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<a href="backend_2metal_2kernels_2complex_8h.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a id="l00001" name="l00001"></a><span class="lineno"> 1</span><span class="comment">// Copyright © 2023 Apple Inc.</span></div>
<div class="line"><a id="l00002" name="l00002"></a><span class="lineno"> 2</span> </div>
<div class="line"><a id="l00003" name="l00003"></a><span class="lineno"> 3</span><span class="preprocessor">#pragma once</span></div>
<div class="line"><a id="l00004" name="l00004"></a><span class="lineno"> 4</span> </div>
<div class="line"><a id="l00005" name="l00005"></a><span class="lineno"> 5</span><span class="preprocessor">#include &lt;metal_stdlib&gt;</span></div>
<div class="line"><a id="l00006" name="l00006"></a><span class="lineno"> 6</span> </div>
<div class="line"><a id="l00007" name="l00007"></a><span class="lineno"> 7</span><span class="keyword">using namespace </span><a class="code hl_namespace" href="namespacemetal.html">metal</a>;</div>
<div class="line"><a id="l00008" name="l00008"></a><span class="lineno"> 8</span> </div>
<div class="line"><a id="l00009" name="l00009"></a><span class="lineno"> 9</span><span class="keyword">struct </span><a class="code hl_struct" href="structcomplex64__t.html">complex64_t</a>;</div>
<div class="line"><a id="l00010" name="l00010"></a><span class="lineno"> 10</span> </div>
<div class="line"><a id="l00011" name="l00011"></a><span class="lineno"> 11</span><span class="keyword">template</span> &lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a id="l00012" name="l00012"></a><span class="lineno"><a class="line" href="backend_2metal_2kernels_2complex_8h.html#a4f90ad54f4fae363e8d3cc41d539557b"> 12</a></span><span class="keyword">static</span> <span class="keyword">constexpr</span> constant <span class="keywordtype">bool</span> <a class="code hl_variable" href="backend_2metal_2kernels_2complex_8h.html#a4f90ad54f4fae363e8d3cc41d539557b">can_convert_to_complex64</a> =</div>
<div class="line"><a id="l00013" name="l00013"></a><span class="lineno"> 13</span> !is_same_v&lt;T, complex64_t&gt; &amp;&amp; is_convertible_v&lt;T, float&gt;;</div>
<div class="line"><a id="l00014" name="l00014"></a><span class="lineno"> 14</span> </div>
<div class="line"><a id="l00015" name="l00015"></a><span class="lineno"> 15</span><span class="keyword">template</span> &lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a id="l00016" name="l00016"></a><span class="lineno"><a class="line" href="backend_2metal_2kernels_2complex_8h.html#ab149db78f6f19b8da6297dac4c36d893"> 16</a></span><span class="keyword">static</span> <span class="keyword">constexpr</span> constant <span class="keywordtype">bool</span> <a class="code hl_variable" href="backend_2metal_2kernels_2complex_8h.html#ab149db78f6f19b8da6297dac4c36d893">can_convert_from_complex64</a> =</div>
<div class="line"><a id="l00017" name="l00017"></a><span class="lineno"> 17</span> !is_same_v&lt;T, complex64_t&gt; &amp;&amp;</div>
<div class="line"><a id="l00018" name="l00018"></a><span class="lineno"> 18</span> (is_convertible_v&lt;float, T&gt; || is_convertible_v&lt;bfloat16_t, T&gt;);</div>
<div class="line"><a id="l00019" name="l00019"></a><span class="lineno"> 19</span> </div>
<div class="foldopen" id="foldopen00020" data-start="{" data-end="};">
<div class="line"><a id="l00020" name="l00020"></a><span class="lineno"><a class="line" href="structcomplex64__t.html"> 20</a></span><span class="keyword">struct </span><a class="code hl_struct" href="structcomplex64__t.html">complex64_t</a> {</div>
<div class="line"><a id="l00021" name="l00021"></a><span class="lineno"><a class="line" href="structcomplex64__t.html#abbd4a0092eca9f112c1c5ae1a133a27e"> 21</a></span> <span class="keywordtype">float</span> <a class="code hl_variable" href="structcomplex64__t.html#abbd4a0092eca9f112c1c5ae1a133a27e">real</a>;</div>
<div class="line"><a id="l00022" name="l00022"></a><span class="lineno"><a class="line" href="structcomplex64__t.html#a94037c0cf8451aaff7cb4d154a8426de"> 22</a></span> <span class="keywordtype">float</span> <a class="code hl_variable" href="structcomplex64__t.html#a94037c0cf8451aaff7cb4d154a8426de">imag</a>;</div>
<div class="line"><a id="l00023" name="l00023"></a><span class="lineno"> 23</span> </div>
<div class="line"><a id="l00024" name="l00024"></a><span class="lineno"> 24</span> <span class="comment">// Constructors</span></div>
<div class="line"><a id="l00025" name="l00025"></a><span class="lineno"><a class="line" href="structcomplex64__t.html#adbd392a5e92d31997380ad0a38be4be8"> 25</a></span> <span class="keyword">constexpr</span> <a class="code hl_function" href="structcomplex64__t.html#adbd392a5e92d31997380ad0a38be4be8">complex64_t</a>(<span class="keywordtype">float</span> <a class="code hl_variable" href="structcomplex64__t.html#abbd4a0092eca9f112c1c5ae1a133a27e">real</a>, <span class="keywordtype">float</span> <a class="code hl_variable" href="structcomplex64__t.html#a94037c0cf8451aaff7cb4d154a8426de">imag</a>) : <a class="code hl_variable" href="structcomplex64__t.html#abbd4a0092eca9f112c1c5ae1a133a27e">real</a>(<a class="code hl_variable" href="structcomplex64__t.html#abbd4a0092eca9f112c1c5ae1a133a27e">real</a>), <a class="code hl_variable" href="structcomplex64__t.html#a94037c0cf8451aaff7cb4d154a8426de">imag</a>(<a class="code hl_variable" href="structcomplex64__t.html#a94037c0cf8451aaff7cb4d154a8426de">imag</a>) {};</div>
<div class="line"><a id="l00026" name="l00026"></a><span class="lineno"><a class="line" href="structcomplex64__t.html#a29782289bb90d6294099667b86509cd3"> 26</a></span> <span class="keyword">constexpr</span> <a class="code hl_function" href="structcomplex64__t.html#a29782289bb90d6294099667b86509cd3">complex64_t</a>() : <a class="code hl_variable" href="structcomplex64__t.html#abbd4a0092eca9f112c1c5ae1a133a27e">real</a>(0), <a class="code hl_variable" href="structcomplex64__t.html#a94037c0cf8451aaff7cb4d154a8426de">imag</a>(0) {};</div>
<div class="line"><a id="l00027" name="l00027"></a><span class="lineno"><a class="line" href="structcomplex64__t.html#a905b048d70eb8d748a62454268242291"> 27</a></span> <span class="keyword">constexpr</span> <a class="code hl_function" href="structcomplex64__t.html#a905b048d70eb8d748a62454268242291">complex64_t</a>() threadgroup : <a class="code hl_variable" href="structcomplex64__t.html#abbd4a0092eca9f112c1c5ae1a133a27e">real</a>(0), <a class="code hl_variable" href="structcomplex64__t.html#a94037c0cf8451aaff7cb4d154a8426de">imag</a>(0) {};</div>
<div class="line"><a id="l00028" name="l00028"></a><span class="lineno"> 28</span> </div>
<div class="line"><a id="l00029" name="l00029"></a><span class="lineno"> 29</span> <span class="comment">// Conversions to complex64_t</span></div>
<div class="line"><a id="l00030" name="l00030"></a><span class="lineno"> 30</span> <span class="keyword">template</span> &lt;</div>
<div class="line"><a id="l00031" name="l00031"></a><span class="lineno"> 31</span> <span class="keyword">typename</span> T,</div>
<div class="line"><a id="l00032" name="l00032"></a><span class="lineno"> 32</span> <span class="keyword">typename</span> = <span class="keyword">typename</span> enable_if&lt;can_convert_to_complex64&lt;T&gt;&gt;::type&gt;</div>
<div class="line"><a id="l00033" name="l00033"></a><span class="lineno"><a class="line" href="structcomplex64__t.html#a33a2452eb33b5ed53655773539c357a5"> 33</a></span> <span class="keyword">constexpr</span> <a class="code hl_function" href="structcomplex64__t.html#a33a2452eb33b5ed53655773539c357a5">complex64_t</a>(T x) thread : <a class="code hl_variable" href="structcomplex64__t.html#abbd4a0092eca9f112c1c5ae1a133a27e">real</a>(x), <a class="code hl_variable" href="structcomplex64__t.html#a94037c0cf8451aaff7cb4d154a8426de">imag</a>(0) {}</div>
<div class="line"><a id="l00034" name="l00034"></a><span class="lineno"> 34</span> </div>
<div class="line"><a id="l00035" name="l00035"></a><span class="lineno"> 35</span> <span class="keyword">template</span> &lt;</div>
<div class="line"><a id="l00036" name="l00036"></a><span class="lineno"> 36</span> <span class="keyword">typename</span> T,</div>
<div class="line"><a id="l00037" name="l00037"></a><span class="lineno"> 37</span> <span class="keyword">typename</span> = <span class="keyword">typename</span> enable_if&lt;can_convert_to_complex64&lt;T&gt;&gt;::type&gt;</div>
<div class="line"><a id="l00038" name="l00038"></a><span class="lineno"><a class="line" href="structcomplex64__t.html#a89b65ace8588b7bf215355f705eb23d9"> 38</a></span> <span class="keyword">constexpr</span> <a class="code hl_function" href="structcomplex64__t.html#a89b65ace8588b7bf215355f705eb23d9">complex64_t</a>(T x) threadgroup : <a class="code hl_variable" href="structcomplex64__t.html#abbd4a0092eca9f112c1c5ae1a133a27e">real</a>(x), <a class="code hl_variable" href="structcomplex64__t.html#a94037c0cf8451aaff7cb4d154a8426de">imag</a>(0) {}</div>
<div class="line"><a id="l00039" name="l00039"></a><span class="lineno"> 39</span> </div>
<div class="line"><a id="l00040" name="l00040"></a><span class="lineno"> 40</span> <span class="keyword">template</span> &lt;</div>
<div class="line"><a id="l00041" name="l00041"></a><span class="lineno"> 41</span> <span class="keyword">typename</span> T,</div>
<div class="line"><a id="l00042" name="l00042"></a><span class="lineno"> 42</span> <span class="keyword">typename</span> = <span class="keyword">typename</span> enable_if&lt;can_convert_to_complex64&lt;T&gt;&gt;::type&gt;</div>
<div class="line"><a id="l00043" name="l00043"></a><span class="lineno"><a class="line" href="structcomplex64__t.html#ac81b486f642fb3b26c5d659917bdbcd0"> 43</a></span> <span class="keyword">constexpr</span> <a class="code hl_function" href="structcomplex64__t.html#ac81b486f642fb3b26c5d659917bdbcd0">complex64_t</a>(T x) device : <a class="code hl_variable" href="structcomplex64__t.html#abbd4a0092eca9f112c1c5ae1a133a27e">real</a>(x), <a class="code hl_variable" href="structcomplex64__t.html#a94037c0cf8451aaff7cb4d154a8426de">imag</a>(0) {}</div>
<div class="line"><a id="l00044" name="l00044"></a><span class="lineno"> 44</span> </div>
<div class="line"><a id="l00045" name="l00045"></a><span class="lineno"> 45</span> <span class="keyword">template</span> &lt;</div>
<div class="line"><a id="l00046" name="l00046"></a><span class="lineno"> 46</span> <span class="keyword">typename</span> T,</div>
<div class="line"><a id="l00047" name="l00047"></a><span class="lineno"> 47</span> <span class="keyword">typename</span> = <span class="keyword">typename</span> enable_if&lt;can_convert_to_complex64&lt;T&gt;&gt;::type&gt;</div>
<div class="line"><a id="l00048" name="l00048"></a><span class="lineno"><a class="line" href="structcomplex64__t.html#a0a27a41206400f1e62b60ceb56960c93"> 48</a></span> <span class="keyword">constexpr</span> <a class="code hl_function" href="structcomplex64__t.html#a0a27a41206400f1e62b60ceb56960c93">complex64_t</a>(T x) constant : <a class="code hl_variable" href="structcomplex64__t.html#abbd4a0092eca9f112c1c5ae1a133a27e">real</a>(x), <a class="code hl_variable" href="structcomplex64__t.html#a94037c0cf8451aaff7cb4d154a8426de">imag</a>(0) {}</div>
<div class="line"><a id="l00049" name="l00049"></a><span class="lineno"> 49</span> </div>
<div class="line"><a id="l00050" name="l00050"></a><span class="lineno"> 50</span> <span class="comment">// Conversions from complex64_t</span></div>
<div class="line"><a id="l00051" name="l00051"></a><span class="lineno"> 51</span> <span class="keyword">template</span> &lt;</div>
<div class="line"><a id="l00052" name="l00052"></a><span class="lineno"> 52</span> <span class="keyword">typename</span> T,</div>
<div class="line"><a id="l00053" name="l00053"></a><span class="lineno"> 53</span> <span class="keyword">typename</span> = <span class="keyword">typename</span> enable_if&lt;can_convert_from_complex64&lt;T&gt;&gt;::type&gt;</div>
<div class="foldopen" id="foldopen00054" data-start="{" data-end="}">
<div class="line"><a id="l00054" name="l00054"></a><span class="lineno"><a class="line" href="structcomplex64__t.html#a70e9b16031eeaff3baa601f400023fcd"> 54</a></span> <span class="keyword">constexpr</span> <span class="keyword">operator</span> T() const thread {</div>
<div class="line"><a id="l00055" name="l00055"></a><span class="lineno"> 55</span> <span class="keywordflow">return</span> <span class="keyword">static_cast&lt;</span>T<span class="keyword">&gt;</span>(<a class="code hl_variable" href="structcomplex64__t.html#abbd4a0092eca9f112c1c5ae1a133a27e">real</a>);</div>
<div class="line"><a id="l00056" name="l00056"></a><span class="lineno"> 56</span> }</div>
</div>
<div class="line"><a id="l00057" name="l00057"></a><span class="lineno"> 57</span> </div>
<div class="line"><a id="l00058" name="l00058"></a><span class="lineno"> 58</span> <span class="keyword">template</span> &lt;</div>
<div class="line"><a id="l00059" name="l00059"></a><span class="lineno"> 59</span> <span class="keyword">typename</span> T,</div>
<div class="line"><a id="l00060" name="l00060"></a><span class="lineno"> 60</span> <span class="keyword">typename</span> = <span class="keyword">typename</span> enable_if&lt;can_convert_from_complex64&lt;T&gt;&gt;::type&gt;</div>
<div class="foldopen" id="foldopen00061" data-start="{" data-end="}">
<div class="line"><a id="l00061" name="l00061"></a><span class="lineno"><a class="line" href="structcomplex64__t.html#a4f3beea7ab6001189b782a74d1746b67"> 61</a></span> <span class="keyword">constexpr</span> <span class="keyword">operator</span> T() const threadgroup {</div>
<div class="line"><a id="l00062" name="l00062"></a><span class="lineno"> 62</span> <span class="keywordflow">return</span> <span class="keyword">static_cast&lt;</span>T<span class="keyword">&gt;</span>(<a class="code hl_variable" href="structcomplex64__t.html#abbd4a0092eca9f112c1c5ae1a133a27e">real</a>);</div>
<div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</span> }</div>
</div>
<div class="line"><a id="l00064" name="l00064"></a><span class="lineno"> 64</span> </div>
<div class="line"><a id="l00065" name="l00065"></a><span class="lineno"> 65</span> <span class="keyword">template</span> &lt;</div>
<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"> 66</span> <span class="keyword">typename</span> T,</div>
<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"> 67</span> <span class="keyword">typename</span> = <span class="keyword">typename</span> enable_if&lt;can_convert_from_complex64&lt;T&gt;&gt;::type&gt;</div>
<div class="foldopen" id="foldopen00068" data-start="{" data-end="}">
<div class="line"><a id="l00068" name="l00068"></a><span class="lineno"><a class="line" href="structcomplex64__t.html#a9f4f7eca89ffe6c8d126a4145df6d9f2"> 68</a></span> <span class="keyword">constexpr</span> <span class="keyword">operator</span> T() const device {</div>
<div class="line"><a id="l00069" name="l00069"></a><span class="lineno"> 69</span> <span class="keywordflow">return</span> <span class="keyword">static_cast&lt;</span>T<span class="keyword">&gt;</span>(<a class="code hl_variable" href="structcomplex64__t.html#abbd4a0092eca9f112c1c5ae1a133a27e">real</a>);</div>
<div class="line"><a id="l00070" name="l00070"></a><span class="lineno"> 70</span> }</div>
</div>
<div class="line"><a id="l00071" name="l00071"></a><span class="lineno"> 71</span> </div>
<div class="line"><a id="l00072" name="l00072"></a><span class="lineno"> 72</span> <span class="keyword">template</span> &lt;</div>
<div class="line"><a id="l00073" name="l00073"></a><span class="lineno"> 73</span> <span class="keyword">typename</span> T,</div>
<div class="line"><a id="l00074" name="l00074"></a><span class="lineno"> 74</span> <span class="keyword">typename</span> = <span class="keyword">typename</span> enable_if&lt;can_convert_from_complex64&lt;T&gt;&gt;::type&gt;</div>
<div class="foldopen" id="foldopen00075" data-start="{" data-end="}">
<div class="line"><a id="l00075" name="l00075"></a><span class="lineno"><a class="line" href="structcomplex64__t.html#ac33e2e5263fec76a4fb4418c6e1d8d14"> 75</a></span> <span class="keyword">constexpr</span> <span class="keyword">operator</span> T() const constant {</div>
<div class="line"><a id="l00076" name="l00076"></a><span class="lineno"> 76</span> <span class="keywordflow">return</span> <span class="keyword">static_cast&lt;</span>T<span class="keyword">&gt;</span>(<a class="code hl_variable" href="structcomplex64__t.html#abbd4a0092eca9f112c1c5ae1a133a27e">real</a>);</div>
<div class="line"><a id="l00077" name="l00077"></a><span class="lineno"> 77</span> }</div>
</div>
<div class="line"><a id="l00078" name="l00078"></a><span class="lineno"> 78</span>};</div>
</div>
<div class="line"><a id="l00079" name="l00079"></a><span class="lineno"> 79</span> </div>
<div class="foldopen" id="foldopen00080" data-start="{" data-end="}">
<div class="line"><a id="l00080" name="l00080"></a><span class="lineno"><a class="line" href="backend_2metal_2kernels_2complex_8h.html#a226cfd54d49f02e35c5aab3139c7596b"> 80</a></span><span class="keyword">constexpr</span> <a class="code hl_struct" href="structcomplex64__t.html">complex64_t</a> <a class="code hl_function" href="backend_2metal_2kernels_2complex_8h.html#a226cfd54d49f02e35c5aab3139c7596b">operator-</a>(<a class="code hl_struct" href="structcomplex64__t.html">complex64_t</a> x) {</div>
<div class="line"><a id="l00081" name="l00081"></a><span class="lineno"> 81</span> <span class="keywordflow">return</span> {-x.<a class="code hl_variable" href="structcomplex64__t.html#abbd4a0092eca9f112c1c5ae1a133a27e">real</a>, -x.<a class="code hl_variable" href="structcomplex64__t.html#a94037c0cf8451aaff7cb4d154a8426de">imag</a>};</div>
<div class="line"><a id="l00082" name="l00082"></a><span class="lineno"> 82</span>}</div>
</div>
<div class="line"><a id="l00083" name="l00083"></a><span class="lineno"> 83</span> </div>
<div class="foldopen" id="foldopen00084" data-start="{" data-end="}">
<div class="line"><a id="l00084" name="l00084"></a><span class="lineno"><a class="line" href="backend_2metal_2kernels_2complex_8h.html#aafbd686c180398c98b33d7643f893a46"> 84</a></span><span class="keyword">constexpr</span> <span class="keywordtype">bool</span> <a class="code hl_function" href="backend_2metal_2kernels_2complex_8h.html#aafbd686c180398c98b33d7643f893a46">operator&gt;=</a>(<a class="code hl_struct" href="structcomplex64__t.html">complex64_t</a> a, <a class="code hl_struct" href="structcomplex64__t.html">complex64_t</a> b) {</div>
<div class="line"><a id="l00085" name="l00085"></a><span class="lineno"> 85</span> <span class="keywordflow">return</span> (a.<a class="code hl_variable" href="structcomplex64__t.html#abbd4a0092eca9f112c1c5ae1a133a27e">real</a> &gt; b.<a class="code hl_variable" href="structcomplex64__t.html#abbd4a0092eca9f112c1c5ae1a133a27e">real</a>) || (a.<a class="code hl_variable" href="structcomplex64__t.html#abbd4a0092eca9f112c1c5ae1a133a27e">real</a> == b.<a class="code hl_variable" href="structcomplex64__t.html#abbd4a0092eca9f112c1c5ae1a133a27e">real</a> &amp;&amp; a.<a class="code hl_variable" href="structcomplex64__t.html#a94037c0cf8451aaff7cb4d154a8426de">imag</a> &gt;= b.<a class="code hl_variable" href="structcomplex64__t.html#a94037c0cf8451aaff7cb4d154a8426de">imag</a>);</div>
<div class="line"><a id="l00086" name="l00086"></a><span class="lineno"> 86</span>}</div>
</div>
<div class="line"><a id="l00087" name="l00087"></a><span class="lineno"> 87</span> </div>
<div class="foldopen" id="foldopen00088" data-start="{" data-end="}">
<div class="line"><a id="l00088" name="l00088"></a><span class="lineno"><a class="line" href="backend_2metal_2kernels_2complex_8h.html#a032a8d3eec2384c9f03066f7fd945995"> 88</a></span><span class="keyword">constexpr</span> <span class="keywordtype">bool</span> <a class="code hl_function" href="backend_2metal_2kernels_2complex_8h.html#a032a8d3eec2384c9f03066f7fd945995">operator&gt;</a>(<a class="code hl_struct" href="structcomplex64__t.html">complex64_t</a> a, <a class="code hl_struct" href="structcomplex64__t.html">complex64_t</a> b) {</div>
<div class="line"><a id="l00089" name="l00089"></a><span class="lineno"> 89</span> <span class="keywordflow">return</span> (a.<a class="code hl_variable" href="structcomplex64__t.html#abbd4a0092eca9f112c1c5ae1a133a27e">real</a> &gt; b.<a class="code hl_variable" href="structcomplex64__t.html#abbd4a0092eca9f112c1c5ae1a133a27e">real</a>) || (a.<a class="code hl_variable" href="structcomplex64__t.html#abbd4a0092eca9f112c1c5ae1a133a27e">real</a> == b.<a class="code hl_variable" href="structcomplex64__t.html#abbd4a0092eca9f112c1c5ae1a133a27e">real</a> &amp;&amp; a.<a class="code hl_variable" href="structcomplex64__t.html#a94037c0cf8451aaff7cb4d154a8426de">imag</a> &gt; b.<a class="code hl_variable" href="structcomplex64__t.html#a94037c0cf8451aaff7cb4d154a8426de">imag</a>);</div>
<div class="line"><a id="l00090" name="l00090"></a><span class="lineno"> 90</span>}</div>
</div>
<div class="line"><a id="l00091" name="l00091"></a><span class="lineno"> 91</span> </div>
<div class="foldopen" id="foldopen00092" data-start="{" data-end="}">
<div class="line"><a id="l00092" name="l00092"></a><span class="lineno"><a class="line" href="backend_2metal_2kernels_2complex_8h.html#aee04c9a63c6716a99a027418354debb0"> 92</a></span><span class="keyword">constexpr</span> <span class="keywordtype">bool</span> <a class="code hl_function" href="backend_2metal_2kernels_2complex_8h.html#aee04c9a63c6716a99a027418354debb0">operator&lt;=</a>(<a class="code hl_struct" href="structcomplex64__t.html">complex64_t</a> a, <a class="code hl_struct" href="structcomplex64__t.html">complex64_t</a> b) {</div>
<div class="line"><a id="l00093" name="l00093"></a><span class="lineno"> 93</span> <span class="keywordflow">return</span> <a class="code hl_function" href="backend_2metal_2kernels_2complex_8h.html#aafbd686c180398c98b33d7643f893a46">operator&gt;=</a>(b, a);</div>
<div class="line"><a id="l00094" name="l00094"></a><span class="lineno"> 94</span>}</div>
</div>
<div class="line"><a id="l00095" name="l00095"></a><span class="lineno"> 95</span> </div>
<div class="foldopen" id="foldopen00096" data-start="{" data-end="}">
<div class="line"><a id="l00096" name="l00096"></a><span class="lineno"><a class="line" href="backend_2metal_2kernels_2complex_8h.html#a67674e32596a9dae2258bb8e0e6a2058"> 96</a></span><span class="keyword">constexpr</span> <span class="keywordtype">bool</span> <a class="code hl_function" href="backend_2metal_2kernels_2complex_8h.html#a67674e32596a9dae2258bb8e0e6a2058">operator&lt;</a>(<a class="code hl_struct" href="structcomplex64__t.html">complex64_t</a> a, <a class="code hl_struct" href="structcomplex64__t.html">complex64_t</a> b) {</div>
<div class="line"><a id="l00097" name="l00097"></a><span class="lineno"> 97</span> <span class="keywordflow">return</span> <a class="code hl_function" href="backend_2metal_2kernels_2complex_8h.html#a032a8d3eec2384c9f03066f7fd945995">operator&gt;</a>(b, a);</div>
<div class="line"><a id="l00098" name="l00098"></a><span class="lineno"> 98</span>}</div>
</div>
<div class="line"><a id="l00099" name="l00099"></a><span class="lineno"> 99</span> </div>
<div class="foldopen" id="foldopen00100" data-start="{" data-end="}">
<div class="line"><a id="l00100" name="l00100"></a><span class="lineno"><a class="line" href="backend_2metal_2kernels_2complex_8h.html#abfc19f03616441245dfc7726b278f190"> 100</a></span><span class="keyword">constexpr</span> <span class="keywordtype">bool</span> <a class="code hl_function" href="backend_2metal_2kernels_2complex_8h.html#abfc19f03616441245dfc7726b278f190">operator==</a>(<a class="code hl_struct" href="structcomplex64__t.html">complex64_t</a> a, <a class="code hl_struct" href="structcomplex64__t.html">complex64_t</a> b) {</div>
<div class="line"><a id="l00101" name="l00101"></a><span class="lineno"> 101</span> <span class="keywordflow">return</span> a.<a class="code hl_variable" href="structcomplex64__t.html#abbd4a0092eca9f112c1c5ae1a133a27e">real</a> == b.<a class="code hl_variable" href="structcomplex64__t.html#abbd4a0092eca9f112c1c5ae1a133a27e">real</a> &amp;&amp; a.<a class="code hl_variable" href="structcomplex64__t.html#a94037c0cf8451aaff7cb4d154a8426de">imag</a> == b.<a class="code hl_variable" href="structcomplex64__t.html#a94037c0cf8451aaff7cb4d154a8426de">imag</a>;</div>
<div class="line"><a id="l00102" name="l00102"></a><span class="lineno"> 102</span>}</div>
</div>
<div class="line"><a id="l00103" name="l00103"></a><span class="lineno"> 103</span> </div>
<div class="foldopen" id="foldopen00104" data-start="{" data-end="}">
<div class="line"><a id="l00104" name="l00104"></a><span class="lineno"><a class="line" href="backend_2metal_2kernels_2complex_8h.html#ad6af5c6c5ed4898b49758618e5aee189"> 104</a></span><span class="keyword">constexpr</span> <a class="code hl_struct" href="structcomplex64__t.html">complex64_t</a> <a class="code hl_function" href="backend_2metal_2kernels_2complex_8h.html#ad6af5c6c5ed4898b49758618e5aee189">operator+</a>(<a class="code hl_struct" href="structcomplex64__t.html">complex64_t</a> a, <a class="code hl_struct" href="structcomplex64__t.html">complex64_t</a> b) {</div>
<div class="line"><a id="l00105" name="l00105"></a><span class="lineno"> 105</span> <span class="keywordflow">return</span> {a.<a class="code hl_variable" href="structcomplex64__t.html#abbd4a0092eca9f112c1c5ae1a133a27e">real</a> + b.<a class="code hl_variable" href="structcomplex64__t.html#abbd4a0092eca9f112c1c5ae1a133a27e">real</a>, a.<a class="code hl_variable" href="structcomplex64__t.html#a94037c0cf8451aaff7cb4d154a8426de">imag</a> + b.<a class="code hl_variable" href="structcomplex64__t.html#a94037c0cf8451aaff7cb4d154a8426de">imag</a>};</div>
<div class="line"><a id="l00106" name="l00106"></a><span class="lineno"> 106</span>}</div>
</div>
<div class="line"><a id="l00107" name="l00107"></a><span class="lineno"> 107</span> </div>
<div class="foldopen" id="foldopen00108" data-start="{" data-end="}">
<div class="line"><a id="l00108" name="l00108"></a><span class="lineno"><a class="line" href="backend_2metal_2kernels_2complex_8h.html#af5608264cf920688607059b4e8cd3117"> 108</a></span><span class="keyword">constexpr</span> <a class="code hl_struct" href="structcomplex64__t.html">complex64_t</a> <a class="code hl_function" href="backend_2metal_2kernels_2complex_8h.html#a226cfd54d49f02e35c5aab3139c7596b">operator-</a>(<a class="code hl_struct" href="structcomplex64__t.html">complex64_t</a> a, <a class="code hl_struct" href="structcomplex64__t.html">complex64_t</a> b) {</div>
<div class="line"><a id="l00109" name="l00109"></a><span class="lineno"> 109</span> <span class="keywordflow">return</span> {a.<a class="code hl_variable" href="structcomplex64__t.html#abbd4a0092eca9f112c1c5ae1a133a27e">real</a> - b.<a class="code hl_variable" href="structcomplex64__t.html#abbd4a0092eca9f112c1c5ae1a133a27e">real</a>, a.<a class="code hl_variable" href="structcomplex64__t.html#a94037c0cf8451aaff7cb4d154a8426de">imag</a> - b.<a class="code hl_variable" href="structcomplex64__t.html#a94037c0cf8451aaff7cb4d154a8426de">imag</a>};</div>
<div class="line"><a id="l00110" name="l00110"></a><span class="lineno"> 110</span>}</div>
</div>
<div class="line"><a id="l00111" name="l00111"></a><span class="lineno"> 111</span> </div>
<div class="foldopen" id="foldopen00112" data-start="{" data-end="}">
<div class="line"><a id="l00112" name="l00112"></a><span class="lineno"><a class="line" href="backend_2metal_2kernels_2complex_8h.html#a681d4fb076973f58f7dac894ec62a385"> 112</a></span><span class="keyword">constexpr</span> <a class="code hl_struct" href="structcomplex64__t.html">complex64_t</a> <a class="code hl_function" href="backend_2metal_2kernels_2complex_8h.html#a681d4fb076973f58f7dac894ec62a385">operator*</a>(<a class="code hl_struct" href="structcomplex64__t.html">complex64_t</a> a, <a class="code hl_struct" href="structcomplex64__t.html">complex64_t</a> b) {</div>
<div class="line"><a id="l00113" name="l00113"></a><span class="lineno"> 113</span> <span class="keywordflow">return</span> {a.<a class="code hl_variable" href="structcomplex64__t.html#abbd4a0092eca9f112c1c5ae1a133a27e">real</a> * b.<a class="code hl_variable" href="structcomplex64__t.html#abbd4a0092eca9f112c1c5ae1a133a27e">real</a> - a.<a class="code hl_variable" href="structcomplex64__t.html#a94037c0cf8451aaff7cb4d154a8426de">imag</a> * b.<a class="code hl_variable" href="structcomplex64__t.html#a94037c0cf8451aaff7cb4d154a8426de">imag</a>, a.<a class="code hl_variable" href="structcomplex64__t.html#abbd4a0092eca9f112c1c5ae1a133a27e">real</a> * b.<a class="code hl_variable" href="structcomplex64__t.html#a94037c0cf8451aaff7cb4d154a8426de">imag</a> + a.<a class="code hl_variable" href="structcomplex64__t.html#a94037c0cf8451aaff7cb4d154a8426de">imag</a> * b.<a class="code hl_variable" href="structcomplex64__t.html#abbd4a0092eca9f112c1c5ae1a133a27e">real</a>};</div>
<div class="line"><a id="l00114" name="l00114"></a><span class="lineno"> 114</span>}</div>
</div>
<div class="line"><a id="l00115" name="l00115"></a><span class="lineno"> 115</span> </div>
<div class="foldopen" id="foldopen00116" data-start="{" data-end="}">
<div class="line"><a id="l00116" name="l00116"></a><span class="lineno"><a class="line" href="backend_2metal_2kernels_2complex_8h.html#ae6a708f67d6fd9b0962aa8877cec6d35"> 116</a></span><span class="keyword">constexpr</span> <a class="code hl_struct" href="structcomplex64__t.html">complex64_t</a> <a class="code hl_function" href="backend_2metal_2kernels_2complex_8h.html#ae6a708f67d6fd9b0962aa8877cec6d35">operator/</a>(<a class="code hl_struct" href="structcomplex64__t.html">complex64_t</a> a, <a class="code hl_struct" href="structcomplex64__t.html">complex64_t</a> b) {</div>
<div class="line"><a id="l00117" name="l00117"></a><span class="lineno"> 117</span> <span class="keyword">auto</span> denom = b.<a class="code hl_variable" href="structcomplex64__t.html#abbd4a0092eca9f112c1c5ae1a133a27e">real</a> * b.<a class="code hl_variable" href="structcomplex64__t.html#abbd4a0092eca9f112c1c5ae1a133a27e">real</a> + b.<a class="code hl_variable" href="structcomplex64__t.html#a94037c0cf8451aaff7cb4d154a8426de">imag</a> * b.<a class="code hl_variable" href="structcomplex64__t.html#a94037c0cf8451aaff7cb4d154a8426de">imag</a>;</div>
<div class="line"><a id="l00118" name="l00118"></a><span class="lineno"> 118</span> <span class="keyword">auto</span> x = a.<a class="code hl_variable" href="structcomplex64__t.html#abbd4a0092eca9f112c1c5ae1a133a27e">real</a> * b.<a class="code hl_variable" href="structcomplex64__t.html#abbd4a0092eca9f112c1c5ae1a133a27e">real</a> + a.<a class="code hl_variable" href="structcomplex64__t.html#a94037c0cf8451aaff7cb4d154a8426de">imag</a> * b.<a class="code hl_variable" href="structcomplex64__t.html#a94037c0cf8451aaff7cb4d154a8426de">imag</a>;</div>
<div class="line"><a id="l00119" name="l00119"></a><span class="lineno"> 119</span> <span class="keyword">auto</span> y = a.<a class="code hl_variable" href="structcomplex64__t.html#a94037c0cf8451aaff7cb4d154a8426de">imag</a> * b.<a class="code hl_variable" href="structcomplex64__t.html#abbd4a0092eca9f112c1c5ae1a133a27e">real</a> - a.<a class="code hl_variable" href="structcomplex64__t.html#abbd4a0092eca9f112c1c5ae1a133a27e">real</a> * b.<a class="code hl_variable" href="structcomplex64__t.html#a94037c0cf8451aaff7cb4d154a8426de">imag</a>;</div>
<div class="line"><a id="l00120" name="l00120"></a><span class="lineno"> 120</span> <span class="keywordflow">return</span> {x / denom, y / denom};</div>
<div class="line"><a id="l00121" name="l00121"></a><span class="lineno"> 121</span>}</div>
</div>
<div class="line"><a id="l00122" name="l00122"></a><span class="lineno"> 122</span> </div>
<div class="foldopen" id="foldopen00123" data-start="{" data-end="}">
<div class="line"><a id="l00123" name="l00123"></a><span class="lineno"><a class="line" href="backend_2metal_2kernels_2complex_8h.html#aaf53122a07c8eca858b5a8e38ae280e0"> 123</a></span><span class="keyword">constexpr</span> <a class="code hl_struct" href="structcomplex64__t.html">complex64_t</a> <a class="code hl_function" href="backend_2metal_2kernels_2complex_8h.html#aaf53122a07c8eca858b5a8e38ae280e0">operator%</a>(<a class="code hl_struct" href="structcomplex64__t.html">complex64_t</a> a, <a class="code hl_struct" href="structcomplex64__t.html">complex64_t</a> b) {</div>
<div class="line"><a id="l00124" name="l00124"></a><span class="lineno"> 124</span> <span class="keyword">auto</span> real = a.<a class="code hl_variable" href="structcomplex64__t.html#abbd4a0092eca9f112c1c5ae1a133a27e">real</a> - (b.<a class="code hl_variable" href="structcomplex64__t.html#abbd4a0092eca9f112c1c5ae1a133a27e">real</a> * <span class="keyword">static_cast&lt;</span>int64_t<span class="keyword">&gt;</span>(a.<a class="code hl_variable" href="structcomplex64__t.html#abbd4a0092eca9f112c1c5ae1a133a27e">real</a> / b.<a class="code hl_variable" href="structcomplex64__t.html#abbd4a0092eca9f112c1c5ae1a133a27e">real</a>));</div>
<div class="line"><a id="l00125" name="l00125"></a><span class="lineno"> 125</span> <span class="keyword">auto</span> imag = a.<a class="code hl_variable" href="structcomplex64__t.html#a94037c0cf8451aaff7cb4d154a8426de">imag</a> - (b.<a class="code hl_variable" href="structcomplex64__t.html#a94037c0cf8451aaff7cb4d154a8426de">imag</a> * <span class="keyword">static_cast&lt;</span>int64_t<span class="keyword">&gt;</span>(a.<a class="code hl_variable" href="structcomplex64__t.html#a94037c0cf8451aaff7cb4d154a8426de">imag</a> / b.<a class="code hl_variable" href="structcomplex64__t.html#a94037c0cf8451aaff7cb4d154a8426de">imag</a>));</div>
<div class="line"><a id="l00126" name="l00126"></a><span class="lineno"> 126</span> <span class="keywordflow">if</span> (real != 0 &amp;&amp; (real &lt; 0 != b.<a class="code hl_variable" href="structcomplex64__t.html#abbd4a0092eca9f112c1c5ae1a133a27e">real</a> &lt; 0)) {</div>
<div class="line"><a id="l00127" name="l00127"></a><span class="lineno"> 127</span> real += b.<a class="code hl_variable" href="structcomplex64__t.html#abbd4a0092eca9f112c1c5ae1a133a27e">real</a>;</div>
<div class="line"><a id="l00128" name="l00128"></a><span class="lineno"> 128</span> }</div>
<div class="line"><a id="l00129" name="l00129"></a><span class="lineno"> 129</span> <span class="keywordflow">if</span> (imag != 0 &amp;&amp; (imag &lt; 0 != b.<a class="code hl_variable" href="structcomplex64__t.html#a94037c0cf8451aaff7cb4d154a8426de">imag</a> &lt; 0)) {</div>
<div class="line"><a id="l00130" name="l00130"></a><span class="lineno"> 130</span> imag += b.<a class="code hl_variable" href="structcomplex64__t.html#a94037c0cf8451aaff7cb4d154a8426de">imag</a>;</div>
<div class="line"><a id="l00131" name="l00131"></a><span class="lineno"> 131</span> }</div>
<div class="line"><a id="l00132" name="l00132"></a><span class="lineno"> 132</span> <span class="keywordflow">return</span> {real, imag};</div>
<div class="line"><a id="l00133" name="l00133"></a><span class="lineno"> 133</span>}</div>
</div>
<div class="ttc" id="abackend_2metal_2kernels_2complex_8h_html_a032a8d3eec2384c9f03066f7fd945995"><div class="ttname"><a href="backend_2metal_2kernels_2complex_8h.html#a032a8d3eec2384c9f03066f7fd945995">operator&gt;</a></div><div class="ttdeci">constexpr bool operator&gt;(complex64_t a, complex64_t b)</div><div class="ttdef"><b>Definition</b> complex.h:88</div></div>
<div class="ttc" id="abackend_2metal_2kernels_2complex_8h_html_a226cfd54d49f02e35c5aab3139c7596b"><div class="ttname"><a href="backend_2metal_2kernels_2complex_8h.html#a226cfd54d49f02e35c5aab3139c7596b">operator-</a></div><div class="ttdeci">constexpr complex64_t operator-(complex64_t x)</div><div class="ttdef"><b>Definition</b> complex.h:80</div></div>
<div class="ttc" id="abackend_2metal_2kernels_2complex_8h_html_a4f90ad54f4fae363e8d3cc41d539557b"><div class="ttname"><a href="backend_2metal_2kernels_2complex_8h.html#a4f90ad54f4fae363e8d3cc41d539557b">can_convert_to_complex64</a></div><div class="ttdeci">static constexpr constant bool can_convert_to_complex64</div><div class="ttdef"><b>Definition</b> complex.h:12</div></div>
<div class="ttc" id="abackend_2metal_2kernels_2complex_8h_html_a67674e32596a9dae2258bb8e0e6a2058"><div class="ttname"><a href="backend_2metal_2kernels_2complex_8h.html#a67674e32596a9dae2258bb8e0e6a2058">operator&lt;</a></div><div class="ttdeci">constexpr bool operator&lt;(complex64_t a, complex64_t b)</div><div class="ttdef"><b>Definition</b> complex.h:96</div></div>
<div class="ttc" id="abackend_2metal_2kernels_2complex_8h_html_a681d4fb076973f58f7dac894ec62a385"><div class="ttname"><a href="backend_2metal_2kernels_2complex_8h.html#a681d4fb076973f58f7dac894ec62a385">operator*</a></div><div class="ttdeci">constexpr complex64_t operator*(complex64_t a, complex64_t b)</div><div class="ttdef"><b>Definition</b> complex.h:112</div></div>
<div class="ttc" id="abackend_2metal_2kernels_2complex_8h_html_aaf53122a07c8eca858b5a8e38ae280e0"><div class="ttname"><a href="backend_2metal_2kernels_2complex_8h.html#aaf53122a07c8eca858b5a8e38ae280e0">operator%</a></div><div class="ttdeci">constexpr complex64_t operator%(complex64_t a, complex64_t b)</div><div class="ttdef"><b>Definition</b> complex.h:123</div></div>
<div class="ttc" id="abackend_2metal_2kernels_2complex_8h_html_aafbd686c180398c98b33d7643f893a46"><div class="ttname"><a href="backend_2metal_2kernels_2complex_8h.html#aafbd686c180398c98b33d7643f893a46">operator&gt;=</a></div><div class="ttdeci">constexpr bool operator&gt;=(complex64_t a, complex64_t b)</div><div class="ttdef"><b>Definition</b> complex.h:84</div></div>
<div class="ttc" id="abackend_2metal_2kernels_2complex_8h_html_ab149db78f6f19b8da6297dac4c36d893"><div class="ttname"><a href="backend_2metal_2kernels_2complex_8h.html#ab149db78f6f19b8da6297dac4c36d893">can_convert_from_complex64</a></div><div class="ttdeci">static constexpr constant bool can_convert_from_complex64</div><div class="ttdef"><b>Definition</b> complex.h:16</div></div>
<div class="ttc" id="abackend_2metal_2kernels_2complex_8h_html_abfc19f03616441245dfc7726b278f190"><div class="ttname"><a href="backend_2metal_2kernels_2complex_8h.html#abfc19f03616441245dfc7726b278f190">operator==</a></div><div class="ttdeci">constexpr bool operator==(complex64_t a, complex64_t b)</div><div class="ttdef"><b>Definition</b> complex.h:100</div></div>
<div class="ttc" id="abackend_2metal_2kernels_2complex_8h_html_ad6af5c6c5ed4898b49758618e5aee189"><div class="ttname"><a href="backend_2metal_2kernels_2complex_8h.html#ad6af5c6c5ed4898b49758618e5aee189">operator+</a></div><div class="ttdeci">constexpr complex64_t operator+(complex64_t a, complex64_t b)</div><div class="ttdef"><b>Definition</b> complex.h:104</div></div>
<div class="ttc" id="abackend_2metal_2kernels_2complex_8h_html_ae6a708f67d6fd9b0962aa8877cec6d35"><div class="ttname"><a href="backend_2metal_2kernels_2complex_8h.html#ae6a708f67d6fd9b0962aa8877cec6d35">operator/</a></div><div class="ttdeci">constexpr complex64_t operator/(complex64_t a, complex64_t b)</div><div class="ttdef"><b>Definition</b> complex.h:116</div></div>
<div class="ttc" id="abackend_2metal_2kernels_2complex_8h_html_aee04c9a63c6716a99a027418354debb0"><div class="ttname"><a href="backend_2metal_2kernels_2complex_8h.html#aee04c9a63c6716a99a027418354debb0">operator&lt;=</a></div><div class="ttdeci">constexpr bool operator&lt;=(complex64_t a, complex64_t b)</div><div class="ttdef"><b>Definition</b> complex.h:92</div></div>
<div class="ttc" id="anamespacemetal_html"><div class="ttname"><a href="namespacemetal.html">metal</a></div><div class="ttdef"><b>Definition</b> bf16_math.h:226</div></div>
<div class="ttc" id="astructcomplex64__t_html"><div class="ttname"><a href="structcomplex64__t.html">complex64_t</a></div><div class="ttdef"><b>Definition</b> complex.h:20</div></div>
<div class="ttc" id="astructcomplex64__t_html_a0a27a41206400f1e62b60ceb56960c93"><div class="ttname"><a href="structcomplex64__t.html#a0a27a41206400f1e62b60ceb56960c93">complex64_t::complex64_t</a></div><div class="ttdeci">constexpr complex64_t(T x) const ant</div><div class="ttdef"><b>Definition</b> complex.h:48</div></div>
<div class="ttc" id="astructcomplex64__t_html_a29782289bb90d6294099667b86509cd3"><div class="ttname"><a href="structcomplex64__t.html#a29782289bb90d6294099667b86509cd3">complex64_t::complex64_t</a></div><div class="ttdeci">constexpr complex64_t()</div><div class="ttdef"><b>Definition</b> complex.h:26</div></div>
<div class="ttc" id="astructcomplex64__t_html_a33a2452eb33b5ed53655773539c357a5"><div class="ttname"><a href="structcomplex64__t.html#a33a2452eb33b5ed53655773539c357a5">complex64_t::complex64_t</a></div><div class="ttdeci">constexpr complex64_t(T x) thread</div><div class="ttdef"><b>Definition</b> complex.h:33</div></div>
<div class="ttc" id="astructcomplex64__t_html_a89b65ace8588b7bf215355f705eb23d9"><div class="ttname"><a href="structcomplex64__t.html#a89b65ace8588b7bf215355f705eb23d9">complex64_t::complex64_t</a></div><div class="ttdeci">constexpr complex64_t(T x) threadgroup</div><div class="ttdef"><b>Definition</b> complex.h:38</div></div>
<div class="ttc" id="astructcomplex64__t_html_a905b048d70eb8d748a62454268242291"><div class="ttname"><a href="structcomplex64__t.html#a905b048d70eb8d748a62454268242291">complex64_t::complex64_t</a></div><div class="ttdeci">constexpr complex64_t() threadgroup</div><div class="ttdef"><b>Definition</b> complex.h:27</div></div>
<div class="ttc" id="astructcomplex64__t_html_a94037c0cf8451aaff7cb4d154a8426de"><div class="ttname"><a href="structcomplex64__t.html#a94037c0cf8451aaff7cb4d154a8426de">complex64_t::imag</a></div><div class="ttdeci">float imag</div><div class="ttdef"><b>Definition</b> complex.h:22</div></div>
<div class="ttc" id="astructcomplex64__t_html_abbd4a0092eca9f112c1c5ae1a133a27e"><div class="ttname"><a href="structcomplex64__t.html#abbd4a0092eca9f112c1c5ae1a133a27e">complex64_t::real</a></div><div class="ttdeci">float real</div><div class="ttdef"><b>Definition</b> complex.h:21</div></div>
<div class="ttc" id="astructcomplex64__t_html_ac81b486f642fb3b26c5d659917bdbcd0"><div class="ttname"><a href="structcomplex64__t.html#ac81b486f642fb3b26c5d659917bdbcd0">complex64_t::complex64_t</a></div><div class="ttdeci">constexpr complex64_t(T x) device</div><div class="ttdef"><b>Definition</b> complex.h:43</div></div>
<div class="ttc" id="astructcomplex64__t_html_adbd392a5e92d31997380ad0a38be4be8"><div class="ttname"><a href="structcomplex64__t.html#adbd392a5e92d31997380ad0a38be4be8">complex64_t::complex64_t</a></div><div class="ttdeci">constexpr complex64_t(float real, float imag)</div><div class="ttdef"><b>Definition</b> complex.h:25</div></div>
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