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CHAPTER 7 HISTOGRAMS
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Isn t that an amazing coincidence No, not really, because from 9i onward, you can enable SQL trace while using the dbms_stats package to generate a histogram, and find that behind the scenes, the package is running SQL like the following: select min(minbkt), maxbkt, substrb(dump(min(val),16,0,32),1,120) substrb(dump(max(val),16,0,32),1,120) sum(rep) sum(repsq) max(rep) count(*) sum(case when rep=1 then 1 else 0 end) from ( select val, min(bkt) max(bkt) count(val) count(val) * count(val) from ( select /*+ cursor_sharing_exact dynamic_sampling(0) no_monitoring */ "NORMAL" val, ntile(10) over(order by "NORMAL") bkt from "TEST_USER"."T1" t where "NORMAL" is not null ) group by val ) group by maxbkt order by maxbkt ; Look very carefully at the innermost of the inline views. Note the line where the ntile(10) appears. Apart from a few cosmetic changes, and a few extra figures used for dealing with extreme conditions and the value of user_tab_columns.density, the SQL that generates the figures stored in user_tab_histograms is exactly the same as my original graph-drawing SQL. A histogram is just a picture of your data set. minbkt, maxbkt, rep, repsq
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minval, maxval, sumrep, sumrepsq, maxrep, bktndv, unqrep
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Look back at the graph one more time, and say to yourself, Oracle Corp. calls this type of graph a height balanced histogram. If you ve ever had trouble understanding Oracle s concept of height balanced histograms, you now know why ... they aren t height-balanced, they re just the straightforward style of histogram that most people probably first learned about at the age of 12, and have never had to think about since.
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When I searched Google for height balanced and histogram, every reference I found pointed me back to Oracle. It was only after a tip-off from Wolfgang Breitling that I did a search for equi-depth and histogram and found that the histograms that Oracle describes as height balanced are commonly called equi-depth (or sometimes equi-height) in the standard literature. None of the terms gives me an intuitive understanding of how the graphs represent the data so I tend to avoid using the expression height balanced, and just call the things histograms.
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Oracle uses histograms to improve its selectivity and cardinality calculations for nonuniform data distributions. But you can actually use two different strategies: one for data sets with only a few (fewer than 255) distinct values, and one for data sets with lots of distinct values. Oracle calls the former a frequency histogram (although technically it probably ought to be a cumulative frequency histogram) and the latter a height balanced histogram (although, as you saw earlier, the heights involved are not balanced in any way that a non-mathematician would appreciate). Although the two types of histogram have their own special features, there are many common areas in their use that I plan to cover in this section. At the simplest level, irrespective of type, a histogram is simply a collection of pairs of numbers (stored in views like user_tab_histograms, user_part_histograms, user_subpart_histograms) that can be used to draw pictures of the data. However, while collecting the histogram data, Oracle also collects some extra information that it uses to calculate a modified density for the column. After generating a histogram for a column, you will usually find that the density value reported in user_tab_columns (et al.) is no longer equal to 1 / num_distinct. When working out selectivities and cardinalities, Oracle may be able to make use of the full detail of the histogram, but sometimes has to fall back on using just the density. It is this fallback position that can cause surprises, so the rest of this section is a quick tour of features that interfere with the best use of histograms.
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Histograms and Bind Variables
We have seen in earlier chapters that the optimizer uses the density as the selectivity for predicates of the form column = constant or column = :bind_variable. So with histograms in place, the selectivity of a simple equality predicate changes, even for a query involving a bind variable. If you ve ever heard that histograms become irrelevant when you use (un-peeked) bind variables, it s not quite true the detail cannot be used, but the effect of the density may be very relevant. Unfortunately, as I noted earlier, if there is a particular area of the graph that you are really interested in, you may need to override Oracle s estimated density and create a business-relevant density.
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