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<a href="common_2hadamard_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 © 2024 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;map&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="preprocessor">#include &quot;<a class="code" href="utils_8h.html">mlx/utils.h</a>&quot;</span></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">namespace </span><a class="code hl_namespace" href="namespacemlx_1_1core.html">mlx::core</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="comment">// From http://neilsloane.com/hadamard/</span></div>
<div class="line"><a id="l00012" name="l00012"></a><span class="lineno"><a class="line" href="namespacemlx_1_1core.html#a4beeeec4413be7adcfb14feaa9cf0e2e"> 12</a></span><span class="keyword">constexpr</span> std::string_view <a class="code hl_variable" href="namespacemlx_1_1core.html#a4beeeec4413be7adcfb14feaa9cf0e2e">h12</a> = R<span class="stringliteral">&quot;(</span></div>
<div class="line"><a id="l00013" name="l00013"></a><span class="lineno"> 13</span><span class="stringliteral">+-++++++++++</span></div>
<div class="line"><a id="l00014" name="l00014"></a><span class="lineno"> 14</span><span class="stringliteral">--+-+-+-+-+-</span></div>
<div class="line"><a id="l00015" name="l00015"></a><span class="lineno"> 15</span><span class="stringliteral">+++-++----++</span></div>
<div class="line"><a id="l00016" name="l00016"></a><span class="lineno"> 16</span><span class="stringliteral">+---+--+-++-</span></div>
<div class="line"><a id="l00017" name="l00017"></a><span class="lineno"> 17</span><span class="stringliteral">+++++-++----</span></div>
<div class="line"><a id="l00018" name="l00018"></a><span class="lineno"> 18</span><span class="stringliteral">+-+---+--+-+</span></div>
<div class="line"><a id="l00019" name="l00019"></a><span class="lineno"> 19</span><span class="stringliteral">++--+++-++--</span></div>
<div class="line"><a id="l00020" name="l00020"></a><span class="lineno"> 20</span><span class="stringliteral">+--++---+--+</span></div>
<div class="line"><a id="l00021" name="l00021"></a><span class="lineno"> 21</span><span class="stringliteral">++----+++-++</span></div>
<div class="line"><a id="l00022" name="l00022"></a><span class="lineno"> 22</span><span class="stringliteral">+--+-++---+-</span></div>
<div class="line"><a id="l00023" name="l00023"></a><span class="lineno"> 23</span><span class="stringliteral">++++----+++-</span></div>
<div class="line"><a id="l00024" name="l00024"></a><span class="lineno"> 24</span><span class="stringliteral">+-+--+-++---</span></div>
<div class="line"><a id="l00025" name="l00025"></a><span class="lineno"> 25</span><span class="stringliteral">)&quot;;</span></div>
<div class="line"><a id="l00026" name="l00026"></a><span class="lineno"> 26</span><span class="stringliteral"></span> </div>
<div class="line"><a id="l00027" name="l00027"></a><span class="lineno"><a class="line" href="namespacemlx_1_1core.html#a862c6b94fec384c34a699ced64d01404"> 27</a></span><span class="stringliteral"></span><span class="keyword">constexpr</span> std::string_view <a class="code hl_variable" href="namespacemlx_1_1core.html#a862c6b94fec384c34a699ced64d01404">h20</a> = R<span class="stringliteral">&quot;(</span></div>
<div class="line"><a id="l00028" name="l00028"></a><span class="lineno"> 28</span><span class="stringliteral">+----+----++--++-++-</span></div>
<div class="line"><a id="l00029" name="l00029"></a><span class="lineno"> 29</span><span class="stringliteral">-+----+---+++---+-++</span></div>
<div class="line"><a id="l00030" name="l00030"></a><span class="lineno"> 30</span><span class="stringliteral">--+----+---+++-+-+-+</span></div>
<div class="line"><a id="l00031" name="l00031"></a><span class="lineno"> 31</span><span class="stringliteral">---+----+---+++++-+-</span></div>
<div class="line"><a id="l00032" name="l00032"></a><span class="lineno"> 32</span><span class="stringliteral">----+----++--++-++-+</span></div>
<div class="line"><a id="l00033" name="l00033"></a><span class="lineno"> 33</span><span class="stringliteral">-+++++-----+--+++--+</span></div>
<div class="line"><a id="l00034" name="l00034"></a><span class="lineno"> 34</span><span class="stringliteral">+-+++-+---+-+--+++--</span></div>
<div class="line"><a id="l00035" name="l00035"></a><span class="lineno"> 35</span><span class="stringliteral">++-++--+---+-+--+++-</span></div>
<div class="line"><a id="l00036" name="l00036"></a><span class="lineno"> 36</span><span class="stringliteral">+++-+---+---+-+--+++</span></div>
<div class="line"><a id="l00037" name="l00037"></a><span class="lineno"> 37</span><span class="stringliteral">++++-----++--+-+--++</span></div>
<div class="line"><a id="l00038" name="l00038"></a><span class="lineno"> 38</span><span class="stringliteral">--++-+-++-+-----++++</span></div>
<div class="line"><a id="l00039" name="l00039"></a><span class="lineno"> 39</span><span class="stringliteral">---++-+-++-+---+-+++</span></div>
<div class="line"><a id="l00040" name="l00040"></a><span class="lineno"> 40</span><span class="stringliteral">+---++-+-+--+--++-++</span></div>
<div class="line"><a id="l00041" name="l00041"></a><span class="lineno"> 41</span><span class="stringliteral">++---++-+----+-+++-+</span></div>
<div class="line"><a id="l00042" name="l00042"></a><span class="lineno"> 42</span><span class="stringliteral">-++---++-+----+++++-</span></div>
<div class="line"><a id="l00043" name="l00043"></a><span class="lineno"> 43</span><span class="stringliteral">-+--+--++-+----+----</span></div>
<div class="line"><a id="l00044" name="l00044"></a><span class="lineno"> 44</span><span class="stringliteral">+-+-----++-+----+---</span></div>
<div class="line"><a id="l00045" name="l00045"></a><span class="lineno"> 45</span><span class="stringliteral">-+-+-+---+--+----+--</span></div>
<div class="line"><a id="l00046" name="l00046"></a><span class="lineno"> 46</span><span class="stringliteral">--+-+++------+----+-</span></div>
<div class="line"><a id="l00047" name="l00047"></a><span class="lineno"> 47</span><span class="stringliteral">+--+--++------+----+</span></div>
<div class="line"><a id="l00048" name="l00048"></a><span class="lineno"> 48</span><span class="stringliteral">)&quot;;</span></div>
<div class="line"><a id="l00049" name="l00049"></a><span class="lineno"> 49</span><span class="stringliteral"></span> </div>
<div class="line"><a id="l00050" name="l00050"></a><span class="lineno"><a class="line" href="namespacemlx_1_1core.html#ac447ad59592dd06435adca7df37e33ad"> 50</a></span><span class="stringliteral"></span><span class="keyword">constexpr</span> std::string_view <a class="code hl_variable" href="namespacemlx_1_1core.html#ac447ad59592dd06435adca7df37e33ad">h28</a> = R<span class="stringliteral">&quot;(</span></div>
<div class="line"><a id="l00051" name="l00051"></a><span class="lineno"> 51</span><span class="stringliteral">+------++----++-+--+-+--++--</span></div>
<div class="line"><a id="l00052" name="l00052"></a><span class="lineno"> 52</span><span class="stringliteral">-+-----+++-----+-+--+-+--++-</span></div>
<div class="line"><a id="l00053" name="l00053"></a><span class="lineno"> 53</span><span class="stringliteral">--+-----+++---+-+-+----+--++</span></div>
<div class="line"><a id="l00054" name="l00054"></a><span class="lineno"> 54</span><span class="stringliteral">---+-----+++---+-+-+-+--+--+</span></div>
<div class="line"><a id="l00055" name="l00055"></a><span class="lineno"> 55</span><span class="stringliteral">----+-----+++---+-+-+++--+--</span></div>
<div class="line"><a id="l00056" name="l00056"></a><span class="lineno"> 56</span><span class="stringliteral">-----+-----++++--+-+--++--+-</span></div>
<div class="line"><a id="l00057" name="l00057"></a><span class="lineno"> 57</span><span class="stringliteral">------++----++-+--+-+--++--+</span></div>
<div class="line"><a id="l00058" name="l00058"></a><span class="lineno"> 58</span><span class="stringliteral">--++++-+-------++--+++-+--+-</span></div>
<div class="line"><a id="l00059" name="l00059"></a><span class="lineno"> 59</span><span class="stringliteral">---++++-+-----+-++--+-+-+--+</span></div>
<div class="line"><a id="l00060" name="l00060"></a><span class="lineno"> 60</span><span class="stringliteral">+---+++--+----++-++--+-+-+--</span></div>
<div class="line"><a id="l00061" name="l00061"></a><span class="lineno"> 61</span><span class="stringliteral">++---++---+----++-++--+-+-+-</span></div>
<div class="line"><a id="l00062" name="l00062"></a><span class="lineno"> 62</span><span class="stringliteral">+++---+----+----++-++--+-+-+</span></div>
<div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</span><span class="stringliteral">++++--------+-+--++-++--+-+-</span></div>
<div class="line"><a id="l00064" name="l00064"></a><span class="lineno"> 64</span><span class="stringliteral">-++++--------+++--++--+--+-+</span></div>
<div class="line"><a id="l00065" name="l00065"></a><span class="lineno"> 65</span><span class="stringliteral">-+-++-++--++--+--------++++-</span></div>
<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"> 66</span><span class="stringliteral">+-+-++--+--++--+--------++++</span></div>
<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"> 67</span><span class="stringliteral">-+-+-++--+--++--+----+---+++</span></div>
<div class="line"><a id="l00068" name="l00068"></a><span class="lineno"> 68</span><span class="stringliteral">+-+-+-++--+--+---+---++---++</span></div>
<div class="line"><a id="l00069" name="l00069"></a><span class="lineno"> 69</span><span class="stringliteral">++-+-+-++--+------+--+++---+</span></div>
<div class="line"><a id="l00070" name="l00070"></a><span class="lineno"> 70</span><span class="stringliteral">-++-+-+-++--+------+-++++---</span></div>
<div class="line"><a id="l00071" name="l00071"></a><span class="lineno"> 71</span><span class="stringliteral">+-++-+---++--+------+-++++--</span></div>
<div class="line"><a id="l00072" name="l00072"></a><span class="lineno"> 72</span><span class="stringliteral">-++--++-+-++-+++----++------</span></div>
<div class="line"><a id="l00073" name="l00073"></a><span class="lineno"> 73</span><span class="stringliteral">+-++--++-+-++-+++-----+-----</span></div>
<div class="line"><a id="l00074" name="l00074"></a><span class="lineno"> 74</span><span class="stringliteral">++-++---+-+-++-+++-----+----</span></div>
<div class="line"><a id="l00075" name="l00075"></a><span class="lineno"> 75</span><span class="stringliteral">-++-++-+-+-+-+--+++-----+---</span></div>
<div class="line"><a id="l00076" name="l00076"></a><span class="lineno"> 76</span><span class="stringliteral">--++-++++-+-+----+++-----+--</span></div>
<div class="line"><a id="l00077" name="l00077"></a><span class="lineno"> 77</span><span class="stringliteral">+--++-+-++-+-+----+++-----+-</span></div>
<div class="line"><a id="l00078" name="l00078"></a><span class="lineno"> 78</span><span class="stringliteral">++--++-+-++-+-+----++------+</span></div>
<div class="line"><a id="l00079" name="l00079"></a><span class="lineno"> 79</span><span class="stringliteral">)&quot;;</span></div>
<div class="line"><a id="l00080" name="l00080"></a><span class="lineno"> 80</span><span class="stringliteral"></span> </div>
<div class="foldopen" id="foldopen00081" data-start="{" data-end="}">
<div class="line"><a id="l00081" name="l00081"></a><span class="lineno"><a class="line" href="namespacemlx_1_1core.html#a50214cf406957fab27c8bef32046f030"> 81</a></span><span class="stringliteral"></span><span class="keyword">inline</span> <span class="keyword">const</span> std::map&lt;int, std::string_view&gt; <a class="code hl_function" href="namespacemlx_1_1core.html#a50214cf406957fab27c8bef32046f030">hadamard_matrices</a>() {</div>
<div class="line"><a id="l00082" name="l00082"></a><span class="lineno"> 82</span> <span class="keywordflow">return</span> {{12, <a class="code hl_variable" href="namespacemlx_1_1core.html#a4beeeec4413be7adcfb14feaa9cf0e2e">h12</a>}, {20, <a class="code hl_variable" href="namespacemlx_1_1core.html#a862c6b94fec384c34a699ced64d01404">h20</a>}, {28, <a class="code hl_variable" href="namespacemlx_1_1core.html#ac447ad59592dd06435adca7df37e33ad">h28</a>}};</div>
<div class="line"><a id="l00083" name="l00083"></a><span class="lineno"> 83</span>}</div>
</div>
<div class="line"><a id="l00084" name="l00084"></a><span class="lineno"> 84</span> </div>
<div class="foldopen" id="foldopen00085" data-start="{" data-end="}">
<div class="line"><a id="l00085" name="l00085"></a><span class="lineno"><a class="line" href="namespacemlx_1_1core.html#a3a8fe7ba84714dbb5fdc81e93a07abc8"> 85</a></span><span class="keyword">inline</span> std::pair&lt;int, int&gt; <a class="code hl_function" href="namespacemlx_1_1core.html#a3a8fe7ba84714dbb5fdc81e93a07abc8">decompose_hadamard</a>(<span class="keywordtype">int</span> n) {</div>
<div class="line"><a id="l00086" name="l00086"></a><span class="lineno"> 86</span> <span class="comment">// n = m*2^k</span></div>
<div class="line"><a id="l00087" name="l00087"></a><span class="lineno"> 87</span> <span class="keywordtype">int</span> m = 1;</div>
<div class="line"><a id="l00088" name="l00088"></a><span class="lineno"> 88</span> <span class="keywordflow">if</span> (!<a class="code hl_function" href="namespacemlx_1_1core.html#adacbc4526e8964b267a8ec3eb1bc1a32">is_power_of_2</a>(n)) {</div>
<div class="line"><a id="l00089" name="l00089"></a><span class="lineno"> 89</span> <span class="keyword">auto</span> h_matrices = <a class="code hl_function" href="namespacemlx_1_1core.html#a50214cf406957fab27c8bef32046f030">hadamard_matrices</a>();</div>
<div class="line"><a id="l00090" name="l00090"></a><span class="lineno"> 90</span> <span class="keywordflow">for</span> (<span class="keyword">auto</span> [factor, _] : h_matrices) {</div>
<div class="line"><a id="l00091" name="l00091"></a><span class="lineno"> 91</span> <span class="keywordflow">if</span> (n % factor == 0) {</div>
<div class="line"><a id="l00092" name="l00092"></a><span class="lineno"> 92</span> m = factor;</div>
<div class="line"><a id="l00093" name="l00093"></a><span class="lineno"> 93</span> n /= factor;</div>
<div class="line"><a id="l00094" name="l00094"></a><span class="lineno"> 94</span> <span class="keywordflow">break</span>;</div>
<div class="line"><a id="l00095" name="l00095"></a><span class="lineno"> 95</span> }</div>
<div class="line"><a id="l00096" name="l00096"></a><span class="lineno"> 96</span> }</div>
<div class="line"><a id="l00097" name="l00097"></a><span class="lineno"> 97</span> <span class="keywordflow">if</span> (m == 1) {</div>
<div class="line"><a id="l00098" name="l00098"></a><span class="lineno"> 98</span> <span class="keywordflow">throw</span> std::invalid_argument(</div>
<div class="line"><a id="l00099" name="l00099"></a><span class="lineno"> 99</span> <span class="stringliteral">&quot;[hadamard] Only supports n = m*2^k where m in (1, 12, 20, 28).&quot;</span>);</div>
<div class="line"><a id="l00100" name="l00100"></a><span class="lineno"> 100</span> }</div>
<div class="line"><a id="l00101" name="l00101"></a><span class="lineno"> 101</span> }</div>
<div class="line"><a id="l00102" name="l00102"></a><span class="lineno"> 102</span> <span class="keywordflow">return</span> {n, m};</div>
<div class="line"><a id="l00103" name="l00103"></a><span class="lineno"> 103</span>}</div>
</div>
<div class="line"><a id="l00104" name="l00104"></a><span class="lineno"> 104</span> </div>
<div class="line"><a id="l00105" name="l00105"></a><span class="lineno"> 105</span>} <span class="comment">// namespace mlx::core</span></div>
<div class="ttc" id="anamespacemlx_1_1core_html"><div class="ttname"><a href="namespacemlx_1_1core.html">mlx::core</a></div><div class="ttdef"><b>Definition</b> allocator.h:7</div></div>
<div class="ttc" id="anamespacemlx_1_1core_html_a3a8fe7ba84714dbb5fdc81e93a07abc8"><div class="ttname"><a href="namespacemlx_1_1core.html#a3a8fe7ba84714dbb5fdc81e93a07abc8">mlx::core::decompose_hadamard</a></div><div class="ttdeci">std::pair&lt; int, int &gt; decompose_hadamard(int n)</div><div class="ttdef"><b>Definition</b> hadamard.h:85</div></div>
<div class="ttc" id="anamespacemlx_1_1core_html_a4beeeec4413be7adcfb14feaa9cf0e2e"><div class="ttname"><a href="namespacemlx_1_1core.html#a4beeeec4413be7adcfb14feaa9cf0e2e">mlx::core::h12</a></div><div class="ttdeci">constexpr std::string_view h12</div><div class="ttdef"><b>Definition</b> hadamard.h:12</div></div>
<div class="ttc" id="anamespacemlx_1_1core_html_a50214cf406957fab27c8bef32046f030"><div class="ttname"><a href="namespacemlx_1_1core.html#a50214cf406957fab27c8bef32046f030">mlx::core::hadamard_matrices</a></div><div class="ttdeci">const std::map&lt; int, std::string_view &gt; hadamard_matrices()</div><div class="ttdef"><b>Definition</b> hadamard.h:81</div></div>
<div class="ttc" id="anamespacemlx_1_1core_html_a862c6b94fec384c34a699ced64d01404"><div class="ttname"><a href="namespacemlx_1_1core.html#a862c6b94fec384c34a699ced64d01404">mlx::core::h20</a></div><div class="ttdeci">constexpr std::string_view h20</div><div class="ttdef"><b>Definition</b> hadamard.h:27</div></div>
<div class="ttc" id="anamespacemlx_1_1core_html_ac447ad59592dd06435adca7df37e33ad"><div class="ttname"><a href="namespacemlx_1_1core.html#ac447ad59592dd06435adca7df37e33ad">mlx::core::h28</a></div><div class="ttdeci">constexpr std::string_view h28</div><div class="ttdef"><b>Definition</b> hadamard.h:50</div></div>
<div class="ttc" id="anamespacemlx_1_1core_html_adacbc4526e8964b267a8ec3eb1bc1a32"><div class="ttname"><a href="namespacemlx_1_1core.html#adacbc4526e8964b267a8ec3eb1bc1a32">mlx::core::is_power_of_2</a></div><div class="ttdeci">bool is_power_of_2(int n)</div><div class="ttdef"><b>Definition</b> utils.h:122</div></div>
<div class="ttc" id="autils_8h_html"><div class="ttname"><a href="utils_8h.html">utils.h</a></div></div>
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