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Title:Optimizing Iterator/UFunc Performance
Author: Mark Wiebe <mwwiebe@gmail.com>
Content-Type:text/x-rst
Created:25-Nov-2010

Table of Contents

Abstract

This NEP proposes to replace the NumPy iterator and multi-iterator with a single new iterator, designed to be more flexible and allow for more cache-friendly data access. The new iterator also subsumes much of the core ufunc functionality, making it easy to get the current ufunc benefits in contexts which don't precisely fit the ufunc mold. Key benefits include:

  • automatic reordering to find a cache-friendly access pattern
  • standard and customizable broadcasting
  • automatic type/byte-order/alignment conversions
  • optional buffering to minimize conversion memory usage
  • optional output arrays, with automatic allocation when unsupplied
  • automatic output or common type selection

A large fraction of this iterator design has already been implemented with promising results. Construction overhead is slightly greater (a.flat: 0.5 us, nditer(a): 1.4 us and broadcast(a,b): 1.4 us, nditer([a,b]): 2.2 us), but, as shown in an example, it is already possible to improve on the performance of the built-in NumPy mechanisms in pure Python code together with the iterator. One example rewrites np.add, getting a four times improvement with some Fortran-contiguous arrays, and another improves image compositing code from 1.4s to 180ms.

The implementation attempts to take into account the design decisions made in the NumPy 2.0 refactor, to make its future integration into libndarray relatively simple.

Motivation

NumPy defaults to returning C-contiguous arrays from UFuncs. This can result in extremely poor memory access patterns when dealing with data that is structured differently. A simple timing example illustrates this with a more than eight times performance hit from adding Fortran-contiguous arrays together. All timings are done using Numpy 2.0dev (Nov 22, 2010) on an Athlon 64 X2 4200+, with a 64-bit OS.:

In [1]: import numpy as np
In [2]: a = np.arange(1000000,dtype=np.float32).reshape(10,10,10,10,10,10)
In [3]: b, c, d = a.copy(), a.copy(), a.copy()

In [4]: timeit a+b+c+d
10 loops, best of 3: 28.5 ms per loop

In [5]: timeit a.T+b.T+c.T+d.T
1 loops, best of 3: 237 ms per loop

In [6]: timeit a.T.ravel('A')+b.T.ravel('A')+c.T.ravel('A')+d.T.ravel('A')
10 loops, best of 3: 29.6 ms per loop

In this case, it is simple to recover the performance by switching to a view of the memory, adding, then reshaping back. To further examine the problem and see how it isn’t always as trivial to work around, let’s consider simple code for working with image buffers in NumPy.

Image Compositing Example

For a more realistic example, consider an image buffer. Images are generally stored in a Fortran-contiguous order, and the colour channel can be treated as either a structured 'RGB' type or an extra dimension of length three. The resulting memory layout is neither C- nor Fortran-contiguous, but is easy to work with directly in NumPy, because of the flexibility of the ndarray. This appears ideal, because it makes the memory layout compatible with typical C or C++ image code, while simultaneously giving natural access in Python. Getting the color of pixel (x,y) is just ‘image[x,y]’.

The performance of this layout in NumPy turns out to be very poor. Here is code which creates two black images, and does an ‘over’ compositing operation on them.:

In [9]: image1 = np.zeros((1080,1920,3), dtype=np.float32).swapaxes(0,1)
In [10]: alpha1 = np.zeros((1080,1920,1), dtype=np.float32).swapaxes(0,1)
In [11]: image2 = np.zeros((1080,1920,3), dtype=np.float32).swapaxes(0,1)
In [12]: alpha2 = np.zeros((1080,1920,1), dtype=np.float32).swapaxes(0,1)
In [13]: def composite_over(im1, al1, im2, al2):
   ....:     return (im1 + (1-al1)*im2, al1 + (1-al1)*al2)

In [14]: timeit composite_over(image1,alpha1,image2,alpha2)
1 loops, best of 3: 3.51 s per loop

If we give up the convenient layout, and use the C-contiguous default, the performance is about seven times better.:

In [16]: image1 = np.zeros((1080,1920,3), dtype=np.float32)
In [17]: alpha1 = np.zeros((1080,1920,1), dtype=np.float32)
In [18]: image2 = np.zeros((1080,1920,3), dtype=np.float32)
In [19]: alpha2 = np.zeros((1080,1920,1), dtype=np.float32)

In [20]: timeit composite_over(image1,alpha1,image2,alpha2)
1 loops, best of 3: 581 ms per loop

But this is not all, since it turns out that broadcasting the alpha channel is exacting a performance price as well. If we use an alpha channel with 3 values instead of one, we get:

In [21]: image1 = np.zeros((1080,1920,3), dtype=np.float32)
In [22]: alpha1 = np.zeros((1080,1920,3), dtype=np.float32)
In [23]: image2 = np.zeros((1080,1920,3), dtype=np.float32)
In [24]: alpha2 = np.zeros((1080,1920,3), dtype=np.float32)

In [25]: timeit composite_over(image1,alpha1,image2,alpha2)
1 loops, best of 3: 313 ms per loop

For a final comparison, let’s see how it performs when we use one-dimensional arrays to ensure just a single loop does the calculation.:

In [26]: image1 = np.zeros((1080*1920*3), dtype=np.float32)
In [27]: alpha1 = np.zeros((1080*1920*3), dtype=np.float32)
In [28]: image2 = np.zeros((1080*1920*3), dtype=np.float32)
In [29]: alpha2 = np.zeros((1080*1920*3), dtype=np.float32)

In [30]: timeit composite_over(image1,alpha1,image2,alpha2)
1 loops, best of 3: 312 ms per loop

To get a reference performance number, I implemented this simple operation straightforwardly in C (careful to use the same compile options as NumPy). If I emulated the memory allocation and layout of the Python code, the performance was roughly 0.3 seconds, very much in line with NumPy’s performance. Combining the operations into one pass reduced the time to roughly 0.15 seconds.

A slight variation of this example is to use a single memory block with four channels (1920,1080,4) instead of separate image and alpha. This is more typical in image processing applications, and here’s how that looks with a C-contiguous layout.:

In [31]: image1 = np.zeros((1080,1920,4), dtype=np.float32)
In [32]: image2 = np.zeros((1080,1920,4), dtype=np.float32)
In [33]: def composite_over(im1, im2):
   ....:     ret = (1-im1[:,:,-1])[:,:,np.newaxis]*im2
   ....:     ret += im1
   ....:     return ret

In [34]: timeit composite_over(image1,image2)
1 loops, best of 3: 481 ms per loop

To see the improvements that implementation of the new iterator as proposed can produce, go to the example continued after the proposed API, near the bottom of the document.

Improving Cache-Coherency

In order to get the best performance from UFunc calls, the pattern of memory reads should be as regular as possible. Modern CPUs attempt to predict the memory read/write pattern and fill the cache ahead of time. The most predictable pattern is for all the inputs and outputs to be sequentially processed in the same order.

I propose that by default, the memory layout of the UFunc outputs be as close to that of the inputs as possible. Whenever there is an ambiguity or a mismatch, it defaults to a C-contiguous layout.

To understand how to accomplish this, we first consider the strides of all the inputs after the shapes have been normalized for broadcasting. By determining whether a set of strides are compatible and/or ambiguous, we can determine an output memory layout which maximizes coherency.

In broadcasting, the input shapes are first transformed to broadcast shapes by prepending singular dimensions, then the broadcast strides are created, where any singular dimension’s stride is set to zero.

Strides may be negative as well, and in certain cases this can be normalized to fit the following discussion. If all the strides for a particular axis are negative or zero, the strides for that dimension can be negated after adjusting the base data pointers appropriately.

Here's an example of how three inputs with C-contiguous layouts result in broadcast strides. To simplify things, the examples use an itemsize of 1.

Input shapes: (5,3,7) (5,3,1) (1,7)
Broadcast shapes: (5,3,7) (5,3,1) (1,1,7)
Broadcast strides: (21,7,1) (3,1,0) (0,0,1)

Compatible Strides - A set of strides are compatible if there exists a permutation of the axes such that the strides are decreasing for every stride in the set, excluding entries that are zero.

The example above satisfies the definition with the identity permutation. In the motivation image example, the strides are slightly different if we separate the colour and alpha information or not. The permutation which demonstrates compatibility here is the transposition (0,1).

Input/Broadcast shapes: Image (1920, 1080, 3) Alpha (1920, 1080, 1)
Broadcast strides (separate): (3,5760,1) (1,1920,0)
Broadcast strides (together): (4,7680,1) (4,7680,0)

Ambiguous Strides - A set of compatible strides are ambiguous if more than one permutation of the axes exists such that the strides are decreasing for every stride in the set, excluding entries that are zero.

This typically occurs when every axis has a 0-stride somewhere in the set of strides. The simplest example is in two dimensions, as follows.

Broadcast shapes: (1,3) (5,1)
Broadcast strides: (0,1) (1,0)

There may, however, be unambiguous compatible strides without a single input forcing the entire layout, as in this example:

Broadcast shapes: (1,3,4) (5,3,1)
Broadcast strides: (0,4,1) (3,1,0)

In the face of ambiguity, we have a choice to either completely throw away the fact that the strides are compatible, or try to resolve the ambiguity by adding an additional constraint. I think the appropriate choice is to resolve it by picking the memory layout closest to C-contiguous, but still compatible with the input strides.

Output Layout Selection Algorithm

The output ndarray memory layout we would like to produce is as follows:

Consistent/Unambiguous strides: The single consistent layout
Consistent/Ambiguous strides: The consistent layout closest to C-contiguous
Inconsistent strides: C-contiguous

Here is pseudo-code for an algorithm to compute the permutation for the output layout.:

perm = range(ndim) # Identity, i.e. C-contiguous
# Insertion sort, ignoring 0-strides
# Note that the sort must be stable, and 0-strides may
# be reordered if necessary, but should be moved as little
# as possible.
for i0 = 1 to ndim-1:
    # ipos is where perm[i0] will get inserted
    ipos = i0
    j0 = perm[i0]
    for i1 = i0-1 to 0:
        j1 = perm[i1]
        ambig, shouldswap = True, False
        # Check whether any strides are ordered wrong
        for strides in broadcast_strides:
            if strides[j0] != 0 and strides[j1] != 0:
                if strides[j0] > strides[j1]:
                    # Only set swap if it's still ambiguous.
                    if ambig:
                        shouldswap = True
                else:
                    # Set swap even if it's not ambiguous,
                    # because not swapping is the choice
                    # for conflicts as well.
                    shouldswap = False
                ambig = False
        # If there was an unambiguous comparison, either shift ipos
        # to i1 or stop looking for the comparison
        if not ambig:
            if shouldswap:
                ipos = i1
            else:
                break
    # Insert perm[i0] into the right place
    if ipos != i0:
       for i1 = i0-1 to ipos:
         perm[i1+1] = perm[i1]
       perm[ipos] = j0
# perm is now the closest consistent ordering to C-contiguous
return perm

Coalescing Dimensions

In many cases, the memory layout allows for the use of a one-dimensional loop instead of tracking multiple coordinates within the iterator. The existing code already exploits this when the data is C-contiguous, but since we're reordering the axes, we can apply this optimization more generally.

Once the iteration strides have been sorted to be monotonically decreasing, any dimensions which could be coalesced are side by side. If for all the operands, incrementing by strides[i+1] shape[i+1] times is the same as incrementing by strides[i], or strides[i+1]*shape[i+1] == strides[i], dimensions i and i+1 can be coalesced into a single dimension.

Here is pseudo-code for coalescing.:

# Figure out which pairs of dimensions can be coalesced
can_coalesce = [False]*ndim
for strides, shape in zip(broadcast_strides, broadcast_shape):
    for i = 0 to ndim-2:
        if strides[i+1]*shape[i+1] == strides[i]:
            can_coalesce[i] = True
# Coalesce the types
new_ndim = ndim - count_nonzero(can_coalesce)
for strides, shape in zip(broadcast_strides, broadcast_shape):
    j = 0
    for i = 0 to ndim-1:
        # Note that can_coalesce[ndim-1] is always False, so
        # there is no out-of-bounds access here.
        if can_coalesce[i]:
            shape[i+1] = shape[i]*shape[i+1]
        else:
            strides[j] = strides[i]
            shape[j] = shape[i]
            j += 1

Inner Loop Specialization

Specialization is handled purely by the inner loop function, so this optimization is independent of the others. Some specialization is already done, like for the reduce operation. The idea is mentioned in http://projects.scipy.org/numpy/wiki/ProjectIdeas, “use intrinsics (SSE-instructions) to speed up low-level loops in NumPy.”

Here are some possibilities for two-argument functions, covering the important cases of add/subtract/multiply/divide.

  • The first or second argument is a single value (i.e. a 0 stride value) and does not alias the output. arr = arr + 1; arr = 1 + arr
    • Can load the constant once instead of reloading it from memory every time
  • The strides match the size of the data type. C- or Fortran-contiguous data, for example
    • Can do a simple loop without using strides
  • The strides match the size of the data type, and they are both 16-byte aligned (or differ from 16-byte aligned by the same offset)
    • Can use SSE to process multiple values at once
  • The first input and the output are the same single value (i.e. a reduction operation).
    • This is already specialized for many UFuncs in the existing code

The above cases are not generally mutually exclusive, for example a constant argument may be combined with SSE when the strides match the data type size, and reductions can be optimized with SSE as well.

Implementation Details

Except for inner loop specialization, the discussed optimizations significantly affect ufunc_object.c and the PyArrayIterObject/PyArrayMultiIterObject used to do the broadcasting. In general, it should be possible to emulate the current behavior where it is desired, but I believe the default should be to produce and manipulate memory layouts which will give the best performance.

To support the new cache-friendly behavior, we introduce a new option ‘K’ (for “keep”) for any order= parameter.

The proposed ‘order=’ flags become as follows:

‘C’ C-contiguous layout
‘F’ Fortran-contiguous layout
‘A’ ‘F’ if the input(s) have a Fortran-contiguous layout, ‘C’ otherwise (“Any Contiguous”)
‘K’ a layout equivalent to ‘C’ followed by some permutation of the axes, as close to the layout of the input(s) as possible (“Keep Layout”)

Or as an enum:

/* For specifying array memory layout or iteration order */
typedef enum {
        /* Fortran order if inputs are all Fortran, C otherwise */
        NPY_ANYORDER=-1,
        /* C order */
        NPY_CORDER=0,
        /* Fortran order */
        NPY_FORTRANORDER=1,
        /* An order as close to the inputs as possible */
        NPY_KEEPORDER=2
} NPY_ORDER;

Perhaps a good strategy is to first implement the capabilities discussed here without changing the defaults. Once they are implemented and well-tested, the defaults can change from order='C' to order='K' everywhere appropriate. UFuncs additionally should gain an order= parameter to control the layout of their output(s).

The iterator can do automatic casting, and I have created a sequence of progressively more permissive casting rules. Perhaps for 2.0, NumPy could adopt this enum as its prefered way of dealing with casting.:

/* For specifying allowed casting in operations which support it */
typedef enum {
        /* Only allow identical types */
        NPY_NO_CASTING=0,
        /* Allow identical and byte swapped types */
        NPY_EQUIV_CASTING=1,
        /* Only allow safe casts */
        NPY_SAFE_CASTING=2,
        /* Allow safe casts and casts within the same kind */
        NPY_SAME_KIND_CASTING=3,
        /* Allow any casts */
        NPY_UNSAFE_CASTING=4
} NPY_CASTING;

Iterator Rewrite

Based on an analysis of the code, it appears that refactoring the existing iteration objects to implement these optimizations is prohibitively difficult. Additionally, some usage of the iterator requires modifying internal values or flags, so code using the iterator would have to change anyway. Thus we propose creating a new iterator object which subsumes the existing iterator functionality and expands it to account for the optimizations.

High level goals for the replacement iterator include:

  • Small memory usage and a low number of memory allocations.
  • Simple cases (like flat arrays) should have very little overhead.
  • Combine single and multiple iteration into one object.

Capabilities that should be provided to user code:

  • Iterate in C, Fortran, or “Fastest” (default) order.
  • Track a C-style or Fortran-style flat index if requested (existing iterator always tracks a C-style index). This can be done independently of the iteration order.
  • Track the coordinates if requested (the existing iterator requires manually changing an internal iterator flag to guarantee this).
  • Skip iteration of the last internal dimension so that it can be processed with an inner loop.
  • Jump to a specific coordinate in the array.
  • Iterate an arbitrary subset of axes (to support, for example, reduce with multiple axes at once).
  • Ability to automatically allocate output parameters if a NULL input is provided, These outputs should have a memory layout matching the iteration order, and are the mechanism for the order='K' support.
  • Automatic copying and/or buffering of inputs which do not satisfy type/byte-order/alignment requirements. The caller's iteration inner loop should be the same no matter what buffering or copying is done.

Notes for implementation:

  • User code must never touch the inside of the iterator. This allows for drastic changes of the internal memory layout in the future, if higher-performance implementation strategies are found.
  • Use a function pointer instead of a macro for iteration. This way, specializations can be created for the common cases, like when ndim is small, for different flag settings, and when the number of arrays iterated is small. Also, an iteration pattern can be prescribed that makes a copy of the function pointer first to allow the compiler to keep the function pointer in a register.
  • Dynamically create the memory layout, to minimize the number of cache lines taken up by the iterator (for LP64, sizeof(PyArrayIterObject) is about 2.5KB, and a binary operation like plus needs three of these for the Multi-Iterator).
  • Isolate the C-API object from Python reference counting, so that it can be used naturally from C. The Python object then becomes a wrapper around the C iterator. This is analogous to the PEP 3118 design separation of Py_buffer and memoryview.

Proposed Iterator Memory Layout

The following struct describes the iterator memory. All items are packed together, which means that different values of the flags, ndim, and niter will produce slightly different layouts.

struct {
    /* Flags indicate what optimizations have been applied, and
     * affect the layout of this struct. */
    uint32 itflags;
    /* Number of iteration dimensions.  If FLAGS_HASCOORDS is set,
     * it matches the creation ndim, otherwise it may be smaller.  */
    uint16 ndim;
    /* Number of objects being iterated.  This is fixed at creation time. */
    uint16 niter;

    /* The number of times the iterator will iterate */
    intp itersize;

    /* The permutation is only used when FLAGS_HASCOORDS is set,
     * and is placed here so its position depends on neither ndim
     * nor niter. */
    intp perm[ndim];

    /* The data types of all the operands */
    PyArray_Descr *dtypes[niter];
    /* Backups of the starting axisdata 'ptr' values, to support Reset */
    char *resetdataptr[niter];
    /* Backup of the starting index value, to support Reset */
    npy_intp resetindex;

    /* When the iterator is destroyed, Py_XDECREF is called on all
       these objects */
    PyObject *objects[niter];

    /* Flags indicating read/write status and buffering
     * for each operand. */
    uint8 opitflags[niter];
    /* Padding to make things intp-aligned again */
    uint8 padding[];

    /* If some or all of the inputs are being buffered */
    #if (flags&FLAGS_BUFFERED)
    struct buffer_data {
        /* The size of the buffer, and which buffer we're on.
         * the i-th iteration has i = buffersize*bufferindex+pos
         */
        intp buffersize;
        /* For tracking position inside the buffer */
        intp size, pos;
        /* The strides for the pointers */
        intp stride[niter];
        /* Pointers to the data for the current iterator position.
         * The buffer_data.value ptr[i] equals either
         * axis_data[0].ptr[i] or buffer_data.buffers[i] depending
         * on whether copying to the buffer was necessary.
         */
        char* ptr[niter];
        /* Functions to do the copyswap and casting necessary */
        transferfn_t readtransferfn[niter];
        void *readtransferdata[niter];
        transferfn_t writetransferfn[niter];
        void *writetransferdata[niter];
        /* Pointers to the allocated buffers for operands
         * which the iterator determined needed buffering
         */
        char *buffers[niter];
    };
    #endif /* FLAGS_BUFFERED */

    /* Data per axis, starting with the most-frequently
     * updated, and in decreasing order after that. */
    struct axis_data {
        /* The shape of this axis */
        intp shape;
        /* The current coordinate along this axis */
        intp coord;
        /* The operand and index strides for this axis
        intp stride[niter];
        {intp indexstride;} #if (flags&FLAGS_HASINDEX);
        /* The operand pointers and index values for this axis */
        char* ptr[niter];
        {intp index;} #if (flags&FLAGS_HASINDEX);
    }[ndim];
};

The array of axis_data structs is ordered to be in increasing rapidity of increment updates. If the perm is the identity, this means it’s reversed from the C-order. This is done so data items touched most often are closest to the beginning of the struct, where the common properties are, resulting in increased cache coherency. It also simplifies the iternext call, while making getcoord and related functions slightly more complicated.

Proposed Iterator API

The existing iterator API includes functions like PyArrayIter_Check, PyArray_Iter* and PyArray_ITER_*. The multi-iterator array includes PyArray_MultiIter*, PyArray_Broadcast, and PyArray_RemoveSmallest. The new iterator design replaces all of this functionality with a single object and associated API. One goal of the new API is that all uses of the existing iterator should be replaceable with the new iterator without significant effort.

The C-API naming convention chosen is based on the one in the numpy-refactor branch, where libndarray has the array named NpyArray and functions named NpyArray_*. The iterator is named NpyIter and functions are named NpyIter_*.

The Python exposure has the iterator named np.nditer. One possible release strategy for this iterator would be to release a 1.X (1.6?) version with the iterator added, but not used by the NumPy code. Then, 2.0 can be release with it fully integrated. If this strategy is chosen, the naming convention and API should be finalized as much as possible before the 1.X release. The name np.iter can't be used because it conflicts with the Python built-in iter. I would suggest the name np.nditer within Python, as it is currently unused.

In addition to the performance goals set out for the new iterator, it appears the API can be refactored to better support some common NumPy programming idioms.

By moving some functionality currently in the UFunc code into the iterator, it should make it easier for extension code which wants to emulate UFunc behavior in cases which don't quite fit the UFunc paradigm. In particular, emulating the UFunc buffering behavior is not a trivial enterprise.

Old -> New Iterator API Conversion

For the regular iterator:

PyArray_IterNew NpyIter_New
PyArray_IterAllButAxis NpyIter_New + axes parameter or Iterator flag NPY_ITER_NO_INNER_ITERATION
PyArray_BroadcastToShape NOT SUPPORTED (but could be, if needed)
PyArrayIter_Check Will need to add this in Python exposure
PyArray_ITER_RESET NpyIter_Reset
PyArray_ITER_NEXT Function pointer from NpyIter_GetIterNext
PyArray_ITER_DATA NpyIter_GetDataPtrArray
PyArray_ITER_GOTO NpyIter_GotoCoords
PyArray_ITER_GOTO1D NpyIter_GotoIndex
PyArray_ITER_NOTDONE Return value of iternext function pointer

For the multi-iterator:

PyArray_MultiIterNew NpyIter_MultiNew
PyArray_MultiIter_RESET NpyIter_Reset
PyArray_MultiIter_NEXT Function pointer from NpyIter_GetIterNext
PyArray_MultiIter_DATA NpyIter_GetDataPtrArray
PyArray_MultiIter_NEXTi NOT SUPPORTED (always lock-step iteration)
PyArray_MultiIter_GOTO NpyIter_GotoCoords
PyArray_MultiIter_GOTO1D NpyIter_GotoIndex
PyArray_MultiIter_NOTDONE Return value of iternext function pointer
PyArray_Broadcast Handled by NpyIter_MultiNew
PyArray_RemoveSmallest Iterator flag NPY_ITER_NO_INNER_ITERATION

For other API calls:

PyArray_ConvertToCommonType Iterator flag NPY_ITER_COMMON_DTYPE

Iterator Pointer Type

The iterator structure is internally generated, but a type is still needed to provide warnings and/or errors when the wrong type is passed to the API. We do this with a typedef of an incomplete struct

typedef struct NpyIter_InternalOnly NpyIter;

Construction and Destruction

NpyIter* NpyIter_New(PyArrayObject* op, npy_uint32 flags, NPY_ORDER order, NPY_CASTING casting, PyArray_Descr* dtype, npy_intp a_ndim, npy_intp *axes, npy_intp buffersize)

Creates an iterator for the given numpy array object op.

Flags that may be passed in flags are any combination of the global and per-operand flags documented in NpyIter_MultiNew, except for NPY_ITER_ALLOCATE.

Any of the NPY_ORDER enum values may be passed to order. For efficient iteration, NPY_KEEPORDER is the best option, and the other orders enforce the particular iteration pattern.

Any of the NPY_CASTING enum values may be passed to casting. The values include NPY_NO_CASTING, NPY_EQUIV_CASTING, NPY_SAFE_CASTING, NPY_SAME_KIND_CASTING, and NPY_UNSAFE_CASTING. To allow the casts to occur, copying or buffering must also be enabled.

If dtype isn't NULL, then it requires that data type. If copying is allowed, it will make a temporary copy if the data is castable. If UPDATEIFCOPY is enabled, it will also copy the data back with another cast upon iterator destruction.

If a_ndim is greater than zero, axes must also be provided. In this case, axes is an a_ndim-sized array of op's axes. A value of -1 in axes means newaxis. Within the axes array, axes may not be repeated.

If buffersize is zero, a default buffer size is used, otherwise it specifies how big of a buffer to use. Buffers which are powers of 2 such as 512 or 1024 are recommended.

Returns NULL if there is an error, otherwise returns the allocated iterator.

To make an iterator similar to the old iterator, this should work.:

iter = NpyIter_New(op, NPY_ITER_READWRITE,
                    NPY_CORDER, NPY_NO_CASTING, NULL, 0, NULL);

If you want to edit an array with aligned double code, but the order doesn't matter, you would use this.:

dtype = PyArray_DescrFromType(NPY_DOUBLE);
iter = NpyIter_New(op, NPY_ITER_READWRITE |
                    NPY_ITER_BUFFERED |
                    NPY_ITER_NBO,
                    NPY_ITER_ALIGNED,
                    NPY_KEEPORDER,
                    NPY_SAME_KIND_CASTING,
                    dtype, 0, NULL);
Py_DECREF(dtype);

NpyIter* NpyIter_MultiNew(npy_intp niter, PyArrayObject** op, npy_uint32 flags, NPY_ORDER order, NPY_CASTING casting, npy_uint32 *op_flags, PyArray_Descr** op_dtypes, npy_intp oa_ndim, npy_intp **op_axes, npy_intp buffersize)

Creates an iterator for broadcasting the niter array objects provided in op.

For normal usage, use 0 for oa_ndim and NULL for op_axes. See below for a description of these parameters, which allow for custom manual broadcasting as well as reordering and leaving out axes.

Any of the NPY_ORDER enum values may be passed to order. For efficient iteration, NPY_KEEPORDER is the best option, and the other orders enforce the particular iteration pattern. When using NPY_KEEPORDER, if you also want to ensure that the iteration is not reversed along an axis, you should pass the flag NPY_ITER_DONT_NEGATE_STRIDES.

Any of the NPY_CASTING enum values may be passed to casting. The values include NPY_NO_CASTING, NPY_EQUIV_CASTING, NPY_SAFE_CASTING, NPY_SAME_KIND_CASTING, and NPY_UNSAFE_CASTING. To allow the casts to occur, copying or buffering must also be enabled.

If op_dtypes isn't NULL, it specifies a data type or NULL for each op[i].

The parameter oa_ndim, when non-zero, specifies the number of dimensions that will be iterated with customized broadcasting. If it is provided, op_axes must also be provided. These two parameters let you control in detail how the axes of the operand arrays get matched together and iterated. In op_axes, you must provide an array of niter pointers to oa_ndim-sized arrays of type npy_intp. If an entry in op_axes is NULL, normal broadcasting rules will apply. In op_axes[j][i] is stored either a valid axis of op[j], or -1 which means newaxis. Within each op_axes[j] array, axes may not be repeated. The following example is how normal broadcasting applies to a 3-D array, a 2-D array, a 1-D array and a scalar.:

npy_intp oa_ndim = 3;               /* # iteration axes */
npy_intp op0_axes[] = {0, 1, 2};    /* 3-D operand */
npy_intp op1_axes[] = {-1, 0, 1};   /* 2-D operand */
npy_intp op2_axes[] = {-1, -1, 0};  /* 1-D operand */
npy_intp op3_axes[] = {-1, -1, -1}  /* 0-D (scalar) operand */
npy_intp *op_axes[] = {op0_axes, op1_axes, op2_axes, op3_axes};

If buffersize is zero, a default buffer size is used, otherwise it specifies how big of a buffer to use. Buffers which are powers of 2 such as 512 or 1024 are recommended.

Returns NULL if there is an error, otherwise returns the allocated iterator.

Flags that may be passed in flags, applying to the whole iterator, are:

NPY_ITER_C_INDEX, NPY_ITER_F_INDEX

Causes the iterator to track an index matching C or Fortran order. These options are mutually exclusive.

NPY_ITER_COORDS

Causes the iterator to track array coordinates. This prevents the iterator from coalescing axes to produce bigger inner loops.

NPY_ITER_NO_INNER_ITERATION

Causes the iterator to skip iteration of the innermost loop, allowing the user of the iterator to handle it.

This flag is incompatible with NPY_ITER_C_INDEX, NPY_ITER_F_INDEX, and NPY_ITER_COORDS.

NPY_ITER_DONT_NEGATE_STRIDES

This only affects the iterator when NPY_KEEPORDER is specified for the order parameter. By default with NPY_KEEPORDER, the iterator reverses axes which have negative strides, so that memory is traversed in a forward direction. This disables this step. Use this flag if you want to use the underlying memory-ordering of the axes, but don't want an axis reversed. This is the behavior of numpy.ravel(a, order='K'), for instance.

NPY_ITER_COMMON_DTYPE

Causes the iterator to convert all the operands to a common data type, calculated based on the ufunc type promotion rules. The flags for each operand must be set so that the appropriate casting is permitted, and copying or buffering must be enabled.

If the common data type is known ahead of time, don't use this flag. Instead, set the requested dtype for all the operands.

NPY_ITER_REFS_OK

Indicates that arrays with reference types (object arrays or structured arrays containing an object type) may be accepted and used in the iterator. If this flag is enabled, the caller must be sure to check whether NpyIter_IterationNeedsAPI(iter) is true, in which case it may not release the GIL during iteration.

NPY_ITER_ZEROSIZE_OK

Indicates that arrays with a size of zero should be permitted. Since the typical iteration loop does not naturally work with zero-sized arrays, you must check that the IterSize is non-zero before entering the iteration loop.

NPY_ITER_REDUCE_OK

Permits writeable operands with a dimension with zero stride and size greater than one. Note that such operands must be read/write.

When buffering is enabled, this also switches to a special buffering mode which reduces the loop length as necessary to not trample on values being reduced.

Note that if you want to do a reduction on an automatically allocated output, you must use NpyIter_GetOperandArray to get its reference, then set every value to the reduction unit before doing the iteration loop. In the case of a buffered reduction, this means you must also specify the flag NPY_ITER_DELAY_BUFALLOC, then reset the iterator after initializing the allocated operand to prepare the buffers.

NPY_ITER_RANGED

Enables support for iteration of sub-ranges of the full iterindex range [0, NpyIter_IterSize(iter)). Use the function NpyIter_ResetToIterIndexRange to specify a range for iteration.

This flag can only be used with NPY_ITER_NO_INNER_ITERATION when NPY_ITER_BUFFERED is enabled. This is because without buffering, the inner loop is always the size of the innermost iteration dimension, and allowing it to get cut up would require special handling, effectively making it more like the buffered version.

NPY_ITER_BUFFERED

Causes the iterator to store buffering data, and use buffering to satisfy data type, alignment, and byte-order requirements. To buffer an operand, do not specify the NPY_ITER_COPY or NPY_ITER_UPDATEIFCOPY flags, because they will override buffering. Buffering is especially useful for Python code using the iterator, allowing for larger chunks of data at once to amortize the Python interpreter overhead.

If used with NPY_ITER_NO_INNER_ITERATION, the inner loop for the caller may get larger chunks than would be possible without buffering, because of how the strides are laid out.

Note that if an operand is given the flag NPY_ITER_COPY or NPY_ITER_UPDATEIFCOPY, a copy will be made in preference to buffering. Buffering will still occur when the array was broadcast so elements need to be duplicated to get a constant stride.

In normal buffering, the size of each inner loop is equal to the buffer size, or possibly larger if NPY_ITER_GROWINNER is specified. If NPY_ITER_REDUCE_OK is enabled and a reduction occurs, the inner loops may become smaller depending on the structure of the reduction.

NPY_ITER_GROWINNER

When buffering is enabled, this allows the size of the inner loop to grow when buffering isn't necessary. This option is best used if you're doing a straight pass through all the data, rather than anything with small cache-friendly arrays of temporary values for each inner loop.

NPY_ITER_DELAY_BUFALLOC

When buffering is enabled, this delays allocation of the buffers until one of the NpyIter_Reset* functions is called. This flag exists to avoid wasteful copying of buffer data when making multiple copies of a buffered iterator for multi-threaded iteration.

Another use of this flag is for setting up reduction operations. After the iterator is created, and a reduction output is allocated automatically by the iterator (be sure to use READWRITE access), its value may be initialized to the reduction unit. Use NpyIter_GetOperandArray to get the object. Then, call NpyIter_Reset to allocate and fill the buffers with their initial values.

Flags that may be passed in op_flags[i], where 0 <= i < niter:

NPY_ITER_READWRITE, NPY_ITER_READONLY, NPY_ITER_WRITEONLY

Indicate how the user of the iterator will read or write to op[i]. Exactly one of these flags must be specified per operand.

NPY_ITER_COPY

Allow a copy of op[i] to be made if it does not meet the data type or alignment requirements as specified by the constructor flags and parameters.

NPY_ITER_UPDATEIFCOPY

Triggers NPY_ITER_COPY, and when an array operand is flagged for writing and is copied, causes the data in a copy to be copied back to op[i] when the iterator is destroyed.

If the operand is flagged as write-only and a copy is needed, an uninitialized temporary array will be created and then copied to back to op[i] on destruction, instead of doing the unecessary copy operation.

NPY_ITER_NBO, NPY_ITER_ALIGNED, NPY_ITER_CONTIG

Causes the iterator to provide data for op[i] that is in native byte order, aligned according to the dtype requirements, contiguous, or any combination.

By default, the iterator produces pointers into the arrays provided, which may be aligned or unaligned, and with any byte order. If copying or buffering is not enabled and the operand data doesn't satisfy the constraints, an error will be raised.

The contiguous constraint applies only to the inner loop, successive inner loops may have arbitrary pointer changes.

If the requested data type is in non-native byte order, the NBO flag overrides it and the requested data type is converted to be in native byte order.

NPY_ITER_ALLOCATE

This is for output arrays, and requires that the flag NPY_ITER_WRITEONLY be set. If op[i] is NULL, creates a new array with the final broadcast dimensions, and a layout matching the iteration order of the iterator.

When op[i] is NULL, the requested data type op_dtypes[i] may be NULL as well, in which case it is automatically generated from the dtypes of the arrays which are flagged as readable. The rules for generating the dtype are the same is for UFuncs. Of special note is handling of byte order in the selected dtype. If there is exactly one input, the input's dtype is used as is. Otherwise, if more than one input dtypes are combined together, the output will be in native byte order.

After being allocated with this flag, the caller may retrieve the new array by calling NpyIter_GetOperandArray and getting the i-th object in the returned C array. The caller must call Py_INCREF on it to claim a reference to the array.

NPY_ITER_NO_SUBTYPE

For use with NPY_ITER_ALLOCATE, this flag disables allocating an array subtype for the output, forcing it to be a straight ndarray.

TODO: Maybe it would be better to introduce a function NpyIter_GetWrappedOutput and remove this flag?

NPY_ITER_NO_BROADCAST

Ensures that the input or output matches the iteration dimensions exactly.

NPY_ITER_WRITEABLE_REFERENCES

By default, the iterator fails on creation if the iterator has a writeable operand where the data type involves Python references. Adding this flag indicates that the code using the iterator is aware of this possibility and handles it correctly.

NpyIter *NpyIter_Copy(NpyIter *iter)

Makes a copy of the given iterator. This function is provided primarily to enable multi-threaded iteration of the data.

TODO: Move this to a section about multithreaded iteration.

The recommended approach to multithreaded iteration is to first create an iterator with the flags NPY_ITER_NO_INNER_ITERATION, NPY_ITER_RANGED, NPY_ITER_BUFFERED, NPY_ITER_DELAY_BUFALLOC, and possibly NPY_ITER_GROWINNER. Create a copy of this iterator for each thread (minus one for the first iterator). Then, take the iteration index range [0, NpyIter_GetIterSize(iter)) and split it up into tasks, for example using a TBB parallel_for loop. When a thread gets a task to execute, it then uses its copy of the iterator by calling NpyIter_ResetToIterIndexRange and iterating over the full range.

When using the iterator in multi-threaded code or in code not holding the Python GIL, care must be taken to only call functions which are safe in that context. NpyIter_Copy cannot be safely called without the Python GIL, because it increments Python references. The Reset* and some other functions may be safely called by passing in the errmsg parameter as non-NULL, so that the functions will pass back errors through it instead of setting a Python exception.

int NpyIter_UpdateIter(NpyIter *iter, npy_intp i, npy_uint32 op_flags, NPY_CASTING casting, PyArray_Descr *dtype) UNIMPLEMENTED

Updates the i-th operand within the iterator to possibly have a new data type or more restrictive flag attributes. A use-case for this is to allow the automatic allocation to determine an output data type based on the standard NumPy type promotion rules, then use this function to convert the inputs and possibly the automatic output to a different data type during processing.

This operation can only be done if NPY_ITER_COORDS was passed as a flag to the iterator. If coordinates are not needed, call the function NpyIter_RemoveCoords() once no more calls to NpyIter_UpdateIter are needed.

If the i-th operand has already been copied, an error is thrown. To avoid this, leave all the flags out except the read/write indicators for any operand that later has NpyIter_UpdateIter called on it.

The flags that may be passed in op_flags are NPY_ITER_COPY, NPY_ITER_UPDATEIFCOPY, NPY_ITER_NBO, NPY_ITER_ALIGNED, NPY_ITER_CONTIG.

int NpyIter_RemoveAxis(NpyIter *iter, npy_intp axis)

Removes an axis from iteration. This requires that NPY_ITER_COORDS was set for iterator creation, and does not work if buffering is enabled or an index is being tracked. This function also resets the iterator to its initial state.

This is useful for setting up an accumulation loop, for example. The iterator can first be created with all the dimensions, including the accumulation axis, so that the output gets created correctly. Then, the accumulation axis can be removed, and the calculation done in a nested fashion.

WARNING: This function may change the internal memory layout of the iterator. Any cached functions or pointers from the iterator must be retrieved again!

Returns NPY_SUCCEED or NPY_FAIL.

int NpyIter_RemoveCoords(NpyIter *iter)

If the iterator has coordinates, this strips support for them, and does further iterator optimizations that are possible if coordinates are not needed. This function also resets the iterator to its initial state.

WARNING: This function may change the internal memory layout of the iterator. Any cached functions or pointers from the iterator must be retrieved again!

After calling this function, NpyIter_HasCoords(iter) will return false.

Returns NPY_SUCCEED or NPY_FAIL.

int NpyIter_RemoveInnerLoop(NpyIter *iter)

If UpdateIter/RemoveCoords was used, you may want to specify the flag NPY_ITER_NO_INNER_ITERATION. This flag is not permitted together with NPY_ITER_COORDS, so this function is provided to enable the feature after NpyIter_RemoveCoords is called. This function also resets the iterator to its initial state.

WARNING: This function changes the internal logic of the iterator. Any cached functions or pointers from the iterator must be retrieved again!

Returns NPY_SUCCEED or NPY_FAIL.

int NpyIter_Deallocate(NpyIter *iter)

Deallocates the iterator object. This additionally frees any copies made, triggering UPDATEIFCOPY behavior where necessary.

Returns NPY_SUCCEED or NPY_FAIL.

int NpyIter_Reset(NpyIter *iter, char **errmsg)

Resets the iterator back to its initial state, at the beginning of the iteration range.

Returns NPY_SUCCEED or NPY_FAIL. If errmsg is non-NULL, no Python exception is set when NPY_FAIL is returned. Instead, *errmsg is set to an error message. When errmsg is non-NULL, the function may be safely called without holding the Python GIL.

int NpyIter_ResetToIterIndexRange(NpyIter *iter, npy_intp istart, npy_intp iend, char **errmsg)

Resets the iterator and restricts it to the iterindex range [istart, iend). See NpyIter_Copy for an explanation of how to use this for multi-threaded iteration. This requires that the flag NPY_ITER_RANGED was passed to the iterator constructor.

If you want to reset both the iterindex range and the base pointers at the same time, you can do the following to avoid extra buffer copying (be sure to add the return code error checks when you copy this code).:

/* Set to a trivial empty range */
NpyIter_ResetToIterIndexRange(iter, 0, 0);
/* Set the base pointers */
NpyIter_ResetBasePointers(iter, baseptrs);
/* Set to the desired range */
NpyIter_ResetToIterIndexRange(iter, istart, iend);

Returns NPY_SUCCEED or NPY_FAIL. If errmsg is non-NULL, no Python exception is set when NPY_FAIL is returned. Instead, *errmsg is set to an error message. When errmsg is non-NULL, the function may be safely called without holding the Python GIL.

int NpyIter_ResetBasePointers(NpyIter *iter, char **baseptrs, char **errmsg)

Resets the iterator back to its initial state, but using the values in baseptrs for the data instead of the pointers from the arrays being iterated. This functions is intended to be used, together with the op_axes parameter, by nested iteration code with two or more iterators.

Returns NPY_SUCCEED or NPY_FAIL. If errmsg is non-NULL, no Python exception is set when NPY_FAIL is returned. Instead, *errmsg is set to an error message. When errmsg is non-NULL, the function may be safely called without holding the Python GIL.

TODO: Move the following into a special section on nested iterators.

Creating iterators for nested iteration requires some care. All the iterator operands must match exactly, or the calls to NpyIter_ResetBasePointers will be invalid. This means that automatic copies and output allocation should not be used haphazardly. It is possible to still use the automatic data conversion and casting features of the iterator by creating one of the iterators with all the conversion parameters enabled, then grabbing the allocated operands with the NpyIter_GetOperandArray function and passing them into the constructors for the rest of the iterators.

WARNING: When creating iterators for nested iteration, the code must not use a dimension more than once in the different iterators. If this is done, nested iteration will produce out-of-bounds pointers during iteration.

WARNING: When creating iterators for nested iteration, buffering can only be applied to the innermost iterator. If a buffered iterator is used as the source for baseptrs, it will point into a small buffer instead of the array and the inner iteration will be invalid.

The pattern for using nested iterators is as follows.:

NpyIter *iter1, *iter1;
NpyIter_IterNext_Fn iternext1, iternext2;
char **dataptrs1;

/*
 * With the exact same operands, no copies allowed, and
 * no axis in op_axes used both in iter1 and iter2.
 * Buffering may be enabled for iter2, but not for iter1.
 */
iter1 = ...; iter2 = ...;

iternext1 = NpyIter_GetIterNext(iter1);
iternext2 = NpyIter_GetIterNext(iter2);
dataptrs1 = NpyIter_GetDataPtrArray(iter1);

do {
    NpyIter_ResetBasePointers(iter2, dataptrs1);
    do {
        /* Use the iter2 values */
    } while (iternext2(iter2));
} while (iternext1(iter1));

int NpyIter_GotoCoords(NpyIter *iter, npy_intp *coords)

Adjusts the iterator to point to the ndim coordinates pointed to by coords. Returns an error if coordinates are not being tracked, the coordinates are out of bounds, or inner loop iteration is disabled.

Returns NPY_SUCCEED or NPY_FAIL.

int NpyIter_GotoIndex(NpyIter *iter, npy_intp index)

Adjusts the iterator to point to the index specified. If the iterator was constructed with the flag NPY_ITER_C_INDEX, index is the C-order index, and if the iterator was constructed with the flag NPY_ITER_F_INDEX, index is the Fortran-order index. Returns an error if there is no index being tracked, the index is out of bounds, or inner loop iteration is disabled.

Returns NPY_SUCCEED or NPY_FAIL.

npy_intp NpyIter_GetIterSize(NpyIter *iter)

Returns the number of elements being iterated. This is the product of all the dimensions in the shape.

npy_intp NpyIter_GetReduceBlockSizeFactor(NpyIter *iter) UNIMPLEMENTED

This provides a factor that must divide into the blocksize used for ranged iteration to safely multithread a reduction. If the iterator has no reduction, it returns 1.

When using ranged iteration to multithread a reduction, there are two possible ways to do the reduction:

If there is a big reduction to a small output, make a temporary array initialized to the reduction unit for each thread, then have each thread reduce into its temporary. When that is complete, combine the temporaries together. You can detect this case by observing that NpyIter_GetReduceBlockSizeFactor returns a large value, for instance half or a third of NpyIter_GetIterSize. You should also check that the output is small just to be sure.

If there are many small reductions to a big output, and the reduction dimensions are inner dimensions, NpyIter_GetReduceBlockSizeFactor will return a small number, and as long as the block size you choose for multithreading is NpyIter_GetReduceBlockSizeFactor(iter)*n for some n, the operation will be safe.

The bad case is when the a reduction dimension is the outermost loop in the iterator. For example, if you have a C-order array with shape (3,1000,1000), and you reduce on dimension 0, NpyIter_GetReduceBlockSizeFactor will return a size equal to NpyIter_GetIterSize for NPY_KEEPORDER or NPY_CORDER iteration orders. While it is bad for the CPU cache, perhaps in the future another order possibility could be provided, maybe NPY_REDUCEORDER, which pushes the reduction axes to the inner loop, but otherwise is the same as NPY_KEEPORDER.

npy_intp NpyIter_GetIterIndex(NpyIter *iter)

Gets the iterindex of the iterator, which is an index matching the iteration order of the iterator.

void NpyIter_GetIterIndexRange(NpyIter *iter, npy_intp *istart, npy_intp *iend)

Gets the iterindex sub-range that is being iterated. If NPY_ITER_RANGED was not specified, this always returns the range [0, NpyIter_IterSize(iter)).

int NpyIter_GotoIterIndex(NpyIter *iter, npy_intp iterindex)

Adjusts the iterator to point to the iterindex specified. The IterIndex is an index matching the iteration order of the iterator. Returns an error if the iterindex is out of bounds, buffering is enabled, or inner loop iteration is disabled.

Returns NPY_SUCCEED or NPY_FAIL.

int NpyIter_HasInnerLoop(NpyIter *iter

Returns 1 if the iterator handles the inner loop, or 0 if the caller needs to handle it. This is controlled by the constructor flag NPY_ITER_NO_INNER_ITERATION.

int NpyIter_HasCoords(NpyIter *iter)

Returns 1 if the iterator was created with the NPY_ITER_COORDS flag, 0 otherwise.

int NpyIter_HasIndex(NpyIter *iter)

Returns 1 if the iterator was created with the NPY_ITER_C_INDEX or NPY_ITER_F_INDEX flag, 0 otherwise.

int NpyIter_IsBuffered(NpyIter *iter)

Returns 1 if the iterator was created with the NPY_ITER_BUFFERED flag, 0 otherwise.

int NpyIter_IsGrowInner(NpyIter *iter)

Returns 1 if the iterator was created with the NPY_ITER_GROWINNER flag, 0 otherwise.

npy_intp NpyIter_GetBufferSize(NpyIter *iter)

If the iterator is buffered, returns the size of the buffer being used, otherwise returns 0.

npy_intp NpyIter_GetNDim(NpyIter *iter)

Returns the number of dimensions being iterated. If coordinates were not requested in the iterator constructor, this value may be smaller than the number of dimensions in the original objects.

npy_intp NpyIter_GetNIter(NpyIter *iter)

Returns the number of objects being iterated.

npy_intp *NpyIter_GetAxisStrideArray(NpyIter *iter, npy_intp axis)

Gets the array of strides for the specified axis. Requires that the iterator be tracking coordinates, and that buffering not be enabled.

This may be used when you want to match up operand axes in some fashion, then remove them with NpyIter_RemoveAxis to handle their processing manually. By calling this function before removing the axes, you can get the strides for the manual processing.

Returns NULL on error.

int NpyIter_GetShape(NpyIter *iter, npy_intp *outshape)

Returns the broadcast shape of the iterator in outshape. This can only be called on an iterator which supports coordinates.

Returns NPY_SUCCEED or NPY_FAIL.

PyArray_Descr **NpyIter_GetDescrArray(NpyIter *iter)

This gives back a pointer to the niter data type Descrs for the objects being iterated. The result points into iter, so the caller does not gain any references to the Descrs.

This pointer may be cached before the iteration loop, calling iternext will not change it.

PyObject **NpyIter_GetOperandArray(NpyIter *iter)

This gives back a pointer to the niter operand PyObjects that are being iterated. The result points into iter, so the caller does not gain any references to the PyObjects.

PyObject *NpyIter_GetIterView(NpyIter *iter, npy_intp i)

This gives back a reference to a new ndarray view, which is a view into the i-th object in the array NpyIter_GetOperandArray(), whose dimensions and strides match the internal optimized iteration pattern. A C-order iteration of this view is equivalent to the iterator's iteration order.

For example, if an iterator was created with a single array as its input, and it was possible to rearrange all its axes and then collapse it into a single strided iteration, this would return a view that is a one-dimensional array.

void NpyIter_GetReadFlags(NpyIter *iter, char *outreadflags)

Fills niter flags. Sets outreadflags[i] to 1 if op[i] can be read from, and to 0 if not.

void NpyIter_GetWriteFlags(NpyIter *iter, char *outwriteflags)

Fills niter flags. Sets outwriteflags[i] to 1 if op[i] can be written to, and to 0 if not.

Functions For Iteration

NpyIter_IterNext_Fn NpyIter_GetIterNext(NpyIter *iter, char **errmsg)

Returns a function pointer for iteration. A specialized version of the function pointer may be calculated by this function instead of being stored in the iterator structure. Thus, to get good performance, it is required that the function pointer be saved in a variable rather than retrieved for each loop iteration.

Returns NULL if there is an error. If errmsg is non-NULL, no Python exception is set when NPY_FAIL is returned. Instead, *errmsg is set to an error message. When errmsg is non-NULL, the function may be safely called without holding the Python GIL.

The typical looping construct is as follows.:

NpyIter_IterNext_Fn iternext = NpyIter_GetIterNext(iter, NULL);
char **dataptr = NpyIter_GetDataPtrArray(iter);

do {
    /* use the addresses dataptr[0], ... dataptr[niter-1] */
} while(iternext(iter));

When NPY_ITER_NO_INNER_ITERATION is specified, the typical inner loop construct is as follows.:

NpyIter_IterNext_Fn iternext = NpyIter_GetIterNext(iter, NULL);
char **dataptr = NpyIter_GetDataPtrArray(iter);
npy_intp *stride = NpyIter_GetInnerStrideArray(iter);
npy_intp *size_ptr = NpyIter_GetInnerLoopSizePtr(iter), size;
npy_intp iiter, niter = NpyIter_GetNIter(iter);

do {
    size = *size_ptr;
    while (size--) {
        /* use the addresses dataptr[0], ... dataptr[niter-1] */
        for (iiter = 0; iiter < niter; ++iiter) {
            dataptr[iiter] += stride[iiter];
        }
    }
} while (iternext());

Observe that we are using the dataptr array inside the iterator, not copying the values to a local temporary. This is possible because when iternext() is called, these pointers will be overwritten with fresh values, not incrementally updated.

If a compile-time fixed buffer is being used (both flags NPY_ITER_BUFFERED and NPY_ITER_NO_INNER_ITERATION), the inner size may be used as a signal as well. The size is guaranteed to become zero when iternext() returns false, enabling the following loop construct. Note that if you use this construct, you should not pass NPY_ITER_GROWINNER as a flag, because it will cause larger sizes under some circumstances.:

/* The constructor should have buffersize passed as this value */
#define FIXED_BUFFER_SIZE 1024

NpyIter_IterNext_Fn iternext = NpyIter_GetIterNext(iter, NULL);
char **dataptr = NpyIter_GetDataPtrArray(iter);
npy_intp *stride = NpyIter_GetInnerStrideArray(iter);
npy_intp *size_ptr = NpyIter_GetInnerLoopSizePtr(iter), size;
npy_intp i, iiter, niter = NpyIter_GetNIter(iter);

/* One loop with a fixed inner size */
size = *size_ptr;
while (size == FIXED_BUFFER_SIZE) {
    /*
     * This loop could be manually unrolled by a factor
     * which divides into FIXED_BUFFER_SIZE
     */
    for (i = 0; i < FIXED_BUFFER_SIZE; ++i) {
        /* use the addresses dataptr[0], ... dataptr[niter-1] */
        for (iiter = 0; iiter < niter; ++iiter) {
            dataptr[iiter] += stride[iiter];
        }
    }
    iternext();
    size = *size_ptr;
}

/* Finish-up loop with variable inner size */
if (size > 0) do {
    size = *size_ptr;
    while (size--) {
        /* use the addresses dataptr[0], ... dataptr[niter-1] */
        for (iiter = 0; iiter < niter; ++iiter) {
            dataptr[iiter] += stride[iiter];
        }
    }
} while (iternext());

NpyIter_GetCoords_Fn NpyIter_GetGetCoords(NpyIter *iter, char **errmsg)

Returns a function pointer for getting the coordinates of the iterator. Returns NULL if the iterator does not support coordinates. It is recommended that this function pointer be cached in a local variable before the iteration loop.

Returns NULL if there is an error. If errmsg is non-NULL, no Python exception is set when NPY_FAIL is returned. Instead, *errmsg is set to an error message. When errmsg is non-NULL, the function may be safely called without holding the Python GIL.

char **NpyIter_GetDataPtrArray(NpyIter *iter)

This gives back a pointer to the niter data pointers. If NPY_ITER_NO_INNER_ITERATION was not specified, each data pointer points to the current data item of the iterator. If no inner iteration was specified, it points to the first data item of the inner loop.

This pointer may be cached before the iteration loop, calling iternext will not change it. This function may be safely called without holding the Python GIL.

npy_intp *NpyIter_GetIndexPtr(NpyIter *iter)

This gives back a pointer to the index being tracked, or NULL if no index is being tracked. It is only useable if one of the flags NPY_ITER_C_INDEX or NPY_ITER_F_INDEX were specified during construction.

When the flag NPY_ITER_NO_INNER_ITERATION is used, the code needs to know the parameters for doing the inner loop. These functions provide that information.

npy_intp *NpyIter_GetInnerStrideArray(NpyIter *iter)

Returns a pointer to an array of the niter strides, one for each iterated object, to be used by the inner loop.

This pointer may be cached before the iteration loop, calling iternext will not change it. This function may be safely called without holding the Python GIL.

npy_intp* NpyIter_GetInnerLoopSizePtr(NpyIter *iter)

Returns a pointer to the number of iterations the inner loop should execute.

This address may be cached before the iteration loop, calling iternext will not change it. The value itself may change during iteration, in particular if buffering is enabled. This function may be safely called without holding the Python GIL.

void NpyIter_GetInnerFixedStrideArray(NpyIter *iter, npy_intp *out_strides)

Gets an array of strides which are fixed, or will not change during the entire iteration. For strides that may change, the value NPY_MAX_INTP is placed in the stride.

Once the iterator is prepared for iteration (after a reset if NPY_DELAY_BUFALLOC was used), call this to get the strides which may be used to select a fast inner loop function. For example, if the stride is 0, that means the inner loop can always load its value into a variable once, then use the variable throughout the loop, or if the stride equals the itemsize, a contiguous version for that operand may be used.

This function may be safely called without holding the Python GIL.

Examples

A copy function using the iterator. The order parameter is used to control the memory layout of the allocated result.

If the input is a reference type, this function will fail. To fix this, the code must be changed to specially handle writeable references, and add NPY_ITER_WRITEABLE_REFERENCES to the flags.:

/* NOTE: This code has not been compiled/tested */
PyObject *CopyArray(PyObject *arr, NPY_ORDER order)
{
    NpyIter *iter;
    NpyIter_IterNext_Fn iternext;
    PyObject *op[2], *ret;
    npy_uint32 flags;
    npy_uint32 op_flags[2];
    npy_intp itemsize, *innersizeptr, innerstride;
    char **dataptrarray;

    /*
     * No inner iteration - inner loop is handled by CopyArray code
     */
    flags = NPY_ITER_NO_INNER_ITERATION;
    /*
     * Tell the constructor to automatically allocate the output.
     * The data type of the output will match that of the input.
     */
    op[0] = arr;
    op[1] = NULL;
    op_flags[0] = NPY_ITER_READONLY;
    op_flags[1] = NPY_ITER_WRITEONLY | NPY_ITER_ALLOCATE;

    /* Construct the iterator */
    iter = NpyIter_MultiNew(2, op, flags, order, NPY_NO_CASTING,
                            op_flags, NULL, 0, NULL);
    if (iter == NULL) {
        return NULL;
    }

    /*
     * Make a copy of the iternext function pointer and
     * a few other variables the inner loop needs.
     */
    iternext = NpyIter_GetIterNext(iter);
    innerstride = NpyIter_GetInnerStrideArray(iter)[0];
    itemsize = NpyIter_GetDescrArray(iter)[0]->elsize;
    /*
     * The inner loop size and data pointers may change during the
     * loop, so just cache the addresses.
     */
    innersizeptr = NpyIter_GetInnerLoopSizePtr(iter);
    dataptrarray = NpyIter_GetDataPtrArray(iter);

    /*
     * Note that because the iterator allocated the output,
     * it matches the iteration order and is packed tightly,
     * so we don't need to check it like the input.
     */
    if (innerstride == itemsize) {
        do {
            memcpy(dataptrarray[1], dataptrarray[0],
                                    itemsize * (*innersizeptr));
        } while (iternext(iter));
    } else {
        /* Should specialize this further based on item size... */
        npy_intp i;
        do {
            npy_intp size = *innersizeptr;
            char *src = dataaddr[0], *dst = dataaddr[1];
            for(i = 0; i < size; i++, src += innerstride, dst += itemsize) {
                memcpy(dst, src, itemsize);
            }
        } while (iternext(iter));
    }

    /* Get the result from the iterator object array */
    ret = NpyIter_GetOperandArray(iter)[1];
    Py_INCREF(ret);

    if (NpyIter_Deallocate(iter) != NPY_SUCCEED) {
        Py_DECREF(ret);
        return NULL;
    }

    return ret;
}

Python Lambda UFunc Example

To show how the new iterator allows the definition of efficient UFunc-like functions in pure Python, we demonstrate the function luf, which makes a lambda-expression act like a UFunc. This is very similar to the numexpr library, but only takes a few lines of code.

First, here is the definition of the luf function.:

def luf(lamdaexpr, *args, **kwargs):
    """Lambda UFunc

        e.g.
        c = luf(lambda i,j:i+j, a, b, order='K',
                            casting='safe', buffersize=8192)

        c = np.empty(...)
        luf(lambda i,j:i+j, a, b, out=c, order='K',
                            casting='safe', buffersize=8192)
    """

    nargs = len(args)
    op = args + (kwargs.get('out',None),)
    it = np.nditer(op, ['buffered','no_inner_iteration'],
            [['readonly','nbo_aligned']]*nargs +
                            [['writeonly','allocate','no_broadcast']],
            order=kwargs.get('order','K'),
            casting=kwargs.get('casting','safe'),
            buffersize=kwargs.get('buffersize',0))
    while not it.finished:
        it[-1] = lamdaexpr(*it[:-1])
        it.iternext()

    return it.operands[-1]

Then, by using luf instead of straight Python expressions, we can gain some performance from better cache behavior.:

In [2]: a = np.random.random((50,50,50,10))
In [3]: b = np.random.random((50,50,1,10))
In [4]: c = np.random.random((50,50,50,1))

In [5]: timeit 3*a+b-(a/c)
1 loops, best of 3: 138 ms per loop

In [6]: timeit luf(lambda a,b,c:3*a+b-(a/c), a, b, c)
10 loops, best of 3: 60.9 ms per loop

In [7]: np.all(3*a+b-(a/c) == luf(lambda a,b,c:3*a+b-(a/c), a, b, c))
Out[7]: True

Python Addition Example

The iterator has been mostly written and exposed to Python. To see how it behaves, let's see what we can do with the np.add ufunc. Even without changing the core of NumPy, we will be able to use the iterator to make a faster add function.

The Python exposure supplies two iteration interfaces, one which follows the Python iterator protocol, and another which mirrors the C-style do-while pattern. The native Python approach is better in most cases, but if you need the iterator's coordinates or index, use the C-style pattern.

Here is how we might write an iter_add function, using the Python iterator protocol.:

def iter_add_py(x, y, out=None):
    addop = np.add

    it = np.nditer([x,y,out], [],
                [['readonly'],['readonly'],['writeonly','allocate']])

    for (a, b, c) in it:
        addop(a, b, c)

    return it.operands[2]

Here is the same function, but following the C-style pattern.:

def iter_add(x, y, out=None):
    addop = np.add

    it = np.nditer([x,y,out], [],
                [['readonly'],['readonly'],['writeonly','allocate']])

    while not it.finished:
        addop(it[0], it[1], it[2])
        it.iternext()

    return it.operands[2]

Some noteworthy points about this function:

  • Cache np.add as a local variable to reduce namespace lookups
  • Inputs are readonly, output is writeonly, and will be allocated automatically if it is None.
  • Uses np.add's out parameter to avoid an extra copy.

Let's create some test variables, and time this function as well as the built-in np.add.:

In [1]: a = np.arange(1000000,dtype='f4').reshape(100,100,100)
In [2]: b = np.arange(10000,dtype='f4').reshape(1,100,100)
In [3]: c = np.arange(10000,dtype='f4').reshape(100,100,1)

In [4]: timeit iter_add(a, b)
1 loops, best of 3: 7.03 s per loop

In [5]: timeit np.add(a, b)
100 loops, best of 3: 6.73 ms per loop

At a thousand times slower, this is clearly not very good. One feature of the iterator, designed to help speed up the inner loops, is the flag no_inner_iteration. This is the same idea as the old iterator's PyArray_IterAllButAxis, but slightly smarter. Let's modify iter_add to use this feature.:

def iter_add_noinner(x, y, out=None):
    addop = np.add

    it = np.nditer([x,y,out], ['no_inner_iteration'],
                [['readonly'],['readonly'],['writeonly','allocate']])

    for (a, b, c) in it:
        addop(a, b, c)

    return it.operands[2]

The performance improves dramatically.:

In[6]: timeit iter_add_noinner(a, b)
100 loops, best of 3: 7.1 ms per loop

The performance is basically as good as the built-in function! It turns out this is because the iterator was able to coalesce the last two dimensions, resulting in 100 adds of 10000 elements each. If the inner loop doesn't become as large, the performance doesn't improve as dramatically. Let's use c instead of b to see how this works.:

In[7]: timeit iter_add_noinner(a, c)
10 loops, best of 3: 76.4 ms per loop

It's still a lot better than seven seconds, but still over ten times worse than the built-in function. Here, the inner loop has 100 elements, and it's iterating 10000 times. If we were coding in C, our performance would already be as good as the built-in performance, but in Python there is too much overhead.

This leads us to another feature of the iterator, its ability to give us views of the iterated memory. The views it gives us are structured so that processing them in C-order, like the built-in NumPy code does, gives the same access order as the iterator itself. Effectively, we are using the iterator to solve for a good memory access pattern, then using other NumPy machinery to efficiently execute it. Let's modify iter_add once again.:

def iter_add_itview(x, y, out=None):
    it = np.nditer([x,y,out], [],
                [['readonly'],['readonly'],['writeonly','allocate']])

    (a, b, c) = it.itviews
    np.add(a, b, c)

    return it.operands[2]

Now the performance pretty closely matches the built-in function's.:

In [8]: timeit iter_add_itview(a, b)
100 loops, best of 3: 6.18 ms per loop

In [9]: timeit iter_add_itview(a, c)
100 loops, best of 3: 6.69 ms per loop

Let us now step back to a case similar to the original motivation for the new iterator. Here are the same calculations in Fortran memory order instead Of C memory order.:

In [10]: a = np.arange(1000000,dtype='f4').reshape(100,100,100).T
In [12]: b = np.arange(10000,dtype='f4').reshape(100,100,1).T
In [11]: c = np.arange(10000,dtype='f4').reshape(1,100,100).T

In [39]: timeit np.add(a, b)
10 loops, best of 3: 34.3 ms per loop

In [41]: timeit np.add(a, c)
10 loops, best of 3: 31.6 ms per loop

In [44]: timeit iter_add_itview(a, b)
100 loops, best of 3: 6.58 ms per loop

In [43]: timeit iter_add_itview(a, c)
100 loops, best of 3: 6.33 ms per loop

As you can see, the performance of the built-in function dropped significantly, but our newly-written add function maintained essentially the same performance. As one final test, let's try several adds chained together.:

In [4]: timeit np.add(np.add(np.add(a,b), c), a)
1 loops, best of 3: 99.5 ms per loop

In [9]: timeit iter_add_itview(iter_add_itview(iter_add_itview(a,b), c), a)
10 loops, best of 3: 29.3 ms per loop

Also, just to check that it's doing the same thing,:

In [22]: np.all(
   ....: iter_add_itview(iter_add_itview(iter_add_itview(a,b), c), a) ==
   ....: np.add(np.add(np.add(a,b), c), a)
   ....: )

Out[22]: True

Image Compositing Example Revisited

For motivation, we had an example that did an 'over' composite operation on two images. Now let's see how we can write the function with the new iterator.

Here is one of the original functions, for reference, and some random image data.:

In [5]: rand1 = np.random.random_sample(1080*1920*4).astype(np.float32)
In [6]: rand2 = np.random.random_sample(1080*1920*4).astype(np.float32)
In [7]: image1 = rand1.reshape(1080,1920,4).swapaxes(0,1)
In [8]: image2 = rand2.reshape(1080,1920,4).swapaxes(0,1)

In [3]: def composite_over(im1, im2):
  ....:     ret = (1-im1[:,:,-1])[:,:,np.newaxis]*im2
  ....:     ret += im1
  ....:     return ret

In [4]: timeit composite_over(image1,image2)
1 loops, best of 3: 1.39 s per loop

Here's the same function, rewritten to use a new iterator. Note how easy it was to add an optional output parameter.:

In [5]: def composite_over_it(im1, im2, out=None, buffersize=4096):
  ....:     it = np.nditer([im1, im1[:,:,-1], im2, out],
  ....:                     ['buffered','no_inner_iteration'],
  ....:                     [['readonly']]*3+[['writeonly','allocate']],
  ....:                     op_axes=[None,[0,1,np.newaxis],None,None],
  ....:                     buffersize=buffersize)
  ....:     while not it.finished:
  ....:         np.multiply(1-it[1], it[2], it[3])
  ....:         it[3] += it[0]
  ....:         it.iternext()
  ....:     return it.operands[3]

In [6]: timeit composite_over_it(image1, image2)
1 loops, best of 3: 197 ms per loop

A big speed improvement, over even the best previous attempt using straight NumPy and a C-order array! By playing with the buffer size, we can see how the speed improves until we hit the limits of the CPU cache in the inner loop.:

In [7]: timeit composite_over_it(image1, image2, buffersize=2**7)
1 loops, best of 3: 1.23 s per loop

In [8]: timeit composite_over_it(image1, image2, buffersize=2**8)
1 loops, best of 3: 699 ms per loop

In [9]: timeit composite_over_it(image1, image2, buffersize=2**9)
1 loops, best of 3: 418 ms per loop

In [10]: timeit composite_over_it(image1, image2, buffersize=2**10)
1 loops, best of 3: 287 ms per loop

In [11]: timeit composite_over_it(image1, image2, buffersize=2**11)
1 loops, best of 3: 225 ms per loop

In [12]: timeit composite_over_it(image1, image2, buffersize=2**12)
1 loops, best of 3: 194 ms per loop

In [13]: timeit composite_over_it(image1, image2, buffersize=2**13)
1 loops, best of 3: 180 ms per loop

In [14]: timeit composite_over_it(image1, image2, buffersize=2**14)
1 loops, best of 3: 192 ms per loop

In [15]: timeit composite_over_it(image1, image2, buffersize=2**15)
1 loops, best of 3: 280 ms per loop

In [16]: timeit composite_over_it(image1, image2, buffersize=2**16)
1 loops, best of 3: 328 ms per loop

In [17]: timeit composite_over_it(image1, image2, buffersize=2**17)
1 loops, best of 3: 345 ms per loop

And finally, to double check that it's working, we can compare the two functions.:

In [18]: np.all(composite_over(image1, image2) ==
    ...:        composite_over_it(image1, image2))
Out[18]: True

Image Compositing With NumExpr

As a test of the iterator, numexpr has been enhanced to allow use of the iterator instead of its internal broadcasting code. First, let's implement the composite operation with numexpr.:

In [22]: def composite_over_ne(im1, im2, out=None):
   ....:     ima = im1[:,:,-1][:,:,np.newaxis]
   ....:     return ne.evaluate("im1+(1-ima)*im2")

In [23]: timeit composite_over_ne(image1,image2)
1 loops, best of 3: 1.25 s per loop

This beats the straight NumPy operation, but isn't very good. Switching to the iterator version of numexpr, we get a big improvement over the straight Python function using the iterator. Note that this is on a dual core machine.:

In [29]: def composite_over_ne_it(im1, im2, out=None):
   ....:     ima = im1[:,:,-1][:,:,np.newaxis]
   ....:     return ne.evaluate_iter("im1+(1-ima)*im2")

In [30]: timeit composite_over_ne_it(image1,image2)
10 loops, best of 3: 67.2 ms per loop

In [31]: ne.set_num_threads(1)
In [32]: timeit composite_over_ne_it(image1,image2)
10 loops, best of 3: 91.1 ms per loop
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