complexpack/README.html at master · nkkav/complexpack · GitHub

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<div class="document" id="complexpack-user-manual">
<h1 class="title">complexpack user manual</h1>

<img alt="complexpack.png" class="align-center" src="complexpack.png" style="width: 95.5px; height: 70.25px;" />
<table border="1" class="docutils">
<colgroup>
<col width="25%" />
<col width="75%" />
</colgroup>
<tbody valign="top">
<tr><td><strong>Title</strong></td>
<td>complexpack (VHDL complex arithmetic package).</td>
</tr>
<tr><td><strong>Author</strong></td>
<td>Nikolaos Kavvadias 2009-2020</td>
</tr>
<tr><td><strong>Contact</strong></td>
<td><a class="reference external" href="mailto:nikolaos.kavvadias&#64;gmail.com">nikolaos.kavvadias&#64;gmail.com</a></td>
</tr>
<tr><td><strong>Website</strong></td>
<td><a class="reference external" href="http://www.nkavvadias.com">http://www.nkavvadias.com</a></td>
</tr>
<tr><td><strong>Release Date</strong></td>
<td>09 December 2020</td>
</tr>
<tr><td><strong>Version</strong></td>
<td>0.2.4</td>
</tr>
<tr><td><strong>Rev. history</strong></td>
<td>&nbsp;</td>
</tr>
<tr><td><strong>v0.2.4</strong></td>
<td><p class="first">2020-12-09</p>
<p class="last">Self-checking test.</p>
</td>
</tr>
<tr><td><strong>v0.2.3</strong></td>
<td><p class="first">2017-06-16</p>
<p class="last">Add complex reciprocal.</p>
</td>
</tr>
<tr><td><strong>v0.2.2</strong></td>
<td><p class="first">2017-06-10</p>
<p class="last">Add complex mac.</p>
</td>
</tr>
<tr><td><strong>v0.2.1</strong></td>
<td><p class="first">2017-06-07</p>
<p class="last">Add arg (argument).</p>
</td>
</tr>
<tr><td><strong>v0.2.0</strong></td>
<td><p class="first">2017-06-05</p>
<p class="last">Add polar form, to_polar, to_cartesian, exp, log, pow,
sqrt, sin, cos, tan, arcsin, arccos, arctan.</p>
</td>
</tr>
<tr><td><strong>v0.1.5</strong></td>
<td><p class="first">2016-23-07</p>
<p class="last">Use sim/rtl_sim/bin dir, ignores for git, clean script</p>
</td>
</tr>
<tr><td><strong>v0.1.4</strong></td>
<td><p class="first">2016-03-13</p>
<p class="last">Update date information.</p>
</td>
</tr>
<tr><td><strong>v0.1.3</strong></td>
<td><p class="first">2014-11-30</p>
<p class="last">Added project logo to README.rst.</p>
</td>
</tr>
<tr><td><strong>v0.1.2</strong></td>
<td><p class="first">2014-06-17</p>
<p class="last">Changed README to README.rst.</p>
</td>
</tr>
<tr><td><strong>v0.1.1</strong></td>
<td><p class="first">2014-03-04</p>
<p class="last">Added support for the &quot;abs&quot; and the negation (&quot;-&quot;)
operators as those are needed by the complexarrpack
package project.</p>
</td>
</tr>
<tr><td><strong>v0.1.0</strong></td>
<td><p class="first">2014-03-03</p>
<p class="last">Added get_real, get_imaginary, magnitude, and operators:
lt, gt, le, ge, eq, ne. New library dependency:
IEEE.math_real.</p>
</td>
</tr>
<tr><td><strong>v0.0.1</strong></td>
<td><p class="first">2014-02-24</p>
<p class="last">Changed documentation format to RestructuredText.
Code has been reorganized into new directory structure.</p>
</td>
</tr>
<tr><td><strong>v0.0.0</strong></td>
<td><p class="first">2009-10-02</p>
<p class="last">First public release.</p>
</td>
</tr>
</tbody>
</table>
<div class="section" id="introduction">
<h1>1. Introduction</h1>
<p><tt class="docutils literal">complexpack</tt> is a simple complex arithmetic package written in VHDL. It is
based ona code example present in the RASSP series of VHDL lectures. Compared to
the RASSP version, the following have beed added:</p>
<ul class="simple">
<li>conjugate function.</li>
<li>magnitude function.</li>
<li>comparison operators.</li>
<li>get real and get imaginary part functions.</li>
</ul>
<p>A complex number is defined by the pair (real-part, imaginary-part) where both
items of the pair are numbers. A common algebraic representation for complex
numbers is:</p>
<div class="line-block">
<div class="line"><tt class="docutils literal">z = a + i*b,</tt></div>
</div>
<p>where:</p>
<ul class="simple">
<li><tt class="docutils literal">z</tt> is the resulting complex number</li>
<li><tt class="docutils literal">a</tt> is the real part of the number also written as <tt class="docutils literal">a = Re(z)</tt></li>
<li><tt class="docutils literal">b</tt> is the imaginary part of the number also written as <tt class="docutils literal">b = Im(z)</tt></li>
<li><tt class="docutils literal">i</tt> is the imaginary unit and has the value of <tt class="docutils literal"><span class="pre">sqrt(-1)</span></tt>.</li>
</ul>
<p>Currently, the <tt class="docutils literal">complexpack</tt> package implements the following:</p>
<ul class="simple">
<li>the constants re and im, which specify addresses for an array-based
representation of a complex number</li>
<li>type definition for a complex number</li>
<li>interface and implementation for complex arithmetic functionality</li>
</ul>
<div class="section" id="implemented-functions-and-operators">
<h2>1.1. Implemented functions and operators</h2>
<p>This is a summary of the currently supported functions, procedures and operators
by the <tt class="docutils literal">complexpack</tt> package.</p>
<ul class="simple">
<li><tt class="docutils literal">to_complex(real, real)</tt>: form a complex number</li>
<li><tt class="docutils literal">+</tt>: add two complex numbers</li>
<li><tt class="docutils literal">-</tt>: subtract one complex number from another</li>
<li><tt class="docutils literal">-</tt>: negate a complex number</li>
<li><tt class="docutils literal">*</tt>: multiply two complex numbers</li>
<li><tt class="docutils literal">/</tt>: divide two complex numbers</li>
<li><tt class="docutils literal">mac</tt>: multiply-and accumulate (<tt class="docutils literal">a * b + c</tt>)</li>
<li><tt class="docutils literal">reciprocal</tt>: the reciprocal of a complex number</li>
<li><tt class="docutils literal">conjugate(complex)</tt>: return the conjugate of the given complex
number</li>
<li><tt class="docutils literal">exp(complex)</tt>: return the complex exponent</li>
<li><tt class="docutils literal">log(complex)</tt>: return the complex logarithm</li>
<li><tt class="docutils literal">pow(complex, complex)</tt>: return the complex power</li>
<li><tt class="docutils literal">sqrt(complex)</tt>: return the complex square root</li>
<li><tt class="docutils literal">sin(complex)</tt>: return the complex sine</li>
<li><tt class="docutils literal">cos(complex)</tt>: return the complex cosine</li>
<li><tt class="docutils literal">tan(complex)</tt>: return the complex tangent</li>
<li><tt class="docutils literal">arcsin(complex)</tt>: return the complex arcsine</li>
<li><tt class="docutils literal">arccos(complex)</tt>: return the complex arccosine</li>
<li><tt class="docutils literal">arctan(complex)</tt>: return the complex arctangent</li>
<li><tt class="docutils literal">to_cartesian(polar)</tt>: convert from polar form to Cartesian</li>
</ul>
<p>All functions above return an item of the complex data type.</p>
<ul class="simple">
<li><tt class="docutils literal">get_real(complex)</tt>: get the real part of a complex number</li>
<li><tt class="docutils literal">get_imaginary(complex)</tt>: get the imaginary part of a complex number</li>
<li><tt class="docutils literal">magnitude(complex)</tt>: return the magnitude (distance from point 0,0)
of the complex number</li>
<li><tt class="docutils literal">arg(complex)</tt>: return the argument (phase) of the complex number</li>
<li><tt class="docutils literal">abs(complex)</tt>: alias for <tt class="docutils literal">magnitude</tt></li>
</ul>
<p>All functions above return an item of the real data type (a scalar quantity).</p>
<ul class="simple">
<li><tt class="docutils literal">&lt;</tt>: less than comparison for two complex numbers</li>
<li><tt class="docutils literal">&gt;</tt>: greater than comparison for two complex numbers</li>
<li><tt class="docutils literal">&lt;=</tt>: less than or equal comparison for two complex numbers</li>
<li><tt class="docutils literal">&gt;=</tt>: greater than or equal comparison for two complex numbers</li>
<li><tt class="docutils literal">=</tt>: equality comparison for two complex numbers</li>
<li><tt class="docutils literal">/=</tt>: non-equality comparison for two complex numbers</li>
</ul>
<p>All functions above return an item of the boolean data type (TRUE or FALSE).</p>
<ul class="simple">
<li><tt class="docutils literal">to_polar(complex)</tt>: convert the complex (Cartesian) to polar coordinates</li>
</ul>
<p>The function above returns a complex number in polar form.</p>
<p>The definition of <tt class="docutils literal">magnitude</tt> requires a square root computation. For this
task, a call to the <tt class="docutils literal">sqrt</tt> function found in the <tt class="docutils literal">IEEE.math_real</tt> library
is used.</p>
<p><tt class="docutils literal">complexpack</tt> is distributed along with a simple VHDL testbench exercising
basic functionalities.</p>
</div>
</div>
<div class="section" id="file-listing">
<h1>2. File listing</h1>
<p>The <tt class="docutils literal">complexpack</tt> distribution includes the following files:</p>
<table border="1" class="docutils">
<colgroup>
<col width="30%" />
<col width="70%" />
</colgroup>
<tbody valign="top">
<tr><td>/complexpack</td>
<td>Top-level directory</td>
</tr>
<tr><td>ChangeLog</td>
<td>A log for code changes.</td>
</tr>
<tr><td>LICENSE</td>
<td>The modified BSD license governs <tt class="docutils literal">complexpack</tt>
since version 0.2.0.</td>
</tr>
<tr><td>README.rst</td>
<td>This file.</td>
</tr>
<tr><td>README.html</td>
<td>HTML version of README.rst.</td>
</tr>
<tr><td>README.pdf</td>
<td>PDF version of README.rst.</td>
</tr>
<tr><td>VERSION</td>
<td>Current version of the project sources.</td>
</tr>
<tr><td>complexpack.png</td>
<td>PNG image for the <tt class="docutils literal">complexpack</tt> project logo.</td>
</tr>
<tr><td>rst2docs.sh</td>
<td>Bash script for generating the HTML and PDF versions.</td>
</tr>
<tr><td>/bench/vhdl</td>
<td>Benchmarks VHDL directory</td>
</tr>
<tr><td>complexpack_tb.vhd</td>
<td>A simple testbench.</td>
</tr>
<tr><td>/doc</td>
<td>Documentation directory</td>
</tr>
<tr><td>/rtl/vhdl</td>
<td>RTL source code directory for the package</td>
</tr>
<tr><td>complexpack.vhd</td>
<td>The complex arithmetic package.</td>
</tr>
<tr><td>/sim/rtl_sim</td>
<td>RTL simulation files directory</td>
</tr>
<tr><td>/sim/rtl_sim/bin</td>
<td>RTL simulation makefiles directory</td>
</tr>
<tr><td>complexpack.mk</td>
<td>GNU Makefile for running GHDL simulations.</td>
</tr>
<tr><td>/sim/rtl_sim/out</td>
<td>RTL simulation output files directory</td>
</tr>
<tr><td>complexpack_results-
.txt</td>
<td>Output generated by the <tt class="docutils literal">complexpack_tb.vhd</tt> test.</td>
</tr>
<tr><td>/sim/rtl_sim/run</td>
<td>RTL simulation run scripts directory</td>
</tr>
<tr><td>clean.sh</td>
<td>A bash script for cleaning simulation artifacts.</td>
</tr>
<tr><td>run.sh</td>
<td>A bash script for running the GNU Makefile for GHDL.</td>
</tr>
</tbody>
</table>
</div>
<div class="section" id="complexpack-usage">
<h1>3. <tt class="docutils literal">complexpack</tt> usage</h1>
<p>The <tt class="docutils literal">complexpack</tt> package test script can be used as follows:</p>
<div class="line-block">
<div class="line"><tt class="docutils literal">$ ./run.sh</tt></div>
</div>
<p>as run from within the <tt class="docutils literal">./sim/rtl_sim/run</tt> subdirectory. The run script
expects that the GHDL simulator is installed and its <tt class="docutils literal">bin</tt> directory is in the
<tt class="docutils literal">$PATH</tt>.</p>
<p>After this process, the <tt class="docutils literal">complexpack_results.txt</tt> file is generated containing
simulation results.</p>
<p>A reference <tt class="docutils literal">complexpack_results.txt</tt> is kept under <tt class="docutils literal">./sim/rtl_sim/out</tt> for
comparison.</p>
<p>To clean up afterwards, use:</p>
<div class="line-block">
<div class="line"><tt class="docutils literal">$ ./clean.sh</tt></div>
</div>
</div>
<div class="section" id="prerequisites">
<h1>4. Prerequisites</h1>
<ul>
<li><p class="first">Standard UNIX-based tools (tested on cygwin/x86 and MinGW/x86 and MinGW/x64)</p>
<ul class="simple">
<li>make</li>
<li>bash</li>
</ul>
</li>
<li><p class="first">GHDL simulator (<a class="reference external" href="http://ghdl.free.fr">http://ghdl.free.fr</a>)</p>
<p>Provides the &quot;ghdl&quot; executable and corresponding simulation environment.
Versions 0.26 to 0.37 have been used for testing.</p>
</li>
</ul>
</div>
</div>
</body>
</html>