Selectivity for non-pupular value in Height based Histograms.

Question

Hi,
I wanted to check how optimizer calculates the cardinality/selectivity for a value which is not popular and histogram is height based histograms.
Following is the small test case (Version is 11.2.0.1) platform hpux
create table t1 (
       skew    not null,
       padding
as
/* with generator as (
select --+ materialize
       rownum id
from all_objects
where rownum <= 5000
select /*+ ordered use_nl(v2) */
     v1.id,
     rpad('x',400)
from
    generator  v1,
    generator v2
where
   v1.id <= 80
and
   v2.id <= 80
and
   v2.id <= v1.id
;Following is the table stats:
SQL> select count(*) from t1;
  COUNT(*)
      3240
SQL> exec dbms_stats.gather_table_stats('SYS','T1',cascade=>TRUE, estimate_percent => null, method_opt => 'for all columns size 75');
PL/SQL procedure successfully completed.
SQL> select column_name,num_distinct,density,num_buckets from dba_tab_columns where table_name='T1';
COLUMN_NAME                    NUM_DISTINCT    DENSITY NUM_BUCKETS
SKEW                                     80 .013973812          75
PADDING                                   1 .000154321           1
SQL> select endpoint_number, endpoint_value from dba_tab_histograms where column_name='SKEW' and table_name='T1' order by endpoint_number;
ENDPOINT_NUMBER ENDPOINT_VALUE
              0              1
              1              9
              2             13
              3             16
              4             19
              5             21
              6             23
              7             25
              8             26
              9             28
             10             29
ENDPOINT_NUMBER ENDPOINT_VALUE
             11             31
             12             32
             13             33
             14             35
             15             36
             16             37
             17             38
             18             39
             19             40
             20             41
             21             42
ENDPOINT_NUMBER ENDPOINT_VALUE
             22             43
             23             44
             24             45
             25             46
             26             47
             27             48
             28             49
             29             50
             30             51
             32             52
             33             53
ENDPOINT_NUMBER ENDPOINT_VALUE
             34             54
             35             55
             37             56
             38             57
             39             58
             41             59
             42             60
             43             61
             45             62
             46             63
             48             64
ENDPOINT_NUMBER ENDPOINT_VALUE
             49             65
             51             66
             52             67
             54             68
             56             69
             57             70
             59             71
             60             72
             62             73
             64             74
             66             75
ENDPOINT_NUMBER ENDPOINT_VALUE
             67             76
             69             77
             71             78
             73             79
             75             80
60 rows selected.Checking the selectivity for value 75(which is the popular value as per information from dba_tab_histograms
SQL> set autotrace on
SQL> select count(*) from t1 where skew=75;
  COUNT(*)
        75
Execution Plan
Plan hash value: 4273422929
| Id  | Operation         | Name  | Rows  | Bytes | Cost (%CPU)| Time     |
|   0 | SELECT STATEMENT  |       |     1 |     3 |     1   (0)| 00:00:01 |
|   1 |  SORT AGGREGATE   |       |     1 |     3 |            |          |
|*  2 |   INDEX RANGE SCAN| T1_I1 |    86 |   258 |     1   (0)| 00:00:01 |
Predicate Information (identified by operation id):
   2 - access("SKEW"=75)Skipped the Statistics information for keep example short.
selectivity for 75 (popular value) = 2/75 = 0.02666
Cardinality for 75 is = selectivity * num_rows = 0.02666*3240 = 86.3784 (rounded to 86) >> Here selectivity and cardinality are correct and displayed in autotrace.
SQL> select count(*) from t1 where skew=8;
  COUNT(*)
         8
Execution Plan
Plan hash value: 4273422929
| Id  | Operation         | Name  | Rows  | Bytes | Cost (%CPU)| Time     |
|   0 | SELECT STATEMENT  |       |     1 |     3 |     1   (0)| 00:00:01 |
|   1 |  SORT AGGREGATE   |       |     1 |     3 |            |          |
|*  2 |   INDEX RANGE SCAN| T1_I1 |    29 |    87 |     1   (0)| 00:00:01 |
Predicate Information (identified by operation id):
   2 - access("SKEW"=8)how the cardinality is 29 calculated. I think the formula for selectivity is
select for 1(non popular value) = density * num_rows = .013973812 * num_rows (which is 45 approx) but in autotrace its 29
SQL> select count(*) from t1 where skew = 46;
  COUNT(*)
        46
Execution Plan
Plan hash value: 4273422929
| Id  | Operation         | Name  | Rows  | Bytes | Cost (%CPU)| Time     |
|   0 | SELECT STATEMENT  |       |     1 |     3 |     1   (0)| 00:00:01 |
|   1 |  SORT AGGREGATE   |       |     1 |     3 |            |          |
|*  2 |   INDEX RANGE SCAN| T1_I1 |    29 |    87 |     1   (0)| 00:00:01 |
Predicate Information (identified by operation id):
   2 - access("SKEW"=46)46 is also non popular value
So how the value is calculated for these values?

Answer 1

Your example seems to be based on Jonathan Lewis's article:
http://jonathanlewis.wordpress.com/2012/01/03/newdensity/
In this article, he does walk through the calculation of selectivity for non-popular values.
The calculation is not density but NewDensity, as seen in a 10053 trace, which takes into account the number of non-popular values AND the number of non-popular buckets
The article describes exactly how 29 is derived.Hi Dom,
Yes i used the same sample script of create the data sets. I should have checked Jonathan's blog for new density calculations. So selectivity works out as two either ways
1) selectivity(non popular) = Newdensity(took from 10053 traces) * rum_rows
or
2) non-popular rows/ non_popular values (where non-popular values can be derived from 10053 traces and non popular rows are (3240 * (74-31)/74 = ) 1883
Thanks for pointing to right blog