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<?xml version="1.0" encoding="UTF-8" standalone="no"?>
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>67.3. B-Tree Support Functions</title><link rel="stylesheet" type="text/css" href="stylesheet.css" /><link rev="made" href="pgsql-docs@lists.postgresql.org" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="prev" href="btree-behavior.html" title="67.2. Behavior of B-Tree Operator Classes" /><link rel="next" href="btree-implementation.html" title="67.4. Implementation" /></head><body id="docContent" class="container-fluid col-10"><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="5" align="center">67.3. B-Tree Support Functions</th></tr><tr><td width="10%" align="left"><a accesskey="p" href="btree-behavior.html" title="67.2. Behavior of B-Tree Operator Classes">Prev</a> </td><td width="10%" align="left"><a accesskey="u" href="btree.html" title="Chapter 67. B-Tree Indexes">Up</a></td><th width="60%" align="center">Chapter 67. B-Tree Indexes</th><td width="10%" align="right"><a accesskey="h" href="index.html" title="PostgreSQL 15.7 Documentation">Home</a></td><td width="10%" align="right"> <a accesskey="n" href="btree-implementation.html" title="67.4. Implementation">Next</a></td></tr></table><hr /></div><div class="sect1" id="BTREE-SUPPORT-FUNCS"><div class="titlepage"><div><div><h2 class="title" style="clear: both">67.3. B-Tree Support Functions</h2></div></div></div><p>
As shown in <a class="xref" href="xindex.html#XINDEX-BTREE-SUPPORT-TABLE" title="Table 38.9. B-Tree Support Functions">Table 38.9</a>, btree defines
one required and four optional support functions. The five
user-defined methods are:
</p><div class="variablelist"><dl class="variablelist"><dt><span class="term"><code class="function">order</code></span></dt><dd><p>
For each combination of data types that a btree operator family
provides comparison operators for, it must provide a comparison
support function, registered in
<code class="structname">pg_amproc</code> with support function number 1
and
<code class="structfield">amproclefttype</code>/<code class="structfield">amprocrighttype</code>
equal to the left and right data types for the comparison (i.e.,
the same data types that the matching operators are registered
with in <code class="structname">pg_amop</code>). The comparison
function must take two non-null values
<em class="replaceable"><code>A</code></em> and <em class="replaceable"><code>B</code></em> and
return an <code class="type">int32</code> value that is
<code class="literal"><</code> <code class="literal">0</code>,
<code class="literal">0</code>, or <code class="literal">></code>
<code class="literal">0</code> when <em class="replaceable"><code>A</code></em>
<code class="literal"><</code> <em class="replaceable"><code>B</code></em>,
<em class="replaceable"><code>A</code></em> <code class="literal">=</code>
<em class="replaceable"><code>B</code></em>, or <em class="replaceable"><code>A</code></em>
<code class="literal">></code> <em class="replaceable"><code>B</code></em>,
respectively. A null result is disallowed: all values of the
data type must be comparable. See
<code class="filename">src/backend/access/nbtree/nbtcompare.c</code> for
examples.
</p><p>
If the compared values are of a collatable data type, the
appropriate collation OID will be passed to the comparison
support function, using the standard
<code class="function">PG_GET_COLLATION()</code> mechanism.
</p></dd><dt><span class="term"><code class="function">sortsupport</code></span></dt><dd><p>
Optionally, a btree operator family may provide <em class="firstterm">sort
support</em> function(s), registered under support
function number 2. These functions allow implementing
comparisons for sorting purposes in a more efficient way than
naively calling the comparison support function. The APIs
involved in this are defined in
<code class="filename">src/include/utils/sortsupport.h</code>.
</p></dd><dt><span class="term"><code class="function">in_range</code></span></dt><dd><a id="id-1.10.18.5.3.3.2.1" class="indexterm"></a><a id="id-1.10.18.5.3.3.2.2" class="indexterm"></a><p>
Optionally, a btree operator family may provide
<em class="firstterm">in_range</em> support function(s), registered
under support function number 3. These are not used during btree
index operations; rather, they extend the semantics of the
operator family so that it can support window clauses containing
the <code class="literal">RANGE</code> <em class="replaceable"><code>offset</code></em>
<code class="literal">PRECEDING</code> and <code class="literal">RANGE</code>
<em class="replaceable"><code>offset</code></em> <code class="literal">FOLLOWING</code>
frame bound types (see <a class="xref" href="sql-expressions.html#SYNTAX-WINDOW-FUNCTIONS" title="4.2.8. Window Function Calls">Section 4.2.8</a>). Fundamentally, the extra
information provided is how to add or subtract an
<em class="replaceable"><code>offset</code></em> value in a way that is
compatible with the family's data ordering.
</p><p>
An <code class="function">in_range</code> function must have the signature
</p><pre class="synopsis">
in_range(<em class="replaceable"><code>val</code></em> type1, <em class="replaceable"><code>base</code></em> type1, <em class="replaceable"><code>offset</code></em> type2, <em class="replaceable"><code>sub</code></em> bool, <em class="replaceable"><code>less</code></em> bool)
returns bool
</pre><p>
<em class="replaceable"><code>val</code></em> and
<em class="replaceable"><code>base</code></em> must be of the same type, which
is one of the types supported by the operator family (i.e., a
type for which it provides an ordering). However,
<em class="replaceable"><code>offset</code></em> could be of a different type,
which might be one otherwise unsupported by the family. An
example is that the built-in <code class="literal">time_ops</code> family
provides an <code class="function">in_range</code> function that has
<em class="replaceable"><code>offset</code></em> of type <code class="type">interval</code>.
A family can provide <code class="function">in_range</code> functions for
any of its supported types and one or more
<em class="replaceable"><code>offset</code></em> types. Each
<code class="function">in_range</code> function should be entered in
<code class="structname">pg_amproc</code> with
<code class="structfield">amproclefttype</code> equal to
<code class="type">type1</code> and <code class="structfield">amprocrighttype</code>
equal to <code class="type">type2</code>.
</p><p>
The essential semantics of an <code class="function">in_range</code>
function depend on the two Boolean flag parameters. It should
add or subtract <em class="replaceable"><code>base</code></em> and
<em class="replaceable"><code>offset</code></em>, then compare
<em class="replaceable"><code>val</code></em> to the result, as follows:
</p><div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "><li class="listitem"><p>
if <code class="literal">!</code><em class="replaceable"><code>sub</code></em> and
<code class="literal">!</code><em class="replaceable"><code>less</code></em>, return
<em class="replaceable"><code>val</code></em> <code class="literal">>=</code>
(<em class="replaceable"><code>base</code></em> <code class="literal">+</code>
<em class="replaceable"><code>offset</code></em>)
</p></li><li class="listitem"><p>
if <code class="literal">!</code><em class="replaceable"><code>sub</code></em> and
<em class="replaceable"><code>less</code></em>, return
<em class="replaceable"><code>val</code></em> <code class="literal"><=</code>
(<em class="replaceable"><code>base</code></em> <code class="literal">+</code>
<em class="replaceable"><code>offset</code></em>)
</p></li><li class="listitem"><p>
if <em class="replaceable"><code>sub</code></em> and
<code class="literal">!</code><em class="replaceable"><code>less</code></em>, return
<em class="replaceable"><code>val</code></em> <code class="literal">>=</code>
(<em class="replaceable"><code>base</code></em> <code class="literal">-</code>
<em class="replaceable"><code>offset</code></em>)
</p></li><li class="listitem"><p>
if <em class="replaceable"><code>sub</code></em> and
<em class="replaceable"><code>less</code></em>, return
<em class="replaceable"><code>val</code></em> <code class="literal"><=</code>
(<em class="replaceable"><code>base</code></em> <code class="literal">-</code>
<em class="replaceable"><code>offset</code></em>)
</p></li></ul></div><p>
Before doing so, the function should check the sign of
<em class="replaceable"><code>offset</code></em>: if it is less than zero, raise
error
<code class="literal">ERRCODE_INVALID_PRECEDING_OR_FOLLOWING_SIZE</code>
(22013) with error text like <span class="quote">“<span class="quote">invalid preceding or
following size in window function</span>”</span>. (This is required by
the SQL standard, although nonstandard operator families might
perhaps choose to ignore this restriction, since there seems to
be little semantic necessity for it.) This requirement is
delegated to the <code class="function">in_range</code> function so that
the core code needn't understand what <span class="quote">“<span class="quote">less than
zero</span>”</span> means for a particular data type.
</p><p>
An additional expectation is that <code class="function">in_range</code>
functions should, if practical, avoid throwing an error if
<em class="replaceable"><code>base</code></em> <code class="literal">+</code>
<em class="replaceable"><code>offset</code></em> or
<em class="replaceable"><code>base</code></em> <code class="literal">-</code>
<em class="replaceable"><code>offset</code></em> would overflow. The correct
comparison result can be determined even if that value would be
out of the data type's range. Note that if the data type
includes concepts such as <span class="quote">“<span class="quote">infinity</span>”</span> or
<span class="quote">“<span class="quote">NaN</span>”</span>, extra care may be needed to ensure that
<code class="function">in_range</code>'s results agree with the normal
sort order of the operator family.
</p><p>
The results of the <code class="function">in_range</code> function must be
consistent with the sort ordering imposed by the operator family.
To be precise, given any fixed values of
<em class="replaceable"><code>offset</code></em> and
<em class="replaceable"><code>sub</code></em>, then:
</p><div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "><li class="listitem"><p>
If <code class="function">in_range</code> with
<em class="replaceable"><code>less</code></em> = true is true for some
<em class="replaceable"><code>val1</code></em> and
<em class="replaceable"><code>base</code></em>, it must be true for every
<em class="replaceable"><code>val2</code></em> <code class="literal"><=</code>
<em class="replaceable"><code>val1</code></em> with the same
<em class="replaceable"><code>base</code></em>.
</p></li><li class="listitem"><p>
If <code class="function">in_range</code> with
<em class="replaceable"><code>less</code></em> = true is false for some
<em class="replaceable"><code>val1</code></em> and
<em class="replaceable"><code>base</code></em>, it must be false for every
<em class="replaceable"><code>val2</code></em> <code class="literal">>=</code>
<em class="replaceable"><code>val1</code></em> with the same
<em class="replaceable"><code>base</code></em>.
</p></li><li class="listitem"><p>
If <code class="function">in_range</code> with
<em class="replaceable"><code>less</code></em> = true is true for some
<em class="replaceable"><code>val</code></em> and
<em class="replaceable"><code>base1</code></em>, it must be true for every
<em class="replaceable"><code>base2</code></em> <code class="literal">>=</code>
<em class="replaceable"><code>base1</code></em> with the same
<em class="replaceable"><code>val</code></em>.
</p></li><li class="listitem"><p>
If <code class="function">in_range</code> with
<em class="replaceable"><code>less</code></em> = true is false for some
<em class="replaceable"><code>val</code></em> and
<em class="replaceable"><code>base1</code></em>, it must be false for every
<em class="replaceable"><code>base2</code></em> <code class="literal"><=</code>
<em class="replaceable"><code>base1</code></em> with the same
<em class="replaceable"><code>val</code></em>.
</p></li></ul></div><p>
Analogous statements with inverted conditions hold when
<em class="replaceable"><code>less</code></em> = false.
</p><p>
If the type being ordered (<code class="type">type1</code>) is collatable, the
appropriate collation OID will be passed to the
<code class="function">in_range</code> function, using the standard
PG_GET_COLLATION() mechanism.
</p><p>
<code class="function">in_range</code> functions need not handle NULL
inputs, and typically will be marked strict.
</p></dd><dt><span class="term"><code class="function">equalimage</code></span></dt><dd><p>
Optionally, a btree operator family may provide
<code class="function">equalimage</code> (<span class="quote">“<span class="quote">equality implies image
equality</span>”</span>) support functions, registered under support
function number 4. These functions allow the core code to
determine when it is safe to apply the btree deduplication
optimization. Currently, <code class="function">equalimage</code>
functions are only called when building or rebuilding an index.
</p><p>
An <code class="function">equalimage</code> function must have the
signature
</p><pre class="synopsis">
equalimage(<em class="replaceable"><code>opcintype</code></em> <code class="type">oid</code>) returns bool
</pre><p>
The return value is static information about an operator class
and collation. Returning <code class="literal">true</code> indicates that
the <code class="function">order</code> function for the operator class is
guaranteed to only return <code class="literal">0</code> (<span class="quote">“<span class="quote">arguments
are equal</span>”</span>) when its <em class="replaceable"><code>A</code></em> and
<em class="replaceable"><code>B</code></em> arguments are also interchangeable
without any loss of semantic information. Not registering an
<code class="function">equalimage</code> function or returning
<code class="literal">false</code> indicates that this condition cannot be
assumed to hold.
</p><p>
The <em class="replaceable"><code>opcintype</code></em> argument is the
<code class="literal"><code class="structname">pg_type</code>.oid</code> of the
data type that the operator class indexes. This is a convenience
that allows reuse of the same underlying
<code class="function">equalimage</code> function across operator classes.
If <em class="replaceable"><code>opcintype</code></em> is a collatable data
type, the appropriate collation OID will be passed to the
<code class="function">equalimage</code> function, using the standard
<code class="function">PG_GET_COLLATION()</code> mechanism.
</p><p>
As far as the operator class is concerned, returning
<code class="literal">true</code> indicates that deduplication is safe (or
safe for the collation whose OID was passed to its
<code class="function">equalimage</code> function). However, the core
code will only deem deduplication safe for an index when
<span class="emphasis"><em>every</em></span> indexed column uses an operator class
that registers an <code class="function">equalimage</code> function, and
each function actually returns <code class="literal">true</code> when
called.
</p><p>
Image equality is <span class="emphasis"><em>almost</em></span> the same condition
as simple bitwise equality. There is one subtle difference: When
indexing a varlena data type, the on-disk representation of two
image equal datums may not be bitwise equal due to inconsistent
application of <acronym class="acronym">TOAST</acronym> compression on input.
Formally, when an operator class's
<code class="function">equalimage</code> function returns
<code class="literal">true</code>, it is safe to assume that the
<code class="literal">datum_image_eq()</code> C function will always agree
with the operator class's <code class="function">order</code> function
(provided that the same collation OID is passed to both the
<code class="function">equalimage</code> and <code class="function">order</code>
functions).
</p><p>
The core code is fundamentally unable to deduce anything about
the <span class="quote">“<span class="quote">equality implies image equality</span>”</span> status of an
operator class within a multiple-data-type family based on
details from other operator classes in the same family. Also, it
is not sensible for an operator family to register a cross-type
<code class="function">equalimage</code> function, and attempting to do so
will result in an error. This is because <span class="quote">“<span class="quote">equality implies
image equality</span>”</span> status does not just depend on
sorting/equality semantics, which are more or less defined at the
operator family level. In general, the semantics that one
particular data type implements must be considered separately.
</p><p>
The convention followed by the operator classes included with the
core <span class="productname">PostgreSQL</span> distribution is to
register a stock, generic <code class="function">equalimage</code>
function. Most operator classes register
<code class="function">btequalimage()</code>, which indicates that
deduplication is safe unconditionally. Operator classes for
collatable data types such as <code class="type">text</code> register
<code class="function">btvarstrequalimage()</code>, which indicates that
deduplication is safe with deterministic collations. Best
practice for third-party extensions is to register their own
custom function to retain control.
</p></dd><dt><span class="term"><code class="function">options</code></span></dt><dd><p>
Optionally, a B-tree operator family may provide
<code class="function">options</code> (<span class="quote">“<span class="quote">operator class specific
options</span>”</span>) support functions, registered under support
function number 5. These functions define a set of user-visible
parameters that control operator class behavior.
</p><p>
An <code class="function">options</code> support function must have the
signature
</p><pre class="synopsis">
options(<em class="replaceable"><code>relopts</code></em> <code class="type">local_relopts *</code>) returns void
</pre><p>
The function is passed a pointer to a <code class="structname">local_relopts</code>
struct, which needs to be filled with a set of operator class
specific options. The options can be accessed from other support
functions using the <code class="literal">PG_HAS_OPCLASS_OPTIONS()</code> and
<code class="literal">PG_GET_OPCLASS_OPTIONS()</code> macros.
</p><p>
Currently, no B-Tree operator class has an <code class="function">options</code>
support function. B-tree doesn't allow flexible representation of keys
like GiST, SP-GiST, GIN and BRIN do. So, <code class="function">options</code>
probably doesn't have much application in the current B-tree index
access method. Nevertheless, this support function was added to B-tree
for uniformity, and will probably find uses during further
evolution of B-tree in <span class="productname">PostgreSQL</span>.
</p></dd></dl></div></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="btree-behavior.html" title="67.2. Behavior of B-Tree Operator Classes">Prev</a> </td><td width="20%" align="center"><a accesskey="u" href="btree.html" title="Chapter 67. B-Tree Indexes">Up</a></td><td width="40%" align="right"> <a accesskey="n" href="btree-implementation.html" title="67.4. Implementation">Next</a></td></tr><tr><td width="40%" align="left" valign="top">67.2. Behavior of B-Tree Operator Classes </td><td width="20%" align="center"><a accesskey="h" href="index.html" title="PostgreSQL 15.7 Documentation">Home</a></td><td width="40%" align="right" valign="top"> 67.4. Implementation</td></tr></table></div></body></html>
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