### Re: [HACKERS] Statistics and selectivity estimation for ranges

On 01.03.2013 16:22, Alexander Korotkov wrote: On Wed, Mar 13, 2013 at 11:10 PM, Heikki Linnakangas hlinnakan...@vmware.com wrote: On 01.03.2013 16:22, Alexander Korotkov wrote: frac = area / (length2 - length1); you can get NaN result. I've especially adjusted the code to get more of less correct result in this case. Hmm, good point. I think I managed to fix those cases in the attached version. Is there any other corner case that I missed? Did you try test case by Jeff Davis on this thread? http://www.postgresql.org/message-id/1355167304.3896.37.camel@jdavis I try it with attached version of patch and get NaN estimate. Thanks, fixed that too. Committed with a little bit more clean up and fixes. Thank you for bearing with this long process :-). And many thanks Jeff for the review, and sorry that I forgot to credit you for that in the commit message. - Heikki -- Sent via pgsql-hackers mailing list (pgsql-hackers@postgresql.org) To make changes to your subscription: http://www.postgresql.org/mailpref/pgsql-hackers

### Re: [HACKERS] Statistics and selectivity estimation for ranges

Hi! Thanks for your work on this patch! On Tue, Mar 12, 2013 at 8:03 PM, Heikki Linnakangas hlinnakan...@vmware.com wrote: So, after some hacking, I ended up with this version. I find it more readable, I hope I didn't miss anything. This seems to produce results that are close, but not identical, to the original patch. I'm not sure where the discrepancy is coming from, or which patch is more correct in that respect. I'll continue from this tomorrow, but if you have the time, please take a look and let me know what you think. I've read your explanation and version of patch. In general it seems correct to me. There is one point why I have breaked up abstraction in some functions is infinities. For example, in calc_length_hist_frac one or both of length1 and length2 can be infinity. In the line frac = area / (length2 - length1); you can get NaN result. I've especially adjusted the code to get more of less correct result in this case. Another minor note about this line bin_width *= get_position(typcache, lower, hist_lower[i], hist_lower[i + 1]); ITSM it sould looks like bin_width -= 1.0 - get_position(typcache, lower, hist_lower[i], hist_lower[i + 1]); Imagine lower and upper bounds fall into same histogram bin. In this case we should subtract lengths of both parts which were cut in the left and in the right. -- With best regards, Alexander Korotkov.

### Re: [HACKERS] Statistics and selectivity estimation for ranges

On 01.03.2013 16:22, Alexander Korotkov wrote: On Tue, Mar 12, 2013 at 8:03 PM, Heikki Linnakangashlinnakan...@vmware.com wrote: So, after some hacking, I ended up with this version. I find it more readable, I hope I didn't miss anything. This seems to produce results that are close, but not identical, to the original patch. I'm not sure where the discrepancy is coming from, or which patch is more correct in that respect. I'll continue from this tomorrow, but if you have the time, please take a look and let me know what you think. I've read your explanation and version of patch. In general it seems correct to me. There is one point why I have breaked up abstraction in some functions is infinities. For example, in calc_length_hist_frac one or both of length1 and length2 can be infinity. In the line frac = area / (length2 - length1); you can get NaN result. I've especially adjusted the code to get more of less correct result in this case. Hmm, good point. I think I managed to fix those cases in the attached version. Is there any other corner case that I missed? Another minor note about this line bin_width *= get_position(typcache, lower,hist_lower[i], hist_lower[i + 1]); ITSM it sould looks like bin_width -= 1.0 - get_position(typcache, lower,hist_lower[i], hist_lower[i + 1]); Imagine lower and upper bounds fall into same histogram bin. In this case we should subtract lengths of both parts which were cut in the left and in the right. Yes, true. There's one negation too many above, though; should be: bin_width -= get_position(typcache, lower,hist_lower[i], hist_lower[i + 1]); Fixed that. Barring any more issues, I'll read through this once more tomorrow and commit. - Heikki *** a/src/backend/utils/adt/rangetypes_selfuncs.c --- b/src/backend/utils/adt/rangetypes_selfuncs.c *** *** 20,25 --- 20,26 #include access/htup_details.h #include catalog/pg_operator.h #include catalog/pg_statistic.h + #include utils/builtins.h #include utils/lsyscache.h #include utils/rangetypes.h #include utils/selfuncs.h *** *** 39,44 static int rbound_bsearch(TypeCacheEntry *typcache, RangeBound *value, --- 40,60 RangeBound *hist, int hist_length, bool equal); static float8 get_position(TypeCacheEntry *typcache, RangeBound *value, RangeBound *hist1, RangeBound *hist2); + static float8 get_len_position(double value, double hist1, double hist2); + static float8 get_distance(TypeCacheEntry *typcache, RangeBound *bound1, + RangeBound *bound2); + static int length_hist_bsearch(Datum *length_hist_values, + int length_hist_nvalues, double value, bool equal); + static double calc_length_hist_frac(Datum *length_hist_values, + int length_hist_nvalues, double length1, double length2, bool equal); + static double calc_hist_selectivity_contained(TypeCacheEntry *typcache, + RangeBound *lower, RangeBound *upper, + RangeBound *hist_lower, int hist_nvalues, + Datum *length_hist_values, int length_hist_nvalues); + static double calc_hist_selectivity_contains(TypeCacheEntry *typcache, + RangeBound *lower, RangeBound *upper, + RangeBound *hist_lower, int hist_nvalues, + Datum *length_hist_values, int length_hist_nvalues); /* * Returns a default selectivity estimate for given operator, when we don't *** *** 213,219 calc_rangesel(TypeCacheEntry *typcache, VariableStatData *vardata, /* Try to get fraction of empty ranges */ if (get_attstatsslot(vardata-statsTuple, vardata-atttype, vardata-atttypmod, ! STATISTIC_KIND_RANGE_EMPTY_FRAC, InvalidOid, NULL, NULL, NULL, numbers, nnumbers)) --- 229,235 /* Try to get fraction of empty ranges */ if (get_attstatsslot(vardata-statsTuple, vardata-atttype, vardata-atttypmod, ! STATISTIC_KIND_RANGE_LENGTH_HISTOGRAM, InvalidOid, NULL, NULL, NULL, numbers, nnumbers)) *** *** 332,337 calc_hist_selectivity(TypeCacheEntry *typcache, VariableStatData *vardata, --- 348,355 { Datum *hist_values; int nhist; + Datum *length_hist_values; + int length_nhist; RangeBound *hist_lower; RangeBound *hist_upper; int i; *** *** 365,370 calc_hist_selectivity(TypeCacheEntry *typcache, VariableStatData *vardata, --- 383,403 elog(ERROR, bounds histogram contains an empty range); } + /* @ and @ also need a histogram of range lengths */ + if (operator == OID_RANGE_CONTAINS_OP || + operator == OID_RANGE_CONTAINED_OP) + { + if (!(HeapTupleIsValid(vardata-statsTuple) + get_attstatsslot(vardata-statsTuple, + vardata-atttype, vardata-atttypmod, + STATISTIC_KIND_RANGE_LENGTH_HISTOGRAM, + InvalidOid, + NULL, + length_hist_values, length_nhist, + NULL, NULL))) + return

### Re: [HACKERS] Statistics and selectivity estimation for ranges

On Wed, Mar 13, 2013 at 11:10 PM, Heikki Linnakangas hlinnakan...@vmware.com wrote: On 01.03.2013 16:22, Alexander Korotkov wrote: On Tue, Mar 12, 2013 at 8:03 PM, Heikki Linnakangashlinnakangas@** vmware.com hlinnakan...@vmware.com wrote: So, after some hacking, I ended up with this version. I find it more readable, I hope I didn't miss anything. This seems to produce results that are close, but not identical, to the original patch. I'm not sure where the discrepancy is coming from, or which patch is more correct in that respect. I'll continue from this tomorrow, but if you have the time, please take a look and let me know what you think. I've read your explanation and version of patch. In general it seems correct to me. There is one point why I have breaked up abstraction in some functions is infinities. For example, in calc_length_hist_frac one or both of length1 and length2 can be infinity. In the line frac = area / (length2 - length1); you can get NaN result. I've especially adjusted the code to get more of less correct result in this case. Hmm, good point. I think I managed to fix those cases in the attached version. Is there any other corner case that I missed? Did you try test case by Jeff Davis on this thread? http://www.postgresql.org/message-id/1355167304.3896.37.camel@jdavis I try it with attached version of patch and get NaN estimate. -- With best regards, Alexander Korotkov.

### Re: [HACKERS] Statistics and selectivity estimation for ranges

On 01.03.2013 16:22, Alexander Korotkov wrote: These changes were made in attached patch. Thanks. I've been staring at this code for a very long time now, trying to understand how the math in calc_hist_selectivity_contained works. I think I understand it now, but it probably needs a lot more comments and perhaps some refactoring, so that the next reader won't need to spend hours deciphering it. I'll walk through an example of a calc_hist_selectivity_contained invocation, to verify that my understanding is correct. This isn't 100% identical to how the function works; I explain it as if it holds some temporary bins in memory and modifies them in steps, but in reality, it keeps the bin distances and some other information only for the current/previous bin it's processing, in local variables. Assume that the query is col @ int4range(15, 50), and the lower bounds histogram is (10, 20, 40, 100, 120). Visually, the histogram looks like this: Boundary 10 20 40100120 -+--+--+--+--+- Fraction 0.25 0.25 0.25 0.25 Each bin, 10-20, 20-40, 40-100 and 100-120, contains the same proportion, 25%, of all the tuples in the table. The function first finds the bins containing the lower and upper bounds, 15 and 55. All the bins outside those bounds are ignored, as there are no matching tuples there. The fractions and the bounds of first and last bin, ie. those containing the lower and upper bounds, are adjusted according to the boundary values, using linear interpolation. The lower bound, 15, falls in the middle of the bin 10-20, and the upper bound, 55, splits the 40-100 bin at ratio of 1/5. The adjusted bins look like this: Boundary 15 20 40 55 -+--+--+--+ Fraction 0.125 0.25 0.05 Next, we need to calculate what proportion of tuples in each bin has a small enough length to be contained withing the query range. For that, the distance of each bin boundary to the upper bound is calculated: Distance 40 35 15 0 -+--+--+--+ Fraction 0.125 0.25 0.05 The bins are walked starting from the highest bin, ie. starting from distance 0, walking up in increasing order of distance. For each bin, the proportion of tuples within that range that have a suitable length is calculated. The calc_length_hist_frac function does that. That calculation is more complicated than it sounds: for example, for the middle bin above, calc_length_hist_frac is passed both distance boundaries, 15 and 35. calc_length_hist frac calculates the average of P(x), when x slides linearly from 15 to 35, where P(x) is the fraction of tuples with length = x. Now, here's a question, on something I didn't quite understand: * Returns average fraction of histogram which is greater than given length. * While this length is increasing from length1 to *length2. If histogram * ends up before *length2 then set covered fraction of (length1, *length2) * interval to *fraction and set end of histogram to *length2. */ static double calc_length_hist_frac(Datum *length_hist_values, int length_hist_nvalues, double length1, double *length2, double *fraction) { Why the behavior explained in the last sentence in the above comment? It seems that the abstraction provided by calc_length_hist_frac() is leaky; the caller shouldn't need to know anything about the boundaries of the length bins. Ignoring that, I believe that calc_length_hist_frac can also be explained like this: /* * Let P(x) be the fraction of tuples with length = x. * * calc_length_hist_frac calculates the average of P(x), in the interval [A, B]. * * This can be calculated by the formula: * * B *1 / * --- | P(x)dx * B - A / * A */ static double calc_length_hist_frac(Datum *length_hist_values, int length_hist_nvalues, double A, double B) Am I correct this far? The function doesn't use the above formula as is, but it could.. I'll continue trying to understand this and add comments.. - Heikki -- Sent via pgsql-hackers mailing list (pgsql-hackers@postgresql.org) To make changes to your subscription: http://www.postgresql.org/mailpref/pgsql-hackers

### Re: [HACKERS] Statistics and selectivity estimation for ranges

On 01.03.2013 16:22, Alexander Korotkov wrote: I've been staring at this code for a very long time now, trying to understand how the math in calc_hist_selectivity_contained works. I think I understand it now, but it probably needs a lot more comments and perhaps some refactoring, so that the next reader won't need to spend hours deciphering it. I'll walk through an example of a calc_hist_selectivity_contained invocation, to verify that my understanding is correct. This isn't 100% identical to how the function works; I explain it as if it holds some temporary bins in memory and modifies them in steps, but in reality, it keeps the bin distances and some other information only for the current/previous bin it's processing, in local variables. Assume that the query is col @ int4range(15, 50), and the lower bounds histogram is (10, 20, 40, 100, 120). Visually, the histogram looks like this: Boundary 10 20 40 100 120 -+--+--+--+--+- Fraction 0.25 0.25 0.25 0.25 Each bin, 10-20, 20-40, 40-100 and 100-120, contains the same proportion, 25%, of all the tuples in the table. The function first finds the bins containing the lower and upper bounds, 15 and 55. All the bins outside those bounds are ignored, as there are no matching tuples there. The fractions and the bounds of first and last bin, ie. those containing the lower and upper bounds, are adjusted according to the boundary values, using linear interpolation. The lower bound, 15, falls in the middle of the bin 10-20, and the upper bound, 55, splits the 40-100 bin at ratio of 1/5. The adjusted bins look like this: Boundary 15 20 40 55 -+--+--+--+ Fraction 0.125 0.25 0.05 Next, we need to calculate what proportion of tuples in each bin has a small enough length to be contained withing the query range. For that, the distance of each bin boundary to the upper bound is calculated: Distance 40 35 15 0 -+--+--+--+ Fraction 0.125 0.25 0.05 The bins are walked starting from the highest bin, ie. starting from distance 0, walking up in increasing order of distance. For each bin, the proportion of tuples within that range that have a suitable length is calculated. The calc_length_hist_frac function does that. That calculation is more complicated than it sounds: for example, for the middle bin above, calc_length_hist_frac is passed both distance boundaries, 15 and 35. calc_length_hist frac calculates the average of P(x), when x slides linearly from 15 to 35, where P(x) is the fraction of tuples with length = x. Now, here's a question, on something I didn't quite understand: * Returns average fraction of histogram which is greater than given length. * While this length is increasing from length1 to *length2. If histogram * ends up before *length2 then set covered fraction of (length1, *length2) * interval to *fraction and set end of histogram to *length2. */ static double calc_length_hist_frac(Datum *length_hist_values, int length_hist_nvalues, double length1, double *length2, double *fraction) { Why the behavior explained in the last sentence in the above comment? It seems that the abstraction provided by calc_length_hist_frac() is leaky; the caller shouldn't need to know anything about the boundaries of the length bins. Ignoring that, I believe that calc_length_hist_frac can also be explained like this: /* * Let P(x) be the fraction of tuples with length = x. * * calc_length_hist_frac calculates the average of P(x), in the interval [A, B]. * * This can be calculated by the formula: * * B * 1 / * --- | P(x)dx * B - A / * A */ static double calc_length_hist_frac(Datum *length_hist_values, int length_hist_nvalues, double A, double B) Am I correct this far? The function doesn't use the above formula as is, but it could.. I'll continue trying to understand this and add comments.. So, after some hacking, I ended up with this version. I find it more readable, I hope I didn't miss anything. This seems to produce results that are close, but not identical, to the original patch. I'm not sure where the discrepancy is coming from, or which patch is more correct in that respect. I'll continue from this tomorrow, but if you have the time, please take a look and let me know what you think. - Heikki *** a/src/backend/utils/adt/rangetypes_selfuncs.c --- b/src/backend/utils/adt/rangetypes_selfuncs.c *** *** 20,25 --- 20,26 #include access/htup_details.h #include catalog/pg_operator.h #include catalog/pg_statistic.h + #include utils/builtins.h #include utils/lsyscache.h #include utils/rangetypes.h #include utils/selfuncs.h *** *** 39,44 static int rbound_bsearch(TypeCacheEntry *typcache, RangeBound *value, --- 40,58 RangeBound *hist, int hist_length, bool equal); static float8 get_position(TypeCacheEntry *typcache, RangeBound *value, RangeBound *hist1, RangeBound *hist2); + static float8 get_len_position(double value, double hist1, double hist2); +

### Re: [HACKERS] Statistics and selectivity estimation for ranges

On Wed, Feb 13, 2013 at 5:55 PM, Alexander Korotkov aekorot...@gmail.comwrote: On Wed, Feb 13, 2013 at 5:28 PM, Heikki Linnakangas hlinnakan...@vmware.com wrote: On 04.01.2013 10:42, Alexander Korotkov wrote: /* * Calculate selectivity of operator using histograms of range lower bounds * and histogram of range lengths. */ static double calc_hist_selectivity_overlap(**TypeCacheEntry *typcache, RangeBound *lower, RangeBound *upper, RangeBound *hist_lower, int hist_nvalues, Datum *length_hist_values, int length_hist_nvalues) We already have code to estimate , based on the lower and upper bound histograms: case OID_RANGE_OVERLAP_OP: case OID_RANGE_CONTAINS_ELEM_OP: /* * A B = NOT (A B OR A B). * * range @ elem is equivalent to range [elem,elem]. The * caller already constructed the singular range from the element * constant, so just treat it the same as . */ hist_selec = calc_hist_selectivity_scalar(**typcache, const_lower, hist_upper, nhist, false); hist_selec += (1.0 - calc_hist_selectivity_scalar(**typcache, const_upper, hist_lower, nhist, true)); hist_selec = 1.0 - hist_selec; break; I don't think the method based on lower bound and length histograms is any better. In fact, my gut feeling is that it's less accurate. I'd suggest dropping that part of the patch. Right. This estimation has an accuracy of histogram, while estimation based on lower bound and length histograms rely on additional assumption about independence of lower bound and length histogram. We can sum A B and A B probabilities because they are mutually exclusive. It's pretty evident but I would like to mention it in the comments, because typical assumption about events in statistics calculation is their independence. These changes were made in attached patch. -- With best regards, Alexander Korotkov. range_stat-0.11.patch.gz Description: GNU Zip compressed data -- Sent via pgsql-hackers mailing list (pgsql-hackers@postgresql.org) To make changes to your subscription: http://www.postgresql.org/mailpref/pgsql-hackers

### Re: [HACKERS] Statistics and selectivity estimation for ranges

On 04.01.2013 10:42, Alexander Korotkov wrote: /* * Calculate selectivity of operator using histograms of range lower bounds * and histogram of range lengths. */ static double calc_hist_selectivity_overlap(TypeCacheEntry *typcache, RangeBound *lower, RangeBound *upper, RangeBound *hist_lower, int hist_nvalues, Datum *length_hist_values, int length_hist_nvalues) We already have code to estimate , based on the lower and upper bound histograms: case OID_RANGE_OVERLAP_OP: case OID_RANGE_CONTAINS_ELEM_OP: /* * A B = NOT (A B OR A B). * * range @ elem is equivalent to range [elem,elem]. The * caller already constructed the singular range from the element * constant, so just treat it the same as . */ hist_selec = calc_hist_selectivity_scalar(typcache, const_lower, hist_upper, nhist, false); hist_selec += (1.0 - calc_hist_selectivity_scalar(typcache, const_upper, hist_lower, nhist, true)); hist_selec = 1.0 - hist_selec; break; I don't think the method based on lower bound and length histograms is any better. In fact, my gut feeling is that it's less accurate. I'd suggest dropping that part of the patch. - Heikki -- Sent via pgsql-hackers mailing list (pgsql-hackers@postgresql.org) To make changes to your subscription: http://www.postgresql.org/mailpref/pgsql-hackers

### Re: [HACKERS] Statistics and selectivity estimation for ranges

On Wed, Feb 13, 2013 at 5:28 PM, Heikki Linnakangas hlinnakan...@vmware.com wrote: On 04.01.2013 10:42, Alexander Korotkov wrote: /* * Calculate selectivity of operator using histograms of range lower bounds * and histogram of range lengths. */ static double calc_hist_selectivity_overlap(**TypeCacheEntry *typcache, RangeBound *lower, RangeBound *upper, RangeBound *hist_lower, int hist_nvalues, Datum *length_hist_values, int length_hist_nvalues) We already have code to estimate , based on the lower and upper bound histograms: case OID_RANGE_OVERLAP_OP: case OID_RANGE_CONTAINS_ELEM_OP: /* * A B = NOT (A B OR A B). * * range @ elem is equivalent to range [elem,elem]. The * caller already constructed the singular range from the element * constant, so just treat it the same as . */ hist_selec = calc_hist_selectivity_scalar(**typcache, const_lower, hist_upper, nhist, false); hist_selec += (1.0 - calc_hist_selectivity_scalar(**typcache, const_upper, hist_lower, nhist, true)); hist_selec = 1.0 - hist_selec; break; I don't think the method based on lower bound and length histograms is any better. In fact, my gut feeling is that it's less accurate. I'd suggest dropping that part of the patch. Right. This estimation has an accuracy of histogram, while estimation based on lower bound and length histograms rely on additional assumption about independence of lower bound and length histogram. We can sum A B and A B probabilities because they are mutually exclusive. It's pretty evident but I would like to mention it in the comments, because typical assumption about events in statistics calculation is their independence. -- With best regards, Alexander Korotkov.

### Re: [HACKERS] Statistics and selectivity estimation for ranges

On Mon, Dec 10, 2012 at 11:21 PM, Jeff Davis pg...@j-davis.com wrote: And I have a few other questions/comments: * Why is summ spelled with two ms? Is it short for summation? If so, might be good to use summation of instead of integrate in the comment. Fixed. * Why does get_length_hist_frac return 0.0 when i is the last value? Is that a mistake? Comment was wrong. Actually it return fraction fraction of ranges which length is *greater*. * I am still confused by the distinction between rbound_bsearch and rbound_bsearch_bin. What is the intuitive purpose of each? I've added corresponding comments. rbound_bsearch is for scalar operators and for bin corresponding to upper bound. rbound_bsearch_bin is now rbound_bsearch_bin_lower. It is for bin corresponding to lower bound. * You use constant value in the comments in several places. Would query value or search key be better? Yes. Fixed. I also renamed get_length_hist_frac to get_length_hist_summ and rewrote comments about it. Hope it becomes more understandable. -- With best regards, Alexander Korotkov. range_stat-0.10.patch.gz Description: GNU Zip compressed data -- Sent via pgsql-hackers mailing list (pgsql-hackers@postgresql.org) To make changes to your subscription: http://www.postgresql.org/mailpref/pgsql-hackers

### Re: [HACKERS] Statistics and selectivity estimation for ranges

Hi, Jeff! Thanks a lot for review! On Mon, Dec 10, 2012 at 11:21 PM, Jeff Davis pg...@j-davis.com wrote: It looks like there are still some problems with this patch. CREATE TABLE foo(ir int4range); insert into foo select 'empty' from generate_series(1,1); insert into foo select int4range(NULL, g, '(]') from generate_series(1,100) g; insert into foo select int4range(g, NULL, '[)') from generate_series(1,100) g; insert into foo select int4range(g, ((g*1.01)+10)::int4, '[]') from generate_series(1,100) g; CREATE TABLE bar(ir) AS select * from foo order by random(); ANALYZE bar; Now: EXPLAIN ANALYZE SELECT * FROM bar WHERE ir @ int4range(1,2); The estimates are -nan. Similar for many other queries. Oh, yeah! It appears that infinities require much more cautious work with them than I supposed. That should be fixes in the attached version of patch. However, it require significant rethinking of comments. Will update comments and address your questions in a couple of days. Could you recheck if attached patch really fixes problem you reported? -- With best regards, Alexander Korotkov. range_stat-0.9.patch.gz Description: GNU Zip compressed data -- Sent via pgsql-hackers mailing list (pgsql-hackers@postgresql.org) To make changes to your subscription: http://www.postgresql.org/mailpref/pgsql-hackers

### Re: [HACKERS] Statistics and selectivity estimation for ranges

It looks like there are still some problems with this patch. CREATE TABLE foo(ir int4range); insert into foo select 'empty' from generate_series(1,1); insert into foo select int4range(NULL, g, '(]') from generate_series(1,100) g; insert into foo select int4range(g, NULL, '[)') from generate_series(1,100) g; insert into foo select int4range(g, ((g*1.01)+10)::int4, '[]') from generate_series(1,100) g; CREATE TABLE bar(ir) AS select * from foo order by random(); ANALYZE bar; Now: EXPLAIN ANALYZE SELECT * FROM bar WHERE ir @ int4range(1,2); The estimates are -nan. Similar for many other queries. And I have a few other questions/comments: * Why is summ spelled with two ms? Is it short for summation? If so, might be good to use summation of instead of integrate in the comment. * Why does get_length_hist_frac return 0.0 when i is the last value? Is that a mistake? * I am still confused by the distinction between rbound_bsearch and rbound_bsearch_bin. What is the intuitive purpose of each? * You use constant value in the comments in several places. Would query value or search key be better? Regards, Jeff Davis -- Sent via pgsql-hackers mailing list (pgsql-hackers@postgresql.org) To make changes to your subscription: http://www.postgresql.org/mailpref/pgsql-hackers

### Re: [HACKERS] Statistics and selectivity estimation for ranges

On 2012-11-05 22:10:50 -0800, Jeff Davis wrote: On Mon, 2012-11-05 at 11:12 -0300, Alvaro Herrera wrote: What's going on with this patch? I haven't seen any activity in a while. Should I just move this to the next commitfest? Sorry, I dropped the ball here. I will still review it, whether it makes this commitfest or not. Sorry to nag, but it starts to look like it might fall of the end of the next CF... Greetings, Andres Freund -- Andres Freund http://www.2ndQuadrant.com/ PostgreSQL Development, 24x7 Support, Training Services -- Sent via pgsql-hackers mailing list (pgsql-hackers@postgresql.org) To make changes to your subscription: http://www.postgresql.org/mailpref/pgsql-hackers

### Re: [HACKERS] Statistics and selectivity estimation for ranges

What's going on with this patch? I haven't seen any activity in a while. Should I just move this to the next commitfest? -- Álvaro Herrerahttp://www.2ndQuadrant.com/ PostgreSQL Development, 24x7 Support, Training Services -- Sent via pgsql-hackers mailing list (pgsql-hackers@postgresql.org) To make changes to your subscription: http://www.postgresql.org/mailpref/pgsql-hackers

### Re: [HACKERS] Statistics and selectivity estimation for ranges

On Mon, 2012-11-05 at 11:12 -0300, Alvaro Herrera wrote: What's going on with this patch? I haven't seen any activity in a while. Should I just move this to the next commitfest? Sorry, I dropped the ball here. I will still review it, whether it makes this commitfest or not. Regards, Jeff Davis -- Sent via pgsql-hackers mailing list (pgsql-hackers@postgresql.org) To make changes to your subscription: http://www.postgresql.org/mailpref/pgsql-hackers

### Re: [HACKERS] Statistics and selectivity estimation for ranges

Heikki, would you be able to give this patch a look and perhaps commit it? -- Álvaro Herrerahttp://www.2ndQuadrant.com/ PostgreSQL Development, 24x7 Support, Training Services -- Sent via pgsql-hackers mailing list (pgsql-hackers@postgresql.org) To make changes to your subscription: http://www.postgresql.org/mailpref/pgsql-hackers

### Re: [HACKERS] Statistics and selectivity estimation for ranges

On Tue, 2012-09-04 at 17:27 +0400, Alexander Korotkov wrote: Addon patch is attached. Actually, I don't get your intention of introducing STATISTIC_KIND_RANGE_EMPTY_FRAC stakind. Did you plan to leave it as empty frac in distinct stakind or replace this stakind with STATISTIC_KIND_LENGTH_HISTOGRAM? In the attached patch STATISTIC_KIND_RANGE_EMPTY_FRAC is replaced with STATISTIC_KIND_LENGTH_HISTOGRAM. Review comments: 1. In compute_range_stats, you need to guard against the case where there is no subdiff function. Perhaps default to 1.0 or something? 2. I think it would be helpful to add comments regarding what happens when lengths are identical, right now it's a little confusing. For instance, the comment: Generate a length histogram slot entry if there are at least two length values doesn't seem right, because the condition still matches even if there is only one distinct value. 3. It looks like get_distance also needs to guard against a missing subdiff. 4. There are 3 binary search functions, which seems a little excessive: * rbound_bsearch: greatest i such that hist[i] v; or -1 * rbound_bsearch_equal: greatest i such that: hist[i] = v and (i=0 or hist[i-1] != hist[i]); or -1 * length_hist_bsearch: least i such that hist[i] = v; or length of hist (let me know if I misunderstood the definitions) At a minimum, we need more consistent and informative names. Also, the definition of rbound_bsearch_equal is a little confusing because it's looking for the highest index among distinct values, but the lowest index among identical values. Do you see a way to refactor these to be a little easier to understand? Regards, Jeff Davis -- Sent via pgsql-hackers mailing list (pgsql-hackers@postgresql.org) To make changes to your subscription: http://www.postgresql.org/mailpref/pgsql-hackers

### Re: [HACKERS] Statistics and selectivity estimation for ranges

On Mon, Aug 27, 2012 at 5:00 PM, Heikki Linnakangas heikki.linnakan...@enterprisedb.com wrote: On 24.08.2012 18:51, Heikki Linnakangas wrote: On 20.08.2012 00:31, Alexander Korotkov wrote: New version of patch. * Collect new stakind STATISTIC_KIND_BOUNDS_**HISTOGRAM, which is lower and upper bounds histograms combined into single ranges array, instead of STATISTIC_KIND_HISTOGRAM. One worry I have about that format for the histogram is that you deserialize all the values in the histogram, before you do the binary searches. That seems expensive if stats target is very high. I guess you could deserialize them lazily to alleviate that, though. * Selectivity estimations for,=,,= using this histogram. Thanks! I'm going to do the same for this that I did for the sp-gist patch, and punt on the more complicated parts for now, and review them separately. Attached is a heavily edited version that doesn't include the length histogram, and consequently doesn't do anything smart for the and operators. is estimated using the bounds histograms. There's now a separate stakind for the empty range fraction, since it's not included in the length-histogram. I tested this on a dataset containing birth and death dates of persons that have a wikipedia page, obtained from the dbpedia.org project. I can send a copy if someone wants it. The estimates seem pretty accurate. Please take a look, to see if I messed up something. Committed this with some further changes. Addon patch is attached. Actually, I don't get your intention of introducing STATISTIC_KIND_RANGE_EMPTY_FRAC stakind. Did you plan to leave it as empty frac in distinct stakind or replace this stakind with STATISTIC_KIND_LENGTH_HISTOGRAM? In the attached patch STATISTIC_KIND_RANGE_EMPTY_FRAC is replaced with STATISTIC_KIND_LENGTH_HISTOGRAM. -- With best regards, Alexander Korotkov. range_stat-addon-0.1.patch.gz Description: GNU Zip compressed data -- Sent via pgsql-hackers mailing list (pgsql-hackers@postgresql.org) To make changes to your subscription: http://www.postgresql.org/mailpref/pgsql-hackers

### Re: [HACKERS] Statistics and selectivity estimation for ranges

On 24.08.2012 18:51, Heikki Linnakangas wrote: On 20.08.2012 00:31, Alexander Korotkov wrote: New version of patch. * Collect new stakind STATISTIC_KIND_BOUNDS_HISTOGRAM, which is lower and upper bounds histograms combined into single ranges array, instead of STATISTIC_KIND_HISTOGRAM. One worry I have about that format for the histogram is that you deserialize all the values in the histogram, before you do the binary searches. That seems expensive if stats target is very high. I guess you could deserialize them lazily to alleviate that, though. * Selectivity estimations for,=,,= using this histogram. Thanks! I'm going to do the same for this that I did for the sp-gist patch, and punt on the more complicated parts for now, and review them separately. Attached is a heavily edited version that doesn't include the length histogram, and consequently doesn't do anything smart for the and operators. is estimated using the bounds histograms. There's now a separate stakind for the empty range fraction, since it's not included in the length-histogram. I tested this on a dataset containing birth and death dates of persons that have a wikipedia page, obtained from the dbpedia.org project. I can send a copy if someone wants it. The estimates seem pretty accurate. Please take a look, to see if I messed up something. Committed this with some further changes. -- Heikki Linnakangas EnterpriseDB http://www.enterprisedb.com -- Sent via pgsql-hackers mailing list (pgsql-hackers@postgresql.org) To make changes to your subscription: http://www.postgresql.org/mailpref/pgsql-hackers

### Re: [HACKERS] Statistics and selectivity estimation for ranges

On Mon, Aug 27, 2012 at 5:00 PM, Heikki Linnakangas heikki.linnakan...@enterprisedb.com wrote: On 24.08.2012 18:51, Heikki Linnakangas wrote: On 20.08.2012 00:31, Alexander Korotkov wrote: New version of patch. * Collect new stakind STATISTIC_KIND_BOUNDS_**HISTOGRAM, which is lower and upper bounds histograms combined into single ranges array, instead of STATISTIC_KIND_HISTOGRAM. One worry I have about that format for the histogram is that you deserialize all the values in the histogram, before you do the binary searches. That seems expensive if stats target is very high. I guess you could deserialize them lazily to alleviate that, though. * Selectivity estimations for,=,,= using this histogram. Thanks! I'm going to do the same for this that I did for the sp-gist patch, and punt on the more complicated parts for now, and review them separately. Attached is a heavily edited version that doesn't include the length histogram, and consequently doesn't do anything smart for the and operators. is estimated using the bounds histograms. There's now a separate stakind for the empty range fraction, since it's not included in the length-histogram. I tested this on a dataset containing birth and death dates of persons that have a wikipedia page, obtained from the dbpedia.org project. I can send a copy if someone wants it. The estimates seem pretty accurate. Please take a look, to see if I messed up something. Committed this with some further changes. Thanks! Sorry for I didn't provide a feedback for previous message. Commited patch looks nice for me. I'm going to provide additional patch with length-histogram and more selectivity estimates. -- With best regards, Alexander Korotkov.

### Re: [HACKERS] Statistics and selectivity estimation for ranges

On 20.08.2012 00:31, Alexander Korotkov wrote: On Thu, Aug 16, 2012 at 4:40 PM, Heikki Linnakangas heikki.linnakan...@enterprisedb.com wrote: On 15.08.2012 11:34, Alexander Korotkov wrote: Ok, we've to decide if we need standard histogram. In some cases it can be used for more accurate estimation of and operators. But I think it is not so important. So, we can replace standard histogram with histograms of lower and upper bounds? Yeah, I think that makes more sense. The lower bound histogram is still useful for and operators, just not as accurate if there are lots of values with the same lower bound but different upper bound. New version of patch. * Collect new stakind STATISTIC_KIND_BOUNDS_HISTOGRAM, which is lower and upper bounds histograms combined into single ranges array, instead of STATISTIC_KIND_HISTOGRAM. One worry I have about that format for the histogram is that you deserialize all the values in the histogram, before you do the binary searches. That seems expensive if stats target is very high. I guess you could deserialize them lazily to alleviate that, though. * Selectivity estimations for,=,,= using this histogram. Thanks! I'm going to do the same for this that I did for the sp-gist patch, and punt on the more complicated parts for now, and review them separately. Attached is a heavily edited version that doesn't include the length histogram, and consequently doesn't do anything smart for the and operators. is estimated using the bounds histograms. There's now a separate stakind for the empty range fraction, since it's not included in the length-histogram. I tested this on a dataset containing birth and death dates of persons that have a wikipedia page, obtained from the dbpedia.org project. I can send a copy if someone wants it. The estimates seem pretty accurate. Please take a look, to see if I messed up something. -- Heikki Linnakangas EnterpriseDB http://www.enterprisedb.com diff --git a/src/backend/utils/adt/Makefile b/src/backend/utils/adt/Makefile index a692086..a929f4a 100644 --- a/src/backend/utils/adt/Makefile +++ b/src/backend/utils/adt/Makefile @@ -30,7 +30,8 @@ OBJS = acl.o arrayfuncs.o array_selfuncs.o array_typanalyze.o \ tsginidx.o tsgistidx.o tsquery.o tsquery_cleanup.o tsquery_gist.o \ tsquery_op.o tsquery_rewrite.o tsquery_util.o tsrank.o \ tsvector.o tsvector_op.o tsvector_parser.o \ - txid.o uuid.o windowfuncs.o xml.o rangetypes_spgist.o + txid.o uuid.o windowfuncs.o xml.o rangetypes_spgist.o \ + rangetypes_typanalyze.o rangetypes_selfuncs.o like.o: like.c like_match.c diff --git a/src/backend/utils/adt/rangetypes.c b/src/backend/utils/adt/rangetypes.c index fe9e0c4..f229a9d 100644 --- a/src/backend/utils/adt/rangetypes.c +++ b/src/backend/utils/adt/rangetypes.c @@ -1228,23 +1228,6 @@ hash_range(PG_FUNCTION_ARGS) PG_RETURN_INT32(result); } -/* ANALYZE support */ - -/* typanalyze function for range datatypes */ -Datum -range_typanalyze(PG_FUNCTION_ARGS) -{ - /* - * For the moment, just punt and don't analyze range columns. If we get - * close to release without having a better answer, we could consider - * letting std_typanalyze do what it can ... but those stats are probably - * next door to useless for most activity with range columns, so it's not - * clear it's worth gathering them. - */ - PG_RETURN_BOOL(false); -} - - /* *-- * CANONICAL FUNCTIONS diff --git a/src/backend/utils/adt/rangetypes_selfuncs.c b/src/backend/utils/adt/rangetypes_selfuncs.c new file mode 100644 index 000..ebfc427 --- /dev/null +++ b/src/backend/utils/adt/rangetypes_selfuncs.c @@ -0,0 +1,560 @@ +/*- + * + * rangetypes_selfuncs.c + * Functions for selectivity estimation of range operators + * + * Estimates are based on histograms of lower and upper bounds. + * + * Portions Copyright (c) 1996-2012, PostgreSQL Global Development Group + * Portions Copyright (c) 1994, Regents of the University of California + * + * + * IDENTIFICATION + * src/backend/utils/adt/rangetypes_selfuncs.c + * + *- + */ +#include postgres.h + +#include math.h + +#include catalog/pg_operator.h +#include catalog/pg_statistic.h +#include utils/lsyscache.h +#include utils/rangetypes.h +#include utils/selfuncs.h +#include utils/typcache.h + +static double calc_hist_selectivity(TypeCacheEntry *typcache, + VariableStatData *vardata, RangeType *constval, Oid operator); +static double calc_hist_selectivity_scalar(TypeCacheEntry *typcache, + RangeBound *constbound, + RangeBound *hist, int hist_nvalues, + bool equal); + +static int range_bsearch(TypeCacheEntry *typcache, RangeBound *value, + RangeBound *hist, int hist_length, bool equal); +static double calc_rangesel(TypeCacheEntry *typcache, VariableStatData *vardata,

### Re: [HACKERS] Statistics and selectivity estimation for ranges

On 20.08.2012 00:31, Alexander Korotkov wrote: On Thu, Aug 16, 2012 at 4:40 PM, Heikki Linnakangas heikki.linnakan...@enterprisedb.com wrote: On 15.08.2012 11:34, Alexander Korotkov wrote: Ok, we've to decide if we need standard histogram. In some cases it can be used for more accurate estimation of and operators. But I think it is not so important. So, we can replace standard histogram with histograms of lower and upper bounds? Yeah, I think that makes more sense. The lower bound histogram is still useful for and operators, just not as accurate if there are lots of values with the same lower bound but different upper bound. New version of patch. * Collect new stakind STATISTIC_KIND_BOUNDS_HISTOGRAM, which is lower and upper bounds histograms combined into single ranges array, instead of STATISTIC_KIND_HISTOGRAM. Ah, that's an interesting approach. So essentially, the histogram looks just like a normal STATISTIC_KIND_HISTOGRAM histogram, but the values stored in it are not picked the usual way. The usual way would be to pick N evenly-spaced values from the column, and store those. Instead, you pick N evenly-spaced lower bounds, and N evenly-spaced upper bounds, and construct N range values from those. Looking at a single value in the histogram, its lower bound comes from a different row than its upper bound. That's pretty clever - the histogram has a shape and order that's compatible with a histogram you'd get with the standard scalar typanalyze function. In fact, I think you could just let the standard scalar estimators for and to use that histogram as is. Perhaps we should use STATISTIC_KIND_HISTOGRAM for this after all... -- Heikki Linnakangas EnterpriseDB http://www.enterprisedb.com -- Sent via pgsql-hackers mailing list (pgsql-hackers@postgresql.org) To make changes to your subscription: http://www.postgresql.org/mailpref/pgsql-hackers

### Re: [HACKERS] Statistics and selectivity estimation for ranges

On Thu, Aug 16, 2012 at 4:40 PM, Heikki Linnakangas heikki.linnakan...@enterprisedb.com wrote: On 15.08.2012 11:34, Alexander Korotkov wrote: Ok, we've to decide if we need standard histogram. In some cases it can be used for more accurate estimation of and operators. But I think it is not so important. So, we can replace standard histogram with histograms of lower and upper bounds? Yeah, I think that makes more sense. The lower bound histogram is still useful for and operators, just not as accurate if there are lots of values with the same lower bound but different upper bound. New version of patch. * Collect new stakind STATISTIC_KIND_BOUNDS_HISTOGRAM, which is lower and upper bounds histograms combined into single ranges array, instead of STATISTIC_KIND_HISTOGRAM. * Selectivity estimations for , =, , =, , , , using this histogram. -- With best regards, Alexander Korotkov. range_stat-0.7.patch.gz Description: GNU Zip compressed data -- Sent via pgsql-hackers mailing list (pgsql-hackers@postgresql.org) To make changes to your subscription: http://www.postgresql.org/mailpref/pgsql-hackers

### Re: [HACKERS] Statistics and selectivity estimation for ranges

On 15.08.2012 11:34, Alexander Korotkov wrote: On Wed, Aug 15, 2012 at 12:14 PM, Heikki Linnakangas heikki.linnakan...@enterprisedb.com wrote: Histogram of upper bounds would be both more accurate and natural for some operators. However, it requires collecting additional statistics while AFAICS it doesn't liberate us from having histogram of range lengths. Hmm, if we collected a histogram of lower bounds and a histogram of upper bounds, that would be roughly the same amount of data as for the standard histogram with both bounds in the same histogram. Ok, we've to decide if we need standard histogram. In some cases it can be used for more accurate estimation of and operators. But I think it is not so important. So, we can replace standard histogram with histograms of lower and upper bounds? Yeah, I think that makes more sense. The lower bound histogram is still useful for and operators, just not as accurate if there are lots of values with the same lower bound but different upper bound. -- Heikki Linnakangas EnterpriseDB http://www.enterprisedb.com -- Sent via pgsql-hackers mailing list (pgsql-hackers@postgresql.org) To make changes to your subscription: http://www.postgresql.org/mailpref/pgsql-hackers

### Re: [HACKERS] Statistics and selectivity estimation for ranges

On 15.08.2012 11:34, Alexander Korotkov wrote: On Wed, Aug 15, 2012 at 12:14 PM, Heikki Linnakangas heikki.linnakan...@enterprisedb.com wrote: Histogram of upper bounds would be both more accurate and natural for some operators. However, it requires collecting additional statistics while AFAICS it doesn't liberate us from having histogram of range lengths. Hmm, if we collected a histogram of lower bounds and a histogram of upper bounds, that would be roughly the same amount of data as for the standard histogram with both bounds in the same histogram. Ok, we've to decide if we need standard histogram. In some cases it can be used for more accurate estimation of and operators. But I think it is not so important. So, we can replace standard histogram with histograms of lower and upper bounds? Yeah, I think that makes more sense. The lower bound histogram is still useful for and operators, just not as accurate if there are lots of values with the same lower bound but different upper bound. -- Heikki Linnakangas EnterpriseDB http://www.enterprisedb.com -- Sent via pgsql-hackers mailing list (pgsql-hackers@postgresql.org) To make changes to your subscription: http://www.postgresql.org/mailpref/pgsql-hackers

### Re: [HACKERS] Statistics and selectivity estimation for ranges

On Tue, Aug 14, 2012 at 7:46 PM, Heikki Linnakangas heikki.linnakan...@enterprisedb.com wrote: On 14.08.2012 09:45, Alexander Korotkov wrote: After fixing few more bugs, I've a version with much more reasonable accuracy. Great! One little thing just occurred to me: You're relying on the regular scalar selectivity estimators for the , , and operators. That seems bogus, in particular for and , because ineq_histogram_selectivity then performs a binary search of the histogram using those operators. and compare the *upper* bound of the value in table against the lower bound of constant, but the histogram is constructed using regular operator, which sorts the entries by lower bound. I think the estimates you now get for those operators are quite bogus if there is a non-trivial amount of overlap between ranges. For example: postgres=# create table range_test as select int4range(-a, a) as r from generate_series(1,100) a; analyze range_test; SELECT 100 ANALYZE postgres=# EXPLAIN ANALYZE SELECT * FROM range_test WHERE r int4range(20, 21); QUERY PLAN --**--** --**- Seq Scan on range_test (cost=0.00..17906.00 rows=100 width=14) (actual time=0. 060..1340.147 rows=20 loops=1) Filter: (r '[20,21)'::int4range) Rows Removed by Filter: 80 Total runtime: 1371.865 ms (4 rows) It would be quite easy to provide reasonable estimates for those operators, if we had a separate histogram of upper bounds. I also note that the estimation of overlap selectivity could be implemented using separate histograms of lower bounds and upper bounds, without requiring a histogram of range lengths, because a b == NOT (a b OR a b). I'm not sure if the estimates we'd get that way would be better or worse than your current method, but I think it would be easier to understand. I don't think the and operators could be implemented in terms of a lower and upper bound histogram, though, so you'd still need the current length histogram method for that. Oh, actually I didn't touch those operators. Selectivity estimation functions for them were already in the catalog, they didn't work previously just because no statistics. Histogram of upper bounds would be both more accurate and natural for some operators. However, it requires collecting additional statistics while AFAICS it doesn't liberate us from having histogram of range lengths. The code in that traverses the lower bound and length histograms in lockstep looks quite scary. Any ideas on how to simplify that? My first thought is that there should be helper function that gets a range length as argument, and returns the fraction of tuples with length = argument. It would do the lookup in the length histogram to find the right histogram bin, and do the linear interpolation within the bin. You're assuming that length is independent of lower/upper bound, so you shouldn't need any other parameters than range length for that estimation. You could then loop through only the lower bounds, and call the helper function for each bin to get the fraction of ranges long enough in that bin, instead dealing with both histograms in the same loop. I think a helper function like that might simplify those scary loops significantly, but I wasn't sure if there's some more intelligence in the way you combine values from the length and lower bound histograms that you couldn't do with such a helper function. Yes, I also thought about something like this. But, in order to save current estimate accuracy, it should be more complicated in following reasons: 1) In last version, I don't estimate just fraction of tuples with length = argument, but area under length histogram between two length bounds (length_hist_summ). 2) In histogram ends up before reaching given length bound we also need to return place where it happened. Now it is performed by hist_frac *= (length - prev_dist) / (dist - prev_dist). I'm going to try some simplification with taking care about both mentioned aspects. -- With best regards, Alexander Korotkov.

### Re: [HACKERS] Statistics and selectivity estimation for ranges

On 15.08.2012 10:38, Alexander Korotkov wrote: On Tue, Aug 14, 2012 at 7:46 PM, Heikki Linnakangas heikki.linnakan...@enterprisedb.com wrote: It would be quite easy to provide reasonable estimates for those operators, if we had a separate histogram of upper bounds. I also note that the estimation of overlap selectivity could be implemented using separate histograms of lower bounds and upper bounds, without requiring a histogram of range lengths, because a b == NOT (a b OR a b). I'm not sure if the estimates we'd get that way would be better or worse than your current method, but I think it would be easier to understand. I don't think the and operators could be implemented in terms of a lower and upper bound histogram, though, so you'd still need the current length histogram method for that. Oh, actually I didn't touch those operators. Selectivity estimation functions for them were already in the catalog, they didn't work previously just because no statistics. Yeah, without the histogram, the scalar selectivity estimator sort-of works, in that it returns the estimate just based on the most common values and a constant. Histogram of upper bounds would be both more accurate and natural for some operators. However, it requires collecting additional statistics while AFAICS it doesn't liberate us from having histogram of range lengths. Hmm, if we collected a histogram of lower bounds and a histogram of upper bounds, that would be roughly the same amount of data as for the standard histogram with both bounds in the same histogram. The code in that traverses the lower bound and length histograms in lockstep looks quite scary. Any ideas on how to simplify that? My first thought is that there should be helper function that gets a range length as argument, and returns the fraction of tuples with length= argument. It would do the lookup in the length histogram to find the right histogram bin, and do the linear interpolation within the bin. You're assuming that length is independent of lower/upper bound, so you shouldn't need any other parameters than range length for that estimation. You could then loop through only the lower bounds, and call the helper function for each bin to get the fraction of ranges long enough in that bin, instead dealing with both histograms in the same loop. I think a helper function like that might simplify those scary loops significantly, but I wasn't sure if there's some more intelligence in the way you combine values from the length and lower bound histograms that you couldn't do with such a helper function. Yes, I also thought about something like this. But, in order to save current estimate accuracy, it should be more complicated in following reasons: 1) In last version, I don't estimate just fraction of tuples with length= argument, but area under length histogram between two length bounds (length_hist_summ). 2) In histogram ends up before reaching given length bound we also need to return place where it happened. Now it is performed by hist_frac *= (length - prev_dist) / (dist - prev_dist). I'm going to try some simplification with taking care about both mentioned aspects. Thanks. -- Heikki Linnakangas EnterpriseDB http://www.enterprisedb.com -- Sent via pgsql-hackers mailing list (pgsql-hackers@postgresql.org) To make changes to your subscription: http://www.postgresql.org/mailpref/pgsql-hackers

### Re: [HACKERS] Statistics and selectivity estimation for ranges

On Wed, Aug 15, 2012 at 12:14 PM, Heikki Linnakangas heikki.linnakan...@enterprisedb.com wrote: Histogram of upper bounds would be both more accurate and natural for some operators. However, it requires collecting additional statistics while AFAICS it doesn't liberate us from having histogram of range lengths. Hmm, if we collected a histogram of lower bounds and a histogram of upper bounds, that would be roughly the same amount of data as for the standard histogram with both bounds in the same histogram. Ok, we've to decide if we need standard histogram. In some cases it can be used for more accurate estimation of and operators. But I think it is not so important. So, we can replace standard histogram with histograms of lower and upper bounds? -- With best regards, Alexander Korotkov.

### Re: [HACKERS] Statistics and selectivity estimation for ranges

Alexander Korotkov aekorot...@gmail.com writes: Ok, we've to decide if we need standard histogram. In some cases it can be used for more accurate estimation of and operators. But I think it is not so important. So, we can replace standard histogram with histograms of lower and upper bounds? You should assign a new pg_statistic kind value (see pg_statistic.h) rather than mislabel this as being a standard histogram. However, there's nothing wrong with a data-type-specific stats collection function choosing to gather only this type of histogram and not the standard one. regards, tom lane -- Sent via pgsql-hackers mailing list (pgsql-hackers@postgresql.org) To make changes to your subscription: http://www.postgresql.org/mailpref/pgsql-hackers

### Re: [HACKERS] Statistics and selectivity estimation for ranges

On Mon, Aug 13, 2012 at 1:11 AM, Alexander Korotkov aekorot...@gmail.comwrote: On Thu, Aug 9, 2012 at 12:44 AM, Alexander Korotkov aekorot...@gmail.comwrote: My conclusion is so, that current errors are probably ok for selectivity estimation. But taking into attention that generated datasets ideally fits assumptions of estimation, there could be room for improvement. Especially, it's unclear why estimate for @ and @ have much greater error than estimate for . Possibly, it's caused by some bugs. ITSM, I found reason of inaccuracy. Implementation of linear interpolation was wrong. Fixed version is attached. Now, need to rerun tests, possible refactoring and comments rework. After fixing few more bugs, I've a version with much more reasonable accuracy. Statistics target = 100. Relatively large result sets (= 10) test=# select operator, avg(estimate_count::float8/actual_count::float8) as avg_ratio, avg(exp(abs(ln(estimate_count::float8/actual_count::float8 - 1.0 as avg_error from datasets d join test_results tr on tr.test_id = d.idwhere d.stat_target = 100 and actual_count = 10 group by operator; operator |avg_ratio | avg_error --+--+ @ | 1.00404179116863 | 0.0504415454560903 @ | 1.06364108531688 | 0.105646077989812 | 1.00757984721409 | 0.0420984234933233 (3 rows) Small result sets (1 - 9) test=# select operator, avg(estimate_count::float8/actual_count::float8) as avg_ratio, avg(exp(abs(ln(estimate_count::float8/actual_count::float8 - 1.0 as avg_error from datasets d join test_results tr on tr.test_id = d.idwhere d.stat_target = 100 and actual_count between 1 and 9 group by operator; operator |avg_ratio | avg_error --+--+--- @ | 1.31530838062865 | 0.654886592410495 @ | 2.78708078320147 | 1.94124123003433 | 1.93268112525538 | 1.09904919063335 (3 rows) Empty result sets test=# select operator, avg(estimate_count) as avg_estimate, count(*) as tests_count from datasets d join test_results tr on tr.test_id = d.id where d.stat_target = 100 and actual_count = 0 group by operator; operator |avg_estimate| tests_count --++- @ | 1.1437670609645132 |1099 @ | 1.0479430126460701 | 87458 (2 rows) Statistics target = 1000. Relatively large result sets (= 10) test=# select operator, avg(estimate_count::float8/actual_count::float8) as avg_ratio, avg(exp(abs(ln(estimate_count::float8/actual_count::float8 - 1.0 as avg_error from datasets d join test_results tr on tr.test_id = d.idwhere d.stat_target = 1000 and actual_count = 10 group by operator; operator |avg_ratio | avg_error --+--+ @ | 1.00073999445381 | 0.045099762607524 @ | 1.05296320350853 | 0.0907489633452971 | 1.00217602359039 | 0.0353421159150165 (3 rows) Small result sets (1 - 9) test=# select operator, avg(estimate_count::float8/actual_count::float8) as avg_ratio, avg(exp(abs(ln(estimate_count::float8/actual_count::float8 - 1.0 as avg_error from datasets d join test_results tr on tr.test_id = d.idwhere d.stat_target = 1000 and actual_count between 1 and 9 group by operator; operator |avg_ratio | avg_error --+--+--- @ | 1.26946358795998 | 0.577803898836364 @ | 2.69000633430211 | 1.83165424646645 | 1.48715184186882 | 0.577998652291105 (3 rows) Empty result sets test=# select operator, avg(estimate_count) as avg_estimate, count(*) as tests_count from datasets d join test_results tr on tr.test_id = d.id where d.stat_target = 1000 and actual_count = 0 group by operator; operator |avg_estimate| tests_count --++- @ | 1.0887096774193548 |1364 @ | 1.0423876983771183 | 89224 | 5. | 1 (3 rows) -- With best regards, Alexander Korotkov. range_stat-0.6.patch.gz Description: GNU Zip compressed data -- Sent via pgsql-hackers mailing list (pgsql-hackers@postgresql.org) To make changes to your subscription: http://www.postgresql.org/mailpref/pgsql-hackers

### Re: [HACKERS] Statistics and selectivity estimation for ranges

On 14.08.2012 09:45, Alexander Korotkov wrote: After fixing few more bugs, I've a version with much more reasonable accuracy. Great! One little thing just occurred to me: You're relying on the regular scalar selectivity estimators for the , , and operators. That seems bogus, in particular for and , because ineq_histogram_selectivity then performs a binary search of the histogram using those operators. and compare the *upper* bound of the value in table against the lower bound of constant, but the histogram is constructed using regular operator, which sorts the entries by lower bound. I think the estimates you now get for those operators are quite bogus if there is a non-trivial amount of overlap between ranges. For example: postgres=# create table range_test as select int4range(-a, a) as r from generate_series(1,100) a; analyze range_test; SELECT 100 ANALYZE postgres=# EXPLAIN ANALYZE SELECT * FROM range_test WHERE r int4range(20, 21); QUERY PLAN --- Seq Scan on range_test (cost=0.00..17906.00 rows=100 width=14) (actual time=0. 060..1340.147 rows=20 loops=1) Filter: (r '[20,21)'::int4range) Rows Removed by Filter: 80 Total runtime: 1371.865 ms (4 rows) It would be quite easy to provide reasonable estimates for those operators, if we had a separate histogram of upper bounds. I also note that the estimation of overlap selectivity could be implemented using separate histograms of lower bounds and upper bounds, without requiring a histogram of range lengths, because a b == NOT (a b OR a b). I'm not sure if the estimates we'd get that way would be better or worse than your current method, but I think it would be easier to understand. I don't think the and operators could be implemented in terms of a lower and upper bound histogram, though, so you'd still need the current length histogram method for that. The code in that traverses the lower bound and length histograms in lockstep looks quite scary. Any ideas on how to simplify that? My first thought is that there should be helper function that gets a range length as argument, and returns the fraction of tuples with length = argument. It would do the lookup in the length histogram to find the right histogram bin, and do the linear interpolation within the bin. You're assuming that length is independent of lower/upper bound, so you shouldn't need any other parameters than range length for that estimation. You could then loop through only the lower bounds, and call the helper function for each bin to get the fraction of ranges long enough in that bin, instead dealing with both histograms in the same loop. I think a helper function like that might simplify those scary loops significantly, but I wasn't sure if there's some more intelligence in the way you combine values from the length and lower bound histograms that you couldn't do with such a helper function. -- Heikki Linnakangas EnterpriseDB http://www.enterprisedb.com -- Sent via pgsql-hackers mailing list (pgsql-hackers@postgresql.org) To make changes to your subscription: http://www.postgresql.org/mailpref/pgsql-hackers

### Re: [HACKERS] Statistics and selectivity estimation for ranges

On Thu, Aug 9, 2012 at 12:44 AM, Alexander Korotkov aekorot...@gmail.comwrote: My conclusion is so, that current errors are probably ok for selectivity estimation. But taking into attention that generated datasets ideally fits assumptions of estimation, there could be room for improvement. Especially, it's unclear why estimate for @ and @ have much greater error than estimate for . Possibly, it's caused by some bugs. ITSM, I found reason of inaccuracy. Implementation of linear interpolation was wrong. Fixed version is attached. Now, need to rerun tests, possible refactoring and comments rework. -- With best regards, Alexander Korotkov. range_stat-0.4.patch.gz Description: GNU Zip compressed data -- Sent via pgsql-hackers mailing list (pgsql-hackers@postgresql.org) To make changes to your subscription: http://www.postgresql.org/mailpref/pgsql-hackers

### Re: [HACKERS] Statistics and selectivity estimation for ranges

New revision of patch with two fixes: 1) Check if histogram bin width is zero in get_position. 2) Check statsTuple is valid tuple in rangecontsel. -- With best regards, Alexander Korotkov. range_stat-0.3.patch.gz Description: GNU Zip compressed data -- Sent via pgsql-hackers mailing list (pgsql-hackers@postgresql.org) To make changes to your subscription: http://www.postgresql.org/mailpref/pgsql-hackers

### Re: [HACKERS] Statistics and selectivity estimation for ranges

Having statistics on ranges was really missing! The planner was doing some really, really bad choices on bigger tables regarding seq/random scans, nested loop/other joins etc. Is there any chance this makes it into 9.2 final? It would really round-off the introduction of range types and maybe avoid problems like the new range types are slow (just due to the bad row estimates). Thanks for implementing this feature, -Matthias -- Sent via pgsql-hackers mailing list (pgsql-hackers@postgresql.org) To make changes to your subscription: http://www.postgresql.org/mailpref/pgsql-hackers

### Re: [HACKERS] Statistics and selectivity estimation for ranges

On 04.08.2012 12:31, Alexander Korotkov wrote: Hackers, attached patch is for collecting statistics and selectivity estimation for ranges. In order to make our estimations accurate for every distribution of ranges, we would collect 2d-distribution of lower and upper bounds of range into some kind of 2d-histogram. However, this patch use some simplification and assume distribution of lower bound and distribution of length to be independent. Sounds reasonable. Another possibility would be to calculate the average length for each lower-bound bin. So you would e.g know the average length of values with lower bound between 1-10, and the average length of values with lower bound between 10-20, and so forth. Within a bin, you would have to assume that the distribution of the lengths is fixed. PS. get_position() should guard against division by zero, when subdiff returns zero. -- Heikki Linnakangas EnterpriseDB http://www.enterprisedb.com -- Sent via pgsql-hackers mailing list (pgsql-hackers@postgresql.org) To make changes to your subscription: http://www.postgresql.org/mailpref/pgsql-hackers

### Re: [HACKERS] Statistics and selectivity estimation for ranges

On Mon, Aug 6, 2012 at 6:09 PM, Heikki Linnakangas heikki.linnakan...@enterprisedb.com wrote: On 04.08.2012 12:31, Alexander Korotkov wrote: Hackers, attached patch is for collecting statistics and selectivity estimation for ranges. In order to make our estimations accurate for every distribution of ranges, we would collect 2d-distribution of lower and upper bounds of range into some kind of 2d-histogram. However, this patch use some simplification and assume distribution of lower bound and distribution of length to be independent. Sounds reasonable. Another possibility would be to calculate the average length for each lower-bound bin. So you would e.g know the average length of values with lower bound between 1-10, and the average length of values with lower bound between 10-20, and so forth. Within a bin, you would have to assume that the distribution of the lengths is fixed. Interesting idea. AFAICS, if we store average length for each lower-bound bin, we still have to assume some kind of distribution of range length in order to do estimates. For example, assume that range length have exponential distribution. Correspondingly, we've following trade off: we don't have to assume lower bound distribution to be independent from length distribution, but we have to assume kind of length distribution. Actually, I don't know what is better. Ideally, we would have range length histogram for each lower-bound bin, or upper-bound histogram for each lower-bound bin. But, storing such amount of data seems too expensive. -- With best regards, Alexander Korotkov.