mirror of https://gitlab.com/rnger/amath
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<div id="projectname">amath
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 <span id="projectnumber">1.6.2</span>
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<div id="projectbrief">Simple command line calculator</div>
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<div class="title">cbrt.c File Reference</div> </div>
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<div class="textblock"><code>#include "<a class="el" href="real_2prim_8h_source.html">prim.h</a>"</code><br />
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Include dependency graph for cbrt.c:</div>
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<p><a href="cbrt_8c_source.html">Go to the source code of this file.</a></p>
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Functions</h2></td></tr>
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<tr class="memitem:a8af00e2203928978e0242b4afd1d899f"><td class="memItemLeft" align="right" valign="top">double </td><td class="memItemRight" valign="bottom"><a class="el" href="cbrt_8c.html#a8af00e2203928978e0242b4afd1d899f">cbrt</a> (double x)</td></tr>
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<tr class="memdesc:a8af00e2203928978e0242b4afd1d899f"><td class="mdescLeft"> </td><td class="mdescRight">Cube root function. <a href="#a8af00e2203928978e0242b4afd1d899f">More...</a><br /></td></tr>
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Variables</h2></td></tr>
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<tr class="memitem:a0340375b1c4fd28d44d3d8f2c21ef4c2"><td class="memItemLeft" align="right" valign="top">static const unsigned </td><td class="memItemRight" valign="bottom"><a class="el" href="cbrt_8c.html#a0340375b1c4fd28d44d3d8f2c21ef4c2">B1</a> = 715094163</td></tr>
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<tr class="separator:a0340375b1c4fd28d44d3d8f2c21ef4c2"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:a63d271d6b952319d904e32c7319dbacd"><td class="memItemLeft" align="right" valign="top">static const unsigned </td><td class="memItemRight" valign="bottom"><a class="el" href="cbrt_8c.html#a63d271d6b952319d904e32c7319dbacd">B2</a> = 696219795</td></tr>
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<tr class="separator:a63d271d6b952319d904e32c7319dbacd"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:a9e8a46a0e00368ad98642587ca4ebdbe"><td class="memItemLeft" align="right" valign="top">static const double </td><td class="memItemRight" valign="bottom"><a class="el" href="cbrt_8c.html#a9e8a46a0e00368ad98642587ca4ebdbe">C</a> = 5.42857142857142815906e-01</td></tr>
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<tr class="separator:a9e8a46a0e00368ad98642587ca4ebdbe"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:a412464ee5e4d4e873c365d926d1970bb"><td class="memItemLeft" align="right" valign="top">static const double </td><td class="memItemRight" valign="bottom"><a class="el" href="cbrt_8c.html#a412464ee5e4d4e873c365d926d1970bb">D</a> = -7.05306122448979611050e-01</td></tr>
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<tr class="separator:a412464ee5e4d4e873c365d926d1970bb"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:ab587ba72a9c23f238cb4fd70e2fdb545"><td class="memItemLeft" align="right" valign="top">static const double </td><td class="memItemRight" valign="bottom"><a class="el" href="cbrt_8c.html#ab587ba72a9c23f238cb4fd70e2fdb545">E</a> = 1.41428571428571436819e+00</td></tr>
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<tr class="memitem:a480d6423b1e9ca40c69c5a83458b49b0"><td class="memItemLeft" align="right" valign="top">static const double </td><td class="memItemRight" valign="bottom"><a class="el" href="cbrt_8c.html#a480d6423b1e9ca40c69c5a83458b49b0">F</a> = 1.60714285714285720630e+00</td></tr>
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<tr class="memitem:ab97e4616d23ed4c2961295010c1afc3c"><td class="memItemLeft" align="right" valign="top">static const double </td><td class="memItemRight" valign="bottom"><a class="el" href="cbrt_8c.html#ab97e4616d23ed4c2961295010c1afc3c">G</a> = 3.57142857142857150787e-01</td></tr>
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</table>
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<h2 class="groupheader">Function Documentation</h2>
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<td class="memname">double cbrt </td>
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<td>(</td>
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<td class="paramtype">double </td>
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<td class="paramname"><em>x</em></td><td>)</td>
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<td></td>
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<p>Cube root function. </p>
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<dl class="section version"><dt>Version</dt><dd>1.3 </dd></dl>
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<dl class="section date"><dt>Date</dt><dd>95/01/18 </dd></dl>
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<dl class="section copyright"><dt>Copyright</dt><dd>Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. Developed at SunSoft, a Sun Microsystems, Inc. business. Permission to use, copy, modify, and distribute this software is freely granted, provided that this notice is preserved. </dd></dl>
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<p>Definition at line <a class="el" href="cbrt_8c_source.html#l00067">67</a> of file <a class="el" href="cbrt_8c_source.html">cbrt.c</a>.</p>
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<p>References <a class="el" href="cbrt_8c_source.html#l00047">B1</a>, <a class="el" href="cbrt_8c_source.html#l00048">B2</a>, <a class="el" href="cbrt_8c_source.html#l00051">C</a>, <a class="el" href="cbrt_8c_source.html#l00052">D</a>, <a class="el" href="cbrt_8c_source.html#l00053">E</a>, <a class="el" href="cbrt_8c_source.html#l00054">F</a>, and <a class="el" href="cbrt_8c_source.html#l00055">G</a>.</p>
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<div class="fragment"><div class="line"><a name="l00068"></a><span class="lineno"> 68</span> {</div><div class="line"><a name="l00069"></a><span class="lineno"> 69</span>  <a class="code" href="real_2prim_8h.html#ae91287c8a5f73a8a22a100f50dc4de77">sword</a> hx, lx, ht;</div><div class="line"><a name="l00070"></a><span class="lineno"> 70</span>  <span class="keywordtype">double</span> r,s,t=0.0,w;</div><div class="line"><a name="l00071"></a><span class="lineno"> 71</span>  <a class="code" href="real_2prim_8h.html#a6e60fe0e0f9f8801507e15fe2d893751">uword</a> sign;</div><div class="line"><a name="l00072"></a><span class="lineno"> 72</span> </div><div class="line"><a name="l00073"></a><span class="lineno"> 73</span>  <a class="code" href="real_2prim_8h.html#ae62ee08d06ab4cc06d61dc1246b73195">GET_HIGH_WORD</a>(hx,x); <span class="comment">/* high word of x */</span></div><div class="line"><a name="l00074"></a><span class="lineno"> 74</span>  sign=hx&0x80000000; <span class="comment">/* sign= sign(x) */</span></div><div class="line"><a name="l00075"></a><span class="lineno"> 75</span>  hx ^=sign;</div><div class="line"><a name="l00076"></a><span class="lineno"> 76</span>  <span class="keywordflow">if</span>(hx>=0x7ff00000) <span class="keywordflow">return</span>(x+x); <span class="comment">/* cbrt(NaN,INF) is itself */</span></div><div class="line"><a name="l00077"></a><span class="lineno"> 77</span>  <a class="code" href="real_2prim_8h.html#adee023704c856ea8f310e8e3fd765a22">GET_LOW_WORD</a>(lx, x);</div><div class="line"><a name="l00078"></a><span class="lineno"> 78</span>  <span class="keywordflow">if</span>((hx|lx)==0)</div><div class="line"><a name="l00079"></a><span class="lineno"> 79</span>  <span class="keywordflow">return</span>(x); <span class="comment">/* cbrt(0) is itself */</span></div><div class="line"><a name="l00080"></a><span class="lineno"> 80</span> </div><div class="line"><a name="l00081"></a><span class="lineno"> 81</span>  <a class="code" href="real_2prim_8h.html#a6ca54776127e20149f84c290bf52f89e">SET_HIGH_WORD</a>(x,hx); <span class="comment">/* x <- |x| */</span></div><div class="line"><a name="l00082"></a><span class="lineno"> 82</span>  <span class="comment">/* rough cbrt to 5 bits */</span></div><div class="line"><a name="l00083"></a><span class="lineno"> 83</span>  <span class="keywordflow">if</span>(hx<0x00100000) <span class="comment">/* subnormal number */</span></div><div class="line"><a name="l00084"></a><span class="lineno"> 84</span>  {</div><div class="line"><a name="l00085"></a><span class="lineno"> 85</span>  <a class="code" href="real_2prim_8h.html#a6ca54776127e20149f84c290bf52f89e">SET_HIGH_WORD</a>(t,0x43500000); <span class="comment">/* set t= 2**54 */</span></div><div class="line"><a name="l00086"></a><span class="lineno"> 86</span>  t*=x;</div><div class="line"><a name="l00087"></a><span class="lineno"> 87</span>  <a class="code" href="real_2prim_8h.html#ae62ee08d06ab4cc06d61dc1246b73195">GET_HIGH_WORD</a>(ht,t);</div><div class="line"><a name="l00088"></a><span class="lineno"> 88</span>  <a class="code" href="real_2prim_8h.html#a6ca54776127e20149f84c290bf52f89e">SET_HIGH_WORD</a>(t,ht/3+<a class="code" href="cbrt_8c.html#a63d271d6b952319d904e32c7319dbacd">B2</a>);</div><div class="line"><a name="l00089"></a><span class="lineno"> 89</span>  }</div><div class="line"><a name="l00090"></a><span class="lineno"> 90</span>  <span class="keywordflow">else</span></div><div class="line"><a name="l00091"></a><span class="lineno"> 91</span>  <a class="code" href="real_2prim_8h.html#a6ca54776127e20149f84c290bf52f89e">SET_HIGH_WORD</a>(t,hx/3+<a class="code" href="cbrt_8c.html#a0340375b1c4fd28d44d3d8f2c21ef4c2">B1</a>);</div><div class="line"><a name="l00092"></a><span class="lineno"> 92</span> </div><div class="line"><a name="l00093"></a><span class="lineno"> 93</span>  <span class="comment">/* new cbrt to 23 bits, may be implemented in single precision */</span></div><div class="line"><a name="l00094"></a><span class="lineno"> 94</span>  r=t*t/x;</div><div class="line"><a name="l00095"></a><span class="lineno"> 95</span>  s=<a class="code" href="cbrt_8c.html#a9e8a46a0e00368ad98642587ca4ebdbe">C</a>+r*t;</div><div class="line"><a name="l00096"></a><span class="lineno"> 96</span>  t*=<a class="code" href="cbrt_8c.html#ab97e4616d23ed4c2961295010c1afc3c">G</a>+<a class="code" href="cbrt_8c.html#a480d6423b1e9ca40c69c5a83458b49b0">F</a>/(s+<a class="code" href="cbrt_8c.html#ab587ba72a9c23f238cb4fd70e2fdb545">E</a>+<a class="code" href="cbrt_8c.html#a412464ee5e4d4e873c365d926d1970bb">D</a>/s);</div><div class="line"><a name="l00097"></a><span class="lineno"> 97</span> </div><div class="line"><a name="l00098"></a><span class="lineno"> 98</span>  <span class="comment">/* chopped to 20 bits and make it larger than cbrt(x) */</span></div><div class="line"><a name="l00099"></a><span class="lineno"> 99</span>  <a class="code" href="real_2prim_8h.html#af4776e0b45c17da39fce08bc7b211a03">SET_LOW_WORD</a>(t,0);</div><div class="line"><a name="l00100"></a><span class="lineno"> 100</span>  <a class="code" href="real_2prim_8h.html#ae62ee08d06ab4cc06d61dc1246b73195">GET_HIGH_WORD</a>(ht,t);</div><div class="line"><a name="l00101"></a><span class="lineno"> 101</span>  <a class="code" href="real_2prim_8h.html#a6ca54776127e20149f84c290bf52f89e">SET_HIGH_WORD</a>(t,ht + 0x00000001);</div><div class="line"><a name="l00102"></a><span class="lineno"> 102</span> </div><div class="line"><a name="l00103"></a><span class="lineno"> 103</span>  <span class="comment">/* one step newton iteration to 53 bits with error less than 0.667 ulps */</span></div><div class="line"><a name="l00104"></a><span class="lineno"> 104</span>  s=t*t; <span class="comment">/* t*t is exact */</span></div><div class="line"><a name="l00105"></a><span class="lineno"> 105</span>  r=x/s;</div><div class="line"><a name="l00106"></a><span class="lineno"> 106</span>  w=t+t;</div><div class="line"><a name="l00107"></a><span class="lineno"> 107</span>  r=(r-t)/(w+r); <span class="comment">/* r-s is exact */</span></div><div class="line"><a name="l00108"></a><span class="lineno"> 108</span>  t=t+t*r;</div><div class="line"><a name="l00109"></a><span class="lineno"> 109</span> </div><div class="line"><a name="l00110"></a><span class="lineno"> 110</span>  <span class="comment">/* retore the sign bit */</span></div><div class="line"><a name="l00111"></a><span class="lineno"> 111</span>  <a class="code" href="real_2prim_8h.html#ae62ee08d06ab4cc06d61dc1246b73195">GET_HIGH_WORD</a>(ht,t);</div><div class="line"><a name="l00112"></a><span class="lineno"> 112</span>  <a class="code" href="real_2prim_8h.html#a6ca54776127e20149f84c290bf52f89e">SET_HIGH_WORD</a>(t,ht|sign);</div><div class="line"><a name="l00113"></a><span class="lineno"> 113</span> </div><div class="line"><a name="l00114"></a><span class="lineno"> 114</span>  <span class="keywordflow">return</span>(t);</div><div class="line"><a name="l00115"></a><span class="lineno"> 115</span> }</div><div class="ttc" id="cbrt_8c_html_a412464ee5e4d4e873c365d926d1970bb"><div class="ttname"><a href="cbrt_8c.html#a412464ee5e4d4e873c365d926d1970bb">D</a></div><div class="ttdeci">static const double D</div><div class="ttdef"><b>Definition:</b> <a href="cbrt_8c_source.html#l00052">cbrt.c:52</a></div></div>
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<div class="ttc" id="cbrt_8c_html_ab587ba72a9c23f238cb4fd70e2fdb545"><div class="ttname"><a href="cbrt_8c.html#ab587ba72a9c23f238cb4fd70e2fdb545">E</a></div><div class="ttdeci">static const double E</div><div class="ttdef"><b>Definition:</b> <a href="cbrt_8c_source.html#l00053">cbrt.c:53</a></div></div>
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<div class="ttc" id="real_2prim_8h_html_ae62ee08d06ab4cc06d61dc1246b73195"><div class="ttname"><a href="real_2prim_8h.html#ae62ee08d06ab4cc06d61dc1246b73195">GET_HIGH_WORD</a></div><div class="ttdeci">#define GET_HIGH_WORD(i, d)</div><div class="ttdoc">Get the more significant 32 bit int from a double. </div><div class="ttdef"><b>Definition:</b> <a href="real_2prim_8h_source.html#l00165">prim.h:165</a></div></div>
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<div class="ttc" id="real_2prim_8h_html_adee023704c856ea8f310e8e3fd765a22"><div class="ttname"><a href="real_2prim_8h.html#adee023704c856ea8f310e8e3fd765a22">GET_LOW_WORD</a></div><div class="ttdeci">#define GET_LOW_WORD(i, d)</div><div class="ttdoc">Get the less significant 32 bit int from a double. </div><div class="ttdef"><b>Definition:</b> <a href="real_2prim_8h_source.html#l00176">prim.h:176</a></div></div>
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<div class="ttc" id="cbrt_8c_html_a480d6423b1e9ca40c69c5a83458b49b0"><div class="ttname"><a href="cbrt_8c.html#a480d6423b1e9ca40c69c5a83458b49b0">F</a></div><div class="ttdeci">static const double F</div><div class="ttdef"><b>Definition:</b> <a href="cbrt_8c_source.html#l00054">cbrt.c:54</a></div></div>
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<div class="ttc" id="real_2prim_8h_html_ae91287c8a5f73a8a22a100f50dc4de77"><div class="ttname"><a href="real_2prim_8h.html#ae91287c8a5f73a8a22a100f50dc4de77">sword</a></div><div class="ttdeci">signed int sword</div><div class="ttdoc">32 bit signed integer. </div><div class="ttdef"><b>Definition:</b> <a href="real_2prim_8h_source.html#l00107">prim.h:107</a></div></div>
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<div class="ttc" id="real_2prim_8h_html_a6e60fe0e0f9f8801507e15fe2d893751"><div class="ttname"><a href="real_2prim_8h.html#a6e60fe0e0f9f8801507e15fe2d893751">uword</a></div><div class="ttdeci">unsigned int uword</div><div class="ttdoc">32 bit unsigned integer. </div><div class="ttdef"><b>Definition:</b> <a href="real_2prim_8h_source.html#l00101">prim.h:101</a></div></div>
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<div class="ttc" id="cbrt_8c_html_a63d271d6b952319d904e32c7319dbacd"><div class="ttname"><a href="cbrt_8c.html#a63d271d6b952319d904e32c7319dbacd">B2</a></div><div class="ttdeci">static const unsigned B2</div><div class="ttdef"><b>Definition:</b> <a href="cbrt_8c_source.html#l00048">cbrt.c:48</a></div></div>
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<div class="ttc" id="cbrt_8c_html_ab97e4616d23ed4c2961295010c1afc3c"><div class="ttname"><a href="cbrt_8c.html#ab97e4616d23ed4c2961295010c1afc3c">G</a></div><div class="ttdeci">static const double G</div><div class="ttdef"><b>Definition:</b> <a href="cbrt_8c_source.html#l00055">cbrt.c:55</a></div></div>
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<div class="ttc" id="cbrt_8c_html_a0340375b1c4fd28d44d3d8f2c21ef4c2"><div class="ttname"><a href="cbrt_8c.html#a0340375b1c4fd28d44d3d8f2c21ef4c2">B1</a></div><div class="ttdeci">static const unsigned B1</div><div class="ttdef"><b>Definition:</b> <a href="cbrt_8c_source.html#l00047">cbrt.c:47</a></div></div>
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<div class="ttc" id="cbrt_8c_html_a9e8a46a0e00368ad98642587ca4ebdbe"><div class="ttname"><a href="cbrt_8c.html#a9e8a46a0e00368ad98642587ca4ebdbe">C</a></div><div class="ttdeci">static const double C</div><div class="ttdef"><b>Definition:</b> <a href="cbrt_8c_source.html#l00051">cbrt.c:51</a></div></div>
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<div class="ttc" id="real_2prim_8h_html_af4776e0b45c17da39fce08bc7b211a03"><div class="ttname"><a href="real_2prim_8h.html#af4776e0b45c17da39fce08bc7b211a03">SET_LOW_WORD</a></div><div class="ttdeci">#define SET_LOW_WORD(d, v)</div><div class="ttdoc">Set the less significant 32 bits of a double from an int. </div><div class="ttdef"><b>Definition:</b> <a href="real_2prim_8h_source.html#l00211">prim.h:211</a></div></div>
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<div class="ttc" id="real_2prim_8h_html_a6ca54776127e20149f84c290bf52f89e"><div class="ttname"><a href="real_2prim_8h.html#a6ca54776127e20149f84c290bf52f89e">SET_HIGH_WORD</a></div><div class="ttdeci">#define SET_HIGH_WORD(d, v)</div><div class="ttdoc">Set the more significant 32 bits of a double from an int. </div><div class="ttdef"><b>Definition:</b> <a href="real_2prim_8h_source.html#l00199">prim.h:199</a></div></div>
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<h2 class="groupheader">Variable Documentation</h2>
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<td class="memname">const unsigned B1 = 715094163</td>
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<p>Definition at line <a class="el" href="cbrt_8c_source.html#l00047">47</a> of file <a class="el" href="cbrt_8c_source.html">cbrt.c</a>.</p>
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<p>Referenced by <a class="el" href="cbrt_8c_source.html#l00067">cbrt()</a>.</p>
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<p>Definition at line <a class="el" href="cbrt_8c_source.html#l00048">48</a> of file <a class="el" href="cbrt_8c_source.html">cbrt.c</a>.</p>
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<p>Referenced by <a class="el" href="cbrt_8c_source.html#l00067">cbrt()</a>.</p>
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<p>Definition at line <a class="el" href="cbrt_8c_source.html#l00051">51</a> of file <a class="el" href="cbrt_8c_source.html">cbrt.c</a>.</p>
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<p>Referenced by <a class="el" href="cbrt_8c_source.html#l00067">cbrt()</a>.</p>
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<p>Definition at line <a class="el" href="cbrt_8c_source.html#l00052">52</a> of file <a class="el" href="cbrt_8c_source.html">cbrt.c</a>.</p>
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<p>Referenced by <a class="el" href="cbrt_8c_source.html#l00067">cbrt()</a>.</p>
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<p>Definition at line <a class="el" href="cbrt_8c_source.html#l00053">53</a> of file <a class="el" href="cbrt_8c_source.html">cbrt.c</a>.</p>
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<p>Referenced by <a class="el" href="cbrt_8c_source.html#l00067">cbrt()</a>.</p>
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<p>Definition at line <a class="el" href="cbrt_8c_source.html#l00054">54</a> of file <a class="el" href="cbrt_8c_source.html">cbrt.c</a>.</p>
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<p>Referenced by <a class="el" href="cbrt_8c_source.html#l00067">cbrt()</a>.</p>
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<p>Definition at line <a class="el" href="cbrt_8c_source.html#l00055">55</a> of file <a class="el" href="cbrt_8c_source.html">cbrt.c</a>.</p>
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<p>Referenced by <a class="el" href="cbrt_8c_source.html#l00067">cbrt()</a>.</p>
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