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 <span id="projectnumber">1.6.2</span>
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<div class="title">atan.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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<code>#include "<a class="el" href="math_8h_source.html">math.h</a>"</code><br />
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Include dependency graph for atan.c:</div>
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<p><a href="atan_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:a1e2f8f6d64eaa95131bc63fee34970ea"><td class="memItemLeft" align="right" valign="top">double </td><td class="memItemRight" valign="bottom"><a class="el" href="atan_8c.html#a1e2f8f6d64eaa95131bc63fee34970ea">atan</a> (double x)</td></tr>
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<tr class="memdesc:a1e2f8f6d64eaa95131bc63fee34970ea"><td class="mdescLeft"> </td><td class="mdescRight">Inverse trigonometric tangent function. <a href="#a1e2f8f6d64eaa95131bc63fee34970ea">More...</a><br /></td></tr>
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Variables</h2></td></tr>
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<tr class="memitem:a3ad59cecebe81954b05adb6655a3522d"><td class="memItemLeft" align="right" valign="top">static const double </td><td class="memItemRight" valign="bottom"><a class="el" href="atan_8c.html#a3ad59cecebe81954b05adb6655a3522d">atanhi</a> []</td></tr>
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<tr class="separator:a3ad59cecebe81954b05adb6655a3522d"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:a8e27d24e02eed00dd09eecee7230b8a7"><td class="memItemLeft" align="right" valign="top">static const double </td><td class="memItemRight" valign="bottom"><a class="el" href="atan_8c.html#a8e27d24e02eed00dd09eecee7230b8a7">atanlo</a> []</td></tr>
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<tr class="separator:a8e27d24e02eed00dd09eecee7230b8a7"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:a728d3c586fb7556699ef98d4e277da73"><td class="memItemLeft" align="right" valign="top">static const double </td><td class="memItemRight" valign="bottom"><a class="el" href="atan_8c.html#a728d3c586fb7556699ef98d4e277da73">aT</a> []</td></tr>
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<tr class="memitem:ada85e349d35971b32c8ea4238881ff8b"><td class="memItemLeft" align="right" valign="top">static const double </td><td class="memItemRight" valign="bottom"><a class="el" href="atan_8c.html#ada85e349d35971b32c8ea4238881ff8b">one</a> = 1.0</td></tr>
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<tr class="memitem:acbd466133274923cc0785707fbdeea9a"><td class="memItemLeft" align="right" valign="top">static const double </td><td class="memItemRight" valign="bottom"><a class="el" href="atan_8c.html#acbd466133274923cc0785707fbdeea9a">huge</a> = 1.0e300</td></tr>
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<tr class="separator:acbd466133274923cc0785707fbdeea9a"><td class="memSeparator" colspan="2"> </td></tr>
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</table>
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<h2 class="groupheader">Function Documentation</h2>
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<a class="anchor" id="a1e2f8f6d64eaa95131bc63fee34970ea"></a>
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<td class="memname">double atan </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>Inverse trigonometric tangent 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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<pre>
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Method
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1. Reduce x to positive by atan(x) = -atan(-x).
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2. According to the integer k=4t+0.25 chopped, t=x, the argument
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is further reduced to one of the following intervals and the
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arctangent of t is evaluated by the corresponding formula:</pre><pre> [0,7/16] atan(x) = t-t^3*(a1+t^2*(a2+...(a10+t^2*a11)...)
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[7/16,11/16] atan(x) = atan(1/2) + atan( (t-0.5)/(1+t/2) )
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[11/16.19/16] atan(x) = atan( 1 ) + atan( (t-1)/(1+t) )
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[19/16,39/16] atan(x) = atan(3/2) + atan( (t-1.5)/(1+1.5t) )
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[39/16,INF] atan(x) = atan(INF) + atan( -1/t )</pre><pre>Constants:
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The hexadecimal values are the intended ones for the following
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constants. The decimal values may be used, provided that the
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compiler will convert from decimal to binary accurately enough
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to produce the hexadecimal values shown.
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</pre> <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="atan_8c_source.html#l00109">109</a> of file <a class="el" href="atan_8c_source.html">atan.c</a>.</p>
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<p>References <a class="el" href="atan_8c_source.html#l00061">aT</a>, <a class="el" href="atan_8c_source.html#l00047">atanhi</a>, <a class="el" href="atan_8c_source.html#l00054">atanlo</a>, <a class="el" href="atan_8c_source.html#l00077">huge</a>, and <a class="el" href="atan_8c_source.html#l00076">one</a>.</p>
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<p>Referenced by <a class="el" href="real_8cpp_source.html#l00447">RealNumber::ArcCotangent()</a>, <a class="el" href="real_8cpp_source.html#l00437">RealNumber::ArcTangent()</a>, and <a class="el" href="atan2_8c_source.html#l00086">atan2()</a>.</p>
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<div class="fragment"><div class="line"><a name="l00110"></a><span class="lineno"> 110</span> {</div><div class="line"><a name="l00111"></a><span class="lineno"> 111</span>  <span class="keywordtype">double</span> w,s1,s2,z;</div><div class="line"><a name="l00112"></a><span class="lineno"> 112</span>  <a class="code" href="real_2prim_8h.html#ae91287c8a5f73a8a22a100f50dc4de77">sword</a> ix,hx,id;</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>  <a class="code" href="real_2prim_8h.html#ae62ee08d06ab4cc06d61dc1246b73195">GET_HIGH_WORD</a>(hx,x);</div><div class="line"><a name="l00115"></a><span class="lineno"> 115</span>  ix = hx&0x7fffffff;</div><div class="line"><a name="l00116"></a><span class="lineno"> 116</span>  <span class="keywordflow">if</span>(ix>=0x44100000) { <span class="comment">/* if |x| >= 2^66 */</span></div><div class="line"><a name="l00117"></a><span class="lineno"> 117</span>  <a class="code" href="real_2prim_8h.html#a6e60fe0e0f9f8801507e15fe2d893751">uword</a> low;</div><div class="line"><a name="l00118"></a><span class="lineno"> 118</span> </div><div class="line"><a name="l00119"></a><span class="lineno"> 119</span>  <a class="code" href="real_2prim_8h.html#adee023704c856ea8f310e8e3fd765a22">GET_LOW_WORD</a>(low,x);</div><div class="line"><a name="l00120"></a><span class="lineno"> 120</span>  <span class="keywordflow">if</span>(ix>0x7ff00000||</div><div class="line"><a name="l00121"></a><span class="lineno"> 121</span>  (ix==0x7ff00000&&(low!=0)))</div><div class="line"><a name="l00122"></a><span class="lineno"> 122</span>  <span class="keywordflow">return</span> x+x; <span class="comment">/* NaN */</span></div><div class="line"><a name="l00123"></a><span class="lineno"> 123</span>  <span class="keywordflow">if</span>(hx>0) <span class="keywordflow">return</span> <a class="code" href="atan_8c.html#a3ad59cecebe81954b05adb6655a3522d">atanhi</a>[3]+<a class="code" href="atan_8c.html#a8e27d24e02eed00dd09eecee7230b8a7">atanlo</a>[3];</div><div class="line"><a name="l00124"></a><span class="lineno"> 124</span>  <span class="keywordflow">else</span> <span class="keywordflow">return</span> -<a class="code" href="atan_8c.html#a3ad59cecebe81954b05adb6655a3522d">atanhi</a>[3]-atanlo[3];</div><div class="line"><a name="l00125"></a><span class="lineno"> 125</span>  }</div><div class="line"><a name="l00126"></a><span class="lineno"> 126</span>  <span class="keywordflow">if</span> (ix < 0x3fdc0000) { <span class="comment">/* |x| < 0.4375 */</span></div><div class="line"><a name="l00127"></a><span class="lineno"> 127</span>  <span class="keywordflow">if</span> (ix < 0x3e200000) { <span class="comment">/* |x| < 2^-29 */</span></div><div class="line"><a name="l00128"></a><span class="lineno"> 128</span>  <span class="keywordflow">if</span>(<a class="code" href="atan_8c.html#acbd466133274923cc0785707fbdeea9a">huge</a>+x><a class="code" href="atan_8c.html#ada85e349d35971b32c8ea4238881ff8b">one</a>) <span class="keywordflow">return</span> x; <span class="comment">/* raise inexact */</span></div><div class="line"><a name="l00129"></a><span class="lineno"> 129</span>  }</div><div class="line"><a name="l00130"></a><span class="lineno"> 130</span>  <span class="keywordtype">id</span> = -1;</div><div class="line"><a name="l00131"></a><span class="lineno"> 131</span>  } <span class="keywordflow">else</span> {</div><div class="line"><a name="l00132"></a><span class="lineno"> 132</span>  x = <a class="code" href="math_8h.html#a8fb5c0b9b43a108724b355136d29d2f9">fabs</a>(x);</div><div class="line"><a name="l00133"></a><span class="lineno"> 133</span>  <span class="keywordflow">if</span> (ix < 0x3ff30000) { <span class="comment">/* |x| < 1.1875 */</span></div><div class="line"><a name="l00134"></a><span class="lineno"> 134</span>  <span class="keywordflow">if</span> (ix < 0x3fe60000) { <span class="comment">/* 7/16 <=|x|<11/16 */</span></div><div class="line"><a name="l00135"></a><span class="lineno"> 135</span>  <span class="keywordtype">id</span> = 0;</div><div class="line"><a name="l00136"></a><span class="lineno"> 136</span>  x = (2.0*x-<a class="code" href="atan_8c.html#ada85e349d35971b32c8ea4238881ff8b">one</a>)/(2.0+x);</div><div class="line"><a name="l00137"></a><span class="lineno"> 137</span>  } <span class="keywordflow">else</span> { <span class="comment">/* 11/16<=|x|< 19/16 */</span></div><div class="line"><a name="l00138"></a><span class="lineno"> 138</span>  <span class="keywordtype">id</span> = 1;</div><div class="line"><a name="l00139"></a><span class="lineno"> 139</span>  x = (x-<a class="code" href="atan_8c.html#ada85e349d35971b32c8ea4238881ff8b">one</a>)/(x+<a class="code" href="atan_8c.html#ada85e349d35971b32c8ea4238881ff8b">one</a>);</div><div class="line"><a name="l00140"></a><span class="lineno"> 140</span>  }</div><div class="line"><a name="l00141"></a><span class="lineno"> 141</span>  } <span class="keywordflow">else</span> {</div><div class="line"><a name="l00142"></a><span class="lineno"> 142</span>  <span class="keywordflow">if</span> (ix < 0x40038000) { <span class="comment">/* |x| < 2.4375 */</span></div><div class="line"><a name="l00143"></a><span class="lineno"> 143</span>  <span class="keywordtype">id</span> = 2;</div><div class="line"><a name="l00144"></a><span class="lineno"> 144</span>  x = (x-1.5)/(<a class="code" href="atan_8c.html#ada85e349d35971b32c8ea4238881ff8b">one</a>+1.5*x);</div><div class="line"><a name="l00145"></a><span class="lineno"> 145</span>  } <span class="keywordflow">else</span> { <span class="comment">/* 2.4375 <= |x| < 2^66 */</span></div><div class="line"><a name="l00146"></a><span class="lineno"> 146</span>  <span class="keywordtype">id</span> = 3;</div><div class="line"><a name="l00147"></a><span class="lineno"> 147</span>  x = -1.0/x;</div><div class="line"><a name="l00148"></a><span class="lineno"> 148</span>  }</div><div class="line"><a name="l00149"></a><span class="lineno"> 149</span>  }</div><div class="line"><a name="l00150"></a><span class="lineno"> 150</span>  }</div><div class="line"><a name="l00151"></a><span class="lineno"> 151</span>  <span class="comment">/* end of argument reduction */</span></div><div class="line"><a name="l00152"></a><span class="lineno"> 152</span>  z = x*x;</div><div class="line"><a name="l00153"></a><span class="lineno"> 153</span>  w = z*z;</div><div class="line"><a name="l00154"></a><span class="lineno"> 154</span>  <span class="comment">/* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */</span></div><div class="line"><a name="l00155"></a><span class="lineno"> 155</span>  s1 = z*(<a class="code" href="atan_8c.html#a728d3c586fb7556699ef98d4e277da73">aT</a>[0]+w*(<a class="code" href="atan_8c.html#a728d3c586fb7556699ef98d4e277da73">aT</a>[2]+w*(<a class="code" href="atan_8c.html#a728d3c586fb7556699ef98d4e277da73">aT</a>[4]+w*(<a class="code" href="atan_8c.html#a728d3c586fb7556699ef98d4e277da73">aT</a>[6]+w*(<a class="code" href="atan_8c.html#a728d3c586fb7556699ef98d4e277da73">aT</a>[8]+w*<a class="code" href="atan_8c.html#a728d3c586fb7556699ef98d4e277da73">aT</a>[10])))));</div><div class="line"><a name="l00156"></a><span class="lineno"> 156</span>  s2 = w*(<a class="code" href="atan_8c.html#a728d3c586fb7556699ef98d4e277da73">aT</a>[1]+w*(<a class="code" href="atan_8c.html#a728d3c586fb7556699ef98d4e277da73">aT</a>[3]+w*(<a class="code" href="atan_8c.html#a728d3c586fb7556699ef98d4e277da73">aT</a>[5]+w*(<a class="code" href="atan_8c.html#a728d3c586fb7556699ef98d4e277da73">aT</a>[7]+w*<a class="code" href="atan_8c.html#a728d3c586fb7556699ef98d4e277da73">aT</a>[9]))));</div><div class="line"><a name="l00157"></a><span class="lineno"> 157</span>  <span class="keywordflow">if</span> (<span class="keywordtype">id</span><0) <span class="keywordflow">return</span> x - x*(s1+s2);</div><div class="line"><a name="l00158"></a><span class="lineno"> 158</span>  <span class="keywordflow">else</span> {</div><div class="line"><a name="l00159"></a><span class="lineno"> 159</span>  z = <a class="code" href="atan_8c.html#a3ad59cecebe81954b05adb6655a3522d">atanhi</a>[id] - ((x*(s1+s2) - <a class="code" href="atan_8c.html#a8e27d24e02eed00dd09eecee7230b8a7">atanlo</a>[<span class="keywordtype">id</span>]) - x);</div><div class="line"><a name="l00160"></a><span class="lineno"> 160</span>  <span class="keywordflow">return</span> (hx<0)? -z:z;</div><div class="line"><a name="l00161"></a><span class="lineno"> 161</span>  }</div><div class="line"><a name="l00162"></a><span class="lineno"> 162</span> }</div><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="atan_8c_html_acbd466133274923cc0785707fbdeea9a"><div class="ttname"><a href="atan_8c.html#acbd466133274923cc0785707fbdeea9a">huge</a></div><div class="ttdeci">static const double huge</div><div class="ttdef"><b>Definition:</b> <a href="atan_8c_source.html#l00077">atan.c:77</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="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="math_8h_html_a8fb5c0b9b43a108724b355136d29d2f9"><div class="ttname"><a href="math_8h.html#a8fb5c0b9b43a108724b355136d29d2f9">fabs</a></div><div class="ttdeci">double fabs(double x)</div><div class="ttdoc">Returns the absolute value of x. </div><div class="ttdef"><b>Definition:</b> <a href="fabs_8c_source.html#l00051">fabs.c:51</a></div></div>
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<div class="ttc" id="atan_8c_html_a728d3c586fb7556699ef98d4e277da73"><div class="ttname"><a href="atan_8c.html#a728d3c586fb7556699ef98d4e277da73">aT</a></div><div class="ttdeci">static const double aT[]</div><div class="ttdef"><b>Definition:</b> <a href="atan_8c_source.html#l00061">atan.c:61</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="atan_8c_html_a3ad59cecebe81954b05adb6655a3522d"><div class="ttname"><a href="atan_8c.html#a3ad59cecebe81954b05adb6655a3522d">atanhi</a></div><div class="ttdeci">static const double atanhi[]</div><div class="ttdef"><b>Definition:</b> <a href="atan_8c_source.html#l00047">atan.c:47</a></div></div>
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<div class="ttc" id="atan_8c_html_ada85e349d35971b32c8ea4238881ff8b"><div class="ttname"><a href="atan_8c.html#ada85e349d35971b32c8ea4238881ff8b">one</a></div><div class="ttdeci">static const double one</div><div class="ttdef"><b>Definition:</b> <a href="atan_8c_source.html#l00076">atan.c:76</a></div></div>
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<div class="ttc" id="atan_8c_html_a8e27d24e02eed00dd09eecee7230b8a7"><div class="ttname"><a href="atan_8c.html#a8e27d24e02eed00dd09eecee7230b8a7">atanlo</a></div><div class="ttdeci">static const double atanlo[]</div><div class="ttdef"><b>Definition:</b> <a href="atan_8c_source.html#l00054">atan.c:54</a></div></div>
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</div><!-- fragment -->
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<p><div class="dynheader">
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Here is the caller graph for this function:</div>
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<div class="center"><img src="atan_8c_a1e2f8f6d64eaa95131bc63fee34970ea_icgraph.png" border="0" usemap="#atan_8c_a1e2f8f6d64eaa95131bc63fee34970ea_icgraph" alt=""/></div>
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<h2 class="groupheader">Variable Documentation</h2>
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<td class="memname">const double aT[]</td>
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<span class="mlabels"><span class="mlabel">static</span></span> </td>
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<b>Initial value:</b><div class="fragment"><div class="line">= {</div><div class="line"> 3.33333333333329318027e-01, </div><div class="line"> -1.99999999998764832476e-01, </div><div class="line"> 1.42857142725034663711e-01, </div><div class="line"> -1.11111104054623557880e-01, </div><div class="line"> 9.09088713343650656196e-02, </div><div class="line"> -7.69187620504482999495e-02, </div><div class="line"> 6.66107313738753120669e-02, </div><div class="line"> -5.83357013379057348645e-02, </div><div class="line"> 4.97687799461593236017e-02, </div><div class="line"> -3.65315727442169155270e-02, </div><div class="line"> 1.62858201153657823623e-02, </div><div class="line">}</div></div><!-- fragment -->
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<p>Definition at line <a class="el" href="atan_8c_source.html#l00061">61</a> of file <a class="el" href="atan_8c_source.html">atan.c</a>.</p>
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<p>Referenced by <a class="el" href="atan_8c_source.html#l00109">atan()</a>.</p>
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<td class="memname">const double atanhi[]</td>
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<b>Initial value:</b><div class="fragment"><div class="line">= {</div><div class="line"> 4.63647609000806093515e-01, </div><div class="line"> 7.85398163397448278999e-01, </div><div class="line"> 9.82793723247329054082e-01, </div><div class="line"> 1.57079632679489655800e+00, </div><div class="line">}</div></div><!-- fragment -->
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<p>Definition at line <a class="el" href="atan_8c_source.html#l00047">47</a> of file <a class="el" href="atan_8c_source.html">atan.c</a>.</p>
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<p>Referenced by <a class="el" href="atan_8c_source.html#l00109">atan()</a>.</p>
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<td class="memname">const double atanlo[]</td>
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<b>Initial value:</b><div class="fragment"><div class="line">= {</div><div class="line"> 2.26987774529616870924e-17, </div><div class="line"> 3.06161699786838301793e-17, </div><div class="line"> 1.39033110312309984516e-17, </div><div class="line"> 6.12323399573676603587e-17, </div><div class="line">}</div></div><!-- fragment -->
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<p>Definition at line <a class="el" href="atan_8c_source.html#l00054">54</a> of file <a class="el" href="atan_8c_source.html">atan.c</a>.</p>
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<p>Referenced by <a class="el" href="atan_8c_source.html#l00109">atan()</a>.</p>
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<td class="memname">const double huge = 1.0e300</td>
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<p>Definition at line <a class="el" href="atan_8c_source.html#l00077">77</a> of file <a class="el" href="atan_8c_source.html">atan.c</a>.</p>
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<p>Referenced by <a class="el" href="atan_8c_source.html#l00109">atan()</a>.</p>
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<td class="memname">const double one = 1.0</td>
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<p>Definition at line <a class="el" href="atan_8c_source.html#l00076">76</a> of file <a class="el" href="atan_8c_source.html">atan.c</a>.</p>
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<p>Referenced by <a class="el" href="atan_8c_source.html#l00109">atan()</a>.</p>
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<img class="footer" src="doxygen.png" alt="doxygen"/></a> 1.8.11 </li>
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