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<title>9.3.Mathematical Functions and Operators</title>
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<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"><div class="sect1" lang="en">
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
<a name="functions-math"></a>9.3.Mathematical Functions and Operators</h2></div></div></div>
<p> Mathematical operators are provided for many
<span class="productname">PostgreSQL</span> types. For types without
common mathematical conventions for all possible permutations
(e.g., date/time types) we
describe the actual behavior in subsequent sections.
</p>
<p> <a href="functions-math.html#functions-math-op-table" title="Table9.2.Mathematical Operators">Table9.2, “Mathematical Operators”</a> shows the available mathematical operators.
</p>
<div class="table">
<a name="functions-math-op-table"></a><p class="title"><b>Table9.2.Mathematical Operators</b></p>
<div class="table-contents"><table summary="Mathematical Operators" border="1">
<colgroup>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>Operator</th>
<th>Description</th>
<th>Example</th>
<th>Result</th>
</tr></thead>
<tbody>
<tr>
<td> <code class="literal">+</code> </td>
<td>addition</td>
<td><code class="literal">2 + 3</code></td>
<td><code class="literal">5</code></td>
</tr>
<tr>
<td> <code class="literal">-</code> </td>
<td>subtraction</td>
<td><code class="literal">2 - 3</code></td>
<td><code class="literal">-1</code></td>
</tr>
<tr>
<td> <code class="literal">*</code> </td>
<td>multiplication</td>
<td><code class="literal">2 * 3</code></td>
<td><code class="literal">6</code></td>
</tr>
<tr>
<td> <code class="literal">/</code> </td>
<td>division (integer division truncates results)</td>
<td><code class="literal">4 / 2</code></td>
<td><code class="literal">2</code></td>
</tr>
<tr>
<td> <code class="literal">%</code> </td>
<td>modulo (remainder)</td>
<td><code class="literal">5 % 4</code></td>
<td><code class="literal">1</code></td>
</tr>
<tr>
<td> <code class="literal">^</code> </td>
<td>exponentiation</td>
<td><code class="literal">2.0 ^ 3.0</code></td>
<td><code class="literal">8</code></td>
</tr>
<tr>
<td> <code class="literal">|/</code> </td>
<td>square root</td>
<td><code class="literal">|/ 25.0</code></td>
<td><code class="literal">5</code></td>
</tr>
<tr>
<td> <code class="literal">||/</code> </td>
<td>cube root</td>
<td><code class="literal">||/ 27.0</code></td>
<td><code class="literal">3</code></td>
</tr>
<tr>
<td> <code class="literal">!</code> </td>
<td>factorial</td>
<td><code class="literal">5 !</code></td>
<td><code class="literal">120</code></td>
</tr>
<tr>
<td> <code class="literal">!!</code> </td>
<td>factorial (prefix operator)</td>
<td><code class="literal">!! 5</code></td>
<td><code class="literal">120</code></td>
</tr>
<tr>
<td> <code class="literal">@</code> </td>
<td>absolute value</td>
<td><code class="literal">@ -5.0</code></td>
<td><code class="literal">5</code></td>
</tr>
<tr>
<td> <code class="literal">&</code> </td>
<td>bitwise AND</td>
<td><code class="literal">91 & 15</code></td>
<td><code class="literal">11</code></td>
</tr>
<tr>
<td> <code class="literal">|</code> </td>
<td>bitwise OR</td>
<td><code class="literal">32 | 3</code></td>
<td><code class="literal">35</code></td>
</tr>
<tr>
<td> <code class="literal">#</code> </td>
<td>bitwise XOR</td>
<td><code class="literal">17 # 5</code></td>
<td><code class="literal">20</code></td>
</tr>
<tr>
<td> <code class="literal">~</code> </td>
<td>bitwise NOT</td>
<td><code class="literal">~1</code></td>
<td><code class="literal">-2</code></td>
</tr>
<tr>
<td> <code class="literal"><<</code> </td>
<td>bitwise shift left</td>
<td><code class="literal">1 << 4</code></td>
<td><code class="literal">16</code></td>
</tr>
<tr>
<td> <code class="literal">>></code> </td>
<td>bitwise shift right</td>
<td><code class="literal">8 >> 2</code></td>
<td><code class="literal">2</code></td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><p> The bitwise operators work only on integral data types, whereas
the others are available for all numeric data types. The bitwise
operators are also available for the bit
string types <code class="type">bit</code> and <code class="type">bit varying</code>, as
shown in <a href="functions-bitstring.html#functions-bit-string-op-table" title="Table9.10.Bit String Operators">Table9.10, “Bit String Operators”</a>.
</p>
<p> <a href="functions-math.html#functions-math-func-table" title="Table9.3.Mathematical Functions">Table9.3, “Mathematical Functions”</a> shows the available
mathematical functions. In the table, <code class="literal">dp</code>
indicates <code class="type">double precision</code>. Many of these functions
are provided in multiple forms with different argument types.
Except where noted, any given form of a function returns the same
data type as its argument.
The functions working with <code class="type">double precision</code> data are mostly
implemented on top of the host system's C library; accuracy and behavior in
boundary cases may therefore vary depending on the host system.
</p>
<a name="id595448"></a><a name="id595454"></a><a name="id595460"></a><a name="id595467"></a><a name="id595473"></a><a name="id595479"></a><a name="id595485"></a><a name="id595492"></a><a name="id595498"></a><a name="id595504"></a><a name="id595510"></a><a name="id595517"></a><a name="id595523"></a><a name="id595529"></a><a name="id595535"></a><a name="id595542"></a><a name="id595548"></a><a name="id595554"></a><a name="id595560"></a><div class="table">
<a name="functions-math-func-table"></a><p class="title"><b>Table9.3.Mathematical Functions</b></p>
<div class="table-contents"><table summary="Mathematical Functions" border="1">
<colgroup>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>Function</th>
<th>Return Type</th>
<th>Description</th>
<th>Example</th>
<th>Result</th>
</tr></thead>
<tbody>
<tr>
<td><code class="literal"><code class="function">abs</code>(<em class="replaceable"><code>x</code></em>)</code></td>
<td>(same as <em class="replaceable"><code>x</code></em>)</td>
<td>absolute value</td>
<td><code class="literal">abs(-17.4)</code></td>
<td><code class="literal">17.4</code></td>
</tr>
<tr>
<td><code class="literal"><code class="function">cbrt</code>(<code class="type">dp</code>)</code></td>
<td><code class="type">dp</code></td>
<td>cube root</td>
<td><code class="literal">cbrt(27.0)</code></td>
<td><code class="literal">3</code></td>
</tr>
<tr>
<td><code class="literal"><code class="function">ceil</code>(<code class="type">dp</code> or <code class="type">numeric</code>)</code></td>
<td>(same as input)</td>
<td>smallest integer not less than argument</td>
<td><code class="literal">ceil(-42.8)</code></td>
<td><code class="literal">-42</code></td>
</tr>
<tr>
<td><code class="literal"><code class="function">ceiling</code>(<code class="type">dp</code> or <code class="type">numeric</code>)</code></td>
<td>(same as input)</td>
<td>smallest integer not less than argument (alias for <code class="function">ceil</code>)</td>
<td><code class="literal">ceiling(-95.3)</code></td>
<td><code class="literal">-95</code></td>
</tr>
<tr>
<td><code class="literal"><code class="function">degrees</code>(<code class="type">dp</code>)</code></td>
<td><code class="type">dp</code></td>
<td>radians to degrees</td>
<td><code class="literal">degrees(0.5)</code></td>
<td><code class="literal">28.6478897565412</code></td>
</tr>
<tr>
<td><code class="literal"><code class="function">exp</code>(<code class="type">dp</code> or <code class="type">numeric</code>)</code></td>
<td>(same as input)</td>
<td>exponential</td>
<td><code class="literal">exp(1.0)</code></td>
<td><code class="literal">2.71828182845905</code></td>
</tr>
<tr>
<td><code class="literal"><code class="function">floor</code>(<code class="type">dp</code> or <code class="type">numeric</code>)</code></td>
<td>(same as input)</td>
<td>largest integer not greater than argument</td>
<td><code class="literal">floor(-42.8)</code></td>
<td><code class="literal">-43</code></td>
</tr>
<tr>
<td><code class="literal"><code class="function">ln</code>(<code class="type">dp</code> or <code class="type">numeric</code>)</code></td>
<td>(same as input)</td>
<td>natural logarithm</td>
<td><code class="literal">ln(2.0)</code></td>
<td><code class="literal">0.693147180559945</code></td>
</tr>
<tr>
<td><code class="literal"><code class="function">log</code>(<code class="type">dp</code> or <code class="type">numeric</code>)</code></td>
<td>(same as input)</td>
<td>base 10 logarithm</td>
<td><code class="literal">log(100.0)</code></td>
<td><code class="literal">2</code></td>
</tr>
<tr>
<td><code class="literal"><code class="function">log</code>(<em class="parameter"><code>b</code></em> <code class="type">numeric</code>,
<em class="parameter"><code>x</code></em> <code class="type">numeric</code>)</code></td>
<td><code class="type">numeric</code></td>
<td>logarithm to base <em class="parameter"><code>b</code></em>
</td>
<td><code class="literal">log(2.0, 64.0)</code></td>
<td><code class="literal">6.0000000000</code></td>
</tr>
<tr>
<td><code class="literal"><code class="function">mod</code>(<em class="parameter"><code>y</code></em>,
<em class="parameter"><code>x</code></em>)</code></td>
<td>(same as argument types)</td>
<td>remainder of <em class="parameter"><code>y</code></em>/<em class="parameter"><code>x</code></em>
</td>
<td><code class="literal">mod(9,4)</code></td>
<td><code class="literal">1</code></td>
</tr>
<tr>
<td><code class="literal"><code class="function">pi</code>()</code></td>
<td><code class="type">dp</code></td>
<td>“<span class="quote">[pi ]</span>” constant</td>
<td><code class="literal">pi()</code></td>
<td><code class="literal">3.14159265358979</code></td>
</tr>
<tr>
<td><code class="literal"><code class="function">power</code>(<em class="parameter"><code>a</code></em> <code class="type">dp</code>,
<em class="parameter"><code>b</code></em> <code class="type">dp</code>)</code></td>
<td><code class="type">dp</code></td>
<td>
<em class="parameter"><code>a</code></em> raised to the power of <em class="parameter"><code>b</code></em>
</td>
<td><code class="literal">power(9.0, 3.0)</code></td>
<td><code class="literal">729</code></td>
</tr>
<tr>
<td><code class="literal"><code class="function">power</code>(<em class="parameter"><code>a</code></em> <code class="type">numeric</code>,
<em class="parameter"><code>b</code></em> <code class="type">numeric</code>)</code></td>
<td><code class="type">numeric</code></td>
<td>
<em class="parameter"><code>a</code></em> raised to the power of <em class="parameter"><code>b</code></em>
</td>
<td><code class="literal">power(9.0, 3.0)</code></td>
<td><code class="literal">729</code></td>
</tr>
<tr>
<td><code class="literal"><code class="function">radians</code>(<code class="type">dp</code>)</code></td>
<td><code class="type">dp</code></td>
<td>degrees to radians</td>
<td><code class="literal">radians(45.0)</code></td>
<td><code class="literal">0.785398163397448</code></td>
</tr>
<tr>
<td><code class="literal"><code class="function">random</code>()</code></td>
<td><code class="type">dp</code></td>
<td>random value between 0.0 and 1.0</td>
<td><code class="literal">random()</code></td>
<td></td>
</tr>
<tr>
<td><code class="literal"><code class="function">round</code>(<code class="type">dp</code> or <code class="type">numeric</code>)</code></td>
<td>(same as input)</td>
<td>round to nearest integer</td>
<td><code class="literal">round(42.4)</code></td>
<td><code class="literal">42</code></td>
</tr>
<tr>
<td><code class="literal"><code class="function">round</code>(<em class="parameter"><code>v</code></em> <code class="type">numeric</code>, <em class="parameter"><code>s</code></em> <code class="type">int</code>)</code></td>
<td><code class="type">numeric</code></td>
<td>round to <em class="parameter"><code>s</code></em> decimal places</td>
<td><code class="literal">round(42.4382, 2)</code></td>
<td><code class="literal">42.44</code></td>
</tr>
<tr>
<td><code class="literal"><code class="function">setseed</code>(<code class="type">dp</code>)</code></td>
<td><code class="type">int</code></td>
<td>set seed for subsequent <code class="literal">random()</code> calls</td>
<td><code class="literal">setseed(0.54823)</code></td>
<td><code class="literal">1177314959</code></td>
</tr>
<tr>
<td><code class="literal"><code class="function">sign</code>(<code class="type">dp</code> or <code class="type">numeric</code>)</code></td>
<td>(same as input)</td>
<td>sign of the argument (-1, 0, +1)</td>
<td><code class="literal">sign(-8.4)</code></td>
<td><code class="literal">-1</code></td>
</tr>
<tr>
<td><code class="literal"><code class="function">sqrt</code>(<code class="type">dp</code> or <code class="type">numeric</code>)</code></td>
<td>(same as input)</td>
<td>square root</td>
<td><code class="literal">sqrt(2.0)</code></td>
<td><code class="literal">1.4142135623731</code></td>
</tr>
<tr>
<td><code class="literal"><code class="function">trunc</code>(<code class="type">dp</code> or <code class="type">numeric</code>)</code></td>
<td>(same as input)</td>
<td>truncate toward zero</td>
<td><code class="literal">trunc(42.8)</code></td>
<td><code class="literal">42</code></td>
</tr>
<tr>
<td><code class="literal"><code class="function">trunc</code>(<em class="parameter"><code>v</code></em> <code class="type">numeric</code>, <em class="parameter"><code>s</code></em> <code class="type">int</code>)</code></td>
<td><code class="type">numeric</code></td>
<td>truncate to <em class="parameter"><code>s</code></em> decimal places</td>
<td><code class="literal">trunc(42.4382, 2)</code></td>
<td><code class="literal">42.43</code></td>
</tr>
<tr>
<td><code class="literal"><code class="function">width_bucket</code>(<em class="parameter"><code>op</code></em> <code class="type">numeric</code>, <em class="parameter"><code>b1</code></em> <code class="type">numeric</code>, <em class="parameter"><code>b2</code></em> <code class="type">numeric</code>, <em class="parameter"><code>count</code></em> <code class="type">int</code>)</code></td>
<td><code class="type">int</code></td>
<td>return the bucket to which <em class="parameter"><code>operand</code></em> would
be assigned in an equidepth histogram with <em class="parameter"><code>count</code></em>
buckets, an upper bound of <em class="parameter"><code>b1</code></em>, and a lower bound
of <em class="parameter"><code>b2</code></em>
</td>
<td><code class="literal">width_bucket(5.35, 0.024, 10.06, 5)</code></td>
<td><code class="literal">3</code></td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><p> Finally, <a href="functions-math.html#functions-math-trig-table" title="Table9.4.Trigonometric Functions">Table9.4, “Trigonometric Functions”</a> shows the
available trigonometric functions. All trigonometric functions
take arguments and return values of type <code class="type">double
precision</code>.
</p>
<a name="id596694"></a><a name="id596700"></a><a name="id596706"></a><a name="id596712"></a><a name="id596719"></a><a name="id596725"></a><a name="id596731"></a><a name="id596737"></a><div class="table">
<a name="functions-math-trig-table"></a><p class="title"><b>Table9.4.Trigonometric Functions</b></p>
<div class="table-contents"><table summary="Trigonometric Functions" border="1">
<colgroup>
<col>
<col>
</colgroup>
<thead><tr>
<th>Function</th>
<th>Description</th>
</tr></thead>
<tbody>
<tr>
<td><code class="literal"><code class="function">acos</code>(<em class="replaceable"><code>x</code></em>)</code></td>
<td>inverse cosine</td>
</tr>
<tr>
<td><code class="literal"><code class="function">asin</code>(<em class="replaceable"><code>x</code></em>)</code></td>
<td>inverse sine</td>
</tr>
<tr>
<td><code class="literal"><code class="function">atan</code>(<em class="replaceable"><code>x</code></em>)</code></td>
<td>inverse tangent</td>
</tr>
<tr>
<td><code class="literal"><code class="function">atan2</code>(<em class="replaceable"><code>x</code></em>,
<em class="replaceable"><code>y</code></em>)</code></td>
<td>inverse tangent of
<code class="literal"><em class="replaceable"><code>x</code></em>/<em class="replaceable"><code>y</code></em></code>
</td>
</tr>
<tr>
<td><code class="literal"><code class="function">cos</code>(<em class="replaceable"><code>x</code></em>)</code></td>
<td>cosine</td>
</tr>
<tr>
<td><code class="literal"><code class="function">cot</code>(<em class="replaceable"><code>x</code></em>)</code></td>
<td>cotangent</td>
</tr>
<tr>
<td><code class="literal"><code class="function">sin</code>(<em class="replaceable"><code>x</code></em>)</code></td>
<td>sine</td>
</tr>
<tr>
<td><code class="literal"><code class="function">tan</code>(<em class="replaceable"><code>x</code></em>)</code></td>
<td>tangent</td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break">
</div></body>
</html>
|
