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AI Engine API User Guide (AIE) 2023.2
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The AIE API offers a stage-based interface for carrying out decimation-in-time FFTs. More...
Overview
The AIE API offers a stage-based interface for carrying out decimation-in-time FFTs.
For example, assuming twiddle pointer visibility, a 1024 point FFT can be computed as follows:
void fft_1024pt(const cint16 * __restrict x, // Input pointer
unsigned shift_tw, // Indicates the decimal point of the twiddles
// e.g. The twiddle 1.0+0.0i can be represented with cint16(32767, 0) and a shift_tw of 15
unsigned shift, // Shift applied to apply to dit outputs
bool inv, // Run inverse FFT
cint16 * __restrict tmp, // Scratch space for intermediate results
cint16 * __restrict y // Output pointer
)
{
aie::fft_dit_r2_stage<512>(x, tw1, 1024, shift_tw, shift, inv, tmp);
aie::fft_dit_r2_stage<256>(tmp, tw2, 1024, shift_tw, shift, inv, y);
aie::fft_dit_r2_stage<128>(y, tw4, 1024, shift_tw, shift, inv, tmp);
aie::fft_dit_r2_stage<64> (tmp, tw8, 1024, shift_tw, shift, inv, y);
aie::fft_dit_r2_stage<32> (y, tw16, 1024, shift_tw, shift, inv, tmp);
aie::fft_dit_r2_stage<16> (tmp, tw32, 1024, shift_tw, shift, inv, y);
aie::fft_dit_r2_stage<8> (y, tw64, 1024, shift_tw, shift, inv, tmp);
aie::fft_dit_r2_stage<4> (tmp, tw128, 1024, shift_tw, shift, inv, y);
aie::fft_dit_r2_stage<2> (y, tw256, 1024, shift_tw, shift, inv, tmp);
aie::fft_dit_r2_stage<1> (tmp, tw512, 1024, shift_tw, shift, inv, y);
}
An R-radix, N-point FFT typically requires R-1 twiddle tables, each with N / R entries. The entries, in floating point, are given by
for (unsigned r = 1; r < R; ++r) {
for (unsigned i = 0; i < N / R; ++i) {
tw[r-1][i] = exp(-2j * pi * r * i / n);
}
}
For fixed point implementations, the twiddle value should be multiplied by (1 << shift_tw) before casting to the output type.
Given that earlier stages of an N-point FFT are smaller, batched FFTs, the same equation for the twiddle values hold. However, N is divided by the Vectorization to give N_stage = N / Vectorization.
Typedefs | |
| template<unsigned Vectorization, unsigned Radix, typename Input , typename Output = Input, typename Twiddle = detail::default_twiddle_type_t<Input, Output>> | |
| using | aie::fft_dit = detail::fft_dit< Vectorization, detail::fft_get_stage< Vectorization, Radix, Input, Output, Twiddle >(), Radix, Input, Output, Twiddle > |
| Type that encapsulates the functionality for decimation-in-time FFTs. | |
Functions | |
| template<unsigned Vectorization, typename Input , typename Output , typename Twiddle > requires (arch::is(arch::AIE) && detail::is_floating_point_v<Input>) | |
| void | aie::fft_dit_r2_stage (const Input *__restrict x, const Twiddle *__restrict tw, unsigned n, bool inv, Output *__restrict out) |
| A function to perform a single floating point radix 2 FFT stage. | |
| template<unsigned Vectorization, typename Input , typename Output , typename Twiddle > | |
| void | aie::fft_dit_r2_stage (const Input *__restrict x, const Twiddle *__restrict tw, unsigned n, unsigned shift_tw, unsigned shift, bool inv, Output *__restrict out) |
| A function to perform a single radix 2 FFT stage. | |
| template<unsigned Vectorization, typename Input , typename Output , typename Twiddle > requires (arch::is(arch::AIE)) | |
| void | aie::fft_dit_r3_stage (const Input *__restrict x, const Twiddle *__restrict tw0, const Twiddle *__restrict tw1, unsigned n, unsigned shift_tw, unsigned shift, bool inv, Output *__restrict out) |
| A function to perform a single radix 3 FFT stage. | |
| template<unsigned Vectorization, typename Input , typename Output , typename Twiddle > | |
| void | aie::fft_dit_r4_stage (const Input *__restrict x, const Twiddle *__restrict tw0, const Twiddle *__restrict tw1, const Twiddle *__restrict tw2, unsigned n, unsigned shift_tw, unsigned shift, bool inv, Output *__restrict out) |
| A function to perform a single radix 4 FFT stage. | |
| template<unsigned Vectorization, typename Input , typename Output , typename Twiddle > requires (arch::is(arch::AIE)) | |
| void | aie::fft_dit_r5_stage (const Input *__restrict x, const Twiddle *__restrict tw0, const Twiddle *__restrict tw1, const Twiddle *__restrict tw2, const Twiddle *__restrict tw3, unsigned n, unsigned shift_tw, unsigned shift, bool inv, Output *out) |
| A function to perform a single radix 5 FFT stage. | |
Supported Fast Fourier Transform Modes
| Input Type | Output Type | Twiddle Type | AIE Supported Radices | AIE-ML Supported Radices |
|---|---|---|---|---|
| c16b | c16b | c16b | 2, 4 | 2, 4 |
| c16b | c32b | c16b | 2, 3, 4, 5 | 2, 4 |
| c32b | c16b | c16b | 2, 4, | 2, 4 |
| c32b | c32b | c16b | 2, 3, 4, 5 | 2, 4 |
| c32b | c16b | c32b | 2 | |
| c32b | c32b | c32b | 2, 3, 4, 5 | |
| cfloat | cfloat | cfloat | 2 |
Typedef Documentation
◆ fft_dit
template<unsigned Vectorization, unsigned Radix, typename Input , typename Output = Input, typename Twiddle = detail::default_twiddle_type_t<Input, Output>>
| using aie::fft_dit = typedef detail::fft_dit<Vectorization, detail::fft_get_stage<Vectorization, Radix, Input, Output, Twiddle>(), Radix, Input, Output, Twiddle> |
Type that encapsulates the functionality for decimation-in-time FFTs.
- Deprecated:
- The iterator interface is deprecated and the stage-based interface should be preferred.
- Template Parameters
-
Vectorization Vectorization of the FFT stage Radix Number which selects the FFT radix. Input Type of the input elements. Output Type of the output elements, defaults to input type. Twiddle Type of the twiddle elements, defaults to cint16 for integral types and cfloat for floating point.
Function Documentation
◆ fft_dit_r2_stage() [1/2]
template<unsigned Vectorization, typename Input , typename Output , typename Twiddle >
requires (arch::is(arch::AIE) && detail::is_floating_point_v<Input>)
requires (arch::is(arch::AIE) && detail::is_floating_point_v<Input>)
| void aie::fft_dit_r2_stage | ( | const Input *__restrict | x, |
| const Twiddle *__restrict | tw, | ||
| unsigned | n, | ||
| bool | inv, | ||
| Output *__restrict | out | ||
| ) |
A function to perform a single floating point radix 2 FFT stage.
- Parameters
-
x Input data pointer tw Twiddle group pointer n Number of samples inv Run inverse FFT stage out Output data pointer
- Template Parameters
-
Vectorization Vectorization of the FFT stage Input Type of the input elements. Output Type of the output elements, defaults to input type. Twiddle Type of the twiddle elements, defaults to cint16 for integral types and cfloat for floating point.
◆ fft_dit_r2_stage() [2/2]
template<unsigned Vectorization, typename Input , typename Output , typename Twiddle >
| void aie::fft_dit_r2_stage | ( | const Input *__restrict | x, |
| const Twiddle *__restrict | tw, | ||
| unsigned | n, | ||
| unsigned | shift_tw, | ||
| unsigned | shift, | ||
| bool | inv, | ||
| Output *__restrict | out | ||
| ) |
A function to perform a single radix 2 FFT stage.
- Parameters
-
x Input data pointer tw Twiddle group pointer n Number of samples shift_tw Indicates the decimal point of the twiddles shift Shift applied to apply to dit outputs inv Run inverse FFT stage out Output data pointer
- Template Parameters
-
Vectorization Vectorization of the FFT stage Input Type of the input elements. Output Type of the output elements, defaults to input type. Twiddle Type of the twiddle elements, defaults to cint16 for integral types and cfloat for floating point.
◆ fft_dit_r3_stage()
template<unsigned Vectorization, typename Input , typename Output , typename Twiddle >
requires (arch::is(arch::AIE))
requires (arch::is(arch::AIE))
| void aie::fft_dit_r3_stage | ( | const Input *__restrict | x, |
| const Twiddle *__restrict | tw0, | ||
| const Twiddle *__restrict | tw1, | ||
| unsigned | n, | ||
| unsigned | shift_tw, | ||
| unsigned | shift, | ||
| bool | inv, | ||
| Output *__restrict | out | ||
| ) |
A function to perform a single radix 3 FFT stage.
- Parameters
-
x Input data pointer tw0 First twiddle group pointer tw1 Second twiddle group pointer n Number of samples shift_tw Indicates the decimal point of the twiddles shift Shift applied to apply to dit outputs inv Run inverse FFT stage out Output data pointer
- Template Parameters
-
Vectorization Vectorization of the FFT stage Input Type of the input elements. Output Type of the output elements, defaults to input type. Twiddle Type of the twiddle elements, defaults to cint16 for integral types and cfloat for floating point.
◆ fft_dit_r4_stage()
template<unsigned Vectorization, typename Input , typename Output , typename Twiddle >
| void aie::fft_dit_r4_stage | ( | const Input *__restrict | x, |
| const Twiddle *__restrict | tw0, | ||
| const Twiddle *__restrict | tw1, | ||
| const Twiddle *__restrict | tw2, | ||
| unsigned | n, | ||
| unsigned | shift_tw, | ||
| unsigned | shift, | ||
| bool | inv, | ||
| Output *__restrict | out | ||
| ) |
A function to perform a single radix 4 FFT stage.
- Parameters
-
x Input data pointer tw0 First twiddle group pointer tw1 Second twiddle group pointer tw2 Third twiddle group pointer n Number of samples shift_tw Indicates the decimal point of the twiddles shift Shift applied to apply to dit outputs inv Run inverse FFT stage out Output data pointer
- Template Parameters
-
Vectorization Vectorization of the FFT stage Input Type of the input elements. Output Type of the output elements, defaults to input type. Twiddle Type of the twiddle elements, defaults to cint16 for integral types and cfloat for floating point.
◆ fft_dit_r5_stage()
template<unsigned Vectorization, typename Input , typename Output , typename Twiddle >
requires (arch::is(arch::AIE))
requires (arch::is(arch::AIE))
| void aie::fft_dit_r5_stage | ( | const Input *__restrict | x, |
| const Twiddle *__restrict | tw0, | ||
| const Twiddle *__restrict | tw1, | ||
| const Twiddle *__restrict | tw2, | ||
| const Twiddle *__restrict | tw3, | ||
| unsigned | n, | ||
| unsigned | shift_tw, | ||
| unsigned | shift, | ||
| bool | inv, | ||
| Output * | out | ||
| ) |
A function to perform a single radix 5 FFT stage.
- Parameters
-
x Input data pointer tw0 First twiddle group pointer tw1 Second twiddle group pointer tw2 Third twiddle group pointer tw3 Fourth twiddle group pointer n Number of samples shift_tw Indicates the decimal point of the twiddles shift Shift applied to apply to dit outputs inv Run inverse FFT stage out Output data pointer
- Template Parameters
-
Vectorization Vectorization of the FFT stage Input Type of the input elements. Output Type of the output elements, defaults to input type. Twiddle Type of the twiddle elements, defaults to cint16 for integral types and cfloat for floating point.