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diff --git a/devdocs/c/numeric%2Fcomplex%2Fcatan.html b/devdocs/c/numeric%2Fcomplex%2Fcatan.html new file mode 100644 index 00000000..c74f6eef --- /dev/null +++ b/devdocs/c/numeric%2Fcomplex%2Fcatan.html @@ -0,0 +1,56 @@ + <h1 id="firstHeading" class="firstHeading">catanf, catan, catanl</h1> <table class="t-dcl-begin"> <tr class="t-dsc-header"> <th> Defined in header <code><complex.h></code> </th> <th> </th> <th> </th> </tr> <tr class="t-dcl t-since-c99"> <td> <pre data-language="c">float complex catanf( float complex z );</pre> +</td> <td> (1) </td> <td> <span class="t-mark-rev t-since-c99">(since C99)</span> </td> </tr> <tr class="t-dcl t-since-c99"> <td> <pre data-language="c">double complex catan( double complex z );</pre> +</td> <td> (2) </td> <td> <span class="t-mark-rev t-since-c99">(since C99)</span> </td> </tr> <tr class="t-dcl t-since-c99"> <td> <pre data-language="c">long double complex catanl( long double complex z );</pre> +</td> <td> (3) </td> <td> <span class="t-mark-rev t-since-c99">(since C99)</span> </td> </tr> <tr class="t-dsc-header"> <th> Defined in header <code><tgmath.h></code> </th> <th> </th> <th> </th> </tr> <tr class="t-dcl t-since-c99"> <td> <pre data-language="c">#define atan( z )</pre> +</td> <td> (4) </td> <td> <span class="t-mark-rev t-since-c99">(since C99)</span> </td> </tr> </table> <div class="t-li1"> +<span class="t-li">1-3)</span> Computes the complex arc tangent of <code>z</code> with branch cuts outside the interval [−i,+i] along the imaginary axis.</div> <div class="t-li1"> +<span class="t-li">4)</span> Type-generic macro: If <code>z</code> has type <code><span class="kw4">long</span> <span class="kw4">double</span> <a href="http://en.cppreference.com/w/c/numeric/complex/complex"><span class="kw743">complex</span></a></code>, <code>catanl</code> is called. if <code>z</code> has type <code><span class="kw4">double</span> <a href="http://en.cppreference.com/w/c/numeric/complex/complex"><span class="kw743">complex</span></a></code>, <code>catan</code> is called, if <code>z</code> has type <code><span class="kw4">float</span> <a href="http://en.cppreference.com/w/c/numeric/complex/complex"><span class="kw743">complex</span></a></code>, <code>catanf</code> is called. If <code>z</code> is real or integer, then the macro invokes the corresponding real function (<code>atanf</code>, <code><a href="http://en.cppreference.com/w/c/numeric/math/atan"><span class="kw674">atan</span></a></code>, <code>atanl</code>). If <code>z</code> is imaginary, then the macro invokes the corresponding real version of the function <code><a href="../math/atanh" title="c/numeric/math/atanh">atanh</a></code>, implementing the formula atan(iy) = i atanh(y), and the return type of the macro is imaginary.</div> <h3 id="Parameters"> Parameters</h3> <table class="t-par-begin"> <tr class="t-par"> <td> z </td> <td> - </td> <td> complex argument </td> +</tr> +</table> <h3 id="Return_value"> Return value</h3> <p>If no errors occur, complex arc tangent of <code>z</code> is returned, in the range of a strip unbounded along the imaginary axis and in the interval [−π/2; +π/2] along the real axis.</p> +<p>Errors and special cases are handled as if the operation is implemented by <code><span class="sy2">-</span>I <span class="sy2">*</span> <a href="http://en.cppreference.com/w/c/numeric/complex/catanh"><span class="kw802">catanh</span></a><span class="br0">(</span>I<span class="sy2">*</span>z<span class="br0">)</span></code>.</p> +<h3 id="Notes"> Notes</h3> <p>Inverse tangent (or arc tangent) is a multivalued function and requires a branch cut on the complex plane. The branch cut is conventionally placed at the line segments (-∞i,-i) and (+i,+∞i) of the imaginary axis. The mathematical definition of the principal value of inverse tangent is atan z = -</p> +<span><span>1</span><span>/</span><span>2</span></span> i [ln(1 - iz) - ln (1 + iz] <h3 id="Example"> Example</h3> <div class="t-example"> <div class="c source-c"><pre data-language="c">#include <stdio.h> +#include <float.h> +#include <complex.h> + +int main(void) +{ + double complex z = catan(2*I); + printf("catan(+0+2i) = %f%+fi\n", creal(z), cimag(z)); + + double complex z2 = catan(-conj(2*I)); // or CMPLX(-0.0, 2) + printf("catan(-0+2i) (the other side of the cut) = %f%+fi\n", creal(z2), cimag(z2)); + + double complex z3 = 2*catan(2*I*DBL_MAX); // or CMPLX(0, INFINITY) + printf("2*catan(+0+i*Inf) = %f%+fi\n", creal(z3), cimag(z3)); +}</pre></div> <p>Output:</p> +<div class="text source-text"><pre data-language="c">catan(+0+2i) = 1.570796+0.549306i +catan(-0+2i) (the other side of the cut) = -1.570796+0.549306i +2*catan(+0+i*Inf) = 3.141593+0.000000i</pre></div> </div> <h3 id="References"> References</h3> <ul> +<li> C11 standard (ISO/IEC 9899:2011): </li> +<ul> +<li> 7.3.5.3 The catan functions (p: 191) </li> +<li> 7.25 Type-generic math <tgmath.h> (p: 373-375) </li> +<li> G.7 Type-generic math <tgmath.h> (p: 545) </li> +</ul> +<li> C99 standard (ISO/IEC 9899:1999): </li> +<ul> +<li> 7.3.5.3 The catan functions (p: 173) </li> +<li> 7.22 Type-generic math <tgmath.h> (p: 335-337) </li> +<li> G.7 Type-generic math <tgmath.h> (p: 480) </li> +</ul> +</ul> <h3 id="See_also"> See also</h3> <table class="t-dsc-begin"> <tr class="t-dsc"> <td> <div><a href="casin" title="c/numeric/complex/casin"> <span class="t-lines"><span>casin</span><span>casinf</span><span>casinl</span></span></a></div> +<div><span class="t-lines"><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span></span></div> </td> <td> computes the complex arc sine <br> <span class="t-mark">(function)</span> </td> +</tr> <tr class="t-dsc"> <td> <div><a href="cacos" title="c/numeric/complex/cacos"> <span class="t-lines"><span>cacos</span><span>cacosf</span><span>cacosl</span></span></a></div> +<div><span class="t-lines"><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span></span></div> </td> <td> computes the complex arc cosine <br> <span class="t-mark">(function)</span> </td> +</tr> <tr class="t-dsc"> <td> <div><a href="ctan" title="c/numeric/complex/ctan"> <span class="t-lines"><span>ctan</span><span>ctanf</span><span>ctanl</span></span></a></div> +<div><span class="t-lines"><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span></span></div> </td> <td> computes the complex tangent <br> <span class="t-mark">(function)</span> </td> +</tr> <tr class="t-dsc"> <td> <div><a href="../math/atan" title="c/numeric/math/atan"> <span class="t-lines"><span>atan</span><span>atanf</span><span>atanl</span></span></a></div> +<div><span class="t-lines"><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span></span></div> </td> <td> computes arc tangent (\({\small\arctan{x} }\)arctan(x)) <br> <span class="t-mark">(function)</span> </td> +</tr> <tr class="t-dsc"> <td colspan="2"> <span><a href="https://en.cppreference.com/w/cpp/numeric/complex/atan" title="cpp/numeric/complex/atan">C++ documentation</a></span> for <code>atan</code> </td> +</tr> </table> <div class="_attribution"> + <p class="_attribution-p"> + © cppreference.com<br>Licensed under the Creative Commons Attribution-ShareAlike Unported License v3.0.<br> + <a href="https://en.cppreference.com/w/c/numeric/complex/catan" class="_attribution-link">https://en.cppreference.com/w/c/numeric/complex/catan</a> + </p> +</div> |