# rocFFT#

## Introduction#

The rocFFT library is an implementation of the discrete Fast Fourier Transform (FFT) written in HIP for GPU devices. The code is open and hosted here: ROCmSoftwarePlatform/rocFFT

The rocFFT library:

• Provides a fast and accurate platform for calculating discrete FFTs.

• Supports half (FP16), single, and double precision floating point formats.

• Supports 1D, 2D, and 3D transforms.

• Supports computation of transforms in batches.

• Supports real and complex FFTs.

• Supports arbitrary lengths, with optimizations for combinations of powers of 2, 3, 5, 7, 11, 13, and 17.

## FFT Computation#

The FFT is an implementation of the Discrete Fourier Transform (DFT) that makes use of symmetries in the DFT definition to reduce the mathematical complexity from $$O(N^2)$$ to $$O(N \log N)$$.

What is computed by the library? Here are the formulas:

For a 1D complex DFT:

$${\tilde{x}}_j = \sum_{k=0}^{n-1}x_k\exp\left({\pm i}{{2\pi jk}\over{n}}\right)\hbox{ for } j=0,1,\ldots,n-1$$

where, $$x_k$$ are the complex data to be transformed, $$\tilde{x}_j$$ are the transformed data, and the sign $$\pm$$ determines the direction of the transform: $$-$$ for forward and $$+$$ for backward.

For a 2D complex DFT:

$${\tilde{x}}_{jk} = \sum_{q=0}^{m-1}\sum_{r=0}^{n-1}x_{rq}\exp\left({\pm i} {{2\pi jr}\over{n}}\right)\exp\left({\pm i}{{2\pi kq}\over{m}}\right)$$

for $$j=0,1,\ldots,n-1\hbox{ and } k=0,1,\ldots,m-1$$, where, $$x_{rq}$$ are the complex data to be transformed, $$\tilde{x}_{jk}$$ are the transformed data, and the sign $$\pm$$ determines the direction of the transform.

For a 3D complex DFT:

$$\tilde{x}_{jkl} = \sum_{s=0}^{p-1}\sum_{q=0}^{m-1}\sum_{r=0}^{n-1}x_{rqs}\exp\left({\pm i} {{2\pi jr}\over{n}}\right)\exp\left({\pm i}{{2\pi kq}\over{m}}\right)\exp\left({\pm i}{{2\pi ls}\over{p}}\right)$$

for $$j=0,1,\ldots,n-1\hbox{ and } k=0,1,\ldots,m-1\hbox{ and } l=0,1,\ldots,p-1$$, where $$x_{rqs}$$ are the complex data to be transformed, $$\tilde{x}_{jkl}$$ are the transformed data, and the sign $$\pm$$ determines the direction of the transform.

## Library Setup and Cleanup#

At the beginning of the program, before any of the library APIs are called, the function rocfft_setup() has to be called. Similarly, the function rocfft_cleanup() has to be called at the end of the program. These APIs ensure resources are properly allocated and freed.

## Workflow#

In order to compute an FFT with rocFFT, a plan has to be created first. A plan is a handle to an internal data structure that holds the details about the transform that the user wishes to compute. After the plan is created, it can be executed (a separate API call) with the specified data buffers. The execution step can be repeated any number of times with the same plan on different input/output buffers as needed. And when the plan is no longer needed, it gets destroyed.

To do a transform,

1. Initialize the library by calling rocfft_setup().

2. Create a plan, for each distinct type of FFT needed:

3. Execute the plan:

4. If a work buffer was allocated:

5. Destroy the plan by calling rocfft_plan_destroy().

6. Terminate the library by calling rocfft_cleanup().

## Example#

#include <iostream>
#include <vector>
#include "hip/hip_runtime_api.h"
#include "hip/hip_vector_types.h"
#include "rocfft.h"

int main()
{
// rocFFT gpu compute
// ========================================

rocfft_setup();

size_t N = 16;
size_t Nbytes = N * sizeof(float2);

// Create HIP device buffer
float2 *x;
hipMalloc(&x, Nbytes);

// Initialize data
std::vector<float2> cx(N);
for (size_t i = 0; i < N; i++)
{
cx[i].x = 1;
cx[i].y = -1;
}

//  Copy data to device
hipMemcpy(x, cx.data(), Nbytes, hipMemcpyHostToDevice);

// Create rocFFT plan
rocfft_plan plan = nullptr;
size_t length = N;
rocfft_plan_create(&plan, rocfft_placement_inplace,
rocfft_transform_type_complex_forward, rocfft_precision_single,
1, &length, 1, nullptr);

// Check if the plan requires a work buffer
size_t work_buf_size = 0;
rocfft_plan_get_work_buffer_size(plan, &work_buf_size);
void* work_buf = nullptr;
rocfft_execution_info info = nullptr;
if(work_buf_size)
{
rocfft_execution_info_create(&info);
hipMalloc(&work_buf, work_buf_size);
rocfft_execution_info_set_work_buffer(info, work_buf, work_buf_size);
}

// Execute plan
rocfft_execute(plan, (void**) &x, nullptr, info);

// Wait for execution to finish
hipDeviceSynchronize();

// Clean up work buffer
if(work_buf_size)
{
hipFree(work_buf);
rocfft_execution_info_destroy(info);
}

// Destroy plan
rocfft_plan_destroy(plan);

// Copy result back to host
std::vector<float2> y(N);
hipMemcpy(y.data(), x, Nbytes, hipMemcpyDeviceToHost);

// Print results
for (size_t i = 0; i < N; i++)
{
std::cout << y[i].x << ", " << y[i].y << std::endl;
}

// Free device buffer
hipFree(x);

rocfft_cleanup();

return 0;
}


## Plans#

A plan is the collection of (almost) all the parameters needed to specify an FFT computation. A rocFFT plan includes the following information:

• Type of transform (complex or real)

• Dimension of the transform (1D, 2D, or 3D)

• Length or extent of data in each dimension

• Number of datasets that are transformed (batch size)

• Floating-point precision of the data

• In-place or not in-place transform

• Format (array type) of the input/output buffer

• Layout of data in the input/output buffer

• Scaling factor to apply to the output of the transform

The rocFFT plan does not include the following parameters:

• The handles to the input and output data buffers.

• The handle to a temporary work buffer (if needed).

• Other information to control execution on the device.

These parameters are specified when the plan is executed.

## Data#

The input/output buffers that hold the data for the transform must be allocated, initialized and specified to the library by the user. For larger transforms, temporary work buffers may be needed. Because the library tries to minimize its own allocation of memory regions on the device, it expects the user to manage work buffers. The size of the buffer needed can be queried using rocfft_plan_get_work_buffer_size() and after their allocation can be passed to the library by rocfft_execution_info_set_work_buffer(). The samples in the source repository show how to use these.

## Transform and Array types#

There are two main types of FFTs in the library:

• Complex FFT - Transformation of complex data (forward or backward); the library supports the following two array types to store complex numbers:

1. Planar format - where the real and imaginary components are kept in 2 separate arrays:

• Buffer1: RRRRR...

• Buffer2: IIIII...

2. Interleaved format - where the real and imaginary components are stored as contiguous pairs in the same array:

• Buffer: RIRIRIRIRIRI...

• Real FFT - Transformation of real data. For transforms involving real data, there are two possibilities:

• Real data being subject to forward FFT that results in complex data (Hermitian).

• Complex data (Hermitian) being subject to backward FFT that results in real data.

Note

Real backward FFTs require that the input data be Hermitian-symmetric, as would naturally happen in the output of a real forward FFT. rocFFT will produce undefined results if this requirement is not met.

The library provides the rocfft_transform_type and rocfft_array_type enums to specify transform and array types, respectively.

## Batches#

The efficiency of the library is improved by utilizing transforms in batches. Sending as much data as possible in a single transform call leverages the parallel compute capabilities of devices (GPU devices in particular), and minimizes the penalty of control transfer. It is best to think of a device as a high-throughput, high-latency device. Using a networking analogy as an example, this approach is similar to having a massively high-bandwidth pipe with very high ping response times. If the client is ready to send data to the device for compute, it should be sent in as few API calls as possible, and this can be done by batching. rocFFT plans have a parameter number_of_transforms (this value is also referred to as batch size in various places in the document) in rocfft_plan_create() to describe the number of transforms being requested. All 1D, 2D, and 3D transforms can be batched.

## Result placement#

The API supports both in-place and not in-place transforms via the rocfft_result_placement enum. With in-place transforms, only input buffers are provided to the execution API, and the resulting data is written to the same buffer, overwriting the input data. With not in-place transforms, distinct output buffers are provided, and the results are written into the output buffer.

Note that rocFFT may still modify the input buffer even if a transform is requested to be not in-place. Real-complex transforms in particular are more efficient if they can modify the original input.

## Strides and Distances#

Strides and distances enable users to specify custom layout of data using rocfft_plan_description_set_data_layout().

For 1D data, if strides == strideX == 1, successive elements in the first dimension (dimension index 0) are stored contiguously in memory. If strideX is a value greater than 1, gaps in memory exist between each element of the vector. For multi-dimensional cases; if strides == strideY == LenX for 2D data and strides == strideZ == LenX * LenY for 3D data, no gaps exist in memory between each element, and all vectors are stored tightly packed in memory. Here, LenX, LenY, and LenZ denote the transform lengths lengths, lengths, and lengths, respectively, which are used to set up the plan.

Distance is the stride that exists between corresponding elements of successive FFT data instances (primitives) in a batch. Distance is measured in units of the memory type; complex data measures in complex units, and real data measures in real units. For tightly packed data, the distance between FFT primitives is the size of the FFT primitive, such that dist == LenX for 1D data, dist == LenX * LenY for 2D data, and dist == LenX * LenY * LenZ for 3D data. It is possible to set the distance of a plan to be less than the size of the FFT vector; typically 1 when doing column (strided) access on packed data. When computing a batch of 1D FFT vectors, if distance == 1, and strideX == length(vector), it means data for each logical FFT is read along columns (in this case along the batch). You must verify that the distance and strides are valid, such that each logical FFT instance is not overlapping with any other; if not valid, undefined results may occur. A simple example would be to perform a 1D length 4096 on each row of an array of 1024 rows x 4096 columns of values stored in a column-major array, such as a FORTRAN program might provide. (This would be equivalent to a C or C++ program that has an array of 4096 rows x 1024 columns stored in a row-major manner, on which you want to perform a 1D length 4096 transform on each column.) In this case, specify the strides as  and distance as 1.

### Overwriting non-contiguous buffers#

rocFFT guarantees that both the reading of FFT input and the writing of FFT output will respect the specified strides. However, temporary results can potentially be written to these buffers contiguously, which may be unexpected if the strides would avoid certain memory locations completely for reading and writing.

For example, a 1D FFT of length $$N$$ with input and output stride of 2 is transforming only even-indexed elements in the input and output buffers. But if temporary data needs to be written to the buffers, odd-indexed elements may be overwritten.

However, rocFFT is guaranteed to respect the size of buffers. In the above example, the input/output buffers are $$2N$$ elements long, even if only $$N$$ even-indexed elements are being transformed. No more than $$2N$$ elements of temporary data will be written to the buffers during the transform.

These policies apply to both input and output buffers, because not in-place transforms may overwrite input data.

## Result Scaling#

The output of a forward or backward FFT often needs to be multiplied by a scaling factor before the data can be passed to the next step of a computation. While users of rocFFT can launch a separate GPU kernel to do this work, rocFFT provides a rocfft_plan_description_set_scale_factor() function to more efficiently combine this scaling multiplication with the FFT work.

The scaling factor is set on the plan description prior to plan creation.

rocFFT includes experimental functionality to call user-defined device functions when loading input from global memory at the start of a transform, or when storing output to global memory at the end of a transform.

These user-defined callback functions may be optionally supplied to the library using rocfft_execution_info_set_load_callback() and rocfft_execution_info_set_store_callback().

Device functions supplied as callbacks must load and store element data types that are appropriate for the transform being performed.

Transform type

Store element type

Complex-to-complex, half-precision

_Float16_2

_Float16_2

Complex-to-complex, single-precision

float2

float2

Complex-to-complex, double-precision

double2

double2

Real-to-complex, single-precision

float

float2

Real-to-complex, half-precision

_Float16

_Float16_2

Real-to-complex, double-precision

double

double2

Complex-to-real, half-precision

_Float16_2

_Float16

Complex-to-real, single-precision

float2

float

Complex-to-real, double-precision

double2

double

The callback function signatures must match the specifications below.

T load_callback(T* buffer, size_t offset, void* callback_data, void* shared_memory);
void store_callback(T* buffer, size_t offset, T element, void* callback_data, void* shared_memory);


The parameters for the functions are defined as:

• T: The data type of each element being loaded or stored from the input or output.

• buffer: Pointer to the input (for load callbacks) or output (for store callbacks) in device memory that was passed to rocfft_execute().

• offset: The offset of the location being read from or written to. This counts in elements, from the buffer pointer.

• element: For store callbacks only, the element to be stored.

• callback_data: A pointer value accepted by rocfft_execution_info_set_load_callback() and rocfft_execution_info_set_store_callback() which is passed through to the callback function.

• shared_memory: A pointer to an amount of shared memory requested when the callback is set. Currently, shared memory is not supported and this parameter is always null.

Callback functions are called exactly once for each element being loaded or stored in a transform. Note that multiple kernels may be launched to decompose a transform, which means that separate kernels may call the load and store callbacks for a transform if both are specified.

Currently, callbacks functions are only supported for transforms that do not use planar format for input or output.

## Runtime compilation#

rocFFT includes many kernels for common FFT problems. Some plans may require additional kernels aside from what is built in to the library. In these cases, rocFFT will compile optimized kernels for the plan when the plan is created.

Compiled kernels are stored in memory by default and will be reused if they are required again for plans in the same process.

If the ROCFFT_RTC_CACHE_PATH environment variable is set to a writable file location, rocFFT will write compiled kernels to this location. rocFFT will read kernels from this location for plans in other processes that need runtime-compiled kernels. rocFFT will create the specified file if it does not already exist.