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<div class="refentry" title="GEN03">
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<h2>
<span class="refentrytitle">GEN03</span>
</h2>
<p>GEN03 —
Generates a stored function table by evaluating a polynomial.
</p>
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<div class="refsect1" title="Description">
<a id="id3729240"></a>
<h2>Description</h2>
<p>
This subroutine generates a stored function table by evaluating a polynomial in x over a fixed interval and with specified coefficients.
</p>
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<div class="refsect1" title="Syntax">
<a id="id3729255"></a>
<h2>Syntax</h2>
<pre class="synopsis"><span class="command"><strong>f</strong></span> # time size 3 xval1 xval2 c0 c1 c2 ... cn</pre>
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<div class="refsect1" title="Initialization">
<a id="id3730093"></a>
<h2>Initialization</h2>
<p>
<span class="emphasis"><em>size </em></span> -- number of points in the table. Must be a power of 2 or a power-of-2 plus 1.
</p>
<p>
<span class="emphasis"><em>xval1, xval2 </em></span> -- left and right values of the x interval over which the polynomial is defined (<span class="emphasis"><em>xval1</em></span> < <span class="emphasis"><em>xval2</em></span>). These will produce the 1st stored value and the (power-of-2 plus l)th stored value respectively in the generated function table.
</p>
<p>
<span class="emphasis"><em>c0, c1, c2, ..., cn</em></span> -- coefficients of the nth-order polynomial
</p>
<p>
<span class="emphasis"><em>C<sub>0</sub></em></span> + <span class="emphasis"><em>C<sub>1</sub>x</em></span> +
<span class="emphasis"><em>C<sub>2</sub>x<sup>2</sup></em></span> + . . . +
<span class="emphasis"><em>C<sub>n</sub>x<sup>n</sup></em></span>
</p>
<p>
Coefficients may be positive or negative real numbers; a zero denotes a missing term in the polynomial. The coefficient list begins in p7, providing a current upper limit of 144 terms.
</p>
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<p>
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<p>
The defined segment [fn(<span class="emphasis"><em>xval1</em></span>), fn(<span class="emphasis"><em>xval2</em></span>)] is evenly distributed. Thus a 512-point table over the interval [-1,1] will have its origin at location 257 (at the start of the 2nd half). Provided the extended guard point is requested, both fn(-1) and fn(1) will exist in the table.
</p>
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<li class="listitem">
<p>
<span class="emphasis"><em>GEN03</em></span> is useful in conjunction with <a class="link" href="table.html" title="table"><em class="citetitle">table</em></a> or <a class="link" href="tablei.html" title="tablei"><em class="citetitle">tablei</em></a> for audio waveshaping (sound modification by non-linear distortion). Coefficients to produce a particular formant from a sinusoidal lookup index of known amplitude can be determined at preprocessing time using algorithms such as Chebyshev formulae. See also <a class="link" href="GEN13.html" title="GEN13"><em class="citetitle">GEN13</em></a>.
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<div class="refsect1" title="Examples">
<a id="id3730256"></a>
<h2>Examples</h2>
<p>
Here is a simple example of the GEN03 routine. It uses the files <a class="ulink" href="examples/gen03.csd" target="_top"><em class="citetitle">gen03.csd</em></a>. It fills a table with a 4th order polynomial function over the x-interval -1 to 1. The origin will be at the offset position 512. The function is post-normalized. Here is its diagram:
</p>
<div class="mediaobject">
<img src="images/gen03.png" alt="Diagram of the waveform generated by GEN03." />
<div class="caption">
<p>Diagram of the waveform generated by GEN03.</p>
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<p>
</p>
<div class="example">
<a id="id3730307"></a>
<p class="title">
<b>Example 735. A simple example of the GEN03 routine.</b>
</p>
<div class="example-contents">
<pre class="programlisting">
<span class="csdtag"><CsoundSynthesizer></span>
<span class="csdtag"><CsOptions></span>
<span class="comment">; Select audio/midi flags here according to platform</span>
<span class="comment">; Audio out Audio in</span>
-odac -iadc <span class="comment">;;;RT audio I/O</span>
<span class="comment">; For Non-realtime ouput leave only the line below:</span>
<span class="comment">; -o gen03.wav -W ;;; for file output any platform</span>
<span class="csdtag"></CsOptions></span>
<span class="csdtag"><CsInstruments></span>
<span class="comment">; Initialize the global variables.</span>
<span class="ohdr">sr</span> <span class="op">=</span> 44100
<span class="ohdr">kr</span> <span class="op">=</span> 4410
<span class="ohdr">ksmps</span> <span class="op">=</span> 10
<span class="ohdr">nchnls</span> <span class="op">=</span> 1
<span class="comment">; Instrument #1.</span>
<span class="oblock">instr</span> 1
<span class="comment">; Create an index over the length of our entire note.</span>
kcps <span class="opc">init</span> 1<span class="op">/</span>p3
kndx <span class="opc">phasor</span> kcps
<span class="comment">; Read Table #1 with our index.</span>
ifn <span class="op">=</span> 1
ixmode <span class="op">=</span> 1
kamp <span class="opc">table</span> kndx, ifn, ixmode
<span class="comment">; Create a sine wave, use the Table #1 values to control</span>
<span class="comment">; the amplitude.</span>
a1 <span class="opc">oscil</span> kamp<span class="op">*</span>30000, 440, 2
<span class="opc">out</span> a1
<span class="oblock">endin</span>
<span class="csdtag"></CsInstruments></span>
<span class="csdtag"><CsScore></span>
<span class="comment">; Table #1: a polynomial function (using GEN03).</span>
<span class="stamnt">f</span> 1 0 1025 3 -1 1 5 4 3 2 2 1
<span class="comment">; Table #2, a sine wave.</span>
<span class="stamnt">f</span> 2 0 16384 10 1
<span class="comment">; Play Instrument #1 for 2 seconds.</span>
<span class="stamnt">i</span> 1 0 2
<span class="stamnt">e</span>
<span class="csdtag"></CsScore></span>
<span class="csdtag"></CsoundSynthesizer></span>
</pre>
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<p><br class="example-break" />
</p>
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<div class="refsect1" title="See Also">
<a id="id3730325"></a>
<h2>See Also</h2>
<p>
<a class="link" href="GEN13.html" title="GEN13"><em class="citetitle">GEN13</em></a>,
<a class="link" href="GEN14.html" title="GEN14"><em class="citetitle">GEN14</em></a>, and
<a class="link" href="GEN15.html" title="GEN15"><em class="citetitle">GEN15</em></a>.
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