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<p class=MsoTitle>ThreadWeave </p>

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<h2>Introduction</h2>

<p class=MsoNormal>In a nutshell, ThreadWeave aims to bring the type of functionality
found in scipy.weave to the GPU, or SIMD architectures, more generally. That
is, ThreadWeave allows one to write concise inline SIMD kernels directly in Python,
while providing both complete imperative backwards compatibility, as well as a
useful set of higher level abstractions.</p>

<p class=MsoNormal>Most significantly, nd-arrays are first class citizens of
the ThreadWeave world. They can be passed around, indexed, have their
attributes read, and have boundary handling modes applied to them, all within
the kernel.</p>

<p class=MsoNormal>An example says more than a thousand words, so here are two
short ones:</p>

<table class=MsoTableGrid border=1 cellspacing=0 cellpadding=0
 style='border-collapse:collapse;border:none;mso-border-alt:solid windowtext .5pt;
 mso-yfti-tbllook:1184;mso-padding-alt:5.75pt 5.75pt 5.75pt 5.75pt'>
 <tr style='mso-yfti-irow:0;mso-yfti-firstrow:yes;mso-yfti-lastrow:yes'>
  <td width=1277 style='width:6.65in;border:solid windowtext 1.0pt;mso-border-alt:
  solid windowtext .5pt;padding:5.75pt 5.75pt 5.75pt 5.75pt'>
  <p class=MsoNoSpacing><span style='font-size:8.0pt;font-family:"Courier New"'>import
  numpy as np<o:p></o:p></span></p>
  <p class=MsoNoSpacing><span style='font-size:8.0pt;font-family:"Courier New"'>from
  threadweave.backend import OpenCL as Backend<o:p></o:p></span></p>
  <p class=MsoNoSpacing><span style='font-size:8.0pt;font-family:"Courier New"'>from
  threadweave.stencil import laplacian<o:p></o:p></span></p>
  <p class=MsoNoSpacing><span style='font-size:8.0pt;font-family:"Courier New"'><o:p>&nbsp;</o:p></span></p>
  <p class=MsoNoSpacing><span style='font-size:8.0pt;font-family:"Courier New"'>with
  Backend.Context(device = 0) as ctx:<o:p></o:p></span></p>
  <p class=MsoNoSpacing><span style='font-size:8.0pt;font-family:"Courier New"'><o:p>&nbsp;</o:p></span></p>
  <p class=MsoNoSpacing><span style='font-size:8.0pt;font-family:"Courier New"'><span
  style='mso-spacerun:yes'>    </span>laplacian_kernel =
  ctx.kernel(&quot;&quot;&quot;<o:p></o:p></span></p>
  <p class=MsoNoSpacing><span style='font-size:8.0pt;font-family:"Courier New"'><span
  style='mso-spacerun:yes'>        </span>(&lt;type&gt;[d,n,m] output) &lt;&lt;
  [d,n,m] &lt;&lt; (&lt;type&gt;[d,n,m] input):<o:p></o:p></span></p>
  <p class=MsoNoSpacing><span style='font-size:8.0pt;font-family:"Courier New"'><span
  style='mso-spacerun:yes'>            </span>n:<span
  style='mso-spacerun:yes'>      </span>serial<o:p></o:p></span></p>
  <p class=MsoNoSpacing><span style='font-size:8.0pt;font-family:"Courier New"'><span
  style='mso-spacerun:yes'>            </span>d:<span
  style='mso-spacerun:yes'>      </span>variable<o:p></o:p></span></p>
  <p class=MsoNoSpacing><span style='font-size:8.0pt;font-family:"Courier New"'><span
  style='mso-spacerun:yes'>            </span>input:<span
  style='mso-spacerun:yes'>  </span>padded(stencil)<o:p></o:p></span></p>
  <p class=MsoNoSpacing><span style='font-size:8.0pt;font-family:"Courier New"'><span
  style='mso-spacerun:yes'>        </span>{<o:p></o:p></span></p>
  <p class=MsoNoSpacing><span style='font-size:8.0pt;font-family:"Courier New"'><span
  style='mso-spacerun:yes'>            </span>&lt;type&gt; r = 0;<o:p></o:p></span></p>
  <p class=MsoNoSpacing><span style='font-size:8.0pt;font-family:"Courier New"'><span
  style='mso-spacerun:yes'>            </span>for (s in stencil(input))<o:p></o:p></span></p>
  <p class=MsoNoSpacing><span style='font-size:8.0pt;font-family:"Courier New"'><span
  style='mso-spacerun:yes'>                 </span>r += input(s.d,s.n,s.m) *
  s.weight;<o:p></o:p></span></p>
  <p class=MsoNoSpacing><span style='font-size:8.0pt;font-family:"Courier New"'><span
  style='mso-spacerun:yes'>            </span>output(d,n,m) = r;<o:p></o:p></span></p>
  <p class=MsoNoSpacing><span style='font-size:8.0pt;font-family:"Courier New"'><span
  style='mso-spacerun:yes'>        </span>}&quot;&quot;&quot;)<o:p></o:p></span></p>
  <p class=MsoNoSpacing><span style='font-size:8.0pt;font-family:"Courier New"'><o:p>&nbsp;</o:p></span></p>
  <p class=MsoNoSpacing><span style='font-size:8.0pt;font-family:"Courier New"'><span
  style='mso-spacerun:yes'>    </span>shape = (2,6,6)<o:p></o:p></span></p>
  <p class=MsoNoSpacing><span style='font-size:8.0pt;font-family:"Courier New"'><span
  style='mso-spacerun:yes'>    </span>input =
  ctx.array(np.arange(np.prod(shape)).astype(np.float32).reshape(shape) ** 2)<o:p></o:p></span></p>
  <p class=MsoNoSpacing><span style='font-size:8.0pt;font-family:"Courier New"'><span
  style='mso-spacerun:yes'>    </span>print input<span
  style='mso-spacerun:yes'>    </span>#some arbitrary input data<o:p></o:p></span></p>
  <p class=MsoNoSpacing><span style='font-size:8.0pt;font-family:"Courier New"'><o:p>&nbsp;</o:p></span></p>
  <p class=MsoNoSpacing><span style='font-size:8.0pt;font-family:"Courier New"'><span
  style='mso-spacerun:yes'>    </span>stencil = laplacian(2,5)[np.newaxis,:,:]
  #construct 2-dim 5-pts laplacian, with broadcasting<o:p></o:p></span></p>
  <p class=MsoNoSpacing><span style='font-size:8.0pt;font-family:"Courier New"'><span
  style='mso-spacerun:yes'>    </span>output = laplacian_kernel(input, stencil
  = stencil)<o:p></o:p></span></p>
  <p class=MsoNoSpacing><span style='font-size:8.0pt;font-family:"Courier New"'><span
  style='mso-spacerun:yes'>    </span>print output</span></p>
  </td>
 </tr>
</table>

<p class=MsoNormal><o:p>&nbsp;</o:p></p>

<p class=MsoNormal>Without going into the details; this example shows the
declaration and invocation of a Laplacian filter applied to a stack of 2d
arrays; these few lines of code are converted into 70 lines of dense CUDA or OpenCL
boilerplate. Of course good libraries exist already to perform convolutions; the
added value, aside from demonstration purposes, is that ThreadWeave allows for
greatly expanded flexibility. By acting on a stack of 2d arrays, we can expose
additional parallelism, and we have full control over boundary handling, as
well as the way in which axes are iterated over. Also, the iteration over the
stencil is transparently unrolled.</p>

<p class=MsoNormal>Aside from eliminating boilerplate from imperative C code, the
functionality at the core of ThreadWeave also makes for a good platform for
building higher level abstractions:</p>

<table class=MsoTableGrid border=1 cellspacing=0 cellpadding=0
 style='border-collapse:collapse;border:none;mso-border-alt:solid windowtext .5pt;
 mso-yfti-tbllook:1184;mso-padding-alt:5.75pt 5.75pt 5.75pt 5.75pt'>
 <tr style='mso-yfti-irow:0;mso-yfti-firstrow:yes;mso-yfti-lastrow:yes'>
  <td width=1277 style='width:6.65in;border:solid windowtext 1.0pt;mso-border-alt:
  solid windowtext .5pt;padding:5.75pt 5.75pt 5.75pt 5.75pt'>
  <p class=MsoNoSpacing><span style='font-size:8.0pt;font-family:"Courier New"'>import
  numpy as np<o:p></o:p></span></p>
  <p class=MsoNoSpacing><span style='font-size:8.0pt;font-family:"Courier New"'>from
  threadweave.backend import CUDA as Backend<o:p></o:p></span></p>
  <p class=MsoNoSpacing><span style='font-size:8.0pt;font-family:"Courier New"'><o:p>&nbsp;</o:p></span></p>
  <p class=MsoNoSpacing><span style='font-size:8.0pt;font-family:"Courier New"'>with
  Backend.Context(device = 0) as ctx:<o:p></o:p></span></p>
  <p class=MsoNoSpacing><span style='font-size:8.0pt;font-family:"Courier New"'><span
  style='mso-spacerun:yes'>    </span>#some example data<o:p></o:p></span></p>
  <p class=MsoNoSpacing><span style='font-size:8.0pt;font-family:"Courier New"'><span
  style='mso-spacerun:yes'>    </span>shape = 2,3,4<o:p></o:p></span></p>
  <p class=MsoNoSpacing><span style='font-size:8.0pt;font-family:"Courier New"'><span
  style='mso-spacerun:yes'>    </span>A =
  ctx.arange(np.prod(shape),np.float32).reshape(shape)<o:p></o:p></span></p>
  <p class=MsoNoSpacing><span style='font-size:8.0pt;font-family:"Courier New"'><span
  style='mso-spacerun:yes'>    </span>shape = 2,4,3<o:p></o:p></span></p>
  <p class=MsoNoSpacing><span style='font-size:8.0pt;font-family:"Courier New"'><span
  style='mso-spacerun:yes'>    </span>B =
  ctx.arange(np.prod(shape),np.float32).reshape(shape)<o:p></o:p></span></p>
  <p class=MsoNoSpacing><span style='font-size:8.0pt;font-family:"Courier New"'><o:p>&nbsp;</o:p></span></p>
  <p class=MsoNoSpacing><span style='font-size:8.0pt;font-family:"Courier New"'><span
  style='mso-spacerun:yes'>    </span>#declare product, contracted over j<o:p></o:p></span></p>
  <p class=MsoNoSpacing><span style='font-size:8.0pt;font-family:"Courier New"'><span
  style='mso-spacerun:yes'>    </span>stacked_matrix_product =
  ctx.tensor_product('nij,njk-&gt;nik')<o:p></o:p></span></p>
  <p class=MsoNoSpacing><span style='font-size:8.0pt;font-family:"Courier New"'><span
  style='mso-spacerun:yes'>    </span>C = stacked_matrix_product(A, B)<o:p></o:p></span></p>
  <p class=MsoNoSpacing><span style='font-size:8.0pt;font-family:"Courier New"'><o:p>&nbsp;</o:p></span></p>
  <p class=MsoNoSpacing><span style='font-size:8.0pt;font-family:"Courier New"'><span
  style='mso-spacerun:yes'>    </span>print C<o:p></o:p></span></p>
  <p class=MsoNoSpacing><span style='font-size:8.0pt;font-family:"Courier New"'><span
  style='mso-spacerun:yes'>    </span>print ctx.tensor_product('nii-&gt;ni')(C)<span
  style='mso-spacerun:yes'>   </span>#print the diagonals of C too, for good measure<o:p></o:p></span></p>
  </td>
 </tr>
</table>

<p class=MsoNormal><o:p>&nbsp;</o:p></p>

<p class=MsoNormal>This short example declares and invokes a contracting tensor
product; more specifically, it multiplies a stack of matrices. The function
ctx.tensor_product is a work-alike of the invaluable numpy.einsum, and can be
used to concisely express inner products, outer products, diagonal extractions,
transposes, and any other operation which can be expressed as a tensor product
with Einstein summation convention.</p>

<p class=MsoNormal>By building on top of the abstractions at the core of ThreadWeave,
the functionality in ctx. tensor_product can be implemented in just a handful
of lines. (in its current fully functional yet suboptimal form, that is). </p>

<p class=MsoNormal>To give an impression of how this happens: both
tensor_product and laplacian_kernel have the same type; KernelFactory, which
wraps a KernelDeclaration and a cache of compiled KernelInstances, which are
created by letting a backend specific CodeGenerator act on a KernelDeclaration
for a given set of template arguments. </p>

<p class=MsoNormal>You get the idea; quite a few of the same things going on
behind the scenes, which are identical for both examples. The methods
Context.prod and Context.kernel merely wrap two different front-ends for
parsing their respective grammars into a KernelDeclaration; many more can be created
with relatively little effort to cater to specific wants. This frees one from
grave discussions, with oneself or others, over syntactical details; if your
problem domain asks for different syntax, it should be easy to implement on top
of ThreadWeave.</p>

<p class=MsoNormal><o:p>&nbsp;</o:p></p>

<h2>Feature summary</h2>

<p class=MsoNormal>Here is a concise listing of the core features that
ThreadWeave provides at present.</p>

<p class=MsoListParagraphCxSpFirst style='margin-left:20.65pt;mso-add-space:
auto;text-indent:-.25in;mso-list:l1 level1 lfo1'><![if !supportLists]><span
style='mso-ascii-font-family:Calibri;mso-fareast-font-family:Calibri;
mso-hansi-font-family:Calibri;mso-bidi-font-family:Calibri'><span
style='mso-list:Ignore'>-<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span></span></span><![endif]>Nd-array awareness:</p>

<p class=MsoListParagraphCxSpMiddle style='margin-left:56.65pt;mso-add-space:
auto;text-indent:-.25in;mso-list:l1 level2 lfo1'><![if !supportLists]><span
style='font-family:"Courier New";mso-fareast-font-family:"Courier New"'><span
style='mso-list:Ignore'>o<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;
</span></span></span><![endif]>Passing nd-arrays in and out of kernels</p>

<p class=MsoListParagraphCxSpMiddle style='margin-left:56.65pt;mso-add-space:
auto;text-indent:-.25in;mso-list:l1 level2 lfo1'><![if !supportLists]><span
style='font-family:"Courier New";mso-fareast-font-family:"Courier New"'><span
style='mso-list:Ignore'>o<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;
</span></span></span><![endif]>Indexing of nd-arrays</p>

<p class=MsoListParagraphCxSpMiddle style='margin-left:56.65pt;mso-add-space:
auto;text-indent:-.25in;mso-list:l1 level2 lfo1'><![if !supportLists]><span
style='font-family:"Courier New";mso-fareast-font-family:"Courier New"'><span
style='mso-list:Ignore'>o<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;
</span></span></span><![endif]>Various boundary handling modes (padded,
wrapped, clamped, fixed)</p>

<p class=MsoListParagraphCxSpMiddle style='margin-left:56.65pt;mso-add-space:
auto;text-indent:-.25in;mso-list:l1 level2 lfo1'><![if !supportLists]><span
style='font-family:"Courier New";mso-fareast-font-family:"Courier New"'><span
style='mso-list:Ignore'>o<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;
</span></span></span><![endif]>Accessing of array attributes such as shape with
numpythonic syntax.</p>

<p class=MsoListParagraphCxSpMiddle style='margin-left:20.65pt;mso-add-space:
auto;text-indent:-.25in;mso-list:l1 level1 lfo1'><![if !supportLists]><span
style='mso-ascii-font-family:Calibri;mso-fareast-font-family:Calibri;
mso-hansi-font-family:Calibri;mso-bidi-font-family:Calibri'><span
style='mso-list:Ignore'>-<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span></span></span><![endif]>Axes:</p>

<p class=MsoListParagraphCxSpMiddle style='margin-left:56.65pt;mso-add-space:
auto;text-indent:-.25in;mso-list:l1 level2 lfo1'><![if !supportLists]><span
style='font-family:"Courier New";mso-fareast-font-family:"Courier New"'><span
style='mso-list:Ignore'>o<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;
</span></span></span><![endif]>Declaratively relate kernel and array axes to
one another. This gives a highly flexible and compact notation.</p>

<p class=MsoListParagraphCxSpMiddle style='margin-left:56.65pt;mso-add-space:
auto;text-indent:-.25in;mso-list:l1 level2 lfo1'><![if !supportLists]><span
style='font-family:"Courier New";mso-fareast-font-family:"Courier New"'><span
style='mso-list:Ignore'>o<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;
</span></span></span><![endif]>Decoupling between the grid of work items to be
performed, and the grid of threads that perform them. This allows us to
overcome hardware limitations on threadgrids, but more importantly, allows one
to declaratively optimize the relation between the work to be performed, and
the arrangement of threads to accomplish this goal.</p>

<p class=MsoListParagraphCxSpMiddle style='margin-left:20.65pt;mso-add-space:
auto;text-indent:-.25in;mso-list:l1 level1 lfo1'><![if !supportLists]><span
style='mso-ascii-font-family:Calibri;mso-fareast-font-family:Calibri;
mso-hansi-font-family:Calibri;mso-bidi-font-family:Calibri'><span
style='mso-list:Ignore'>-<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span></span></span><![endif]>Runtime features:</p>

<p class=MsoListParagraphCxSpMiddle style='margin-left:56.65pt;mso-add-space:
auto;text-indent:-.25in;mso-list:l1 level2 lfo1'><![if !supportLists]><span
style='font-family:"Courier New";mso-fareast-font-family:"Courier New"'><span
style='mso-list:Ignore'>o<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;
</span></span></span><![endif]>JIT compilation of kernels templated on shape,
type and stencil arguments</p>

<p class=MsoListParagraphCxSpMiddle style='margin-left:56.65pt;mso-add-space:
auto;text-indent:-.25in;mso-list:l1 level2 lfo1'><![if !supportLists]><span
style='font-family:"Courier New";mso-fareast-font-family:"Courier New"'><span
style='mso-list:Ignore'>o<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;
</span></span></span><![endif]>Runtime type &amp; shape validation of kernel
arguments</p>

<p class=MsoListParagraphCxSpMiddle style='margin-left:56.65pt;mso-add-space:
auto;text-indent:-.25in;mso-list:l1 level2 lfo1'><![if !supportLists]><span
style='font-family:"Courier New";mso-fareast-font-family:"Courier New"'><span
style='mso-list:Ignore'>o<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;
</span></span></span><![endif]>Output shape inference and allocation (if not
given to the kernel)</p>

<p class=MsoListParagraphCxSpMiddle style='margin-left:56.65pt;mso-add-space:
auto;text-indent:-.25in;mso-list:l1 level2 lfo1'><![if !supportLists]><span
style='font-family:"Courier New";mso-fareast-font-family:"Courier New"'><span
style='mso-list:Ignore'>o<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;
</span></span></span><![endif]>Computation of sensible defaults for grid/block
parameters</p>

<p class=MsoListParagraphCxSpLast style='margin-left:20.65pt;mso-add-space:
auto;text-indent:-.25in;mso-list:l1 level1 lfo1'><![if !supportLists]><span
style='mso-ascii-font-family:Calibri;mso-fareast-font-family:Calibri;
mso-hansi-font-family:Calibri;mso-bidi-font-family:Calibri'><span
style='mso-list:Ignore'>-<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span></span></span><![endif]>Abstracting away the differences between
different backends; they can be switched out by changing a single import. As of
now, CUDA and OpenCL are supported. This applies to both the Python side of
things, where ThreadPy presents a uniform interface, as well as papering over
the superficial syntactical differences between the two C-dialects, like
atomicAdd / atomic_add. </p>

<p class=MsoNormal><o:p>&nbsp;</o:p></p>

<h2>ThreadWeave Concepts</h2>

<h3>Nd-arrays</h3>

<p class=MsoNormal>The two primary SIMD languages, CUDA and OpenCL, are both C
dialects, which is the natural choice in many ways. However, C was never
designed with SIMD in mind; and although both dialects offer some abstractions
for dealing with multiple threads, one is left with the minimal array
abstractions C offers for the multiple data part of the equation. By extending
C with nd-array capabilities, we not only gain the immediate benefits of this
tried and true abstraction, but it also enables the introduction of novel
concepts, aimed at harnassing the typically tight relationship between the grid
of threads and the data they act on.</p>

<p class=MsoNormal>ThreadWeave facilitates working with nd-arrays both within
the kernel code, as well as during declaration and invocation.</p>

<p class=MsoNormal>In order to provide access to arrays within the kernel, a pointer
to the device memory is passed into the kernel (shocker). In addition, all
shape information is either passed into the kernel at compile time or runtime.
This information is then used to compute all strides, which in turn is used to
provide clean syntax for indexation of nd-arrays. All the array properties
passed into or computed within the kernel are accessible within the kernel by
means of numpythonic syntax.</p>

<p class=MsoNormal>Each array axis can be given a boundary handling mode. By
default, array access is not bounds checked. But when working with stencil
operations for instance, one needs a consistent way of handling array
boundaries. All typical boundary handling modes are planned functionality
(clamped, fixed, reflected); for now, ThreadWeave only supports wrapped
boundaries, and padded boundaries. By marking an array as padded (with a given
stencil), it is treated as a view upon a larger array (with enough padding such
that all access through the stencil is safe). This is both a very flexible way
of specifying boundary conditions, and it is the most efficient in terms of
overhead inside the kernel.</p>

<p class=MsoNormal>At the moment, only C-contiguous arrays are supported (plus
a restricted notion of views on these, in the form of padded arrays). Support
for arbitrary strides would be nice to have, but the nd-array classes included
in the current stable branch of pycuda and pyopencl do not support such. This
functionality is however around the corner, in the form on the package compyte,
which provides a closer analogue of numpy�s ndarray, with a shared code base
between pycuda and pyopencl. It�s probably best to wait for the public release
of compyte and its integration into pycuda/pyopencl rather than reinventing
that wheel.</p>

<h3>Kernels and axes</h3>

<p class=MsoNormal>In ThreadWeave, kernels are declared as having an arbitrary
number of axes, with these axes spanning a grid of repetitive work items, which
all have the same kernel body applied to them. As opposed to the typical SIMD model,
not all these work items are necessarily performed in parallel; many kernels
benefit from having a thread act serially along an axis, such as to minimize
thread launch overhead, and maximize reuse of computed terms which are constant
between work items. This is opposed to the CUDA/OpenCL model, where the kernel
grid has a one to one mapping to a grid of physical threads.</p>

<p class=MsoNormal>An axis can have its iteration type set to serial, parallel,
or hybrid iteration, with the latter meaning the work items along the axes are
divided among a number of threads, each of which having responsibility for looping
over a part of the axis, and the other two iteration modes denoting the logical
extremes of that scenario. By being able to declaratively change an axis� iteration
behavior, one can rapidly find a balance between the benefits of exposing
parallelism and its drawbacks, without rewriting a single line of kernel body code.</p>

<p class=MsoNormal>Within a kernel declaration, we can create size relations
between kernel axes and array axes. This allows the kernel shape and output
arguments� shape to be deduced from the input arguments� shape. In typical use,
most array axes are directly related to a kernel axis in this manner.</p>

<h3>Stencil operations</h3>

<p class=MsoNormal>Stencil operations are a staple of GPU computing, and as
such, ThreadWeave attempts to accommodate them. Most importantly, ThreadWeave
supports special syntax for iterating over (unrolled) stencils. The syntax is �for
(voxel_id in stencil_id)�, where any properties of the individual voxels of a
stencil can be accessed through the loop dummy variable, as in voxel_id.weight,
for instance.</p>

<p class=MsoNormal>For a comprehensive hands on tutorial of stencil operations
in ThreadWeave, see the watershed segmentation unittest in the source.</p>

<h3>Context objects</h3>

<p class=MsoNormal>ThreadWeave adds a thin wrapper around native
pycuda/pyopencl context objects. This is useful for abstracting away some of the
superficial differences between the two, as well as hiding some of their rather
C-like characteristics behind a more pythonic interface. This context object
aims to be a work-alike of the numpy namespace, providing a comprehensive
toolbox of functionality in a familiar interface. For more information, see
ThreadPy.</p>

<p class=MsoNormal><o:p>&nbsp;</o:p></p>

<h2>Frontend Syntax</h2>

<p class=MsoNormal>ThreadWeave at present supports several front-end syntaxes
for accessing its functionality; a general imperative syntax, which allows for
the most flexibility, and two more derived ways of declaring stencils, for pure
elementwise kernels and tensor products.</p>

<h3>General imperative syntax</h3>

<p class=MsoNormal>The imperative syntax is largely familiar C code, with some
extensions. The most visible difference is in the signature of the kernel
declaration. Fully writing out all details of this syntax is more cluttered
than just reading the relevant parser definitions in the source (which is quite
concise and readable, thanks to pyparsing), and arguably the syntax is most
easily grasped by looking at the examples, but nonetheless, a coarse
description of the syntax is given here.</p>

<p class=MsoNormal>The global structure of the syntax is thus: </p>

<p class=MsoNormal><span style='font-size:8.0pt;line-height:115%;font-family:
"Courier New"'>Colon_terminated_signature_line:<o:p></o:p></span></p>

<p class=MsoNormal style='text-indent:.5in'><span style='font-size:8.0pt;
line-height:115%;font-family:"Courier New"'>Indented_annotations_block<o:p></o:p></span></p>

<p class=MsoNormal><span style='font-size:8.0pt;line-height:115%;font-family:
"Courier New"'>Curly_braced_body<o:p></o:p></span></p>

<p class=MsoNormal>The signature has the following grammar:</p>

<p class=MsoNormal><span style='font-family:"Courier New"'>(output arguments)
&lt;&lt; [kernel axes] &lt;&lt; (input arguments)<o:p></o:p></span></p>

<p class=MsoNormal>Which is supposed to be read as �the input arguments mapped
over a kernel of the given shape yield the output arguments�.</p>

<p class=MsoNormal>Kernel axis identifiers should be a single lowercase
character. Constraints on the size of the axis can be written inline with their
declaration.</p>

<p class=MsoNormal>Arguments have the form <span style='font-family:"Courier New"'>typename[array
axes] array_identifier</span>, with an optional assignment of default values
for output arguments (constants value or copy of input argument).</p>

<p class=MsoNormal>The array and axes identifiers declared in the signature can
be further specified with annotations in the proceeding annotations section.</p>

<p class=MsoNormal>For axes, we can specify an iteration mode (serial,
parallel, hybrid), and binding behavior (compile-time or run-time). By default,
templated size arguments bind at compile time; this leads to less arguments to
pass in, and enables more compiler optimizations. However, while kernels are
typically called often with the same size parameters, this need not be the
case, and template arguments can be annotated as variable, to defer binding of
their size value to runtime, to avoid excessive compilation overhead.</p>

<p class=MsoNormal>For arrays, the only possible annotation is in specifying a
boundary handling method for now, but more features are planned, such the
ability to specify caching behavior.</p>

<p class=MsoNormal>The syntax was designed so that the signature prominently
displays the important information, being the public interface of the kernel,
as well as lucidly summarizing the relationship between the nd-kernel and the
nd-arrays it acts upon. The annotation section defines additional properties of
axes and arrays declared on the signature line. It would be possible to allow such
annotations to be written inline with the signature, but considering the number
of possible (future) keywords, this could get rather cluttered; plus these
annotations are at most of secondary semantic significance; more about the how
than the what.</p>

<p class=MsoNormal>The last section is the kernel body. Any valid C code is
valid body code, but in addition, a set of preprocessing transformations are
applied. The recognized constructs are:</p>

<p class=MsoListParagraphCxSpFirst style='margin-left:20.65pt;mso-add-space:
auto;text-indent:-.25in;mso-list:l1 level1 lfo1'><![if !supportLists]><span
style='mso-ascii-font-family:Calibri;mso-fareast-font-family:Calibri;
mso-hansi-font-family:Calibri;mso-bidi-font-family:Calibri'><span
style='mso-list:Ignore'>-<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span></span></span><![endif]>Array indexing <span style='mso-tab-count:1'>        </span>(round
brackets, to avoid conflicts with native C indexing)</p>

<p class=MsoListParagraphCxSpMiddle style='margin-left:20.65pt;mso-add-space:
auto;text-indent:-.25in;mso-list:l1 level1 lfo1'><![if !supportLists]><span
style='mso-ascii-font-family:Calibri;mso-fareast-font-family:Calibri;
mso-hansi-font-family:Calibri;mso-bidi-font-family:Calibri'><span
style='mso-list:Ignore'>-<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span></span></span><![endif]>Array properties <span style='mso-tab-count:
1'>     </span>(.shape[], .strides[], .size, andsoforth)</p>

<p class=MsoListParagraphCxSpMiddle style='margin-left:20.65pt;mso-add-space:
auto;text-indent:-.25in;mso-list:l1 level1 lfo1'><![if !supportLists]><span
style='mso-ascii-font-family:Calibri;mso-fareast-font-family:Calibri;
mso-hansi-font-family:Calibri;mso-bidi-font-family:Calibri'><span
style='mso-list:Ignore'>-<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span></span></span><![endif]>Stencil iteration <span style='mso-tab-count:
1'>      </span>(�for voxel_id in stencil_id) {}�)</p>

<p class=MsoListParagraphCxSpMiddle style='margin-left:20.65pt;mso-add-space:
auto;text-indent:-.25in;mso-list:l1 level1 lfo1'><![if !supportLists]><span
style='mso-ascii-font-family:Calibri;mso-fareast-font-family:Calibri;
mso-hansi-font-family:Calibri;mso-bidi-font-family:Calibri'><span
style='mso-list:Ignore'>-<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span></span></span><![endif]>Voxel properties<span style='mso-tab-count:1'>      </span>(voxel_id.axis_id,
voxel_id.weight)</p>

<p class=MsoListParagraphCxSpMiddle style='margin-left:20.65pt;mso-add-space:
auto;text-indent:-.25in;mso-list:l1 level1 lfo1'><![if !supportLists]><span
style='mso-ascii-font-family:Calibri;mso-fareast-font-family:Calibri;
mso-hansi-font-family:Calibri;mso-bidi-font-family:Calibri'><span
style='mso-list:Ignore'>-<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span></span></span><![endif]>Stencil properties <span style='mso-tab-count:
1'>   </span>(stencil_id.size &lt;- gives number of active (non-masked) voxels)</p>

<p class=MsoListParagraphCxSpMiddle style='margin-left:20.65pt;mso-add-space:
auto;text-indent:-.25in;mso-list:l1 level1 lfo1'><![if !supportLists]><span
style='mso-ascii-font-family:Calibri;mso-fareast-font-family:Calibri;
mso-hansi-font-family:Calibri;mso-bidi-font-family:Calibri'><span
style='mso-list:Ignore'>-<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span></span></span><![endif]>Integer range iteration (�for (dummy in
0:array_id.shape[1])�)</p>

<p class=MsoListParagraphCxSpMiddle style='margin-left:20.65pt;mso-add-space:
auto;text-indent:-.25in;mso-list:l1 level1 lfo1'><![if !supportLists]><span
style='mso-ascii-font-family:Calibri;mso-fareast-font-family:Calibri;
mso-hansi-font-family:Calibri;mso-bidi-font-family:Calibri'><span
style='mso-list:Ignore'>-<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span></span></span><![endif]>Numpythonic type names<span style='mso-tab-count:
1'>    </span>(�uint64� just looks so much better than �unsigned long long�)</p>

<p class=MsoListParagraphCxSpMiddle style='margin-left:20.65pt;mso-add-space:
auto;text-indent:-.25in;mso-list:l1 level1 lfo1'><![if !supportLists]><span
style='mso-ascii-font-family:Calibri;mso-fareast-font-family:Calibri;
mso-hansi-font-family:Calibri;mso-bidi-font-family:Calibri'><span
style='mso-list:Ignore'>-<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span></span></span><![endif]>Template types<span style='mso-tab-count:1'>       </span>(angle
bracketed template identifiers. To be used in both body and signature)</p>

<p class=MsoListParagraphCxSpLast style='margin-left:20.65pt;mso-add-space:
auto;text-indent:-.25in;mso-list:l1 level1 lfo1'><![if !supportLists]><span
style='mso-ascii-font-family:Calibri;mso-fareast-font-family:Calibri;
mso-hansi-font-family:Calibri;mso-bidi-font-family:Calibri'><span
style='mso-list:Ignore'>-<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span></span></span><![endif]>Backend-specific translations<span
style='mso-tab-count:1'>            </span>(atomic operations, synchronization
statements)</p>

<h3>Elementwise kernels</h3>

<p class=MsoNormal>This provides an nd-array aware, and thus broadcastable
equivalent of pycuda/pyopencl elementwise kernels. Basic usage is shown in the
examples folder. </p>

<h3>Tensor products</h3>

<p class=MsoNormal>The syntax and use is entirely similar to numpy.einsum,
aside from the fact that ThreadWeave employs a separate declaration and
invocation stage. The syntax is likely to be enriched in the future, for
instance to cleanly specify axes size hints or iteration modes. So far this
function is more a demonstration of concept than something that is efficient in
many circumstances; though non-contracting products should work well enough.
Again, basic usage is demonstrated in the examples folder.</p>

<p class=MsoNormal><o:p>&nbsp;</o:p></p>

<h2>Software design</h2>

<p class=MsoNormal>Here is a short conceptual description of the classes in
ThreadWeave</p>

<p class=MsoNormal>Class overview:</p>

<p class=MsoListParagraphCxSpFirst style='text-indent:-.25in;mso-list:l0 level1 lfo2'><![if !supportLists]><span
style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
Symbol'><span style='mso-list:Ignore'>·<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span></span></span><![endif]>KernelDeclaration: Contains all information that
defines the kernel. It provides a rich set of accessor properties, such that
other pieces of code that depend on it, like the CodeGenerator and runtime
components, can be written in a readable and safe manner. Also, it presents an
interface for building declaration objects in a concise and consistent manner;
see parsing_tensor.py and parsing_declaration.py for an example of use. <br>
Building KernelDeclarations in end-user code is entirely possible as well, but
so far the power of the front-end declaration language has been able to keep
pace with the features in the KernelDeclaration, so there should not be any
real use for this.</p>

<p class=MsoListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l0 level1 lfo2'><![if !supportLists]><span
style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
Symbol'><span style='mso-list:Ignore'>·<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span></span></span><![endif]>KernelFactory: The public Kernel interface one
is dealing with in typical use. It transparently handles JIT compilation of its
associated KernelDeclaration, based on inferred or explicitly specified
template arguments.</p>

<p class=MsoListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l0 level1 lfo2'><![if !supportLists]><span
style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
Symbol'><span style='mso-list:Ignore'>·<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span></span></span><![endif]>KernelInstance: Kernel object compiled against a
complete set of template arguments. It provides methods for runtime argument
checking, collection of required runtime arguments, and automatic thread/block
assignment.</p>

<p class=MsoListParagraphCxSpLast style='text-indent:-.25in;mso-list:l0 level1 lfo2'><![if !supportLists]><span
style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
Symbol'><span style='mso-list:Ignore'>·<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span></span></span><![endif]>CodeGenerator: class responsible for translating
a KernelDeclaration into valid backend-specific code. Most lines of code are in
a general C_Code_Generator baseclass; the parts which are backend specific are
delegated to subclasses.</p>

<p class=MsoNormal><o:p>&nbsp;</o:p></p>

<h2>Relation to other projects</h2>

<p class=MsoNormal>In terms of overall intent and approach, ThreadWeave is most
similar to scipy.weave, which is where it derives its name from. ThreadWeave is
built as a layer on top of pycuda and pyopencl; infact, ThreadWeave was
inspired by the elementwise function from these packages, which is similar in
intent, if much more limited in functionality.</p>

<p class=MsoNormal>There exist many python libraries for facilitating SIMD
programming with higher level concepts; notable ones are Loo.py, Theano,
copperhead (seems to be inactive), and CUDA Thrust (as used within pycuda).</p>

<p class=MsoNormal>They all share an intention to bring functional programming
techniques to the GPU; which is a sensible aim, given the highly formulaic nature
of much C SIMD code. However, not every SIMD programming problem can be
naturally expressed in a functional framework, and often some hacky C code is
the more natural solution, especially considering the performance oriented
nature of most applications. Most of the repetitive nature of kernel code can
be eliminated with a simple C preprocessor, which is the approach ThreadWeave
takes. If you cannot fit your problem into one of ThreadWeave abstractions,
that does not mean it is back to square one of plain old C; you simply handcode
that part, while still enjoying its other conveniences. This is the niche that
ThreadWeave aims to fill.</p>

<p class=MsoNormal>ThreadWeave aspires to expand its higher level and more
functional layer in the future. It is my hope that ThreadWeave and loo.py become
integrated. They both have their own application domains, but they also share a
lot of functionality and intent. Ideally, loo.py could be built on top of
ThreadWeave, relying on it for backend independence, front end syntax, nd-array
handling and other basics like JIT-compilation of template arguments, while
bringing its excellent functional programming capabilities to a wider audience.
</p>

<p class=MsoNormal>Theano in turn, (another python package much beloved by me) might
in an ideal world be built on top of such a software stack. At present the
Theano development team has to maintain its own GPU nd-array kernel code, while
without a doubt, that is a cause worthy of its own development team. Whether it
comes to the point where this package will be general and robust enough to
serve such needs, I do not know, but this is certainly the direction that I
believe this project should take.</p>

<h2><o:p>&nbsp;</o:p></h2>

<h2>Planned functionality</h2>

<p class=MsoNormal>This project has so far been a one man effort. It has gone
through several rewrites from the ground up, and I would not be surprised if it
went through a few more, after going public and receiving feedback. At present,
ThreadWeave does what I set out for it to do, but as it has become a bit of a
goal in itself, I expect to be actively developing it in the future. </p>

<p class=MsoNormal>Here is a short list of the functionality I feel is
currently missing, and which I might add in the near future, or would encourage
others to help with; but I am sure many obvious features are missing, and your
input is much appreciated:</p>

<p class=MsoListParagraphCxSpFirst style='margin-left:20.65pt;mso-add-space:
auto;text-indent:-.25in;mso-list:l1 level1 lfo1'><![if !supportLists]><span
style='mso-ascii-font-family:Calibri;mso-fareast-font-family:Calibri;
mso-hansi-font-family:Calibri;mso-bidi-font-family:Calibri'><span
style='mso-list:Ignore'>-<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span></span></span><![endif]>A natural way to include auxiliary functions, or
other pieces of C code. Of course one can just append anything desirable to the
source string, but it would be nice to have the ability to pass arrays around,
and so forth. </p>

<p class=MsoListParagraphCxSpMiddle style='margin-left:20.65pt;mso-add-space:
auto;text-indent:-.25in;mso-list:l1 level1 lfo1'><![if !supportLists]><span
style='mso-ascii-font-family:Calibri;mso-fareast-font-family:Calibri;
mso-hansi-font-family:Calibri;mso-bidi-font-family:Calibri'><span
style='mso-list:Ignore'>-<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span></span></span><![endif]>Support for arbitrarily strided arrays. This
should be a breeze to add, once the latest compyte nd-array is merged with
pycuda and pyopencl. Also, if such is supported, it would be good to be able to
place declarative constraints on the ordering of arrays; either to ensure an
input argument has the expected layout, and cast or raise otherwise, or to
allocate an output array in a specific manner. Control over strides is
important, considering their implications for memory coalescing.</p>

<p class=MsoListParagraphCxSpMiddle style='margin-left:20.65pt;mso-add-space:
auto;text-indent:-.25in;mso-list:l1 level1 lfo1'><![if !supportLists]><span
style='mso-ascii-font-family:Calibri;mso-fareast-font-family:Calibri;
mso-hansi-font-family:Calibri;mso-bidi-font-family:Calibri'><span
style='mso-list:Ignore'>-<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span></span></span><![endif]>Support for various array caching schemes. Two
very common cases come to mind where shared memory makes the difference, and
which should not be too hard to generalize and abstract away: a front of
threads iterating through an array to perform a stencil operation, and matrix
multiplication or transpose type operations. Also, small and frequently
accessed arrays may be hoisted into shared mem entirely, to take pressure off
the cache.</p>

<p class=MsoListParagraphCxSpMiddle style='margin-left:20.65pt;mso-add-space:
auto;text-indent:-.25in;mso-list:l1 level1 lfo1'><![if !supportLists]><span
style='mso-ascii-font-family:Calibri;mso-fareast-font-family:Calibri;
mso-hansi-font-family:Calibri;mso-bidi-font-family:Calibri'><span
style='mso-list:Ignore'>-<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span></span></span><![endif]>Support for arrays of structs, and structs of
arrays. That includes complex arrays of both kinds. It would be nice if both
were supported elegantly on both the python and kernel side of things; ie,
automatic struct declaration generation from the python typedef, and structs of
arrays being passable into the function as a single entity. Perhaps it is a bit
too voodoo, but there is something to be said for translating
array_id[index].field to array_id_field[index] if array_id is a struct of
arrays, so memory layout can be switched declaratively, without changing a
single line of body code, analogous to the way strides abstract away memory layout.</p>

<p class=MsoListParagraphCxSpMiddle style='margin-left:20.65pt;mso-add-space:
auto;text-indent:-.25in;mso-list:l1 level1 lfo1'><![if !supportLists]><span
style='mso-ascii-font-family:Calibri;mso-fareast-font-family:Calibri;
mso-hansi-font-family:Calibri;mso-bidi-font-family:Calibri'><span
style='mso-list:Ignore'>-<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span></span></span><![endif]>A rich way of specifying symbolic constraints
between axes sizes. At present, only equal and constant size constraints are
fully supported. But it would be nice to support arbitrary arithmetic relations
and inequalities between the array and kernel axes; for instance, when tiling
an array, the output dimensions are N times the input dimensions; when
differentiating along an axis, that dimension shrinks by one; and so forth (the
latter can actually be expressed as a stencil operation, size constraints and
all). One could use sympy to solve these symbolic relations at declaration time
for the missing quantities, and derive explicit expressions that can
efficiently be evaluated by the runtime components.</p>

<p class=MsoListParagraphCxSpMiddle style='margin-left:20.65pt;mso-add-space:
auto;text-indent:-.25in;mso-list:l1 level1 lfo1'><![if !supportLists]><span
style='mso-ascii-font-family:Calibri;mso-fareast-font-family:Calibri;
mso-hansi-font-family:Calibri;mso-bidi-font-family:Calibri'><span
style='mso-list:Ignore'>-<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span></span></span><![endif]>Improvements to grid and block allocations. The
current implementation works, but is not particularly intelligent. Considering
how problem dependent this is, there should probably be the option to choose
from different strategies during kernel declaration, and provide a manual
override as well.</p>

<p class=MsoListParagraphCxSpMiddle style='margin-left:20.65pt;mso-add-space:
auto;text-indent:-.25in;mso-list:l1 level1 lfo1'><![if !supportLists]><span
style='mso-ascii-font-family:Calibri;mso-fareast-font-family:Calibri;
mso-hansi-font-family:Calibri;mso-bidi-font-family:Calibri'><span
style='mso-list:Ignore'>-<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span></span></span><![endif]>Provide virtual parallel axes. CUDA supports
only up to three parallel axes (or two for old hardware). It has not been a
practical concern yet, but there should not be a limit to their number. If
there are more parallel axes than hardware axes, multiple axes should be packed
into a single hardware axis. Similarly; the length of any particular axis
should not be limited by hardware constraints, and should be virtualized where
necessary.</p>

<p class=MsoListParagraphCxSpLast style='margin-left:20.65pt;mso-add-space:
auto;text-indent:-.25in;mso-list:l1 level1 lfo1'><![if !supportLists]><span
style='mso-ascii-font-family:Calibri;mso-fareast-font-family:Calibri;
mso-hansi-font-family:Calibri;mso-bidi-font-family:Calibri'><span
style='mso-list:Ignore'>-<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span></span></span><![endif]>Provide syntax to explicitly structure code involving
serial axes iteration. By default, the whole kernel is the loop body, but we
may wish to place code before, in, or after any given axis loop. Something like
�axis(axis_identifier) {body}� should do the trick, where this construct is
translated into the actual for loop over the axis, or is simply taken out in
case of a parallel axis.<br>
It is probably more typical to wish to structure code relative to the whole of
all serial axes iteration though (declaring a dummy, serially reducing, and
then atomically reducing an array comes to mind). Just �for {body}� or
something like it should work for that. Both syntaxes could coexist.</p>

<h2>Acknowledgement</h2>

<p class=MsoNormal>Andreas Kloenckner, of pycuda and pyopencl fame, which makes
all of this possible.</p>

<p class=MsoNormal>Paul McGuire, for the awesome pyparsing, without which
starting a project of this kind would never have crossed my mind.</p>

<p class=MsoNormal>And the terrific python community as a whole, whom I hope to
repay a small part of my debt to.</p>

<h2>Terms of use</h2>

<p class=MsoNormal>To do with as you please. Acknowledgement or citations, where
applicable, are appreciated. Ideas and suggestions for improvements are always
welcome, as are actual improvements themselves.</p>

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