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  45 <a href="#func-members">Functions</a> &#124;
  46 <a href="#var-members">Variables</a>  </div>
  47   <div class="headertitle">
  48 <h1>Cosine<br/>
  49 <small>
  50 [<a class="el" href="group__group_fast_math.html">Fast Math Functions</a>]</small>
  51 </h1>  </div>
  52 </div>
  53 <div class="contents">
  54 <table class="memberdecls">
  55 <tr><td colspan="2"><h2><a name="func-members"></a>
  56 Functions</h2></td></tr>
  57 <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__cos.html#gace15287f9c64b9b4084d1c797d4c49d8">arm_cos_f32</a> (<a class="el" href="arm__math_8h.html#a4611b605e45ab401f02cab15c5e38715">float32_t</a> x)</td></tr>
  58 <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__cos.html#gad80f121949ef885a77d83ab36e002567">arm_cos_q31</a> (<a class="el" href="arm__math_8h.html#adc89a3547f5324b7b3b95adec3806bc0">q31_t</a> x)</td></tr>
  59 <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__cos.html#gadfd60c24def501638c0d5db20f4c869b">arm_cos_q15</a> (<a class="el" href="arm__math_8h.html#ab5a8fb21a5b3b983d5f54f31614052ea">q15_t</a> x)</td></tr>
  60 <tr><td colspan="2"><h2><a name="var-members"></a>
  61 Variables</h2></td></tr>
  62 <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__cos.html#ga9588015a9447c6e124d36339e273bd53">cosTable</a> [259]</td></tr>
  63 <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__cos.html#gafe999a5fcf1774a2292220071096b834">cosTableQ31</a> [259]</td></tr>
  64 <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__cos.html#ga012ad965e3493ffcc6dd7f9a12569e58">cosTableQ15</a> [259]</td></tr>
  65 </table>
  66 <hr/><a name="_details"></a><h2>Detailed Description</h2>
  67 <p>Computes the trigonometric cosine 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 1) mapping to [0 2*pi).</p>
  68 <p>The implementation is based on table lookup using 256 values together with cubic interpolation. The steps used are:</p>
  69 <ol type="1">
  70 <li>Calculation of the nearest integer table index</li>
  71 <li>Fetch the four table values a, b, c, and d</li>
  72 <li>Compute the fractional portion (fract) of the table index.</li>
  73 <li>Calculation of wa, wb, wc, wd</li>
  74 <li>The final result equals <code>a*wa + b*wb + c*wc + d*wd</code></li>
  75 </ol>
  76 <p>where </p>
  77 <pre>
  78     a=Table[index-1];
  79     b=Table[index+0];
  80     c=Table[index+1];
  81     d=Table[index+2];
  82  </pre><p> and </p>
  83 <pre>
  84     wa=-(1/6)*fract.^3 + (1/2)*fract.^2 - (1/3)*fract;
  85     wb=(1/2)*fract.^3 - fract.^2 - (1/2)*fract + 1;
  86     wc=-(1/2)*fract.^3+(1/2)*fract.^2+fract;
  87     wd=(1/6)*fract.^3 - (1/6)*fract;
  88  </pre> <hr/><h2>Function Documentation</h2>
  89 <a class="anchor" id="gace15287f9c64b9b4084d1c797d4c49d8"></a><!-- doxytag: member="arm_cos_f32.c::arm_cos_f32" ref="gace15287f9c64b9b4084d1c797d4c49d8" args="(float32_t x)" -->
  90 <div class="memitem">
  91 <div class="memproto">
  92       <table class="memname">
  93         <tr>
  94           <td class="memname"><a class="el" href="arm__math_8h.html#a4611b605e45ab401f02cab15c5e38715">float32_t</a> arm_cos_f32 </td>
  95           <td>(</td>
  96           <td class="paramtype"><a class="el" href="arm__math_8h.html#a4611b605e45ab401f02cab15c5e38715">float32_t</a>&#160;</td>
  97           <td class="paramname"> <em>x</em>&#160;)</td>
  98           <td></td>
  99         </tr>
 100       </table>
 101 </div>
 102 <div class="memdoc">
 103
 104 <p>Fast approximation to the trigonometric cosine function for floating-point data. </p>
 105 <dl><dt><b>Parameters:</b></dt><dd>
 106   <table class="params">
 107     <tr><td class="paramdir">[in]</td><td class="paramname">x</td><td>input value in radians. </td></tr>
 108   </table>
 109   </dd>
 110 </dl>
 111 <dl class="return"><dt><b>Returns:</b></dt><dd>cos(x). </dd></dl>
 112 <dl><dt><b>Examples: </b></dt><dd><a class="el" href="arm_sin_cos_example_f32_8c-example.html#a11">arm_sin_cos_example_f32.c</a>.</dd>
 113 </dl>
 114 <p>Definition at line <a class="el" href="arm__cos__f32_8c_source.html#l00192">192</a> of file <a class="el" href="arm__cos__f32_8c_source.html">arm_cos_f32.c</a>.</p>
 115
 116 </div>
 117 </div>
 118 <a class="anchor" id="gad80f121949ef885a77d83ab36e002567"></a><!-- doxytag: member="arm_cos_q31.c::arm_cos_q31" ref="gad80f121949ef885a77d83ab36e002567" args="(q31_t x)" -->
 119 <div class="memitem">
 120 <div class="memproto">
 121       <table class="memname">
 122         <tr>
 123           <td class="memname"><a class="el" href="arm__math_8h.html#adc89a3547f5324b7b3b95adec3806bc0">q31_t</a> arm_cos_q31 </td>
 124           <td>(</td>
 125           <td class="paramtype"><a class="el" href="arm__math_8h.html#adc89a3547f5324b7b3b95adec3806bc0">q31_t</a>&#160;</td>
 126           <td class="paramname"> <em>x</em>&#160;)</td>
 127           <td></td>
 128         </tr>
 129       </table>
 130 </div>
 131 <div class="memdoc">
 132
 133 <p>Fast approximation to the trigonometric cosine function for Q31 data. </p>
 134 <dl><dt><b>Parameters:</b></dt><dd>
 135   <table class="params">
 136     <tr><td class="paramdir">[in]</td><td class="paramname">x</td><td>Scaled input value in radians. </td></tr>
 137   </table>
 138   </dd>
 139 </dl>
 140 <dl class="return"><dt><b>Returns:</b></dt><dd>cos(x).</dd></dl>
 141 <p>The Q31 input value is in the range [0 +1) and is mapped to a radian value in the range [0 2*pi). </p>
 142
 143 <p>Definition at line <a class="el" href="arm__cos__q31_8c_source.html#l00136">136</a> of file <a class="el" href="arm__cos__q31_8c_source.html">arm_cos_q31.c</a>.</p>
 144
 145 </div>
 146 </div>
 147 <a class="anchor" id="gadfd60c24def501638c0d5db20f4c869b"></a><!-- doxytag: member="arm_cos_q15.c::arm_cos_q15" ref="gadfd60c24def501638c0d5db20f4c869b" args="(q15_t x)" -->
 148 <div class="memitem">
 149 <div class="memproto">
 150       <table class="memname">
 151         <tr>
 152           <td class="memname"><a class="el" href="arm__math_8h.html#ab5a8fb21a5b3b983d5f54f31614052ea">q15_t</a> arm_cos_q15 </td>
 153           <td>(</td>
 154           <td class="paramtype"><a class="el" href="arm__math_8h.html#ab5a8fb21a5b3b983d5f54f31614052ea">q15_t</a>&#160;</td>
 155           <td class="paramname"> <em>x</em>&#160;)</td>
 156           <td></td>
 157         </tr>
 158       </table>
 159 </div>
 160 <div class="memdoc">
 161
 162 <p>Fast approximation to the trigonometric cosine function for Q15 data. </p>
 163 <dl><dt><b>Parameters:</b></dt><dd>
 164   <table class="params">
 165     <tr><td class="paramdir">[in]</td><td class="paramname">x</td><td>Scaled input value in radians. </td></tr>
 166   </table>
 167   </dd>
 168 </dl>
 169 <dl class="return"><dt><b>Returns:</b></dt><dd>cos(x).</dd></dl>
 170 <p>The Q15 input value is in the range [0 +1) and is mapped to a radian value in the range [0 2*pi). </p>
 171
 172 <p>Definition at line <a class="el" href="arm__cos__q15_8c_source.html#l00105">105</a> of file <a class="el" href="arm__cos__q15_8c_source.html">arm_cos_q15.c</a>.</p>
 173
 174 </div>
 175 </div>
 176 <hr/><h2>Variable Documentation</h2>
 177 <a class="anchor" id="ga9588015a9447c6e124d36339e273bd53"></a><!-- doxytag: member="arm_cos_f32.c::cosTable" ref="ga9588015a9447c6e124d36339e273bd53" args="[259]" -->
 178 <div class="memitem">
 179 <div class="memproto">
 180       <table class="memname">
 181         <tr>
 182           <td class="memname">const <a class="el" href="arm__math_8h.html#a4611b605e45ab401f02cab15c5e38715">float32_t</a> <a class="el" href="group__cos.html#ga9588015a9447c6e124d36339e273bd53">cosTable</a>[259]<code> [static]</code></td>
 183         </tr>
 184       </table>
 185 </div>
 186 <div class="memdoc">
 187 <dl class="user"><dt><b></b></dt><dd><b>Example code for Generation of Cos Table:</b> tableSize = 256; <pre>for(n = -1; n &lt; (tableSize + 1); n++)
 188  {
 189         cosTable[n+1]= cos(2*pi*n/tableSize);
 190  } </pre> where pi value is 3.14159265358979 </dd></dl>
 191
 192 <p>Definition at line <a class="el" href="arm__cos__f32_8c_source.html#l00086">86</a> of file <a class="el" href="arm__cos__f32_8c_source.html">arm_cos_f32.c</a>.</p>
 193
 194 </div>
 195 </div>
 196 <a class="anchor" id="gafe999a5fcf1774a2292220071096b834"></a><!-- doxytag: member="arm_cos_q31.c::cosTableQ31" ref="gafe999a5fcf1774a2292220071096b834" args="[259]" -->
 197 <div class="memitem">
 198 <div class="memproto">
 199       <table class="memname">
 200         <tr>
 201           <td class="memname">const <a class="el" href="arm__math_8h.html#adc89a3547f5324b7b3b95adec3806bc0">q31_t</a> <a class="el" href="group__cos.html#gafe999a5fcf1774a2292220071096b834">cosTableQ31</a>[259]<code> [static]</code></td>
 202         </tr>
 203       </table>
 204 </div>
 205 <div class="memdoc">
 206 <dl class="user"><dt><b></b></dt><dd>Table Values are in Q31(1.31 Fixed point format) and generation is done in three steps First Generate cos values in floating point: tableSize = 256; <pre>for(n = -1; n &lt; (tableSize + 1); n++)
 207  {
 208         cosTable[n+1]= cos(2*pi*n/tableSize);
 209  } </pre> where pi value is 3.14159265358979 </dd></dl>
 210 <dl class="user"><dt><b></b></dt><dd>Secondly Convert Floating point to Q31(Fixed point): (cosTable[i] * pow(2, 31)) </dd></dl>
 211 <dl class="user"><dt><b></b></dt><dd>Finally Rounding to nearest integer is done cosTable[i] += (cosTable[i] &gt; 0 ? 0.5 :-0.5); </dd></dl>
 212
 213 <p>Definition at line <a class="el" href="arm__cos__q31_8c_source.html#l00060">60</a> of file <a class="el" href="arm__cos__q31_8c_source.html">arm_cos_q31.c</a>.</p>
 214
 215 </div>
 216 </div>
 217 <a class="anchor" id="ga012ad965e3493ffcc6dd7f9a12569e58"></a><!-- doxytag: member="arm_cos_q15.c::cosTableQ15" ref="ga012ad965e3493ffcc6dd7f9a12569e58" args="[259]" -->
 218 <div class="memitem">
 219 <div class="memproto">
 220       <table class="memname">
 221         <tr>
 222           <td class="memname">const <a class="el" href="arm__math_8h.html#ab5a8fb21a5b3b983d5f54f31614052ea">q15_t</a> <a class="el" href="group__cos.html#ga012ad965e3493ffcc6dd7f9a12569e58">cosTableQ15</a>[259]<code> [static]</code></td>
 223         </tr>
 224       </table>
 225 </div>
 226 <div class="memdoc">
 227 <dl class="user"><dt><b></b></dt><dd>Table Values are in Q15(1.15 Fixed point format) and generation is done in three steps </dd></dl>
 228 <dl class="user"><dt><b></b></dt><dd>First Generate cos values in floating point: tableSize = 256; <pre>for(n = -1; n &lt; (tableSize + 1); n++)
 229  {
 230         cosTable[n+1]= cos(2*pi*n/tableSize);
 231  }</pre> where pi value is 3.14159265358979 </dd></dl>
 232 <dl class="user"><dt><b></b></dt><dd>Secondly Convert Floating point to Q15(Fixed point): (cosTable[i] * pow(2, 15)) </dd></dl>
 233 <dl class="user"><dt><b></b></dt><dd>Finally Rounding to nearest integer is done cosTable[i] += (cosTable[i] &gt; 0 ? 0.5 :-0.5); </dd></dl>
 234
 235 <p>Definition at line <a class="el" href="arm__cos__q15_8c_source.html#l00060">60</a> of file <a class="el" href="arm__cos__q15_8c_source.html">arm_cos_q15.c</a>.</p>
 236
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