# FFTW¶

Usage

use FFTW;


Submodules

FFT computations via key routines from FFTW (version 3)

This module defines Chapel wrappers for key 64-bit routines from FFTW (http://www.fftw.org), version 3. The routines in this module exposes the simple FFTW interface. The full C API may be accessed through the C_FFTW submodule. Over time, the intention is to expand these modules to support additional routines, prioritizing based on requests and feedback from users.

To use this module:

1. Ensure that FFTW (version 3) is installed on your system. The current version of the Chapel module only supports double precision real(64) transforms. We do support using the FFTW compatible wrappers provided by the Intel Math Kernel Library (MKL) (see below for usage).
2. Add use FFTW; to your Chapel code.
3. Include the appropriate libraries in your compilation command.
1. For a standard FFTW installation, this may be as simple as including -lfftw3 when compiling. You may also need to use the -I and -L flags to specify the locations of the header and library files if these are in non-standard locations.
2. Intel MKL : To use the MKL FFTW wrappers, compile with -sisFFTW_MKL to include the fftw3_mkl.h header in addition to the usual fftw3.h header file. You may also need to add -I\${MKLROOT}/include/fftw to point the compiler to the location of these header files. Refer to the Intel MKL documentation for the appropriate libraries to include.
4. If you wish to run FFTW in a multi-threaded mode:
1. Initialize FFTW for multithreaded support. You may do this by either setting the compile-time config parameter autoInitFFTW_MT to true or calling init_FFTW_MT.
2. Set the number of threads for subsequent FFTW plans with plan_with_nthreads. If you initialized automatically, this module defaults to using here.maxTaskPar. There is no limit on the number of times you can call plan_with_nthreads.
3. Link with the appropriate multi-threaded FFTW libraries.
4. Note the both init_FFTW_MT and plan_with_nthreads are multi-locale aware and will automatically run on all locales. However, the FFTW plans created by this routine are not distributed.
5. When all multi-threaded usage is complete, call cleanup_threads.

As in standard FFTW usage, the flow is to:

1. Create plan(s) using the plan_dft* routines.
2. Execute the plan(s) one or more times using execute.
3. Destroy the plan(s) using destroy_plan.
4. Cleanup, using cleanup (and cleanup_threads if multi-threaded).

Note that each of the Chapel plan_dft* routines support both in-place and out-of-place versions of the transforms, where the former versions use a single array for both input and output, and the latter use two distinct arrays.

In future versions of this module, we anticipate improving the plan_dft*() interfaces to make better use of Chapel features and move further away from C-isms (like the overloaded role of flags and the use of C-based types). Such features are expected to take advantage of Chapel's support for default argument values and keyword-based argument passing. We are also thinking about changing the interface for the in-place routines to use array slicing rather than separate arguments for the array and domain.

config param isFFTW_MKL = false

Set this to true if you are using the Intel MKL FFTW wrappers

config param autoInitFFTW_MT = false

Set this config parameter to true to automatically initialize FFTW for thread support, and setup FFTW to generate multi-threaded plans (with the number of threads equal to maxTaskPar in Chapel).

If you keep the default value of false, then call init_FFTW_MT() to initialize thread-support for Chapel.

Note that plan_with_nthreads can be called at any time and changes the number of threads used by plans created after the call.

config param noFFTWsizeChecks = false

Controls execution-time array size checks in the FFTW plan_dft routines (set to true to disable checks).

type fftw_plan

An opaque type used to store and reuse FFTW plans across multiple routines.

proc plan_dft(input: [?Din] complex(128), output: [?Dout] complex(128), sign: c_int, flags: c_uint): fftw_plan

Creates a plan for an out-of-place complex-to-complex DFT.

Arguments: input : [] complex(128) -- The input array, which can be of any rank output : [] complex(128) -- The output array, whose size and shape must match the input array's sign : c_int -- FFTW_FORWARD or FFTW_BACKWARD flags : c_int -- the bitwise-or of any planning-rigor or algorithm-restriction flags that should be used in creating the plan (e.g., FFTW_MEASURE | FFTW_PRESERVE_INPUT) The fftw_plan representing the resulting plan
proc plan_dft(arr: [] complex(128), sign: c_int, flags: c_uint): fftw_plan

Creates a plan for an in-place complex-to-complex DFT.

Arguments: arr : [] complex(128) -- The array to use as the in-place input/output array. sign : c_int -- FFTW_FORWARD or FFTW_BACKWARD flags : c_int -- the bitwise-or of any planning-rigor or algorithm-restriction flags that should be used in creating the plan (e.g., FFTW_MEASURE | FFTW_PRESERVE_INPUT) The fftw_plan representing the resulting plan
proc plan_dft_r2c(input: [?Din] real(64), output: [?Dout] complex(128), flags: c_uint): fftw_plan

Create a plan for a real-to-complex, out-of-place DFT.

Arguments: input : [] real(64) -- The input array, which can be of any rank output : [] complex(128) -- The output array, whose size and shape must match the input array's, except for the leading dimension which should be n/2 + 1, where n is the size of the input array's leading dimension. See the FFTW documentation for more information. flags : c_int -- the bitwise-or of any planning-rigor or algorithm-restriction flags that should be used in creating the plan (e.g., FFTW_MEASURE | FFTW_PRESERVE_INPUT) The fftw_plan representing the resulting plan
proc plan_dft_r2c(realDom: domain, arr: [?D] ?t, flags: c_uint): fftw_plan

Create a plan for a real-to-complex, in-place DFT.

Arguments: realDom : domain -- Describes the indices of the 'real' view of the array arr : [] T where T is of type real(64) or complex(128) -- The array to be used as the in-place input/output array. If passing in an array of real elements, the leading dimension of the array must be padded to store 2(n/2 + 1) elements, where n is the size of the corresponding dimension of realDom. If passing in an array of complex elements, the leading dimension should be (n/2 + 1). See the FFTW documentation for more information. flags : c_int -- the bitwise-or of any planning-rigor or algorithm-restriction flags that should be used in creating the plan (e.g., FFTW_MEASURE | FFTW_PRESERVE_INPUT) The fftw_plan representing the resulting plan
proc plan_dft_c2r(input: [?Din] complex(128), output: [?Dout] real(64), flags: c_uint): fftw_plan

Create a plan for a complex-to-real, out-of-place DFT.

Arguments: input : [] complex(128) -- The input array, whose size and shape must match the output array's, except for the leading dimension which should be n/2 + 1, where n is the size of the output array's leading dimension. See the FFTW documentation for more information. output : [] real(64) -- The output array flags : c_int -- the bitwise-or of any planning-rigor or algorithm-restriction flags that should be used in creating the plan (e.g., FFTW_MEASURE | FFTW_PRESERVE_INPUT) The fftw_plan representing the resulting plan
proc plan_dft_c2r(realDom: domain, arr: [?D] ?t, flags: c_uint): fftw_plan

Create a plan for a complex-to-real, in-place DFT.

Arguments: realDom : domain -- Describes the indices of the 'real' view of the array arr : [] T where T is of type real(64) or complex(128) -- The array to be used as the in-place input/output array. If passing in an array of real elements, the leading dimension of the array must be padded to store 2(n/2 + 1) elements, where n is the size of the corresponding dimension of realDom. If passing in an array of complex elements, the leading dimension should be (n/2 + 1). See the FFTW documentation for more information. flags : c_int -- the bitwise-or of any planning-rigor or algorithm-restriction flags that should be used in creating the plan (e.g., FFTW_MEASURE | FFTW_PRESERVE_INPUT) The fftw_plan representing the resulting plan
proc execute(const plan: fftw_plan)

Execute an FFTW plan.

Arguments: plan : fftw_plan -- The plan to execute, as computed by a plan_dft*() routine.
proc destroy_plan(plan: fftw_plan)

Destroy an FFTW plan.

Arguments: plan : fftw_plan -- The plan to destroy
proc cleanup()

Clean up FFTW overall.

const FFTW_FORWARD: c_int

Request a forward transform (i.e., use a negative exponent in the transform).

const FFTW_BACKWARD: c_int

Request a backward transform (i.e., use a positive exponent in the transform).

const FFTW_ESTIMATE: c_uint

Specify that a simple heuristic should be used to pick a plan quickly. This will prevent the input/output arrays from being overwritten during planning.

const FFTW_MEASURE: c_uint

Specify that FFTW should try and find an optimized plan by computing several FFTs and measuring their execution time. This can consume some time.

const FFTW_PATIENT: c_uint

Specify that FFTW should expend a greater effort finding an optimized plan.

const FFTW_EXHAUSTIVE: c_uint

Specify that FFTW should expend an even greater effort finding an optimized plan.

const FFTW_WISDOM_ONLY: c_uint

This is a special planning mode that is useful for querying whether wisdom is available. When using it, the plan is only created when wisdom is available for the given problem; otherwise a null plan is returned. This can be combined with other flags to create a plan if the wisdom available was created in that mode (e.g., FFTW_WISDOM_ONLY | FFTW_PATIENT). For more details on this flag and the previous four, refer to Section 4.3.2 of the FFTW manual

const FFTW_DESTROY_INPUT: c_uint

Specify that an out-of-place transform is permitted to overwrite its input array with arbitrary data. This permits more efficient algorithms to be used in some cases.

const FFTW_PRESERVE_INPUT: c_uint

Specify that an out-of-place transform cannot change its input array.

const FFTW_UNALIGNED: c_uint

Specify that the algorithm may not impose any unusual alignment requirements on the input/output arrays. This flag should not be necessary for current Chapel use since the planner will automatically detect such cases. For more details on this flag and the previous two, refer to Section 4.3.2 of the FFTW manual.

const FFTW_R2HC: c_int

Use the halfcomplex form of array storage

const FFTW_HC2R: c_int
const FFTW_DHT: c_int

Discrete Hartley Transforms.

const FFTW_REDFT00: c_int

Specify the type of discrete cosine and discrete sine transforms to use.

const FFTW_REDFT01: c_int
const FFTW_REDFT10: c_int
const FFTW_REDFT11: c_int
const FFTW_RODFT00: c_int
const FFTW_RODFT01: c_int
const FFTW_RODFT10: c_int
const FFTW_RODFT11: c_int
proc init_FFTW_MT()

Initialize the FFTW module to support multithreading. This has the effect of calling the FFTW C routine fftw_init_threads() on all locales, halting the Chapel program if any of the calls generate an error.

proc plan_with_nthreads(nthreads: int = 0)

Register the number of threads to use for multi-threaded FFTW plans on all locales. If fewer than one thread is requested, each locale will default to here.maxTaskPar threads. Note that this routine can be called multiple times, overwriting previous values.

Arguments: nthreads : int -- The number of threads to use.
proc cleanup_threads()

Clean up the memory used by FFTW threads on all locales.