[sql] Import SQLite 3.17.0.

third_party/sqlite/src/src/in-operator.md

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+IN-Operator Implementation Notes
+================================
+
+## Definitions:
+
+An IN operator has one of the following formats:
+
+>
+     x IN (y1,y2,y3,...,yN)
+     x IN (subquery)
+
+The "x" is referred to as the LHS (left-hand side).  The list or subquery
+on the right is called the RHS (right-hand side).  If the RHS is a list
+it must be a non-empty list.  But if the RHS is a subquery, it can be an
+empty set.
+
+The LHS can be a scalar (a single quantity) or a vector (a list of
+two or or more values) or a subquery that returns one or more columns.
+We use the term "vector" to mean an actually list of values or a
+subquery that returns two or more columns.  An isolated value or
+a subquery that returns a single columns is called a scalar.
+
+The RHS can be a subquery that returns a single column, a subquery
+that returns two or more columns, or a list of scalars.  It is not
+currently support for the RHS to be a list of vectors.
+
+The number of columns for LHS must match the number of columns for
+the RHS.  If the RHS is a list of values, then the LHS must be a 
+scalar.  If the RHS is a subquery returning N columns, then the LHS
+must be a vector of size N.
+
+NULL values can occur in either or both of the LHS and RHS.
+If the LHS contains only
+NULL values then we say that it is a "total-NULL".  If the LHS contains
+some NULL values and some non-NULL values, then it is a "partial-NULL".
+For a scalar, there is no difference between a partial-NULL and a total-NULL.
+The RHS is a partial-NULL if any row contains a NULL value.  The RHS is
+a total-NULL if it contains one or more rows that contain only NULL values.
+The LHS is called "non-NULL" if it contains no NULL values.  The RHS is
+called "non-NULL" if it contains no NULL values in any row.
+
+The result of an IN operator is one of TRUE, FALSE, or NULL.  A NULL result
+means that it cannot be determined if the LHS is contained in the RHS due
+to the presence of NULL values.  In some contexts (for example, when the IN
+operator occurs in a WHERE clause)
+the system only needs a binary result: TRUE or NOT-TRUE.  One can also
+to define a binary result of FALSE and NOT-FALSE, but
+it turns out that no extra optimizations are possible in that case, so if
+the FALSE/NOT-FALSE binary is needed, we have to compute the three-state
+TRUE/FALSE/NULL result and then combine the TRUE and NULL values into 
+NOT-FALSE.
+
+A "NOT IN" operator is computed by first computing the equivalent IN
+operator, then interchanging the TRUE and FALSE results.
+
+## Simple Full-Scan Algorithm
+
+The following algorithm always compute the correct answer.  However, this
+algorithm is suboptimal, especially if there are many rows on the RHS.
+
+  1.  Set the null-flag to false
+  2.  For each row in the RHS:
+      <ol type='a'>
+      <li>  Compare the LHS against the RHS
+      <li>  If the LHS exactly matches the RHS, immediately return TRUE
+      <li>  If the comparison result is NULL, set the null-flag to true
+      </ol>
+  3.  If the null-flag is true, return NULL.
+  4.  Return FALSE
+
+## Optimized Algorithm
+
+The following procedure computes the same answer as the simple full-scan
+algorithm, though it does so with less work in the common case.  This
+is the algorithm that is implemented in SQLite.
+
+  1.  If the RHS is a constant list of length 1 or 2, then rewrite the
+      IN operator as a simple expression.  Implement
+
+            x IN (y1,y2)
+
+      as if it were
+
+            x=y1 OR x=y2
+
+      This is the INDEX_NOOP optimization and is only undertaken if the
+      IN operator is used for membership testing.  If the IN operator is
+      driving a loop, then skip this step entirely.
+
+  2.  Check the LHS to see if it is a partial-NULL and if it is, jump
+      ahead to step 5.
+
+  3.  Do a binary search of the RHS using the LHS as a probe.  If
+      an exact match is found, return TRUE.
+
+  4.  If the RHS is non-NULL then return FALSE.
+
+  5.  If we do not need to distinguish between FALSE and NULL,
+      then return FALSE.
+  
+  6.  For each row in the RHS, compare that row against the LHS and
+      if the result is NULL, immediately return NULL.  In the case
+      of a scalar IN operator, we only need to look at the very first
+      row the RHS because for a scalar RHS, all NULLs will always come 
+      first.  If the RHS is empty, this step is a no-op.
+
+  7.  Return FALSE.