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| </script></nav></div><div class="container mainContainer docsContainer"><div class="wrapper"><div class="post"><header class="postHeader"><a class="edit-page-link button" href="https://github.com/apache/singa-doc/blob/master/docs-site/docs/half-precision.md" target="_blank" rel="noreferrer noopener">Edit</a><h1 id="__docusaurus" class="postHeaderTitle">Half Precision</h1></header><article><div><span><!--- Licensed to the Apache Software Foundation (ASF) under one or more contributor license agreements. See the NOTICE file distributed with this work for additional information regarding copyright ownership. The ASF licenses this file to you under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. --> |
| <p>Half precision training could bring benefits:</p> |
| <ul> |
| <li>using less GPU memory, supporting larger network.</li> |
| <li>training faster.</li> |
| </ul> |
| <h2><a class="anchor" aria-hidden="true" id="half-data-type"></a><a href="#half-data-type" aria-hidden="true" class="hash-link"><svg class="hash-link-icon" aria-hidden="true" height="16" version="1.1" viewBox="0 0 16 16" width="16"><path fill-rule="evenodd" d="M4 9h1v1H4c-1.5 0-3-1.69-3-3.5S2.55 3 4 3h4c1.45 0 3 1.69 3 3.5 0 1.41-.91 2.72-2 3.25V8.59c.58-.45 1-1.27 1-2.09C10 5.22 8.98 4 8 4H4c-.98 0-2 1.22-2 2.5S3 9 4 9zm9-3h-1v1h1c1 0 2 1.22 2 2.5S13.98 12 13 12H9c-.98 0-2-1.22-2-2.5 0-.83.42-1.64 1-2.09V6.25c-1.09.53-2 1.84-2 3.25C6 11.31 7.55 13 9 13h4c1.45 0 3-1.69 3-3.5S14.5 6 13 6z"></path></svg></a>Half data type</h2> |
| <h3><a class="anchor" aria-hidden="true" id="half-data-type-definition"></a><a href="#half-data-type-definition" aria-hidden="true" class="hash-link"><svg class="hash-link-icon" aria-hidden="true" height="16" version="1.1" viewBox="0 0 16 16" width="16"><path fill-rule="evenodd" d="M4 9h1v1H4c-1.5 0-3-1.69-3-3.5S2.55 3 4 3h4c1.45 0 3 1.69 3 3.5 0 1.41-.91 2.72-2 3.25V8.59c.58-.45 1-1.27 1-2.09C10 5.22 8.98 4 8 4H4c-.98 0-2 1.22-2 2.5S3 9 4 9zm9-3h-1v1h1c1 0 2 1.22 2 2.5S13.98 12 13 12H9c-.98 0-2-1.22-2-2.5 0-.83.42-1.64 1-2.09V6.25c-1.09.53-2 1.84-2 3.25C6 11.31 7.55 13 9 13h4c1.45 0 3-1.69 3-3.5S14.5 6 13 6z"></path></svg></a>Half data type definition</h3> |
| <p>The IEEE 754 standard specifies a binary16 as having the following |
| <a href="https://en.wikipedia.org/wiki/Half-precision_floating-point_format">format</a>: |
| Sign bit: 1 bit |
| Exponent width: 5 bits |
| Significand precision: 11 bits (10 explicitly stored)</p> |
| <h3><a class="anchor" aria-hidden="true" id="half-data-type-operation"></a><a href="#half-data-type-operation" aria-hidden="true" class="hash-link"><svg class="hash-link-icon" aria-hidden="true" height="16" version="1.1" viewBox="0 0 16 16" width="16"><path fill-rule="evenodd" d="M4 9h1v1H4c-1.5 0-3-1.69-3-3.5S2.55 3 4 3h4c1.45 0 3 1.69 3 3.5 0 1.41-.91 2.72-2 3.25V8.59c.58-.45 1-1.27 1-2.09C10 5.22 8.98 4 8 4H4c-.98 0-2 1.22-2 2.5S3 9 4 9zm9-3h-1v1h1c1 0 2 1.22 2 2.5S13.98 12 13 12H9c-.98 0-2-1.22-2-2.5 0-.83.42-1.64 1-2.09V6.25c-1.09.53-2 1.84-2 3.25C6 11.31 7.55 13 9 13h4c1.45 0 3-1.69 3-3.5S14.5 6 13 6z"></path></svg></a>Half data type operation</h3> |
| <p>Load data in fp32 and easily convert to fp16 by casting.</p> |
| <pre><code class="hljs css language-python"><span class="hljs-meta">>>> </span><span class="hljs-keyword">from</span> singa <span class="hljs-keyword">import</span> tensor, device |
| <span class="hljs-meta">>>> </span>dev = device.create_cuda_gpu() |
| <span class="hljs-meta">>>> </span>x = tensor.random((<span class="hljs-number">2</span>,<span class="hljs-number">3</span>),dev) |
| <span class="hljs-meta">>>> </span>x |
| [[<span class="hljs-number">0.7703407</span> <span class="hljs-number">0.42764223</span> <span class="hljs-number">0.5872884</span> ] |
| [<span class="hljs-number">0.78362167</span> <span class="hljs-number">0.70469785</span> <span class="hljs-number">0.64975065</span>]], float32 |
| <span class="hljs-meta">>>> </span>y = x.as_type(tensor.float16) |
| <span class="hljs-meta">>>> </span>y |
| [[<span class="hljs-number">0.7705</span> <span class="hljs-number">0.4277</span> <span class="hljs-number">0.5874</span>] |
| [<span class="hljs-number">0.7837</span> <span class="hljs-number">0.7046</span> <span class="hljs-number">0.65</span> ]], float16 |
| </code></pre> |
| <p>Primary operations are supported in fp16.</p> |
| <pre><code class="hljs css language-python"><span class="hljs-meta">>>> </span>y+y |
| [[<span class="hljs-number">1.541</span> <span class="hljs-number">0.8555</span> <span class="hljs-number">1.175</span> ] |
| [<span class="hljs-number">1.567</span> <span class="hljs-number">1.409</span> <span class="hljs-number">1.3</span> ]], float16 |
| </code></pre> |
| <h2><a class="anchor" aria-hidden="true" id="training-in-half"></a><a href="#training-in-half" aria-hidden="true" class="hash-link"><svg class="hash-link-icon" aria-hidden="true" height="16" version="1.1" viewBox="0 0 16 16" width="16"><path fill-rule="evenodd" d="M4 9h1v1H4c-1.5 0-3-1.69-3-3.5S2.55 3 4 3h4c1.45 0 3 1.69 3 3.5 0 1.41-.91 2.72-2 3.25V8.59c.58-.45 1-1.27 1-2.09C10 5.22 8.98 4 8 4H4c-.98 0-2 1.22-2 2.5S3 9 4 9zm9-3h-1v1h1c1 0 2 1.22 2 2.5S13.98 12 13 12H9c-.98 0-2-1.22-2-2.5 0-.83.42-1.64 1-2.09V6.25c-1.09.53-2 1.84-2 3.25C6 11.31 7.55 13 9 13h4c1.45 0 3-1.69 3-3.5S14.5 6 13 6z"></path></svg></a>Training in Half</h2> |
| <h3><a class="anchor" aria-hidden="true" id="training-in-half-three-step"></a><a href="#training-in-half-three-step" aria-hidden="true" class="hash-link"><svg class="hash-link-icon" aria-hidden="true" height="16" version="1.1" viewBox="0 0 16 16" width="16"><path fill-rule="evenodd" d="M4 9h1v1H4c-1.5 0-3-1.69-3-3.5S2.55 3 4 3h4c1.45 0 3 1.69 3 3.5 0 1.41-.91 2.72-2 3.25V8.59c.58-.45 1-1.27 1-2.09C10 5.22 8.98 4 8 4H4c-.98 0-2 1.22-2 2.5S3 9 4 9zm9-3h-1v1h1c1 0 2 1.22 2 2.5S13.98 12 13 12H9c-.98 0-2-1.22-2-2.5 0-.83.42-1.64 1-2.09V6.25c-1.09.53-2 1.84-2 3.25C6 11.31 7.55 13 9 13h4c1.45 0 3-1.69 3-3.5S14.5 6 13 6z"></path></svg></a>Training in Half three step</h3> |
| <p>Training in half precision could be done easily in three steps:</p> |
| <ol> |
| <li>Load data and convert to half</li> |
| <li>Set data type of optimizer</li> |
| <li>Train model as usual</li> |
| </ol> |
| <pre><code class="hljs css language-python"><span class="hljs-comment"># cast input data to fp16</span> |
| x = load_data() |
| x = x.astype(np.float16) |
| tx = tensor.from_numpy(x) |
| |
| <span class="hljs-comment"># load model</span> |
| model = build_model() |
| <span class="hljs-comment"># set optimizer dtype to fp16</span> |
| sgd = opt.SGD(lr=<span class="hljs-number">0.1</span>, dtype=tensor.float16) |
| |
| <span class="hljs-comment"># train as usual</span> |
| out, loss = model(tx, ty) |
| </code></pre> |
| <h3><a class="anchor" aria-hidden="true" id="example"></a><a href="#example" aria-hidden="true" class="hash-link"><svg class="hash-link-icon" aria-hidden="true" height="16" version="1.1" viewBox="0 0 16 16" width="16"><path fill-rule="evenodd" d="M4 9h1v1H4c-1.5 0-3-1.69-3-3.5S2.55 3 4 3h4c1.45 0 3 1.69 3 3.5 0 1.41-.91 2.72-2 3.25V8.59c.58-.45 1-1.27 1-2.09C10 5.22 8.98 4 8 4H4c-.98 0-2 1.22-2 2.5S3 9 4 9zm9-3h-1v1h1c1 0 2 1.22 2 2.5S13.98 12 13 12H9c-.98 0-2-1.22-2-2.5 0-.83.42-1.64 1-2.09V6.25c-1.09.53-2 1.84-2 3.25C6 11.31 7.55 13 9 13h4c1.45 0 3-1.69 3-3.5S14.5 6 13 6z"></path></svg></a>Example</h3> |
| <p>An example script is <code>train_cnn.py</code>, run below command to train in half.</p> |
| <pre><code class="hljs css language-python">python examples/cnn/train_cnn.py cnn mnist -pfloat16 |
| </code></pre> |
| <h2><a class="anchor" aria-hidden="true" id="implementation"></a><a href="#implementation" aria-hidden="true" class="hash-link"><svg class="hash-link-icon" aria-hidden="true" height="16" version="1.1" viewBox="0 0 16 16" width="16"><path fill-rule="evenodd" d="M4 9h1v1H4c-1.5 0-3-1.69-3-3.5S2.55 3 4 3h4c1.45 0 3 1.69 3 3.5 0 1.41-.91 2.72-2 3.25V8.59c.58-.45 1-1.27 1-2.09C10 5.22 8.98 4 8 4H4c-.98 0-2 1.22-2 2.5S3 9 4 9zm9-3h-1v1h1c1 0 2 1.22 2 2.5S13.98 12 13 12H9c-.98 0-2-1.22-2-2.5 0-.83.42-1.64 1-2.09V6.25c-1.09.53-2 1.84-2 3.25C6 11.31 7.55 13 9 13h4c1.45 0 3-1.69 3-3.5S14.5 6 13 6z"></path></svg></a>Implementation</h2> |
| <h3><a class="anchor" aria-hidden="true" id="half-type-dependency"></a><a href="#half-type-dependency" aria-hidden="true" class="hash-link"><svg class="hash-link-icon" aria-hidden="true" height="16" version="1.1" viewBox="0 0 16 16" width="16"><path fill-rule="evenodd" d="M4 9h1v1H4c-1.5 0-3-1.69-3-3.5S2.55 3 4 3h4c1.45 0 3 1.69 3 3.5 0 1.41-.91 2.72-2 3.25V8.59c.58-.45 1-1.27 1-2.09C10 5.22 8.98 4 8 4H4c-.98 0-2 1.22-2 2.5S3 9 4 9zm9-3h-1v1h1c1 0 2 1.22 2 2.5S13.98 12 13 12H9c-.98 0-2-1.22-2-2.5 0-.83.42-1.64 1-2.09V6.25c-1.09.53-2 1.84-2 3.25C6 11.31 7.55 13 9 13h4c1.45 0 3-1.69 3-3.5S14.5 6 13 6z"></path></svg></a>Half Type Dependency</h3> |
| <p>This half implementation is integrated in C++ backend as general half type |
| support.</p> |
| <p>To run on GPU, <code>__half</code> is available in Cuda math API. To support <code>__half</code> |
| math operation, it is required to compile against Nvidia compute arch > 6.0 |
| (Pascal).</p> |
| <h3><a class="anchor" aria-hidden="true" id="nvidia-hardware-acceleration-tensor-core"></a><a href="#nvidia-hardware-acceleration-tensor-core" aria-hidden="true" class="hash-link"><svg class="hash-link-icon" aria-hidden="true" height="16" version="1.1" viewBox="0 0 16 16" width="16"><path fill-rule="evenodd" d="M4 9h1v1H4c-1.5 0-3-1.69-3-3.5S2.55 3 4 3h4c1.45 0 3 1.69 3 3.5 0 1.41-.91 2.72-2 3.25V8.59c.58-.45 1-1.27 1-2.09C10 5.22 8.98 4 8 4H4c-.98 0-2 1.22-2 2.5S3 9 4 9zm9-3h-1v1h1c1 0 2 1.22 2 2.5S13.98 12 13 12H9c-.98 0-2-1.22-2-2.5 0-.83.42-1.64 1-2.09V6.25c-1.09.53-2 1.84-2 3.25C6 11.31 7.55 13 9 13h4c1.45 0 3-1.69 3-3.5S14.5 6 13 6z"></path></svg></a>Nvidia Hardware Acceleration: Tensor Core</h3> |
| <p>Tensor Core released by Nvidia further accelerates half precision and multiples |
| throughput for operations like GEMM(CuBlas) and convolution(CuDNN). To enable |
| Tensor core operation, there are a few restriction on GEMM dimensions, |
| convolution channel size, Cuda version, and GPU version(Turing or later) and etc.</p> |
| <h3><a class="anchor" aria-hidden="true" id="implement-operations"></a><a href="#implement-operations" aria-hidden="true" class="hash-link"><svg class="hash-link-icon" aria-hidden="true" height="16" version="1.1" viewBox="0 0 16 16" width="16"><path fill-rule="evenodd" d="M4 9h1v1H4c-1.5 0-3-1.69-3-3.5S2.55 3 4 3h4c1.45 0 3 1.69 3 3.5 0 1.41-.91 2.72-2 3.25V8.59c.58-.45 1-1.27 1-2.09C10 5.22 8.98 4 8 4H4c-.98 0-2 1.22-2 2.5S3 9 4 9zm9-3h-1v1h1c1 0 2 1.22 2 2.5S13.98 12 13 12H9c-.98 0-2-1.22-2-2.5 0-.83.42-1.64 1-2.09V6.25c-1.09.53-2 1.84-2 3.25C6 11.31 7.55 13 9 13h4c1.45 0 3-1.69 3-3.5S14.5 6 13 6z"></path></svg></a>Implement Operations</h3> |
| <p>Half operations are primarily implemented in <code>tensor_math_cuda.h</code>, by specializing |
| operation template with half type and implementation the low level computation.</p> |
| <p>For example, GEMM operation is implemented as:</p> |
| <pre><code class="hljs css language-c++"><span class="hljs-keyword">template</span> <> |
| <span class="hljs-keyword">void</span> GEMM<half_float::half, lang::Cuda>(<span class="hljs-keyword">const</span> half_float::half alpha, |
| <span class="hljs-keyword">const</span> Tensor& A, <span class="hljs-keyword">const</span> Tensor& B, |
| <span class="hljs-keyword">const</span> half_float::half beta, Tensor* C, |
| Context* ctx) { |
| <span class="hljs-comment">// ...</span> |
| CUBLAS_CHECK(cublasGemmEx(handle, transb, transa, ncolB, nrowA, ncolA, |
| alphaPtr, BPtr, Btype, ldb, APtr, Atype, lda, |
| betaPtr, CPtr, Ctype, ldc, computeType, algo)); |
| <span class="hljs-comment">// ...</span> |
| } |
| </code></pre> |
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