FFT library for PyCuda and PyOpenCL
Project description
Introduction
This module contains implementation of batched FFT, ported from Apple’s OpenCL implementation. OpenCL’s ideology of constructing kernel code on the fly maps perfectly on PyCuda/PyOpenCL, and variety of Python’s templating engines makes code generation simpler. I used mako templating engine, simply because of the personal preference. The code can be easily changed to use any other engine.
Warning: “Cuda” part of pyfft requires PyCuda 0.94 or newer; “CL” part requires PyOpenCL 0.92 or newer.
Quick Start
The usage is quite simple. First, import numpy and plan creation interface from pyfft (let us use cuda in this example):
>>> from pyfft.cuda import Plan >>> import numpy
Since we are using Cuda, it must be initialized before any Cuda functions are called (by default, the plan will use existing context, but there are other possibilities; see reference entry for Plan for further information). In addition, we will need gpuarray module to pass data to and from GPU:
>>> from pycuda.tools import make_default_context >>> import pycuda.gpuarray as gpuarray >>> import pycuda.driver as cuda >>> cuda.init() >>> context = make_default_context()
Then the plan must be created. The creation is not very fast, mainly because of the compilation speed. But, fortunately, PyCuda and PyOpenCL cache compiled sources, so if you use the same plan for each run of your program, it will be created pretty fast.
>>> plan = Plan((16, 16))
Now, let’s prepare simple test array and try to execute plan over it:
>>> data = numpy.ones((16, 16), dtype=numpy.complex64)
>>> gpu_data = gpuarray.to_gpu(data)
>>> plan.execute(gpu_data)
>>> result = gpu_data.get()
>>> print result # doctest: +ELLIPSIS
[[ 256.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j
0.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j
0.+0.j 0.+0.j]
...
[ 0.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j
0.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j
0.+0.j 0.+0.j]]
As expected, we got array with the first non-zero element, equal to array size. Let’s now perform the inverse transform:
>>> plan.execute(gpu_data, inverse=True) >>> result = gpu_data.get()
Since data is non-integer, we cannot simply compare it. We will just calculate error instead.
>>> error = numpy.abs(numpy.sum(numpy.abs(data) - numpy.abs(result)) / data.size) >>> error < 1e-6 True
That’s good enough for single precision numbers.
Last step is releasing Cuda context:
>>> context.pop()
Reference
cuda.Plan, cl.Plan
Creates class, containing precalculated FFT plan.
Arguments: Plan(shape, dtype=numpy.complex64, mempool=None, context=None, normalize=True, wait_for_finish=None, fast_math=True, stream=None, queue=None)
- shape:
Problem size. Can be integer or tuple with 1, 2 or 3 integer elements. Each dimension must be a power of two.
Warning: 2D and 3D plans with y == 1 or z == 1 are not supported at the moment.
- dtype:
Numpy data type for input/output arrays. If complex data type is given, plan for interleaved arrays will be created. If scalar data type is given, plan will work for data arrays with separate real and imaginary parts. Depending on this parameter, execute() will have different signatures; see its reference entry for details.
Currently supported: numpy.complex64, numpy.float32 (single precision) and numpy.complex128, numpy.float64 (double precision).
- mempool:
Cuda-specific. If specified, method allocate of this object will be used to create temporary buffers.
- normalize:
Whether to normalize inverse FFT so that IFFT(FFT(signal)) == signal. If equals to False, IFFT(FFT(signal)) == signal * x * y * z.
- wait_for_finish:
Boolean variable, which tells whether it is necessary to wait on stream after scheduling all FFT kernels. Default value depends on context, stream and queue parameters — see Contexts and streams usage logic for details. Can be overridden by wait_for_finish parameter to execute()
- fast_math:
If True, additional compiler options will be used, which increase performance at the expense of accuracy. For Cuda it is -use_fast_math, for OpenCL — -cl-mad-enable and -cl-fast-relaxed-math. In addition, in case of OpenCL, native_cos and native_sin are used instead of cos and sin (Cuda uses intrinsincs automatically when -use_fast_math is set).
- context:
Context, which will be used to compile kernels and execute plan. See Contexts and streams usage logic entry for details.
- stream:
Cuda-specific. An object of class pycuda.driver.Stream, which will be used to schedule plan execution.
- queue:
OpenCL-specific. An object of class pyopencl.CommandQueue, which will be used to schedule plan execution.
Plan.execute()
Execute plan for interleaved data arrays. Signature depends on dtype given to constructor:
Interleaved: execute(data_in, data_out=None, inverse=False, batch=1, wait_for_finish=None)
Split: executeSplit(data_in_re, data_in_im, data_out_re=None, data_out_im=None, inverse=False, batch=1, wait_for_finish=None)
- data_in or data_in_re, data_in_im:
Input array(s). For Cuda plan PyCuda’s GPUArray or anything that can be cast to memory pointer is supported; for OpenCL Buffer objects are supported.
- data_out or data_out_re, data_out_im:
Output array(s). If not defined, the execution will be performed in-place and the results will be stored in data_in or data_in_re, data_in_im.
- inverse:
If True, inverse transform will be performed.
- batch:
Number of data sets to process. They should be located successively in data_in.
- wait_for_finish:
Whether to wait for scheduled FFT kernels to finish. Overrides setting, which was specified during plan creation.
- Returns
None if waiting for scheduled kernels; Stream or CommandQueue object otherwise. User is expected to handle this object with care, since it can be reused during the next call to execute().
Contexts and streams usage logic
Plan behavior can differ depending on values of context, stream/queue and wait_for_finish parameters. These differences should, in theory, make the module more convenient to use.
wait_for_finish parameter can be set on three levels. First, there is a default value which depends on context and stream/queue parameters (see details below). It can be overridden by explicitly passing it as an argument to constructor. This setting, in turn, can be overridden by passing wait_for_finish keyword to execute().
Cuda
context and stream are None:
Current (at the moment of plan creation) context and device will be used to create kernels.
Stream will be created internally and used for each execute() call.
Default value of wait_for_finish is True.
stream is not None:
context is ignored.
stream is remembered and used.
execute() will assume that context, corresponding to given stream is active at the time of the call.
Default value of wait_for_finish is False.
context is not None:
OpenCL
Either context or queue must be set.
queue is not None:
queue is remembered and used.
Target context and device are obtained from queue.
Default value of wait_for_finish is False.
context is not None:
context is remembered.
CommandQueue will be created internally and used for each execute() call.
Default value of wait_for_finish is True.
Performance
Here is the comparison to pure Cuda program using CUFFT. Since CUFFT supports batched FFT only for 1D, tests for other dimensions were performed using 1D FFT and matrix transposes (that’s why CUFFT performance is so non-uniform, but it is the only way of getting FFT for large batches). See cuda folder in distribution for details. Pyfft tests were executed with fast_math==True.
In the following tables “sp” stands for “single precision”, “dp” for “double precision”.
Mac OS 10.6.4, Python 3.1, Cuda 3.1, PyCuda 0.94, GF9600, 32 Mb buffer:
Problem size / GFLOPS |
CUFFT, sp |
pyfft, sp |
|---|---|---|
[16, 1, 1], batch 131072 |
1.61 |
7.63 |
[1024, 1, 1], batch 2048 |
16.54 |
15.71 |
[8192, 1, 1], batch 256 |
13.13 |
12.25 |
[16, 16, 1], batch 8192 |
1.65 |
10.04 |
[128, 128, 1], batch 128 |
15.08 |
15.14 |
[1024, 1024, 1], batch 2 |
14.80 |
13.38 |
[16, 16, 16], batch 512 |
1.77 |
11.42 |
[32, 32, 128], batch 16 |
5.32 |
15.65 |
[128, 128, 128], batch 1 |
12.27 |
14.53 |
CentOS 5.5, Python 2.6, Cuda 3.1, PyCuda 0.94, nVidia Tesla C1060, 32 Mb buffer:
Problem size / GFLOPS |
CUFFT, sp |
pyfft, sp |
CUFFT, dp |
pyfft, dp |
|---|---|---|---|---|
[16, 1, 1], batch 131072 |
99.83 |
81.17 |
27.16 |
11.02 |
[1024, 1, 1], batch 2048 |
206.27 |
185.73 |
38.05 |
11.98 |
[8192, 1, 1], batch 256 |
132.84 |
116.53 |
35.60 |
11.59 |
[16, 16, 1], batch 8192 |
4.97 |
90.04 |
3.14 |
14.04 |
[128, 128, 1], batch 128 |
71.03 |
127.53 |
22.64 |
15.80 |
[1024, 1024, 1], batch 2 |
49.71 |
122.26 |
17.45 |
11.75 |
[16, 16, 16], batch 512 |
6.77 |
93.40 |
4.17 |
15.25 |
[32, 32, 128], batch 16 |
25.66 |
127.94 |
11.02 |
14.85 |
[128, 128, 128], batch 1 |
52.26 |
115.22 |
16.35 |
15.30 |
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