Collect and use element-frequency statistics for arrays.

[postgresql] / src / backend / tsearch / ts_typanalyze.c

/*-------------------------------------------------------------------------
 *
 * ts_typanalyze.c
 *        functions for gathering statistics from tsvector columns
 *
 * Portions Copyright (c) 1996-2012, PostgreSQL Global Development Group
 *
 *
 * IDENTIFICATION
 *        src/backend/tsearch/ts_typanalyze.c
 *
 *-------------------------------------------------------------------------
 */
#include "postgres.h"

#include "access/hash.h"
#include "catalog/pg_operator.h"
#include "commands/vacuum.h"
#include "tsearch/ts_type.h"
#include "utils/builtins.h"


/* A hash key for lexemes */
typedef struct
{
        char       *lexeme;                     /* lexeme (not NULL terminated!) */
        int                     length;                 /* its length in bytes */
} LexemeHashKey;

/* A hash table entry for the Lossy Counting algorithm */
typedef struct
{
        LexemeHashKey key;                      /* This is 'e' from the LC algorithm. */
        int                     frequency;              /* This is 'f'. */
        int                     delta;                  /* And this is 'delta'. */
} TrackItem;

static void compute_tsvector_stats(VacAttrStats *stats,
                                           AnalyzeAttrFetchFunc fetchfunc,
                                           int samplerows,
                                           double totalrows);
static void prune_lexemes_hashtable(HTAB *lexemes_tab, int b_current);
static uint32 lexeme_hash(const void *key, Size keysize);
static int      lexeme_match(const void *key1, const void *key2, Size keysize);
static int      lexeme_compare(const void *key1, const void *key2);
static int      trackitem_compare_frequencies_desc(const void *e1, const void *e2);
static int      trackitem_compare_lexemes(const void *e1, const void *e2);


/*
 *      ts_typanalyze -- a custom typanalyze function for tsvector columns
 */
Datum
ts_typanalyze(PG_FUNCTION_ARGS)
{
        VacAttrStats *stats = (VacAttrStats *) PG_GETARG_POINTER(0);
        Form_pg_attribute attr = stats->attr;

        /* If the attstattarget column is negative, use the default value */
        /* NB: it is okay to scribble on stats->attr since it's a copy */
        if (attr->attstattarget < 0)
                attr->attstattarget = default_statistics_target;

        stats->compute_stats = compute_tsvector_stats;
        /* see comment about the choice of minrows in commands/analyze.c */
        stats->minrows = 300 * attr->attstattarget;

        PG_RETURN_BOOL(true);
}

/*
 *      compute_tsvector_stats() -- compute statistics for a tsvector column
 *
 *      This functions computes statistics that are useful for determining @@
 *      operations' selectivity, along with the fraction of non-null rows and
 *      average width.
 *
 *      Instead of finding the most common values, as we do for most datatypes,
 *      we're looking for the most common lexemes. This is more useful, because
 *      there most probably won't be any two rows with the same tsvector and thus
 *      the notion of a MCV is a bit bogus with this datatype. With a list of the
 *      most common lexemes we can do a better job at figuring out @@ selectivity.
 *
 *      For the same reasons we assume that tsvector columns are unique when
 *      determining the number of distinct values.
 *
 *      The algorithm used is Lossy Counting, as proposed in the paper "Approximate
 *      frequency counts over data streams" by G. S. Manku and R. Motwani, in
 *      Proceedings of the 28th International Conference on Very Large Data Bases,
 *      Hong Kong, China, August 2002, section 4.2. The paper is available at
 *      http://www.vldb.org/conf/2002/S10P03.pdf
 *
 *      The Lossy Counting (aka LC) algorithm goes like this:
 *      Let s be the threshold frequency for an item (the minimum frequency we
 *      are interested in) and epsilon the error margin for the frequency. Let D
 *      be a set of triples (e, f, delta), where e is an element value, f is that
 *      element's frequency (actually, its current occurrence count) and delta is
 *      the maximum error in f. We start with D empty and process the elements in
 *      batches of size w. (The batch size is also known as "bucket size" and is
 *      equal to 1/epsilon.) Let the current batch number be b_current, starting
 *      with 1. For each element e we either increment its f count, if it's
 *      already in D, or insert a new triple into D with values (e, 1, b_current
 *      - 1). After processing each batch we prune D, by removing from it all
 *      elements with f + delta <= b_current.  After the algorithm finishes we
 *      suppress all elements from D that do not satisfy f >= (s - epsilon) * N,
 *      where N is the total number of elements in the input.  We emit the
 *      remaining elements with estimated frequency f/N.  The LC paper proves
 *      that this algorithm finds all elements with true frequency at least s,
 *      and that no frequency is overestimated or is underestimated by more than
 *      epsilon.  Furthermore, given reasonable assumptions about the input
 *      distribution, the required table size is no more than about 7 times w.
 *
 *      We set s to be the estimated frequency of the K'th word in a natural
 *      language's frequency table, where K is the target number of entries in
 *      the MCELEM array plus an arbitrary constant, meant to reflect the fact
 *      that the most common words in any language would usually be stopwords
 *      so we will not actually see them in the input.  We assume that the
 *      distribution of word frequencies (including the stopwords) follows Zipf's
 *      law with an exponent of 1.
 *
 *      Assuming Zipfian distribution, the frequency of the K'th word is equal
 *      to 1/(K * H(W)) where H(n) is 1/2 + 1/3 + ... + 1/n and W is the number of
 *      words in the language.  Putting W as one million, we get roughly 0.07/K.
 *      Assuming top 10 words are stopwords gives s = 0.07/(K + 10).  We set
 *      epsilon = s/10, which gives bucket width w = (K + 10)/0.007 and
 *      maximum expected hashtable size of about 1000 * (K + 10).
 *
 *      Note: in the above discussion, s, epsilon, and f/N are in terms of a
 *      lexeme's frequency as a fraction of all lexemes seen in the input.
 *      However, what we actually want to store in the finished pg_statistic
 *      entry is each lexeme's frequency as a fraction of all rows that it occurs
 *      in.  Assuming that the input tsvectors are correctly constructed, no
 *      lexeme occurs more than once per tsvector, so the final count f is a
 *      correct estimate of the number of input tsvectors it occurs in, and we
 *      need only change the divisor from N to nonnull_cnt to get the number we
 *      want.
 */
static void
compute_tsvector_stats(VacAttrStats *stats,
                                           AnalyzeAttrFetchFunc fetchfunc,
                                           int samplerows,
                                           double totalrows)
{
        int                     num_mcelem;
        int                     null_cnt = 0;
        double          total_width = 0;

        /* This is D from the LC algorithm. */
        HTAB       *lexemes_tab;
        HASHCTL         hash_ctl;
        HASH_SEQ_STATUS scan_status;

        /* This is the current bucket number from the LC algorithm */
        int                     b_current;

        /* This is 'w' from the LC algorithm */
        int                     bucket_width;
        int                     vector_no,
                                lexeme_no;
        LexemeHashKey hash_key;
        TrackItem  *item;

        /*
         * We want statistics_target * 10 lexemes in the MCELEM array.  This
         * multiplier is pretty arbitrary, but is meant to reflect the fact that
         * the number of individual lexeme values tracked in pg_statistic ought to
         * be more than the number of values for a simple scalar column.
         */
        num_mcelem = stats->attr->attstattarget * 10;

        /*
         * We set bucket width equal to (num_mcelem + 10) / 0.007 as per the
         * comment above.
         */
        bucket_width = (num_mcelem + 10) * 1000 / 7;

        /*
         * Create the hashtable. It will be in local memory, so we don't need to
         * worry about overflowing the initial size. Also we don't need to pay any
         * attention to locking and memory management.
         */
        MemSet(&hash_ctl, 0, sizeof(hash_ctl));
        hash_ctl.keysize = sizeof(LexemeHashKey);
        hash_ctl.entrysize = sizeof(TrackItem);
        hash_ctl.hash = lexeme_hash;
        hash_ctl.match = lexeme_match;
        hash_ctl.hcxt = CurrentMemoryContext;
        lexemes_tab = hash_create("Analyzed lexemes table",
                                                          bucket_width * 7,
                                                          &hash_ctl,
                                        HASH_ELEM | HASH_FUNCTION | HASH_COMPARE | HASH_CONTEXT);

        /* Initialize counters. */
        b_current = 1;
        lexeme_no = 0;

        /* Loop over the tsvectors. */
        for (vector_no = 0; vector_no < samplerows; vector_no++)
        {
                Datum           value;
                bool            isnull;
                TSVector        vector;
                WordEntry  *curentryptr;
                char       *lexemesptr;
                int                     j;

                vacuum_delay_point();

                value = fetchfunc(stats, vector_no, &isnull);

                /*
                 * Check for null/nonnull.
                 */
                if (isnull)
                {
                        null_cnt++;
                        continue;
                }

                /*
                 * Add up widths for average-width calculation.  Since it's a
                 * tsvector, we know it's varlena.  As in the regular
                 * compute_minimal_stats function, we use the toasted width for this
                 * calculation.
                 */
                total_width += VARSIZE_ANY(DatumGetPointer(value));

                /*
                 * Now detoast the tsvector if needed.
                 */
                vector = DatumGetTSVector(value);

                /*
                 * We loop through the lexemes in the tsvector and add them to our
                 * tracking hashtable.  Note: the hashtable entries will point into
                 * the (detoasted) tsvector value, therefore we cannot free that
                 * storage until we're done.
                 */
                lexemesptr = STRPTR(vector);
                curentryptr = ARRPTR(vector);
                for (j = 0; j < vector->size; j++)
                {
                        bool            found;

                        /* Construct a hash key */
                        hash_key.lexeme = lexemesptr + curentryptr->pos;
                        hash_key.length = curentryptr->len;

                        /* Lookup current lexeme in hashtable, adding it if new */
                        item = (TrackItem *) hash_search(lexemes_tab,
                                                                                         (const void *) &hash_key,
                                                                                         HASH_ENTER, &found);

                        if (found)
                        {
                                /* The lexeme is already on the tracking list */
                                item->frequency++;
                        }
                        else
                        {
                                /* Initialize new tracking list element */
                                item->frequency = 1;
                                item->delta = b_current - 1;
                        }

                        /* lexeme_no is the number of elements processed (ie N) */
                        lexeme_no++;

                        /* We prune the D structure after processing each bucket */
                        if (lexeme_no % bucket_width == 0)
                        {
                                prune_lexemes_hashtable(lexemes_tab, b_current);
                                b_current++;
                        }

                        /* Advance to the next WordEntry in the tsvector */
                        curentryptr++;
                }
        }

        /* We can only compute real stats if we found some non-null values. */
        if (null_cnt < samplerows)
        {
                int                     nonnull_cnt = samplerows - null_cnt;
                int                     i;
                TrackItem **sort_table;
                int                     track_len;
                int                     cutoff_freq;
                int                     minfreq,
                                        maxfreq;

                stats->stats_valid = true;
                /* Do the simple null-frac and average width stats */
                stats->stanullfrac = (double) null_cnt / (double) samplerows;
                stats->stawidth = total_width / (double) nonnull_cnt;

                /* Assume it's a unique column (see notes above) */
                stats->stadistinct = -1.0;

                /*
                 * Construct an array of the interesting hashtable items, that is,
                 * those meeting the cutoff frequency (s - epsilon)*N.  Also identify
                 * the minimum and maximum frequencies among these items.
                 *
                 * Since epsilon = s/10 and bucket_width = 1/epsilon, the cutoff
                 * frequency is 9*N / bucket_width.
                 */
                cutoff_freq = 9 * lexeme_no / bucket_width;

                i = hash_get_num_entries(lexemes_tab);  /* surely enough space */
                sort_table = (TrackItem **) palloc(sizeof(TrackItem *) * i);

                hash_seq_init(&scan_status, lexemes_tab);
                track_len = 0;
                minfreq = lexeme_no;
                maxfreq = 0;
                while ((item = (TrackItem *) hash_seq_search(&scan_status)) != NULL)
                {
                        if (item->frequency > cutoff_freq)
                        {
                                sort_table[track_len++] = item;
                                minfreq = Min(minfreq, item->frequency);
                                maxfreq = Max(maxfreq, item->frequency);
                        }
                }
                Assert(track_len <= i);

                /* emit some statistics for debug purposes */
                elog(DEBUG3, "tsvector_stats: target # mces = %d, bucket width = %d, "
                         "# lexemes = %d, hashtable size = %d, usable entries = %d",
                         num_mcelem, bucket_width, lexeme_no, i, track_len);

                /*
                 * If we obtained more lexemes than we really want, get rid of those
                 * with least frequencies.      The easiest way is to qsort the array into
                 * descending frequency order and truncate the array.
                 */
                if (num_mcelem < track_len)
                {
                        qsort(sort_table, track_len, sizeof(TrackItem *),
                                  trackitem_compare_frequencies_desc);
                        /* reset minfreq to the smallest frequency we're keeping */
                        minfreq = sort_table[num_mcelem - 1]->frequency;
                }
                else
                        num_mcelem = track_len;

                /* Generate MCELEM slot entry */
                if (num_mcelem > 0)
                {
                        MemoryContext old_context;
                        Datum      *mcelem_values;
                        float4     *mcelem_freqs;

                        /*
                         * We want to store statistics sorted on the lexeme value using
                         * first length, then byte-for-byte comparison. The reason for
                         * doing length comparison first is that we don't care about the
                         * ordering so long as it's consistent, and comparing lengths
                         * first gives us a chance to avoid a strncmp() call.
                         *
                         * This is different from what we do with scalar statistics --
                         * they get sorted on frequencies. The rationale is that we
                         * usually search through most common elements looking for a
                         * specific value, so we can grab its frequency.  When values are
                         * presorted we can employ binary search for that.      See
                         * ts_selfuncs.c for a real usage scenario.
                         */
                        qsort(sort_table, num_mcelem, sizeof(TrackItem *),
                                  trackitem_compare_lexemes);

                        /* Must copy the target values into anl_context */
                        old_context = MemoryContextSwitchTo(stats->anl_context);

                        /*
                         * We sorted statistics on the lexeme value, but we want to be
                         * able to find out the minimal and maximal frequency without
                         * going through all the values.  We keep those two extra
                         * frequencies in two extra cells in mcelem_freqs.
                         *
                         * (Note: the MCELEM statistics slot definition allows for a third
                         * extra number containing the frequency of nulls, but we don't
                         * create that for a tsvector column, since null elements aren't
                         * possible.)
                         */
                        mcelem_values = (Datum *) palloc(num_mcelem * sizeof(Datum));
                        mcelem_freqs = (float4 *) palloc((num_mcelem + 2) * sizeof(float4));

                        /*
                         * See comments above about use of nonnull_cnt as the divisor for
                         * the final frequency estimates.
                         */
                        for (i = 0; i < num_mcelem; i++)
                        {
                                TrackItem  *item = sort_table[i];

                                mcelem_values[i] =
                                        PointerGetDatum(cstring_to_text_with_len(item->key.lexeme,
                                                                                                                  item->key.length));
                                mcelem_freqs[i] = (double) item->frequency / (double) nonnull_cnt;
                        }
                        mcelem_freqs[i++] = (double) minfreq / (double) nonnull_cnt;
                        mcelem_freqs[i] = (double) maxfreq / (double) nonnull_cnt;
                        MemoryContextSwitchTo(old_context);

                        stats->stakind[0] = STATISTIC_KIND_MCELEM;
                        stats->staop[0] = TextEqualOperator;
                        stats->stanumbers[0] = mcelem_freqs;
                        /* See above comment about two extra frequency fields */
                        stats->numnumbers[0] = num_mcelem + 2;
                        stats->stavalues[0] = mcelem_values;
                        stats->numvalues[0] = num_mcelem;
                        /* We are storing text values */
                        stats->statypid[0] = TEXTOID;
                        stats->statyplen[0] = -1;       /* typlen, -1 for varlena */
                        stats->statypbyval[0] = false;
                        stats->statypalign[0] = 'i';
                }
        }
        else
        {
                /* We found only nulls; assume the column is entirely null */
                stats->stats_valid = true;
                stats->stanullfrac = 1.0;
                stats->stawidth = 0;    /* "unknown" */
                stats->stadistinct = 0.0;               /* "unknown" */
        }

        /*
         * We don't need to bother cleaning up any of our temporary palloc's. The
         * hashtable should also go away, as it used a child memory context.
         */
}

/*
 *      A function to prune the D structure from the Lossy Counting algorithm.
 *      Consult compute_tsvector_stats() for wider explanation.
 */
static void
prune_lexemes_hashtable(HTAB *lexemes_tab, int b_current)
{
        HASH_SEQ_STATUS scan_status;
        TrackItem  *item;

        hash_seq_init(&scan_status, lexemes_tab);
        while ((item = (TrackItem *) hash_seq_search(&scan_status)) != NULL)
        {
                if (item->frequency + item->delta <= b_current)
                {
                        if (hash_search(lexemes_tab, (const void *) &item->key,
                                                        HASH_REMOVE, NULL) == NULL)
                                elog(ERROR, "hash table corrupted");
                }
        }
}

/*
 * Hash functions for lexemes. They are strings, but not NULL terminated,
 * so we need a special hash function.
 */
static uint32
lexeme_hash(const void *key, Size keysize)
{
        const LexemeHashKey *l = (const LexemeHashKey *) key;

        return DatumGetUInt32(hash_any((const unsigned char *) l->lexeme,
                                                                   l->length));
}

/*
 *      Matching function for lexemes, to be used in hashtable lookups.
 */
static int
lexeme_match(const void *key1, const void *key2, Size keysize)
{
        /* The keysize parameter is superfluous, the keys store their lengths */
        return lexeme_compare(key1, key2);
}

/*
 *      Comparison function for lexemes.
 */
static int
lexeme_compare(const void *key1, const void *key2)
{
        const LexemeHashKey *d1 = (const LexemeHashKey *) key1;
        const LexemeHashKey *d2 = (const LexemeHashKey *) key2;

        /* First, compare by length */
        if (d1->length > d2->length)
                return 1;
        else if (d1->length < d2->length)
                return -1;
        /* Lengths are equal, do a byte-by-byte comparison */
        return strncmp(d1->lexeme, d2->lexeme, d1->length);
}

/*
 *      qsort() comparator for sorting TrackItems on frequencies (descending sort)
 */
static int
trackitem_compare_frequencies_desc(const void *e1, const void *e2)
{
        const TrackItem *const * t1 = (const TrackItem *const *) e1;
        const TrackItem *const * t2 = (const TrackItem *const *) e2;

        return (*t2)->frequency - (*t1)->frequency;
}

/*
 *      qsort() comparator for sorting TrackItems on lexemes
 */
static int
trackitem_compare_lexemes(const void *e1, const void *e2)
{
        const TrackItem *const * t1 = (const TrackItem *const *) e1;
        const TrackItem *const * t2 = (const TrackItem *const *) e2;

        return lexeme_compare(&(*t1)->key, &(*t2)->key);
}