Reproducing the reltuples analyze estimate bug.
-----------------------------------------------

The script "reltuples_analyze_bug.sql" creates a table that is large
compared to the analyze sample size and then repeatedly updates about
10% of it followed by an analyze each iteration. The bug is that the
calculation analyze uses to update pg_class.reltuples will tend to
increase each time even though the actual rowcount does not change.

To run:

Given a postgresql 10.x server with >= 1GB of shared buffers:

  createdb test
  psql --no-psqlrc -f analyze_reltuples_bug.sql test > test_standard.out 2>&1
  awk -f analyze_counts.awk test_standard.out

To verify the fix, restart postgres with a patched binary and repeat
the above.

Here are the results with an unpatched server:

After 10 interations of:
  update 10% of rows;
  analyze

reltuples has almost doubled.

               / estimated rows  /    /   pages   /   /sampled rows/
   relname       current  proposed    total scanned    live    dead
reltuples_test  10000001  10000055   153847   3000   195000       0
reltuples_test  10981367   9951346   169231   3000   176410   18590
reltuples_test  11948112  10039979   184615   3000   163150   31850
reltuples_test  12900718  10070666   200000   3000   151060   43940
reltuples_test  13835185   9739305   215384   3000   135655   59345
reltuples_test  14758916   9864947   230768   3000   128245   66755
reltuples_test  15674572  10138631   246153   3000   123565   71435
reltuples_test  16576847   9910944   261537   3000   113685   81315
reltuples_test  17470388  10019961   276922   3000   108550   86450
reltuples_test  18356707  10234607   292306   3000   105040   89960
reltuples_test  19228409   9639927   307690   3000    93990  101010