algorithm.rst

Parallel Algorithms

Element-wise expression evalution ("map")

Evaluating involved expressions on :class:`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 :mod:`pyopencl.elementwise` contains tools to help generate kernels that evaluate multi-stage expressions on one or several operands in a single pass.

Here's a usage example:

import pyopencl as cl
import pyopencl.array as cl_array
import numpy

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

n = 10
a_gpu = cl_array.to_device(
        ctx, queue, numpy.random.randn(n).astype(numpy.float32))
b_gpu = cl_array.to_device(
        ctx, queue, numpy.random.randn(n).astype(numpy.float32))

from pyopencl.elementwise import ElementwiseKernel
lin_comb = ElementwiseKernel(ctx,
        "float a, float *x, "
        "float b, float *y, "
        "float *z",
        "z[i] = a*x[i] + b*y[i]",
        "linear_combination")

c_gpu = cl_array.empty_like(a_gpu)
lin_comb(5, a_gpu, 6, b_gpu, c_gpu)

import numpy.linalg as la
assert la.norm((c_gpu - (5*a_gpu+6*b_gpu)).get()) < 1e-5

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

Sums and counts ("reduce")

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 :class:`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 :meth:`pyopencl.Program.build`. preamble specifies a string of code that is inserted before the actual kernels.

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. :mod:`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 :func:`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 :func:`unique` for an example.

Making Custom Scan Kernels

Debugging aids

Performs the same function and has the same interface as :class:`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

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.

Works like :class:`ExclusiveScanKernel`.

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", ...)

Sorting (radix sort)

Building many variable-size lists