apps/fft/main.cpp

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This source file includes following definitions.
make_real
make_complex
log2
main
// This FFT is an implementation of the algorithm described in
// http://research.microsoft.com/pubs/131400/fftgpusc08.pdf
// This algorithm is more well suited to Halide than in-place
// algorithms.

#include "Halide.h"
#include <cstdio>
#include <vector>
#include "fft.h"
#include "halide_benchmark.h"

#ifdef WITH_FFTW
#include <fftw3.h>
#endif

using namespace Halide;
using namespace Halide::Tools;

Var x("x"), y("y");

template <typename T>
Func make_real(const Buffer<T> &re) {
    Func ret;
    ret(x, y) = re(x, y);
    return ret;
}

template <typename T>
ComplexFunc make_complex(const Buffer<T> &re) {
    ComplexFunc ret;
    ret(x, y) = re(x, y);
    return ret;
}

double log2(double x) {
    return log(x)/log(2.0);
}

int main(int argc, char **argv) {
    int W = 32;
    int H = 32;
    if (argc >= 3) {
        W = atoi(argv[1]);
        H = atoi(argv[2]);
    }
    std::string output_dir;
    if (argc >= 4) {
        output_dir = argv[3];
    }

    // Generate a random image to convolve with.
    Buffer<float> in(W, H);
    for (int y = 0; y < H; y++) {
        for (int x = 0; x < W; x++) {
            in(x, y) = (float)rand()/(float)RAND_MAX;
        }
    }

    // Construct a box filter kernel centered on the origin.
    const int box = 3;
    Buffer<float> kernel(W, H);
    for (int y = 0; y < H; y++) {
        for (int x = 0; x < W; x++) {
            int u = x < (W - x) ? x : (W - x);
            int v = y < (H - y) ? y : (H - y);
            kernel(x, y) = u <= box/2 && v <= box/2 ? 1.0f/(box*box) : 0.0f;
        }
    }

    Target target = get_jit_target_from_environment();

    Fft2dDesc fwd_desc;
    Fft2dDesc inv_desc;
    inv_desc.gain = 1.0f/(W*H);

    Func filtered_c2c;
    {
        // Compute the DFT of the input and the kernel.
        ComplexFunc dft_in = fft2d_c2c(make_complex(in), W, H, -1, target, fwd_desc);
        ComplexFunc dft_kernel = fft2d_c2c(make_complex(kernel), W, H, -1, target, fwd_desc);
        dft_in.compute_root();
        dft_kernel.compute_root();

        // Compute the convolution.
        ComplexFunc dft_filtered("dft_filtered");
        dft_filtered(x, y) = dft_in(x, y) * dft_kernel(x, y);

        // Compute the inverse DFT to get the result.
        ComplexFunc dft_out = fft2d_c2c(dft_filtered, W, H, 1, target, inv_desc);
        dft_out.compute_root();

        // Extract the real component and normalize.
        filtered_c2c(x, y) = re(dft_out(x, y));
    }

    Func filtered_r2c;
    {
        // Compute the DFT of the input and the kernel.
        ComplexFunc dft_in = fft2d_r2c(make_real(in), W, H, target, fwd_desc);
        ComplexFunc dft_kernel = fft2d_r2c(make_real(kernel), W, H, target, fwd_desc);
        dft_in.compute_root();
        dft_kernel.compute_root();

        // Compute the convolution.
        ComplexFunc dft_filtered("dft_filtered");
        dft_filtered(x, y) = dft_in(x, y) * dft_kernel(x, y);

        // Compute the inverse DFT to get the result.
        filtered_r2c = fft2d_c2r(dft_filtered, W, H, target, inv_desc);
    }

    Buffer<float> result_c2c = filtered_c2c.realize(W, H, target);
    Buffer<float> result_r2c = filtered_r2c.realize(W, H, target);

    for (int y = 0; y < H; y++) {
        for (int x = 0; x < W; x++) {
            float correct = 0;
            for (int i = -box/2; i <= box/2; i++) {
                for (int j = -box/2; j <= box/2; j++) {
                    correct += in((x + j + W)%W, (y + i + H)%H);
                }
            }
            correct /= box*box;
            if (fabs(result_c2c(x, y) - correct) > 1e-6f) {
                printf("result_c2c(%d, %d) = %f instead of %f\n", x, y, result_c2c(x, y), correct);
                return -1;
            }
            if (fabs(result_r2c(x, y) - correct) > 1e-6f) {
                printf("result_r2c(%d, %d) = %f instead of %f\n", x, y, result_r2c(x, y), correct);
                return -1;
            }
        }
    }

    // For a description of the methodology used here, see
    // http://www.fftw.org/speed/method.html

    // Take the minimum time over many of iterations to minimize
    // noise.
    const int samples = 100;
    const int reps = 1000;

    Var rep("rep");

    Buffer<float> re_in = lambda(x, y, 0.0f).realize(W, H);
    Buffer<float> im_in = lambda(x, y, 0.0f).realize(W, H);

    printf("%12s %5s%11s%5s %5s%11s%5s\n", "", "", "Halide", "", "", "FFTW", "");
    printf("%12s %10s %10s %10s %10s %10s\n", "DFT type", "Time (us)", "MFLOP/s", "Time (us)", "MFLOP/s", "Ratio");

    ComplexFunc c2c_in;
    // Read all reps from the same place in memory. This effectively
    // benchmarks taking the FFT of cached inputs, which is a
    // reasonable assumption for a well optimized program with good
    // locality.
    c2c_in(x, y, rep) = {re_in(x, y), im_in(x, y)};
    Func bench_c2c = fft2d_c2c(c2c_in, W, H, -1, target, fwd_desc);
    bench_c2c.compile_to_lowered_stmt(output_dir + "c2c.html", bench_c2c.infer_arguments(), HTML);
    Realization R_c2c = bench_c2c.realize(W, H, reps, target);
    // Write all reps to the same place in memory. This means the
    // output appears to be cached on all but the first
    // iteration. This seems to match the behavior of FFTW's benchmark
    // code, and like the input, it is a reasonable assumption for a well
    // optimized real world system.
    R_c2c[0].raw_buffer()->dim[2].stride = 0;
    R_c2c[1].raw_buffer()->dim[2].stride = 0;

    double halide_t = benchmark(samples, 1, [&]() { bench_c2c.realize(R_c2c); })*1e6/reps;
#ifdef WITH_FFTW
    std::vector<std::pair<float, float>> fftw_c1(W * H);
    std::vector<std::pair<float, float>> fftw_c2(W * H);
    fftwf_plan c2c_plan = fftwf_plan_dft_2d(W, H, (fftwf_complex*)&fftw_c1[0], (fftwf_complex*)&fftw_c2[0], FFTW_FORWARD, FFTW_EXHAUSTIVE);
    double fftw_t = benchmark(samples, reps, [&]() { fftwf_execute(c2c_plan); })*1e6;
#else
    double fftw_t = 0;
#endif
    printf("%12s %10.3f %10.2f %10.3f %10.2f %10.3g\n",
           "c2c",
           halide_t,
           5*W*H*(log2(W) + log2(H))/halide_t,
           fftw_t,
           5*W*H*(log2(W) + log2(H))/fftw_t,
           fftw_t / halide_t);

    Func r2c_in;
    // All reps read from the same input. See notes on c2c_in.
    r2c_in(x, y, rep) = re_in(x, y);
    Func bench_r2c = fft2d_r2c(r2c_in, W, H, target, fwd_desc);
    bench_r2c.compile_to_lowered_stmt(output_dir + "r2c.html", bench_r2c.infer_arguments(), HTML);
    Realization R_r2c = bench_r2c.realize(W, H/2 + 1, reps, target);
    // Write all reps to the same place in memory. See notes on R_c2c.
    R_r2c[0].raw_buffer()->dim[2].stride = 0;
    R_r2c[1].raw_buffer()->dim[2].stride = 0;

    halide_t = benchmark(samples, 1, [&]() { bench_r2c.realize(R_r2c); })*1e6/reps;
#ifdef WITH_FFTW
    std::vector<float> fftw_r(W * H);
    fftwf_plan r2c_plan = fftwf_plan_dft_r2c_2d(W, H, &fftw_r[0], (fftwf_complex*)&fftw_c1[0], FFTW_EXHAUSTIVE);
    fftw_t = benchmark(samples, reps, [&]() { fftwf_execute(r2c_plan); })*1e6;
#else
    fftw_t = 0;
#endif
    printf("%12s %10.3f %10.2f %10.3f %10.2f %10.3g\n",
           "r2c",
           halide_t,
           2.5*W*H*(log2(W) + log2(H))/halide_t,
           fftw_t,
           2.5*W*H*(log2(W) + log2(H))/fftw_t,
           fftw_t / halide_t);

    ComplexFunc c2r_in;
    // All reps read from the same input. See notes on c2c_in.
    c2r_in(x, y, rep) = {re_in(x, y), im_in(x, y)};
    Func bench_c2r = fft2d_c2r(c2r_in, W, H, target, inv_desc);
    bench_c2r.compile_to_lowered_stmt(output_dir + "c2r.html", bench_c2r.infer_arguments(), HTML);
    Realization R_c2r = bench_c2r.realize(W, H, reps, target);
    // Write all reps to the same place in memory. See notes on R_c2c.
    R_c2r[0].raw_buffer()->dim[2].stride = 0;

    halide_t = benchmark(samples, 1, [&]() { bench_c2r.realize(R_c2r); })*1e6/reps;
#ifdef WITH_FFTW
    fftwf_plan c2r_plan = fftwf_plan_dft_c2r_2d(W, H, (fftwf_complex*)&fftw_c1[0], &fftw_r[0], FFTW_EXHAUSTIVE);
    fftw_t = benchmark(samples, reps, [&]() { fftwf_execute(c2r_plan); })*1e6;
#else
    fftw_t = 0;
#endif
    printf("%12s %10.3f %10.2f %10.3f %10.2f %10.3g\n",
           "c2r",
           halide_t,
           2.5*W*H*(log2(W) + log2(H))/halide_t,
           fftw_t,
           2.5*W*H*(log2(W) + log2(H))/fftw_t,
           fftw_t / halide_t);

#ifdef WITH_FFTW
    fftwf_destroy_plan(c2c_plan);
    fftwf_destroy_plan(r2c_plan);
    fftwf_destroy_plan(c2r_plan);
#endif

    return 0;
}
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root/apps/fft/main.cpp

DEFINITIONS
