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# Indexes On Expressions

Normally, an SQL index references columns of a table. But an index can also be formed on expressions involving table columns.

As an example, consider the following table that tracks dollar-amount changes on various "accounts":

>     CREATE TABLE account_change(
>       chng_id INTEGER PRIMARY KEY,
>       acct_no INTEGER REFERENCES account,
>       location INTEGER REFERENCES locations,
>       amt INTEGER,  -- in cents
>       authority TEXT,
>       comment TEXT
>     );
>     CREATE INDEX acctchng_magnitude ON account_change(acct_no, abs(amt));

Each entry in the account_change table records a deposit or a withdrawal into an account. Deposits have a positive "amt" and withdrawals have a negative "amt".

The acctchng_magnitude index is over the account number ("acct_no") and on the absolute value of the amount. This index allows one to do efficient queries over the magnitude of a change to the account. For example, to list all changes to account number $xyz that are more than $100.00, one can say:

>     SELECT * FROM account_change WHERE acct_no=$xyz AND abs(amt)>=10000;

Or, to list all changes to one particular account ($xyz) in order of decreasing magnitude, one can write:

>     SELECT * FROM account_change WHERE acct_no=$xyz
>      ORDER BY abs(amt) DESC;

Both of the above example queries would work fine without the acctchng_magnitude index. The acctchng_magnitude index index merely helps the queries to run faster, especially on databases where there are many entries in the table for each account.

## How To Use Indexes On Expressions

Use a CREATE INDEX statement to create a new index on one or more expressions just like you would to create an index on columns. The only difference is that expressions are listed as the elements to be indexed rather than column names.

The SQLite query planner will consider using an index on an expression when the expression that is indexed appears in the WHERE clause or in the ORDER BY clause of a query, exactly as it is written in the CREATE INDEX statement. The query planner does not do algebra. In order to match WHERE clause constraints and ORDER BY terms to indexes, SQLite requires that the expressions be the same, except for minor syntactic differences such as white-space changes. So if you have:

>     CREATE TABLE t2(x,y,z);
>     CREATE INDEX t2xy ON t2(x+y);

And then you run the query:

>     SELECT * FROM t2 WHERE y+x=22;

Then the index will not be used because the expression on the CREATE INDEX statement (x+y) is not the same as the expression as it appears in the query (y+x). The two expressions might be mathematically equivalent, but the SQLite query planner insists that they be the same, not merely equivalent. Consider rewriting the query thusly:

>     SELECT * FROM t2 WHERE x+y=22;

This second query will likely use the index because now the expression in the WHERE clause (x+y) matches the expression in the index exactly.

## Restrictions

There are certain reasonable restrictions on expressions that appear in CREATE INDEX statements:

1. Expressions in CREATE INDEX statements may only refer to columns of the table being indexed, not to columns in other tables.

2. Expressions in CREATE INDEX statements may contain function calls, but only to functions whose output is always determined completely by its input parameters (a.k.a.: "deterministic" functions). Obviously, functions like random() will not work well in an index. But also functions like sqlite_version(), though they are constant across any one database connection, are not constant across the life of the underlying database file, and hence may not be used in a CREATE INDEX statement.

   Note that application-defined SQL functions are by default considered non-deterministic and may not be used in a CREATE INDEX statement unless the SQLITE_DETERMINISTIC flag is used when the function is registered.

3. Expressions in CREATE INDEX statements may not use subqueries.

4. Expressions may only be used in CREATE INDEX statements, not within UNIQUE or PRIMARY KEY constraints within the CREATE TABLE statement.

## Compatibility

The ability to index expressions was added to SQLite with version 3.9.0 in October of 2015. A database that uses an index on expressions will not be usable by earlier versions of SQLite.