index SP-GiST SP-GiST is an abbreviation for space-partitioned GiST. SP-GiST supports partitioned search trees, which facilitate development of a wide range of different non-balanced data structures, such as quad-trees, k-d trees, and radix trees (tries). The common feature of these structures is that they repeatedly divide the search space into partitions that need not be of equal size. Searches that are well matched to the partitioning rule can be very fast. These popular data structures were originally developed for in-memory usage. In main memory, they are usually designed as a set of dynamically allocated nodes linked by pointers. This is not suitable for direct storing on disk, since these chains of pointers can be rather long which would require too many disk accesses. In contrast, disk-based data structures should have a high fanout to minimize I/O. The challenge addressed by SP-GiST is to map search tree nodes to disk pages in such a way that a search need access only a few disk pages, even if it traverses many nodes. Like GiST, SP-GiST is meant to allow the development of custom data types with the appropriate access methods, by an expert in the domain of the data type, rather than a database expert. Some of the information here is derived from Purdue University's SP-GiST Indexing Project web site. The SP-GiST implementation in PostgreSQL is primarily maintained by Teodor Sigaev and Oleg Bartunov, and there is more information on their web site. The core PostgreSQL distribution includes the SP-GiST operator classes shown in . Name Indexed Data Type Indexable Operators kd_point_ops point << <@ <^ >> >^ ~= quad_point_ops point << <@ <^ >> >^ ~= range_ops any range type && &< &> -|- << <@ = >> @> text_ops text < <= = > >= ~<=~ ~<~ ~>=~ ~>~ Of the two operator classes for type point, quad_point_ops is the default. kd_point_ops supports the same operators but uses a different index data structure which may offer better performance in some applications. SP-GiST offers an interface with a high level of abstraction, requiring the access method developer to implement only methods specific to a given data type. The SP-GiST core is responsible for efficient disk mapping and searching the tree structure. It also takes care of concurrency and logging considerations. Leaf tuples of an SP-GiST tree contain values of the same data type as the indexed column. Leaf tuples at the root level will always contain the original indexed data value, but leaf tuples at lower levels might contain only a compressed representation, such as a suffix. In that case the operator class support functions must be able to reconstruct the original value using information accumulated from the inner tuples that are passed through to reach the leaf level. Inner tuples are more complex, since they are branching points in the search tree. Each inner tuple contains a set of one or more nodes, which represent groups of similar leaf values. A node contains a downlink that leads to either another, lower-level inner tuple, or a short list of leaf tuples that all lie on the same index page. Each node has a label that describes it; for example, in a radix tree the node label could be the next character of the string value. Optionally, an inner tuple can have a prefix value that describes all its members. In a radix tree this could be the common prefix of the represented strings. The prefix value is not necessarily really a prefix, but can be any data needed by the operator class; for example, in a quad-tree it can store the central point that the four quadrants are measured with respect to. A quad-tree inner tuple would then also contain four nodes corresponding to the quadrants around this central point. Some tree algorithms require knowledge of level (or depth) of the current tuple, so the SP-GiST core provides the possibility for operator classes to manage level counting while descending the tree. There is also support for incrementally reconstructing the represented value when that is needed. The SP-GiST core code takes care of null entries. Although SP-GiST indexes do store entries for nulls in indexed columns, this is hidden from the index operator class code: no null index entries or search conditions will ever be passed to the operator class methods. (It is assumed that SP-GiST operators are strict and so cannot succeed for null values.) Null values are therefore not discussed further here. There are five user-defined methods that an index operator class for SP-GiST must provide. All five follow the convention of accepting two internal arguments, the first of which is a pointer to a C struct containing input values for the support method, while the second argument is a pointer to a C struct where output values must be placed. Four of the methods just return void, since all their results appear in the output struct; but leaf_consistent additionally returns a boolean result. The methods must not modify any fields of their input structs. In all cases, the output struct is initialized to zeroes before calling the user-defined method. The five user-defined methods are: config Returns static information about the index implementation, including the data type OIDs of the prefix and node label data types. The SQL declaration of the function must look like this: CREATE FUNCTION my_config(internal, internal) RETURNS void ... The first argument is a pointer to a spgConfigIn C struct, containing input data for the function. The second argument is a pointer to a spgConfigOut C struct, which the function must fill with result data. typedef struct spgConfigIn { Oid attType; /* Data type to be indexed */ } spgConfigIn; typedef struct spgConfigOut { Oid prefixType; /* Data type of inner-tuple prefixes */ Oid labelType; /* Data type of inner-tuple node labels */ bool canReturnData; /* Opclass can reconstruct original data */ bool longValuesOK; /* Opclass can cope with values > 1 page */ } spgConfigOut; attType is passed in order to support polymorphic index operator classes; for ordinary fixed-data-type operator classes, it will always have the same value and so can be ignored. For operator classes that do not use prefixes, prefixType can be set to VOIDOID. Likewise, for operator classes that do not use node labels, labelType can be set to VOIDOID. canReturnData should be set true if the operator class is capable of reconstructing the originally-supplied index value. longValuesOK should be set true only when the attType is of variable length and the operator class is capable of segmenting long values by repeated suffixing (see ). choose Chooses a method for inserting a new value into an inner tuple. The SQL declaration of the function must look like this: CREATE FUNCTION my_choose(internal, internal) RETURNS void ... The first argument is a pointer to a spgChooseIn C struct, containing input data for the function. The second argument is a pointer to a spgChooseOut C struct, which the function must fill with result data. typedef struct spgChooseIn { Datum datum; /* original datum to be indexed */ Datum leafDatum; /* current datum to be stored at leaf */ int level; /* current level (counting from zero) */ /* Data from current inner tuple */ bool allTheSame; /* tuple is marked all-the-same? */ bool hasPrefix; /* tuple has a prefix? */ Datum prefixDatum; /* if so, the prefix value */ int nNodes; /* number of nodes in the inner tuple */ Datum *nodeLabels; /* node label values (NULL if none) */ } spgChooseIn; typedef enum spgChooseResultType { spgMatchNode = 1, /* descend into existing node */ spgAddNode, /* add a node to the inner tuple */ spgSplitTuple /* split inner tuple (change its prefix) */ } spgChooseResultType; typedef struct spgChooseOut { spgChooseResultType resultType; /* action code, see above */ union { struct /* results for spgMatchNode */ { int nodeN; /* descend to this node (index from 0) */ int levelAdd; /* increment level by this much */ Datum restDatum; /* new leaf datum */ } matchNode; struct /* results for spgAddNode */ { Datum nodeLabel; /* new node's label */ int nodeN; /* where to insert it (index from 0) */ } addNode; struct /* results for spgSplitTuple */ { /* Info to form new inner tuple with one node */ bool prefixHasPrefix; /* tuple should have a prefix? */ Datum prefixPrefixDatum; /* if so, its value */ Datum nodeLabel; /* node's label */ /* Info to form new lower-level inner tuple with all old nodes */ bool postfixHasPrefix; /* tuple should have a prefix? */ Datum postfixPrefixDatum; /* if so, its value */ } splitTuple; } result; } spgChooseOut; datum is the original datum that was to be inserted into the index. leafDatum is initially the same as datum, but can change at lower levels of the tree if the choose or picksplit methods change it. When the insertion search reaches a leaf page, the current value of leafDatum is what will be stored in the newly created leaf tuple. level is the current inner tuple's level, starting at zero for the root level. allTheSame is true if the current inner tuple is marked as containing multiple equivalent nodes (see ). hasPrefix is true if the current inner tuple contains a prefix; if so, prefixDatum is its value. nNodes is the number of child nodes contained in the inner tuple, and nodeLabels is an array of their label values, or NULL if there are no labels. The choose function can determine either that the new value matches one of the existing child nodes, or that a new child node must be added, or that the new value is inconsistent with the tuple prefix and so the inner tuple must be split to create a less restrictive prefix. If the new value matches one of the existing child nodes, set resultType to spgMatchNode. Set nodeN to the index (from zero) of that node in the node array. Set levelAdd to the increment in level caused by descending through that node, or leave it as zero if the operator class does not use levels. Set restDatum to equal datum if the operator class does not modify datums from one level to the next, or otherwise set it to the modified value to be used as leafDatum at the next level. If a new child node must be added, set resultType to spgAddNode. Set nodeLabel to the label to be used for the new node, and set nodeN to the index (from zero) at which to insert the node in the node array. After the node has been added, the choose function will be called again with the modified inner tuple; that call should result in an spgMatchNode result. If the new value is inconsistent with the tuple prefix, set resultType to spgSplitTuple. This action moves all the existing nodes into a new lower-level inner tuple, and replaces the existing inner tuple with a tuple having a single node that links to the new lower-level inner tuple. Set prefixHasPrefix to indicate whether the new upper tuple should have a prefix, and if so set prefixPrefixDatum to the prefix value. This new prefix value must be sufficiently less restrictive than the original to accept the new value to be indexed, and it should be no longer than the original prefix. Set nodeLabel to the label to be used for the node that will point to the new lower-level inner tuple. Set postfixHasPrefix to indicate whether the new lower-level inner tuple should have a prefix, and if so set postfixPrefixDatum to the prefix value. The combination of these two prefixes and the additional label must have the same meaning as the original prefix, because there is no opportunity to alter the node labels that are moved to the new lower-level tuple, nor to change any child index entries. After the node has been split, the choose function will be called again with the replacement inner tuple. That call will usually result in an spgAddNode result, since presumably the node label added in the split step will not match the new value; so after that, there will be a third call that finally returns spgMatchNode and allows the insertion to descend to the leaf level. picksplit Decides how to create a new inner tuple over a set of leaf tuples. The SQL declaration of the function must look like this: CREATE FUNCTION my_picksplit(internal, internal) RETURNS void ... The first argument is a pointer to a spgPickSplitIn C struct, containing input data for the function. The second argument is a pointer to a spgPickSplitOut C struct, which the function must fill with result data. typedef struct spgPickSplitIn { int nTuples; /* number of leaf tuples */ Datum *datums; /* their datums (array of length nTuples) */ int level; /* current level (counting from zero) */ } spgPickSplitIn; typedef struct spgPickSplitOut { bool hasPrefix; /* new inner tuple should have a prefix? */ Datum prefixDatum; /* if so, its value */ int nNodes; /* number of nodes for new inner tuple */ Datum *nodeLabels; /* their labels (or NULL for no labels) */ int *mapTuplesToNodes; /* node index for each leaf tuple */ Datum *leafTupleDatums; /* datum to store in each new leaf tuple */ } spgPickSplitOut; nTuples is the number of leaf tuples provided. datums is an array of their datum values. level is the current level that all the leaf tuples share, which will become the level of the new inner tuple. Set hasPrefix to indicate whether the new inner tuple should have a prefix, and if so set prefixDatum to the prefix value. Set nNodes to indicate the number of nodes that the new inner tuple will contain, and set nodeLabels to an array of their label values. (If the nodes do not require labels, set nodeLabels to NULL; see for details.) Set mapTuplesToNodes to an array that gives the index (from zero) of the node that each leaf tuple should be assigned to. Set leafTupleDatums to an array of the values to be stored in the new leaf tuples (these will be the same as the input datums if the operator class does not modify datums from one level to the next). Note that the picksplit function is responsible for palloc'ing the nodeLabels, mapTuplesToNodes and leafTupleDatums arrays. If more than one leaf tuple is supplied, it is expected that the picksplit function will classify them into more than one node; otherwise it is not possible to split the leaf tuples across multiple pages, which is the ultimate purpose of this operation. Therefore, if the picksplit function ends up placing all the leaf tuples in the same node, the core SP-GiST code will override that decision and generate an inner tuple in which the leaf tuples are assigned at random to several identically-labeled nodes. Such a tuple is marked allTheSame to signify that this has happened. The choose and inner_consistent functions must take suitable care with such inner tuples. See for more information. picksplit can be applied to a single leaf tuple only in the case that the config function set longValuesOK to true and a larger-than-a-page input value has been supplied. In this case the point of the operation is to strip off a prefix and produce a new, shorter leaf datum value. The call will be repeated until a leaf datum short enough to fit on a page has been produced. See for more information. inner_consistent Returns set of nodes (branches) to follow during tree search. The SQL declaration of the function must look like this: CREATE FUNCTION my_inner_consistent(internal, internal) RETURNS void ... The first argument is a pointer to a spgInnerConsistentIn C struct, containing input data for the function. The second argument is a pointer to a spgInnerConsistentOut C struct, which the function must fill with result data. typedef struct spgInnerConsistentIn { ScanKey scankeys; /* array of operators and comparison values */ int nkeys; /* length of array */ Datum reconstructedValue; /* value reconstructed at parent */ int level; /* current level (counting from zero) */ bool returnData; /* original data must be returned? */ /* Data from current inner tuple */ bool allTheSame; /* tuple is marked all-the-same? */ bool hasPrefix; /* tuple has a prefix? */ Datum prefixDatum; /* if so, the prefix value */ int nNodes; /* number of nodes in the inner tuple */ Datum *nodeLabels; /* node label values (NULL if none) */ } spgInnerConsistentIn; typedef struct spgInnerConsistentOut { int nNodes; /* number of child nodes to be visited */ int *nodeNumbers; /* their indexes in the node array */ int *levelAdds; /* increment level by this much for each */ Datum *reconstructedValues; /* associated reconstructed values */ } spgInnerConsistentOut; The array scankeys, of length nkeys, describes the index search condition(s). These conditions are combined with AND — only index entries that satisfy all of them are interesting. (Note that nkeys = 0 implies that all index entries satisfy the query.) Usually the consistent function only cares about the sk_strategy and sk_argument fields of each array entry, which respectively give the indexable operator and comparison value. In particular it is not necessary to check sk_flags to see if the comparison value is NULL, because the SP-GiST core code will filter out such conditions. reconstructedValue is the value reconstructed for the parent tuple; it is (Datum) 0 at the root level or if the inner_consistent function did not provide a value at the parent level. level is the current inner tuple's level, starting at zero for the root level. returnData is true if reconstructed data is required for this query; this will only be so if the config function asserted canReturnData. allTheSame is true if the current inner tuple is marked all-the-same; in this case all the nodes have the same label (if any) and so either all or none of them match the query (see ). hasPrefix is true if the current inner tuple contains a prefix; if so, prefixDatum is its value. nNodes is the number of child nodes contained in the inner tuple, and nodeLabels is an array of their label values, or NULL if the nodes do not have labels. nNodes must be set to the number of child nodes that need to be visited by the search, and nodeNumbers must be set to an array of their indexes. If the operator class keeps track of levels, set levelAdds to an array of the level increments required when descending to each node to be visited. (Often these increments will be the same for all the nodes, but that's not necessarily so, so an array is used.) If value reconstruction is needed, set reconstructedValues to an array of the values reconstructed for each child node to be visited; otherwise, leave reconstructedValues as NULL. Note that the inner_consistent function is responsible for palloc'ing the nodeNumbers, levelAdds and reconstructedValues arrays. leaf_consistent Returns true if a leaf tuple satisfies a query. The SQL declaration of the function must look like this: CREATE FUNCTION my_leaf_consistent(internal, internal) RETURNS bool ... The first argument is a pointer to a spgLeafConsistentIn C struct, containing input data for the function. The second argument is a pointer to a spgLeafConsistentOut C struct, which the function must fill with result data. typedef struct spgLeafConsistentIn { ScanKey scankeys; /* array of operators and comparison values */ int nkeys; /* length of array */ Datum reconstructedValue; /* value reconstructed at parent */ int level; /* current level (counting from zero) */ bool returnData; /* original data must be returned? */ Datum leafDatum; /* datum in leaf tuple */ } spgLeafConsistentIn; typedef struct spgLeafConsistentOut { Datum leafValue; /* reconstructed original data, if any */ bool recheck; /* set true if operator must be rechecked */ } spgLeafConsistentOut; The array scankeys, of length nkeys, describes the index search condition(s). These conditions are combined with AND — only index entries that satisfy all of them satisfy the query. (Note that nkeys = 0 implies that all index entries satisfy the query.) Usually the consistent function only cares about the sk_strategy and sk_argument fields of each array entry, which respectively give the indexable operator and comparison value. In particular it is not necessary to check sk_flags to see if the comparison value is NULL, because the SP-GiST core code will filter out such conditions. reconstructedValue is the value reconstructed for the parent tuple; it is (Datum) 0 at the root level or if the inner_consistent function did not provide a value at the parent level. level is the current leaf tuple's level, starting at zero for the root level. returnData is true if reconstructed data is required for this query; this will only be so if the config function asserted canReturnData. leafDatum is the key value stored in the current leaf tuple. The function must return true if the leaf tuple matches the query, or false if not. In the true case, if returnData is true then leafValue must be set to the value originally supplied to be indexed for this leaf tuple. Also, recheck may be set to true if the match is uncertain and so the operator(s) must be re-applied to the actual heap tuple to verify the match. All the SP-GiST support methods are normally called in a short-lived memory context; that is, CurrentMemoryContext will be reset after processing of each tuple. It is therefore not very important to worry about pfree'ing everything you palloc. (The config method is an exception: it should try to avoid leaking memory. But usually the config method need do nothing but assign constants into the passed parameter struct.) If the indexed column is of a collatable data type, the index collation will be passed to all the support methods, using the standard PG_GET_COLLATION() mechanism. This section covers implementation details and other tricks that are useful for implementers of SP-GiST operator classes to know. Individual leaf tuples and inner tuples must fit on a single index page (8KB by default). Therefore, when indexing values of variable-length data types, long values can only be supported by methods such as radix trees, in which each level of the tree includes a prefix that is short enough to fit on a page, and the final leaf level includes a suffix also short enough to fit on a page. The operator class should set longValuesOK to TRUE only if it is prepared to arrange for this to happen. Otherwise, the SP-GiST core will reject any request to index a value that is too large to fit on an index page. Likewise, it is the operator class's responsibility that inner tuples do not grow too large to fit on an index page; this limits the number of child nodes that can be used in one inner tuple, as well as the maximum size of a prefix value. Another limitation is that when an inner tuple's node points to a set of leaf tuples, those tuples must all be in the same index page. (This is a design decision to reduce seeking and save space in the links that chain such tuples together.) If the set of leaf tuples grows too large for a page, a split is performed and an intermediate inner tuple is inserted. For this to fix the problem, the new inner tuple must divide the set of leaf values into more than one node group. If the operator class's picksplit function fails to do that, the SP-GiST core resorts to extraordinary measures described in . Some tree algorithms use a fixed set of nodes for each inner tuple; for example, in a quad-tree there are always exactly four nodes corresponding to the four quadrants around the inner tuple's centroid point. In such a case the code typically works with the nodes by number, and there is no need for explicit node labels. To suppress node labels (and thereby save some space), the picksplit function can return NULL for the nodeLabels array. This will in turn result in nodeLabels being NULL during subsequent calls to choose and inner_consistent. In principle, node labels could be used for some inner tuples and omitted for others in the same index. When working with an inner tuple having unlabeled nodes, it is an error for choose to return spgAddNode, since the set of nodes is supposed to be fixed in such cases. Also, there is no provision for generating an unlabeled node in spgSplitTuple actions, since it is expected that an spgAddNode action will be needed as well. The SP-GiST core can override the results of the operator class's picksplit function when picksplit fails to divide the supplied leaf values into at least two node categories. When this happens, the new inner tuple is created with multiple nodes that each have the same label (if any) that picksplit gave to the one node it did use, and the leaf values are divided at random among these equivalent nodes. The allTheSame flag is set on the inner tuple to warn the choose and inner_consistent functions that the tuple does not have the node set that they might otherwise expect. When dealing with an allTheSame tuple, a choose result of spgMatchNode is interpreted to mean that the new value can be assigned to any of the equivalent nodes; the core code will ignore the supplied nodeN value and descend into one of the nodes at random (so as to keep the tree balanced). It is an error for choose to return spgAddNode, since that would make the nodes not all equivalent; the spgSplitTuple action must be used if the value to be inserted doesn't match the existing nodes. When dealing with an allTheSame tuple, the inner_consistent function should return either all or none of the nodes as targets for continuing the index search, since they are all equivalent. This may or may not require any special-case code, depending on how much the inner_consistent function normally assumes about the meaning of the nodes. The PostgreSQL source distribution includes several examples of index operator classes for SP-GiST. The core system currently provides radix trees over text columns and two types of trees over points: quad-tree and k-d tree. Look into src/backend/access/spgist/ to see the code.