The problem is that there is only one autoinc value associated with 
the query when binlogging. If more than one autoinc values are used 
in the query, the autoinc values after the first one can be inserted 
wrongly on slave. So these autoinc values can become inconsistent on 
master and slave.

The problem is resolved by marking all the statements that invoke 
a trigger or call a function that updated autoinc fields as unsafe, 
and will switch to row-format in Mixed mode. Actually, the statement 
is safe if just one autoinc value is used in sub-statement, but it's 
impossible to check how many autoinc values are used in sub-statement.)

mysql-test/suite/rpl/r/rpl_auto_increment_update_failure.result:
  Test result for bug#45677
mysql-test/suite/rpl/t/rpl_auto_increment_update_failure.test:
  Added test to verify the following two properties:
  P1) insert/update in an autoinc column causes statement to 
  be logged in row format if binlog_format=mixed
  P2) if binlog_format=mixed, and a trigger or function contains 
      two or more inserts/updates in a table that has an autoinc 
      column, then the slave should not go out of sync, even if 
      there are concurrent transactions.
sql/sql_base.cc:
  Added function 'has_write_table_with_auto_increment' to check 
  if one (or more) write tables have auto_increment columns.
  
  Removed function 'has_two_write_locked_tables_with_auto_increment', 
  because the function is included in function 
  'has_write_table_with_auto_increment'.