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<a id="polynomial"></a>
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<a id="IndexPolynomial" class="indexterm"></a>
<div class="refnamediv">
<h2>
<span class="refentrytitle">polynomial</span>
</h2>
<p>polynomial —
Efficiently evaluates a polynomial of arbitrary order.
</p>
</div>
<div class="refsect1">
<a id="idm281472902888424"></a>
<h2>Description</h2>
<p>
The <span class="emphasis"><em>polynomial</em></span> opcode calculates a polynomial with a single a-rate input variable. The polynomial is a sum of any number of terms in the form <span class="emphasis"><em>kn*x^n</em></span> where <span class="emphasis"><em>kn</em></span> is the nth coefficient of the expression. These coefficients are k-rate values.
</p>
</div>
<div class="refsect1">
<a id="idm281472902814200"></a>
<h2>Syntax</h2>
<pre class="synopsis">aout <span class="command"><strong>polynomial</strong></span> ain, k0 [, k1 [, k2 [...]]]</pre>
</div>
<div class="refsect1">
<a id="idm281472902811976"></a>
<h2>Performance</h2>
<p>
<span class="emphasis"><em>ain</em></span> -- the input signal used as the independent variable of the polynomial ("x").
</p>
<p>
<span class="emphasis"><em>aout</em></span> -- the output signal ("y").
</p>
<p>
<span class="emphasis"><em>k0, k1, k2, ...</em></span> -- the coefficients for each term of the polynomial.
</p>
<p>
If we consider the input parameter <span class="emphasis"><em>ain</em></span> to be "x" and the output <span class="emphasis"><em>aout</em></span> to be "y", then the <span class="emphasis"><em>polynomial</em></span> opcode calculates the following equation:
</p>
<div class="literallayout">
<p><br />
y = k0 + k1*x + k2*x^2 + k3*x^3 + ...<br />
</p>
</div>
<p>
</p>
</div>
<div class="refsect1">
<a id="idm281472902805784"></a>
<h2>Examples</h2>
<p>
Here is an example of the polynomial opcode. It uses the file <a class="ulink" href="examples/polynomial.csd" target="_top"><em class="citetitle">polynomial.csd</em></a>.
</p>
<div class="example">
<a id="idm281472902803928"></a>
<p class="title">
<strong>Example 705. Example of the polynomial opcode.</strong>
</p>
<div class="example-contents">
<p>See the sections <a class="link" href="UsingRealTime.html" title="Real-Time Audio"><em class="citetitle">Real-time Audio</em></a> and <a class="link" href="CommandFlags.html" title="Csound command line"><em class="citetitle">Command Line Flags</em></a> for more information on using command line flags.</p>
<div class="refsect1">
<a id="idm281472723981800"></a>
<pre class="programlisting">
<span class="nt"><CsoundSynthesizer></span>
<span class="nt"><CsOptions></span>
<span class="c1">; Select audio/midi flags here according to platform</span>
-odac <span class="c1">;;;realtime audio</span>
<span class="c1">;-iadc ;;;uncomment -iadc if realtime audio input is needed too</span>
<span class="c1">; For Non-realtime ouput leave only the line below:</span>
<span class="c1">; -o polynomial.wav -W ;;; for file output any platform</span>
<span class="nt"></CsOptions></span>
<span class="nt"><CsInstruments></span>
<span class="vg">sr</span> <span class="o">=</span> <span class="mi">44100</span>
<span class="vg">ksmps</span> <span class="o">=</span> <span class="mi">32</span>
<span class="vg">nchnls</span> <span class="o">=</span> <span class="mi">2</span>
<span class="vg">0dbfs</span> <span class="o">=</span> <span class="mi">1</span>
<span class="c1">; The polynomial y=x^n where n is odd always produces a curve</span>
<span class="c1">; that traverses the range [-1, 1] when the input is within</span>
<span class="c1">; the same range. Therefore, we can use one of these curves</span>
<span class="c1">; to make a nonlinear phasor that repeatedly reads a table </span>
<span class="c1">; from beginning to end like a linear phasor (maintaining </span>
<span class="c1">; continuity) but that distorts the waveform in the table.</span>
<span class="kd">instr</span> <span class="nf">4</span> <span class="c1">; This instrument demonstrates phase distortion with x^3</span>
i<span class="n">dur</span> <span class="o">=</span> <span class="nb">p3</span>
i<span class="n">amp</span> <span class="o">=</span> <span class="nb">p4</span>
i<span class="n">freq</span> <span class="o">=</span> <span class="nb">p5</span>
i<span class="n">table</span> <span class="o">=</span> <span class="nb">p6</span>
a<span class="n">env</span> <span class="nb">linseg</span> <span class="mi">0</span><span class="p">,</span> <span class="mf">.001</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">,</span> i<span class="n">dur</span> <span class="o">-</span> <span class="mf">.051</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">,</span> <span class="mf">.05</span><span class="p">,</span> <span class="mi">0</span> <span class="c1">; declicking envelope</span>
a<span class="n">osc</span> <span class="nb">phasor</span> i<span class="n">freq</span> <span class="c1">; create a linear phasor</span>
a<span class="n">pd</span> <span class="nb">polynomial</span> a<span class="n">osc</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">1</span> <span class="c1">; distort the phasor with x^3</span>
a<span class="n">out</span> <span class="nb">tablei</span> a<span class="n">pd</span><span class="p">,</span> i<span class="n">table</span><span class="p">,</span> <span class="mi">1</span> <span class="c1">; read a sine table with the nonlinear phasor</span>
<span class="nb">outs</span> a<span class="n">env</span><span class="o">*</span>a<span class="n">out</span><span class="o">*</span>i<span class="n">amp</span><span class="p">,</span> a<span class="n">env</span><span class="o">*</span>a<span class="n">out</span><span class="o">*</span>i<span class="n">amp</span>
<span class="kd">endin</span>
<span class="kd">instr</span> <span class="nf">5</span> <span class="c1">; This instrument demonstrates phase distortion with x^11</span>
i<span class="n">dur</span> <span class="o">=</span> <span class="nb">p3</span>
i<span class="n">amp</span> <span class="o">=</span> <span class="nb">p4</span>
i<span class="n">freq</span> <span class="o">=</span> <span class="nb">p5</span>
i<span class="n">table</span> <span class="o">=</span> <span class="nb">p6</span>
a<span class="n">env</span> <span class="nb">linseg</span> <span class="mi">0</span><span class="p">,</span> <span class="mf">.001</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">,</span> i<span class="n">dur</span> <span class="o">-</span> <span class="mf">.051</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">,</span> <span class="mf">.05</span><span class="p">,</span> <span class="mi">0</span> <span class="c1">; declicking envelope</span>
a<span class="n">osc</span> <span class="nb">phasor</span> i<span class="n">freq</span> <span class="c1">; create a linear phasor</span>
a<span class="n">pd</span> <span class="nb">polynomial</span> a<span class="n">osc</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">1</span> <span class="c1">; distort the phasor with x^11</span>
a<span class="n">out</span> <span class="nb">tablei</span> a<span class="n">pd</span><span class="p">,</span> i<span class="n">table</span><span class="p">,</span> <span class="mi">1</span> <span class="c1">; read a sine table with the nonlinear phasor</span>
<span class="nb">outs</span> a<span class="n">env</span><span class="o">*</span>a<span class="n">out</span><span class="o">*</span>i<span class="n">amp</span><span class="p">,</span> a<span class="n">env</span><span class="o">*</span>a<span class="n">out</span><span class="o">*</span>i<span class="n">amp</span>
<span class="kd">endin</span>
<span class="kd">instr</span> <span class="nf">6</span> <span class="c1">; This instrument crossfades between a pure sine and one distorted with x^11</span>
i<span class="n">dur</span> <span class="o">=</span> <span class="nb">p3</span>
i<span class="n">amp</span> <span class="o">=</span> <span class="nb">p4</span>
i<span class="n">freq</span> <span class="o">=</span> <span class="nb">p5</span>
i<span class="n">table</span> <span class="o">=</span> <span class="nb">p6</span>
a<span class="n">env</span> <span class="nb">linseg</span> <span class="mi">0</span><span class="p">,</span> <span class="mf">.001</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">,</span> i<span class="n">dur</span> <span class="o">-</span> <span class="mf">.051</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">,</span> <span class="mf">.05</span><span class="p">,</span> <span class="mi">0</span> <span class="c1">; declicking envelope</span>
a<span class="n">osc</span> <span class="nb">phasor</span> i<span class="n">freq</span> <span class="c1">; create a linear phasor</span>
a<span class="n">out3</span> <span class="nb">tablei</span> a<span class="n">osc</span><span class="p">,</span> i<span class="n">table</span><span class="p">,</span> <span class="mi">1</span> <span class="c1">; read a sine table without the linear phasor</span>
a<span class="n">pd11</span> <span class="nb">polynomial</span> a<span class="n">osc</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">1</span> <span class="c1">; distort the phasor with x^11</span>
a<span class="n">out11</span> <span class="nb">tablei</span> a<span class="n">pd11</span><span class="p">,</span> i<span class="n">table</span><span class="p">,</span> <span class="mi">1</span> <span class="c1">; read a sine table with the nonlinear phasor</span>
k<span class="n">amount</span> <span class="nb">linseg</span> <span class="mf">1.0</span><span class="p">,</span> <span class="mf">0.05</span><span class="p">,</span> <span class="mf">0.9</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">,</span> <span class="mf">0.0</span> <span class="c1">; crossfade between two outputs</span>
a<span class="n">out</span> <span class="o">=</span> a<span class="n">out3</span><span class="o">*</span>k<span class="n">amount</span> <span class="o">+</span> a<span class="n">out11</span><span class="o">*</span><span class="p">(</span><span class="mf">1.0</span> <span class="o">-</span> k<span class="n">amount</span><span class="p">)</span>
<span class="nb">outs</span> a<span class="n">env</span><span class="o">*</span>a<span class="n">out</span><span class="o">*</span>i<span class="n">amp</span><span class="p">,</span> a<span class="n">env</span><span class="o">*</span>a<span class="n">out</span><span class="o">*</span>i<span class="n">amp</span>
<span class="kd">endin</span>
<span class="nt"></CsInstruments></span>
<span class="nt"><CsScore></span>
<span class="nb">f</span><span class="mi">1</span> <span class="mi">0</span> <span class="mi">16385</span> <span class="mi">10</span> <span class="mi">1</span> <span class="c1">; sine wave</span>
<span class="c1">; descending "just blues" scale</span>
<span class="nb">t</span> <span class="mi">0</span> <span class="mi">100</span>
<span class="nb">i</span><span class="mi">4</span> <span class="mi">0</span> <span class="mf">.333</span> <span class="mf">.7</span> <span class="mi">512</span> <span class="mi">1</span>
<span class="nb">i</span><span class="o">.</span> <span class="o">+</span> <span class="o">.</span> <span class="o">.</span> <span class="mi">448</span>
<span class="nb">i</span><span class="o">.</span> <span class="o">+</span> <span class="o">.</span> <span class="o">.</span> <span class="mi">384</span>
<span class="nb">i</span><span class="o">.</span> <span class="o">+</span> <span class="o">.</span> <span class="o">.</span> <span class="mi">360</span>
<span class="nb">i</span><span class="o">.</span> <span class="o">+</span> <span class="o">.</span> <span class="o">.</span> <span class="mf">341.33</span>
<span class="nb">i</span><span class="o">.</span> <span class="o">+</span> <span class="o">.</span> <span class="o">.</span> <span class="mf">298.67</span>
<span class="nb">i</span><span class="o">.</span> <span class="o">+</span> <span class="mi">2</span> <span class="o">.</span> <span class="mi">256</span>
<span class="nb">s</span>
<span class="nb">t</span> <span class="mi">0</span> <span class="mi">100</span>
<span class="nb">i</span><span class="mi">5</span> <span class="mi">0</span> <span class="mf">.333</span> <span class="mf">.7</span> <span class="mi">512</span> <span class="mi">1</span>
<span class="nb">i</span><span class="o">.</span> <span class="o">+</span> <span class="o">.</span> <span class="o">.</span> <span class="mi">448</span>
<span class="nb">i</span><span class="o">.</span> <span class="o">+</span> <span class="o">.</span> <span class="o">.</span> <span class="mi">384</span>
<span class="nb">i</span><span class="o">.</span> <span class="o">+</span> <span class="o">.</span> <span class="o">.</span> <span class="mi">360</span>
<span class="nb">i</span><span class="o">.</span> <span class="o">+</span> <span class="o">.</span> <span class="o">.</span> <span class="mf">341.33</span>
<span class="nb">i</span><span class="o">.</span> <span class="o">+</span> <span class="o">.</span> <span class="o">.</span> <span class="mf">298.67</span>
<span class="nb">i</span><span class="o">.</span> <span class="o">+</span> <span class="mi">2</span> <span class="o">.</span> <span class="mi">256</span>
<span class="nb">s</span>
<span class="nb">t</span> <span class="mi">0</span> <span class="mi">100</span>
<span class="nb">i</span><span class="mi">6</span> <span class="mi">0</span> <span class="mf">.333</span> <span class="mf">.7</span> <span class="mi">512</span> <span class="mi">1</span>
<span class="nb">i</span><span class="o">.</span> <span class="o">+</span> <span class="o">.</span> <span class="o">.</span> <span class="mi">448</span>
<span class="nb">i</span><span class="o">.</span> <span class="o">+</span> <span class="o">.</span> <span class="o">.</span> <span class="mi">384</span>
<span class="nb">i</span><span class="o">.</span> <span class="o">+</span> <span class="o">.</span> <span class="o">.</span> <span class="mi">360</span>
<span class="nb">i</span><span class="o">.</span> <span class="o">+</span> <span class="o">.</span> <span class="o">.</span> <span class="mf">341.33</span>
<span class="nb">i</span><span class="o">.</span> <span class="o">+</span> <span class="o">.</span> <span class="o">.</span> <span class="mf">298.67</span>
<span class="nb">i</span><span class="o">.</span> <span class="o">+</span> <span class="mi">2</span> <span class="o">.</span> <span class="mi">256</span>
<span class="nb">e</span>
<span class="nt"></CsScore></span>
<span class="nt"></CsoundSynthesizer></span>
</pre>
</div>
</div>
</div>
<p><br class="example-break" />
</p>
</div>
<div class="refsect1">
<a id="idm281472902799640"></a>
<h2>See Also</h2>
<p>
<a class="link" href="chebyshevpoly.html" title="chebyshevpoly"><em class="citetitle">chebyshevpoly</em></a>,
<a class="link" href="mac.html" title="mac"><em class="citetitle">mac</em></a>
<a class="link" href="maca.html" title="maca"><em class="citetitle">maca</em></a>
</p>
</div>
<div class="refsect1">
<a id="idm281472902795768"></a>
<h2>Credits</h2>
<p>
</p>
<table border="0" summary="Simple list" class="simplelist">
<tr>
<td>Author: Anthony Kozar</td>
</tr>
<tr>
<td>January 2008</td>
</tr>
</table>
<p>
</p>
<p>New in Csound version 5.08</p>
</div>
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