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<a href="metal_2kernels_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><span class="preprocessor">#include &lt;metal_common&gt;</span></div>
<div class="line"><a id="l00003" name="l00003"></a><span class="lineno"> 3</span><span class="preprocessor">#include &lt;metal_compute&gt;</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 &quot;<a class="code" href="steel_2defines_8h.html">mlx/backend/metal/kernels/steel/defines.h</a>&quot;</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="comment">// Thread local Hadamard transform for 2^R</span></div>
<div class="line"><a id="l00010" name="l00010"></a><span class="lineno"> 10</span><span class="keyword">template</span> &lt;<span class="keywordtype">short</span> R&gt;</div>
<div class="foldopen" id="foldopen00011" data-start="{" data-end="}">
<div class="line"><a id="l00011" name="l00011"></a><span class="lineno"><a class="line" href="metal_2kernels_2hadamard_8h.html#a590e5366adc78bab4fe44e37885d413f"> 11</a></span>METAL_FUNC <span class="keywordtype">void</span> <a class="code hl_function" href="metal_2kernels_2hadamard_8h.html#a590e5366adc78bab4fe44e37885d413f">radix_func</a>(thread <span class="keywordtype">float</span>* x) {</div>
<div class="line"><a id="l00012" name="l00012"></a><span class="lineno"> 12</span> <span class="keyword">constexpr</span> <span class="keywordtype">short</span> logR = __builtin_ctz(R);</div>
<div class="line"><a id="l00013" name="l00013"></a><span class="lineno"> 13</span> <span class="keywordtype">short</span> h = 1;</div>
<div class="line"><a id="l00014" name="l00014"></a><span class="lineno"> 14</span> <a class="code hl_define" href="steel_2defines_8h.html#a5a5c3095b132a7589bc19cd5cb80e2c6">STEEL_PRAGMA_UNROLL</a></div>
<div class="line"><a id="l00015" name="l00015"></a><span class="lineno"> 15</span> <span class="keywordflow">for</span> (<span class="keywordtype">short</span> s = 0; s &lt; logR; s++) {</div>
<div class="line"><a id="l00016" name="l00016"></a><span class="lineno"> 16</span> <a class="code hl_define" href="steel_2defines_8h.html#a5a5c3095b132a7589bc19cd5cb80e2c6">STEEL_PRAGMA_UNROLL</a></div>
<div class="line"><a id="l00017" name="l00017"></a><span class="lineno"> 17</span> <span class="keywordflow">for</span> (<span class="keywordtype">short</span> i = 0; i &lt; R / 2; i++) {</div>
<div class="line"><a id="l00018" name="l00018"></a><span class="lineno"> 18</span> <span class="keywordtype">short</span> k = i &amp; (h - 1);</div>
<div class="line"><a id="l00019" name="l00019"></a><span class="lineno"> 19</span> <span class="keywordtype">short</span> j = ((i - k) &lt;&lt; 1) + k;</div>
<div class="line"><a id="l00020" name="l00020"></a><span class="lineno"> 20</span> <span class="keywordtype">float</span> a = x[j];</div>
<div class="line"><a id="l00021" name="l00021"></a><span class="lineno"> 21</span> <span class="keywordtype">float</span> b = x[j + h];</div>
<div class="line"><a id="l00022" name="l00022"></a><span class="lineno"> 22</span> x[j] = a + b;</div>
<div class="line"><a id="l00023" name="l00023"></a><span class="lineno"> 23</span> x[j + h] = a - b;</div>
<div class="line"><a id="l00024" name="l00024"></a><span class="lineno"> 24</span> }</div>
<div class="line"><a id="l00025" name="l00025"></a><span class="lineno"> 25</span> h &lt;&lt;= 1;</div>
<div class="line"><a id="l00026" name="l00026"></a><span class="lineno"> 26</span> }</div>
<div class="line"><a id="l00027" name="l00027"></a><span class="lineno"> 27</span>}</div>
</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="keyword">template</span> &lt;<span class="keyword">typename</span> T, <span class="keywordtype">int</span> N, <span class="keywordtype">int</span> max_radix, <span class="keywordtype">int</span> read_w<span class="keywordtype">id</span>th&gt;</div>
<div class="foldopen" id="foldopen00030" data-start="{" data-end="}">
<div class="line"><a id="l00030" name="l00030"></a><span class="lineno"><a class="line" href="metal_2kernels_2hadamard_8h.html#a63c0e8510e555cd065e1f0ddfb33ce18"> 30</a></span>[[kernel]] <span class="keywordtype">void</span> <a class="code hl_function" href="metal_2kernels_2hadamard_8h.html#a63c0e8510e555cd065e1f0ddfb33ce18">hadamard_n</a>(</div>
<div class="line"><a id="l00031" name="l00031"></a><span class="lineno"> 31</span> <span class="keyword">const</span> device T* in [[buffer(0)]],</div>
<div class="line"><a id="l00032" name="l00032"></a><span class="lineno"> 32</span> device T* out [[buffer(1)]],</div>
<div class="line"><a id="l00033" name="l00033"></a><span class="lineno"> 33</span> constant <span class="keyword">const</span> <span class="keywordtype">float</span>&amp; scale,</div>
<div class="line"><a id="l00034" name="l00034"></a><span class="lineno"> 34</span> uint3 elem [[thread_position_in_grid]],</div>
<div class="line"><a id="l00035" name="l00035"></a><span class="lineno"> 35</span> uint3 grid [[threads_per_grid]]) {</div>
<div class="line"><a id="l00036" name="l00036"></a><span class="lineno"> 36</span> <span class="comment">// Compute a Hadamard transform of size N = 2^k</span></div>
<div class="line"><a id="l00037" name="l00037"></a><span class="lineno"> 37</span> <span class="comment">//</span></div>
<div class="line"><a id="l00038" name="l00038"></a><span class="lineno"> 38</span> <span class="comment">// Equivalent to:</span></div>
<div class="line"><a id="l00039" name="l00039"></a><span class="lineno"> 39</span> <span class="comment">// from scipy.linalg import hadamard</span></div>
<div class="line"><a id="l00040" name="l00040"></a><span class="lineno"> 40</span> <span class="comment">// y = hadamard(len(x)) @ x</span></div>
<div class="line"><a id="l00041" name="l00041"></a><span class="lineno"> 41</span> </div>
<div class="line"><a id="l00042" name="l00042"></a><span class="lineno"> 42</span> <span class="keyword">constexpr</span> <span class="keywordtype">short</span> num_threads = N / max_radix;</div>
<div class="line"><a id="l00043" name="l00043"></a><span class="lineno"> 43</span> <span class="keyword">constexpr</span> <span class="keywordtype">short</span> logN = __builtin_ctz(N);</div>
<div class="line"><a id="l00044" name="l00044"></a><span class="lineno"> 44</span> <span class="keyword">constexpr</span> <span class="keywordtype">short</span> logR = __builtin_ctz(max_radix);</div>
<div class="line"><a id="l00045" name="l00045"></a><span class="lineno"> 45</span> <span class="keyword">constexpr</span> <span class="keywordtype">short</span> num_steps = logN / logR;</div>
<div class="line"><a id="l00046" name="l00046"></a><span class="lineno"> 46</span> <span class="keyword">constexpr</span> <span class="keywordtype">short</span> logFinal = logN % logR;</div>
<div class="line"><a id="l00047" name="l00047"></a><span class="lineno"> 47</span> <span class="keyword">constexpr</span> <span class="keywordtype">short</span> final_radix = 1 &lt;&lt; (logFinal);</div>
<div class="line"><a id="l00048" name="l00048"></a><span class="lineno"> 48</span> </div>
<div class="line"><a id="l00049" name="l00049"></a><span class="lineno"> 49</span> <span class="keywordtype">int</span> batch_idx = elem.x * N;</div>
<div class="line"><a id="l00050" name="l00050"></a><span class="lineno"> 50</span> <span class="keywordtype">short</span> i = elem.y;</div>
<div class="line"><a id="l00051" name="l00051"></a><span class="lineno"> 51</span> </div>
<div class="line"><a id="l00052" name="l00052"></a><span class="lineno"> 52</span> threadgroup T <a class="code hl_variable" href="backend_2metal_2allocator_8h.html#a15aa5cc1baf29be08d55cca88509e697">buf</a>[N];</div>
<div class="line"><a id="l00053" name="l00053"></a><span class="lineno"> 53</span> </div>
<div class="line"><a id="l00054" name="l00054"></a><span class="lineno"> 54</span> <span class="comment">// Read values from device</span></div>
<div class="line"><a id="l00055" name="l00055"></a><span class="lineno"> 55</span> <a class="code hl_define" href="steel_2defines_8h.html#a5a5c3095b132a7589bc19cd5cb80e2c6">STEEL_PRAGMA_UNROLL</a></div>
<div class="line"><a id="l00056" name="l00056"></a><span class="lineno"> 56</span> <span class="keywordflow">for</span> (<span class="keywordtype">short</span> j = 0; j &lt; max_radix / read_width; j++) {</div>
<div class="line"><a id="l00057" name="l00057"></a><span class="lineno"> 57</span> <span class="keywordtype">short</span> index = j * read_width * num_threads + i * read_width;</div>
<div class="line"><a id="l00058" name="l00058"></a><span class="lineno"> 58</span> <a class="code hl_define" href="steel_2defines_8h.html#a5a5c3095b132a7589bc19cd5cb80e2c6">STEEL_PRAGMA_UNROLL</a></div>
<div class="line"><a id="l00059" name="l00059"></a><span class="lineno"> 59</span> <span class="keywordflow">for</span> (<span class="keywordtype">short</span> r = 0; r &lt; read_width; r++) {</div>
<div class="line"><a id="l00060" name="l00060"></a><span class="lineno"> 60</span> <a class="code hl_variable" href="backend_2metal_2allocator_8h.html#a15aa5cc1baf29be08d55cca88509e697">buf</a>[index + r] = in[batch_idx + index + r];</div>
<div class="line"><a id="l00061" name="l00061"></a><span class="lineno"> 61</span> }</div>
<div class="line"><a id="l00062" name="l00062"></a><span class="lineno"> 62</span> }</div>
<div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</span> </div>
<div class="line"><a id="l00064" name="l00064"></a><span class="lineno"> 64</span> threadgroup_barrier(mem_flags::mem_threadgroup);</div>
<div class="line"><a id="l00065" name="l00065"></a><span class="lineno"> 65</span> </div>
<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"> 66</span> <span class="keywordtype">float</span> x[max_radix];</div>
<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"> 67</span> <span class="keywordtype">short</span> h = 1;</div>
<div class="line"><a id="l00068" name="l00068"></a><span class="lineno"> 68</span> </div>
<div class="line"><a id="l00069" name="l00069"></a><span class="lineno"> 69</span> <a class="code hl_define" href="steel_2defines_8h.html#a5a5c3095b132a7589bc19cd5cb80e2c6">STEEL_PRAGMA_UNROLL</a></div>
<div class="line"><a id="l00070" name="l00070"></a><span class="lineno"> 70</span> <span class="keywordflow">for</span> (<span class="keywordtype">short</span> s = 0; s &lt; num_steps; s++) {</div>
<div class="line"><a id="l00071" name="l00071"></a><span class="lineno"> 71</span> <span class="keywordtype">short</span> k = i &amp; (h - 1);</div>
<div class="line"><a id="l00072" name="l00072"></a><span class="lineno"> 72</span> <span class="keywordtype">short</span> j = ((i - k) &lt;&lt; logR) + k;</div>
<div class="line"><a id="l00073" name="l00073"></a><span class="lineno"> 73</span> </div>
<div class="line"><a id="l00074" name="l00074"></a><span class="lineno"> 74</span> <a class="code hl_define" href="steel_2defines_8h.html#a5a5c3095b132a7589bc19cd5cb80e2c6">STEEL_PRAGMA_UNROLL</a></div>
<div class="line"><a id="l00075" name="l00075"></a><span class="lineno"> 75</span> <span class="keywordflow">for</span> (<span class="keywordtype">short</span> r = 0; r &lt; max_radix; r++) {</div>
<div class="line"><a id="l00076" name="l00076"></a><span class="lineno"> 76</span> x[r] = <a class="code hl_variable" href="backend_2metal_2allocator_8h.html#a15aa5cc1baf29be08d55cca88509e697">buf</a>[j + h * r];</div>
<div class="line"><a id="l00077" name="l00077"></a><span class="lineno"> 77</span> }</div>
<div class="line"><a id="l00078" name="l00078"></a><span class="lineno"> 78</span> </div>
<div class="line"><a id="l00079" name="l00079"></a><span class="lineno"> 79</span> <a class="code hl_function" href="metal_2kernels_2hadamard_8h.html#a590e5366adc78bab4fe44e37885d413f">radix_func&lt;max_radix&gt;</a>(x);</div>
<div class="line"><a id="l00080" name="l00080"></a><span class="lineno"> 80</span> </div>
<div class="line"><a id="l00081" name="l00081"></a><span class="lineno"> 81</span> <a class="code hl_define" href="steel_2defines_8h.html#a5a5c3095b132a7589bc19cd5cb80e2c6">STEEL_PRAGMA_UNROLL</a></div>
<div class="line"><a id="l00082" name="l00082"></a><span class="lineno"> 82</span> <span class="keywordflow">for</span> (<span class="keywordtype">short</span> r = 0; r &lt; max_radix; r++) {</div>
<div class="line"><a id="l00083" name="l00083"></a><span class="lineno"> 83</span> <a class="code hl_variable" href="backend_2metal_2allocator_8h.html#a15aa5cc1baf29be08d55cca88509e697">buf</a>[j + h * r] = T(x[r]);</div>
<div class="line"><a id="l00084" name="l00084"></a><span class="lineno"> 84</span> }</div>
<div class="line"><a id="l00085" name="l00085"></a><span class="lineno"> 85</span> </div>
<div class="line"><a id="l00086" name="l00086"></a><span class="lineno"> 86</span> h &lt;&lt;= logR;</div>
<div class="line"><a id="l00087" name="l00087"></a><span class="lineno"> 87</span> threadgroup_barrier(mem_flags::mem_threadgroup);</div>
<div class="line"><a id="l00088" name="l00088"></a><span class="lineno"> 88</span> }</div>
<div class="line"><a id="l00089" name="l00089"></a><span class="lineno"> 89</span> </div>
<div class="line"><a id="l00090" name="l00090"></a><span class="lineno"> 90</span> <span class="comment">// Do the final radix</span></div>
<div class="line"><a id="l00091" name="l00091"></a><span class="lineno"> 91</span> <span class="comment">// e.g. max_radix = 16</span></div>
<div class="line"><a id="l00092" name="l00092"></a><span class="lineno"> 92</span> <span class="comment">// N = 1024 = 16 * 16 * 4</span></div>
<div class="line"><a id="l00093" name="l00093"></a><span class="lineno"> 93</span> <span class="keywordflow">if</span> (final_radix &gt; 1) {</div>
<div class="line"><a id="l00094" name="l00094"></a><span class="lineno"> 94</span> <span class="comment">// Each thread does multiple butterflies</span></div>
<div class="line"><a id="l00095" name="l00095"></a><span class="lineno"> 95</span> <a class="code hl_define" href="steel_2defines_8h.html#a5a5c3095b132a7589bc19cd5cb80e2c6">STEEL_PRAGMA_UNROLL</a></div>
<div class="line"><a id="l00096" name="l00096"></a><span class="lineno"> 96</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> t = 0; t &lt; max_radix / final_radix; t++) {</div>
<div class="line"><a id="l00097" name="l00097"></a><span class="lineno"> 97</span> <span class="keywordtype">short</span> index = i + t * num_threads;</div>
<div class="line"><a id="l00098" name="l00098"></a><span class="lineno"> 98</span> <span class="keywordtype">short</span> k = index &amp; (h - 1);</div>
<div class="line"><a id="l00099" name="l00099"></a><span class="lineno"> 99</span> <span class="keywordtype">short</span> j = ((index - k) &lt;&lt; logFinal) + k;</div>
<div class="line"><a id="l00100" name="l00100"></a><span class="lineno"> 100</span> <a class="code hl_define" href="steel_2defines_8h.html#a5a5c3095b132a7589bc19cd5cb80e2c6">STEEL_PRAGMA_UNROLL</a></div>
<div class="line"><a id="l00101" name="l00101"></a><span class="lineno"> 101</span> <span class="keywordflow">for</span> (<span class="keywordtype">short</span> r = 0; r &lt; final_radix; r++) {</div>
<div class="line"><a id="l00102" name="l00102"></a><span class="lineno"> 102</span> x[r] = <a class="code hl_variable" href="backend_2metal_2allocator_8h.html#a15aa5cc1baf29be08d55cca88509e697">buf</a>[j + h * r];</div>
<div class="line"><a id="l00103" name="l00103"></a><span class="lineno"> 103</span> }</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> <a class="code hl_function" href="metal_2kernels_2hadamard_8h.html#a590e5366adc78bab4fe44e37885d413f">radix_func&lt;final_radix&gt;</a>(x);</div>
<div class="line"><a id="l00106" name="l00106"></a><span class="lineno"> 106</span> </div>
<div class="line"><a id="l00107" name="l00107"></a><span class="lineno"> 107</span> <a class="code hl_define" href="steel_2defines_8h.html#a5a5c3095b132a7589bc19cd5cb80e2c6">STEEL_PRAGMA_UNROLL</a></div>
<div class="line"><a id="l00108" name="l00108"></a><span class="lineno"> 108</span> <span class="keywordflow">for</span> (<span class="keywordtype">short</span> r = 0; r &lt; final_radix; r++) {</div>
<div class="line"><a id="l00109" name="l00109"></a><span class="lineno"> 109</span> <a class="code hl_variable" href="backend_2metal_2allocator_8h.html#a15aa5cc1baf29be08d55cca88509e697">buf</a>[j + h * r] = T(x[r]);</div>
<div class="line"><a id="l00110" name="l00110"></a><span class="lineno"> 110</span> }</div>
<div class="line"><a id="l00111" name="l00111"></a><span class="lineno"> 111</span> }</div>
<div class="line"><a id="l00112" name="l00112"></a><span class="lineno"> 112</span> threadgroup_barrier(mem_flags::mem_threadgroup);</div>
<div class="line"><a id="l00113" name="l00113"></a><span class="lineno"> 113</span> }</div>
<div class="line"><a id="l00114" name="l00114"></a><span class="lineno"> 114</span> </div>
<div class="line"><a id="l00115" name="l00115"></a><span class="lineno"> 115</span> <span class="comment">// Write values to device</span></div>
<div class="line"><a id="l00116" name="l00116"></a><span class="lineno"> 116</span> <a class="code hl_define" href="steel_2defines_8h.html#a5a5c3095b132a7589bc19cd5cb80e2c6">STEEL_PRAGMA_UNROLL</a></div>
<div class="line"><a id="l00117" name="l00117"></a><span class="lineno"> 117</span> <span class="keywordflow">for</span> (<span class="keywordtype">short</span> j = 0; j &lt; max_radix / read_width; j++) {</div>
<div class="line"><a id="l00118" name="l00118"></a><span class="lineno"> 118</span> <span class="keywordtype">short</span> index = j * read_width * num_threads + i * read_width;</div>
<div class="line"><a id="l00119" name="l00119"></a><span class="lineno"> 119</span> <a class="code hl_define" href="steel_2defines_8h.html#a5a5c3095b132a7589bc19cd5cb80e2c6">STEEL_PRAGMA_UNROLL</a></div>
<div class="line"><a id="l00120" name="l00120"></a><span class="lineno"> 120</span> <span class="keywordflow">for</span> (<span class="keywordtype">short</span> r = 0; r &lt; read_width; r++) {</div>
<div class="line"><a id="l00121" name="l00121"></a><span class="lineno"> 121</span> out[batch_idx + index + r] = T(<a class="code hl_variable" href="backend_2metal_2allocator_8h.html#a15aa5cc1baf29be08d55cca88509e697">buf</a>[index + r] * scale);</div>
<div class="line"><a id="l00122" name="l00122"></a><span class="lineno"> 122</span> }</div>
<div class="line"><a id="l00123" name="l00123"></a><span class="lineno"> 123</span> }</div>
<div class="line"><a id="l00124" name="l00124"></a><span class="lineno"> 124</span>}</div>
</div>
<div class="line"><a id="l00125" name="l00125"></a><span class="lineno"> 125</span> </div>
<div class="line"><a id="l00126" name="l00126"></a><span class="lineno"> 126</span><span class="keyword">template</span> &lt;<span class="keyword">typename</span> T, <span class="keywordtype">int</span> N, <span class="keywordtype">int</span> M, <span class="keywordtype">int</span> read_w<span class="keywordtype">id</span>th&gt;</div>
<div class="foldopen" id="foldopen00127" data-start="{" data-end="}">
<div class="line"><a id="l00127" name="l00127"></a><span class="lineno"><a class="line" href="metal_2kernels_2hadamard_8h.html#ab0bd478f2051af35aed1869005e3370a"> 127</a></span>[[kernel]] <span class="keywordtype">void</span> <a class="code hl_function" href="metal_2kernels_2hadamard_8h.html#ab0bd478f2051af35aed1869005e3370a">hadamard_m</a>(</div>
<div class="line"><a id="l00128" name="l00128"></a><span class="lineno"> 128</span> <span class="keyword">const</span> device T* in [[buffer(0)]],</div>
<div class="line"><a id="l00129" name="l00129"></a><span class="lineno"> 129</span> device T* out [[buffer(1)]],</div>
<div class="line"><a id="l00130" name="l00130"></a><span class="lineno"> 130</span> constant <span class="keyword">const</span> <span class="keywordtype">float</span>&amp; scale,</div>
<div class="line"><a id="l00131" name="l00131"></a><span class="lineno"> 131</span> uint3 elem [[thread_position_in_grid]],</div>
<div class="line"><a id="l00132" name="l00132"></a><span class="lineno"> 132</span> uint3 grid [[threads_per_grid]]) {</div>
<div class="line"><a id="l00133" name="l00133"></a><span class="lineno"> 133</span> <span class="comment">// Compute a Hadamard transform of size M</span></div>
<div class="line"><a id="l00134" name="l00134"></a><span class="lineno"> 134</span> <span class="comment">// using a naive O(M^2) codelet.</span></div>
<div class="line"><a id="l00135" name="l00135"></a><span class="lineno"> 135</span> <span class="comment">//</span></div>
<div class="line"><a id="l00136" name="l00136"></a><span class="lineno"> 136</span> <span class="comment">// This kernel is the second stage in the computation</span></div>
<div class="line"><a id="l00137" name="l00137"></a><span class="lineno"> 137</span> <span class="comment">// of a Hadamard transform of size M*N where N = 2^k.</span></div>
<div class="line"><a id="l00138" name="l00138"></a><span class="lineno"> 138</span> </div>
<div class="line"><a id="l00139" name="l00139"></a><span class="lineno"> 139</span> <span class="keywordtype">int</span> index = elem.x * grid.y + elem.y;</div>
<div class="line"><a id="l00140" name="l00140"></a><span class="lineno"> 140</span> <span class="keywordtype">short</span> i = index % (N / read_width);</div>
<div class="line"><a id="l00141" name="l00141"></a><span class="lineno"> 141</span> <span class="keywordtype">int</span> batch_idx = index / (N / read_width) * M * N;</div>
<div class="line"><a id="l00142" name="l00142"></a><span class="lineno"> 142</span> </div>
<div class="line"><a id="l00143" name="l00143"></a><span class="lineno"> 143</span> <span class="keywordtype">float</span> x[read_width][M];</div>
<div class="line"><a id="l00144" name="l00144"></a><span class="lineno"> 144</span> <a class="code hl_define" href="steel_2defines_8h.html#a5a5c3095b132a7589bc19cd5cb80e2c6">STEEL_PRAGMA_UNROLL</a></div>
<div class="line"><a id="l00145" name="l00145"></a><span class="lineno"> 145</span> <span class="keywordflow">for</span> (<span class="keywordtype">short</span> c = 0; c &lt; M; c++) {</div>
<div class="line"><a id="l00146" name="l00146"></a><span class="lineno"> 146</span> <a class="code hl_define" href="steel_2defines_8h.html#a5a5c3095b132a7589bc19cd5cb80e2c6">STEEL_PRAGMA_UNROLL</a></div>
<div class="line"><a id="l00147" name="l00147"></a><span class="lineno"> 147</span> <span class="keywordflow">for</span> (<span class="keywordtype">short</span> r = 0; r &lt; read_width; r++) {</div>
<div class="line"><a id="l00148" name="l00148"></a><span class="lineno"> 148</span> x[r][c] = in[batch_idx + c * N + i * read_width + r];</div>
<div class="line"><a id="l00149" name="l00149"></a><span class="lineno"> 149</span> }</div>
<div class="line"><a id="l00150" name="l00150"></a><span class="lineno"> 150</span> }</div>
<div class="line"><a id="l00151" name="l00151"></a><span class="lineno"> 151</span> </div>
<div class="line"><a id="l00152" name="l00152"></a><span class="lineno"> 152</span> <a class="code hl_define" href="steel_2defines_8h.html#a5a5c3095b132a7589bc19cd5cb80e2c6">STEEL_PRAGMA_UNROLL</a></div>
<div class="line"><a id="l00153" name="l00153"></a><span class="lineno"> 153</span> <span class="keywordflow">for</span> (<span class="keywordtype">short</span> r = 0; r &lt; read_width; r++) {</div>
<div class="line"><a id="l00154" name="l00154"></a><span class="lineno"> 154</span> <span class="comment">// This function is JIT compiled for M</span></div>
<div class="line"><a id="l00155" name="l00155"></a><span class="lineno"> 155</span> <span class="comment">// using the Hadamard matrix strings in `metal/hadamard.cpp`</span></div>
<div class="line"><a id="l00156" name="l00156"></a><span class="lineno"> 156</span> hadamard_radix_m(x[r]);</div>
<div class="line"><a id="l00157" name="l00157"></a><span class="lineno"> 157</span> }</div>
<div class="line"><a id="l00158" name="l00158"></a><span class="lineno"> 158</span> </div>
<div class="line"><a id="l00159" name="l00159"></a><span class="lineno"> 159</span> <span class="comment">// Write back to device</span></div>
<div class="line"><a id="l00160" name="l00160"></a><span class="lineno"> 160</span> <a class="code hl_define" href="steel_2defines_8h.html#a5a5c3095b132a7589bc19cd5cb80e2c6">STEEL_PRAGMA_UNROLL</a></div>
<div class="line"><a id="l00161" name="l00161"></a><span class="lineno"> 161</span> <span class="keywordflow">for</span> (<span class="keywordtype">short</span> c = 0; c &lt; M; c++) {</div>
<div class="line"><a id="l00162" name="l00162"></a><span class="lineno"> 162</span> <a class="code hl_define" href="steel_2defines_8h.html#a5a5c3095b132a7589bc19cd5cb80e2c6">STEEL_PRAGMA_UNROLL</a></div>
<div class="line"><a id="l00163" name="l00163"></a><span class="lineno"> 163</span> <span class="keywordflow">for</span> (<span class="keywordtype">short</span> r = 0; r &lt; read_width; r++) {</div>
<div class="line"><a id="l00164" name="l00164"></a><span class="lineno"> 164</span> out[batch_idx + c * N + i * read_width + r] = T(x[r][c] * scale);</div>
<div class="line"><a id="l00165" name="l00165"></a><span class="lineno"> 165</span> }</div>
<div class="line"><a id="l00166" name="l00166"></a><span class="lineno"> 166</span> }</div>
<div class="line"><a id="l00167" name="l00167"></a><span class="lineno"> 167</span>}</div>
</div>
<div class="ttc" id="abackend_2metal_2allocator_8h_html_a15aa5cc1baf29be08d55cca88509e697"><div class="ttname"><a href="backend_2metal_2allocator_8h.html#a15aa5cc1baf29be08d55cca88509e697">buf</a></div><div class="ttdeci">MTL::Buffer * buf</div><div class="ttdef"><b>Definition</b> allocator.h:39</div></div>
<div class="ttc" id="ametal_2kernels_2hadamard_8h_html_a590e5366adc78bab4fe44e37885d413f"><div class="ttname"><a href="metal_2kernels_2hadamard_8h.html#a590e5366adc78bab4fe44e37885d413f">radix_func</a></div><div class="ttdeci">METAL_FUNC void radix_func(thread float *x)</div><div class="ttdef"><b>Definition</b> hadamard.h:11</div></div>
<div class="ttc" id="ametal_2kernels_2hadamard_8h_html_a63c0e8510e555cd065e1f0ddfb33ce18"><div class="ttname"><a href="metal_2kernels_2hadamard_8h.html#a63c0e8510e555cd065e1f0ddfb33ce18">hadamard_n</a></div><div class="ttdeci">void hadamard_n(const device T *in, device T *out, constant const float &amp;scale, uint3 elem, uint3 grid)</div><div class="ttdef"><b>Definition</b> hadamard.h:30</div></div>
<div class="ttc" id="ametal_2kernels_2hadamard_8h_html_ab0bd478f2051af35aed1869005e3370a"><div class="ttname"><a href="metal_2kernels_2hadamard_8h.html#ab0bd478f2051af35aed1869005e3370a">hadamard_m</a></div><div class="ttdeci">void hadamard_m(const device T *in, device T *out, constant const float &amp;scale, uint3 elem, uint3 grid)</div><div class="ttdef"><b>Definition</b> hadamard.h:127</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.h:265</div></div>
<div class="ttc" id="asteel_2defines_8h_html"><div class="ttname"><a href="steel_2defines_8h.html">defines.h</a></div></div>
<div class="ttc" id="asteel_2defines_8h_html_a5a5c3095b132a7589bc19cd5cb80e2c6"><div class="ttname"><a href="steel_2defines_8h.html#a5a5c3095b132a7589bc19cd5cb80e2c6">STEEL_PRAGMA_UNROLL</a></div><div class="ttdeci">#define STEEL_PRAGMA_UNROLL</div><div class="ttdef"><b>Definition</b> defines.h:4</div></div>
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