DOC: Moved NumPy Internals into Under-the-hood docs

1 files changed, 3 insertions, 612 deletions

diff --git a/doc/source/reference/internals.code-explanations.rst b/doc/source/reference/internals.code-explanations.rst
index e8e428f2e..d34314610 100644
--- a/doc/source/reference/internals.code-explanations.rst
+++ b/doc/source/reference/internals.code-explanations.rst
@@ -1,618 +1,9 @@
-.. currentmodule:: numpy
+:orphan:
 
 *************************
 NumPy C Code Explanations
 *************************
 
-    Fanaticism consists of redoubling your efforts when you have forgotten
-    your aim.
-    --- *George Santayana*
+.. This document has been moved to ../dev/internals.code-explanations.rst.
 
-    An authority is a person who can tell you more about something than
-    you really care to know.
-    --- *Unknown*
-
-This Chapter 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.
-
-
-Memory model
-============
-
-.. index::
-   pair: ndarray; memory model
-
-One fundamental aspect of the ndarray is that an array is seen as a
-"chunk" of memory starting at some location. The interpretation of
-this memory depends on the stride information. For each dimension in
-an :math:`N` -dimensional array, an integer (stride) dictates how many
-bytes must be skipped to get to the next element in that dimension.
-Unless you have a single-segment array, this stride information must
-be consulted when traversing through an array. It is not difficult to
-write code that accepts strides, you just have to use (char \*)
-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 rank-0 array), then the strides and dimensions variables are
-NULL.
-
-Besides the structural information contained in the strides and
-dimensions members of the :c:type:`PyArrayObject`, the flags contain
-important information about how the data may be accessed. In particular,
-the :c:data:`NPY_ARRAY_ALIGNED` flag is set when the memory is on a
-suitable boundary according to the data-type array. Even if you have
-a contiguous chunk of memory, you cannot just assume it is safe to
-dereference a data- type-specific pointer to an element. Only if the
-:c:data:`NPY_ARRAY_ALIGNED` flag is set is this a safe operation (on
-some platforms it will work but on others, like Solaris, it will cause
-a bus error). The :c:data:`NPY_ARRAY_WRITEABLE` 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 :c:data:`NPY_ARRAY_WRITEABLE` flag is not
-set will just be rude. Other times it can cause program crashes ( *e.g.*
-a data-area that is a read-only memory-mapped file).
-
-
-Data-type encapsulation
-=======================
-
-.. index::
-   single: dtype
-
-The data-type is an important abstraction of the ndarray. Operations
-will look to the data-type 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 'f' member of the
-:c:type:`PyArray_Descr` structure. In this way, the number of data-types can be
-extended simply by providing a :c:type:`PyArray_Descr` structure with suitable
-function pointers in the 'f' member. For built-in types there are some
-optimizations that by-pass this mechanism, but the point of the data-
-type abstraction is to allow new data-types to be added.
-
-One of the built-in data-types, the void data-type allows for
-arbitrary structured types containing 1 or more fields as elements of the
-array. A field is simply another data-type object along with an offset
-into the current structured type. In order to support arbitrarily nested
-fields, several recursive implementations of data-type 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 data-type object stored at the given offset. These offsets can be
-arbitrary numbers. Therefore, the possibility of encountering mis-
-aligned data must be recognized and taken into account if necessary.
-
-
-N-D Iterators
-=============
-
-.. index::
-   single: array iterator
-
-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
-dataptr member of the iterator object structure and call the macro
-:c:func:`PyArray_ITER_NEXT` (it) on the iterator object to move to the next
-element. The "next" 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.
-
-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 dataptr 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 dataptr 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 backstrides
-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 dataptr is adjusted appropriately for
-arbitrary striding.
-
-The coordinates member of the :c:type:`PyArrayIterObject` structure maintains
-the current N-d counter unless the underlying array is C-contiguous in
-which case the coordinate counting is by-passed. The index member of
-the :c:type:`PyArrayIterObject` keeps track of the current flat index of the
-iterator. It is updated by the :c:func:`PyArray_ITER_NEXT` macro.
-
-
-Broadcasting
-============
-
-.. index::
-   single: broadcasting
-
-In Numeric, the ancestor of Numpy, broadcasting was implemented in several
-lines of code buried deep in ufuncobject.c. In NumPy, the notion of broadcasting
-has been abstracted so that it can be performed in multiple places.
-Broadcasting is handled by the function :c:func:`PyArray_Broadcast`. This
-function requires a :c:type:`PyArrayMultiIterObject` (or something that is a
-binary equivalent) to be passed in. The :c:type:`PyArrayMultiIterObject` 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.
-
-The :c:func:`PyArray_Broadcast` 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 :c:func:`PyArray_MultiIterNew` 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 shape 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.
-
-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 :c:type:`PyArrayIterObject`, the iterators involved in a
-broadcast result are kept track of in a :c:type:`PyArrayMultiIterObject`,
-and the :c:func:`PyArray_Broadcast` call implements the broad-casting rules.
-
-
-Array Scalars
-=============
-
-.. index::
-   single: array scalars
-
-The array scalars offer a hierarchy of Python types that allow a one-
-to-one correspondence between the data-type 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).
-
-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
-(a[0]['f1'] = ``value`` ).
-
-
-Indexing
-========
-
-.. index::
-   single: indexing
-
-All python indexing operations ``arr[index]`` are organized by first preparing
-the index and finding the index type. The supported index types are:
-
-* integer
-* newaxis
-* slice
-* ellipsis
-* integer arrays/array-likes (fancy)
-* boolean (single boolean array); if there is more than one boolean array as
-  index or the shape does not match exactly, the boolean array will be
-  converted to an integer array instead.
-* 0-d boolean (and also integer); 0-d boolean arrays are a special
-  case which 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.
-
-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 ellipsis is added for incomplete indices for example when
-a two dimensional array is indexed with a single integer.
-
-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 ellipsis or slice 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 :c:func:`PyArray_CopyObject`. Note that `PyArray_CopyObject`
-may also be called on temporary arrays in other branches to support
-complicated assignments when the array is of object dtype.
-
-Advanced indexing
------------------
-
-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:
-
-* 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 `intp` type and the value array in assignments
-  should be of the correct type. This is purely a fast path.
-* There are only integer array indices so that no subarray exists.
-* 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, ``arr[[1, 2, 3], :]`` is created by
-  vertically stacking the subarrays ``arr[1, :]``, ``arr[2,:]``, and
-  ``arr[3, :]``.
-* 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.
-
-Deciding what case applies, checking broadcasting, and determining the kind
-of transposition needed are all done in `PyArray_MapIterNew`. 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 *as well as* 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 to restart the subarray
-iteration.
-
-When advanced indices are next to each other transposing may be necessary.
-All necessary transposing is handled by :c:func:`PyArray_MapIterSwapAxes` and
-has to be handled by the caller unless `PyArray_MapIterNew` is asked to
-allocate the result.
-
-After preparation, getting and setting is relatively straight forward,
-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.
-
-
-Universal Functions
-===================
-
-.. index::
-   single: ufunc
-
-Universal functions are callable objects that take :math:`N` inputs
-and produce :math:`M` outputs by wrapping basic 1-D loops that work
-element-by-element into full easy-to use functions that seamlessly
-implement broadcasting, type-checking and buffered coercion, and
-output-argument handling. New universal functions are normally created
-in C, although there is a mechanism for creating ufuncs from Python
-functions (:func:`frompyfunc`). 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.
-
-
-Setup
------
-
-Every ufunc 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 scalarmath module exists
-precisely to give array scalars the look-and-feel of ufunc based
-calculations with significantly reduced overhead).
-
-When a ufunc 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 PyArray_Broadcast so that
-the broadcasting can be handled in the same way as it is handled in
-other sections of code.
-
-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.
-
-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.
-
-Next, an appropriate 1-D loop is selected from the 1-D loops available
-to the ufunc based on the input array types. This 1-D loop is selected
-by trying to match the signature of the data-types of the inputs
-against the available signatures. The signatures corresponding to
-built-in types are stored in the types 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
-``CObject`` in the userloops dictionary keyed by the data-type 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 argument_list
-is updated with the stored signature --- in case casting is necessary
-and to fix the output types assumed by the 1-D loop.
-
-If the ufunc has 2 inputs and 1 output and the second input is an
-Object array then a special-case check is performed so that
-NotImplemented is returned if the second input is not an ndarray, has
-the __array_priority\__ attribute, and has an __r{op}\__ 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.
-
-For input arrays that are smaller than the specified buffer size,
-copies are made of all non-contiguous, mis-aligned, 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.
-
-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 mis-aligned) and is smaller than the
-buffer size, then a new output array is constructed with the special
-:c:data:`NPY_ARRAY_WRITEBACKIFCOPY` flag set. At the end of the function,
-:c:func:`PyArray_ResolveWritebackIfCopy` is called so that 
-its contents will be copied back into the output array.
-Iterators for the output arguments are then processed.
-
-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 contiguous, aligned, and correct data
-type), strided-loop (for non-contiguous but still aligned and correct
-data type), and a buffered loop (for mis-aligned or incorrect data
-type situations). Depending on which execution method is called for,
-the loop is then setup and computed.
-
-
-Function call
--------------
-
-This section describes how the basic universal function computation loop is
-setup and executed for each of the three different kinds of execution. If
-:c:data:`NPY_ALLOW_THREADS` 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.
-
-
-One Loop
-^^^^^^^^
-
-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 byte-order) for both input
-and output and all arrays have uniform strides (either contiguous,
-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.
-
-
-Strided Loop
-^^^^^^^^^^^^
-
-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.
-
-
-Buffered Loop
-^^^^^^^^^^^^^
-
-This is the code that handles the situation whenever the input and/or
-output arrays are either misaligned or of the wrong data-type
-(including being byte-swapped) 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 bufsize chunks (where
-bufsize 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:
-
-- memory allocation of the temporary buffers
-
-- deciding whether or not to use buffers on the input and output data
-  (mis-aligned and/or wrong data-type)
-
-- copying and possibly casting data for any inputs or outputs for which
-  buffers are necessary.
-
-- special-casing Object arrays so that reference counts are properly
-  handled when copies and/or casts are necessary.
-
-- breaking up the inner 1-D loop into bufsize chunks (with a possible
-  remainder).
-
-Again, the hardware error flags are checked at the end of each 1-D
-loop.
-
-
-Final output manipulation
--------------------------
-
-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
-:obj:`~numpy.class.__array_wrap__` method, then the class with the largest
-:obj:`~numpy.class.__array_priority__` attribute determines the type of all the
-outputs (with the exception of any output arrays passed in). The
-:obj:`~numpy.class.__array_wrap__` method of the input array will be called with the
-ndarray being returned from the ufunc as it's input. There are two
-calling styles of the :obj:`~numpy.class.__array_wrap__` 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 TypeError occurs, then the
-function is called with just the ndarray as the first argument.
-
-
-Methods
--------
-
-There are three methods of ufuncs that require calculation similar to
-the general-purpose ufuncs. These are reduce, accumulate, and
-reduceat. 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.
-
-
-Setup
-^^^^^
-
-The setup function for all three methods is ``construct_reduce``.
-This function creates a reducing loop object and fills it with
-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 [ ``otype``,
-``otype``, ``otype`` ] where ``otype`` is the requested reduction
-data-type. The buffer size and error handling is then retrieved from
-(per-thread) global storage. For small arrays that are mis-aligned or
-have incorrect data-type, 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 mis-aligned and has the
-correct data-type, then strided looping is selected. Otherwise,
-buffered looping must be performed. Looping parameters are then
-established, and the return array is constructed.  The output array is
-of a different shape depending on whether the method is reduce,
-accumulate, or reduceat. If an output array is already provided, then
-it's shape is checked. If the output array is not C-contiguous,
-aligned, and of the correct data type, then a temporary copy is made
-with the WRITEBACKIFCOPY flag set. In this way, the methods will be able
-to work with a well-behaved output array but the result will be copied
-back into the true output array when :c:func:`PyArray_ResolveWritebackIfCopy`
-is called at function completion.
-Finally, iterators are set up to loop over the correct axis
-(depending on the value of axis provided to the method) and the setup
-routine returns to the actual computation routine.
-
-
-Reduce
-^^^^^^
-
-.. index::
-   triple: ufunc; methods; reduce
-
-All of the ufunc methods use the same underlying 1-D computational
-loops with input and output arguments adjusted so that the appropriate
-reduction takes place. For example, the key to the functioning of
-reduce is that the 1-D loop is called with the output and the second
-input pointing to the same position in memory and both having a step-
-size of 0. The first input is pointing to the input array with a step-
-size given by the appropriate stride for the selected axis. In this
-way, the operation performed is
-
-.. math::
-   :nowrap:
-
-   \begin{align*}
-   o & = & i[0] \\
-   o & = & i[k]\textrm{<op>}o\quad k=1\ldots N
-   \end{align*}
-
-where :math:`N+1` is the number of elements in the input, :math:`i`,
-:math:`o` is the output, and :math:`i[k]` is the
-:math:`k^{\textrm{th}}` element of :math:`i` along the selected axis.
-This basic operations is repeated for arrays with greater than 1
-dimension so that the reduction takes place for every 1-D sub-array
-along the selected axis. An iterator with the selected dimension
-removed handles this looping.
-
-For buffered loops, care must be taken to copy and cast data before
-the loop function is called because the underlying loop expects
-aligned data of the correct data-type (including byte-order). The
-buffered loop must handle this copying and casting prior to calling
-the loop function on chunks no greater than the user-specified
-bufsize.
-
-
-Accumulate
-^^^^^^^^^^
-
-.. index::
-   triple: ufunc; methods; accumulate
-
-The accumulate function is very similar to the reduce function in that
-the output and the second input both point to the output. The
-difference is that the second input points to memory one stride behind
-the current output pointer. Thus, the operation performed is
-
-.. math::
-   :nowrap:
-
-   \begin{align*}
-   o[0] & = & i[0] \\
-   o[k] & = & i[k]\textrm{<op>}o[k-1]\quad k=1\ldots N.
-   \end{align*}
-
-The output has the same shape as the input and each 1-D loop operates
-over :math:`N` elements when the shape in the selected axis is :math:`N+1`.
-Again, buffered loops take care to copy and cast the data before
-calling the underlying 1-D computational loop.
-
-
-Reduceat
-^^^^^^^^
-
-.. index::
-   triple: ufunc; methods; reduceat
-   single: ufunc
-
-The reduceat function is a generalization of both the reduce and
-accumulate functions. It implements a reduce over ranges of the input
-array specified by indices. The extra indices argument is checked to
-be sure that every input is not too large for the input array along
-the selected dimension before the loop calculations take place. The
-loop implementation is handled using code that is very similar to the
-reduce code repeated as many times as there are elements in the
-indices input. In particular: the first input pointer passed to the
-underlying 1-D computational loop points to the input array at the
-correct location indicated by the index array. In addition, the output
-pointer and the second input pointer passed to the underlying 1-D loop
-point to the same position in memory. The size of the 1-D
-computational loop is fixed to be the difference between the current
-index and the next index (when the current index is the last index,
-then the next index is assumed to be the length of the array along the
-selected dimension). In this way, the 1-D loop will implement a reduce
-over the specified indices.
-
-Mis-aligned or a loop data-type that does not match the input and/or
-output data-type is handled using buffered code where-in data is
-copied to a temporary buffer and cast to the correct data-type if
-necessary prior to calling the underlying 1-D function. The temporary
-buffers are created in (element) sizes no bigger than the user
-settable buffer-size value. Thus, the loop must be flexible enough to
-call the underlying 1-D computational loop enough times to complete
-the total calculation in chunks no bigger than the buffer-size.
+This document has been moved to :ref:`c-code-explanations`.
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