blob: cb1391ab4e31c5e2371f7007335ad1ea84d6e4ae [file] [log] [blame]
/*
* Copyright (c) 2019-2020 Arm Limited.
*
* SPDX-License-Identifier: MIT
*
* Permission is hereby granted, free of charge, to any person obtaining a copy
* of this software and associated documentation files (the "Software"), to
* deal in the Software without restriction, including without limitation the
* rights to use, copy, modify, merge, publish, distribute, sublicense, and/or
* sell copies of the Software, and to permit persons to whom the Software is
* furnished to do so, subject to the following conditions:
*
* The above copyright notice and this permission notice shall be included in all
* copies or substantial portions of the Software.
*
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
* IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
* FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
* AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
* LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
* OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
* SOFTWARE.
*/
#include "src/core/NEON/kernels/NEFFTRadixStageKernel.h"
#include "arm_compute/core/ITensor.h"
#include "arm_compute/core/TensorInfo.h"
#include "arm_compute/core/Types.h"
#include "arm_compute/core/Utils.h"
#include "arm_compute/core/Window.h"
#include "src/core/NEON/wrapper/traits.h"
#include "src/core/NEON/wrapper/wrapper.h"
#include "src/core/helpers/AutoConfiguration.h"
#include "src/core/helpers/WindowHelpers.h"
#include <arm_neon.h>
#include <cmath>
#include <complex>
#include <map>
namespace arm_compute
{
namespace
{
// PI constant (from cmath)
constexpr float kPi = float(M_PI);
// Constant used in the fft_3 kernel
constexpr float kSqrt3Div2 = 0.866025403784438;
// Constants used in the fft_5 kernel
constexpr float kW5_0 = 0.30901699437494f;
constexpr float kW5_1 = 0.95105651629515f;
constexpr float kW5_2 = 0.80901699437494f;
constexpr float kW5_3 = 0.58778525229247f;
// Constants used in the fft_7 kernel
constexpr float kW7_0 = 0.62348980185873f;
constexpr float kW7_1 = 0.78183148246802f;
constexpr float kW7_2 = 0.22252093395631f;
constexpr float kW7_3 = 0.97492791218182f;
constexpr float kW7_4 = 0.90096886790241f;
constexpr float kW7_5 = 0.43388373911755f;
// Constant used in the fft_8 kernel
constexpr float kSqrt2Div2 = 0.707106781186548;
float32x2_t c_mul_neon(float32x2_t a, float32x2_t b)
{
using ExactTagType = typename wrapper::traits::neon_vector<float, 2>::tag_type;
const float32x2_t mask = { -1.0, 1.0 };
const float32x2_t tmp0 = wrapper::vdup_n(wrapper::vgetlane(a, 0), ExactTagType{});
const float32x2_t tmp1 = wrapper::vdup_n(wrapper::vgetlane(a, 1), ExactTagType{});
float32x2_t res = wrapper::vmul(tmp0, b);
b = wrapper::vrev64(b);
b = wrapper::vmul(b, mask);
res = wrapper::vmla(res, tmp1, b);
return res;
}
float32x2_t c_mul_neon_img(float32x2_t a, float img_constant)
{
const float a_r = wrapper::vgetlane(a, 0);
const float a_i = wrapper::vgetlane(a, 1);
const auto out = wrapper::vmul(float32x2_t{ -a_i, a_r }, float32x2_t{ img_constant, img_constant });
return out;
}
float32x2_t reduce_sum_5(float32x2_t a, float32x2_t b, float32x2_t c, float32x2_t d, float32x2_t e)
{
const auto t0 = wrapper::vadd(a, b);
const auto t1 = wrapper::vadd(c, d);
const auto t2 = wrapper::vadd(t0, t1);
return wrapper::vadd(t2, e);
}
float32x2_t reduce_sum_7(float32x2_t x1, float32x2_t x2, float32x2_t x3, float32x2_t x4, float32x2_t x5, float32x2_t x6, float32x2_t x7)
{
const auto t0 = wrapper::vadd(x1, x2);
const auto t1 = wrapper::vadd(x3, x4);
const auto t2 = wrapper::vadd(x5, x6);
const auto t00 = wrapper::vadd(t0, t1);
const auto t01 = wrapper::vadd(t2, x7);
return wrapper::vadd(t00, t01);
}
float32x2_t reduce_sum_8(float32x2_t x1, float32x2_t x2, float32x2_t x3, float32x2_t x4, float32x2_t x5, float32x2_t x6, float32x2_t x7, float32x2_t x8)
{
const auto t0 = wrapper::vadd(x1, x2);
const auto t1 = wrapper::vadd(x3, x4);
const auto t2 = wrapper::vadd(x5, x6);
const auto t3 = wrapper::vadd(x7, x8);
const auto t00 = wrapper::vadd(t0, t1);
const auto t01 = wrapper::vadd(t2, t3);
return wrapper::vadd(t00, t01);
}
void fft_2(float32x2_t &x, float32x2_t &y, float32x2_t &w)
{
float32x2_t a = x;
float32x2_t b = c_mul_neon(w, y);
x = wrapper::vadd(a, b);
y = wrapper::vsub(a, b);
}
void fft_3(float32x2_t &x, float32x2_t &y, float32x2_t &z, const float32x2_t &w, const float32x2_t &w2)
{
float32x2_t a = x;
float32x2_t b = c_mul_neon(w, y);
float32x2_t c = c_mul_neon(w2, z);
x = wrapper::vadd(a, b);
x = wrapper::vadd(x, c);
const auto v1 = wrapper::vmul(float32x2_t{ 0.5f, 0.5 }, wrapper::vadd(b, c));
const auto v2 = c_mul_neon(float32x2_t{ 0.f, -kSqrt3Div2 }, wrapper::vsub(b, c));
y = z = wrapper::vsub(a, v1);
y = wrapper::vadd(y, v2);
z = wrapper::vsub(z, v2);
}
void fft_4(float32x2_t &x1, float32x2_t &x2, float32x2_t &x3, float32x2_t &x4, const float32x2_t &w, const float32x2_t &w2, const float32x2_t &w3)
{
float32x2_t a = x1;
float32x2_t b = c_mul_neon(w, x2);
float32x2_t c = c_mul_neon(w2, x3);
float32x2_t d = c_mul_neon(w3, x4);
const auto x11 = wrapper::vadd(a, b);
const auto x12 = wrapper::vadd(c, d);
x1 = wrapper::vadd(x11, x12);
const auto x21 = wrapper::vadd(a, c_mul_neon_img(b, -1));
const auto x22 = wrapper::vadd(wrapper::vneg(c), c_mul_neon_img(d, 1.f));
x2 = wrapper::vadd(x21, x22);
const auto x31 = wrapper::vadd(a, wrapper::vneg(b));
const auto x32 = wrapper::vadd(c, wrapper::vneg(d));
x3 = wrapper::vadd(x31, x32);
const auto x41 = wrapper::vadd(a, c_mul_neon_img(b, 1));
const auto x42 = wrapper::vadd(wrapper::vneg(c), c_mul_neon_img(d, -1));
x4 = wrapper::vadd(x41, x42);
}
void fft_5(float32x2_t &x1, float32x2_t &x2, float32x2_t &x3, float32x2_t &x4, float32x2_t &x5, const float32x2_t &w, const float32x2_t &w2, const float32x2_t &w3, const float32x2_t &w4)
{
const auto a = x1;
const auto b = c_mul_neon(w, x2);
const auto c = c_mul_neon(w2, x3);
const auto d = c_mul_neon(w3, x4);
const auto e = c_mul_neon(w4, x5);
const auto b0 = c_mul_neon(float32x2_t{ kW5_0, -kW5_1 }, b);
const auto b1 = c_mul_neon(float32x2_t{ -kW5_2, -kW5_3 }, b);
const auto b2 = c_mul_neon(float32x2_t{ -kW5_2, kW5_3 }, b);
const auto b3 = c_mul_neon(float32x2_t{ kW5_0, kW5_1 }, b);
const auto c0 = c_mul_neon(float32x2_t{ -kW5_2, -kW5_3 }, c);
const auto c1 = c_mul_neon(float32x2_t{ kW5_0, kW5_1 }, c);
const auto c2 = c_mul_neon(float32x2_t{ kW5_0, -kW5_1 }, c);
const auto c3 = c_mul_neon(float32x2_t{ -kW5_2, kW5_3 }, c);
const auto d0 = c_mul_neon(float32x2_t{ -kW5_2, kW5_3 }, d);
const auto d1 = c_mul_neon(float32x2_t{ kW5_0, -kW5_1 }, d);
const auto d2 = c_mul_neon(float32x2_t{ kW5_0, kW5_1 }, d);
const auto d3 = c_mul_neon(float32x2_t{ -kW5_2, -kW5_3 }, d);
const auto e0 = c_mul_neon(float32x2_t{ kW5_0, kW5_1 }, e);
const auto e1 = c_mul_neon(float32x2_t{ -kW5_2, kW5_3 }, e);
const auto e2 = c_mul_neon(float32x2_t{ -kW5_2, -kW5_3 }, e);
const auto e3 = c_mul_neon(float32x2_t{ kW5_0, -kW5_1 }, e);
x1 = reduce_sum_5(a, b, c, d, e);
x2 = reduce_sum_5(a, b0, c0, d0, e0);
x3 = reduce_sum_5(a, b1, c1, d1, e1);
x4 = reduce_sum_5(a, b2, c2, d2, e2);
x5 = reduce_sum_5(a, b3, c3, d3, e3);
}
void fft_7(float32x2_t &x1, float32x2_t &x2, float32x2_t &x3, float32x2_t &x4, float32x2_t &x5, float32x2_t &x6, float32x2_t &x7, const float32x2_t &w, const float32x2_t &w2, const float32x2_t &w3,
const float32x2_t &w4,
const float32x2_t &w5, const float32x2_t &w6)
{
const auto a = x1;
const auto b = c_mul_neon(w, x2);
const auto c = c_mul_neon(w2, x3);
const auto d = c_mul_neon(w3, x4);
const auto e = c_mul_neon(w4, x5);
const auto f = c_mul_neon(w5, x6);
const auto g = c_mul_neon(w6, x7);
const auto b0 = c_mul_neon(float32x2_t{ kW7_0, -kW7_1 }, b);
const auto b1 = c_mul_neon(float32x2_t{ -kW7_2, -kW7_3 }, b);
const auto b2 = c_mul_neon(float32x2_t{ -kW7_4, -kW7_5 }, b);
const auto b3 = c_mul_neon(float32x2_t{ -kW7_4, kW7_5 }, b);
const auto b4 = c_mul_neon(float32x2_t{ -kW7_2, kW7_3 }, b);
const auto b5 = c_mul_neon(float32x2_t{ kW7_0, kW7_1 }, b);
const auto c0 = c_mul_neon(float32x2_t{ -kW7_2, -kW7_3 }, c);
const auto c1 = c_mul_neon(float32x2_t{ -kW7_4, kW7_5 }, c);
const auto c2 = c_mul_neon(float32x2_t{ kW7_0, kW7_1 }, c);
const auto c3 = c_mul_neon(float32x2_t{ kW7_0, -kW7_1 }, c);
const auto c4 = c_mul_neon(float32x2_t{ -kW7_4, -kW7_5 }, c);
const auto c5 = c_mul_neon(float32x2_t{ -kW7_2, kW7_3 }, c);
const auto d0 = c_mul_neon(float32x2_t{ -kW7_4, -kW7_5 }, d);
const auto d1 = c_mul_neon(float32x2_t{ kW7_0, kW7_1 }, d);
const auto d2 = c_mul_neon(float32x2_t{ -kW7_2, -kW7_3 }, d);
const auto d3 = c_mul_neon(float32x2_t{ -kW7_2, +kW7_3 }, d);
const auto d4 = c_mul_neon(float32x2_t{ kW7_0, -kW7_1 }, d);
const auto d5 = c_mul_neon(float32x2_t{ -kW7_4, kW7_5 }, d);
const auto e0 = c_mul_neon(float32x2_t{ -kW7_4, kW7_5 }, e);
const auto e1 = c_mul_neon(float32x2_t{ kW7_0, -kW7_1 }, e);
const auto e2 = c_mul_neon(float32x2_t{ -kW7_2, kW7_3 }, e);
const auto e3 = c_mul_neon(float32x2_t{ -kW7_2, -kW7_3 }, e);
const auto e4 = c_mul_neon(float32x2_t{ kW7_0, kW7_1 }, e);
const auto e5 = c_mul_neon(float32x2_t{ -kW7_4, -kW7_5 }, e);
const auto f0 = c_mul_neon(float32x2_t{ -kW7_2, kW7_3 }, f);
const auto f1 = c_mul_neon(float32x2_t{ -kW7_4, -kW7_5 }, f);
const auto f2 = c_mul_neon(float32x2_t{ kW7_0, -kW7_1 }, f);
const auto f3 = c_mul_neon(float32x2_t{ kW7_0, kW7_1 }, f);
const auto f4 = c_mul_neon(float32x2_t{ -kW7_4, kW7_5 }, f);
const auto f5 = c_mul_neon(float32x2_t{ -kW7_2, -kW7_3 }, f);
const auto g0 = c_mul_neon(float32x2_t{ kW7_0, kW7_1 }, g);
const auto g1 = c_mul_neon(float32x2_t{ -kW7_2, kW7_3 }, g);
const auto g2 = c_mul_neon(float32x2_t{ -kW7_4, kW7_5 }, g);
const auto g3 = c_mul_neon(float32x2_t{ -kW7_4, -kW7_5 }, g);
const auto g4 = c_mul_neon(float32x2_t{ -kW7_2, -kW7_3 }, g);
const auto g5 = c_mul_neon(float32x2_t{ kW7_0, -kW7_1 }, g);
x1 = reduce_sum_7(a, b, c, d, e, f, g);
x2 = reduce_sum_7(a, b0, c0, d0, e0, f0, g0);
x3 = reduce_sum_7(a, b1, c1, d1, e1, f1, g1);
x4 = reduce_sum_7(a, b2, c2, d2, e2, f2, g2);
x5 = reduce_sum_7(a, b3, c3, d3, e3, f3, g3);
x6 = reduce_sum_7(a, b4, c4, d4, e4, f4, g4);
x7 = reduce_sum_7(a, b5, c5, d5, e5, f5, g5);
}
void fft_8(float32x2_t &x1, float32x2_t &x2, float32x2_t &x3, float32x2_t &x4, float32x2_t &x5, float32x2_t &x6, float32x2_t &x7, float32x2_t &x8, const float32x2_t &w, const float32x2_t &w2,
const float32x2_t &w3,
const float32x2_t &w4, const float32x2_t &w5, const float32x2_t &w6,
const float32x2_t &w7)
{
const auto a = x1;
const auto b = c_mul_neon(w, x2);
const auto c = c_mul_neon(w2, x3);
const auto d = c_mul_neon(w3, x4);
const auto e = c_mul_neon(w4, x5);
const auto f = c_mul_neon(w5, x6);
const auto g = c_mul_neon(w6, x7);
const auto h = c_mul_neon(w7, x8);
const auto b0 = c_mul_neon(float32x2_t{ kSqrt2Div2, -kSqrt2Div2 }, b);
const auto b1 = c_mul_neon(float32x2_t{ 0, -1 }, b);
const auto b2 = c_mul_neon(float32x2_t{ -kSqrt2Div2, -kSqrt2Div2 }, b);
const auto b3 = c_mul_neon(float32x2_t{ -1, 0 }, b);
const auto b4 = c_mul_neon(float32x2_t{ -kSqrt2Div2, kSqrt2Div2 }, b);
const auto b5 = c_mul_neon(float32x2_t{ 0, 1 }, b);
const auto b6 = c_mul_neon(float32x2_t{ kSqrt2Div2, kSqrt2Div2 }, b);
const auto c0 = c_mul_neon(float32x2_t{ 0, -1 }, c);
const auto c1 = c_mul_neon(float32x2_t{ -1, 0 }, c);
const auto c2 = c_mul_neon(float32x2_t{ 0, 1 }, c);
const auto c3 = c_mul_neon(float32x2_t{ 1, 0 }, c);
const auto c4 = c_mul_neon(float32x2_t{ 0, -1 }, c);
const auto c5 = c_mul_neon(float32x2_t{ -1, 0 }, c);
const auto c6 = c_mul_neon(float32x2_t{ 0, 1 }, c);
const auto d0 = c_mul_neon(float32x2_t{ -kSqrt2Div2, -kSqrt2Div2 }, d);
const auto d1 = c_mul_neon(float32x2_t{ 0, 1 }, d);
const auto d2 = c_mul_neon(float32x2_t{ kSqrt2Div2, -kSqrt2Div2 }, d);
const auto d3 = c_mul_neon(float32x2_t{ -1, 0 }, d);
const auto d4 = c_mul_neon(float32x2_t{ kSqrt2Div2, kSqrt2Div2 }, d);
const auto d5 = c_mul_neon(float32x2_t{ 0, -1 }, d);
const auto d6 = c_mul_neon(float32x2_t{ -kSqrt2Div2, kSqrt2Div2 }, d);
const auto e0 = c_mul_neon(float32x2_t{ -1, 0 }, e);
const auto e1 = c_mul_neon(float32x2_t{ 1, 0 }, e);
const auto e2 = c_mul_neon(float32x2_t{ -1, 0 }, e);
const auto e3 = c_mul_neon(float32x2_t{ 1, 0 }, e);
const auto e4 = c_mul_neon(float32x2_t{ -1, 0 }, e);
const auto e5 = c_mul_neon(float32x2_t{ 1, 0 }, e);
const auto e6 = c_mul_neon(float32x2_t{ -1, 0 }, e);
const auto f0 = c_mul_neon(float32x2_t{ -kSqrt2Div2, kSqrt2Div2 }, f);
const auto f1 = c_mul_neon(float32x2_t{ 0, -1 }, f);
const auto f2 = c_mul_neon(float32x2_t{ kSqrt2Div2, kSqrt2Div2 }, f);
const auto f3 = c_mul_neon(float32x2_t{ -1, 0 }, f);
const auto f4 = c_mul_neon(float32x2_t{ kSqrt2Div2, -kSqrt2Div2 }, f);
const auto f5 = c_mul_neon(float32x2_t{ 0, 1 }, f);
const auto f6 = c_mul_neon(float32x2_t{ -kSqrt2Div2, -kSqrt2Div2 }, f);
const auto g0 = c_mul_neon(float32x2_t{ 0, 1 }, g);
const auto g1 = c_mul_neon(float32x2_t{ -1, 0 }, g);
const auto g2 = c_mul_neon(float32x2_t{ 0, -1 }, g);
const auto g3 = c_mul_neon(float32x2_t{ 1, 0 }, g);
const auto g4 = c_mul_neon(float32x2_t{ 0, 1 }, g);
const auto g5 = c_mul_neon(float32x2_t{ -1, 0 }, g);
const auto g6 = c_mul_neon(float32x2_t{ 0, -1 }, g);
const auto h0 = c_mul_neon(float32x2_t{ kSqrt2Div2, kSqrt2Div2 }, h);
const auto h1 = c_mul_neon(float32x2_t{ 0, 1 }, h);
const auto h2 = c_mul_neon(float32x2_t{ -kSqrt2Div2, kSqrt2Div2 }, h);
const auto h3 = c_mul_neon(float32x2_t{ -1, 0 }, h);
const auto h4 = c_mul_neon(float32x2_t{ -kSqrt2Div2, -kSqrt2Div2 }, h);
const auto h5 = c_mul_neon(float32x2_t{ 0, -1 }, h);
const auto h6 = c_mul_neon(float32x2_t{ kSqrt2Div2, -kSqrt2Div2 }, h);
x1 = reduce_sum_8(a, b, c, d, e, f, g, h);
x2 = reduce_sum_8(a, b0, c0, d0, e0, f0, g0, h0);
x3 = reduce_sum_8(a, b1, c1, d1, e1, f1, g1, h1);
x4 = reduce_sum_8(a, b2, c2, d2, e2, f2, g2, h2);
x5 = reduce_sum_8(a, b3, c3, d3, e3, f3, g3, h3);
x6 = reduce_sum_8(a, b4, c4, d4, e4, f4, g4, h4);
x7 = reduce_sum_8(a, b5, c5, d5, e5, f5, g5, h5);
x8 = reduce_sum_8(a, b6, c6, d6, e6, f6, g6, h6);
}
template <bool first_stage>
void fft_radix_2_axes_0(float *X, float *x, unsigned int Nx, unsigned int NxRadix, const float32x2_t &w_m, unsigned int N)
{
float32x2_t w{ 1.0f, 0.0f };
for(unsigned int j = 0; j < Nx; j++)
{
for(unsigned int k = 2 * j; k < 2 * N; k += 2 * NxRadix)
{
auto a = float32x2_t{ 0, 0 };
auto b = float32x2_t{ 0, 0 };
// Load inputs
if(first_stage)
{
const auto ab = wrapper::vloadq(x + k);
a = wrapper::vgetlow(ab);
b = wrapper::vgethigh(ab);
}
else
{
a = wrapper::vload(x + k);
b = wrapper::vload(x + k + 2 * Nx);
}
// Base-case prime transform
fft_2(a, b, w);
// Write outputs
if(first_stage)
{
wrapper::vstore(X + k, wrapper::vcombine(a, b));
}
else
{
wrapper::vstore(X + k, a);
wrapper::vstore(X + k + 2 * Nx, b);
}
}
w = c_mul_neon(w, w_m);
}
}
void fft_radix_2_axes_1(float *X, float *x, unsigned int Nx, unsigned int NxRadix, const float32x2_t &w_m, unsigned int M, unsigned int N)
{
float32x2_t w{ 1.0f, 0.0f };
for(unsigned int j = 0; j < Nx; j++)
{
for(unsigned int k = 2 * j; k < 2 * N; k += 2 * NxRadix)
{
// Load inputs
float32x2_t a = wrapper::vload(x + M * k);
float32x2_t b = wrapper::vload(x + M * (k + 2 * Nx));
// Base-case prime transform
fft_2(a, b, w);
// Write outputs
wrapper::vstore(X + M * k, a);
wrapper::vstore(X + M * (k + 2 * Nx), b);
}
w = c_mul_neon(w, w_m);
}
}
template <bool first_stage>
void fft_radix_3_axes_0(float *X, float *x, unsigned int Nx, unsigned int NxRadix, const float32x2_t &w_m, unsigned int N)
{
float32x2_t w{ 1.0f, 0.0f };
for(unsigned int j = 0; j < Nx; j++)
{
const auto w2 = c_mul_neon(w, w);
for(unsigned int k = 2 * j; k < 2 * N; k += 2 * NxRadix)
{
// Load inputs
float32x2_t a = { 0, 0 };
float32x2_t b = { 0, 0 };
float32x2_t c = { 0, 0 };
if(first_stage)
{
const auto ab = wrapper::vloadq(x + k);
a = wrapper::vgetlow(ab);
b = wrapper::vgethigh(ab);
}
else
{
a = wrapper::vload(x + k);
b = wrapper::vload(x + k + 2 * Nx);
}
c = wrapper::vload(x + k + 4 * Nx);
// Base-case prime transform
fft_3(a, b, c, w, w2);
if(first_stage)
{
wrapper::vstore(X + k, wrapper::vcombine(a, b));
}
else
{
wrapper::vstore(X + k, a);
wrapper::vstore(X + k + 2 * Nx, b);
}
wrapper::vstore(X + k + 4 * Nx, c);
}
w = c_mul_neon(w, w_m);
}
}
void fft_radix_3_axes_1(float *X, float *x, unsigned int Nx, unsigned int NxRadix, const float32x2_t &w_m, unsigned int M, unsigned int N)
{
float32x2_t w{ 1.0f, 0.0f };
for(unsigned int j = 0; j < Nx; j++)
{
const auto w2 = c_mul_neon(w, w);
for(unsigned int k = 2 * j; k < 2 * N; k += 2 * NxRadix)
{
// Load inputs
float32x2_t a = wrapper::vload(x + M * k);
float32x2_t b = wrapper::vload(x + M * (k + 2 * Nx));
float32x2_t c = wrapper::vload(x + M * (k + 4 * Nx));
// Base-case prime transform
fft_3(a, b, c, w, w2);
// Store the output
wrapper::vstore(X + M * k, a);
wrapper::vstore(X + M * (k + 2 * Nx), b);
wrapper::vstore(X + M * (k + 4 * Nx), c);
}
w = c_mul_neon(w, w_m);
}
}
template <bool first_stage>
void fft_radix_4_axes_0(float *X, float *x, unsigned int Nx, unsigned int NxRadix, const float32x2_t &w_m, unsigned int N)
{
float32x2_t w{ 1.0f, 0.0f };
for(unsigned int j = 0; j < Nx; j++)
{
const auto w2 = c_mul_neon(w, w);
const auto w3 = c_mul_neon(w2, w);
for(unsigned int k = 2 * j; k < 2 * N; k += 2 * NxRadix)
{
float32x2_t a = { 0, 0 };
float32x2_t b = { 0, 0 };
float32x2_t c = { 0, 0 };
float32x2_t d = { 0, 0 };
if(first_stage)
{
const auto ab = wrapper::vloadq(x + k);
const auto cd = wrapper::vloadq(x + k + 4 * Nx);
a = wrapper::vgetlow(ab);
b = wrapper::vgethigh(ab);
c = wrapper::vgetlow(cd);
d = wrapper::vgethigh(cd);
}
else
{
// Load inputs
a = wrapper::vload(x + k);
b = wrapper::vload(x + k + 2 * Nx);
c = wrapper::vload(x + k + 4 * Nx);
d = wrapper::vload(x + k + 6 * Nx);
}
// Base-case prime transform
fft_4(a, b, c, d, w, w2, w3);
if(first_stage)
{
wrapper::vstore(X + k, wrapper::vcombine(a, b));
wrapper::vstore(X + k + 4 * Nx, wrapper::vcombine(c, d));
}
else
{
wrapper::vstore(X + k, a);
wrapper::vstore(X + k + 2 * Nx, b);
wrapper::vstore(X + k + 4 * Nx, c);
wrapper::vstore(X + k + 6 * Nx, d);
}
}
w = c_mul_neon(w, w_m);
}
}
void fft_radix_4_axes_1(float *X, float *x, unsigned int Nx, unsigned int NxRadix, const float32x2_t &w_m, unsigned int M, unsigned int N)
{
float32x2_t w{ 1.0f, 0.0f };
for(unsigned int j = 0; j < Nx; j++)
{
const auto w2 = c_mul_neon(w, w);
const auto w3 = c_mul_neon(w2, w);
for(unsigned int k = 2 * j; k < 2 * N; k += 2 * NxRadix)
{
// Load inputs
float32x2_t a = wrapper::vload(x + M * k);
float32x2_t b = wrapper::vload(x + M * (k + 2 * Nx));
float32x2_t c = wrapper::vload(x + M * (k + 4 * Nx));
float32x2_t d = wrapper::vload(x + M * (k + 6 * Nx));
// Base-case prime transform
fft_4(a, b, c, d, w, w2, w3);
wrapper::vstore(X + M * k, a);
wrapper::vstore(X + M * (k + 2 * Nx), b);
wrapper::vstore(X + M * (k + 4 * Nx), c);
wrapper::vstore(X + M * (k + 6 * Nx), d);
}
w = c_mul_neon(w, w_m);
}
}
template <bool first_stage>
void fft_radix_5_axes_0(float *X, float *x, unsigned int Nx, unsigned int NxRadix, const float32x2_t &w_m, unsigned int N)
{
float32x2_t w{ 1.0f, 0.0f };
for(unsigned int j = 0; j < Nx; j++)
{
const float32x2_t w2 = c_mul_neon(w, w);
const float32x2_t w3 = c_mul_neon(w2, w);
const float32x2_t w4 = c_mul_neon(w3, w);
for(unsigned int k = 2 * j; k < 2 * N; k += 2 * NxRadix)
{
float32x2_t a = { 0, 0 };
float32x2_t b = { 0, 0 };
float32x2_t c = { 0, 0 };
float32x2_t d = { 0, 0 };
float32x2_t e = { 0, 0 };
// Load inputs
if(first_stage)
{
const auto ab = wrapper::vloadq(x + k);
const auto cd = wrapper::vloadq(x + k + 4 * Nx);
a = wrapper::vgetlow(ab);
b = wrapper::vgethigh(ab);
c = wrapper::vgetlow(cd);
d = wrapper::vgethigh(cd);
}
else
{
a = wrapper::vload(x + k);
b = wrapper::vload(x + k + 2 * Nx);
c = wrapper::vload(x + k + 4 * Nx);
d = wrapper::vload(x + k + 6 * Nx);
}
e = wrapper::vload(x + k + 8 * Nx);
// Base-case prime transform
fft_5(a, b, c, d, e, w, w2, w3, w4);
// Store outputs
if(first_stage)
{
wrapper::vstore(X + k, wrapper::vcombine(a, b));
wrapper::vstore(X + k + 4 * Nx, wrapper::vcombine(c, d));
}
else
{
wrapper::vstore(X + k, a);
wrapper::vstore(X + k + 2 * Nx, b);
wrapper::vstore(X + k + 4 * Nx, c);
wrapper::vstore(X + k + 6 * Nx, d);
}
wrapper::vstore(X + k + 8 * Nx, e);
}
w = c_mul_neon(w, w_m);
}
}
void fft_radix_5_axes_1(float *X, float *x, unsigned int Nx, unsigned int NxRadix, const float32x2_t &w_m, unsigned int M, unsigned int N)
{
float32x2_t w{ 1.0f, 0.0f };
for(unsigned int j = 0; j < Nx; j++)
{
const float32x2_t w2 = c_mul_neon(w, w);
const float32x2_t w3 = c_mul_neon(w2, w);
const float32x2_t w4 = c_mul_neon(w3, w);
for(unsigned int k = 2 * j; k < 2 * N; k += 2 * NxRadix)
{
// Load inputs
float32x2_t a = wrapper::vload(x + M * k);
float32x2_t b = wrapper::vload(x + M * (k + 2 * Nx));
float32x2_t c = wrapper::vload(x + M * (k + 4 * Nx));
float32x2_t d = wrapper::vload(x + M * (k + 6 * Nx));
float32x2_t e = wrapper::vload(x + M * (k + 8 * Nx));
// Base-case prime transform
fft_5(a, b, c, d, e, w, w2, w3, w4);
// Store outputs
wrapper::vstore(X + M * k, a);
wrapper::vstore(X + M * (k + 2 * Nx), b);
wrapper::vstore(X + M * (k + 4 * Nx), c);
wrapper::vstore(X + M * (k + 6 * Nx), d);
wrapper::vstore(X + M * (k + 8 * Nx), e);
}
w = c_mul_neon(w, w_m);
}
}
template <bool first_stage>
void fft_radix_7_axes_0(float *X, float *x, unsigned int Nx, unsigned int NxRadix, const float32x2_t &w_m, unsigned int N)
{
float32x2_t w{ 1.0f, 0.0f };
for(unsigned int j = 0; j < Nx; j++)
{
const float32x2_t w2 = c_mul_neon(w, w);
const float32x2_t w3 = c_mul_neon(w2, w);
const float32x2_t w4 = c_mul_neon(w3, w);
const float32x2_t w5 = c_mul_neon(w4, w);
const float32x2_t w6 = c_mul_neon(w5, w);
for(unsigned int k = 2 * j; k < 2 * N; k += 2 * NxRadix)
{
float32x2_t a = { 0, 0 };
float32x2_t b = { 0, 0 };
float32x2_t c = { 0, 0 };
float32x2_t d = { 0, 0 };
float32x2_t e = { 0, 0 };
float32x2_t f = { 0, 0 };
float32x2_t g = { 0, 0 };
// Load inputs
if(first_stage)
{
const auto ab = wrapper::vloadq(x + k);
const auto cd = wrapper::vloadq(x + k + 4 * Nx);
const auto ef = wrapper::vloadq(x + k + 8 * Nx);
a = wrapper::vgetlow(ab);
b = wrapper::vgethigh(ab);
c = wrapper::vgetlow(cd);
d = wrapper::vgethigh(cd);
e = wrapper::vgetlow(ef);
f = wrapper::vgethigh(ef);
}
else
{
a = wrapper::vload(x + k);
b = wrapper::vload(x + k + 2 * Nx);
c = wrapper::vload(x + k + 4 * Nx);
d = wrapper::vload(x + k + 6 * Nx);
e = wrapper::vload(x + k + 8 * Nx);
f = wrapper::vload(x + k + 10 * Nx);
}
g = wrapper::vload(x + k + 12 * Nx);
// Base-case prime transform
fft_7(a, b, c, d, e, f, g, w, w2, w3, w4, w5, w6);
if(first_stage)
{
wrapper::vstore(X + k, wrapper::vcombine(a, b));
wrapper::vstore(X + k + 4 * Nx, wrapper::vcombine(c, d));
wrapper::vstore(X + k + 8 * Nx, wrapper::vcombine(e, f));
}
else
{
wrapper::vstore(X + k, a);
wrapper::vstore(X + k + 2 * Nx, b);
wrapper::vstore(X + k + 4 * Nx, c);
wrapper::vstore(X + k + 6 * Nx, d);
wrapper::vstore(X + k + 8 * Nx, e);
wrapper::vstore(X + k + 10 * Nx, f);
}
wrapper::vstore(X + k + 12 * Nx, g);
}
w = c_mul_neon(w, w_m);
}
}
void fft_radix_7_axes_1(float *X, float *x, unsigned int Nx, unsigned int NxRadix, const float32x2_t &w_m, unsigned int M, unsigned int N)
{
float32x2_t w{ 1.0f, 0.0f };
for(unsigned int j = 0; j < Nx; j++)
{
const float32x2_t w2 = c_mul_neon(w, w);
const float32x2_t w3 = c_mul_neon(w2, w);
const float32x2_t w4 = c_mul_neon(w3, w);
const float32x2_t w5 = c_mul_neon(w4, w);
const float32x2_t w6 = c_mul_neon(w5, w);
for(unsigned int k = 2 * j; k < 2 * N; k += 2 * NxRadix)
{
// Load inputs
float32x2_t a = wrapper::vload(x + M * k);
float32x2_t b = wrapper::vload(x + M * (k + 2 * Nx));
float32x2_t c = wrapper::vload(x + M * (k + 4 * Nx));
float32x2_t d = wrapper::vload(x + M * (k + 6 * Nx));
float32x2_t e = wrapper::vload(x + M * (k + 8 * Nx));
float32x2_t f = wrapper::vload(x + M * (k + 10 * Nx));
float32x2_t g = wrapper::vload(x + M * (k + 12 * Nx));
// Base-case prime transform
fft_7(a, b, c, d, e, f, g, w, w2, w3, w4, w5, w6);
// Store outputs
wrapper::vstore(X + M * k, a);
wrapper::vstore(X + M * (k + 2 * Nx), b);
wrapper::vstore(X + M * (k + 4 * Nx), c);
wrapper::vstore(X + M * (k + 6 * Nx), d);
wrapper::vstore(X + M * (k + 8 * Nx), e);
wrapper::vstore(X + M * (k + 10 * Nx), f);
wrapper::vstore(X + M * (k + 12 * Nx), g);
}
w = c_mul_neon(w, w_m);
}
}
template <bool first_stage>
void fft_radix_8_axes_0(float *X, float *x, unsigned int Nx, unsigned int NxRadix, const float32x2_t &w_m, unsigned int N)
{
float32x2_t w{ 1.0f, 0.0f };
for(unsigned int j = 0; j < Nx; j++)
{
const float32x2_t w2 = c_mul_neon(w, w);
const float32x2_t w3 = c_mul_neon(w2, w);
const float32x2_t w4 = c_mul_neon(w3, w);
const float32x2_t w5 = c_mul_neon(w4, w);
const float32x2_t w6 = c_mul_neon(w5, w);
const float32x2_t w7 = c_mul_neon(w6, w);
for(unsigned int k = 2 * j; k < 2 * N; k += 2 * NxRadix)
{
// Load inputs
float32x2_t a = { 0, 0 };
float32x2_t b = { 0, 0 };
float32x2_t c = { 0, 0 };
float32x2_t d = { 0, 0 };
float32x2_t e = { 0, 0 };
float32x2_t f = { 0, 0 };
float32x2_t g = { 0, 0 };
float32x2_t h = { 0, 0 };
// Base-case prime transform
if(first_stage)
{
const auto ab = wrapper::vloadq(x + k);
const auto cd = wrapper::vloadq(x + k + 4 * Nx);
const auto ef = wrapper::vloadq(x + k + 8 * Nx);
const auto gh = wrapper::vloadq(x + k + 12 * Nx);
a = wrapper::vgetlow(ab);
b = wrapper::vgethigh(ab);
c = wrapper::vgetlow(cd);
d = wrapper::vgethigh(cd);
e = wrapper::vgetlow(ef);
f = wrapper::vgethigh(ef);
g = wrapper::vgetlow(gh);
h = wrapper::vgethigh(gh);
}
else
{
a = wrapper::vload(x + k);
b = wrapper::vload(x + k + 2 * Nx);
c = wrapper::vload(x + k + 4 * Nx);
d = wrapper::vload(x + k + 6 * Nx);
e = wrapper::vload(x + k + 8 * Nx);
f = wrapper::vload(x + k + 10 * Nx);
g = wrapper::vload(x + k + 12 * Nx);
h = wrapper::vload(x + k + 14 * Nx);
}
// Apply twiddle factors
fft_8(a, b, c, d, e, f, g, h, w, w2, w3, w4, w5, w6, w7);
// Store outputs
if(first_stage)
{
wrapper::vstore(X + k, wrapper::vcombine(a, b));
wrapper::vstore(X + k + 4 * Nx, wrapper::vcombine(c, d));
wrapper::vstore(X + k + 8 * Nx, wrapper::vcombine(e, f));
wrapper::vstore(X + k + 12 * Nx, wrapper::vcombine(g, h));
}
else
{
wrapper::vstore(X + k, a);
wrapper::vstore(X + k + 2 * Nx, b);
wrapper::vstore(X + k + 4 * Nx, c);
wrapper::vstore(X + k + 6 * Nx, d);
wrapper::vstore(X + k + 8 * Nx, e);
wrapper::vstore(X + k + 10 * Nx, f);
wrapper::vstore(X + k + 12 * Nx, g);
wrapper::vstore(X + k + 14 * Nx, h);
}
}
w = c_mul_neon(w, w_m);
}
}
void fft_radix_8_axes_1(float *X, float *x, unsigned int Nx, unsigned int NxRadix, const float32x2_t &w_m, unsigned int M, unsigned int N)
{
float32x2_t w{ 1.0f, 0.0f };
for(unsigned int j = 0; j < Nx; j++)
{
const float32x2_t w2 = c_mul_neon(w, w);
const float32x2_t w3 = c_mul_neon(w2, w);
const float32x2_t w4 = c_mul_neon(w3, w);
const float32x2_t w5 = c_mul_neon(w4, w);
const float32x2_t w6 = c_mul_neon(w5, w);
const float32x2_t w7 = c_mul_neon(w6, w);
for(unsigned int k = 2 * j; k < 2 * N; k += 2 * NxRadix)
{
// Load inputs
float32x2_t a = wrapper::vload(x + M * k);
float32x2_t b = wrapper::vload(x + M * (k + 2 * Nx));
float32x2_t c = wrapper::vload(x + M * (k + 4 * Nx));
float32x2_t d = wrapper::vload(x + M * (k + 6 * Nx));
float32x2_t e = wrapper::vload(x + M * (k + 8 * Nx));
float32x2_t f = wrapper::vload(x + M * (k + 10 * Nx));
float32x2_t g = wrapper::vload(x + M * (k + 12 * Nx));
float32x2_t h = wrapper::vload(x + M * (k + 14 * Nx));
// Base-case prime transform
fft_8(a, b, c, d, e, f, g, h, w, w2, w3, w4, w5, w6, w7);
// Store outputs
wrapper::vstore(X + M * k, a);
wrapper::vstore(X + M * (k + 2 * Nx), b);
wrapper::vstore(X + M * (k + 4 * Nx), c);
wrapper::vstore(X + M * (k + 6 * Nx), d);
wrapper::vstore(X + M * (k + 8 * Nx), e);
wrapper::vstore(X + M * (k + 10 * Nx), f);
wrapper::vstore(X + M * (k + 12 * Nx), g);
wrapper::vstore(X + M * (k + 14 * Nx), h);
}
w = c_mul_neon(w, w_m);
}
}
Status validate_arguments(const ITensorInfo *input, const ITensorInfo *output, const FFTRadixStageKernelInfo &config)
{
ARM_COMPUTE_RETURN_ERROR_ON_DATA_TYPE_CHANNEL_NOT_IN(input, 2, DataType::F32);
ARM_COMPUTE_RETURN_ERROR_ON(config.axis > 1);
ARM_COMPUTE_RETURN_ERROR_ON(NEFFTRadixStageKernel::supported_radix().count(config.radix) == 0);
ARM_COMPUTE_UNUSED(config);
// Checks performed when output is configured
if((output != nullptr) && (output->total_size() != 0))
{
ARM_COMPUTE_RETURN_ERROR_ON_MISMATCHING_SHAPES(input, output);
ARM_COMPUTE_RETURN_ERROR_ON_MISMATCHING_DATA_TYPES(input, output);
}
return Status{};
}
std::pair<Status, Window> validate_and_configure_window(ITensorInfo *input, ITensorInfo *output, const FFTRadixStageKernelInfo &config)
{
ARM_COMPUTE_UNUSED(config);
if(output != nullptr)
{
auto_init_if_empty(*output, *input);
}
Window win = calculate_max_window(*input, Steps());
if(output != nullptr)
{
output->set_valid_region(ValidRegion(Coordinates(), output->tensor_shape()));
}
return std::make_pair(Status{}, win);
}
} // namespace
NEFFTRadixStageKernel::NEFFTRadixStageKernel()
: _input(nullptr), _output(nullptr), _run_in_place(false), _Nx(0), _axis(0), _radix(0), _func_0(), _func_1()
{
}
void NEFFTRadixStageKernel::set_radix_stage_axis0(const FFTRadixStageKernelInfo &config)
{
// FFT table axis 0: [radix, first_stage]
static std::map<unsigned int, std::map<bool, FFTFunctionPointerAxis0>> fft_table_axis0;
if(fft_table_axis0.empty())
{
fft_table_axis0[2][false] = &fft_radix_2_axes_0<false>;
fft_table_axis0[3][false] = &fft_radix_3_axes_0<false>;
fft_table_axis0[4][false] = &fft_radix_4_axes_0<false>;
fft_table_axis0[5][false] = &fft_radix_5_axes_0<false>;
fft_table_axis0[7][false] = &fft_radix_7_axes_0<false>;
fft_table_axis0[8][false] = &fft_radix_8_axes_0<false>;
fft_table_axis0[2][true] = &fft_radix_2_axes_0<true>;
fft_table_axis0[3][true] = &fft_radix_3_axes_0<true>;
fft_table_axis0[4][true] = &fft_radix_4_axes_0<true>;
fft_table_axis0[5][true] = &fft_radix_5_axes_0<true>;
fft_table_axis0[7][true] = &fft_radix_7_axes_0<true>;
fft_table_axis0[8][true] = &fft_radix_8_axes_0<true>;
}
_func_0 = fft_table_axis0[config.radix][config.is_first_stage];
}
void NEFFTRadixStageKernel::set_radix_stage_axis1(const FFTRadixStageKernelInfo &config)
{
// FFT table axis 1: [radix, first_stage]
static std::map<unsigned int, FFTFunctionPointerAxis1> fft_table_axis1;
if(fft_table_axis1.empty())
{
fft_table_axis1[2] = &fft_radix_2_axes_1;
fft_table_axis1[3] = &fft_radix_3_axes_1;
fft_table_axis1[4] = &fft_radix_4_axes_1;
fft_table_axis1[5] = &fft_radix_5_axes_1;
fft_table_axis1[7] = &fft_radix_7_axes_1;
fft_table_axis1[8] = &fft_radix_8_axes_1;
}
_func_1 = fft_table_axis1[config.radix];
}
void NEFFTRadixStageKernel::configure(ITensor *input, ITensor *output, const FFTRadixStageKernelInfo &config)
{
ARM_COMPUTE_ERROR_ON_NULLPTR(input);
// Output auto inizialitation if not yet initialized
if(output != nullptr)
{
auto_init_if_empty(*output->info(), *input->info()->clone());
}
ARM_COMPUTE_ERROR_THROW_ON(validate_arguments(input->info(), (output != nullptr) ? output->info() : nullptr, config));
_input = input;
_output = output;
_run_in_place = (output == nullptr) || (output == input);
_Nx = config.Nx;
_axis = config.axis;
_radix = config.radix;
switch(config.axis)
{
case 0:
set_radix_stage_axis0(config);
break;
case 1:
set_radix_stage_axis1(config);
break;
default:
ARM_COMPUTE_ERROR("Axis not supported");
break;
}
// Configure kernel window
auto win_config = validate_and_configure_window(input->info(), (_run_in_place) ? nullptr : output->info(), config);
ARM_COMPUTE_ERROR_THROW_ON(win_config.first);
INEKernel::configure(win_config.second);
}
Status NEFFTRadixStageKernel::validate(const ITensorInfo *input, const ITensorInfo *output, const FFTRadixStageKernelInfo &config)
{
const bool run_in_place = (output == nullptr) || (output == input);
ARM_COMPUTE_RETURN_ON_ERROR(validate_arguments(input, output, config));
ARM_COMPUTE_RETURN_ON_ERROR(validate_and_configure_window(input->clone().get(),
(run_in_place) ? nullptr : output->clone().get(),
config)
.first);
return Status{};
}
std::set<unsigned int> NEFFTRadixStageKernel::supported_radix()
{
return std::set<unsigned int> { 2, 3, 4, 5, 7, 8 };
}
void NEFFTRadixStageKernel::run(const Window &window, const ThreadInfo &info)
{
ARM_COMPUTE_ERROR_ON_UNCONFIGURED_KERNEL(this);
ARM_COMPUTE_ERROR_ON_INVALID_SUBWINDOW(INEKernel::window(), window);
ARM_COMPUTE_UNUSED(info);
Window input_window = window;
input_window.set(_axis, 0);
Iterator in(_input, input_window);
Iterator out(_run_in_place ? _input : _output, input_window);
// Precompute FFT constants
const unsigned int NxRadix = _radix * _Nx;
const float alpha = 2.0f * kPi / float(NxRadix);
const float32x2_t w_m{ cosf(alpha), -sinf(alpha) };
if(_axis == 0)
{
const unsigned int N = _input->info()->dimension(0);
execute_window_loop(input_window, [&](const Coordinates &)
{
_func_0(reinterpret_cast<float *>(out.ptr()), reinterpret_cast<float *>(in.ptr()), _Nx, NxRadix, w_m, N);
},
in, out);
}
else
{
const unsigned int N = _input->info()->dimension(0);
const unsigned int M = _input->info()->dimension(1);
execute_window_loop(input_window, [&](const Coordinates &)
{
_func_1(reinterpret_cast<float *>(out.ptr()), reinterpret_cast<float *>(in.ptr()), _Nx, NxRadix, w_m, N, M);
},
in, out);
}
ARM_COMPUTE_ERROR_ON_UNCONFIGURED_KERNEL(this);
ARM_COMPUTE_ERROR_ON_INVALID_SUBWINDOW(INEKernel::window(), window);
}
} // namespace arm_compute