Hello,

I'm not sure if I should post here or on pgsql-hackers.

While investigating about a wrong result with my btree bloat estimation query,
I found a strange stat deviation between the average size of a value in its
table and its average size in one index on the "lower" expression.

Take the following scenario:

  postgres@test=# create table test as
  test-# select md5(t::text) AS t 
  test-# from generate_series(1, 1000000) t;
  SELECT 1000000
  
  postgres@test=# create index ON test (lower(t));
  CREATE INDEX
  
  postgres@test=# analyze test;
  ANALYZE
  
  postgres@test=# select tablename, attname, avg_width
  test-# from pg_stats
  test-# where schemaname = 'public';
     tablename    | attname | avg_width 
  ----------------+---------+-----------
   test           | t       |        33
   test_lower_idx | lower   |        36

Md5 values are always 32 bytes long. In the table, pg_stats reports 33 because
of the text header. In the index, the reported value is 36!

Looking at the page layout documentation and in the index using hexdump, I can
not find any answer about this 3 bytes. PFA the "hexdump -C" output from the
index. For each row, we clearly see a 8 bytes row header followed by a ONE byte
value header (43 'C'), the 32 bytes of the md5 and 7 bytes of padding (00).

A wild guess would be that ANALYZE is considering a text field from an
expression has always a 4 bytes header whatever its actual size (text field
header size is one if the value is < 127 bytes long, 4 in other situations).


This tiny difference is the source of a very bad estimation with the Btree bloat
estimation query when values are around an alignement boundary. As instance,
here is the use case that lead me to this:

       tablename      | attname | avg_width 
  --------------------+---------+-----------
   customer           | email   |        23
   customer_lower_idx | lower   |        26

We have an index on email, and another one on lower(index). The first one is
aligned on 24, the second one on 32. Leading to bloat estimation of 17% for
the first one and -1% for the second one (the estimated index size is bigger
than the real one).

Any information about this from a hacker? Do anyone have an explanation about
this? Is it something that's worth posting on pgsql-hackers?


Regards,
00000000  00 00 00 00 00 00 00 00  00 00 00 00 30 00 f0 1f  |............0...|
00000010  f0 1f 04 20 00 00 00 00  62 31 05 00 02 00 00 00  |... ....b1......|
00000020  01 00 00 00 00 00 00 00  01 00 00 00 00 00 00 00  |................|
00000030  00 00 00 00 00 00 00 00  00 00 00 00 00 00 00 00  |................|
*
00001ff0  00 00 00 00 00 00 00 00  00 00 00 00 08 00 00 00  |................|
00002000  00 00 00 00 00 00 00 00  00 00 00 00 a8 01 30 0d  |..............0.|
00002010  f0 1f 04 20 00 00 00 00  c0 9f 60 00 90 9f 60 00  |... ......`...`.|
00002020  60 9f 60 00 30 9f 60 00  00 9f 60 00 d0 9e 60 00  |`.`.0.`...`...`.|
00002030  a0 9e 60 00 70 9e 60 00  40 9e 60 00 10 9e 60 00  |..`.p.`.@.`...`.|
00002040  e0 9d 60 00 b0 9d 60 00  80 9d 60 00 50 9d 60 00  |..`...`...`.P.`.|
00002050  20 9d 60 00 f0 9c 60 00  c0 9c 60 00 90 9c 60 00  | .`...`...`...`.|
00002060  60 9c 60 00 30 9c 60 00  00 9c 60 00 d0 9b 60 00  |`.`.0.`...`...`.|
00002070  a0 9b 60 00 70 9b 60 00  40 9b 60 00 10 9b 60 00  |..`.p.`.@.`...`.|
00002080  e0 9a 60 00 b0 9a 60 00  80 9a 60 00 50 9a 60 00  |..`...`...`.P.`.|
00002090  20 9a 60 00 f0 99 60 00  c0 99 60 00 90 99 60 00  | .`...`...`...`.|
000020a0  60 99 60 00 30 99 60 00  00 99 60 00 d0 98 60 00  |`.`.0.`...`...`.|
000020b0  a0 98 60 00 70 98 60 00  40 98 60 00 10 98 60 00  |..`.p.`.@.`...`.|
000020c0  e0 97 60 00 b0 97 60 00  80 97 60 00 50 97 60 00  |..`...`...`.P.`.|
000020d0  20 97 60 00 f0 96 60 00  c0 96 60 00 90 96 60 00  | .`...`...`...`.|
000020e0  60 96 60 00 30 96 60 00  00 96 60 00 d0 95 60 00  |`.`.0.`...`...`.|
000020f0  a0 95 60 00 70 95 60 00  40 95 60 00 10 95 60 00  |..`.p.`.@.`...`.|
00002100  e0 94 60 00 b0 94 60 00  80 94 60 00 50 94 60 00  |..`...`...`.P.`.|
00002110  20 94 60 00 f0 93 60 00  c0 93 60 00 90 93 60 00  | .`...`...`...`.|
00002120  60 93 60 00 30 93 60 00  00 93 60 00 d0 92 60 00  |`.`.0.`...`...`.|
00002130  a0 92 60 00 70 92 60 00  40 92 60 00 10 92 60 00  |..`.p.`.@.`...`.|
00002140  e0 91 60 00 b0 91 60 00  80 91 60 00 50 91 60 00  |..`...`...`.P.`.|
00002150  20 91 60 00 f0 90 60 00  c0 90 60 00 90 90 60 00  | .`...`...`...`.|
00002160  60 90 60 00 30 90 60 00  00 90 60 00 d0 8f 60 00  |`.`.0.`...`...`.|
00002170  a0 8f 60 00 70 8f 60 00  40 8f 60 00 10 8f 60 00  |..`.p.`.@.`...`.|
00002180  e0 8e 60 00 b0 8e 60 00  80 8e 60 00 50 8e 60 00  |..`...`...`.P.`.|
00002190  20 8e 60 00 f0 8d 60 00  c0 8d 60 00 90 8d 60 00  | .`...`...`...`.|
000021a0  60 8d 60 00 30 8d 60 00  30 8d 60 00 00 00 00 00  |`.`.0.`.0.`.....|
000021b0  00 00 00 00 00 00 00 00  00 00 00 00 00 00 00 00  |................|
*
00002d30  00 00 00 00 53 00 30 40  43 66 65 39 66 63 32 38  |....S.0@Cfe9fc28|
00002d40  39 63 33 66 66 30 61 66  31 34 32 62 36 64 33 62  |9c3ff0af142b6d3b|
00002d50  65 61 64 39 38 61 39 32  33 00 00 00 00 00 00 00  |ead98a923.......|
00002d60  00 00 00 00 41 00 30 40  43 66 63 34 39 30 63 61  |....A.0@Cfc490ca|
00002d70  34 35 63 30 30 62 31 32  34 39 62 62 65 33 35 35  |45c00b1249bbe355|
00002d80  34 61 34 66 64 66 36 66  62 00 00 00 00 00 00 00  |4a4fdf6fb.......|
00002d90  00 00 00 00 4c 00 30 40  43 66 62 64 37 39 33 39  |....L.0@Cfbd7939|
00002da0  64 36 37 34 39 39 37 63  64 62 34 36 39 32 64 33  |d674997cdb4692d3|
00002db0  34 64 65 38 36 33 33 63  34 00 00 00 00 00 00 00  |4de8633c4.......|
00002dc0  00 00 00 00 64 00 30 40  43 66 38 39 39 31 33 39  |....d.0@Cf899139|
00002dd0  64 66 35 65 31 30 35 39  33 39 36 34 33 31 34 31  |df5e105939643141|
00002de0  35 65 37 37 30 63 36 64  64 00 00 00 00 00 00 00  |5e770c6dd.......|
00002df0  00 00 00 00 2c 00 30 40  43 66 37 31 37 37 31 36  |....,.0@Cf717716|
00002e00  33 63 38 33 33 64 66 66  34 62 33 38 66 63 38 64  |3c833dff4b38fc8d|
00002e10  32 38 37 32 66 31 65 63  36 00 00 00 00 00 00 00  |2872f1ec6.......|
00002e20  00 00 00 00 5e 00 30 40  43 66 34 62 39 65 63 33  |....^.0@Cf4b9ec3|
00002e30  30 61 64 39 66 36 38 66  38 39 62 32 39 36 33 39  |0ad9f68f89b29639|
00002e40  37 38 36 63 62 36 32 65  66 00 00 00 00 00 00 00  |786cb62ef.......|
00002e50  00 00 00 00 31 00 30 40  43 66 34 35 37 63 35 34  |....1.0@Cf457c54|
00002e60  35 61 39 64 65 64 38 38  66 31 38 65 63 65 65 34  |5a9ded88f18ecee4|
00002e70  37 31 34 35 61 37 32 63  30 00 00 00 00 00 00 00  |7145a72c0.......|
00002e80  00 00 00 00 50 00 30 40  43 66 30 33 33 61 62 33  |....P.0@Cf033ab3|
00002e90  37 63 33 30 32 30 31 66  37 33 66 31 34 32 34 34  |7c30201f73f14244|
00002ea0  39 64 30 33 37 30 32 38  64 00 00 00 00 00 00 00  |9d037028d.......|
00002eb0  00 00 00 00 62 00 30 40  43 65 64 33 64 32 63 32  |....b.0@Ced3d2c2|
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00002ed0  33 61 66 39 66 61 36 63  61 00 00 00 00 00 00 00  |3af9fa6ca.......|
00002ee0  00 00 00 00 03 00 30 40  43 65 63 63 62 63 38 37  |......0@Ceccbc87|
00002ef0  65 34 62 35 63 65 32 66  65 32 38 33 30 38 66 64  |e4b5ce2fe28308fd|
00002f00  39 66 32 61 37 62 61 66  33 00 00 00 00 00 00 00  |9f2a7baf3.......|
00002f10  00 00 00 00 40 00 30 40  43 65 61 35 64 32 66 31  |....@.0@Cea5d2f1|
00002f20  63 34 36 30 38 32 33 32  65 30 37 64 33 61 61 33  |c4608232e07d3aa3|
00002f30  64 39 39 38 65 35 31 33  35 00 00 00 00 00 00 00  |d998e5135.......|
00002f40  00 00 00 00 05 00 30 40  43 65 34 64 61 33 62 37  |......0@Ce4da3b7|
00002f50  66 62 62 63 65 32 33 34  35 64 37 37 37 32 62 30  |fbbce2345d7772b0|
00002f60  36 37 34 61 33 31 38 64  35 00 00 00 00 00 00 00  |674a318d5.......|
00002f70  00 00 00 00 22 00 30 40  43 65 33 36 39 38 35 33  |....".0@Ce369853|
00002f80  64 66 37 36 36 66 61 34  34 65 31 65 64 30 66 66  |df766fa44e1ed0ff|
00002f90  36 31 33 66 35 36 33 62  64 00 00 00 00 00 00 00  |613f563bd.......|
00002fa0  00 00 00 00 61 00 30 40  43 65 32 65 66 35 32 34  |....a.0@Ce2ef524|
00002fb0  66 62 66 33 64 39 66 65  36 31 31 64 35 61 38 65  |fbf3d9fe611d5a8e|
00002fc0  39 30 66 65 66 64 63 39  63 00 00 00 00 00 00 00  |90fefdc9c.......|
00002fd0  00 00 00 00 47 00 30 40  43 65 32 63 34 32 30 64  |....G.0@Ce2c420d|
00002fe0  39 32 38 64 34 62 66 38  63 65 30 66 66 32 65 63  |928d4bf8ce0ff2ec|
00002ff0  31 39 62 33 37 31 35 31  34 00 00 00 00 00 00 00  |19b371514.......|
00003000  00 00 00 00 2e 00 30 40  43 64 39 64 34 66 34 39  |......0@Cd9d4f49|
00003010  35 65 38 37 35 61 32 65  30 37 35 61 31 61 34 61  |5e875a2e075a1a4a|
00003020  36 65 31 62 39 37 37 30  66 00 00 00 00 00 00 00  |6e1b9770f.......|
00003030  00 00 00 00 35 00 30 40  43 64 38 32 63 38 64 31  |....5.0@Cd82c8d1|
00003040  36 31 39 61 64 38 31 37  36 64 36 36 35 34 35 33  |619ad8176d665453|
00003050  63 66 62 32 65 35 35 66  30 00 00 00 00 00 00 00  |cfb2e55f0.......|
00003060  00 00 00 00 27 00 30 40  43 64 36 37 64 38 61 62  |....'.0@Cd67d8ab|
00003070  34 66 34 63 31 30 62 66  32 32 61 61 33 35 33 65  |4f4c10bf22aa353e|
00003080  32 37 38 37 39 31 33 33  63 00 00 00 00 00 00 00  |27879133c.......|
00003090  00 00 00 00 28 00 30 40  43 64 36 34 35 39 32 30  |....(.0@Cd645920|
000030a0  65 33 39 35 66 65 64 61  64 37 62 62 62 65 64 30  |e395fedad7bbbed0|
000030b0  65 63 61 33 66 65 32 65  30 00 00 00 00 00 00 00  |eca3fe2e0.......|
000030c0  00 00 00 00 0a 00 30 40  43 64 33 64 39 34 34 36  |......0@Cd3d9446|
000030d0  38 30 32 61 34 34 32 35  39 37 35 35 64 33 38 65  |802a44259755d38e|
000030e0  36 64 31 36 33 65 38 32  30 00 00 00 00 00 00 00  |6d163e820.......|
000030f0  00 00 00 00 49 00 30 40  43 64 32 64 64 65 61 31  |....I.0@Cd2ddea1|
00003100  38 66 30 30 36 36 35 63  65 38 36 32 33 65 33 36  |8f00665ce8623e36|
00003110  62 64 34 65 33 63 37 63  35 00 00 00 00 00 00 00  |bd4e3c7c5.......|
00003120  00 00 00 00 4f 00 30 40  43 64 31 66 65 31 37 33  |....O.0@Cd1fe173|
00003130  64 30 38 65 39 35 39 33  39 37 61 64 66 33 34 62  |d08e959397adf34b|
00003140  31 64 37 37 65 38 38 64  37 00 00 00 00 00 00 00  |1d77e88d7.......|
00003150  00 00 00 00 4b 00 30 40  43 64 30 39 62 66 34 31  |....K.0@Cd09bf41|
00003160  35 34 34 61 33 33 36 35  61 34 36 63 39 30 37 37  |544a3365a46c9077|
00003170  65 62 62 35 65 33 35 63  33 00 00 00 00 00 00 00  |ebb5e35c3.......|
00003180  00 00 00 00 08 00 30 40  43 63 39 66 30 66 38 39  |......0@Cc9f0f89|
00003190  35 66 62 39 38 61 62 39  31 35 39 66 35 31 66 64  |5fb98ab9159f51fd|
000031a0  30 32 39 37 65 32 33 36  64 00 00 00 00 00 00 00  |0297e236d.......|
000031b0  00 00 00 00 02 00 30 40  43 63 38 31 65 37 32 38  |......0@Cc81e728|
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000031e0  00 00 00 00 57 00 30 40  43 63 37 65 31 32 34 39  |....W.0@Cc7e1249|
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00003200  33 36 62 64 31 39 39 36  64 00 00 00 00 00 00 00  |36bd1996d.......|
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00003240  00 00 00 00 0d 00 30 40  43 63 35 31 63 65 34 31  |......0@Cc51ce41|
00003250  30 63 31 32 34 61 31 30  65 30 64 62 35 65 34 62  |0c124a10e0db5e4b|
00003260  39 37 66 63 32 61 66 33  39 00 00 00 00 00 00 00  |97fc2af39.......|
00003270  00 00 00 00 01 00 30 40  43 63 34 63 61 34 32 33  |......0@Cc4ca423|
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000032a0  00 00 00 00 0c 00 30 40  43 63 32 30 61 64 34 64  |......0@Cc20ad4d|
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00003300  00 00 00 00 32 00 30 40  43 63 30 63 37 63 37 36  |....2.0@Cc0c7c76|
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00003360  00 00 00 00 37 00 30 40  43 62 35 33 62 33 61 33  |....7.0@Cb53b3a3|
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000033b0  38 33 62 65 36 39 32 35  31 00 00 00 00 00 00 00  |83be69251.......|
000033c0  00 00 00 00 63 00 30 40  43 61 63 36 32 37 61 62  |....c.0@Cac627ab|
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00003450  00 00 00 00 36 00 30 40  43 61 36 38 34 65 63 65  |....6.0@Ca684ece|
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00003600  00 00 00 00 5d 00 30 40  43 39 38 64 63 65 38 33  |....].0@C98dce83|
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00003650  65 66 30 32 39 33 33 31  63 00 00 00 00 00 00 00  |ef029331c.......|
00003660  00 00 00 00 56 00 30 40  43 39 33 64 62 38 35 65  |....V.0@C93db85e|
00003670  64 39 30 39 63 31 33 38  33 38 66 66 39 35 63 63  |d909c13838ff95cc|
00003680  66 61 39 34 63 65 62 64  39 00 00 00 00 00 00 00  |fa94cebd9.......|
00003690  00 00 00 00 5c 00 30 40  43 39 32 63 63 32 32 37  |....\.0@C92cc227|
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000036b0  32 35 34 64 66 61 64 31  30 00 00 00 00 00 00 00  |254dfad10.......|
000036c0  00 00 00 00 07 00 30 40  43 38 66 31 34 65 34 35  |......0@C8f14e45|
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000036e0  64 34 62 65 61 32 35 34  33 00 00 00 00 00 00 00  |d4bea2543.......|
000036f0  00 00 00 00 19 00 30 40  43 38 65 32 39 36 61 30  |......0@C8e296a0|
00003700  36 37 61 33 37 35 36 33  33 37 30 64 65 64 30 35  |67a37563370ded05|
00003710  66 35 61 33 62 66 33 65  63 00 00 00 00 00 00 00  |f5a3bf3ec.......|
00003720  00 00 00 00 5a 00 30 40  43 38 36 31 33 39 38 35  |....Z.0@C8613985|
00003730  65 63 34 39 65 62 38 66  37 35 37 61 65 36 34 33  |ec49eb8f757ae643|
00003740  39 65 38 37 39 62 62 32  61 00 00 00 00 00 00 00  |9e879bb2a.......|
00003750  00 00 00 00 5f 00 30 40  43 38 31 32 62 34 62 61  |...._.0@C812b4ba|
00003760  32 38 37 66 35 65 65 30  62 63 39 64 34 33 62 62  |287f5ee0bc9d43bb|
00003770  66 35 62 62 65 38 37 66  62 00 00 00 00 00 00 00  |f5bbe87fb.......|
00003780  00 00 00 00 3d 00 30 40  43 37 66 33 39 66 38 33  |....=.0@C7f39f83|
00003790  31 37 66 62 64 62 31 39  38 38 65 66 34 63 36 32  |17fbdb1988ef4c62|
000037a0  38 65 62 61 30 32 35 39  31 00 00 00 00 00 00 00  |8eba02591.......|
000037b0  00 00 00 00 46 00 30 40  43 37 63 62 62 63 34 30  |....F.0@C7cbbc40|
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000037d0  64 31 65 30 36 66 32 31  35 00 00 00 00 00 00 00  |d1e06f215.......|
000037e0  00 00 00 00 59 00 30 40  43 37 36 34 37 39 36 36  |....Y.0@C7647966|
000037f0  62 37 33 34 33 63 32 39  30 34 38 36 37 33 32 35  |b7343c2904867325|
00003800  32 65 34 39 30 66 37 33  36 00 00 00 00 00 00 00  |2e490f736.......|
00003810  00 00 00 00 43 00 30 40  43 37 33 35 62 39 30 62  |....C.0@C735b90b|
00003820  34 35 36 38 31 32 35 65  64 36 63 33 66 36 37 38  |4568125ed6c3f678|
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00004000
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