network_selfuncs.c

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/*-------------------------------------------------------------------------
 *
 * network_selfuncs.c
 *    Functions for selectivity estimation of inet/cidr operators
 *
 * This module provides estimators for the subnet inclusion and overlap
 * operators.  Estimates are based on null fraction, most common values,
 * and histogram of inet/cidr columns.
 *
 * Portions Copyright (c) 1996-2024, PostgreSQL Global Development Group
 * Portions Copyright (c) 1994, Regents of the University of California
 *
 *
 * IDENTIFICATION
 *    src/backend/utils/adt/network_selfuncs.c
 *
 *-------------------------------------------------------------------------
 */
#include "postgres.h"
 
#include <math.h>
 
#include "access/htup_details.h"
#include "catalog/pg_operator.h"
#include "catalog/pg_statistic.h"
#include "utils/fmgrprotos.h"
#include "utils/inet.h"
#include "utils/lsyscache.h"
#include "utils/selfuncs.h"
 
 
/* Default selectivity for the inet overlap operator */
#define DEFAULT_OVERLAP_SEL 0.01
 
/* Default selectivity for the various inclusion operators */
#define DEFAULT_INCLUSION_SEL 0.005
 
/* Default selectivity for specified operator */
#define DEFAULT_SEL(operator) \
    ((operator) == OID_INET_OVERLAP_OP ? \
     DEFAULT_OVERLAP_SEL : DEFAULT_INCLUSION_SEL)
 
/* Maximum number of items to consider in join selectivity calculations */
#define MAX_CONSIDERED_ELEMS 1024
 
static Selectivity networkjoinsel_inner(Oid operator,
                                        VariableStatData *vardata1, VariableStatData *vardata2);
static Selectivity networkjoinsel_semi(Oid operator,
                                       VariableStatData *vardata1, VariableStatData *vardata2);
static Selectivity mcv_population(float4 *mcv_numbers, int mcv_nvalues);
static Selectivity inet_hist_value_sel(Datum *values, int nvalues,
                                       Datum constvalue, int opr_codenum);
static Selectivity inet_mcv_join_sel(Datum *mcv1_values,
                                     float4 *mcv1_numbers, int mcv1_nvalues, Datum *mcv2_values,
                                     float4 *mcv2_numbers, int mcv2_nvalues, Oid operator);
static Selectivity inet_mcv_hist_sel(Datum *mcv_values, float4 *mcv_numbers,
                                     int mcv_nvalues, Datum *hist_values, int hist_nvalues,
                                     int opr_codenum);
static Selectivity inet_hist_inclusion_join_sel(Datum *hist1_values,
                                                int hist1_nvalues,
                                                Datum *hist2_values, int hist2_nvalues,
                                                int opr_codenum);
static Selectivity inet_semi_join_sel(Datum lhs_value,
                                      bool mcv_exists, Datum *mcv_values, int mcv_nvalues,
                                      bool hist_exists, Datum *hist_values, int hist_nvalues,
                                      double hist_weight,
                                      FmgrInfo *proc, int opr_codenum);
static int  inet_opr_codenum(Oid operator);
static int  inet_inclusion_cmp(inet *left, inet *right, int opr_codenum);
static int  inet_masklen_inclusion_cmp(inet *left, inet *right,
                                       int opr_codenum);
static int  inet_hist_match_divider(inet *boundary, inet *query,
                                    int opr_codenum);
 
/*
 * Selectivity estimation for the subnet inclusion/overlap operators
 */
Datum
networksel(PG_FUNCTION_ARGS)
{
    PlannerInfo *root = (PlannerInfo *) PG_GETARG_POINTER(0);
    Oid         operator = PG_GETARG_OID(1);
    List       *args = (List *) PG_GETARG_POINTER(2);
    int         varRelid = PG_GETARG_INT32(3);
    VariableStatData vardata;
    Node       *other;
    bool        varonleft;
    Selectivity selec,
                mcv_selec,
                non_mcv_selec;
    Datum       constvalue;
    Form_pg_statistic stats;
    AttStatsSlot hslot;
    double      sumcommon,
                nullfrac;
    FmgrInfo    proc;
 
    /*
     * If expression is not (variable op something) or (something op
     * variable), then punt and return a default estimate.
     */
    if (!get_restriction_variable(root, args, varRelid,
                                  &vardata, &other, &varonleft))
        PG_RETURN_FLOAT8(DEFAULT_SEL(operator));
 
    /*
     * Can't do anything useful if the something is not a constant, either.
     */
    if (!IsA(other, Const))
    {
        ReleaseVariableStats(vardata);
        PG_RETURN_FLOAT8(DEFAULT_SEL(operator));
    }
 
    /* All of the operators handled here are strict. */
    if (((Const *) other)->constisnull)
    {
        ReleaseVariableStats(vardata);
        PG_RETURN_FLOAT8(0.0);
    }
    constvalue = ((Const *) other)->constvalue;
 
    /* Otherwise, we need stats in order to produce a non-default estimate. */
    if (!HeapTupleIsValid(vardata.statsTuple))
    {
        ReleaseVariableStats(vardata);
        PG_RETURN_FLOAT8(DEFAULT_SEL(operator));
    }
 
    stats = (Form_pg_statistic) GETSTRUCT(vardata.statsTuple);
    nullfrac = stats->stanullfrac;
 
    /*
     * If we have most-common-values info, add up the fractions of the MCV
     * entries that satisfy MCV OP CONST.  These fractions contribute directly
     * to the result selectivity.  Also add up the total fraction represented
     * by MCV entries.
     */
    fmgr_info(get_opcode(operator), &proc);
    mcv_selec = mcv_selectivity(&vardata, &proc, InvalidOid,
                                constvalue, varonleft,
                                &sumcommon);
 
    /*
     * If we have a histogram, use it to estimate the proportion of the
     * non-MCV population that satisfies the clause.  If we don't, apply the
     * default selectivity to that population.
     */
    if (get_attstatsslot(&hslot, vardata.statsTuple,
                         STATISTIC_KIND_HISTOGRAM, InvalidOid,
                         ATTSTATSSLOT_VALUES))
    {
        int         opr_codenum = inet_opr_codenum(operator);
 
        /* Commute if needed, so we can consider histogram to be on the left */
        if (!varonleft)
            opr_codenum = -opr_codenum;
        non_mcv_selec = inet_hist_value_sel(hslot.values, hslot.nvalues,
                                            constvalue, opr_codenum);
 
        free_attstatsslot(&hslot);
    }
    else
        non_mcv_selec = DEFAULT_SEL(operator);
 
    /* Combine selectivities for MCV and non-MCV populations */
    selec = mcv_selec + (1.0 - nullfrac - sumcommon) * non_mcv_selec;
 
    /* Result should be in range, but make sure... */
    CLAMP_PROBABILITY(selec);
 
    ReleaseVariableStats(vardata);
 
    PG_RETURN_FLOAT8(selec);
}
 
/*
 * Join selectivity estimation for the subnet inclusion/overlap operators
 *
 * This function has the same structure as eqjoinsel() in selfuncs.c.
 *
 * Throughout networkjoinsel and its subroutines, we have a performance issue
 * in that the amount of work to be done is O(N^2) in the length of the MCV
 * and histogram arrays.  To keep the runtime from getting out of hand when
 * large statistics targets have been set, we arbitrarily limit the number of
 * values considered to 1024 (MAX_CONSIDERED_ELEMS).  For the MCV arrays, this
 * is easy: just consider at most the first N elements.  (Since the MCVs are
 * sorted by decreasing frequency, this correctly gets us the first N MCVs.)
 * For the histogram arrays, we decimate; that is consider only every k'th
 * element, where k is chosen so that no more than MAX_CONSIDERED_ELEMS
 * elements are considered.  This should still give us a good random sample of
 * the non-MCV population.  Decimation is done on-the-fly in the loops that
 * iterate over the histogram arrays.
 */
Datum
networkjoinsel(PG_FUNCTION_ARGS)
{
    PlannerInfo *root = (PlannerInfo *) PG_GETARG_POINTER(0);
    Oid         operator = PG_GETARG_OID(1);
    List       *args = (List *) PG_GETARG_POINTER(2);
#ifdef NOT_USED
    JoinType    jointype = (JoinType) PG_GETARG_INT16(3);
#endif
    SpecialJoinInfo *sjinfo = (SpecialJoinInfo *) PG_GETARG_POINTER(4);
    double      selec;
    VariableStatData vardata1;
    VariableStatData vardata2;
    bool        join_is_reversed;
 
    get_join_variables(root, args, sjinfo,
                       &vardata1, &vardata2, &join_is_reversed);
 
    switch (sjinfo->jointype)
    {
        case JOIN_INNER:
        case JOIN_LEFT:
        case JOIN_FULL:
 
            /*
             * Selectivity for left/full join is not exactly the same as inner
             * join, but we neglect the difference, as eqjoinsel does.
             */
            selec = networkjoinsel_inner(operator, &vardata1, &vardata2);
            break;
        case JOIN_SEMI:
        case JOIN_ANTI:
            /* Here, it's important that we pass the outer var on the left. */
            if (!join_is_reversed)
                selec = networkjoinsel_semi(operator, &vardata1, &vardata2);
            else
                selec = networkjoinsel_semi(get_commutator(operator),
                                            &vardata2, &vardata1);
            break;
        default:
            /* other values not expected here */
            elog(ERROR, "unrecognized join type: %d",
                 (int) sjinfo->jointype);
            selec = 0;          /* keep compiler quiet */
            break;
    }
 
    ReleaseVariableStats(vardata1);
    ReleaseVariableStats(vardata2);
 
    CLAMP_PROBABILITY(selec);
 
    PG_RETURN_FLOAT8((float8) selec);
}
 
/*
 * Inner join selectivity estimation for subnet inclusion/overlap operators
 *
 * Calculates MCV vs MCV, MCV vs histogram and histogram vs histogram
 * selectivity for join using the subnet inclusion operators.  Unlike the
 * join selectivity function for the equality operator, eqjoinsel_inner(),
 * one to one matching of the values is not enough.  Network inclusion
 * operators are likely to match many to many, so we must check all pairs.
 * (Note: it might be possible to exploit understanding of the histogram's
 * btree ordering to reduce the work needed, but we don't currently try.)
 * Also, MCV vs histogram selectivity is not neglected as in eqjoinsel_inner().
 */
static Selectivity
networkjoinsel_inner(Oid operator,
                     VariableStatData *vardata1, VariableStatData *vardata2)
{
    Form_pg_statistic stats;
    double      nullfrac1 = 0.0,
                nullfrac2 = 0.0;
    Selectivity selec = 0.0,
                sumcommon1 = 0.0,
                sumcommon2 = 0.0;
    bool        mcv1_exists = false,
                mcv2_exists = false,
                hist1_exists = false,
                hist2_exists = false;
    int         opr_codenum;
    int         mcv1_length = 0,
                mcv2_length = 0;
    AttStatsSlot mcv1_slot;
    AttStatsSlot mcv2_slot;
    AttStatsSlot hist1_slot;
    AttStatsSlot hist2_slot;
 
    if (HeapTupleIsValid(vardata1->statsTuple))
    {
        stats = (Form_pg_statistic) GETSTRUCT(vardata1->statsTuple);
        nullfrac1 = stats->stanullfrac;
 
        mcv1_exists = get_attstatsslot(&mcv1_slot, vardata1->statsTuple,
                                       STATISTIC_KIND_MCV, InvalidOid,
                                       ATTSTATSSLOT_VALUES | ATTSTATSSLOT_NUMBERS);
        hist1_exists = get_attstatsslot(&hist1_slot, vardata1->statsTuple,
                                        STATISTIC_KIND_HISTOGRAM, InvalidOid,
                                        ATTSTATSSLOT_VALUES);
        /* Arbitrarily limit number of MCVs considered */
        mcv1_length = Min(mcv1_slot.nvalues, MAX_CONSIDERED_ELEMS);
        if (mcv1_exists)
            sumcommon1 = mcv_population(mcv1_slot.numbers, mcv1_length);
    }
    else
    {
        memset(&mcv1_slot, 0, sizeof(mcv1_slot));
        memset(&hist1_slot, 0, sizeof(hist1_slot));
    }
 
    if (HeapTupleIsValid(vardata2->statsTuple))
    {
        stats = (Form_pg_statistic) GETSTRUCT(vardata2->statsTuple);
        nullfrac2 = stats->stanullfrac;
 
        mcv2_exists = get_attstatsslot(&mcv2_slot, vardata2->statsTuple,
                                       STATISTIC_KIND_MCV, InvalidOid,
                                       ATTSTATSSLOT_VALUES | ATTSTATSSLOT_NUMBERS);
        hist2_exists = get_attstatsslot(&hist2_slot, vardata2->statsTuple,
                                        STATISTIC_KIND_HISTOGRAM, InvalidOid,
                                        ATTSTATSSLOT_VALUES);
        /* Arbitrarily limit number of MCVs considered */
        mcv2_length = Min(mcv2_slot.nvalues, MAX_CONSIDERED_ELEMS);
        if (mcv2_exists)
            sumcommon2 = mcv_population(mcv2_slot.numbers, mcv2_length);
    }
    else
    {
        memset(&mcv2_slot, 0, sizeof(mcv2_slot));
        memset(&hist2_slot, 0, sizeof(hist2_slot));
    }
 
    opr_codenum = inet_opr_codenum(operator);
 
    /*
     * Calculate selectivity for MCV vs MCV matches.
     */
    if (mcv1_exists && mcv2_exists)
        selec += inet_mcv_join_sel(mcv1_slot.values, mcv1_slot.numbers,
                                   mcv1_length,
                                   mcv2_slot.values, mcv2_slot.numbers,
                                   mcv2_length,
                                   operator);
 
    /*
     * Add in selectivities for MCV vs histogram matches, scaling according to
     * the fractions of the populations represented by the histograms. Note
     * that the second case needs to commute the operator.
     */
    if (mcv1_exists && hist2_exists)
        selec += (1.0 - nullfrac2 - sumcommon2) *
            inet_mcv_hist_sel(mcv1_slot.values, mcv1_slot.numbers, mcv1_length,
                              hist2_slot.values, hist2_slot.nvalues,
                              opr_codenum);
    if (mcv2_exists && hist1_exists)
        selec += (1.0 - nullfrac1 - sumcommon1) *
            inet_mcv_hist_sel(mcv2_slot.values, mcv2_slot.numbers, mcv2_length,
                              hist1_slot.values, hist1_slot.nvalues,
                              -opr_codenum);
 
    /*
     * Add in selectivity for histogram vs histogram matches, again scaling
     * appropriately.
     */
    if (hist1_exists && hist2_exists)
        selec += (1.0 - nullfrac1 - sumcommon1) *
            (1.0 - nullfrac2 - sumcommon2) *
            inet_hist_inclusion_join_sel(hist1_slot.values, hist1_slot.nvalues,
                                         hist2_slot.values, hist2_slot.nvalues,
                                         opr_codenum);
 
    /*
     * If useful statistics are not available then use the default estimate.
     * We can apply null fractions if known, though.
     */
    if ((!mcv1_exists && !hist1_exists) || (!mcv2_exists && !hist2_exists))
        selec = (1.0 - nullfrac1) * (1.0 - nullfrac2) * DEFAULT_SEL(operator);
 
    /* Release stats. */
    free_attstatsslot(&mcv1_slot);
    free_attstatsslot(&mcv2_slot);
    free_attstatsslot(&hist1_slot);
    free_attstatsslot(&hist2_slot);
 
    return selec;
}
 
/*
 * Semi join selectivity estimation for subnet inclusion/overlap operators
 *
 * Calculates MCV vs MCV, MCV vs histogram, histogram vs MCV, and histogram vs
 * histogram selectivity for semi/anti join cases.
 */
static Selectivity
networkjoinsel_semi(Oid operator,
                    VariableStatData *vardata1, VariableStatData *vardata2)
{
    Form_pg_statistic stats;
    Selectivity selec = 0.0,
                sumcommon1 = 0.0,
                sumcommon2 = 0.0;
    double      nullfrac1 = 0.0,
                nullfrac2 = 0.0,
                hist2_weight = 0.0;
    bool        mcv1_exists = false,
                mcv2_exists = false,
                hist1_exists = false,
                hist2_exists = false;
    int         opr_codenum;
    FmgrInfo    proc;
    int         i,
                mcv1_length = 0,
                mcv2_length = 0;
    AttStatsSlot mcv1_slot;
    AttStatsSlot mcv2_slot;
    AttStatsSlot hist1_slot;
    AttStatsSlot hist2_slot;
 
    if (HeapTupleIsValid(vardata1->statsTuple))
    {
        stats = (Form_pg_statistic) GETSTRUCT(vardata1->statsTuple);
        nullfrac1 = stats->stanullfrac;
 
        mcv1_exists = get_attstatsslot(&mcv1_slot, vardata1->statsTuple,
                                       STATISTIC_KIND_MCV, InvalidOid,
                                       ATTSTATSSLOT_VALUES | ATTSTATSSLOT_NUMBERS);
        hist1_exists = get_attstatsslot(&hist1_slot, vardata1->statsTuple,
                                        STATISTIC_KIND_HISTOGRAM, InvalidOid,
                                        ATTSTATSSLOT_VALUES);
        /* Arbitrarily limit number of MCVs considered */
        mcv1_length = Min(mcv1_slot.nvalues, MAX_CONSIDERED_ELEMS);
        if (mcv1_exists)
            sumcommon1 = mcv_population(mcv1_slot.numbers, mcv1_length);
    }
    else
    {
        memset(&mcv1_slot, 0, sizeof(mcv1_slot));
        memset(&hist1_slot, 0, sizeof(hist1_slot));
    }
 
    if (HeapTupleIsValid(vardata2->statsTuple))
    {
        stats = (Form_pg_statistic) GETSTRUCT(vardata2->statsTuple);
        nullfrac2 = stats->stanullfrac;
 
        mcv2_exists = get_attstatsslot(&mcv2_slot, vardata2->statsTuple,
                                       STATISTIC_KIND_MCV, InvalidOid,
                                       ATTSTATSSLOT_VALUES | ATTSTATSSLOT_NUMBERS);
        hist2_exists = get_attstatsslot(&hist2_slot, vardata2->statsTuple,
                                        STATISTIC_KIND_HISTOGRAM, InvalidOid,
                                        ATTSTATSSLOT_VALUES);
        /* Arbitrarily limit number of MCVs considered */
        mcv2_length = Min(mcv2_slot.nvalues, MAX_CONSIDERED_ELEMS);
        if (mcv2_exists)
            sumcommon2 = mcv_population(mcv2_slot.numbers, mcv2_length);
    }
    else
    {
        memset(&mcv2_slot, 0, sizeof(mcv2_slot));
        memset(&hist2_slot, 0, sizeof(hist2_slot));
    }
 
    opr_codenum = inet_opr_codenum(operator);
    fmgr_info(get_opcode(operator), &proc);
 
    /* Estimate number of input rows represented by RHS histogram. */
    if (hist2_exists && vardata2->rel)
        hist2_weight = (1.0 - nullfrac2 - sumcommon2) * vardata2->rel->rows;
 
    /*
     * Consider each element of the LHS MCV list, matching it to whatever RHS
     * stats we have.  Scale according to the known frequency of the MCV.
     */
    if (mcv1_exists && (mcv2_exists || hist2_exists))
    {
        for (i = 0; i < mcv1_length; i++)
        {
            selec += mcv1_slot.numbers[i] *
                inet_semi_join_sel(mcv1_slot.values[i],
                                   mcv2_exists, mcv2_slot.values, mcv2_length,
                                   hist2_exists,
                                   hist2_slot.values, hist2_slot.nvalues,
                                   hist2_weight,
                                   &proc, opr_codenum);
        }
    }
 
    /*
     * Consider each element of the LHS histogram, except for the first and
     * last elements, which we exclude on the grounds that they're outliers
     * and thus not very representative.  Scale on the assumption that each
     * such histogram element represents an equal share of the LHS histogram
     * population (which is a bit bogus, because the members of its bucket may
     * not all act the same with respect to the join clause, but it's hard to
     * do better).
     *
     * If there are too many histogram elements, decimate to limit runtime.
     */
    if (hist1_exists && hist1_slot.nvalues > 2 && (mcv2_exists || hist2_exists))
    {
        double      hist_selec_sum = 0.0;
        int         k,
                    n;
 
        k = (hist1_slot.nvalues - 3) / MAX_CONSIDERED_ELEMS + 1;
 
        n = 0;
        for (i = 1; i < hist1_slot.nvalues - 1; i += k)
        {
            hist_selec_sum +=
                inet_semi_join_sel(hist1_slot.values[i],
                                   mcv2_exists, mcv2_slot.values, mcv2_length,
                                   hist2_exists,
                                   hist2_slot.values, hist2_slot.nvalues,
                                   hist2_weight,
                                   &proc, opr_codenum);
            n++;
        }
 
        selec += (1.0 - nullfrac1 - sumcommon1) * hist_selec_sum / n;
    }
 
    /*
     * If useful statistics are not available then use the default estimate.
     * We can apply null fractions if known, though.
     */
    if ((!mcv1_exists && !hist1_exists) || (!mcv2_exists && !hist2_exists))
        selec = (1.0 - nullfrac1) * (1.0 - nullfrac2) * DEFAULT_SEL(operator);
 
    /* Release stats. */
    free_attstatsslot(&mcv1_slot);
    free_attstatsslot(&mcv2_slot);
    free_attstatsslot(&hist1_slot);
    free_attstatsslot(&hist2_slot);
 
    return selec;
}
 
/*
 * Compute the fraction of a relation's population that is represented
 * by the MCV list.
 */
static Selectivity
mcv_population(float4 *mcv_numbers, int mcv_nvalues)
{
    Selectivity sumcommon = 0.0;
    int         i;
 
    for (i = 0; i < mcv_nvalues; i++)
    {
        sumcommon += mcv_numbers[i];
    }
 
    return sumcommon;
}
 
/*
 * Inet histogram vs single value selectivity estimation
 *
 * Estimate the fraction of the histogram population that satisfies
 * "value OPR CONST".  (The result needs to be scaled to reflect the
 * proportion of the total population represented by the histogram.)
 *
 * The histogram is originally for the inet btree comparison operators.
 * Only the common bits of the network part and the length of the network part
 * (masklen) are interesting for the subnet inclusion operators.  Fortunately,
 * btree comparison treats the network part as the major sort key.  Even so,
 * the length of the network part would not really be significant in the
 * histogram.  This would lead to big mistakes for data sets with uneven
 * masklen distribution.  To reduce this problem, comparisons with the left
 * and the right sides of the buckets are used together.
 *
 * Histogram bucket matches are calculated in two forms.  If the constant
 * matches both bucket endpoints the bucket is considered as fully matched.
 * The second form is to match the bucket partially; we recognize this when
 * the constant matches just one endpoint, or the two endpoints fall on
 * opposite sides of the constant.  (Note that when the constant matches an
 * interior histogram element, it gets credit for partial matches to the
 * buckets on both sides, while a match to a histogram endpoint gets credit
 * for only one partial match.  This is desirable.)
 *
 * The divider in the partial bucket match is imagined as the distance
 * between the decisive bits and the common bits of the addresses.  It will
 * be used as a power of two as it is the natural scale for the IP network
 * inclusion.  This partial bucket match divider calculation is an empirical
 * formula and subject to change with more experiment.
 *
 * For a partial match, we try to calculate dividers for both of the
 * boundaries.  If the address family of a boundary value does not match the
 * constant or comparison of the length of the network parts is not correct
 * for the operator, the divider for that boundary will not be taken into
 * account.  If both of the dividers are valid, the greater one will be used
 * to minimize the mistake in buckets that have disparate masklens.  This
 * calculation is unfair when dividers can be calculated for both of the
 * boundaries but they are far from each other; but it is not a common
 * situation as the boundaries are expected to share most of their significant
 * bits of their masklens.  The mistake would be greater, if we would use the
 * minimum instead of the maximum, and we don't know a sensible way to combine
 * them.
 *
 * For partial match in buckets that have different address families on the
 * left and right sides, only the boundary with the same address family is
 * taken into consideration.  This can cause more mistakes for these buckets
 * if the masklens of their boundaries are also disparate.  But this can only
 * happen in one bucket, since only two address families exist.  It seems a
 * better option than not considering these buckets at all.
 */
static Selectivity
inet_hist_value_sel(Datum *values, int nvalues, Datum constvalue,
                    int opr_codenum)
{
    Selectivity match = 0.0;
    inet       *query,
               *left,
               *right;
    int         i,
                k,
                n;
    int         left_order,
                right_order,
                left_divider,
                right_divider;
 
    /* guard against zero-divide below */
    if (nvalues <= 1)
        return 0.0;
 
    /* if there are too many histogram elements, decimate to limit runtime */
    k = (nvalues - 2) / MAX_CONSIDERED_ELEMS + 1;
 
    query = DatumGetInetPP(constvalue);
 
    /* "left" is the left boundary value of the current bucket ... */
    left = DatumGetInetPP(values[0]);
    left_order = inet_inclusion_cmp(left, query, opr_codenum);
 
    n = 0;
    for (i = k; i < nvalues; i += k)
    {
        /* ... and "right" is the right boundary value */
        right = DatumGetInetPP(values[i]);
        right_order = inet_inclusion_cmp(right, query, opr_codenum);
 
        if (left_order == 0 && right_order == 0)
        {
            /* The whole bucket matches, since both endpoints do. */
            match += 1.0;
        }
        else if ((left_order <= 0 && right_order >= 0) ||
                 (left_order >= 0 && right_order <= 0))
        {
            /* Partial bucket match. */
            left_divider = inet_hist_match_divider(left, query, opr_codenum);
            right_divider = inet_hist_match_divider(right, query, opr_codenum);
 
            if (left_divider >= 0 || right_divider >= 0)
                match += 1.0 / pow(2.0, Max(left_divider, right_divider));
        }
 
        /* Shift the variables. */
        left = right;
        left_order = right_order;
 
        /* Count the number of buckets considered. */
        n++;
    }
 
    return match / n;
}
 
/*
 * Inet MCV vs MCV join selectivity estimation
 *
 * We simply add up the fractions of the populations that satisfy the clause.
 * The result is exact and does not need to be scaled further.
 */
static Selectivity
inet_mcv_join_sel(Datum *mcv1_values, float4 *mcv1_numbers, int mcv1_nvalues,
                  Datum *mcv2_values, float4 *mcv2_numbers, int mcv2_nvalues,
                  Oid operator)
{
    Selectivity selec = 0.0;
    FmgrInfo    proc;
    int         i,
                j;
 
    fmgr_info(get_opcode(operator), &proc);
 
    for (i = 0; i < mcv1_nvalues; i++)
    {
        for (j = 0; j < mcv2_nvalues; j++)
            if (DatumGetBool(FunctionCall2(&proc,
                                           mcv1_values[i],
                                           mcv2_values[j])))
                selec += mcv1_numbers[i] * mcv2_numbers[j];
    }
    return selec;
}
 
/*
 * Inet MCV vs histogram join selectivity estimation
 *
 * For each MCV on the lefthand side, estimate the fraction of the righthand's
 * histogram population that satisfies the join clause, and add those up,
 * scaling by the MCV's frequency.  The result still needs to be scaled
 * according to the fraction of the righthand's population represented by
 * the histogram.
 */
static Selectivity
inet_mcv_hist_sel(Datum *mcv_values, float4 *mcv_numbers, int mcv_nvalues,
                  Datum *hist_values, int hist_nvalues,
                  int opr_codenum)
{
    Selectivity selec = 0.0;
    int         i;
 
    /*
     * We'll call inet_hist_value_selec with the histogram on the left, so we
     * must commute the operator.
     */
    opr_codenum = -opr_codenum;
 
    for (i = 0; i < mcv_nvalues; i++)
    {
        selec += mcv_numbers[i] *
            inet_hist_value_sel(hist_values, hist_nvalues, mcv_values[i],
                                opr_codenum);
    }
    return selec;
}
 
/*
 * Inet histogram vs histogram join selectivity estimation
 *
 * Here, we take all values listed in the second histogram (except for the
 * first and last elements, which are excluded on the grounds of possibly
 * not being very representative) and treat them as a uniform sample of
 * the non-MCV population for that relation.  For each one, we apply
 * inet_hist_value_selec to see what fraction of the first histogram
 * it matches.
 *
 * We could alternatively do this the other way around using the operator's
 * commutator.  XXX would it be worthwhile to do it both ways and take the
 * average?  That would at least avoid non-commutative estimation results.
 */
static Selectivity
inet_hist_inclusion_join_sel(Datum *hist1_values, int hist1_nvalues,
                             Datum *hist2_values, int hist2_nvalues,
                             int opr_codenum)
{
    double      match = 0.0;
    int         i,
                k,
                n;
 
    if (hist2_nvalues <= 2)
        return 0.0;             /* no interior histogram elements */
 
    /* if there are too many histogram elements, decimate to limit runtime */
    k = (hist2_nvalues - 3) / MAX_CONSIDERED_ELEMS + 1;
 
    n = 0;
    for (i = 1; i < hist2_nvalues - 1; i += k)
    {
        match += inet_hist_value_sel(hist1_values, hist1_nvalues,
                                     hist2_values[i], opr_codenum);
        n++;
    }
 
    return match / n;
}
 
/*
 * Inet semi join selectivity estimation for one value
 *
 * The function calculates the probability that there is at least one row
 * in the RHS table that satisfies the "lhs_value op column" condition.
 * It is used in semi join estimation to check a sample from the left hand
 * side table.
 *
 * The MCV and histogram from the right hand side table should be provided as
 * arguments with the lhs_value from the left hand side table for the join.
 * hist_weight is the total number of rows represented by the histogram.
 * For example, if the table has 1000 rows, and 10% of the rows are in the MCV
 * list, and another 10% are NULLs, hist_weight would be 800.
 *
 * First, the lhs_value will be matched to the most common values.  If it
 * matches any of them, 1.0 will be returned, because then there is surely
 * a match.
 *
 * Otherwise, the histogram will be used to estimate the number of rows in
 * the second table that match the condition.  If the estimate is greater
 * than 1.0, 1.0 will be returned, because it means there is a greater chance
 * that the lhs_value will match more than one row in the table.  If it is
 * between 0.0 and 1.0, it will be returned as the probability.
 */
static Selectivity
inet_semi_join_sel(Datum lhs_value,
                   bool mcv_exists, Datum *mcv_values, int mcv_nvalues,
                   bool hist_exists, Datum *hist_values, int hist_nvalues,
                   double hist_weight,
                   FmgrInfo *proc, int opr_codenum)
{
    if (mcv_exists)
    {
        int         i;
 
        for (i = 0; i < mcv_nvalues; i++)
        {
            if (DatumGetBool(FunctionCall2(proc,
                                           lhs_value,
                                           mcv_values[i])))
                return 1.0;
        }
    }
 
    if (hist_exists && hist_weight > 0)
    {
        Selectivity hist_selec;
 
        /* Commute operator, since we're passing lhs_value on the right */
        hist_selec = inet_hist_value_sel(hist_values, hist_nvalues,
                                         lhs_value, -opr_codenum);
 
        if (hist_selec > 0)
            return Min(1.0, hist_weight * hist_selec);
    }
 
    return 0.0;
}
 
/*
 * Assign useful code numbers for the subnet inclusion/overlap operators
 *
 * Only inet_masklen_inclusion_cmp() and inet_hist_match_divider() depend
 * on the exact codes assigned here; but many other places in this file
 * know that they can negate a code to obtain the code for the commutator
 * operator.
 */
static int
inet_opr_codenum(Oid operator)
{
    switch (operator)
    {
        case OID_INET_SUP_OP:
            return -2;
        case OID_INET_SUPEQ_OP:
            return -1;
        case OID_INET_OVERLAP_OP:
            return 0;
        case OID_INET_SUBEQ_OP:
            return 1;
        case OID_INET_SUB_OP:
            return 2;
        default:
            elog(ERROR, "unrecognized operator %u for inet selectivity",
                 operator);
    }
    return 0;                   /* unreached, but keep compiler quiet */
}
 
/*
 * Comparison function for the subnet inclusion/overlap operators
 *
 * If the comparison is okay for the specified inclusion operator, the return
 * value will be 0.  Otherwise the return value will be less than or greater
 * than 0 as appropriate for the operator.
 *
 * Comparison is compatible with the basic comparison function for the inet
 * type.  See network_cmp_internal() in network.c for the original.  Basic
 * comparison operators are implemented with the network_cmp_internal()
 * function.  It is possible to implement the subnet inclusion operators with
 * this function.
 *
 * Comparison is first on the common bits of the network part, then on the
 * length of the network part (masklen) as in the network_cmp_internal()
 * function.  Only the first part is in this function.  The second part is
 * separated to another function for reusability.  The difference between the
 * second part and the original network_cmp_internal() is that the inclusion
 * operator is considered while comparing the lengths of the network parts.
 * See the inet_masklen_inclusion_cmp() function below.
 */
static int
inet_inclusion_cmp(inet *left, inet *right, int opr_codenum)
{
    if (ip_family(left) == ip_family(right))
    {
        int         order;
 
        order = bitncmp(ip_addr(left), ip_addr(right),
                        Min(ip_bits(left), ip_bits(right)));
        if (order != 0)
            return order;
 
        return inet_masklen_inclusion_cmp(left, right, opr_codenum);
    }
 
    return ip_family(left) - ip_family(right);
}
 
/*
 * Masklen comparison function for the subnet inclusion/overlap operators
 *
 * Compares the lengths of the network parts of the inputs.  If the comparison
 * is okay for the specified inclusion operator, the return value will be 0.
 * Otherwise the return value will be less than or greater than 0 as
 * appropriate for the operator.
 */
static int
inet_masklen_inclusion_cmp(inet *left, inet *right, int opr_codenum)
{
    int         order;
 
    order = (int) ip_bits(left) - (int) ip_bits(right);
 
    /*
     * Return 0 if the operator would accept this combination of masklens.
     * Note that opr_codenum zero (overlaps) will accept all cases.
     */
    if ((order > 0 && opr_codenum >= 0) ||
        (order == 0 && opr_codenum >= -1 && opr_codenum <= 1) ||
        (order < 0 && opr_codenum <= 0))
        return 0;
 
    /*
     * Otherwise, return a negative value for sup/supeq (notionally, the RHS
     * needs to have a larger masklen than it has, which would make it sort
     * later), or a positive value for sub/subeq (vice versa).
     */
    return opr_codenum;
}
 
/*
 * Inet histogram partial match divider calculation
 *
 * First the families and the lengths of the network parts are compared using
 * the subnet inclusion operator.  If those are acceptable for the operator,
 * the divider will be calculated using the masklens and the common bits of
 * the addresses.  -1 will be returned if it cannot be calculated.
 *
 * See commentary for inet_hist_value_sel() for some rationale for this.
 */
static int
inet_hist_match_divider(inet *boundary, inet *query, int opr_codenum)
{
    if (ip_family(boundary) == ip_family(query) &&
        inet_masklen_inclusion_cmp(boundary, query, opr_codenum) == 0)
    {
        int         min_bits,
                    decisive_bits;
 
        min_bits = Min(ip_bits(boundary), ip_bits(query));
 
        /*
         * Set decisive_bits to the masklen of the one that should contain the
         * other according to the operator.
         */
        if (opr_codenum < 0)
            decisive_bits = ip_bits(boundary);
        else if (opr_codenum > 0)
            decisive_bits = ip_bits(query);
        else
            decisive_bits = min_bits;
 
        /*
         * Now return the number of non-common decisive bits.  (This will be
         * zero if the boundary and query in fact match, else positive.)
         */
        if (min_bits > 0)
            return decisive_bits - bitncommon(ip_addr(boundary),
                                              ip_addr(query),
                                              min_bits);
        return decisive_bits;
    }
 
    return -1;
}