The BETWEEN function was comparing DATE/DATETIME values either as ints or as
strings. Both methods have their disadvantages and may lead to a wrong
result.

Now BETWEEN function checks whether all of its arguments has the STRING result
types and at least one of them is a DATE/DATETIME item. If so it sets up
two Arg_comparator obects to compare with the compare_datetime() comparator
and uses them to compare such items.

Added two Arg_comparator object members and one flag to the
Item_func_between class for the correct DATE/DATETIME comparison.
The Item_func_between::fix_length_and_dec() function now detects whether
it's used for DATE/DATETIME comparison and sets up newly added Arg_comparator
objects to do this.
The Item_func_between::val_int() now uses Arg_comparator objects to perform
correct DATE/DATETIME comparison.
The owner variable of the Arg_comparator class now can be set to NULL if the
caller wants to handle NULL values by itself.
Now the Item_date_add_interval::get_date() function ajusts cached_field type according to the detected type.


mysql-test/t/type_datetime.test:
  Added a test case for the bug#16377: Wrong DATE/DATETIME comparison in BETWEEN function.
mysql-test/r/type_datetime.result:
  Added a test case for the bug#16377: Wrong DATE/DATETIME comparison in BETWEEN function.
mysql-test/r/query_cache.result:
  A test case result corrected after the fix for bug#16377.
sql/item_timefunc.cc:
  Bug#16377: Wrong DATE/DATETIME comparison in BETWEEN function.
  Now the Item_date_add_interval::get_date() function ajusts cached_field type according to the detected type.
sql/item_cmpfunc.cc:
  Bug#16377: Wrong DATE/DATETIME comparison in BETWEEN function.
  The Item_func_between::fix_length_and_dec() function now detects whether
  it's used for DATE/DATETIME comparison and sets up newly added Arg_comparator
  objects to do this.
  The Item_func_between::val_int() now uses Arg_comparators to perform correct
  DATE/DATETIME comparison.
  The owner variable of the Arg_comparator class now can be set to NULL if the
  caller wants to handle NULL values by itself.
sql/item_cmpfunc.h:
  Bug#16377: Wrong DATE/DATETIME comparison in BETWEEN function.
  Added two Arg_comparator object members and one flag
  to the Item_func_between class for the correct DATE/DATETIME comparison.