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<div class="headertitle"><div class="title">bf16_math.h</div></div>
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<a href="bf16__math_8h.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a id="l00001" name="l00001"></a><span class="lineno"> 1</span><span class="comment">// Copyright © 2023 Apple Inc.</span></div>
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<div class="line"><a id="l00002" name="l00002"></a><span class="lineno"> 2</span> </div>
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<div class="line"><a id="l00003" name="l00003"></a><span class="lineno"> 3</span><span class="preprocessor">#pragma once</span></div>
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<div class="line"><a id="l00004" name="l00004"></a><span class="lineno"> 4</span> </div>
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<div class="line"><a id="l00005" name="l00005"></a><span class="lineno"> 5</span><span class="preprocessor">#include "<a class="code" href="backend_2metal_2kernels_2bf16_8h.html">mlx/backend/metal/kernels/bf16.h</a>"</span></div>
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<div class="line"><a id="l00006" name="l00006"></a><span class="lineno"> 6</span> </div>
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<div class="line"><a id="l00008" name="l00008"></a><span class="lineno"> 8</span><span class="comment">// Metal math for bfloat16</span></div>
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<div class="line"><a id="l00010" name="l00010"></a><span class="lineno"> 10</span> </div>
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<div class="line"><a id="l00011" name="l00011"></a><span class="lineno"> 11</span><span class="comment">/*</span></div>
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<div class="line"><a id="l00012" name="l00012"></a><span class="lineno"> 12</span><span class="comment"></span> </div>
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<div class="line"><a id="l00013" name="l00013"></a><span class="lineno"> 13</span><span class="comment">Following the Metal Shading Language Specification (Metal 3.1)</span></div>
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<div class="line"><a id="l00014" name="l00014"></a><span class="lineno"> 14</span><span class="comment"></span> </div>
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<div class="line"><a id="l00015" name="l00015"></a><span class="lineno"> 15</span><span class="comment">"bfloat is an extended itypeing point type that only allows implicit conversion</span></div>
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<div class="line"><a id="l00016" name="l00016"></a><span class="lineno"> 16</span><span class="comment"> to a type of greater itypeing point rank. While bfloat can be implicitly</span></div>
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<div class="line"><a id="l00017" name="l00017"></a><span class="lineno"> 17</span><span class="comment"> converted to itype, it cannot be implicitly converted to half, and neither</span></div>
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<div class="line"><a id="l00018" name="l00018"></a><span class="lineno"> 18</span><span class="comment"> itype nor half can be implicitly converted to bfloat."</span></div>
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<div class="line"><a id="l00019" name="l00019"></a><span class="lineno"> 19</span><span class="comment"></span> </div>
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<div class="line"><a id="l00020" name="l00020"></a><span class="lineno"> 20</span><span class="comment">Further, as far as I can tell, the stdlib math/simd functions are not defined</span></div>
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<div class="line"><a id="l00021" name="l00021"></a><span class="lineno"> 21</span><span class="comment">for bfloat and calling with an argument of type bfloat will result in that</span></div>
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<div class="line"><a id="l00022" name="l00022"></a><span class="lineno"> 22</span><span class="comment">argument getting implicitly converted to itype which then returns an output</span></div>
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<div class="line"><a id="l00023" name="l00023"></a><span class="lineno"> 23</span><span class="comment">that is (likely) a itype which cannot be implicitly converted into a bfloat</span></div>
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<div class="line"><a id="l00024" name="l00024"></a><span class="lineno"> 24</span><span class="comment"></span> </div>
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<div class="line"><a id="l00025" name="l00025"></a><span class="lineno"> 25</span><span class="comment">This leads to situations where</span></div>
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<div class="line"><a id="l00026" name="l00026"></a><span class="lineno"> 26</span><span class="comment">bfloat a = 5.0bf;</span></div>
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<div class="line"><a id="l00027" name="l00027"></a><span class="lineno"> 27</span><span class="comment">bfloat b = metal::abs(a); // this will throw an error since abs return itype</span></div>
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<div class="line"><a id="l00028" name="l00028"></a><span class="lineno"> 28</span><span class="comment">bfloat c = static_cast<bfloat>(metal::abs(a)); // this is fine</span></div>
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<div class="line"><a id="l00029" name="l00029"></a><span class="lineno"> 29</span><span class="comment"></span> </div>
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<div class="line"><a id="l00030" name="l00030"></a><span class="lineno"> 30</span><span class="comment">For the moment, I will be adding overloaded instantiations of the math</span></div>
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<div class="line"><a id="l00031" name="l00031"></a><span class="lineno"> 31</span><span class="comment">functions to accordingly automatically handle the casting</span></div>
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<div class="line"><a id="l00032" name="l00032"></a><span class="lineno"> 32</span><span class="comment"></span> </div>
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<div class="line"><a id="l00033" name="l00033"></a><span class="lineno"> 33</span><span class="comment">*/</span></div>
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<div class="line"><a id="l00034" name="l00034"></a><span class="lineno"> 34</span> </div>
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<div class="foldopen" id="foldopen00035" data-start="" data-end="">
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<div class="line"><a id="l00035" name="l00035"></a><span class="lineno"><a class="line" href="bf16__math_8h.html#a9e9f0fdd6e304522bc88acd22c576842"> 35</a></span><span class="preprocessor">#define instantiate_metal_math_funcs(itype, otype, ctype, mfast) \</span></div>
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<div class="line"><a id="l00036" name="l00036"></a><span class="lineno"> 36</span><span class="preprocessor"> \</span></div>
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<div class="line"><a id="l00037" name="l00037"></a><span class="lineno"> 37</span><span class="preprocessor"> METAL_FUNC otype abs(itype x) { \</span></div>
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<div class="line"><a id="l00038" name="l00038"></a><span class="lineno"> 38</span><span class="preprocessor"> return static_cast<otype>(__metal_fabs(static_cast<ctype>(x), mfast)); \</span></div>
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<div class="line"><a id="l00039" name="l00039"></a><span class="lineno"> 39</span><span class="preprocessor"> } \</span></div>
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<div class="line"><a id="l00040" name="l00040"></a><span class="lineno"> 40</span><span class="preprocessor"> METAL_FUNC otype acos(itype x) { \</span></div>
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<div class="line"><a id="l00041" name="l00041"></a><span class="lineno"> 41</span><span class="preprocessor"> return static_cast<otype>(__metal_acos(static_cast<ctype>(x), mfast)); \</span></div>
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<div class="line"><a id="l00042" name="l00042"></a><span class="lineno"> 42</span><span class="preprocessor"> } \</span></div>
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<div class="line"><a id="l00043" name="l00043"></a><span class="lineno"> 43</span><span class="preprocessor"> METAL_FUNC otype acosh(itype x) { \</span></div>
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<div class="line"><a id="l00044" name="l00044"></a><span class="lineno"> 44</span><span class="preprocessor"> return static_cast<otype>(__metal_acosh(static_cast<ctype>(x), mfast)); \</span></div>
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<div class="line"><a id="l00045" name="l00045"></a><span class="lineno"> 45</span><span class="preprocessor"> } \</span></div>
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<div class="line"><a id="l00046" name="l00046"></a><span class="lineno"> 46</span><span class="preprocessor"> METAL_FUNC otype asin(itype x) { \</span></div>
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<div class="line"><a id="l00047" name="l00047"></a><span class="lineno"> 47</span><span class="preprocessor"> return static_cast<otype>(__metal_asin(static_cast<ctype>(x), mfast)); \</span></div>
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<div class="line"><a id="l00048" name="l00048"></a><span class="lineno"> 48</span><span class="preprocessor"> } \</span></div>
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<div class="line"><a id="l00049" name="l00049"></a><span class="lineno"> 49</span><span class="preprocessor"> METAL_FUNC otype asinh(itype x) { \</span></div>
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<div class="line"><a id="l00050" name="l00050"></a><span class="lineno"> 50</span><span class="preprocessor"> return static_cast<otype>(__metal_asinh(static_cast<ctype>(x), mfast)); \</span></div>
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<div class="line"><a id="l00051" name="l00051"></a><span class="lineno"> 51</span><span class="preprocessor"> } \</span></div>
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<div class="line"><a id="l00052" name="l00052"></a><span class="lineno"> 52</span><span class="preprocessor"> METAL_FUNC otype atan(itype y_over_x) { \</span></div>
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<div class="line"><a id="l00053" name="l00053"></a><span class="lineno"> 53</span><span class="preprocessor"> return static_cast<otype>( \</span></div>
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<div class="line"><a id="l00054" name="l00054"></a><span class="lineno"> 54</span><span class="preprocessor"> __metal_atan(static_cast<ctype>(y_over_x), mfast)); \</span></div>
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<div class="line"><a id="l00055" name="l00055"></a><span class="lineno"> 55</span><span class="preprocessor"> } \</span></div>
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<div class="line"><a id="l00056" name="l00056"></a><span class="lineno"> 56</span><span class="preprocessor"> METAL_FUNC otype atan2(itype y, itype x) { \</span></div>
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<div class="line"><a id="l00057" name="l00057"></a><span class="lineno"> 57</span><span class="preprocessor"> return static_cast<otype>( \</span></div>
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<div class="line"><a id="l00058" name="l00058"></a><span class="lineno"> 58</span><span class="preprocessor"> __metal_atan2(static_cast<ctype>(y), static_cast<ctype>(x), mfast)); \</span></div>
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<div class="line"><a id="l00059" name="l00059"></a><span class="lineno"> 59</span><span class="preprocessor"> } \</span></div>
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<div class="line"><a id="l00060" name="l00060"></a><span class="lineno"> 60</span><span class="preprocessor"> METAL_FUNC otype atanh(itype x) { \</span></div>
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<div class="line"><a id="l00061" name="l00061"></a><span class="lineno"> 61</span><span class="preprocessor"> return static_cast<otype>(__metal_atanh(static_cast<ctype>(x), mfast)); \</span></div>
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<div class="line"><a id="l00062" name="l00062"></a><span class="lineno"> 62</span><span class="preprocessor"> } \</span></div>
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<div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</span><span class="preprocessor"> METAL_FUNC otype ceil(itype x) { \</span></div>
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<div class="line"><a id="l00064" name="l00064"></a><span class="lineno"> 64</span><span class="preprocessor"> return static_cast<otype>(__metal_ceil(static_cast<ctype>(x), mfast)); \</span></div>
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<div class="line"><a id="l00065" name="l00065"></a><span class="lineno"> 65</span><span class="preprocessor"> } \</span></div>
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<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"> 66</span><span class="preprocessor"> METAL_FUNC otype cos(itype x) { \</span></div>
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<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"> 67</span><span class="preprocessor"> return static_cast<otype>(__metal_cos(static_cast<ctype>(x), mfast)); \</span></div>
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<div class="line"><a id="l00068" name="l00068"></a><span class="lineno"> 68</span><span class="preprocessor"> } \</span></div>
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<div class="line"><a id="l00069" name="l00069"></a><span class="lineno"> 69</span><span class="preprocessor"> METAL_FUNC otype cosh(itype x) { \</span></div>
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<div class="line"><a id="l00070" name="l00070"></a><span class="lineno"> 70</span><span class="preprocessor"> return static_cast<otype>(__metal_cosh(static_cast<ctype>(x), mfast)); \</span></div>
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<div class="line"><a id="l00071" name="l00071"></a><span class="lineno"> 71</span><span class="preprocessor"> } \</span></div>
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<div class="line"><a id="l00072" name="l00072"></a><span class="lineno"> 72</span><span class="preprocessor"> METAL_FUNC otype cospi(itype x) { \</span></div>
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<div class="line"><a id="l00073" name="l00073"></a><span class="lineno"> 73</span><span class="preprocessor"> return static_cast<otype>(__metal_cospi(static_cast<ctype>(x), mfast)); \</span></div>
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<div class="line"><a id="l00074" name="l00074"></a><span class="lineno"> 74</span><span class="preprocessor"> } \</span></div>
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<div class="line"><a id="l00075" name="l00075"></a><span class="lineno"> 75</span><span class="preprocessor"> METAL_FUNC otype divide(itype x, itype y) { \</span></div>
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<div class="line"><a id="l00076" name="l00076"></a><span class="lineno"> 76</span><span class="preprocessor"> return static_cast<otype>( \</span></div>
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<div class="line"><a id="l00077" name="l00077"></a><span class="lineno"> 77</span><span class="preprocessor"> __metal_divide(static_cast<ctype>(x), static_cast<ctype>(y), mfast)); \</span></div>
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<div class="line"><a id="l00078" name="l00078"></a><span class="lineno"> 78</span><span class="preprocessor"> } \</span></div>
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<div class="line"><a id="l00079" name="l00079"></a><span class="lineno"> 79</span><span class="preprocessor"> METAL_FUNC otype exp(itype x) { \</span></div>
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<div class="line"><a id="l00080" name="l00080"></a><span class="lineno"> 80</span><span class="preprocessor"> return static_cast<otype>(__metal_exp(static_cast<ctype>(x), mfast)); \</span></div>
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<div class="line"><a id="l00081" name="l00081"></a><span class="lineno"> 81</span><span class="preprocessor"> } \</span></div>
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<div class="line"><a id="l00082" name="l00082"></a><span class="lineno"> 82</span><span class="preprocessor"> METAL_FUNC otype exp10(itype x) { \</span></div>
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<div class="line"><a id="l00083" name="l00083"></a><span class="lineno"> 83</span><span class="preprocessor"> return static_cast<otype>(__metal_exp10(static_cast<ctype>(x), mfast)); \</span></div>
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<div class="line"><a id="l00084" name="l00084"></a><span class="lineno"> 84</span><span class="preprocessor"> } \</span></div>
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<div class="line"><a id="l00085" name="l00085"></a><span class="lineno"> 85</span><span class="preprocessor"> METAL_FUNC otype exp2(itype x) { \</span></div>
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<div class="line"><a id="l00086" name="l00086"></a><span class="lineno"> 86</span><span class="preprocessor"> return static_cast<otype>(__metal_exp2(static_cast<ctype>(x), mfast)); \</span></div>
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<div class="line"><a id="l00087" name="l00087"></a><span class="lineno"> 87</span><span class="preprocessor"> } \</span></div>
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<div class="line"><a id="l00088" name="l00088"></a><span class="lineno"> 88</span><span class="preprocessor"> METAL_FUNC otype fabs(itype x) { \</span></div>
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<div class="line"><a id="l00089" name="l00089"></a><span class="lineno"> 89</span><span class="preprocessor"> return static_cast<otype>(__metal_fabs(static_cast<ctype>(x), mfast)); \</span></div>
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<div class="line"><a id="l00090" name="l00090"></a><span class="lineno"> 90</span><span class="preprocessor"> } \</span></div>
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<div class="line"><a id="l00091" name="l00091"></a><span class="lineno"> 91</span><span class="preprocessor"> METAL_FUNC otype fdim(itype x, itype y) { \</span></div>
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<div class="line"><a id="l00092" name="l00092"></a><span class="lineno"> 92</span><span class="preprocessor"> ctype t = static_cast<ctype>(x - y); \</span></div>
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<div class="line"><a id="l00093" name="l00093"></a><span class="lineno"> 93</span><span class="preprocessor"> return static_cast<otype>(select(t, ctype(0), t < ctype(0) || x == y)); \</span></div>
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<div class="line"><a id="l00094" name="l00094"></a><span class="lineno"> 94</span><span class="preprocessor"> } \</span></div>
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<div class="line"><a id="l00095" name="l00095"></a><span class="lineno"> 95</span><span class="preprocessor"> METAL_FUNC otype floor(itype x) { \</span></div>
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<div class="line"><a id="l00096" name="l00096"></a><span class="lineno"> 96</span><span class="preprocessor"> return static_cast<otype>(__metal_floor(static_cast<ctype>(x), mfast)); \</span></div>
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<div class="line"><a id="l00097" name="l00097"></a><span class="lineno"> 97</span><span class="preprocessor"> } \</span></div>
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<div class="line"><a id="l00098" name="l00098"></a><span class="lineno"> 98</span><span class="preprocessor"> METAL_FUNC otype fma(itype x, itype y, itype z) { \</span></div>
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<div class="line"><a id="l00099" name="l00099"></a><span class="lineno"> 99</span><span class="preprocessor"> return static_cast<otype>(__metal_fma( \</span></div>
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<div class="line"><a id="l00100" name="l00100"></a><span class="lineno"> 100</span><span class="preprocessor"> static_cast<ctype>(x), static_cast<ctype>(y), static_cast<ctype>(z))); \</span></div>
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<div class="line"><a id="l00101" name="l00101"></a><span class="lineno"> 101</span><span class="preprocessor"> } \</span></div>
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<div class="line"><a id="l00102" name="l00102"></a><span class="lineno"> 102</span><span class="preprocessor"> METAL_FUNC otype fmax(itype x, itype y) { \</span></div>
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<div class="line"><a id="l00103" name="l00103"></a><span class="lineno"> 103</span><span class="preprocessor"> return static_cast<otype>( \</span></div>
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<div class="line"><a id="l00104" name="l00104"></a><span class="lineno"> 104</span><span class="preprocessor"> __metal_fmax(static_cast<ctype>(x), static_cast<ctype>(y), mfast)); \</span></div>
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<div class="line"><a id="l00105" name="l00105"></a><span class="lineno"> 105</span><span class="preprocessor"> } \</span></div>
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<div class="line"><a id="l00106" name="l00106"></a><span class="lineno"> 106</span><span class="preprocessor"> METAL_FUNC otype fmax3(itype x, itype y, itype z) { \</span></div>
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<div class="line"><a id="l00107" name="l00107"></a><span class="lineno"> 107</span><span class="preprocessor"> return static_cast<otype>(__metal_fmax3( \</span></div>
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<div class="line"><a id="l00108" name="l00108"></a><span class="lineno"> 108</span><span class="preprocessor"> static_cast<ctype>(x), \</span></div>
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<div class="line"><a id="l00109" name="l00109"></a><span class="lineno"> 109</span><span class="preprocessor"> static_cast<ctype>(y), \</span></div>
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<div class="line"><a id="l00110" name="l00110"></a><span class="lineno"> 110</span><span class="preprocessor"> static_cast<ctype>(z), \</span></div>
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<div class="line"><a id="l00111" name="l00111"></a><span class="lineno"> 111</span><span class="preprocessor"> mfast)); \</span></div>
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<div class="line"><a id="l00112" name="l00112"></a><span class="lineno"> 112</span><span class="preprocessor"> } \</span></div>
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<div class="line"><a id="l00113" name="l00113"></a><span class="lineno"> 113</span><span class="preprocessor"> METAL_FUNC otype fmedian3(itype x, itype y, itype z) { \</span></div>
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<div class="line"><a id="l00114" name="l00114"></a><span class="lineno"> 114</span><span class="preprocessor"> return static_cast<otype>(__metal_fmedian3( \</span></div>
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<div class="line"><a id="l00115" name="l00115"></a><span class="lineno"> 115</span><span class="preprocessor"> static_cast<ctype>(x), \</span></div>
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<div class="line"><a id="l00116" name="l00116"></a><span class="lineno"> 116</span><span class="preprocessor"> static_cast<ctype>(y), \</span></div>
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<div class="line"><a id="l00117" name="l00117"></a><span class="lineno"> 117</span><span class="preprocessor"> static_cast<ctype>(z), \</span></div>
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<div class="line"><a id="l00118" name="l00118"></a><span class="lineno"> 118</span><span class="preprocessor"> mfast)); \</span></div>
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<div class="line"><a id="l00119" name="l00119"></a><span class="lineno"> 119</span><span class="preprocessor"> } \</span></div>
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<div class="line"><a id="l00120" name="l00120"></a><span class="lineno"> 120</span><span class="preprocessor"> METAL_FUNC otype fmin(itype x, itype y) { \</span></div>
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<div class="line"><a id="l00121" name="l00121"></a><span class="lineno"> 121</span><span class="preprocessor"> return static_cast<otype>( \</span></div>
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<div class="line"><a id="l00122" name="l00122"></a><span class="lineno"> 122</span><span class="preprocessor"> __metal_fmin(static_cast<ctype>(x), static_cast<ctype>(y), mfast)); \</span></div>
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<div class="line"><a id="l00123" name="l00123"></a><span class="lineno"> 123</span><span class="preprocessor"> } \</span></div>
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<div class="line"><a id="l00124" name="l00124"></a><span class="lineno"> 124</span><span class="preprocessor"> METAL_FUNC otype fmin3(itype x, itype y, itype z) { \</span></div>
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<div class="line"><a id="l00125" name="l00125"></a><span class="lineno"> 125</span><span class="preprocessor"> return static_cast<otype>(__metal_fmin3( \</span></div>
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<div class="line"><a id="l00126" name="l00126"></a><span class="lineno"> 126</span><span class="preprocessor"> static_cast<ctype>(x), \</span></div>
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<div class="line"><a id="l00127" name="l00127"></a><span class="lineno"> 127</span><span class="preprocessor"> static_cast<ctype>(y), \</span></div>
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<div class="line"><a id="l00128" name="l00128"></a><span class="lineno"> 128</span><span class="preprocessor"> static_cast<ctype>(z), \</span></div>
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<div class="line"><a id="l00129" name="l00129"></a><span class="lineno"> 129</span><span class="preprocessor"> mfast)); \</span></div>
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<div class="line"><a id="l00130" name="l00130"></a><span class="lineno"> 130</span><span class="preprocessor"> } \</span></div>
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<div class="line"><a id="l00131" name="l00131"></a><span class="lineno"> 131</span><span class="preprocessor"> METAL_FUNC otype fmod(itype x, itype y) { \</span></div>
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<div class="line"><a id="l00132" name="l00132"></a><span class="lineno"> 132</span><span class="preprocessor"> return static_cast<otype>( \</span></div>
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<div class="line"><a id="l00133" name="l00133"></a><span class="lineno"> 133</span><span class="preprocessor"> __metal_fmod(static_cast<ctype>(x), static_cast<ctype>(y), mfast)); \</span></div>
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<div class="line"><a id="l00134" name="l00134"></a><span class="lineno"> 134</span><span class="preprocessor"> } \</span></div>
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<div class="line"><a id="l00135" name="l00135"></a><span class="lineno"> 135</span><span class="preprocessor"> METAL_FUNC otype fract(itype x) { \</span></div>
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<div class="line"><a id="l00136" name="l00136"></a><span class="lineno"> 136</span><span class="preprocessor"> return static_cast<otype>(__metal_fract(static_cast<ctype>(x), mfast)); \</span></div>
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<div class="line"><a id="l00137" name="l00137"></a><span class="lineno"> 137</span><span class="preprocessor"> } \</span></div>
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<div class="line"><a id="l00138" name="l00138"></a><span class="lineno"> 138</span><span class="preprocessor"> METAL_FUNC otype frexp(itype x, thread int& exp) { \</span></div>
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<div class="line"><a id="l00139" name="l00139"></a><span class="lineno"> 139</span><span class="preprocessor"> return static_cast<otype>(__metal_frexp(static_cast<ctype>(x), &exp)); \</span></div>
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<div class="line"><a id="l00140" name="l00140"></a><span class="lineno"> 140</span><span class="preprocessor"> } \</span></div>
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<div class="line"><a id="l00141" name="l00141"></a><span class="lineno"> 141</span><span class="preprocessor"> METAL_FUNC otype ldexp(itype x, int k) { \</span></div>
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<div class="line"><a id="l00142" name="l00142"></a><span class="lineno"> 142</span><span class="preprocessor"> return static_cast<otype>(__metal_ldexp(static_cast<ctype>(x), k, mfast)); \</span></div>
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<div class="line"><a id="l00143" name="l00143"></a><span class="lineno"> 143</span><span class="preprocessor"> } \</span></div>
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<div class="line"><a id="l00144" name="l00144"></a><span class="lineno"> 144</span><span class="preprocessor"> METAL_FUNC otype log(itype x) { \</span></div>
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<div class="line"><a id="l00145" name="l00145"></a><span class="lineno"> 145</span><span class="preprocessor"> return static_cast<otype>(__metal_log(static_cast<ctype>(x), mfast)); \</span></div>
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<div class="line"><a id="l00146" name="l00146"></a><span class="lineno"> 146</span><span class="preprocessor"> } \</span></div>
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<div class="line"><a id="l00147" name="l00147"></a><span class="lineno"> 147</span><span class="preprocessor"> METAL_FUNC otype log10(itype x) { \</span></div>
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<div class="line"><a id="l00148" name="l00148"></a><span class="lineno"> 148</span><span class="preprocessor"> return static_cast<otype>(__metal_log10(static_cast<ctype>(x), mfast)); \</span></div>
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<div class="line"><a id="l00149" name="l00149"></a><span class="lineno"> 149</span><span class="preprocessor"> } \</span></div>
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<div class="line"><a id="l00150" name="l00150"></a><span class="lineno"> 150</span><span class="preprocessor"> METAL_FUNC otype log2(itype x) { \</span></div>
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<div class="line"><a id="l00151" name="l00151"></a><span class="lineno"> 151</span><span class="preprocessor"> return static_cast<otype>(__metal_log2(static_cast<ctype>(x), mfast)); \</span></div>
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<div class="line"><a id="l00152" name="l00152"></a><span class="lineno"> 152</span><span class="preprocessor"> } \</span></div>
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<div class="line"><a id="l00153" name="l00153"></a><span class="lineno"> 153</span><span class="preprocessor"> METAL_FUNC otype max(itype x, itype y) { \</span></div>
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<div class="line"><a id="l00154" name="l00154"></a><span class="lineno"> 154</span><span class="preprocessor"> return static_cast<otype>( \</span></div>
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<div class="line"><a id="l00155" name="l00155"></a><span class="lineno"> 155</span><span class="preprocessor"> __metal_fmax(static_cast<ctype>(x), static_cast<ctype>(y), mfast)); \</span></div>
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<div class="line"><a id="l00156" name="l00156"></a><span class="lineno"> 156</span><span class="preprocessor"> } \</span></div>
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<div class="line"><a id="l00157" name="l00157"></a><span class="lineno"> 157</span><span class="preprocessor"> METAL_FUNC otype max3(itype x, itype y, itype z) { \</span></div>
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<div class="line"><a id="l00158" name="l00158"></a><span class="lineno"> 158</span><span class="preprocessor"> return static_cast<otype>(__metal_fmax3( \</span></div>
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<div class="line"><a id="l00159" name="l00159"></a><span class="lineno"> 159</span><span class="preprocessor"> static_cast<ctype>(x), \</span></div>
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<div class="line"><a id="l00160" name="l00160"></a><span class="lineno"> 160</span><span class="preprocessor"> static_cast<ctype>(y), \</span></div>
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<div class="line"><a id="l00161" name="l00161"></a><span class="lineno"> 161</span><span class="preprocessor"> static_cast<ctype>(z), \</span></div>
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<div class="line"><a id="l00162" name="l00162"></a><span class="lineno"> 162</span><span class="preprocessor"> mfast)); \</span></div>
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<div class="line"><a id="l00163" name="l00163"></a><span class="lineno"> 163</span><span class="preprocessor"> } \</span></div>
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<div class="line"><a id="l00164" name="l00164"></a><span class="lineno"> 164</span><span class="preprocessor"> METAL_FUNC otype median3(itype x, itype y, itype z) { \</span></div>
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<div class="line"><a id="l00165" name="l00165"></a><span class="lineno"> 165</span><span class="preprocessor"> return static_cast<otype>(__metal_fmedian3( \</span></div>
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<div class="line"><a id="l00166" name="l00166"></a><span class="lineno"> 166</span><span class="preprocessor"> static_cast<ctype>(x), \</span></div>
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<div class="line"><a id="l00167" name="l00167"></a><span class="lineno"> 167</span><span class="preprocessor"> static_cast<ctype>(y), \</span></div>
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<div class="line"><a id="l00168" name="l00168"></a><span class="lineno"> 168</span><span class="preprocessor"> static_cast<ctype>(z), \</span></div>
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<div class="line"><a id="l00169" name="l00169"></a><span class="lineno"> 169</span><span class="preprocessor"> mfast)); \</span></div>
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<div class="line"><a id="l00170" name="l00170"></a><span class="lineno"> 170</span><span class="preprocessor"> } \</span></div>
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<div class="line"><a id="l00171" name="l00171"></a><span class="lineno"> 171</span><span class="preprocessor"> METAL_FUNC otype min(itype x, itype y) { \</span></div>
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<div class="line"><a id="l00172" name="l00172"></a><span class="lineno"> 172</span><span class="preprocessor"> return static_cast<otype>( \</span></div>
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<div class="line"><a id="l00173" name="l00173"></a><span class="lineno"> 173</span><span class="preprocessor"> __metal_fmin(static_cast<ctype>(x), static_cast<ctype>(y), mfast)); \</span></div>
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<div class="line"><a id="l00174" name="l00174"></a><span class="lineno"> 174</span><span class="preprocessor"> } \</span></div>
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<div class="line"><a id="l00175" name="l00175"></a><span class="lineno"> 175</span><span class="preprocessor"> METAL_FUNC otype min3(itype x, itype y, itype z) { \</span></div>
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<div class="line"><a id="l00176" name="l00176"></a><span class="lineno"> 176</span><span class="preprocessor"> return static_cast<otype>(__metal_fmin3( \</span></div>
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<div class="line"><a id="l00177" name="l00177"></a><span class="lineno"> 177</span><span class="preprocessor"> static_cast<ctype>(x), \</span></div>
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<div class="line"><a id="l00178" name="l00178"></a><span class="lineno"> 178</span><span class="preprocessor"> static_cast<ctype>(y), \</span></div>
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<div class="line"><a id="l00179" name="l00179"></a><span class="lineno"> 179</span><span class="preprocessor"> static_cast<ctype>(z), \</span></div>
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<div class="line"><a id="l00180" name="l00180"></a><span class="lineno"> 180</span><span class="preprocessor"> mfast)); \</span></div>
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<div class="line"><a id="l00181" name="l00181"></a><span class="lineno"> 181</span><span class="preprocessor"> } \</span></div>
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<div class="line"><a id="l00182" name="l00182"></a><span class="lineno"> 182</span><span class="preprocessor"> METAL_FUNC otype nextafter(itype x, itype y) { \</span></div>
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<div class="line"><a id="l00183" name="l00183"></a><span class="lineno"> 183</span><span class="preprocessor"> return static_cast<otype>( \</span></div>
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<div class="line"><a id="l00184" name="l00184"></a><span class="lineno"> 184</span><span class="preprocessor"> __metal_nextafter(static_cast<ctype>(x), static_cast<ctype>(y))); \</span></div>
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<div class="line"><a id="l00185" name="l00185"></a><span class="lineno"> 185</span><span class="preprocessor"> } \</span></div>
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<div class="line"><a id="l00186" name="l00186"></a><span class="lineno"> 186</span><span class="preprocessor"> METAL_FUNC otype pow(itype x, itype y) { \</span></div>
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<div class="line"><a id="l00187" name="l00187"></a><span class="lineno"> 187</span><span class="preprocessor"> return static_cast<otype>( \</span></div>
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<div class="line"><a id="l00188" name="l00188"></a><span class="lineno"> 188</span><span class="preprocessor"> __metal_pow(static_cast<ctype>(x), static_cast<ctype>(y), mfast)); \</span></div>
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<div class="line"><a id="l00189" name="l00189"></a><span class="lineno"> 189</span><span class="preprocessor"> } \</span></div>
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<div class="line"><a id="l00190" name="l00190"></a><span class="lineno"> 190</span><span class="preprocessor"> METAL_FUNC otype powr(itype x, itype y) { \</span></div>
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<div class="line"><a id="l00191" name="l00191"></a><span class="lineno"> 191</span><span class="preprocessor"> return static_cast<otype>( \</span></div>
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<div class="line"><a id="l00192" name="l00192"></a><span class="lineno"> 192</span><span class="preprocessor"> __metal_powr(static_cast<ctype>(x), static_cast<ctype>(y), mfast)); \</span></div>
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<div class="line"><a id="l00193" name="l00193"></a><span class="lineno"> 193</span><span class="preprocessor"> } \</span></div>
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<div class="line"><a id="l00194" name="l00194"></a><span class="lineno"> 194</span><span class="preprocessor"> METAL_FUNC otype rint(itype x) { \</span></div>
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<div class="line"><a id="l00195" name="l00195"></a><span class="lineno"> 195</span><span class="preprocessor"> return static_cast<otype>(__metal_rint(static_cast<ctype>(x), mfast)); \</span></div>
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<div class="line"><a id="l00196" name="l00196"></a><span class="lineno"> 196</span><span class="preprocessor"> } \</span></div>
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<div class="line"><a id="l00197" name="l00197"></a><span class="lineno"> 197</span><span class="preprocessor"> METAL_FUNC otype round(itype x) { \</span></div>
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<div class="line"><a id="l00198" name="l00198"></a><span class="lineno"> 198</span><span class="preprocessor"> return static_cast<otype>(__metal_round(static_cast<ctype>(x), mfast)); \</span></div>
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<div class="line"><a id="l00199" name="l00199"></a><span class="lineno"> 199</span><span class="preprocessor"> } \</span></div>
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<div class="line"><a id="l00200" name="l00200"></a><span class="lineno"> 200</span><span class="preprocessor"> METAL_FUNC otype rsqrt(itype x) { \</span></div>
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<div class="line"><a id="l00201" name="l00201"></a><span class="lineno"> 201</span><span class="preprocessor"> return static_cast<otype>(__metal_rsqrt(static_cast<ctype>(x), mfast)); \</span></div>
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<div class="line"><a id="l00202" name="l00202"></a><span class="lineno"> 202</span><span class="preprocessor"> } \</span></div>
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<div class="line"><a id="l00203" name="l00203"></a><span class="lineno"> 203</span><span class="preprocessor"> METAL_FUNC otype sin(itype x) { \</span></div>
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<div class="line"><a id="l00204" name="l00204"></a><span class="lineno"> 204</span><span class="preprocessor"> return static_cast<otype>(__metal_sin(static_cast<ctype>(x), mfast)); \</span></div>
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<div class="line"><a id="l00205" name="l00205"></a><span class="lineno"> 205</span><span class="preprocessor"> } \</span></div>
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<div class="line"><a id="l00206" name="l00206"></a><span class="lineno"> 206</span><span class="preprocessor"> METAL_FUNC otype sinh(itype x) { \</span></div>
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<div class="line"><a id="l00207" name="l00207"></a><span class="lineno"> 207</span><span class="preprocessor"> return static_cast<otype>(__metal_sinh(static_cast<ctype>(x), mfast)); \</span></div>
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<div class="line"><a id="l00208" name="l00208"></a><span class="lineno"> 208</span><span class="preprocessor"> } \</span></div>
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<div class="line"><a id="l00209" name="l00209"></a><span class="lineno"> 209</span><span class="preprocessor"> METAL_FUNC otype sinpi(itype x) { \</span></div>
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<div class="line"><a id="l00210" name="l00210"></a><span class="lineno"> 210</span><span class="preprocessor"> return static_cast<otype>(__metal_sinpi(static_cast<ctype>(x), mfast)); \</span></div>
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<div class="line"><a id="l00211" name="l00211"></a><span class="lineno"> 211</span><span class="preprocessor"> } \</span></div>
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<div class="line"><a id="l00212" name="l00212"></a><span class="lineno"> 212</span><span class="preprocessor"> METAL_FUNC otype sqrt(itype x) { \</span></div>
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<div class="line"><a id="l00213" name="l00213"></a><span class="lineno"> 213</span><span class="preprocessor"> return static_cast<otype>(__metal_sqrt(static_cast<ctype>(x), mfast)); \</span></div>
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<div class="line"><a id="l00214" name="l00214"></a><span class="lineno"> 214</span><span class="preprocessor"> } \</span></div>
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<div class="line"><a id="l00215" name="l00215"></a><span class="lineno"> 215</span><span class="preprocessor"> METAL_FUNC otype tan(itype x) { \</span></div>
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<div class="line"><a id="l00216" name="l00216"></a><span class="lineno"> 216</span><span class="preprocessor"> return static_cast<otype>(__metal_tan(static_cast<ctype>(x), mfast)); \</span></div>
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<div class="line"><a id="l00217" name="l00217"></a><span class="lineno"> 217</span><span class="preprocessor"> } \</span></div>
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<div class="line"><a id="l00218" name="l00218"></a><span class="lineno"> 218</span><span class="preprocessor"> METAL_FUNC otype tanh(itype x) { \</span></div>
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<div class="line"><a id="l00219" name="l00219"></a><span class="lineno"> 219</span><span class="preprocessor"> return static_cast<otype>(__metal_tanh(static_cast<ctype>(x), mfast)); \</span></div>
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<div class="line"><a id="l00220" name="l00220"></a><span class="lineno"> 220</span><span class="preprocessor"> } \</span></div>
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<div class="line"><a id="l00221" name="l00221"></a><span class="lineno"> 221</span><span class="preprocessor"> METAL_FUNC otype tanpi(itype x) { \</span></div>
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<div class="line"><a id="l00222" name="l00222"></a><span class="lineno"> 222</span><span class="preprocessor"> return static_cast<otype>(__metal_tanpi(static_cast<ctype>(x), mfast)); \</span></div>
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<div class="line"><a id="l00223" name="l00223"></a><span class="lineno"> 223</span><span class="preprocessor"> } \</span></div>
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<div class="line"><a id="l00224" name="l00224"></a><span class="lineno"> 224</span><span class="preprocessor"> METAL_FUNC otype trunc(itype x) { \</span></div>
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<div class="line"><a id="l00225" name="l00225"></a><span class="lineno"> 225</span><span class="preprocessor"> return static_cast<otype>(__metal_trunc(static_cast<ctype>(x), mfast)); \</span></div>
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<div class="line"><a id="l00226" name="l00226"></a><span class="lineno"> 226</span><span class="preprocessor"> }</span></div>
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</div>
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<div class="line"><a id="l00227" name="l00227"></a><span class="lineno"> 227</span> </div>
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<div class="line"><a id="l00228" name="l00228"></a><span class="lineno"> 228</span><span class="keyword">namespace </span><a class="code hl_namespace" href="namespacemetal.html">metal</a> {</div>
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<div class="line"><a id="l00229" name="l00229"></a><span class="lineno"> 229</span> </div>
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<div class="line"><a id="l00230" name="l00230"></a><span class="lineno"> 230</span><a class="code hl_define" href="bf16__math_8h.html#a9e9f0fdd6e304522bc88acd22c576842">instantiate_metal_math_funcs</a>(</div>
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<div class="line"><a id="l00231" name="l00231"></a><span class="lineno"> 231</span> <a class="code hl_struct" href="struct___m_l_x___b_float16.html">bfloat16_t</a>,</div>
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<div class="line"><a id="l00232" name="l00232"></a><span class="lineno"> 232</span> <a class="code hl_struct" href="struct___m_l_x___b_float16.html">bfloat16_t</a>,</div>
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<div class="line"><a id="l00233" name="l00233"></a><span class="lineno"> 233</span> <span class="keywordtype">float</span>,</div>
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<div class="line"><a id="l00234" name="l00234"></a><span class="lineno"><a class="line" href="namespacemetal.html#a87c5122c60f9a12afceb9925a5b78ffb"> 234</a></span> __METAL_MAYBE_FAST_MATH__);</div>
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<div class="line"><a id="l00235" name="l00235"></a><span class="lineno"> 235</span> </div>
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<div class="foldopen" id="foldopen00236" data-start="{" data-end="}">
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<div class="line"><a id="l00236" name="l00236"></a><span class="lineno"><a class="line" href="namespacemetal_1_1fast.html"> 236</a></span><span class="keyword">namespace </span>fast {</div>
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<div class="line"><a id="l00237" name="l00237"></a><span class="lineno"> 237</span> </div>
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<div class="line"><a id="l00238" name="l00238"></a><span class="lineno"> 238</span><a class="code hl_define" href="bf16__math_8h.html#a9e9f0fdd6e304522bc88acd22c576842">instantiate_metal_math_funcs</a>(</div>
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<div class="line"><a id="l00239" name="l00239"></a><span class="lineno"> 239</span> <a class="code hl_struct" href="struct___m_l_x___b_float16.html">bfloat16_t</a>,</div>
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<div class="line"><a id="l00240" name="l00240"></a><span class="lineno"> 240</span> <a class="code hl_struct" href="struct___m_l_x___b_float16.html">bfloat16_t</a>,</div>
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<div class="line"><a id="l00241" name="l00241"></a><span class="lineno"> 241</span> <span class="keywordtype">float</span>,</div>
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<div class="line"><a id="l00242" name="l00242"></a><span class="lineno"><a class="line" href="namespacemetal_1_1fast.html#a90d2973f71f83180e7f02e38d11c7a8f"> 242</a></span> __METAL_FAST_MATH__);</div>
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<div class="line"><a id="l00243" name="l00243"></a><span class="lineno"> 243</span> </div>
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<div class="line"><a id="l00244" name="l00244"></a><span class="lineno"> 244</span>} <span class="comment">// namespace fast</span></div>
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</div>
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<div class="line"><a id="l00245" name="l00245"></a><span class="lineno"> 245</span> </div>
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<div class="foldopen" id="foldopen00246" data-start="{" data-end="}">
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<div class="line"><a id="l00246" name="l00246"></a><span class="lineno"><a class="line" href="namespacemetal_1_1precise.html"> 246</a></span><span class="keyword">namespace </span>precise {</div>
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<div class="line"><a id="l00247" name="l00247"></a><span class="lineno"> 247</span> </div>
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<div class="line"><a id="l00248" name="l00248"></a><span class="lineno"> 248</span><a class="code hl_define" href="bf16__math_8h.html#a9e9f0fdd6e304522bc88acd22c576842">instantiate_metal_math_funcs</a>(</div>
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<div class="line"><a id="l00249" name="l00249"></a><span class="lineno"> 249</span> <a class="code hl_struct" href="struct___m_l_x___b_float16.html">bfloat16_t</a>,</div>
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<div class="line"><a id="l00250" name="l00250"></a><span class="lineno"> 250</span> <a class="code hl_struct" href="struct___m_l_x___b_float16.html">bfloat16_t</a>,</div>
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<div class="line"><a id="l00251" name="l00251"></a><span class="lineno"> 251</span> <span class="keywordtype">float</span>,</div>
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<div class="line"><a id="l00252" name="l00252"></a><span class="lineno"><a class="line" href="namespacemetal_1_1precise.html#a99f2b2746e813b9ca7b4249afbaf2a14"> 252</a></span> __METAL_PRECISE_MATH__);</div>
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<div class="line"><a id="l00253" name="l00253"></a><span class="lineno"> 253</span> </div>
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<div class="line"><a id="l00254" name="l00254"></a><span class="lineno"> 254</span>} <span class="comment">// namespace precise</span></div>
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</div>
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<div class="line"><a id="l00255" name="l00255"></a><span class="lineno"> 255</span> </div>
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<div class="line"><a id="l00256" name="l00256"></a><span class="lineno"> 256</span>} <span class="comment">// namespace metal</span></div>
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<div class="line"><a id="l00257" name="l00257"></a><span class="lineno"> 257</span> </div>
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<div class="line"><a id="l00259" name="l00259"></a><span class="lineno"> 259</span><span class="comment">// Metal simd for bfloat16</span></div>
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<div class="line"><a id="l00261" name="l00261"></a><span class="lineno"> 261</span> </div>
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<div class="line"><a id="l00262" name="l00262"></a><span class="lineno"><a class="line" href="bf16__math_8h.html#aecc11cb898846d01bfc9faa109fcf791"> 262</a></span><span class="preprocessor">#define instantiate_metal_simd_comm_funcs( \</span></div>
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<div class="line"><a id="l00263" name="l00263"></a><span class="lineno"> 263</span><span class="preprocessor"> itype, otype, ctype, itype_to_ctype, ctype_to_otype) \</span></div>
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<div class="line"><a id="l00264" name="l00264"></a><span class="lineno"> 264</span><span class="preprocessor"> \</span></div>
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<div class="line"><a id="l00265" name="l00265"></a><span class="lineno"> 265</span><span class="preprocessor"> METAL_FUNC otype simd_broadcast(itype data, ushort broadcast_lane_id) { \</span></div>
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<div class="line"><a id="l00266" name="l00266"></a><span class="lineno"> 266</span><span class="preprocessor"> return ctype_to_otype( \</span></div>
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<div class="line"><a id="l00267" name="l00267"></a><span class="lineno"> 267</span><span class="preprocessor"> __metal_simd_broadcast(itype_to_ctype(data), broadcast_lane_id)); \</span></div>
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<div class="line"><a id="l00268" name="l00268"></a><span class="lineno"> 268</span><span class="preprocessor"> } \</span></div>
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<div class="line"><a id="l00269" name="l00269"></a><span class="lineno"> 269</span><span class="preprocessor"> \</span></div>
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<div class="line"><a id="l00270" name="l00270"></a><span class="lineno"> 270</span><span class="preprocessor"> METAL_FUNC otype simd_shuffle(itype data, ushort simd_lane_id) { \</span></div>
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<div class="line"><a id="l00271" name="l00271"></a><span class="lineno"> 271</span><span class="preprocessor"> return ctype_to_otype( \</span></div>
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<div class="line"><a id="l00272" name="l00272"></a><span class="lineno"> 272</span><span class="preprocessor"> __metal_simd_shuffle(itype_to_ctype(data), simd_lane_id)); \</span></div>
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<div class="line"><a id="l00273" name="l00273"></a><span class="lineno"> 273</span><span class="preprocessor"> } \</span></div>
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<div class="line"><a id="l00274" name="l00274"></a><span class="lineno"> 274</span><span class="preprocessor"> \</span></div>
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<div class="line"><a id="l00275" name="l00275"></a><span class="lineno"> 275</span><span class="preprocessor"> METAL_FUNC otype simd_shuffle_and_fill_down( \</span></div>
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<div class="line"><a id="l00276" name="l00276"></a><span class="lineno"> 276</span><span class="preprocessor"> itype data, itype filling_data, ushort delta, ushort modulo) { \</span></div>
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<div class="line"><a id="l00277" name="l00277"></a><span class="lineno"> 277</span><span class="preprocessor"> return ctype_to_otype(__metal_simd_shuffle_and_fill_down( \</span></div>
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<div class="line"><a id="l00278" name="l00278"></a><span class="lineno"> 278</span><span class="preprocessor"> itype_to_ctype(data), itype_to_ctype(filling_data), delta, modulo)); \</span></div>
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<div class="line"><a id="l00279" name="l00279"></a><span class="lineno"> 279</span><span class="preprocessor"> } \</span></div>
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<div class="line"><a id="l00280" name="l00280"></a><span class="lineno"> 280</span><span class="preprocessor"> \</span></div>
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<div class="line"><a id="l00281" name="l00281"></a><span class="lineno"> 281</span><span class="preprocessor"> METAL_FUNC otype simd_shuffle_and_fill_down( \</span></div>
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<div class="line"><a id="l00282" name="l00282"></a><span class="lineno"> 282</span><span class="preprocessor"> itype data, itype filling_data, ushort delta) { \</span></div>
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<div class="line"><a id="l00283" name="l00283"></a><span class="lineno"> 283</span><span class="preprocessor"> return ctype_to_otype(__metal_simd_shuffle_and_fill_down( \</span></div>
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<div class="line"><a id="l00284" name="l00284"></a><span class="lineno"> 284</span><span class="preprocessor"> itype_to_ctype(data), \</span></div>
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<div class="line"><a id="l00285" name="l00285"></a><span class="lineno"> 285</span><span class="preprocessor"> itype_to_ctype(filling_data), \</span></div>
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<div class="line"><a id="l00286" name="l00286"></a><span class="lineno"> 286</span><span class="preprocessor"> delta, \</span></div>
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<div class="line"><a id="l00287" name="l00287"></a><span class="lineno"> 287</span><span class="preprocessor"> __metal_get_simdgroup_size(ushort()))); \</span></div>
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<div class="line"><a id="l00288" name="l00288"></a><span class="lineno"> 288</span><span class="preprocessor"> } \</span></div>
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<div class="line"><a id="l00289" name="l00289"></a><span class="lineno"> 289</span><span class="preprocessor"> \</span></div>
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<div class="line"><a id="l00290" name="l00290"></a><span class="lineno"> 290</span><span class="preprocessor"> METAL_FUNC otype simd_shuffle_and_fill_up( \</span></div>
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<div class="line"><a id="l00291" name="l00291"></a><span class="lineno"> 291</span><span class="preprocessor"> itype data, itype filling_data, ushort delta, ushort modulo) { \</span></div>
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<div class="line"><a id="l00292" name="l00292"></a><span class="lineno"> 292</span><span class="preprocessor"> return ctype_to_otype(__metal_simd_shuffle_and_fill_up( \</span></div>
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<div class="line"><a id="l00293" name="l00293"></a><span class="lineno"> 293</span><span class="preprocessor"> itype_to_ctype(data), itype_to_ctype(filling_data), delta, modulo)); \</span></div>
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<div class="line"><a id="l00294" name="l00294"></a><span class="lineno"> 294</span><span class="preprocessor"> } \</span></div>
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<div class="line"><a id="l00295" name="l00295"></a><span class="lineno"> 295</span><span class="preprocessor"> \</span></div>
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<div class="line"><a id="l00296" name="l00296"></a><span class="lineno"> 296</span><span class="preprocessor"> METAL_FUNC otype simd_shuffle_and_fill_up( \</span></div>
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<div class="line"><a id="l00297" name="l00297"></a><span class="lineno"> 297</span><span class="preprocessor"> itype data, itype filling_data, ushort delta) { \</span></div>
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<div class="line"><a id="l00298" name="l00298"></a><span class="lineno"> 298</span><span class="preprocessor"> return ctype_to_otype(__metal_simd_shuffle_and_fill_up( \</span></div>
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<div class="line"><a id="l00299" name="l00299"></a><span class="lineno"> 299</span><span class="preprocessor"> itype_to_ctype(data), \</span></div>
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<div class="line"><a id="l00300" name="l00300"></a><span class="lineno"> 300</span><span class="preprocessor"> itype_to_ctype(filling_data), \</span></div>
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<div class="line"><a id="l00301" name="l00301"></a><span class="lineno"> 301</span><span class="preprocessor"> delta, \</span></div>
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<div class="line"><a id="l00302" name="l00302"></a><span class="lineno"> 302</span><span class="preprocessor"> __metal_get_simdgroup_size(ushort()))); \</span></div>
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<div class="line"><a id="l00303" name="l00303"></a><span class="lineno"> 303</span><span class="preprocessor"> } \</span></div>
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<div class="line"><a id="l00304" name="l00304"></a><span class="lineno"> 304</span><span class="preprocessor"> \</span></div>
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<div class="line"><a id="l00305" name="l00305"></a><span class="lineno"> 305</span><span class="preprocessor"> METAL_FUNC otype simd_shuffle_down(itype data, ushort delta) { \</span></div>
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<div class="line"><a id="l00306" name="l00306"></a><span class="lineno"> 306</span><span class="preprocessor"> return ctype_to_otype( \</span></div>
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<div class="line"><a id="l00307" name="l00307"></a><span class="lineno"> 307</span><span class="preprocessor"> __metal_simd_shuffle_down(itype_to_ctype(data), delta)); \</span></div>
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<div class="line"><a id="l00308" name="l00308"></a><span class="lineno"> 308</span><span class="preprocessor"> } \</span></div>
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<div class="line"><a id="l00309" name="l00309"></a><span class="lineno"> 309</span><span class="preprocessor"> \</span></div>
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<div class="line"><a id="l00310" name="l00310"></a><span class="lineno"> 310</span><span class="preprocessor"> METAL_FUNC otype simd_shuffle_rotate_down(itype data, ushort delta) { \</span></div>
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<div class="line"><a id="l00311" name="l00311"></a><span class="lineno"> 311</span><span class="preprocessor"> return ctype_to_otype( \</span></div>
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<div class="line"><a id="l00312" name="l00312"></a><span class="lineno"> 312</span><span class="preprocessor"> __metal_simd_shuffle_rotate_down(itype_to_ctype(data), delta)); \</span></div>
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<div class="line"><a id="l00313" name="l00313"></a><span class="lineno"> 313</span><span class="preprocessor"> } \</span></div>
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<div class="line"><a id="l00314" name="l00314"></a><span class="lineno"> 314</span><span class="preprocessor"> \</span></div>
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<div class="line"><a id="l00315" name="l00315"></a><span class="lineno"> 315</span><span class="preprocessor"> METAL_FUNC otype simd_shuffle_rotate_up(itype data, ushort delta) { \</span></div>
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<div class="line"><a id="l00316" name="l00316"></a><span class="lineno"> 316</span><span class="preprocessor"> return ctype_to_otype( \</span></div>
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<div class="line"><a id="l00317" name="l00317"></a><span class="lineno"> 317</span><span class="preprocessor"> __metal_simd_shuffle_rotate_up(itype_to_ctype(data), delta)); \</span></div>
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<div class="line"><a id="l00318" name="l00318"></a><span class="lineno"> 318</span><span class="preprocessor"> } \</span></div>
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<div class="line"><a id="l00319" name="l00319"></a><span class="lineno"> 319</span><span class="preprocessor"> \</span></div>
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<div class="line"><a id="l00320" name="l00320"></a><span class="lineno"> 320</span><span class="preprocessor"> METAL_FUNC otype simd_shuffle_up(itype data, ushort delta) { \</span></div>
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<div class="line"><a id="l00321" name="l00321"></a><span class="lineno"> 321</span><span class="preprocessor"> return ctype_to_otype( \</span></div>
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<div class="line"><a id="l00322" name="l00322"></a><span class="lineno"> 322</span><span class="preprocessor"> __metal_simd_shuffle_up(itype_to_ctype(data), delta)); \</span></div>
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<div class="line"><a id="l00323" name="l00323"></a><span class="lineno"> 323</span><span class="preprocessor"> } \</span></div>
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<div class="line"><a id="l00324" name="l00324"></a><span class="lineno"> 324</span><span class="preprocessor"> \</span></div>
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<div class="line"><a id="l00325" name="l00325"></a><span class="lineno"> 325</span><span class="preprocessor"> METAL_FUNC otype simd_shuffle_xor(itype data, ushort mask) { \</span></div>
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<div class="line"><a id="l00326" name="l00326"></a><span class="lineno"> 326</span><span class="preprocessor"> return ctype_to_otype( \</span></div>
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<div class="line"><a id="l00327" name="l00327"></a><span class="lineno"> 327</span><span class="preprocessor"> __metal_simd_shuffle_xor(itype_to_ctype(data), mask)); \</span></div>
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<div class="line"><a id="l00328" name="l00328"></a><span class="lineno"> 328</span><span class="preprocessor"> }</span></div>
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<div class="line"><a id="l00329" name="l00329"></a><span class="lineno"> 329</span> </div>
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<div class="foldopen" id="foldopen00330" data-start="" data-end="">
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|
<div class="line"><a id="l00330" name="l00330"></a><span class="lineno"><a class="line" href="bf16__math_8h.html#a51688bc24fc9292aaec5f54a58eaa2d0"> 330</a></span><span class="preprocessor">#define instantiate_metal_simd_reduction_funcs(itype, otype, ctype) \</span></div>
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<div class="line"><a id="l00331" name="l00331"></a><span class="lineno"> 331</span><span class="preprocessor"> \</span></div>
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<div class="line"><a id="l00332" name="l00332"></a><span class="lineno"> 332</span><span class="preprocessor"> METAL_FUNC otype simd_max(itype data) { \</span></div>
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<div class="line"><a id="l00333" name="l00333"></a><span class="lineno"> 333</span><span class="preprocessor"> return static_cast<otype>(__metal_simd_max(static_cast<ctype>(data))); \</span></div>
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<div class="line"><a id="l00334" name="l00334"></a><span class="lineno"> 334</span><span class="preprocessor"> } \</span></div>
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<div class="line"><a id="l00335" name="l00335"></a><span class="lineno"> 335</span><span class="preprocessor"> \</span></div>
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<div class="line"><a id="l00336" name="l00336"></a><span class="lineno"> 336</span><span class="preprocessor"> METAL_FUNC otype simd_min(itype data) { \</span></div>
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<div class="line"><a id="l00337" name="l00337"></a><span class="lineno"> 337</span><span class="preprocessor"> return static_cast<otype>(__metal_simd_min(static_cast<ctype>(data))); \</span></div>
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<div class="line"><a id="l00338" name="l00338"></a><span class="lineno"> 338</span><span class="preprocessor"> } \</span></div>
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<div class="line"><a id="l00339" name="l00339"></a><span class="lineno"> 339</span><span class="preprocessor"> \</span></div>
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<div class="line"><a id="l00340" name="l00340"></a><span class="lineno"> 340</span><span class="preprocessor"> METAL_FUNC otype simd_prefix_exclusive_product(itype data) { \</span></div>
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<div class="line"><a id="l00341" name="l00341"></a><span class="lineno"> 341</span><span class="preprocessor"> return static_cast<otype>( \</span></div>
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<div class="line"><a id="l00342" name="l00342"></a><span class="lineno"> 342</span><span class="preprocessor"> __metal_simd_prefix_exclusive_product(static_cast<ctype>(data))); \</span></div>
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<div class="line"><a id="l00343" name="l00343"></a><span class="lineno"> 343</span><span class="preprocessor"> } \</span></div>
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<div class="line"><a id="l00344" name="l00344"></a><span class="lineno"> 344</span><span class="preprocessor"> \</span></div>
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<div class="line"><a id="l00345" name="l00345"></a><span class="lineno"> 345</span><span class="preprocessor"> METAL_FUNC otype simd_prefix_exclusive_sum(itype data) { \</span></div>
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<div class="line"><a id="l00346" name="l00346"></a><span class="lineno"> 346</span><span class="preprocessor"> return static_cast<otype>( \</span></div>
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<div class="line"><a id="l00347" name="l00347"></a><span class="lineno"> 347</span><span class="preprocessor"> __metal_simd_prefix_exclusive_sum(static_cast<ctype>(data))); \</span></div>
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<div class="line"><a id="l00348" name="l00348"></a><span class="lineno"> 348</span><span class="preprocessor"> } \</span></div>
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<div class="line"><a id="l00349" name="l00349"></a><span class="lineno"> 349</span><span class="preprocessor"> \</span></div>
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<div class="line"><a id="l00350" name="l00350"></a><span class="lineno"> 350</span><span class="preprocessor"> METAL_FUNC otype simd_prefix_inclusive_product(itype data) { \</span></div>
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<div class="line"><a id="l00351" name="l00351"></a><span class="lineno"> 351</span><span class="preprocessor"> return static_cast<otype>( \</span></div>
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<div class="line"><a id="l00352" name="l00352"></a><span class="lineno"> 352</span><span class="preprocessor"> __metal_simd_prefix_inclusive_product(static_cast<ctype>(data))); \</span></div>
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<div class="line"><a id="l00353" name="l00353"></a><span class="lineno"> 353</span><span class="preprocessor"> } \</span></div>
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<div class="line"><a id="l00354" name="l00354"></a><span class="lineno"> 354</span><span class="preprocessor"> \</span></div>
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<div class="line"><a id="l00355" name="l00355"></a><span class="lineno"> 355</span><span class="preprocessor"> METAL_FUNC otype simd_prefix_inclusive_sum(itype data) { \</span></div>
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<div class="line"><a id="l00356" name="l00356"></a><span class="lineno"> 356</span><span class="preprocessor"> return static_cast<otype>( \</span></div>
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<div class="line"><a id="l00357" name="l00357"></a><span class="lineno"> 357</span><span class="preprocessor"> __metal_simd_prefix_inclusive_sum(static_cast<ctype>(data))); \</span></div>
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<div class="line"><a id="l00358" name="l00358"></a><span class="lineno"> 358</span><span class="preprocessor"> } \</span></div>
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<div class="line"><a id="l00359" name="l00359"></a><span class="lineno"> 359</span><span class="preprocessor"> \</span></div>
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<div class="line"><a id="l00360" name="l00360"></a><span class="lineno"> 360</span><span class="preprocessor"> METAL_FUNC otype simd_product(itype data) { \</span></div>
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<div class="line"><a id="l00361" name="l00361"></a><span class="lineno"> 361</span><span class="preprocessor"> return static_cast<otype>(__metal_simd_product(static_cast<ctype>(data))); \</span></div>
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<div class="line"><a id="l00362" name="l00362"></a><span class="lineno"> 362</span><span class="preprocessor"> } \</span></div>
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<div class="line"><a id="l00363" name="l00363"></a><span class="lineno"> 363</span><span class="preprocessor"> \</span></div>
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<div class="line"><a id="l00364" name="l00364"></a><span class="lineno"> 364</span><span class="preprocessor"> METAL_FUNC otype simd_sum(itype data) { \</span></div>
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<div class="line"><a id="l00365" name="l00365"></a><span class="lineno"> 365</span><span class="preprocessor"> return static_cast<otype>(__metal_simd_sum(static_cast<ctype>(data))); \</span></div>
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<div class="line"><a id="l00366" name="l00366"></a><span class="lineno"> 366</span><span class="preprocessor"> } \</span></div>
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<div class="line"><a id="l00367" name="l00367"></a><span class="lineno"> 367</span><span class="preprocessor"> \</span></div>
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<div class="line"><a id="l00368" name="l00368"></a><span class="lineno"> 368</span><span class="preprocessor"> METAL_FUNC otype simd_xor(itype data) { \</span></div>
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<div class="line"><a id="l00369" name="l00369"></a><span class="lineno"> 369</span><span class="preprocessor"> return static_cast<otype>(__metal_simd_xor(static_cast<ctype>(data))); \</span></div>
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<div class="line"><a id="l00370" name="l00370"></a><span class="lineno"> 370</span><span class="preprocessor"> }</span></div>
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</div>
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<div class="line"><a id="l00371" name="l00371"></a><span class="lineno"> 371</span> </div>
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<div class="line"><a id="l00372" name="l00372"></a><span class="lineno"> 372</span><span class="preprocessor">#if (MLX_METAL_VERSION >= 310) || (__METAL_VERSION__ >= 310)</span></div>
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<div class="line"><a id="l00373" name="l00373"></a><span class="lineno"> 373</span> </div>
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<div class="line"><a id="l00374" name="l00374"></a><span class="lineno"> 374</span><span class="preprocessor">#define bfloat16_to_uint16(x) as_type<uint16_t>(x)</span></div>
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<div class="line"><a id="l00375" name="l00375"></a><span class="lineno"> 375</span><span class="preprocessor">#define uint16_to_bfloat16(x) as_type<bfloat16_t>(x)</span></div>
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<div class="line"><a id="l00376" name="l00376"></a><span class="lineno"> 376</span> </div>
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<div class="line"><a id="l00377" name="l00377"></a><span class="lineno"> 377</span><span class="preprocessor">#else</span></div>
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<div class="line"><a id="l00378" name="l00378"></a><span class="lineno"> 378</span> </div>
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<div class="line"><a id="l00379" name="l00379"></a><span class="lineno"><a class="line" href="bf16__math_8h.html#a51cfdd4502e755310f6f3456f039bea7"> 379</a></span><span class="preprocessor">#define bfloat16_to_uint16(x) x.bits_</span></div>
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<div class="line"><a id="l00380" name="l00380"></a><span class="lineno"><a class="line" href="bf16__math_8h.html#a030d871474c0e7d907fccffcc8c047e0"> 380</a></span><span class="preprocessor">#define uint16_to_bfloat16(x) _MLX_BFloat16(x, _MLX_BFloat16::bits_to_bfloat())</span></div>
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<div class="line"><a id="l00381" name="l00381"></a><span class="lineno"> 381</span> </div>
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<div class="line"><a id="l00382" name="l00382"></a><span class="lineno"> 382</span><span class="preprocessor">#endif</span></div>
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<div class="line"><a id="l00383" name="l00383"></a><span class="lineno"> 383</span> </div>
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<div class="line"><a id="l00384" name="l00384"></a><span class="lineno"> 384</span><span class="keyword">namespace </span><a class="code hl_namespace" href="namespacemetal.html">metal</a> {</div>
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<div class="line"><a id="l00385" name="l00385"></a><span class="lineno"> 385</span> </div>
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<div class="line"><a id="l00386" name="l00386"></a><span class="lineno"> 386</span><a class="code hl_define" href="bf16__math_8h.html#aecc11cb898846d01bfc9faa109fcf791">instantiate_metal_simd_comm_funcs</a>(</div>
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<div class="line"><a id="l00387" name="l00387"></a><span class="lineno"> 387</span> <a class="code hl_struct" href="struct___m_l_x___b_float16.html">bfloat16_t</a>,</div>
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<div class="line"><a id="l00388" name="l00388"></a><span class="lineno"> 388</span> <a class="code hl_struct" href="struct___m_l_x___b_float16.html">bfloat16_t</a>,</div>
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<div class="line"><a id="l00389" name="l00389"></a><span class="lineno"> 389</span> uint16_t,</div>
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<div class="line"><a id="l00390" name="l00390"></a><span class="lineno"> 390</span> <a class="code hl_define" href="bf16__math_8h.html#a51cfdd4502e755310f6f3456f039bea7">bfloat16_to_uint16</a>,</div>
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<div class="line"><a id="l00391" name="l00391"></a><span class="lineno"><a class="line" href="namespacemetal.html#a498f1e85107eb5f01ba4435977f8efe0"> 391</a></span> <a class="code hl_define" href="bf16__math_8h.html#a030d871474c0e7d907fccffcc8c047e0">uint16_to_bfloat16</a>);</div>
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<div class="line"><a id="l00392" name="l00392"></a><span class="lineno"><a class="line" href="namespacemetal.html#a048cad0aca52cb737ebf103e76bd1c49"> 392</a></span><a class="code hl_define" href="bf16__math_8h.html#a51688bc24fc9292aaec5f54a58eaa2d0">instantiate_metal_simd_reduction_funcs</a>(<a class="code hl_struct" href="struct___m_l_x___b_float16.html">bfloat16_t</a>, <a class="code hl_struct" href="struct___m_l_x___b_float16.html">bfloat16_t</a>, <span class="keywordtype">float</span>);</div>
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<div class="line"><a id="l00393" name="l00393"></a><span class="lineno"> 393</span> </div>
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<div class="line"><a id="l00394" name="l00394"></a><span class="lineno"> 394</span>} <span class="comment">// namespace metal</span></div>
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<div class="ttc" id="abackend_2metal_2kernels_2bf16_8h_html"><div class="ttname"><a href="backend_2metal_2kernels_2bf16_8h.html">bf16.h</a></div></div>
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<div class="ttc" id="abf16__math_8h_html_a030d871474c0e7d907fccffcc8c047e0"><div class="ttname"><a href="bf16__math_8h.html#a030d871474c0e7d907fccffcc8c047e0">uint16_to_bfloat16</a></div><div class="ttdeci">#define uint16_to_bfloat16(x)</div><div class="ttdef"><b>Definition</b> bf16_math.h:380</div></div>
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<div class="ttc" id="abf16__math_8h_html_a51688bc24fc9292aaec5f54a58eaa2d0"><div class="ttname"><a href="bf16__math_8h.html#a51688bc24fc9292aaec5f54a58eaa2d0">instantiate_metal_simd_reduction_funcs</a></div><div class="ttdeci">#define instantiate_metal_simd_reduction_funcs(itype, otype, ctype)</div><div class="ttdef"><b>Definition</b> bf16_math.h:330</div></div>
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<div class="ttc" id="abf16__math_8h_html_a51cfdd4502e755310f6f3456f039bea7"><div class="ttname"><a href="bf16__math_8h.html#a51cfdd4502e755310f6f3456f039bea7">bfloat16_to_uint16</a></div><div class="ttdeci">#define bfloat16_to_uint16(x)</div><div class="ttdef"><b>Definition</b> bf16_math.h:379</div></div>
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<div class="ttc" id="abf16__math_8h_html_a9e9f0fdd6e304522bc88acd22c576842"><div class="ttname"><a href="bf16__math_8h.html#a9e9f0fdd6e304522bc88acd22c576842">instantiate_metal_math_funcs</a></div><div class="ttdeci">#define instantiate_metal_math_funcs(itype, otype, ctype, mfast)</div><div class="ttdef"><b>Definition</b> bf16_math.h:35</div></div>
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<div class="ttc" id="abf16__math_8h_html_aecc11cb898846d01bfc9faa109fcf791"><div class="ttname"><a href="bf16__math_8h.html#aecc11cb898846d01bfc9faa109fcf791">instantiate_metal_simd_comm_funcs</a></div><div class="ttdeci">#define instantiate_metal_simd_comm_funcs( itype, otype, ctype, itype_to_ctype, ctype_to_otype)</div><div class="ttdef"><b>Definition</b> bf16_math.h:262</div></div>
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<div class="ttc" id="anamespacemetal_html"><div class="ttname"><a href="namespacemetal.html">metal</a></div><div class="ttdef"><b>Definition</b> bf16.h:265</div></div>
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<div class="ttc" id="astruct___m_l_x___b_float16_html"><div class="ttname"><a href="struct___m_l_x___b_float16.html">_MLX_BFloat16</a></div><div class="ttdef"><b>Definition</b> bf16.h:54</div></div>
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