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Window Functions
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Table Of Contents
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<div id="toc_sub"><div class="fancy-toc1"><a href="#introduction_to_window_functions">1. Introduction to Window Functions</a></div>
<div class="fancy-toc1"><a href="#aggregate_window_functions">2. Aggregate Window Functions</a></div>
<div class="fancy-toc2"><a href="#the_partition_by_clause">2.1. The PARTITION BY Clause</a></div>
<div class="fancy-toc2"><a href="#frame_specifications">2.2. Frame Specifications</a></div>
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<div class="fancy-toc3"><a href="#frame_boundaries">2.2.2. Frame Boundaries</a></div>
<div class="fancy-toc3"><a href="#the_exclude_clause">2.2.3. The EXCLUDE Clause</a></div>
<div class="fancy-toc2"><a href="#the_filter_clause">2.3. The FILTER Clause</a></div>
<div class="fancy-toc1"><a href="#built_in_window_functions">3. Built-in Window Functions</a></div>
<div class="fancy-toc1"><a href="#window_chaining">4. Window Chaining</a></div>
<div class="fancy-toc1"><a href="#user_defined_aggregate_window_functions">5. User-Defined Aggregate Window Functions</a></div>
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<h1 id="introduction_to_window_functions"><span>1. </span>Introduction to Window Functions</h1>

<p>A window function is an SQL function where the input
values are taken from
a "window" of one or more rows in the results set of a SELECT statement.

</p><p>Window functions are distinguished from <a href="lang_corefunc.html">scalar functions</a> and
<a href="lang_aggfunc.html">aggregate functions</a> by the
presence of an OVER clause. If a function has an OVER clause,
then it is a window function. If it lacks an OVER clause, then it is an
ordinary aggregate or scalar function. Window functions might also
have a FILTER clause in between the function and the OVER clause.

</p><p>The syntax for a window function is like this:


<p><b><a href="syntax/window-function-invocation.html">window-function-invocation:</a></b>
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</div>
<p><b><a href="syntax/function-arguments.html">function-arguments:</a></b>
<button id='xd8262bee' onclick='hideorshow("xd8262bee","xc4e3ffe6")'>show</button></p>
 <div id='xc4e3ffe6' style='display:none;' class='imgcontainer'>
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<p><b><a href="syntax/ordering-term.html">ordering-term:</a></b>
<button id='x98ae4005' onclick='hideorshow("x98ae4005","x0a87bd5c")'>show</button></p>
 <div id='x0a87bd5c' style='display:none;' class='imgcontainer'>
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<path d="M32,32L81,32L81,2L32,2Z"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
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</svg>
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</div>
</div>
<p><b><a href="syntax/literal-value.html">literal-value:</a></b>
<button id='x4a625953' onclick='hideorshow("x4a625953","x9125574b")'>show</button></p>
 <div id='x9125574b' style='display:none;' class='imgcontainer'>
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<p><b><a href="syntax/over-clause.html">over-clause:</a></b>
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<p><b><a href="syntax/frame-spec.html">frame-spec:</a></b>
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<p><b><a href="syntax/ordering-term.html">ordering-term:</a></b>
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 <div id='x4da0c1d5' style='display:none;' class='imgcontainer'>
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</div>
</div>
<p><b><a href="syntax/raise-function.html">raise-function:</a></b>
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</div>
<p><b><a href="syntax/select-stmt.html">select-stmt:</a></b>
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<p><b><a href="syntax/common-table-expression.html">common-table-expression:</a></b>
<button id='x22e81d6a' onclick='hideorshow("x22e81d6a","x4c1ab371")'>show</button></p>
 <div id='x4c1ab371' style='display:none;' class='imgcontainer'>
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</div>
<p><b><a href="syntax/compound-operator.html">compound-operator:</a></b>
<button id='x89950653' onclick='hideorshow("x89950653","xceff8d96")'>show</button></p>
 <div id='xceff8d96' style='display:none;' class='imgcontainer'>
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</div>
<p><b><a href="syntax/join-clause.html">join-clause:</a></b>
<button id='x5ecb3f06' onclick='hideorshow("x5ecb3f06","x25642fa8")'>show</button></p>
 <div id='x25642fa8' style='display:none;' class='imgcontainer'>
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<path d="M587,62L721,62L721,32L587,32Z"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
<text x="654" y="47" text-anchor="middle" fill="rgb(0,0,0)" dominant-baseline="central">join-constraint</text>
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<path d="M483,17L776,17"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
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</svg>
</div>
<p><b><a href="syntax/join-constraint.html">join-constraint:</a></b>
<button id='x9f0e73e3' onclick='hideorshow("x9f0e73e3","x105195d3")'>show</button></p>
 <div id='x105195d3' style='display:none;' class='imgcontainer'>
 <div style="max-width:483px"><svg xmlns='http://www.w3.org/2000/svg' class="pikchr" viewBox="0 0 483.336 126.576">
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<path d="M9,17 L 16,17 Q 24,17 24,32 L 24,40 Q 24,55 34,55 L 45,55"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
<path d="M66,70L104,70A15 15 0 0 0 120 55L120,55A15 15 0 0 0 104 39L66,39A15 15 0 0 0 50 55L50,55A15 15 0 0 0 66 70Z"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
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<text x="158" y="55" text-anchor="middle" font-weight="bold" fill="rgb(0,0,0)" dominant-baseline="central">(</text>
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<path d="M224,70L318,70A15 15 0 0 0 333 55L333,55A15 15 0 0 0 318 39L224,39A15 15 0 0 0 209 55L209,55A15 15 0 0 0 224 70Z"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
<text x="271" y="55" text-anchor="middle" fill="rgb(0,0,0)" dominant-baseline="central">column-name</text>
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<text x="384" y="55" text-anchor="middle" font-weight="bold" fill="rgb(0,0,0)" dominant-baseline="central">)</text>
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<circle cx="477" cy="17" r="3.6"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
<path d="M271,108A15 15 0 0 0 286 92A15 15 0 0 0 271 77A15 15 0 0 0 256 92A15 15 0 0 0 271 108Z"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
<text x="271" y="92" text-anchor="middle" font-weight="bold" fill="rgb(0,0,0)" dominant-baseline="central">,</text>
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<text x="70" y="17" text-anchor="middle" fill="rgb(0,0,0)" dominant-baseline="central">ON</text>
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<path d="M90,17L107,17"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
<path d="M113,32L162,32L162,2L113,2Z"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
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</svg>
</div>
</div>
<p><b><a href="syntax/join-operator.html">join-operator:</a></b>
<button id='xfa31f036' onclick='hideorshow("xfa31f036","x58a596b4")'>show</button></p>
 <div id='x58a596b4' style='display:none;' class='imgcontainer'>
 <div style="max-width:620px"><svg xmlns='http://www.w3.org/2000/svg' class="pikchr" viewBox="0 0 620.333 255.312">
<circle cx="5" cy="17" r="3.6"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
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<path d="M9,17 L 16,17 Q 24,17 24,32 L 24,56 Q 24,71 34,71 L 45,71"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
<path d="M66,86L133,86A15 15 0 0 0 148 71A15 15 0 0 0 133 56L66,56A15 15 0 0 0 50 71A15 15 0 0 0 66 86Z"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
<text x="99" y="71" text-anchor="middle" fill="rgb(0,0,0)" dominant-baseline="central">NATURAL</text>
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<text x="259" y="71" text-anchor="middle" fill="rgb(0,0,0)" dominant-baseline="central">LEFT</text>
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<text x="415" y="71" text-anchor="middle" fill="rgb(0,0,0)" dominant-baseline="central">OUTER</text>
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<path d="M532,56L554,56A15 15 0 0 0 569 41A15 15 0 0 0 554 26L532,26A15 15 0 0 0 516 41A15 15 0 0 0 532 56Z"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
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<circle cx="614" cy="17" r="3.6"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
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<text x="310" y="17" text-anchor="middle" font-weight="bold" fill="rgb(0,0,0)" dominant-baseline="central">,</text>
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<path d="M99,41L178,41"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
<path d="M189,41L505,41"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
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<path d="M246,124L284,124A15 15 0 0 0 299 109A15 15 0 0 0 284 94L246,94A15 15 0 0 0 231 109A15 15 0 0 0 246 124Z"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
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<path d="M246,207L287,207A15 15 0 0 0 302 192A15 15 0 0 0 287 177L246,177A15 15 0 0 0 231 192A15 15 0 0 0 246 207Z"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
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</svg>
</div>
</div>
</div>
<p><b><a href="syntax/ordering-term.html">ordering-term:</a></b>
<button id='x50e5887c' onclick='hideorshow("x50e5887c","x3985c24c")'>show</button></p>
 <div id='x3985c24c' style='display:none;' class='imgcontainer'>
 <div style="max-width:798px"><svg xmlns='http://www.w3.org/2000/svg' class="pikchr" viewBox="0 0 798.451 99.576">
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<path d="M32,32L81,32L81,2L32,2Z"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
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<p><b><a href="syntax/result-column.html">result-column:</a></b>
<button id='x0857d62f' onclick='hideorshow("x0857d62f","x094cf564")'>show</button></p>
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<p><b><a href="syntax/table-or-subquery.html">table-or-subquery:</a></b>
<button id='xee1e290d' onclick='hideorshow("xee1e290d","x1d3f9721")'>show</button></p>
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<circle cx="715" cy="36" r="3.6"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
<path d="M215,417A15 15 0 0 0 230 402A15 15 0 0 0 215 387A15 15 0 0 0 200 402A15 15 0 0 0 215 417Z"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
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<path d="M296,364 L 303,364 Q 311,364 311,379 L 311,387 Q 311,402 296,402 L 251,402 L 236,402"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
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<text x="173" y="440" text-anchor="middle" fill="rgb(0,0,0)" dominant-baseline="central">join-clause</text>
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</svg>
</div>
</div>
</div>
<p><b><a href="syntax/type-name.html">type-name:</a></b>
<button id='xcf057e45' onclick='hideorshow("xcf057e45","xdd8e2cf1")'>show</button></p>
 <div id='xdd8e2cf1' style='display:none;' class='imgcontainer'>
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<path d="M60,32L87,32A15 15 0 0 0 102 17A15 15 0 0 0 87 2L60,2A15 15 0 0 0 45 17A15 15 0 0 0 60 32Z"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
<text x="74" y="17" text-anchor="middle" fill="rgb(0,0,0)" dominant-baseline="central">name</text>
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<path d="M180,108A15 15 0 0 0 195 92A15 15 0 0 0 180 77A15 15 0 0 0 165 92A15 15 0 0 0 180 108Z"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
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<path d="M212,108L350,108L350,77L212,77Z"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
<text x="281" y="92" text-anchor="middle" fill="rgb(0,0,0)" dominant-baseline="central">signed-number</text>
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<path d="M382,108A15 15 0 0 0 398 92A15 15 0 0 0 382 77A15 15 0 0 0 367 92A15 15 0 0 0 382 108Z"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
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<path d="M102,17L377,17"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
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</svg>
</div>
<p><b><a href="syntax/signed-number.html">signed-number:</a></b>
<button id='xbfbe88e9' onclick='hideorshow("xbfbe88e9","x27d3cd5a")'>show</button></p>
 <div id='x27d3cd5a' style='display:none;' class='imgcontainer'>
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<circle cx="5" cy="17" r="3.6"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
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<path d="M9,17 L 16,17 Q 24,17 24,30 Q 24,44 34,44 L 45,44"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
<path d="M66,59A15 15 0 0 0 81 44L81,44A15 15 0 0 0 66 29A15 15 0 0 0 50 44L50,44A15 15 0 0 0 66 59Z"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
<text x="66" y="44" text-anchor="middle" font-weight="bold" fill="rgb(0,0,0)" dominant-baseline="central">+</text>
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<path d="M81,44 L 88,44 Q 96,44 96,30 Q 96,17 106,17 L 116,17"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
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<text x="191" y="17" text-anchor="middle" fill="rgb(0,0,0)" dominant-baseline="central">numeric-literal</text>
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<circle cx="286" cy="17" r="3.6"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
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<path d="M9,17 L 16,17 Q 24,17 24,32 L 24,67 Q 24,82 34,82 L 45,82"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
<path d="M66,97A15 15 0 0 0 81 82L81,82A15 15 0 0 0 66 67A15 15 0 0 0 50 82L50,82A15 15 0 0 0 66 97Z"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
<text x="66" y="82" text-anchor="middle" font-weight="bold" fill="rgb(0,0,0)" dominant-baseline="central">-</text>
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<path d="M66,17L111,17"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
</svg>
</div>
</div>
</div>
</div>
<p><b><a href="syntax/filter-clause.html">filter-clause:</a></b>
<button id='x42666c57' onclick='hideorshow("x42666c57","x3adc8ba7")'>hide</button></p>
 <div id='x3adc8ba7' class='imgcontainer'>
 <div style="max-width:422px"><svg xmlns='http://www.w3.org/2000/svg' class="pikchr" viewBox="0 0 422.381 34.56">
<circle cx="5" cy="17" r="3.6"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
<polygon points="32,17 20,21 20,12" style="fill:rgb(0,0,0)"/>
<path d="M9,17L26,17"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
<path d="M47,32L93,32A15 15 0 0 0 108 17A15 15 0 0 0 93 2L47,2A15 15 0 0 0 32 17A15 15 0 0 0 47 32Z"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
<text x="70" y="17" text-anchor="middle" fill="rgb(0,0,0)" dominant-baseline="central">FILTER</text>
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<path d="M108,17L125,17"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
<path d="M146,32L146,32A15 15 0 0 0 161 17A15 15 0 0 0 146 2L146,2A15 15 0 0 0 131 17A15 15 0 0 0 146 32Z"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
<text x="146" y="17" text-anchor="middle" font-weight="bold" fill="rgb(0,0,0)" dominant-baseline="central">(</text>
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<path d="M199,32L249,32A15 15 0 0 0 264 17A15 15 0 0 0 249 2L199,2A15 15 0 0 0 184 17A15 15 0 0 0 199 32Z"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
<text x="224" y="17" text-anchor="middle" fill="rgb(0,0,0)" dominant-baseline="central">WHERE</text>
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<path d="M264,17L281,17"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
<path d="M287,32L336,32L336,2L287,2Z"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
<text x="312" y="17" text-anchor="middle" fill="rgb(0,0,0)" dominant-baseline="central">expr</text>
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<path d="M374,32A15 15 0 0 0 389 17A15 15 0 0 0 374 2A15 15 0 0 0 359 17A15 15 0 0 0 374 32Z"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
<text x="374" y="17" text-anchor="middle" font-weight="bold" fill="rgb(0,0,0)" dominant-baseline="central">)</text>
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<circle cx="416" cy="17" r="3.6"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
</svg>
</div>
</div>
<p><b><a href="syntax/window-defn.html">window-defn:</a></b>
<button id='x792b9975' onclick='hideorshow("x792b9975","x477af11c")'>hide</button></p>
 <div id='x477af11c' class='imgcontainer'>
 <div style="max-width:479px"><svg xmlns='http://www.w3.org/2000/svg' class="pikchr" viewBox="0 0 479.765 380.592">
<circle cx="5" cy="17" r="3.6"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
<polygon points="32,17 20,21 20,12" style="fill:rgb(0,0,0)"/>
<path d="M9,17L26,17"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
<path d="M47,32A15 15 0 0 0 62 17A15 15 0 0 0 47 2A15 15 0 0 0 32 17A15 15 0 0 0 47 32Z"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
<text x="47" y="17" text-anchor="middle" font-weight="bold" fill="rgb(0,0,0)" dominant-baseline="central">(</text>
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<path d="M119,59L260,59A15 15 0 0 0 275 44L275,44A15 15 0 0 0 260 29L119,29A15 15 0 0 0 104 44L104,44A15 15 0 0 0 119 59Z"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
<text x="190" y="44" text-anchor="middle" fill="rgb(0,0,0)" dominant-baseline="central">base-window-name</text>
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<text x="159" y="120" text-anchor="middle" fill="rgb(0,0,0)" dominant-baseline="central">PARTITION</text>
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<text x="254" y="120" text-anchor="middle" fill="rgb(0,0,0)" dominant-baseline="central">BY</text>
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<path d="M298,44 L 306,44 Q 313,44 313,51 L 313,59"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
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<p><b><a href="syntax/ordering-term.html">ordering-term:</a></b>
<button id='xe0fe7824' onclick='hideorshow("xe0fe7824","x537a9e34")'>show</button></p>
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</p><p>Unlike ordinary functions, window functions
cannot use the DISTINCT keyword.
Also, Window functions may only appear in the result set and in the
ORDER BY clause of a SELECT statement.

</p><p>Window functions come in two varieties:
<a href="windowfunctions.html#aggwinfunc">aggregate window functions</a> and
<a href="windowfunctions.html#builtins">built-in window functions</a>.  Every aggregate window function
can also work as a ordinary aggregate function, simply by omitting
the OVER and FILTER clauses.  Furthermore, all of the built-in
<a href="lang_aggfunc.html">aggregate functions</a> of SQLite can be used as an
aggregate window function by adding an appropriate OVER clause.
Applications can register new aggregate window functions using
the <a href="c3ref/create_function.html">sqlite3_create_window_function()</a> interface.
The built-in window functions, however, require special-case
handling in the query planner and hence new window functions
that exhibit the exceptional properties found in the built-in
window functions cannot be added by the application.

</p><p>Here is an example using the built-in row_number()
window function:

</p><div class="codeblock"><pre>CREATE TABLE t0(x INTEGER PRIMARY KEY, y TEXT);
INSERT INTO t0 VALUES (1, 'aaa'), (2, 'ccc'), (3, 'bbb');

<i>-- The following SELECT statement returns:</i>
<i>-- </i>
<i>--   x | y | row_number</i>
-----------------------
<i>--   1 | aaa | 1         </i>
<i>--   2 | ccc | 3         </i>
<i>--   3 | bbb | 2         </i>
<i>-- </i>
SELECT x, y, row_number() OVER (ORDER BY y) AS row_number FROM t0 ORDER BY x;
</pre></div>

<p>
The row_number() window function
assigns consecutive integers to each
row in order of the "ORDER BY" clause within the
<span class='yynonterm'>window-defn</span> (in this case "ORDER BY y"). Note that
this does not affect the order in which results are returned from
the overall query.  The order of the final output is
still governed by the ORDER BY clause attached to the SELECT
statement (in this case "ORDER BY x").

</p><p>Named <span class='yynonterm'>window-defn</span> clauses may also be added to a SELECT
statement using a WINDOW clause and then referred to by name within window
function invocations. For example, the following SELECT statement contains
two named <span class='yynonterm'>window-defs</span> clauses, "win1" and "win2":

</p><div class="codeblock"><pre>SELECT x, y, row_number() OVER <b>win1</b>, rank() OVER <b>win2</b>
FROM t0
WINDOW <b>win1</b> AS (ORDER BY y RANGE BETWEEN UNBOUNDED PRECEDING AND CURRENT ROW),
       <b>win2</b> AS (PARTITION BY y ORDER BY x)
ORDER BY x;
</pre></div>

<p>The WINDOW clause, when one is present, comes after any HAVING clause and
before any ORDER BY.

<a name="aggwinfunc"></a>

</p><h1 id="aggregate_window_functions"><span>2. </span>Aggregate Window Functions</h1>

<p> The examples in this section all assume that the database is populated as
follows:

</p><div class="codeblock"><pre>CREATE TABLE t1(a INTEGER PRIMARY KEY, b, c);
INSERT INTO t1 VALUES   (1, 'A', 'one'  ),
                        (2, 'B', 'two'  ),
                        (3, 'C', 'three'),
                        (4, 'D', 'one'  ),
                        (5, 'E', 'two'  ),
                        (6, 'F', 'three'),
                        (7, 'G', 'one'  );
</pre></div>

<p> An aggregate window function is similar to an
<a href="lang_aggfunc.html">ordinary aggregate function</a>, except
adding it to a query does not change the number of rows returned. Instead,
for each row the result of the aggregate window function is as if the
corresponding aggregate were run over all rows in the "window frame"
specified by the OVER clause.


</p><div class="codeblock"><pre><i>-- The following SELECT statement returns:</i>
<i>-- </i>
<i>--   a | b | group_concat</i>
-------------------------
<i>--   1 | A | A.B         </i>
<i>--   2 | B | A.B.C       </i>
<i>--   3 | C | B.C.D       </i>
<i>--   4 | D | C.D.E       </i>
<i>--   5 | E | D.E.F       </i>
<i>--   6 | F | E.F.G       </i>
<i>--   7 | G | F.G         </i>
<i>-- </i>
SELECT a, b, group_concat(b, '.') OVER (
  ORDER BY a ROWS BETWEEN 1 PRECEDING AND 1 FOLLOWING
) AS group_concat FROM t1;
</pre></div>

<p> In the example above, the window frame consists of all rows between the
previous row ("1 PRECEDING") and the following row ("1 FOLLOWING"), inclusive,
where rows are sorted according to the ORDER BY clause in the
<span class='yynonterm'>window-defn</span> (in this case "ORDER BY a").
For example, the frame for the row with (a=3) consists of rows (2, 'B', 'two'),
(3, 'C', 'three') and (4, 'D', 'one'). The result of group_concat(b, '.')
for that row is therefore 'B.C.D'.

</p><p> All of SQLite's <a href="lang_aggfunc.html">aggregate functions</a> may
be used as aggregate window functions. It is also possible to
<a href="windowfunctions.html#udfwinfunc">create user-defined aggregate window functions</a>.


<a name="ptxn"></a>

</p><h2 id="the_partition_by_clause"><span>2.1. </span>The PARTITION BY Clause</h2>

<p> For the purpose of computing window functions, the result set
of a query is divided into one or more "partitions".  A partition consists
of all rows that have the same value for all terms of the PARTITION BY clause
in the <span class='yynonterm'>window-defn</span>.  If there is no PARTITION BY clause,
then the entire result set of the query is a single partition.
Window-function processing is performed separately for each partition.

</p><p> For example:

</p><div class="codeblock"><pre><i>-- The following SELECT statement returns:</i>
<i>-- </i>
<i>--   c     | a | b | group_concat</i>
---------------------------------
<i>--   one   | 1 | A | A.D.G       </i>
<i>--   one   | 4 | D | D.G         </i>
<i>--   one   | 7 | G | G           </i>
<i>--   three | 3 | C | C.F         </i>
<i>--   three | 6 | F | F           </i>
<i>--   two   | 2 | B | B.E         </i>
<i>--   two   | 5 | E | E           </i>
<i>-- </i>
SELECT c, a, b, group_concat(b, '.') OVER (
  PARTITION BY c ORDER BY a RANGE BETWEEN CURRENT ROW AND UNBOUNDED FOLLOWING
) AS group_concat
FROM t1 ORDER BY c, a;
</pre></div>

<p> In the query above, the "PARTITION BY c" clause breaks the
result set up into three partitions. The first partition has
three rows with c=='one'.  The second partition has two rows with
c=='three' and the third partition has two rows with c=='two'.

</p><p> In the example above, all the rows for each partition are
grouped together in the final output.  This is because the PARTITION BY
clause is a prefix of the ORDER BY clause on the overall query.
But that does not have
to be the case.  A partition can be composed of rows scattered
about haphazardly within the result set.  For example:

</p><div class="codeblock"><pre><i>-- The following SELECT statement returns:</i>
<i>-- </i>
<i>--   c     | a | b | group_concat</i>
---------------------------------
<i>--   one   | 1 | A | A.D.G       </i>
<i>--   two   | 2 | B | B.E         </i>
<i>--   three | 3 | C | C.F         </i>
<i>--   one   | 4 | D | D.G         </i>
<i>--   two   | 5 | E | E           </i>
<i>--   three | 6 | F | F           </i>
<i>--   one   | 7 | G | G           </i>
<i>-- </i>
SELECT c, a, b, group_concat(b, '.') OVER (
  PARTITION BY c ORDER BY a RANGE BETWEEN CURRENT ROW AND UNBOUNDED FOLLOWING
) AS group_concat
FROM t1 ORDER BY a;
</pre></div>


<a name="framespec"></a>

<h2 id="frame_specifications"><span>2.2. </span>Frame Specifications</h2>

<p> The <span class='yynonterm'>frame-spec</span> determines which output rows are
read by an aggregate window function.  The
<span class='yynonterm'>frame-spec</span> consists of four parts:

</p><ul>
  <li> A frame type - either ROWS, RANGE or GROUPS,
  </li><li> A starting frame boundary,
  </li><li> An ending frame boundary,
  </li><li> An EXCLUDE clause.
</li></ul>

<p> Here are the syntax details:

<p><b><a href="syntax/frame-spec.html">frame-spec:</a></b>
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<p><b><a href="syntax/expr.html">expr:</a></b>
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<path d="M916,1051 L 924,1051 Q 931,1051 931,1036 L 931,32 Q 931,17 939,17 L 946,17"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
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</svg>
</div>
<p><b><a href="syntax/filter-clause.html">filter-clause:</a></b>
<button id='x6e5adba8' onclick='hideorshow("x6e5adba8","xdbb0e8d4")'>show</button></p>
 <div id='xdbb0e8d4' style='display:none;' class='imgcontainer'>
 <div style="max-width:422px"><svg xmlns='http://www.w3.org/2000/svg' class="pikchr" viewBox="0 0 422.381 34.56">
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<path d="M47,32L93,32A15 15 0 0 0 108 17A15 15 0 0 0 93 2L47,2A15 15 0 0 0 32 17A15 15 0 0 0 47 32Z"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
<text x="70" y="17" text-anchor="middle" fill="rgb(0,0,0)" dominant-baseline="central">FILTER</text>
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<text x="146" y="17" text-anchor="middle" font-weight="bold" fill="rgb(0,0,0)" dominant-baseline="central">(</text>
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<path d="M287,32L336,32L336,2L287,2Z"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
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</svg>
</div>
</div>
<p><b><a href="syntax/function-arguments.html">function-arguments:</a></b>
<button id='x62f7c893' onclick='hideorshow("x62f7c893","x2e28c5e5")'>show</button></p>
 <div id='x2e28c5e5' style='display:none;' class='imgcontainer'>
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<circle cx="5" cy="56" r="3.6"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
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<path d="M245,132L375,132L375,101L245,101Z"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
<text x="310" y="117" text-anchor="middle" fill="rgb(0,0,0)" dominant-baseline="central">ordering-term</text>
<path d="M310,169A15 15 0 0 0 325 154A15 15 0 0 0 310 139A15 15 0 0 0 294 154A15 15 0 0 0 310 169Z"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
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</svg>
</div>
<p><b><a href="syntax/ordering-term.html">ordering-term:</a></b>
<button id='xa4e5c48b' onclick='hideorshow("xa4e5c48b","xf02c44ea")'>show</button></p>
 <div id='xf02c44ea' style='display:none;' class='imgcontainer'>
 <div style="max-width:798px"><svg xmlns='http://www.w3.org/2000/svg' class="pikchr" viewBox="0 0 798.451 99.576">
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<path d="M32,32L81,32L81,2L32,2Z"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
<text x="56" y="17" text-anchor="middle" fill="rgb(0,0,0)" dominant-baseline="central">expr</text>
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<text x="158" y="44" text-anchor="middle" fill="rgb(0,0,0)" dominant-baseline="central">COLLATE</text>
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<text x="296" y="44" text-anchor="middle" fill="rgb(0,0,0)" dominant-baseline="central">collation-name</text>
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</div>
</div>
<p><b><a href="syntax/literal-value.html">literal-value:</a></b>
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<p><b><a href="syntax/over-clause.html">over-clause:</a></b>
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<p><b><a href="syntax/ordering-term.html">ordering-term:</a></b>
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</div>
</div>
<p><b><a href="syntax/raise-function.html">raise-function:</a></b>
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<p><b><a href="syntax/select-stmt.html">select-stmt:</a></b>
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<p><b><a href="syntax/common-table-expression.html">common-table-expression:</a></b>
<button id='xb5f243c6' onclick='hideorshow("xb5f243c6","x9ff2c574")'>show</button></p>
 <div id='x9ff2c574' style='display:none;' class='imgcontainer'>
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<text x="85" y="29" text-anchor="middle" fill="rgb(0,0,0)" dominant-baseline="central">table-name</text>
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</div>
</div>
<p><b><a href="syntax/compound-operator.html">compound-operator:</a></b>
<button id='x91d419e5' onclick='hideorshow("x91d419e5","x5d685770")'>show</button></p>
 <div id='x5d685770' style='display:none;' class='imgcontainer'>
 <div style="max-width:293px"><svg xmlns='http://www.w3.org/2000/svg' class="pikchr" viewBox="0 0 293.842 147.96">
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<text x="105" y="17" text-anchor="middle" fill="rgb(0,0,0)" dominant-baseline="central">UNION</text>
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</svg>
</div>
</div>
<p><b><a href="syntax/join-clause.html">join-clause:</a></b>
<button id='xefb9c824' onclick='hideorshow("xefb9c824","x3aab8e3c")'>show</button></p>
 <div id='x3aab8e3c' style='display:none;' class='imgcontainer'>
 <div style="max-width:793px"><svg xmlns='http://www.w3.org/2000/svg' class="pikchr" viewBox="0 0 793.282 84.24">
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<path d="M9,17L26,17"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
<path d="M32,32L193,32L193,2L32,2Z"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
<text x="112" y="17" text-anchor="middle" fill="rgb(0,0,0)" dominant-baseline="central">table-or-subquery</text>
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<path d="M483,17L776,17"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
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</svg>
</div>
<p><b><a href="syntax/join-constraint.html">join-constraint:</a></b>
<button id='x1bff3899' onclick='hideorshow("x1bff3899","x2354f933")'>show</button></p>
 <div id='x2354f933' style='display:none;' class='imgcontainer'>
 <div style="max-width:483px"><svg xmlns='http://www.w3.org/2000/svg' class="pikchr" viewBox="0 0 483.336 126.576">
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<text x="271" y="55" text-anchor="middle" fill="rgb(0,0,0)" dominant-baseline="central">column-name</text>
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<circle cx="477" cy="17" r="3.6"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
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<text x="70" y="17" text-anchor="middle" fill="rgb(0,0,0)" dominant-baseline="central">ON</text>
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</svg>
</div>
</div>
<p><b><a href="syntax/join-operator.html">join-operator:</a></b>
<button id='xd89646f0' onclick='hideorshow("xd89646f0","x06401d72")'>show</button></p>
 <div id='x06401d72' style='display:none;' class='imgcontainer'>
 <div style="max-width:620px"><svg xmlns='http://www.w3.org/2000/svg' class="pikchr" viewBox="0 0 620.333 255.312">
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<path d="M9,17 L 16,17 Q 24,17 24,32 L 24,56 Q 24,71 34,71 L 45,71"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
<path d="M66,86L133,86A15 15 0 0 0 148 71A15 15 0 0 0 133 56L66,56A15 15 0 0 0 50 71A15 15 0 0 0 66 86Z"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
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<text x="259" y="71" text-anchor="middle" fill="rgb(0,0,0)" dominant-baseline="central">LEFT</text>
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<text x="415" y="71" text-anchor="middle" fill="rgb(0,0,0)" dominant-baseline="central">OUTER</text>
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<circle cx="614" cy="17" r="3.6"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
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<text x="310" y="17" text-anchor="middle" font-weight="bold" fill="rgb(0,0,0)" dominant-baseline="central">,</text>
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<path d="M99,41L178,41"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
<path d="M189,41L505,41"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
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<path d="M246,124L284,124A15 15 0 0 0 299 109A15 15 0 0 0 284 94L246,94A15 15 0 0 0 231 109A15 15 0 0 0 246 124Z"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
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<text x="260" y="147" text-anchor="middle" fill="rgb(0,0,0)" dominant-baseline="central">FULL</text>
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<path d="M246,207L287,207A15 15 0 0 0 302 192A15 15 0 0 0 287 177L246,177A15 15 0 0 0 231 192A15 15 0 0 0 246 207Z"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
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<path d="M475,192 L 482,192 Q 490,192 490,185 L 490,177"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
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<path d="M246,253L287,253A15 15 0 0 0 303 238A15 15 0 0 0 287 222L246,222A15 15 0 0 0 231 238A15 15 0 0 0 246 253Z"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
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<path d="M303,238L469,238"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
<path d="M475,238 L 482,238 Q 490,238 490,223 L 490,71 L 490,56"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
</svg>
</div>
</div>
</div>
<p><b><a href="syntax/ordering-term.html">ordering-term:</a></b>
<button id='xfb6a9b78' onclick='hideorshow("xfb6a9b78","xad22eab0")'>show</button></p>
 <div id='xad22eab0' style='display:none;' class='imgcontainer'>
 <div style="max-width:798px"><svg xmlns='http://www.w3.org/2000/svg' class="pikchr" viewBox="0 0 798.451 99.576">
<circle cx="5" cy="17" r="3.6"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
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<path d="M9,17L26,17"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
<path d="M32,32L81,32L81,2L32,2Z"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
<text x="56" y="17" text-anchor="middle" fill="rgb(0,0,0)" dominant-baseline="central">expr</text>
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<path d="M126,59L190,59A15 15 0 0 0 205 44L205,44A15 15 0 0 0 190 29L126,29A15 15 0 0 0 111 44L111,44A15 15 0 0 0 126 59Z"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
<text x="158" y="44" text-anchor="middle" fill="rgb(0,0,0)" dominant-baseline="central">COLLATE</text>
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<path d="M205,44L223,44"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
<path d="M244,59L349,59A15 15 0 0 0 364 44L364,44A15 15 0 0 0 349 29L244,29A15 15 0 0 0 228 44L228,44A15 15 0 0 0 244 59Z"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
<text x="296" y="44" text-anchor="middle" fill="rgb(0,0,0)" dominant-baseline="central">collation-name</text>
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<path d="M81,17L238,17"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
<path d="M243,17L394,17"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
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<path d="M462,97L492,97A15 15 0 0 0 508 82A15 15 0 0 0 492 67L462,67A15 15 0 0 0 447 82A15 15 0 0 0 462 97Z"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
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<path d="M462,59L479,59A15 15 0 0 0 494 44L494,44A15 15 0 0 0 479 29L462,29A15 15 0 0 0 447 44L447,44A15 15 0 0 0 462 59Z"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
<text x="471" y="44" text-anchor="middle" fill="rgb(0,0,0)" dominant-baseline="central">ASC</text>
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<path d="M494,44 L 508,44 Q 523,44 523,36 L 523,29"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
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<path d="M477,17L538,17"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
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<path d="M606,59L648,59A15 15 0 0 0 663 44L663,44A15 15 0 0 0 648 29L606,29A15 15 0 0 0 591 44L591,44A15 15 0 0 0 606 59Z"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
<text x="627" y="44" text-anchor="middle" fill="rgb(0,0,0)" dominant-baseline="central">NULLS</text>
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<path d="M701,59L735,59A15 15 0 0 0 750 44L750,44A15 15 0 0 0 735 29L701,29A15 15 0 0 0 686 44L686,44A15 15 0 0 0 701 59Z"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
<text x="718" y="44" text-anchor="middle" fill="rgb(0,0,0)" dominant-baseline="central">FIRST</text>
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<path d="M606,97L648,97A15 15 0 0 0 663 82A15 15 0 0 0 648 67L606,67A15 15 0 0 0 591 82A15 15 0 0 0 606 97Z"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
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<path d="M663,82L680,82"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
<path d="M701,97L727,97A15 15 0 0 0 742 82A15 15 0 0 0 727 67L701,67A15 15 0 0 0 686 82A15 15 0 0 0 701 97Z"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
<text x="714" y="82" text-anchor="middle" fill="rgb(0,0,0)" dominant-baseline="central">LAST</text>
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<path d="M742,82 L 754,82 Q 765,82 765,67 L 765,44 L 765,29"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
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<path d="M670,17L780,17"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
</svg>
</div>
</div>
<p><b><a href="syntax/result-column.html">result-column:</a></b>
<button id='xdb83a7b9' onclick='hideorshow("xdb83a7b9","xcca4ae9d")'>show</button></p>
 <div id='xcca4ae9d' style='display:none;' class='imgcontainer'>
 <div style="max-width:398px"><svg xmlns='http://www.w3.org/2000/svg' class="pikchr" viewBox="0 0 398.054 163.08">
<circle cx="5" cy="17" r="3.6"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
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<path d="M9,17L39,17"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
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<p><b><a href="syntax/window-defn.html">window-defn:</a></b>
<button id='xb0d1461b' onclick='hideorshow("xb0d1461b","xa8f015e1")'>show</button></p>
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<p><b><a href="syntax/type-name.html">type-name:</a></b>
<button id='x187bb7f1' onclick='hideorshow("x187bb7f1","x2230c8ce")'>show</button></p>
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<path d="M212,108L350,108L350,77L212,77Z"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
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<p><b><a href="syntax/signed-number.html">signed-number:</a></b>
<button id='x2e27fd13' onclick='hideorshow("x2e27fd13","x3f3bc4fd")'>show</button></p>
 <div id='x3f3bc4fd' style='display:none;' class='imgcontainer'>
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</p><p>The ending frame boundary can be omitted (if the
BETWEEN and&nbsp;AND keywords that surround the starting frame boundary
are also omitted),
in which case the ending frame boundary defaults to CURRENT ROW.

</p><p> If the frame type is RANGE or GROUPS, then rows with the same values for
all ORDER BY expressions are considered "peers". Or, if there are no ORDER BY
terms, all rows are peers. Peers are always within the same frame.

</p><p>The default <span class='yynonterm'>frame-spec</span> is:

</p><div class="codeblock"><pre>RANGE BETWEEN UNBOUNDED PRECEDING AND CURRENT ROW EXCLUDE NO OTHERS
</pre></div>

<p>The default means that aggregate window functions read all
rows from the beginning of the partition up to and including the
current row and its peers. This implies that rows that have the same values for
all ORDER BY expressions will also have the same value for the result of the
window function (as the window frame is the same). For example:

</p><div class="codeblock"><pre><i>-- The following SELECT statement returns:</i>
<i>-- </i>
<i>--   a | b | c | group_concat</i>
-----------------------------
<i>--   1 | A | one   | A.D.G       </i>
<i>--   2 | B | two   | A.D.G.C.F.B.E</i>
<i>--   3 | C | three | A.D.G.C.F   </i>
<i>--   4 | D | one   | A.D.G       </i>
<i>--   5 | E | two   | A.D.G.C.F.B.E</i>
<i>--   6 | F | three | A.D.G.C.F   </i>
<i>--   7 | G | one   | A.D.G       </i>
<i>-- </i>
SELECT a, b, c,
       group_concat(b, '.') OVER (ORDER BY c) AS group_concat
FROM t1 ORDER BY a;
</pre></div>

<a name="frametype"></a>

<h3 id="frame_type"><span>2.2.1. </span>Frame Type</h3>

<p>
There are three frame types:  ROWS, GROUPS, and RANGE.
The frame type determines how the starting and ending boundaries
of the frame are measured.

</p><ul>
<li><p><b>ROWS</b>:
The ROWS frame type means that the starting and ending boundaries
for the frame are determined by counting individual rows relative
to the current row.

<a name="grouptype"></a>

</p></li><li><p><b>GROUPS</b>:
The GROUPS frame type means that the starting and ending boundaries
are determine by counting "groups" relative to the current group.
A "group" is a set of rows that all have equivalent values for all
all terms of the window ORDER BY clause.  ("Equivalent" means that
the <a href="lang_expr.html#isisnot">IS operator</a> is true when comparing the two values.)
In other words, a group consists of all peers of a row.

<a name="rangetype"></a>

</p></li><li><p><b>RANGE</b>:
The RANGE frame type requires that the ORDER BY clause of the
window have exactly one term.  Call that term "X".  With the
RANGE frame type, the elements of the frame are determined by
computing the value of expression X for all rows in the partition
and framing those rows for which the value of X is within a certain
range of the value of X for the current row.  See the description
in the "<a href="windowfunctions.html#exprrange">&lt;expr&gt; PRECEDING</a>" boundary
specification below for details.
</p></li></ul>

<p>The ROWS and GROUPS frame types are similar in that they
both determine the extent of a frame by counting relative to
the current row.  The difference is that ROWS counts individual
rows and GROUPS counts peer groups.
The RANGE frame type is different.
The RANGE frame type determines the extent of a frame by
looking for expression values that are within some band of
values relative to the current row.

<a name="frameboundary"></a>

</p><h3 id="frame_boundaries"><span>2.2.2. </span>Frame Boundaries</h3>

<p> There are five ways to describe starting and ending frame boundaries:

</p><ol>
<li><p> <b>UNBOUNDED PRECEDING</b><br>
     The frame boundary is the first
     row in the <a href="windowfunctions.html#ptxn">partition</a>.

</p></li><li><p> <b>&lt;expr&gt; PRECEDING</b><br>
        &lt;expr&gt; must be a non-negative constant numeric expression.
        The boundary is a row that is &lt;expr&gt; "units" prior to
        the current row.  The meaning of "units" here depends on the
        frame type:
        </p><ul>
        <li><p> <b>ROWS &rarr;</b>
        The frame boundary is the row that is &lt;expr&gt;
        rows before the current row, or the first row of the
        partition if there are fewer than &lt;expr&gt; rows
        before the current row.  &lt;expr&gt; must be an integer.
        </p></li><li><p> <b>GROUPS &rarr;</b>
        A "group" is a set of peer rows - rows that all have
        the same values for every term in the ORDER BY clause.
        The frame boundary is the group that is &lt;expr&gt;
        groups before the group containing the current row, or the
        first group of the partition if there are fewer
        than &lt;expr&gt; groups before the current row.
        For the starting boundary of a frame, the first
        row of the group is used and for the ending boundary
        of a frame, the last row of the group is used.
        &lt;expr&gt; must be an integer.
        <a name="exprrange"></a>

        </p></li><li><p> <b>RANGE &rarr;</b>
        For this form, the ORDER BY clause of the
        <span class='yynonterm'>window-defn</span> must have a single
        term.  Call that ORDER BY term "X".  Let
        X<sub><small>i</small></sub> be the value of the X
        expression for the i-th row in the partition and let
        X<sub><small>c</small></sub> be the value of X for the
        current row.  Informally, a RANGE bound is the first row
        for which X<sub><small>i</small></sub> is within
        the &lt;expr&gt; of X<sub><small>c</small></sub>.
        More precisely:
        </p><ol type="a">
        <li> If either X<sub><small>i</small></sub> or
             X<sub><small>c</small></sub> are non-numeric, then
             the boundary is the first row for which the expression
             "X<sub><small>i</small></sub> IS X<sub><small>c</small></sub>"
             is true.
        </li><li> Else if the ORDER BY is ASC then the boundary
             is the first row for which
             X<sub><small>i</small></sub>&gt;=X<sub><small>c</small></sub>-&lt;expr&gt;.
        </li><li> Else if the ORDER BY is DESC then the boundary
        is the first row for which
        X<sub><small>i</small></sub>&lt;=X<sub><small>c</small></sub>+&lt;expr&gt;.
        </li></ol>
        For this form, the &lt;expr&gt; does not have to be an
        integer. It can evaluate to a real number as long as
        it is constant and non-negative.
        </li></ul>
    The boundary description "0 PRECEDING" always means the same
    thing as "CURRENT ROW".

</li><li><p><b>CURRENT ROW</b><br>
        The current row. For RANGE and GROUPS frame types,
        peers of the current row are also included in the frame,
        unless specifically excluded by the EXCLUDE clause.
        This is true regardless of whether CURRENT ROW is used
        as the starting or ending frame boundary.

</p></li><li><p><b>&lt;expr&gt; FOLLOWING</b><br>
        This is the same as "&lt;expr&gt; PRECEDING" except that
        the boundary is &lt;expr&gt; units after the current
        rather than before the current row.

</p></li><li><p> <b>UNBOUNDED FOLLOWING</b><br>
   The frame boundary is the last
   row in the <a href="windowfunctions.html#ptxn">partition</a>.

</p></li></ol>

<p> The ending frame boundary may not take a form that appears higher in
the above list than the starting frame boundary.

</p><p> In the following example, the window frame for each row consists of all
rows from the current row to the end of the set, where rows are sorted
according to "ORDER BY a".

</p><div class="codeblock"><pre><i>-- The following SELECT statement returns:</i>
<i>-- </i>
<i>--   c     | a | b | group_concat</i>
---------------------------------
<i>--   one   | 1 | A | A.D.G.C.F.B.E</i>
<i>--   one   | 4 | D | D.G.C.F.B.E </i>
<i>--   one   | 7 | G | G.C.F.B.E   </i>
<i>--   three | 3 | C | C.F.B.E     </i>
<i>--   three | 6 | F | F.B.E       </i>
<i>--   two   | 2 | B | B.E         </i>
<i>--   two   | 5 | E | E           </i>
<i>-- </i>
SELECT c, a, b, group_concat(b, '.') OVER (
  ORDER BY c, a ROWS BETWEEN CURRENT ROW AND UNBOUNDED FOLLOWING
) AS group_concat
FROM t1 ORDER BY c, a;
</pre></div>

<a name="wexcls"></a>

<h3 id="the_exclude_clause"><span>2.2.3. </span>The EXCLUDE Clause</h3>

<p> The optional EXCLUDE clause may take any of the following four forms:

</p><ul>
  <li> <p><b> EXCLUDE NO OTHERS</b>: This is the default. In this case no
  rows are excluded from the window frame as defined by its starting and ending
  frame boundaries.

  </p></li><li> <p><b> EXCLUDE CURRENT ROW</b>: In this case the current row is
  excluded from the window frame.  Peers of the current row remain in
  the frame for the GROUPS and RANGE frame types.

  </p></li><li> <p><b> EXCLUDE GROUP</b>: In this case the current row and all other
  rows that are peers of the current row are excluded from the frame. When
  processing an EXCLUDE clause, all rows with the same ORDER BY values, or all
  rows in the partition if there is no ORDER BY clause, are considered peers,
  even if the frame type is ROWS.

  </p></li><li> <p><b> EXCLUDE TIES</b>: In this case the current row is part of the
  frame, but peers of the current row are excluded.
</p></li></ul>

<p> The following example demonstrates the effect of the various
forms of the EXCLUDE clause:

</p><div class="codeblock"><pre><i>-- The following SELECT statement returns:</i>
<i>-- </i>
<i>--   c    | a | b | no_others     | current_row | grp       | ties</i>
<i>--  one   | 1 | A | A.D.G         | D.G         |           | A</i>
<i>--  one   | 4 | D | A.D.G         | A.G         |           | D</i>
<i>--  one   | 7 | G | A.D.G         | A.D         |           | G</i>
<i>--  three | 3 | C | A.D.G.C.F     | A.D.G.F     | A.D.G     | A.D.G.C</i>
<i>--  three | 6 | F | A.D.G.C.F     | A.D.G.C     | A.D.G     | A.D.G.F</i>
<i>--  two   | 2 | B | A.D.G.C.F.B.E | A.D.G.C.F.E | A.D.G.C.F | A.D.G.C.F.B</i>
<i>--  two   | 5 | E | A.D.G.C.F.B.E | A.D.G.C.F.B | A.D.G.C.F | A.D.G.C.F.E</i>
<i>-- </i>
SELECT c, a, b,
  group_concat(b, '.') OVER (
    ORDER BY c GROUPS BETWEEN UNBOUNDED PRECEDING AND CURRENT ROW EXCLUDE NO OTHERS
  ) AS no_others,
  group_concat(b, '.') OVER (
    ORDER BY c GROUPS BETWEEN UNBOUNDED PRECEDING AND CURRENT ROW EXCLUDE CURRENT ROW
  ) AS current_row,
  group_concat(b, '.') OVER (
    ORDER BY c GROUPS BETWEEN UNBOUNDED PRECEDING AND CURRENT ROW EXCLUDE GROUP
  ) AS grp,
  group_concat(b, '.') OVER (
    ORDER BY c GROUPS BETWEEN UNBOUNDED PRECEDING AND CURRENT ROW EXCLUDE TIES
  ) AS ties
FROM t1 ORDER BY c, a;
</pre></div>

<h2 id="the_filter_clause"><span>2.3. </span>The FILTER Clause</h2>

<p><b><a href="syntax/filter-clause.html">filter-clause:</a></b>
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<p><b><a href="syntax/function-arguments.html">function-arguments:</a></b>
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 <div id='xd7a5c5d5' style='display:none;' class='imgcontainer'>
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<p><b><a href="syntax/ordering-term.html">ordering-term:</a></b>
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<p><b><a href="syntax/literal-value.html">literal-value:</a></b>
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<p><b><a href="syntax/over-clause.html">over-clause:</a></b>
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</svg>
</div>
</div>
<p><b><a href="syntax/ordering-term.html">ordering-term:</a></b>
<button id='x1df87fd8' onclick='hideorshow("x1df87fd8","x420baa92")'>show</button></p>
 <div id='x420baa92' style='display:none;' class='imgcontainer'>
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<path d="M9,17L26,17"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
<path d="M32,32L81,32L81,2L32,2Z"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
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<path d="M126,59L190,59A15 15 0 0 0 205 44L205,44A15 15 0 0 0 190 29L126,29A15 15 0 0 0 111 44L111,44A15 15 0 0 0 126 59Z"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
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<text x="296" y="44" text-anchor="middle" fill="rgb(0,0,0)" dominant-baseline="central">collation-name</text>
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<path d="M606,59L648,59A15 15 0 0 0 663 44L663,44A15 15 0 0 0 648 29L606,29A15 15 0 0 0 591 44L591,44A15 15 0 0 0 606 59Z"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
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<path d="M701,59L735,59A15 15 0 0 0 750 44L750,44A15 15 0 0 0 735 29L701,29A15 15 0 0 0 686 44L686,44A15 15 0 0 0 701 59Z"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
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<path d="M701,97L727,97A15 15 0 0 0 742 82A15 15 0 0 0 727 67L701,67A15 15 0 0 0 686 82A15 15 0 0 0 701 97Z"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
<text x="714" y="82" text-anchor="middle" fill="rgb(0,0,0)" dominant-baseline="central">LAST</text>
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<path d="M742,82 L 754,82 Q 765,82 765,67 L 765,44 L 765,29"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
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<path d="M549,17L665,17"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
<path d="M670,17L780,17"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
</svg>
</div>
</div>
</div>
<p><b><a href="syntax/raise-function.html">raise-function:</a></b>
<button id='x4a5943b5' onclick='hideorshow("x4a5943b5","x85d7df8c")'>show</button></p>
 <div id='x85d7df8c' style='display:none;' class='imgcontainer'>
 <div style="max-width:627px"><svg xmlns='http://www.w3.org/2000/svg' class="pikchr" viewBox="0 0 627.302 147.96">
<circle cx="5" cy="17" r="3.6"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
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<path d="M9,17L26,17"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
<path d="M47,32L82,32A15 15 0 0 0 97 17A15 15 0 0 0 82 2L47,2A15 15 0 0 0 32 17A15 15 0 0 0 47 32Z"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
<text x="65" y="17" text-anchor="middle" fill="rgb(0,0,0)" dominant-baseline="central">RAISE</text>
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<path d="M97,17L114,17"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
<path d="M135,32L135,32A15 15 0 0 0 150 17A15 15 0 0 0 135 2L135,2A15 15 0 0 0 120 17A15 15 0 0 0 135 32Z"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
<text x="135" y="17" text-anchor="middle" font-weight="bold" fill="rgb(0,0,0)" dominant-baseline="central">(</text>
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<path d="M207,70L285,70A15 15 0 0 0 300 55L300,55A15 15 0 0 0 285 39L207,39A15 15 0 0 0 192 55L192,55A15 15 0 0 0 207 70Z"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
<text x="246" y="55" text-anchor="middle" fill="rgb(0,0,0)" dominant-baseline="central">ROLLBACK</text>
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<path d="M300,55L330,55"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
<path d="M351,70A15 15 0 0 0 366 55L366,55A15 15 0 0 0 351 39A15 15 0 0 0 336 55L336,55A15 15 0 0 0 351 70Z"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
<text x="351" y="55" text-anchor="middle" font-weight="bold" fill="rgb(0,0,0)" dominant-baseline="central">,</text>
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<path d="M404,70L508,70A15 15 0 0 0 523 55L523,55A15 15 0 0 0 508 39L404,39A15 15 0 0 0 389 55L389,55A15 15 0 0 0 404 70Z"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
<text x="456" y="55" text-anchor="middle" fill="rgb(0,0,0)" dominant-baseline="central">error-message</text>
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<path d="M579,32A15 15 0 0 0 594 17A15 15 0 0 0 579 2A15 15 0 0 0 564 17A15 15 0 0 0 579 32Z"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
<text x="579" y="17" text-anchor="middle" font-weight="bold" fill="rgb(0,0,0)" dominant-baseline="central">)</text>
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<path d="M207,32L259,32A15 15 0 0 0 274 17A15 15 0 0 0 259 2L207,2A15 15 0 0 0 192 17A15 15 0 0 0 207 32Z"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
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<path d="M456,17L553,17"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
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<path d="M300,92 L 307,92 Q 315,92 315,77 L 315,70 Q 315,55 322,55 L 330,55"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
<path d="M207,145L229,145A15 15 0 0 0 244 130A15 15 0 0 0 229 115L207,115A15 15 0 0 0 192 130A15 15 0 0 0 207 145Z"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
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</svg>
</div>
</div>
<p><b><a href="syntax/select-stmt.html">select-stmt:</a></b>
<button id='xb11a1037' onclick='hideorshow("xb11a1037","x12d9418a")'>show</button></p>
 <div id='x12d9418a' style='display:none;' class='imgcontainer'>
 <div style="max-width:669px"><svg xmlns='http://www.w3.org/2000/svg' class="pikchr" viewBox="0 0 669.677 1162.3">
<path d="M55,845L667,845L667,99L55,99Z"  style="fill:none;stroke-width:3.24;stroke:rgb(211,211,211);" />
<circle cx="6" cy="17" r="3.6"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
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<path d="M61,32L92,32A15 15 0 0 0 107 17A15 15 0 0 0 92 2L61,2A15 15 0 0 0 46 17A15 15 0 0 0 61 32Z"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
<text x="76" y="17" text-anchor="middle" fill="rgb(0,0,0)" dominant-baseline="central">WITH</text>
<path d="M167,62L253,62A15 15 0 0 0 268 47L268,47A15 15 0 0 0 253 32L167,32A15 15 0 0 0 152 47L152,47A15 15 0 0 0 167 62Z"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
<text x="210" y="47" text-anchor="middle" fill="rgb(0,0,0)" dominant-baseline="central">RECURSIVE</text>
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<p><b><a href="syntax/common-table-expression.html">common-table-expression:</a></b>
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<p><b><a href="syntax/compound-operator.html">compound-operator:</a></b>
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<text x="105" y="17" text-anchor="middle" fill="rgb(0,0,0)" dominant-baseline="central">UNION</text>
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<text x="105" y="55" text-anchor="middle" fill="rgb(0,0,0)" dominant-baseline="central">UNION</text>
<path d="M83,108L168,108A15 15 0 0 0 183 92A15 15 0 0 0 168 77L83,77A15 15 0 0 0 68 92A15 15 0 0 0 83 108Z"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
<text x="125" y="92" text-anchor="middle" fill="rgb(0,0,0)" dominant-baseline="central">INTERSECT</text>
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<text x="109" y="130" text-anchor="middle" fill="rgb(0,0,0)" dominant-baseline="central">EXCEPT</text>
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<path d="M180,70L195,70A15 15 0 0 0 210 55L210,55A15 15 0 0 0 195 39L180,39A15 15 0 0 0 165 55L165,55A15 15 0 0 0 180 70Z"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
<text x="187" y="55" text-anchor="middle" fill="rgb(0,0,0)" dominant-baseline="central">ALL</text>
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<path d="M233,55 L 240,55 Q 248,55 248,40 L 248,32 Q 248,17 263,17 L 263,17 L 278,17"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
<circle cx="288" cy="17" r="3.6"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
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<path d="M142,17L276,17"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
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<path d="M183,92L227,92"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
<path d="M233,92 L 240,92 Q 248,92 248,77 L 248,54 L 248,39"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
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<path d="M233,130 L 240,130 Q 248,130 248,115 L 248,92 L 248,77"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
</svg>
</div>
</div>
<p><b><a href="syntax/join-clause.html">join-clause:</a></b>
<button id='x09db4fdc' onclick='hideorshow("x09db4fdc","xf6525aa6")'>show</button></p>
 <div id='xf6525aa6' style='display:none;' class='imgcontainer'>
 <div style="max-width:793px"><svg xmlns='http://www.w3.org/2000/svg' class="pikchr" viewBox="0 0 793.282 84.24">
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<polygon points="32,17 20,21 20,12" style="fill:rgb(0,0,0)"/>
<path d="M9,17L26,17"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
<path d="M32,32L193,32L193,2L32,2Z"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
<text x="112" y="17" text-anchor="middle" fill="rgb(0,0,0)" dominant-baseline="central">table-or-subquery</text>
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<path d="M193,17 L 200,17 Q 208,17 208,32 L 208,32 Q 208,47 223,47 L 238,47 L 253,47"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
<path d="M259,62L380,62L380,32L259,32Z"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
<text x="319" y="47" text-anchor="middle" fill="rgb(0,0,0)" dominant-baseline="central">join-operator</text>
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<path d="M380,47L397,47"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
<path d="M403,62L564,62L564,32L403,32Z"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
<text x="483" y="47" text-anchor="middle" fill="rgb(0,0,0)" dominant-baseline="central">table-or-subquery</text>
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<path d="M564,47L581,47"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
<path d="M587,62L721,62L721,32L587,32Z"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
<text x="654" y="47" text-anchor="middle" fill="rgb(0,0,0)" dominant-baseline="central">join-constraint</text>
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<circle cx="787" cy="17" r="3.6"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
<polygon points="483,17 472,21 472,12" style="fill:rgb(0,0,0)"/>
<path d="M193,17L478,17"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
<path d="M483,17L776,17"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
<polygon points="483,77 495,73 495,82" style="fill:rgb(0,0,0)"/>
<path d="M721,47 L 728,47 Q 736,47 736,62 L 736,62 Q 736,77 721,77 L 504,77 L 489,77"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
<path d="M483,77 L 247,77 Q 232,77 232,62 L 232,62 Q 232,47 246,47 L 259,47"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
</svg>
</div>
<p><b><a href="syntax/join-constraint.html">join-constraint:</a></b>
<button id='xf5b07b14' onclick='hideorshow("xf5b07b14","x7d470f23")'>show</button></p>
 <div id='x7d470f23' style='display:none;' class='imgcontainer'>
 <div style="max-width:483px"><svg xmlns='http://www.w3.org/2000/svg' class="pikchr" viewBox="0 0 483.336 126.576">
<circle cx="5" cy="17" r="3.6"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
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<path d="M9,17 L 16,17 Q 24,17 24,32 L 24,40 Q 24,55 34,55 L 45,55"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
<path d="M66,70L104,70A15 15 0 0 0 120 55L120,55A15 15 0 0 0 104 39L66,39A15 15 0 0 0 50 55L50,55A15 15 0 0 0 66 70Z"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
<text x="85" y="55" text-anchor="middle" fill="rgb(0,0,0)" dominant-baseline="central">USING</text>
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<path d="M158,70A15 15 0 0 0 173 55L173,55A15 15 0 0 0 158 39A15 15 0 0 0 143 55L143,55A15 15 0 0 0 158 70Z"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
<text x="158" y="55" text-anchor="middle" font-weight="bold" fill="rgb(0,0,0)" dominant-baseline="central">(</text>
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<path d="M173,55L203,55"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
<path d="M224,70L318,70A15 15 0 0 0 333 55L333,55A15 15 0 0 0 318 39L224,39A15 15 0 0 0 209 55L209,55A15 15 0 0 0 224 70Z"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
<text x="271" y="55" text-anchor="middle" fill="rgb(0,0,0)" dominant-baseline="central">column-name</text>
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<path d="M384,70A15 15 0 0 0 399 55L399,55A15 15 0 0 0 384 39A15 15 0 0 0 369 55L369,55A15 15 0 0 0 384 70Z"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
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<polygon points="473,17 462,21 462,12" style="fill:rgb(0,0,0)"/>
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<circle cx="477" cy="17" r="3.6"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
<path d="M271,108A15 15 0 0 0 286 92A15 15 0 0 0 271 77A15 15 0 0 0 256 92A15 15 0 0 0 271 108Z"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
<text x="271" y="92" text-anchor="middle" font-weight="bold" fill="rgb(0,0,0)" dominant-baseline="central">,</text>
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<path d="M9,17L45,17"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
<path d="M66,32L74,32A15 15 0 0 0 90 17A15 15 0 0 0 74 2L66,2A15 15 0 0 0 50 17A15 15 0 0 0 66 32Z"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
<text x="70" y="17" text-anchor="middle" fill="rgb(0,0,0)" dominant-baseline="central">ON</text>
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<path d="M90,17L107,17"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
<path d="M113,32L162,32L162,2L113,2Z"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
<text x="137" y="17" text-anchor="middle" fill="rgb(0,0,0)" dominant-baseline="central">expr</text>
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<path d="M422,17L462,17"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
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<path d="M209,120 L 422,120 Q 437,120 437,105 L 437,54 L 437,39"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
</svg>
</div>
</div>
<p><b><a href="syntax/join-operator.html">join-operator:</a></b>
<button id='x1f8f067e' onclick='hideorshow("x1f8f067e","x77621cba")'>show</button></p>
 <div id='x77621cba' style='display:none;' class='imgcontainer'>
 <div style="max-width:620px"><svg xmlns='http://www.w3.org/2000/svg' class="pikchr" viewBox="0 0 620.333 255.312">
<circle cx="5" cy="17" r="3.6"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
<polygon points="50,71 39,76 39,67" style="fill:rgb(0,0,0)"/>
<path d="M9,17 L 16,17 Q 24,17 24,32 L 24,56 Q 24,71 34,71 L 45,71"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
<path d="M66,86L133,86A15 15 0 0 0 148 71A15 15 0 0 0 133 56L66,56A15 15 0 0 0 50 71A15 15 0 0 0 66 86Z"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
<text x="99" y="71" text-anchor="middle" fill="rgb(0,0,0)" dominant-baseline="central">NATURAL</text>
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<path d="M246,86L273,86A15 15 0 0 0 288 71A15 15 0 0 0 273 56L246,56A15 15 0 0 0 231 71A15 15 0 0 0 246 86Z"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
<text x="259" y="71" text-anchor="middle" fill="rgb(0,0,0)" dominant-baseline="central">LEFT</text>
<polygon points="378,71 366,76 366,67" style="fill:rgb(0,0,0)"/>
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<path d="M393,86L437,86A15 15 0 0 0 452 71A15 15 0 0 0 437 56L393,56A15 15 0 0 0 378 71A15 15 0 0 0 393 86Z"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
<text x="415" y="71" text-anchor="middle" fill="rgb(0,0,0)" dominant-baseline="central">OUTER</text>
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<path d="M452,71L469,71"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
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<path d="M532,56L554,56A15 15 0 0 0 569 41A15 15 0 0 0 554 26L532,26A15 15 0 0 0 516 41A15 15 0 0 0 532 56Z"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
<text x="543" y="41" text-anchor="middle" fill="rgb(0,0,0)" dominant-baseline="central">JOIN</text>
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<circle cx="614" cy="17" r="3.6"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
<path d="M310,32A15 15 0 0 0 325 17A15 15 0 0 0 310 2A15 15 0 0 0 295 17A15 15 0 0 0 310 32Z"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
<text x="310" y="17" text-anchor="middle" font-weight="bold" fill="rgb(0,0,0)" dominant-baseline="central">,</text>
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<path d="M99,41L178,41"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
<path d="M189,41L505,41"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
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<path d="M246,124L284,124A15 15 0 0 0 299 109A15 15 0 0 0 284 94L246,94A15 15 0 0 0 231 109A15 15 0 0 0 246 124Z"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
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<path d="M189,41 L 197,41 Q 204,41 204,56 L 204,132 Q 204,147 215,147 L 225,147"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
<path d="M246,162L274,162A15 15 0 0 0 289 147A15 15 0 0 0 274 132L246,132A15 15 0 0 0 231 147A15 15 0 0 0 246 162Z"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
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<path d="M246,207L287,207A15 15 0 0 0 302 192A15 15 0 0 0 287 177L246,177A15 15 0 0 0 231 192A15 15 0 0 0 246 207Z"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
<text x="267" y="192" text-anchor="middle" fill="rgb(0,0,0)" dominant-baseline="central">INNER</text>
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<path d="M302,192L469,192"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
<path d="M475,192 L 482,192 Q 490,192 490,185 L 490,177"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
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<path d="M246,253L287,253A15 15 0 0 0 303 238A15 15 0 0 0 287 222L246,222A15 15 0 0 0 231 238A15 15 0 0 0 246 253Z"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
<text x="267" y="238" text-anchor="middle" fill="rgb(0,0,0)" dominant-baseline="central">CROSS</text>
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<path d="M303,238L469,238"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
<path d="M475,238 L 482,238 Q 490,238 490,223 L 490,71 L 490,56"  style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" />
</svg>
</div>
</div>
</div>
<p><b><a href="syntax/ordering-term.html">ordering-term:</a></b>
<button id='x2c2d83da' onclick='hideorshow("x2c2d83da","x4f75c28b")'>show</button></p>
 <div id='x4f75c28b' style='display:none;' class='imgcontainer'>
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<p><b><a href="syntax/result-column.html">result-column:</a></b>
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<p><b><a href="syntax/table-or-subquery.html">table-or-subquery:</a></b>
<button id='xa37b1d70' onclick='hideorshow("xa37b1d70","xdd371957")'>show</button></p>
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</div>
<p><b><a href="syntax/window-defn.html">window-defn:</a></b>
<button id='x5a375ead' onclick='hideorshow("x5a375ead","x050877ef")'>show</button></p>
 <div id='x050877ef' style='display:none;' class='imgcontainer'>
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<p><b><a href="syntax/frame-spec.html">frame-spec:</a></b>
<button id='xc09a2f4d' onclick='hideorshow("xc09a2f4d","xea11e11d")'>show</button></p>
 <div id='xea11e11d' style='display:none;' class='imgcontainer'>
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<p><b><a href="syntax/type-name.html">type-name:</a></b>
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<p><b><a href="syntax/signed-number.html">signed-number:</a></b>
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</div>


<p>If a FILTER clause is provided, then only rows for which the <i>expr</i> is
true are included in the window frame. The aggregate window still returns a
value for every row, but those for which the FILTER expression evaluates to
other than true are not included in the window frame for any row. For example:

</p><div class="codeblock"><pre><i>-- The following SELECT statement returns:</i>
<i>-- </i>
<i>--   c     | a | b | group_concat</i>
---------------------------------
<i>--   one   | 1 | A | A           </i>
<i>--   two   | 2 | B | A           </i>
<i>--   three | 3 | C | A.C         </i>
<i>--   one   | 4 | D | A.C.D       </i>
<i>--   two   | 5 | E | A.C.D       </i>
<i>--   three | 6 | F | A.C.D.F     </i>
<i>--   one   | 7 | G | A.C.D.F.G   </i>
<i>-- </i>
SELECT c, a, b, group_concat(b, '.') FILTER (WHERE c!='two') OVER (
  ORDER BY a
) AS group_concat
FROM t1 ORDER BY a;
</pre></div>


<a name="builtins"></a>

<h1 id="built_in_window_functions"><span>3. </span>Built-in Window Functions</h1>

<p> As well as aggregate window functions, SQLite features a set of built-in
window functions based on
<a href="https://www.postgresql.org/docs/10/static/functions-window.html">
those supported by PostgreSQL</a>.

</p><p> Built-in window functions honor any PARTITION BY clause in the same way
as aggregate window functions - each selected row is assigned to a partition
and each partition is processed separately. The ways in which any ORDER BY
clause affects each built-in window function is described below. Some of
the window functions (rank(), dense_rank(), percent_rank() and ntile()) use
the concept of "peer groups" (rows within the same partition that have the
same values for all ORDER BY expressions). In these cases, it does not matter
whether the <span class='yynonterm'>frame-spec</span> specifies ROWS, GROUPS, or RANGE.
For the purposes of built-in window function processing, rows with the same values
for all ORDER BY expressions are considered peers regardless of the frame type.

</p><p> Most built-in window functions ignore the
<span class='yynonterm'>frame-spec</span>, the exceptions being first_value(),
last_value() and nth_value(). It is a syntax error to specify a FILTER
clause as part of a built-in window function invocation.

<a name="biwinfunc"></a>

</p><p> SQLite supports the following 11 built-in window functions:

</p><dl>
  <dt><p><b>row_number()</b>
  </p></dt><dd><p> The number of the row within the current partition. Rows are
       numbered starting from 1 in the order defined by the ORDER BY clause in
       the window definition, or in arbitrary order otherwise.
  </p></dd><dt><p><b>rank()</b>
  </p></dt><dd><p> The row_number() of the first peer in each group - the rank of the
       current row with gaps. If there is no ORDER BY clause, then all rows
       are considered peers and this function always returns 1.
  </p></dd><dt><p><b>dense_rank()</b>
  </p></dt><dd><p> The number of the current row's peer group within its partition - the
       rank of the current row without gaps. Rows are numbered starting
       from 1 in the order defined by the ORDER BY clause in the window
       definition. If there is no ORDER BY clause, then all rows are
       considered peers and this function always returns 1.
  </p></dd><dt><p><b>percent_rank()</b>
  </p></dt><dd><p> Despite the name, this function always returns a value between 0.0
       and 1.0 equal to (<i>rank</i> - 1)/(<i>partition-rows</i> - 1), where
       <i>rank</i> is the value returned by built-in window function rank()
       and <i>partition-rows</i> is the total number of rows in the
       partition. If the partition contains only one row, this function
       returns 0.0.
  </p></dd><dt><p><b>cume_dist()</b>
  </p></dt><dd><p> The cumulative distribution. Calculated as
       <i>row-number</i>/<i>partition-rows</i>, where <i>row-number</i> is
       the value returned by row_number() for the last peer in the group
       and <i>partition-rows</i> the number of rows in the partition.
  </p></dd><dt><p><b>ntile(N)</b>
  </p></dt><dd><p> Argument <i>N</i> is handled as an integer. This function divides the
       partition into N groups as evenly as possible and assigns an integer
       between 1 and <i>N</i> to each group, in the order defined by the ORDER
       BY clause, or in arbitrary order otherwise. If necessary, larger groups
       occur first. This function returns the integer value assigned to the
       group that the current row is a part of.

  </p></dd><dt><p><b>lag(expr)<br>lag(expr, offset)<br>lag(expr, offset, default)</b>
  </p></dt><dd><p> The first form of the lag() function returns the result of evaluating
       expression <i>expr</i> against the previous row in the partition. Or, if
       there is no previous row (because the current row is the first), NULL.

      </p><p> If the <i>offset</i> argument is provided, then it must be a
       non-negative integer. In this case the value returned is the result
       of evaluating <i>expr</i> against the row <i>offset</i> rows before the
       current row within the partition. If <i>offset</i> is 0, then
       <i>expr</i> is evaluated against the current row. If there is no row
       <i>offset</i> rows before the current row, NULL is returned.

      </p><p> If <i>default</i> is also provided, then it is returned instead of
      NULL if the row identified by <i>offset</i> does not exist.

  </p></dd><dt><p><b>lead(expr)<br>lead(expr, offset)<br>lead(expr, offset, default)</b>
  </p></dt><dd><p> The first form of the lead() function returns the result of evaluating
       expression <i>expr</i> against the next row in the partition. Or, if
       there is no next row (because the current row is the last), NULL.

      </p><p> If the <i>offset</i> argument is provided, then it must be a
       non-negative integer. In this case the value returned is the result
       of evaluating <i>expr</i> against the row <i>offset</i> rows after the
       current row within the partition. If <i>offset</i> is 0, then
       <i>expr</i> is evaluated against the current row. If there is no row
       <i>offset</i> rows after the current row, NULL is returned.

      </p><p> If <i>default</i> is also provided, then it is returned instead of
      NULL if the row identified by <i>offset</i> does not exist.
  </p></dd><dt><p><b>first_value(expr)</b>
  </p></dt><dd><p> This built-in window function calculates the window frame for each
       row in the same way as an aggregate window function. It returns the
       value of <i>expr</i> evaluated against the first row in the window frame
       for each row.
  </p></dd><dt><p><b>last_value(expr)</b>
  </p></dt><dd><p> This built-in window function calculates the window frame for each
       row in the same way as an aggregate window function. It returns the
       value of <i>expr</i> evaluated against the last row in the window frame
       for each row.
  </p></dd><dt><p><b>nth_value(expr, N)</b>
  </p></dt><dd><p> This built-in window function calculates the window frame for each
       row in the same way as an aggregate window function. It returns the
       value of <i>expr</i> evaluated against the row <i>N</i> of the window
       frame. Rows are numbered within the window frame starting from 1 in
       the order defined by the ORDER BY clause if one is present, or in
       arbitrary order otherwise. If there is no <i>N</i>th row in the
       partition, then NULL is returned.
  </p></dd><dd>
</dd></dl>

<p>The examples in this section use the
<a href="windowfunctions.html#aggwinfunc">previously defined T1 table</a>
as well as the following T2 table:

</p><div class="codeblock"><pre>CREATE TABLE t2(a, b);
INSERT INTO t2 VALUES('a', 'one'),
                     ('a', 'two'),
                     ('a', 'three'),
                     ('b', 'four'),
                     ('c', 'five'),
                     ('c', 'six');
</pre></div>

<p>The following example illustrates the behaviour of the five ranking
functions - row_number(), rank(), dense_rank(), percent_rank() and
cume_dist().

</p><div class="codeblock"><pre><i>-- The following SELECT statement returns:</i>
<i>-- </i>
<i>--   a | row_number | rank | dense_rank | percent_rank | cume_dist</i>
------------------------------------------------------------------
<i>--   a |          1 |    1 |          1 |          0.0 |       0.5</i>
<i>--   a |          2 |    1 |          1 |          0.0 |       0.5</i>
<i>--   a |          3 |    1 |          1 |          0.0 |       0.5</i>
<i>--   b |          4 |    4 |          2 |          0.6 |       0.66</i>
<i>--   c |          5 |    5 |          3 |          0.8 |       1.0</i>
<i>--   c |          6 |    5 |          3 |          0.8 |       1.0</i>
<i>-- </i>
SELECT a                        AS a,
       row_number() OVER win    AS row_number,
       rank() OVER win          AS rank,
       dense_rank() OVER win    AS dense_rank,
       percent_rank() OVER win  AS percent_rank,
       cume_dist() OVER win     AS cume_dist
FROM t2
WINDOW win AS (ORDER BY a);
</pre></div>

<p>The example below uses ntile() to divide the six rows into two groups (the
ntile(2) call) and into four groups (the ntile(4) call). For ntile(2), there
are three rows assigned to each group. For ntile(4), there are two groups of
two and two groups of one. The larger groups of two appear first.

</p><div class="codeblock"><pre><i>-- The following SELECT statement returns:</i>
<i>-- </i>
<i>--   a | b     | ntile_2 | ntile_4</i>
----------------------------------
<i>--   a | one   |       1 |       1</i>
<i>--   a | two   |       1 |       1</i>
<i>--   a | three |       1 |       2</i>
<i>--   b | four  |       2 |       2</i>
<i>--   c | five  |       2 |       3</i>
<i>--   c | six   |       2 |       4</i>
<i>-- </i>
SELECT a                        AS a,
       b                        AS b,
       ntile(2) OVER win        AS ntile_2,
       ntile(4) OVER win        AS ntile_4
FROM t2
WINDOW win AS (ORDER BY a);
</pre></div>

<p> The next example demonstrates lag(), lead(), first_value(), last_value()
and nth_value(). The <span class='yynonterm'>frame-spec</span> is ignored by
both lag() and lead(), but respected by first_value(), last_value()
and nth_value().

</p><div class="codeblock"><pre><i>-- The following SELECT statement returns:</i>
<i>-- </i>
<i>--   b | lead | lag  | first_value | last_value | nth_value_3</i>
-------------------------------------------------------------
<i>--   A | C    | NULL | A           | A          | NULL       </i>
<i>--   B | D    | A    | A           | B          | NULL       </i>
<i>--   C | E    | B    | A           | C          | C          </i>
<i>--   D | F    | C    | A           | D          | C          </i>
<i>--   E | G    | D    | A           | E          | C          </i>
<i>--   F | n/a  | E    | A           | F          | C          </i>
<i>--   G | n/a  | F    | A           | G          | C          </i>
<i>-- </i>
SELECT b                          AS b,
       lead(b, 2, 'n/a') OVER win AS lead,
       lag(b) OVER win            AS lag,
       first_value(b) OVER win    AS first_value,
       last_value(b) OVER win     AS last_value,
       nth_value(b, 3) OVER win   AS nth_value_3
FROM t1
WINDOW win AS (ORDER BY b ROWS BETWEEN UNBOUNDED PRECEDING AND CURRENT ROW)
</pre></div>


<a name="wchaining"></a>

<h1 id="window_chaining"><span>4. </span>Window Chaining</h1>

<p>
Window chaining is a shorthand that allows one window to be defined in terms
of another. Specifically, the shorthand allows the new window to implicitly
copy the PARTITION BY and optionally ORDER BY clauses of the base window. For
example, in the following:

</p><div class="codeblock"><pre>SELECT group_concat(b, '.') OVER (
  win ROWS BETWEEN UNBOUNDED PRECEDING AND CURRENT ROW
)
FROM t1
WINDOW win AS (PARTITION BY a ORDER BY c)
</pre></div>

<p>
the window used by the group_concat() function is equivalent
to "PARTITION BY a ORDER BY c ROWS BETWEEN UNBOUNDED PRECEDING
AND CURRENT ROW". In order to use window
chaining, all of the following must be true:

</p><ul>
  <li><p>The new window definition must not include a PARTITION BY clause. The
       PARTITION BY clause, if there is one, must be supplied by the base
       window specification.

  </p></li><li><p>If the base window has an ORDER BY clause, it is copied into the new
       window. In this case the new window must not specify an ORDER BY clause.
       If the base window has no ORDER BY clause, one may be specified as part
       of the new window definition.

  </p></li><li><p>The base window may not specify a frame specification.  The frame
      specification can only be given in the new window specification.
</p></li></ul>

<p>The two fragments of SQL below are similar, but not entirely equivalent, as
the latter will fail if the definition of window "win" contains a frame
specification.

</p><div class="codeblock"><pre>SELECT group_concat(b, '.') OVER win ...
SELECT group_concat(b, '.') OVER (win) ...
</pre></div>

<a name="udfwinfunc"></a>

<h1 id="user_defined_aggregate_window_functions"><span>5. </span>User-Defined Aggregate Window Functions</h1>

<p> User-defined aggregate window functions may be created using the
<a href="c3ref/create_function.html">sqlite3_create_window_function</a>() API. Implementing an aggregate window
function is very similar to an ordinary aggregate function. Any user-defined
aggregate window function may also be used as an ordinary aggregate. To
implement a user-defined aggregate window function the application must
supply four callback functions:

</p><table striped="1" style="margin:1em auto; width:80%; border-spacing:0">
<tr style="text-align:left"><th>Callback </th><th>Description
</th></tr><tr style="text-align:left;background-color:#DDDDDD"><td>xStep </td><td>
      This method is required by both window aggregate and legacy aggregate
      function implementations. It is invoked to add a row to the current
      window. The function arguments, if any, corresponding to the row being
      added are passed to the implementation of xStep.

</td></tr><tr style="text-align:left"><td>xFinal </td><td>
      This method is required by both window aggregate and legacy aggregate
      function implementations. It is invoked to return the current value
      of the aggregate (determined by the contents of the current window),
      and to free any resources allocated by earlier calls to xStep.

</td></tr><tr style="text-align:left;background-color:#DDDDDD"><td>xValue </td><td>
      This method is  only required for window aggregate functions.  The presence
      of this method is what distinguishes a window aggregate function from a
      legacy  aggregate function.  This method is invoked to return the current
      value of the aggregate. Unlike xFinal, the implementation should not
      delete any context.

</td></tr><tr style="text-align:left"><td>xInverse </td><td>
      This method is only required for window aggregate functions, not legacy
      aggregate function implementations. It is invoked to remove the oldest
      presently aggregated result of xStep from the current window.
      The function arguments, if any, are those
      passed to xStep for the row being removed.
</td></tr></table>

<p> The C code below implements a simple window aggregate function named
sumint(). This works in the same way as the built-in sum() function, except
that it throws an exception if passed an argument that is not an integer
value.

</p><div class="codeblock"><pre><pre>
<i>/*</i>
<i>** xStep for sumint().</i>
<i>**</i>
<i>** Add the value of the argument to the aggregate context (an integer).</i>
<i>*/</i>
static void sumintStep(
  <a href="c3ref/context.html">sqlite3_context</a> *ctx,
  int nArg,
  <a href="c3ref/value.html">sqlite3_value</a> *apArg[]
){
  <a href="c3ref/int64.html">sqlite3_int64</a> *pInt;

  assert( nArg==1 );
  if( <a href="c3ref/value_blob.html">sqlite3_value_type</a>(apArg[0])!=SQLITE_INTEGER ){
    <a href="c3ref/result_blob.html">sqlite3_result_error</a>(ctx, "invalid argument", -1);
    return;
  }
  pInt = (sqlite3_int64*)sqlite3_aggregate_context(ctx, sizeof(<a href="c3ref/int64.html">sqlite3_int64</a>));
  if( pInt ){
    *pInt += <a href="c3ref/value_blob.html">sqlite3_value_int64</a>(apArg[0]);
  }
}

<i>/*</i>
<i>** xInverse for sumint().</i>
<i>**</i>
<i>** This does the opposite of xStep() - subtracts the value of the argument</i>
<i>** from the current context value. The error checking can be omitted from</i>
<i>** this function, as it is only ever called after xStep() (so the aggregate</i>
<i>** context has already been allocated) and with a value that has already</i>
<i>** been passed to xStep() without error (so it must be an integer).</i>
<i>*/</i>
static void sumintInverse(
  <a href="c3ref/context.html">sqlite3_context</a> *ctx,
  int nArg,
  <a href="c3ref/value.html">sqlite3_value</a> *apArg[]
){
  <a href="c3ref/int64.html">sqlite3_int64</a> *pInt;
  assert( <a href="c3ref/value_blob.html">sqlite3_value_type</a>(apArg[0])==SQLITE_INTEGER );
  pInt = (sqlite3_int64*)sqlite3_aggregate_context(ctx, sizeof(<a href="c3ref/int64.html">sqlite3_int64</a>));
  *pInt -= <a href="c3ref/value_blob.html">sqlite3_value_int64</a>(apArg[0]);
}

<i>/*</i>
<i>** xFinal for sumint().</i>
<i>**</i>
<i>** Return the current value of the aggregate window function. Because</i>
<i>** this implementation does not allocate any resources beyond the buffer</i>
<i>** returned by <a href="c3ref/aggregate_context.html">sqlite3_aggregate_context</a>, which is automatically freed</i>
<i>** by the system, there are no resources to free. And so this method is</i>
<i>** identical to xValue().</i>
<i>*/</i>
static void sumintFinal(<a href="c3ref/context.html">sqlite3_context</a> *ctx){
  <a href="c3ref/int64.html">sqlite3_int64</a> res = 0;
  <a href="c3ref/int64.html">sqlite3_int64</a> *pInt;
  pInt = (sqlite3_int64*)<a href="c3ref/aggregate_context.html">sqlite3_aggregate_context</a>(ctx, 0);
  if( pInt ) res = *pInt;
  <a href="c3ref/result_blob.html">sqlite3_result_int64</a>(ctx, res);
}

<i>/*</i>
<i>** xValue for sumint().</i>
<i>**</i>
<i>** Return the current value of the aggregate window function.</i>
<i>*/</i>
static void sumintValue(<a href="c3ref/context.html">sqlite3_context</a> *ctx){
  <a href="c3ref/int64.html">sqlite3_int64</a> res = 0;
  <a href="c3ref/int64.html">sqlite3_int64</a> *pInt;
  pInt = (sqlite3_int64*)<a href="c3ref/aggregate_context.html">sqlite3_aggregate_context</a>(ctx, 0);
  if( pInt ) res = *pInt;
  <a href="c3ref/result_blob.html">sqlite3_result_int64</a>(ctx, res);
}

<i>/*</i>
<i>** Register sumint() window aggregate with database handle db.</i>
<i>*/</i>
int register_sumint(<a href="c3ref/sqlite3.html">sqlite3</a> *db){
  return <a href="c3ref/create_function.html">sqlite3_create_window_function</a>(db, "sumint", 1, SQLITE_UTF8, 0,
      sumintStep, sumintFinal, sumintValue, sumintInverse, 0
  );
}
</pre>

</pre></div>

<p> The following example uses the sumint() function implemented by the above
C code. For each row, the window consists of the preceding row (if any), the current row and the following row (again, if any):

</p><div class="codeblock"><pre>CREATE TABLE t3(x, y);
INSERT INTO t3 VALUES('a', 4),
                     ('b', 5),
                     ('c', 3),
                     ('d', 8),
                     ('e', 1);

<i>-- Assuming the database is populated using the above script, the </i>
<i>-- following SELECT statement returns:</i>
<i>-- </i>
<i>--   x | sum_y</i>
--------------
<i>--   a | 9    </i>
<i>--   b | 12   </i>
<i>--   c | 16   </i>
<i>--   d | 12   </i>
<i>--   e | 9    </i>
<i>-- </i>
SELECT x, sumint(y) OVER (
  ORDER BY x ROWS BETWEEN 1 PRECEDING AND 1 FOLLOWING
) AS sum_y
FROM t3 ORDER BY x;
</pre></div>

<p>In processing the query above, SQLite invokes the sumint callbacks as
follows:

</p><p>
</p><ol>
  <li> <b>xStep(4)</b> - add "4" to the current window.
  </li><li> <b>xStep(5)</b> - add "5" to the current window.
  </li><li> <b>xValue()</b> - invoke xValue() to obtain the value of sumint() for
       the row with (x='a'). The window currently consists of values 4 and 5,
       and so the result is 9.
  </li><li> <b>xStep(3)</b> - add "3" to the current window.
  </li><li> <b>xValue()</b> - invoke xValue() to obtain the value of sumint() for
       the row with (x='b'). The window currently consists of values 4, 5 and
       3, and so the result is 12.
  </li><li> <b>xInverse(4)</b> - remove "4" from the window.
  </li><li> <b>xStep(8)</b> - add "8" to the current window. The window now consists
       of values 5, 3 and 8.
  </li><li> <b>xValue()</b> - invoked to obtain the value for the row with (x='c').
       In this case, 16.
  </li><li> <b>xInverse(5)</b> - remove value "5" from the window.
  </li><li> <b>xStep(1)</b> - add value "1" to the window.
  </li><li> <b>xValue()</b> - invoked to obtain the value for row (x='d').
  </li><li> <b>xInverse(3)</b> - remove value "3" from the window. The window now
       contains values 8 and 1 only.
  </li><li> <b>xFinal()</b> - invoked to reclaim any allocated resources and to
                         obtain the value for row (x='e'). 9.     .
</li></ol>

<p>If the user were to abandon query execution by calling sqlite3_reset() or
sqlite3_finalize() on the statement handle before SQLite has called xFinal(),
then xFinal() is called automatically from within the sqlite3_reset() or
sqlite3_finalize() call in order to reclaim any allocated resources, even
though the value is not required. In this case any error returned by the xFinal
implementation is silently discarded.

</p><h1 id="history"><span>6. </span>History</h1>

<p>Window function support was first added to SQLite with release
<a href="releaselog/3_25_0.html">version 3.25.0</a> (2018-09-15). The SQLite developers used
the <a href="http://www.postgresql.org">PostgreSQL</a> window function
documentation as their primary reference for how window functions
ought to behave.  Many test cases have been run against PostgreSQL
to ensure that window functions operate the same way in both
SQLite and PostgreSQL.

</p><p>In SQLite <a href="releaselog/3_28_0.html">version 3.28.0</a> (2019-04-16),
windows function support was extended to include the EXCLUDE clause,
GROUPS frame types, window chaining, and support for
"&lt;expr&gt; PRECEDING" and "&lt;expr&gt; FOLLOWING" boundaries
in RANGE frames.
</p><p align="center"><small><i>This page last modified on  <a href="https://sqlite.org/docsrc/honeypot" id="mtimelink"  data-href="https://sqlite.org/docsrc/finfo/pages/windowfunctions.in?m=9647771778">2023-12-05 14:43:20</a> UTC </small></i></p>
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