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| <span class="mdl-layout-title toc">Table Of Contents</span> |
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| <li class="toctree-l1"><a class="reference internal" href="../tutorials/index.html">Python Tutorials</a><ul> |
| <li class="toctree-l2"><a class="reference internal" href="../tutorials/getting-started/index.html">Getting Started</a><ul> |
| <li class="toctree-l3"><a class="reference internal" href="../tutorials/getting-started/crash-course/index.html">Crash Course</a><ul> |
| <li class="toctree-l4"><a class="reference internal" href="../tutorials/getting-started/crash-course/1-ndarray.html">Manipulate data with <code class="docutils literal notranslate"><span class="pre">ndarray</span></code></a></li> |
| <li class="toctree-l4"><a class="reference internal" href="../tutorials/getting-started/crash-course/2-nn.html">Create a neural network</a></li> |
| <li class="toctree-l4"><a class="reference internal" href="../tutorials/getting-started/crash-course/3-autograd.html">Automatic differentiation with <code class="docutils literal notranslate"><span class="pre">autograd</span></code></a></li> |
| <li class="toctree-l4"><a class="reference internal" href="../tutorials/getting-started/crash-course/4-train.html">Train the neural network</a></li> |
| <li class="toctree-l4"><a class="reference internal" href="../tutorials/getting-started/crash-course/5-predict.html">Predict with a pre-trained model</a></li> |
| <li class="toctree-l4"><a class="reference internal" href="../tutorials/getting-started/crash-course/6-use_gpus.html">Use GPUs</a></li> |
| </ul> |
| </li> |
| <li class="toctree-l3"><a class="reference internal" href="../tutorials/getting-started/to-mxnet/index.html">Moving to MXNet from Other Frameworks</a><ul> |
| <li class="toctree-l4"><a class="reference internal" href="../tutorials/getting-started/to-mxnet/pytorch.html">PyTorch vs Apache MXNet</a></li> |
| </ul> |
| </li> |
| <li class="toctree-l3"><a class="reference internal" href="../tutorials/getting-started/gluon_from_experiment_to_deployment.html">Gluon: from experiment to deployment</a></li> |
| <li class="toctree-l3"><a class="reference internal" href="../tutorials/getting-started/logistic_regression_explained.html">Logistic regression explained</a></li> |
| <li class="toctree-l3"><a class="reference external" href="https://mxnet.apache.org/api/python/docs/tutorials/packages/gluon/image/mnist.html">MNIST</a></li> |
| </ul> |
| </li> |
| <li class="toctree-l2"><a class="reference internal" href="../tutorials/packages/index.html">Packages</a><ul> |
| <li class="toctree-l3"><a class="reference internal" href="../tutorials/packages/autograd/index.html">Automatic Differentiation</a></li> |
| <li class="toctree-l3"><a class="reference internal" href="../tutorials/packages/gluon/index.html">Gluon</a><ul> |
| <li class="toctree-l4"><a class="reference internal" href="../tutorials/packages/gluon/blocks/index.html">Blocks</a><ul> |
| <li class="toctree-l5"><a class="reference internal" href="../tutorials/packages/gluon/blocks/custom-layer.html">Custom Layers</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../tutorials/packages/gluon/blocks/custom_layer_beginners.html">Customer Layers (Beginners)</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../tutorials/packages/gluon/blocks/hybridize.html">Hybridize</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../tutorials/packages/gluon/blocks/init.html">Initialization</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../tutorials/packages/gluon/blocks/naming.html">Parameter and Block Naming</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../tutorials/packages/gluon/blocks/nn.html">Layers and Blocks</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../tutorials/packages/gluon/blocks/parameters.html">Parameter Management</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../tutorials/packages/gluon/blocks/save_load_params.html">Saving and Loading Gluon Models</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../tutorials/packages/gluon/blocks/activations/activations.html">Activation Blocks</a></li> |
| </ul> |
| </li> |
| <li class="toctree-l4"><a class="reference internal" href="../tutorials/packages/gluon/data/index.html">Data Tutorials</a><ul> |
| <li class="toctree-l5"><a class="reference internal" href="../tutorials/packages/gluon/data/data_augmentation.html">Image Augmentation</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../tutorials/packages/gluon/data/data_augmentation.html#Spatial-Augmentation">Spatial Augmentation</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../tutorials/packages/gluon/data/data_augmentation.html#Color-Augmentation">Color Augmentation</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../tutorials/packages/gluon/data/data_augmentation.html#Composed-Augmentations">Composed Augmentations</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../tutorials/packages/gluon/data/datasets.html">Gluon <code class="docutils literal notranslate"><span class="pre">Dataset</span></code>s and <code class="docutils literal notranslate"><span class="pre">DataLoader</span></code></a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../tutorials/packages/gluon/data/datasets.html#Using-own-data-with-included-Datasets">Using own data with included <code class="docutils literal notranslate"><span class="pre">Dataset</span></code>s</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../tutorials/packages/gluon/data/datasets.html#Using-own-data-with-custom-Datasets">Using own data with custom <code class="docutils literal notranslate"><span class="pre">Dataset</span></code>s</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../tutorials/packages/gluon/data/datasets.html#Appendix:-Upgrading-from-Module-DataIter-to-Gluon-DataLoader">Appendix: Upgrading from Module <code class="docutils literal notranslate"><span class="pre">DataIter</span></code> to Gluon <code class="docutils literal notranslate"><span class="pre">DataLoader</span></code></a></li> |
| </ul> |
| </li> |
| <li class="toctree-l4"><a class="reference internal" href="../tutorials/packages/gluon/image/index.html">Image Tutorials</a><ul> |
| <li class="toctree-l5"><a class="reference internal" href="../tutorials/packages/gluon/image/image-augmentation.html">Image Augmentation</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../tutorials/packages/gluon/image/info_gan.html">Image similarity search with InfoGAN</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../tutorials/packages/gluon/image/mnist.html">Handwritten Digit Recognition</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../tutorials/packages/gluon/image/pretrained_models.html">Using pre-trained models in MXNet</a></li> |
| </ul> |
| </li> |
| <li class="toctree-l4"><a class="reference internal" href="../tutorials/packages/gluon/loss/index.html">Losses</a><ul> |
| <li class="toctree-l5"><a class="reference internal" href="../tutorials/packages/gluon/loss/custom-loss.html">Custom Loss Blocks</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../tutorials/packages/gluon/loss/kl_divergence.html">Kullback-Leibler (KL) Divergence</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../tutorials/packages/gluon/loss/loss.html">Loss functions</a></li> |
| </ul> |
| </li> |
| <li class="toctree-l4"><a class="reference internal" href="../tutorials/packages/gluon/text/index.html">Text Tutorials</a><ul> |
| <li class="toctree-l5"><a class="reference internal" href="../tutorials/packages/gluon/text/gnmt.html">Google Neural Machine Translation</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../tutorials/packages/gluon/text/transformer.html">Machine Translation with Transformer</a></li> |
| </ul> |
| </li> |
| <li class="toctree-l4"><a class="reference internal" href="../tutorials/packages/gluon/training/index.html">Training</a><ul> |
| <li class="toctree-l5"><a class="reference internal" href="../tutorials/packages/gluon/training/fit_api_tutorial.html">MXNet Gluon Fit API</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../tutorials/packages/gluon/training/trainer.html">Trainer</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../tutorials/packages/gluon/training/learning_rates/index.html">Learning Rates</a><ul> |
| <li class="toctree-l6"><a class="reference internal" href="../tutorials/packages/gluon/training/learning_rates/learning_rate_finder.html">Learning Rate Finder</a></li> |
| <li class="toctree-l6"><a class="reference internal" href="../tutorials/packages/gluon/training/learning_rates/learning_rate_schedules.html">Learning Rate Schedules</a></li> |
| <li class="toctree-l6"><a class="reference internal" href="../tutorials/packages/gluon/training/learning_rates/learning_rate_schedules_advanced.html">Advanced Learning Rate Schedules</a></li> |
| </ul> |
| </li> |
| <li class="toctree-l5"><a class="reference internal" href="../tutorials/packages/gluon/training/normalization/index.html">Normalization Blocks</a></li> |
| </ul> |
| </li> |
| </ul> |
| </li> |
| <li class="toctree-l3"><a class="reference internal" href="../tutorials/packages/kvstore/index.html">KVStore</a><ul> |
| <li class="toctree-l4"><a class="reference internal" href="../tutorials/packages/kvstore/kvstore.html">Distributed Key-Value Store</a></li> |
| </ul> |
| </li> |
| <li class="toctree-l3"><a class="reference internal" href="../tutorials/packages/ndarray/index.html">NDArray</a><ul> |
| <li class="toctree-l4"><a class="reference internal" href="../tutorials/packages/ndarray/01-ndarray-intro.html">An Intro: Manipulate Data the MXNet Way with NDArray</a></li> |
| <li class="toctree-l4"><a class="reference internal" href="../tutorials/packages/ndarray/02-ndarray-operations.html">NDArray Operations</a></li> |
| <li class="toctree-l4"><a class="reference internal" href="../tutorials/packages/ndarray/03-ndarray-contexts.html">NDArray Contexts</a></li> |
| <li class="toctree-l4"><a class="reference internal" href="../tutorials/packages/ndarray/gotchas_numpy_in_mxnet.html">Gotchas using NumPy in Apache MXNet</a></li> |
| <li class="toctree-l4"><a class="reference internal" href="../tutorials/packages/ndarray/sparse/index.html">Tutorials</a><ul> |
| <li class="toctree-l5"><a class="reference internal" href="../tutorials/packages/ndarray/sparse/csr.html">CSRNDArray - NDArray in Compressed Sparse Row Storage Format</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../tutorials/packages/ndarray/sparse/row_sparse.html">RowSparseNDArray - NDArray for Sparse Gradient Updates</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../tutorials/packages/ndarray/sparse/train.html">Train a Linear Regression Model with Sparse Symbols</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../tutorials/packages/ndarray/sparse/train_gluon.html">Sparse NDArrays with Gluon</a></li> |
| </ul> |
| </li> |
| </ul> |
| </li> |
| <li class="toctree-l3"><a class="reference internal" href="../tutorials/packages/onnx/index.html">ONNX</a><ul> |
| <li class="toctree-l4"><a class="reference internal" href="../tutorials/packages/onnx/fine_tuning_gluon.html">Fine-tuning an ONNX model</a></li> |
| <li class="toctree-l4"><a class="reference internal" href="../tutorials/packages/onnx/inference_on_onnx_model.html">Running inference on MXNet/Gluon from an ONNX model</a></li> |
| <li class="toctree-l4"><a class="reference internal" href="../tutorials/packages/onnx/super_resolution.html">Importing an ONNX model into MXNet</a></li> |
| <li class="toctree-l4"><a class="reference external" href="https://mxnet.apache.org/api/python/docs/tutorials/deploy/export/onnx.html">Export ONNX Models</a></li> |
| </ul> |
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| <li class="toctree-l3"><a class="reference internal" href="../tutorials/packages/optimizer/index.html">Optimizers</a></li> |
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| <li class="toctree-l4"><a class="reference external" href="https://mxnet.apache.org/api/faq/visualize_graph">Visualize networks</a></li> |
| </ul> |
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| <li class="toctree-l2"><a class="reference internal" href="../tutorials/performance/index.html">Performance</a><ul> |
| <li class="toctree-l3"><a class="reference internal" href="../tutorials/performance/compression/index.html">Compression</a><ul> |
| <li class="toctree-l4"><a class="reference internal" href="../tutorials/performance/compression/int8.html">Deploy with int-8</a></li> |
| <li class="toctree-l4"><a class="reference external" href="https://mxnet.apache.org/api/faq/float16">Float16</a></li> |
| <li class="toctree-l4"><a class="reference external" href="https://mxnet.apache.org/api/faq/gradient_compression">Gradient Compression</a></li> |
| <li class="toctree-l4"><a class="reference external" href="https://gluon-cv.mxnet.io/build/examples_deployment/int8_inference.html">GluonCV with Quantized Models</a></li> |
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| <li class="toctree-l4"><a class="reference internal" href="../tutorials/performance/backend/mkldnn/index.html">Intel MKL-DNN</a><ul> |
| <li class="toctree-l5"><a class="reference internal" href="../tutorials/performance/backend/mkldnn/mkldnn_quantization.html">Quantize with MKL-DNN backend</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../tutorials/performance/backend/mkldnn/mkldnn_quantization.html#Improving-accuracy-with-Intel®-Neural-Compressor">Improving accuracy with Intel® Neural Compressor</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../tutorials/performance/backend/mkldnn/mkldnn_readme.html">Install MXNet with MKL-DNN</a></li> |
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| </li> |
| <li class="toctree-l4"><a class="reference internal" href="../tutorials/performance/backend/tensorrt/index.html">TensorRT</a><ul> |
| <li class="toctree-l5"><a class="reference internal" href="../tutorials/performance/backend/tensorrt/tensorrt.html">Optimizing Deep Learning Computation Graphs with TensorRT</a></li> |
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| </li> |
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| <li class="toctree-l4"><a class="reference internal" href="../tutorials/performance/backend/profiler.html">Profiling MXNet Models</a></li> |
| <li class="toctree-l4"><a class="reference internal" href="../tutorials/performance/backend/amp.html">Using AMP: Automatic Mixed Precision</a></li> |
| </ul> |
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| </ul> |
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| <li class="toctree-l2"><a class="reference internal" href="../tutorials/deploy/index.html">Deployment</a><ul> |
| <li class="toctree-l3"><a class="reference internal" href="../tutorials/deploy/export/index.html">Export</a><ul> |
| <li class="toctree-l4"><a class="reference internal" href="../tutorials/deploy/export/onnx.html">Exporting to ONNX format</a></li> |
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| <li class="toctree-l4"><a class="reference internal" href="../tutorials/deploy/inference/wine_detector.html">Real-time Object Detection with MXNet On The Raspberry Pi</a></li> |
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| </ul> |
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| <span class="mdl-layout-title toc">Table Of Contents</span> |
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| <ul> |
| <li class="toctree-l1"><a class="reference internal" href="../tutorials/index.html">Python Tutorials</a><ul> |
| <li class="toctree-l2"><a class="reference internal" href="../tutorials/getting-started/index.html">Getting Started</a><ul> |
| <li class="toctree-l3"><a class="reference internal" href="../tutorials/getting-started/crash-course/index.html">Crash Course</a><ul> |
| <li class="toctree-l4"><a class="reference internal" href="../tutorials/getting-started/crash-course/1-ndarray.html">Manipulate data with <code class="docutils literal notranslate"><span class="pre">ndarray</span></code></a></li> |
| <li class="toctree-l4"><a class="reference internal" href="../tutorials/getting-started/crash-course/2-nn.html">Create a neural network</a></li> |
| <li class="toctree-l4"><a class="reference internal" href="../tutorials/getting-started/crash-course/3-autograd.html">Automatic differentiation with <code class="docutils literal notranslate"><span class="pre">autograd</span></code></a></li> |
| <li class="toctree-l4"><a class="reference internal" href="../tutorials/getting-started/crash-course/4-train.html">Train the neural network</a></li> |
| <li class="toctree-l4"><a class="reference internal" href="../tutorials/getting-started/crash-course/5-predict.html">Predict with a pre-trained model</a></li> |
| <li class="toctree-l4"><a class="reference internal" href="../tutorials/getting-started/crash-course/6-use_gpus.html">Use GPUs</a></li> |
| </ul> |
| </li> |
| <li class="toctree-l3"><a class="reference internal" href="../tutorials/getting-started/to-mxnet/index.html">Moving to MXNet from Other Frameworks</a><ul> |
| <li class="toctree-l4"><a class="reference internal" href="../tutorials/getting-started/to-mxnet/pytorch.html">PyTorch vs Apache MXNet</a></li> |
| </ul> |
| </li> |
| <li class="toctree-l3"><a class="reference internal" href="../tutorials/getting-started/gluon_from_experiment_to_deployment.html">Gluon: from experiment to deployment</a></li> |
| <li class="toctree-l3"><a class="reference internal" href="../tutorials/getting-started/logistic_regression_explained.html">Logistic regression explained</a></li> |
| <li class="toctree-l3"><a class="reference external" href="https://mxnet.apache.org/api/python/docs/tutorials/packages/gluon/image/mnist.html">MNIST</a></li> |
| </ul> |
| </li> |
| <li class="toctree-l2"><a class="reference internal" href="../tutorials/packages/index.html">Packages</a><ul> |
| <li class="toctree-l3"><a class="reference internal" href="../tutorials/packages/autograd/index.html">Automatic Differentiation</a></li> |
| <li class="toctree-l3"><a class="reference internal" href="../tutorials/packages/gluon/index.html">Gluon</a><ul> |
| <li class="toctree-l4"><a class="reference internal" href="../tutorials/packages/gluon/blocks/index.html">Blocks</a><ul> |
| <li class="toctree-l5"><a class="reference internal" href="../tutorials/packages/gluon/blocks/custom-layer.html">Custom Layers</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../tutorials/packages/gluon/blocks/custom_layer_beginners.html">Customer Layers (Beginners)</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../tutorials/packages/gluon/blocks/hybridize.html">Hybridize</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../tutorials/packages/gluon/blocks/init.html">Initialization</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../tutorials/packages/gluon/blocks/naming.html">Parameter and Block Naming</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../tutorials/packages/gluon/blocks/nn.html">Layers and Blocks</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../tutorials/packages/gluon/blocks/parameters.html">Parameter Management</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../tutorials/packages/gluon/blocks/save_load_params.html">Saving and Loading Gluon Models</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../tutorials/packages/gluon/blocks/activations/activations.html">Activation Blocks</a></li> |
| </ul> |
| </li> |
| <li class="toctree-l4"><a class="reference internal" href="../tutorials/packages/gluon/data/index.html">Data Tutorials</a><ul> |
| <li class="toctree-l5"><a class="reference internal" href="../tutorials/packages/gluon/data/data_augmentation.html">Image Augmentation</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../tutorials/packages/gluon/data/data_augmentation.html#Spatial-Augmentation">Spatial Augmentation</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../tutorials/packages/gluon/data/data_augmentation.html#Color-Augmentation">Color Augmentation</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../tutorials/packages/gluon/data/data_augmentation.html#Composed-Augmentations">Composed Augmentations</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../tutorials/packages/gluon/data/datasets.html">Gluon <code class="docutils literal notranslate"><span class="pre">Dataset</span></code>s and <code class="docutils literal notranslate"><span class="pre">DataLoader</span></code></a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../tutorials/packages/gluon/data/datasets.html#Using-own-data-with-included-Datasets">Using own data with included <code class="docutils literal notranslate"><span class="pre">Dataset</span></code>s</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../tutorials/packages/gluon/data/datasets.html#Using-own-data-with-custom-Datasets">Using own data with custom <code class="docutils literal notranslate"><span class="pre">Dataset</span></code>s</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../tutorials/packages/gluon/data/datasets.html#Appendix:-Upgrading-from-Module-DataIter-to-Gluon-DataLoader">Appendix: Upgrading from Module <code class="docutils literal notranslate"><span class="pre">DataIter</span></code> to Gluon <code class="docutils literal notranslate"><span class="pre">DataLoader</span></code></a></li> |
| </ul> |
| </li> |
| <li class="toctree-l4"><a class="reference internal" href="../tutorials/packages/gluon/image/index.html">Image Tutorials</a><ul> |
| <li class="toctree-l5"><a class="reference internal" href="../tutorials/packages/gluon/image/image-augmentation.html">Image Augmentation</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../tutorials/packages/gluon/image/info_gan.html">Image similarity search with InfoGAN</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../tutorials/packages/gluon/image/mnist.html">Handwritten Digit Recognition</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../tutorials/packages/gluon/image/pretrained_models.html">Using pre-trained models in MXNet</a></li> |
| </ul> |
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| <h1>Source code for numbers</h1><div class="highlight"><pre> |
| <span></span><span class="c1"># Copyright 2007 Google, Inc. All Rights Reserved.</span> |
| <span class="c1"># Licensed to PSF under a Contributor Agreement.</span> |
| |
| <span class="sd">"""Abstract Base Classes (ABCs) for numbers, according to PEP 3141.</span> |
| |
| <span class="sd">TODO: Fill out more detailed documentation on the operators."""</span> |
| |
| <span class="kn">from</span> <span class="nn">abc</span> <span class="kn">import</span> <span class="n">ABCMeta</span><span class="p">,</span> <span class="n">abstractmethod</span> |
| |
| <span class="n">__all__</span> <span class="o">=</span> <span class="p">[</span><span class="s2">"Number"</span><span class="p">,</span> <span class="s2">"Complex"</span><span class="p">,</span> <span class="s2">"Real"</span><span class="p">,</span> <span class="s2">"Rational"</span><span class="p">,</span> <span class="s2">"Integral"</span><span class="p">]</span> |
| |
| <div class="viewcode-block" id="Number"><a class="viewcode-back" href="../api/mxnet/image/index.html#mxnet.image.Number">[docs]</a><span class="k">class</span> <span class="nc">Number</span><span class="p">(</span><span class="n">metaclass</span><span class="o">=</span><span class="n">ABCMeta</span><span class="p">):</span> |
| <span class="sd">"""All numbers inherit from this class.</span> |
| |
| <span class="sd"> If you just want to check if an argument x is a number, without</span> |
| <span class="sd"> caring what kind, use isinstance(x, Number).</span> |
| <span class="sd"> """</span> |
| <span class="vm">__slots__</span> <span class="o">=</span> <span class="p">()</span> |
| |
| <span class="c1"># Concrete numeric types must provide their own hash implementation</span> |
| <span class="fm">__hash__</span> <span class="o">=</span> <span class="kc">None</span></div> |
| |
| |
| <span class="c1">## Notes on Decimal</span> |
| <span class="c1">## ----------------</span> |
| <span class="c1">## Decimal has all of the methods specified by the Real abc, but it should</span> |
| <span class="c1">## not be registered as a Real because decimals do not interoperate with</span> |
| <span class="c1">## binary floats (i.e. Decimal('3.14') + 2.71828 is undefined). But,</span> |
| <span class="c1">## abstract reals are expected to interoperate (i.e. R1 + R2 should be</span> |
| <span class="c1">## expected to work if R1 and R2 are both Reals).</span> |
| |
| <span class="k">class</span> <span class="nc">Complex</span><span class="p">(</span><span class="n">Number</span><span class="p">):</span> |
| <span class="sd">"""Complex defines the operations that work on the builtin complex type.</span> |
| |
| <span class="sd"> In short, those are: a conversion to complex, .real, .imag, +, -,</span> |
| <span class="sd"> *, /, **, abs(), .conjugate, ==, and !=.</span> |
| |
| <span class="sd"> If it is given heterogeneous arguments, and doesn't have special</span> |
| <span class="sd"> knowledge about them, it should fall back to the builtin complex</span> |
| <span class="sd"> type as described below.</span> |
| <span class="sd"> """</span> |
| |
| <span class="vm">__slots__</span> <span class="o">=</span> <span class="p">()</span> |
| |
| <span class="nd">@abstractmethod</span> |
| <span class="k">def</span> <span class="fm">__complex__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span> |
| <span class="sd">"""Return a builtin complex instance. Called for complex(self)."""</span> |
| |
| <span class="k">def</span> <span class="fm">__bool__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span> |
| <span class="sd">"""True if self != 0. Called for bool(self)."""</span> |
| <span class="k">return</span> <span class="bp">self</span> <span class="o">!=</span> <span class="mi">0</span> |
| |
| <span class="nd">@property</span> |
| <span class="nd">@abstractmethod</span> |
| <span class="k">def</span> <span class="nf">real</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span> |
| <span class="sd">"""Retrieve the real component of this number.</span> |
| |
| <span class="sd"> This should subclass Real.</span> |
| <span class="sd"> """</span> |
| <span class="k">raise</span> <span class="ne">NotImplementedError</span> |
| |
| <span class="nd">@property</span> |
| <span class="nd">@abstractmethod</span> |
| <span class="k">def</span> <span class="nf">imag</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span> |
| <span class="sd">"""Retrieve the imaginary component of this number.</span> |
| |
| <span class="sd"> This should subclass Real.</span> |
| <span class="sd"> """</span> |
| <span class="k">raise</span> <span class="ne">NotImplementedError</span> |
| |
| <span class="nd">@abstractmethod</span> |
| <span class="k">def</span> <span class="fm">__add__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span> |
| <span class="sd">"""self + other"""</span> |
| <span class="k">raise</span> <span class="ne">NotImplementedError</span> |
| |
| <span class="nd">@abstractmethod</span> |
| <span class="k">def</span> <span class="fm">__radd__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span> |
| <span class="sd">"""other + self"""</span> |
| <span class="k">raise</span> <span class="ne">NotImplementedError</span> |
| |
| <span class="nd">@abstractmethod</span> |
| <span class="k">def</span> <span class="fm">__neg__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span> |
| <span class="sd">"""-self"""</span> |
| <span class="k">raise</span> <span class="ne">NotImplementedError</span> |
| |
| <span class="nd">@abstractmethod</span> |
| <span class="k">def</span> <span class="fm">__pos__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span> |
| <span class="sd">"""+self"""</span> |
| <span class="k">raise</span> <span class="ne">NotImplementedError</span> |
| |
| <span class="k">def</span> <span class="fm">__sub__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span> |
| <span class="sd">"""self - other"""</span> |
| <span class="k">return</span> <span class="bp">self</span> <span class="o">+</span> <span class="o">-</span><span class="n">other</span> |
| |
| <span class="k">def</span> <span class="fm">__rsub__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span> |
| <span class="sd">"""other - self"""</span> |
| <span class="k">return</span> <span class="o">-</span><span class="bp">self</span> <span class="o">+</span> <span class="n">other</span> |
| |
| <span class="nd">@abstractmethod</span> |
| <span class="k">def</span> <span class="fm">__mul__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span> |
| <span class="sd">"""self * other"""</span> |
| <span class="k">raise</span> <span class="ne">NotImplementedError</span> |
| |
| <span class="nd">@abstractmethod</span> |
| <span class="k">def</span> <span class="fm">__rmul__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span> |
| <span class="sd">"""other * self"""</span> |
| <span class="k">raise</span> <span class="ne">NotImplementedError</span> |
| |
| <span class="nd">@abstractmethod</span> |
| <span class="k">def</span> <span class="fm">__truediv__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span> |
| <span class="sd">"""self / other: Should promote to float when necessary."""</span> |
| <span class="k">raise</span> <span class="ne">NotImplementedError</span> |
| |
| <span class="nd">@abstractmethod</span> |
| <span class="k">def</span> <span class="fm">__rtruediv__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span> |
| <span class="sd">"""other / self"""</span> |
| <span class="k">raise</span> <span class="ne">NotImplementedError</span> |
| |
| <span class="nd">@abstractmethod</span> |
| <span class="k">def</span> <span class="fm">__pow__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">exponent</span><span class="p">):</span> |
| <span class="sd">"""self**exponent; should promote to float or complex when necessary."""</span> |
| <span class="k">raise</span> <span class="ne">NotImplementedError</span> |
| |
| <span class="nd">@abstractmethod</span> |
| <span class="k">def</span> <span class="fm">__rpow__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">base</span><span class="p">):</span> |
| <span class="sd">"""base ** self"""</span> |
| <span class="k">raise</span> <span class="ne">NotImplementedError</span> |
| |
| <span class="nd">@abstractmethod</span> |
| <span class="k">def</span> <span class="fm">__abs__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span> |
| <span class="sd">"""Returns the Real distance from 0. Called for abs(self)."""</span> |
| <span class="k">raise</span> <span class="ne">NotImplementedError</span> |
| |
| <span class="nd">@abstractmethod</span> |
| <span class="k">def</span> <span class="nf">conjugate</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span> |
| <span class="sd">"""(x+y*i).conjugate() returns (x-y*i)."""</span> |
| <span class="k">raise</span> <span class="ne">NotImplementedError</span> |
| |
| <span class="nd">@abstractmethod</span> |
| <span class="k">def</span> <span class="fm">__eq__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span> |
| <span class="sd">"""self == other"""</span> |
| <span class="k">raise</span> <span class="ne">NotImplementedError</span> |
| |
| <span class="n">Complex</span><span class="o">.</span><span class="n">register</span><span class="p">(</span><span class="nb">complex</span><span class="p">)</span> |
| |
| |
| <span class="k">class</span> <span class="nc">Real</span><span class="p">(</span><span class="n">Complex</span><span class="p">):</span> |
| <span class="sd">"""To Complex, Real adds the operations that work on real numbers.</span> |
| |
| <span class="sd"> In short, those are: a conversion to float, trunc(), divmod,</span> |
| <span class="sd"> %, <, <=, >, and >=.</span> |
| |
| <span class="sd"> Real also provides defaults for the derived operations.</span> |
| <span class="sd"> """</span> |
| |
| <span class="vm">__slots__</span> <span class="o">=</span> <span class="p">()</span> |
| |
| <span class="nd">@abstractmethod</span> |
| <span class="k">def</span> <span class="fm">__float__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span> |
| <span class="sd">"""Any Real can be converted to a native float object.</span> |
| |
| <span class="sd"> Called for float(self)."""</span> |
| <span class="k">raise</span> <span class="ne">NotImplementedError</span> |
| |
| <span class="nd">@abstractmethod</span> |
| <span class="k">def</span> <span class="nf">__trunc__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span> |
| <span class="sd">"""trunc(self): Truncates self to an Integral.</span> |
| |
| <span class="sd"> Returns an Integral i such that:</span> |
| <span class="sd"> * i>0 iff self>0;</span> |
| <span class="sd"> * abs(i) <= abs(self);</span> |
| <span class="sd"> * for any Integral j satisfying the first two conditions,</span> |
| <span class="sd"> abs(i) >= abs(j) [i.e. i has "maximal" abs among those].</span> |
| <span class="sd"> i.e. "truncate towards 0".</span> |
| <span class="sd"> """</span> |
| <span class="k">raise</span> <span class="ne">NotImplementedError</span> |
| |
| <span class="nd">@abstractmethod</span> |
| <span class="k">def</span> <span class="nf">__floor__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span> |
| <span class="sd">"""Finds the greatest Integral <= self."""</span> |
| <span class="k">raise</span> <span class="ne">NotImplementedError</span> |
| |
| <span class="nd">@abstractmethod</span> |
| <span class="k">def</span> <span class="nf">__ceil__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span> |
| <span class="sd">"""Finds the least Integral >= self."""</span> |
| <span class="k">raise</span> <span class="ne">NotImplementedError</span> |
| |
| <span class="nd">@abstractmethod</span> |
| <span class="k">def</span> <span class="fm">__round__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">ndigits</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span> |
| <span class="sd">"""Rounds self to ndigits decimal places, defaulting to 0.</span> |
| |
| <span class="sd"> If ndigits is omitted or None, returns an Integral, otherwise</span> |
| <span class="sd"> returns a Real. Rounds half toward even.</span> |
| <span class="sd"> """</span> |
| <span class="k">raise</span> <span class="ne">NotImplementedError</span> |
| |
| <span class="k">def</span> <span class="fm">__divmod__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span> |
| <span class="sd">"""divmod(self, other): The pair (self // other, self % other).</span> |
| |
| <span class="sd"> Sometimes this can be computed faster than the pair of</span> |
| <span class="sd"> operations.</span> |
| <span class="sd"> """</span> |
| <span class="k">return</span> <span class="p">(</span><span class="bp">self</span> <span class="o">//</span> <span class="n">other</span><span class="p">,</span> <span class="bp">self</span> <span class="o">%</span> <span class="n">other</span><span class="p">)</span> |
| |
| <span class="k">def</span> <span class="fm">__rdivmod__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span> |
| <span class="sd">"""divmod(other, self): The pair (self // other, self % other).</span> |
| |
| <span class="sd"> Sometimes this can be computed faster than the pair of</span> |
| <span class="sd"> operations.</span> |
| <span class="sd"> """</span> |
| <span class="k">return</span> <span class="p">(</span><span class="n">other</span> <span class="o">//</span> <span class="bp">self</span><span class="p">,</span> <span class="n">other</span> <span class="o">%</span> <span class="bp">self</span><span class="p">)</span> |
| |
| <span class="nd">@abstractmethod</span> |
| <span class="k">def</span> <span class="fm">__floordiv__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span> |
| <span class="sd">"""self // other: The floor() of self/other."""</span> |
| <span class="k">raise</span> <span class="ne">NotImplementedError</span> |
| |
| <span class="nd">@abstractmethod</span> |
| <span class="k">def</span> <span class="fm">__rfloordiv__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span> |
| <span class="sd">"""other // self: The floor() of other/self."""</span> |
| <span class="k">raise</span> <span class="ne">NotImplementedError</span> |
| |
| <span class="nd">@abstractmethod</span> |
| <span class="k">def</span> <span class="fm">__mod__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span> |
| <span class="sd">"""self % other"""</span> |
| <span class="k">raise</span> <span class="ne">NotImplementedError</span> |
| |
| <span class="nd">@abstractmethod</span> |
| <span class="k">def</span> <span class="fm">__rmod__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span> |
| <span class="sd">"""other % self"""</span> |
| <span class="k">raise</span> <span class="ne">NotImplementedError</span> |
| |
| <span class="nd">@abstractmethod</span> |
| <span class="k">def</span> <span class="fm">__lt__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span> |
| <span class="sd">"""self < other</span> |
| |
| <span class="sd"> < on Reals defines a total ordering, except perhaps for NaN."""</span> |
| <span class="k">raise</span> <span class="ne">NotImplementedError</span> |
| |
| <span class="nd">@abstractmethod</span> |
| <span class="k">def</span> <span class="fm">__le__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span> |
| <span class="sd">"""self <= other"""</span> |
| <span class="k">raise</span> <span class="ne">NotImplementedError</span> |
| |
| <span class="c1"># Concrete implementations of Complex abstract methods.</span> |
| <span class="k">def</span> <span class="fm">__complex__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span> |
| <span class="sd">"""complex(self) == complex(float(self), 0)"""</span> |
| <span class="k">return</span> <span class="nb">complex</span><span class="p">(</span><span class="nb">float</span><span class="p">(</span><span class="bp">self</span><span class="p">))</span> |
| |
| <span class="nd">@property</span> |
| <span class="k">def</span> <span class="nf">real</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span> |
| <span class="sd">"""Real numbers are their real component."""</span> |
| <span class="k">return</span> <span class="o">+</span><span class="bp">self</span> |
| |
| <span class="nd">@property</span> |
| <span class="k">def</span> <span class="nf">imag</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span> |
| <span class="sd">"""Real numbers have no imaginary component."""</span> |
| <span class="k">return</span> <span class="mi">0</span> |
| |
| <span class="k">def</span> <span class="nf">conjugate</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span> |
| <span class="sd">"""Conjugate is a no-op for Reals."""</span> |
| <span class="k">return</span> <span class="o">+</span><span class="bp">self</span> |
| |
| <span class="n">Real</span><span class="o">.</span><span class="n">register</span><span class="p">(</span><span class="nb">float</span><span class="p">)</span> |
| |
| |
| <span class="k">class</span> <span class="nc">Rational</span><span class="p">(</span><span class="n">Real</span><span class="p">):</span> |
| <span class="sd">""".numerator and .denominator should be in lowest terms."""</span> |
| |
| <span class="vm">__slots__</span> <span class="o">=</span> <span class="p">()</span> |
| |
| <span class="nd">@property</span> |
| <span class="nd">@abstractmethod</span> |
| <span class="k">def</span> <span class="nf">numerator</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span> |
| <span class="k">raise</span> <span class="ne">NotImplementedError</span> |
| |
| <span class="nd">@property</span> |
| <span class="nd">@abstractmethod</span> |
| <span class="k">def</span> <span class="nf">denominator</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span> |
| <span class="k">raise</span> <span class="ne">NotImplementedError</span> |
| |
| <span class="c1"># Concrete implementation of Real's conversion to float.</span> |
| <span class="k">def</span> <span class="fm">__float__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span> |
| <span class="sd">"""float(self) = self.numerator / self.denominator</span> |
| |
| <span class="sd"> It's important that this conversion use the integer's "true"</span> |
| <span class="sd"> division rather than casting one side to float before dividing</span> |
| <span class="sd"> so that ratios of huge integers convert without overflowing.</span> |
| |
| <span class="sd"> """</span> |
| <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">numerator</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">denominator</span> |
| |
| |
| <span class="k">class</span> <span class="nc">Integral</span><span class="p">(</span><span class="n">Rational</span><span class="p">):</span> |
| <span class="sd">"""Integral adds methods that work on integral numbers.</span> |
| |
| <span class="sd"> In short, these are conversion to int, pow with modulus, and the</span> |
| <span class="sd"> bit-string operations.</span> |
| <span class="sd"> """</span> |
| |
| <span class="vm">__slots__</span> <span class="o">=</span> <span class="p">()</span> |
| |
| <span class="nd">@abstractmethod</span> |
| <span class="k">def</span> <span class="fm">__int__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span> |
| <span class="sd">"""int(self)"""</span> |
| <span class="k">raise</span> <span class="ne">NotImplementedError</span> |
| |
| <span class="k">def</span> <span class="fm">__index__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span> |
| <span class="sd">"""Called whenever an index is needed, such as in slicing"""</span> |
| <span class="k">return</span> <span class="nb">int</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> |
| |
| <span class="nd">@abstractmethod</span> |
| <span class="k">def</span> <span class="fm">__pow__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">exponent</span><span class="p">,</span> <span class="n">modulus</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span> |
| <span class="sd">"""self ** exponent % modulus, but maybe faster.</span> |
| |
| <span class="sd"> Accept the modulus argument if you want to support the</span> |
| <span class="sd"> 3-argument version of pow(). Raise a TypeError if exponent < 0</span> |
| <span class="sd"> or any argument isn't Integral. Otherwise, just implement the</span> |
| <span class="sd"> 2-argument version described in Complex.</span> |
| <span class="sd"> """</span> |
| <span class="k">raise</span> <span class="ne">NotImplementedError</span> |
| |
| <span class="nd">@abstractmethod</span> |
| <span class="k">def</span> <span class="fm">__lshift__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span> |
| <span class="sd">"""self << other"""</span> |
| <span class="k">raise</span> <span class="ne">NotImplementedError</span> |
| |
| <span class="nd">@abstractmethod</span> |
| <span class="k">def</span> <span class="fm">__rlshift__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span> |
| <span class="sd">"""other << self"""</span> |
| <span class="k">raise</span> <span class="ne">NotImplementedError</span> |
| |
| <span class="nd">@abstractmethod</span> |
| <span class="k">def</span> <span class="fm">__rshift__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span> |
| <span class="sd">"""self >> other"""</span> |
| <span class="k">raise</span> <span class="ne">NotImplementedError</span> |
| |
| <span class="nd">@abstractmethod</span> |
| <span class="k">def</span> <span class="fm">__rrshift__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span> |
| <span class="sd">"""other >> self"""</span> |
| <span class="k">raise</span> <span class="ne">NotImplementedError</span> |
| |
| <span class="nd">@abstractmethod</span> |
| <span class="k">def</span> <span class="fm">__and__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span> |
| <span class="sd">"""self & other"""</span> |
| <span class="k">raise</span> <span class="ne">NotImplementedError</span> |
| |
| <span class="nd">@abstractmethod</span> |
| <span class="k">def</span> <span class="fm">__rand__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span> |
| <span class="sd">"""other & self"""</span> |
| <span class="k">raise</span> <span class="ne">NotImplementedError</span> |
| |
| <span class="nd">@abstractmethod</span> |
| <span class="k">def</span> <span class="fm">__xor__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span> |
| <span class="sd">"""self ^ other"""</span> |
| <span class="k">raise</span> <span class="ne">NotImplementedError</span> |
| |
| <span class="nd">@abstractmethod</span> |
| <span class="k">def</span> <span class="fm">__rxor__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span> |
| <span class="sd">"""other ^ self"""</span> |
| <span class="k">raise</span> <span class="ne">NotImplementedError</span> |
| |
| <span class="nd">@abstractmethod</span> |
| <span class="k">def</span> <span class="fm">__or__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span> |
| <span class="sd">"""self | other"""</span> |
| <span class="k">raise</span> <span class="ne">NotImplementedError</span> |
| |
| <span class="nd">@abstractmethod</span> |
| <span class="k">def</span> <span class="fm">__ror__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span> |
| <span class="sd">"""other | self"""</span> |
| <span class="k">raise</span> <span class="ne">NotImplementedError</span> |
| |
| <span class="nd">@abstractmethod</span> |
| <span class="k">def</span> <span class="fm">__invert__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span> |
| <span class="sd">"""~self"""</span> |
| <span class="k">raise</span> <span class="ne">NotImplementedError</span> |
| |
| <span class="c1"># Concrete implementations of Rational and Real abstract methods.</span> |
| <span class="k">def</span> <span class="fm">__float__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span> |
| <span class="sd">"""float(self) == float(int(self))"""</span> |
| <span class="k">return</span> <span class="nb">float</span><span class="p">(</span><span class="nb">int</span><span class="p">(</span><span class="bp">self</span><span class="p">))</span> |
| |
| <span class="nd">@property</span> |
| <span class="k">def</span> <span class="nf">numerator</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span> |
| <span class="sd">"""Integers are their own numerators."""</span> |
| <span class="k">return</span> <span class="o">+</span><span class="bp">self</span> |
| |
| <span class="nd">@property</span> |
| <span class="k">def</span> <span class="nf">denominator</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span> |
| <span class="sd">"""Integers have a denominator of 1."""</span> |
| <span class="k">return</span> <span class="mi">1</span> |
| |
| <span class="n">Integral</span><span class="o">.</span><span class="n">register</span><span class="p">(</span><span class="nb">int</span><span class="p">)</span> |
| </pre></div> |
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