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Diffstat (limited to 'src/backend/statistics/dependencies.c')
| -rw-r--r-- | src/backend/statistics/dependencies.c | 1352 |
1 files changed, 1352 insertions, 0 deletions
diff --git a/src/backend/statistics/dependencies.c b/src/backend/statistics/dependencies.c new file mode 100644 index 0000000..552843f --- /dev/null +++ b/src/backend/statistics/dependencies.c @@ -0,0 +1,1352 @@ +/*------------------------------------------------------------------------- + * + * dependencies.c + * POSTGRES functional dependencies + * + * Portions Copyright (c) 1996-2020, PostgreSQL Global Development Group + * Portions Copyright (c) 1994, Regents of the University of California + * + * IDENTIFICATION + * src/backend/statistics/dependencies.c + * + *------------------------------------------------------------------------- + */ +#include "postgres.h" + +#include "access/htup_details.h" +#include "access/sysattr.h" +#include "catalog/pg_operator.h" +#include "catalog/pg_statistic_ext.h" +#include "catalog/pg_statistic_ext_data.h" +#include "lib/stringinfo.h" +#include "nodes/nodeFuncs.h" +#include "nodes/nodes.h" +#include "nodes/pathnodes.h" +#include "optimizer/clauses.h" +#include "optimizer/optimizer.h" +#include "statistics/extended_stats_internal.h" +#include "statistics/statistics.h" +#include "utils/bytea.h" +#include "utils/fmgroids.h" +#include "utils/fmgrprotos.h" +#include "utils/lsyscache.h" +#include "utils/selfuncs.h" +#include "utils/syscache.h" +#include "utils/typcache.h" + +/* size of the struct header fields (magic, type, ndeps) */ +#define SizeOfHeader (3 * sizeof(uint32)) + +/* size of a serialized dependency (degree, natts, atts) */ +#define SizeOfItem(natts) \ + (sizeof(double) + sizeof(AttrNumber) * (1 + (natts))) + +/* minimal size of a dependency (with two attributes) */ +#define MinSizeOfItem SizeOfItem(2) + +/* minimal size of dependencies, when all deps are minimal */ +#define MinSizeOfItems(ndeps) \ + (SizeOfHeader + (ndeps) * MinSizeOfItem) + +/* + * Internal state for DependencyGenerator of dependencies. Dependencies are similar to + * k-permutations of n elements, except that the order does not matter for the + * first (k-1) elements. That is, (a,b=>c) and (b,a=>c) are equivalent. + */ +typedef struct DependencyGeneratorData +{ + int k; /* size of the dependency */ + int n; /* number of possible attributes */ + int current; /* next dependency to return (index) */ + AttrNumber ndependencies; /* number of dependencies generated */ + AttrNumber *dependencies; /* array of pre-generated dependencies */ +} DependencyGeneratorData; + +typedef DependencyGeneratorData *DependencyGenerator; + +static void generate_dependencies_recurse(DependencyGenerator state, + int index, AttrNumber start, AttrNumber *current); +static void generate_dependencies(DependencyGenerator state); +static DependencyGenerator DependencyGenerator_init(int n, int k); +static void DependencyGenerator_free(DependencyGenerator state); +static AttrNumber *DependencyGenerator_next(DependencyGenerator state); +static double dependency_degree(int numrows, HeapTuple *rows, int k, + AttrNumber *dependency, VacAttrStats **stats, Bitmapset *attrs); +static bool dependency_is_fully_matched(MVDependency *dependency, + Bitmapset *attnums); +static bool dependency_is_compatible_clause(Node *clause, Index relid, + AttrNumber *attnum); +static MVDependency *find_strongest_dependency(MVDependencies **dependencies, + int ndependencies, + Bitmapset *attnums); +static Selectivity clauselist_apply_dependencies(PlannerInfo *root, List *clauses, + int varRelid, JoinType jointype, + SpecialJoinInfo *sjinfo, + MVDependency **dependencies, + int ndependencies, + AttrNumber *list_attnums, + Bitmapset **estimatedclauses); + +static void +generate_dependencies_recurse(DependencyGenerator state, int index, + AttrNumber start, AttrNumber *current) +{ + /* + * The generator handles the first (k-1) elements differently from the + * last element. + */ + if (index < (state->k - 1)) + { + AttrNumber i; + + /* + * The first (k-1) values have to be in ascending order, which we + * generate recursively. + */ + + for (i = start; i < state->n; i++) + { + current[index] = i; + generate_dependencies_recurse(state, (index + 1), (i + 1), current); + } + } + else + { + int i; + + /* + * the last element is the implied value, which does not respect the + * ascending order. We just need to check that the value is not in the + * first (k-1) elements. + */ + + for (i = 0; i < state->n; i++) + { + int j; + bool match = false; + + current[index] = i; + + for (j = 0; j < index; j++) + { + if (current[j] == i) + { + match = true; + break; + } + } + + /* + * If the value is not found in the first part of the dependency, + * we're done. + */ + if (!match) + { + state->dependencies = (AttrNumber *) repalloc(state->dependencies, + state->k * (state->ndependencies + 1) * sizeof(AttrNumber)); + memcpy(&state->dependencies[(state->k * state->ndependencies)], + current, state->k * sizeof(AttrNumber)); + state->ndependencies++; + } + } + } +} + +/* generate all dependencies (k-permutations of n elements) */ +static void +generate_dependencies(DependencyGenerator state) +{ + AttrNumber *current = (AttrNumber *) palloc0(sizeof(AttrNumber) * state->k); + + generate_dependencies_recurse(state, 0, 0, current); + + pfree(current); +} + +/* + * initialize the DependencyGenerator of variations, and prebuild the variations + * + * This pre-builds all the variations. We could also generate them in + * DependencyGenerator_next(), but this seems simpler. + */ +static DependencyGenerator +DependencyGenerator_init(int n, int k) +{ + DependencyGenerator state; + + Assert((n >= k) && (k > 0)); + + /* allocate the DependencyGenerator state */ + state = (DependencyGenerator) palloc0(sizeof(DependencyGeneratorData)); + state->dependencies = (AttrNumber *) palloc(k * sizeof(AttrNumber)); + + state->ndependencies = 0; + state->current = 0; + state->k = k; + state->n = n; + + /* now actually pre-generate all the variations */ + generate_dependencies(state); + + return state; +} + +/* free the DependencyGenerator state */ +static void +DependencyGenerator_free(DependencyGenerator state) +{ + pfree(state->dependencies); + pfree(state); + +} + +/* generate next combination */ +static AttrNumber * +DependencyGenerator_next(DependencyGenerator state) +{ + if (state->current == state->ndependencies) + return NULL; + + return &state->dependencies[state->k * state->current++]; +} + + +/* + * validates functional dependency on the data + * + * An actual work horse of detecting functional dependencies. Given a variation + * of k attributes, it checks that the first (k-1) are sufficient to determine + * the last one. + */ +static double +dependency_degree(int numrows, HeapTuple *rows, int k, AttrNumber *dependency, + VacAttrStats **stats, Bitmapset *attrs) +{ + int i, + nitems; + MultiSortSupport mss; + SortItem *items; + AttrNumber *attnums; + AttrNumber *attnums_dep; + int numattrs; + + /* counters valid within a group */ + int group_size = 0; + int n_violations = 0; + + /* total number of rows supporting (consistent with) the dependency */ + int n_supporting_rows = 0; + + /* Make sure we have at least two input attributes. */ + Assert(k >= 2); + + /* sort info for all attributes columns */ + mss = multi_sort_init(k); + + /* + * Transform the attrs from bitmap to an array to make accessing the i-th + * member easier, and then construct a filtered version with only attnums + * referenced by the dependency we validate. + */ + attnums = build_attnums_array(attrs, &numattrs); + + attnums_dep = (AttrNumber *) palloc(k * sizeof(AttrNumber)); + for (i = 0; i < k; i++) + attnums_dep[i] = attnums[dependency[i]]; + + /* + * Verify the dependency (a,b,...)->z, using a rather simple algorithm: + * + * (a) sort the data lexicographically + * + * (b) split the data into groups by first (k-1) columns + * + * (c) for each group count different values in the last column + * + * We use the column data types' default sort operators and collations; + * perhaps at some point it'd be worth using column-specific collations? + */ + + /* prepare the sort function for the dimensions */ + for (i = 0; i < k; i++) + { + VacAttrStats *colstat = stats[dependency[i]]; + TypeCacheEntry *type; + + type = lookup_type_cache(colstat->attrtypid, TYPECACHE_LT_OPR); + if (type->lt_opr == InvalidOid) /* shouldn't happen */ + elog(ERROR, "cache lookup failed for ordering operator for type %u", + colstat->attrtypid); + + /* prepare the sort function for this dimension */ + multi_sort_add_dimension(mss, i, type->lt_opr, colstat->attrcollid); + } + + /* + * build an array of SortItem(s) sorted using the multi-sort support + * + * XXX This relies on all stats entries pointing to the same tuple + * descriptor. For now that assumption holds, but it might change in the + * future for example if we support statistics on multiple tables. + */ + items = build_sorted_items(numrows, &nitems, rows, stats[0]->tupDesc, + mss, k, attnums_dep); + + /* + * Walk through the sorted array, split it into rows according to the + * first (k-1) columns. If there's a single value in the last column, we + * count the group as 'supporting' the functional dependency. Otherwise we + * count it as contradicting. + */ + + /* start with the first row forming a group */ + group_size = 1; + + /* loop 1 beyond the end of the array so that we count the final group */ + for (i = 1; i <= nitems; i++) + { + /* + * Check if the group ended, which may be either because we processed + * all the items (i==nitems), or because the i-th item is not equal to + * the preceding one. + */ + if (i == nitems || + multi_sort_compare_dims(0, k - 2, &items[i - 1], &items[i], mss) != 0) + { + /* + * If no violations were found in the group then track the rows of + * the group as supporting the functional dependency. + */ + if (n_violations == 0) + n_supporting_rows += group_size; + + /* Reset counters for the new group */ + n_violations = 0; + group_size = 1; + continue; + } + /* first columns match, but the last one does not (so contradicting) */ + else if (multi_sort_compare_dim(k - 1, &items[i - 1], &items[i], mss) != 0) + n_violations++; + + group_size++; + } + + if (items) + pfree(items); + + pfree(mss); + pfree(attnums); + pfree(attnums_dep); + + /* Compute the 'degree of validity' as (supporting/total). */ + return (n_supporting_rows * 1.0 / numrows); +} + +/* + * detects functional dependencies between groups of columns + * + * Generates all possible subsets of columns (variations) and computes + * the degree of validity for each one. For example when creating statistics + * on three columns (a,b,c) there are 9 possible dependencies + * + * two columns three columns + * ----------- ------------- + * (a) -> b (a,b) -> c + * (a) -> c (a,c) -> b + * (b) -> a (b,c) -> a + * (b) -> c + * (c) -> a + * (c) -> b + */ +MVDependencies * +statext_dependencies_build(int numrows, HeapTuple *rows, Bitmapset *attrs, + VacAttrStats **stats) +{ + int i, + k; + int numattrs; + AttrNumber *attnums; + + /* result */ + MVDependencies *dependencies = NULL; + + /* + * Transform the bms into an array, to make accessing i-th member easier. + */ + attnums = build_attnums_array(attrs, &numattrs); + + Assert(numattrs >= 2); + + /* + * We'll try build functional dependencies starting from the smallest ones + * covering just 2 columns, to the largest ones, covering all columns + * included in the statistics object. We start from the smallest ones + * because we want to be able to skip already implied ones. + */ + for (k = 2; k <= numattrs; k++) + { + AttrNumber *dependency; /* array with k elements */ + + /* prepare a DependencyGenerator of variation */ + DependencyGenerator DependencyGenerator = DependencyGenerator_init(numattrs, k); + + /* generate all possible variations of k values (out of n) */ + while ((dependency = DependencyGenerator_next(DependencyGenerator))) + { + double degree; + MVDependency *d; + + /* compute how valid the dependency seems */ + degree = dependency_degree(numrows, rows, k, dependency, stats, attrs); + + /* + * if the dependency seems entirely invalid, don't store it + */ + if (degree == 0.0) + continue; + + d = (MVDependency *) palloc0(offsetof(MVDependency, attributes) + + k * sizeof(AttrNumber)); + + /* copy the dependency (and keep the indexes into stxkeys) */ + d->degree = degree; + d->nattributes = k; + for (i = 0; i < k; i++) + d->attributes[i] = attnums[dependency[i]]; + + /* initialize the list of dependencies */ + if (dependencies == NULL) + { + dependencies + = (MVDependencies *) palloc0(sizeof(MVDependencies)); + + dependencies->magic = STATS_DEPS_MAGIC; + dependencies->type = STATS_DEPS_TYPE_BASIC; + dependencies->ndeps = 0; + } + + dependencies->ndeps++; + dependencies = (MVDependencies *) repalloc(dependencies, + offsetof(MVDependencies, deps) + + dependencies->ndeps * sizeof(MVDependency *)); + + dependencies->deps[dependencies->ndeps - 1] = d; + } + + /* + * we're done with variations of k elements, so free the + * DependencyGenerator + */ + DependencyGenerator_free(DependencyGenerator); + } + + return dependencies; +} + + +/* + * Serialize list of dependencies into a bytea value. + */ +bytea * +statext_dependencies_serialize(MVDependencies *dependencies) +{ + int i; + bytea *output; + char *tmp; + Size len; + + /* we need to store ndeps, with a number of attributes for each one */ + len = VARHDRSZ + SizeOfHeader; + + /* and also include space for the actual attribute numbers and degrees */ + for (i = 0; i < dependencies->ndeps; i++) + len += SizeOfItem(dependencies->deps[i]->nattributes); + + output = (bytea *) palloc0(len); + SET_VARSIZE(output, len); + + tmp = VARDATA(output); + + /* Store the base struct values (magic, type, ndeps) */ + memcpy(tmp, &dependencies->magic, sizeof(uint32)); + tmp += sizeof(uint32); + memcpy(tmp, &dependencies->type, sizeof(uint32)); + tmp += sizeof(uint32); + memcpy(tmp, &dependencies->ndeps, sizeof(uint32)); + tmp += sizeof(uint32); + + /* store number of attributes and attribute numbers for each dependency */ + for (i = 0; i < dependencies->ndeps; i++) + { + MVDependency *d = dependencies->deps[i]; + + memcpy(tmp, &d->degree, sizeof(double)); + tmp += sizeof(double); + + memcpy(tmp, &d->nattributes, sizeof(AttrNumber)); + tmp += sizeof(AttrNumber); + + memcpy(tmp, d->attributes, sizeof(AttrNumber) * d->nattributes); + tmp += sizeof(AttrNumber) * d->nattributes; + + /* protect against overflow */ + Assert(tmp <= ((char *) output + len)); + } + + /* make sure we've produced exactly the right amount of data */ + Assert(tmp == ((char *) output + len)); + + return output; +} + +/* + * Reads serialized dependencies into MVDependencies structure. + */ +MVDependencies * +statext_dependencies_deserialize(bytea *data) +{ + int i; + Size min_expected_size; + MVDependencies *dependencies; + char *tmp; + + if (data == NULL) + return NULL; + + if (VARSIZE_ANY_EXHDR(data) < SizeOfHeader) + elog(ERROR, "invalid MVDependencies size %zd (expected at least %zd)", + VARSIZE_ANY_EXHDR(data), SizeOfHeader); + + /* read the MVDependencies header */ + dependencies = (MVDependencies *) palloc0(sizeof(MVDependencies)); + + /* initialize pointer to the data part (skip the varlena header) */ + tmp = VARDATA_ANY(data); + + /* read the header fields and perform basic sanity checks */ + memcpy(&dependencies->magic, tmp, sizeof(uint32)); + tmp += sizeof(uint32); + memcpy(&dependencies->type, tmp, sizeof(uint32)); + tmp += sizeof(uint32); + memcpy(&dependencies->ndeps, tmp, sizeof(uint32)); + tmp += sizeof(uint32); + + if (dependencies->magic != STATS_DEPS_MAGIC) + elog(ERROR, "invalid dependency magic %d (expected %d)", + dependencies->magic, STATS_DEPS_MAGIC); + + if (dependencies->type != STATS_DEPS_TYPE_BASIC) + elog(ERROR, "invalid dependency type %d (expected %d)", + dependencies->type, STATS_DEPS_TYPE_BASIC); + + if (dependencies->ndeps == 0) + elog(ERROR, "invalid zero-length item array in MVDependencies"); + + /* what minimum bytea size do we expect for those parameters */ + min_expected_size = SizeOfItem(dependencies->ndeps); + + if (VARSIZE_ANY_EXHDR(data) < min_expected_size) + elog(ERROR, "invalid dependencies size %zd (expected at least %zd)", + VARSIZE_ANY_EXHDR(data), min_expected_size); + + /* allocate space for the MCV items */ + dependencies = repalloc(dependencies, offsetof(MVDependencies, deps) + + (dependencies->ndeps * sizeof(MVDependency *))); + + for (i = 0; i < dependencies->ndeps; i++) + { + double degree; + AttrNumber k; + MVDependency *d; + + /* degree of validity */ + memcpy(°ree, tmp, sizeof(double)); + tmp += sizeof(double); + + /* number of attributes */ + memcpy(&k, tmp, sizeof(AttrNumber)); + tmp += sizeof(AttrNumber); + + /* is the number of attributes valid? */ + Assert((k >= 2) && (k <= STATS_MAX_DIMENSIONS)); + + /* now that we know the number of attributes, allocate the dependency */ + d = (MVDependency *) palloc0(offsetof(MVDependency, attributes) + + (k * sizeof(AttrNumber))); + + d->degree = degree; + d->nattributes = k; + + /* copy attribute numbers */ + memcpy(d->attributes, tmp, sizeof(AttrNumber) * d->nattributes); + tmp += sizeof(AttrNumber) * d->nattributes; + + dependencies->deps[i] = d; + + /* still within the bytea */ + Assert(tmp <= ((char *) data + VARSIZE_ANY(data))); + } + + /* we should have consumed the whole bytea exactly */ + Assert(tmp == ((char *) data + VARSIZE_ANY(data))); + + return dependencies; +} + +/* + * dependency_is_fully_matched + * checks that a functional dependency is fully matched given clauses on + * attributes (assuming the clauses are suitable equality clauses) + */ +static bool +dependency_is_fully_matched(MVDependency *dependency, Bitmapset *attnums) +{ + int j; + + /* + * Check that the dependency actually is fully covered by clauses. We have + * to translate all attribute numbers, as those are referenced + */ + for (j = 0; j < dependency->nattributes; j++) + { + int attnum = dependency->attributes[j]; + + if (!bms_is_member(attnum, attnums)) + return false; + } + + return true; +} + +/* + * statext_dependencies_load + * Load the functional dependencies for the indicated pg_statistic_ext tuple + */ +MVDependencies * +statext_dependencies_load(Oid mvoid) +{ + MVDependencies *result; + bool isnull; + Datum deps; + HeapTuple htup; + + htup = SearchSysCache1(STATEXTDATASTXOID, ObjectIdGetDatum(mvoid)); + if (!HeapTupleIsValid(htup)) + elog(ERROR, "cache lookup failed for statistics object %u", mvoid); + + deps = SysCacheGetAttr(STATEXTDATASTXOID, htup, + Anum_pg_statistic_ext_data_stxddependencies, &isnull); + if (isnull) + elog(ERROR, + "requested statistics kind \"%c\" is not yet built for statistics object %u", + STATS_EXT_DEPENDENCIES, mvoid); + + result = statext_dependencies_deserialize(DatumGetByteaPP(deps)); + + ReleaseSysCache(htup); + + return result; +} + +/* + * pg_dependencies_in - input routine for type pg_dependencies. + * + * pg_dependencies is real enough to be a table column, but it has no operations + * of its own, and disallows input too + */ +Datum +pg_dependencies_in(PG_FUNCTION_ARGS) +{ + /* + * pg_node_list stores the data in binary form and parsing text input is + * not needed, so disallow this. + */ + ereport(ERROR, + (errcode(ERRCODE_FEATURE_NOT_SUPPORTED), + errmsg("cannot accept a value of type %s", "pg_dependencies"))); + + PG_RETURN_VOID(); /* keep compiler quiet */ +} + +/* + * pg_dependencies - output routine for type pg_dependencies. + */ +Datum +pg_dependencies_out(PG_FUNCTION_ARGS) +{ + bytea *data = PG_GETARG_BYTEA_PP(0); + MVDependencies *dependencies = statext_dependencies_deserialize(data); + int i, + j; + StringInfoData str; + + initStringInfo(&str); + appendStringInfoChar(&str, '{'); + + for (i = 0; i < dependencies->ndeps; i++) + { + MVDependency *dependency = dependencies->deps[i]; + + if (i > 0) + appendStringInfoString(&str, ", "); + + appendStringInfoChar(&str, '"'); + for (j = 0; j < dependency->nattributes; j++) + { + if (j == dependency->nattributes - 1) + appendStringInfoString(&str, " => "); + else if (j > 0) + appendStringInfoString(&str, ", "); + + appendStringInfo(&str, "%d", dependency->attributes[j]); + } + appendStringInfo(&str, "\": %f", dependency->degree); + } + + appendStringInfoChar(&str, '}'); + + PG_RETURN_CSTRING(str.data); +} + +/* + * pg_dependencies_recv - binary input routine for type pg_dependencies. + */ +Datum +pg_dependencies_recv(PG_FUNCTION_ARGS) +{ + ereport(ERROR, + (errcode(ERRCODE_FEATURE_NOT_SUPPORTED), + errmsg("cannot accept a value of type %s", "pg_dependencies"))); + + PG_RETURN_VOID(); /* keep compiler quiet */ +} + +/* + * pg_dependencies_send - binary output routine for type pg_dependencies. + * + * Functional dependencies are serialized in a bytea value (although the type + * is named differently), so let's just send that. + */ +Datum +pg_dependencies_send(PG_FUNCTION_ARGS) +{ + return byteasend(fcinfo); +} + +/* + * dependency_is_compatible_clause + * Determines if the clause is compatible with functional dependencies + * + * Only clauses that have the form of equality to a pseudoconstant, or can be + * interpreted that way, are currently accepted. Furthermore the variable + * part of the clause must be a simple Var belonging to the specified + * relation, whose attribute number we return in *attnum on success. + */ +static bool +dependency_is_compatible_clause(Node *clause, Index relid, AttrNumber *attnum) +{ + Var *var; + + if (IsA(clause, RestrictInfo)) + { + RestrictInfo *rinfo = (RestrictInfo *) clause; + + /* Pseudoconstants are not interesting (they couldn't contain a Var) */ + if (rinfo->pseudoconstant) + return false; + + /* Clauses referencing multiple, or no, varnos are incompatible */ + if (bms_membership(rinfo->clause_relids) != BMS_SINGLETON) + return false; + + clause = (Node *) rinfo->clause; + } + + if (is_opclause(clause)) + { + /* If it's an opclause, check for Var = Const or Const = Var. */ + OpExpr *expr = (OpExpr *) clause; + + /* Only expressions with two arguments are candidates. */ + if (list_length(expr->args) != 2) + return false; + + /* Make sure non-selected argument is a pseudoconstant. */ + if (is_pseudo_constant_clause(lsecond(expr->args))) + var = linitial(expr->args); + else if (is_pseudo_constant_clause(linitial(expr->args))) + var = lsecond(expr->args); + else + return false; + + /* + * If it's not an "=" operator, just ignore the clause, as it's not + * compatible with functional dependencies. + * + * This uses the function for estimating selectivity, not the operator + * directly (a bit awkward, but well ...). + * + * XXX this is pretty dubious; probably it'd be better to check btree + * or hash opclass membership, so as not to be fooled by custom + * selectivity functions, and to be more consistent with decisions + * elsewhere in the planner. + */ + if (get_oprrest(expr->opno) != F_EQSEL) + return false; + + /* OK to proceed with checking "var" */ + } + else if (IsA(clause, ScalarArrayOpExpr)) + { + /* If it's an scalar array operator, check for Var IN Const. */ + ScalarArrayOpExpr *expr = (ScalarArrayOpExpr *) clause; + + /* + * Reject ALL() variant, we only care about ANY/IN. + * + * FIXME Maybe we should check if all the values are the same, and + * allow ALL in that case? Doesn't seem very practical, though. + */ + if (!expr->useOr) + return false; + + /* Only expressions with two arguments are candidates. */ + if (list_length(expr->args) != 2) + return false; + + /* + * We know it's always (Var IN Const), so we assume the var is the + * first argument, and pseudoconstant is the second one. + */ + if (!is_pseudo_constant_clause(lsecond(expr->args))) + return false; + + var = linitial(expr->args); + + /* + * If it's not an "=" operator, just ignore the clause, as it's not + * compatible with functional dependencies. The operator is identified + * simply by looking at which function it uses to estimate + * selectivity. That's a bit strange, but it's what other similar + * places do. + */ + if (get_oprrest(expr->opno) != F_EQSEL) + return false; + + /* OK to proceed with checking "var" */ + } + else if (is_orclause(clause)) + { + BoolExpr *expr = (BoolExpr *) clause; + ListCell *lc; + + /* start with no attribute number */ + *attnum = InvalidAttrNumber; + + foreach(lc, expr->args) + { + AttrNumber clause_attnum; + + /* + * Had we found incompatible clause in the arguments, treat the + * whole clause as incompatible. + */ + if (!dependency_is_compatible_clause((Node *) lfirst(lc), + relid, &clause_attnum)) + return false; + + if (*attnum == InvalidAttrNumber) + *attnum = clause_attnum; + + if (*attnum != clause_attnum) + return false; + } + + /* the Var is already checked by the recursive call */ + return true; + } + else if (is_notclause(clause)) + { + /* + * "NOT x" can be interpreted as "x = false", so get the argument and + * proceed with seeing if it's a suitable Var. + */ + var = (Var *) get_notclausearg(clause); + } + else + { + /* + * A boolean expression "x" can be interpreted as "x = true", so + * proceed with seeing if it's a suitable Var. + */ + var = (Var *) clause; + } + + /* + * We may ignore any RelabelType node above the operand. (There won't be + * more than one, since eval_const_expressions has been applied already.) + */ + if (IsA(var, RelabelType)) + var = (Var *) ((RelabelType *) var)->arg; + + /* We only support plain Vars for now */ + if (!IsA(var, Var)) + return false; + + /* Ensure Var is from the correct relation */ + if (var->varno != relid) + return false; + + /* We also better ensure the Var is from the current level */ + if (var->varlevelsup != 0) + return false; + + /* Also ignore system attributes (we don't allow stats on those) */ + if (!AttrNumberIsForUserDefinedAttr(var->varattno)) + return false; + + *attnum = var->varattno; + return true; +} + +/* + * find_strongest_dependency + * find the strongest dependency on the attributes + * + * When applying functional dependencies, we start with the strongest + * dependencies. That is, we select the dependency that: + * + * (a) has all attributes covered by equality clauses + * + * (b) has the most attributes + * + * (c) has the highest degree of validity + * + * This guarantees that we eliminate the most redundant conditions first + * (see the comment in dependencies_clauselist_selectivity). + */ +static MVDependency * +find_strongest_dependency(MVDependencies **dependencies, int ndependencies, + Bitmapset *attnums) +{ + int i, + j; + MVDependency *strongest = NULL; + + /* number of attnums in clauses */ + int nattnums = bms_num_members(attnums); + + /* + * Iterate over the MVDependency items and find the strongest one from the + * fully-matched dependencies. We do the cheap checks first, before + * matching it against the attnums. + */ + for (i = 0; i < ndependencies; i++) + { + for (j = 0; j < dependencies[i]->ndeps; j++) + { + MVDependency *dependency = dependencies[i]->deps[j]; + + /* + * Skip dependencies referencing more attributes than available + * clauses, as those can't be fully matched. + */ + if (dependency->nattributes > nattnums) + continue; + + if (strongest) + { + /* skip dependencies on fewer attributes than the strongest. */ + if (dependency->nattributes < strongest->nattributes) + continue; + + /* also skip weaker dependencies when attribute count matches */ + if (strongest->nattributes == dependency->nattributes && + strongest->degree > dependency->degree) + continue; + } + + /* + * this dependency is stronger, but we must still check that it's + * fully matched to these attnums. We perform this check last as + * it's slightly more expensive than the previous checks. + */ + if (dependency_is_fully_matched(dependency, attnums)) + strongest = dependency; /* save new best match */ + } + } + + return strongest; +} + +/* + * clauselist_apply_dependencies + * Apply the specified functional dependencies to a list of clauses and + * return the estimated selecvitity of the clauses that are compatible + * with any of the given dependencies. + * + * This will estimate all not-already-estimated clauses that are compatible + * with functional dependencies, and which have an attribute mentioned by any + * of the given dependencies (either as an implying or implied attribute). + * + * Given (lists of) clauses on attributes (a,b) and a functional dependency + * (a=>b), the per-column selectivities P(a) and P(b) are notionally combined + * using the formula + * + * P(a,b) = f * P(a) + (1-f) * P(a) * P(b) + * + * where 'f' is the degree of dependency. This reflects the fact that we + * expect a fraction f of all rows to be consistent with the dependency + * (a=>b), and so have a selectivity of P(a), while the remaining rows are + * treated as independent. + * + * In practice, we use a slightly modified version of this formula, which uses + * a selectivity of Min(P(a), P(b)) for the dependent rows, since the result + * should obviously not exceed either column's individual selectivity. I.e., + * we actually combine selectivities using the formula + * + * P(a,b) = f * Min(P(a), P(b)) + (1-f) * P(a) * P(b) + * + * This can make quite a difference if the specific values matching the + * clauses are not consistent with the functional dependency. + */ +static Selectivity +clauselist_apply_dependencies(PlannerInfo *root, List *clauses, + int varRelid, JoinType jointype, + SpecialJoinInfo *sjinfo, + MVDependency **dependencies, int ndependencies, + AttrNumber *list_attnums, + Bitmapset **estimatedclauses) +{ + Bitmapset *attnums; + int i; + int j; + int nattrs; + Selectivity *attr_sel; + int attidx; + int listidx; + ListCell *l; + Selectivity s1; + + /* + * Extract the attnums of all implying and implied attributes from all the + * given dependencies. Each of these attributes is expected to have at + * least 1 not-already-estimated compatible clause that we will estimate + * here. + */ + attnums = NULL; + for (i = 0; i < ndependencies; i++) + { + for (j = 0; j < dependencies[i]->nattributes; j++) + { + AttrNumber attnum = dependencies[i]->attributes[j]; + + attnums = bms_add_member(attnums, attnum); + } + } + + /* + * Compute per-column selectivity estimates for each of these attributes, + * and mark all the corresponding clauses as estimated. + */ + nattrs = bms_num_members(attnums); + attr_sel = (Selectivity *) palloc(sizeof(Selectivity) * nattrs); + + attidx = 0; + i = -1; + while ((i = bms_next_member(attnums, i)) >= 0) + { + List *attr_clauses = NIL; + Selectivity simple_sel; + + listidx = -1; + foreach(l, clauses) + { + Node *clause = (Node *) lfirst(l); + + listidx++; + if (list_attnums[listidx] == i) + { + attr_clauses = lappend(attr_clauses, clause); + *estimatedclauses = bms_add_member(*estimatedclauses, listidx); + } + } + + simple_sel = clauselist_selectivity_simple(root, attr_clauses, varRelid, + jointype, sjinfo, NULL); + attr_sel[attidx++] = simple_sel; + } + + /* + * Now combine these selectivities using the dependency information. For + * chains of dependencies such as a -> b -> c, the b -> c dependency will + * come before the a -> b dependency in the array, so we traverse the + * array backwards to ensure such chains are computed in the right order. + * + * As explained above, pairs of selectivities are combined using the + * formula + * + * P(a,b) = f * Min(P(a), P(b)) + (1-f) * P(a) * P(b) + * + * to ensure that the combined selectivity is never greater than either + * individual selectivity. + * + * Where multiple dependencies apply (e.g., a -> b -> c), we use + * conditional probabilities to compute the overall result as follows: + * + * P(a,b,c) = P(c|a,b) * P(a,b) = P(c|a,b) * P(b|a) * P(a) + * + * so we replace the selectivities of all implied attributes with + * conditional probabilities, that are conditional on all their implying + * attributes. The selectivities of all other non-implied attributes are + * left as they are. + */ + for (i = ndependencies - 1; i >= 0; i--) + { + MVDependency *dependency = dependencies[i]; + AttrNumber attnum; + Selectivity s2; + double f; + + /* Selectivity of all the implying attributes */ + s1 = 1.0; + for (j = 0; j < dependency->nattributes - 1; j++) + { + attnum = dependency->attributes[j]; + attidx = bms_member_index(attnums, attnum); + s1 *= attr_sel[attidx]; + } + + /* Original selectivity of the implied attribute */ + attnum = dependency->attributes[j]; + attidx = bms_member_index(attnums, attnum); + s2 = attr_sel[attidx]; + + /* + * Replace s2 with the conditional probability s2 given s1, computed + * using the formula P(b|a) = P(a,b) / P(a), which simplifies to + * + * P(b|a) = f * Min(P(a), P(b)) / P(a) + (1-f) * P(b) + * + * where P(a) = s1, the selectivity of the implying attributes, and + * P(b) = s2, the selectivity of the implied attribute. + */ + f = dependency->degree; + + if (s1 <= s2) + attr_sel[attidx] = f + (1 - f) * s2; + else + attr_sel[attidx] = f * s2 / s1 + (1 - f) * s2; + } + + /* + * The overall selectivity of all the clauses on all these attributes is + * then the product of all the original (non-implied) probabilities and + * the new conditional (implied) probabilities. + */ + s1 = 1.0; + for (i = 0; i < nattrs; i++) + s1 *= attr_sel[i]; + + CLAMP_PROBABILITY(s1); + + pfree(attr_sel); + bms_free(attnums); + + return s1; +} + +/* + * dependencies_clauselist_selectivity + * Return the estimated selectivity of (a subset of) the given clauses + * using functional dependency statistics, or 1.0 if no useful functional + * dependency statistic exists. + * + * 'estimatedclauses' is an input/output argument that gets a bit set + * corresponding to the (zero-based) list index of each clause that is included + * in the estimated selectivity. + * + * Given equality clauses on attributes (a,b) we find the strongest dependency + * between them, i.e. either (a=>b) or (b=>a). Assuming (a=>b) is the selected + * dependency, we then combine the per-clause selectivities using the formula + * + * P(a,b) = f * P(a) + (1-f) * P(a) * P(b) + * + * where 'f' is the degree of the dependency. (Actually we use a slightly + * modified version of this formula -- see clauselist_apply_dependencies()). + * + * With clauses on more than two attributes, the dependencies are applied + * recursively, starting with the widest/strongest dependencies. For example + * P(a,b,c) is first split like this: + * + * P(a,b,c) = f * P(a,b) + (1-f) * P(a,b) * P(c) + * + * assuming (a,b=>c) is the strongest dependency. + */ +Selectivity +dependencies_clauselist_selectivity(PlannerInfo *root, + List *clauses, + int varRelid, + JoinType jointype, + SpecialJoinInfo *sjinfo, + RelOptInfo *rel, + Bitmapset **estimatedclauses) +{ + Selectivity s1 = 1.0; + ListCell *l; + Bitmapset *clauses_attnums = NULL; + AttrNumber *list_attnums; + int listidx; + MVDependencies **func_dependencies; + int nfunc_dependencies; + int total_ndeps; + MVDependency **dependencies; + int ndependencies; + int i; + + /* check if there's any stats that might be useful for us. */ + if (!has_stats_of_kind(rel->statlist, STATS_EXT_DEPENDENCIES)) + return 1.0; + + list_attnums = (AttrNumber *) palloc(sizeof(AttrNumber) * + list_length(clauses)); + + /* + * Pre-process the clauses list to extract the attnums seen in each item. + * We need to determine if there's any clauses which will be useful for + * dependency selectivity estimations. Along the way we'll record all of + * the attnums for each clause in a list which we'll reference later so we + * don't need to repeat the same work again. We'll also keep track of all + * attnums seen. + * + * We also skip clauses that we already estimated using different types of + * statistics (we treat them as incompatible). + */ + listidx = 0; + foreach(l, clauses) + { + Node *clause = (Node *) lfirst(l); + AttrNumber attnum; + + if (!bms_is_member(listidx, *estimatedclauses) && + dependency_is_compatible_clause(clause, rel->relid, &attnum)) + { + list_attnums[listidx] = attnum; + clauses_attnums = bms_add_member(clauses_attnums, attnum); + } + else + list_attnums[listidx] = InvalidAttrNumber; + + listidx++; + } + + /* + * If there's not at least two distinct attnums then reject the whole list + * of clauses. We must return 1.0 so the calling function's selectivity is + * unaffected. + */ + if (bms_num_members(clauses_attnums) < 2) + { + bms_free(clauses_attnums); + pfree(list_attnums); + return 1.0; + } + + /* + * Load all functional dependencies matching at least two parameters. We + * can simply consider all dependencies at once, without having to search + * for the best statistics object. + * + * To not waste cycles and memory, we deserialize dependencies only for + * statistics that match at least two attributes. The array is allocated + * with the assumption that all objects match - we could grow the array to + * make it just the right size, but it's likely wasteful anyway thanks to + * moving the freed chunks to freelists etc. + */ + func_dependencies = (MVDependencies **) palloc(sizeof(MVDependencies *) * + list_length(rel->statlist)); + nfunc_dependencies = 0; + total_ndeps = 0; + + foreach(l, rel->statlist) + { + StatisticExtInfo *stat = (StatisticExtInfo *) lfirst(l); + Bitmapset *matched; + int num_matched; + + /* skip statistics that are not of the correct type */ + if (stat->kind != STATS_EXT_DEPENDENCIES) + continue; + + matched = bms_intersect(clauses_attnums, stat->keys); + num_matched = bms_num_members(matched); + bms_free(matched); + + /* skip objects matching fewer than two attributes from clauses */ + if (num_matched < 2) + continue; + + func_dependencies[nfunc_dependencies] + = statext_dependencies_load(stat->statOid); + + total_ndeps += func_dependencies[nfunc_dependencies]->ndeps; + nfunc_dependencies++; + } + + /* if no matching stats could be found then we've nothing to do */ + if (nfunc_dependencies == 0) + { + pfree(func_dependencies); + bms_free(clauses_attnums); + pfree(list_attnums); + return 1.0; + } + + /* + * Work out which dependencies we can apply, starting with the + * widest/stongest ones, and proceeding to smaller/weaker ones. + */ + dependencies = (MVDependency **) palloc(sizeof(MVDependency *) * + total_ndeps); + ndependencies = 0; + + while (true) + { + MVDependency *dependency; + AttrNumber attnum; + + /* the widest/strongest dependency, fully matched by clauses */ + dependency = find_strongest_dependency(func_dependencies, + nfunc_dependencies, + clauses_attnums); + if (!dependency) + break; + + dependencies[ndependencies++] = dependency; + + /* Ignore dependencies using this implied attribute in later loops */ + attnum = dependency->attributes[dependency->nattributes - 1]; + clauses_attnums = bms_del_member(clauses_attnums, attnum); + } + + /* + * If we found applicable dependencies, use them to estimate all + * compatible clauses on attributes that they refer to. + */ + if (ndependencies != 0) + s1 = clauselist_apply_dependencies(root, clauses, varRelid, jointype, + sjinfo, dependencies, ndependencies, + list_attnums, estimatedclauses); + + /* free deserialized functional dependencies (and then the array) */ + for (i = 0; i < nfunc_dependencies; i++) + pfree(func_dependencies[i]); + + pfree(dependencies); + pfree(func_dependencies); + bms_free(clauses_attnums); + pfree(list_attnums); + + return s1; +} |