In case of two views with subqueries it is dificult to decide about order of injected ORDER BY clauses.
A simple solution is just prohibit ORDER BY injection if there is other order by.

mysql-test/r/view.result:
  New test added, old test changed.
mysql-test/t/view.test:
  New test aded.
sql/share/errmsg.txt:
  new warning added.
sql/sql_view.cc:
  Inject ORDER BY only if there is no other one.
  
  Warning about ignoring ORDER BY in this case for EXPLAIN EXTENDED.

- Correct handling of outer joins + DuplicateWeedout (docs pending)

Fixed explains of previous patch.

mysql-test/r/explain.result:
  Fixed explains of previous patch.
mysql-test/r/join_outer.result:
  Fixed explains of previous patch.
mysql-test/r/negation_elimination.result:
  Fixed explains of previous patch.
mysql-test/r/view.result:
  Fixed explains of previous patch.
mysql-test/suite/innodb/r/innodb_mysql.result:
  Removed duplicate test suite.
mysql-test/suite/innodb/t/innodb_mysql.test:
  Removed duplicate test suite.
mysql-test/suite/innodb_plugin/r/innodb_mysql.result:
  Removed duplicate test suite.
mysql-test/suite/innodb_plugin/t/innodb_mysql.test:
  Removed duplicate test suite.
sql/opt_range.h:
  Removed incorrect fix.
sql/records.cc:
  Removed incorrect fix.

There are 2 volatile condition constructions AND/OR constructions and fields(references) when first
good supported to be top elements of conditions because it is normal practice
(see copy_andor_structure for example) fields without any expression in the condition is really rare
and mostly useless case however it could lead to problems when optimiser changes/moves them unaware
of other variables referring to them. An easy solution of this problem is just to replace single field
in a condition with equivalent expression well supported by the server (<field> -> <field> != 0).

mysql-test/r/view.result:
  New test added.
mysql-test/t/view.test:
  New test added.
sql/sql_parse.cc:
  <field> -> <field> != 0
sql/sql_yacc.yy:
  <field> -> <field> != 0

Do not make substitution of a single-row table if it is an inner
table of an outer join with on expression containing an expensive
subquery.

An aggregating query over an empty set of a join of two tables
with a rejecting HAVING clause erroneously could return a row.
It could happen in the cases when the optimizer made a conclusion
that the aggregating set was empty.
Wrong results were produced because the server missed initial
setting for aggregation functions in the mentioned cases.
      

The function matching_cond should take into account that
there may be always false constant conjunctive conditions
that has not been evaluated yet,for example, conjunctive
conditions with non-correlated subqueries.

of the patch for bug 780386.

ALL subquery should return TRUE if subquery rowa set is empty independently
of left part.  The problem was that Item_func_(eq,ne,gt,ge,lt,le) do not
call execution of second argument if first is NULL no in this case subquery
will not be executed and when Item_func_not_all calls any_value() of the
subquery or aggregation function which report that there was rows. So for
NULL < ALL (SELECT...) result was FALSE instead of TRUE.

Fix is just swapping of arguments of Item_func_(eq,ne,gt,ge,lt,le) (with
changing the operation if it is needed) so that result will be the same
(for examole a < b is equal to b > a). This fix exploit the fact that
first argument will be executed in any case.

mysql-test/r/subselect.result:
  The test suite added.
mysql-test/r/subselect_no_mat.result:
  The test suite added.
mysql-test/r/subselect_no_opts.result:
  The test suite added.
mysql-test/r/subselect_no_semijoin.result:
  The test suite added.
mysql-test/r/subselect_scache.result:
  The test suite added.
mysql-test/t/subselect.test:
  The test suite added.
sql/item_cmpfunc.cc:
  Swap arguments creation methods added.
sql/item_cmpfunc.h:
  Swap arguments creation methods added.
sql/item_subselect.cc:
  Swap arguments of the comparison.

BUG##806524: Assertion `join->best_read < 1.7976931348623157e+308 with table_elimination=on and derived_merge=on 
reset_nj_counters() used to rely on the fact that join nests have 
table->table==NULL. This ceased to be true wit new derived table
optimizations. Use test for table->nested_join!=NULL instead.

The problem was that optimizer removes some outer references (it they are
constant for example) and the list of outer items built during prepare phase is
not actual during execution phase when we need it as the cache parameters.
First solution was use pointer on pointer on outer reference Item and
initialize temporary table on demand. This solved most problem except case
when optimiser also reduce Item which contains outer references ('OR' in
this bug test suite).

The solution is to build the list of outer reference items on execution
phase (after optimization) on demand (just before temporary table creation)
by walking Item tree and finding outer references among Item_ident
(Item_field/Item_ref) and Item_sum items.

Removed depends_on list (because it is not neede any mnore for the cache, in the place where it was used it replaced with upper_refs).

Added processor (collect_outer_ref_processor) and get_cache_parameters() methods to collect outer references (or other expression parameters in future).

mysql-test/r/subselect_cache.result:
  A new test added.
mysql-test/r/subselect_scache.result:
  Changes in creating the cache and its paremeters order or adding arguments of aggregate function (which is a parameter also, but this has no influence on the result).
mysql-test/t/subselect_cache.test:
  Added a new test.
sql/item.cc:
  depends_on removed.
  
  Added processor (collect_outer_ref_processor) and get_cache_parameters() methods to collect outer references.
  
  Item_cache_wrapper collect parameters befor initialization of its cache.
sql/item.h:
  depends_on removed.
  
  Added processor (collect_outer_ref_processor) and get_cache_parameters() methods to collect outer references.
sql/item_cmpfunc.cc:
  depends_on removed.
  
  Added processor (collect_outer_ref_processor) to collect outer references.
sql/item_cmpfunc.h:
  Added processor (collect_outer_ref_processor) to collect outer references.
sql/item_subselect.cc:
  depends_on removed.
  Added processor get_cache_parameters() method to collect outer references.
sql/item_subselect.h:
  depends_on removed.
  Added processor get_cache_parameters() method to collect outer references.
sql/item_sum.cc:
  Added processor (collect_outer_ref_processor) method to collect outer references.
sql/item_sum.h:
  Added processor (collect_outer_ref_processor) and get_cache_parameters() methods to collect outer references.
sql/opt_range.cc:
  depends_on removed.
sql/sql_base.cc:
  depends_on removed.
sql/sql_class.h:
  New iterator added.
sql/sql_expression_cache.cc:
  Build of list of items resolved in outer query done just before creating expression cache on the first execution of the subquery which removes influence of optimizer removing items (all optimization already done).
sql/sql_expression_cache.h:
  Build of list of items resolved in outer query done just before creating expression cache on the first execution of the subquery which removes influence of optimizer removing items (all optimization already done).
sql/sql_lex.cc:
  depends_on removed.
sql/sql_lex.h:
  depends_on removed.
sql/sql_list.h:
  Added add_unique method to add only unique elements to the list.
sql/sql_select.cc:
  Support of new Item list added.
sql/sql_select.h:
  Support of new Item list added.

- Add testcase.

Analysis:
Both the wrong result and the valgrind warning were a result
of incomplete cleanup of the MIN/MAX subquery rewrite. At the
first execution of the query, the non-aggregate subquery is
transformed into an aggregate MIN/MAX subquery. During the
fix_fields phase of the MIN/MAX function, it sets the property
st_select_lex::with_sum_func to true.

The second execution of the query finds this flag to be ON.
When optimization reaches the same MIN/MAX subquery
transformation, it tests if the subquery is an aggregate or not.
Since select_lex->with_sum_func == true from the previous
execution, the transformation executes the second branch that
handles aggregate subqueries. This substitutes the subquery
Item into a Item_maxmin_subselect. At the same time elsewhere
it is assumed that the subquery Item is of type
Item_allany_subselect. Ultimately this results in casting the
actual object to the wrong class, and calling the wrong
any_value() method from empty_underlying_subquery().

Solution:
Cleanup the st_select_lex::with_sum_func property in the case
when the MIN/MAX transformation was performed for a non-aggregate
subquery, so that the transformation can be repeated.

This bug could lead to wrong result sets for a query over a
materialized derived table or view accessed by a multi-component
key.
It happened because the function get_next_field_for_derived_key
was supposed to update its argument, and it did not do it.

Also:
1. simplified the code of the function mysql_derived_merge_for_insert.
2. moved merge of views/dt for multi-update/delete to the prepare stage.
3. the list of the references to the candidates for semi-join now is
   allocated in the statement memory.

mysql-test/r/subselect_scache.result:
  Test with subquery cache on.
mysql-test/t/subselect_scache.test:
  Test with subquery cache on.

Made it 'off' by default.

- {ha_myisam,ha_maria}::index_read_idx_map should also initialize end_range, because index condition 
  function will attempt to check it. We initialize it like index_init() does.

(This is not a real fix for this bug, even though it makes it to no longer repeat)
- Semi-join subquery predicates, i.e. ... WHERE outer_expr IN (SELECT ...) may have null-rejecting properties,
  may allow to convert outer joins into inner.
- When convert_subq_to_sj() injected IN-equality into parent's WHERE/ON clause, it didn't call 
  $new_cond->top_level_item(), which would cause null-rejecting properties to be lost.
- Fixed, now the mentioned outer-to-inner conversion will really take place.

- Added an initial set of feature-specific test cases
- Handled the special case where the materialized subquery of an
  IN predicates consists of only NULL values.
- Fixed a bug where making Item_in_subselect a constant,
  didn't respect its null_value value.

- Make {ha_myisam,ha_maria}::index_read_idx_map check pushed index condition.
- Address review feedback (added comments)