Parallel Algorithms¶

Element-wise expression evalution (“map”)¶

Evaluating involved expressions on pyopencl.array.Array instances by using overloaded operators can be somewhat inefficient, because a new temporary is created for each intermediate result. The functionality in the module pyopencl.elementwise contains tools to help generate kernels that evaluate multi-stage expressions on one or several operands in a single pass.

class pyopencl.elementwise.ElementwiseKernel(context, arguments, operation, name='kernel', preamble='', options=[])¶

A kernel that takes a number of scalar or vector arguments and performs an operation specified as a snippet of C on these arguments.

Parameters

arguments – a string formatted as a C argument list.
operation – a snippet of C that carries out the desired ‘map’ operation. The current index is available as the variable i. operation may contain the statement PYOPENCL_ELWISE_CONTINUE, which will terminate processing for the current element.
name – the function name as which the kernel is compiled
options – passed unmodified to pyopencl.Program.build().
preamble – a piece of C source code that gets inserted outside of the function context in the elementwise operation’s kernel source code.

Warning

Using a return statement in operation will lead to incorrect results, as some elements may never get processed. Use PYOPENCL_ELWISE_CONTINUE instead.

Changed in version 2013.1: Added PYOPENCL_ELWISE_CONTINUE.

__call__(*args, wait_for=None)¶

Invoke the generated scalar kernel. The arguments may either be scalars or pyopencl.array.Array instances.

Returns a new pyopencl.Event. wait_for may either be None or a list of pyopencl.Event instances for whose completion this command waits before starting exeuction.

Here’s a usage example:

#!/usr/bin/env python3

import numpy as np
import pyopencl as cl
import pyopencl.array
from pyopencl.elementwise import ElementwiseKernel

n = 10
a_np = np.random.randn(n).astype(np.float32)
b_np = np.random.randn(n).astype(np.float32)

ctx = cl.create_some_context()
queue = cl.CommandQueue(ctx)

a_g = cl.array.to_device(queue, a_np)
b_g = cl.array.to_device(queue, b_np)

lin_comb = ElementwiseKernel(ctx,
    "float k1, float *a_g, float k2, float *b_g, float *res_g",
    "res_g[i] = k1 * a_g[i] + k2 * b_g[i]",
    "lin_comb")

res_g = cl.array.empty_like(a_g)
lin_comb(2, a_g, 3, b_g, res_g)

# Check on GPU with PyOpenCL Array:
print((res_g - (2 * a_g + 3 * b_g)).get())

# Check on CPU with Numpy:
res_np = res_g.get()
print(res_np - (2 * a_np + 3 * b_np))
print(np.linalg.norm(res_np - (2 * a_np + 3 * b_np)))

(You can find this example as examples/demo_elementwise.py in the PyOpenCL distribution.)

Sums and counts (“reduce”)¶

class pyopencl.reduction.ReductionKernel(ctx, dtype_out, neutral, reduce_expr, map_expr=None, arguments=None, name='reduce_kernel', options=[], preamble='')¶

Generate a kernel that takes a number of scalar or vector arguments (at least one vector argument), performs the map_expr on each entry of the vector argument and then the reduce_expr on the outcome of that. neutral serves as an initial value. preamble offers the possibility to add preprocessor directives and other code (such as helper functions) to be added before the actual reduction kernel code.

Vectors in map_expr should be indexed by the variable i. reduce_expr uses the formal values “a” and “b” to indicate two operands of a binary reduction operation. If you do not specify a map_expr, in[i] is automatically assumed and treated as the only one input argument.

dtype_out specifies the numpy.dtype in which the reduction is performed and in which the result is returned. neutral is specified as float or integer formatted as string. reduce_expr and map_expr are specified as string formatted operations and arguments is specified as a string formatted as a C argument list. name specifies the name as which the kernel is compiled. options are passed unmodified to pyopencl.Program.build(). preamble specifies a string of code that is inserted before the actual kernels.

__call__(*args, queue=None, wait_for=None, return_event=False, out=None)¶

wait_for may either be None or a list of pyopencl.Event instances for whose completion this command waits before starting exeuction.

With out the resulting single-entry pyopencl.array.Array can be specified. Because offsets are supported one can store results anywhere (e.g. out=a[3]).

Returns: the resulting scalar as a single-entry pyopencl.array.Array if return_event is False, otherwise a tuple (scalar_array, event).

Note

The returned pyopencl.Event corresponds only to part of the execution of the reduction. It is not suitable for profiling.

New in version 2011.1.

Changed in version 2014.2: Added out parameter.

Here’s a usage example:

a = pyopencl.array.arange(queue, 400, dtype=numpy.float32)
b = pyopencl.array.arange(queue, 400, dtype=numpy.float32)

krnl = ReductionKernel(ctx, numpy.float32, neutral="0",
        reduce_expr="a+b", map_expr="x[i]*y[i]",
        arguments="__global float *x, __global float *y")

my_dot_prod = krnl(a, b).get()

Prefix Sums (“scan”)¶

A prefix sum is a running sum of an array, as provided by e.g. numpy.cumsum():

>>> import numpy as np
>>> a = [1,1,1,1,1,2,2,2,2,2]
>>> np.cumsum(a)
array([ 1,  2,  3,  4,  5,  7,  9, 11, 13, 15])

This is a very simple example of what a scan can do. It turns out that scans are significantly more versatile. They are a basic building block of many non-trivial parallel algorithms. Many of the operations enabled by scans seem difficult to parallelize because of loop-carried dependencies.

Usage Example¶

This example illustrates the implementation of a simplified version of pyopencl.algorithm.copy_if(), which copies integers from an array into the (variable-size) output if they are greater than 300:

knl = GenericScanKernel(
        ctx, np.int32,
        arguments="__global int *ary, __global int *out",
        input_expr="(ary[i] > 300) ? 1 : 0",
        scan_expr="a+b", neutral="0",
        output_statement="""
            if (prev_item != item) out[item-1] = ary[i];
            """)

out = a.copy()
knl(a, out)

a_host = a.get()
out_host = a_host[a_host > 300]

assert (out_host == out.get()[:len(out_host)]).all()

The value being scanned over is a number of flags indicating whether each array element is greater than 300. These flags are computed by input_expr. The prefix sum over this array gives a running count of array items greater than 300. The output_statement the compares prev_item (the previous item’s scan result, i.e. index) to item (the current item’s scan result, i.e. index). If they differ, i.e. if the predicate was satisfied at this position, then the item is stored in the output at the computed index.

This example does not make use of the following advanced features also available in PyOpenCL:

Segmented scans
Access to the previous item in input_expr (e.g. for comparisons) See the implementation of pyopencl.algorithm.unique() for an example.

Making Custom Scan Kernels¶

New in version 2013.1.

class pyopencl.scan.GenericScanKernel(ctx, dtype, arguments, input_expr, scan_expr, neutral, output_statement, is_segment_start_expr=None, input_fetch_exprs=None, index_dtype=<class 'numpy.int32'>, name_prefix='scan', options=None, preamble='', devices=None)¶

Generates and executes code that performs prefix sums (“scans”) on arbitrary types, with many possible tweaks.

Usage example:

from pyopencl.scan import GenericScanKernel
knl = GenericScanKernel(
        context, np.int32,
        arguments="__global int *ary",
        input_expr="ary[i]",
        scan_expr="a+b", neutral="0",
        output_statement="ary[i+1] = item;")

a = cl.array.arange(queue, 10000, dtype=np.int32)
knl(a, queue=queue)

__call__(*args, allocator=None, queue=None, size=None, wait_for=None)¶

queue and allocator default to the ones provided on the first pyopencl.array.Array in args. size may specify the length of the scan to be carried out. If not given, this length is inferred from the first array argument passed.

Returns a new pyopencl.Event. wait_for may either be None or a list of pyopencl.Event instances for whose completion this command waits before starting exeuction.

Note

The returned pyopencl.Event corresponds only to part of the execution of the scan. It is not suitable for profiling.

Debugging aids¶

class pyopencl.scan.GenericDebugScanKernel¶: Performs the same function and has the same interface as GenericScanKernel, but uses a dead-simple, sequential scan. Works best on CPU platforms, and helps isolate bugs in scans by removing the potential for issues originating in parallel execution.

Simple / Legacy Interface¶

class pyopencl.scan.ExclusiveScanKernel(ctx, dtype, scan_expr, neutral, name_prefix='scan', options=[], preamble='', devices=None)¶

Generates a kernel that can compute a prefix sum using any associative operation given as scan_expr. scan_expr uses the formal values “a” and “b” to indicate two operands of an associative binary operation. neutral is the neutral element of scan_expr, obeying scan_expr(a, neutral) == a.

dtype specifies the type of the arrays being operated on. name_prefix is used for kernel names to ensure recognizability in profiles and logs. options is a list of compiler options to use when building. preamble specifies a string of code that is inserted before the actual kernels. devices may be used to restrict the set of devices on which the kernel is meant to run. (defaults to all devices in the context ctx.

__call__(self, input_ary, output_ary=None, allocator=None, queue=None)¶

class pyopencl.scan.InclusiveScanKernel(ctx, dtype, scan_expr, neutral=None, name_prefix='scan', options=[], preamble='', devices=None)¶: Works like ExclusiveScanKernel.

Changed in version 2013.1: neutral is now always required.

For the array [1,2,3], inclusive scan results in [1,3,6], and exclusive scan results in [0,1,3].

Here’s a usage example:

knl = InclusiveScanKernel(context, np.int32, "a+b")

n = 2**20-2**18+5
host_data = np.random.randint(0, 10, n).astype(np.int32)
dev_data = cl_array.to_device(queue, host_data)

knl(dev_data)
assert (dev_data.get() == np.cumsum(host_data, axis=0)).all()

Predicated copies (“partition”, “unique”, …)¶

pyopencl.algorithm.copy_if(ary, predicate, extra_args=None, preamble='', queue=None, wait_for=None)¶

Copy the elements of ary satisfying predicate to an output array.

Parameters

predicate – a C expression evaluating to a bool, represented as a string. The value to test is available as ary[i], and if the expression evaluates to true, then this value ends up in the output.
extra_args – a list of tuples (name, value) specifying extra arguments to pass to the scan procedure. For version 2013.1, value must be a of a numpy sized scalar type. As of version 2013.2, value may also be a pyopencl.array.Array.
preamble – A snippet of C that is inserted into the compiled kernel before the actual kernel function. May be used for, e.g. type definitions or include statements.
wait_for – wait_for may either be None or a list of pyopencl.Event instances for whose completion this command waits before starting exeuction.

Returns

a tuple (out, count, event) where out is the output array, count is an on-device scalar (fetch to host with count.get()) indicating how many elements satisfied predicate, and event is a pyopencl.Event for dependency management. out is allocated to the same length as ary, but only the first count entries carry meaning.

New in version 2013.1.

pyopencl.algorithm.remove_if(ary, predicate, extra_args=None, preamble='', queue=None, wait_for=None)¶

Copy the elements of ary not satisfying predicate to an output array.

Parameters

predicate – a C expression evaluating to a bool, represented as a string. The value to test is available as ary[i], and if the expression evaluates to false, then this value ends up in the output.
extra_args – a list of tuples (name, value) specifying extra arguments to pass to the scan procedure. For version 2013.1, value must be a of a numpy sized scalar type. As of version 2013.2, value may also be a pyopencl.array.Array.
preamble – A snippet of C that is inserted into the compiled kernel before the actual kernel function. May be used for, e.g. type definitions or include statements.
wait_for – wait_for may either be None or a list of pyopencl.Event instances for whose completion this command waits before starting exeuction.

Returns

a tuple (out, count, event) where out is the output array, count is an on-device scalar (fetch to host with count.get()) indicating how many elements did not satisfy predicate, and event is a pyopencl.Event for dependency management.

New in version 2013.1.

pyopencl.algorithm.partition(ary, predicate, extra_args=None, preamble='', queue=None, wait_for=None)¶

Copy the elements of ary into one of two arrays depending on whether they satisfy predicate.

Parameters

predicate – a C expression evaluating to a bool, represented as a string. The value to test is available as ary[i].
extra_args – a list of tuples (name, value) specifying extra arguments to pass to the scan procedure. For version 2013.1, value must be a of a numpy sized scalar type. As of version 2013.2, value may also be a pyopencl.array.Array.
preamble – A snippet of C that is inserted into the compiled kernel before the actual kernel function. May be used for, e.g. type definitions or include statements.
wait_for – wait_for may either be None or a list of pyopencl.Event instances for whose completion this command waits before starting exeuction.

Returns

a tuple (out_true, out_false, count, event) where count is an on-device scalar (fetch to host with count.get()) indicating how many elements satisfied the predicate, and event is a pyopencl.Event for dependency management.

New in version 2013.1.

pyopencl.algorithm.unique(ary, is_equal_expr='a == b', extra_args=None, preamble='', queue=None, wait_for=None)¶

Copy the elements of ary into the output if is_equal_expr, applied to the array element and its predecessor, yields false.

Works like the UNIX command uniq, with a potentially custom comparison. This operation is often used on sorted sequences.

Parameters

is_equal_expr – a C expression evaluating to a bool, represented as a string. The elements being compared are available as a and b. If this expression yields false, the two are considered distinct.
extra_args – a list of tuples (name, value) specifying extra arguments to pass to the scan procedure. For version 2013.1, value must be a of a numpy sized scalar type. As of version 2013.2, value may also be a pyopencl.array.Array.
preamble – A snippet of C that is inserted into the compiled kernel before the actual kernel function. May be used for, e.g. type definitions or include statements.
wait_for – wait_for may either be None or a list of pyopencl.Event instances for whose completion this command waits before starting exeuction.

Returns

a tuple (out, count, event) where out is the output array, count is an on-device scalar (fetch to host with count.get()) indicating how many elements satisfied the predicate, and event is a pyopencl.Event for dependency management.

New in version 2013.1.

Sorting (radix sort)¶

class pyopencl.algorithm.RadixSort(context, arguments, key_expr, sort_arg_names, bits_at_a_time=2, index_dtype=<class 'numpy.int32'>, key_dtype=<class 'numpy.uint32'>, scan_kernel=<class 'pyopencl.scan.GenericScanKernel'>, options=None)¶

Provides a general radix sort on the compute device.

Building many variable-size lists¶

class pyopencl.algorithm.ListOfListsBuilder(context, list_names_and_dtypes, generate_template, arg_decls, count_sharing=None, devices=None, name_prefix='plb_build_list', options=None, preamble='', debug=False, complex_kernel=False, eliminate_empty_output_lists=False)¶

Generates and executes code to produce a large number of variable-size lists, simply.

Note

This functionality is provided as a preview. Its interface is subject to change until this notice is removed.

New in version 2013.1.

Here’s a usage example:

from pyopencl.algorithm import ListOfListsBuilder
builder = ListOfListsBuilder(context, [("mylist", np.int32)], """
        void generate(LIST_ARG_DECL USER_ARG_DECL index_type i)
        {
            int count = i % 4;
            for (int j = 0; j < count; ++j)
            {
                APPEND_mylist(count);
            }
        }
        """, arg_decls=[])

result, event = builder(queue, 2000)

inf = result["mylist"]
assert inf.count == 3000
assert (inf.list.get()[-6:] == [1, 2, 2, 3, 3, 3]).all()

The function generate above is called once for each “input object”. Each input object can then generate zero or more list entries. The number of these input objects is given to __call__() as n_objects. List entries are generated by calls to APPEND_<list name>(value). Multiple lists may be generated at once.

__init__(context, list_names_and_dtypes, generate_template, arg_decls, count_sharing=None, devices=None, name_prefix='plb_build_list', options=None, preamble='', debug=False, complex_kernel=False, eliminate_empty_output_lists=False)¶

Parameters

context – A pyopencl.Context.
list_names_and_dtypes – a list of (name, dtype) tuples indicating the lists to be built.
generate_template – a snippet of C as described below
arg_decls – A string of comma-separated C argument declarations.
count_sharing – A mapping consisting of (child, mother) indicating that mother and child will always have the same number of indices, and the APPEND to mother will always happen before the APPEND to the child.
name_prefix – the name prefix to use for the compiled kernels
options – OpenCL compilation options for kernels using generate_template.
complex_kernel – If True, prevents vectorization on CPUs.
eliminate_empty_output_lists – A Python list of list names for which the empty output lists are eliminated.

generate_template may use the following C macros/identifiers:

index_type: expands to C identifier for the index type used for the calculation
USER_ARG_DECL: expands to the C declarator for arg_decls
USER_ARGS: a list of C argument values corresponding to user_arg_decl
LIST_ARG_DECL: expands to a C argument list representing the data for the output lists. These are escaped prefixed with “plg_” so as to not interfere with user-provided names.
LIST_ARGS: a list of C argument values corresponding to LIST_ARG_DECL
APPEND_name(entry): inserts entry into the list name. entry must be a valid C expression of the correct type.

All argument-list related macros have a trailing comma included if they are non-empty.

generate_template must supply a function:

void generate(USER_ARG_DECL LIST_ARG_DECL index_type i)
{
    APPEND_mylist(5);
}

Internally, the kernel_template is expanded (at least) twice. Once, for a ‘counting’ stage where the size of all the lists is determined, and a second time, for a ‘generation’ stage where the lists are actually filled. A generate function that has side effects beyond calling append is therefore ill-formed.

Changed in version 2018.1: Change eliminate_empty_output_lists argument type from bool to list.

__call__(queue, n_objects, *args, **kwargs)¶

Parameters

args – arguments corresponding to arg_decls in the constructor. Array-like arguments must be either 1D pyopencl.array.Array objects or pyopencl.MemoryObject objects, of which the latter can be obtained from a pyopencl.array.Array using the pyopencl.array.Array.data attribute.
allocator – optionally, the allocator to use to allocate new arrays.
omit_lists – An iterable of list names that should not be built with this invocation. The kernel code may not call APPEND_name for these omitted lists. If it does, undefined behavior will result. The returned lists dictionary will not contain an entry for names in omit_lists.
wait_for – wait_for may either be None or a list of pyopencl.Event instances for whose completion this command waits before starting exeuction.

Returns

a tuple (lists, event), where lists a mapping from (built) list names to objects which have attributes

count for the total number of entries in all lists combined
lists for the array containing all lists.
starts for the array of starting indices in lists. starts is built so that it has n+1 entries, so that the i’th entry is the start of the i’th list, and the i’th entry is the index one past the i’th list’s end, even for the last list.

This implies that all lists are contiguous.

If the list name is specified in eliminate_empty_output_lists constructor argument, lists has two additional attributes num_nonempty_lists and nonempty_indices

num_nonempty_lists for the number of nonempty lists.
nonempty_indices for the index of nonempty list in input objects.

In this case, starts has num_nonempty_lists + 1 entries. The i’s entry is the start of the i’th nonempty list, which is generated by the object with index nonempty_indices[i].

event is a pyopencl.Event for dependency management.

Changed in version 2016.2: Added omit_lists.

Bitonic Sort¶

class pyopencl.bitonic_sort.BitonicSort(context)¶

Sort an array (or one axis of one) using a sorting network.

Will only work if the axis of the array to be sorted has a length that is a power of 2.

New in version 2015.2.

Parallel Algorithms¶

Element-wise expression evalution (“map”)¶

Sums and counts (“reduce”)¶

Prefix Sums (“scan”)¶

Usage Example¶

Making Custom Scan Kernels¶

Debugging aids¶

Simple / Legacy Interface¶

Predicated copies (“partition”, “unique”, …)¶

Sorting (radix sort)¶

Building many variable-size lists¶

Bitonic Sort¶

PyOpenCL

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