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Awni Hannun 6269c69d0e docs update
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<li class="navelem"><a class="el" href="dir_938ab0ecf10b8b860ff766c820f665fd.html">mlx</a></li><li class="navelem"><a class="el" href="dir_1d446c9bd3c99228254c9484e0bc5c06.html">backend</a></li><li class="navelem"><a class="el" href="dir_d0c977ea65824390717cdb7efc36c157.html">metal</a></li><li class="navelem"><a class="el" href="dir_70a37effa88bcbd6b791977fa1e64356.html">kernels</a></li> </ul>
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<a href="backend_2metal_2kernels_2utils_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 © 2023-2024 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;metal_math&gt;</span></div>
<div class="line"><a id="l00006" name="l00006"></a><span class="lineno"> 6</span><span class="preprocessor">#include &quot;<a class="code" href="backend_2metal_2kernels_2bf16_8h.html">mlx/backend/metal/kernels/bf16.h</a>&quot;</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="backend_2metal_2kernels_2complex_8h.html">mlx/backend/metal/kernels/complex.h</a>&quot;</span></div>
<div class="line"><a id="l00008" name="l00008"></a><span class="lineno"> 8</span><span class="preprocessor">#include &quot;<a class="code" href="defines_8h.html">mlx/backend/metal/kernels/defines.h</a>&quot;</span></div>
<div class="line"><a id="l00009" name="l00009"></a><span class="lineno"> 9</span> </div>
<div class="line"><a id="l00010" name="l00010"></a><span class="lineno"><a class="line" href="backend_2metal_2kernels_2utils_8h.html#acb8ddf4a29129846b673c50ba7078773"> 10</a></span><span class="keyword">typedef</span> half <a class="code hl_typedef" href="backend_2metal_2kernels_2utils_8h.html#acb8ddf4a29129846b673c50ba7078773">float16_t</a>;</div>
<div class="line"><a id="l00011" name="l00011"></a><span class="lineno"> 11</span> </div>
<div class="line"><a id="l00013" name="l00013"></a><span class="lineno"> 13</span><span class="comment">// Type limits utils</span></div>
<div class="line"><a id="l00015" name="l00015"></a><span class="lineno"> 15</span> </div>
<div class="line"><a id="l00016" name="l00016"></a><span class="lineno"> 16</span><span class="keyword">template</span> &lt;<span class="keyword">typename</span> U&gt;</div>
<div class="foldopen" id="foldopen00017" data-start="{" data-end="};">
<div class="line"><a id="l00017" name="l00017"></a><span class="lineno"><a class="line" href="struct_limits.html"> 17</a></span><span class="keyword">struct </span><a class="code hl_struct" href="struct_limits.html">Limits</a> {</div>
<div class="line"><a id="l00018" name="l00018"></a><span class="lineno"><a class="line" href="struct_limits.html#a2f0673b6f9da89ce1d64f9f3d74f50a8"> 18</a></span> <span class="keyword">static</span> <span class="keyword">const</span> constant U <a class="code hl_variable" href="struct_limits.html#a2f0673b6f9da89ce1d64f9f3d74f50a8">max</a> = metal::numeric_limits&lt;U&gt;::max();</div>
<div class="line"><a id="l00019" name="l00019"></a><span class="lineno"><a class="line" href="struct_limits.html#a6e81584ba65a4dc6ff9366b458e3a20e"> 19</a></span> <span class="keyword">static</span> <span class="keyword">const</span> constant U <a class="code hl_variable" href="struct_limits.html#a6e81584ba65a4dc6ff9366b458e3a20e">min</a> = metal::numeric_limits&lt;U&gt;::min();</div>
<div class="line"><a id="l00020" name="l00020"></a><span class="lineno"><a class="line" href="struct_limits.html#a5a3eae6d244fbea2aa7b9200001463e5"> 20</a></span> <span class="keyword">static</span> <span class="keyword">const</span> constant U <a class="code hl_variable" href="struct_limits.html#a5a3eae6d244fbea2aa7b9200001463e5">finite_max</a> = metal::numeric_limits&lt;U&gt;::max();</div>
<div class="line"><a id="l00021" name="l00021"></a><span class="lineno"><a class="line" href="struct_limits.html#ae7469d21f2688797ca3e388d919ef05e"> 21</a></span> <span class="keyword">static</span> <span class="keyword">const</span> constant U <a class="code hl_variable" href="struct_limits.html#ae7469d21f2688797ca3e388d919ef05e">finite_min</a> = metal::numeric_limits&lt;U&gt;::min();</div>
<div class="line"><a id="l00022" name="l00022"></a><span class="lineno"> 22</span>};</div>
</div>
<div class="line"><a id="l00023" name="l00023"></a><span class="lineno"> 23</span> </div>
<div class="foldopen" id="foldopen00024" data-start="" data-end="">
<div class="line"><a id="l00024" name="l00024"></a><span class="lineno"><a class="line" href="backend_2metal_2kernels_2utils_8h.html#abedffa358e7ba7782cc78d6772064c7c"> 24</a></span><span class="preprocessor">#define instantiate_default_limit(type) \</span></div>
<div class="line"><a id="l00025" name="l00025"></a><span class="lineno"> 25</span><span class="preprocessor"> template &lt;&gt; \</span></div>
<div class="line"><a id="l00026" name="l00026"></a><span class="lineno"> 26</span><span class="preprocessor"> struct Limits&lt;type&gt; { \</span></div>
<div class="line"><a id="l00027" name="l00027"></a><span class="lineno"> 27</span><span class="preprocessor"> static constexpr constant type max = metal::numeric_limits&lt;type&gt;::max(); \</span></div>
<div class="line"><a id="l00028" name="l00028"></a><span class="lineno"> 28</span><span class="preprocessor"> static constexpr constant type min = metal::numeric_limits&lt;type&gt;::min(); \</span></div>
<div class="line"><a id="l00029" name="l00029"></a><span class="lineno"> 29</span><span class="preprocessor"> static constexpr constant type finite_max = \</span></div>
<div class="line"><a id="l00030" name="l00030"></a><span class="lineno"> 30</span><span class="preprocessor"> metal::numeric_limits&lt;type&gt;::max(); \</span></div>
<div class="line"><a id="l00031" name="l00031"></a><span class="lineno"> 31</span><span class="preprocessor"> static constexpr constant type finite_min = \</span></div>
<div class="line"><a id="l00032" name="l00032"></a><span class="lineno"> 32</span><span class="preprocessor"> metal::numeric_limits&lt;type&gt;::min(); \</span></div>
<div class="line"><a id="l00033" name="l00033"></a><span class="lineno"> 33</span><span class="preprocessor"> };</span></div>
</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"><a class="line" href="struct_limits_3_01uint8__t_01_4.html#a55f48b89033e8c8683f8540ec6b23f02"> 35</a></span><a class="code hl_define" href="backend_2metal_2kernels_2utils_8h.html#abedffa358e7ba7782cc78d6772064c7c">instantiate_default_limit</a>(uint8_t);</div>
<div class="line"><a id="l00036" name="l00036"></a><span class="lineno"><a class="line" href="struct_limits_3_01uint16__t_01_4.html#a9d517d8265ea1898b6b16e91b8595146"> 36</a></span><a class="code hl_define" href="backend_2metal_2kernels_2utils_8h.html#abedffa358e7ba7782cc78d6772064c7c">instantiate_default_limit</a>(uint16_t);</div>
<div class="line"><a id="l00037" name="l00037"></a><span class="lineno"><a class="line" href="struct_limits_3_01uint32__t_01_4.html#a0698139f3fe440d7aa08ac5029d72235"> 37</a></span><a class="code hl_define" href="backend_2metal_2kernels_2utils_8h.html#abedffa358e7ba7782cc78d6772064c7c">instantiate_default_limit</a>(uint32_t);</div>
<div class="line"><a id="l00038" name="l00038"></a><span class="lineno"><a class="line" href="struct_limits_3_01uint64__t_01_4.html#aff101ff38be5ccdbb9790aecb3069071"> 38</a></span><a class="code hl_define" href="backend_2metal_2kernels_2utils_8h.html#abedffa358e7ba7782cc78d6772064c7c">instantiate_default_limit</a>(uint64_t);</div>
<div class="line"><a id="l00039" name="l00039"></a><span class="lineno"><a class="line" href="struct_limits_3_01int8__t_01_4.html#a24cdab873e0fb778393c69f1dc9ecf73"> 39</a></span><a class="code hl_define" href="backend_2metal_2kernels_2utils_8h.html#abedffa358e7ba7782cc78d6772064c7c">instantiate_default_limit</a>(int8_t);</div>
<div class="line"><a id="l00040" name="l00040"></a><span class="lineno"><a class="line" href="struct_limits_3_01int16__t_01_4.html#acb2936d1cdbf347a9a014c8e036a5782"> 40</a></span><a class="code hl_define" href="backend_2metal_2kernels_2utils_8h.html#abedffa358e7ba7782cc78d6772064c7c">instantiate_default_limit</a>(int16_t);</div>
<div class="line"><a id="l00041" name="l00041"></a><span class="lineno"><a class="line" href="struct_limits_3_01int32__t_01_4.html#aa9ed9f0e8c7400d8fc92e1cba9588794"> 41</a></span><a class="code hl_define" href="backend_2metal_2kernels_2utils_8h.html#abedffa358e7ba7782cc78d6772064c7c">instantiate_default_limit</a>(int32_t);</div>
<div class="line"><a id="l00042" name="l00042"></a><span class="lineno"><a class="line" href="struct_limits_3_01int64__t_01_4.html#a6c7254b641878fa0fb9538814c45457a"> 42</a></span><a class="code hl_define" href="backend_2metal_2kernels_2utils_8h.html#abedffa358e7ba7782cc78d6772064c7c">instantiate_default_limit</a>(int64_t);</div>
<div class="line"><a id="l00043" name="l00043"></a><span class="lineno"> 43</span> </div>
<div class="foldopen" id="foldopen00044" data-start="" data-end="">
<div class="line"><a id="l00044" name="l00044"></a><span class="lineno"><a class="line" href="backend_2metal_2kernels_2utils_8h.html#a1e520e23f58ca645dea1ac20998d987a"> 44</a></span><span class="preprocessor">#define instantiate_float_limit(type) \</span></div>
<div class="line"><a id="l00045" name="l00045"></a><span class="lineno"> 45</span><span class="preprocessor"> template &lt;&gt; \</span></div>
<div class="line"><a id="l00046" name="l00046"></a><span class="lineno"> 46</span><span class="preprocessor"> struct Limits&lt;type&gt; { \</span></div>
<div class="line"><a id="l00047" name="l00047"></a><span class="lineno"> 47</span><span class="preprocessor"> static constexpr constant type max = \</span></div>
<div class="line"><a id="l00048" name="l00048"></a><span class="lineno"> 48</span><span class="preprocessor"> metal::numeric_limits&lt;type&gt;::infinity(); \</span></div>
<div class="line"><a id="l00049" name="l00049"></a><span class="lineno"> 49</span><span class="preprocessor"> static constexpr constant type min = \</span></div>
<div class="line"><a id="l00050" name="l00050"></a><span class="lineno"> 50</span><span class="preprocessor"> -metal::numeric_limits&lt;type&gt;::infinity(); \</span></div>
<div class="line"><a id="l00051" name="l00051"></a><span class="lineno"> 51</span><span class="preprocessor"> static constexpr constant type finite_max = \</span></div>
<div class="line"><a id="l00052" name="l00052"></a><span class="lineno"> 52</span><span class="preprocessor"> metal::numeric_limits&lt;type&gt;::max(); \</span></div>
<div class="line"><a id="l00053" name="l00053"></a><span class="lineno"> 53</span><span class="preprocessor"> static constexpr constant type finite_min = \</span></div>
<div class="line"><a id="l00054" name="l00054"></a><span class="lineno"> 54</span><span class="preprocessor"> -metal::numeric_limits&lt;type&gt;::max(); \</span></div>
<div class="line"><a id="l00055" name="l00055"></a><span class="lineno"> 55</span><span class="preprocessor"> };</span></div>
</div>
<div class="line"><a id="l00056" name="l00056"></a><span class="lineno"> 56</span> </div>
<div class="line"><a id="l00057" name="l00057"></a><span class="lineno"><a class="line" href="struct_limits_3_01half_01_4.html#aedaf0190aabf23da20510e558e2690b4"> 57</a></span><a class="code hl_define" href="backend_2metal_2kernels_2utils_8h.html#a1e520e23f58ca645dea1ac20998d987a">instantiate_float_limit</a>(half);</div>
<div class="line"><a id="l00058" name="l00058"></a><span class="lineno"><a class="line" href="struct_limits_3_01float_01_4.html#a291eea590113fc1858b7f83f2e0c977d"> 58</a></span><a class="code hl_define" href="backend_2metal_2kernels_2utils_8h.html#a1e520e23f58ca645dea1ac20998d987a">instantiate_float_limit</a>(<span class="keywordtype">float</span>);</div>
<div class="line"><a id="l00059" name="l00059"></a><span class="lineno"><a class="line" href="struct_limits_3_01bfloat16__t_01_4.html#a6337dc35207b3f6f7185cd73eabac211"> 59</a></span><a class="code hl_define" href="backend_2metal_2kernels_2utils_8h.html#a1e520e23f58ca645dea1ac20998d987a">instantiate_float_limit</a>(<a class="code hl_struct" href="struct___m_l_x___b_float16.html">bfloat16_t</a>);</div>
<div class="line"><a id="l00060" name="l00060"></a><span class="lineno"> 60</span> </div>
<div class="line"><a id="l00061" name="l00061"></a><span class="lineno"> 61</span><span class="keyword">template</span> &lt;&gt;</div>
<div class="foldopen" id="foldopen00062" data-start="{" data-end="};">
<div class="line"><a id="l00062" name="l00062"></a><span class="lineno"><a class="line" href="struct_limits_3_01bool_01_4.html"> 62</a></span><span class="keyword">struct </span><a class="code hl_struct" href="struct_limits.html">Limits</a>&lt;bool&gt; {</div>
<div class="line"><a id="l00063" name="l00063"></a><span class="lineno"><a class="line" href="struct_limits_3_01bool_01_4.html#acbd2132145888d51220558a101ffcff4"> 63</a></span> <span class="keyword">static</span> <span class="keyword">constexpr</span> constant <span class="keywordtype">bool</span> <a class="code hl_variable" href="struct_limits.html#a2f0673b6f9da89ce1d64f9f3d74f50a8">max</a> = <span class="keyword">true</span>;</div>
<div class="line"><a id="l00064" name="l00064"></a><span class="lineno"><a class="line" href="struct_limits_3_01bool_01_4.html#a139f787b57536d455490b8ef801d37cc"> 64</a></span> <span class="keyword">static</span> <span class="keyword">constexpr</span> constant <span class="keywordtype">bool</span> <a class="code hl_variable" href="struct_limits.html#a6e81584ba65a4dc6ff9366b458e3a20e">min</a> = <span class="keyword">false</span>;</div>
<div class="line"><a id="l00065" name="l00065"></a><span class="lineno"> 65</span>};</div>
</div>
<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"> 66</span> </div>
<div class="line"><a id="l00068" name="l00068"></a><span class="lineno"> 68</span><span class="comment">// Indexing utils</span></div>
<div class="line"><a id="l00070" name="l00070"></a><span class="lineno"> 70</span> </div>
<div class="line"><a id="l00071" name="l00071"></a><span class="lineno"><a class="line" href="backend_2metal_2kernels_2utils_8h.html#a069b682d7d21827461544817d722bfd3"> 71</a></span><span class="preprocessor">#define MLX_MTL_PRAGMA_UNROLL _Pragma(&quot;clang loop unroll(full)&quot;)</span></div>
<div class="line"><a id="l00072" name="l00072"></a><span class="lineno"> 72</span> </div>
<div class="line"><a id="l00074" name="l00074"></a><span class="lineno"> 74</span><span class="comment">// Single Array with generic dims</span></div>
<div class="line"><a id="l00075" name="l00075"></a><span class="lineno"> 75</span> </div>
<div class="line"><a id="l00076" name="l00076"></a><span class="lineno"> 76</span><span class="keyword">template</span> &lt;<span class="keyword">typename</span> str<span class="keywordtype">id</span>e_t&gt;</div>
<div class="foldopen" id="foldopen00077" data-start="{" data-end="}">
<div class="line"><a id="l00077" name="l00077"></a><span class="lineno"><a class="line" href="backend_2metal_2kernels_2utils_8h.html#a2e49fa7ab8f6348543455c6c45d7e2a9"> 77</a></span>METAL_FUNC stride_t <a class="code hl_function" href="backend_2metal_2kernels_2utils_8h.html#a2e49fa7ab8f6348543455c6c45d7e2a9">elem_to_loc</a>(</div>
<div class="line"><a id="l00078" name="l00078"></a><span class="lineno"> 78</span> uint elem,</div>
<div class="line"><a id="l00079" name="l00079"></a><span class="lineno"> 79</span> device <span class="keyword">const</span> <span class="keywordtype">int</span>* shape,</div>
<div class="line"><a id="l00080" name="l00080"></a><span class="lineno"> 80</span> device <span class="keyword">const</span> stride_t* strides,</div>
<div class="line"><a id="l00081" name="l00081"></a><span class="lineno"> 81</span> <span class="keywordtype">int</span> ndim) {</div>
<div class="line"><a id="l00082" name="l00082"></a><span class="lineno"> 82</span> stride_t loc = 0;</div>
<div class="line"><a id="l00083" name="l00083"></a><span class="lineno"> 83</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = ndim - 1; i &gt;= 0 &amp;&amp; elem &gt; 0; --i) {</div>
<div class="line"><a id="l00084" name="l00084"></a><span class="lineno"> 84</span> loc += (elem % shape[i]) * strides[i];</div>
<div class="line"><a id="l00085" name="l00085"></a><span class="lineno"> 85</span> elem /= shape[i];</div>
<div class="line"><a id="l00086" name="l00086"></a><span class="lineno"> 86</span> }</div>
<div class="line"><a id="l00087" name="l00087"></a><span class="lineno"> 87</span> <span class="keywordflow">return</span> loc;</div>
<div class="line"><a id="l00088" name="l00088"></a><span class="lineno"> 88</span>}</div>
</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="keyword">template</span> &lt;<span class="keyword">typename</span> str<span class="keywordtype">id</span>e_t&gt;</div>
<div class="foldopen" id="foldopen00091" data-start="{" data-end="}">
<div class="line"><a id="l00091" name="l00091"></a><span class="lineno"><a class="line" href="backend_2metal_2kernels_2utils_8h.html#a8fd0c8fc6058e650fc99bca8b6acd7d1"> 91</a></span>METAL_FUNC stride_t <a class="code hl_function" href="backend_2metal_2kernels_2utils_8h.html#a2e49fa7ab8f6348543455c6c45d7e2a9">elem_to_loc</a>(</div>
<div class="line"><a id="l00092" name="l00092"></a><span class="lineno"> 92</span> uint elem,</div>
<div class="line"><a id="l00093" name="l00093"></a><span class="lineno"> 93</span> constant <span class="keyword">const</span> <span class="keywordtype">int</span>* shape,</div>
<div class="line"><a id="l00094" name="l00094"></a><span class="lineno"> 94</span> constant <span class="keyword">const</span> stride_t* strides,</div>
<div class="line"><a id="l00095" name="l00095"></a><span class="lineno"> 95</span> <span class="keywordtype">int</span> ndim) {</div>
<div class="line"><a id="l00096" name="l00096"></a><span class="lineno"> 96</span> stride_t loc = 0;</div>
<div class="line"><a id="l00097" name="l00097"></a><span class="lineno"> 97</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = ndim - 1; i &gt;= 0 &amp;&amp; elem &gt; 0; --i) {</div>
<div class="line"><a id="l00098" name="l00098"></a><span class="lineno"> 98</span> loc += (elem % shape[i]) * strides[i];</div>
<div class="line"><a id="l00099" name="l00099"></a><span class="lineno"> 99</span> elem /= shape[i];</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> <span class="keywordflow">return</span> loc;</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="line"><a id="l00104" name="l00104"></a><span class="lineno"> 104</span><span class="comment">// Non templated version to handle arbitrary dims</span></div>
<div class="line"><a id="l00105" name="l00105"></a><span class="lineno"> 105</span><span class="keyword">template</span> &lt;<span class="keyword">typename</span> str<span class="keywordtype">id</span>e_t&gt;</div>
<div class="foldopen" id="foldopen00106" data-start="{" data-end="}">
<div class="line"><a id="l00106" name="l00106"></a><span class="lineno"><a class="line" href="backend_2metal_2kernels_2utils_8h.html#a37e00d94751710e81c9632bca2f91e51"> 106</a></span>METAL_FUNC stride_t <a class="code hl_function" href="backend_2metal_2kernels_2utils_8h.html#a2e49fa7ab8f6348543455c6c45d7e2a9">elem_to_loc</a>(</div>
<div class="line"><a id="l00107" name="l00107"></a><span class="lineno"> 107</span> uint3 elem,</div>
<div class="line"><a id="l00108" name="l00108"></a><span class="lineno"> 108</span> constant <span class="keyword">const</span> <span class="keywordtype">int</span>* shape,</div>
<div class="line"><a id="l00109" name="l00109"></a><span class="lineno"> 109</span> constant <span class="keyword">const</span> stride_t* strides,</div>
<div class="line"><a id="l00110" name="l00110"></a><span class="lineno"> 110</span> <span class="keywordtype">int</span> ndim) {</div>
<div class="line"><a id="l00111" name="l00111"></a><span class="lineno"> 111</span> stride_t loc = elem.x * strides[ndim - 1] + elem.y * strides[ndim - 2];</div>
<div class="line"><a id="l00112" name="l00112"></a><span class="lineno"> 112</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> d = ndim - 3; d &gt;= 0; --d) {</div>
<div class="line"><a id="l00113" name="l00113"></a><span class="lineno"> 113</span> loc += (elem.z % shape[d]) * strides[d];</div>
<div class="line"><a id="l00114" name="l00114"></a><span class="lineno"> 114</span> elem.z /= shape[d];</div>
<div class="line"><a id="l00115" name="l00115"></a><span class="lineno"> 115</span> }</div>
<div class="line"><a id="l00116" name="l00116"></a><span class="lineno"> 116</span> <span class="keywordflow">return</span> loc;</div>
<div class="line"><a id="l00117" name="l00117"></a><span class="lineno"> 117</span>}</div>
</div>
<div class="line"><a id="l00118" name="l00118"></a><span class="lineno"> 118</span> </div>
<div class="line"><a id="l00120" name="l00120"></a><span class="lineno"> 120</span><span class="comment">// Single Array with fixed N dims</span></div>
<div class="line"><a id="l00121" name="l00121"></a><span class="lineno"> 121</span> </div>
<div class="line"><a id="l00122" name="l00122"></a><span class="lineno"> 122</span><span class="keyword">template</span> &lt;<span class="keyword">typename</span> str<span class="keywordtype">id</span>e_t&gt;</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_2utils_8h.html#a196a07022b812b241d4c06192c0fa83d"> 123</a></span>METAL_FUNC stride_t <a class="code hl_function" href="backend_2metal_2kernels_2utils_8h.html#a196a07022b812b241d4c06192c0fa83d">elem_to_loc_1</a>(uint elem, constant <span class="keyword">const</span> stride_t&amp; stride) {</div>
<div class="line"><a id="l00124" name="l00124"></a><span class="lineno"> 124</span> <span class="keywordflow">return</span> elem * stride;</div>
<div class="line"><a id="l00125" name="l00125"></a><span class="lineno"> 125</span>}</div>
</div>
<div class="line"><a id="l00126" name="l00126"></a><span class="lineno"> 126</span> </div>
<div class="line"><a id="l00127" name="l00127"></a><span class="lineno"> 127</span><span class="keyword">template</span> &lt;<span class="keyword">typename</span> str<span class="keywordtype">id</span>e_t&gt;</div>
<div class="line"><a id="l00128" name="l00128"></a><span class="lineno"> 128</span>METAL_FUNC stride_t</div>
<div class="foldopen" id="foldopen00129" data-start="{" data-end="}">
<div class="line"><a id="l00129" name="l00129"></a><span class="lineno"><a class="line" href="backend_2metal_2kernels_2utils_8h.html#ad6c45cacca97899cd362df49c06fea79"> 129</a></span><a class="code hl_function" href="backend_2metal_2kernels_2utils_8h.html#ad6c45cacca97899cd362df49c06fea79">elem_to_loc_2</a>(uint2 elem, constant <span class="keyword">const</span> stride_t strides[2]) {</div>
<div class="line"><a id="l00130" name="l00130"></a><span class="lineno"> 130</span> <span class="keywordflow">return</span> elem.x * strides[1] + elem.y * strides[0];</div>
<div class="line"><a id="l00131" name="l00131"></a><span class="lineno"> 131</span>}</div>
</div>
<div class="line"><a id="l00132" name="l00132"></a><span class="lineno"> 132</span> </div>
<div class="line"><a id="l00133" name="l00133"></a><span class="lineno"> 133</span><span class="keyword">template</span> &lt;<span class="keyword">typename</span> str<span class="keywordtype">id</span>e_t&gt;</div>
<div class="line"><a id="l00134" name="l00134"></a><span class="lineno"> 134</span>METAL_FUNC stride_t</div>
<div class="foldopen" id="foldopen00135" data-start="{" data-end="}">
<div class="line"><a id="l00135" name="l00135"></a><span class="lineno"><a class="line" href="backend_2metal_2kernels_2utils_8h.html#a2c34ed54714c69e6e1b44344f9e6e330"> 135</a></span><a class="code hl_function" href="backend_2metal_2kernels_2utils_8h.html#a2c34ed54714c69e6e1b44344f9e6e330">elem_to_loc_3</a>(uint3 elem, constant <span class="keyword">const</span> stride_t strides[3]) {</div>
<div class="line"><a id="l00136" name="l00136"></a><span class="lineno"> 136</span> <span class="keywordflow">return</span> elem.x * strides[2] + elem.y * strides[1] + elem.z * strides[0];</div>
<div class="line"><a id="l00137" name="l00137"></a><span class="lineno"> 137</span>}</div>
</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="keyword">template</span> &lt;<span class="keywordtype">int</span> NDIM&gt;</div>
<div class="foldopen" id="foldopen00140" data-start="{" data-end="}">
<div class="line"><a id="l00140" name="l00140"></a><span class="lineno"><a class="line" href="backend_2metal_2kernels_2utils_8h.html#aa25c926e32ba8f05de765c662326d955"> 140</a></span>METAL_FUNC <span class="keywordtype">size_t</span> <a class="code hl_function" href="backend_2metal_2kernels_2utils_8h.html#aa25c926e32ba8f05de765c662326d955">elem_to_loc_nd</a>(</div>
<div class="line"><a id="l00141" name="l00141"></a><span class="lineno"> 141</span> uint elem,</div>
<div class="line"><a id="l00142" name="l00142"></a><span class="lineno"> 142</span> device <span class="keyword">const</span> <span class="keywordtype">int</span>* shape,</div>
<div class="line"><a id="l00143" name="l00143"></a><span class="lineno"> 143</span> device <span class="keyword">const</span> <span class="keywordtype">size_t</span>* strides) {</div>
<div class="line"><a id="l00144" name="l00144"></a><span class="lineno"> 144</span> <span class="keywordtype">size_t</span> loc = (elem % shape[NDIM - 1]) * strides[NDIM - 1];</div>
<div class="line"><a id="l00145" name="l00145"></a><span class="lineno"> 145</span> </div>
<div class="line"><a id="l00146" name="l00146"></a><span class="lineno"> 146</span> <a class="code hl_define" href="backend_2metal_2kernels_2utils_8h.html#a069b682d7d21827461544817d722bfd3">MLX_MTL_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">int</span> d = NDIM - 2; d &gt;= 0; --d) {</div>
<div class="line"><a id="l00148" name="l00148"></a><span class="lineno"> 148</span> elem /= shape[d + 1];</div>
<div class="line"><a id="l00149" name="l00149"></a><span class="lineno"> 149</span> loc += (elem % shape[d]) * strides[d];</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> <span class="keywordflow">return</span> loc;</div>
<div class="line"><a id="l00153" name="l00153"></a><span class="lineno"> 153</span>}</div>
</div>
<div class="line"><a id="l00154" name="l00154"></a><span class="lineno"> 154</span> </div>
<div class="line"><a id="l00155" name="l00155"></a><span class="lineno"> 155</span><span class="keyword">template</span> &lt;<span class="keywordtype">int</span> NDIM&gt;</div>
<div class="foldopen" id="foldopen00156" data-start="{" data-end="}">
<div class="line"><a id="l00156" name="l00156"></a><span class="lineno"><a class="line" href="backend_2metal_2kernels_2utils_8h.html#a0d04f0d0718d0a5796ce5ca1a289d942"> 156</a></span>METAL_FUNC <span class="keywordtype">size_t</span> <a class="code hl_function" href="backend_2metal_2kernels_2utils_8h.html#aa25c926e32ba8f05de765c662326d955">elem_to_loc_nd</a>(</div>
<div class="line"><a id="l00157" name="l00157"></a><span class="lineno"> 157</span> uint3 elem,</div>
<div class="line"><a id="l00158" name="l00158"></a><span class="lineno"> 158</span> constant <span class="keyword">const</span> <span class="keywordtype">int</span> shape[NDIM],</div>
<div class="line"><a id="l00159" name="l00159"></a><span class="lineno"> 159</span> constant <span class="keyword">const</span> <span class="keywordtype">size_t</span> strides[NDIM]) {</div>
<div class="line"><a id="l00160" name="l00160"></a><span class="lineno"> 160</span> <span class="keywordtype">size_t</span> loc = elem.x * strides[NDIM - 1] + elem.y * strides[NDIM - 2];</div>
<div class="line"><a id="l00161" name="l00161"></a><span class="lineno"> 161</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> d = NDIM - 3; d &gt;= 0; --d) {</div>
<div class="line"><a id="l00162" name="l00162"></a><span class="lineno"> 162</span> loc += (elem.z % shape[d]) * strides[d];</div>
<div class="line"><a id="l00163" name="l00163"></a><span class="lineno"> 163</span> elem.z /= shape[d];</div>
<div class="line"><a id="l00164" name="l00164"></a><span class="lineno"> 164</span> }</div>
<div class="line"><a id="l00165" name="l00165"></a><span class="lineno"> 165</span> <span class="keywordflow">return</span> loc;</div>
<div class="line"><a id="l00166" name="l00166"></a><span class="lineno"> 166</span>}</div>
</div>
<div class="line"><a id="l00167" name="l00167"></a><span class="lineno"> 167</span> </div>
<div class="line"><a id="l00168" name="l00168"></a><span class="lineno"> 168</span><span class="keyword">template</span> &lt;<span class="keywordtype">int</span> NDIM&gt;</div>
<div class="foldopen" id="foldopen00169" data-start="{" data-end="}">
<div class="line"><a id="l00169" name="l00169"></a><span class="lineno"><a class="line" href="backend_2metal_2kernels_2utils_8h.html#ac7d74fb6d5fed31513b6b7defcf45921"> 169</a></span>METAL_FUNC int64_t <a class="code hl_function" href="backend_2metal_2kernels_2utils_8h.html#aa25c926e32ba8f05de765c662326d955">elem_to_loc_nd</a>(</div>
<div class="line"><a id="l00170" name="l00170"></a><span class="lineno"> 170</span> uint elem,</div>
<div class="line"><a id="l00171" name="l00171"></a><span class="lineno"> 171</span> constant <span class="keyword">const</span> <span class="keywordtype">int</span> shape[NDIM],</div>
<div class="line"><a id="l00172" name="l00172"></a><span class="lineno"> 172</span> constant <span class="keyword">const</span> int64_t strides[NDIM]) {</div>
<div class="line"><a id="l00173" name="l00173"></a><span class="lineno"> 173</span> int64_t loc = (elem % shape[NDIM - 1]) * strides[NDIM - 1];</div>
<div class="line"><a id="l00174" name="l00174"></a><span class="lineno"> 174</span> </div>
<div class="line"><a id="l00175" name="l00175"></a><span class="lineno"> 175</span> <a class="code hl_define" href="backend_2metal_2kernels_2utils_8h.html#a069b682d7d21827461544817d722bfd3">MLX_MTL_PRAGMA_UNROLL</a></div>
<div class="line"><a id="l00176" name="l00176"></a><span class="lineno"> 176</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> d = NDIM - 2; d &gt;= 0; --d) {</div>
<div class="line"><a id="l00177" name="l00177"></a><span class="lineno"> 177</span> elem /= shape[d + 1];</div>
<div class="line"><a id="l00178" name="l00178"></a><span class="lineno"> 178</span> loc += (elem % shape[d]) * strides[d];</div>
<div class="line"><a id="l00179" name="l00179"></a><span class="lineno"> 179</span> }</div>
<div class="line"><a id="l00180" name="l00180"></a><span class="lineno"> 180</span> </div>
<div class="line"><a id="l00181" name="l00181"></a><span class="lineno"> 181</span> <span class="keywordflow">return</span> loc;</div>
<div class="line"><a id="l00182" name="l00182"></a><span class="lineno"> 182</span>}</div>
</div>
<div class="line"><a id="l00183" name="l00183"></a><span class="lineno"> 183</span> </div>
<div class="line"><a id="l00184" name="l00184"></a><span class="lineno"> 184</span><span class="keyword">template</span> &lt;<span class="keywordtype">int</span> NDIM&gt;</div>
<div class="foldopen" id="foldopen00185" data-start="{" data-end="}">
<div class="line"><a id="l00185" name="l00185"></a><span class="lineno"><a class="line" href="backend_2metal_2kernels_2utils_8h.html#a4fec636fff34a288ccd56ce202703232"> 185</a></span>METAL_FUNC int64_t <a class="code hl_function" href="backend_2metal_2kernels_2utils_8h.html#aa25c926e32ba8f05de765c662326d955">elem_to_loc_nd</a>(</div>
<div class="line"><a id="l00186" name="l00186"></a><span class="lineno"> 186</span> uint3 elem,</div>
<div class="line"><a id="l00187" name="l00187"></a><span class="lineno"> 187</span> constant <span class="keyword">const</span> <span class="keywordtype">int</span> shape[NDIM],</div>
<div class="line"><a id="l00188" name="l00188"></a><span class="lineno"> 188</span> constant <span class="keyword">const</span> int64_t strides[NDIM]) {</div>
<div class="line"><a id="l00189" name="l00189"></a><span class="lineno"> 189</span> int64_t loc = elem.x * strides[NDIM - 1] + elem.y * strides[NDIM - 2];</div>
<div class="line"><a id="l00190" name="l00190"></a><span class="lineno"> 190</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> d = NDIM - 3; d &gt;= 0; --d) {</div>
<div class="line"><a id="l00191" name="l00191"></a><span class="lineno"> 191</span> loc += (elem.z % shape[d]) * strides[d];</div>
<div class="line"><a id="l00192" name="l00192"></a><span class="lineno"> 192</span> elem.z /= shape[d];</div>
<div class="line"><a id="l00193" name="l00193"></a><span class="lineno"> 193</span> }</div>
<div class="line"><a id="l00194" name="l00194"></a><span class="lineno"> 194</span> <span class="keywordflow">return</span> loc;</div>
<div class="line"><a id="l00195" name="l00195"></a><span class="lineno"> 195</span>}</div>
</div>
<div class="line"><a id="l00196" name="l00196"></a><span class="lineno"> 196</span> </div>
<div class="line"><a id="l00198" name="l00198"></a><span class="lineno"> 198</span><span class="comment">// Multiple Arrays with generic dims</span></div>
<div class="line"><a id="l00199" name="l00199"></a><span class="lineno"> 199</span> </div>
<div class="foldopen" id="foldopen00200" data-start="{" data-end="}">
<div class="line"><a id="l00200" name="l00200"></a><span class="lineno"><a class="line" href="backend_2metal_2kernels_2utils_8h.html#a4069a6398757e8158c14551539083181"> 200</a></span>METAL_FUNC uint2 <a class="code hl_function" href="backend_2metal_2kernels_2utils_8h.html#a4069a6398757e8158c14551539083181">elem_to_loc_2_nd</a>(</div>
<div class="line"><a id="l00201" name="l00201"></a><span class="lineno"> 201</span> uint3 elem,</div>
<div class="line"><a id="l00202" name="l00202"></a><span class="lineno"> 202</span> constant <span class="keyword">const</span> <span class="keywordtype">int</span>* shape,</div>
<div class="line"><a id="l00203" name="l00203"></a><span class="lineno"> 203</span> constant <span class="keyword">const</span> <span class="keywordtype">size_t</span>* a_strides,</div>
<div class="line"><a id="l00204" name="l00204"></a><span class="lineno"> 204</span> constant <span class="keyword">const</span> <span class="keywordtype">size_t</span>* b_strides,</div>
<div class="line"><a id="l00205" name="l00205"></a><span class="lineno"> 205</span> <span class="keywordtype">int</span> ndim) {</div>
<div class="line"><a id="l00206" name="l00206"></a><span class="lineno"> 206</span> uint2 loc = {</div>
<div class="line"><a id="l00207" name="l00207"></a><span class="lineno"> 207</span> <span class="keyword">static_cast&lt;</span>uint<span class="keyword">&gt;</span>(</div>
<div class="line"><a id="l00208" name="l00208"></a><span class="lineno"> 208</span> elem.x * a_strides[ndim - 1] + elem.y * a_strides[ndim - 2]),</div>
<div class="line"><a id="l00209" name="l00209"></a><span class="lineno"> 209</span> <span class="keyword">static_cast&lt;</span>uint<span class="keyword">&gt;</span>(</div>
<div class="line"><a id="l00210" name="l00210"></a><span class="lineno"> 210</span> elem.x * b_strides[ndim - 1] + elem.y * b_strides[ndim - 2])};</div>
<div class="line"><a id="l00211" name="l00211"></a><span class="lineno"> 211</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> d = ndim - 3; d &gt;= 0; --d) {</div>
<div class="line"><a id="l00212" name="l00212"></a><span class="lineno"> 212</span> uint l = elem.z % shape[d];</div>
<div class="line"><a id="l00213" name="l00213"></a><span class="lineno"> 213</span> loc.x += l * a_strides[d];</div>
<div class="line"><a id="l00214" name="l00214"></a><span class="lineno"> 214</span> loc.y += l * b_strides[d];</div>
<div class="line"><a id="l00215" name="l00215"></a><span class="lineno"> 215</span> elem.z /= shape[d];</div>
<div class="line"><a id="l00216" name="l00216"></a><span class="lineno"> 216</span> }</div>
<div class="line"><a id="l00217" name="l00217"></a><span class="lineno"> 217</span> <span class="keywordflow">return</span> loc;</div>
<div class="line"><a id="l00218" name="l00218"></a><span class="lineno"> 218</span>}</div>
</div>
<div class="line"><a id="l00219" name="l00219"></a><span class="lineno"> 219</span> </div>
<div class="foldopen" id="foldopen00220" data-start="{" data-end="}">
<div class="line"><a id="l00220" name="l00220"></a><span class="lineno"><a class="line" href="backend_2metal_2kernels_2utils_8h.html#a59d3221f4fbcc7e340af0a743fae054b"> 220</a></span>METAL_FUNC uint3 <a class="code hl_function" href="backend_2metal_2kernels_2utils_8h.html#a59d3221f4fbcc7e340af0a743fae054b">elem_to_loc_3_nd</a>(</div>
<div class="line"><a id="l00221" name="l00221"></a><span class="lineno"> 221</span> uint3 elem,</div>
<div class="line"><a id="l00222" name="l00222"></a><span class="lineno"> 222</span> constant <span class="keyword">const</span> <span class="keywordtype">int</span>* shape,</div>
<div class="line"><a id="l00223" name="l00223"></a><span class="lineno"> 223</span> constant <span class="keyword">const</span> <span class="keywordtype">size_t</span>* a_strides,</div>
<div class="line"><a id="l00224" name="l00224"></a><span class="lineno"> 224</span> constant <span class="keyword">const</span> <span class="keywordtype">size_t</span>* b_strides,</div>
<div class="line"><a id="l00225" name="l00225"></a><span class="lineno"> 225</span> constant <span class="keyword">const</span> <span class="keywordtype">size_t</span>* c_strides,</div>
<div class="line"><a id="l00226" name="l00226"></a><span class="lineno"> 226</span> <span class="keywordtype">int</span> ndim) {</div>
<div class="line"><a id="l00227" name="l00227"></a><span class="lineno"> 227</span> uint3 loc = {</div>
<div class="line"><a id="l00228" name="l00228"></a><span class="lineno"> 228</span> <span class="keyword">static_cast&lt;</span>uint<span class="keyword">&gt;</span>(</div>
<div class="line"><a id="l00229" name="l00229"></a><span class="lineno"> 229</span> elem.x * a_strides[ndim - 1] + elem.y * a_strides[ndim - 2]),</div>
<div class="line"><a id="l00230" name="l00230"></a><span class="lineno"> 230</span> <span class="keyword">static_cast&lt;</span>uint<span class="keyword">&gt;</span>(</div>
<div class="line"><a id="l00231" name="l00231"></a><span class="lineno"> 231</span> elem.x * b_strides[ndim - 1] + elem.y * b_strides[ndim - 2]),</div>
<div class="line"><a id="l00232" name="l00232"></a><span class="lineno"> 232</span> <span class="keyword">static_cast&lt;</span>uint<span class="keyword">&gt;</span>(</div>
<div class="line"><a id="l00233" name="l00233"></a><span class="lineno"> 233</span> elem.x * c_strides[ndim - 1] + elem.y * c_strides[ndim - 2])};</div>
<div class="line"><a id="l00234" name="l00234"></a><span class="lineno"> 234</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> d = ndim - 3; d &gt;= 0; --d) {</div>
<div class="line"><a id="l00235" name="l00235"></a><span class="lineno"> 235</span> uint l = elem.z % shape[d];</div>
<div class="line"><a id="l00236" name="l00236"></a><span class="lineno"> 236</span> loc.x += l * a_strides[d];</div>
<div class="line"><a id="l00237" name="l00237"></a><span class="lineno"> 237</span> loc.y += l * b_strides[d];</div>
<div class="line"><a id="l00238" name="l00238"></a><span class="lineno"> 238</span> loc.z += l * c_strides[d];</div>
<div class="line"><a id="l00239" name="l00239"></a><span class="lineno"> 239</span> elem.z /= shape[d];</div>
<div class="line"><a id="l00240" name="l00240"></a><span class="lineno"> 240</span> }</div>
<div class="line"><a id="l00241" name="l00241"></a><span class="lineno"> 241</span> <span class="keywordflow">return</span> loc;</div>
<div class="line"><a id="l00242" name="l00242"></a><span class="lineno"> 242</span>}</div>
</div>
<div class="line"><a id="l00243" name="l00243"></a><span class="lineno"> 243</span> </div>
<div class="line"><a id="l00245" name="l00245"></a><span class="lineno"> 245</span><span class="comment">// Multiple Arrays with fixed N dims</span></div>
<div class="line"><a id="l00246" name="l00246"></a><span class="lineno"> 246</span> </div>
<div class="line"><a id="l00247" name="l00247"></a><span class="lineno"> 247</span><span class="keyword">template</span> &lt;<span class="keywordtype">int</span> NDIM&gt;</div>
<div class="foldopen" id="foldopen00248" data-start="{" data-end="}">
<div class="line"><a id="l00248" name="l00248"></a><span class="lineno"><a class="line" href="backend_2metal_2kernels_2utils_8h.html#a2eae434d62466c9a072a8339162113ca"> 248</a></span>METAL_FUNC uint2 <a class="code hl_function" href="backend_2metal_2kernels_2utils_8h.html#a4069a6398757e8158c14551539083181">elem_to_loc_2_nd</a>(</div>
<div class="line"><a id="l00249" name="l00249"></a><span class="lineno"> 249</span> uint3 elem,</div>
<div class="line"><a id="l00250" name="l00250"></a><span class="lineno"> 250</span> constant <span class="keyword">const</span> <span class="keywordtype">int</span> shape[NDIM],</div>
<div class="line"><a id="l00251" name="l00251"></a><span class="lineno"> 251</span> constant <span class="keyword">const</span> <span class="keywordtype">size_t</span> a_strides[NDIM],</div>
<div class="line"><a id="l00252" name="l00252"></a><span class="lineno"> 252</span> constant <span class="keyword">const</span> <span class="keywordtype">size_t</span> b_strides[NDIM]) {</div>
<div class="line"><a id="l00253" name="l00253"></a><span class="lineno"> 253</span> uint2 loc = {</div>
<div class="line"><a id="l00254" name="l00254"></a><span class="lineno"> 254</span> <span class="keyword">static_cast&lt;</span>uint<span class="keyword">&gt;</span>(</div>
<div class="line"><a id="l00255" name="l00255"></a><span class="lineno"> 255</span> elem.x * a_strides[NDIM - 1] + elem.y * a_strides[NDIM - 2]),</div>
<div class="line"><a id="l00256" name="l00256"></a><span class="lineno"> 256</span> <span class="keyword">static_cast&lt;</span>uint<span class="keyword">&gt;</span>(</div>
<div class="line"><a id="l00257" name="l00257"></a><span class="lineno"> 257</span> elem.x * b_strides[NDIM - 1] + elem.y * b_strides[NDIM - 2])};</div>
<div class="line"><a id="l00258" name="l00258"></a><span class="lineno"> 258</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> d = NDIM - 3; d &gt;= 0; --d) {</div>
<div class="line"><a id="l00259" name="l00259"></a><span class="lineno"> 259</span> uint l = elem.z % shape[d];</div>
<div class="line"><a id="l00260" name="l00260"></a><span class="lineno"> 260</span> loc.x += l * a_strides[d];</div>
<div class="line"><a id="l00261" name="l00261"></a><span class="lineno"> 261</span> loc.y += l * b_strides[d];</div>
<div class="line"><a id="l00262" name="l00262"></a><span class="lineno"> 262</span> elem.z /= shape[d];</div>
<div class="line"><a id="l00263" name="l00263"></a><span class="lineno"> 263</span> }</div>
<div class="line"><a id="l00264" name="l00264"></a><span class="lineno"> 264</span> <span class="keywordflow">return</span> loc;</div>
<div class="line"><a id="l00265" name="l00265"></a><span class="lineno"> 265</span>}</div>
</div>
<div class="line"><a id="l00266" name="l00266"></a><span class="lineno"> 266</span> </div>
<div class="line"><a id="l00267" name="l00267"></a><span class="lineno"> 267</span><span class="keyword">template</span> &lt;<span class="keywordtype">int</span> NDIM&gt;</div>
<div class="foldopen" id="foldopen00268" data-start="{" data-end="}">
<div class="line"><a id="l00268" name="l00268"></a><span class="lineno"><a class="line" href="backend_2metal_2kernels_2utils_8h.html#a418562e11bdfc92130e445ac01e53924"> 268</a></span>METAL_FUNC uint3 <a class="code hl_function" href="backend_2metal_2kernels_2utils_8h.html#a59d3221f4fbcc7e340af0a743fae054b">elem_to_loc_3_nd</a>(</div>
<div class="line"><a id="l00269" name="l00269"></a><span class="lineno"> 269</span> uint3 elem,</div>
<div class="line"><a id="l00270" name="l00270"></a><span class="lineno"> 270</span> constant <span class="keyword">const</span> <span class="keywordtype">int</span> shape[NDIM],</div>
<div class="line"><a id="l00271" name="l00271"></a><span class="lineno"> 271</span> constant <span class="keyword">const</span> <span class="keywordtype">size_t</span> a_strides[NDIM],</div>
<div class="line"><a id="l00272" name="l00272"></a><span class="lineno"> 272</span> constant <span class="keyword">const</span> <span class="keywordtype">size_t</span> b_strides[NDIM],</div>
<div class="line"><a id="l00273" name="l00273"></a><span class="lineno"> 273</span> constant <span class="keyword">const</span> <span class="keywordtype">size_t</span> c_strides[NDIM]) {</div>
<div class="line"><a id="l00274" name="l00274"></a><span class="lineno"> 274</span> uint3 loc = {</div>
<div class="line"><a id="l00275" name="l00275"></a><span class="lineno"> 275</span> <span class="keyword">static_cast&lt;</span>uint<span class="keyword">&gt;</span>(</div>
<div class="line"><a id="l00276" name="l00276"></a><span class="lineno"> 276</span> elem.x * a_strides[NDIM - 1] + elem.y * a_strides[NDIM - 2]),</div>
<div class="line"><a id="l00277" name="l00277"></a><span class="lineno"> 277</span> <span class="keyword">static_cast&lt;</span>uint<span class="keyword">&gt;</span>(</div>
<div class="line"><a id="l00278" name="l00278"></a><span class="lineno"> 278</span> elem.x * b_strides[NDIM - 1] + elem.y * b_strides[NDIM - 2]),</div>
<div class="line"><a id="l00279" name="l00279"></a><span class="lineno"> 279</span> <span class="keyword">static_cast&lt;</span>uint<span class="keyword">&gt;</span>(</div>
<div class="line"><a id="l00280" name="l00280"></a><span class="lineno"> 280</span> elem.x * c_strides[NDIM - 1] + elem.y * c_strides[NDIM - 2])};</div>
<div class="line"><a id="l00281" name="l00281"></a><span class="lineno"> 281</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> d = NDIM - 3; d &gt;= 0; --d) {</div>
<div class="line"><a id="l00282" name="l00282"></a><span class="lineno"> 282</span> uint l = elem.z % shape[d];</div>
<div class="line"><a id="l00283" name="l00283"></a><span class="lineno"> 283</span> loc.x += l * a_strides[d];</div>
<div class="line"><a id="l00284" name="l00284"></a><span class="lineno"> 284</span> loc.y += l * b_strides[d];</div>
<div class="line"><a id="l00285" name="l00285"></a><span class="lineno"> 285</span> loc.z += l * c_strides[d];</div>
<div class="line"><a id="l00286" name="l00286"></a><span class="lineno"> 286</span> elem.z /= shape[d];</div>
<div class="line"><a id="l00287" name="l00287"></a><span class="lineno"> 287</span> }</div>
<div class="line"><a id="l00288" name="l00288"></a><span class="lineno"> 288</span> <span class="keywordflow">return</span> loc;</div>
<div class="line"><a id="l00289" name="l00289"></a><span class="lineno"> 289</span>}</div>
</div>
<div class="line"><a id="l00290" name="l00290"></a><span class="lineno"> 290</span> </div>
<div class="line"><a id="l00292" name="l00292"></a><span class="lineno"> 292</span><span class="comment">// Calculation utils</span></div>
<div class="line"><a id="l00294" name="l00294"></a><span class="lineno"> 294</span> </div>
<div class="foldopen" id="foldopen00296" data-start="{" data-end="}">
<div class="line"><a id="l00296" name="l00296"></a><span class="lineno"><a class="line" href="backend_2metal_2kernels_2utils_8h.html#a51c19db777f43943e4b35f25dd88d49d"> 296</a></span><span class="keyword">inline</span> <span class="keywordtype">size_t</span> <a class="code hl_function" href="backend_2metal_2kernels_2utils_8h.html#a51c19db777f43943e4b35f25dd88d49d">ceildiv</a>(<span class="keywordtype">size_t</span> N, <span class="keywordtype">size_t</span> M) {</div>
<div class="line"><a id="l00297" name="l00297"></a><span class="lineno"> 297</span> <span class="keywordflow">return</span> (N + M - 1) / M;</div>
<div class="line"><a id="l00298" name="l00298"></a><span class="lineno"> 298</span>}</div>
</div>
<div class="line"><a id="l00299" name="l00299"></a><span class="lineno"> 299</span> </div>
<div class="line"><a id="l00300" name="l00300"></a><span class="lineno"> 300</span><span class="comment">// https://docs.oracle.com/cd/E19957-01/806-3568/ncg_goldberg.html#1202</span></div>
<div class="foldopen" id="foldopen00301" data-start="{" data-end="}">
<div class="line"><a id="l00301" name="l00301"></a><span class="lineno"><a class="line" href="backend_2metal_2kernels_2utils_8h.html#a27c03f2f90ab56db2e4d59559a3d2e9a"> 301</a></span><span class="keyword">inline</span> <span class="keywordtype">float</span> <a class="code hl_function" href="backend_2metal_2kernels_2utils_8h.html#a27c03f2f90ab56db2e4d59559a3d2e9a">log1p</a>(<span class="keywordtype">float</span> x) {</div>
<div class="line"><a id="l00302" name="l00302"></a><span class="lineno"> 302</span> <span class="keywordtype">float</span> xp1 = 1.0f + x;</div>
<div class="line"><a id="l00303" name="l00303"></a><span class="lineno"> 303</span> <span class="keywordflow">if</span> (xp1 == <a class="code hl_struct" href="struct_limits.html">Limits&lt;float&gt;::max</a>) {</div>
<div class="line"><a id="l00304" name="l00304"></a><span class="lineno"> 304</span> <span class="keywordflow">return</span> <a class="code hl_struct" href="struct_limits.html">Limits&lt;float&gt;::max</a>;</div>
<div class="line"><a id="l00305" name="l00305"></a><span class="lineno"> 305</span> }</div>
<div class="line"><a id="l00306" name="l00306"></a><span class="lineno"> 306</span> <span class="keywordflow">if</span> (xp1 == 1.0f) {</div>
<div class="line"><a id="l00307" name="l00307"></a><span class="lineno"> 307</span> <span class="keywordflow">return</span> x;</div>
<div class="line"><a id="l00308" name="l00308"></a><span class="lineno"> 308</span> }</div>
<div class="line"><a id="l00309" name="l00309"></a><span class="lineno"> 309</span> </div>
<div class="line"><a id="l00310" name="l00310"></a><span class="lineno"> 310</span> <span class="keywordflow">return</span> x * (<a class="code hl_function" href="namespacemetal.html#a423a9f4f2fc7ef5ec7eda061277b51b6">metal::log</a>(xp1) / (xp1 - 1.0f));</div>
<div class="line"><a id="l00311" name="l00311"></a><span class="lineno"> 311</span>}</div>
</div>
<div class="line"><a id="l00312" name="l00312"></a><span class="lineno"> 312</span> </div>
<div class="foldopen" id="foldopen00313" data-start="{" data-end="}">
<div class="line"><a id="l00313" name="l00313"></a><span class="lineno"><a class="line" href="backend_2metal_2kernels_2utils_8h.html#a3501b665c8837eabf9789ea27a7d6946"> 313</a></span><span class="keyword">inline</span> <a class="code hl_struct" href="struct___m_l_x___b_float16.html">bfloat16_t</a> <a class="code hl_function" href="backend_2metal_2kernels_2utils_8h.html#a27c03f2f90ab56db2e4d59559a3d2e9a">log1p</a>(<a class="code hl_struct" href="struct___m_l_x___b_float16.html">bfloat16_t</a> x) {</div>
<div class="line"><a id="l00314" name="l00314"></a><span class="lineno"> 314</span> <span class="keywordtype">float</span> xp1 = 1.0f + <span class="keyword">static_cast&lt;</span><span class="keywordtype">float</span><span class="keyword">&gt;</span>(x);</div>
<div class="line"><a id="l00315" name="l00315"></a><span class="lineno"> 315</span> <span class="keywordflow">if</span> (xp1 == <a class="code hl_struct" href="struct_limits.html">Limits&lt;float&gt;::max</a>) {</div>
<div class="line"><a id="l00316" name="l00316"></a><span class="lineno"> 316</span> <span class="keywordflow">return</span> <a class="code hl_struct" href="struct_limits.html">Limits&lt;bfloat16_t&gt;::max</a>;</div>
<div class="line"><a id="l00317" name="l00317"></a><span class="lineno"> 317</span> }</div>
<div class="line"><a id="l00318" name="l00318"></a><span class="lineno"> 318</span> <span class="keywordflow">if</span> (xp1 == 1.0f) {</div>
<div class="line"><a id="l00319" name="l00319"></a><span class="lineno"> 319</span> <span class="keywordflow">return</span> x;</div>
<div class="line"><a id="l00320" name="l00320"></a><span class="lineno"> 320</span> }</div>
<div class="line"><a id="l00321" name="l00321"></a><span class="lineno"> 321</span> </div>
<div class="line"><a id="l00322" name="l00322"></a><span class="lineno"> 322</span> <span class="keywordflow">return</span> <a class="code hl_typedef" href="backend_2metal_2kernels_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82">bfloat16_t</a>(x * (<a class="code hl_function" href="namespacemetal.html#a423a9f4f2fc7ef5ec7eda061277b51b6">metal::log</a>(xp1) / (xp1 - 1.0f)));</div>
<div class="line"><a id="l00323" name="l00323"></a><span class="lineno"> 323</span>}</div>
</div>
<div class="line"><a id="l00324" name="l00324"></a><span class="lineno"> 324</span> </div>
<div class="line"><a id="l00326" name="l00326"></a><span class="lineno"> 326</span><span class="comment">// SIMD shuffle ops</span></div>
<div class="line"><a id="l00328" name="l00328"></a><span class="lineno"> 328</span> </div>
<div class="foldopen" id="foldopen00329" data-start="{" data-end="}">
<div class="line"><a id="l00329" name="l00329"></a><span class="lineno"><a class="line" href="backend_2metal_2kernels_2utils_8h.html#aba6279624b1d30c525efee856a222b5c"> 329</a></span><span class="keyword">inline</span> uint64_t <a class="code hl_function" href="namespacemetal.html#af6e2dd7ae087aba6abac4f0350b7611c">simd_shuffle_down</a>(uint64_t data, uint16_t delta) {</div>
<div class="line"><a id="l00330" name="l00330"></a><span class="lineno"> 330</span> <span class="keywordflow">return</span> as_type&lt;uint64_t&gt;(</div>
<div class="line"><a id="l00331" name="l00331"></a><span class="lineno"> 331</span> <a class="code hl_function" href="namespacemetal.html#af6e2dd7ae087aba6abac4f0350b7611c">metal::simd_shuffle_down</a>(as_type&lt;uint2&gt;(data), delta));</div>
<div class="line"><a id="l00332" name="l00332"></a><span class="lineno"> 332</span>}</div>
</div>
<div class="line"><a id="l00333" name="l00333"></a><span class="lineno"> 333</span> </div>
<div class="foldopen" id="foldopen00334" data-start="{" data-end="}">
<div class="line"><a id="l00334" name="l00334"></a><span class="lineno"><a class="line" href="backend_2metal_2kernels_2utils_8h.html#a0c1e4d782fcc56e1ab5565cef12430dd"> 334</a></span><span class="keyword">inline</span> int64_t <a class="code hl_function" href="namespacemetal.html#af6e2dd7ae087aba6abac4f0350b7611c">simd_shuffle_down</a>(int64_t data, uint16_t delta) {</div>
<div class="line"><a id="l00335" name="l00335"></a><span class="lineno"> 335</span> <span class="keywordflow">return</span> as_type&lt;int64_t&gt;(</div>
<div class="line"><a id="l00336" name="l00336"></a><span class="lineno"> 336</span> <a class="code hl_function" href="namespacemetal.html#af6e2dd7ae087aba6abac4f0350b7611c">metal::simd_shuffle_down</a>(as_type&lt;uint2&gt;(data), delta));</div>
<div class="line"><a id="l00337" name="l00337"></a><span class="lineno"> 337</span>}</div>
</div>
<div class="line"><a id="l00338" name="l00338"></a><span class="lineno"> 338</span> </div>
<div class="foldopen" id="foldopen00339" data-start="{" data-end="}">
<div class="line"><a id="l00339" name="l00339"></a><span class="lineno"><a class="line" href="backend_2metal_2kernels_2utils_8h.html#a48ae83a8caf5c74810df60b6c6cdb062"> 339</a></span><span class="keyword">inline</span> <span class="keywordtype">bool</span> <a class="code hl_function" href="namespacemetal.html#af6e2dd7ae087aba6abac4f0350b7611c">simd_shuffle_down</a>(<span class="keywordtype">bool</span> data, uint16_t delta) {</div>
<div class="line"><a id="l00340" name="l00340"></a><span class="lineno"> 340</span> <span class="keywordflow">return</span> <a class="code hl_function" href="namespacemetal.html#af6e2dd7ae087aba6abac4f0350b7611c">simd_shuffle_down</a>(<span class="keyword">static_cast&lt;</span>uint32_t<span class="keyword">&gt;</span>(data), delta);</div>
<div class="line"><a id="l00341" name="l00341"></a><span class="lineno"> 341</span>}</div>
</div>
<div class="ttc" id="abackend_2metal_2kernels_2bf16_8h_html"><div class="ttname"><a href="backend_2metal_2kernels_2bf16_8h.html">bf16.h</a></div></div>
<div class="ttc" id="abackend_2metal_2kernels_2bf16_8h_html_a7782de82393104dd4ad754ce3b316e82"><div class="ttname"><a href="backend_2metal_2kernels_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82">bfloat16_t</a></div><div class="ttdeci">struct _MLX_BFloat16 bfloat16_t</div><div class="ttdef"><b>Definition</b> bf16.h:257</div></div>
<div class="ttc" id="abackend_2metal_2kernels_2complex_8h_html"><div class="ttname"><a href="backend_2metal_2kernels_2complex_8h.html">complex.h</a></div></div>
<div class="ttc" id="abackend_2metal_2kernels_2utils_8h_html_a069b682d7d21827461544817d722bfd3"><div class="ttname"><a href="backend_2metal_2kernels_2utils_8h.html#a069b682d7d21827461544817d722bfd3">MLX_MTL_PRAGMA_UNROLL</a></div><div class="ttdeci">#define MLX_MTL_PRAGMA_UNROLL</div><div class="ttdef"><b>Definition</b> utils.h:71</div></div>
<div class="ttc" id="abackend_2metal_2kernels_2utils_8h_html_a196a07022b812b241d4c06192c0fa83d"><div class="ttname"><a href="backend_2metal_2kernels_2utils_8h.html#a196a07022b812b241d4c06192c0fa83d">elem_to_loc_1</a></div><div class="ttdeci">METAL_FUNC stride_t elem_to_loc_1(uint elem, constant const stride_t &amp;stride)</div><div class="ttdef"><b>Definition</b> utils.h:123</div></div>
<div class="ttc" id="abackend_2metal_2kernels_2utils_8h_html_a1e520e23f58ca645dea1ac20998d987a"><div class="ttname"><a href="backend_2metal_2kernels_2utils_8h.html#a1e520e23f58ca645dea1ac20998d987a">instantiate_float_limit</a></div><div class="ttdeci">#define instantiate_float_limit(type)</div><div class="ttdef"><b>Definition</b> utils.h:44</div></div>
<div class="ttc" id="abackend_2metal_2kernels_2utils_8h_html_a27c03f2f90ab56db2e4d59559a3d2e9a"><div class="ttname"><a href="backend_2metal_2kernels_2utils_8h.html#a27c03f2f90ab56db2e4d59559a3d2e9a">log1p</a></div><div class="ttdeci">float log1p(float x)</div><div class="ttdef"><b>Definition</b> utils.h:301</div></div>
<div class="ttc" id="abackend_2metal_2kernels_2utils_8h_html_a2c34ed54714c69e6e1b44344f9e6e330"><div class="ttname"><a href="backend_2metal_2kernels_2utils_8h.html#a2c34ed54714c69e6e1b44344f9e6e330">elem_to_loc_3</a></div><div class="ttdeci">METAL_FUNC stride_t elem_to_loc_3(uint3 elem, constant const stride_t strides[3])</div><div class="ttdef"><b>Definition</b> utils.h:135</div></div>
<div class="ttc" id="abackend_2metal_2kernels_2utils_8h_html_a2e49fa7ab8f6348543455c6c45d7e2a9"><div class="ttname"><a href="backend_2metal_2kernels_2utils_8h.html#a2e49fa7ab8f6348543455c6c45d7e2a9">elem_to_loc</a></div><div class="ttdeci">METAL_FUNC stride_t elem_to_loc(uint elem, device const int *shape, device const stride_t *strides, int ndim)</div><div class="ttdef"><b>Definition</b> utils.h:77</div></div>
<div class="ttc" id="abackend_2metal_2kernels_2utils_8h_html_a4069a6398757e8158c14551539083181"><div class="ttname"><a href="backend_2metal_2kernels_2utils_8h.html#a4069a6398757e8158c14551539083181">elem_to_loc_2_nd</a></div><div class="ttdeci">METAL_FUNC uint2 elem_to_loc_2_nd(uint3 elem, constant const int *shape, constant const size_t *a_strides, constant const size_t *b_strides, int ndim)</div><div class="ttdef"><b>Definition</b> utils.h:200</div></div>
<div class="ttc" id="abackend_2metal_2kernels_2utils_8h_html_a51c19db777f43943e4b35f25dd88d49d"><div class="ttname"><a href="backend_2metal_2kernels_2utils_8h.html#a51c19db777f43943e4b35f25dd88d49d">ceildiv</a></div><div class="ttdeci">size_t ceildiv(size_t N, size_t M)</div><div class="ttdoc">Compute ceil((float)N/(float)M)</div><div class="ttdef"><b>Definition</b> utils.h:296</div></div>
<div class="ttc" id="abackend_2metal_2kernels_2utils_8h_html_a59d3221f4fbcc7e340af0a743fae054b"><div class="ttname"><a href="backend_2metal_2kernels_2utils_8h.html#a59d3221f4fbcc7e340af0a743fae054b">elem_to_loc_3_nd</a></div><div class="ttdeci">METAL_FUNC uint3 elem_to_loc_3_nd(uint3 elem, constant const int *shape, constant const size_t *a_strides, constant const size_t *b_strides, constant const size_t *c_strides, int ndim)</div><div class="ttdef"><b>Definition</b> utils.h:220</div></div>
<div class="ttc" id="abackend_2metal_2kernels_2utils_8h_html_aa25c926e32ba8f05de765c662326d955"><div class="ttname"><a href="backend_2metal_2kernels_2utils_8h.html#aa25c926e32ba8f05de765c662326d955">elem_to_loc_nd</a></div><div class="ttdeci">METAL_FUNC size_t elem_to_loc_nd(uint elem, device const int *shape, device const size_t *strides)</div><div class="ttdef"><b>Definition</b> utils.h:140</div></div>
<div class="ttc" id="abackend_2metal_2kernels_2utils_8h_html_abedffa358e7ba7782cc78d6772064c7c"><div class="ttname"><a href="backend_2metal_2kernels_2utils_8h.html#abedffa358e7ba7782cc78d6772064c7c">instantiate_default_limit</a></div><div class="ttdeci">#define instantiate_default_limit(type)</div><div class="ttdef"><b>Definition</b> utils.h:24</div></div>
<div class="ttc" id="abackend_2metal_2kernels_2utils_8h_html_acb8ddf4a29129846b673c50ba7078773"><div class="ttname"><a href="backend_2metal_2kernels_2utils_8h.html#acb8ddf4a29129846b673c50ba7078773">float16_t</a></div><div class="ttdeci">half float16_t</div><div class="ttdef"><b>Definition</b> utils.h:10</div></div>
<div class="ttc" id="abackend_2metal_2kernels_2utils_8h_html_ad6c45cacca97899cd362df49c06fea79"><div class="ttname"><a href="backend_2metal_2kernels_2utils_8h.html#ad6c45cacca97899cd362df49c06fea79">elem_to_loc_2</a></div><div class="ttdeci">METAL_FUNC stride_t elem_to_loc_2(uint2 elem, constant const stride_t strides[2])</div><div class="ttdef"><b>Definition</b> utils.h:129</div></div>
<div class="ttc" id="adefines_8h_html"><div class="ttname"><a href="defines_8h.html">defines.h</a></div></div>
<div class="ttc" id="anamespacemetal_html_a423a9f4f2fc7ef5ec7eda061277b51b6"><div class="ttname"><a href="namespacemetal.html#a423a9f4f2fc7ef5ec7eda061277b51b6">metal::log</a></div><div class="ttdeci">METAL_FUNC bfloat16_t log(bfloat16_t x)</div><div class="ttdef"><b>Definition</b> bf16_math.h:234</div></div>
<div class="ttc" id="anamespacemetal_html_af6e2dd7ae087aba6abac4f0350b7611c"><div class="ttname"><a href="namespacemetal.html#af6e2dd7ae087aba6abac4f0350b7611c">metal::simd_shuffle_down</a></div><div class="ttdeci">METAL_FUNC bfloat16_t simd_shuffle_down(bfloat16_t data, ushort delta)</div><div class="ttdef"><b>Definition</b> bf16_math.h:391</div></div>
<div class="ttc" id="astruct___m_l_x___b_float16_html"><div class="ttname"><a href="struct___m_l_x___b_float16.html">_MLX_BFloat16</a></div><div class="ttdef"><b>Definition</b> bf16.h:54</div></div>
<div class="ttc" id="astruct_limits_html"><div class="ttname"><a href="struct_limits.html">Limits</a></div><div class="ttdef"><b>Definition</b> utils.h:17</div></div>
<div class="ttc" id="astruct_limits_html_a2f0673b6f9da89ce1d64f9f3d74f50a8"><div class="ttname"><a href="struct_limits.html#a2f0673b6f9da89ce1d64f9f3d74f50a8">Limits::max</a></div><div class="ttdeci">static const constant U max</div><div class="ttdef"><b>Definition</b> utils.h:18</div></div>
<div class="ttc" id="astruct_limits_html_a5a3eae6d244fbea2aa7b9200001463e5"><div class="ttname"><a href="struct_limits.html#a5a3eae6d244fbea2aa7b9200001463e5">Limits::finite_max</a></div><div class="ttdeci">static const constant U finite_max</div><div class="ttdef"><b>Definition</b> utils.h:20</div></div>
<div class="ttc" id="astruct_limits_html_a6e81584ba65a4dc6ff9366b458e3a20e"><div class="ttname"><a href="struct_limits.html#a6e81584ba65a4dc6ff9366b458e3a20e">Limits::min</a></div><div class="ttdeci">static const constant U min</div><div class="ttdef"><b>Definition</b> utils.h:19</div></div>
<div class="ttc" id="astruct_limits_html_ae7469d21f2688797ca3e388d919ef05e"><div class="ttname"><a href="struct_limits.html#ae7469d21f2688797ca3e388d919ef05e">Limits::finite_min</a></div><div class="ttdeci">static const constant U finite_min</div><div class="ttdef"><b>Definition</b> utils.h:21</div></div>
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