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PX4-Autopilot/CMSIS/Documentation/DSP/html/group__sin.html
jgoppert 1579630efe Added CMSIS library.
2013-01-06 13:57:31 -05:00

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&#160;<span id="projectnumber">Verison 1.1.0</span>
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<a href="#var-members">Variables</a> &#124;
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<div class="title">Sine</div> </div>
<div class="ingroups"><a class="el" href="group__group_fast_math.html">Fast Math Functions</a></div></div>
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<table class="memberdecls">
<tr><td colspan="2"><h2><a name="var-members"></a>
Variables</h2></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">static const <a class="el" href="arm__math_8h.html#a4611b605e45ab401f02cab15c5e38715">float32_t</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="group__sin.html#ga71a0a466c6d42c65526968509b04790c">sinTable</a> [259]</td></tr>
<tr><td class="memItemLeft" align="right" valign="top">static const <a class="el" href="arm__math_8h.html#ab5a8fb21a5b3b983d5f54f31614052ea">q15_t</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="group__sin.html#ga0bb9449f52f04f5241f073864a72930a">sinTableQ15</a> [259]</td></tr>
<tr><td class="memItemLeft" align="right" valign="top">static const <a class="el" href="arm__math_8h.html#adc89a3547f5324b7b3b95adec3806bc0">q31_t</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="group__sin.html#gab1ffde7f3deee5adc75ba8b3d0a53106">sinTableQ31</a> [259]</td></tr>
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Functions</h2></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="el" href="arm__math_8h.html#a4611b605e45ab401f02cab15c5e38715">float32_t</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="group__sin.html#gae164899c4a3fc0e946dc5d55555fe541">arm_sin_f32</a> (<a class="el" href="arm__math_8h.html#a4611b605e45ab401f02cab15c5e38715">float32_t</a> x)</td></tr>
<tr><td class="mdescLeft">&#160;</td><td class="mdescRight">Fast approximation to the trigonometric sine function for floating-point data. <a href="#gae164899c4a3fc0e946dc5d55555fe541"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="el" href="arm__math_8h.html#ab5a8fb21a5b3b983d5f54f31614052ea">q15_t</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="group__sin.html#ga1fc6d6640be6cfa688a8bea0a48397ee">arm_sin_q15</a> (<a class="el" href="arm__math_8h.html#ab5a8fb21a5b3b983d5f54f31614052ea">q15_t</a> x)</td></tr>
<tr><td class="mdescLeft">&#160;</td><td class="mdescRight">Fast approximation to the trigonometric sine function for Q15 data. <a href="#ga1fc6d6640be6cfa688a8bea0a48397ee"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="el" href="arm__math_8h.html#adc89a3547f5324b7b3b95adec3806bc0">q31_t</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="group__sin.html#ga57aade7d8892585992cdc6375bd82f9c">arm_sin_q31</a> (<a class="el" href="arm__math_8h.html#adc89a3547f5324b7b3b95adec3806bc0">q31_t</a> x)</td></tr>
<tr><td class="mdescLeft">&#160;</td><td class="mdescRight">Fast approximation to the trigonometric sine function for Q31 data. <a href="#ga57aade7d8892585992cdc6375bd82f9c"></a><br/></td></tr>
</table>
<hr/><a name="details" id="details"></a><h2>Description</h2>
<p>Computes the trigonometric sine function using a combination of table lookup and cubic interpolation. There are separate functions for Q15, Q31, and floating-point data types. The input to the floating-point version is in radians while the fixed-point Q15 and Q31 have a scaled input with the range [0 +0.9999] mapping to [0 2*pi), Where range excludes 2*pi.</p>
<p>The implementation is based on table lookup using 256 values together with cubic interpolation. The steps used are:</p>
<ol type="1">
<li>Calculation of the nearest integer table index</li>
<li>Fetch the four table values a, b, c, and d</li>
<li>Compute the fractional portion (fract) of the table index.</li>
<li>Calculation of wa, wb, wc, wd</li>
<li>The final result equals <code>a*wa + b*wb + c*wc + d*wd</code></li>
</ol>
<p>where </p>
<pre>
a=Table[index-1];
b=Table[index+0];
c=Table[index+1];
d=Table[index+2];
</pre><p> and </p>
<pre>
wa=-(1/6)*fract.^3 + (1/2)*fract.^2 - (1/3)*fract;
wb=(1/2)*fract.^3 - fract.^2 - (1/2)*fract + 1;
wc=-(1/2)*fract.^3+(1/2)*fract.^2+fract;
wd=(1/6)*fract.^3 - (1/6)*fract;
</pre> <hr/><h2>Variable Documentation</h2>
<a class="anchor" id="ga71a0a466c6d42c65526968509b04790c"></a><!-- doxytag: member="arm_sin_f32.c::sinTable" ref="ga71a0a466c6d42c65526968509b04790c" args="[259]" -->
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<td class="memname">const <a class="el" href="arm__math_8h.html#a4611b605e45ab401f02cab15c5e38715">float32_t</a> <a class="el" href="group__sin.html#ga71a0a466c6d42c65526968509b04790c">sinTable</a>[259]<code> [static]</code></td>
</tr>
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</div>
<div class="memdoc">
<dl class="user"><dt><b></b></dt><dd>Example code for Generation of Floating-point Sin Table: tableSize = 256; <pre>for(n = -1; n &lt; (tableSize + 1); n++)
{
sinTable[n+1]=sin(2*pi*n/tableSize);
}</pre> </dd></dl>
<dl class="user"><dt><b></b></dt><dd>where pi value is 3.14159265358979 </dd></dl>
<p>Referenced by <a class="el" href="group__sin.html#gae164899c4a3fc0e946dc5d55555fe541">arm_sin_f32()</a>.</p>
</div>
</div>
<a class="anchor" id="ga0bb9449f52f04f5241f073864a72930a"></a><!-- doxytag: member="arm_sin_q15.c::sinTableQ15" ref="ga0bb9449f52f04f5241f073864a72930a" args="[259]" -->
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<td class="memname">const <a class="el" href="arm__math_8h.html#ab5a8fb21a5b3b983d5f54f31614052ea">q15_t</a> <a class="el" href="group__sin.html#ga0bb9449f52f04f5241f073864a72930a">sinTableQ15</a>[259]<code> [static]</code></td>
</tr>
</table>
</div>
<div class="memdoc">
<dl class="user"><dt><b></b></dt><dd>Example code for Generation of Q15 Sin Table: </dd></dl>
<dl class="user"><dt><b></b></dt><dd><pre>tableSize = 256;
for(n = -1; n &lt; (tableSize + 1); n++)
{
sinTable[n+1]=sin(2*pi*n/tableSize);
} </pre> where pi value is 3.14159265358979 </dd></dl>
<dl class="user"><dt><b></b></dt><dd>Convert Floating point to Q15(Fixed point): (sinTable[i] * pow(2, 15)) </dd></dl>
<dl class="user"><dt><b></b></dt><dd>rounding to nearest integer is done sinTable[i] += (sinTable[i] &gt; 0 ? 0.5 :-0.5); </dd></dl>
<p>Referenced by <a class="el" href="group__sin.html#ga1fc6d6640be6cfa688a8bea0a48397ee">arm_sin_q15()</a>.</p>
</div>
</div>
<a class="anchor" id="gab1ffde7f3deee5adc75ba8b3d0a53106"></a><!-- doxytag: member="arm_sin_q31.c::sinTableQ31" ref="gab1ffde7f3deee5adc75ba8b3d0a53106" args="[259]" -->
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<td class="memname">const <a class="el" href="arm__math_8h.html#adc89a3547f5324b7b3b95adec3806bc0">q31_t</a> <a class="el" href="group__sin.html#gab1ffde7f3deee5adc75ba8b3d0a53106">sinTableQ31</a>[259]<code> [static]</code></td>
</tr>
</table>
</div>
<div class="memdoc">
<dl class="user"><dt><b></b></dt><dd>Tables generated are in Q31(1.31 Fixed point format) Generation of sin values in floating point: <pre>tableSize = 256;
for(n = -1; n &lt; (tableSize + 1); n++)
{
sinTable[n+1]= sin(2*pi*n/tableSize);
} </pre> where pi value is 3.14159265358979 </dd></dl>
<dl class="user"><dt><b></b></dt><dd>Convert Floating point to Q31(Fixed point): (sinTable[i] * pow(2, 31)) </dd></dl>
<dl class="user"><dt><b></b></dt><dd>rounding to nearest integer is done sinTable[i] += (sinTable[i] &gt; 0 ? 0.5 :-0.5); </dd></dl>
<p>Referenced by <a class="el" href="group__sin.html#ga57aade7d8892585992cdc6375bd82f9c">arm_sin_q31()</a>.</p>
</div>
</div>
<hr/><h2>Function Documentation</h2>
<a class="anchor" id="gae164899c4a3fc0e946dc5d55555fe541"></a><!-- doxytag: member="arm_sin_f32.c::arm_sin_f32" ref="gae164899c4a3fc0e946dc5d55555fe541" args="(float32_t x)" -->
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<td class="memname"><a class="el" href="arm__math_8h.html#a4611b605e45ab401f02cab15c5e38715">float32_t</a> arm_sin_f32 </td>
<td>(</td>
<td class="paramtype"><a class="el" href="arm__math_8h.html#a4611b605e45ab401f02cab15c5e38715">float32_t</a>&#160;</td>
<td class="paramname"><em>x</em></td><td>)</td>
<td></td>
</tr>
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<div class="memdoc">
<dl><dt><b>Parameters:</b></dt><dd>
<table class="params">
<tr><td class="paramdir">[in]</td><td class="paramname">x</td><td>input value in radians. </td></tr>
</table>
</dd>
</dl>
<dl class="return"><dt><b>Returns:</b></dt><dd>sin(x). </dd></dl>
<dl><dt><b>Examples: </b></dt><dd><a class="el" href="arm_linear_interp_example_f32_8c-example.html#a12">arm_linear_interp_example_f32.c</a>, and <a class="el" href="arm_sin_cos_example_f32_8c-example.html#a12">arm_sin_cos_example_f32.c</a>.</dd>
</dl>
<p>References <a class="el" href="group__sin.html#ga71a0a466c6d42c65526968509b04790c">sinTable</a>, and <a class="el" href="arm__math_8h.html#a032503e76d6f69bc67e99e909c8125da">TABLE_SIZE</a>.</p>
<p>Referenced by <a class="el" href="arm__linear__interp__example__f32_8c.html#a52d2cba30e6946c95578be946ac12a65">main()</a>.</p>
</div>
</div>
<a class="anchor" id="ga1fc6d6640be6cfa688a8bea0a48397ee"></a><!-- doxytag: member="arm_sin_q15.c::arm_sin_q15" ref="ga1fc6d6640be6cfa688a8bea0a48397ee" args="(q15_t x)" -->
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<td class="memname"><a class="el" href="arm__math_8h.html#ab5a8fb21a5b3b983d5f54f31614052ea">q15_t</a> arm_sin_q15 </td>
<td>(</td>
<td class="paramtype"><a class="el" href="arm__math_8h.html#ab5a8fb21a5b3b983d5f54f31614052ea">q15_t</a>&#160;</td>
<td class="paramname"><em>x</em></td><td>)</td>
<td></td>
</tr>
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<div class="memdoc">
<dl><dt><b>Parameters:</b></dt><dd>
<table class="params">
<tr><td class="paramdir">[in]</td><td class="paramname">x</td><td>Scaled input value in radians. </td></tr>
</table>
</dd>
</dl>
<dl class="return"><dt><b>Returns:</b></dt><dd>sin(x).</dd></dl>
<p>The Q15 input value is in the range [0 +0.9999] and is mapped to a radian value in the range [0 2*pi), Here range excludes 2*pi. </p>
<p>References <a class="el" href="group__sin.html#ga0bb9449f52f04f5241f073864a72930a">sinTableQ15</a>, and <a class="el" href="arm__math_8h.html#a60b0142af7be007902142add27919b82">TABLE_SPACING_Q15</a>.</p>
</div>
</div>
<a class="anchor" id="ga57aade7d8892585992cdc6375bd82f9c"></a><!-- doxytag: member="arm_sin_q31.c::arm_sin_q31" ref="ga57aade7d8892585992cdc6375bd82f9c" args="(q31_t x)" -->
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<td class="memname"><a class="el" href="arm__math_8h.html#adc89a3547f5324b7b3b95adec3806bc0">q31_t</a> arm_sin_q31 </td>
<td>(</td>
<td class="paramtype"><a class="el" href="arm__math_8h.html#adc89a3547f5324b7b3b95adec3806bc0">q31_t</a>&#160;</td>
<td class="paramname"><em>x</em></td><td>)</td>
<td></td>
</tr>
</table>
</div>
<div class="memdoc">
<dl><dt><b>Parameters:</b></dt><dd>
<table class="params">
<tr><td class="paramdir">[in]</td><td class="paramname">x</td><td>Scaled input value in radians. </td></tr>
</table>
</dd>
</dl>
<dl class="return"><dt><b>Returns:</b></dt><dd>sin(x).</dd></dl>
<p>The Q31 input value is in the range [0 +0.9999] and is mapped to a radian value in the range [0 2*pi), Here range excludes 2*pi. </p>
<p>References <a class="el" href="group__sin.html#gab1ffde7f3deee5adc75ba8b3d0a53106">sinTableQ31</a>, and <a class="el" href="arm__math_8h.html#a8407c9e1347d10e3bcf0a7014f1fb2ff">TABLE_SPACING_Q31</a>.</p>
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