zhangyiss/mlx
1
0
Fork 0
mirror of https://github.com/ml-explore/mlx.git synced 2025-06-26 02:33:21 +08:00
Code Issues Actions Packages Projects Releases Wiki Activity
c7080f89ca
mlx/docs/build/html/backend_2metal_2kernels_2fft_8h_source.html
CircleCI Docs c7080f89ca rebase
2025-06-04 01:01:55 +00:00

675 lines
109 KiB
HTML
Raw Blame History

<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "https://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
<html xmlns="http://www.w3.org/1999/xhtml" lang="en-US">
<head>
<meta http-equiv="Content-Type" content="text/xhtml;charset=UTF-8"/>
<meta http-equiv="X-UA-Compatible" content="IE=11"/>
<meta name="generator" content="Doxygen 1.13.2"/>
<meta name="viewport" content="width=device-width, initial-scale=1"/>
<title>MLX: mlx/backend/metal/kernels/fft.h Source File</title>
<link href="tabs.css" rel="stylesheet" type="text/css"/>
<script type="text/javascript" src="jquery.js"></script>
<script type="text/javascript" src="dynsections.js"></script>
<script type="text/javascript" src="clipboard.js"></script>
<link href="navtree.css" rel="stylesheet" type="text/css"/>
<script type="text/javascript" src="navtreedata.js"></script>
<script type="text/javascript" src="navtree.js"></script>
<script type="text/javascript" src="resize.js"></script>
<script type="text/javascript" src="cookie.js"></script>
<link href="search/search.css" rel="stylesheet" type="text/css"/>
<script type="text/javascript" src="search/searchdata.js"></script>
<script type="text/javascript" src="search/search.js"></script>
<script type="text/javascript">
/* @license magnet:?xt=urn:btih:d3d9a9a6595521f9666a5e94cc830dab83b65699&amp;dn=expat.txt MIT */
$(function() { init_search(); });
/* @license-end */
</script>
<link href="doxygen.css" rel="stylesheet" type="text/css" />
</head>
<body>
<div id="top"><!-- do not remove this div, it is closed by doxygen! -->
<div id="titlearea">
<table cellspacing="0" cellpadding="0">
<tbody>
<tr id="projectrow">
<td id="projectalign">
<div id="projectname">MLX
</div>
</td>
<td> <div id="MSearchBox" class="MSearchBoxInactive">
<span class="left">
<span id="MSearchSelect" onmouseover="return searchBox.OnSearchSelectShow()" onmouseout="return searchBox.OnSearchSelectHide()">&#160;</span>
<input type="text" id="MSearchField" value="" placeholder="Search" accesskey="S"
onfocus="searchBox.OnSearchFieldFocus(true)"
onblur="searchBox.OnSearchFieldFocus(false)"
onkeyup="searchBox.OnSearchFieldChange(event)"/>
</span><span class="right">
<a id="MSearchClose" href="javascript:searchBox.CloseResultsWindow()"><img id="MSearchCloseImg" border="0" src="search/close.svg" alt=""/></a>
</span>
</div>
</td>
</tr>
</tbody>
</table>
</div>
<!-- end header part -->
<!-- Generated by Doxygen 1.13.2 -->
<script type="text/javascript">
/* @license magnet:?xt=urn:btih:d3d9a9a6595521f9666a5e94cc830dab83b65699&amp;dn=expat.txt MIT */
var searchBox = new SearchBox("searchBox", "search/",'.html');
/* @license-end */
</script>
<script type="text/javascript">
/* @license magnet:?xt=urn:btih:d3d9a9a6595521f9666a5e94cc830dab83b65699&amp;dn=expat.txt MIT */
$(function() { codefold.init(0); });
/* @license-end */
</script>
</div><!-- top -->
<div id="side-nav" class="ui-resizable side-nav-resizable">
<div id="nav-tree">
<div id="nav-tree-contents">
<div id="nav-sync" class="sync"></div>
</div>
</div>
<div id="splitbar" style="-moz-user-select:none;"
class="ui-resizable-handle">
</div>
</div>
<script type="text/javascript">
/* @license magnet:?xt=urn:btih:d3d9a9a6595521f9666a5e94cc830dab83b65699&amp;dn=expat.txt MIT */
$(function(){initNavTree('backend_2metal_2kernels_2fft_8h_source.html',''); initResizable(true); });
/* @license-end */
</script>
<div id="doc-content">
<!-- window showing the filter options -->
<div id="MSearchSelectWindow"
onmouseover="return searchBox.OnSearchSelectShow()"
onmouseout="return searchBox.OnSearchSelectHide()"
onkeydown="return searchBox.OnSearchSelectKey(event)">
</div>
<!-- iframe showing the search results (closed by default) -->
<div id="MSearchResultsWindow">
<div id="MSearchResults">
<div class="SRPage">
<div id="SRIndex">
<div id="SRResults"></div>
<div class="SRStatus" id="Loading">Loading...</div>
<div class="SRStatus" id="Searching">Searching...</div>
<div class="SRStatus" id="NoMatches">No Matches</div>
</div>
</div>
</div>
</div>
<div class="header">
<div class="headertitle"><div class="title">fft.h</div></div>
</div><!--header-->
<div class="contents">
<a href="backend_2metal_2kernels_2fft_8h.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a id="l00001" name="l00001"></a><span class="lineno"> 1</span><span class="comment">// Copyright © 2024 Apple Inc.</span></div>
<div class="line"><a id="l00002" name="l00002"></a><span class="lineno"> 2</span> </div>
<div class="line"><a id="l00003" name="l00003"></a><span class="lineno"> 3</span><span class="comment">// Metal FFT using Stockham&#39;s algorithm</span></div>
<div class="line"><a id="l00004" name="l00004"></a><span class="lineno"> 4</span><span class="comment">//</span></div>
<div class="line"><a id="l00005" name="l00005"></a><span class="lineno"> 5</span><span class="comment">// References:</span></div>
<div class="line"><a id="l00006" name="l00006"></a><span class="lineno"> 6</span><span class="comment">// - VkFFT (https://github.com/DTolm/VkFFT)</span></div>
<div class="line"><a id="l00007" name="l00007"></a><span class="lineno"> 7</span><span class="comment">// - Eric Bainville&#39;s excellent page (http://www.bealto.com/gpu-fft.html)</span></div>
<div class="line"><a id="l00008" name="l00008"></a><span class="lineno"> 8</span> </div>
<div class="line"><a id="l00009" name="l00009"></a><span class="lineno"> 9</span><span class="preprocessor">#include &lt;metal_common&gt;</span></div>
<div class="line"><a id="l00010" name="l00010"></a><span class="lineno"> 10</span> </div>
<div class="line"><a id="l00011" name="l00011"></a><span class="lineno"> 11</span><span class="preprocessor">#include &quot;<a class="code" href="radix_8h.html">mlx/backend/metal/kernels/fft/radix.h</a>&quot;</span></div>
<div class="line"><a id="l00012" name="l00012"></a><span class="lineno"> 12</span><span class="preprocessor">#include &quot;<a class="code" href="readwrite_8h.html">mlx/backend/metal/kernels/fft/readwrite.h</a>&quot;</span></div>
<div class="line"><a id="l00013" name="l00013"></a><span class="lineno"> 13</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="l00014" name="l00014"></a><span class="lineno"> 14</span> </div>
<div class="line"><a id="l00015" name="l00015"></a><span class="lineno"> 15</span><span class="keyword">using namespace </span><a class="code hl_namespace" href="namespacemetal.html">metal</a>;</div>
<div class="line"><a id="l00016" name="l00016"></a><span class="lineno"> 16</span> </div>
<div class="line"><a id="l00017" name="l00017"></a><span class="lineno"><a class="line" href="backend_2metal_2kernels_2fft_8h.html#a7b6e56afa21f022c5e754b000955735a"> 17</a></span><span class="preprocessor">#define MAX_RADIX 13</span></div>
<div class="line"><a id="l00018" name="l00018"></a><span class="lineno"> 18</span><span class="comment">// Reached when elems_per_thread_ = 6, max_radix = 13</span></div>
<div class="line"><a id="l00019" name="l00019"></a><span class="lineno"> 19</span><span class="comment">// and some threads have to do 3 radix 6s requiring 18 float2s.</span></div>
<div class="line"><a id="l00020" name="l00020"></a><span class="lineno"><a class="line" href="backend_2metal_2kernels_2fft_8h.html#a28d683cf067736d76f867f30c066317e"> 20</a></span><span class="preprocessor">#define MAX_OUTPUT_SIZE 18</span></div>
<div class="line"><a id="l00021" name="l00021"></a><span class="lineno"> 21</span> </div>
<div class="line"><a id="l00022" name="l00022"></a><span class="lineno"> 22</span><span class="comment">// Specialize for a particular value of N at runtime</span></div>
<div class="line"><a id="l00023" name="l00023"></a><span class="lineno"><a class="line" href="backend_2metal_2kernels_2fft_8h.html#a7a83318497519ff3ff0141b7d511ed38"> 23</a></span><a class="code hl_define" href="steel_2defines_8h.html#a90b91c866313ffa46eff6d9cc944ad2b">STEEL_CONST</a> <span class="keywordtype">bool</span> <a class="code hl_variable" href="backend_2metal_2kernels_2fft_8h.html#a7a83318497519ff3ff0141b7d511ed38">inv_</a> [[function_constant(0)]];</div>
<div class="line"><a id="l00024" name="l00024"></a><span class="lineno"><a class="line" href="backend_2metal_2kernels_2fft_8h.html#a2a4df90e329b84ee6c1890ba7c265c9c"> 24</a></span><a class="code hl_define" href="steel_2defines_8h.html#a90b91c866313ffa46eff6d9cc944ad2b">STEEL_CONST</a> <span class="keywordtype">bool</span> <a class="code hl_variable" href="backend_2metal_2kernels_2fft_8h.html#a2a4df90e329b84ee6c1890ba7c265c9c">is_power_of_2_</a> [[function_constant(1)]];</div>
<div class="line"><a id="l00025" name="l00025"></a><span class="lineno"><a class="line" href="backend_2metal_2kernels_2fft_8h.html#ad395c11e6f2aee72cd1928fba93a35a3"> 25</a></span><a class="code hl_define" href="steel_2defines_8h.html#a90b91c866313ffa46eff6d9cc944ad2b">STEEL_CONST</a> <span class="keywordtype">int</span> <a class="code hl_variable" href="backend_2metal_2kernels_2fft_8h.html#ad395c11e6f2aee72cd1928fba93a35a3">elems_per_thread_</a> [[function_constant(2)]];</div>
<div class="line"><a id="l00026" name="l00026"></a><span class="lineno"> 26</span><span class="comment">// rader_m = n / rader_n</span></div>
<div class="line"><a id="l00027" name="l00027"></a><span class="lineno"><a class="line" href="backend_2metal_2kernels_2fft_8h.html#ac309c77ef775a3ef13850c5287a86480"> 27</a></span><a class="code hl_define" href="steel_2defines_8h.html#a90b91c866313ffa46eff6d9cc944ad2b">STEEL_CONST</a> <span class="keywordtype">int</span> <a class="code hl_variable" href="backend_2metal_2kernels_2fft_8h.html#ac309c77ef775a3ef13850c5287a86480">rader_m_</a> [[function_constant(3)]];</div>
<div class="line"><a id="l00028" name="l00028"></a><span class="lineno"> 28</span><span class="comment">// Stockham steps</span></div>
<div class="line"><a id="l00029" name="l00029"></a><span class="lineno"><a class="line" href="backend_2metal_2kernels_2fft_8h.html#abb079b86e89ca88ce13a179d9ec566af"> 29</a></span><a class="code hl_define" href="steel_2defines_8h.html#a90b91c866313ffa46eff6d9cc944ad2b">STEEL_CONST</a> <span class="keywordtype">int</span> <a class="code hl_variable" href="backend_2metal_2kernels_2fft_8h.html#abb079b86e89ca88ce13a179d9ec566af">radix_13_steps_</a> [[function_constant(4)]];</div>
<div class="line"><a id="l00030" name="l00030"></a><span class="lineno"><a class="line" href="backend_2metal_2kernels_2fft_8h.html#a7cd17bff8bc567f71d4789ee31fa07f2"> 30</a></span><a class="code hl_define" href="steel_2defines_8h.html#a90b91c866313ffa46eff6d9cc944ad2b">STEEL_CONST</a> <span class="keywordtype">int</span> <a class="code hl_variable" href="backend_2metal_2kernels_2fft_8h.html#a7cd17bff8bc567f71d4789ee31fa07f2">radix_11_steps_</a> [[function_constant(5)]];</div>
<div class="line"><a id="l00031" name="l00031"></a><span class="lineno"><a class="line" href="backend_2metal_2kernels_2fft_8h.html#a3cb03a97a209ba1346375e720ee76177"> 31</a></span><a class="code hl_define" href="steel_2defines_8h.html#a90b91c866313ffa46eff6d9cc944ad2b">STEEL_CONST</a> <span class="keywordtype">int</span> <a class="code hl_variable" href="backend_2metal_2kernels_2fft_8h.html#a3cb03a97a209ba1346375e720ee76177">radix_8_steps_</a> [[function_constant(6)]];</div>
<div class="line"><a id="l00032" name="l00032"></a><span class="lineno"><a class="line" href="backend_2metal_2kernels_2fft_8h.html#a2145cc8ab4d07583a735317b3cf60d55"> 32</a></span><a class="code hl_define" href="steel_2defines_8h.html#a90b91c866313ffa46eff6d9cc944ad2b">STEEL_CONST</a> <span class="keywordtype">int</span> <a class="code hl_variable" href="backend_2metal_2kernels_2fft_8h.html#a2145cc8ab4d07583a735317b3cf60d55">radix_7_steps_</a> [[function_constant(7)]];</div>
<div class="line"><a id="l00033" name="l00033"></a><span class="lineno"><a class="line" href="backend_2metal_2kernels_2fft_8h.html#a2f7f7cc2423cfcd4998d1a2a0363c3e2"> 33</a></span><a class="code hl_define" href="steel_2defines_8h.html#a90b91c866313ffa46eff6d9cc944ad2b">STEEL_CONST</a> <span class="keywordtype">int</span> <a class="code hl_variable" href="backend_2metal_2kernels_2fft_8h.html#a2f7f7cc2423cfcd4998d1a2a0363c3e2">radix_6_steps_</a> [[function_constant(8)]];</div>
<div class="line"><a id="l00034" name="l00034"></a><span class="lineno"><a class="line" href="backend_2metal_2kernels_2fft_8h.html#a903d5239b5f73577c559e97ff910892d"> 34</a></span><a class="code hl_define" href="steel_2defines_8h.html#a90b91c866313ffa46eff6d9cc944ad2b">STEEL_CONST</a> <span class="keywordtype">int</span> <a class="code hl_variable" href="backend_2metal_2kernels_2fft_8h.html#a903d5239b5f73577c559e97ff910892d">radix_5_steps_</a> [[function_constant(9)]];</div>
<div class="line"><a id="l00035" name="l00035"></a><span class="lineno"><a class="line" href="backend_2metal_2kernels_2fft_8h.html#a12d99a846c3686806bab6c42148e1039"> 35</a></span><a class="code hl_define" href="steel_2defines_8h.html#a90b91c866313ffa46eff6d9cc944ad2b">STEEL_CONST</a> <span class="keywordtype">int</span> <a class="code hl_variable" href="backend_2metal_2kernels_2fft_8h.html#a12d99a846c3686806bab6c42148e1039">radix_4_steps_</a> [[function_constant(10)]];</div>
<div class="line"><a id="l00036" name="l00036"></a><span class="lineno"><a class="line" href="backend_2metal_2kernels_2fft_8h.html#a579123b7be825f08f3076287dded08e3"> 36</a></span><a class="code hl_define" href="steel_2defines_8h.html#a90b91c866313ffa46eff6d9cc944ad2b">STEEL_CONST</a> <span class="keywordtype">int</span> <a class="code hl_variable" href="backend_2metal_2kernels_2fft_8h.html#a579123b7be825f08f3076287dded08e3">radix_3_steps_</a> [[function_constant(11)]];</div>
<div class="line"><a id="l00037" name="l00037"></a><span class="lineno"><a class="line" href="backend_2metal_2kernels_2fft_8h.html#a53fdc660e99e6b5db6808bbd596cd374"> 37</a></span><a class="code hl_define" href="steel_2defines_8h.html#a90b91c866313ffa46eff6d9cc944ad2b">STEEL_CONST</a> <span class="keywordtype">int</span> <a class="code hl_variable" href="backend_2metal_2kernels_2fft_8h.html#a53fdc660e99e6b5db6808bbd596cd374">radix_2_steps_</a> [[function_constant(12)]];</div>
<div class="line"><a id="l00038" name="l00038"></a><span class="lineno"> 38</span><span class="comment">// Rader steps</span></div>
<div class="line"><a id="l00039" name="l00039"></a><span class="lineno"><a class="line" href="backend_2metal_2kernels_2fft_8h.html#a20d24f3e040d3d226a70d4dd7c9ac6a9"> 39</a></span><a class="code hl_define" href="steel_2defines_8h.html#a90b91c866313ffa46eff6d9cc944ad2b">STEEL_CONST</a> <span class="keywordtype">int</span> <a class="code hl_variable" href="backend_2metal_2kernels_2fft_8h.html#a20d24f3e040d3d226a70d4dd7c9ac6a9">rader_13_steps_</a> [[function_constant(13)]];</div>
<div class="line"><a id="l00040" name="l00040"></a><span class="lineno"><a class="line" href="backend_2metal_2kernels_2fft_8h.html#a1f3c377d05da52429172e64132dba750"> 40</a></span><a class="code hl_define" href="steel_2defines_8h.html#a90b91c866313ffa46eff6d9cc944ad2b">STEEL_CONST</a> <span class="keywordtype">int</span> <a class="code hl_variable" href="backend_2metal_2kernels_2fft_8h.html#a1f3c377d05da52429172e64132dba750">rader_11_steps_</a> [[function_constant(14)]];</div>
<div class="line"><a id="l00041" name="l00041"></a><span class="lineno"><a class="line" href="backend_2metal_2kernels_2fft_8h.html#ac6123e111816dd62a11ccb86b66fa3e9"> 41</a></span><a class="code hl_define" href="steel_2defines_8h.html#a90b91c866313ffa46eff6d9cc944ad2b">STEEL_CONST</a> <span class="keywordtype">int</span> <a class="code hl_variable" href="backend_2metal_2kernels_2fft_8h.html#ac6123e111816dd62a11ccb86b66fa3e9">rader_8_steps_</a> [[function_constant(15)]];</div>
<div class="line"><a id="l00042" name="l00042"></a><span class="lineno"><a class="line" href="backend_2metal_2kernels_2fft_8h.html#a0d437aef17faf8d9707ae7ffe68fdb30"> 42</a></span><a class="code hl_define" href="steel_2defines_8h.html#a90b91c866313ffa46eff6d9cc944ad2b">STEEL_CONST</a> <span class="keywordtype">int</span> <a class="code hl_variable" href="backend_2metal_2kernels_2fft_8h.html#a0d437aef17faf8d9707ae7ffe68fdb30">rader_7_steps_</a> [[function_constant(16)]];</div>
<div class="line"><a id="l00043" name="l00043"></a><span class="lineno"><a class="line" href="backend_2metal_2kernels_2fft_8h.html#a020469d1aca557ff1b49414f121dedbb"> 43</a></span><a class="code hl_define" href="steel_2defines_8h.html#a90b91c866313ffa46eff6d9cc944ad2b">STEEL_CONST</a> <span class="keywordtype">int</span> <a class="code hl_variable" href="backend_2metal_2kernels_2fft_8h.html#a020469d1aca557ff1b49414f121dedbb">rader_6_steps_</a> [[function_constant(17)]];</div>
<div class="line"><a id="l00044" name="l00044"></a><span class="lineno"><a class="line" href="backend_2metal_2kernels_2fft_8h.html#afea05e9a7105bafbaafca25042f4d1b4"> 44</a></span><a class="code hl_define" href="steel_2defines_8h.html#a90b91c866313ffa46eff6d9cc944ad2b">STEEL_CONST</a> <span class="keywordtype">int</span> <a class="code hl_variable" href="backend_2metal_2kernels_2fft_8h.html#afea05e9a7105bafbaafca25042f4d1b4">rader_5_steps_</a> [[function_constant(18)]];</div>
<div class="line"><a id="l00045" name="l00045"></a><span class="lineno"><a class="line" href="backend_2metal_2kernels_2fft_8h.html#ac7c58404df0434d4f861db62d3471870"> 45</a></span><a class="code hl_define" href="steel_2defines_8h.html#a90b91c866313ffa46eff6d9cc944ad2b">STEEL_CONST</a> <span class="keywordtype">int</span> <a class="code hl_variable" href="backend_2metal_2kernels_2fft_8h.html#ac7c58404df0434d4f861db62d3471870">rader_4_steps_</a> [[function_constant(19)]];</div>
<div class="line"><a id="l00046" name="l00046"></a><span class="lineno"><a class="line" href="backend_2metal_2kernels_2fft_8h.html#adb129cc3808c08fd95af9795bfc7ae63"> 46</a></span><a class="code hl_define" href="steel_2defines_8h.html#a90b91c866313ffa46eff6d9cc944ad2b">STEEL_CONST</a> <span class="keywordtype">int</span> <a class="code hl_variable" href="backend_2metal_2kernels_2fft_8h.html#adb129cc3808c08fd95af9795bfc7ae63">rader_3_steps_</a> [[function_constant(20)]];</div>
<div class="line"><a id="l00047" name="l00047"></a><span class="lineno"><a class="line" href="backend_2metal_2kernels_2fft_8h.html#a2d725bfd4c30be4c605b5c4559a62892"> 47</a></span><a class="code hl_define" href="steel_2defines_8h.html#a90b91c866313ffa46eff6d9cc944ad2b">STEEL_CONST</a> <span class="keywordtype">int</span> <a class="code hl_variable" href="backend_2metal_2kernels_2fft_8h.html#a2d725bfd4c30be4c605b5c4559a62892">rader_2_steps_</a> [[function_constant(21)]];</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="comment">// See &quot;radix.h&quot; for radix codelets</span></div>
<div class="line"><a id="l00050" name="l00050"></a><span class="lineno"><a class="line" href="backend_2metal_2kernels_2fft_8h.html#a6ba62eabfd5428644aabf89ddaa0128d"> 50</a></span><span class="keyword">typedef</span> void (*<a class="code hl_typedef" href="backend_2metal_2kernels_2fft_8h.html#a6ba62eabfd5428644aabf89ddaa0128d">RadixFunc</a>)(thread float2*, thread float2*);</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><span class="comment">// Perform a single radix n butterfly with appropriate twiddles</span></div>
<div class="line"><a id="l00053" name="l00053"></a><span class="lineno"> 53</span><span class="keyword">template</span> &lt;<span class="keywordtype">int</span> radix, RadixFunc radix_func&gt;</div>
<div class="foldopen" id="foldopen00054" data-start="{" data-end="}">
<div class="line"><a id="l00054" name="l00054"></a><span class="lineno"><a class="line" href="backend_2metal_2kernels_2fft_8h.html#a278d980ed397e6841ce0af44b9aa4396"> 54</a></span>METAL_FUNC <span class="keywordtype">void</span> <a class="code hl_function" href="backend_2metal_2kernels_2fft_8h.html#a278d980ed397e6841ce0af44b9aa4396">radix_butterfly</a>(</div>
<div class="line"><a id="l00055" name="l00055"></a><span class="lineno"> 55</span> <span class="keywordtype">int</span> i,</div>
<div class="line"><a id="l00056" name="l00056"></a><span class="lineno"> 56</span> <span class="keywordtype">int</span> p,</div>
<div class="line"><a id="l00057" name="l00057"></a><span class="lineno"> 57</span> thread float2* x,</div>
<div class="line"><a id="l00058" name="l00058"></a><span class="lineno"> 58</span> thread <span class="keywordtype">short</span>* indices,</div>
<div class="line"><a id="l00059" name="l00059"></a><span class="lineno"> 59</span> thread float2* y) {</div>
<div class="line"><a id="l00060" name="l00060"></a><span class="lineno"> 60</span> <span class="comment">// i: the index in the overall DFT that we&#39;re processing.</span></div>
<div class="line"><a id="l00061" name="l00061"></a><span class="lineno"> 61</span> <span class="comment">// p: the size of the DFTs we&#39;re merging at this step.</span></div>
<div class="line"><a id="l00062" name="l00062"></a><span class="lineno"> 62</span> <span class="comment">// m: how many threads are working on this DFT.</span></div>
<div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</span> <span class="keywordtype">int</span> k, j;</div>
<div class="line"><a id="l00064" name="l00064"></a><span class="lineno"> 64</span> </div>
<div class="line"><a id="l00065" name="l00065"></a><span class="lineno"> 65</span> <span class="comment">// Use faster bitwise operations when working with powers of two</span></div>
<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"> 66</span> <span class="keyword">constexpr</span> <span class="keywordtype">bool</span> radix_p_2 = (radix &amp; (radix - 1)) == 0;</div>
<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"> 67</span> <span class="keywordflow">if</span> (radix_p_2 &amp;&amp; <a class="code hl_variable" href="backend_2metal_2kernels_2fft_8h.html#a2a4df90e329b84ee6c1890ba7c265c9c">is_power_of_2_</a>) {</div>
<div class="line"><a id="l00068" name="l00068"></a><span class="lineno"> 68</span> <span class="keyword">constexpr</span> <span class="keywordtype">short</span> power = __builtin_ctz(radix);</div>
<div class="line"><a id="l00069" name="l00069"></a><span class="lineno"> 69</span> k = i &amp; (p - 1);</div>
<div class="line"><a id="l00070" name="l00070"></a><span class="lineno"> 70</span> j = ((i - k) &lt;&lt; power) + k;</div>
<div class="line"><a id="l00071" name="l00071"></a><span class="lineno"> 71</span> } <span class="keywordflow">else</span> {</div>
<div class="line"><a id="l00072" name="l00072"></a><span class="lineno"> 72</span> k = i % p;</div>
<div class="line"><a id="l00073" name="l00073"></a><span class="lineno"> 73</span> j = (i / p) * radix * p + k;</div>
<div class="line"><a id="l00074" name="l00074"></a><span class="lineno"> 74</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="comment">// Apply twiddles</span></div>
<div class="line"><a id="l00077" name="l00077"></a><span class="lineno"> 77</span> <span class="keywordflow">if</span> (p &gt; 1) {</div>
<div class="line"><a id="l00078" name="l00078"></a><span class="lineno"> 78</span> float2 twiddle_1 = <a class="code hl_function" href="radix_8h.html#ac5cf950316b9445296ee9ecfc56a56bd">get_twiddle</a>(k, radix * p);</div>
<div class="line"><a id="l00079" name="l00079"></a><span class="lineno"> 79</span> float2 twiddle = twiddle_1;</div>
<div class="line"><a id="l00080" name="l00080"></a><span class="lineno"> 80</span> x[1] = <a class="code hl_function" href="radix_8h.html#a5bfc53b531214c9ce277bebc18aa67d6">complex_mul</a>(x[1], twiddle);</div>
<div class="line"><a id="l00081" name="l00081"></a><span class="lineno"> 81</span> </div>
<div class="line"><a id="l00082" name="l00082"></a><span class="lineno"> 82</span> <a class="code hl_define" href="steel_2defines_8h.html#a5a5c3095b132a7589bc19cd5cb80e2c6">STEEL_PRAGMA_UNROLL</a></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> t = 2; t &lt; radix; t++) {</div>
<div class="line"><a id="l00084" name="l00084"></a><span class="lineno"> 84</span> twiddle = <a class="code hl_function" href="radix_8h.html#a5bfc53b531214c9ce277bebc18aa67d6">complex_mul</a>(twiddle, twiddle_1);</div>
<div class="line"><a id="l00085" name="l00085"></a><span class="lineno"> 85</span> x[t] = <a class="code hl_function" href="radix_8h.html#a5bfc53b531214c9ce277bebc18aa67d6">complex_mul</a>(x[t], twiddle);</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> }</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> <a class="code hl_function" href="metal_2kernels_2hadamard_8h.html#a590e5366adc78bab4fe44e37885d413f">radix_func</a>(x, y);</div>
<div class="line"><a id="l00090" name="l00090"></a><span class="lineno"> 90</span> </div>
<div class="line"><a id="l00091" name="l00091"></a><span class="lineno"> 91</span> <a class="code hl_define" href="steel_2defines_8h.html#a5a5c3095b132a7589bc19cd5cb80e2c6">STEEL_PRAGMA_UNROLL</a></div>
<div class="line"><a id="l00092" name="l00092"></a><span class="lineno"> 92</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> t = 0; t &lt; radix; t++) {</div>
<div class="line"><a id="l00093" name="l00093"></a><span class="lineno"> 93</span> indices[t] = j + t * p;</div>
<div class="line"><a id="l00094" name="l00094"></a><span class="lineno"> 94</span> }</div>
<div class="line"><a id="l00095" name="l00095"></a><span class="lineno"> 95</span>}</div>
</div>
<div class="line"><a id="l00096" name="l00096"></a><span class="lineno"> 96</span> </div>
<div class="line"><a id="l00097" name="l00097"></a><span class="lineno"> 97</span><span class="comment">// Perform all the radix steps required for a</span></div>
<div class="line"><a id="l00098" name="l00098"></a><span class="lineno"> 98</span><span class="comment">// particular radix size n.</span></div>
<div class="line"><a id="l00099" name="l00099"></a><span class="lineno"> 99</span><span class="keyword">template</span> &lt;<span class="keywordtype">int</span> radix, RadixFunc radix_func&gt;</div>
<div class="foldopen" id="foldopen00100" data-start="{" data-end="}">
<div class="line"><a id="l00100" name="l00100"></a><span class="lineno"><a class="line" href="backend_2metal_2kernels_2fft_8h.html#aba8d32e0911499671df93678f39da08b"> 100</a></span>METAL_FUNC <span class="keywordtype">void</span> <a class="code hl_function" href="backend_2metal_2kernels_2fft_8h.html#aba8d32e0911499671df93678f39da08b">radix_n_steps</a>(</div>
<div class="line"><a id="l00101" name="l00101"></a><span class="lineno"> 101</span> <span class="keywordtype">int</span> i,</div>
<div class="line"><a id="l00102" name="l00102"></a><span class="lineno"> 102</span> thread <span class="keywordtype">int</span>* p,</div>
<div class="line"><a id="l00103" name="l00103"></a><span class="lineno"> 103</span> <span class="keywordtype">int</span> m,</div>
<div class="line"><a id="l00104" name="l00104"></a><span class="lineno"> 104</span> <span class="keywordtype">int</span> n,</div>
<div class="line"><a id="l00105" name="l00105"></a><span class="lineno"> 105</span> <span class="keywordtype">int</span> num_steps,</div>
<div class="line"><a id="l00106" name="l00106"></a><span class="lineno"> 106</span> thread float2* inputs,</div>
<div class="line"><a id="l00107" name="l00107"></a><span class="lineno"> 107</span> thread <span class="keywordtype">short</span>* indices,</div>
<div class="line"><a id="l00108" name="l00108"></a><span class="lineno"> 108</span> thread float2* values,</div>
<div class="line"><a id="l00109" name="l00109"></a><span class="lineno"> 109</span> threadgroup float2* buf) {</div>
<div class="line"><a id="l00110" name="l00110"></a><span class="lineno"> 110</span> <span class="keywordtype">int</span> m_r = n / radix;</div>
<div class="line"><a id="l00111" name="l00111"></a><span class="lineno"> 111</span> <span class="comment">// When combining different sized radices, we have to do</span></div>
<div class="line"><a id="l00112" name="l00112"></a><span class="lineno"> 112</span> <span class="comment">// multiple butterflies in a single thread.</span></div>
<div class="line"><a id="l00113" name="l00113"></a><span class="lineno"> 113</span> <span class="comment">// E.g. n = 28 = 4 * 7</span></div>
<div class="line"><a id="l00114" name="l00114"></a><span class="lineno"> 114</span> <span class="comment">// 4 threads, 7 elems_per_thread</span></div>
<div class="line"><a id="l00115" name="l00115"></a><span class="lineno"> 115</span> <span class="comment">// All threads do 1 radix7 butterfly.</span></div>
<div class="line"><a id="l00116" name="l00116"></a><span class="lineno"> 116</span> <span class="comment">// 3 threads do 2 radix4 butterflies.</span></div>
<div class="line"><a id="l00117" name="l00117"></a><span class="lineno"> 117</span> <span class="comment">// 1 thread does 1 radix4 butterfly.</span></div>
<div class="line"><a id="l00118" name="l00118"></a><span class="lineno"> 118</span> <span class="keywordtype">int</span> max_radices_per_thread = (<a class="code hl_variable" href="backend_2metal_2kernels_2fft_8h.html#ad395c11e6f2aee72cd1928fba93a35a3">elems_per_thread_</a> + radix - 1) / radix;</div>
<div class="line"><a id="l00119" name="l00119"></a><span class="lineno"> 119</span> </div>
<div class="line"><a id="l00120" name="l00120"></a><span class="lineno"> 120</span> <span class="keywordtype">int</span> index = 0;</div>
<div class="line"><a id="l00121" name="l00121"></a><span class="lineno"> 121</span> <span class="keywordtype">int</span> r_index = 0;</div>
<div class="line"><a id="l00122" name="l00122"></a><span class="lineno"> 122</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> s = 0; s &lt; num_steps; s++) {</div>
<div class="line"><a id="l00123" name="l00123"></a><span class="lineno"> 123</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> t = 0; t &lt; max_radices_per_thread; t++) {</div>
<div class="line"><a id="l00124" name="l00124"></a><span class="lineno"> 124</span> index = i + t * m;</div>
<div class="line"><a id="l00125" name="l00125"></a><span class="lineno"> 125</span> <span class="keywordflow">if</span> (index &lt; m_r) {</div>
<div class="line"><a id="l00126" name="l00126"></a><span class="lineno"> 126</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> r = 0; r &lt; radix; r++) {</div>
<div class="line"><a id="l00127" name="l00127"></a><span class="lineno"> 127</span> inputs[r] = buf[index + r * m_r];</div>
<div class="line"><a id="l00128" name="l00128"></a><span class="lineno"> 128</span> }</div>
<div class="line"><a id="l00129" name="l00129"></a><span class="lineno"> 129</span> <a class="code hl_function" href="backend_2metal_2kernels_2fft_8h.html#a278d980ed397e6841ce0af44b9aa4396">radix_butterfly&lt;radix, radix_func&gt;</a>(</div>
<div class="line"><a id="l00130" name="l00130"></a><span class="lineno"> 130</span> index, *p, inputs, indices + t * radix, values + t * radix);</div>
<div class="line"><a id="l00131" name="l00131"></a><span class="lineno"> 131</span> }</div>
<div class="line"><a id="l00132" name="l00132"></a><span class="lineno"> 132</span> }</div>
<div class="line"><a id="l00133" name="l00133"></a><span class="lineno"> 133</span> </div>
<div class="line"><a id="l00134" name="l00134"></a><span class="lineno"> 134</span> <span class="comment">// Wait until all threads have read their inputs into thread local mem</span></div>
<div class="line"><a id="l00135" name="l00135"></a><span class="lineno"> 135</span> threadgroup_barrier(mem_flags::mem_threadgroup);</div>
<div class="line"><a id="l00136" name="l00136"></a><span class="lineno"> 136</span> </div>
<div class="line"><a id="l00137" name="l00137"></a><span class="lineno"> 137</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> t = 0; t &lt; max_radices_per_thread; t++) {</div>
<div class="line"><a id="l00138" name="l00138"></a><span class="lineno"> 138</span> index = i + t * m;</div>
<div class="line"><a id="l00139" name="l00139"></a><span class="lineno"> 139</span> <span class="keywordflow">if</span> (index &lt; m_r) {</div>
<div class="line"><a id="l00140" name="l00140"></a><span class="lineno"> 140</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> r = 0; r &lt; radix; r++) {</div>
<div class="line"><a id="l00141" name="l00141"></a><span class="lineno"> 141</span> r_index = t * radix + r;</div>
<div class="line"><a id="l00142" name="l00142"></a><span class="lineno"> 142</span> buf[indices[r_index]] = values[r_index];</div>
<div class="line"><a id="l00143" name="l00143"></a><span class="lineno"> 143</span> }</div>
<div class="line"><a id="l00144" name="l00144"></a><span class="lineno"> 144</span> }</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> </div>
<div class="line"><a id="l00147" name="l00147"></a><span class="lineno"> 147</span> <span class="comment">// Wait until all threads have written back to threadgroup mem</span></div>
<div class="line"><a id="l00148" name="l00148"></a><span class="lineno"> 148</span> threadgroup_barrier(mem_flags::mem_threadgroup);</div>
<div class="line"><a id="l00149" name="l00149"></a><span class="lineno"> 149</span> *p *= radix;</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>
<div class="line"><a id="l00152" name="l00152"></a><span class="lineno"> 152</span> </div>
<div class="foldopen" id="foldopen00153" data-start="" data-end="">
<div class="line"><a id="l00153" name="l00153"></a><span class="lineno"><a class="line" href="backend_2metal_2kernels_2fft_8h.html#a794032d3a9acff0e31c77c69d0007f10"> 153</a></span><span class="preprocessor">#define RADIX_STEP(radix, radix_func, num_steps) \</span></div>
<div class="line"><a id="l00154" name="l00154"></a><span class="lineno"> 154</span><span class="preprocessor"> radix_n_steps&lt;radix, radix_func&gt;( \</span></div>
<div class="line"><a id="l00155" name="l00155"></a><span class="lineno"> 155</span><span class="preprocessor"> fft_idx, p, m, n, num_steps, inputs, indices, values, buf);</span></div>
</div>
<div class="line"><a id="l00156" name="l00156"></a><span class="lineno"> 156</span> </div>
<div class="line"><a id="l00157" name="l00157"></a><span class="lineno"> 157</span><span class="keyword">template</span> &lt;<span class="keywordtype">bool</span> rader = false&gt;</div>
<div class="line"><a id="l00158" name="l00158"></a><span class="lineno"> 158</span>METAL_FUNC <span class="keywordtype">void</span></div>
<div class="foldopen" id="foldopen00159" data-start="{" data-end="}">
<div class="line"><a id="l00159" name="l00159"></a><span class="lineno"><a class="line" href="backend_2metal_2kernels_2fft_8h.html#a050ead8fa5cacdaec13d68ca3c0dcb81"> 159</a></span><a class="code hl_function" href="backend_2metal_2kernels_2fft_8h.html#a050ead8fa5cacdaec13d68ca3c0dcb81">perform_fft</a>(<span class="keywordtype">int</span> fft_idx, thread <span class="keywordtype">int</span>* p, <span class="keywordtype">int</span> m, <span class="keywordtype">int</span> n, threadgroup float2* buf) {</div>
<div class="line"><a id="l00160" name="l00160"></a><span class="lineno"> 160</span> float2 inputs[<a class="code hl_define" href="backend_2metal_2kernels_2fft_8h.html#a7b6e56afa21f022c5e754b000955735a">MAX_RADIX</a>];</div>
<div class="line"><a id="l00161" name="l00161"></a><span class="lineno"> 161</span> <span class="keywordtype">short</span> indices[<a class="code hl_define" href="backend_2metal_2kernels_2fft_8h.html#a28d683cf067736d76f867f30c066317e">MAX_OUTPUT_SIZE</a>];</div>
<div class="line"><a id="l00162" name="l00162"></a><span class="lineno"> 162</span> float2 values[<a class="code hl_define" href="backend_2metal_2kernels_2fft_8h.html#a28d683cf067736d76f867f30c066317e">MAX_OUTPUT_SIZE</a>];</div>
<div class="line"><a id="l00163" name="l00163"></a><span class="lineno"> 163</span> </div>
<div class="line"><a id="l00164" name="l00164"></a><span class="lineno"> 164</span> <a class="code hl_define" href="backend_2metal_2kernels_2fft_8h.html#a794032d3a9acff0e31c77c69d0007f10">RADIX_STEP</a>(2, <a class="code hl_function" href="radix_8h.html#a745e50244f1470bba233d8b6b993729c">radix2</a>, rader ? <a class="code hl_variable" href="backend_2metal_2kernels_2fft_8h.html#a2d725bfd4c30be4c605b5c4559a62892">rader_2_steps_</a> : <a class="code hl_variable" href="backend_2metal_2kernels_2fft_8h.html#a53fdc660e99e6b5db6808bbd596cd374">radix_2_steps_</a>);</div>
<div class="line"><a id="l00165" name="l00165"></a><span class="lineno"> 165</span> <a class="code hl_define" href="backend_2metal_2kernels_2fft_8h.html#a794032d3a9acff0e31c77c69d0007f10">RADIX_STEP</a>(3, <a class="code hl_function" href="radix_8h.html#a497b31cfa28418e1c2fad53d09f7bc0b">radix3</a>, rader ? <a class="code hl_variable" href="backend_2metal_2kernels_2fft_8h.html#adb129cc3808c08fd95af9795bfc7ae63">rader_3_steps_</a> : <a class="code hl_variable" href="backend_2metal_2kernels_2fft_8h.html#a579123b7be825f08f3076287dded08e3">radix_3_steps_</a>);</div>
<div class="line"><a id="l00166" name="l00166"></a><span class="lineno"> 166</span> <a class="code hl_define" href="backend_2metal_2kernels_2fft_8h.html#a794032d3a9acff0e31c77c69d0007f10">RADIX_STEP</a>(4, <a class="code hl_function" href="radix_8h.html#a12cb26bd3ad635d16a195ccea750256d">radix4</a>, rader ? <a class="code hl_variable" href="backend_2metal_2kernels_2fft_8h.html#ac7c58404df0434d4f861db62d3471870">rader_4_steps_</a> : <a class="code hl_variable" href="backend_2metal_2kernels_2fft_8h.html#a12d99a846c3686806bab6c42148e1039">radix_4_steps_</a>);</div>
<div class="line"><a id="l00167" name="l00167"></a><span class="lineno"> 167</span> <a class="code hl_define" href="backend_2metal_2kernels_2fft_8h.html#a794032d3a9acff0e31c77c69d0007f10">RADIX_STEP</a>(5, <a class="code hl_function" href="radix_8h.html#a026e6779e6d2ecdef39ff4aad186091e">radix5</a>, rader ? <a class="code hl_variable" href="backend_2metal_2kernels_2fft_8h.html#afea05e9a7105bafbaafca25042f4d1b4">rader_5_steps_</a> : <a class="code hl_variable" href="backend_2metal_2kernels_2fft_8h.html#a903d5239b5f73577c559e97ff910892d">radix_5_steps_</a>);</div>
<div class="line"><a id="l00168" name="l00168"></a><span class="lineno"> 168</span> <a class="code hl_define" href="backend_2metal_2kernels_2fft_8h.html#a794032d3a9acff0e31c77c69d0007f10">RADIX_STEP</a>(6, <a class="code hl_function" href="radix_8h.html#afaaa5de58a97f0a5e6a84fc0d598a884">radix6</a>, rader ? <a class="code hl_variable" href="backend_2metal_2kernels_2fft_8h.html#a020469d1aca557ff1b49414f121dedbb">rader_6_steps_</a> : <a class="code hl_variable" href="backend_2metal_2kernels_2fft_8h.html#a2f7f7cc2423cfcd4998d1a2a0363c3e2">radix_6_steps_</a>);</div>
<div class="line"><a id="l00169" name="l00169"></a><span class="lineno"> 169</span> <a class="code hl_define" href="backend_2metal_2kernels_2fft_8h.html#a794032d3a9acff0e31c77c69d0007f10">RADIX_STEP</a>(7, <a class="code hl_function" href="radix_8h.html#a6d37e483d806c550deefabf56caf4ec8">radix7</a>, rader ? <a class="code hl_variable" href="backend_2metal_2kernels_2fft_8h.html#a0d437aef17faf8d9707ae7ffe68fdb30">rader_7_steps_</a> : <a class="code hl_variable" href="backend_2metal_2kernels_2fft_8h.html#a2145cc8ab4d07583a735317b3cf60d55">radix_7_steps_</a>);</div>
<div class="line"><a id="l00170" name="l00170"></a><span class="lineno"> 170</span> <a class="code hl_define" href="backend_2metal_2kernels_2fft_8h.html#a794032d3a9acff0e31c77c69d0007f10">RADIX_STEP</a>(8, <a class="code hl_function" href="radix_8h.html#a6b306e1afe1c5b6af4cd80aa02adb138">radix8</a>, rader ? <a class="code hl_variable" href="backend_2metal_2kernels_2fft_8h.html#ac6123e111816dd62a11ccb86b66fa3e9">rader_8_steps_</a> : <a class="code hl_variable" href="backend_2metal_2kernels_2fft_8h.html#a3cb03a97a209ba1346375e720ee76177">radix_8_steps_</a>);</div>
<div class="line"><a id="l00171" name="l00171"></a><span class="lineno"> 171</span> <a class="code hl_define" href="backend_2metal_2kernels_2fft_8h.html#a794032d3a9acff0e31c77c69d0007f10">RADIX_STEP</a>(11, <a class="code hl_function" href="radix_8h.html#a34f7dcefd29f8a7f6bddf9a17609a8a7">radix11</a>, rader ? <a class="code hl_variable" href="backend_2metal_2kernels_2fft_8h.html#a1f3c377d05da52429172e64132dba750">rader_11_steps_</a> : <a class="code hl_variable" href="backend_2metal_2kernels_2fft_8h.html#a7cd17bff8bc567f71d4789ee31fa07f2">radix_11_steps_</a>);</div>
<div class="line"><a id="l00172" name="l00172"></a><span class="lineno"> 172</span> <a class="code hl_define" href="backend_2metal_2kernels_2fft_8h.html#a794032d3a9acff0e31c77c69d0007f10">RADIX_STEP</a>(13, <a class="code hl_function" href="radix_8h.html#a833b7b31facbd62f6971bb108c54d1db">radix13</a>, rader ? <a class="code hl_variable" href="backend_2metal_2kernels_2fft_8h.html#a20d24f3e040d3d226a70d4dd7c9ac6a9">rader_13_steps_</a> : <a class="code hl_variable" href="backend_2metal_2kernels_2fft_8h.html#abb079b86e89ca88ce13a179d9ec566af">radix_13_steps_</a>);</div>
<div class="line"><a id="l00173" name="l00173"></a><span class="lineno"> 173</span>}</div>
</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><span class="comment">// Each FFT is computed entirely in shared GPU memory.</span></div>
<div class="line"><a id="l00176" name="l00176"></a><span class="lineno"> 176</span><span class="comment">//</span></div>
<div class="line"><a id="l00177" name="l00177"></a><span class="lineno"> 177</span><span class="comment">// N is decomposed into radix-n DFTs:</span></div>
<div class="line"><a id="l00178" name="l00178"></a><span class="lineno"> 178</span><span class="comment">// e.g. 128 = 2 * 4 * 4 * 4</span></div>
<div class="line"><a id="l00179" name="l00179"></a><span class="lineno"> 179</span><span class="keyword">template</span> &lt;<span class="keywordtype">int</span> tg_mem_size, <span class="keyword">typename</span> in_T, <span class="keyword">typename</span> out_T&gt;</div>
<div class="foldopen" id="foldopen00180" data-start="{" data-end="}">
<div class="line"><a id="l00180" name="l00180"></a><span class="lineno"><a class="line" href="backend_2metal_2kernels_2fft_8h.html#a4010b0e151e5f01e610e9c32234458c7"> 180</a></span>[[kernel]] <span class="keywordtype">void</span> <a class="code hl_function" href="backend_2metal_2kernels_2fft_8h.html#a4010b0e151e5f01e610e9c32234458c7">fft</a>(</div>
<div class="line"><a id="l00181" name="l00181"></a><span class="lineno"> 181</span> <span class="keyword">const</span> device in_T* in [[buffer(0)]],</div>
<div class="line"><a id="l00182" name="l00182"></a><span class="lineno"> 182</span> device out_T* out [[buffer(1)]],</div>
<div class="line"><a id="l00183" name="l00183"></a><span class="lineno"> 183</span> constant <span class="keyword">const</span> <span class="keywordtype">int</span>&amp; n,</div>
<div class="line"><a id="l00184" name="l00184"></a><span class="lineno"> 184</span> constant <span class="keyword">const</span> <span class="keywordtype">int</span>&amp; batch_size,</div>
<div class="line"><a id="l00185" name="l00185"></a><span class="lineno"> 185</span> uint3 elem [[thread_position_in_grid]],</div>
<div class="line"><a id="l00186" name="l00186"></a><span class="lineno"> 186</span> uint3 grid [[threads_per_grid]]) {</div>
<div class="line"><a id="l00187" name="l00187"></a><span class="lineno"> 187</span> threadgroup float2 shared_in[tg_mem_size];</div>
<div class="line"><a id="l00188" name="l00188"></a><span class="lineno"> 188</span> </div>
<div class="line"><a id="l00189" name="l00189"></a><span class="lineno"> 189</span> thread <a class="code hl_struct" href="struct_read_writer.html">ReadWriter&lt;in_T, out_T&gt;</a> read_writer = <a class="code hl_struct" href="struct_read_writer.html">ReadWriter&lt;in_T, out_T&gt;</a>(</div>
<div class="line"><a id="l00190" name="l00190"></a><span class="lineno"> 190</span> in,</div>
<div class="line"><a id="l00191" name="l00191"></a><span class="lineno"> 191</span> &amp;shared_in[0],</div>
<div class="line"><a id="l00192" name="l00192"></a><span class="lineno"> 192</span> out,</div>
<div class="line"><a id="l00193" name="l00193"></a><span class="lineno"> 193</span> n,</div>
<div class="line"><a id="l00194" name="l00194"></a><span class="lineno"> 194</span> batch_size,</div>
<div class="line"><a id="l00195" name="l00195"></a><span class="lineno"> 195</span> <a class="code hl_variable" href="backend_2metal_2kernels_2fft_8h.html#ad395c11e6f2aee72cd1928fba93a35a3">elems_per_thread_</a>,</div>
<div class="line"><a id="l00196" name="l00196"></a><span class="lineno"> 196</span> elem,</div>
<div class="line"><a id="l00197" name="l00197"></a><span class="lineno"> 197</span> grid,</div>
<div class="line"><a id="l00198" name="l00198"></a><span class="lineno"> 198</span> <a class="code hl_variable" href="backend_2metal_2kernels_2fft_8h.html#a7a83318497519ff3ff0141b7d511ed38">inv_</a>);</div>
<div class="line"><a id="l00199" name="l00199"></a><span class="lineno"> 199</span> </div>
<div class="line"><a id="l00200" name="l00200"></a><span class="lineno"> 200</span> <span class="keywordflow">if</span> (read_writer.out_of_bounds()) {</div>
<div class="line"><a id="l00201" name="l00201"></a><span class="lineno"> 201</span> <span class="keywordflow">return</span>;</div>
<div class="line"><a id="l00202" name="l00202"></a><span class="lineno"> 202</span> };</div>
<div class="line"><a id="l00203" name="l00203"></a><span class="lineno"> 203</span> read_writer.load();</div>
<div class="line"><a id="l00204" name="l00204"></a><span class="lineno"> 204</span> </div>
<div class="line"><a id="l00205" name="l00205"></a><span class="lineno"> 205</span> threadgroup_barrier(mem_flags::mem_threadgroup);</div>
<div class="line"><a id="l00206" name="l00206"></a><span class="lineno"> 206</span> </div>
<div class="line"><a id="l00207" name="l00207"></a><span class="lineno"> 207</span> <span class="keywordtype">int</span> p = 1;</div>
<div class="line"><a id="l00208" name="l00208"></a><span class="lineno"> 208</span> <span class="keywordtype">int</span> fft_idx = elem.z; <span class="comment">// Thread index in DFT</span></div>
<div class="line"><a id="l00209" name="l00209"></a><span class="lineno"> 209</span> <span class="keywordtype">int</span> m = grid.z; <span class="comment">// Threads per DFT</span></div>
<div class="line"><a id="l00210" name="l00210"></a><span class="lineno"> 210</span> <span class="keywordtype">int</span> tg_idx = elem.y * n; <span class="comment">// Index of this DFT in threadgroup</span></div>
<div class="line"><a id="l00211" name="l00211"></a><span class="lineno"> 211</span> threadgroup float2* buf = &amp;shared_in[tg_idx];</div>
<div class="line"><a id="l00212" name="l00212"></a><span class="lineno"> 212</span> </div>
<div class="line"><a id="l00213" name="l00213"></a><span class="lineno"> 213</span> <a class="code hl_function" href="backend_2metal_2kernels_2fft_8h.html#a050ead8fa5cacdaec13d68ca3c0dcb81">perform_fft</a>(fft_idx, &amp;p, m, n, buf);</div>
<div class="line"><a id="l00214" name="l00214"></a><span class="lineno"> 214</span> </div>
<div class="line"><a id="l00215" name="l00215"></a><span class="lineno"> 215</span> read_writer.write();</div>
<div class="line"><a id="l00216" name="l00216"></a><span class="lineno"> 216</span>}</div>
</div>
<div class="line"><a id="l00217" name="l00217"></a><span class="lineno"> 217</span> </div>
<div class="line"><a id="l00218" name="l00218"></a><span class="lineno"> 218</span><span class="keyword">template</span> &lt;<span class="keywordtype">int</span> tg_mem_size, <span class="keyword">typename</span> in_T, <span class="keyword">typename</span> out_T&gt;</div>
<div class="foldopen" id="foldopen00219" data-start="{" data-end="}">
<div class="line"><a id="l00219" name="l00219"></a><span class="lineno"><a class="line" href="backend_2metal_2kernels_2fft_8h.html#ad123452303f6415904f3592f660769b8"> 219</a></span>[[kernel]] <span class="keywordtype">void</span> <a class="code hl_function" href="backend_2metal_2kernels_2fft_8h.html#ad123452303f6415904f3592f660769b8">rader_fft</a>(</div>
<div class="line"><a id="l00220" name="l00220"></a><span class="lineno"> 220</span> <span class="keyword">const</span> device in_T* in [[buffer(0)]],</div>
<div class="line"><a id="l00221" name="l00221"></a><span class="lineno"> 221</span> device out_T* out [[buffer(1)]],</div>
<div class="line"><a id="l00222" name="l00222"></a><span class="lineno"> 222</span> <span class="keyword">const</span> device float2* raders_b_q [[buffer(2)]],</div>
<div class="line"><a id="l00223" name="l00223"></a><span class="lineno"> 223</span> <span class="keyword">const</span> device <span class="keywordtype">short</span>* raders_g_q [[buffer(3)]],</div>
<div class="line"><a id="l00224" name="l00224"></a><span class="lineno"> 224</span> <span class="keyword">const</span> device <span class="keywordtype">short</span>* raders_g_minus_q [[buffer(4)]],</div>
<div class="line"><a id="l00225" name="l00225"></a><span class="lineno"> 225</span> constant <span class="keyword">const</span> <span class="keywordtype">int</span>&amp; n,</div>
<div class="line"><a id="l00226" name="l00226"></a><span class="lineno"> 226</span> constant <span class="keyword">const</span> <span class="keywordtype">int</span>&amp; batch_size,</div>
<div class="line"><a id="l00227" name="l00227"></a><span class="lineno"> 227</span> constant <span class="keyword">const</span> <span class="keywordtype">int</span>&amp; rader_n,</div>
<div class="line"><a id="l00228" name="l00228"></a><span class="lineno"> 228</span> uint3 elem [[thread_position_in_grid]],</div>
<div class="line"><a id="l00229" name="l00229"></a><span class="lineno"> 229</span> uint3 grid [[threads_per_grid]]) {</div>
<div class="line"><a id="l00230" name="l00230"></a><span class="lineno"> 230</span> <span class="comment">// Use Rader&#39;s algorithm to compute fast FFTs</span></div>
<div class="line"><a id="l00231" name="l00231"></a><span class="lineno"> 231</span> <span class="comment">// when a prime factor `p` of `n` is greater than 13 but</span></div>
<div class="line"><a id="l00232" name="l00232"></a><span class="lineno"> 232</span> <span class="comment">// has `p - 1` Stockham decomposable into to prime factors &lt;= 13.</span></div>
<div class="line"><a id="l00233" name="l00233"></a><span class="lineno"> 233</span> <span class="comment">//</span></div>
<div class="line"><a id="l00234" name="l00234"></a><span class="lineno"> 234</span> <span class="comment">// E.g. n = 102</span></div>
<div class="line"><a id="l00235" name="l00235"></a><span class="lineno"> 235</span> <span class="comment">// = 2 * 3 * 17</span></div>
<div class="line"><a id="l00236" name="l00236"></a><span class="lineno"> 236</span> <span class="comment">// . = 2 * 3 * RADER(16)</span></div>
<div class="line"><a id="l00237" name="l00237"></a><span class="lineno"> 237</span> <span class="comment">// . = 2 * 3 * RADER(4 * 4)</span></div>
<div class="line"><a id="l00238" name="l00238"></a><span class="lineno"> 238</span> <span class="comment">//</span></div>
<div class="line"><a id="l00239" name="l00239"></a><span class="lineno"> 239</span> <span class="comment">// In numpy:</span></div>
<div class="line"><a id="l00240" name="l00240"></a><span class="lineno"> 240</span> <span class="comment">// x_perm = x[g_q]</span></div>
<div class="line"><a id="l00241" name="l00241"></a><span class="lineno"> 241</span> <span class="comment">// y = np.fft.fft(x_perm) * b_q</span></div>
<div class="line"><a id="l00242" name="l00242"></a><span class="lineno"> 242</span> <span class="comment">// z = np.fft.ifft(y) + x[0]</span></div>
<div class="line"><a id="l00243" name="l00243"></a><span class="lineno"> 243</span> <span class="comment">// out = z[g_minus_q]</span></div>
<div class="line"><a id="l00244" name="l00244"></a><span class="lineno"> 244</span> <span class="comment">// out[0] = x[1:].sum()</span></div>
<div class="line"><a id="l00245" name="l00245"></a><span class="lineno"> 245</span> <span class="comment">//</span></div>
<div class="line"><a id="l00246" name="l00246"></a><span class="lineno"> 246</span> <span class="comment">// Where the g_q and g_minus_q are permutations formed</span></div>
<div class="line"><a id="l00247" name="l00247"></a><span class="lineno"> 247</span> <span class="comment">// by the group under multiplicative modulo N using the</span></div>
<div class="line"><a id="l00248" name="l00248"></a><span class="lineno"> 248</span> <span class="comment">// primitive root of N and b_q is a constant.</span></div>
<div class="line"><a id="l00249" name="l00249"></a><span class="lineno"> 249</span> <span class="comment">// See https://en.wikipedia.org/wiki/Rader%27s_FFT_algorithm</span></div>
<div class="line"><a id="l00250" name="l00250"></a><span class="lineno"> 250</span> <span class="comment">//</span></div>
<div class="line"><a id="l00251" name="l00251"></a><span class="lineno"> 251</span> <span class="comment">// Rader&#39;s uses fewer operations than Bluestein&#39;s and so</span></div>
<div class="line"><a id="l00252" name="l00252"></a><span class="lineno"> 252</span> <span class="comment">// is more accurate. It&#39;s also faster in most cases.</span></div>
<div class="line"><a id="l00253" name="l00253"></a><span class="lineno"> 253</span> threadgroup float2 shared_in[tg_mem_size];</div>
<div class="line"><a id="l00254" name="l00254"></a><span class="lineno"> 254</span> </div>
<div class="line"><a id="l00255" name="l00255"></a><span class="lineno"> 255</span> thread <a class="code hl_struct" href="struct_read_writer.html">ReadWriter&lt;in_T, out_T&gt;</a> read_writer = <a class="code hl_struct" href="struct_read_writer.html">ReadWriter&lt;in_T, out_T&gt;</a>(</div>
<div class="line"><a id="l00256" name="l00256"></a><span class="lineno"> 256</span> in,</div>
<div class="line"><a id="l00257" name="l00257"></a><span class="lineno"> 257</span> &amp;shared_in[0],</div>
<div class="line"><a id="l00258" name="l00258"></a><span class="lineno"> 258</span> out,</div>
<div class="line"><a id="l00259" name="l00259"></a><span class="lineno"> 259</span> n,</div>
<div class="line"><a id="l00260" name="l00260"></a><span class="lineno"> 260</span> batch_size,</div>
<div class="line"><a id="l00261" name="l00261"></a><span class="lineno"> 261</span> <a class="code hl_variable" href="backend_2metal_2kernels_2fft_8h.html#ad395c11e6f2aee72cd1928fba93a35a3">elems_per_thread_</a>,</div>
<div class="line"><a id="l00262" name="l00262"></a><span class="lineno"> 262</span> elem,</div>
<div class="line"><a id="l00263" name="l00263"></a><span class="lineno"> 263</span> grid,</div>
<div class="line"><a id="l00264" name="l00264"></a><span class="lineno"> 264</span> <a class="code hl_variable" href="backend_2metal_2kernels_2fft_8h.html#a7a83318497519ff3ff0141b7d511ed38">inv_</a>);</div>
<div class="line"><a id="l00265" name="l00265"></a><span class="lineno"> 265</span> </div>
<div class="line"><a id="l00266" name="l00266"></a><span class="lineno"> 266</span> <span class="keywordflow">if</span> (read_writer.out_of_bounds()) {</div>
<div class="line"><a id="l00267" name="l00267"></a><span class="lineno"> 267</span> <span class="keywordflow">return</span>;</div>
<div class="line"><a id="l00268" name="l00268"></a><span class="lineno"> 268</span> };</div>
<div class="line"><a id="l00269" name="l00269"></a><span class="lineno"> 269</span> read_writer.load();</div>
<div class="line"><a id="l00270" name="l00270"></a><span class="lineno"> 270</span> </div>
<div class="line"><a id="l00271" name="l00271"></a><span class="lineno"> 271</span> threadgroup_barrier(mem_flags::mem_threadgroup);</div>
<div class="line"><a id="l00272" name="l00272"></a><span class="lineno"> 272</span> </div>
<div class="line"><a id="l00273" name="l00273"></a><span class="lineno"> 273</span> <span class="comment">// The number of the threads we&#39;re using for each DFT</span></div>
<div class="line"><a id="l00274" name="l00274"></a><span class="lineno"> 274</span> <span class="keywordtype">int</span> m = grid.z;</div>
<div class="line"><a id="l00275" name="l00275"></a><span class="lineno"> 275</span> </div>
<div class="line"><a id="l00276" name="l00276"></a><span class="lineno"> 276</span> <span class="keywordtype">int</span> fft_idx = elem.z;</div>
<div class="line"><a id="l00277" name="l00277"></a><span class="lineno"> 277</span> <span class="keywordtype">int</span> tg_idx = elem.y * n;</div>
<div class="line"><a id="l00278" name="l00278"></a><span class="lineno"> 278</span> threadgroup float2* buf = &amp;shared_in[tg_idx];</div>
<div class="line"><a id="l00279" name="l00279"></a><span class="lineno"> 279</span> </div>
<div class="line"><a id="l00280" name="l00280"></a><span class="lineno"> 280</span> <span class="comment">// rader_m = n / rader_n;</span></div>
<div class="line"><a id="l00281" name="l00281"></a><span class="lineno"> 281</span> <span class="keywordtype">int</span> rader_m = <a class="code hl_variable" href="backend_2metal_2kernels_2fft_8h.html#ac309c77ef775a3ef13850c5287a86480">rader_m_</a>;</div>
<div class="line"><a id="l00282" name="l00282"></a><span class="lineno"> 282</span> </div>
<div class="line"><a id="l00283" name="l00283"></a><span class="lineno"> 283</span> <span class="comment">// We have to load two x_0s for each thread since sometimes</span></div>
<div class="line"><a id="l00284" name="l00284"></a><span class="lineno"> 284</span> <span class="comment">// elems_per_thread_ crosses a boundary.</span></div>
<div class="line"><a id="l00285" name="l00285"></a><span class="lineno"> 285</span> <span class="comment">// E.g. with n = 34, rader_n = 17, elems_per_thread_ = 4</span></div>
<div class="line"><a id="l00286" name="l00286"></a><span class="lineno"> 286</span> <span class="comment">// 0 0 0 0 1 1 1 1 2 2 2 2 3 3 3 3 4 4 4 4 5 5 5 5 6 6 6 6 7 7 7 7 8 8</span></div>
<div class="line"><a id="l00287" name="l00287"></a><span class="lineno"> 287</span> <span class="comment">// 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1</span></div>
<div class="line"><a id="l00288" name="l00288"></a><span class="lineno"> 288</span> <span class="keywordtype">short</span> x_0_index =</div>
<div class="line"><a id="l00289" name="l00289"></a><span class="lineno"> 289</span> <a class="code hl_function" href="namespacemetal.html#a6653b28c9473087141eddce39878d4d3">metal::min</a>(fft_idx * <a class="code hl_variable" href="backend_2metal_2kernels_2fft_8h.html#ad395c11e6f2aee72cd1928fba93a35a3">elems_per_thread_</a> / (rader_n - 1), rader_m - 1);</div>
<div class="line"><a id="l00290" name="l00290"></a><span class="lineno"> 290</span> float2 x_0[2] = {buf[x_0_index], buf[x_0_index + 1]};</div>
<div class="line"><a id="l00291" name="l00291"></a><span class="lineno"> 291</span> </div>
<div class="line"><a id="l00292" name="l00292"></a><span class="lineno"> 292</span> <span class="comment">// Do the Rader permutation in shared memory</span></div>
<div class="line"><a id="l00293" name="l00293"></a><span class="lineno"> 293</span> float2 temp[<a class="code hl_define" href="backend_2metal_2kernels_2fft_8h.html#a7b6e56afa21f022c5e754b000955735a">MAX_RADIX</a>];</div>
<div class="line"><a id="l00294" name="l00294"></a><span class="lineno"> 294</span> <span class="keywordtype">int</span> max_index = n - rader_m - 1;</div>
<div class="line"><a id="l00295" name="l00295"></a><span class="lineno"> 295</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> e = 0; e &lt; <a class="code hl_variable" href="backend_2metal_2kernels_2fft_8h.html#ad395c11e6f2aee72cd1928fba93a35a3">elems_per_thread_</a>; e++) {</div>
<div class="line"><a id="l00296" name="l00296"></a><span class="lineno"> 296</span> <span class="keywordtype">short</span> index = <a class="code hl_function" href="namespacemetal.html#a6653b28c9473087141eddce39878d4d3">metal::min</a>(fft_idx * <a class="code hl_variable" href="backend_2metal_2kernels_2fft_8h.html#ad395c11e6f2aee72cd1928fba93a35a3">elems_per_thread_</a> + e, max_index);</div>
<div class="line"><a id="l00297" name="l00297"></a><span class="lineno"> 297</span> <span class="keywordtype">short</span> g_q = raders_g_q[index / rader_m];</div>
<div class="line"><a id="l00298" name="l00298"></a><span class="lineno"> 298</span> temp[e] = buf[rader_m + (g_q - 1) * rader_m + index % rader_m];</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> </div>
<div class="line"><a id="l00301" name="l00301"></a><span class="lineno"> 301</span> threadgroup_barrier(mem_flags::mem_threadgroup);</div>
<div class="line"><a id="l00302" name="l00302"></a><span class="lineno"> 302</span> </div>
<div class="line"><a id="l00303" name="l00303"></a><span class="lineno"> 303</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> e = 0; e &lt; <a class="code hl_variable" href="backend_2metal_2kernels_2fft_8h.html#ad395c11e6f2aee72cd1928fba93a35a3">elems_per_thread_</a>; e++) {</div>
<div class="line"><a id="l00304" name="l00304"></a><span class="lineno"> 304</span> <span class="keywordtype">short</span> index = <a class="code hl_function" href="namespacemetal.html#a6653b28c9473087141eddce39878d4d3">metal::min</a>(fft_idx * <a class="code hl_variable" href="backend_2metal_2kernels_2fft_8h.html#ad395c11e6f2aee72cd1928fba93a35a3">elems_per_thread_</a> + e, max_index);</div>
<div class="line"><a id="l00305" name="l00305"></a><span class="lineno"> 305</span> buf[index + rader_m] = temp[e];</div>
<div class="line"><a id="l00306" name="l00306"></a><span class="lineno"> 306</span> }</div>
<div class="line"><a id="l00307" name="l00307"></a><span class="lineno"> 307</span> </div>
<div class="line"><a id="l00308" name="l00308"></a><span class="lineno"> 308</span> threadgroup_barrier(mem_flags::mem_threadgroup);</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="comment">// Rader FFT on x[rader_m:]</span></div>
<div class="line"><a id="l00311" name="l00311"></a><span class="lineno"> 311</span> <span class="keywordtype">int</span> p = 1;</div>
<div class="line"><a id="l00312" name="l00312"></a><span class="lineno"> 312</span> <a class="code hl_function" href="backend_2metal_2kernels_2fft_8h.html#a050ead8fa5cacdaec13d68ca3c0dcb81">perform_fft</a>&lt;<span class="comment">/*rader=*/</span><span class="keyword">true</span>&gt;(fft_idx, &amp;p, m, n - rader_m, buf + rader_m);</div>
<div class="line"><a id="l00313" name="l00313"></a><span class="lineno"> 313</span> </div>
<div class="line"><a id="l00314" name="l00314"></a><span class="lineno"> 314</span> <span class="comment">// x_1 + ... + x_n is computed for us in the first FFT step so</span></div>
<div class="line"><a id="l00315" name="l00315"></a><span class="lineno"> 315</span> <span class="comment">// we save it in the first rader_m indices of the array for later.</span></div>
<div class="line"><a id="l00316" name="l00316"></a><span class="lineno"> 316</span> <span class="keywordtype">int</span> x_sum_index = <a class="code hl_function" href="namespacemetal.html#a6653b28c9473087141eddce39878d4d3">metal::min</a>(fft_idx, rader_m - 1);</div>
<div class="line"><a id="l00317" name="l00317"></a><span class="lineno"> 317</span> buf[x_sum_index] = buf[rader_m + x_sum_index * (rader_n - 1)];</div>
<div class="line"><a id="l00318" name="l00318"></a><span class="lineno"> 318</span> </div>
<div class="line"><a id="l00319" name="l00319"></a><span class="lineno"> 319</span> float2 inv = {1.0f, -1.0f};</div>
<div class="line"><a id="l00320" name="l00320"></a><span class="lineno"> 320</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> e = 0; e &lt; <a class="code hl_variable" href="backend_2metal_2kernels_2fft_8h.html#ad395c11e6f2aee72cd1928fba93a35a3">elems_per_thread_</a>; e++) {</div>
<div class="line"><a id="l00321" name="l00321"></a><span class="lineno"> 321</span> <span class="keywordtype">short</span> index = <a class="code hl_function" href="namespacemetal.html#a6653b28c9473087141eddce39878d4d3">metal::min</a>(fft_idx * <a class="code hl_variable" href="backend_2metal_2kernels_2fft_8h.html#ad395c11e6f2aee72cd1928fba93a35a3">elems_per_thread_</a> + e, max_index);</div>
<div class="line"><a id="l00322" name="l00322"></a><span class="lineno"> 322</span> <span class="keywordtype">short</span> interleaved_index =</div>
<div class="line"><a id="l00323" name="l00323"></a><span class="lineno"> 323</span> index / rader_m + (index % rader_m) * (rader_n - 1);</div>
<div class="line"><a id="l00324" name="l00324"></a><span class="lineno"> 324</span> temp[e] = <a class="code hl_function" href="radix_8h.html#a5bfc53b531214c9ce277bebc18aa67d6">complex_mul</a>(</div>
<div class="line"><a id="l00325" name="l00325"></a><span class="lineno"> 325</span> buf[rader_m + interleaved_index],</div>
<div class="line"><a id="l00326" name="l00326"></a><span class="lineno"> 326</span> raders_b_q[interleaved_index % (rader_n - 1)]);</div>
<div class="line"><a id="l00327" name="l00327"></a><span class="lineno"> 327</span> }</div>
<div class="line"><a id="l00328" name="l00328"></a><span class="lineno"> 328</span> </div>
<div class="line"><a id="l00329" name="l00329"></a><span class="lineno"> 329</span> threadgroup_barrier(mem_flags::mem_threadgroup);</div>
<div class="line"><a id="l00330" name="l00330"></a><span class="lineno"> 330</span> </div>
<div class="line"><a id="l00331" name="l00331"></a><span class="lineno"> 331</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> e = 0; e &lt; <a class="code hl_variable" href="backend_2metal_2kernels_2fft_8h.html#ad395c11e6f2aee72cd1928fba93a35a3">elems_per_thread_</a>; e++) {</div>
<div class="line"><a id="l00332" name="l00332"></a><span class="lineno"> 332</span> <span class="keywordtype">short</span> index = <a class="code hl_function" href="namespacemetal.html#a6653b28c9473087141eddce39878d4d3">metal::min</a>(fft_idx * <a class="code hl_variable" href="backend_2metal_2kernels_2fft_8h.html#ad395c11e6f2aee72cd1928fba93a35a3">elems_per_thread_</a> + e, max_index);</div>
<div class="line"><a id="l00333" name="l00333"></a><span class="lineno"> 333</span> buf[rader_m + index] = temp[e] * inv;</div>
<div class="line"><a id="l00334" name="l00334"></a><span class="lineno"> 334</span> }</div>
<div class="line"><a id="l00335" name="l00335"></a><span class="lineno"> 335</span> </div>
<div class="line"><a id="l00336" name="l00336"></a><span class="lineno"> 336</span> threadgroup_barrier(mem_flags::mem_threadgroup);</div>
<div class="line"><a id="l00337" name="l00337"></a><span class="lineno"> 337</span> </div>
<div class="line"><a id="l00338" name="l00338"></a><span class="lineno"> 338</span> <span class="comment">// Rader IFFT on x[rader_m:]</span></div>
<div class="line"><a id="l00339" name="l00339"></a><span class="lineno"> 339</span> p = 1;</div>
<div class="line"><a id="l00340" name="l00340"></a><span class="lineno"> 340</span> <a class="code hl_function" href="backend_2metal_2kernels_2fft_8h.html#a050ead8fa5cacdaec13d68ca3c0dcb81">perform_fft</a>&lt;<span class="comment">/*rader=*/</span><span class="keyword">true</span>&gt;(fft_idx, &amp;p, m, n - rader_m, buf + rader_m);</div>
<div class="line"><a id="l00341" name="l00341"></a><span class="lineno"> 341</span> </div>
<div class="line"><a id="l00342" name="l00342"></a><span class="lineno"> 342</span> float2 rader_inv_factor = {1.0f / (rader_n - 1), -1.0f / (rader_n - 1)};</div>
<div class="line"><a id="l00343" name="l00343"></a><span class="lineno"> 343</span> </div>
<div class="line"><a id="l00344" name="l00344"></a><span class="lineno"> 344</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> e = 0; e &lt; <a class="code hl_variable" href="backend_2metal_2kernels_2fft_8h.html#ad395c11e6f2aee72cd1928fba93a35a3">elems_per_thread_</a>; e++) {</div>
<div class="line"><a id="l00345" name="l00345"></a><span class="lineno"> 345</span> <span class="keywordtype">short</span> index = <a class="code hl_function" href="namespacemetal.html#a6653b28c9473087141eddce39878d4d3">metal::min</a>(fft_idx * <a class="code hl_variable" href="backend_2metal_2kernels_2fft_8h.html#ad395c11e6f2aee72cd1928fba93a35a3">elems_per_thread_</a> + e, n - rader_m - 1);</div>
<div class="line"><a id="l00346" name="l00346"></a><span class="lineno"> 346</span> <span class="keywordtype">short</span> diff_index = index / (rader_n - 1) - x_0_index;</div>
<div class="line"><a id="l00347" name="l00347"></a><span class="lineno"> 347</span> temp[e] = buf[rader_m + index] * rader_inv_factor + x_0[diff_index];</div>
<div class="line"><a id="l00348" name="l00348"></a><span class="lineno"> 348</span> }</div>
<div class="line"><a id="l00349" name="l00349"></a><span class="lineno"> 349</span> </div>
<div class="line"><a id="l00350" name="l00350"></a><span class="lineno"> 350</span> <span class="comment">// Use the sum of elements that was computed in the first FFT</span></div>
<div class="line"><a id="l00351" name="l00351"></a><span class="lineno"> 351</span> float2 x_sum = buf[x_0_index] + x_0[0];</div>
<div class="line"><a id="l00352" name="l00352"></a><span class="lineno"> 352</span> </div>
<div class="line"><a id="l00353" name="l00353"></a><span class="lineno"> 353</span> threadgroup_barrier(mem_flags::mem_threadgroup);</div>
<div class="line"><a id="l00354" name="l00354"></a><span class="lineno"> 354</span> </div>
<div class="line"><a id="l00355" name="l00355"></a><span class="lineno"> 355</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> e = 0; e &lt; <a class="code hl_variable" href="backend_2metal_2kernels_2fft_8h.html#ad395c11e6f2aee72cd1928fba93a35a3">elems_per_thread_</a>; e++) {</div>
<div class="line"><a id="l00356" name="l00356"></a><span class="lineno"> 356</span> <span class="keywordtype">short</span> index = <a class="code hl_function" href="namespacemetal.html#a6653b28c9473087141eddce39878d4d3">metal::min</a>(fft_idx * <a class="code hl_variable" href="backend_2metal_2kernels_2fft_8h.html#ad395c11e6f2aee72cd1928fba93a35a3">elems_per_thread_</a> + e, max_index);</div>
<div class="line"><a id="l00357" name="l00357"></a><span class="lineno"> 357</span> <span class="keywordtype">short</span> g_q_index = index % (rader_n - 1);</div>
<div class="line"><a id="l00358" name="l00358"></a><span class="lineno"> 358</span> <span class="keywordtype">short</span> g_q = raders_g_minus_q[g_q_index];</div>
<div class="line"><a id="l00359" name="l00359"></a><span class="lineno"> 359</span> <span class="keywordtype">short</span> out_index = index - g_q_index + g_q + (index / (rader_n - 1));</div>
<div class="line"><a id="l00360" name="l00360"></a><span class="lineno"> 360</span> buf[out_index] = temp[e];</div>
<div class="line"><a id="l00361" name="l00361"></a><span class="lineno"> 361</span> }</div>
<div class="line"><a id="l00362" name="l00362"></a><span class="lineno"> 362</span> </div>
<div class="line"><a id="l00363" name="l00363"></a><span class="lineno"> 363</span> buf[x_0_index * rader_n] = x_sum;</div>
<div class="line"><a id="l00364" name="l00364"></a><span class="lineno"> 364</span> </div>
<div class="line"><a id="l00365" name="l00365"></a><span class="lineno"> 365</span> threadgroup_barrier(mem_flags::mem_threadgroup);</div>
<div class="line"><a id="l00366" name="l00366"></a><span class="lineno"> 366</span> </div>
<div class="line"><a id="l00367" name="l00367"></a><span class="lineno"> 367</span> p = rader_n;</div>
<div class="line"><a id="l00368" name="l00368"></a><span class="lineno"> 368</span> <a class="code hl_function" href="backend_2metal_2kernels_2fft_8h.html#a050ead8fa5cacdaec13d68ca3c0dcb81">perform_fft</a>(fft_idx, &amp;p, m, n, buf);</div>
<div class="line"><a id="l00369" name="l00369"></a><span class="lineno"> 369</span> </div>
<div class="line"><a id="l00370" name="l00370"></a><span class="lineno"> 370</span> read_writer.write();</div>
<div class="line"><a id="l00371" name="l00371"></a><span class="lineno"> 371</span>}</div>
</div>
<div class="line"><a id="l00372" name="l00372"></a><span class="lineno"> 372</span> </div>
<div class="line"><a id="l00373" name="l00373"></a><span class="lineno"> 373</span><span class="keyword">template</span> &lt;<span class="keywordtype">int</span> tg_mem_size, <span class="keyword">typename</span> in_T, <span class="keyword">typename</span> out_T&gt;</div>
<div class="foldopen" id="foldopen00374" data-start="{" data-end="}">
<div class="line"><a id="l00374" name="l00374"></a><span class="lineno"><a class="line" href="backend_2metal_2kernels_2fft_8h.html#a0abc609e9756475800e996775a96a87e"> 374</a></span>[[kernel]] <span class="keywordtype">void</span> <a class="code hl_function" href="backend_2metal_2kernels_2fft_8h.html#a0abc609e9756475800e996775a96a87e">bluestein_fft</a>(</div>
<div class="line"><a id="l00375" name="l00375"></a><span class="lineno"> 375</span> <span class="keyword">const</span> device in_T* in [[buffer(0)]],</div>
<div class="line"><a id="l00376" name="l00376"></a><span class="lineno"> 376</span> device out_T* out [[buffer(1)]],</div>
<div class="line"><a id="l00377" name="l00377"></a><span class="lineno"> 377</span> <span class="keyword">const</span> device float2* w_q [[buffer(2)]],</div>
<div class="line"><a id="l00378" name="l00378"></a><span class="lineno"> 378</span> <span class="keyword">const</span> device float2* w_k [[buffer(3)]],</div>
<div class="line"><a id="l00379" name="l00379"></a><span class="lineno"> 379</span> constant <span class="keyword">const</span> <span class="keywordtype">int</span>&amp; length,</div>
<div class="line"><a id="l00380" name="l00380"></a><span class="lineno"> 380</span> constant <span class="keyword">const</span> <span class="keywordtype">int</span>&amp; n,</div>
<div class="line"><a id="l00381" name="l00381"></a><span class="lineno"> 381</span> constant <span class="keyword">const</span> <span class="keywordtype">int</span>&amp; batch_size,</div>
<div class="line"><a id="l00382" name="l00382"></a><span class="lineno"> 382</span> uint3 elem [[thread_position_in_grid]],</div>
<div class="line"><a id="l00383" name="l00383"></a><span class="lineno"> 383</span> uint3 grid [[threads_per_grid]]) {</div>
<div class="line"><a id="l00384" name="l00384"></a><span class="lineno"> 384</span> <span class="comment">// Computes arbitrary length FFTs with Bluestein&#39;s algorithm</span></div>
<div class="line"><a id="l00385" name="l00385"></a><span class="lineno"> 385</span> <span class="comment">//</span></div>
<div class="line"><a id="l00386" name="l00386"></a><span class="lineno"> 386</span> <span class="comment">// In numpy:</span></div>
<div class="line"><a id="l00387" name="l00387"></a><span class="lineno"> 387</span> <span class="comment">// bluestein_n = next_power_of_2(2*n - 1)</span></div>
<div class="line"><a id="l00388" name="l00388"></a><span class="lineno"> 388</span> <span class="comment">// out = w_k * np.fft.ifft(np.fft.fft(w_k * in, bluestein_n) * w_q)</span></div>
<div class="line"><a id="l00389" name="l00389"></a><span class="lineno"> 389</span> <span class="comment">//</span></div>
<div class="line"><a id="l00390" name="l00390"></a><span class="lineno"> 390</span> <span class="comment">// Where w_k and w_q are precomputed on CPU in high precision as:</span></div>
<div class="line"><a id="l00391" name="l00391"></a><span class="lineno"> 391</span> <span class="comment">// w_k = np.exp(-1j * np.pi / n * (np.arange(-n + 1, n) ** 2))</span></div>
<div class="line"><a id="l00392" name="l00392"></a><span class="lineno"> 392</span> <span class="comment">// w_q = np.fft.fft(1/w_k[-n:])</span></div>
<div class="line"><a id="l00393" name="l00393"></a><span class="lineno"> 393</span> threadgroup float2 shared_in[tg_mem_size];</div>
<div class="line"><a id="l00394" name="l00394"></a><span class="lineno"> 394</span> </div>
<div class="line"><a id="l00395" name="l00395"></a><span class="lineno"> 395</span> thread <a class="code hl_struct" href="struct_read_writer.html">ReadWriter&lt;in_T, out_T&gt;</a> read_writer = <a class="code hl_struct" href="struct_read_writer.html">ReadWriter&lt;in_T, out_T&gt;</a>(</div>
<div class="line"><a id="l00396" name="l00396"></a><span class="lineno"> 396</span> in,</div>
<div class="line"><a id="l00397" name="l00397"></a><span class="lineno"> 397</span> &amp;shared_in[0],</div>
<div class="line"><a id="l00398" name="l00398"></a><span class="lineno"> 398</span> out,</div>
<div class="line"><a id="l00399" name="l00399"></a><span class="lineno"> 399</span> n,</div>
<div class="line"><a id="l00400" name="l00400"></a><span class="lineno"> 400</span> batch_size,</div>
<div class="line"><a id="l00401" name="l00401"></a><span class="lineno"> 401</span> <a class="code hl_variable" href="backend_2metal_2kernels_2fft_8h.html#ad395c11e6f2aee72cd1928fba93a35a3">elems_per_thread_</a>,</div>
<div class="line"><a id="l00402" name="l00402"></a><span class="lineno"> 402</span> elem,</div>
<div class="line"><a id="l00403" name="l00403"></a><span class="lineno"> 403</span> grid,</div>
<div class="line"><a id="l00404" name="l00404"></a><span class="lineno"> 404</span> <a class="code hl_variable" href="backend_2metal_2kernels_2fft_8h.html#a7a83318497519ff3ff0141b7d511ed38">inv_</a>);</div>
<div class="line"><a id="l00405" name="l00405"></a><span class="lineno"> 405</span> </div>
<div class="line"><a id="l00406" name="l00406"></a><span class="lineno"> 406</span> <span class="keywordflow">if</span> (read_writer.out_of_bounds()) {</div>
<div class="line"><a id="l00407" name="l00407"></a><span class="lineno"> 407</span> <span class="keywordflow">return</span>;</div>
<div class="line"><a id="l00408" name="l00408"></a><span class="lineno"> 408</span> };</div>
<div class="line"><a id="l00409" name="l00409"></a><span class="lineno"> 409</span> read_writer.load_padded(length, w_k);</div>
<div class="line"><a id="l00410" name="l00410"></a><span class="lineno"> 410</span> </div>
<div class="line"><a id="l00411" name="l00411"></a><span class="lineno"> 411</span> threadgroup_barrier(mem_flags::mem_threadgroup);</div>
<div class="line"><a id="l00412" name="l00412"></a><span class="lineno"> 412</span> </div>
<div class="line"><a id="l00413" name="l00413"></a><span class="lineno"> 413</span> <span class="keywordtype">int</span> p = 1;</div>
<div class="line"><a id="l00414" name="l00414"></a><span class="lineno"> 414</span> <span class="keywordtype">int</span> fft_idx = elem.z; <span class="comment">// Thread index in DFT</span></div>
<div class="line"><a id="l00415" name="l00415"></a><span class="lineno"> 415</span> <span class="keywordtype">int</span> m = grid.z; <span class="comment">// Threads per DFT</span></div>
<div class="line"><a id="l00416" name="l00416"></a><span class="lineno"> 416</span> <span class="keywordtype">int</span> tg_idx = elem.y * n; <span class="comment">// Index of this DFT in threadgroup</span></div>
<div class="line"><a id="l00417" name="l00417"></a><span class="lineno"> 417</span> threadgroup float2* buf = &amp;shared_in[tg_idx];</div>
<div class="line"><a id="l00418" name="l00418"></a><span class="lineno"> 418</span> </div>
<div class="line"><a id="l00419" name="l00419"></a><span class="lineno"> 419</span> <span class="comment">// fft</span></div>
<div class="line"><a id="l00420" name="l00420"></a><span class="lineno"> 420</span> <a class="code hl_function" href="backend_2metal_2kernels_2fft_8h.html#a050ead8fa5cacdaec13d68ca3c0dcb81">perform_fft</a>(fft_idx, &amp;p, m, n, buf);</div>
<div class="line"><a id="l00421" name="l00421"></a><span class="lineno"> 421</span> </div>
<div class="line"><a id="l00422" name="l00422"></a><span class="lineno"> 422</span> float2 inv = float2(1.0f, -1.0f);</div>
<div class="line"><a id="l00423" name="l00423"></a><span class="lineno"> 423</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> t = 0; t &lt; <a class="code hl_variable" href="backend_2metal_2kernels_2fft_8h.html#ad395c11e6f2aee72cd1928fba93a35a3">elems_per_thread_</a>; t++) {</div>
<div class="line"><a id="l00424" name="l00424"></a><span class="lineno"> 424</span> <span class="keywordtype">int</span> index = fft_idx + t * m;</div>
<div class="line"><a id="l00425" name="l00425"></a><span class="lineno"> 425</span> buf[index] = <a class="code hl_function" href="radix_8h.html#a5bfc53b531214c9ce277bebc18aa67d6">complex_mul</a>(buf[index], w_q[index]) * inv;</div>
<div class="line"><a id="l00426" name="l00426"></a><span class="lineno"> 426</span> }</div>
<div class="line"><a id="l00427" name="l00427"></a><span class="lineno"> 427</span> </div>
<div class="line"><a id="l00428" name="l00428"></a><span class="lineno"> 428</span> threadgroup_barrier(mem_flags::mem_threadgroup);</div>
<div class="line"><a id="l00429" name="l00429"></a><span class="lineno"> 429</span> </div>
<div class="line"><a id="l00430" name="l00430"></a><span class="lineno"> 430</span> <span class="comment">// ifft</span></div>
<div class="line"><a id="l00431" name="l00431"></a><span class="lineno"> 431</span> p = 1;</div>
<div class="line"><a id="l00432" name="l00432"></a><span class="lineno"> 432</span> <a class="code hl_function" href="backend_2metal_2kernels_2fft_8h.html#a050ead8fa5cacdaec13d68ca3c0dcb81">perform_fft</a>(fft_idx, &amp;p, m, n, buf);</div>
<div class="line"><a id="l00433" name="l00433"></a><span class="lineno"> 433</span> </div>
<div class="line"><a id="l00434" name="l00434"></a><span class="lineno"> 434</span> read_writer.write_padded(length, w_k);</div>
<div class="line"><a id="l00435" name="l00435"></a><span class="lineno"> 435</span>}</div>
</div>
<div class="line"><a id="l00436" name="l00436"></a><span class="lineno"> 436</span> </div>
<div class="line"><a id="l00437" name="l00437"></a><span class="lineno"> 437</span><span class="keyword">template</span> &lt;</div>
<div class="line"><a id="l00438" name="l00438"></a><span class="lineno"> 438</span> <span class="keywordtype">int</span> tg_mem_size,</div>
<div class="line"><a id="l00439" name="l00439"></a><span class="lineno"> 439</span> <span class="keyword">typename</span> in_T,</div>
<div class="line"><a id="l00440" name="l00440"></a><span class="lineno"> 440</span> <span class="keyword">typename</span> out_T,</div>
<div class="line"><a id="l00441" name="l00441"></a><span class="lineno"> 441</span> <span class="keywordtype">int</span> step,</div>
<div class="line"><a id="l00442" name="l00442"></a><span class="lineno"> 442</span> <span class="keywordtype">bool</span> <a class="code hl_function" href="namespacemlx_1_1core_1_1simd.html#acdf822b7626bbab6a495552aea3457b5">real</a> = <span class="keyword">false</span>&gt;</div>
<div class="foldopen" id="foldopen00443" data-start="{" data-end="}">
<div class="line"><a id="l00443" name="l00443"></a><span class="lineno"><a class="line" href="backend_2metal_2kernels_2fft_8h.html#a6558a8205ee4c3e4767bafa93f7606de"> 443</a></span>[[kernel]] <span class="keywordtype">void</span> <a class="code hl_function" href="backend_2metal_2kernels_2fft_8h.html#a6558a8205ee4c3e4767bafa93f7606de">four_step_fft</a>(</div>
<div class="line"><a id="l00444" name="l00444"></a><span class="lineno"> 444</span> <span class="keyword">const</span> device in_T* in [[buffer(0)]],</div>
<div class="line"><a id="l00445" name="l00445"></a><span class="lineno"> 445</span> device out_T* out [[buffer(1)]],</div>
<div class="line"><a id="l00446" name="l00446"></a><span class="lineno"> 446</span> constant <span class="keyword">const</span> <span class="keywordtype">int</span>&amp; n1,</div>
<div class="line"><a id="l00447" name="l00447"></a><span class="lineno"> 447</span> constant <span class="keyword">const</span> <span class="keywordtype">int</span>&amp; n2,</div>
<div class="line"><a id="l00448" name="l00448"></a><span class="lineno"> 448</span> constant <span class="keyword">const</span> <span class="keywordtype">int</span>&amp; batch_size,</div>
<div class="line"><a id="l00449" name="l00449"></a><span class="lineno"> 449</span> uint3 elem [[thread_position_in_grid]],</div>
<div class="line"><a id="l00450" name="l00450"></a><span class="lineno"> 450</span> uint3 grid [[threads_per_grid]]) {</div>
<div class="line"><a id="l00451" name="l00451"></a><span class="lineno"> 451</span> <span class="comment">// Fast four step FFT implementation for powers of 2.</span></div>
<div class="line"><a id="l00452" name="l00452"></a><span class="lineno"> 452</span> <span class="keywordtype">int</span> overall_n = n1 * n2;</div>
<div class="line"><a id="l00453" name="l00453"></a><span class="lineno"> 453</span> <span class="keywordtype">int</span> n = step == 0 ? n1 : n2;</div>
<div class="line"><a id="l00454" name="l00454"></a><span class="lineno"> 454</span> <span class="keywordtype">int</span> stride = step == 0 ? n2 : n1;</div>
<div class="line"><a id="l00455" name="l00455"></a><span class="lineno"> 455</span> </div>
<div class="line"><a id="l00456" name="l00456"></a><span class="lineno"> 456</span> <span class="comment">// The number of the threads we&#39;re using for each DFT</span></div>
<div class="line"><a id="l00457" name="l00457"></a><span class="lineno"> 457</span> <span class="keywordtype">int</span> m = grid.z;</div>
<div class="line"><a id="l00458" name="l00458"></a><span class="lineno"> 458</span> <span class="keywordtype">int</span> fft_idx = elem.z;</div>
<div class="line"><a id="l00459" name="l00459"></a><span class="lineno"> 459</span> </div>
<div class="line"><a id="l00460" name="l00460"></a><span class="lineno"> 460</span> threadgroup float2 shared_in[tg_mem_size];</div>
<div class="line"><a id="l00461" name="l00461"></a><span class="lineno"> 461</span> threadgroup float2* buf = &amp;shared_in[elem.y * n];</div>
<div class="line"><a id="l00462" name="l00462"></a><span class="lineno"> 462</span> </div>
<div class="line"><a id="l00463" name="l00463"></a><span class="lineno"> 463</span> <span class="keyword">using </span>read_writer_t = <a class="code hl_struct" href="struct_read_writer.html">ReadWriter&lt;in_T, out_T, step, real&gt;</a>;</div>
<div class="line"><a id="l00464" name="l00464"></a><span class="lineno"> 464</span> read_writer_t read_writer = read_writer_t(</div>
<div class="line"><a id="l00465" name="l00465"></a><span class="lineno"> 465</span> in,</div>
<div class="line"><a id="l00466" name="l00466"></a><span class="lineno"> 466</span> &amp;shared_in[0],</div>
<div class="line"><a id="l00467" name="l00467"></a><span class="lineno"> 467</span> out,</div>
<div class="line"><a id="l00468" name="l00468"></a><span class="lineno"> 468</span> n,</div>
<div class="line"><a id="l00469" name="l00469"></a><span class="lineno"> 469</span> batch_size,</div>
<div class="line"><a id="l00470" name="l00470"></a><span class="lineno"> 470</span> <a class="code hl_variable" href="backend_2metal_2kernels_2fft_8h.html#ad395c11e6f2aee72cd1928fba93a35a3">elems_per_thread_</a>,</div>
<div class="line"><a id="l00471" name="l00471"></a><span class="lineno"> 471</span> elem,</div>
<div class="line"><a id="l00472" name="l00472"></a><span class="lineno"> 472</span> grid,</div>
<div class="line"><a id="l00473" name="l00473"></a><span class="lineno"> 473</span> <a class="code hl_variable" href="backend_2metal_2kernels_2fft_8h.html#a7a83318497519ff3ff0141b7d511ed38">inv_</a>);</div>
<div class="line"><a id="l00474" name="l00474"></a><span class="lineno"> 474</span> </div>
<div class="line"><a id="l00475" name="l00475"></a><span class="lineno"> 475</span> <span class="keywordflow">if</span> (read_writer.out_of_bounds()) {</div>
<div class="line"><a id="l00476" name="l00476"></a><span class="lineno"> 476</span> <span class="keywordflow">return</span>;</div>
<div class="line"><a id="l00477" name="l00477"></a><span class="lineno"> 477</span> };</div>
<div class="line"><a id="l00478" name="l00478"></a><span class="lineno"> 478</span> read_writer.load_strided(stride, overall_n);</div>
<div class="line"><a id="l00479" name="l00479"></a><span class="lineno"> 479</span> </div>
<div class="line"><a id="l00480" name="l00480"></a><span class="lineno"> 480</span> threadgroup_barrier(mem_flags::mem_threadgroup);</div>
<div class="line"><a id="l00481" name="l00481"></a><span class="lineno"> 481</span> </div>
<div class="line"><a id="l00482" name="l00482"></a><span class="lineno"> 482</span> <span class="keywordtype">int</span> p = 1;</div>
<div class="line"><a id="l00483" name="l00483"></a><span class="lineno"> 483</span> <a class="code hl_function" href="backend_2metal_2kernels_2fft_8h.html#a050ead8fa5cacdaec13d68ca3c0dcb81">perform_fft</a>(fft_idx, &amp;p, m, n, buf);</div>
<div class="line"><a id="l00484" name="l00484"></a><span class="lineno"> 484</span> </div>
<div class="line"><a id="l00485" name="l00485"></a><span class="lineno"> 485</span> read_writer.write_strided(stride, overall_n);</div>
<div class="line"><a id="l00486" name="l00486"></a><span class="lineno"> 486</span>}</div>
</div>
<div class="ttc" id="abackend_2metal_2kernels_2fft_8h_html_a020469d1aca557ff1b49414f121dedbb"><div class="ttname"><a href="backend_2metal_2kernels_2fft_8h.html#a020469d1aca557ff1b49414f121dedbb">rader_6_steps_</a></div><div class="ttdeci">static constant constexpr const int rader_6_steps_</div><div class="ttdef"><b>Definition</b> fft.h:43</div></div>
<div class="ttc" id="abackend_2metal_2kernels_2fft_8h_html_a050ead8fa5cacdaec13d68ca3c0dcb81"><div class="ttname"><a href="backend_2metal_2kernels_2fft_8h.html#a050ead8fa5cacdaec13d68ca3c0dcb81">perform_fft</a></div><div class="ttdeci">METAL_FUNC void perform_fft(int fft_idx, thread int *p, int m, int n, threadgroup float2 *buf)</div><div class="ttdef"><b>Definition</b> fft.h:159</div></div>
<div class="ttc" id="abackend_2metal_2kernels_2fft_8h_html_a0abc609e9756475800e996775a96a87e"><div class="ttname"><a href="backend_2metal_2kernels_2fft_8h.html#a0abc609e9756475800e996775a96a87e">bluestein_fft</a></div><div class="ttdeci">void bluestein_fft(const device in_T *in, device out_T *out, const device float2 *w_q, const device float2 *w_k, constant const int &amp;length, constant const int &amp;n, constant const int &amp;batch_size, uint3 elem, uint3 grid)</div><div class="ttdef"><b>Definition</b> fft.h:374</div></div>
<div class="ttc" id="abackend_2metal_2kernels_2fft_8h_html_a0d437aef17faf8d9707ae7ffe68fdb30"><div class="ttname"><a href="backend_2metal_2kernels_2fft_8h.html#a0d437aef17faf8d9707ae7ffe68fdb30">rader_7_steps_</a></div><div class="ttdeci">static constant constexpr const int rader_7_steps_</div><div class="ttdef"><b>Definition</b> fft.h:42</div></div>
<div class="ttc" id="abackend_2metal_2kernels_2fft_8h_html_a12d99a846c3686806bab6c42148e1039"><div class="ttname"><a href="backend_2metal_2kernels_2fft_8h.html#a12d99a846c3686806bab6c42148e1039">radix_4_steps_</a></div><div class="ttdeci">static constant constexpr const int radix_4_steps_</div><div class="ttdef"><b>Definition</b> fft.h:35</div></div>
<div class="ttc" id="abackend_2metal_2kernels_2fft_8h_html_a1f3c377d05da52429172e64132dba750"><div class="ttname"><a href="backend_2metal_2kernels_2fft_8h.html#a1f3c377d05da52429172e64132dba750">rader_11_steps_</a></div><div class="ttdeci">static constant constexpr const int rader_11_steps_</div><div class="ttdef"><b>Definition</b> fft.h:40</div></div>
<div class="ttc" id="abackend_2metal_2kernels_2fft_8h_html_a20d24f3e040d3d226a70d4dd7c9ac6a9"><div class="ttname"><a href="backend_2metal_2kernels_2fft_8h.html#a20d24f3e040d3d226a70d4dd7c9ac6a9">rader_13_steps_</a></div><div class="ttdeci">static constant constexpr const int rader_13_steps_</div><div class="ttdef"><b>Definition</b> fft.h:39</div></div>
<div class="ttc" id="abackend_2metal_2kernels_2fft_8h_html_a2145cc8ab4d07583a735317b3cf60d55"><div class="ttname"><a href="backend_2metal_2kernels_2fft_8h.html#a2145cc8ab4d07583a735317b3cf60d55">radix_7_steps_</a></div><div class="ttdeci">static constant constexpr const int radix_7_steps_</div><div class="ttdef"><b>Definition</b> fft.h:32</div></div>
<div class="ttc" id="abackend_2metal_2kernels_2fft_8h_html_a278d980ed397e6841ce0af44b9aa4396"><div class="ttname"><a href="backend_2metal_2kernels_2fft_8h.html#a278d980ed397e6841ce0af44b9aa4396">radix_butterfly</a></div><div class="ttdeci">METAL_FUNC void radix_butterfly(int i, int p, thread float2 *x, thread short *indices, thread float2 *y)</div><div class="ttdef"><b>Definition</b> fft.h:54</div></div>
<div class="ttc" id="abackend_2metal_2kernels_2fft_8h_html_a28d683cf067736d76f867f30c066317e"><div class="ttname"><a href="backend_2metal_2kernels_2fft_8h.html#a28d683cf067736d76f867f30c066317e">MAX_OUTPUT_SIZE</a></div><div class="ttdeci">#define MAX_OUTPUT_SIZE</div><div class="ttdef"><b>Definition</b> fft.h:20</div></div>
<div class="ttc" id="abackend_2metal_2kernels_2fft_8h_html_a2a4df90e329b84ee6c1890ba7c265c9c"><div class="ttname"><a href="backend_2metal_2kernels_2fft_8h.html#a2a4df90e329b84ee6c1890ba7c265c9c">is_power_of_2_</a></div><div class="ttdeci">static constant constexpr const bool is_power_of_2_</div><div class="ttdef"><b>Definition</b> fft.h:24</div></div>
<div class="ttc" id="abackend_2metal_2kernels_2fft_8h_html_a2d725bfd4c30be4c605b5c4559a62892"><div class="ttname"><a href="backend_2metal_2kernels_2fft_8h.html#a2d725bfd4c30be4c605b5c4559a62892">rader_2_steps_</a></div><div class="ttdeci">static constant constexpr const int rader_2_steps_</div><div class="ttdef"><b>Definition</b> fft.h:47</div></div>
<div class="ttc" id="abackend_2metal_2kernels_2fft_8h_html_a2f7f7cc2423cfcd4998d1a2a0363c3e2"><div class="ttname"><a href="backend_2metal_2kernels_2fft_8h.html#a2f7f7cc2423cfcd4998d1a2a0363c3e2">radix_6_steps_</a></div><div class="ttdeci">static constant constexpr const int radix_6_steps_</div><div class="ttdef"><b>Definition</b> fft.h:33</div></div>
<div class="ttc" id="abackend_2metal_2kernels_2fft_8h_html_a3cb03a97a209ba1346375e720ee76177"><div class="ttname"><a href="backend_2metal_2kernels_2fft_8h.html#a3cb03a97a209ba1346375e720ee76177">radix_8_steps_</a></div><div class="ttdeci">static constant constexpr const int radix_8_steps_</div><div class="ttdef"><b>Definition</b> fft.h:31</div></div>
<div class="ttc" id="abackend_2metal_2kernels_2fft_8h_html_a4010b0e151e5f01e610e9c32234458c7"><div class="ttname"><a href="backend_2metal_2kernels_2fft_8h.html#a4010b0e151e5f01e610e9c32234458c7">fft</a></div><div class="ttdeci">void fft(const device in_T *in, device out_T *out, constant const int &amp;n, constant const int &amp;batch_size, uint3 elem, uint3 grid)</div><div class="ttdef"><b>Definition</b> fft.h:180</div></div>
<div class="ttc" id="abackend_2metal_2kernels_2fft_8h_html_a53fdc660e99e6b5db6808bbd596cd374"><div class="ttname"><a href="backend_2metal_2kernels_2fft_8h.html#a53fdc660e99e6b5db6808bbd596cd374">radix_2_steps_</a></div><div class="ttdeci">static constant constexpr const int radix_2_steps_</div><div class="ttdef"><b>Definition</b> fft.h:37</div></div>
<div class="ttc" id="abackend_2metal_2kernels_2fft_8h_html_a579123b7be825f08f3076287dded08e3"><div class="ttname"><a href="backend_2metal_2kernels_2fft_8h.html#a579123b7be825f08f3076287dded08e3">radix_3_steps_</a></div><div class="ttdeci">static constant constexpr const int radix_3_steps_</div><div class="ttdef"><b>Definition</b> fft.h:36</div></div>
<div class="ttc" id="abackend_2metal_2kernels_2fft_8h_html_a6558a8205ee4c3e4767bafa93f7606de"><div class="ttname"><a href="backend_2metal_2kernels_2fft_8h.html#a6558a8205ee4c3e4767bafa93f7606de">four_step_fft</a></div><div class="ttdeci">void four_step_fft(const device in_T *in, device out_T *out, constant const int &amp;n1, constant const int &amp;n2, constant const int &amp;batch_size, uint3 elem, uint3 grid)</div><div class="ttdef"><b>Definition</b> fft.h:443</div></div>
<div class="ttc" id="abackend_2metal_2kernels_2fft_8h_html_a6ba62eabfd5428644aabf89ddaa0128d"><div class="ttname"><a href="backend_2metal_2kernels_2fft_8h.html#a6ba62eabfd5428644aabf89ddaa0128d">RadixFunc</a></div><div class="ttdeci">void(* RadixFunc)(thread float2 *, thread float2 *)</div><div class="ttdef"><b>Definition</b> fft.h:50</div></div>
<div class="ttc" id="abackend_2metal_2kernels_2fft_8h_html_a794032d3a9acff0e31c77c69d0007f10"><div class="ttname"><a href="backend_2metal_2kernels_2fft_8h.html#a794032d3a9acff0e31c77c69d0007f10">RADIX_STEP</a></div><div class="ttdeci">#define RADIX_STEP(radix, radix_func, num_steps)</div><div class="ttdef"><b>Definition</b> fft.h:153</div></div>
<div class="ttc" id="abackend_2metal_2kernels_2fft_8h_html_a7a83318497519ff3ff0141b7d511ed38"><div class="ttname"><a href="backend_2metal_2kernels_2fft_8h.html#a7a83318497519ff3ff0141b7d511ed38">inv_</a></div><div class="ttdeci">static constant constexpr const bool inv_</div><div class="ttdef"><b>Definition</b> fft.h:23</div></div>
<div class="ttc" id="abackend_2metal_2kernels_2fft_8h_html_a7b6e56afa21f022c5e754b000955735a"><div class="ttname"><a href="backend_2metal_2kernels_2fft_8h.html#a7b6e56afa21f022c5e754b000955735a">MAX_RADIX</a></div><div class="ttdeci">#define MAX_RADIX</div><div class="ttdef"><b>Definition</b> fft.h:17</div></div>
<div class="ttc" id="abackend_2metal_2kernels_2fft_8h_html_a7cd17bff8bc567f71d4789ee31fa07f2"><div class="ttname"><a href="backend_2metal_2kernels_2fft_8h.html#a7cd17bff8bc567f71d4789ee31fa07f2">radix_11_steps_</a></div><div class="ttdeci">static constant constexpr const int radix_11_steps_</div><div class="ttdef"><b>Definition</b> fft.h:30</div></div>
<div class="ttc" id="abackend_2metal_2kernels_2fft_8h_html_a903d5239b5f73577c559e97ff910892d"><div class="ttname"><a href="backend_2metal_2kernels_2fft_8h.html#a903d5239b5f73577c559e97ff910892d">radix_5_steps_</a></div><div class="ttdeci">static constant constexpr const int radix_5_steps_</div><div class="ttdef"><b>Definition</b> fft.h:34</div></div>
<div class="ttc" id="abackend_2metal_2kernels_2fft_8h_html_aba8d32e0911499671df93678f39da08b"><div class="ttname"><a href="backend_2metal_2kernels_2fft_8h.html#aba8d32e0911499671df93678f39da08b">radix_n_steps</a></div><div class="ttdeci">METAL_FUNC void radix_n_steps(int i, thread int *p, int m, int n, int num_steps, thread float2 *inputs, thread short *indices, thread float2 *values, threadgroup float2 *buf)</div><div class="ttdef"><b>Definition</b> fft.h:100</div></div>
<div class="ttc" id="abackend_2metal_2kernels_2fft_8h_html_abb079b86e89ca88ce13a179d9ec566af"><div class="ttname"><a href="backend_2metal_2kernels_2fft_8h.html#abb079b86e89ca88ce13a179d9ec566af">radix_13_steps_</a></div><div class="ttdeci">static constant constexpr const int radix_13_steps_</div><div class="ttdef"><b>Definition</b> fft.h:29</div></div>
<div class="ttc" id="abackend_2metal_2kernels_2fft_8h_html_ac309c77ef775a3ef13850c5287a86480"><div class="ttname"><a href="backend_2metal_2kernels_2fft_8h.html#ac309c77ef775a3ef13850c5287a86480">rader_m_</a></div><div class="ttdeci">static constant constexpr const int rader_m_</div><div class="ttdef"><b>Definition</b> fft.h:27</div></div>
<div class="ttc" id="abackend_2metal_2kernels_2fft_8h_html_ac6123e111816dd62a11ccb86b66fa3e9"><div class="ttname"><a href="backend_2metal_2kernels_2fft_8h.html#ac6123e111816dd62a11ccb86b66fa3e9">rader_8_steps_</a></div><div class="ttdeci">static constant constexpr const int rader_8_steps_</div><div class="ttdef"><b>Definition</b> fft.h:41</div></div>
<div class="ttc" id="abackend_2metal_2kernels_2fft_8h_html_ac7c58404df0434d4f861db62d3471870"><div class="ttname"><a href="backend_2metal_2kernels_2fft_8h.html#ac7c58404df0434d4f861db62d3471870">rader_4_steps_</a></div><div class="ttdeci">static constant constexpr const int rader_4_steps_</div><div class="ttdef"><b>Definition</b> fft.h:45</div></div>
<div class="ttc" id="abackend_2metal_2kernels_2fft_8h_html_ad123452303f6415904f3592f660769b8"><div class="ttname"><a href="backend_2metal_2kernels_2fft_8h.html#ad123452303f6415904f3592f660769b8">rader_fft</a></div><div class="ttdeci">void rader_fft(const device in_T *in, device out_T *out, const device float2 *raders_b_q, const device short *raders_g_q, const device short *raders_g_minus_q, constant const int &amp;n, constant const int &amp;batch_size, constant const int &amp;rader_n, uint3 elem, uint3 grid)</div><div class="ttdef"><b>Definition</b> fft.h:219</div></div>
<div class="ttc" id="abackend_2metal_2kernels_2fft_8h_html_ad395c11e6f2aee72cd1928fba93a35a3"><div class="ttname"><a href="backend_2metal_2kernels_2fft_8h.html#ad395c11e6f2aee72cd1928fba93a35a3">elems_per_thread_</a></div><div class="ttdeci">static constant constexpr const int elems_per_thread_</div><div class="ttdef"><b>Definition</b> fft.h:25</div></div>
<div class="ttc" id="abackend_2metal_2kernels_2fft_8h_html_adb129cc3808c08fd95af9795bfc7ae63"><div class="ttname"><a href="backend_2metal_2kernels_2fft_8h.html#adb129cc3808c08fd95af9795bfc7ae63">rader_3_steps_</a></div><div class="ttdeci">static constant constexpr const int rader_3_steps_</div><div class="ttdef"><b>Definition</b> fft.h:46</div></div>
<div class="ttc" id="abackend_2metal_2kernels_2fft_8h_html_afea05e9a7105bafbaafca25042f4d1b4"><div class="ttname"><a href="backend_2metal_2kernels_2fft_8h.html#afea05e9a7105bafbaafca25042f4d1b4">rader_5_steps_</a></div><div class="ttdeci">static constant constexpr const int rader_5_steps_</div><div class="ttdef"><b>Definition</b> fft.h:44</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="anamespacemetal_html"><div class="ttname"><a href="namespacemetal.html">metal</a></div><div class="ttdef"><b>Definition</b> bf16_math.h:226</div></div>
<div class="ttc" id="anamespacemetal_html_a6653b28c9473087141eddce39878d4d3"><div class="ttname"><a href="namespacemetal.html#a6653b28c9473087141eddce39878d4d3">metal::min</a></div><div class="ttdeci">METAL_FUNC bfloat16_t min(bfloat16_t x, bfloat16_t y)</div><div class="ttdef"><b>Definition</b> bf16_math.h:232</div></div>
<div class="ttc" id="anamespacemlx_1_1core_1_1simd_html_acdf822b7626bbab6a495552aea3457b5"><div class="ttname"><a href="namespacemlx_1_1core_1_1simd.html#acdf822b7626bbab6a495552aea3457b5">mlx::core::simd::real</a></div><div class="ttdeci">auto real(Simd&lt; T, 1 &gt; in) -&gt; Simd&lt; decltype(std::real(in.value)), 1 &gt;</div><div class="ttdef"><b>Definition</b> base_simd.h:98</div></div>
<div class="ttc" id="aradix_8h_html"><div class="ttname"><a href="radix_8h.html">radix.h</a></div></div>
<div class="ttc" id="aradix_8h_html_a026e6779e6d2ecdef39ff4aad186091e"><div class="ttname"><a href="radix_8h.html#a026e6779e6d2ecdef39ff4aad186091e">radix5</a></div><div class="ttdeci">METAL_FUNC void radix5(thread float2 *x, thread float2 *y)</div><div class="ttdef"><b>Definition</b> radix.h:69</div></div>
<div class="ttc" id="aradix_8h_html_a12cb26bd3ad635d16a195ccea750256d"><div class="ttname"><a href="radix_8h.html#a12cb26bd3ad635d16a195ccea750256d">radix4</a></div><div class="ttdeci">METAL_FUNC void radix4(thread float2 *x, thread float2 *y)</div><div class="ttdef"><b>Definition</b> radix.h:56</div></div>
<div class="ttc" id="aradix_8h_html_a34f7dcefd29f8a7f6bddf9a17609a8a7"><div class="ttname"><a href="radix_8h.html#a34f7dcefd29f8a7f6bddf9a17609a8a7">radix11</a></div><div class="ttdeci">METAL_FUNC void radix11(thread float2 *x, thread float2 *y)</div><div class="ttdef"><b>Definition</b> radix.h:201</div></div>
<div class="ttc" id="aradix_8h_html_a497b31cfa28418e1c2fad53d09f7bc0b"><div class="ttname"><a href="radix_8h.html#a497b31cfa28418e1c2fad53d09f7bc0b">radix3</a></div><div class="ttdeci">METAL_FUNC void radix3(thread float2 *x, thread float2 *y)</div><div class="ttdef"><b>Definition</b> radix.h:41</div></div>
<div class="ttc" id="aradix_8h_html_a5bfc53b531214c9ce277bebc18aa67d6"><div class="ttname"><a href="radix_8h.html#a5bfc53b531214c9ce277bebc18aa67d6">complex_mul</a></div><div class="ttdeci">METAL_FUNC float2 complex_mul(float2 a, float2 b)</div><div class="ttdef"><b>Definition</b> radix.h:19</div></div>
<div class="ttc" id="aradix_8h_html_a6b306e1afe1c5b6af4cd80aa02adb138"><div class="ttname"><a href="radix_8h.html#a6b306e1afe1c5b6af4cd80aa02adb138">radix8</a></div><div class="ttdeci">METAL_FUNC void radix8(thread float2 *x, thread float2 *y)</div><div class="ttdef"><b>Definition</b> radix.h:151</div></div>
<div class="ttc" id="aradix_8h_html_a6d37e483d806c550deefabf56caf4ec8"><div class="ttname"><a href="radix_8h.html#a6d37e483d806c550deefabf56caf4ec8">radix7</a></div><div class="ttdeci">METAL_FUNC void radix7(thread float2 *x, thread float2 *y)</div><div class="ttdef"><b>Definition</b> radix.h:122</div></div>
<div class="ttc" id="aradix_8h_html_a745e50244f1470bba233d8b6b993729c"><div class="ttname"><a href="radix_8h.html#a745e50244f1470bba233d8b6b993729c">radix2</a></div><div class="ttdeci">METAL_FUNC void radix2(thread float2 *x, thread float2 *y)</div><div class="ttdef"><b>Definition</b> radix.h:36</div></div>
<div class="ttc" id="aradix_8h_html_a833b7b31facbd62f6971bb108c54d1db"><div class="ttname"><a href="radix_8h.html#a833b7b31facbd62f6971bb108c54d1db">radix13</a></div><div class="ttdeci">METAL_FUNC void radix13(thread float2 *x, thread float2 *y)</div><div class="ttdef"><b>Definition</b> radix.h:290</div></div>
<div class="ttc" id="aradix_8h_html_ac5cf950316b9445296ee9ecfc56a56bd"><div class="ttname"><a href="radix_8h.html#ac5cf950316b9445296ee9ecfc56a56bd">get_twiddle</a></div><div class="ttdeci">METAL_FUNC float2 get_twiddle(int k, int p)</div><div class="ttdef"><b>Definition</b> radix.h:29</div></div>
<div class="ttc" id="aradix_8h_html_afaaa5de58a97f0a5e6a84fc0d598a884"><div class="ttname"><a href="radix_8h.html#afaaa5de58a97f0a5e6a84fc0d598a884">radix6</a></div><div class="ttdeci">METAL_FUNC void radix6(thread float2 *x, thread float2 *y)</div><div class="ttdef"><b>Definition</b> radix.h:96</div></div>
<div class="ttc" id="areadwrite_8h_html"><div class="ttname"><a href="readwrite_8h.html">readwrite.h</a></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>
<div class="ttc" id="asteel_2defines_8h_html_a90b91c866313ffa46eff6d9cc944ad2b"><div class="ttname"><a href="steel_2defines_8h.html#a90b91c866313ffa46eff6d9cc944ad2b">STEEL_CONST</a></div><div class="ttdeci">#define STEEL_CONST</div><div class="ttdef"><b>Definition</b> defines.h:3</div></div>
<div class="ttc" id="astruct_read_writer_html"><div class="ttname"><a href="struct_read_writer.html">ReadWriter</a></div><div class="ttdef"><b>Definition</b> readwrite.h:35</div></div>
</div><!-- fragment --></div><!-- contents -->
</div><!-- doc-content -->
<!-- start footer part -->
<div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
<ul>
<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><li class="navelem"><a class="el" href="backend_2metal_2kernels_2fft_8h.html">fft.h</a></li>
<li class="footer">Generated by <a href="https://www.doxygen.org/index.html"><img class="footer" src="doxygen.svg" width="104" height="31" alt="doxygen"/></a> 1.13.2 </li>
</ul>
</div>
</body>
</html>
Reference in New Issue View Git Blame Copy Permalink