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<section id="data-types">
<span id="basics-types"></span><h1>Data types<a class="headerlink" href="#data-types" title="Link to this heading">#</a></h1>
<div class="admonition seealso">
<p class="admonition-title">See also</p>
<p><a class="reference internal" href="../reference/arrays.dtypes.html#arrays-dtypes"><span class="std std-ref">Data type objects</span></a></p>
</div>
<section id="array-types-and-conversions-between-types">
<h2>Array types and conversions between types<a class="headerlink" href="#array-types-and-conversions-between-types" title="Link to this heading">#</a></h2>
<p>NumPy supports a much greater variety of numerical types than Python does.
This section shows which are available, and how to modify an array’s data-type.</p>
<p>NumPy numerical types are instances of <a class="reference internal" href="../reference/generated/numpy.dtype.html#numpy.dtype" title="numpy.dtype"><code class="xref py py-obj docutils literal notranslate"><span class="pre">numpy.dtype</span></code></a> (data-type) objects, each
having unique characteristics. Once you have imported NumPy using <code class="docutils literal notranslate"><span class="pre">import</span>
<span class="pre">numpy</span> <span class="pre">as</span> <span class="pre">np</span></code> you can create arrays with a specified dtype using the scalar
types in the numpy top-level API, e.g. <a class="reference internal" href="../reference/arrays.scalars.html#numpy.bool" title="numpy.bool"><code class="xref py py-obj docutils literal notranslate"><span class="pre">numpy.bool</span></code></a>, <a class="reference internal" href="../reference/arrays.scalars.html#numpy.float32" title="numpy.float32"><code class="xref py py-obj docutils literal notranslate"><span class="pre">numpy.float32</span></code></a>, etc.</p>
<p>These scalar types as arguments to the dtype keyword that many numpy functions
or methods accept. For example:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">z</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">uint8</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">z</span>
<span class="go">array([0, 1, 2], dtype=uint8)</span>
</pre></div>
</div>
<p>Array types can also be referred to by character codes, for example:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">],</span> <span class="n">dtype</span><span class="o">=</span><span class="s1">'f'</span><span class="p">)</span>
<span class="go">array([1., 2., 3.], dtype=float32)</span>
<span class="gp">>>> </span><span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">],</span> <span class="n">dtype</span><span class="o">=</span><span class="s1">'d'</span><span class="p">)</span>
<span class="go">array([1., 2., 3.], dtype=float64)</span>
</pre></div>
</div>
<p>See <a class="reference internal" href="../reference/arrays.dtypes.html#arrays-dtypes-constructing"><span class="std std-ref">Specifying and constructing data types</span></a> for more information about specifying and
constructing data type objects, including how to specify parameters like the
byte order.</p>
<p>To determine the type of an array, look at the dtype attribute:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">z</span><span class="o">.</span><span class="n">dtype</span>
<span class="go">dtype('uint8')</span>
</pre></div>
</div>
<p>dtype objects also contain information about the type, such as its bit-width
and its byte-order. The data type can also be used indirectly to query
properties of the type, such as whether it is an integer:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">d</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">dtype</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">int64</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">d</span>
<span class="go">dtype('int64')</span>
<span class="gp">>>> </span><span class="n">np</span><span class="o">.</span><span class="n">issubdtype</span><span class="p">(</span><span class="n">d</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">integer</span><span class="p">)</span>
<span class="go">True</span>
<span class="gp">>>> </span><span class="n">np</span><span class="o">.</span><span class="n">issubdtype</span><span class="p">(</span><span class="n">d</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">floating</span><span class="p">)</span>
<span class="go">False</span>
</pre></div>
</div>
<p>To convert the type of an array, use the .astype() method. For example:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">z</span><span class="o">.</span><span class="n">astype</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">float64</span><span class="p">)</span>
<span class="go">array([0., 1., 2.])</span>
</pre></div>
</div>
<p>Note that, above, we could have used the <em>Python</em> float object as a dtype
instead of <a class="reference internal" href="../reference/arrays.scalars.html#numpy.float64" title="numpy.float64"><code class="xref py py-obj docutils literal notranslate"><span class="pre">numpy.float64</span></code></a>. NumPy knows that
<a class="reference external" href="https://docs.python.org/3/library/functions.html#int" title="(in Python v3.14)"><code class="xref py py-class docutils literal notranslate"><span class="pre">int</span></code></a> refers to <a class="reference internal" href="../reference/arrays.scalars.html#numpy.int_" title="numpy.int_"><code class="xref py py-obj docutils literal notranslate"><span class="pre">numpy.int_</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.14)"><code class="xref py py-class docutils literal notranslate"><span class="pre">bool</span></code></a> means
<a class="reference internal" href="../reference/arrays.scalars.html#numpy.bool" title="numpy.bool"><code class="xref py py-obj docutils literal notranslate"><span class="pre">numpy.bool</span></code></a>, that <a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.14)"><code class="xref py py-class docutils literal notranslate"><span class="pre">float</span></code></a> is <a class="reference internal" href="../reference/arrays.scalars.html#numpy.float64" title="numpy.float64"><code class="xref py py-obj docutils literal notranslate"><span class="pre">numpy.float64</span></code></a> and
<a class="reference external" href="https://docs.python.org/3/library/functions.html#complex" title="(in Python v3.14)"><code class="xref py py-class docutils literal notranslate"><span class="pre">complex</span></code></a> is <a class="reference internal" href="../reference/arrays.scalars.html#numpy.complex128" title="numpy.complex128"><code class="xref py py-obj docutils literal notranslate"><span class="pre">numpy.complex128</span></code></a>. The other data-types do not have
Python equivalents.</p>
<p>Sometimes the conversion can overflow, for instance when converting a <a class="reference internal" href="../reference/arrays.scalars.html#numpy.int64" title="numpy.int64"><code class="xref py py-obj docutils literal notranslate"><span class="pre">numpy.int64</span></code></a> value
300 to <a class="reference internal" href="../reference/arrays.scalars.html#numpy.int8" title="numpy.int8"><code class="xref py py-obj docutils literal notranslate"><span class="pre">numpy.int8</span></code></a>. NumPy follows C casting rules, so that value would overflow and
become 44 <code class="docutils literal notranslate"><span class="pre">(300</span> <span class="pre">-</span> <span class="pre">256)</span></code>. If you wish to avoid such overflows, you can specify that the
overflow action fail by using <code class="docutils literal notranslate"><span class="pre">same_value</span></code> for the <code class="docutils literal notranslate"><span class="pre">casting</span></code> argument (see also
<a class="reference internal" href="#overflow-errors"><span class="std std-ref">Overflow errors</span></a>):</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">z</span><span class="o">.</span><span class="n">astype</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">float64</span><span class="p">,</span> <span class="n">casting</span><span class="o">=</span><span class="s2">"same_value"</span><span class="p">)</span>
<span class="go">array([0., 1., 2.])</span>
</pre></div>
</div>
<section id="numerical-data-types">
<h3>Numerical Data Types<a class="headerlink" href="#numerical-data-types" title="Link to this heading">#</a></h3>
<p>There are 5 basic numerical types representing booleans (<code class="docutils literal notranslate"><span class="pre">bool</span></code>), integers
(<code class="docutils literal notranslate"><span class="pre">int</span></code>), unsigned integers (<code class="docutils literal notranslate"><span class="pre">uint</span></code>) floating point (<code class="docutils literal notranslate"><span class="pre">float</span></code>) and
<code class="docutils literal notranslate"><span class="pre">complex</span></code>. A basic numerical type name combined with a numeric bitsize defines
a concrete type. The bitsize is the number of bits that are needed to represent
a single value in memory. For example, <a class="reference internal" href="../reference/arrays.scalars.html#numpy.float64" title="numpy.float64"><code class="xref py py-obj docutils literal notranslate"><span class="pre">numpy.float64</span></code></a> is a 64 bit
floating point data type. Some types, such as <a class="reference internal" href="../reference/arrays.scalars.html#numpy.int_" title="numpy.int_"><code class="xref py py-obj docutils literal notranslate"><span class="pre">numpy.int_</span></code></a> and
<a class="reference internal" href="../reference/arrays.scalars.html#numpy.intp" title="numpy.intp"><code class="xref py py-obj docutils literal notranslate"><span class="pre">numpy.intp</span></code></a>, have differing bitsizes, dependent on the platforms
(e.g. 32-bit vs. 64-bit CPU architectures). This should be taken into account
when interfacing with low-level code (such as C or Fortran) where the raw memory
is addressed.</p>
</section>
<section id="data-types-for-strings-and-bytes">
<h3>Data Types for Strings and Bytes<a class="headerlink" href="#data-types-for-strings-and-bytes" title="Link to this heading">#</a></h3>
<p>In addition to numerical types, NumPy also supports storing unicode strings, via
the <a class="reference internal" href="../reference/arrays.scalars.html#numpy.str_" title="numpy.str_"><code class="xref py py-obj docutils literal notranslate"><span class="pre">numpy.str_</span></code></a> dtype (<code class="docutils literal notranslate"><span class="pre">U</span></code> character code), null-terminated byte sequences via
<a class="reference internal" href="../reference/arrays.scalars.html#numpy.bytes_" title="numpy.bytes_"><code class="xref py py-obj docutils literal notranslate"><span class="pre">numpy.bytes_</span></code></a> (<code class="docutils literal notranslate"><span class="pre">S</span></code> character code), and arbitrary byte sequences, via
<a class="reference internal" href="../reference/arrays.scalars.html#numpy.void" title="numpy.void"><code class="xref py py-obj docutils literal notranslate"><span class="pre">numpy.void</span></code></a> (<code class="docutils literal notranslate"><span class="pre">V</span></code> character code).</p>
<p>All of the above are <em>fixed-width</em> data types. They are parameterized by a
width, in either bytes or unicode points, that a single data element in the
array must fit inside. This means that storing an array of byte sequences or
strings using this dtype requires knowing or calculating the sizes of the
longest text or byte sequence in advance.</p>
<p>As an example, we can create an array storing the words <code class="docutils literal notranslate"><span class="pre">"hello"</span></code> and
<code class="docutils literal notranslate"><span class="pre">"world!"</span></code>:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="s2">"hello"</span><span class="p">,</span> <span class="s2">"world!"</span><span class="p">])</span>
<span class="go">array(['hello', 'world!'], dtype='<U6')</span>
</pre></div>
</div>
<p>Here the data type is detected as a unicode string that is a maximum of 6 code
points long, enough to store both entries without truncation. If we specify a
shorter or longer data type, the string is either truncated or zero-padded to
fit in the specified width:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="s2">"hello"</span><span class="p">,</span> <span class="s2">"world!"</span><span class="p">],</span> <span class="n">dtype</span><span class="o">=</span><span class="s2">"U5"</span><span class="p">)</span>
<span class="go">array(['hello', 'world'], dtype='<U5')</span>
<span class="gp">>>> </span><span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="s2">"hello"</span><span class="p">,</span> <span class="s2">"world!"</span><span class="p">],</span> <span class="n">dtype</span><span class="o">=</span><span class="s2">"U7"</span><span class="p">)</span>
<span class="go">array(['hello', 'world!'], dtype='<U7')</span>
</pre></div>
</div>
<p>We can see the zero-padding a little more clearly if we use the bytes data
type and ask NumPy to print out the bytes in the array buffer:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="s2">"hello"</span><span class="p">,</span> <span class="s2">"world"</span><span class="p">],</span> <span class="n">dtype</span><span class="o">=</span><span class="s2">"S7"</span><span class="p">)</span><span class="o">.</span><span class="n">tobytes</span><span class="p">()</span>
<span class="go">b'hello\x00\x00world\x00\x00'</span>
</pre></div>
</div>
<p>Each entry is padded with two extra null bytes. Note however that NumPy cannot
tell the difference between intentionally stored trailing nulls and padding
nulls:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">x</span> <span class="o">=</span> <span class="p">[</span><span class="sa">b</span><span class="s2">"hello</span><span class="se">\0\0</span><span class="s2">"</span><span class="p">,</span> <span class="sa">b</span><span class="s2">"world"</span><span class="p">]</span>
<span class="gp">>>> </span><span class="n">a</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="s2">"S7"</span><span class="p">)</span>
<span class="gp">>>> </span><span class="nb">print</span><span class="p">(</span><span class="n">a</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span>
<span class="go">b"hello"</span>
<span class="gp">>>> </span><span class="n">a</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">==</span> <span class="n">x</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
<span class="go">False</span>
</pre></div>
</div>
<p>If you need to store and round-trip any trailing null bytes, you will need to
use an unstructured void data type:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">a</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="s2">"V7"</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">a</span>
<span class="go">array([b'\x68\x65\x6C\x6C\x6F\x00\x00', b'\x77\x6F\x72\x6C\x64\x00\x00'],</span>
<span class="go"> dtype='|V7')</span>
<span class="gp">>>> </span><span class="n">a</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">==</span> <span class="n">np</span><span class="o">.</span><span class="n">void</span><span class="p">(</span><span class="n">x</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span>
<span class="go">True</span>
</pre></div>
</div>
<p>Advanced types, not listed above, are explored in section
<a class="reference internal" href="basics.rec.html#structured-arrays"><span class="std std-ref">Structured arrays</span></a>.</p>
</section>
</section>
<section id="relationship-between-numpy-data-types-and-c-data-types">
<span id="canonical-python-and-c-types"></span><h2>Relationship Between NumPy Data Types and C Data Types<a class="headerlink" href="#relationship-between-numpy-data-types-and-c-data-types" title="Link to this heading">#</a></h2>
<p>NumPy provides both bit sized type names and names based on the names of C types.
Since the definition of C types are platform dependent, this means the explicitly
bit sized should be preferred to avoid platform-dependent behavior in programs
using NumPy.</p>
<p>To ease integration with C code, where it is more natural to refer to
platform-dependent C types, NumPy also provides type aliases that correspond
to the C types for the platform. Some dtypes have trailing underscore to avoid
confusion with builtin python type names, such as <a class="reference internal" href="../reference/arrays.scalars.html#numpy.bool_" title="numpy.bool_"><code class="xref py py-obj docutils literal notranslate"><span class="pre">numpy.bool_</span></code></a>.</p>
<div class="pst-scrollable-table-container"><table class="table">
<thead>
<tr class="row-odd"><th class="head"><p>Canonical Python API name</p></th>
<th class="head"><p>Python API “C-like” name</p></th>
<th class="head"><p>Actual C type</p></th>
<th class="head"><p>Description</p></th>
</tr>
</thead>
<tbody>
<tr class="row-even"><td><p><a class="reference internal" href="../reference/arrays.scalars.html#numpy.bool" title="numpy.bool"><code class="xref py py-obj docutils literal notranslate"><span class="pre">numpy.bool</span></code></a> or <a class="reference internal" href="../reference/arrays.scalars.html#numpy.bool_" title="numpy.bool_"><code class="xref py py-obj docutils literal notranslate"><span class="pre">numpy.bool_</span></code></a></p></td>
<td><p>N/A</p></td>
<td><p><code class="docutils literal notranslate"><span class="pre">bool</span></code> (defined in <code class="docutils literal notranslate"><span class="pre">stdbool.h</span></code>)</p></td>
<td><p>Boolean (True or False) stored as a byte.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="../reference/arrays.scalars.html#numpy.int8" title="numpy.int8"><code class="xref py py-obj docutils literal notranslate"><span class="pre">numpy.int8</span></code></a></p></td>
<td><p><a class="reference internal" href="../reference/arrays.scalars.html#numpy.byte" title="numpy.byte"><code class="xref py py-obj docutils literal notranslate"><span class="pre">numpy.byte</span></code></a></p></td>
<td><p><code class="docutils literal notranslate"><span class="pre">signed</span> <span class="pre">char</span></code></p></td>
<td><p>Platform-defined integer type with 8 bits.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="../reference/arrays.scalars.html#numpy.uint8" title="numpy.uint8"><code class="xref py py-obj docutils literal notranslate"><span class="pre">numpy.uint8</span></code></a></p></td>
<td><p><a class="reference internal" href="../reference/arrays.scalars.html#numpy.ubyte" title="numpy.ubyte"><code class="xref py py-obj docutils literal notranslate"><span class="pre">numpy.ubyte</span></code></a></p></td>
<td><p><code class="docutils literal notranslate"><span class="pre">unsigned</span> <span class="pre">char</span></code></p></td>
<td><p>Platform-defined integer type with 8 bits without sign.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="../reference/arrays.scalars.html#numpy.int16" title="numpy.int16"><code class="xref py py-obj docutils literal notranslate"><span class="pre">numpy.int16</span></code></a></p></td>
<td><p><a class="reference internal" href="../reference/arrays.scalars.html#numpy.short" title="numpy.short"><code class="xref py py-obj docutils literal notranslate"><span class="pre">numpy.short</span></code></a></p></td>
<td><p><code class="docutils literal notranslate"><span class="pre">short</span></code></p></td>
<td><p>Platform-defined integer type with 16 bits.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="../reference/arrays.scalars.html#numpy.uint16" title="numpy.uint16"><code class="xref py py-obj docutils literal notranslate"><span class="pre">numpy.uint16</span></code></a></p></td>
<td><p><a class="reference internal" href="../reference/arrays.scalars.html#numpy.ushort" title="numpy.ushort"><code class="xref py py-obj docutils literal notranslate"><span class="pre">numpy.ushort</span></code></a></p></td>
<td><p><code class="docutils literal notranslate"><span class="pre">unsigned</span> <span class="pre">short</span></code></p></td>
<td><p>Platform-defined integer type with 16 bits without sign.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="../reference/arrays.scalars.html#numpy.int32" title="numpy.int32"><code class="xref py py-obj docutils literal notranslate"><span class="pre">numpy.int32</span></code></a></p></td>
<td><p><a class="reference internal" href="../reference/arrays.scalars.html#numpy.intc" title="numpy.intc"><code class="xref py py-obj docutils literal notranslate"><span class="pre">numpy.intc</span></code></a></p></td>
<td><p><code class="docutils literal notranslate"><span class="pre">int</span></code></p></td>
<td><p>Platform-defined integer type with 32 bits.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="../reference/arrays.scalars.html#numpy.uint32" title="numpy.uint32"><code class="xref py py-obj docutils literal notranslate"><span class="pre">numpy.uint32</span></code></a></p></td>
<td><p><a class="reference internal" href="../reference/arrays.scalars.html#numpy.uintc" title="numpy.uintc"><code class="xref py py-obj docutils literal notranslate"><span class="pre">numpy.uintc</span></code></a></p></td>
<td><p><code class="docutils literal notranslate"><span class="pre">unsigned</span> <span class="pre">int</span></code></p></td>
<td><p>Platform-defined integer type with 32 bits without sign.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="../reference/arrays.scalars.html#numpy.intp" title="numpy.intp"><code class="xref py py-obj docutils literal notranslate"><span class="pre">numpy.intp</span></code></a></p></td>
<td><p>N/A</p></td>
<td><p><code class="docutils literal notranslate"><span class="pre">ssize_t</span></code>/<code class="docutils literal notranslate"><span class="pre">Py_ssize_t</span></code></p></td>
<td><p>Platform-defined integer of size <code class="docutils literal notranslate"><span class="pre">size_t</span></code>; used e.g. for sizes.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="../reference/arrays.scalars.html#numpy.uintp" title="numpy.uintp"><code class="xref py py-obj docutils literal notranslate"><span class="pre">numpy.uintp</span></code></a></p></td>
<td><p>N/A</p></td>
<td><p><code class="docutils literal notranslate"><span class="pre">size_t</span></code></p></td>
<td><p>Platform-defined integer type capable of storing the maximum
allocation size.</p></td>
</tr>
<tr class="row-odd"><td><p>N/A</p></td>
<td><p><code class="docutils literal notranslate"><span class="pre">'p'</span></code></p></td>
<td><p><code class="docutils literal notranslate"><span class="pre">intptr_t</span></code></p></td>
<td><p>Guaranteed to hold pointers. Character code only (Python and C).</p></td>
</tr>
<tr class="row-even"><td><p>N/A</p></td>
<td><p><code class="docutils literal notranslate"><span class="pre">'P'</span></code></p></td>
<td><p><code class="docutils literal notranslate"><span class="pre">uintptr_t</span></code></p></td>
<td><p>Guaranteed to hold pointers without sign. Character code only (Python and C).</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="../reference/arrays.scalars.html#numpy.int32" title="numpy.int32"><code class="xref py py-obj docutils literal notranslate"><span class="pre">numpy.int32</span></code></a> or <a class="reference internal" href="../reference/arrays.scalars.html#numpy.int64" title="numpy.int64"><code class="xref py py-obj docutils literal notranslate"><span class="pre">numpy.int64</span></code></a></p></td>
<td><p><a class="reference internal" href="../reference/arrays.scalars.html#numpy.long" title="numpy.long"><code class="xref py py-obj docutils literal notranslate"><span class="pre">numpy.long</span></code></a></p></td>
<td><p><code class="docutils literal notranslate"><span class="pre">long</span></code></p></td>
<td><p>Platform-defined integer type with at least 32 bits.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="../reference/arrays.scalars.html#numpy.uint32" title="numpy.uint32"><code class="xref py py-obj docutils literal notranslate"><span class="pre">numpy.uint32</span></code></a> or <a class="reference internal" href="../reference/arrays.scalars.html#numpy.uint64" title="numpy.uint64"><code class="xref py py-obj docutils literal notranslate"><span class="pre">numpy.uint64</span></code></a></p></td>
<td><p><a class="reference internal" href="../reference/arrays.scalars.html#numpy.ulong" title="numpy.ulong"><code class="xref py py-obj docutils literal notranslate"><span class="pre">numpy.ulong</span></code></a></p></td>
<td><p><code class="docutils literal notranslate"><span class="pre">unsigned</span> <span class="pre">long</span></code></p></td>
<td><p>Platform-defined integer type with at least 32 bits without sign.</p></td>
</tr>
<tr class="row-odd"><td><p>N/A</p></td>
<td><p><a class="reference internal" href="../reference/arrays.scalars.html#numpy.longlong" title="numpy.longlong"><code class="xref py py-obj docutils literal notranslate"><span class="pre">numpy.longlong</span></code></a></p></td>
<td><p><code class="docutils literal notranslate"><span class="pre">long</span> <span class="pre">long</span></code></p></td>
<td><p>Platform-defined integer type with at least 64 bits.</p></td>
</tr>
<tr class="row-even"><td><p>N/A</p></td>
<td><p><a class="reference internal" href="../reference/arrays.scalars.html#numpy.ulonglong" title="numpy.ulonglong"><code class="xref py py-obj docutils literal notranslate"><span class="pre">numpy.ulonglong</span></code></a></p></td>
<td><p><code class="docutils literal notranslate"><span class="pre">unsigned</span> <span class="pre">long</span> <span class="pre">long</span></code></p></td>
<td><p>Platform-defined integer type with at least 64 bits without sign.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="../reference/arrays.scalars.html#numpy.float16" title="numpy.float16"><code class="xref py py-obj docutils literal notranslate"><span class="pre">numpy.float16</span></code></a></p></td>
<td><p><a class="reference internal" href="../reference/arrays.scalars.html#numpy.half" title="numpy.half"><code class="xref py py-obj docutils literal notranslate"><span class="pre">numpy.half</span></code></a></p></td>
<td><p>N/A</p></td>
<td><p>Half precision float:
sign bit, 5 bits exponent, 10 bits mantissa.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="../reference/arrays.scalars.html#numpy.float32" title="numpy.float32"><code class="xref py py-obj docutils literal notranslate"><span class="pre">numpy.float32</span></code></a></p></td>
<td><p><a class="reference internal" href="../reference/arrays.scalars.html#numpy.single" title="numpy.single"><code class="xref py py-obj docutils literal notranslate"><span class="pre">numpy.single</span></code></a></p></td>
<td><p><code class="docutils literal notranslate"><span class="pre">float</span></code></p></td>
<td><p>Platform-defined single precision float:
typically sign bit, 8 bits exponent, 23 bits mantissa.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="../reference/arrays.scalars.html#numpy.float64" title="numpy.float64"><code class="xref py py-obj docutils literal notranslate"><span class="pre">numpy.float64</span></code></a></p></td>
<td><p><a class="reference internal" href="../reference/arrays.scalars.html#numpy.double" title="numpy.double"><code class="xref py py-obj docutils literal notranslate"><span class="pre">numpy.double</span></code></a></p></td>
<td><p><code class="docutils literal notranslate"><span class="pre">double</span></code></p></td>
<td><p>Platform-defined double precision float:
typically sign bit, 11 bits exponent, 52 bits mantissa.</p></td>
</tr>
<tr class="row-even"><td><p><code class="docutils literal notranslate"><span class="pre">numpy.float96</span></code> or <a class="reference internal" href="../reference/arrays.scalars.html#numpy.float128" title="numpy.float128"><code class="xref py py-obj docutils literal notranslate"><span class="pre">numpy.float128</span></code></a></p></td>
<td><p><a class="reference internal" href="../reference/arrays.scalars.html#numpy.longdouble" title="numpy.longdouble"><code class="xref py py-obj docutils literal notranslate"><span class="pre">numpy.longdouble</span></code></a></p></td>
<td><p><code class="docutils literal notranslate"><span class="pre">long</span> <span class="pre">double</span></code></p></td>
<td><p>Platform-defined extended-precision float.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="../reference/arrays.scalars.html#numpy.complex64" title="numpy.complex64"><code class="xref py py-obj docutils literal notranslate"><span class="pre">numpy.complex64</span></code></a></p></td>
<td><p><a class="reference internal" href="../reference/arrays.scalars.html#numpy.csingle" title="numpy.csingle"><code class="xref py py-obj docutils literal notranslate"><span class="pre">numpy.csingle</span></code></a></p></td>
<td><p><code class="docutils literal notranslate"><span class="pre">float</span> <span class="pre">complex</span></code></p></td>
<td><p>Complex number, represented by two single-precision floats (real and imaginary components).</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="../reference/arrays.scalars.html#numpy.complex128" title="numpy.complex128"><code class="xref py py-obj docutils literal notranslate"><span class="pre">numpy.complex128</span></code></a></p></td>
<td><p><a class="reference internal" href="../reference/arrays.scalars.html#numpy.cdouble" title="numpy.cdouble"><code class="xref py py-obj docutils literal notranslate"><span class="pre">numpy.cdouble</span></code></a></p></td>
<td><p><code class="docutils literal notranslate"><span class="pre">double</span> <span class="pre">complex</span></code></p></td>
<td><p>Complex number, represented by two double-precision floats (real and imaginary components).</p></td>
</tr>
<tr class="row-odd"><td><p><code class="docutils literal notranslate"><span class="pre">numpy.complex192</span></code> or <a class="reference internal" href="../reference/arrays.scalars.html#numpy.complex256" title="numpy.complex256"><code class="xref py py-obj docutils literal notranslate"><span class="pre">numpy.complex256</span></code></a></p></td>
<td><p><a class="reference internal" href="../reference/arrays.scalars.html#numpy.clongdouble" title="numpy.clongdouble"><code class="xref py py-obj docutils literal notranslate"><span class="pre">numpy.clongdouble</span></code></a></p></td>
<td><p><code class="docutils literal notranslate"><span class="pre">long</span> <span class="pre">double</span> <span class="pre">complex</span></code></p></td>
<td><p>Complex number, represented by two extended-precision floats (real and imaginary components).</p></td>
</tr>
</tbody>
</table>
</div>
<p>Since many of these have platform-dependent definitions, a set of fixed-size
aliases are provided (See <a class="reference internal" href="../reference/arrays.scalars.html#sized-aliases"><span class="std std-ref">Sized aliases</span></a>).</p>
</section>
<section id="array-scalars">
<h2>Array scalars<a class="headerlink" href="#array-scalars" title="Link to this heading">#</a></h2>
<p>NumPy generally returns elements of arrays as array scalars (a scalar
with an associated dtype). Array scalars differ from Python scalars, but
for the most part they can be used interchangeably (the primary
exception is for versions of Python older than v2.x, where integer array
scalars cannot act as indices for lists and tuples). There are some
exceptions, such as when code requires very specific attributes of a scalar
or when it checks specifically whether a value is a Python scalar. Generally,
problems are easily fixed by explicitly converting array scalars
to Python scalars, using the corresponding Python type function
(e.g., <a class="reference external" href="https://docs.python.org/3/library/functions.html#int" title="(in Python v3.14)"><code class="xref py py-class docutils literal notranslate"><span class="pre">int</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.14)"><code class="xref py py-class docutils literal notranslate"><span class="pre">float</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/functions.html#complex" title="(in Python v3.14)"><code class="xref py py-class docutils literal notranslate"><span class="pre">complex</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#str" title="(in Python v3.14)"><code class="xref py py-class docutils literal notranslate"><span class="pre">str</span></code></a>).</p>
<p>The primary advantage of using array scalars is that
they preserve the array type (Python may not have a matching scalar type
available, e.g. <code class="docutils literal notranslate"><span class="pre">int16</span></code>). Therefore, the use of array scalars ensures
identical behaviour between arrays and scalars, irrespective of whether the
value is inside an array or not. NumPy scalars also have many of the same
methods arrays do.</p>
</section>
<section id="overflow-errors">
<span id="id1"></span><h2>Overflow errors<a class="headerlink" href="#overflow-errors" title="Link to this heading">#</a></h2>
<p>The fixed size of NumPy numeric types may cause overflow errors when a value
requires more memory than available in the data type. For example,
<a class="reference internal" href="../reference/generated/numpy.power.html#numpy.power" title="numpy.power"><code class="xref py py-obj docutils literal notranslate"><span class="pre">numpy.power</span></code></a> evaluates <code class="docutils literal notranslate"><span class="pre">100</span> <span class="pre">**</span> <span class="pre">9</span></code> correctly for 64-bit integers,
but gives -1486618624 (incorrect) for a 32-bit integer.</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">np</span><span class="o">.</span><span class="n">power</span><span class="p">(</span><span class="mi">100</span><span class="p">,</span> <span class="mi">9</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">int64</span><span class="p">)</span>
<span class="go">1000000000000000000</span>
<span class="gp">>>> </span><span class="n">np</span><span class="o">.</span><span class="n">power</span><span class="p">(</span><span class="mi">100</span><span class="p">,</span> <span class="mi">9</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">int32</span><span class="p">)</span>
<span class="go">np.int32(-1486618624)</span>
</pre></div>
</div>
<p>The behaviour of NumPy and Python integer types differs significantly for
integer overflows and may confuse users expecting NumPy integers to behave
similar to Python’s <a class="reference external" href="https://docs.python.org/3/library/functions.html#int" title="(in Python v3.14)"><code class="xref py py-class docutils literal notranslate"><span class="pre">int</span></code></a>. Unlike NumPy, the size of Python’s
<a class="reference external" href="https://docs.python.org/3/library/functions.html#int" title="(in Python v3.14)"><code class="xref py py-class docutils literal notranslate"><span class="pre">int</span></code></a> is flexible. This means Python integers may expand to accommodate
any integer and will not overflow.</p>
<p>NumPy provides <a class="reference internal" href="../reference/generated/numpy.iinfo.html#numpy.iinfo" title="numpy.iinfo"><code class="xref py py-obj docutils literal notranslate"><span class="pre">numpy.iinfo</span></code></a> and <a class="reference internal" href="../reference/generated/numpy.finfo.html#numpy.finfo" title="numpy.finfo"><code class="xref py py-obj docutils literal notranslate"><span class="pre">numpy.finfo</span></code></a> to verify the
minimum or maximum values of NumPy integer and floating point values
respectively</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">np</span><span class="o">.</span><span class="n">iinfo</span><span class="p">(</span><span class="nb">int</span><span class="p">)</span> <span class="c1"># Bounds of the default integer on this system.</span>
<span class="go">iinfo(min=-9223372036854775808, max=9223372036854775807, dtype=int64)</span>
<span class="gp">>>> </span><span class="n">np</span><span class="o">.</span><span class="n">iinfo</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">int32</span><span class="p">)</span> <span class="c1"># Bounds of a 32-bit integer</span>
<span class="go">iinfo(min=-2147483648, max=2147483647, dtype=int32)</span>
<span class="gp">>>> </span><span class="n">np</span><span class="o">.</span><span class="n">iinfo</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">int64</span><span class="p">)</span> <span class="c1"># Bounds of a 64-bit integer</span>
<span class="go">iinfo(min=-9223372036854775808, max=9223372036854775807, dtype=int64)</span>
</pre></div>
</div>
<p>If 64-bit integers are still too small the result may be cast to a
floating point number. Floating point numbers offer a larger, but inexact,
range of possible values.</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">np</span><span class="o">.</span><span class="n">power</span><span class="p">(</span><span class="mi">100</span><span class="p">,</span> <span class="mi">100</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">int64</span><span class="p">)</span> <span class="c1"># Incorrect even with 64-bit int</span>
<span class="go">0</span>
<span class="gp">>>> </span><span class="n">np</span><span class="o">.</span><span class="n">power</span><span class="p">(</span><span class="mi">100</span><span class="p">,</span> <span class="mi">100</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">float64</span><span class="p">)</span>
<span class="go">1e+200</span>
</pre></div>
</div>
</section>
<section id="floating-point-precision">
<h2>Floating point precision<a class="headerlink" href="#floating-point-precision" title="Link to this heading">#</a></h2>
<p>Many functions in NumPy, especially those in <a class="reference internal" href="../reference/routines.linalg.html#module-numpy.linalg" title="numpy.linalg"><code class="xref py py-obj docutils literal notranslate"><span class="pre">numpy.linalg</span></code></a>, involve floating-point
arithmetic, which can introduce small inaccuracies due to the way computers
represent decimal numbers. For instance, when performing basic arithmetic operations
involving floating-point numbers:</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="mf">0.3</span> <span class="o">-</span> <span class="mf">0.2</span> <span class="o">-</span> <span class="mf">0.1</span> <span class="c1"># This does not equal 0 due to floating-point precision</span>
<span class="go">-2.7755575615628914e-17</span>
</pre></div>
</div>
<p>To handle such cases, it’s advisable to use functions like <em class="xref py py-obj">np.isclose</em> to compare
values, rather than checking for exact equality:</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">np</span><span class="o">.</span><span class="n">isclose</span><span class="p">(</span><span class="mf">0.3</span> <span class="o">-</span> <span class="mf">0.2</span> <span class="o">-</span> <span class="mf">0.1</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="n">rtol</span><span class="o">=</span><span class="mf">1e-05</span><span class="p">)</span> <span class="c1"># Check for closeness to 0</span>
<span class="go">True</span>
</pre></div>
</div>
<p>In this example, <em class="xref py py-obj">np.isclose</em> accounts for the minor inaccuracies that occur in
floating-point calculations by applying a relative tolerance, ensuring that results
within a small threshold are considered close.</p>
<p>For information about precision in calculations, see <a class="reference external" href="https://docs.oracle.com/cd/E19957-01/806-3568/ncg_goldberg.html">Floating-Point Arithmetic</a>.</p>
</section>
<section id="extended-precision">
<h2>Extended precision<a class="headerlink" href="#extended-precision" title="Link to this heading">#</a></h2>
<p>Python’s floating-point numbers are usually 64-bit floating-point numbers,
nearly equivalent to <a class="reference internal" href="../reference/arrays.scalars.html#numpy.float64" title="numpy.float64"><code class="xref py py-obj docutils literal notranslate"><span class="pre">numpy.float64</span></code></a>. In some unusual situations it may be
useful to use floating-point numbers with more precision. Whether this
is possible in numpy depends on the hardware and on the development
environment: specifically, x86 machines provide hardware floating-point
with 80-bit precision, and while most C compilers provide this as their
<code class="docutils literal notranslate"><span class="pre">long</span> <span class="pre">double</span></code> type, MSVC (standard for Windows builds) makes
<code class="docutils literal notranslate"><span class="pre">long</span> <span class="pre">double</span></code> identical to <code class="docutils literal notranslate"><span class="pre">double</span></code> (64 bits). NumPy makes the
compiler’s <code class="docutils literal notranslate"><span class="pre">long</span> <span class="pre">double</span></code> available as <a class="reference internal" href="../reference/arrays.scalars.html#numpy.longdouble" title="numpy.longdouble"><code class="xref py py-obj docutils literal notranslate"><span class="pre">numpy.longdouble</span></code></a> (and
<code class="docutils literal notranslate"><span class="pre">np.clongdouble</span></code> for the complex numbers). You can find out what your
numpy provides with <code class="docutils literal notranslate"><span class="pre">np.finfo(np.longdouble)</span></code>.</p>
<p>NumPy does not provide a dtype with more precision than C’s
<code class="docutils literal notranslate"><span class="pre">long</span> <span class="pre">double</span></code>; in particular, the 128-bit IEEE quad precision
data type (FORTRAN’s <code class="docutils literal notranslate"><span class="pre">REAL*16</span></code>) is not available.</p>
<p>For efficient memory alignment, <a class="reference internal" href="../reference/arrays.scalars.html#numpy.longdouble" title="numpy.longdouble"><code class="xref py py-obj docutils literal notranslate"><span class="pre">numpy.longdouble</span></code></a> is usually stored
padded with zero bits, either to 96 or 128 bits. Which is more efficient
depends on hardware and development environment; typically on 32-bit
systems they are padded to 96 bits, while on 64-bit systems they are
typically padded to 128 bits. <code class="docutils literal notranslate"><span class="pre">np.longdouble</span></code> is padded to the system
default; <code class="docutils literal notranslate"><span class="pre">np.float96</span></code> and <code class="docutils literal notranslate"><span class="pre">np.float128</span></code> are provided for users who
want specific padding. In spite of the names, <code class="docutils literal notranslate"><span class="pre">np.float96</span></code> and
<code class="docutils literal notranslate"><span class="pre">np.float128</span></code> provide only as much precision as <code class="docutils literal notranslate"><span class="pre">np.longdouble</span></code>,
that is, 80 bits on most x86 machines and 64 bits in standard
Windows builds.</p>
<p>Be warned that even if <a class="reference internal" href="../reference/arrays.scalars.html#numpy.longdouble" title="numpy.longdouble"><code class="xref py py-obj docutils literal notranslate"><span class="pre">numpy.longdouble</span></code></a> offers more precision than
python <a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.14)"><code class="xref py py-class docutils literal notranslate"><span class="pre">float</span></code></a>, it is easy to lose that extra precision, since
python often forces values to pass through <code class="docutils literal notranslate"><span class="pre">float</span></code>. For example,
the <code class="docutils literal notranslate"><span class="pre">%</span></code> formatting operator requires its arguments to be converted
to standard python types, and it is therefore impossible to preserve
extended precision even if many decimal places are requested. It can
be useful to test your code with the value
<code class="docutils literal notranslate"><span class="pre">1</span> <span class="pre">+</span> <span class="pre">np.finfo(np.longdouble).eps</span></code>.</p>
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