Thread

1. POC: Comparison of partitioning key values

   John Mikk <jomikk2706@gmail.com> — 2026-04-13T21:11:34Z

   Hackers, Hi!
   
   When executing the SQL script, we discovered strange behavior — one of
   the partitions cannot be created.
   
   
   ```sql
   drop table if exists grid2 cascade;
   
   create table grid2(x bigint, y bigint) partition by range (x,y);
   
   create table g2_part1 partition of grid2 for values from (1,3) to (7,11);
   create table g2_part2 partition of grid2 for values from (7,11) to (13,15);
   create table g2_part3 partition of grid2 for values from (13,15) to (15,17);
   create table g2_part4 partition of grid2 for values from (15,17) to (19,21);
   --
   create table g2_part5 partition of grid2 for values from (5,15) to (13,17);
   -- [42P17] ERROR: partition "g2_part5" would overlap partition "g2_part1"
   ```
   
   Why is that?
   
   According to the documentation, the row comparison rule for tables applies
   (subsection 9.25.5).
   However, in the case of row comparison, it is possible to override
   comparison operators, which is not the case when defining partitions.
   There is no way to override the comparison operator for partition ranges.
   And is this general approach always correct in the case of partitioning?
   
   For example, the following approach seems quite valid:
   
   If we look at the relative positions of the ranges for each partitioning
   key (of a single table) on a plane, assuming that the from and to values of
   the partitioning key in for values are points on the main diagonal of a
   rectangle representing possible key values for the partition, then there
   appear to be no obstacles to creating the last partition in the provided
   SQL script.
   
   Illustrative Python script:
   
   ```python
   import matplotlib.pyplot as plt
   import matplotlib.patches as patches
   
   fig, ax = plt.subplots()
   
   def key(point, radius=0.1, color='red', ax=ax):
   circle = patches.Circle(point, radius=radius, color=color, alpha=1)
   ax.add_patch(circle)
   return
   
   def range(lower, upper, label='', facecolor='blue', edgecolor='red',
   alpha=0.5, ax=ax):
   x1, y1 = lower
   x2, y2 = upper
   
   x_min, y_min = (min(x1, x2), min(y1, y2))
   width, height = (abs(x2 - x1), abs(y2 - y1))
   
   rectangle = patches.Rectangle(
   (x_min, y_min), width, height,
   facecolor=facecolor, edgecolor=edgecolor, alpha=alpha
   )
   
   ax.add_patch(rectangle)
   
   if label:
   text_x, text_y = (x_min, y_min)
   ax.text(text_x, text_y, label, fontsize=8, color='white', ha='left',
   va='bottom')
   
   return rectangle
   
   # Range, Key. -------------------------
   range( (1, 3, ), (7, 11, ), 'g2_part1')
   range( (7, 11, ), (13, 15, ), 'g2_part2')
   range( (13, 15, ), (15, 17, ), 'g2_part3')
   range( (15, 17, ), (19, 21, ), 'g2_part4')
   range( (5, 15, ), (13, 17, ), 'g2_part5', 'black')
   
   # Show. -------------------------------
   plt.xlim(0, 25)
   plt.ylim(0, 25)
   plt.gca().set_aspect('equal')
   plt.grid(True, alpha=0.3)
   plt.show()
   ```
   
   Let us provide a generalized reasoning:
   
   Suppose we have a range-partitioned table with a partitioning key
   consisting of n attributes.
   Let us consider the from and to values of the partitioning key from the for
   values clause as points on the main diagonal of an n-dimensional
   parallelepiped of permissible key values for a specific partition.
   Of course, our set is finite, but this perspective on the partitioning key
   allows us to use a fact from multidimensional geometry:
   
   Let the first parallelepiped be defined by the main diagonal points
   A = (a_1, a_2, ..., a_n) and A' = (a_1', a_2', ..., a_n'), where a_i < a_i'
   for all i,
   and the second parallelepiped be defined by the main diagonal points
   B = (b_1, b_2, ..., b_n) and B' = (b_1', b_2', ..., b_n'), where b_i < b_i'
   for all i.
   
   In this case, the following theorem (statement) holds true:
   
   Two parallelepipeds do not intersect if and only if there exists at least
   one coordinate k (from 1 to n) for which the projection intervals on this
   axis do not intersect; that is, the intersection of [a_k, a_k'] and [b_k,
   b_k'] is an empty set, or equivalently, the condition (a_k' < b_k) OR (b_k'
   < a_k) holds for one of the k values.
   
   In other words, this fact establishes: first, when two figures do not
   intersect and are separated by a hyperplane x_k = const; and second, the
   necessary and sufficient condition for the figures to intersect, given that
   all projections intersect. The latter remains valid for a parallelepiped
   reduced to a point and can determine whether a new key belongs to a
   particular partition.
   
   The experimental patch I am proposing (v1-0001-partition-by-range.patch)
   introduces changes to the source code based on the described approach, so
   that the partition from the example can be created.
   
   Moreover, the algorithm for determining the partition of a new key during
   an insert operation is even more mysterious in the current implementation;
   my patch corrects this.
   
   In the proposed patch, writing to output directly via fprintf is hardcoded.
   This allows obtaining a plain text list of existing and added ranges after
   each operation for the illustrative Python script.
   
   A segmentation fault will occur during update and delete operations.
   
   Or would adding an override for the range comparison operator be a more
   flexible and correct approach?
   
   I would like to hear your opinion, dear hackers!
   

2. Re: POC: Comparison of partitioning key values

   David Rowley <dgrowleyml@gmail.com> — 2026-04-14T05:19:08Z

   On Tue, 14 Apr 2026 at 09:11, John Mikk <jomikk2706@gmail.com> wrote:
   > ```sql
   > drop table if exists grid2 cascade;
   >
   > create table grid2(x bigint, y bigint) partition by range (x,y);
   >
   > create table g2_part1 partition of grid2 for values from (1,3) to (7,11);
   > create table g2_part2 partition of grid2 for values from (7,11) to (13,15);
   > create table g2_part3 partition of grid2 for values from (13,15) to (15,17);
   > create table g2_part4 partition of grid2 for values from (15,17) to (19,21);
   > --
   > create table g2_part5 partition of grid2 for values from (5,15) to (13,17);
   > -- [42P17] ERROR: partition "g2_part5" would overlap partition "g2_part1"
   > ```
   >
   > Why is that?
   
   Because (5,15) is between (1,3) (inclusive) and (7,11) (non-inclusive)
   
   > According to the documentation, the row comparison rule for tables applies (subsection 9.25.5).
   > However, in the case of row comparison, it is possible to override comparison operators, which is not the case when defining partitions.
   > There is no way to override the comparison operator for partition ranges. And is this general approach always correct in the case of partitioning?
   
   You're free to create your own type and own btree opfamily, but I
   don't see how you're going to tell it that (5,15) isn't above or equal
   to (1,3), and separately, isn't below (7,11). This all works with the
   notion of sorting on a single dimention, where "y" is the tiebreaker
   for equal "x" values. There's just no way to map that into
   2-dimentional space with table partitioning.
   
   Note the part of the documentation in [1]:
   
   "For example, given PARTITION BY RANGE (x,y), a partition bound FROM
   (1, 2) TO (3, 4) allows x=1 with any y>=2, x=2 with any non-null y,
   and x=3 with any y<4."
   
   > Let us provide a generalized reasoning:
   >
   > Suppose we have a range-partitioned table with a partitioning key consisting of n attributes.
   > Let us consider the from and to values of the partitioning key from the for values clause as points on the main diagonal of an n-dimensional parallelepiped of permissible key values for a specific partition.
   > Of course, our set is finite, but this perspective on the partitioning key allows us to use a fact from multidimensional geometry:
   >
   > Let the first parallelepiped be defined by the main diagonal points
   > A = (a_1, a_2, ..., a_n) and A' = (a_1', a_2', ..., a_n'), where a_i < a_i' for all i,
   > and the second parallelepiped be defined by the main diagonal points
   > B = (b_1, b_2, ..., b_n) and B' = (b_1', b_2', ..., b_n'), where b_i < b_i' for all i.
   >
   > In this case, the following theorem (statement) holds true:
   
   So I think you must be thinking that another RANGE column adds another
   dimention. That's not the case. It's still 1 dimention, you just have
   more tiebreaker columns in the notion sorting by the partition bound.
   
   > Two parallelepipeds do not intersect if and only if there exists at least one coordinate k (from 1 to n) for which the projection intervals on this axis do not intersect; that is, the intersection of [a_k, a_k'] and [b_k, b_k'] is an empty set, or equivalently, the condition (a_k' < b_k) OR (b_k' < a_k) holds for one of the k values.
   >
   > In other words, this fact establishes: first, when two figures do not intersect and are separated by a hyperplane x_k = const; and second, the necessary and sufficient condition for the figures to intersect, given that all projections intersect. The latter remains valid for a parallelepiped reduced to a point and can determine whether a new key belongs to a particular partition.
   >
   > The experimental patch I am proposing (v1-0001-partition-by-range.patch) introduces changes to the source code based on the described approach, so that the partition from the example can be created.
   >
   > Moreover, the algorithm for determining the partition of a new key during an insert operation is even more mysterious in the current implementation; my patch corrects this.
   
   It uses a binary search to determine if the partition key columns in
   the inserted tuple falls within a partition's bound. It's not clear to
   me what exactly isn't correct about that.
   
   > In the proposed patch, writing to output directly via fprintf is hardcoded. This allows obtaining a plain text list of existing and added ranges after each operation for the illustrative Python script.
   >
   > A segmentation fault will occur during update and delete operations.
   >
   > Or would adding an override for the range comparison operator be a more flexible and correct approach?
   >
   > I would like to hear your opinion, dear hackers!
   
   You can't change how RANGE partitioning works and not break things for
   everyone using RANGE partitioning when they upgrade. If your patch is
   proposing that, then it's going to fail. If you're proposing a new
   partitioning method, then that's different. It's still a hefty amount
   of work. If you're proposing that then do a detailed proposal here
   before doing too much work. Remember that with declarative
   partitioning, there can be only (at most) a single partition for any
   given tuple. The tuple routing done during INSERT and UPDATE requires
   that. Finding the correct partition must also be fast as INSERT/UPDATE
   performance needs to run that code for every affected tuple.
   
   David
   
   [1] https://www.postgresql.org/docs/current/sql-createtable.html
   
   
   
   

3. Re: POC: Comparison of partitioning key values

   John Mikk <jomikk2706@gmail.com> — 2026-04-16T20:35:34Z

   Dear David, thank you for the detailed response.
   
   I understand your concerns, so I have rethought my approach a bit and
   would like to discuss,
   in general terms, the concept that I would try to implement.
   
   The ability to define a B-tree operator class (opclass) in the clause:
   `PARTITION BY RANGE ( { column_name | ( expression ) } [ opclass ] [, ...] )`
   allows partitioning over a fairly broad class of sets with a defined
   order relation.
   For example, one can obtain an elegant example using an extension
   for ordinary fractions (p/q) represented as `row(p,q)` with a natural
   B-tree operator class for the order relation of ordinary fractions:
   
   ```sql
   drop table if exists axis cascade;
   
   create table axis (
       id serial,
       key fraction,
       label text
   ) partition by range (key fraction_ops);
   
   create table segment_1 partition of axis for values from
   ((0,1)::fraction) to ((1,3)::fraction);
   create table segment_2 partition of axis for values from
   ((2,5)::fraction) to ((4,5)::fraction);
   create table segment_3 partition of axis for values from
   ((15,45)::fraction) to ((2,5)::fraction);
   -- segment_1,2,3 : [0, 1/3], [2/5, 4/5], [1/3, 2/5], where 15/45 == 1/3
   
   insert into axis(key,label) select (1,5)::fraction, '1/5';
   -- insert to segment_1
   insert into axis(key,label) select (1,2)::fraction, '1/2';
   -- insert to segment_2
   insert into axis(key,label) select (1,3)::fraction, '1/3';
   -- insert to segment_3
   ```
   
   However, for multidimensional data structures where one desires
   a multidimensional partitioning key using a B-tree, the necessary
   ordering cannot be established.
   It is easy to prove that when attempting to introduce
   the concept of "to the left" (less than) / "to the right" (greater
   than) for rectangles on a plane,
   the transitivity of such a relation is violated.
   
   To achieve the intended goal,
   it would likely be necessary to use the GiST access method.
   According to the documentation, however,
   only B-tree is applicable when defining an operator class for a range
   partitioning key.
   
   **Proposal:** Make GiST available for partitioning in the `opclass`
   clause of `PARTITION BY RANGE`.
   
   John.
   
   
   On Tue, Apr 14, 2026 at 8:19 AM David Rowley <dgrowleyml@gmail.com> wrote:
   
   > On Tue, 14 Apr 2026 at 09:11, John Mikk <jomikk2706@gmail.com> wrote:
   > ...
   > You can't change how RANGE partitioning works and not break things for
   > everyone using RANGE partitioning when they upgrade. If your patch is
   > proposing that, then it's going to fail. If you're proposing a new
   > partitioning method, then that's different. It's still a hefty amount
   > of work. If you're proposing that then do a detailed proposal here
   > before doing too much work. Remember that with declarative
   > partitioning, there can be only (at most) a single partition for any
   > given tuple. The tuple routing done during INSERT and UPDATE requires
   > that. Finding the correct partition must also be fast as INSERT/UPDATE
   > performance needs to run that code for every affected tuple.
   >
   > David
   >
   > [1] https://www.postgresql.org/docs/current/sql-createtable.html
   >
   

4. Re: POC: Comparison of partitioning key values

   amit <amitlangote09@gmail.com> — 2026-04-20T04:49:16Z

   Hi John,
   
   On Fri, Apr 17, 2026 at 5:35 AM John Mikk <jomikk2706@gmail.com> wrote:
   >
   > Dear David, thank you for the detailed response.
   >
   > I understand your concerns, so I have rethought my approach a bit and would like to discuss,
   > in general terms, the concept that I would try to implement.
   >
   > The ability to define a B-tree operator class (opclass) in the clause:
   > `PARTITION BY RANGE ( { column_name | ( expression ) } [ opclass ] [, ...] )`
   > allows partitioning over a fairly broad class of sets with a defined order relation.
   > For example, one can obtain an elegant example using an extension
   > for ordinary fractions (p/q) represented as `row(p,q)` with a natural
   > B-tree operator class for the order relation of ordinary fractions:
   >
   > ```sql
   > drop table if exists axis cascade;
   >
   > create table axis (
   >     id serial,
   >     key fraction,
   >     label text
   > ) partition by range (key fraction_ops);
   >
   > create table segment_1 partition of axis for values from ((0,1)::fraction) to ((1,3)::fraction);
   > create table segment_2 partition of axis for values from ((2,5)::fraction) to ((4,5)::fraction);
   > create table segment_3 partition of axis for values from ((15,45)::fraction) to ((2,5)::fraction);
   > -- segment_1,2,3 : [0, 1/3], [2/5, 4/5], [1/3, 2/5], where 15/45 == 1/3
   >
   > insert into axis(key,label) select (1,5)::fraction, '1/5';
   > -- insert to segment_1
   > insert into axis(key,label) select (1,2)::fraction, '1/2';
   > -- insert to segment_2
   > insert into axis(key,label) select (1,3)::fraction, '1/3';
   > -- insert to segment_3
   > ```
   >
   > However, for multidimensional data structures where one desires
   > a multidimensional partitioning key using a B-tree, the necessary ordering cannot be established.
   > It is easy to prove that when attempting to introduce
   > the concept of "to the left" (less than) / "to the right" (greater than) for rectangles on a plane,
   > the transitivity of such a relation is violated.
   >
   > To achieve the intended goal,
   > it would likely be necessary to use the GiST access method.
   > According to the documentation, however,
   > only B-tree is applicable when defining an operator class for a range partitioning key.
   >
   > **Proposal:** Make GiST available for partitioning in the `opclass` clause of `PARTITION BY RANGE`.
   
   Thanks for the follow-up and the fraction example. The fraction case
   already works under RANGE today, as you show, and nothing needs to
   change there, or at least that's how I read that part.
   
   I agree with David that the grid case wants a new strategy rather than
   a reinterpretation of RANGE, and I'd push back on making GiST
   available in RANGE's opclass slot specifically.  The GiST opclasses
   you'd actually want for this use case describe overlap and
   containment, not order, so applying the RANGE machinery here seems
   wrong to me. PARTITION BY RANGE has been around for about ~9 years and
   most users understand what it means, so making it accept GiST
   opclasses would be more confusing than helpful. But the fact that you
   reached for GiST tells me the grid case wants something spatial, and
   I've sometimes wondered whether something along the lines of PARTITION
   BY BOX for rectangular partitioning could work as a new strategy. The
   per-dimension non-overlap check you describe would cover partition
   creation. The same logic applies to tuple routing and pruning, though
   the algorithms and data structures would require careful design to
   scale with many partitions.
   
   Part of what got me thinking about BOX partitioning is the growth of
   pgvector, where smaller indexes per partition could help when index
   design hits scaling limits. Whether the decompositions there would
   actually look like boxes is another question that I haven't studied
   very deeply, but it's one more reason to think about spatial
   partitioning strategies.
   
   -- 
   Thanks, Amit Langote