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<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN"
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<html xmlns="http://www.w3.org/1999/xhtml">
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<title>6.6. Mathematical Functions and Operators — Presto 0.204 Documentation</title>
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<div class="header">
<h1 class="heading"><a href="../index.html">
<span>Presto 0.204 Documentation</span></a></h1>
<h2 class="heading"><span>6.6. Mathematical Functions and Operators</span></h2>
</div>
<div class="topnav">
<p class="nav">
<span class="left">
« <a href="conversion.html">6.5. Conversion Functions</a>
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<div class="content">
<div class="section" id="mathematical-functions-and-operators">
<h1>6.6. Mathematical Functions and Operators</h1>
<div class="section" id="mathematical-operators">
<h2>Mathematical Operators</h2>
<table border="1" class="docutils">
<colgroup>
<col width="15%" />
<col width="85%" />
</colgroup>
<thead valign="bottom">
<tr class="row-odd"><th class="head">Operator</th>
<th class="head">Description</th>
</tr>
</thead>
<tbody valign="top">
<tr class="row-even"><td><code class="docutils literal"><span class="pre">+</span></code></td>
<td>Addition</td>
</tr>
<tr class="row-odd"><td><code class="docutils literal"><span class="pre">-</span></code></td>
<td>Subtraction</td>
</tr>
<tr class="row-even"><td><code class="docutils literal"><span class="pre">*</span></code></td>
<td>Multiplication</td>
</tr>
<tr class="row-odd"><td><code class="docutils literal"><span class="pre">/</span></code></td>
<td>Division (integer division performs truncation)</td>
</tr>
<tr class="row-even"><td><code class="docutils literal"><span class="pre">%</span></code></td>
<td>Modulus (remainder)</td>
</tr>
</tbody>
</table>
</div>
<div class="section" id="mathematical-functions">
<h2>Mathematical Functions</h2>
<dl class="function">
<dt id="abs">
<code class="descname">abs</code><span class="sig-paren">(</span><em>x</em><span class="sig-paren">)</span> → [same as input]</dt>
<dd><p>Returns the absolute value of <code class="docutils literal"><span class="pre">x</span></code>.</p>
</dd></dl>
<dl class="function">
<dt id="cbrt">
<code class="descname">cbrt</code><span class="sig-paren">(</span><em>x</em><span class="sig-paren">)</span> → double</dt>
<dd><p>Returns the cube root of <code class="docutils literal"><span class="pre">x</span></code>.</p>
</dd></dl>
<dl class="function">
<dt id="ceil">
<code class="descname">ceil</code><span class="sig-paren">(</span><em>x</em><span class="sig-paren">)</span> → [same as input]</dt>
<dd><p>This is an alias for <a class="reference internal" href="#ceiling" title="ceiling"><code class="xref py py-func docutils literal"><span class="pre">ceiling()</span></code></a>.</p>
</dd></dl>
<dl class="function">
<dt id="ceiling">
<code class="descname">ceiling</code><span class="sig-paren">(</span><em>x</em><span class="sig-paren">)</span> → [same as input]</dt>
<dd><p>Returns <code class="docutils literal"><span class="pre">x</span></code> rounded up to the nearest integer.</p>
</dd></dl>
<dl class="function">
<dt id="cosine_similarity">
<code class="descname">cosine_similarity</code><span class="sig-paren">(</span><em>x</em>, <em>y</em><span class="sig-paren">)</span> → double</dt>
<dd><p>Returns the cosine similarity between the sparse vectors <code class="docutils literal"><span class="pre">x</span></code> and <code class="docutils literal"><span class="pre">y</span></code>:</p>
<div class="highlight-sql"><div class="highlight"><pre><span></span><span class="k">SELECT</span> <span class="n">cosine_similarity</span><span class="p">(</span><span class="k">MAP</span><span class="p">(</span><span class="nb">ARRAY</span><span class="p">[</span><span class="s1">'a'</span><span class="p">],</span> <span class="nb">ARRAY</span><span class="p">[</span><span class="mi">1</span><span class="p">.</span><span class="mi">0</span><span class="p">]),</span> <span class="k">MAP</span><span class="p">(</span><span class="nb">ARRAY</span><span class="p">[</span><span class="s1">'a'</span><span class="p">],</span> <span class="nb">ARRAY</span><span class="p">[</span><span class="mi">2</span><span class="p">.</span><span class="mi">0</span><span class="p">]));</span> <span class="c1">-- 1.0</span>
</pre></div>
</div>
</dd></dl>
<dl class="function">
<dt id="degrees">
<code class="descname">degrees</code><span class="sig-paren">(</span><em>x</em><span class="sig-paren">)</span> → double</dt>
<dd><p>Converts angle <code class="docutils literal"><span class="pre">x</span></code> in radians to degrees.</p>
</dd></dl>
<dl class="function">
<dt id="e">
<code class="descname">e</code><span class="sig-paren">(</span><span class="sig-paren">)</span> → double</dt>
<dd><p>Returns the constant Euler’s number.</p>
</dd></dl>
<dl class="function">
<dt id="exp">
<code class="descname">exp</code><span class="sig-paren">(</span><em>x</em><span class="sig-paren">)</span> → double</dt>
<dd><p>Returns Euler’s number raised to the power of <code class="docutils literal"><span class="pre">x</span></code>.</p>
</dd></dl>
<dl class="function">
<dt id="floor">
<code class="descname">floor</code><span class="sig-paren">(</span><em>x</em><span class="sig-paren">)</span> → [same as input]</dt>
<dd><p>Returns <code class="docutils literal"><span class="pre">x</span></code> rounded down to the nearest integer.</p>
</dd></dl>
<dl class="function">
<dt id="from_base">
<code class="descname">from_base</code><span class="sig-paren">(</span><em>string</em>, <em>radix</em><span class="sig-paren">)</span> → bigint</dt>
<dd><p>Returns the value of <code class="docutils literal"><span class="pre">string</span></code> interpreted as a base-<code class="docutils literal"><span class="pre">radix</span></code> number.</p>
</dd></dl>
<dl class="function">
<dt id="inverse_normal_cdf">
<code class="descname">inverse_normal_cdf</code><span class="sig-paren">(</span><em>mean</em>, <em>sd</em>, <em>p</em><span class="sig-paren">)</span> → double</dt>
<dd><p>Compute the inverse of the Normal cdf with given mean and standard
deviation (sd) for the cumulative probability (p): P(N < n). The mean must be
a real value and the standard deviation must be a real and positive value.
The probability p must lie on the interval (0, 1).</p>
</dd></dl>
<dl class="function">
<dt id="normal_cdf">
<code class="descname">normal_cdf</code><span class="sig-paren">(</span><em>mean</em>, <em>sd</em>, <em>v</em><span class="sig-paren">)</span> → double</dt>
<dd><p>Compute the Normal cdf with given mean and standard deviation (sd): P(N < v; mean, sd).
The mean and value v must be real values and the standard deviation must be a real
and positive value.</p>
</dd></dl>
<dl class="function">
<dt id="ln">
<code class="descname">ln</code><span class="sig-paren">(</span><em>x</em><span class="sig-paren">)</span> → double</dt>
<dd><p>Returns the natural logarithm of <code class="docutils literal"><span class="pre">x</span></code>.</p>
</dd></dl>
<dl class="function">
<dt id="log2">
<code class="descname">log2</code><span class="sig-paren">(</span><em>x</em><span class="sig-paren">)</span> → double</dt>
<dd><p>Returns the base 2 logarithm of <code class="docutils literal"><span class="pre">x</span></code>.</p>
</dd></dl>
<dl class="function">
<dt id="log10">
<code class="descname">log10</code><span class="sig-paren">(</span><em>x</em><span class="sig-paren">)</span> → double</dt>
<dd><p>Returns the base 10 logarithm of <code class="docutils literal"><span class="pre">x</span></code>.</p>
</dd></dl>
<dl class="function">
<dt id="mod">
<code class="descname">mod</code><span class="sig-paren">(</span><em>n</em>, <em>m</em><span class="sig-paren">)</span> → [same as input]</dt>
<dd><p>Returns the modulus (remainder) of <code class="docutils literal"><span class="pre">n</span></code> divided by <code class="docutils literal"><span class="pre">m</span></code>.</p>
</dd></dl>
<dl class="function">
<dt id="pi">
<code class="descname">pi</code><span class="sig-paren">(</span><span class="sig-paren">)</span> → double</dt>
<dd><p>Returns the constant Pi.</p>
</dd></dl>
<dl class="function">
<dt id="pow">
<code class="descname">pow</code><span class="sig-paren">(</span><em>x</em>, <em>p</em><span class="sig-paren">)</span> → double</dt>
<dd><p>This is an alias for <a class="reference internal" href="#power" title="power"><code class="xref py py-func docutils literal"><span class="pre">power()</span></code></a>.</p>
</dd></dl>
<dl class="function">
<dt id="power">
<code class="descname">power</code><span class="sig-paren">(</span><em>x</em>, <em>p</em><span class="sig-paren">)</span> → double</dt>
<dd><p>Returns <code class="docutils literal"><span class="pre">x</span></code> raised to the power of <code class="docutils literal"><span class="pre">p</span></code>.</p>
</dd></dl>
<dl class="function">
<dt id="radians">
<code class="descname">radians</code><span class="sig-paren">(</span><em>x</em><span class="sig-paren">)</span> → double</dt>
<dd><p>Converts angle <code class="docutils literal"><span class="pre">x</span></code> in degrees to radians.</p>
</dd></dl>
<dl class="function">
<dt id="rand">
<code class="descname">rand</code><span class="sig-paren">(</span><span class="sig-paren">)</span> → double</dt>
<dd><p>This is an alias for <a class="reference internal" href="#random" title="random"><code class="xref py py-func docutils literal"><span class="pre">random()</span></code></a>.</p>
</dd></dl>
<dl class="function">
<dt id="random">
<code class="descname">random</code><span class="sig-paren">(</span><span class="sig-paren">)</span> → double</dt>
<dd><p>Returns a pseudo-random value in the range 0.0 <= x < 1.0.</p>
</dd></dl>
<dl class="function">
<dt>
<code class="descname">random</code><span class="sig-paren">(</span><em>n</em><span class="sig-paren">)</span> → [same as input]</dt>
<dd><p>Returns a pseudo-random number between 0 and n (exclusive).</p>
</dd></dl>
<dl class="function">
<dt id="round">
<code class="descname">round</code><span class="sig-paren">(</span><em>x</em><span class="sig-paren">)</span> → [same as input]</dt>
<dd><p>Returns <code class="docutils literal"><span class="pre">x</span></code> rounded to the nearest integer.</p>
</dd></dl>
<dl class="function">
<dt>
<code class="descname">round</code><span class="sig-paren">(</span><em>x</em>, <em>d</em><span class="sig-paren">)</span> → [same as input]</dt>
<dd><p>Returns <code class="docutils literal"><span class="pre">x</span></code> rounded to <code class="docutils literal"><span class="pre">d</span></code> decimal places.</p>
</dd></dl>
<dl class="function">
<dt id="sign">
<code class="descname">sign</code><span class="sig-paren">(</span><em>x</em><span class="sig-paren">)</span> → [same as input]</dt>
<dd><p>Returns the signum function of <code class="docutils literal"><span class="pre">x</span></code>, that is:</p>
<ul class="simple">
<li>0 if the argument is 0,</li>
<li>1 if the argument is greater than 0,</li>
<li>-1 if the argument is less than 0.</li>
</ul>
<p>For double arguments, the function additionally returns:</p>
<ul class="simple">
<li>NaN if the argument is NaN,</li>
<li>1 if the argument is +Infinity,</li>
<li>-1 if the argument is -Infinity.</li>
</ul>
</dd></dl>
<dl class="function">
<dt id="sqrt">
<code class="descname">sqrt</code><span class="sig-paren">(</span><em>x</em><span class="sig-paren">)</span> → double</dt>
<dd><p>Returns the square root of <code class="docutils literal"><span class="pre">x</span></code>.</p>
</dd></dl>
<dl class="function">
<dt id="to_base">
<code class="descname">to_base</code><span class="sig-paren">(</span><em>x</em>, <em>radix</em><span class="sig-paren">)</span> → varchar</dt>
<dd><p>Returns the base-<code class="docutils literal"><span class="pre">radix</span></code> representation of <code class="docutils literal"><span class="pre">x</span></code>.</p>
</dd></dl>
<dl class="function">
<dt id="truncate">
<code class="descname">truncate</code><span class="sig-paren">(</span><em>x</em><span class="sig-paren">)</span> → double</dt>
<dd><p>Returns <code class="docutils literal"><span class="pre">x</span></code> rounded to integer by dropping digits after decimal point.</p>
</dd></dl>
<dl class="function">
<dt id="width_bucket">
<code class="descname">width_bucket</code><span class="sig-paren">(</span><em>x</em>, <em>bound1</em>, <em>bound2</em>, <em>n</em><span class="sig-paren">)</span> → bigint</dt>
<dd><p>Returns the bin number of <code class="docutils literal"><span class="pre">x</span></code> in an equi-width histogram with the
specified <code class="docutils literal"><span class="pre">bound1</span></code> and <code class="docutils literal"><span class="pre">bound2</span></code> bounds and <code class="docutils literal"><span class="pre">n</span></code> number of buckets.</p>
</dd></dl>
<dl class="function">
<dt>
<code class="descname">width_bucket</code><span class="sig-paren">(</span><em>x</em>, <em>bins</em><span class="sig-paren">)</span> → bigint</dt>
<dd><p>Returns the bin number of <code class="docutils literal"><span class="pre">x</span></code> according to the bins specified by the
array <code class="docutils literal"><span class="pre">bins</span></code>. The <code class="docutils literal"><span class="pre">bins</span></code> parameter must be an array of doubles and is
assumed to be in sorted ascending order.</p>
</dd></dl>
</div>
<div class="section" id="statistical-functions">
<h2>Statistical Functions</h2>
<dl class="function">
<dt id="wilson_interval_lower">
<code class="descname">wilson_interval_lower</code><span class="sig-paren">(</span><em>successes</em>, <em>trials</em>, <em>z</em><span class="sig-paren">)</span> → double</dt>
<dd><p>Returns the lower bound of the Wilson score interval of a Bernoulli trial process
at a confidence specified by the z-score <code class="docutils literal"><span class="pre">z</span></code>.</p>
</dd></dl>
<dl class="function">
<dt id="wilson_interval_upper">
<code class="descname">wilson_interval_upper</code><span class="sig-paren">(</span><em>successes</em>, <em>trials</em>, <em>z</em><span class="sig-paren">)</span> → double</dt>
<dd><p>Returns the upper bound of the Wilson score interval of a Bernoulli trial process
at a confidence specified by the z-score <code class="docutils literal"><span class="pre">z</span></code>.</p>
</dd></dl>
</div>
<div class="section" id="trigonometric-functions">
<h2>Trigonometric Functions</h2>
<p>All trigonometric function arguments are expressed in radians.
See unit conversion functions <a class="reference internal" href="#degrees" title="degrees"><code class="xref py py-func docutils literal"><span class="pre">degrees()</span></code></a> and <a class="reference internal" href="#radians" title="radians"><code class="xref py py-func docutils literal"><span class="pre">radians()</span></code></a>.</p>
<dl class="function">
<dt id="acos">
<code class="descname">acos</code><span class="sig-paren">(</span><em>x</em><span class="sig-paren">)</span> → double</dt>
<dd><p>Returns the arc cosine of <code class="docutils literal"><span class="pre">x</span></code>.</p>
</dd></dl>
<dl class="function">
<dt id="asin">
<code class="descname">asin</code><span class="sig-paren">(</span><em>x</em><span class="sig-paren">)</span> → double</dt>
<dd><p>Returns the arc sine of <code class="docutils literal"><span class="pre">x</span></code>.</p>
</dd></dl>
<dl class="function">
<dt id="atan">
<code class="descname">atan</code><span class="sig-paren">(</span><em>x</em><span class="sig-paren">)</span> → double</dt>
<dd><p>Returns the arc tangent of <code class="docutils literal"><span class="pre">x</span></code>.</p>
</dd></dl>
<dl class="function">
<dt id="atan2">
<code class="descname">atan2</code><span class="sig-paren">(</span><em>y</em>, <em>x</em><span class="sig-paren">)</span> → double</dt>
<dd><p>Returns the arc tangent of <code class="docutils literal"><span class="pre">y</span> <span class="pre">/</span> <span class="pre">x</span></code>.</p>
</dd></dl>
<dl class="function">
<dt id="cos">
<code class="descname">cos</code><span class="sig-paren">(</span><em>x</em><span class="sig-paren">)</span> → double</dt>
<dd><p>Returns the cosine of <code class="docutils literal"><span class="pre">x</span></code>.</p>
</dd></dl>
<dl class="function">
<dt id="cosh">
<code class="descname">cosh</code><span class="sig-paren">(</span><em>x</em><span class="sig-paren">)</span> → double</dt>
<dd><p>Returns the hyperbolic cosine of <code class="docutils literal"><span class="pre">x</span></code>.</p>
</dd></dl>
<dl class="function">
<dt id="sin">
<code class="descname">sin</code><span class="sig-paren">(</span><em>x</em><span class="sig-paren">)</span> → double</dt>
<dd><p>Returns the sine of <code class="docutils literal"><span class="pre">x</span></code>.</p>
</dd></dl>
<dl class="function">
<dt id="tan">
<code class="descname">tan</code><span class="sig-paren">(</span><em>x</em><span class="sig-paren">)</span> → double</dt>
<dd><p>Returns the tangent of <code class="docutils literal"><span class="pre">x</span></code>.</p>
</dd></dl>
<dl class="function">
<dt id="tanh">
<code class="descname">tanh</code><span class="sig-paren">(</span><em>x</em><span class="sig-paren">)</span> → double</dt>
<dd><p>Returns the hyperbolic tangent of <code class="docutils literal"><span class="pre">x</span></code>.</p>
</dd></dl>
</div>
<div class="section" id="floating-point-functions">
<h2>Floating Point Functions</h2>
<dl class="function">
<dt id="infinity">
<code class="descname">infinity</code><span class="sig-paren">(</span><span class="sig-paren">)</span> → double</dt>
<dd><p>Returns the constant representing positive infinity.</p>
</dd></dl>
<dl class="function">
<dt id="is_finite">
<code class="descname">is_finite</code><span class="sig-paren">(</span><em>x</em><span class="sig-paren">)</span> → boolean</dt>
<dd><p>Determine if <code class="docutils literal"><span class="pre">x</span></code> is finite.</p>
</dd></dl>
<dl class="function">
<dt id="is_infinite">
<code class="descname">is_infinite</code><span class="sig-paren">(</span><em>x</em><span class="sig-paren">)</span> → boolean</dt>
<dd><p>Determine if <code class="docutils literal"><span class="pre">x</span></code> is infinite.</p>
</dd></dl>
<dl class="function">
<dt id="is_nan">
<code class="descname">is_nan</code><span class="sig-paren">(</span><em>x</em><span class="sig-paren">)</span> → boolean</dt>
<dd><p>Determine if <code class="docutils literal"><span class="pre">x</span></code> is not-a-number.</p>
</dd></dl>
<dl class="function">
<dt id="nan">
<code class="descname">nan</code><span class="sig-paren">(</span><span class="sig-paren">)</span> → double</dt>
<dd><p>Returns the constant representing not-a-number.</p>
</dd></dl>
</div>
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