A database index is a data structure that improves the speed of data retrieval operations on a database table at the cost of additional writes and storage space to maintain the index data structure. Indexes are used to quickly locate data without having to search every row in a database table every time said table is accessed. Indexes can be created using one or more columns of a database table, providing the basis for both rapid random lookups and efficient access of ordered records. An index is a copy of selected columns of data, from a table, that is designed to enable very efficient search. An index normally includes a "key" or direct link to the original row of data from which it was copied, to allow the complete row to be retrieved efficiently. Some databases extend the power of indexing by letting developers create indexes on column values that have been transformed by functions or expressions. For example, an index could be created on upper(last_name), which would only store the upper-case versions of the last_name field in the index. Another option sometimes supported is the use of partial indices, where index entries are created only for those records that satisfy some conditional expression. A further aspect of flexibility is to permit indexing on user-defined functions, as well as expressions formed from an assortment of built-in functions. Most database software includes indexing technology that enables sub-linear time lookup to improve performance, as linear search is inefficient for large databases. Suppose a database contains N data items and one must be retrieved based on the value of one of the fields. A simple implementation retrieves and examines each item according to the test. If there is only one matching item, this can stop when it finds that single item, but if there are multiple matches, it must test everything. This means that the number of operations in the average case is O(N) or linear time. Since databases may contain many objects, and since lookup is a common operation, it is often desirable to improve performance.