_item, right_item)))
return FALSE;
eq_item->set_cmp_func();
eq_item->quick_fix_field();
item= eq_item;
}
if ((cs != ((Item_func *) item)->compare_collation()) ||
!cs->coll->propagate(cs, 0, 0))
return FALSE;
}
......@@ -6584,10 +6591,116 @@ static bool check_equality(Item *item, COND_EQUAL *cond_equal)
return TRUE;
}
}
return FALSE;
}
/*
Convert row equalities into a conjunction of regular equalities
SYNOPSIS
check_row_equality()
left_row left term of the row equality to be processed
right_row right term of the row equality to be processed
cond_equal multiple equalities that must hold together with the predicate
eq_list results of conversions of row equalities that are not simple
enough to form multiple equalities
DESCRIPTION
The function converts a row equality of the form (E1,...,En)=(E'1,...,E'n)
into a list of equalities E1=E'1,...,En=E'n. For each of these equalities
Ei=E'i the function checks whether it is a simple equality or a row equality.
If it is a simple equality it is used to expand multiple equalities of
cond_equal. If it is a row equality it converted to a sequence of equalities
between row elements. If Ei=E'i is neither a simple equality nor a row
equality the item for this predicate is added to eq_list.
RETURN
TRUE if conversion has succeeded (no fatal error)
FALSE otherwise
*/
static bool check_row_equality(Item *left_row, Item_row *right_row,
COND_EQUAL *cond_equal, List<Item>* eq_list)
{
uint n= left_row->cols();
for (uint i= 0 ; i < n; i++)
{
bool is_converted;
Item *left_item= left_row->el(i);
Item *right_item= right_row->el(i);
if (left_item->type() == Item::ROW_ITEM &&
right_item->type() == Item::ROW_ITEM)
is_converted= check_row_equality((Item_row *) left_item,
(Item_row *) right_item,
cond_equal, eq_list);
else
is_converted= check_simple_equality(left_item, right_item, 0, cond_equal);
if (!is_converted)
{
Item_func_eq *eq_item;
if (!(eq_item= new Item_func_eq(left_item, right_item)))
return FALSE;
eq_item->set_cmp_func();
eq_item->quick_fix_field();
eq_list->push_back(eq_item);
}
}
return TRUE;
}
/*
Eliminate row equalities and form multiple equalities predicates
SYNOPSIS
check_equality()
item predicate to process
cond_equal multiple equalities that must hold together with the predicate
eq_list results of conversions of row equalities that are not simple
enough to form multiple equalities
DESCRIPTION
This function checks whether the item is a simple equality
i.e. the one that equates a field with another field or a constant
(field=field_item or field=constant_item), or, a row equality.
For a simple equality the function looks for a multiple equality
in the lists referenced directly or indirectly by cond_equal inferring
the given simple equality. If it doesn't find any, it builds/expands
multiple equality that covers the predicate.
Row equalities are eliminated substituted for conjunctive regular equalities
which are treated in the same way as original equality predicates.
RETURN
TRUE if re-writing rules have been applied
FALSE otherwise, i.e.
if the predicate is not an equality,
or, if the equality is neither a simple one nor a row equality,
or, if the procedure fails by a fatal error.
*/
static bool check_equality(Item *item, COND_EQUAL *cond_equal,
List<Item> *eq_list)
{
if (item->type() == Item::FUNC_ITEM &&
((Item_func*) item)->functype() == Item_func::EQ_FUNC)
{
Item *left_item= ((Item_func*) item)->arguments()[0];
Item *right_item= ((Item_func*) item)->arguments()[1];
if (left_item->type() == Item::ROW_ITEM &&
right_item->type() == Item::ROW_ITEM)
return check_row_equality((Item_row *) left_item,
(Item_row *) right_item,
cond_equal, eq_list);
else
return check_simple_equality(left_item, right_item, item, cond_equal);
}
return FALSE;
}
/*
Replace all equality predicates in a condition by multiple equality items
......@@ -6659,10 +6772,12 @@ static COND *build_equal_items_for_cond(COND *cond,
Item_equal *item_equal;
uint members;
COND_EQUAL cond_equal;
COND *new_cond;
cond_equal.upper_levels= inherited;
if (cond->type() == Item::COND_ITEM)
{
List<Item> eq_list;
bool and_level= ((Item_cond*) cond)->functype() ==
Item_func::COND_AND_FUNC;
List<Item> *args= ((Item_cond*) cond)->argument_list();
......@@ -6685,7 +6800,7 @@ static COND *build_equal_items_for_cond(COND *cond,
structure here because it's restored before each
re-execution of any prepared statement/stored procedure.
*/
if (check_equality(item, &cond_equal))
if (check_equality(item, &cond_equal, &eq_list))
li.remove();
}
......@@ -6732,10 +6847,14 @@ static COND *build_equal_items_for_cond(COND *cond,
}
}
if (and_level)
{
args->concat(&eq_list);
args->concat((List<Item> *)&cond_equal.current_level);
}
}
else if (cond->type() == Item::FUNC_ITEM)
{
List<Item> eq_list;
/*
If an equality predicate forms the whole and level,
we call it standalone equality and it's processed here.
......@@ -6746,13 +6865,46 @@ static COND *build_equal_items_for_cond(COND *cond,
for WHERE a=b AND c=d AND (b=c OR d=5)
b=c is replaced by =(a,b,c,d).
*/
if (check_equality(cond, &cond_equal) &&
(item_equal= cond_equal.current_level.pop()))
if (check_equality(cond, &cond_equal, &eq_list))
{
int n= cond_equal.current_level.elements + eq_list.elements;
if (n == 0)
return new Item_int((longlong) 1,1);
else if (n == 1)
{
if ((item_equal= cond_equal.current_level.pop()))
{
item_equal->fix_length_and_dec();
item_equal->update_used_tables();
return item_equal;
}
else
return eq_list.pop();
}
else
{
/*
Here a new AND level must be created. It can happen only
when a row equality is processed as a standalone predicate.
*/
Item_cond_and *and_cond= new Item_cond_and(eq_list);
and_cond->quick_fix_field();
List<Item> *args= and_cond->argument_list();
List_iterator_fast<Item_equal> it(cond_equal.current_level);
while ((item_equal= it++))
{
item_equal->fix_length_and_dec();
item_equal->update_used_tables();
members= item_equal->members();
if (cond_equal.max_members < members)
cond_equal.max_members= members;
}
and_cond->cond_equal= cond_equal;
args->concat((List<Item> *)&cond_equal.current_level);
return and_cond;
}
}
/*
For each field reference in cond, not from equal item predicates,
set a pointer to the multiple equality it belongs to (if there is any)
......@@ -7038,7 +7190,7 @@ static Item *eliminate_item_equal(COND *cond, COND_EQUAL *upper_levels,
/*
Substitute every field reference in a condition by the best equal field
and eliminate all multiplle equality predicates
and eliminate all multiple equality predicates
SYNOPSIS
substitute_for_best_equal_field()
......
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