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<title>The GNU Fortran Compiler: ATAN2</title>

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<a name="ATAN2"></a>
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<p>
Next: <a href="ATAN2D.html#ATAN2D" accesskey="n" rel="next">ATAN2D</a>, Previous: <a href="ATAND.html#ATAND" accesskey="p" rel="prev">ATAND</a>, Up: <a href="Intrinsic-Procedures.html#Intrinsic-Procedures" accesskey="u" rel="up">Intrinsic Procedures</a> &nbsp; [<a href="index.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="Option-Index.html#Option-Index" title="Index" rel="index">Index</a>]</p>
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<hr>
<a name="ATAN2-_002d_002d_002d-Arctangent-function"></a>
<h3 class="section">9.25 <code>ATAN2</code> &mdash; Arctangent function</h3>
<a name="index-ATAN2"></a>
<a name="index-DATAN2"></a>
<a name="index-trigonometric-function_002c-tangent_002c-inverse-1"></a>
<a name="index-tangent_002c-inverse-1"></a>

<dl compact="compact">
<dt><em>Description</em>:</dt>
<dd><p><code>ATAN2(Y, X)</code> computes the principal value of the argument
function of the complex number <em>X + i Y</em>.  This function can
be used to transform from Cartesian into polar coordinates and
allows to determine the angle in the correct quadrant.
</p>
</dd>
<dt><em>Standard</em>:</dt>
<dd><p>Fortran 77 and later
</p>
</dd>
<dt><em>Class</em>:</dt>
<dd><p>Elemental function
</p>
</dd>
<dt><em>Syntax</em>:</dt>
<dd><p><code>RESULT = ATAN2(Y, X)</code>
</p>
</dd>
<dt><em>Arguments</em>:</dt>
<dd><table>
<tr><td width="15%"><var>Y</var></td><td width="70%">The type shall be <code>REAL</code>.</td></tr>
<tr><td width="15%"><var>X</var></td><td width="70%">The type and kind type parameter shall be the same as <var>Y</var>.
If <var>Y</var> is zero, then <var>X</var> must be nonzero.</td></tr>
</table>

</dd>
<dt><em>Return value</em>:</dt>
<dd><p>The return value has the same type and kind type parameter as <var>Y</var>. It
is the principal value of the complex number <em>X + i Y</em>.  If <var>X</var>
is nonzero, then it lies in the range <em>-\pi \le \atan (x) \leq \pi</em>.
The sign is positive if <var>Y</var> is positive.  If <var>Y</var> is zero, then
the return value is zero if <var>X</var> is strictly positive, <em>\pi</em> if
<var>X</var> is negative and <var>Y</var> is positive zero (or the processor does
not handle signed zeros), and <em>-\pi</em> if <var>X</var> is negative and
<var>Y</var> is negative zero.  Finally, if <var>X</var> is zero, then the
magnitude of the result is <em>\pi/2</em>.
</p>
</dd>
<dt><em>Example</em>:</dt>
<dd><div class="smallexample">
<pre class="smallexample">program test_atan2
  real(4) :: x = 1.e0_4, y = 0.5e0_4
  x = atan2(y,x)
end program test_atan2
</pre></div>

</dd>
<dt><em>Specific names</em>:</dt>
<dd><table>
<tr><td width="20%">Name</td><td width="20%">Argument</td><td width="20%">Return type</td><td width="25%">Standard</td></tr>
<tr><td width="20%"><code>ATAN2(X, Y)</code></td><td width="20%"><code>REAL(4) X, Y</code></td><td width="20%"><code>REAL(4)</code></td><td width="25%">Fortran 77 and later</td></tr>
<tr><td width="20%"><code>DATAN2(X, Y)</code></td><td width="20%"><code>REAL(8) X, Y</code></td><td width="20%"><code>REAL(8)</code></td><td width="25%">Fortran 77 and later</td></tr>
</table>

</dd>
<dt><em>See also</em>:</dt>
<dd><p>Alias: <a href="ATAN.html#ATAN">ATAN</a>
Degrees function: <a href="ATAN2D.html#ATAN2D">ATAN2D</a>
</p>
</dd>
</dl>


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