Descriptor format

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Descriptor format#

The bbfft-aot-generate and bbfft-offline-generate tools use a short FFT descriptor format. The general form of a FFT descriptor is (in ABNF syntax):

fft_descriptor  =  precision domain direction placement shape [istride] [ostride]
precision       =  "s" / "d"
domain          =  "c" / "r"
direction       =  "f" / "b"
placement       =  "i" / "o"
shape           =  [number "."] number *2("x" number) ["*" number]
number          =  1*DIGIT
istride         =  "i" stride
ostride         =  "o" stride
stride          =  number 2*4("," number)

The precision, domain, direction, and placement options are:

Option

Meaning

s

Single precision

d

Double precision

c

Complex input and complex output

r

Real input and complex output in forward direction; complex input and real output in backward direction

f

Forward direction

b

Backward direction

i

In-place

o

Out-of-place

The shape rule defines the shape of the \(M \times N_1 \times \dots \times N_D \times K\) tensor (see Understanding data layouts). Here, the number before the dot is the left-batch size \(M\). If omitted, then \(M=1\).

The numbers before and after “x” correspond to \(N_1,N_2,N_3\) and the number of “x” is equal to the FFT dimension plus 1. E.g., “5” corresponds to \(N_1=5\) and FFT dimension 1, and “8x16x32” corresponds to \(N_1=8,N_2=16,N_3=32\) and FFT dimension 3.

The last number, after “*”, is the right-batch size \(K\). If omitted, then \(K=1\).

The istride and ostride rules can be used to override the default strides of the input and output tensor. The sequence of numbers corresponds to \(s_0,\dots,s_{D+1}\) (see Understanding data layouts). The length of the sequence of numbers must be equal to the FFT dimension plus two.

Note

Custom strides for in-place transforms need to be repeated, i.e. both istride and ostride need to be given.

Examples#

Gibberish

English

srfi5

Single precision real-to-complex 5-point FFT with in-place data layout.

dcbi4*5

Double precision complex-to-complex 4-point FFT in backward direction with in-place data layout and right-batch size of 5.

dcbi4.5

Double precision complex-to-complex 5-point FFT in backward direction with in-place data layout and left-batch size of 4.

drfo5x6x7

Double precision real-to-complex 3-D FFT on \(5x6x7\) tensor with out-of-place data layout.

srbo4.5x6*7

Double precision complex-to-real 2-D FFT on \(5x6\) tensor with left-batch size 4 and right-batch size 7 with out-of-place data layout.

scfo16*32i1,1,20

Single precision complex-to-complex 16-point FFT with right-batch size 32 with out-place data-layout and input stride override (20 complex numbers between batch elements in input tensor).
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