/*
* 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",
num_mcelem,
&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.
*/
lexemesptr = STRPTR(vector);
curentryptr = ARRPTR(vector);
for (j = 0; j < vector->size; j++)
{
bool found;
/*
* Construct a hash key. The key points into the (detoasted)
* tsvector value at this point, but if a new entry is created, we
* make a copy of it. This way we can free the tsvector value
* once we've processed all its lexemes.
*/
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;
item->key.lexeme = palloc(hash_key.length);
memcpy(item->key.lexeme, hash_key.lexeme, hash_key.length);
}
/* 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++;
}
/* If the vector was toasted, free the detoasted copy. */
if (TSVectorGetDatum(vector) != value)
pfree(vector);
}
/* 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 * (1.0 - stats->stanullfrac);
/*
* 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->stacoll[0] = DEFAULT_COLLATION_OID;
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.
*/
}
/*
* 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 D be a set of triples (e, f, d), where e is an element value, f is
* that element's frequency (occurrence count) and d 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".) 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 + d <= b_current. Finally, we
* gather elements with largest f. The LC paper proves error bounds on f
* dependent on the batch size w, and shows that the required table size
* is no more than a few times w.
*
* We use a hashtable for the D structure and a bucket width of
* statistics_target * 10, where 10 is an arbitrarily chosen constant,
* meant to approximate the number of lexemes in a single tsvector.
*/
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 */
num_mcelem = stats->attr->attstattarget * 10;
/*
* We set bucket width equal to the target number of result lexemes. This
* is probably about right but perhaps might need to be scaled up or down
* a bit?
*/
bucket_width = num_mcelem;
/*
* Create the hashtable. It will be in local memory, so we don't need to
* worry about initial size too much. 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 * 4,
&hash_ctl,
HASH_ELEM | HASH_FUNCTION | HASH_COMPARE | HASH_CONTEXT);
/* Initialize counters. */
b_current = 1;
lexeme_no = 1;
/* 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;
}
/* 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 */
lexeme_no++;
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 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;
/*
* Determine the top-N lexemes by simply copying pointers from the
* hashtable into an array and applying qsort()
*/
track_len = hash_get_num_entries(lexemes_tab);
sort_table = (TrackItem **) palloc(sizeof(TrackItem *) * track_len);
hash_seq_init(&scan_status, lexemes_tab);
i = 0;
while ((item = (TrackItem *) hash_seq_search(&scan_status)) != NULL)
{
sort_table[i++] = item;
}
Assert(i == track_len);
qsort(sort_table, track_len, sizeof(TrackItem *),
trackitem_compare_frequencies_desc);
/* Suppress any single-occurrence items */
while (track_len > 0)
{
if (sort_table[track_len - 1]->frequency > 1)
break;
track_len--;
}
/* Determine the number of most common lexemes to be stored */
if (num_mcelem > track_len)
num_mcelem = track_len;
/* Generate MCELEM slot entry */
if (num_mcelem > 0)
{
MemoryContext old_context;
Datum *mcelem_values;
float4 *mcelem_freqs;
/* Grab the minimal and maximal frequencies that will get stored */
minfreq = sort_table[num_mcelem - 1]->frequency;
maxfreq = sort_table[0]->frequency;
/*
* 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.
*/
mcelem_values = (Datum *) palloc(num_mcelem * sizeof(Datum));
mcelem_freqs = (float4 *) palloc((num_mcelem + 2) * sizeof(float4));
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.
*/
}
