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OperatorFormulas.html
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OperatorFormulas.html
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<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="utf-8"/>
<title>ML Operator Formulas</title>
<style>
body
{
font-family: Calibri, Segoe UI, sans-serif;
background-color: #FFFFFF;
}
table tr:nth-child(odd) td{
background-color: #FFFFFF;
}
table tr:nth-child(even) td{
background-color: #F8F8FF;
}
td
{
white-space: pre; /*not pre-wrap;*/
vertical-align: top;
}
th {
background: #E8E8FF;
position: sticky;
top: 0; /* Don't forget this, required for the stickiness */
}
details {
display: inline;
white-space: pre; /*not pre-wrap;*/
}
summary {
display: inline;
white-space: pre; /*not pre-wrap;*/
cursor: zoom-in;
}
summary::after {
content: " details...";
color: blue;
}
/* Hide expandable content by default */
.elementwiseOperator { visibility: collapse; }
.activationOperator { visibility: collapse; }
.reorganizationOperator { visibility: collapse; }
.poolingOperator { visibility: collapse; }
.controlFlowOperator { visibility: collapse; }
.reductionOperator { visibility: collapse; }
.normalizationOperator { visibility: collapse; }
.generationOperator { visibility: collapse; }
.randomOperator { visibility: collapse; }
.matrixMultiplicationOperator { visibility: collapse; }
.imagingOperator { visibility: collapse; }
.aggregateOperator { visibility: collapse; }
.uncategorizedOperator { visibility: collapse; }
/* visibility: collapse doesn't appear to work as expected for columns using Chrome. So use display: none instead. */
.detailsColumn { display: none; }
.webnnColumn { display: none; }
.onnxColumn { display: none; }
.dmlColumn { display: none; }
.xnnPackColumn { display: none; }
.stableHloColumn { display: none; }
.tosaColumn { display: none; }
.numpyColumn { display: none; }
.tensorFlowColumn { display: none; }
.tensorFlowLiteColumn { display: none; }
.pytorchColumn { display: none; }
.coreMlColumn { display: none; }
.bnnsColumn { display: none; }
.mpsColumn { display: none; }
.mlxColumn { display: none; }
.ncnnColumn { display: none; }
.cntkColumn { display: none; }
.openVinoColumn { display: none; }
.oneDnnColumn { display: none; }
.annColumn { display: none; }
.futureColumn { display: none; }
/* Show hidden content when the checkbox is checked */
#toggleElementwiseOperators:checked ~ * .elementwiseOperator { visibility: visible; }
#toggleActivationOperators:checked ~ * .activationOperator { visibility: visible; }
#toggleReorganizationOperators:checked ~ * .reorganizationOperator { visibility: visible; }
#togglePoolingOperators:checked ~ * .poolingOperator { visibility: visible; }
#toggleControlFlowOperators:checked ~ * .controlFlowOperator { visibility: visible; }
#toggleReductionOperators:checked ~ * .reductionOperator { visibility: visible; }
#toggleNormalizationOperators:checked ~ * .normalizationOperator { visibility: visible; }
#toggleGenerationOperators:checked ~ * .generationOperator { visibility: visible; }
#toggleRandomOperators:checked ~ * .randomOperator { visibility: visible; }
#toggleMatrixMultiplicationOperators:checked ~ * .matrixMultiplicationOperator { visibility: visible; }
#toggleImagingOperators:checked ~ * .imagingOperator { visibility: visible; }
#toggleAggregateOperators:checked ~ * .aggregateOperator { visibility: visible; }
#toggleUncategorizedOperators:checked ~ * .uncategorizedOperator { visibility: visible; }
#toggleDetailsColumn:checked ~ * .detailsColumn { display: table-cell; }
#toggleWebnnColumn:checked ~ * .webnnColumn { display: table-cell; }
#toggleOnnxColumn:checked ~ * .onnxColumn { display: table-cell; }
#toggleDmlColumn:checked ~ * .dmlColumn { display: table-cell; }
#toggleXnnPackColumn:checked ~ * .xnnPackColumn { display: table-cell; }
#toggleStableHloColumn:checked ~ * .stableHloColumn { display: table-cell; }
#toggleTosaColumn:checked ~ * .tosaColumn { display: table-cell; }
#toggleNumpyColumn:checked ~ * .numpyColumn { display: table-cell; }
#toggleTensorFlowColumn:checked ~ * .tensorFlowColumn { display: table-cell; }
#toggleTensorFlowLiteColumn:checked ~ * .tensorFlowLiteColumn { display: table-cell; }
#togglePytorchColumn:checked ~ * .pytorchColumn { display: table-cell; }
#toggleCoreMlColumn:checked ~ * .coreMlColumn { display: table-cell; }
#toggleBnnsColumn:checked ~ * .bnnsColumn { display: table-cell; }
#toggleMpsColumn:checked ~ * .mpsColumn { display: table-cell; }
#toggleMlxColumn:checked ~ * .mlxColumn { display: table-cell; }
#toggleNcnnColumn:checked ~ * .ncnnColumn { display: table-cell; }
#toggleCntkColumn:checked ~ * .cntkColumn { display: table-cell; }
#toggleOpenVinoColumn:checked ~ * .openVinoColumn { display: table-cell; }
#toggleAnnColumn:checked ~ * .annColumn { display: table-cell; }
#toggleOneDnnColumn:checked ~ * .oneDnnColumn { display: table-cell; }
</style>
</head>
<body>
<h1>Links</h1>
<ul>
<li>This document
<ul>
<li><a href="https://fdwr.github.io/MachineLearningOperators/OperatorFormulas.html">Original document location</a><br/></li>
<li><a href="https://github.com/fdwr/MachineLearningOperators/">GitHub repo</a><br/></li>
</ul>
</li>
<li><a href="#DataTypes">Data Types table</a></li>
<li><a href="#Operators">Operator Formulas table</a></li>
</ul>
<br/>
<h1>Notation</h1>
<ul style="list-style: inside; padding-left: 0;">
<li>Any multiplication signs '*' mean elementwise multiplication (per NumPy, PyTorch, TensorFlow).</li>
<li>Any matrix style compound dot product will explicitly use MatMul() rather than '*' to avoid unacceptable notation ambiguity.</li>
<li>Any addition signs '+' mean elementwise addition, never the horrible notation abuse of concatenation.</li>
<li>All exp() and log() use the natural logarithm 2.718281828 (not base 10 or 2).</li>
<li>The pseudocode below uses a few undefined functions, but their trivial behavior should be obvious to implement. e.g. min, max, ones, zeroes, iif, assert</li>
<li>Data type field components are listed in logical bit order (not backwards right-to-left order).</li>
</ul>
<br/>
<noscript>*This checkbox will not work without Javascript enabled:<br/></noscript>
<input type="checkbox" id="toggleAllOperators" checked="checked" onclick="toggleAllOperatorsOfIdSuffix(this, 'Operators')"/><label for="toggleAllOperators"><All operator categories></label><br/>
<input type="checkbox" id="toggleElementwiseOperators" checked="checked"/><label for="toggleElementwiseOperators">Elementwise operators (pointwise operation, input.dimensions == output.dimensions)</label><br/>
<input type="checkbox" id="toggleActivationOperators" checked="checked"/><label for="toggleActivationOperators">Activation operators (signal <a href="https://en.wikipedia.org/wiki/Activation_function">remapping function</a>)</label><br/>
<input type="checkbox" id="toggleReorganizationOperators" checked="checked"/><label for="toggleReorganizationOperators">Reorganization operators (data movement, no value calculations)</label><br/>
<input type="checkbox" id="toggleReductionOperators" checked="checked"/><label for="toggleReductionOperators">Reduction operators (reduce multiple inputs to output via a formula)</label><br/>
<input type="checkbox" id="togglePoolingOperators" checked="checked"/><label for="togglePoolingOperators">Pooling operators (overlapping reduction)</label><br/>
<input type="checkbox" id="toggleNormalizationOperators" checked="checked"/><label for="toggleNormalizationOperators">Normalization operators (normalize values based on neighbors)</label><br/>
<input type="checkbox" id="toggleControlFlowOperators" checked="checked"/><label for="toggleControlFlowOperators">Control flow operators (graph level branches and loops)</label><br/>
<input type="checkbox" id="toggleGenerationOperators" checked="checked"/><label for="toggleGenerationOperators">Generation operators (generate data)</label><br/>
<input type="checkbox" id="toggleRandomOperators" checked="checked"/><label for="toggleRandomOperators">Random operators (random number values)</label><br/>
<input type="checkbox" id="toggleMatrixMultiplicationOperators" checked="checked"/><label for="toggleMatrixMultiplicationOperators">Matrix multiplication (multiply and sum)</label><br/>
<input type="checkbox" id="toggleImagingOperators" checked="checked"/><label for="toggleImagingOperators">Imaging operators (for image manipulation)</label><br/>
<input type="checkbox" id="toggleAggregateOperators" checked="checked"/><label for="toggleAggregateOperators">Aggregate operators (multiple combined operators in tiny graph)</label><br/>
<input type="checkbox" id="toggleUncategorizedOperators" checked="checked"/><label for="toggleUncategorizedOperators">Uncategorized operators (no clear category to assign)</label><br/>
<br/>
<noscript>*This checkbox will not work without Javascript enabled:<br/></noscript>
<input type="checkbox" id="toggleAllColumns" checked="checked" onclick="toggleAllOperatorsOfIdSuffix(this, 'Column')"/><label for="toggleAllColumns">All library columns</label><br/>
<input type="checkbox" id="toggleDetailsColumn" checked="checked"/><label for="toggleDetailsColumn">Details</label><br/>
<input type="checkbox" id="toggleWebnnColumn" checked="checked"/><label for="toggleWebnnColumn">WebNN (W3C <b>Web</b> <b>N</b>eural <b>N</b>etwork) <a href="https://www.w3.org/TR/webnn/">(info)</a></label><br/>
<input type="checkbox" id="toggleOnnxColumn" checked="checked"/><label for="toggleOnnxColumn">ONNX (<b>O</b>pen <b>N</b>eural <b>N</b>etwork E<b>x</b>change) <a href="https://onnx.ai/">(info)</a> <a href="https://onnx.ai/onnx/operators/index.html">(ops)</a></label><br/>
<input type="checkbox" id="toggleDmlColumn" checked="checked"/><label for="toggleDmlColumn">DirectML (Microsoft <b>Direct</b> <b>M</b>achine <b>L</b>earning) <a href="https://learn.microsoft.com/en-us/windows/ai/directml/dml-intro">(info)</a> <a href="https://learn.microsoft.com/en-us/windows/win32/api/directml/ne-directml-dml_operator_type">(ops)</a></label><br/>
<input type="checkbox" id="toggleXnnPackColumn" checked="checked"/><label for="toggleXnnPackColumn">XNNPACK (Google <b>X</b> <b>N</b>eural <b>N</b>etwork <b>Pack</b>age) <a href="https://github.com/google/XNNPACK">(info)</a></label><br/>
<input type="checkbox" id="toggleStableHloColumn" checked="checked"/><label for="toggleStableHloColumn">StableHLO (OpenXLA <b>Stable</b> <b>H</b>igh <b>L</b>evel <b>O</b>ptimizer) <a href="https://github.com/openxla/stablehlo/blob/main/docs/spec.md">(info)</a></label><br/>
<input type="checkbox" id="toggleTosaColumn" checked="checked"/><label for="toggleTosaColumn">TOSA (ARM <b>T</b>ensor <b>O</b>perator <b>S</b>et <b>A</b>rchitecture) <a href="https://mlir.llvm.org/docs/Dialects/TOSA/">(info)</a></label><br/>
<input type="checkbox" id="toggleNumpyColumn" checked="checked"/><label for="toggleNumpyColumn">NumPy (<b>Num</b>erical <b>Py</b>thon) <a href="https://numpy.org/">(info)</a> <a href="https://numpy.org/doc/stable/reference/routines.html">(ops)</a></label><br/>
<input type="checkbox" id="toggleTensorFlowColumn" checked="checked"/><label for="toggleTensorFlowColumn">TensorFlow (Google's TensorFlow) <a href="https://www.tensorflow.org/">(info)</a></label><br/>
<input type="checkbox" id="toggleTensorFlowLiteColumn" checked="checked"/><label for="toggleTensorFlowLiteColumn">TensorFlow Lite (Google's TensorFlowLite) <a href="https://www.tensorflow.org/">(info)</a></label><br/>
<input type="checkbox" id="togglePytorchColumn" checked="checked"/><label for="togglePytorchColumn">PyTorch (<b>Py</b>thon <b>Torch</b>, originally by Meta) <a href="https://pytorch.org/">(info)</a> <a href="https://pytorch.org/docs/stable/torch.html">(ops)</a> <a href="https://pytorch.org/docs/stable/nn.html">NN ops</a></label><br/>
<input type="checkbox" id="toggleCoreMlColumn" checked="checked"/><label for="toggleCoreMlColumn">CoreML (Apple <b>Core</b> <b>M</b>achine <b>L</b>earning) <a href="https://developer.apple.com/machine-learning/core-ml/">(info)</a> <a href="https://apple.github.io/coremltools/mlmodel/Format/NeuralNetwork.html">(ops)</a></label><br/>
<input type="checkbox" id="toggleBnnsColumn" checked="checked"/><label for="toggleBnnsColumn">BNNS (Apple <b>B</b>asic <b>N</b>eural <b>N</b>etwork <b>S</b>ubroutines) <a href="https://developer.apple.com/documentation/accelerate/bnns">(info)</a></label><br/>
<input type="checkbox" id="toggleMpsColumn" checked="checked"/><label for="toggleMpsColumn">MPS (Apple <b>M</b>etal <b>P</b>erformance <b>S</b>haders) <a href="https://developer.apple.com/documentation/metalperformanceshaders">(info)</a></label><br/>
<input type="checkbox" id="toggleMlxColumn" checked="checked"/><label for="toggleMlxColumn">MLX (Apple <b>M</b>achine <b>L</b>earning E<b>x</b>plore) <a href="https://ml-explore.github.io/mlx/build/html/python/ops.html">(info)</a></label><br/>
<input type="checkbox" id="toggleNcnnColumn" checked="checked"/><label for="toggleNcnnColumn">NCNN (Tencent <b>N</b>eon <b>C</b>onvolutional <b>N</b>eural <b>N</b>etwork) <a href="https://github.com/Tencent/ncnn/">(info)</a> <a href="https://github.com/Tencent/ncnn/blob/54a9a563e9913d3142782dac0e497f2be50075b5/docs/developer-guide/operators.md">(ops)</a></label><br/>
<input type="checkbox" id="toggleCntkColumn" checked="checked"/><label for="toggleCntkColumn">CNTK (Microsoft <b>C</b>og<b>n</b>itive <b>T</b>ool<b>k</b>it) <a href="https://github.com/microsoft/CNTK">(info)</a> <a href="https://microsoft.github.io/CNTK-R/reference/index.html">(ops)</a></label><br/>
<input type="checkbox" id="toggleOpenVinoColumn" checked="checked"/><label for="toggleOpenVinoColumn">OpenVINO (Intel <b>V</b>isual <b>I</b>nference and <b>N</b>eural Network <b>O</b>ptimization) <a href="https://www.intel.com/content/www/us/en/developer/tools/openvino-toolkit/overview.html">(info)</a> <a href="https://docs.openvino.ai/2023.0/api/ie_python_api/_autosummary/openvino.runtime.opset1.html">(ops)</a></label><br/>
<input type="checkbox" id="toggleOneDnnColumn" checked="checked"/><label for="toggleOneDnnColumn">OneDNN (Intel <b>D</b>eep <b>N</b>eural <b>N</b>etwork Library <a href="https://oneapi-src.github.io/oneDNN/group_dnnl_api_primitives.html">(ops)</a></label><br/>
<input type="checkbox" id="toggleAnnColumn" checked="checked"/><label for="toggleAnnColumn">Android NDK (Google <b>N</b>neural Network <b>D</b>evelopment <b>K</b>it) <a href="https://developer.android.com/ndk/guides">(info)</a> <a href="https://developer.android.com/ndk/reference/group/neural-networks">(ops)</a></label><br/>
<br/>
<br/><br/>
<h1 id="DataTypes">Data Types</h1>
<table border="1" cellpadding="1" cellspacing="0" style="border-collapse:collapse; border:none">
<tbody>
<tr>
<th style="width:12em">Categories</th>
<th>Name</th>
<th class="detailsColumn" valign="top">Details</th>
<th class="webnnColumn"><span title="Updated 2024-01-19"><a href="https://www.w3.org/TR/webnn/#enumdef-mloperanddatatype">WebNN</a></span></th>
<th class="onnxColumn"><span title="Updated 2024-01-19"><a href="https://github.com/onnx/onnx/blob/8a782415a69faf626abc032ff6b2a16187e13c4f/onnx/onnx.proto#L485">ONNX</a></span></th>
<th class="dmlColumn"><span title="Updated 2024-01-19"><a href="https://learn.microsoft.com/en-us/windows/win32/api/directml/ne-directml-dml_tensor_data_type">DML</a></span></th>
<th class="xnnPackColumn"><span title="Updated 2024-01-19"><a href="https://github.com/google/XNNPACK/blob/03d2a24b53f18103a2bb0f62e2c7123c5cea8890/include/xnnpack.h#L211-L232">XNNPACK</a></span></th>
<th class="stableHloColumn"><span title="Updated 2024-01-19"><a href="https://github.com/openxla/stablehlo/blob/main/docs/spec.md#types">StableHLO</a></span></th>
<th class="tosaColumn"><span title="Updated 2024-01-19"><a href="https://www.mlplatform.org/tosa/tosa_spec.html">TOSA</a></span></th>
<th class="numpyColumn"><span title="Updated 2024-01-19"><a href="https://numpy.org/devdocs/user/basics.types.html">NumPy</a></span></th>
<th class="tensorFlowColumn"><span title="Updated 2024-01-19"><a href="https://www.tensorflow.org/api_docs/python/tf/dtypes">TensorFlow</a></span></th>
<th class="tensorFlowLiteColumn"><span title="Updated 2024-08-01"><a href="https://www.tensorflow.org/api_docs/python/tf/dtypes">TensorFlow Lite</a></span></th>
<th class="pytorchColumn"><span title="Updated 2024-01-19"><a href="https://pytorch.org/docs/stable/tensor_attributes.html">PyTorch</a></span></th>
<th class="coreMlColumn"><span title="Updated 2024-01-19"><a href="https://chromium-review.googlesource.com/c/chromium/src/+/5075312/12/services/webnn/coreml/ModelFormat/FeatureTypes.proto">CoreML</a></span></th>
<th class="bnnsColumn"><span title="Updated 2024-01-19"><a href="https://github.com/alexey-lysiuk/macos-sdk/blob/6c1513f5b0667b76e24aaadcad130e90c545f046/MacOSX14.0.sdk/System/Library/Frameworks/Accelerate.framework/Versions/A/Frameworks/vecLib.framework/Versions/A/Headers/BNNS/bnns_constants.h#L33-L91">BNNS</a></span></th>
<th class="mpsColumn"><span title="Updated 2024-01-19"><a href="https://developer.apple.com/documentation/metalperformanceshadersgraph/mpsgraphtensor/3564663-datatype">MPS</a></span></th>
<th class="mlxColumn"><span title="Updated 2024-01-19"><a href="https://ml-explore.github.io/mlx/build/html/python/data_types.html">MLX</a></span></th>
<th class="ncnnColumn"><span title="Updated 2024-01-19"><a href="https://github.com/Tencent/ncnn/blob/54a9a563e9913d3142782dac0e497f2be50075b5/docs/developer-guide/operators.md#cast">NCNN</a></span></th>
<th class="cntkColumn"><span title="Updated 2024-01-19"><a href="https://github.com/microsoft/CNTK/blob/ae9c9c7c5f9e6072cc9c94c254f816dbdc1c5be6/Source/CNTKv2LibraryDll/API/CNTKLibrary.h#L82">CNTK</a></span></th>
<th class="openVinoColumn"><span title="Updated 2024-01-19"><a href="https://docs.openvino.ai/2023.0/groupov_element_cpp_api.html#doxid-group-ov-element-cpp-api">OpenVINO</a></span></th>
<th class="oneDnnColumn"><span title="Updated 2024-01-19"><a href="https://oneapi-src.github.io/oneDNN/enum_dnnl_data_type_t.html">OneDNN</a></span></th>
<th class="annColumn"><span title="Updated 2024-03-26"><a href="https://developer.android.com/ndk/reference/group/neural-networks#operandcode">ANN</a></span></th>
<th class="futureColumn">(for future additions)</th>
</tr>
<tr>
<td>Integer Unsigned</td>
<td>uint1</td>
<td class="detailsColumn"></td>
<td class="webnnColumn">x</td>
<td class="onnxColumn">x</td>
<td class="dmlColumn">x</td>
<td class="xnnPackColumn">x</td>
<td class="stableHloColumn">i1 (bool)</td>
<td class="tosaColumn">x</td>
<td class="numpyColumn">x</td>
<td class="tensorFlowColumn">x</td>
<td class="tensorFlowLiteColumn">x</td>
<td class="pytorchColumn">x</td>
<td class="coreMlColumn">x</td>
<td class="bnnsColumn">x</td>
<td class="mpsColumn">x</td>
<td class="mlxColumn">x</td>
<td class="ncnnColumn">x</td>
<td class="cntkColumn">?</td>
<td class="openVinoColumn">ov::element::Type_t::u1</td>
<td class="oneDnnColumn">x</td>
<td class="annColumn">?</td>
<td class="futureColumn">?</td>
</tr>
<tr>
<td>Integer Unsigned</td>
<td>uint4</td>
<td class="detailsColumn"></td>
<td class="webnnColumn">x</td>
<td class="onnxColumn">x</td>
<td class="dmlColumn">DML_TENSOR_DATA_TYPE_UINT4</td>
<td class="xnnPackColumn">x</td>
<td class="stableHloColumn">ui4</td>
<td class="tosaColumn">x</td>
<td class="numpyColumn">x</td>
<td class="tensorFlowColumn">x</td>
<td class="tensorFlowLiteColumn">x</td>
<td class="pytorchColumn">x</td>
<td class="coreMlColumn">x</td>
<td class="bnnsColumn">x</td>
<td class="mpsColumn">x</td>
<td class="mlxColumn">x</td>
<td class="ncnnColumn">x</td>
<td class="cntkColumn">?</td>
<td class="openVinoColumn">ov::element::Type_t::u4</td>
<td class="oneDnnColumn">x</td>
<td class="annColumn">?</td>
<td class="futureColumn">?</td>
</tr>
<tr>
<td>Integer Unsigned</td>
<td>uint8</td>
<td class="detailsColumn"></td>
<td class="webnnColumn">uint8</td>
<td class="onnxColumn">ONNX.TensorProto.DataType.UINT8</td>
<td class="dmlColumn">DML_TENSOR_DATA_TYPE_UINT8</td>
<td class="xnnPackColumn">x</td>
<td class="stableHloColumn">ui8</td>
<td class="tosaColumn">tosa.uint8_t</td>
<td class="numpyColumn">numpy.uint8 / ubyte</td>
<td class="tensorFlowColumn">tensorflow.uint8</td>
<td class="tensorFlowLiteColumn">tensorflow.uint8</td>
<td class="pytorchColumn">torch.uint8</td>
<td class="coreMlColumn">x</td>
<td class="bnnsColumn">BNNSDataTypeUInt8</td>
<td class="mpsColumn">MPSDataType.uInt8</td>
<td class="mlxColumn">mx.uint8</td>
<td class="ncnnColumn">x</td>
<td class="cntkColumn">CNTK.DataType.UChar</td>
<td class="openVinoColumn">ov::element::Type_t::u8</td>
<td class="oneDnnColumn">dnnl_data_type_t::dnnl_u8</td>
<td class="annColumn">?</td>
<td class="futureColumn">?</td>
</tr>
<tr>
<td>Integer Unsigned</td>
<td>uint16</td>
<td class="detailsColumn"></td>
<td class="webnnColumn">x</td>
<td class="onnxColumn">ONNX.TensorProto.DataType.UINT16</td>
<td class="dmlColumn">DML_TENSOR_DATA_TYPE_UINT16</td>
<td class="xnnPackColumn">x</td>
<td class="stableHloColumn">ui16</td>
<td class="tosaColumn">tosa.uint16_t</td>
<td class="numpyColumn">numpy.uint16 / ushort</td>
<td class="tensorFlowColumn">tensorflow.uint16</td>
<td class="tensorFlowLiteColumn">tensorflow.uint16</td>
<td class="pytorchColumn">x</td>
<td class="coreMlColumn">x</td>
<td class="bnnsColumn">BNNSDataTypeUInt16</td>
<td class="mpsColumn">MPSDataType.uInt16</td>
<td class="mlxColumn">mx.uint16</td>
<td class="ncnnColumn">x</td>
<td class="cntkColumn">x</td>
<td class="openVinoColumn">ov::element::Type_t::u16</td>
<td class="oneDnnColumn">x</td>
<td class="annColumn">?</td>
<td class="futureColumn">?</td>
</tr>
<tr>
<td>Integer Unsigned</td>
<td>uint32</td>
<td class="detailsColumn"></td>
<td class="webnnColumn">uint32</td>
<td class="onnxColumn">ONNX.TensorProto.DataType.UINT32</td>
<td class="dmlColumn">DML_TENSOR_DATA_TYPE_UINT32</td>
<td class="xnnPackColumn">x</td>
<td class="stableHloColumn">ui32</td>
<td class="tosaColumn">x</td>
<td class="numpyColumn">numpy.uint32 / uintc</td>
<td class="tensorFlowColumn">tensorflow.uint32</td>
<td class="tensorFlowLiteColumn">tensorflow.uint32</td>
<td class="pytorchColumn">x</td>
<td class="coreMlColumn">x</td>
<td class="bnnsColumn">BNNSDataTypeUInt32</td>
<td class="mpsColumn">MPSDataType.uInt32</td>
<td class="mlxColumn">mx.uint32</td>
<td class="ncnnColumn">x</td>
<td class="cntkColumn">x</td>
<td class="openVinoColumn">ov::element::Type_t::u32</td>
<td class="oneDnnColumn">x</td>
<td class="annColumn">ANEURALNETWORKS_UINT32</td>
<td class="futureColumn">?</td>
</tr>
<tr>
<td>Integer Unsigned</td>
<td>uint48</td>
<td class="detailsColumn"></td>
<td class="webnnColumn">x</td>
<td class="onnxColumn">x</td>
<td class="dmlColumn">x</td>
<td class="xnnPackColumn">x</td>
<td class="stableHloColumn">x</td>
<td class="tosaColumn">x</td>
<td class="numpyColumn">x</td>
<td class="tensorFlowColumn">x</td>
<td class="tensorFlowLiteColumn">x</td>
<td class="pytorchColumn">x</td>
<td class="coreMlColumn">x</td>
<td class="bnnsColumn">x</td>
<td class="mpsColumn">x</td>
<td class="mlxColumn">x</td>
<td class="ncnnColumn">x</td>
<td class="cntkColumn">x</td>
<td class="openVinoColumn">x</td>
<td class="oneDnnColumn">x</td>
<td class="annColumn">?</td>
<td class="futureColumn">?</td>
</tr>
<tr>
<td>Integer Signed</td>
<td>uint64</td>
<td class="detailsColumn"></td>
<td class="webnnColumn">uint64</td>
<td class="onnxColumn">ONNX.TensorProto.DataType.UINT64</td>
<td class="dmlColumn">DML_TENSOR_DATA_TYPE_UINT64</td>
<td class="xnnPackColumn">x</td>
<td class="stableHloColumn">ui64</td>
<td class="tosaColumn">x</td>
<td class="numpyColumn">numpy.uint64 / uint</td>
<td class="tensorFlowColumn">tensorflow.uint64</td>
<td class="tensorFlowLiteColumn">tensorflow.uint64</td>
<td class="pytorchColumn">x</td>
<td class="coreMlColumn">x</td>
<td class="bnnsColumn">BNNSDataTypeUInt64</td>
<td class="mpsColumn">MPSDataType.uInt64</td>
<td class="mlxColumn">mx.uint64</td>
<td class="ncnnColumn">x</td>
<td class="cntkColumn">x</td>
<td class="openVinoColumn">ov::element::Type_t::u64</td>
<td class="oneDnnColumn">x</td>
<td class="annColumn">?</td>
<td class="futureColumn">?</td>
</tr>
<tr>
<td>Integer Signed</td>
<td>int4</td>
<td class="detailsColumn">int=3, sign=1, twos complement</td>
<td class="webnnColumn">x</td>
<td class="onnxColumn">x</td>
<td class="dmlColumn">DML_TENSOR_DATA_TYPE_INT4</td>
<td class="xnnPackColumn">x</td>
<td class="stableHloColumn">si4</td>
<td class="tosaColumn">tosa.int4_t</td>
<td class="numpyColumn">x</td>
<td class="tensorFlowColumn">x</td>
<td class="tensorFlowLiteColumn">x</td>
<td class="pytorchColumn">x</td>
<td class="coreMlColumn">x</td>
<td class="bnnsColumn">x</td>
<td class="mpsColumn">x</td>
<td class="mlxColumn">x</td>
<td class="ncnnColumn">x</td>
<td class="cntkColumn">x</td>
<td class="openVinoColumn">ov::element::Type_t::i4</td>
<td class="oneDnnColumn">x</td>
<td class="annColumn">?</td>
<td class="futureColumn">?</td>
</tr>
<tr>
<td>Integer Signed</td>
<td>int8</td>
<td class="detailsColumn">int=7, sign=1, twos complement</td>
<td class="webnnColumn">int8</td>
<td class="onnxColumn">ONNX.TensorProto.DataType.INT8</td>
<td class="dmlColumn">DML_TENSOR_DATA_TYPE_INT8</td>
<td class="xnnPackColumn">x</td>
<td class="stableHloColumn">si8</td>
<td class="tosaColumn">tosa.int8_t</td>
<td class="numpyColumn">numpy.int8 / byte</td>
<td class="tensorFlowColumn">tensorflow.int8</td>
<td class="tensorFlowLiteColumn">tensorflow.int8</td>
<td class="pytorchColumn">torch.int8</td>
<td class="coreMlColumn">x</td>
<td class="bnnsColumn">BNNSDataTypeInt8</td>
<td class="mpsColumn">MPSDataType.int8</td>
<td class="mlxColumn">mx.int8</td>
<td class="ncnnColumn">int8</td>
<td class="cntkColumn">CNTK.DataType.Int8</td>
<td class="openVinoColumn">ov::element::Type_t::i8</td>
<td class="oneDnnColumn">dnnl_data_type_t::dnnl_s8</td>
<td class="annColumn">?</td>
<td class="futureColumn">?</td>
</tr>
<tr>
<td>Integer Signed</td>
<td>int16</td>
<td class="detailsColumn">int=15, sign=1, twos complement</td>
<td class="webnnColumn">x</td>
<td class="onnxColumn">ONNX.TensorProto.DataType.INT16</td>
<td class="dmlColumn">DML_TENSOR_DATA_TYPE_INT16</td>
<td class="xnnPackColumn">x</td>
<td class="stableHloColumn">si16</td>
<td class="tosaColumn">tosa.int16_t</td>
<td class="numpyColumn">numpy.int16 / short</td>
<td class="tensorFlowColumn">tensorflow.int16</td>
<td class="tensorFlowLiteColumn">tensorflow.int16</td>
<td class="pytorchColumn">torch.int16 / short</td>
<td class="coreMlColumn">x</td>
<td class="bnnsColumn">BNNSDataTypeInt16</td>
<td class="mpsColumn">MPSDataType.int16</td>
<td class="mlxColumn">mx.int16</td>
<td class="ncnnColumn">x</td>
<td class="cntkColumn">CNTK.DataType.Int16</td>
<td class="openVinoColumn">ov::element::Type_t::i16</td>
<td class="oneDnnColumn">x</td>
<td class="annColumn">?</td>
<td class="futureColumn">?</td>
</tr>
<tr>
<td>Integer Signed</td>
<td>int32</td>
<td class="detailsColumn">int=31, sign=1, twos complement</td>
<td class="webnnColumn">int32</td>
<td class="onnxColumn">ONNX.TensorProto.DataType.INT32</td>
<td class="dmlColumn">DML_TENSOR_DATA_TYPE_INT32</td>
<td class="xnnPackColumn">x</td>
<td class="stableHloColumn">si32</td>
<td class="tosaColumn">tosa.int32_t</td>
<td class="numpyColumn">numpy.int32 / intc</td>
<td class="tensorFlowColumn">tensorflow.int32</td>
<td class="tensorFlowLiteColumn">tensorflow.int32</td>
<td class="pytorchColumn">torch.int32 / int</td>
<td class="coreMlColumn">ArrayFeatureType.ArrayDataType.INT32</td>
<td class="bnnsColumn">BNNSDataTypeInt32</td>
<td class="mpsColumn">MPSDataType.int32</td>
<td class="mlxColumn">mx.int32</td>
<td class="ncnnColumn">x</td>
<td class="cntkColumn">x</td>
<td class="openVinoColumn">ov::element::Type_t::i32</td>
<td class="oneDnnColumn">dnnl_data_type_t::dnnl_s32</td>
<td class="annColumn">ANEURALNETWORKS_INT32</td>
<td class="futureColumn">?</td>
</tr>
<tr>
<td>Integer Signed</td>
<td>int48</td>
<td class="detailsColumn">int=47, sign=1, twos complement</td>
<td class="webnnColumn">x</td>
<td class="onnxColumn">x</td>
<td class="dmlColumn">x</td>
<td class="xnnPackColumn">x</td>
<td class="stableHloColumn">x</td>
<td class="tosaColumn">tosa.int48_t</td>
<td class="numpyColumn">x</td>
<td class="tensorFlowColumn">x</td>
<td class="tensorFlowLiteColumn">x</td>
<td class="pytorchColumn">x</td>
<td class="coreMlColumn">x</td>
<td class="bnnsColumn">x</td>
<td class="mpsColumn">x</td>
<td class="mlxColumn">x</td>
<td class="ncnnColumn">x</td>
<td class="cntkColumn">x</td>
<td class="openVinoColumn">x</td>
<td class="oneDnnColumn">x</td>
<td class="annColumn">?</td>
<td class="futureColumn">?</td>
</tr>
<tr>
<td>Integer Signed</td>
<td>int64</td>
<td class="detailsColumn">int=63, sign=1, twos complement</td>
<td class="webnnColumn">int64</td>
<td class="onnxColumn">ONNX.TensorProto.DataType.INT64</td>
<td class="dmlColumn">DML_TENSOR_DATA_TYPE_INT64</td>
<td class="xnnPackColumn">x</td>
<td class="stableHloColumn">si64</td>
<td class="tosaColumn">x</td>
<td class="numpyColumn">numpy.int64 / int_</td>
<td class="tensorFlowColumn">tensorflow.int64</td>
<td class="tensorFlowLiteColumn">tensorflow.int64</td>
<td class="pytorchColumn">torch.int64 / long</td>
<td class="coreMlColumn">x</td>
<td class="bnnsColumn">BNNSDataTypeInt64</td>
<td class="mpsColumn">MPSDataType.int64</td>
<td class="mlxColumn">mx.int64</td>
<td class="ncnnColumn">x</td>
<td class="cntkColumn">x</td>
<td class="openVinoColumn">ov::element::Type_t::i64</td>
<td class="oneDnnColumn">x</td>
<td class="annColumn">?</td>
<td class="futureColumn">?</td>
</tr>
<tr>
<td>Float Signed</td>
<td>float8f3e4s1Fn</td>
<td class="detailsColumn">frac=3 exp=4 sign=1 <a href="https://arxiv.org/abs/2209.05433">(1)</a> <a href="https://arxiv.org/pdf/2206.02915.pdf">(2)</a> <a href="https://onnx.ai/onnx/technical/float8.html">(3)</a>, has nan, no inf</td>
<td class="webnnColumn">x</td>
<td class="onnxColumn">ONNX.TensorProto.DataType.FLOAT8E4M3FN</td>
<td class="dmlColumn">x</td>
<td class="xnnPackColumn">x</td>
<td class="stableHloColumn">f8E4M3FN</td>
<td class="tosaColumn">x</td>
<td class="numpyColumn">x</td>
<td class="tensorFlowColumn">x</td>
<td class="tensorFlowLiteColumn">x</td>
<td class="pytorchColumn">x</td>
<td class="coreMlColumn">x</td>
<td class="bnnsColumn">x</td>
<td class="mpsColumn">x</td>
<td class="mlxColumn">x</td>
<td class="ncnnColumn">x</td>
<td class="cntkColumn">x</td>
<td class="openVinoColumn">x</td>
<td class="oneDnnColumn">dnnl_data_type_t::dnnl_f8_e4m3</td>
<td class="annColumn">?</td>
<td class="futureColumn">?</td>
</tr>
<tr>
<td>Float Signed</td>
<td>float8f3e4s1FnUz</td>
<td class="detailsColumn">frac=3 exp=4 sign=1 <a href="https://arxiv.org/abs/2209.05433">(1)</a> <a href="https://arxiv.org/pdf/2206.02915.pdf">(2)</a> <a href="https://onnx.ai/onnx/technical/float8.html">(3)</a>, has nan, no inf, no negative zero</td>
<td class="webnnColumn">x</td>
<td class="onnxColumn">ONNX.TensorProto.DataType.FLOAT8E4M3FNUZ</td>
<td class="dmlColumn">x</td>
<td class="xnnPackColumn">x</td>
<td class="stableHloColumn">f8E4M3FNUZ</td>
<td class="tosaColumn">x</td>
<td class="numpyColumn">x</td>
<td class="tensorFlowColumn">x</td>
<td class="tensorFlowLiteColumn">x</td>
<td class="pytorchColumn">x</td>
<td class="coreMlColumn">x</td>
<td class="bnnsColumn">x</td>
<td class="mpsColumn">x</td>
<td class="mlxColumn">x</td>
<td class="ncnnColumn">x</td>
<td class="cntkColumn">x</td>
<td class="openVinoColumn">x</td>
<td class="oneDnnColumn">x</td>
<td class="annColumn">?</td>
<td class="futureColumn">?</td>
</tr>
<tr>
<td>Float Signed</td>
<td>float8f2e5s1</td>
<td class="detailsColumn">frac=2 exp=5 sign=1 <a href="https://arxiv.org/abs/2209.05433">(1)</a> <a href="https://arxiv.org/pdf/2206.02915.pdf">(2)</a> <a href="https://onnx.ai/onnx/technical/float8.html">(3)</a>, has nan, has inf, has negative zero</td>
<td class="webnnColumn">x</td>
<td class="onnxColumn">ONNX.TensorProto.DataType.FLOAT8E5M2</td>
<td class="dmlColumn">x</td>
<td class="xnnPackColumn">x</td>
<td class="stableHloColumn">f8E5M2</td>
<td class="tosaColumn">x</td>
<td class="numpyColumn">x</td>
<td class="tensorFlowColumn">x</td>
<td class="tensorFlowLiteColumn">x</td>
<td class="pytorchColumn">x</td>
<td class="coreMlColumn">x</td>
<td class="bnnsColumn">x</td>
<td class="mpsColumn">x</td>
<td class="mlxColumn">x</td>
<td class="ncnnColumn">x</td>
<td class="cntkColumn">x</td>
<td class="openVinoColumn">x</td>
<td class="oneDnnColumn">dnnl_data_type_t::dnnl_f8_e5m2</td>
<td class="annColumn">?</td>
<td class="futureColumn">?</td>
</tr>
<tr>
<td>Float Signed</td>
<td>float8f2e5s1FnUz</td>
<td class="detailsColumn">frac=2 exp=5 sign=1 <a href="https://arxiv.org/abs/2209.05433">(1)</a> <a href="https://arxiv.org/pdf/2206.02915.pdf">(2)</a> <a href="https://onnx.ai/onnx/technical/float8.html">(3)</a>, has nan, no inf, no negative zero</td>
<td class="webnnColumn">x</td>
<td class="onnxColumn">ONNX.TensorProto.DataType.FLOAT8E5M2FNUZ</td>
<td class="dmlColumn">x</td>
<td class="xnnPackColumn">x</td>
<td class="stableHloColumn">f8E5M2FNUZ</td>
<td class="tosaColumn">x</td>
<td class="numpyColumn">x</td>
<td class="tensorFlowColumn">x</td>
<td class="tensorFlowLiteColumn">x</td>
<td class="pytorchColumn">x</td>
<td class="coreMlColumn">x</td>
<td class="bnnsColumn">x</td>
<td class="mpsColumn">x</td>
<td class="mlxColumn">x</td>
<td class="ncnnColumn">x</td>
<td class="cntkColumn">x</td>
<td class="openVinoColumn">x</td>
<td class="oneDnnColumn">x</td>
<td class="annColumn">?</td>
<td class="futureColumn">?</td>
</tr>
<tr>
<td>Float Signed</td>
<td>float8f2e5bias4s1FnUz</td>
<td class="detailsColumn">frac=2 exp=5 sign=1 <a href="https://proceedings.neurips.cc/paper_files/paper/2019/file/65fc9fb4897a89789352e211ca2d398f-Paper.pdf">(1)</a> TODO: Figure out details</td>
<td class="webnnColumn">x</td>
<td class="onnxColumn">x</td>
<td class="dmlColumn">x</td>
<td class="xnnPackColumn">x</td>
<td class="stableHloColumn">f8E4M3B11FNUZ</td>
<td class="tosaColumn">x</td>
<td class="numpyColumn">x</td>
<td class="tensorFlowColumn">x</td>
<td class="tensorFlowLiteColumn">x</td>
<td class="pytorchColumn">x</td>
<td class="coreMlColumn">x</td>
<td class="bnnsColumn">x</td>
<td class="mpsColumn">x</td>
<td class="mlxColumn">x</td>
<td class="ncnnColumn">x</td>
<td class="cntkColumn">x</td>
<td class="openVinoColumn">x</td>
<td class="oneDnnColumn">x</td>
<td class="annColumn">?</td>
<td class="futureColumn">?</td>
</tr>
<tr>
<td>Float Signed</td>
<td>float16f10e5s1 IEEE</td>
<td class="detailsColumn">frac=10 exp=5 sign=1</td>
<td class="webnnColumn">float16</td>
<td class="onnxColumn">ONNX.TensorProto.DataType.FLOAT16</td>
<td class="dmlColumn">DML_TENSOR_DATA_TYPE_FLOAT16</td>
<td class="xnnPackColumn">xnn_datatype_fp16</td>
<td class="stableHloColumn">f16</td>
<td class="tosaColumn">tosa.fp16_t</td>
<td class="numpyColumn">numpy.float16 / half</td>
<td class="tensorFlowColumn">tensorflow.float16 / half</td>
<td class="tensorFlowLiteColumn">tensorflow.float16 / half</td>
<td class="pytorchColumn">torch.float16 / half</td>
<td class="coreMlColumn">ArrayFeatureType.ArrayDataType.FLOAT16</td>
<td class="bnnsColumn">BNNSDataTypeFloat16</td>
<td class="mpsColumn">MPSDataType.float16</td>
<td class="mlxColumn">mx.float16</td>
<td class="ncnnColumn">float16</td>
<td class="cntkColumn">CNTK.DataType.Float16</td>
<td class="openVinoColumn">ov::element::Type_t::f16</td>
<td class="oneDnnColumn">dnnl_data_type_t::dnnl_f16</td>
<td class="annColumn">ANEURALNETWORKS_FLOAT16</td>
<td class="futureColumn">?</td>
</tr>
<tr>
<td>Float Signed</td>
<td>float16f7e8s1 Brain</td>
<td class="detailsColumn">frac=7 exp=8 sign=1</td>
<td class="webnnColumn">x</td>
<td class="onnxColumn">ONNX.TensorProto.DataType.BFLOAT16</td>
<td class="dmlColumn">x</td>
<td class="xnnPackColumn">x</td>
<td class="stableHloColumn">bf16</td>
<td class="tosaColumn">tosa.bf16_t</td>
<td class="numpyColumn">x</td>
<td class="tensorFlowColumn">tensorflow.bfloat16</td>
<td class="tensorFlowLiteColumn">tensorflow.bfloat16</td>
<td class="pytorchColumn">torch.bfloat16</td>
<td class="coreMlColumn">x</td>
<td class="bnnsColumn">BNNSDataTypeBFloat16</td>
<td class="mpsColumn">MPSDataType.bFloat16</td>
<td class="mlxColumn">x</td>
<td class="ncnnColumn">bfloat16</td>
<td class="cntkColumn">x</td>
<td class="openVinoColumn">ov::element::Type_t::bf16</td>
<td class="oneDnnColumn">dnnl_data_type_t::dnnl_bf16</td>
<td class="annColumn">?</td>
<td class="futureColumn">?</td>
</tr>
<tr>
<td>Float Signed</td>
<td>float32f23e8s1 IEEE</td>
<td class="detailsColumn">frac=23 exp=8 sign=1</td>
<td class="webnnColumn">float32</td>
<td class="onnxColumn">ONNX.TensorProto.DataType.FLOAT</td>
<td class="dmlColumn">DML_TENSOR_DATA_TYPE_FLOAT32</td>
<td class="xnnPackColumn">xnn_datatype_fp32</td>
<td class="stableHloColumn">f32</td>
<td class="tosaColumn">tosa.fp32_t</td>
<td class="numpyColumn">numpy.float32 / single</td>
<td class="tensorFlowColumn">tensorflow.float32 / float</td>
<td class="tensorFlowLiteColumn">tensorflow.float32 / float</td>
<td class="pytorchColumn">torch.float32 / float</td>
<td class="coreMlColumn">ArrayFeatureType.ArrayDataType.FLOAT32</td>
<td class="bnnsColumn">BNNSDataTypeFloat32</td>
<td class="mpsColumn">MPSDataType.float32</td>
<td class="mlxColumn">mx.float32</td>
<td class="ncnnColumn">float32</td>
<td class="cntkColumn">CNTK.DataType.Float</td>
<td class="openVinoColumn">ov::element::Type_t::f32</td>
<td class="oneDnnColumn">dnnl_data_type_t::dnnl_f32</td>
<td class="annColumn">ANEURALNETWORKS_FLOAT32</td>
<td class="futureColumn">?</td>
</tr>
<tr>
<td>Float Signed</td>
<td>float64f52e11s1 IEEE</td>
<td class="detailsColumn">frac=52 exp=11 sign=1</td>
<td class="webnnColumn">float64</td>
<td class="onnxColumn">ONNX.TensorProto.DataType.DOUBLE</td>
<td class="dmlColumn">DML_TENSOR_DATA_TYPE_FLOAT64</td>
<td class="xnnPackColumn">x</td>
<td class="stableHloColumn">f64</td>
<td class="tosaColumn">tosa.fp64_t</td>
<td class="numpyColumn">numpy.float64 / double / float_</td>
<td class="tensorFlowColumn">tensorflow.float64 / double</td>
<td class="tensorFlowLiteColumn">tensorflow.float64 / double</td>
<td class="pytorchColumn">torch.float64 / double</td>
<td class="coreMlColumn">ArrayFeatureType.ArrayDataType.DOUBLE</td>
<td class="bnnsColumn">x</td>
<td class="mpsColumn">x</td>
<td class="mlxColumn">x</td>
<td class="ncnnColumn">x</td>
<td class="cntkColumn">CNTK.DataType.Double</td>
<td class="openVinoColumn">ov::element::Type_t::f64</td>
<td class="oneDnnColumn">dnnl_data_type_t::dnnl_f64</td>
<td class="annColumn">?</td>
<td class="futureColumn">?</td>
</tr>
<tr>
<td>Float Signed</td>
<td>float16 x 2</td>
<td class="detailsColumn"></td>
<td class="webnnColumn">NA</td>
<td class="onnxColumn">x</td>
<td class="dmlColumn">x</td>
<td class="xnnPackColumn">x</td>
<td class="stableHloColumn">x</td>
<td class="tosaColumn">x</td>
<td class="numpyColumn">x</td>
<td class="tensorFlowColumn">x</td>
<td class="tensorFlowLiteColumn">x</td>
<td class="pytorchColumn">x</td>
<td class="coreMlColumn">x</td>
<td class="bnnsColumn">x</td>
<td class="mpsColumn">MPSDataType.complexFloat16</td>
<td class="mlxColumn">x</td>
<td class="ncnnColumn">x</td>
<td class="cntkColumn">x</td>
<td class="openVinoColumn">x</td>
<td class="oneDnnColumn">x</td>
<td class="annColumn">?</td>
<td class="futureColumn">?</td>
</tr>
<tr>
<td>Float Signed</td>
<td>float32 x 2</td>
<td class="detailsColumn"></td>
<td class="webnnColumn">NA</td>
<td class="onnxColumn">ONNX.TensorProto.DataType.COMPLEX64</td>
<td class="dmlColumn">x</td>
<td class="xnnPackColumn">x</td>
<td class="stableHloColumn">x</td>
<td class="tosaColumn">x</td>
<td class="numpyColumn">numpy.complex64 / singlecomplex</td>
<td class="tensorFlowColumn">tensorflow.complex64</td>
<td class="tensorFlowLiteColumn">tensorflow.complex64</td>
<td class="pytorchColumn">torch.complex64 / cfloat</td>
<td class="coreMlColumn">x</td>
<td class="bnnsColumn">x</td>
<td class="mpsColumn">MPSDataType.complexFloat32</td>
<td class="mlxColumn">x</td>
<td class="ncnnColumn">x</td>
<td class="cntkColumn">x</td>
<td class="openVinoColumn">x</td>
<td class="oneDnnColumn">x</td>
<td class="annColumn">?</td>
<td class="futureColumn">?</td>
</tr>
<tr>
<td>Float Signed</td>
<td>float64 x 2</td>
<td class="detailsColumn"></td>
<td class="webnnColumn">NA</td>
<td class="onnxColumn">ONNX.TensorProto.DataType.COMPLEX128</td>
<td class="dmlColumn">x</td>
<td class="xnnPackColumn">x</td>
<td class="stableHloColumn">x</td>
<td class="tosaColumn">x</td>
<td class="numpyColumn">numpy.complex128 / doublecomplex</td>
<td class="tensorFlowColumn">tensorflow.complex128</td>
<td class="tensorFlowLiteColumn">tensorflow.complex128</td>
<td class="pytorchColumn">torch.complex128 / cdouble</td>
<td class="coreMlColumn">x</td>
<td class="bnnsColumn">x</td>
<td class="mpsColumn">x</td>
<td class="mlxColumn">x</td>
<td class="ncnnColumn">x</td>
<td class="cntkColumn">x</td>
<td class="openVinoColumn">x</td>
<td class="oneDnnColumn">x</td>
<td class="annColumn">?</td>
<td class="futureColumn">?</td>
</tr>
<tr>
<td>Boolean</td>
<td>bool8</td>
<td class="detailsColumn">typically just lowest bit is used, but anything != 0 is true</td>
<td class="webnnColumn">uint8</td>
<td class="onnxColumn">ONNX.TensorProto.DataType.BOOL</td>
<td class="dmlColumn">DML_TENSOR_DATA_TYPE_UINT8</td>
<td class="xnnPackColumn">x</td>
<td class="stableHloColumn">x</td>
<td class="tosaColumn">tosa.bool_t</td>
<td class="numpyColumn">numpy.bool</td>
<td class="tensorFlowColumn">tensorflow.bool</td>
<td class="tensorFlowLiteColumn">tensorflow.bool</td>
<td class="pytorchColumn">torch.bool</td>
<td class="coreMlColumn">x</td>
<td class="bnnsColumn">BNNSDataTypeBoolean (bit size?)</td>
<td class="mpsColumn">MPSDataType.bool (bit size?)</td>
<td class="mlxColumn">bool_</td>
<td class="ncnnColumn">x</td>
<td class="cntkColumn">x</td>
<td class="openVinoColumn">ov::element::Type_t::boolean</td>
<td class="oneDnnColumn">dnnl_data_type_t::dnnl_boolean</td>
<td class="annColumn">ANEURALNETWORKS_BOOL8</td>
<td class="futureColumn">?</td>
</tr>
<tr>
<td>String</td>
<td>string8</td>
<td class="detailsColumn">array of char8's (typically UTF-8)</td>
<td class="webnnColumn">NA</td>
<td class="onnxColumn">ONNX.TensorProto.DataType.STRING</td>
<td class="dmlColumn">x</td>
<td class="xnnPackColumn">x</td>
<td class="stableHloColumn">x</td>
<td class="tosaColumn">x</td>
<td class="numpyColumn">x</td>
<td class="tensorFlowColumn">tensorflow.string</td>
<td class="tensorFlowLiteColumn">tensorflow.string</td>
<td class="pytorchColumn">x</td>
<td class="coreMlColumn">x</td>
<td class="bnnsColumn">x</td>
<td class="mpsColumn">x</td>
<td class="mlxColumn">x</td>
<td class="ncnnColumn">x</td>
<td class="cntkColumn">x</td>
<td class="openVinoColumn">x</td>
<td class="oneDnnColumn">x</td>
<td class="annColumn">?</td>
<td class="futureColumn">?</td>
</tr>
<!--
<tr>
<td>categories</td>
<td>name</td>
<td class="detailsColumn"></td>
<td class="webnnColumn">?</td>
<td class="onnxColumn">?</td>
<td class="dmlColumn">?</td>
<td class="xnnPackColumn">?</td>
<td class="stableHloColumn">?</td>
<td class="tosaColumn">?</td>
<td class="numpyColumn">?</td>
<td class="tensorFlowColumn">?</td>
<td class="tensorFlowLiteColumn">?</td>
<td class="pytorchColumn">?</td>
<td class="coreMlColumn">?</td>
<td class="bnnsColumn">?</td>
<td class="mpsColumn">?</td>
<td class="mlxColumn">?</td>
<td class="ncnnColumn">?</td>
<td class="cntkColumn">?</td>
<td class="openVinoColumn">?</td>
<td class="oneDnnColumn">?</td>
<td class="annColumn">?</td>
<td class="futureColumn">?</td>
</tr>
-->
</tbody>
</table>
<!-- ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- -->
<h1 id="Operators">Operators</h1>
<table border=1 cellspacing=0 cellpadding=1 style='border-collapse:collapse; border:none'>
<tr>
<th style="width:15em">Categories</th>
<th>Name</th>
<th class="detailsColumn" valign="top">Details/Formula</th>
<th class="webnnColumn"><a href="https://www.w3.org/TR/webnn/">WebNN</a></th>
<th class="onnxColumn"><a href="https://onnx.ai/onnx/operators/index.html">ONNX</a></th>
<th class="dmlColumn"><a href="https://learn.microsoft.com/en-us/windows/win32/api/directml/ne-directml-dml_operator_type">DML</a></th>
<th class="xnnPackColumn">XNNPACK</th>
<th class="stableHloColumn"><a href="https://github.com/openxla/stablehlo/blob/main/docs/spec.md">StableHLO</a></th>
<th class="tosaColumn"><a href="https://mlir.llvm.org/docs/Dialects/TOSA/">TOSA</a></th>
<th class="numpyColumn"><a href="https://numpy.org/doc/stable/reference/routines.html">NumPy</a></th>
<th class="tensorFlowColumn">TensorFlow</th>
<th class="tensorFlowLiteColumn">TensorFlowLite</th>
<th class="pytorchColumn"><a href="https://pytorch.org/docs/stable/torch.html">PyTorch</a></th>
<th class="coreMlColumn"><a href="https://apple.github.io/coremltools/mlmodel/Format/NeuralNetwork.html">CoreML</a></th>
<th class="bnnsColumn">BNNS</th>
<th class="mpsColumn">MPS</th>
<th class="mlxColumn"><a href="https://ml-explore.github.io/mlx/build/html/python/ops.html">MLX</a></th>
<th class="ncnnColumn"><a href="https://github.com/Tencent/ncnn/blob/54a9a563e9913d3142782dac0e497f2be50075b5/docs/developer-guide/operators.md">NCNN</a></th>
<th class="cntkColumn"><a href="https://microsoft.github.io/CNTK-R/reference/index.html">CNTK</a></th>
<th class="openVinoColumn"><a href="https://docs.openvino.ai/2023.0/api/ie_python_api/_autosummary/openvino.runtime.opset1.html">OpenVINO</a></th>
<th class="oneDnnColumn"><a href="https://oneapi-src.github.io/oneDNN/group_dnnl_api_primitives.html">OneDNN</a></th>
<th class="annColumn"><a href="https://developer.android.com/ndk/reference/group/neural-networks">ANN</a></th>
<th class="futureColumn">(for future additions)</th>
<th>Precision</th>
</tr>
<tr class="elementwiseOperator">
<td>Elementwise</td>
<td>Elementwise Generic</td>
<td class="detailsColumn"><code><details><summary>function elementwiseNullary(functor, dataType, dimensions)</summary>
output = new Tensor(dataType, dimensions)
for each coordinate in output.coordinates
output[coordinate] = functor()
endfor
return output
endfunction
</details>
<details><summary>function elementwiseUnary(input, functor)</summary>
output = new Tensor(input.dataType, input.dimensions)
for each coordinate in input.coordinates
output[coordinate] = functor(input[coordinate])
endfor
return output
endfunction
</details>
<details><summary>function elementwiseBinary(a, b, functor)</summary>
outputDimensions = broadcastDimensions(a.dimensions, b.dimensions)
output = new Tensor(a.dataType, outputDimensions)
aBroadcast = broadcast(a, outputDimensions) // Some implementations can directly use strides to avoid intermediates.
bBroadcast = broadcast(b, outputDimensions)
for each coordinate in input.coordinates
output[coordinate] = functor(aBroadcast[coordinate], bBroadcast[coordinate])
endfor
return output
endfunction
</details>
<details><summary>function elementwiseTrinary(a, b, c, functor)</summary>
outputDimensions = broadcastDimensions(a.dimensions, b.dimensions, c.dimensions)
output = new Tensor(a.dataType, outputDimensions)
aBroadcast = broadcast(a, outputDimensions) // Some implementations can directly use strides to avoid intermediates.
bBroadcast = broadcast(b, outputDimensions)
cBroadcast = broadcast(c, outputDimensions)
for each coordinate in input.coordinates
output[coordinate] = functor(aBroadcast[coordinate], bBroadcast[coordinate], cBroadcast[coordinate])
endfor
return output
endfunction</details></code></td>
<td class="webnnColumn">NA</td>
<td class="onnxColumn">NA</td>
<td class="dmlColumn">NA</td>
<td class="xnnPackColumn">NA</td>
<td class="stableHloColumn">NA</td>
<td class="tosaColumn">NA</td>
<td class="numpyColumn">NA</td>