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<section id="numpy-c-code-explanations">
<span id="c-code-explanations"></span><h1>NumPy C code explanations<a class="headerlink" href="#numpy-c-code-explanations" title="Link to this heading">#</a></h1>
<blockquote>
<div><p>Fanaticism consists of redoubling your efforts when you have forgotten
your aim.
— <em>George Santayana</em></p>
<p>An authority is a person who can tell you more about something than
you really care to know.
— <em>Unknown</em></p>
</div></blockquote>
<p>This page attempts to explain the logic behind some of the new
pieces of code. The purpose behind these explanations is to enable
somebody to be able to understand the ideas behind the implementation
somewhat more easily than just staring at the code. Perhaps in this
way, the algorithms can be improved on, borrowed from, and/or
optimized by more people.</p>
<section id="memory-model">
<h2>Memory model<a class="headerlink" href="#memory-model" title="Link to this heading">#</a></h2>
<p id="index-0">One fundamental aspect of the <a class="reference internal" href="../reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray"><code class="xref py py-class docutils literal notranslate"><span class="pre">ndarray</span></code></a> is that an array is seen as a
“chunk” of memory starting at some location. The interpretation of
this memory depends on the <a class="reference internal" href="../glossary.html#term-stride"><span class="xref std std-term">stride</span></a> information. For each dimension in
an <span class="math notranslate nohighlight">\(N\)</span>-dimensional array, an integer (<a class="reference internal" href="../glossary.html#term-stride"><span class="xref std std-term">stride</span></a>) dictates how many
bytes must be skipped to get to the next element in that dimension.
Unless you have a single-segment array, this <a class="reference internal" href="../glossary.html#term-stride"><span class="xref std std-term">stride</span></a> information must
be consulted when traversing through an array. It is not difficult to
write code that accepts strides, you just have to use <code class="docutils literal notranslate"><span class="pre">char*</span></code>
pointers because strides are in units of bytes. Keep in mind also that
strides do not have to be unit-multiples of the element size. Also,
remember that if the number of dimensions of the array is 0 (sometimes
called a <code class="docutils literal notranslate"><span class="pre">rank-0</span></code> array), then the <a class="reference internal" href="../glossary.html#term-stride"><span class="xref std std-term">strides</span></a> and
<a class="reference internal" href="../glossary.html#term-dimension"><span class="xref std std-term">dimensions</span></a> variables are <code class="docutils literal notranslate"><span class="pre">NULL</span></code>.</p>
<p>Besides the structural information contained in the strides and
dimensions members of the <a class="reference internal" href="../reference/c-api/types-and-structures.html#c.PyArrayObject" title="PyArrayObject"><code class="xref c c-type docutils literal notranslate"><span class="pre">PyArrayObject</span></code></a>, the flags contain
important information about how the data may be accessed. In particular,
the <a class="reference internal" href="../reference/c-api/array.html#c.NPY_ARRAY_ALIGNED" title="NPY_ARRAY_ALIGNED"><code class="xref c c-data docutils literal notranslate"><span class="pre">NPY_ARRAY_ALIGNED</span></code></a> flag is set when the memory is on a
suitable boundary according to the datatype array. Even if you have
a <a class="reference internal" href="../glossary.html#term-contiguous"><span class="xref std std-term">contiguous</span></a> chunk of memory, you cannot just assume it is safe to
dereference a datatype-specific pointer to an element. Only if the
<a class="reference internal" href="../reference/c-api/array.html#c.NPY_ARRAY_ALIGNED" title="NPY_ARRAY_ALIGNED"><code class="xref c c-data docutils literal notranslate"><span class="pre">NPY_ARRAY_ALIGNED</span></code></a> flag is set, this is a safe operation. On
some platforms it will work but on others, like Solaris, it will cause
a bus error. The <a class="reference internal" href="../reference/c-api/array.html#c.NPY_ARRAY_WRITEABLE" title="NPY_ARRAY_WRITEABLE"><code class="xref c c-data docutils literal notranslate"><span class="pre">NPY_ARRAY_WRITEABLE</span></code></a> should also be ensured
if you plan on writing to the memory area of the array. It is also
possible to obtain a pointer to an unwritable memory area. Sometimes,
writing to the memory area when the <a class="reference internal" href="../reference/c-api/array.html#c.NPY_ARRAY_WRITEABLE" title="NPY_ARRAY_WRITEABLE"><code class="xref c c-data docutils literal notranslate"><span class="pre">NPY_ARRAY_WRITEABLE</span></code></a> flag is not
set will just be rude. Other times it can cause program crashes (<em>e.g.</em>
a data-area that is a read-only memory-mapped file).</p>
</section>
<section id="data-type-encapsulation">
<h2>Data-type encapsulation<a class="headerlink" href="#data-type-encapsulation" title="Link to this heading">#</a></h2>
<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 (dtype)</span></a></p>
</div>
<p id="index-1">The <a class="reference internal" href="../reference/arrays.dtypes.html#arrays-dtypes"><span class="std std-ref">datatype</span></a> is an important abstraction of the
<a class="reference internal" href="../reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray"><code class="xref py py-class docutils literal notranslate"><span class="pre">ndarray</span></code></a>. Operations
will look to the datatype to provide the key functionality that is
needed to operate on the array. This functionality is provided in the
list of function pointers pointed to by the <code class="docutils literal notranslate"><span class="pre">f</span></code> member of the
<a class="reference internal" href="../reference/c-api/types-and-structures.html#c.PyArray_Descr" title="PyArray_Descr"><code class="xref c c-type docutils literal notranslate"><span class="pre">PyArray_Descr</span></code></a> structure. In this way, the number of datatypes can be
extended simply by providing a <a class="reference internal" href="../reference/c-api/types-and-structures.html#c.PyArray_Descr" title="PyArray_Descr"><code class="xref c c-type docutils literal notranslate"><span class="pre">PyArray_Descr</span></code></a> structure with suitable
function pointers in the <code class="docutils literal notranslate"><span class="pre">f</span></code> member. For built-in types, there are some
optimizations that bypass this mechanism, but the point of the datatype
abstraction is to allow new datatypes to be added.</p>
<p>One of the built-in datatypes, the <a class="reference internal" href="../reference/arrays.scalars.html#numpy.void" title="numpy.void"><code class="xref py py-class docutils literal notranslate"><span class="pre">void</span></code></a> datatype allows for
arbitrary <a class="reference internal" href="../glossary.html#term-structured-data-type"><span class="xref std std-term">structured types</span></a> containing 1 or more
fields as elements of the array. A <a class="reference internal" href="../glossary.html#term-field"><span class="xref std std-term">field</span></a> is simply another datatype
object along with an offset into the current structured type. In order to
support arbitrarily nested fields, several recursive implementations of
datatype access are implemented for the void type. A common idiom is to cycle
through the elements of the dictionary and perform a specific operation based on
the datatype object stored at the given offset. These offsets can be
arbitrary numbers. Therefore, the possibility of encountering misaligned
data must be recognized and taken into account if necessary.</p>
</section>
<section id="n-d-iterators">
<h2>N-D iterators<a class="headerlink" href="#n-d-iterators" title="Link to this heading">#</a></h2>
<div class="admonition seealso">
<p class="admonition-title">See also</p>
<p><a class="reference internal" href="../reference/arrays.nditer.html#arrays-nditer"><span class="std std-ref">Iterating over arrays</span></a></p>
</div>
<p id="index-2">A very common operation in much of NumPy code is the need to iterate
over all the elements of a general, strided, N-dimensional array. This
operation of a general-purpose N-dimensional loop is abstracted in the
notion of an iterator object. To write an N-dimensional loop, you only
have to create an iterator object from an ndarray, work with the
<a class="reference internal" href="../reference/c-api/types-and-structures.html#c.PyArrayIterObject.dataptr" title="PyArrayIterObject.dataptr"><code class="xref c c-member docutils literal notranslate"><span class="pre">dataptr</span></code></a> member of the iterator object
structure and call the macro <a class="reference internal" href="../reference/c-api/array.html#c.PyArray_ITER_NEXT" title="PyArray_ITER_NEXT"><code class="xref c c-func docutils literal notranslate"><span class="pre">PyArray_ITER_NEXT</span></code></a> on the iterator
object to move to the next element. The <code class="docutils literal notranslate"><span class="pre">next</span></code> element is always in
C-contiguous order. The macro works by first special-casing the C-contiguous,
1-D, and 2-D cases which work very simply.</p>
<p>For the general case, the iteration works by keeping track of a list
of coordinate counters in the iterator object. At each iteration, the
last coordinate counter is increased (starting from 0). If this
counter is smaller than one less than the size of the array in that
dimension (a pre-computed and stored value), then the counter is
increased and the <a class="reference internal" href="../reference/c-api/types-and-structures.html#c.PyArrayIterObject.dataptr" title="PyArrayIterObject.dataptr"><code class="xref c c-member docutils literal notranslate"><span class="pre">dataptr</span></code></a> member is
increased by the strides in that
dimension and the macro ends. If the end of a dimension is reached,
the counter for the last dimension is reset to zero and the
<a class="reference internal" href="../reference/c-api/types-and-structures.html#c.PyArrayIterObject.dataptr" title="PyArrayIterObject.dataptr"><code class="xref c c-member docutils literal notranslate"><span class="pre">dataptr</span></code></a> is
moved back to the beginning of that dimension by subtracting the
strides value times one less than the number of elements in that
dimension (this is also pre-computed and stored in the
<a class="reference internal" href="../reference/c-api/types-and-structures.html#c.PyArrayIterObject.backstrides" title="PyArrayIterObject.backstrides"><code class="xref c c-member docutils literal notranslate"><span class="pre">backstrides</span></code></a>
member of the iterator object). In this case, the macro does not end,
but a local dimension counter is decremented so that the next-to-last
dimension replaces the role that the last dimension played and the
previously-described tests are executed again on the next-to-last
dimension. In this way, the <a class="reference internal" href="../reference/c-api/types-and-structures.html#c.PyArrayIterObject.dataptr" title="PyArrayIterObject.dataptr"><code class="xref c c-member docutils literal notranslate"><span class="pre">dataptr</span></code></a>
is adjusted appropriately for arbitrary striding.</p>
<p>The <a class="reference internal" href="../reference/c-api/types-and-structures.html#c.PyArrayIterObject.coordinates" title="PyArrayIterObject.coordinates"><code class="xref c c-member docutils literal notranslate"><span class="pre">coordinates</span></code></a> member of the
<a class="reference internal" href="../reference/c-api/types-and-structures.html#c.PyArrayIterObject" title="PyArrayIterObject"><code class="xref c c-type docutils literal notranslate"><span class="pre">PyArrayIterObject</span></code></a> structure maintains
the current N-d counter unless the underlying array is C-contiguous in
which case the coordinate counting is bypassed. The
<a class="reference internal" href="../reference/c-api/types-and-structures.html#c.PyArrayIterObject.index" title="PyArrayIterObject.index"><code class="xref c c-member docutils literal notranslate"><span class="pre">index</span></code></a> member of
the <a class="reference internal" href="../reference/c-api/types-and-structures.html#c.PyArrayIterObject" title="PyArrayIterObject"><code class="xref c c-type docutils literal notranslate"><span class="pre">PyArrayIterObject</span></code></a> keeps track of the current flat index of the
iterator. It is updated by the <a class="reference internal" href="../reference/c-api/array.html#c.PyArray_ITER_NEXT" title="PyArray_ITER_NEXT"><code class="xref c c-func docutils literal notranslate"><span class="pre">PyArray_ITER_NEXT</span></code></a> macro.</p>
</section>
<section id="broadcasting">
<h2>Broadcasting<a class="headerlink" href="#broadcasting" title="Link to this heading">#</a></h2>
<div class="admonition seealso">
<p class="admonition-title">See also</p>
<p><a class="reference internal" href="../user/basics.broadcasting.html#basics-broadcasting"><span class="std std-ref">Broadcasting</span></a></p>
</div>
<p id="index-3">In Numeric, the ancestor of NumPy, broadcasting was implemented in several
lines of code buried deep in <code class="docutils literal notranslate"><span class="pre">ufuncobject.c</span></code>. In NumPy, the notion of
broadcasting has been abstracted so that it can be performed in multiple places.
Broadcasting is handled by the function <a class="reference internal" href="../reference/c-api/array.html#c.PyArray_Broadcast" title="PyArray_Broadcast"><code class="xref c c-func docutils literal notranslate"><span class="pre">PyArray_Broadcast</span></code></a>. This
function requires a <a class="reference internal" href="../reference/c-api/types-and-structures.html#c.PyArrayMultiIterObject" title="PyArrayMultiIterObject"><code class="xref c c-type docutils literal notranslate"><span class="pre">PyArrayMultiIterObject</span></code></a> (or something that is a
binary equivalent) to be passed in. The <a class="reference internal" href="../reference/c-api/types-and-structures.html#c.PyArrayMultiIterObject" title="PyArrayMultiIterObject"><code class="xref c c-type docutils literal notranslate"><span class="pre">PyArrayMultiIterObject</span></code></a> keeps
track of the broadcast number of dimensions and size in each
dimension along with the total size of the broadcast result. It also
keeps track of the number of arrays being broadcast and a pointer to
an iterator for each of the arrays being broadcast.</p>
<p>The <a class="reference internal" href="../reference/c-api/array.html#c.PyArray_Broadcast" title="PyArray_Broadcast"><code class="xref c c-func docutils literal notranslate"><span class="pre">PyArray_Broadcast</span></code></a> function takes the iterators that have already
been defined and uses them to determine the broadcast shape in each
dimension (to create the iterators at the same time that broadcasting
occurs then use the <a class="reference internal" href="../reference/c-api/array.html#c.PyArray_MultiIterNew" title="PyArray_MultiIterNew"><code class="xref c c-func docutils literal notranslate"><span class="pre">PyArray_MultiIterNew</span></code></a> function).
Then, the iterators are
adjusted so that each iterator thinks it is iterating over an array
with the broadcast size. This is done by adjusting the iterators
number of dimensions, and the <a class="reference internal" href="../glossary.html#term-shape"><span class="xref std std-term">shape</span></a> in each dimension. This works
because the iterator strides are also adjusted. Broadcasting only
adjusts (or adds) length-1 dimensions. For these dimensions, the
strides variable is simply set to 0 so that the data-pointer for the
iterator over that array doesn’t move as the broadcasting operation
operates over the extended dimension.</p>
<p>Broadcasting was always implemented in Numeric using 0-valued strides
for the extended dimensions. It is done in exactly the same way in
NumPy. The big difference is that now the array of strides is kept
track of in a <a class="reference internal" href="../reference/c-api/types-and-structures.html#c.PyArrayIterObject" title="PyArrayIterObject"><code class="xref c c-type docutils literal notranslate"><span class="pre">PyArrayIterObject</span></code></a>, the iterators involved in a
broadcast result are kept track of in a <a class="reference internal" href="../reference/c-api/types-and-structures.html#c.PyArrayMultiIterObject" title="PyArrayMultiIterObject"><code class="xref c c-type docutils literal notranslate"><span class="pre">PyArrayMultiIterObject</span></code></a>,
and the <a class="reference internal" href="../reference/c-api/array.html#c.PyArray_Broadcast" title="PyArray_Broadcast"><code class="xref c c-func docutils literal notranslate"><span class="pre">PyArray_Broadcast</span></code></a> call implements the
<a class="reference internal" href="../user/basics.broadcasting.html#general-broadcasting-rules"><span class="std std-ref">General broadcasting rules</span></a>.</p>
</section>
<section id="array-scalars">
<h2>Array scalars<a class="headerlink" href="#array-scalars" title="Link to this heading">#</a></h2>
<div class="admonition seealso">
<p class="admonition-title">See also</p>
<p><a class="reference internal" href="../reference/arrays.scalars.html#arrays-scalars"><span class="std std-ref">Scalars</span></a></p>
</div>
<p id="index-4">The array scalars offer a hierarchy of Python types that allow a one-to-one
correspondence between the datatype stored in an array and the
Python-type that is returned when an element is extracted from the
array. An exception to this rule was made with object arrays. Object
arrays are heterogeneous collections of arbitrary Python objects. When
you select an item from an object array, you get back the original
Python object (and not an object array scalar which does exist but is
rarely used for practical purposes).</p>
<p>The array scalars also offer the same methods and attributes as arrays
with the intent that the same code can be used to support arbitrary
dimensions (including 0-dimensions). The array scalars are read-only
(immutable) with the exception of the void scalar which can also be
written to so that structured array field setting works more naturally
(<code class="docutils literal notranslate"><span class="pre">a[0]['f1']</span> <span class="pre">=</span> <span class="pre">value</span></code>).</p>
</section>
<section id="indexing">
<h2>Indexing<a class="headerlink" href="#indexing" title="Link to this heading">#</a></h2>
<div class="admonition seealso">
<p class="admonition-title">See also</p>
<p><a class="reference internal" href="../user/basics.indexing.html#basics-indexing"><span class="std std-ref">Indexing on ndarrays</span></a>, <a class="reference internal" href="../reference/routines.indexing.html#arrays-indexing"><span class="std std-ref">Indexing routines</span></a></p>
</div>
<p id="index-5">All Python indexing operations <code class="docutils literal notranslate"><span class="pre">arr[index]</span></code> are organized by first preparing
the index and finding the index type. The supported index types are:</p>
<ul class="simple">
<li><p>integer</p></li>
<li><p><a class="reference internal" href="../reference/constants.html#numpy.newaxis" title="numpy.newaxis"><code class="xref py py-const docutils literal notranslate"><span class="pre">newaxis</span></code></a></p></li>
<li><p><a class="reference external" href="https://docs.python.org/3/glossary.html#term-slice" title="(in Python v3.14)"><span>slice</span></a></p></li>
<li><p><a class="reference external" href="https://docs.python.org/3/library/constants.html#Ellipsis" title="(in Python v3.14)"><code class="xref py py-data docutils literal notranslate"><span class="pre">Ellipsis</span></code></a></p></li>
<li><p>integer arrays/array-likes (advanced)</p></li>
<li><p>boolean (single boolean array); if there is more than one boolean array as
the index or the shape does not match exactly, the boolean array will be
converted to an integer array instead.</p></li>
<li><p>0-d boolean (and also integer); 0-d boolean arrays are a special
case that has to be handled in the advanced indexing code. They signal
that a 0-d boolean array had to be interpreted as an integer array.</p></li>
</ul>
<p>As well as the scalar array special case signaling that an integer array
was interpreted as an integer index, which is important because an integer
array index forces a copy but is ignored if a scalar is returned (full integer
index). The prepared index is guaranteed to be valid with the exception of
out of bound values and broadcasting errors for advanced indexing. This
includes that an <a class="reference external" href="https://docs.python.org/3/library/constants.html#Ellipsis" title="(in Python v3.14)"><code class="xref py py-data docutils literal notranslate"><span class="pre">Ellipsis</span></code></a> is added for incomplete indices for
example when a two-dimensional array is indexed with a single integer.</p>
<p>The next step depends on the type of index which was found. If all
dimensions are indexed with an integer a scalar is returned or set. A
single boolean indexing array will call specialized boolean functions.
Indices containing an <a class="reference external" href="https://docs.python.org/3/library/constants.html#Ellipsis" title="(in Python v3.14)"><code class="xref py py-data docutils literal notranslate"><span class="pre">Ellipsis</span></code></a> or <a class="reference external" href="https://docs.python.org/3/glossary.html#term-slice" title="(in Python v3.14)"><span>slice</span></a> but no
advanced indexing will always create a view into the old array by calculating
the new strides and memory offset. This view can then either be returned or,
for assignments, filled using <code class="docutils literal notranslate"><span class="pre">PyArray_CopyObject</span></code>. Note that
<code class="docutils literal notranslate"><span class="pre">PyArray_CopyObject</span></code> may also be called on temporary arrays in other branches
to support complicated assignments when the array is of object <a class="reference internal" href="../reference/generated/numpy.dtype.html#numpy.dtype" title="numpy.dtype"><code class="xref py py-class docutils literal notranslate"><span class="pre">dtype</span></code></a>.</p>
<section id="advanced-indexing">
<h3>Advanced indexing<a class="headerlink" href="#advanced-indexing" title="Link to this heading">#</a></h3>
<p>By far the most complex case is advanced indexing, which may or may not be
combined with typical view-based indexing. Here integer indices are
interpreted as view-based. Before trying to understand this, you may want
to make yourself familiar with its subtleties. The advanced indexing code
has three different branches and one special case:</p>
<ul class="simple">
<li><p>There is one indexing array and it, as well as the assignment array, can
be iterated trivially. For example, they may be contiguous. Also, the
indexing array must be of <a class="reference internal" href="../reference/arrays.scalars.html#numpy.intp" title="numpy.intp"><code class="xref py py-class docutils literal notranslate"><span class="pre">intp</span></code></a> type and the value array in
assignments should be of the correct type. This is purely a fast path.</p></li>
<li><p>There are only integer array indices so that no subarray exists.</p></li>
<li><p>View-based and advanced indexing is mixed. In this case, the view-based
indexing defines a collection of subarrays that are combined by the
advanced indexing. For example, <code class="docutils literal notranslate"><span class="pre">arr[[1,</span> <span class="pre">2,</span> <span class="pre">3],</span> <span class="pre">:]</span></code> is created by
vertically stacking the subarrays <code class="docutils literal notranslate"><span class="pre">arr[1,</span> <span class="pre">:]</span></code>, <code class="docutils literal notranslate"><span class="pre">arr[2,</span> <span class="pre">:]</span></code>, and
<code class="docutils literal notranslate"><span class="pre">arr[3,</span> <span class="pre">:]</span></code>.</p></li>
<li><p>There is a subarray but it has exactly one element. This case can be handled
as if there is no subarray but needs some care during setup.</p></li>
</ul>
<p>Deciding what case applies, checking broadcasting, and determining the kind
of transposition needed are all done in <code class="docutils literal notranslate"><span class="pre">PyArray_MapIterNew</span></code>. After
setting up, there are two cases. If there is no subarray or it only has one
element, no subarray iteration is necessary and an iterator is prepared
which iterates all indexing arrays <em>as well as</em> the result or value array.
If there is a subarray, there are three iterators prepared. One for the
indexing arrays, one for the result or value array (minus its subarray),
and one for the subarrays of the original and the result/assignment array.
The first two iterators give (or allow calculation) of the pointers into
the start of the subarray, which then allows restarting the subarray
iteration.</p>
<p>When advanced indices are next to each other transposing may be necessary.
All necessary transposing is handled by <code class="docutils literal notranslate"><span class="pre">PyArray_MapIterSwapAxes</span></code> and
has to be handled by the caller unless <code class="docutils literal notranslate"><span class="pre">PyArray_MapIterNew</span></code> is asked to
allocate the result.</p>
<p>After preparation, getting and setting are relatively straightforward,
although the different modes of iteration need to be considered. Unless
there is only a single indexing array during item getting, the validity of
the indices is checked beforehand. Otherwise, it is handled in the inner
loop itself for optimization.</p>
</section>
</section>
<section id="universal-functions">
<span id="ufuncs-internals"></span><h2>Universal functions<a class="headerlink" href="#universal-functions" title="Link to this heading">#</a></h2>
<div class="admonition seealso">
<p class="admonition-title">See also</p>
<p><a class="reference internal" href="../reference/ufuncs.html#ufuncs"><span class="std std-ref">Universal functions (ufunc)</span></a>, <a class="reference internal" href="../user/basics.ufuncs.html#ufuncs-basics"><span class="std std-ref">Universal functions (ufunc) basics</span></a></p>
</div>
<p id="index-6">Universal functions are callable objects that take <span class="math notranslate nohighlight">\(N\)</span> inputs
and produce <span class="math notranslate nohighlight">\(M\)</span> outputs by wrapping basic 1-D loops that work
element-by-element into full easy-to-use functions that seamlessly
implement <a class="reference internal" href="../user/basics.broadcasting.html#basics-broadcasting"><span class="std std-ref">broadcasting</span></a>,
<a class="reference internal" href="../user/basics.ufuncs.html#ufuncs-casting"><span class="std std-ref">type-checking</span></a>,
<a class="reference internal" href="../user/basics.ufuncs.html#use-of-internal-buffers"><span class="std std-ref">buffered coercion</span></a>, and
<a class="reference internal" href="../user/basics.ufuncs.html#ufuncs-output-type"><span class="std std-ref">output-argument handling</span></a>. New universal functions
are normally created in C, although there is a mechanism for creating ufuncs
from Python functions (<a class="reference internal" href="../reference/generated/numpy.frompyfunc.html#numpy.frompyfunc" title="numpy.frompyfunc"><code class="xref py py-func docutils literal notranslate"><span class="pre">frompyfunc</span></code></a>). The user must supply a 1-D loop that
implements the basic function taking the input scalar values and
placing the resulting scalars into the appropriate output slots as
explained in implementation.</p>
<section id="setup">
<h3>Setup<a class="headerlink" href="#setup" title="Link to this heading">#</a></h3>
<p>Every <a class="reference internal" href="../reference/generated/numpy.ufunc.html#numpy.ufunc" title="numpy.ufunc"><code class="xref py py-class docutils literal notranslate"><span class="pre">ufunc</span></code></a> calculation involves some overhead related to setting up
the calculation. The practical significance of this overhead is that
even though the actual calculation of the ufunc is very fast, you will
be able to write array and type-specific code that will work faster
for small arrays than the ufunc. In particular, using ufuncs to
perform many calculations on 0-D arrays will be slower than other
Python-based solutions (the silently-imported <code class="docutils literal notranslate"><span class="pre">scalarmath</span></code> module exists
precisely to give array scalars the look-and-feel of ufunc based
calculations with significantly reduced overhead).</p>
<p>When a <a class="reference internal" href="../reference/generated/numpy.ufunc.html#numpy.ufunc" title="numpy.ufunc"><code class="xref py py-class docutils literal notranslate"><span class="pre">ufunc</span></code></a> is called, many things must be done. The information
collected from these setup operations is stored in a loop object. This
loop object is a C-structure (that could become a Python object but is
not initialized as such because it is only used internally). This loop
object has the layout needed to be used with <a class="reference internal" href="../reference/c-api/array.html#c.PyArray_Broadcast" title="PyArray_Broadcast"><code class="xref c c-func docutils literal notranslate"><span class="pre">PyArray_Broadcast</span></code></a>
so that the broadcasting can be handled in the same way as it is handled in
other sections of code.</p>
<p>The first thing done is to look up in the thread-specific global
dictionary the current values for the buffer-size, the error mask, and
the associated error object. The state of the error mask controls what
happens when an error condition is found. It should be noted that
checking of the hardware error flags is only performed after each 1-D
loop is executed. This means that if the input and output arrays are
contiguous and of the correct type so that a single 1-D loop is
performed, then the flags may not be checked until all elements of the
array have been calculated. Looking up these values in a thread-specific
dictionary takes time which is easily ignored for all but
very small arrays.</p>
<p>After checking, the thread-specific global variables, the inputs are
evaluated to determine how the ufunc should proceed and the input and
output arrays are constructed if necessary. Any inputs which are not
arrays are converted to arrays (using context if necessary). Which of
the inputs are scalars (and therefore converted to 0-D arrays) is
noted.</p>
<p>Next, an appropriate 1-D loop is selected from the 1-D loops available
to the <a class="reference internal" href="../reference/generated/numpy.ufunc.html#numpy.ufunc" title="numpy.ufunc"><code class="xref py py-class docutils literal notranslate"><span class="pre">ufunc</span></code></a> based on the input array types. This 1-D loop is selected
by trying to match the signature of the datatypes of the inputs
against the available signatures. The signatures corresponding to
built-in types are stored in the <a class="reference internal" href="../reference/generated/numpy.ufunc.types.html#numpy.ufunc.types" title="numpy.ufunc.types"><code class="xref py py-attr docutils literal notranslate"><span class="pre">ufunc.types</span></code></a> member of the ufunc
structure. The signatures corresponding to user-defined types are stored in a
linked list of function information with the head element stored as a
<code class="docutils literal notranslate"><span class="pre">CObject</span></code> in the <code class="docutils literal notranslate"><span class="pre">userloops</span></code> dictionary keyed by the datatype number
(the first user-defined type in the argument list is used as the key).
The signatures are searched until a signature is found to which the
input arrays can all be cast safely (ignoring any scalar arguments
which are not allowed to determine the type of the result). The
implication of this search procedure is that “lesser types” should be
placed below “larger types” when the signatures are stored. If no 1-D
loop is found, then an error is reported. Otherwise, the <code class="docutils literal notranslate"><span class="pre">argument_list</span></code>
is updated with the stored signature — in case casting is necessary
and to fix the output types assumed by the 1-D loop.</p>
<p>If the ufunc has 2 inputs and 1 output and the second input is an
<code class="docutils literal notranslate"><span class="pre">Object</span></code> array then a special-case check is performed so that
<code class="docutils literal notranslate"><span class="pre">NotImplemented</span></code> is returned if the second input is not an ndarray, has
the <a class="reference internal" href="../reference/arrays.classes.html#numpy.class.__array_priority__" title="numpy.class.__array_priority__"><code class="xref py py-obj docutils literal notranslate"><span class="pre">__array_priority__</span></code></a> attribute, and has an <code class="docutils literal notranslate"><span class="pre">__r{op}__</span></code>
special method. In this way, Python is signaled to give the other object a
chance to complete the operation instead of using generic object-array
calculations. This allows (for example) sparse matrices to override
the multiplication operator 1-D loop.</p>
<p>For input arrays that are smaller than the specified buffer size,
copies are made of all non-contiguous, misaligned, or out-of-byteorder
arrays to ensure that for small arrays, a single loop is
used. Then, array iterators are created for all the input arrays and
the resulting collection of iterators is broadcast to a single shape.</p>
<p>The output arguments (if any) are then processed and any missing
return arrays are constructed. If any provided output array doesn’t
have the correct type (or is misaligned) and is smaller than the
buffer size, then a new output array is constructed with the special
<a class="reference internal" href="../reference/c-api/array.html#c.NPY_ARRAY_WRITEBACKIFCOPY" title="NPY_ARRAY_WRITEBACKIFCOPY"><code class="xref c c-data docutils literal notranslate"><span class="pre">NPY_ARRAY_WRITEBACKIFCOPY</span></code></a> flag set. At the end of the function,
<a class="reference internal" href="../reference/c-api/array.html#c.PyArray_ResolveWritebackIfCopy" title="PyArray_ResolveWritebackIfCopy"><code class="xref c c-func docutils literal notranslate"><span class="pre">PyArray_ResolveWritebackIfCopy</span></code></a> is called so that
its contents will be copied back into the output array.
Iterators for the output arguments are then processed.</p>
<p>Finally, the decision is made about how to execute the looping
mechanism to ensure that all elements of the input arrays are combined
to produce the output arrays of the correct type. The options for loop
execution are one-loop (for <a class="reference internal" href="../glossary.html#term-contiguous"><span class="xref std std-term">contiguous</span></a>, aligned, and correct data
type), strided-loop (for non-contiguous but still aligned and correct
data type), and a buffered loop (for misaligned or incorrect data
type situations). Depending on which execution method is called for,
the loop is then set up and computed.</p>
</section>
<section id="function-call">
<h3>Function call<a class="headerlink" href="#function-call" title="Link to this heading">#</a></h3>
<p>This section describes how the basic universal function computation loop is
set up and executed for each of the three different kinds of execution. If
<a class="reference internal" href="../reference/c-api/array.html#c.NPY_ALLOW_THREADS" title="NPY_ALLOW_THREADS"><code class="xref c c-data docutils literal notranslate"><span class="pre">NPY_ALLOW_THREADS</span></code></a> is defined during compilation, then as long as
no object arrays are involved, the Python Global Interpreter Lock (GIL) is
released prior to calling the loops. It is re-acquired if necessary to
handle error conditions. The hardware error flags are checked only after
the 1-D loop is completed.</p>
<section id="one-loop">
<h4>One loop<a class="headerlink" href="#one-loop" title="Link to this heading">#</a></h4>
<p>This is the simplest case of all. The ufunc is executed by calling the
underlying 1-D loop exactly once. This is possible only when we have
aligned data of the correct type (including byteorder) for both input
and output and all arrays have uniform strides (either <a class="reference internal" href="../glossary.html#term-contiguous"><span class="xref std std-term">contiguous</span></a>,
0-D, or 1-D). In this case, the 1-D computational loop is called once
to compute the calculation for the entire array. Note that the
hardware error flags are only checked after the entire calculation is
complete.</p>
</section>
<section id="strided-loop">
<h4>Strided loop<a class="headerlink" href="#strided-loop" title="Link to this heading">#</a></h4>
<p>When the input and output arrays are aligned and of the correct type,
but the striding is not uniform (non-contiguous and 2-D or larger),
then a second looping structure is employed for the calculation. This
approach converts all of the iterators for the input and output
arguments to iterate over all but the largest dimension. The inner
loop is then handled by the underlying 1-D computational loop. The
outer loop is a standard iterator loop on the converted iterators. The
hardware error flags are checked after each 1-D loop is completed.</p>
</section>
<section id="buffered-loop">
<h4>Buffered loop<a class="headerlink" href="#buffered-loop" title="Link to this heading">#</a></h4>
<p>This is the code that handles the situation whenever the input and/or
output arrays are either misaligned or of the wrong datatype
(including being byteswapped) from what the underlying 1-D loop
expects. The arrays are also assumed to be non-contiguous. The code
works very much like the strided-loop except for the inner 1-D loop is
modified so that pre-processing is performed on the inputs and post-processing
is performed on the outputs in <code class="docutils literal notranslate"><span class="pre">bufsize</span></code> chunks (where
<code class="docutils literal notranslate"><span class="pre">bufsize</span></code> is a user-settable parameter). The underlying 1-D
computational loop is called on data that is copied over (if it needs
to be). The setup code and the loop code is considerably more
complicated in this case because it has to handle:</p>
<ul class="simple">
<li><p>memory allocation of the temporary buffers</p></li>
<li><p>deciding whether or not to use buffers on the input and output data
(misaligned and/or wrong datatype)</p></li>
<li><p>copying and possibly casting data for any inputs or outputs for which
buffers are necessary.</p></li>
<li><p>special-casing <code class="docutils literal notranslate"><span class="pre">Object</span></code> arrays so that reference counts are properly
handled when copies and/or casts are necessary.</p></li>
<li><p>breaking up the inner 1-D loop into <code class="docutils literal notranslate"><span class="pre">bufsize</span></code> chunks (with a possible
remainder).</p></li>
</ul>
<p>Again, the hardware error flags are checked at the end of each 1-D
loop.</p>
</section>
</section>
<section id="final-output-manipulation">
<h3>Final output manipulation<a class="headerlink" href="#final-output-manipulation" title="Link to this heading">#</a></h3>
<p>Ufuncs allow other array-like classes to be passed seamlessly through
the interface in that inputs of a particular class will induce the
outputs to be of that same class. The mechanism by which this works is
the following. If any of the inputs are not ndarrays and define the
<a class="reference internal" href="../reference/arrays.classes.html#numpy.class.__array_wrap__" title="numpy.class.__array_wrap__"><code class="xref py py-obj docutils literal notranslate"><span class="pre">__array_wrap__</span></code></a> method, then the class with the largest
<a class="reference internal" href="../reference/arrays.classes.html#numpy.class.__array_priority__" title="numpy.class.__array_priority__"><code class="xref py py-obj docutils literal notranslate"><span class="pre">__array_priority__</span></code></a> attribute determines the type of all the
outputs (with the exception of any output arrays passed in). The
<a class="reference internal" href="../reference/arrays.classes.html#numpy.class.__array_wrap__" title="numpy.class.__array_wrap__"><code class="xref py py-obj docutils literal notranslate"><span class="pre">__array_wrap__</span></code></a> method of the input array will be called
with the ndarray being returned from the ufunc as its input. There are two
calling styles of the <a class="reference internal" href="../reference/arrays.classes.html#numpy.class.__array_wrap__" title="numpy.class.__array_wrap__"><code class="xref py py-obj docutils literal notranslate"><span class="pre">__array_wrap__</span></code></a> function supported.
The first takes the ndarray as the first argument and a tuple of “context” as
the second argument. The context is (ufunc, arguments, output argument
number). This is the first call tried. If a <code class="docutils literal notranslate"><span class="pre">TypeError</span></code> occurs, then the
function is called with just the ndarray as the first argument.</p>
</section>
<section id="methods">
<h3>Methods<a class="headerlink" href="#methods" title="Link to this heading">#</a></h3>
<p>There are three methods of ufuncs that require calculation similar to
the general-purpose ufuncs. These are <a class="reference internal" href="../reference/generated/numpy.ufunc.reduce.html#numpy.ufunc.reduce" title="numpy.ufunc.reduce"><code class="xref py py-meth docutils literal notranslate"><span class="pre">ufunc.reduce</span></code></a>,
<a class="reference internal" href="../reference/generated/numpy.ufunc.accumulate.html#numpy.ufunc.accumulate" title="numpy.ufunc.accumulate"><code class="xref py py-meth docutils literal notranslate"><span class="pre">ufunc.accumulate</span></code></a>, and <a class="reference internal" href="../reference/generated/numpy.ufunc.reduceat.html#numpy.ufunc.reduceat" title="numpy.ufunc.reduceat"><code class="xref py py-meth docutils literal notranslate"><span class="pre">ufunc.reduceat</span></code></a>. Each of these
methods requires a setup command followed by a
loop. There are four loop styles possible for the methods
corresponding to no-elements, one-element, strided-loop, and buffered-loop.
These are the same basic loop styles as implemented for the
general-purpose function call except for the no-element and one-element
cases which are special-cases occurring when the input array
objects have 0 and 1 elements respectively.</p>
<section id="id1">
<h4>Setup<a class="headerlink" href="#id1" title="Link to this heading">#</a></h4>
<p>The setup function for all three methods is <code class="docutils literal notranslate"><span class="pre">construct_reduce</span></code>.
This function creates a reducing loop object and fills it with the
parameters needed to complete the loop. All of the methods only work
on ufuncs that take 2-inputs and return 1 output. Therefore, the
underlying 1-D loop is selected assuming a signature of <code class="docutils literal notranslate"><span class="pre">[otype,</span>
<span class="pre">otype,</span> <span class="pre">otype]</span></code> where <code class="docutils literal notranslate"><span class="pre">otype</span></code> is the requested reduction
datatype. The buffer size and error handling are then retrieved from
(per-thread) global storage. For small arrays that are misaligned or
have incorrect datatype, a copy is made so that the un-buffered
section of code is used. Then, the looping strategy is selected. If
there is 1 element or 0 elements in the array, then a simple looping
method is selected. If the array is not misaligned and has the
correct datatype, then strided looping is selected. Otherwise,