<!DOCTYPE html><html lang="en"><head><meta charSet="utf-8"/><meta http-equiv="X-UA-Compatible" content="IE=edge"/><title>Half Precision · Apache SINGA</title><meta name="viewport" content="width=device-width"/><meta name="generator" content="Docusaurus"/><meta name="description" content="&lt;!--- 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 &quot;License&quot;); 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 &quot;AS IS&quot; 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.  --&gt;"/><meta name="docsearch:version" content="4.0.0"/><meta name="docsearch:language" content="en"/><meta property="og:title" content="Half Precision · Apache SINGA"/><meta property="og:type" content="website"/><meta property="og:url" content="https://singa.apache.org/"/><meta property="og:description" content="&lt;!--- 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 &quot;License&quot;); 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 &quot;AS IS&quot; 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.  --&gt;"/><meta property="og:image" content="https://singa.apache.org/img/singa_twitter_banner.jpeg"/><meta name="twitter:card" content="summary"/><meta name="twitter:image" content="https://singa.apache.org/img/singa_twitter_banner.jpeg"/><link rel="shortcut icon" href="/img/favicon.ico"/><link rel="stylesheet" href="https://cdn.jsdelivr.net/docsearch.js/1/docsearch.min.css"/><link rel="stylesheet" href="//cdnjs.cloudflare.com/ajax/libs/highlight.js/9.12.0/styles/atom-one-dark.min.css"/><link rel="alternate" type="application/atom+xml" href="https://singa.apache.org/blog/atom.xml" title="Apache SINGA Blog ATOM Feed"/><link rel="alternate" type="application/rss+xml" href="https://singa.apache.org/blog/feed.xml" title="Apache SINGA Blog RSS Feed"/><link rel="stylesheet" href="https://fonts.googleapis.com/css?family=Source+Sans+Pro:400,400i,700"/><link rel="stylesheet" href="https://fonts.googleapis.com/css2?family=Baloo+Paaji+2&amp;family=Source+Sans+Pro:wght@200;300&amp;display=swap"/><script type="text/javascript" src="https://buttons.github.io/buttons.js"></script><script src="https://unpkg.com/vanilla-back-to-top@7.1.14/dist/vanilla-back-to-top.min.js"></script><script>
        document.addEventListener('DOMContentLoaded', function() {
          addBackToTop(
            {"zIndex":100}
          )
        });
        </script><script src="/js/scrollSpy.js"></script><link rel="stylesheet" href="/css/main.css"/><script src="/js/codetabs.js"></script></head><body class="sideNavVisible separateOnPageNav"><div class="fixedHeaderContainer"><div class="headerWrapper wrapper"><header><a href="/"><img class="logo" src="/img/singa.png" alt="Apache SINGA"/></a><a href="/versions"><h3>4.0.0</h3></a><div class="navigationWrapper navigationSlider"><nav class="slidingNav"><ul class="nav-site nav-site-internal"><li class="siteNavGroupActive"><a href="/docs/installation" target="_self">Docs</a></li><li class=""><a href="/docs/source-repository" target="_self">Community</a></li><li class=""><a href="/blog/" target="_self">News</a></li><li class=""><a href="https://apache-singa.readthedocs.io/en/latest/" target="_self">API</a></li><li class="navSearchWrapper reactNavSearchWrapper"><input type="text" id="search_input_react" placeholder="Search" title="Search"/></li><li class=""><a href="https://github.com/apache/singa" target="_self">GitHub</a></li></ul></nav></div></header></div></div><div class="navPusher"><div class="docMainWrapper wrapper"><div class="docsNavContainer" id="docsNav"><nav class="toc"><div class="toggleNav"><section class="navWrapper wrapper"><div class="navBreadcrumb wrapper"><div class="navToggle" id="navToggler"><div class="hamburger-menu"><div class="line1"></div><div class="line2"></div><div class="line3"></div></div></div><h2><i>›</i><span>Guides</span></h2><div class="tocToggler" id="tocToggler"><i class="icon-toc"></i></div></div><div class="navGroups"><div class="navGroup"><h3 class="navGroupCategoryTitle">Getting Started</h3><ul class=""><li class="navListItem"><a class="navItem" href="/docs/installation">Installation</a></li><li class="navListItem"><a class="navItem" href="/docs/software-stack">Software Stack</a></li><li class="navListItem"><a class="navItem" href="/docs/examples">Examples</a></li></ul></div><div class="navGroup"><h3 class="navGroupCategoryTitle">Guides</h3><ul class=""><li class="navListItem"><a class="navItem" href="/docs/device">Device</a></li><li class="navListItem"><a class="navItem" href="/docs/tensor">Tensor</a></li><li class="navListItem"><a class="navItem" href="/docs/autograd">Autograd</a></li><li class="navListItem"><a class="navItem" href="/docs/optimizer">Optimizer</a></li><li class="navListItem"><a class="navItem" href="/docs/graph">Model</a></li><li class="navListItem"><a class="navItem" href="/docs/onnx">ONNX</a></li><li class="navListItem"><a class="navItem" href="/docs/dist-train">Distributed Training</a></li><li class="navListItem"><a class="navItem" href="/docs/time-profiling">Time Profiling</a></li><li class="navListItem navListItemActive"><a class="navItem" href="/docs/half-precision">Half Precision</a></li></ul></div><div class="navGroup"><h3 class="navGroupCategoryTitle">Development</h3><ul class=""><li class="navListItem"><a class="navItem" href="/docs/downloads">Download SINGA</a></li><li class="navListItem"><a class="navItem" href="/docs/build">Build SINGA from Source</a></li><li class="navListItem"><a class="navItem" href="/docs/contribute-code">How to Contribute Code</a></li><li class="navListItem"><a class="navItem" href="/docs/contribute-docs">How to Contribute to Documentation</a></li><li class="navListItem"><a class="navItem" href="/docs/how-to-release">How to Prepare a Release</a></li><li class="navListItem"><a class="navItem" href="/docs/git-workflow">Git Workflow</a></li></ul></div></div></section></div><script>
            var coll = document.getElementsByClassName('collapsible');
            var checkActiveCategory = true;
            for (var i = 0; i < coll.length; i++) {
              var links = coll[i].nextElementSibling.getElementsByTagName('*');
              if (checkActiveCategory){
                for (var j = 0; j < links.length; j++) {
                  if (links[j].classList.contains('navListItemActive')){
                    coll[i].nextElementSibling.classList.toggle('hide');
                    coll[i].childNodes[1].classList.toggle('rotate');
                    checkActiveCategory = false;
                    break;
                  }
                }
              }

              coll[i].addEventListener('click', function() {
                var arrow = this.childNodes[1];
                arrow.classList.toggle('rotate');
                var content = this.nextElementSibling;
                content.classList.toggle('hide');
              });
            }

            document.addEventListener('DOMContentLoaded', function() {
              createToggler('#navToggler', '#docsNav', 'docsSliderActive');
              createToggler('#tocToggler', 'body', 'tocActive');

              var headings = document.querySelector('.toc-headings');
              headings && headings.addEventListener('click', function(event) {
                var el = event.target;
                while(el !== headings){
                  if (el.tagName === 'A') {
                    document.body.classList.remove('tocActive');
                    break;
                  } else{
                    el = el.parentNode;
                  }
                }
              }, false);

              function createToggler(togglerSelector, targetSelector, className) {
                var toggler = document.querySelector(togglerSelector);
                var target = document.querySelector(targetSelector);

                if (!toggler) {
                  return;
                }

                toggler.onclick = function(event) {
                  event.preventDefault();

                  target.classList.toggle(className);
                };
              }
            });
        </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">&gt;&gt;&gt; </span><span class="hljs-keyword">from</span> singa <span class="hljs-keyword">import</span> tensor, device
<span class="hljs-meta">&gt;&gt;&gt; </span>dev = device.create_cuda_gpu()
<span class="hljs-meta">&gt;&gt;&gt; </span>x = tensor.random((<span class="hljs-number">2</span>,<span class="hljs-number">3</span>),dev)
<span class="hljs-meta">&gt;&gt;&gt; </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">&gt;&gt;&gt; </span>y = x.as_type(tensor.float16)
<span class="hljs-meta">&gt;&gt;&gt; </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">&gt;&gt;&gt; </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 &gt; 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> &lt;&gt;
<span class="hljs-keyword">void</span> GEMM&lt;half_float::half, lang::Cuda&gt;(<span class="hljs-keyword">const</span> half_float::half alpha,
                                        <span class="hljs-keyword">const</span> Tensor&amp; A, <span class="hljs-keyword">const</span> Tensor&amp; 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>
</span></div></article></div><div class="docLastUpdate"><em>Last updated on 10/16/2020</em></div><div class="docs-prevnext"><a class="docs-prev button" href="/docs/time-profiling"><span class="arrow-prev">← </span><span>Time Profiling</span></a><a class="docs-next button" href="/docs/downloads"><span>Download SINGA</span><span class="arrow-next"> →</span></a></div></div></div><nav class="onPageNav"><ul class="toc-headings"><li><a href="#half-data-type">Half data type</a><ul class="toc-headings"><li><a href="#half-data-type-definition">Half data type definition</a></li><li><a href="#half-data-type-operation">Half data type operation</a></li></ul></li><li><a href="#training-in-half">Training in Half</a><ul class="toc-headings"><li><a href="#training-in-half-three-step">Training in Half three step</a></li><li><a href="#example">Example</a></li></ul></li><li><a href="#implementation">Implementation</a><ul class="toc-headings"><li><a href="#half-type-dependency">Half Type Dependency</a></li><li><a href="#nvidia-hardware-acceleration-tensor-core">Nvidia Hardware Acceleration: Tensor Core</a></li><li><a href="#implement-operations">Implement Operations</a></li></ul></li></ul></nav></div><footer class="nav-footer" id="footer"><section class="sitemap"><a href="/" class="nav-home"><img src="/img/singa-logo-square.png" alt="Apache SINGA" width="66" height="58"/></a><div><h5>Docs</h5><a href="/docs/installation">Getting Started</a><a href="/docs/device">Guides</a><a href="/en/https://apache-singa.readthedocs.io/en/latest/">API Reference</a><a href="/docs/examples">Examples</a><a href="/docs/download-singa">Development</a></div><div><h5>Community</h5><a href="/en/users.html">User Showcase</a><a href="/docs/history-singa">SINGA History</a><a href="/docs/team-list">SINGA Team</a><a href="/blog">SINGA News</a><a href="https://github.com/apache/singa">GitHub</a><div class="social"><a class="github-button" href="https://github.com/apache/singa" data-count-href="/apache/singa/stargazers" data-show-count="true" data-count-aria-label="# stargazers on GitHub" aria-label="Star this project on GitHub">apache/singa-doc</a></div><div class="social"><a href="https://twitter.com/ApacheSINGA" class="twitter-follow-button">Follow @ApacheSINGA</a></div></div><div><h5>Apache Software Foundation</h5><a href="https://apache.org/" target="_blank" rel="noreferrer noopener">Foundation</a><a href="http://www.apache.org/licenses/" target="_blank" rel="noreferrer noopener">License</a><a href="http://www.apache.org/foundation/sponsorship.html" target="_blank" rel="noreferrer noopener">Sponsorship</a><a href="http://www.apache.org/foundation/thanks.html" target="_blank" rel="noreferrer noopener">Thanks</a><a href="http://www.apache.org/events/current-event" target="_blank" rel="noreferrer noopener">Events</a><a href="http://www.apache.org/security/" target="_blank" rel="noreferrer noopener">Security</a></div></section><div style="width:100%;text-align:center"><a href="https://apache.org/" target="_blank" rel="noreferrer noopener" class="ApacheOpenSource"><img src="/img/asf_logo_wide.svg" alt="Apache Open Source"/></a><section class="copyright" style="max-width:60%;margin:0 auto">Copyright © 2023
   The Apache Software Foundation. All rights reserved.
   Apache SINGA, Apache, the Apache feather logo, and
   the Apache SINGA project logos are trademarks of The
   Apache Software Foundation. All other marks mentioned
   may be trademarks or registered trademarks of their
   respective owners.</section></div></footer></div><script type="text/javascript" src="https://cdn.jsdelivr.net/docsearch.js/1/docsearch.min.js"></script><script>window.twttr=(function(d,s, id){var js,fjs=d.getElementsByTagName(s)[0],t=window.twttr||{};if(d.getElementById(id))return t;js=d.createElement(s);js.id=id;js.src='https://platform.twitter.com/widgets.js';fjs.parentNode.insertBefore(js, fjs);t._e = [];t.ready = function(f) {t._e.push(f);};return t;}(document, 'script', 'twitter-wjs'));</script><script>
                document.addEventListener('keyup', function(e) {
                  if (e.target !== document.body) {
                    return;
                  }
                  // keyCode for '/' (slash)
                  if (e.keyCode === 191) {
                    const search = document.getElementById('search_input_react');
                    search && search.focus();
                  }
                });
              </script><script>
              var search = docsearch({
                
                apiKey: '45202133606c0b5fa6d21cddc4725dd8',
                indexName: 'apache_singa',
                inputSelector: '#search_input_react',
                algoliaOptions: {"facetFilters":["language:en","version:3.0.0"]}
              });
            </script></body></html>