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<a href="radix_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">/* Radix kernels</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">We provide optimized, single threaded Radix codelets</span></div>
<div class="line"><a id="l00006" name="l00006"></a><span class="lineno"> 6</span><span class="comment">for n=2,3,4,5,6,7,8,10,11,12,13.</span></div>
<div class="line"><a id="l00007" name="l00007"></a><span class="lineno"> 7</span><span class="comment"></span> </div>
<div class="line"><a id="l00008" name="l00008"></a><span class="lineno"> 8</span><span class="comment">For n=2,3,4,5,6 we hand write the codelets.</span></div>
<div class="line"><a id="l00009" name="l00009"></a><span class="lineno"> 9</span><span class="comment">For n=8,10,12 we combine smaller codelets.</span></div>
<div class="line"><a id="l00010" name="l00010"></a><span class="lineno"> 10</span><span class="comment">For n=7,11,13 we use Rader&#39;s algorithm which decomposes</span></div>
<div class="line"><a id="l00011" name="l00011"></a><span class="lineno"> 11</span><span class="comment">them into (n-1)=6,10,12 codelets. */</span></div>
<div class="line"><a id="l00012" name="l00012"></a><span class="lineno"> 12</span> </div>
<div class="line"><a id="l00013" name="l00013"></a><span class="lineno"> 13</span><span class="preprocessor">#pragma once</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="preprocessor">#include &lt;metal_common&gt;</span></div>
<div class="line"><a id="l00016" name="l00016"></a><span class="lineno"> 16</span><span class="preprocessor">#include &lt;metal_math&gt;</span></div>
<div class="line"><a id="l00017" name="l00017"></a><span class="lineno"> 17</span><span class="preprocessor">#include &lt;metal_stdlib&gt;</span></div>
<div class="line"><a id="l00018" name="l00018"></a><span class="lineno"> 18</span> </div>
<div class="foldopen" id="foldopen00019" data-start="{" data-end="}">
<div class="line"><a id="l00019" name="l00019"></a><span class="lineno"><a class="line" href="radix_8h.html#a5bfc53b531214c9ce277bebc18aa67d6"> 19</a></span>METAL_FUNC float2 <a class="code hl_function" href="radix_8h.html#a5bfc53b531214c9ce277bebc18aa67d6">complex_mul</a>(float2 a, float2 b) {</div>
<div class="line"><a id="l00020" name="l00020"></a><span class="lineno"> 20</span> <span class="keywordflow">return</span> float2(a.x * b.x - a.y * b.y, a.x * b.y + a.y * b.x);</div>
<div class="line"><a id="l00021" name="l00021"></a><span class="lineno"> 21</span>}</div>
</div>
<div class="line"><a id="l00022" name="l00022"></a><span class="lineno"> 22</span> </div>
<div class="line"><a id="l00023" name="l00023"></a><span class="lineno"> 23</span><span class="comment">// Complex mul followed by conjugate</span></div>
<div class="foldopen" id="foldopen00024" data-start="{" data-end="}">
<div class="line"><a id="l00024" name="l00024"></a><span class="lineno"><a class="line" href="radix_8h.html#a0e2dfd3d1dda09f47ccc64eec35629f3"> 24</a></span>METAL_FUNC float2 <a class="code hl_function" href="radix_8h.html#a0e2dfd3d1dda09f47ccc64eec35629f3">complex_mul_conj</a>(float2 a, float2 b) {</div>
<div class="line"><a id="l00025" name="l00025"></a><span class="lineno"> 25</span> <span class="keywordflow">return</span> float2(a.x * b.x - a.y * b.y, -a.x * b.y - a.y * b.x);</div>
<div class="line"><a id="l00026" name="l00026"></a><span class="lineno"> 26</span>}</div>
</div>
<div class="line"><a id="l00027" name="l00027"></a><span class="lineno"> 27</span> </div>
<div class="line"><a id="l00028" name="l00028"></a><span class="lineno"> 28</span><span class="comment">// Compute an FFT twiddle factor</span></div>
<div class="foldopen" id="foldopen00029" data-start="{" data-end="}">
<div class="line"><a id="l00029" name="l00029"></a><span class="lineno"><a class="line" href="radix_8h.html#ac5cf950316b9445296ee9ecfc56a56bd"> 29</a></span>METAL_FUNC float2 <a class="code hl_function" href="radix_8h.html#ac5cf950316b9445296ee9ecfc56a56bd">get_twiddle</a>(<span class="keywordtype">int</span> k, <span class="keywordtype">int</span> p) {</div>
<div class="line"><a id="l00030" name="l00030"></a><span class="lineno"> 30</span> <span class="keywordtype">float</span> theta = -2.0f * k * M_PI_F / p;</div>
<div class="line"><a id="l00031" name="l00031"></a><span class="lineno"> 31</span> </div>
<div class="line"><a id="l00032" name="l00032"></a><span class="lineno"> 32</span> float2 twiddle = {<a class="code hl_function" href="namespacemetal_1_1fast.html#a75b6bb32fa3870eda46a7bfc9f481f88">metal::fast::cos</a>(theta), <a class="code hl_function" href="namespacemetal_1_1fast.html#a3af771cfe7a135104f9d063147dba270">metal::fast::sin</a>(theta)};</div>
<div class="line"><a id="l00033" name="l00033"></a><span class="lineno"> 33</span> <span class="keywordflow">return</span> twiddle;</div>
<div class="line"><a id="l00034" name="l00034"></a><span class="lineno"> 34</span>}</div>
</div>
<div class="line"><a id="l00035" name="l00035"></a><span class="lineno"> 35</span> </div>
<div class="foldopen" id="foldopen00036" data-start="{" data-end="}">
<div class="line"><a id="l00036" name="l00036"></a><span class="lineno"><a class="line" href="radix_8h.html#a745e50244f1470bba233d8b6b993729c"> 36</a></span>METAL_FUNC <span class="keywordtype">void</span> <a class="code hl_function" href="radix_8h.html#a745e50244f1470bba233d8b6b993729c">radix2</a>(thread float2* x, thread float2* y) {</div>
<div class="line"><a id="l00037" name="l00037"></a><span class="lineno"> 37</span> y[0] = x[0] + x[1];</div>
<div class="line"><a id="l00038" name="l00038"></a><span class="lineno"> 38</span> y[1] = x[0] - x[1];</div>
<div class="line"><a id="l00039" name="l00039"></a><span class="lineno"> 39</span>}</div>
</div>
<div class="line"><a id="l00040" name="l00040"></a><span class="lineno"> 40</span> </div>
<div class="foldopen" id="foldopen00041" data-start="{" data-end="}">
<div class="line"><a id="l00041" name="l00041"></a><span class="lineno"><a class="line" href="radix_8h.html#a497b31cfa28418e1c2fad53d09f7bc0b"> 41</a></span>METAL_FUNC <span class="keywordtype">void</span> <a class="code hl_function" href="radix_8h.html#a497b31cfa28418e1c2fad53d09f7bc0b">radix3</a>(thread float2* x, thread float2* y) {</div>
<div class="line"><a id="l00042" name="l00042"></a><span class="lineno"> 42</span> <span class="keywordtype">float</span> pi_2_3 = -0.8660254037844387;</div>
<div class="line"><a id="l00043" name="l00043"></a><span class="lineno"> 43</span> </div>
<div class="line"><a id="l00044" name="l00044"></a><span class="lineno"> 44</span> float2 a_1 = x[1] + x[2];</div>
<div class="line"><a id="l00045" name="l00045"></a><span class="lineno"> 45</span> float2 a_2 = x[1] - x[2];</div>
<div class="line"><a id="l00046" name="l00046"></a><span class="lineno"> 46</span> </div>
<div class="line"><a id="l00047" name="l00047"></a><span class="lineno"> 47</span> y[0] = x[0] + a_1;</div>
<div class="line"><a id="l00048" name="l00048"></a><span class="lineno"> 48</span> float2 b_1 = x[0] - 0.5 * a_1;</div>
<div class="line"><a id="l00049" name="l00049"></a><span class="lineno"> 49</span> float2 b_2 = pi_2_3 * a_2;</div>
<div class="line"><a id="l00050" name="l00050"></a><span class="lineno"> 50</span> </div>
<div class="line"><a id="l00051" name="l00051"></a><span class="lineno"> 51</span> float2 b_2_j = {-b_2.y, b_2.x};</div>
<div class="line"><a id="l00052" name="l00052"></a><span class="lineno"> 52</span> y[1] = b_1 + b_2_j;</div>
<div class="line"><a id="l00053" name="l00053"></a><span class="lineno"> 53</span> y[2] = b_1 - b_2_j;</div>
<div class="line"><a id="l00054" name="l00054"></a><span class="lineno"> 54</span>}</div>
</div>
<div class="line"><a id="l00055" name="l00055"></a><span class="lineno"> 55</span> </div>
<div class="foldopen" id="foldopen00056" data-start="{" data-end="}">
<div class="line"><a id="l00056" name="l00056"></a><span class="lineno"><a class="line" href="radix_8h.html#a12cb26bd3ad635d16a195ccea750256d"> 56</a></span>METAL_FUNC <span class="keywordtype">void</span> <a class="code hl_function" href="radix_8h.html#a12cb26bd3ad635d16a195ccea750256d">radix4</a>(thread float2* x, thread float2* y) {</div>
<div class="line"><a id="l00057" name="l00057"></a><span class="lineno"> 57</span> float2 z_0 = x[0] + x[2];</div>
<div class="line"><a id="l00058" name="l00058"></a><span class="lineno"> 58</span> float2 z_1 = x[0] - x[2];</div>
<div class="line"><a id="l00059" name="l00059"></a><span class="lineno"> 59</span> float2 z_2 = x[1] + x[3];</div>
<div class="line"><a id="l00060" name="l00060"></a><span class="lineno"> 60</span> float2 z_3 = x[1] - x[3];</div>
<div class="line"><a id="l00061" name="l00061"></a><span class="lineno"> 61</span> float2 z_3_i = {z_3.y, -z_3.x};</div>
<div class="line"><a id="l00062" name="l00062"></a><span class="lineno"> 62</span> </div>
<div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</span> y[0] = z_0 + z_2;</div>
<div class="line"><a id="l00064" name="l00064"></a><span class="lineno"> 64</span> y[1] = z_1 + z_3_i;</div>
<div class="line"><a id="l00065" name="l00065"></a><span class="lineno"> 65</span> y[2] = z_0 - z_2;</div>
<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"> 66</span> y[3] = z_1 - z_3_i;</div>
<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"> 67</span>}</div>
</div>
<div class="line"><a id="l00068" name="l00068"></a><span class="lineno"> 68</span> </div>
<div class="foldopen" id="foldopen00069" data-start="{" data-end="}">
<div class="line"><a id="l00069" name="l00069"></a><span class="lineno"><a class="line" href="radix_8h.html#a026e6779e6d2ecdef39ff4aad186091e"> 69</a></span>METAL_FUNC <span class="keywordtype">void</span> <a class="code hl_function" href="radix_8h.html#a026e6779e6d2ecdef39ff4aad186091e">radix5</a>(thread float2* x, thread float2* y) {</div>
<div class="line"><a id="l00070" name="l00070"></a><span class="lineno"> 70</span> float2 root_5_4 = 0.5590169943749475;</div>
<div class="line"><a id="l00071" name="l00071"></a><span class="lineno"> 71</span> float2 sin_2pi_5 = 0.9510565162951535;</div>
<div class="line"><a id="l00072" name="l00072"></a><span class="lineno"> 72</span> float2 sin_1pi_5 = 0.5877852522924731;</div>
<div class="line"><a id="l00073" name="l00073"></a><span class="lineno"> 73</span> </div>
<div class="line"><a id="l00074" name="l00074"></a><span class="lineno"> 74</span> float2 a_1 = x[1] + x[4];</div>
<div class="line"><a id="l00075" name="l00075"></a><span class="lineno"> 75</span> float2 a_2 = x[2] + x[3];</div>
<div class="line"><a id="l00076" name="l00076"></a><span class="lineno"> 76</span> float2 a_3 = x[1] - x[4];</div>
<div class="line"><a id="l00077" name="l00077"></a><span class="lineno"> 77</span> float2 a_4 = x[2] - x[3];</div>
<div class="line"><a id="l00078" name="l00078"></a><span class="lineno"> 78</span> </div>
<div class="line"><a id="l00079" name="l00079"></a><span class="lineno"> 79</span> float2 a_5 = a_1 + a_2;</div>
<div class="line"><a id="l00080" name="l00080"></a><span class="lineno"> 80</span> float2 a_6 = root_5_4 * (a_1 - a_2);</div>
<div class="line"><a id="l00081" name="l00081"></a><span class="lineno"> 81</span> float2 a_7 = x[0] - a_5 / 4;</div>
<div class="line"><a id="l00082" name="l00082"></a><span class="lineno"> 82</span> float2 a_8 = a_7 + a_6;</div>
<div class="line"><a id="l00083" name="l00083"></a><span class="lineno"> 83</span> float2 a_9 = a_7 - a_6;</div>
<div class="line"><a id="l00084" name="l00084"></a><span class="lineno"> 84</span> float2 a_10 = sin_2pi_5 * a_3 + sin_1pi_5 * a_4;</div>
<div class="line"><a id="l00085" name="l00085"></a><span class="lineno"> 85</span> float2 a_11 = sin_1pi_5 * a_3 - sin_2pi_5 * a_4;</div>
<div class="line"><a id="l00086" name="l00086"></a><span class="lineno"> 86</span> float2 a_10_j = {a_10.y, -a_10.x};</div>
<div class="line"><a id="l00087" name="l00087"></a><span class="lineno"> 87</span> float2 a_11_j = {a_11.y, -a_11.x};</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> y[0] = x[0] + a_5;</div>
<div class="line"><a id="l00090" name="l00090"></a><span class="lineno"> 90</span> y[1] = a_8 + a_10_j;</div>
<div class="line"><a id="l00091" name="l00091"></a><span class="lineno"> 91</span> y[2] = a_9 + a_11_j;</div>
<div class="line"><a id="l00092" name="l00092"></a><span class="lineno"> 92</span> y[3] = a_9 - a_11_j;</div>
<div class="line"><a id="l00093" name="l00093"></a><span class="lineno"> 93</span> y[4] = a_8 - a_10_j;</div>
<div class="line"><a id="l00094" name="l00094"></a><span class="lineno"> 94</span>}</div>
</div>
<div class="line"><a id="l00095" name="l00095"></a><span class="lineno"> 95</span> </div>
<div class="foldopen" id="foldopen00096" data-start="{" data-end="}">
<div class="line"><a id="l00096" name="l00096"></a><span class="lineno"><a class="line" href="radix_8h.html#afaaa5de58a97f0a5e6a84fc0d598a884"> 96</a></span>METAL_FUNC <span class="keywordtype">void</span> <a class="code hl_function" href="radix_8h.html#afaaa5de58a97f0a5e6a84fc0d598a884">radix6</a>(thread float2* x, thread float2* y) {</div>
<div class="line"><a id="l00097" name="l00097"></a><span class="lineno"> 97</span> <span class="keywordtype">float</span> sin_pi_3 = 0.8660254037844387;</div>
<div class="line"><a id="l00098" name="l00098"></a><span class="lineno"> 98</span> float2 a_1 = x[2] + x[4];</div>
<div class="line"><a id="l00099" name="l00099"></a><span class="lineno"> 99</span> float2 a_2 = x[0] - a_1 / 2;</div>
<div class="line"><a id="l00100" name="l00100"></a><span class="lineno"> 100</span> float2 a_3 = sin_pi_3 * (x[2] - x[4]);</div>
<div class="line"><a id="l00101" name="l00101"></a><span class="lineno"> 101</span> float2 a_4 = x[5] + x[1];</div>
<div class="line"><a id="l00102" name="l00102"></a><span class="lineno"> 102</span> float2 a_5 = x[3] - a_4 / 2;</div>
<div class="line"><a id="l00103" name="l00103"></a><span class="lineno"> 103</span> float2 a_6 = sin_pi_3 * (x[5] - x[1]);</div>
<div class="line"><a id="l00104" name="l00104"></a><span class="lineno"> 104</span> float2 a_7 = x[0] + a_1;</div>
<div class="line"><a id="l00105" name="l00105"></a><span class="lineno"> 105</span> </div>
<div class="line"><a id="l00106" name="l00106"></a><span class="lineno"> 106</span> float2 a_3_i = {a_3.y, -a_3.x};</div>
<div class="line"><a id="l00107" name="l00107"></a><span class="lineno"> 107</span> float2 a_6_i = {a_6.y, -a_6.x};</div>
<div class="line"><a id="l00108" name="l00108"></a><span class="lineno"> 108</span> float2 a_8 = a_2 + a_3_i;</div>
<div class="line"><a id="l00109" name="l00109"></a><span class="lineno"> 109</span> float2 a_9 = a_2 - a_3_i;</div>
<div class="line"><a id="l00110" name="l00110"></a><span class="lineno"> 110</span> float2 a_10 = x[3] + a_4;</div>
<div class="line"><a id="l00111" name="l00111"></a><span class="lineno"> 111</span> float2 a_11 = a_5 + a_6_i;</div>
<div class="line"><a id="l00112" name="l00112"></a><span class="lineno"> 112</span> float2 a_12 = a_5 - a_6_i;</div>
<div class="line"><a id="l00113" name="l00113"></a><span class="lineno"> 113</span> </div>
<div class="line"><a id="l00114" name="l00114"></a><span class="lineno"> 114</span> y[0] = a_7 + a_10;</div>
<div class="line"><a id="l00115" name="l00115"></a><span class="lineno"> 115</span> y[1] = a_8 - a_11;</div>
<div class="line"><a id="l00116" name="l00116"></a><span class="lineno"> 116</span> y[2] = a_9 + a_12;</div>
<div class="line"><a id="l00117" name="l00117"></a><span class="lineno"> 117</span> y[3] = a_7 - a_10;</div>
<div class="line"><a id="l00118" name="l00118"></a><span class="lineno"> 118</span> y[4] = a_8 + a_11;</div>
<div class="line"><a id="l00119" name="l00119"></a><span class="lineno"> 119</span> y[5] = a_9 - a_12;</div>
<div class="line"><a id="l00120" name="l00120"></a><span class="lineno"> 120</span>}</div>
</div>
<div class="line"><a id="l00121" name="l00121"></a><span class="lineno"> 121</span> </div>
<div class="foldopen" id="foldopen00122" data-start="{" data-end="}">
<div class="line"><a id="l00122" name="l00122"></a><span class="lineno"><a class="line" href="radix_8h.html#a6d37e483d806c550deefabf56caf4ec8"> 122</a></span>METAL_FUNC <span class="keywordtype">void</span> <a class="code hl_function" href="radix_8h.html#a6d37e483d806c550deefabf56caf4ec8">radix7</a>(thread float2* x, thread float2* y) {</div>
<div class="line"><a id="l00123" name="l00123"></a><span class="lineno"> 123</span> <span class="comment">// Rader&#39;s algorithm</span></div>
<div class="line"><a id="l00124" name="l00124"></a><span class="lineno"> 124</span> float2 inv = {1 / 6.0, -1 / 6.0};</div>
<div class="line"><a id="l00125" name="l00125"></a><span class="lineno"> 125</span> </div>
<div class="line"><a id="l00126" name="l00126"></a><span class="lineno"> 126</span> <span class="comment">// fft</span></div>
<div class="line"><a id="l00127" name="l00127"></a><span class="lineno"> 127</span> float2 in1[6] = {x[1], x[3], x[2], x[6], x[4], x[5]};</div>
<div class="line"><a id="l00128" name="l00128"></a><span class="lineno"> 128</span> <a class="code hl_function" href="radix_8h.html#afaaa5de58a97f0a5e6a84fc0d598a884">radix6</a>(in1, y + 1);</div>
<div class="line"><a id="l00129" name="l00129"></a><span class="lineno"> 129</span> </div>
<div class="line"><a id="l00130" name="l00130"></a><span class="lineno"> 130</span> y[0] = y[1] + x[0];</div>
<div class="line"><a id="l00131" name="l00131"></a><span class="lineno"> 131</span> </div>
<div class="line"><a id="l00132" name="l00132"></a><span class="lineno"> 132</span> <span class="comment">// b_q</span></div>
<div class="line"><a id="l00133" name="l00133"></a><span class="lineno"> 133</span> y[1] = <a class="code hl_function" href="radix_8h.html#a0e2dfd3d1dda09f47ccc64eec35629f3">complex_mul_conj</a>(y[1], float2(-1, 0));</div>
<div class="line"><a id="l00134" name="l00134"></a><span class="lineno"> 134</span> y[2] = <a class="code hl_function" href="radix_8h.html#a0e2dfd3d1dda09f47ccc64eec35629f3">complex_mul_conj</a>(y[2], float2(2.44013336, -1.02261879));</div>
<div class="line"><a id="l00135" name="l00135"></a><span class="lineno"> 135</span> y[3] = <a class="code hl_function" href="radix_8h.html#a0e2dfd3d1dda09f47ccc64eec35629f3">complex_mul_conj</a>(y[3], float2(2.37046941, -1.17510629));</div>
<div class="line"><a id="l00136" name="l00136"></a><span class="lineno"> 136</span> y[4] = <a class="code hl_function" href="radix_8h.html#a0e2dfd3d1dda09f47ccc64eec35629f3">complex_mul_conj</a>(y[4], float2(0, -2.64575131));</div>
<div class="line"><a id="l00137" name="l00137"></a><span class="lineno"> 137</span> y[5] = <a class="code hl_function" href="radix_8h.html#a0e2dfd3d1dda09f47ccc64eec35629f3">complex_mul_conj</a>(y[5], float2(2.37046941, 1.17510629));</div>
<div class="line"><a id="l00138" name="l00138"></a><span class="lineno"> 138</span> y[6] = <a class="code hl_function" href="radix_8h.html#a0e2dfd3d1dda09f47ccc64eec35629f3">complex_mul_conj</a>(y[6], float2(-2.44013336, -1.02261879));</div>
<div class="line"><a id="l00139" name="l00139"></a><span class="lineno"> 139</span> </div>
<div class="line"><a id="l00140" name="l00140"></a><span class="lineno"> 140</span> <span class="comment">// ifft</span></div>
<div class="line"><a id="l00141" name="l00141"></a><span class="lineno"> 141</span> <a class="code hl_function" href="radix_8h.html#afaaa5de58a97f0a5e6a84fc0d598a884">radix6</a>(y + 1, x + 1);</div>
<div class="line"><a id="l00142" name="l00142"></a><span class="lineno"> 142</span> </div>
<div class="line"><a id="l00143" name="l00143"></a><span class="lineno"> 143</span> y[1] = x[1] * inv + x[0];</div>
<div class="line"><a id="l00144" name="l00144"></a><span class="lineno"> 144</span> y[5] = x[2] * inv + x[0];</div>
<div class="line"><a id="l00145" name="l00145"></a><span class="lineno"> 145</span> y[4] = x[3] * inv + x[0];</div>
<div class="line"><a id="l00146" name="l00146"></a><span class="lineno"> 146</span> y[6] = x[4] * inv + x[0];</div>
<div class="line"><a id="l00147" name="l00147"></a><span class="lineno"> 147</span> y[2] = x[5] * inv + x[0];</div>
<div class="line"><a id="l00148" name="l00148"></a><span class="lineno"> 148</span> y[3] = x[6] * inv + x[0];</div>
<div class="line"><a id="l00149" name="l00149"></a><span class="lineno"> 149</span>}</div>
</div>
<div class="line"><a id="l00150" name="l00150"></a><span class="lineno"> 150</span> </div>
<div class="foldopen" id="foldopen00151" data-start="{" data-end="}">
<div class="line"><a id="l00151" name="l00151"></a><span class="lineno"><a class="line" href="radix_8h.html#a6b306e1afe1c5b6af4cd80aa02adb138"> 151</a></span>METAL_FUNC <span class="keywordtype">void</span> <a class="code hl_function" href="radix_8h.html#a6b306e1afe1c5b6af4cd80aa02adb138">radix8</a>(thread float2* x, thread float2* y) {</div>
<div class="line"><a id="l00152" name="l00152"></a><span class="lineno"> 152</span> <span class="keywordtype">float</span> cos_pi_4 = 0.7071067811865476;</div>
<div class="line"><a id="l00153" name="l00153"></a><span class="lineno"> 153</span> float2 w_0 = {cos_pi_4, -cos_pi_4};</div>
<div class="line"><a id="l00154" name="l00154"></a><span class="lineno"> 154</span> float2 w_1 = {-cos_pi_4, -cos_pi_4};</div>
<div class="line"><a id="l00155" name="l00155"></a><span class="lineno"> 155</span> float2 temp[8] = {x[0], x[2], x[4], x[6], x[1], x[3], x[5], x[7]};</div>
<div class="line"><a id="l00156" name="l00156"></a><span class="lineno"> 156</span> <a class="code hl_function" href="radix_8h.html#a12cb26bd3ad635d16a195ccea750256d">radix4</a>(temp, x);</div>
<div class="line"><a id="l00157" name="l00157"></a><span class="lineno"> 157</span> <a class="code hl_function" href="radix_8h.html#a12cb26bd3ad635d16a195ccea750256d">radix4</a>(temp + 4, x + 4);</div>
<div class="line"><a id="l00158" name="l00158"></a><span class="lineno"> 158</span> </div>
<div class="line"><a id="l00159" name="l00159"></a><span class="lineno"> 159</span> y[0] = x[0] + x[4];</div>
<div class="line"><a id="l00160" name="l00160"></a><span class="lineno"> 160</span> y[4] = x[0] - x[4];</div>
<div class="line"><a id="l00161" name="l00161"></a><span class="lineno"> 161</span> float2 x_5 = <a class="code hl_function" href="radix_8h.html#a5bfc53b531214c9ce277bebc18aa67d6">complex_mul</a>(x[5], w_0);</div>
<div class="line"><a id="l00162" name="l00162"></a><span class="lineno"> 162</span> y[1] = x[1] + x_5;</div>
<div class="line"><a id="l00163" name="l00163"></a><span class="lineno"> 163</span> y[5] = x[1] - x_5;</div>
<div class="line"><a id="l00164" name="l00164"></a><span class="lineno"> 164</span> float2 x_6 = {x[6].y, -x[6].x};</div>
<div class="line"><a id="l00165" name="l00165"></a><span class="lineno"> 165</span> y[2] = x[2] + x_6;</div>
<div class="line"><a id="l00166" name="l00166"></a><span class="lineno"> 166</span> y[6] = x[2] - x_6;</div>
<div class="line"><a id="l00167" name="l00167"></a><span class="lineno"> 167</span> float2 x_7 = <a class="code hl_function" href="radix_8h.html#a5bfc53b531214c9ce277bebc18aa67d6">complex_mul</a>(x[7], w_1);</div>
<div class="line"><a id="l00168" name="l00168"></a><span class="lineno"> 168</span> y[3] = x[3] + x_7;</div>
<div class="line"><a id="l00169" name="l00169"></a><span class="lineno"> 169</span> y[7] = x[3] - x_7;</div>
<div class="line"><a id="l00170" name="l00170"></a><span class="lineno"> 170</span>}</div>
</div>
<div class="line"><a id="l00171" name="l00171"></a><span class="lineno"> 171</span> </div>
<div class="line"><a id="l00172" name="l00172"></a><span class="lineno"> 172</span><span class="keyword">template</span> &lt;<span class="keywordtype">bool</span> raders_perm&gt;</div>
<div class="foldopen" id="foldopen00173" data-start="{" data-end="}">
<div class="line"><a id="l00173" name="l00173"></a><span class="lineno"><a class="line" href="radix_8h.html#a27054992e148bfcd9f7a69c96d75d926"> 173</a></span>METAL_FUNC <span class="keywordtype">void</span> <a class="code hl_function" href="radix_8h.html#a27054992e148bfcd9f7a69c96d75d926">radix10</a>(thread float2* x, thread float2* y) {</div>
<div class="line"><a id="l00174" name="l00174"></a><span class="lineno"> 174</span> float2 w[4];</div>
<div class="line"><a id="l00175" name="l00175"></a><span class="lineno"> 175</span> w[0] = {0.8090169943749475, -0.5877852522924731};</div>
<div class="line"><a id="l00176" name="l00176"></a><span class="lineno"> 176</span> w[1] = {0.30901699437494745, -0.9510565162951535};</div>
<div class="line"><a id="l00177" name="l00177"></a><span class="lineno"> 177</span> w[2] = {-w[1].x, w[1].y};</div>
<div class="line"><a id="l00178" name="l00178"></a><span class="lineno"> 178</span> w[3] = {-w[0].x, w[0].y};</div>
<div class="line"><a id="l00179" name="l00179"></a><span class="lineno"> 179</span> </div>
<div class="line"><a id="l00180" name="l00180"></a><span class="lineno"> 180</span> <span class="keywordflow">if</span> (raders_perm) {</div>
<div class="line"><a id="l00181" name="l00181"></a><span class="lineno"> 181</span> float2 temp[10] = {</div>
<div class="line"><a id="l00182" name="l00182"></a><span class="lineno"> 182</span> x[0], x[3], x[4], x[8], x[2], x[1], x[7], x[9], x[6], x[5]};</div>
<div class="line"><a id="l00183" name="l00183"></a><span class="lineno"> 183</span> <a class="code hl_function" href="radix_8h.html#a026e6779e6d2ecdef39ff4aad186091e">radix5</a>(temp, x);</div>
<div class="line"><a id="l00184" name="l00184"></a><span class="lineno"> 184</span> <a class="code hl_function" href="radix_8h.html#a026e6779e6d2ecdef39ff4aad186091e">radix5</a>(temp + 5, x + 5);</div>
<div class="line"><a id="l00185" name="l00185"></a><span class="lineno"> 185</span> } <span class="keywordflow">else</span> {</div>
<div class="line"><a id="l00186" name="l00186"></a><span class="lineno"> 186</span> float2 temp[10] = {</div>
<div class="line"><a id="l00187" name="l00187"></a><span class="lineno"> 187</span> x[0], x[2], x[4], x[6], x[8], x[1], x[3], x[5], x[7], x[9]};</div>
<div class="line"><a id="l00188" name="l00188"></a><span class="lineno"> 188</span> <a class="code hl_function" href="radix_8h.html#a026e6779e6d2ecdef39ff4aad186091e">radix5</a>(temp, x);</div>
<div class="line"><a id="l00189" name="l00189"></a><span class="lineno"> 189</span> <a class="code hl_function" href="radix_8h.html#a026e6779e6d2ecdef39ff4aad186091e">radix5</a>(temp + 5, x + 5);</div>
<div class="line"><a id="l00190" name="l00190"></a><span class="lineno"> 190</span> }</div>
<div class="line"><a id="l00191" name="l00191"></a><span class="lineno"> 191</span> </div>
<div class="line"><a id="l00192" name="l00192"></a><span class="lineno"> 192</span> y[0] = x[0] + x[5];</div>
<div class="line"><a id="l00193" name="l00193"></a><span class="lineno"> 193</span> y[5] = x[0] - x[5];</div>
<div class="line"><a id="l00194" name="l00194"></a><span class="lineno"> 194</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> t = 1; t &lt; 5; t++) {</div>
<div class="line"><a id="l00195" name="l00195"></a><span class="lineno"> 195</span> float2 a = <a class="code hl_function" href="radix_8h.html#a5bfc53b531214c9ce277bebc18aa67d6">complex_mul</a>(x[t + 5], w[t - 1]);</div>
<div class="line"><a id="l00196" name="l00196"></a><span class="lineno"> 196</span> y[t] = x[t] + a;</div>
<div class="line"><a id="l00197" name="l00197"></a><span class="lineno"> 197</span> y[t + 5] = x[t] - a;</div>
<div class="line"><a id="l00198" name="l00198"></a><span class="lineno"> 198</span> }</div>
<div class="line"><a id="l00199" name="l00199"></a><span class="lineno"> 199</span>}</div>
</div>
<div class="line"><a id="l00200" name="l00200"></a><span class="lineno"> 200</span> </div>
<div class="foldopen" id="foldopen00201" data-start="{" data-end="}">
<div class="line"><a id="l00201" name="l00201"></a><span class="lineno"><a class="line" href="radix_8h.html#a34f7dcefd29f8a7f6bddf9a17609a8a7"> 201</a></span>METAL_FUNC <span class="keywordtype">void</span> <a class="code hl_function" href="radix_8h.html#a34f7dcefd29f8a7f6bddf9a17609a8a7">radix11</a>(thread float2* x, thread float2* y) {</div>
<div class="line"><a id="l00202" name="l00202"></a><span class="lineno"> 202</span> <span class="comment">// Raders Algorithm</span></div>
<div class="line"><a id="l00203" name="l00203"></a><span class="lineno"> 203</span> float2 inv = {1 / 10.0, -1 / 10.0};</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> <span class="comment">// fft</span></div>
<div class="line"><a id="l00206" name="l00206"></a><span class="lineno"> 206</span> <a class="code hl_function" href="radix_8h.html#a27054992e148bfcd9f7a69c96d75d926">radix10&lt;true&gt;</a>(x + 1, y + 1);</div>
<div class="line"><a id="l00207" name="l00207"></a><span class="lineno"> 207</span> </div>
<div class="line"><a id="l00208" name="l00208"></a><span class="lineno"> 208</span> y[0] = y[1] + x[0];</div>
<div class="line"><a id="l00209" name="l00209"></a><span class="lineno"> 209</span> </div>
<div class="line"><a id="l00210" name="l00210"></a><span class="lineno"> 210</span> <span class="comment">// b_q</span></div>
<div class="line"><a id="l00211" name="l00211"></a><span class="lineno"> 211</span> y[1] = <a class="code hl_function" href="radix_8h.html#a0e2dfd3d1dda09f47ccc64eec35629f3">complex_mul_conj</a>(y[1], float2(-1, 0));</div>
<div class="line"><a id="l00212" name="l00212"></a><span class="lineno"> 212</span> y[2] = <a class="code hl_function" href="radix_8h.html#a0e2dfd3d1dda09f47ccc64eec35629f3">complex_mul_conj</a>(y[2], float2(0.955301878, -3.17606649));</div>
<div class="line"><a id="l00213" name="l00213"></a><span class="lineno"> 213</span> y[3] = <a class="code hl_function" href="radix_8h.html#a0e2dfd3d1dda09f47ccc64eec35629f3">complex_mul_conj</a>(y[3], float2(2.63610556, 2.01269656));</div>
<div class="line"><a id="l00214" name="l00214"></a><span class="lineno"> 214</span> y[4] = <a class="code hl_function" href="radix_8h.html#a0e2dfd3d1dda09f47ccc64eec35629f3">complex_mul_conj</a>(y[4], float2(2.54127802, 2.13117479));</div>
<div class="line"><a id="l00215" name="l00215"></a><span class="lineno"> 215</span> y[5] = <a class="code hl_function" href="radix_8h.html#a0e2dfd3d1dda09f47ccc64eec35629f3">complex_mul_conj</a>(y[5], float2(2.07016210, 2.59122150));</div>
<div class="line"><a id="l00216" name="l00216"></a><span class="lineno"> 216</span> y[6] = <a class="code hl_function" href="radix_8h.html#a0e2dfd3d1dda09f47ccc64eec35629f3">complex_mul_conj</a>(y[6], float2(0, -3.31662479));</div>
<div class="line"><a id="l00217" name="l00217"></a><span class="lineno"> 217</span> y[7] = <a class="code hl_function" href="radix_8h.html#a0e2dfd3d1dda09f47ccc64eec35629f3">complex_mul_conj</a>(y[7], float2(2.07016210, -2.59122150));</div>
<div class="line"><a id="l00218" name="l00218"></a><span class="lineno"> 218</span> y[8] = <a class="code hl_function" href="radix_8h.html#a0e2dfd3d1dda09f47ccc64eec35629f3">complex_mul_conj</a>(y[8], float2(-2.54127802, 2.13117479));</div>
<div class="line"><a id="l00219" name="l00219"></a><span class="lineno"> 219</span> y[9] = <a class="code hl_function" href="radix_8h.html#a0e2dfd3d1dda09f47ccc64eec35629f3">complex_mul_conj</a>(y[9], float2(2.63610556, -2.01269656));</div>
<div class="line"><a id="l00220" name="l00220"></a><span class="lineno"> 220</span> y[10] = <a class="code hl_function" href="radix_8h.html#a0e2dfd3d1dda09f47ccc64eec35629f3">complex_mul_conj</a>(y[10], float2(-0.955301878, -3.17606649));</div>
<div class="line"><a id="l00221" name="l00221"></a><span class="lineno"> 221</span> </div>
<div class="line"><a id="l00222" name="l00222"></a><span class="lineno"> 222</span> <span class="comment">// ifft</span></div>
<div class="line"><a id="l00223" name="l00223"></a><span class="lineno"> 223</span> <a class="code hl_function" href="radix_8h.html#a27054992e148bfcd9f7a69c96d75d926">radix10&lt;false&gt;</a>(y + 1, x + 1);</div>
<div class="line"><a id="l00224" name="l00224"></a><span class="lineno"> 224</span> </div>
<div class="line"><a id="l00225" name="l00225"></a><span class="lineno"> 225</span> y[1] = x[1] * inv + x[0];</div>
<div class="line"><a id="l00226" name="l00226"></a><span class="lineno"> 226</span> y[6] = x[2] * inv + x[0];</div>
<div class="line"><a id="l00227" name="l00227"></a><span class="lineno"> 227</span> y[3] = x[3] * inv + x[0];</div>
<div class="line"><a id="l00228" name="l00228"></a><span class="lineno"> 228</span> y[7] = x[4] * inv + x[0];</div>
<div class="line"><a id="l00229" name="l00229"></a><span class="lineno"> 229</span> y[9] = x[5] * inv + x[0];</div>
<div class="line"><a id="l00230" name="l00230"></a><span class="lineno"> 230</span> y[10] = x[6] * inv + x[0];</div>
<div class="line"><a id="l00231" name="l00231"></a><span class="lineno"> 231</span> y[5] = x[7] * inv + x[0];</div>
<div class="line"><a id="l00232" name="l00232"></a><span class="lineno"> 232</span> y[8] = x[8] * inv + x[0];</div>
<div class="line"><a id="l00233" name="l00233"></a><span class="lineno"> 233</span> y[4] = x[9] * inv + x[0];</div>
<div class="line"><a id="l00234" name="l00234"></a><span class="lineno"> 234</span> y[2] = x[10] * inv + x[0];</div>
<div class="line"><a id="l00235" name="l00235"></a><span class="lineno"> 235</span>}</div>
</div>
<div class="line"><a id="l00236" name="l00236"></a><span class="lineno"> 236</span> </div>
<div class="line"><a id="l00237" name="l00237"></a><span class="lineno"> 237</span><span class="keyword">template</span> &lt;<span class="keywordtype">bool</span> raders_perm&gt;</div>
<div class="foldopen" id="foldopen00238" data-start="{" data-end="}">
<div class="line"><a id="l00238" name="l00238"></a><span class="lineno"><a class="line" href="radix_8h.html#a3c61aa04a4b38575722d864cc9ffd0b7"> 238</a></span>METAL_FUNC <span class="keywordtype">void</span> <a class="code hl_function" href="radix_8h.html#a3c61aa04a4b38575722d864cc9ffd0b7">radix12</a>(thread float2* x, thread float2* y) {</div>
<div class="line"><a id="l00239" name="l00239"></a><span class="lineno"> 239</span> float2 w[6];</div>
<div class="line"><a id="l00240" name="l00240"></a><span class="lineno"> 240</span> <span class="keywordtype">float</span> sin_pi_3 = 0.8660254037844387;</div>
<div class="line"><a id="l00241" name="l00241"></a><span class="lineno"> 241</span> w[0] = {sin_pi_3, -0.5};</div>
<div class="line"><a id="l00242" name="l00242"></a><span class="lineno"> 242</span> w[1] = {0.5, -sin_pi_3};</div>
<div class="line"><a id="l00243" name="l00243"></a><span class="lineno"> 243</span> w[2] = {0, -1};</div>
<div class="line"><a id="l00244" name="l00244"></a><span class="lineno"> 244</span> w[3] = {-0.5, -sin_pi_3};</div>
<div class="line"><a id="l00245" name="l00245"></a><span class="lineno"> 245</span> w[4] = {-sin_pi_3, -0.5};</div>
<div class="line"><a id="l00246" name="l00246"></a><span class="lineno"> 246</span> </div>
<div class="line"><a id="l00247" name="l00247"></a><span class="lineno"> 247</span> <span class="keywordflow">if</span> (raders_perm) {</div>
<div class="line"><a id="l00248" name="l00248"></a><span class="lineno"> 248</span> float2 temp[12] = {</div>
<div class="line"><a id="l00249" name="l00249"></a><span class="lineno"> 249</span> x[0],</div>
<div class="line"><a id="l00250" name="l00250"></a><span class="lineno"> 250</span> x[3],</div>
<div class="line"><a id="l00251" name="l00251"></a><span class="lineno"> 251</span> x[2],</div>
<div class="line"><a id="l00252" name="l00252"></a><span class="lineno"> 252</span> x[11],</div>
<div class="line"><a id="l00253" name="l00253"></a><span class="lineno"> 253</span> x[8],</div>
<div class="line"><a id="l00254" name="l00254"></a><span class="lineno"> 254</span> x[9],</div>
<div class="line"><a id="l00255" name="l00255"></a><span class="lineno"> 255</span> x[1],</div>
<div class="line"><a id="l00256" name="l00256"></a><span class="lineno"> 256</span> x[7],</div>
<div class="line"><a id="l00257" name="l00257"></a><span class="lineno"> 257</span> x[5],</div>
<div class="line"><a id="l00258" name="l00258"></a><span class="lineno"> 258</span> x[10],</div>
<div class="line"><a id="l00259" name="l00259"></a><span class="lineno"> 259</span> x[4],</div>
<div class="line"><a id="l00260" name="l00260"></a><span class="lineno"> 260</span> x[6]};</div>
<div class="line"><a id="l00261" name="l00261"></a><span class="lineno"> 261</span> <a class="code hl_function" href="radix_8h.html#afaaa5de58a97f0a5e6a84fc0d598a884">radix6</a>(temp, x);</div>
<div class="line"><a id="l00262" name="l00262"></a><span class="lineno"> 262</span> <a class="code hl_function" href="radix_8h.html#afaaa5de58a97f0a5e6a84fc0d598a884">radix6</a>(temp + 6, x + 6);</div>
<div class="line"><a id="l00263" name="l00263"></a><span class="lineno"> 263</span> } <span class="keywordflow">else</span> {</div>
<div class="line"><a id="l00264" name="l00264"></a><span class="lineno"> 264</span> float2 temp[12] = {</div>
<div class="line"><a id="l00265" name="l00265"></a><span class="lineno"> 265</span> x[0],</div>
<div class="line"><a id="l00266" name="l00266"></a><span class="lineno"> 266</span> x[2],</div>
<div class="line"><a id="l00267" name="l00267"></a><span class="lineno"> 267</span> x[4],</div>
<div class="line"><a id="l00268" name="l00268"></a><span class="lineno"> 268</span> x[6],</div>
<div class="line"><a id="l00269" name="l00269"></a><span class="lineno"> 269</span> x[8],</div>
<div class="line"><a id="l00270" name="l00270"></a><span class="lineno"> 270</span> x[10],</div>
<div class="line"><a id="l00271" name="l00271"></a><span class="lineno"> 271</span> x[1],</div>
<div class="line"><a id="l00272" name="l00272"></a><span class="lineno"> 272</span> x[3],</div>
<div class="line"><a id="l00273" name="l00273"></a><span class="lineno"> 273</span> x[5],</div>
<div class="line"><a id="l00274" name="l00274"></a><span class="lineno"> 274</span> x[7],</div>
<div class="line"><a id="l00275" name="l00275"></a><span class="lineno"> 275</span> x[9],</div>
<div class="line"><a id="l00276" name="l00276"></a><span class="lineno"> 276</span> x[11]};</div>
<div class="line"><a id="l00277" name="l00277"></a><span class="lineno"> 277</span> <a class="code hl_function" href="radix_8h.html#afaaa5de58a97f0a5e6a84fc0d598a884">radix6</a>(temp, x);</div>
<div class="line"><a id="l00278" name="l00278"></a><span class="lineno"> 278</span> <a class="code hl_function" href="radix_8h.html#afaaa5de58a97f0a5e6a84fc0d598a884">radix6</a>(temp + 6, x + 6);</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> </div>
<div class="line"><a id="l00281" name="l00281"></a><span class="lineno"> 281</span> y[0] = x[0] + x[6];</div>
<div class="line"><a id="l00282" name="l00282"></a><span class="lineno"> 282</span> y[6] = x[0] - x[6];</div>
<div class="line"><a id="l00283" name="l00283"></a><span class="lineno"> 283</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> t = 1; t &lt; 6; t++) {</div>
<div class="line"><a id="l00284" name="l00284"></a><span class="lineno"> 284</span> float2 a = <a class="code hl_function" href="radix_8h.html#a5bfc53b531214c9ce277bebc18aa67d6">complex_mul</a>(x[t + 6], w[t - 1]);</div>
<div class="line"><a id="l00285" name="l00285"></a><span class="lineno"> 285</span> y[t] = x[t] + a;</div>
<div class="line"><a id="l00286" name="l00286"></a><span class="lineno"> 286</span> y[t + 6] = x[t] - a;</div>
<div class="line"><a id="l00287" name="l00287"></a><span class="lineno"> 287</span> }</div>
<div class="line"><a id="l00288" name="l00288"></a><span class="lineno"> 288</span>}</div>
</div>
<div class="line"><a id="l00289" name="l00289"></a><span class="lineno"> 289</span> </div>
<div class="foldopen" id="foldopen00290" data-start="{" data-end="}">
<div class="line"><a id="l00290" name="l00290"></a><span class="lineno"><a class="line" href="radix_8h.html#a833b7b31facbd62f6971bb108c54d1db"> 290</a></span>METAL_FUNC <span class="keywordtype">void</span> <a class="code hl_function" href="radix_8h.html#a833b7b31facbd62f6971bb108c54d1db">radix13</a>(thread float2* x, thread float2* y) {</div>
<div class="line"><a id="l00291" name="l00291"></a><span class="lineno"> 291</span> <span class="comment">// Raders Algorithm</span></div>
<div class="line"><a id="l00292" name="l00292"></a><span class="lineno"> 292</span> float2 inv = {1 / 12.0, -1 / 12.0};</div>
<div class="line"><a id="l00293" name="l00293"></a><span class="lineno"> 293</span> </div>
<div class="line"><a id="l00294" name="l00294"></a><span class="lineno"> 294</span> <span class="comment">// fft</span></div>
<div class="line"><a id="l00295" name="l00295"></a><span class="lineno"> 295</span> <a class="code hl_function" href="radix_8h.html#a3c61aa04a4b38575722d864cc9ffd0b7">radix12&lt;true&gt;</a>(x + 1, y + 1);</div>
<div class="line"><a id="l00296" name="l00296"></a><span class="lineno"> 296</span> </div>
<div class="line"><a id="l00297" name="l00297"></a><span class="lineno"> 297</span> y[0] = y[1] + x[0];</div>
<div class="line"><a id="l00298" name="l00298"></a><span class="lineno"> 298</span> </div>
<div class="line"><a id="l00299" name="l00299"></a><span class="lineno"> 299</span> <span class="comment">// b_q</span></div>
<div class="line"><a id="l00300" name="l00300"></a><span class="lineno"> 300</span> y[1] = <a class="code hl_function" href="radix_8h.html#a0e2dfd3d1dda09f47ccc64eec35629f3">complex_mul_conj</a>(y[1], float2(-1, 0));</div>
<div class="line"><a id="l00301" name="l00301"></a><span class="lineno"> 301</span> y[2] = <a class="code hl_function" href="radix_8h.html#a0e2dfd3d1dda09f47ccc64eec35629f3">complex_mul_conj</a>(y[2], float2(3.07497206, -1.88269669));</div>
<div class="line"><a id="l00302" name="l00302"></a><span class="lineno"> 302</span> y[3] = <a class="code hl_function" href="radix_8h.html#a0e2dfd3d1dda09f47ccc64eec35629f3">complex_mul_conj</a>(y[3], float2(3.09912468, 1.84266823));</div>
<div class="line"><a id="l00303" name="l00303"></a><span class="lineno"> 303</span> y[4] = <a class="code hl_function" href="radix_8h.html#a0e2dfd3d1dda09f47ccc64eec35629f3">complex_mul_conj</a>(y[4], float2(3.45084438, -1.04483161));</div>
<div class="line"><a id="l00304" name="l00304"></a><span class="lineno"> 304</span> y[5] = <a class="code hl_function" href="radix_8h.html#a0e2dfd3d1dda09f47ccc64eec35629f3">complex_mul_conj</a>(y[5], float2(0.91083583, 3.48860690));</div>
<div class="line"><a id="l00305" name="l00305"></a><span class="lineno"> 305</span> y[6] = <a class="code hl_function" href="radix_8h.html#a0e2dfd3d1dda09f47ccc64eec35629f3">complex_mul_conj</a>(y[6], float2(-3.60286363, 0.139189267));</div>
<div class="line"><a id="l00306" name="l00306"></a><span class="lineno"> 306</span> y[7] = <a class="code hl_function" href="radix_8h.html#a0e2dfd3d1dda09f47ccc64eec35629f3">complex_mul_conj</a>(y[7], float2(3.60555128, 0));</div>
<div class="line"><a id="l00307" name="l00307"></a><span class="lineno"> 307</span> y[8] = <a class="code hl_function" href="radix_8h.html#a0e2dfd3d1dda09f47ccc64eec35629f3">complex_mul_conj</a>(y[8], float2(3.60286363, 0.139189267));</div>
<div class="line"><a id="l00308" name="l00308"></a><span class="lineno"> 308</span> y[9] = <a class="code hl_function" href="radix_8h.html#a0e2dfd3d1dda09f47ccc64eec35629f3">complex_mul_conj</a>(y[9], float2(0.91083583, -3.48860690));</div>
<div class="line"><a id="l00309" name="l00309"></a><span class="lineno"> 309</span> y[10] = <a class="code hl_function" href="radix_8h.html#a0e2dfd3d1dda09f47ccc64eec35629f3">complex_mul_conj</a>(y[10], float2(-3.45084438, -1.04483161));</div>
<div class="line"><a id="l00310" name="l00310"></a><span class="lineno"> 310</span> y[11] = <a class="code hl_function" href="radix_8h.html#a0e2dfd3d1dda09f47ccc64eec35629f3">complex_mul_conj</a>(y[11], float2(3.09912468, -1.84266823));</div>
<div class="line"><a id="l00311" name="l00311"></a><span class="lineno"> 311</span> y[12] = <a class="code hl_function" href="radix_8h.html#a0e2dfd3d1dda09f47ccc64eec35629f3">complex_mul_conj</a>(y[12], float2(-3.07497206, -1.88269669));</div>
<div class="line"><a id="l00312" name="l00312"></a><span class="lineno"> 312</span> </div>
<div class="line"><a id="l00313" name="l00313"></a><span class="lineno"> 313</span> <span class="comment">// ifft</span></div>
<div class="line"><a id="l00314" name="l00314"></a><span class="lineno"> 314</span> <a class="code hl_function" href="radix_8h.html#a3c61aa04a4b38575722d864cc9ffd0b7">radix12&lt;false&gt;</a>(y + 1, x + 1);</div>
<div class="line"><a id="l00315" name="l00315"></a><span class="lineno"> 315</span> </div>
<div class="line"><a id="l00316" name="l00316"></a><span class="lineno"> 316</span> y[1] = x[1] * inv + x[0];</div>
<div class="line"><a id="l00317" name="l00317"></a><span class="lineno"> 317</span> y[7] = x[2] * inv + x[0];</div>
<div class="line"><a id="l00318" name="l00318"></a><span class="lineno"> 318</span> y[10] = x[3] * inv + x[0];</div>
<div class="line"><a id="l00319" name="l00319"></a><span class="lineno"> 319</span> y[5] = x[4] * inv + x[0];</div>
<div class="line"><a id="l00320" name="l00320"></a><span class="lineno"> 320</span> y[9] = x[5] * inv + x[0];</div>
<div class="line"><a id="l00321" name="l00321"></a><span class="lineno"> 321</span> y[11] = x[6] * inv + x[0];</div>
<div class="line"><a id="l00322" name="l00322"></a><span class="lineno"> 322</span> y[12] = x[7] * inv + x[0];</div>
<div class="line"><a id="l00323" name="l00323"></a><span class="lineno"> 323</span> y[6] = x[8] * inv + x[0];</div>
<div class="line"><a id="l00324" name="l00324"></a><span class="lineno"> 324</span> y[3] = x[9] * inv + x[0];</div>
<div class="line"><a id="l00325" name="l00325"></a><span class="lineno"> 325</span> y[8] = x[10] * inv + x[0];</div>
<div class="line"><a id="l00326" name="l00326"></a><span class="lineno"> 326</span> y[4] = x[11] * inv + x[0];</div>
<div class="line"><a id="l00327" name="l00327"></a><span class="lineno"> 327</span> y[2] = x[12] * inv + x[0];</div>
<div class="line"><a id="l00328" name="l00328"></a><span class="lineno"> 328</span>}</div>
</div>
<div class="ttc" id="anamespacemetal_1_1fast_html_a3af771cfe7a135104f9d063147dba270"><div class="ttname"><a href="namespacemetal_1_1fast.html#a3af771cfe7a135104f9d063147dba270">metal::fast::sin</a></div><div class="ttdeci">METAL_FUNC bfloat16_t sin(bfloat16_t x)</div><div class="ttdef"><b>Definition</b> bf16_math.h:240</div></div>
<div class="ttc" id="anamespacemetal_1_1fast_html_a75b6bb32fa3870eda46a7bfc9f481f88"><div class="ttname"><a href="namespacemetal_1_1fast.html#a75b6bb32fa3870eda46a7bfc9f481f88">metal::fast::cos</a></div><div class="ttdeci">METAL_FUNC bfloat16_t cos(bfloat16_t x)</div><div class="ttdef"><b>Definition</b> bf16_math.h:240</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_a0e2dfd3d1dda09f47ccc64eec35629f3"><div class="ttname"><a href="radix_8h.html#a0e2dfd3d1dda09f47ccc64eec35629f3">complex_mul_conj</a></div><div class="ttdeci">METAL_FUNC float2 complex_mul_conj(float2 a, float2 b)</div><div class="ttdef"><b>Definition</b> radix.h:24</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_a27054992e148bfcd9f7a69c96d75d926"><div class="ttname"><a href="radix_8h.html#a27054992e148bfcd9f7a69c96d75d926">radix10</a></div><div class="ttdeci">METAL_FUNC void radix10(thread float2 *x, thread float2 *y)</div><div class="ttdef"><b>Definition</b> radix.h:173</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_a3c61aa04a4b38575722d864cc9ffd0b7"><div class="ttname"><a href="radix_8h.html#a3c61aa04a4b38575722d864cc9ffd0b7">radix12</a></div><div class="ttdeci">METAL_FUNC void radix12(thread float2 *x, thread float2 *y)</div><div class="ttdef"><b>Definition</b> radix.h:238</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>
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