brin_minmax_multi.c

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/*
 * brin_minmax_multi.c
 *      Implementation of Multi Min/Max opclass for BRIN
 *
 * Portions Copyright (c) 1996-2021, PostgreSQL Global Development Group
 * Portions Copyright (c) 1994, Regents of the University of California
 *
 *
 * Implements a variant of minmax opclass, where the summary is composed of
 * multiple smaller intervals. This allows us to handle outliers, which
 * usually make the simple minmax opclass inefficient.
 *
 * Consider for example page range with simple minmax interval [1000,2000],
 * and assume a new row gets inserted into the range with value 1000000.
 * Due to that the interval gets [1000,1000000]. I.e. the minmax interval
 * got 1000x wider and won't be useful to eliminate scan keys between 2001
 * and 1000000.
 *
 * With minmax-multi opclass, we may have [1000,2000] interval initially,
 * but after adding the new row we start tracking it as two interval:
 *
 *   [1000,2000] and [1000000,1000000]
 *
 * This allows us to still eliminate the page range when the scan keys hit
 * the gap between 2000 and 1000000, making it useful in cases when the
 * simple minmax opclass gets inefficient.
 *
 * The number of intervals tracked per page range is somewhat flexible.
 * What is restricted is the number of values per page range, and the limit
 * is currently 32 (see values_per_range reloption). Collapsed intervals
 * (with equal minimum and maximum value) are stored as a single value,
 * while regular intervals require two values.
 *
 * When the number of values gets too high (by adding new values to the
 * summary), we merge some of the intervals to free space for more values.
 * This is done in a greedy way - we simply pick the two closest intervals,
 * merge them, and repeat this until the number of values to store gets
 * sufficiently low (below 50% of maximum values), but that is mostly
 * arbitrary threshold and may be changed easily).
 *
 * To pick the closest intervals we use the "distance" support procedure,
 * which measures space between two ranges (i.e. the length of an interval).
 * The computed value may be an approximation - in the worst case we will
 * merge two ranges that are slightly less optimal at that step, but the
 * index should still produce correct results.
 *
 * The compactions (reducing the number of values) is fairly expensive, as
 * it requires calling the distance functions, sorting etc. So when building
 * the summary, we use a significantly larger buffer, and only enforce the
 * exact limit at the very end. This improves performance, and it also helps
 * with building better ranges (due to the greedy approach).
 *
 *
 * IDENTIFICATION
 *    src/backend/access/brin/brin_minmax_multi.c
 */
#include "postgres.h"

/* needed for PGSQL_AF_INET */
#include <sys/socket.h>

#include "access/genam.h"
#include "access/brin.h"
#include "access/brin_internal.h"
#include "access/brin_tuple.h"
#include "access/reloptions.h"
#include "access/stratnum.h"
#include "access/htup_details.h"
#include "catalog/pg_type.h"
#include "catalog/pg_am.h"
#include "catalog/pg_amop.h"
#include "utils/array.h"
#include "utils/builtins.h"
#include "utils/date.h"
#include "utils/datum.h"
#include "utils/inet.h"
#include "utils/lsyscache.h"
#include "utils/memutils.h"
#include "utils/numeric.h"
#include "utils/pg_lsn.h"
#include "utils/rel.h"
#include "utils/syscache.h"
#include "utils/timestamp.h"
#include "utils/uuid.h"

/*
 * Additional SQL level support functions
 *
 * Procedure numbers must not use values reserved for BRIN itself; see
 * brin_internal.h.
 */
#define     MINMAX_MAX_PROCNUMS     1   /* maximum support procs we need */
#define     PROCNUM_DISTANCE        11  /* required, distance between values */

/*
 * Subtract this from procnum to obtain index in MinmaxMultiOpaque arrays
 * (Must be equal to minimum of private procnums).
 */
#define     PROCNUM_BASE            11

/*
 * Sizing the insert buffer - we use 10x the number of values specified
 * in the reloption, but we cap it to 8192 not to get too large. When
 * the buffer gets full, we reduce the number of values by half.
 */
#define     MINMAX_BUFFER_FACTOR            10
#define     MINMAX_BUFFER_MIN               256
#define     MINMAX_BUFFER_MAX               8192
#define     MINMAX_BUFFER_LOAD_FACTOR       0.5

typedef struct MinmaxMultiOpaque
{
    FmgrInfo    extra_procinfos[MINMAX_MAX_PROCNUMS];
    bool        extra_proc_missing[MINMAX_MAX_PROCNUMS];
    Oid         cached_subtype;
    FmgrInfo    strategy_procinfos[BTMaxStrategyNumber];
} MinmaxMultiOpaque;

/*
 * Storage type for BRIN's minmax reloptions
 */
typedef struct MinMaxMultiOptions
{
    int32       vl_len_;        /* varlena header (do not touch directly!) */
    int         valuesPerRange; /* number of values per range */
} MinMaxMultiOptions;

#define MINMAX_MULTI_DEFAULT_VALUES_PER_PAGE        32

#define MinMaxMultiGetValuesPerRange(opts) \
        ((opts) && (((MinMaxMultiOptions *) (opts))->valuesPerRange != 0) ? \
         ((MinMaxMultiOptions *) (opts))->valuesPerRange : \
         MINMAX_MULTI_DEFAULT_VALUES_PER_PAGE)

#define SAMESIGN(a,b) (((a) < 0) == ((b) < 0))

/*
 * The summary of minmax-multi indexes has two representations - Ranges for
 * convenient processing, and SerializedRanges for storage in bytea value.
 *
 * The Ranges struct stores the boundary values in a single array, but we
 * treat regular and single-point ranges differently to save space. For
 * regular ranges (with different boundary values) we have to store both
 * values, while for "single-point ranges" we only need to save one value.
 *
 * The 'values' array stores boundary values for regular ranges first (there
 * are 2*nranges values to store), and then the nvalues boundary values for
 * single-point ranges. That is, we have (2*nranges + nvalues) boundary
 * values in the array.
 *
 * +---------------------------------+-------------------------------+
 * | ranges (sorted pairs of values) | sorted values (single points) |
 * +---------------------------------+-------------------------------+
 *
 * This allows us to quickly add new values, and store outliers without
 * making the other ranges very wide.
 *
 * We never store more than maxvalues values (as set by values_per_range
 * reloption). If needed we merge some of the ranges.
 *
 * To minimize palloc overhead, we always allocate the full array with
 * space for maxvalues elements. This should be fine as long as the
 * maxvalues is reasonably small (64 seems fine), which is the case
 * thanks to values_per_range reloption being limited to 256.
 */
typedef struct Ranges
{
    /* Cache information that we need quite often. */
    Oid         typid;
    Oid         colloid;
    AttrNumber  attno;
    FmgrInfo   *cmp;

    /* (2*nranges + nvalues) <= maxvalues */
    int         nranges;        /* number of ranges in the array (stored) */
    int         nsorted;        /* number of sorted values (ranges + points) */
    int         nvalues;        /* number of values in the data array (all) */
    int         maxvalues;      /* maximum number of values (reloption) */

    /*
     * We simply add the values into a large buffer, without any expensive
     * steps (sorting, deduplication, ...). The buffer is a multiple of the
     * target number of values, so the compaction happens less often,
     * amortizing the costs. We keep the actual target and compact to the
     * requested number of values at the very end, before serializing to
     * on-disk representation.
     */
    /* requested number of values */
    int         target_maxvalues;

    /* values stored for this range - either raw values, or ranges */
    Datum       values[FLEXIBLE_ARRAY_MEMBER];
} Ranges;

/*
 * On-disk the summary is stored as a bytea value, with a simple header
 * with basic metadata, followed by the boundary values. It has a varlena
 * header, so can be treated as varlena directly.
 *
 * See range_serialize/range_deserialize for serialization details.
 */
typedef struct SerializedRanges
{
    /* varlena header (do not touch directly!) */
    int32       vl_len_;

    /* type of values stored in the data array */
    Oid         typid;

    /* (2*nranges + nvalues) <= maxvalues */
    int         nranges;        /* number of ranges in the array (stored) */
    int         nvalues;        /* number of values in the data array (all) */
    int         maxvalues;      /* maximum number of values (reloption) */

    /* contains the actual data */
    char        data[FLEXIBLE_ARRAY_MEMBER];
} SerializedRanges;

static SerializedRanges *range_serialize(Ranges *range);

static Ranges *range_deserialize(int maxvalues, SerializedRanges *range);


/*
 * Used to represent ranges expanded to make merging and combining easier.
 *
 * Each expanded range is essentially an interval, represented by min/max
 * values, along with a flag whether it's a collapsed range (in which case
 * the min and max values are equal). We have the flag to handle by-ref
 * data types - we can't simply compare the datums, and this saves some
 * calls to the type-specific comparator function.
 */
typedef struct ExpandedRange
{
    Datum       minval;         /* lower boundary */
    Datum       maxval;         /* upper boundary */
    bool        collapsed;      /* true if minval==maxval */
} ExpandedRange;

/*
 * Represents a distance between two ranges (identified by index into
 * an array of extended ranges).
 */
typedef struct DistanceValue
{
    int         index;
    double      value;
} DistanceValue;


/* Cache for support and strategy procedures. */

static FmgrInfo *minmax_multi_get_procinfo(BrinDesc *bdesc, uint16 attno,
                                           uint16 procnum);

static FmgrInfo *minmax_multi_get_strategy_procinfo(BrinDesc *bdesc,
                                                    uint16 attno, Oid subtype,
                                                    uint16 strategynum);

typedef struct compare_context
{
    FmgrInfo   *cmpFn;
    Oid         colloid;
} compare_context;

static int  compare_values(const void *a, const void *b, void *arg);


#ifdef USE_ASSERT_CHECKING
/*
 * Check that the order of the array values is correct, using the cmp
 * function (which should be BTLessStrategyNumber).
 */
static void
AssertArrayOrder(FmgrInfo *cmp, Oid colloid, Datum *values, int nvalues)
{
    int         i;
    Datum       lt;

    for (i = 0; i < (nvalues - 1); i++)
    {
        lt = FunctionCall2Coll(cmp, colloid, values[i], values[i + 1]);
        Assert(DatumGetBool(lt));
    }
}
#endif

/*
 * Comprehensive check of the Ranges structure.
 */
static void
AssertCheckRanges(Ranges *ranges, FmgrInfo *cmpFn, Oid colloid)
{
#ifdef USE_ASSERT_CHECKING
    int         i;

    /* some basic sanity checks */
    Assert(ranges->nranges >= 0);
    Assert(ranges->nsorted >= 0);
    Assert(ranges->nvalues >= ranges->nsorted);
    Assert(ranges->maxvalues >= 2 * ranges->nranges + ranges->nvalues);
    Assert(ranges->typid != InvalidOid);

    /*
     * First the ranges - there are 2*nranges boundary values, and the values
     * have to be strictly ordered (equal values would mean the range is
     * collapsed, and should be stored as a point). This also guarantees that
     * the ranges do not overlap.
     */
    AssertArrayOrder(cmpFn, colloid, ranges->values, 2 * ranges->nranges);

    /* then the single-point ranges (with nvalues boundar values ) */
    AssertArrayOrder(cmpFn, colloid, &ranges->values[2 * ranges->nranges],
                     ranges->nsorted);

    /*
     * Check that none of the values are not covered by ranges (both sorted
     * and unsorted)
     */
    for (i = 0; i < ranges->nvalues; i++)
    {
        Datum       compar;
        int         start,
                    end;
        Datum       minvalue,
                    maxvalue;

        Datum       value = ranges->values[2 * ranges->nranges + i];

        if (ranges->nranges == 0)
            break;

        minvalue = ranges->values[0];
        maxvalue = ranges->values[2 * ranges->nranges - 1];

        /*
         * Is the value smaller than the minval? If yes, we'll recurse to the
         * left side of range array.
         */
        compar = FunctionCall2Coll(cmpFn, colloid, value, minvalue);

        /* smaller than the smallest value in the first range */
        if (DatumGetBool(compar))
            continue;

        /*
         * Is the value greater than the maxval? If yes, we'll recurse to the
         * right side of range array.
         */
        compar = FunctionCall2Coll(cmpFn, colloid, maxvalue, value);

        /* larger than the largest value in the last range */
        if (DatumGetBool(compar))
            continue;

        start = 0;              /* first range */
        end = ranges->nranges - 1;  /* last range */
        while (true)
        {
            int         midpoint = (start + end) / 2;

            /* this means we ran out of ranges in the last step */
            if (start > end)
                break;

            /* copy the min/max values from the ranges */
            minvalue = ranges->values[2 * midpoint];
            maxvalue = ranges->values[2 * midpoint + 1];

            /*
             * Is the value smaller than the minval? If yes, we'll recurse to
             * the left side of range array.
             */
            compar = FunctionCall2Coll(cmpFn, colloid, value, minvalue);

            /* smaller than the smallest value in this range */
            if (DatumGetBool(compar))
            {
                end = (midpoint - 1);
                continue;
            }

            /*
             * Is the value greater than the minval? If yes, we'll recurse to
             * the right side of range array.
             */
            compar = FunctionCall2Coll(cmpFn, colloid, maxvalue, value);

            /* larger than the largest value in this range */
            if (DatumGetBool(compar))
            {
                start = (midpoint + 1);
                continue;
            }

            /* hey, we found a matching range */
            Assert(false);
        }
    }

    /* and values in the unsorted part must not be in sorted part */
    for (i = ranges->nsorted; i < ranges->nvalues; i++)
    {
        compare_context cxt;
        Datum       value = ranges->values[2 * ranges->nranges + i];

        if (ranges->nsorted == 0)
            break;

        cxt.colloid = ranges->colloid;
        cxt.cmpFn = ranges->cmp;

        Assert(bsearch_arg(&value, &ranges->values[2 * ranges->nranges],
                           ranges->nsorted, sizeof(Datum),
                           compare_values, (void *) &cxt) == NULL);
    }
#endif
}

/*
 * Check that the expanded ranges (built when reducing the number of ranges
 * by combining some of them) are correctly sorted and do not overlap.
 */
static void
AssertCheckExpandedRanges(BrinDesc *bdesc, Oid colloid, AttrNumber attno,
                          Form_pg_attribute attr, ExpandedRange *ranges,
                          int nranges)
{
#ifdef USE_ASSERT_CHECKING
    int         i;
    FmgrInfo   *eq;
    FmgrInfo   *lt;

    eq = minmax_multi_get_strategy_procinfo(bdesc, attno, attr->atttypid,
                                            BTEqualStrategyNumber);

    lt = minmax_multi_get_strategy_procinfo(bdesc, attno, attr->atttypid,
                                            BTLessStrategyNumber);

    /*
     * Each range independently should be valid, i.e. that for the boundary
     * values (lower <= upper).
     */
    for (i = 0; i < nranges; i++)
    {
        Datum       r;
        Datum       minval = ranges[i].minval;
        Datum       maxval = ranges[i].maxval;

        if (ranges[i].collapsed)    /* collapsed: minval == maxval */
            r = FunctionCall2Coll(eq, colloid, minval, maxval);
        else                    /* non-collapsed: minval < maxval */
            r = FunctionCall2Coll(lt, colloid, minval, maxval);

        Assert(DatumGetBool(r));
    }

    /*
     * And the ranges should be ordered and must not overlap, i.e. upper <
     * lower for boundaries of consecutive ranges.
     */
    for (i = 0; i < nranges - 1; i++)
    {
        Datum       r;
        Datum       maxval = ranges[i].maxval;
        Datum       minval = ranges[i + 1].minval;

        r = FunctionCall2Coll(lt, colloid, maxval, minval);

        Assert(DatumGetBool(r));
    }
#endif
}


/*
 * minmax_multi_init
 *      Initialize the deserialized range list, allocate all the memory.
 *
 * This is only in-memory representation of the ranges, so we allocate
 * enough space for the maximum number of values (so as not to have to do
 * repallocs as the ranges grow).
 */
static Ranges *
minmax_multi_init(int maxvalues)
{
    Size        len;
    Ranges     *ranges;

    Assert(maxvalues > 0);

    len = offsetof(Ranges, values); /* fixed header */
    len += maxvalues * sizeof(Datum);   /* Datum values */

    ranges = (Ranges *) palloc0(len);

    ranges->maxvalues = maxvalues;

    return ranges;
}


/*
 * range_deduplicate_values
 *      Deduplicate the part with values in the simple points.
 *
 * This is meant to be a cheaper way of reducing the size of the ranges. It
 * does not touch the ranges, and only sorts the other values - it does not
 * call the distance functions, which may be quite expensive, etc.
 *
 * We do know the values are not duplicate with the ranges, because we check
 * that before adding a new value. Same for the sorted part of values.
 */
static void
range_deduplicate_values(Ranges *range)
{
    int         i,
                n;
    int         start;
    compare_context cxt;

    /*
     * If there are no unsorted values, we're done (this probably can't
     * happen, as we're adding values to unsorted part).
     */
    if (range->nsorted == range->nvalues)
        return;

    /* sort the values */
    cxt.colloid = range->colloid;
    cxt.cmpFn = range->cmp;

    /* the values start right after the ranges (which are always sorted) */
    start = 2 * range->nranges;

    /*
     * XXX This might do a merge sort, to leverage that the first part of the
     * array is already sorted. If the sorted part is large, it might be quite
     * a bit faster.
     */
    qsort_arg(&range->values[start],
              range->nvalues, sizeof(Datum),
              compare_values, (void *) &cxt);

    n = 1;
    for (i = 1; i < range->nvalues; i++)
    {
        /* same as preceding value, so store it */
        if (compare_values(&range->values[start + i - 1],
                           &range->values[start + i],
                           (void *) &cxt) == 0)
            continue;

        range->values[start + n] = range->values[start + i];

        n++;
    }

    /* now all the values are sorted */
    range->nvalues = n;
    range->nsorted = n;

    AssertCheckRanges(range, range->cmp, range->colloid);
}


/*
 * range_serialize
 *    Serialize the in-memory representation into a compact varlena value.
 *
 * Simply copy the header and then also the individual values, as stored
 * in the in-memory value array.
 */
static SerializedRanges *
range_serialize(Ranges *range)
{
    Size        len;
    int         nvalues;
    SerializedRanges *serialized;
    Oid         typid;
    int         typlen;
    bool        typbyval;

    int         i;
    char       *ptr;

    /* simple sanity checks */
    Assert(range->nranges >= 0);
    Assert(range->nsorted >= 0);
    Assert(range->nvalues >= 0);
    Assert(range->maxvalues > 0);
    Assert(range->target_maxvalues > 0);

    /* at this point the range should be compacted to the target size */
    Assert(2 * range->nranges + range->nvalues <= range->target_maxvalues);

    Assert(range->target_maxvalues <= range->maxvalues);

    /* range boundaries are always sorted */
    Assert(range->nvalues >= range->nsorted);

    /* deduplicate values, if there's unsorted part */
    range_deduplicate_values(range);

    /* see how many Datum values we actually have */
    nvalues = 2 * range->nranges + range->nvalues;

    typid = range->typid;
    typbyval = get_typbyval(typid);
    typlen = get_typlen(typid);

    /* header is always needed */
    len = offsetof(SerializedRanges, data);

    /*
     * The space needed depends on data type - for fixed-length data types
     * (by-value and some by-reference) it's pretty simple, just multiply
     * (attlen * nvalues) and we're done. For variable-length by-reference
     * types we need to actually walk all the values and sum the lengths.
     */
    if (typlen == -1)           /* varlena */
    {
        int         i;

        for (i = 0; i < nvalues; i++)
        {
            len += VARSIZE_ANY(range->values[i]);
        }
    }
    else if (typlen == -2)      /* cstring */
    {
        int         i;

        for (i = 0; i < nvalues; i++)
        {
            /* don't forget to include the null terminator ;-) */
            len += strlen(DatumGetCString(range->values[i])) + 1;
        }
    }
    else                        /* fixed-length types (even by-reference) */
    {
        Assert(typlen > 0);
        len += nvalues * typlen;
    }

    /*
     * Allocate the serialized object, copy the basic information. The
     * serialized object is a varlena, so update the header.
     */
    serialized = (SerializedRanges *) palloc0(len);
    SET_VARSIZE(serialized, len);

    serialized->typid = typid;
    serialized->nranges = range->nranges;
    serialized->nvalues = range->nvalues;
    serialized->maxvalues = range->target_maxvalues;

    /*
     * And now copy also the boundary values (like the length calculation this
     * depends on the particular data type).
     */
    ptr = serialized->data;     /* start of the serialized data */

    for (i = 0; i < nvalues; i++)
    {
        if (typbyval)           /* simple by-value data types */
        {
            Datum       tmp;

            /*
             * For byval types, we need to copy just the significant bytes -
             * we can't use memcpy directly, as that assumes little-endian
             * behavior.  store_att_byval does almost what we need, but it
             * requires a properly aligned buffer - the output buffer does not
             * guarantee that. So we simply use a local Datum variable (which
             * guarantees proper alignment), and then copy the value from it.
             */
            store_att_byval(&tmp, range->values[i], typlen);

            memcpy(ptr, &tmp, typlen);
            ptr += typlen;
        }
        else if (typlen > 0)    /* fixed-length by-ref types */
        {
            memcpy(ptr, DatumGetPointer(range->values[i]), typlen);
            ptr += typlen;
        }
        else if (typlen == -1)  /* varlena */
        {
            int         tmp = VARSIZE_ANY(DatumGetPointer(range->values[i]));

            memcpy(ptr, DatumGetPointer(range->values[i]), tmp);
            ptr += tmp;
        }
        else if (typlen == -2)  /* cstring */
        {
            int         tmp = strlen(DatumGetCString(range->values[i])) + 1;

            memcpy(ptr, DatumGetCString(range->values[i]), tmp);
            ptr += tmp;
        }

        /* make sure we haven't overflown the buffer end */
        Assert(ptr <= ((char *) serialized + len));
    }

    /* exact size */
    Assert(ptr == ((char *) serialized + len));

    return serialized;
}

/*
 * range_deserialize
 *    Serialize the in-memory representation into a compact varlena value.
 *
 * Simply copy the header and then also the individual values, as stored
 * in the in-memory value array.
 */
static Ranges *
range_deserialize(int maxvalues, SerializedRanges *serialized)
{
    int         i,
                nvalues;
    char       *ptr,
               *dataptr;
    bool        typbyval;
    int         typlen;
    Size        datalen;

    Ranges     *range;

    Assert(serialized->nranges >= 0);
    Assert(serialized->nvalues >= 0);
    Assert(serialized->maxvalues > 0);

    nvalues = 2 * serialized->nranges + serialized->nvalues;

    Assert(nvalues <= serialized->maxvalues);
    Assert(serialized->maxvalues <= maxvalues);

    range = minmax_multi_init(maxvalues);

    /* copy the header info */
    range->nranges = serialized->nranges;
    range->nvalues = serialized->nvalues;
    range->nsorted = serialized->nvalues;
    range->maxvalues = maxvalues;
    range->target_maxvalues = serialized->maxvalues;

    range->typid = serialized->typid;

    typbyval = get_typbyval(serialized->typid);
    typlen = get_typlen(serialized->typid);

    /*
     * And now deconstruct the values into Datum array. We have to copy the
     * data because the serialized representation ignores alignment, and we
     * don't want to rely on it being kept around anyway.
     */
    ptr = serialized->data;

    /*
     * We don't want to allocate many pieces, so we just allocate everything
     * in one chunk. How much space will we need?
     *
     * XXX We don't need to copy simple by-value data types.
     */
    datalen = 0;
    dataptr = NULL;
    for (i = 0; (i < nvalues) && (!typbyval); i++)
    {
        if (typlen > 0)         /* fixed-length by-ref types */
            datalen += MAXALIGN(typlen);
        else if (typlen == -1)  /* varlena */
        {
            datalen += MAXALIGN(VARSIZE_ANY(DatumGetPointer(ptr)));
            ptr += VARSIZE_ANY(DatumGetPointer(ptr));
        }
        else if (typlen == -2)  /* cstring */
        {
            Size        slen = strlen(DatumGetCString(ptr)) + 1;

            datalen += MAXALIGN(slen);
            ptr += slen;
        }
    }

    if (datalen > 0)
        dataptr = palloc(datalen);

    /*
     * Restore the source pointer (might have been modified when calculating
     * the space we need to allocate).
     */
    ptr = serialized->data;

    for (i = 0; i < nvalues; i++)
    {
        if (typbyval)           /* simple by-value data types */
        {
            Datum       v = 0;

            memcpy(&v, ptr, typlen);

            range->values[i] = fetch_att(&v, true, typlen);
            ptr += typlen;
        }
        else if (typlen > 0)    /* fixed-length by-ref types */
        {
            range->values[i] = PointerGetDatum(dataptr);

            memcpy(dataptr, ptr, typlen);
            dataptr += MAXALIGN(typlen);

            ptr += typlen;
        }
        else if (typlen == -1)  /* varlena */
        {
            range->values[i] = PointerGetDatum(dataptr);

            memcpy(dataptr, ptr, VARSIZE_ANY(ptr));
            dataptr += MAXALIGN(VARSIZE_ANY(ptr));
            ptr += VARSIZE_ANY(ptr);
        }
        else if (typlen == -2)  /* cstring */
        {
            Size        slen = strlen(ptr) + 1;

            range->values[i] = PointerGetDatum(dataptr);

            memcpy(dataptr, ptr, slen);
            dataptr += MAXALIGN(slen);
            ptr += slen;
        }

        /* make sure we haven't overflown the buffer end */
        Assert(ptr <= ((char *) serialized + VARSIZE_ANY(serialized)));
    }

    /* should have consumed the whole input value exactly */
    Assert(ptr == ((char *) serialized + VARSIZE_ANY(serialized)));

    /* return the deserialized value */
    return range;
}

/*
 * compare_expanded_ranges
 *    Compare the expanded ranges - first by minimum, then by maximum.
 *
 * We do guarantee that ranges in a single Ranges object do not overlap, so it
 * may seem strange that we don't order just by minimum. But when merging two
 * Ranges (which happens in the union function), the ranges may in fact
 * overlap. So we do compare both.
 */
static int
compare_expanded_ranges(const void *a, const void *b, void *arg)
{
    ExpandedRange *ra = (ExpandedRange *) a;
    ExpandedRange *rb = (ExpandedRange *) b;
    Datum       r;

    compare_context *cxt = (compare_context *) arg;

    /* first compare minvals */
    r = FunctionCall2Coll(cxt->cmpFn, cxt->colloid, ra->minval, rb->minval);

    if (DatumGetBool(r))
        return -1;

    r = FunctionCall2Coll(cxt->cmpFn, cxt->colloid, rb->minval, ra->minval);

    if (DatumGetBool(r))
        return 1;

    /* then compare maxvals */
    r = FunctionCall2Coll(cxt->cmpFn, cxt->colloid, ra->maxval, rb->maxval);

    if (DatumGetBool(r))
        return -1;

    r = FunctionCall2Coll(cxt->cmpFn, cxt->colloid, rb->maxval, ra->maxval);

    if (DatumGetBool(r))
        return 1;

    return 0;
}

/*
 * compare_values
 *    Compare the values.
 */
static int
compare_values(const void *a, const void *b, void *arg)
{
    Datum      *da = (Datum *) a;
    Datum      *db = (Datum *) b;
    Datum       r;

    compare_context *cxt = (compare_context *) arg;

    r = FunctionCall2Coll(cxt->cmpFn, cxt->colloid, *da, *db);

    if (DatumGetBool(r))
        return -1;

    r = FunctionCall2Coll(cxt->cmpFn, cxt->colloid, *db, *da);

    if (DatumGetBool(r))
        return 1;

    return 0;
}

/*
 * Check if the new value matches one of the existing ranges.
 */
static bool
has_matching_range(BrinDesc *bdesc, Oid colloid, Ranges *ranges,
                   Datum newval, AttrNumber attno, Oid typid)
{
    Datum       compar;

    Datum       minvalue = ranges->values[0];
    Datum       maxvalue = ranges->values[2 * ranges->nranges - 1];

    FmgrInfo   *cmpLessFn;
    FmgrInfo   *cmpGreaterFn;

    /* binary search on ranges */
    int         start,
                end;

    if (ranges->nranges == 0)
        return false;

    /*
     * Otherwise, need to compare the new value with boundaries of all the
     * ranges. First check if it's less than the absolute minimum, which is
     * the first value in the array.
     */
    cmpLessFn = minmax_multi_get_strategy_procinfo(bdesc, attno, typid,
                                                   BTLessStrategyNumber);
    compar = FunctionCall2Coll(cmpLessFn, colloid, newval, minvalue);

    /* smaller than the smallest value in the range list */
    if (DatumGetBool(compar))
        return false;

    /*
     * And now compare it to the existing maximum (last value in the data
     * array). But only if we haven't already ruled out a possible match in
     * the minvalue check.
     */
    cmpGreaterFn = minmax_multi_get_strategy_procinfo(bdesc, attno, typid,
                                                      BTGreaterStrategyNumber);
    compar = FunctionCall2Coll(cmpGreaterFn, colloid, newval, maxvalue);

    if (DatumGetBool(compar))
        return false;

    /*
     * So we know it's in the general min/max, the question is whether it
     * falls in one of the ranges or gaps. We'll do a binary search on
     * individual ranges - for each range we check equality (value falls into
     * the range), and then check ranges either above or below the current
     * range.
     */
    start = 0;                  /* first range */
    end = (ranges->nranges - 1);    /* last range */
    while (true)
    {
        int         midpoint = (start + end) / 2;

        /* this means we ran out of ranges in the last step */
        if (start > end)
            return false;

        /* copy the min/max values from the ranges */
        minvalue = ranges->values[2 * midpoint];
        maxvalue = ranges->values[2 * midpoint + 1];

        /*
         * Is the value smaller than the minval? If yes, we'll recurse to the
         * left side of range array.
         */
        compar = FunctionCall2Coll(cmpLessFn, colloid, newval, minvalue);

        /* smaller than the smallest value in this range */
        if (DatumGetBool(compar))
        {
            end = (midpoint - 1);
            continue;
        }

        /*
         * Is the value greater than the minval? If yes, we'll recurse to the
         * right side of range array.
         */
        compar = FunctionCall2Coll(cmpGreaterFn, colloid, newval, maxvalue);

        /* larger than the largest value in this range */
        if (DatumGetBool(compar))
        {
            start = (midpoint + 1);
            continue;
        }

        /* hey, we found a matching range */
        return true;
    }

    return false;
}


/*
 * range_contains_value
 *      See if the new value is already contained in the range list.
 *
 * We first inspect the list of intervals. We use a small trick - we check
 * the value against min/max of the whole range (min of the first interval,
 * max of the last one) first, and only inspect the individual intervals if
 * this passes.
 *
 * If the value matches none of the intervals, we check the exact values.
 * We simply loop through them and invoke equality operator on them.
 *
 * The last parameter (full) determines whether we need to search all the
 * values, including the unsorted part. With full=false, the unsorted part
 * is not searched, which may produce false negatives and duplicate values
 * (in the unsorted part only), but when we're building the range that's
 * fine - we'll deduplicate before serialization, and it can only happen
 * if there already are unsorted values (so it was already modified).
 *
 * Serialized ranges don't have any unsorted values, so this can't cause
 * false negatives during querying.
 */
static bool
range_contains_value(BrinDesc *bdesc, Oid colloid,
                     AttrNumber attno, Form_pg_attribute attr,
                     Ranges *ranges, Datum newval, bool full)
{
    int         i;
    FmgrInfo   *cmpEqualFn;
    Oid         typid = attr->atttypid;

    /*
     * First inspect the ranges, if there are any. We first check the whole
     * range, and only when there's still a chance of getting a match we
     * inspect the individual ranges.
     */
    if (has_matching_range(bdesc, colloid, ranges, newval, attno, typid))
        return true;

    cmpEqualFn = minmax_multi_get_strategy_procinfo(bdesc, attno, typid,
                                                    BTEqualStrategyNumber);

    /*
     * There is no matching range, so let's inspect the sorted values.
     *
     * We do a sequential search for small numbers of values, and binary
     * search once we have more than 16 values. This threshold is somewhat
     * arbitrary, as it depends on how expensive the comparison function is.
     *
     * XXX If we use the threshold here, maybe we should do the same thing in
     * has_matching_range? Or maybe we should do the bin search all the time?
     *
     * XXX We could use the same optimization as for ranges, to check if the
     * value is between min/max, to maybe rule out all sorted values without
     * having to inspect all of them.
     */
    if (ranges->nsorted >= 16)
    {
        compare_context cxt;

        cxt.colloid = ranges->colloid;
        cxt.cmpFn = ranges->cmp;

        if (bsearch_arg(&newval, &ranges->values[2 * ranges->nranges],
                        ranges->nsorted, sizeof(Datum),
                        compare_values, (void *) &cxt) != NULL)
            return true;
    }
    else
    {
        for (i = 2 * ranges->nranges; i < 2 * ranges->nranges + ranges->nsorted; i++)
        {
            Datum       compar;

            compar = FunctionCall2Coll(cmpEqualFn, colloid, newval, ranges->values[i]);

            /* found an exact match */
            if (DatumGetBool(compar))
                return true;
        }
    }

    /* If not asked to inspect the unsorted part, we're done. */
    if (!full)
        return false;

    /* Inspect the unsorted part. */
    for (i = 2 * ranges->nranges + ranges->nsorted; i < 2 * ranges->nranges + ranges->nvalues; i++)
    {
        Datum       compar;

        compar = FunctionCall2Coll(cmpEqualFn, colloid, newval, ranges->values[i]);

        /* found an exact match */
        if (DatumGetBool(compar))
            return true;
    }

    /* the value is not covered by this BRIN tuple */
    return false;
}

/*
 * Expand ranges from Ranges into ExpandedRange array. This expects the
 * eranges to be pre-allocated and with the correct size - there needs to be
 * (nranges + nvalues) elements.
 *
 * The order of expanded ranges is arbitrary. We do expand the ranges first,
 * and this part is sorted. But then we expand the values, and this part may
 * be unsorted.
 */
static void
fill_expanded_ranges(ExpandedRange *eranges, int neranges, Ranges *ranges)
{
    int         idx;
    int         i;

    /* Check that the output array has the right size. */
    Assert(neranges == (ranges->nranges + ranges->nvalues));

    idx = 0;
    for (i = 0; i < ranges->nranges; i++)
    {
        eranges[idx].minval = ranges->values[2 * i];
        eranges[idx].maxval = ranges->values[2 * i + 1];
        eranges[idx].collapsed = false;
        idx++;

        Assert(idx <= neranges);
    }

    for (i = 0; i < ranges->nvalues; i++)
    {
        eranges[idx].minval = ranges->values[2 * ranges->nranges + i];
        eranges[idx].maxval = ranges->values[2 * ranges->nranges + i];
        eranges[idx].collapsed = true;
        idx++;

        Assert(idx <= neranges);
    }

    /* Did we produce the expected number of elements? */
    Assert(idx == neranges);

    return;
}

/*
 * Sort and deduplicate expanded ranges.
 *
 * The ranges may be deduplicated - we're simply appending values, without
 * checking for duplicates etc. So maybe the deduplication will reduce the
 * number of ranges enough, and we won't have to compute the distances etc.
 *
 * Returns the number of expanded ranges.
 */
static int
sort_expanded_ranges(FmgrInfo *cmp, Oid colloid,
                     ExpandedRange *eranges, int neranges)
{
    int         n;
    int         i;
    compare_context cxt;

    Assert(neranges > 0);

    /* sort the values */
    cxt.colloid = colloid;
    cxt.cmpFn = cmp;

    /*
     * XXX We do qsort on all the values, but we could also leverage the fact
     * that some of the input data is already sorted (all the ranges and maybe
     * some of the points) and do merge sort.
     */
    qsort_arg(eranges, neranges, sizeof(ExpandedRange),
              compare_expanded_ranges, (void *) &cxt);

    /*
     * Deduplicate the ranges - simply compare each range to the preceding
     * one, and skip the duplicate ones.
     */
    n = 1;
    for (i = 1; i < neranges; i++)
    {
        /* if the current range is equal to the preceding one, do nothing */
        if (!compare_expanded_ranges(&eranges[i - 1], &eranges[i], (void *) &cxt))
            continue;

        /* otherwise, copy it to n-th place (if not already there) */
        if (i != n)
            memcpy(&eranges[n], &eranges[i], sizeof(ExpandedRange));

        n++;
    }

    Assert((n > 0) && (n <= neranges));

    return n;
}

/*
 * When combining multiple Range values (in union function), some of the
 * ranges may overlap. We simply merge the overlapping ranges to fix that.
 *
 * XXX This assumes the expanded ranges were previously sorted (by minval
 * and then maxval). We leverage this when detecting overlap.
 */
static int
merge_overlapping_ranges(FmgrInfo *cmp, Oid colloid,
                         ExpandedRange *eranges, int neranges)
{
    int         idx;

    /* Merge ranges (idx) and (idx+1) if they overlap. */
    idx = 0;
    while (idx < (neranges - 1))
    {
        Datum       r;

        /*
         * comparing [?,maxval] vs. [minval,?] - the ranges overlap if (minval
         * < maxval)
         */
        r = FunctionCall2Coll(cmp, colloid,
                              eranges[idx].maxval,
                              eranges[idx + 1].minval);

        /*
         * Nope, maxval < minval, so no overlap. And we know the ranges are
         * ordered, so there are no more overlaps, because all the remaining
         * ranges have greater or equal minval.
         */
        if (DatumGetBool(r))
        {
            /* proceed to the next range */
            idx += 1;
            continue;
        }

        /*
         * So ranges 'idx' and 'idx+1' do overlap, but we don't know if
         * 'idx+1' is contained in 'idx', or if they overlap only partially.
         * So compare the upper bounds and keep the larger one.
         */
        r = FunctionCall2Coll(cmp, colloid,
                              eranges[idx].maxval,
                              eranges[idx + 1].maxval);

        if (DatumGetBool(r))
            eranges[idx].maxval = eranges[idx + 1].maxval;

        /*
         * The range certainly is no longer collapsed (irrespectively of the
         * previous state).
         */
        eranges[idx].collapsed = false;

        /*
         * Now get rid of the (idx+1) range entirely by shifting the remaining
         * ranges by 1. There are neranges elements, and we need to move
         * elements from (idx+2). That means the number of elements to move is
         * [ncranges - (idx+2)].
         */
        memmove(&eranges[idx + 1], &eranges[idx + 2],
                (neranges - (idx + 2)) * sizeof(ExpandedRange));

        /*
         * Decrease the number of ranges, and repeat (with the same range, as
         * it might overlap with additional ranges thanks to the merge).
         */
        neranges--;
    }

    return neranges;
}

/*
 * Simple comparator for distance values, comparing the double value.
 * This is intentionally sorting the distances in descending order, i.e.
 * the longer gaps will be at the front.
 */
static int
compare_distances(const void *a, const void *b)
{
    DistanceValue *da = (DistanceValue *) a;
    DistanceValue *db = (DistanceValue *) b;

    if (da->value < db->value)
        return 1;
    else if (da->value > db->value)
        return -1;

    return 0;
}

/*
 * Given an array of expanded ranges, compute size of the gaps between each
 * range.  For neranges there are (neranges-1) gaps.
 *
 * We simply call the "distance" function to compute the (max-min) for pairs
 * of consecutive ranges. The function may be fairly expensive, so we do that
 * just once (and then use it to pick as many ranges to merge as possible).
 *
 * See reduce_expanded_ranges for details.
 */
static DistanceValue *
build_distances(FmgrInfo *distanceFn, Oid colloid,
                ExpandedRange *eranges, int neranges)
{
    int         i;
    int         ndistances;
    DistanceValue *distances;

    Assert(neranges >= 2);

    ndistances = (neranges - 1);
    distances = (DistanceValue *) palloc0(sizeof(DistanceValue) * ndistances);

    /*
     * Walk through the ranges once and compute the distance between the
     * ranges so that we can sort them once.
     */
    for (i = 0; i < ndistances; i++)
    {
        Datum       a1,
                    a2,
                    r;

        a1 = eranges[i].maxval;
        a2 = eranges[i + 1].minval;

        /* compute length of the gap (between max/min) */
        r = FunctionCall2Coll(distanceFn, colloid, a1, a2);

        /* remember the index of the gap the distance is for */
        distances[i].index = i;
        distances[i].value = DatumGetFloat8(r);
    }

    /*
     * Sort the distances in descending order, so that the longest gaps are at
     * the front.
     */
    pg_qsort(distances, ndistances, sizeof(DistanceValue), compare_distances);

    return distances;
}

/*
 * Builds expanded ranges for the existing ranges (and single-point ranges),
 * and also the new value (which did not fit into the array).  This expanded
 * representation makes the processing a bit easier, as it allows handling
 * ranges and points the same way.
 *
 * We sort and deduplicate the expanded ranges - this is necessary, because
 * the points may be unsorted. And moreover the two parts (ranges and
 * points) are sorted on their own.
 */
static ExpandedRange *
build_expanded_ranges(FmgrInfo *cmp, Oid colloid, Ranges *ranges,
                      int *nranges)
{
    int         neranges;
    ExpandedRange *eranges;

    /* both ranges and points are expanded into a separate element */
    neranges = ranges->nranges + ranges->nvalues;

    eranges = (ExpandedRange *) palloc0(neranges * sizeof(ExpandedRange));

    /* fill the expanded ranges */
    fill_expanded_ranges(eranges, neranges, ranges);

    /* sort and deduplicate the expanded ranges */
    neranges = sort_expanded_ranges(cmp, colloid, eranges, neranges);

    /* remember how many ranges we built */
    *nranges = neranges;

    return eranges;
}

#ifdef USE_ASSERT_CHECKING
/*
 * Counts boundary values needed to store the ranges. Each single-point
 * range is stored using a single value, each regular range needs two.
 */
static int
count_values(ExpandedRange *cranges, int ncranges)
{
    int         i;
    int         count;

    count = 0;
    for (i = 0; i < ncranges; i++)
    {
        if (cranges[i].collapsed)
            count += 1;
        else
            count += 2;
    }

    return count;
}
#endif

/*
 * reduce_expanded_ranges
 *      reduce the ranges until the number of values is low enough
 *
 * Combines ranges until the number of boundary values drops below the
 * threshold specified by max_values. This happens by merging enough
 * ranges by the distance between them.
 *
 * Returns the number of result ranges.
 *
 * We simply use the global min/max and then add boundaries for enough
 * largest gaps. Each gap adds 2 values, so we simply use (target/2-1)
 * distances. Then we simply sort all the values - each two values are
 * a boundary of a range (possibly collapsed).
 *
 * XXX Some of the ranges may be collapsed (i.e. the min/max values are
 * equal), but we ignore that for now. We could repeat the process,
 * adding a couple more gaps recursively.
 *
 * XXX The ranges to merge are selected solely using the distance. But
 * that may not be the best strategy, for example when multiple gaps
 * are of equal (or very similar) length.
 *
 * Consider for example points 1, 2, 3, .., 64, which have gaps of the
 * same length 1 of course. In that case, we tend to pick the first
 * gap of that length, which leads to this:
 *
 *    step 1:  [1, 2], 3, 4, 5, .., 64
 *    step 2:  [1, 3], 4, 5,    .., 64
 *    step 3:  [1, 4], 5,       .., 64
 *    ...
 *
 * So in the end we'll have one "large" range and multiple small points.
 * That may be fine, but it seems a bit strange and non-optimal. Maybe
 * we should consider other things when picking ranges to merge - e.g.
 * length of the ranges? Or perhaps randomize the choice of ranges, with
 * probability inversely proportional to the distance (the gap lengths
 * may be very close, but not exactly the same).
 *
 * XXX Or maybe we could just handle this by using random value as a
 * tie-break, or by adding random noise to the actual distance.
 */
static int
reduce_expanded_ranges(ExpandedRange *eranges, int neranges,
                       DistanceValue *distances, int max_values,
                       FmgrInfo *cmp, Oid colloid)
{
    int         i;
    int         nvalues;
    Datum      *values;

    compare_context cxt;

    /* total number of gaps between ranges */
    int         ndistances = (neranges - 1);

    /* number of gaps to keep */
    int         keep = (max_values / 2 - 1);

    /*
     * Maybe we have a sufficiently low number of ranges already?
     *
     * XXX This should happen before we actually do the expensive stuff like
     * sorting, so maybe this should be just an assert.
     */
    if (keep >= ndistances)
        return neranges;

    /* sort the values */
    cxt.colloid = colloid;
    cxt.cmpFn = cmp;

    /* allocate space for the boundary values */
    nvalues = 0;
    values = (Datum *) palloc(sizeof(Datum) * max_values);

    /* add the global min/max values, from the first/last range */
    values[nvalues++] = eranges[0].minval;
    values[nvalues++] = eranges[neranges - 1].maxval;

    /* add boundary values for enough gaps */
    for (i = 0; i < keep; i++)
    {
        /* index of the gap between (index) and (index+1) ranges */
        int         index = distances[i].index;

        Assert((index >= 0) && ((index + 1) < neranges));

        /* add max from the preceding range, minval from the next one */
        values[nvalues++] = eranges[index].maxval;
        values[nvalues++] = eranges[index + 1].minval;

        Assert(nvalues <= max_values);
    }

    /* We should have an even number of range values. */
    Assert(nvalues % 2 == 0);

    /*
     * Sort the values using the comparator function, and form ranges from the
     * sorted result.
     */
    qsort_arg(values, nvalues, sizeof(Datum),
              compare_values, (void *) &cxt);

    /* We have nvalues boundary values, which means nvalues/2 ranges. */
    for (i = 0; i < (nvalues / 2); i++)
    {
        eranges[i].minval = values[2 * i];
        eranges[i].maxval = values[2 * i + 1];

        /* if the boundary values are the same, it's a collapsed range */
        eranges[i].collapsed = (compare_values(&values[2 * i],
                                               &values[2 * i + 1],
                                               &cxt) == 0);
    }

    return (nvalues / 2);
}

/*
 * Store the boundary values from ExpandedRanges back into 'ranges' (using
 * only the minimal number of values needed).
 */
static void
store_expanded_ranges(Ranges *ranges, ExpandedRange *eranges, int neranges)
{
    int         i;
    int         idx = 0;

    /* first copy in the regular ranges */
    ranges->nranges = 0;
    for (i = 0; i < neranges; i++)
    {
        if (!eranges[i].collapsed)
        {
            ranges->values[idx++] = eranges[i].minval;
            ranges->values[idx++] = eranges[i].maxval;
            ranges->nranges++;
        }
    }

    /* now copy in the collapsed ones */
    ranges->nvalues = 0;
    for (i = 0; i < neranges; i++)
    {
        if (eranges[i].collapsed)
        {
            ranges->values[idx++] = eranges[i].minval;
            ranges->nvalues++;
        }
    }

    /* all the values are sorted */
    ranges->nsorted = ranges->nvalues;

    Assert(count_values(eranges, neranges) == 2 * ranges->nranges + ranges->nvalues);
    Assert(2 * ranges->nranges + ranges->nvalues <= ranges->maxvalues);
}


/*
 * Consider freeing space in the ranges. Checks if there's space for at least
 * one new value, and performs compaction if needed.
 *
 * Returns true if the value was actually modified.
 */
static bool
ensure_free_space_in_buffer(BrinDesc *bdesc, Oid colloid,
                            AttrNumber attno, Form_pg_attribute attr,
                            Ranges *range)
{
    MemoryContext ctx;
    MemoryContext oldctx;

    FmgrInfo   *cmpFn,
               *distanceFn;

    /* expanded ranges */
    ExpandedRange *eranges;
    int         neranges;
    DistanceValue *distances;

    /*
     * If there is free space in the buffer, we're done without having to
     * modify anything.
     */
    if (2 * range->nranges + range->nvalues < range->maxvalues)
        return false;

    /* we'll certainly need the comparator, so just look it up now */
    cmpFn = minmax_multi_get_strategy_procinfo(bdesc, attno, attr->atttypid,
                                               BTLessStrategyNumber);

    /* deduplicate values, if there's an unsorted part */
    range_deduplicate_values(range);

    /*
     * Did we reduce enough free space by just the deduplication?
     *
     * We don't simply check against range->maxvalues again. The deduplication
     * might have freed very little space (e.g. just one value), forcing us to
     * do deduplication very often. In that case, it's better to do the
     * compaction and reduce more space.
     */
    if (2 * range->nranges + range->nvalues <= range->maxvalues * MINMAX_BUFFER_LOAD_FACTOR)
        return true;

    /*
     * We need to combine some of the existing ranges, to reduce the number of
     * values we have to store.
     *
     * The distanceFn calls (which may internally call e.g. numeric_le) may
     * allocate quite a bit of memory, and we must not leak it (we might have
     * to do this repeatedly, even for a single BRIN page range). Otherwise
     * we'd have problems e.g. when building new indexes. So we use a memory
     * context and make sure we free the memory at the end (so if we call the
     * distance function many times, it might be an issue, but meh).
     */
    ctx = AllocSetContextCreate(CurrentMemoryContext,
                                "minmax-multi context",
                                ALLOCSET_DEFAULT_SIZES);

    oldctx = MemoryContextSwitchTo(ctx);

    /* build the expanded ranges */
    eranges = build_expanded_ranges(cmpFn, colloid, range, &neranges);

    /* and we'll also need the 'distance' procedure */
    distanceFn = minmax_multi_get_procinfo(bdesc, attno, PROCNUM_DISTANCE);

    /* build array of gap distances and sort them in ascending order */
    distances = build_distances(distanceFn, colloid, eranges, neranges);

    /*
     * Combine ranges until we release at least 50% of the space. This
     * threshold is somewhat arbitrary, perhaps needs tuning. We must not use
     * too low or high value.
     */
    neranges = reduce_expanded_ranges(eranges, neranges, distances,
                                      range->maxvalues * MINMAX_BUFFER_LOAD_FACTOR,
                                      cmpFn, colloid);

    /* Make sure we've sufficiently reduced the number of ranges. */
    Assert(count_values(eranges, neranges) <= range->maxvalues * MINMAX_BUFFER_LOAD_FACTOR);

    /* decompose the expanded ranges into regular ranges and single values */
    store_expanded_ranges(range, eranges, neranges);

    MemoryContextSwitchTo(oldctx);
    MemoryContextDelete(ctx);

    /* Did we break the ranges somehow? */
    AssertCheckRanges(range, cmpFn, colloid);

    return true;
}

/*
 * range_add_value
 *      Add the new value to the minmax-multi range.
 */
static bool
range_add_value(BrinDesc *bdesc, Oid colloid,
                AttrNumber attno, Form_pg_attribute attr,
                Ranges *ranges, Datum newval)
{
    FmgrInfo   *cmpFn;
    bool        modified = false;

    /* we'll certainly need the comparator, so just look it up now */
    cmpFn = minmax_multi_get_strategy_procinfo(bdesc, attno, attr->atttypid,
                                               BTLessStrategyNumber);

    /* comprehensive checks of the input ranges */
    AssertCheckRanges(ranges, cmpFn, colloid);

    /*
     * Make sure there's enough free space in the buffer. We only trigger this
     * when the buffer is full, which means it had to be modified as we size
     * it to be larger than what is stored on disk.
     *
     * This needs to happen before we check if the value is contained in the
     * range, because the value might be in the unsorted part, and we don't
     * check that in range_contains_value. The deduplication would then move
     * it to the sorted part, and we'd add the value too, which violates the
     * rule that we never have duplicates with the ranges or sorted values.
     *
     * We might also deduplicate and recheck if the value is contained, but
     * that seems like overkill. We'd need to deduplicate anyway, so why not
     * do it now.
     */
    modified = ensure_free_space_in_buffer(bdesc, colloid,
                                           attno, attr, ranges);

    /*
     * Bail out if the value already is covered by the range.
     *
     * We could also add values until we hit values_per_range, and then do the
     * deduplication in a batch, hoping for better efficiency. But that would
     * mean we actually modify the range every time, which means having to
     * serialize the value, which does palloc, walks the values, copies them,
     * etc. Not exactly cheap.
     *
     * So instead we do the check, which should be fairly cheap - assuming the
     * comparator function is not very expensive.
     *
     * This also implies the values array can't contain duplicate values.
     */
    if (range_contains_value(bdesc, colloid, attno, attr, ranges, newval, false))
        return modified;

    /* Make a copy of the value, if needed. */
    newval = datumCopy(newval, attr->attbyval, attr->attlen);

    /*
     * If there's space in the values array, copy it in and we're done.
     *
     * We do want to keep the values sorted (to speed up searches), so we do a
     * simple insertion sort. We could do something more elaborate, e.g. by
     * sorting the values only now and then, but for small counts (e.g. when
     * maxvalues is 64) this should be fine.
     */
    ranges->values[2 * ranges->nranges + ranges->nvalues] = newval;
    ranges->nvalues++;

    /* If we added the first value, we can consider it as sorted. */
    if (ranges->nvalues == 1)
        ranges->nsorted = 1;

    /*
     * Check we haven't broken the ordering of boundary values (checks both
     * parts, but that doesn't hurt).
     */
    AssertCheckRanges(ranges, cmpFn, colloid);

    /* Check the range contains the value we just added. */
    Assert(range_contains_value(bdesc, colloid, attno, attr, ranges, newval, true));

    /* yep, we've modified the range */
    return true;
}

/*
 * Generate range representation of data collected during "batch mode".
 * This is similar to reduce_expanded_ranges, except that we can't assume
 * the values are sorted and there may be duplicate values.
 */
static void
compactify_ranges(BrinDesc *bdesc, Ranges *ranges, int max_values)
{
    FmgrInfo   *cmpFn,
               *distanceFn;

    /* expanded ranges */
    ExpandedRange *eranges;
    int         neranges;
    DistanceValue *distances;

    MemoryContext ctx;
    MemoryContext oldctx;

    /*
     * Do we need to actually compactify anything?
     *
     * There are two reasons why compaction may be needed - firstly, there may
     * be too many values, or some of the values may be unsorted.
     */
    if ((ranges->nranges * 2 + ranges->nvalues <= max_values) &&
        (ranges->nsorted == ranges->nvalues))
        return;

    /* we'll certainly need the comparator, so just look it up now */
    cmpFn = minmax_multi_get_strategy_procinfo(bdesc, ranges->attno, ranges->typid,
                                               BTLessStrategyNumber);

    /* and we'll also need the 'distance' procedure */
    distanceFn = minmax_multi_get_procinfo(bdesc, ranges->attno, PROCNUM_DISTANCE);

    /*
     * The distanceFn calls (which may internally call e.g. numeric_le) may
     * allocate quite a bit of memory, and we must not leak it. Otherwise,
     * we'd have problems e.g. when building indexes. So we create a local
     * memory context and make sure we free the memory before leaving this
     * function (not after every call).
     */
    ctx = AllocSetContextCreate(CurrentMemoryContext,
                                "minmax-multi context",
                                ALLOCSET_DEFAULT_SIZES);

    oldctx = MemoryContextSwitchTo(ctx);

    /* build the expanded ranges */
    eranges = build_expanded_ranges(cmpFn, ranges->colloid, ranges, &neranges);

    /* build array of gap distances and sort them in ascending order */
    distances = build_distances(distanceFn, ranges->colloid,
                                eranges, neranges);

    /*
     * Combine ranges until we get below max_values. We don't use any scale
     * factor, because this is used during serialization, and we don't expect
     * more tuples to be inserted anytime soon.
     */
    neranges = reduce_expanded_ranges(eranges, neranges, distances,
                                      max_values, cmpFn, ranges->colloid);

    Assert(count_values(eranges, neranges) <= max_values);

    /* transform back into regular ranges and single values */
    store_expanded_ranges(ranges, eranges, neranges);

    /* check all the range invariants */
    AssertCheckRanges(ranges, cmpFn, ranges->colloid);

    MemoryContextSwitchTo(oldctx);
    MemoryContextDelete(ctx);
}

Datum
brin_minmax_multi_opcinfo(PG_FUNCTION_ARGS)
{
    BrinOpcInfo *result;

    /*
     * opaque->strategy_procinfos is initialized lazily; here it is set to
     * all-uninitialized by palloc0 which sets fn_oid to InvalidOid.
     */

    result = palloc0(MAXALIGN(SizeofBrinOpcInfo(1)) +
                     sizeof(MinmaxMultiOpaque));
    result->oi_nstored = 1;
    result->oi_regular_nulls = true;
    result->oi_opaque = (MinmaxMultiOpaque *)
        MAXALIGN((char *) result + SizeofBrinOpcInfo(1));
    result->oi_typcache[0] = lookup_type_cache(PG_BRIN_MINMAX_MULTI_SUMMARYOID, 0);

    PG_RETURN_POINTER(result);
}

/*
 * Compute the distance between two float4 values (plain subtraction).
 */
Datum
brin_minmax_multi_distance_float4(PG_FUNCTION_ARGS)
{
    float       a1 = PG_GETARG_FLOAT4(0);
    float       a2 = PG_GETARG_FLOAT4(1);

    /*
     * We know the values are range boundaries, but the range may be collapsed
     * (i.e. single points), with equal values.
     */
    Assert(a1 <= a2);

    PG_RETURN_FLOAT8((double) a2 - (double) a1);
}

/*
 * Compute the distance between two float8 values (plain subtraction).
 */
Datum
brin_minmax_multi_distance_float8(PG_FUNCTION_ARGS)
{
    double      a1 = PG_GETARG_FLOAT8(0);
    double      a2 = PG_GETARG_FLOAT8(1);

    /*
     * We know the values are range boundaries, but the range may be collapsed
     * (i.e. single points), with equal values.
     */
    Assert(a1 <= a2);

    PG_RETURN_FLOAT8(a2 - a1);
}

/*
 * Compute the distance between two int2 values (plain subtraction).
 */
Datum
brin_minmax_multi_distance_int2(PG_FUNCTION_ARGS)
{
    int16       a1 = PG_GETARG_INT16(0);
    int16       a2 = PG_GETARG_INT16(1);

    /*
     * We know the values are range boundaries, but the range may be collapsed
     * (i.e. single points), with equal values.
     */
    Assert(a1 <= a2);

    PG_RETURN_FLOAT8((double) a2 - (double) a1);
}

/*
 * Compute the distance between two int4 values (plain subtraction).
 */
Datum
brin_minmax_multi_distance_int4(PG_FUNCTION_ARGS)
{
    int32       a1 = PG_GETARG_INT32(0);
    int32       a2 = PG_GETARG_INT32(1);

    /*
     * We know the values are range boundaries, but the range may be collapsed
     * (i.e. single points), with equal values.
     */
    Assert(a1 <= a2);

    PG_RETURN_FLOAT8((double) a2 - (double) a1);
}

/*
 * Compute the distance between two int8 values (plain subtraction).
 */
Datum
brin_minmax_multi_distance_int8(PG_FUNCTION_ARGS)
{
    int64       a1 = PG_GETARG_INT64(0);
    int64       a2 = PG_GETARG_INT64(1);

    /*
     * We know the values are range boundaries, but the range may be collapsed
     * (i.e. single points), with equal values.
     */
    Assert(a1 <= a2);

    PG_RETURN_FLOAT8((double) a2 - (double) a1);
}

/*
 * Compute the distance between two tid values (by mapping them to float8 and
 * then subtracting them).
 */
Datum
brin_minmax_multi_distance_tid(PG_FUNCTION_ARGS)
{
    double      da1,
                da2;

    ItemPointer pa1 = (ItemPointer) PG_GETARG_DATUM(0);
    ItemPointer pa2 = (ItemPointer) PG_GETARG_DATUM(1);

    /*
     * We know the values are range boundaries, but the range may be collapsed
     * (i.e. single points), with equal values.
     */
    Assert(ItemPointerCompare(pa1, pa2) <= 0);

    /*
     * We use the no-check variants here, because user-supplied values may
     * have (ip_posid == 0). See ItemPointerCompare.
     */
    da1 = ItemPointerGetBlockNumberNoCheck(pa1) * MaxHeapTuplesPerPage +
        ItemPointerGetOffsetNumberNoCheck(pa1);

    da2 = ItemPointerGetBlockNumberNoCheck(pa2) * MaxHeapTuplesPerPage +
        ItemPointerGetOffsetNumberNoCheck(pa2);

    PG_RETURN_FLOAT8(da2 - da1);
}

/*
 * Compute the distance between two numeric values (plain subtraction).
 */
Datum
brin_minmax_multi_distance_numeric(PG_FUNCTION_ARGS)
{
    Datum       d;
    Datum       a1 = PG_GETARG_DATUM(0);
    Datum       a2 = PG_GETARG_DATUM(1);

    /*
     * We know the values are range boundaries, but the range may be collapsed
     * (i.e. single points), with equal values.
     */
    Assert(DatumGetBool(DirectFunctionCall2(numeric_le, a1, a2)));

    d = DirectFunctionCall2(numeric_sub, a2, a1);   /* a2 - a1 */

    PG_RETURN_FLOAT8(DirectFunctionCall1(numeric_float8, d));
}

/*
 * Compute the approximate distance between two UUID values.
 *
 * XXX We do not need a perfectly accurate value, so we approximate the
 * deltas (which would have to be 128-bit integers) with a 64-bit float.
 * The small inaccuracies do not matter in practice, in the worst case
 * we'll decide to merge ranges that are not the closest ones.
 */
Datum
brin_minmax_multi_distance_uuid(PG_FUNCTION_ARGS)
{
    int         i;
    float8      delta = 0;

    Datum       a1 = PG_GETARG_DATUM(0);
    Datum       a2 = PG_GETARG_DATUM(1);

    pg_uuid_t  *u1 = DatumGetUUIDP(a1);
    pg_uuid_t  *u2 = DatumGetUUIDP(a2);

    /*
     * We know the values are range boundaries, but the range may be collapsed
     * (i.e. single points), with equal values.
     */
    Assert(DatumGetBool(DirectFunctionCall2(uuid_le, a1, a2)));

    /* compute approximate delta as a double precision value */
    for (i = UUID_LEN - 1; i >= 0; i--)
    {
        delta += (int) u2->data[i] - (int) u1->data[i];
        delta /= 256;
    }

    Assert(delta >= 0);

    PG_RETURN_FLOAT8(delta);
}

/*
 * Compute the approximate distance between two dates.
 */
Datum
brin_minmax_multi_distance_date(PG_FUNCTION_ARGS)
{
    DateADT     dateVal1 = PG_GETARG_DATEADT(0);
    DateADT     dateVal2 = PG_GETARG_DATEADT(1);

    if (DATE_NOT_FINITE(dateVal1) || DATE_NOT_FINITE(dateVal2))
        PG_RETURN_FLOAT8(0);

    PG_RETURN_FLOAT8(dateVal1 - dateVal2);
}

/*
 * Compute the approximate distance between two time (without tz) values.
 *
 * TimeADT is just an int64, so we simply subtract the values directly.
 */
Datum
brin_minmax_multi_distance_time(PG_FUNCTION_ARGS)
{
    float8      delta = 0;

    TimeADT     ta = PG_GETARG_TIMEADT(0);
    TimeADT     tb = PG_GETARG_TIMEADT(1);

    delta = (tb - ta);

    Assert(delta >= 0);

    PG_RETURN_FLOAT8(delta);
}

/*
 * Compute the approximate distance between two timetz values.
 *
 * Simply subtracts the TimeADT (int64) values embedded in TimeTzADT.
 */
Datum
brin_minmax_multi_distance_timetz(PG_FUNCTION_ARGS)
{
    float8      delta = 0;

    TimeTzADT  *ta = PG_GETARG_TIMETZADT_P(0);
    TimeTzADT  *tb = PG_GETARG_TIMETZADT_P(1);

    delta = (tb->time - ta->time) + (tb->zone - ta->zone) * USECS_PER_SEC;

    Assert(delta >= 0);

    PG_RETURN_FLOAT8(delta);
}

/*
 * Compute the distance between two timestamp values.
 */
Datum
brin_minmax_multi_distance_timestamp(PG_FUNCTION_ARGS)
{
    float8      delta = 0;

    Timestamp   dt1 = PG_GETARG_TIMESTAMP(0);
    Timestamp   dt2 = PG_GETARG_TIMESTAMP(1);

    if (TIMESTAMP_NOT_FINITE(dt1) || TIMESTAMP_NOT_FINITE(dt2))
        PG_RETURN_FLOAT8(0);

    delta = dt2 - dt1;

    Assert(delta >= 0);

    PG_RETURN_FLOAT8(delta);
}

/*
 * Compute the distance between two interval values.
 */
Datum
brin_minmax_multi_distance_interval(PG_FUNCTION_ARGS)
{
    float8      delta = 0;

    Interval   *ia = PG_GETARG_INTERVAL_P(0);
    Interval   *ib = PG_GETARG_INTERVAL_P(1);
    Interval   *result;

    int64       dayfraction;
    int64       days;

    result = (Interval *) palloc(sizeof(Interval));

    result->month = ib->month - ia->month;
    /* overflow check copied from int4mi */
    if (!SAMESIGN(ib->month, ia->month) &&
        !SAMESIGN(result->month, ib->month))
        ereport(ERROR,
                (errcode(ERRCODE_DATETIME_VALUE_OUT_OF_RANGE),
                 errmsg("interval out of range")));

    result->day = ib->day - ia->day;
    if (!SAMESIGN(ib->day, ia->day) &&
        !SAMESIGN(result->day, ib->day))
        ereport(ERROR,
                (errcode(ERRCODE_DATETIME_VALUE_OUT_OF_RANGE),
                 errmsg("interval out of range")));

    result->time = ib->time - ia->time;
    if (!SAMESIGN(ib->time, ia->time) &&
        !SAMESIGN(result->time, ib->time))
        ereport(ERROR,
                (errcode(ERRCODE_DATETIME_VALUE_OUT_OF_RANGE),
                 errmsg("interval out of range")));

    /*
     * Delta is (fractional) number of days between the intervals. Assume
     * months have 30 days for consistency with interval_cmp_internal. We
     * don't need to be exact, in the worst case we'll build a bit less
     * efficient ranges. But we should not contradict interval_cmp.
     */
    dayfraction = result->time % USECS_PER_DAY;
    days = result->time / USECS_PER_DAY;
    days += result->month * INT64CONST(30);
    days += result->day;

    /* convert to double precision */
    delta = (double) days + dayfraction / (double) USECS_PER_DAY;

    Assert(delta >= 0);

    PG_RETURN_FLOAT8(delta);
}

/*
 * Compute the distance between two pg_lsn values.
 *
 * LSN is just an int64 encoding position in the stream, so just subtract
 * those int64 values directly.
 */
Datum
brin_minmax_multi_distance_pg_lsn(PG_FUNCTION_ARGS)
{
    float8      delta = 0;

    XLogRecPtr  lsna = PG_GETARG_LSN(0);
    XLogRecPtr  lsnb = PG_GETARG_LSN(1);

    delta = (lsnb - lsna);

    Assert(delta >= 0);

    PG_RETURN_FLOAT8(delta);
}

/*
 * Compute the distance between two macaddr values.
 *
 * mac addresses are treated as 6 unsigned chars, so do the same thing we
 * already do for UUID values.
 */
Datum
brin_minmax_multi_distance_macaddr(PG_FUNCTION_ARGS)
{
    float8      delta;

    macaddr    *a = PG_GETARG_MACADDR_P(0);
    macaddr    *b = PG_GETARG_MACADDR_P(1);

    delta = ((float8) b->f - (float8) a->f);
    delta /= 256;

    delta += ((float8) b->e - (float8) a->e);
    delta /= 256;

    delta += ((float8) b->d - (float8) a->d);
    delta /= 256;

    delta += ((float8) b->c - (float8) a->c);
    delta /= 256;

    delta += ((float8) b->b - (float8) a->b);
    delta /= 256;

    delta += ((float8) b->a - (float8) a->a);
    delta /= 256;

    Assert(delta >= 0);

    PG_RETURN_FLOAT8(delta);
}

/*
 * Compute the distance between two macaddr8 values.
 *
 * macaddr8 addresses are 8 unsigned chars, so do the same thing we
 * already do for UUID values.
 */
Datum
brin_minmax_multi_distance_macaddr8(PG_FUNCTION_ARGS)
{
    float8      delta;

    macaddr8   *a = PG_GETARG_MACADDR8_P(0);
    macaddr8   *b = PG_GETARG_MACADDR8_P(1);

    delta = ((float8) b->h - (float8) a->h);
    delta /= 256;

    delta += ((float8) b->g - (float8) a->g);
    delta /= 256;

    delta += ((float8) b->f - (float8) a->f);
    delta /= 256;

    delta += ((float8) b->e - (float8) a->e);
    delta /= 256;

    delta += ((float8) b->d - (float8) a->d);
    delta /= 256;

    delta += ((float8) b->c - (float8) a->c);
    delta /= 256;

    delta += ((float8) b->b - (float8) a->b);
    delta /= 256;

    delta += ((float8) b->a - (float8) a->a);
    delta /= 256;

    Assert(delta >= 0);

    PG_RETURN_FLOAT8(delta);
}

/*
 * Compute the distance between two inet values.
 *
 * The distance is defined as the difference between 32-bit/128-bit values,
 * depending on the IP version. The distance is computed by subtracting
 * the bytes and normalizing it to [0,1] range for each IP family.
 * Addresses from different families are considered to be in maximum
 * distance, which is 1.0.
 *
 * XXX Does this need to consider the mask (bits)?  For now, it's ignored.
 */
Datum
brin_minmax_multi_distance_inet(PG_FUNCTION_ARGS)
{
    float8      delta;
    int         i;
    int         len;
    unsigned char *addra,
               *addrb;

    inet       *ipa = PG_GETARG_INET_PP(0);
    inet       *ipb = PG_GETARG_INET_PP(1);

    int         lena,
                lenb;

    /*
     * If the addresses are from different families, consider them to be in
     * maximal possible distance (which is 1.0).
     */
    if (ip_family(ipa) != ip_family(ipb))
        PG_RETURN_FLOAT8(1.0);

    addra = (unsigned char *) palloc(ip_addrsize(ipa));
    memcpy(addra, ip_addr(ipa), ip_addrsize(ipa));

    addrb = (unsigned char *) palloc(ip_addrsize(ipb));
    memcpy(addrb, ip_addr(ipb), ip_addrsize(ipb));

    /*
     * The length is calculated from the mask length, because we sort the
     * addresses by first address in the range, so A.B.C.D/24 < A.B.C.1 (the
     * first range starts at A.B.C.0, which is before A.B.C.1). We don't want
     * to produce a negative delta in this case, so we just cut the extra
     * bytes.
     *
     * XXX Maybe this should be a bit more careful and cut the bits, not just
     * whole bytes.
     */
    lena = ip_bits(ipa);
    lenb = ip_bits(ipb);

    len = ip_addrsize(ipa);

    /* apply the network mask to both addresses */
    for (i = 0; i < len; i++)
    {
        unsigned char mask;
        int         nbits;

        nbits = lena - (i * 8);
        if (nbits < 8)
        {
            mask = (0xFF << (8 - nbits));
            addra[i] = (addra[i] & mask);
        }

        nbits = lenb - (i * 8);
        if (nbits < 8)
        {
            mask = (0xFF << (8 - nbits));
            addrb[i] = (addrb[i] & mask);
        }
    }

    /* Calculate the difference between the addresses. */
    delta = 0;
    for (i = len - 1; i >= 0; i--)
    {
        unsigned char a = addra[i];
        unsigned char b = addrb[i];

        delta += (float8) b - (float8) a;
        delta /= 256;
    }

    Assert((delta >= 0) && (delta <= 1));

    pfree(addra);
    pfree(addrb);

    PG_RETURN_FLOAT8(delta);
}

static void
brin_minmax_multi_serialize(BrinDesc *bdesc, Datum src, Datum *dst)
{
    Ranges     *ranges = (Ranges *) DatumGetPointer(src);
    SerializedRanges *s;

    /*
     * In batch mode, we need to compress the accumulated values to the
     * actually requested number of values/ranges.
     */
    compactify_ranges(bdesc, ranges, ranges->target_maxvalues);

    /* At this point everything has to be fully sorted. */
    Assert(ranges->nsorted == ranges->nvalues);

    s = range_serialize(ranges);
    dst[0] = PointerGetDatum(s);
}

static int
brin_minmax_multi_get_values(BrinDesc *bdesc, MinMaxMultiOptions *opts)
{
    return MinMaxMultiGetValuesPerRange(opts);
}

/*
 * Examine the given index tuple (which contains the partial status of a
 * certain page range) by comparing it to the given value that comes from
 * another heap tuple.  If the new value is outside the min/max range
 * specified by the existing tuple values, update the index tuple and return
 * true.  Otherwise, return false and do not modify in this case.
 */
Datum
brin_minmax_multi_add_value(PG_FUNCTION_ARGS)
{
    BrinDesc   *bdesc = (BrinDesc *) PG_GETARG_POINTER(0);
    BrinValues *column = (BrinValues *) PG_GETARG_POINTER(1);
    Datum       newval = PG_GETARG_DATUM(2);
    bool        isnull PG_USED_FOR_ASSERTS_ONLY = PG_GETARG_DATUM(3);
    MinMaxMultiOptions *opts = (MinMaxMultiOptions *) PG_GET_OPCLASS_OPTIONS();
    Oid         colloid = PG_GET_COLLATION();
    bool        modified = false;
    Form_pg_attribute attr;
    AttrNumber  attno;
    Ranges     *ranges;
    SerializedRanges *serialized = NULL;

    Assert(!isnull);

    attno = column->bv_attno;
    attr = TupleDescAttr(bdesc->bd_tupdesc, attno - 1);

    /* use the already deserialized value, if possible */
    ranges = (Ranges *) DatumGetPointer(column->bv_mem_value);

    /*
     * If this is the first non-null value, we need to initialize the range
     * list. Otherwise, just extract the existing range list from BrinValues.
     *
     * When starting with an empty range, we assume this is a batch mode and
     * we use a larger buffer. The buffer size is derived from the BRIN range
     * size, number of rows per page, with some sensible min/max values. A
     * small buffer would be bad for performance, but a large buffer might
     * require a lot of memory (because of keeping all the values).
     */
    if (column->bv_allnulls)
    {
        MemoryContext oldctx;

        int         target_maxvalues;
        int         maxvalues;
        BlockNumber pagesPerRange = BrinGetPagesPerRange(bdesc->bd_index);

        /* what was specified as a reloption? */
        target_maxvalues = brin_minmax_multi_get_values(bdesc, opts);

        /*
         * Determine the insert buffer size - we use 10x the target, capped to
         * the maximum number of values in the heap range. This is more than
         * enough, considering the actual number of rows per page is likely
         * much lower, but meh.
         */
        maxvalues = Min(target_maxvalues * MINMAX_BUFFER_FACTOR,
                        MaxHeapTuplesPerPage * pagesPerRange);

        /* but always at least the original value */
        maxvalues = Max(maxvalues, target_maxvalues);

        /* always cap by MIN/MAX */
        maxvalues = Max(maxvalues, MINMAX_BUFFER_MIN);
        maxvalues = Min(maxvalues, MINMAX_BUFFER_MAX);

        oldctx = MemoryContextSwitchTo(column->bv_context);
        ranges = minmax_multi_init(maxvalues);
        ranges->attno = attno;
        ranges->colloid = colloid;
        ranges->typid = attr->atttypid;
        ranges->target_maxvalues = target_maxvalues;

        /* we'll certainly need the comparator, so just look it up now */
        ranges->cmp = minmax_multi_get_strategy_procinfo(bdesc, attno, attr->atttypid,
                                                         BTLessStrategyNumber);

        MemoryContextSwitchTo(oldctx);

        column->bv_allnulls = false;
        modified = true;

        column->bv_mem_value = PointerGetDatum(ranges);
        column->bv_serialize = brin_minmax_multi_serialize;
    }
    else if (!ranges)
    {
        MemoryContext oldctx;

        int         maxvalues;
        BlockNumber pagesPerRange = BrinGetPagesPerRange(bdesc->bd_index);

        oldctx = MemoryContextSwitchTo(column->bv_context);

        serialized = (SerializedRanges *) PG_DETOAST_DATUM(column->bv_values[0]);

        /*
         * Determine the insert buffer size - we use 10x the target, capped to
         * the maximum number of values in the heap range. This is more than
         * enough, considering the actual number of rows per page is likely
         * much lower, but meh.
         */
        maxvalues = Min(serialized->maxvalues * MINMAX_BUFFER_FACTOR,
                        MaxHeapTuplesPerPage * pagesPerRange);

        /* but always at least the original value */
        maxvalues = Max(maxvalues, serialized->maxvalues);

        /* always cap by MIN/MAX */
        maxvalues = Max(maxvalues, MINMAX_BUFFER_MIN);
        maxvalues = Min(maxvalues, MINMAX_BUFFER_MAX);

        ranges = range_deserialize(maxvalues, serialized);

        ranges->attno = attno;
        ranges->colloid = colloid;
        ranges->typid = attr->atttypid;

        /* we'll certainly need the comparator, so just look it up now */
        ranges->cmp = minmax_multi_get_strategy_procinfo(bdesc, attno, attr->atttypid,
                                                         BTLessStrategyNumber);

        column->bv_mem_value = PointerGetDatum(ranges);
        column->bv_serialize = brin_minmax_multi_serialize;

        MemoryContextSwitchTo(oldctx);
    }

    /*
     * Try to add the new value to the range. We need to update the modified
     * flag, so that we serialize the updated summary later.
     */
    modified |= range_add_value(bdesc, colloid, attno, attr, ranges, newval);


    PG_RETURN_BOOL(modified);
}

/*
 * Given an index tuple corresponding to a certain page range and a scan key,
 * return whether the scan key is consistent with the index tuple's min/max
 * values.  Return true if so, false otherwise.
 */
Datum
brin_minmax_multi_consistent(PG_FUNCTION_ARGS)
{
    BrinDesc   *bdesc = (BrinDesc *) PG_GETARG_POINTER(0);
    BrinValues *column = (BrinValues *) PG_GETARG_POINTER(1);
    ScanKey    *keys = (ScanKey *) PG_GETARG_POINTER(2);
    int         nkeys = PG_GETARG_INT32(3);

    Oid         colloid = PG_GET_COLLATION(),
                subtype;
    AttrNumber  attno;
    Datum       value;
    FmgrInfo   *finfo;
    SerializedRanges *serialized;
    Ranges     *ranges;
    int         keyno;
    int         rangeno;
    int         i;

    attno = column->bv_attno;

    serialized = (SerializedRanges *) PG_DETOAST_DATUM(column->bv_values[0]);
    ranges = range_deserialize(serialized->maxvalues, serialized);

    /* inspect the ranges, and for each one evaluate the scan keys */
    for (rangeno = 0; rangeno < ranges->nranges; rangeno++)
    {
        Datum       minval = ranges->values[2 * rangeno];
        Datum       maxval = ranges->values[2 * rangeno + 1];

        /* assume the range is matching, and we'll try to prove otherwise */
        bool        matching = true;

        for (keyno = 0; keyno < nkeys; keyno++)
        {
            Datum       matches;
            ScanKey     key = keys[keyno];

            /* NULL keys are handled and filtered-out in bringetbitmap */
            Assert(!(key->sk_flags & SK_ISNULL));

            attno = key->sk_attno;
            subtype = key->sk_subtype;
            value = key->sk_argument;
            switch (key->sk_strategy)
            {
                case BTLessStrategyNumber:
                case BTLessEqualStrategyNumber:
                    finfo = minmax_multi_get_strategy_procinfo(bdesc, attno, subtype,
                                                               key->sk_strategy);
                    /* first value from the array */
                    matches = FunctionCall2Coll(finfo, colloid, minval, value);
                    break;

                case BTEqualStrategyNumber:
                    {
                        Datum       compar;
                        FmgrInfo   *cmpFn;

                        /* by default this range does not match */
                        matches = false;

                        /*
                         * Otherwise, need to compare the new value with
                         * boundaries of all the ranges. First check if it's
                         * less than the absolute minimum, which is the first
                         * value in the array.
                         */
                        cmpFn = minmax_multi_get_strategy_procinfo(bdesc, attno, subtype,
                                                                   BTGreaterStrategyNumber);
                        compar = FunctionCall2Coll(cmpFn, colloid, minval, value);

                        /* smaller than the smallest value in this range */
                        if (DatumGetBool(compar))
                            break;

                        cmpFn = minmax_multi_get_strategy_procinfo(bdesc, attno, subtype,
                                                                   BTLessStrategyNumber);
                        compar = FunctionCall2Coll(cmpFn, colloid, maxval, value);

                        /* larger than the largest value in this range */
                        if (DatumGetBool(compar))
                            break;

                        /*
                         * We haven't managed to eliminate this range, so
                         * consider it matching.
                         */
                        matches = true;

                        break;
                    }
                case BTGreaterEqualStrategyNumber:
                case BTGreaterStrategyNumber:
                    finfo = minmax_multi_get_strategy_procinfo(bdesc, attno, subtype,
                                                               key->sk_strategy);
                    /* last value from the array */
                    matches = FunctionCall2Coll(finfo, colloid, maxval, value);
                    break;

                default:
                    /* shouldn't happen */
                    elog(ERROR, "invalid strategy number %d", key->sk_strategy);
                    matches = 0;
                    break;
            }

            /* the range has to match all the scan keys */
            matching &= DatumGetBool(matches);

            /* once we find a non-matching key, we're done */
            if (!matching)
                break;
        }

        /*
         * have we found a range matching all scan keys? if yes, we're done
         */
        if (matching)
            PG_RETURN_DATUM(BoolGetDatum(true));
    }

    /*
     * And now inspect the values. We don't bother with doing a binary search
     * here, because we're dealing with serialized / fully compacted ranges,
     * so there should be only very few values.
     */
    for (i = 0; i < ranges->nvalues; i++)
    {
        Datum       val = ranges->values[2 * ranges->nranges + i];

        /* assume the range is matching, and we'll try to prove otherwise */
        bool        matching = true;

        for (keyno = 0; keyno < nkeys; keyno++)
        {
            Datum       matches;
            ScanKey     key = keys[keyno];

            /* we've already dealt with NULL keys at the beginning */
            if (key->sk_flags & SK_ISNULL)
                continue;

            attno = key->sk_attno;
            subtype = key->sk_subtype;
            value = key->sk_argument;
            switch (key->sk_strategy)
            {
                case BTLessStrategyNumber:
                case BTLessEqualStrategyNumber:
                case BTEqualStrategyNumber:
                case BTGreaterEqualStrategyNumber:
                case BTGreaterStrategyNumber:

                    finfo = minmax_multi_get_strategy_procinfo(bdesc, attno, subtype,
                                                               key->sk_strategy);
                    matches = FunctionCall2Coll(finfo, colloid, val, value);
                    break;

                default:
                    /* shouldn't happen */
                    elog(ERROR, "invalid strategy number %d", key->sk_strategy);
                    matches = 0;
                    break;
            }

            /* the range has to match all the scan keys */
            matching &= DatumGetBool(matches);

            /* once we find a non-matching key, we're done */
            if (!matching)
                break;
        }

        /* have we found a range matching all scan keys? if yes, we're done */
        if (matching)
            PG_RETURN_DATUM(BoolGetDatum(true));
    }

    PG_RETURN_DATUM(BoolGetDatum(false));
}

/*
 * Given two BrinValues, update the first of them as a union of the summary
 * values contained in both.  The second one is untouched.
 */
Datum
brin_minmax_multi_union(PG_FUNCTION_ARGS)
{
    BrinDesc   *bdesc = (BrinDesc *) PG_GETARG_POINTER(0);
    BrinValues *col_a = (BrinValues *) PG_GETARG_POINTER(1);
    BrinValues *col_b = (BrinValues *) PG_GETARG_POINTER(2);

    Oid         colloid = PG_GET_COLLATION();
    SerializedRanges *serialized_a;
    SerializedRanges *serialized_b;
    Ranges     *ranges_a;
    Ranges     *ranges_b;
    AttrNumber  attno;
    Form_pg_attribute attr;
    ExpandedRange *eranges;
    int         neranges;
    FmgrInfo   *cmpFn,
               *distanceFn;
    DistanceValue *distances;
    MemoryContext ctx;
    MemoryContext oldctx;

    Assert(col_a->bv_attno == col_b->bv_attno);
    Assert(!col_a->bv_allnulls && !col_b->bv_allnulls);

    attno = col_a->bv_attno;
    attr = TupleDescAttr(bdesc->bd_tupdesc, attno - 1);

    serialized_a = (SerializedRanges *) PG_DETOAST_DATUM(col_a->bv_values[0]);
    serialized_b = (SerializedRanges *) PG_DETOAST_DATUM(col_b->bv_values[0]);

    ranges_a = range_deserialize(serialized_a->maxvalues, serialized_a);
    ranges_b = range_deserialize(serialized_b->maxvalues, serialized_b);

    /* make sure neither of the ranges is NULL */
    Assert(ranges_a && ranges_b);

    neranges = (ranges_a->nranges + ranges_a->nvalues) +
        (ranges_b->nranges + ranges_b->nvalues);

    /*
     * The distanceFn calls (which may internally call e.g. numeric_le) may
     * allocate quite a bit of memory, and we must not leak it. Otherwise,
     * we'd have problems e.g. when building indexes. So we create a local
     * memory context and make sure we free the memory before leaving this
     * function (not after every call).
     */
    ctx = AllocSetContextCreate(CurrentMemoryContext,
                                "minmax-multi context",
                                ALLOCSET_DEFAULT_SIZES);

    oldctx = MemoryContextSwitchTo(ctx);

    /* allocate and fill */
    eranges = (ExpandedRange *) palloc0(neranges * sizeof(ExpandedRange));

    /* fill the expanded ranges with entries for the first range */
    fill_expanded_ranges(eranges, ranges_a->nranges + ranges_a->nvalues,
                         ranges_a);

    /* and now add combine ranges for the second range */
    fill_expanded_ranges(&eranges[ranges_a->nranges + ranges_a->nvalues],
                         ranges_b->nranges + ranges_b->nvalues,
                         ranges_b);

    cmpFn = minmax_multi_get_strategy_procinfo(bdesc, attno, attr->atttypid,
                                               BTLessStrategyNumber);

    /* sort the expanded ranges */
    neranges = sort_expanded_ranges(cmpFn, colloid, eranges, neranges);

    /*
     * We've loaded two different lists of expanded ranges, so some of them
     * may be overlapping. So walk through them and merge them.
     */
    neranges = merge_overlapping_ranges(cmpFn, colloid, eranges, neranges);

    /* check that the combine ranges are correct (no overlaps, ordering) */
    AssertCheckExpandedRanges(bdesc, colloid, attno, attr, eranges, neranges);

    /*
     * If needed, reduce some of the ranges.
     *
     * XXX This may be fairly expensive, so maybe we should do it only when
     * it's actually needed (when we have too many ranges).
     */

    /* build array of gap distances and sort them in ascending order */
    distanceFn = minmax_multi_get_procinfo(bdesc, attno, PROCNUM_DISTANCE);
    distances = build_distances(distanceFn, colloid, eranges, neranges);

    /*
     * See how many values would be needed to store the current ranges, and if
     * needed combine as many of them to get below the threshold. The
     * collapsed ranges will be stored as a single value.
     *
     * XXX This does not apply the load factor, as we don't expect to add more
     * values to the range, so we prefer to keep as many ranges as possible.
     *
     * XXX Can the maxvalues be different in the two ranges? Perhaps we should
     * use maximum of those?
     */
    neranges = reduce_expanded_ranges(eranges, neranges, distances,
                                      ranges_a->maxvalues,
                                      cmpFn, colloid);

    /* update the first range summary */
    store_expanded_ranges(ranges_a, eranges, neranges);

    MemoryContextSwitchTo(oldctx);
    MemoryContextDelete(ctx);

    /* cleanup and update the serialized value */
    pfree(serialized_a);
    col_a->bv_values[0] = PointerGetDatum(range_serialize(ranges_a));

    PG_RETURN_VOID();
}

/*
 * Cache and return minmax multi opclass support procedure
 *
 * Return the procedure corresponding to the given function support number
 * or null if it does not exist.
 */
static FmgrInfo *
minmax_multi_get_procinfo(BrinDesc *bdesc, uint16 attno, uint16 procnum)
{
    MinmaxMultiOpaque *opaque;
    uint16      basenum = procnum - PROCNUM_BASE;

    /*
     * We cache these in the opaque struct, to avoid repetitive syscache
     * lookups.
     */
    opaque = (MinmaxMultiOpaque *) bdesc->bd_info[attno - 1]->oi_opaque;

    /*
     * If we already searched for this proc and didn't find it, don't bother
     * searching again.
     */
    if (opaque->extra_proc_missing[basenum])
        return NULL;

    if (opaque->extra_procinfos[basenum].fn_oid == InvalidOid)
    {
        if (RegProcedureIsValid(index_getprocid(bdesc->bd_index, attno,
                                                procnum)))
        {
            fmgr_info_copy(&opaque->extra_procinfos[basenum],
                           index_getprocinfo(bdesc->bd_index, attno, procnum),
                           bdesc->bd_context);
        }
        else
        {
            opaque->extra_proc_missing[basenum] = true;
            return NULL;
        }
    }

    return &opaque->extra_procinfos[basenum];
}

/*
 * Cache and return the procedure for the given strategy.
 *
 * Note: this function mirrors minmax_multi_get_strategy_procinfo; see notes
 * there.  If changes are made here, see that function too.
 */
static FmgrInfo *
minmax_multi_get_strategy_procinfo(BrinDesc *bdesc, uint16 attno, Oid subtype,
                                   uint16 strategynum)
{
    MinmaxMultiOpaque *opaque;

    Assert(strategynum >= 1 &&
           strategynum <= BTMaxStrategyNumber);

    opaque = (MinmaxMultiOpaque *) bdesc->bd_info[attno - 1]->oi_opaque;

    /*
     * We cache the procedures for the previous subtype in the opaque struct,
     * to avoid repetitive syscache lookups.  If the subtype changed,
     * invalidate all the cached entries.
     */
    if (opaque->cached_subtype != subtype)
    {
        uint16      i;

        for (i = 1; i <= BTMaxStrategyNumber; i++)
            opaque->strategy_procinfos[i - 1].fn_oid = InvalidOid;
        opaque->cached_subtype = subtype;
    }

    if (opaque->strategy_procinfos[strategynum - 1].fn_oid == InvalidOid)
    {
        Form_pg_attribute attr;
        HeapTuple   tuple;
        Oid         opfamily,
                    oprid;
        bool        isNull;

        opfamily = bdesc->bd_index->rd_opfamily[attno - 1];
        attr = TupleDescAttr(bdesc->bd_tupdesc, attno - 1);
        tuple = SearchSysCache4(AMOPSTRATEGY, ObjectIdGetDatum(opfamily),
                                ObjectIdGetDatum(attr->atttypid),
                                ObjectIdGetDatum(subtype),
                                Int16GetDatum(strategynum));
        if (!HeapTupleIsValid(tuple))
            elog(ERROR, "missing operator %d(%u,%u) in opfamily %u",
                 strategynum, attr->atttypid, subtype, opfamily);

        oprid = DatumGetObjectId(SysCacheGetAttr(AMOPSTRATEGY, tuple,
                                                 Anum_pg_amop_amopopr, &isNull));
        ReleaseSysCache(tuple);
        Assert(!isNull && RegProcedureIsValid(oprid));

        fmgr_info_cxt(get_opcode(oprid),
                      &opaque->strategy_procinfos[strategynum - 1],
                      bdesc->bd_context);
    }

    return &opaque->strategy_procinfos[strategynum - 1];
}

Datum
brin_minmax_multi_options(PG_FUNCTION_ARGS)
{
    local_relopts *relopts = (local_relopts *) PG_GETARG_POINTER(0);

    init_local_reloptions(relopts, sizeof(MinMaxMultiOptions));

    add_local_int_reloption(relopts, "values_per_range", "desc",
                            MINMAX_MULTI_DEFAULT_VALUES_PER_PAGE, 8, 256,
                            offsetof(MinMaxMultiOptions, valuesPerRange));

    PG_RETURN_VOID();
}

/*
 * brin_minmax_multi_summary_in
 *      - input routine for type brin_minmax_multi_summary.
 *
 * brin_minmax_multi_summary is only used internally to represent summaries
 * in BRIN minmax-multi indexes, so it has no operations of its own, and we
 * disallow input too.
 */
Datum
brin_minmax_multi_summary_in(PG_FUNCTION_ARGS)
{
    /*
     * brin_minmax_multi_summary 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", "brin_minmax_multi_summary")));

    PG_RETURN_VOID();           /* keep compiler quiet */
}


/*
 * brin_minmax_multi_summary_out
 *      - output routine for type brin_minmax_multi_summary.
 *
 * BRIN minmax-multi summaries are serialized into a bytea value, but we
 * want to output something nicer humans can understand.
 */
Datum
brin_minmax_multi_summary_out(PG_FUNCTION_ARGS)
{
    int         i;
    int         idx;
    SerializedRanges *ranges;
    Ranges     *ranges_deserialized;
    StringInfoData str;
    bool        isvarlena;
    Oid         outfunc;
    FmgrInfo    fmgrinfo;
    ArrayBuildState *astate_values = NULL;

    initStringInfo(&str);
    appendStringInfoChar(&str, '{');

    /*
     * Detoast to get value with full 4B header (can't be stored in a toast
     * table, but can use 1B header).
     */
    ranges = (SerializedRanges *) PG_DETOAST_DATUM(PG_GETARG_BYTEA_PP(0));

    /* lookup output func for the type */
    getTypeOutputInfo(ranges->typid, &outfunc, &isvarlena);
    fmgr_info(outfunc, &fmgrinfo);

    /* deserialize the range info easy-to-process pieces */
    ranges_deserialized = range_deserialize(ranges->maxvalues, ranges);

    appendStringInfo(&str, "nranges: %u  nvalues: %u  maxvalues: %u",
                     ranges_deserialized->nranges,
                     ranges_deserialized->nvalues,
                     ranges_deserialized->maxvalues);

    /* serialize ranges */
    idx = 0;
    for (i = 0; i < ranges_deserialized->nranges; i++)
    {
        char       *a,
                   *b;
        text       *c;
        StringInfoData str;

        initStringInfo(&str);

        a = OutputFunctionCall(&fmgrinfo, ranges_deserialized->values[idx++]);
        b = OutputFunctionCall(&fmgrinfo, ranges_deserialized->values[idx++]);

        appendStringInfo(&str, "%s ... %s", a, b);

        c = cstring_to_text(str.data);

        astate_values = accumArrayResult(astate_values,
                                         PointerGetDatum(c),
                                         false,
                                         TEXTOID,
                                         CurrentMemoryContext);
    }

    if (ranges_deserialized->nranges > 0)
    {
        Oid         typoutput;
        bool        typIsVarlena;
        Datum       val;
        char       *extval;

        getTypeOutputInfo(ANYARRAYOID, &typoutput, &typIsVarlena);

        val = PointerGetDatum(makeArrayResult(astate_values, CurrentMemoryContext));

        extval = OidOutputFunctionCall(typoutput, val);

        appendStringInfo(&str, " ranges: %s", extval);
    }

    /* serialize individual values */
    astate_values = NULL;

    for (i = 0; i < ranges_deserialized->nvalues; i++)
    {
        Datum       a;
        text       *b;
        StringInfoData str;

        initStringInfo(&str);

        a = FunctionCall1(&fmgrinfo, ranges_deserialized->values[idx++]);

        appendStringInfoString(&str, DatumGetCString(a));

        b = cstring_to_text(str.data);

        astate_values = accumArrayResult(astate_values,
                                         PointerGetDatum(b),
                                         false,
                                         TEXTOID,
                                         CurrentMemoryContext);
    }

    if (ranges_deserialized->nvalues > 0)
    {
        Oid         typoutput;
        bool        typIsVarlena;
        Datum       val;
        char       *extval;

        getTypeOutputInfo(ANYARRAYOID, &typoutput, &typIsVarlena);

        val = PointerGetDatum(makeArrayResult(astate_values, CurrentMemoryContext));

        extval = OidOutputFunctionCall(typoutput, val);

        appendStringInfo(&str, " values: %s", extval);
    }


    appendStringInfoChar(&str, '}');

    PG_RETURN_CSTRING(str.data);
}

/*
 * brin_minmax_multi_summary_recv
 *      - binary input routine for type brin_minmax_multi_summary.
 */
Datum
brin_minmax_multi_summary_recv(PG_FUNCTION_ARGS)
{
    ereport(ERROR,
            (errcode(ERRCODE_FEATURE_NOT_SUPPORTED),
             errmsg("cannot accept a value of type %s", "brin_minmax_multi_summary")));

    PG_RETURN_VOID();           /* keep compiler quiet */
}

/*
 * brin_minmax_multi_summary_send
 *      - binary output routine for type brin_minmax_multi_summary.
 *
 * BRIN minmax-multi summaries are serialized in a bytea value (although
 * the type is named differently), so let's just send that.
 */
Datum
brin_minmax_multi_summary_send(PG_FUNCTION_ARGS)
{
    return byteasend(fcinfo);
}