10.2.1.2 Range Optimization

Range Access Method for Single-Part Indexes

For a single-part index, index value intervals can be conveniently represented by corresponding conditions in the WHERE clause, denoted as range conditions rather than “intervals.”

The definition of a range condition for a single-part index is as follows:

For both BTREE and HASH indexes, comparison of a key part with a constant value is a range condition when using the =, <=>, IN(), IS NULL, or IS NOT NULL operators.
Additionally, for BTREE indexes, comparison of a key part with a constant value is a range condition when using the >, <, >=, <=, BETWEEN, !=, or <> operators, or LIKE comparisons if the argument to LIKE is a constant string that does not start with a wildcard character.
For all index types, multiple range conditions combined with OR or AND form a range condition.

“Constant value” in the preceding descriptions means one of the following:

A constant from the query string
A column of a const or system table from the same join
The result of an uncorrelated subquery
Any expression composed entirely from subexpressions of the preceding types

Here are some examples of queries with range conditions in the WHERE clause:

SELECT * FROM t1
  WHERE key_col > 1
  AND key_col < 10;

SELECT * FROM t1
  WHERE key_col = 1
  OR key_col IN (15,18,20);

SELECT * FROM t1
  WHERE key_col LIKE 'ab%'
  OR key_col BETWEEN 'bar' AND 'foo';

Some nonconstant values may be converted to constants during the optimizer constant propagation phase.

MySQL tries to extract range conditions from the WHERE clause for each of the possible indexes. During the extraction process, conditions that cannot be used for constructing the range condition are dropped, conditions that produce overlapping ranges are combined, and conditions that produce empty ranges are removed.

Consider the following statement, where key1 is an indexed column and nonkey is not indexed:

SELECT * FROM t1 WHERE
  (key1 < 'abc' AND (key1 LIKE 'abcde%' OR key1 LIKE '%b')) OR
  (key1 < 'bar' AND nonkey = 4) OR
  (key1 < 'uux' AND key1 > 'z');

The extraction process for key key1 is as follows:

Start with original WHERE clause:

(key1 < 'abc' AND (key1 LIKE 'abcde%' OR key1 LIKE '%b')) OR
(key1 < 'bar' AND nonkey = 4) OR
(key1 < 'uux' AND key1 > 'z')

Remove nonkey = 4 and key1 LIKE '%b' because they cannot be used for a range scan. The correct way to remove them is to replace them with TRUE, so that we do not miss any matching rows when doing the range scan. Replacing them with TRUE yields:
```
(key1 < 'abc' AND (key1 LIKE 'abcde%' OR TRUE)) OR
(key1 < 'bar' AND TRUE) OR
(key1 < 'uux' AND key1 > 'z')
```
Collapse conditions that are always true or false:
- (key1 LIKE 'abcde%' OR TRUE) is always true
- (key1 < 'uux' AND key1 > 'z') is always false
Replacing these conditions with constants yields:
```
(key1 < 'abc' AND TRUE) OR (key1 < 'bar' AND TRUE) OR (FALSE)
```
Removing unnecessary TRUE and FALSE constants yields:
```
(key1 < 'abc') OR (key1 < 'bar')
```
Combining overlapping intervals into one yields the final condition to be used for the range scan:
```
(key1 < 'bar')
```

In general (and as demonstrated by the preceding example), the condition used for a range scan is less restrictive than the WHERE clause. MySQL performs an additional check to filter out rows that satisfy the range condition but not the full WHERE clause.

The range condition extraction algorithm can handle nested AND/OR constructs of arbitrary depth, and its output does not depend on the order in which conditions appear in WHERE clause.

MySQL does not support merging multiple ranges for the range access method for spatial indexes. To work around this limitation, you can use a UNION with identical SELECT statements, except that you put each spatial predicate in a different SELECT.

Range Access Method for Multiple-Part Indexes

Range conditions on a multiple-part index are an extension of range conditions for a single-part index. A range condition on a multiple-part index restricts index rows to lie within one or several key tuple intervals. Key tuple intervals are defined over a set of key tuples, using ordering from the index.

For example, consider a multiple-part index defined as key1(key_part1, key_part2, key_part3), and the following set of key tuples listed in key order:

key_part1  key_part2  key_part3
  NULL       1          'abc'
  NULL       1          'xyz'
  NULL       2          'foo'
   1         1          'abc'
   1         1          'xyz'
   1         2          'abc'
   2         1          'aaa'

The condition key_part1 = 1 defines this interval:

(1,-inf,-inf) <= (key_part1,key_part2,key_part3) < (1,+inf,+inf)

The interval covers the 4th, 5th, and 6th tuples in the preceding data set and can be used by the range access method.

By contrast, the condition key_part3 = 'abc' does not define a single interval and cannot be used by the range access method.

The following descriptions indicate how range conditions work for multiple-part indexes in greater detail.

For HASH indexes, each interval containing identical values can be used. This means that the interval can be produced only for conditions in the following form:
```
    key_part1 cmp const1
AND key_part2 cmp const2
AND ...
AND key_partN cmp constN;
```
Here, const1, const2, … are constants, cmp is one of the =, <=>, or IS NULL comparison operators, and the conditions cover all index parts. (That is, there are N conditions, one for each part of an N-part index.) For example, the following is a range condition for a three-part HASH index:
```
key_part1 = 1 AND key_part2 IS NULL AND key_part3 = 'foo'
```
For the definition of what is considered to be a constant, see Range Access Method for Single-Part Indexes.
For a BTREE index, an interval might be usable for conditions combined with AND, where each condition compares a key part with a constant value using =, <=>, IS NULL, >, <, >=, <=, !=, <>, BETWEEN, or LIKE 'pattern' (where 'pattern' does not start with a wildcard). An interval can be used as long as it is possible to determine a single key tuple containing all rows that match the condition (or two intervals if <> or != is used).
The optimizer attempts to use additional key parts to determine the interval as long as the comparison operator is =, <=>, or IS NULL. If the operator is >, <, >=, <=, !=, <>, BETWEEN, or LIKE, the optimizer uses it but considers no more key parts. For the following expression, the optimizer uses = from the first comparison. It also uses >= from the second comparison but considers no further key parts and does not use the third comparison for interval construction:
```
key_part1 = 'foo' AND key_part2 >= 10 AND key_part3 > 10
```
The single interval is:
```
('foo',10,-inf) < (key_part1,key_part2,key_part3) < ('foo',+inf,+inf)
```
It is possible that the created interval contains more rows than the initial condition. For example, the preceding interval includes the value ('foo', 11, 0), which does not satisfy the original condition.
If conditions that cover sets of rows contained within intervals are combined with OR, they form a condition that covers a set of rows contained within the union of their intervals. If the conditions are combined with AND, they form a condition that covers a set of rows contained within the intersection of their intervals. For example, for this condition on a two-part index:
```
(key_part1 = 1 AND key_part2 < 2) OR (key_part1 > 5)
```
The intervals are:
```
(1,-inf) < (key_part1,key_part2) < (1,2)
(5,-inf) < (key_part1,key_part2)
```
In this example, the interval on the first line uses one key part for the left bound and two key parts for the right bound. The interval on the second line uses only one key part. The key_len column in the EXPLAIN output indicates the maximum length of the key prefix used.
In some cases, key_len may indicate that a key part was used, but that might be not what you would expect. Suppose that key_part1 and key_part2 can be NULL. Then the key_len column displays two key part lengths for the following condition:
```
key_part1 >= 1 AND key_part2 < 2
```
But, in fact, the condition is converted to this:
```
key_part1 >= 1 AND key_part2 IS NOT NULL
```

For a description of how optimizations are performed to combine or eliminate intervals for range conditions on a single-part index, see Range Access Method for Single-Part Indexes. Analogous steps are performed for range conditions on multiple-part indexes.

Equality Range Optimization of Many-Valued Comparisons

Consider these expressions, where col_name is an indexed column:

col_name IN(val1, ..., valN)
col_name = val1 OR ... OR col_name = valN

Each expression is true if col_name is equal to any of several values. These comparisons are equality range comparisons (where the “range” is a single value). The optimizer estimates the cost of reading qualifying rows for equality range comparisons as follows:

If there is a unique index on col_name, the row estimate for each range is 1 because at most one row can have the given value.
Otherwise, any index on col_name is nonunique and the optimizer can estimate the row count for each range using dives into the index or index statistics.

With index dives, the optimizer makes a dive at each end of a range and uses the number of rows in the range as the estimate. For example, the expression col_name IN (10, 20, 30) has three equality ranges and the optimizer makes two dives per range to generate a row estimate. Each pair of dives yields an estimate of the number of rows that have the given value.

Index dives provide accurate row estimates, but as the number of comparison values in the expression increases, the optimizer takes longer to generate a row estimate. Use of index statistics is less accurate than index dives but permits faster row estimation for large value lists.

The eq_range_index_dive_limit system variable enables you to configure the number of values at which the optimizer switches from one row estimation strategy to the other. To permit use of index dives for comparisons of up to N equality ranges, set eq_range_index_dive_limit to N + 1. To disable use of statistics and always use index dives regardless of N, set eq_range_index_dive_limit to 0.

To update table index statistics for best estimates, use ANALYZE TABLE.

Prior to MySQL 9.3, there is no way of skipping the use of index dives to estimate index usefulness, except by using the eq_range_index_dive_limit system variable. In MySQL 9.3, index dive skipping is possible for queries that satisfy all these conditions:

The query is for a single table, not a join on multiple tables.
A single-index FORCE INDEX index hint is present. The idea is that if index use is forced, there is nothing to be gained from the additional overhead of performing dives into the index.
The index is nonunique and not a FULLTEXT index.
No subquery is present.
No DISTINCT, GROUP BY, or ORDER BY clause is present.

For EXPLAIN FOR CONNECTION, the output changes as follows if index dives are skipped:

For traditional output, the rows and filtered values are NULL.
For JSON output, rows_examined_per_scan and rows_produced_per_join do not appear, skip_index_dive_due_to_force is true, and cost calculations are not accurate.

Without FOR CONNECTION, EXPLAIN output does not change when index dives are skipped.

After execution of a query for which index dives are skipped, the corresponding row in the Information Schema OPTIMIZER_TRACE table contains an index_dives_for_range_access value of skipped_due_to_force_index.

Skip Scan Range Access Method

Consider the following scenario:

CREATE TABLE t1 (f1 INT NOT NULL, f2 INT NOT NULL, PRIMARY KEY(f1, f2));
INSERT INTO t1 VALUES
  (1,1), (1,2), (1,3), (1,4), (1,5),
  (2,1), (2,2), (2,3), (2,4), (2,5);
INSERT INTO t1 SELECT f1, f2 + 5 FROM t1;
INSERT INTO t1 SELECT f1, f2 + 10 FROM t1;
INSERT INTO t1 SELECT f1, f2 + 20 FROM t1;
INSERT INTO t1 SELECT f1, f2 + 40 FROM t1;
ANALYZE TABLE t1;

EXPLAIN SELECT f1, f2 FROM t1 WHERE f2 > 40;

To execute this query, MySQL can choose an index scan to fetch all rows (the index includes all columns to be selected), then apply the f2 > 40 condition from the WHERE clause to produce the final result set.

A range scan is more efficient than a full index scan, but cannot be used in this case because there is no condition on f1, the first index column. The optimizer can perform multiple range scans, one for each value of f1, using a method called Skip Scan that is similar to Loose Index Scan (see Section 10.2.1.17, “GROUP BY Optimization”):

Skip between distinct values of the first index part, f1 (the index prefix).
Perform a subrange scan on each distinct prefix value for the f2 > 40 condition on the remaining index part.

For the data set shown earlier, the algorithm operates like this:

Get the first distinct value of the first key part (f1 = 1).
Construct the range based on the first and second key parts (f1 = 1 AND f2 > 40).
Perform a range scan.
Get the next distinct value of the first key part (f1 = 2).
Construct the range based on the first and second key parts (f1 = 2 AND f2 > 40).
Perform a range scan.

Using this strategy decreases the number of accessed rows because MySQL skips the rows that do not qualify for each constructed range. This Skip Scan access method is applicable under the following conditions:

Table T has at least one compound index with key parts of the form ([A_1, ..., A_k,] B_1, ..., B_m, C [, D_1, ..., D_n]). Key parts A and D may be empty, but B and C must be nonempty.
The query references only one table.
The query does not use GROUP BY or DISTINCT.
The query references only columns in the index.
The predicates on A_1, ..., A_k must be equality predicates and they must be constants. This includes the IN() operator.
The query must be a conjunctive query; that is, an AND of OR conditions: (cond1(key_part1) OR cond2(key_part1)) AND (cond1(key_part2) OR ...) AND ...
There must be a range condition on C.
Conditions on D columns are permitted. Conditions on D must be in conjunction with the range condition on C.

Use of Skip Scan is indicated in EXPLAIN output as follows:

Using index for skip scan in the Extra column indicates that the loose index Skip Scan access method is used.
If the index can be used for Skip Scan, the index should be visible in the possible_keys column.

Use of Skip Scan is indicated in optimizer trace output by a "skip scan" element of this form:

"skip_scan_range": {
  "type": "skip_scan",
  "index": index_used_for_skip_scan,
  "key_parts_used_for_access": [key_parts_used_for_access],
  "range": [range]
}

You may also see a "best_skip_scan_summary" element. If Skip Scan is chosen as the best range access variant, a "chosen_range_access_summary" is written. If Skip Scan is chosen as the overall best access method, a "best_access_path" element is present.

Use of Skip Scan is subject to the value of the skip_scan flag of the optimizer_switch system variable. See Section 10.9.2, “Switchable Optimizations”. By default, this flag is on. To disable it, set skip_scan to off.

In addition to using the optimizer_switch system variable to control optimizer use of Skip Scan session-wide, MySQL supports optimizer hints to influence the optimizer on a per-statement basis. See Section 10.9.3, “Optimizer Hints”.

Range Optimization of Row Constructor Expressions

The optimizer is able to apply the range scan access method to queries of this form:

SELECT ... FROM t1 WHERE ( col_1, col_2 ) IN (( 'a', 'b' ), ( 'c', 'd' ));

Previously, for range scans to be used, it was necessary to write the query as:

SELECT ... FROM t1 WHERE ( col_1 = 'a' AND col_2 = 'b' )
OR ( col_1 = 'c' AND col_2 = 'd' );

For the optimizer to use a range scan, queries must satisfy these conditions:

Only IN() predicates are used, not NOT IN().
On the left side of the IN() predicate, the row constructor contains only column references.
On the right side of the IN() predicate, row constructors contain only runtime constants, which are either literals or local column references that are bound to constants during execution.
On the right side of the IN() predicate, there is more than one row constructor.

For more information about the optimizer and row constructors, see Section 10.2.1.22, “Row Constructor Expression Optimization”

Limiting Memory Use for Range Optimization

To control the memory available to the range optimizer, use the range_optimizer_max_mem_size system variable:

A value of 0 means “no limit.”
With a value greater than 0, the optimizer tracks the memory consumed when considering the range access method. If the specified limit is about to be exceeded, the range access method is abandoned and other methods, including a full table scan, are considered instead. This could be less optimal. If this happens, the following warning occurs (where N is the current range_optimizer_max_mem_size value):
```
Warning    3170    Memory capacity of N bytes for
                   'range_optimizer_max_mem_size' exceeded. Range
                   optimization was not done for this query.
```
For UPDATE and DELETE statements, if the optimizer falls back to a full table scan and the sql_safe_updates system variable is enabled, an error occurs rather than a warning because, in effect, no key is used to determine which rows to modify. For more information, see Using Safe-Updates Mode (--safe-updates).

For individual queries that exceed the available range optimization memory and for which the optimizer falls back to less optimal plans, increasing the range_optimizer_max_mem_size value may improve performance.

To estimate the amount of memory needed to process a range expression, use these guidelines:

For a simple query such as the following, where there is one candidate key for the range access method, each predicate combined with OR uses approximately 230 bytes:
```
SELECT COUNT(*) FROM t
WHERE a=1 OR a=2 OR a=3 OR .. . a=N;
```
Similarly for a query such as the following, each predicate combined with AND uses approximately 125 bytes:
```
SELECT COUNT(*) FROM t
WHERE a=1 AND b=1 AND c=1 ... N;
```
For a query with IN() predicates:
```
SELECT COUNT(*) FROM t
WHERE a IN (1,2, ..., M) AND b IN (1,2, ..., N);
```
Each literal value in an IN() list counts as a predicate combined with OR. If there are two IN() lists, the number of predicates combined with OR is the product of the number of literal values in each list. Thus, the number of predicates combined with OR in the preceding case is M × N.