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/*
! Content:
! A simple example of single-precision complex-to-complex in-place 2D
! FFT using Intel(R) MKL DFTI
!
!****************************************************************************/

#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <float.h>
#include "mkl_service.h"
#include "mkl_dfti.h"

static void init(MKL_Complex8 *x, int N1, int N2, int H1, int H2);
static int verify(MKL_Complex8 *x, int N1, int N2, int H1, int H2);

/* Define the format to printf MKL_LONG values */
#if !defined(MKL_ILP64)
#define LI "%li"
#else
#define LI "%lli"
#endif

int main(void)
{
    /* Sizes of 2D transform */
    int N1 = 7, N2 = 13;

    /* Arbitrary harmonic used to verify FFT */
    int H1 = -1, H2 = -2;

    /* Pointer to input/output data */
    MKL_Complex8 *x = 0;

    /* Execution status */
    MKL_LONG status = 0;

    DFTI_DESCRIPTOR_HANDLE hand = 0;

    char version[DFTI_VERSION_LENGTH];

    DftiGetValue(0, DFTI_VERSION, version);
    printf("%s\n", version);

    printf("Example basic_sp_complex_dft_2d\n");
    printf("Forward and backward single-precision complex in-place 2D FFTs\n");
    printf("Configuration parameters:\n");
    printf(" DFTI_PRECISION      = DFTI_SINGLE\n");
    printf(" DFTI_FORWARD_DOMAIN = DFTI_COMPLEX\n");
    printf(" DFTI_DIMENSION      = 2\n");
    printf(" DFTI_LENGTHS        = {%i, %i}\n", N1, N2);


    printf("Create DFTI descriptor\n");
    {
        MKL_LONG N[2]; N[0] = N1; N[1] = N2;
        status = DftiCreateDescriptor(&hand, DFTI_SINGLE, DFTI_COMPLEX, 2, N);
        if (0 != status) goto failed;
    }

    printf("Commit DFTI descriptor\n");
    status = DftiCommitDescriptor(hand);
    if (0 != status) goto failed;

    printf("Allocate input array\n");
    x = (MKL_Complex8*)mkl_malloc(N1*N2*sizeof(MKL_Complex8), 64);
    if (0 == x) goto failed;

    printf("Initialize input for forward transform\n");
    init(x, N1, N2, H1, H2);

    printf("Compute forward transform\n");
    status = DftiComputeForward(hand, x);
    if (0 != status) goto failed;

    printf("Verify the result of forward FFT\n");
    status = verify(x, N1, N2, H1, H2);
    if (0 != status) goto failed;

    printf("Initialize input for backward transform\n");
    init(x, N1, N2, -H1, -H2);

    printf("Compute backward transform\n");
    status = DftiComputeBackward(hand, x);
    if (0 != status) goto failed;

    printf("Verify the result of backward FFT\n");
    status = verify(x, N1, N2, H1, H2);
    if (0 != status) goto failed;

 cleanup:

    printf("Free DFTI descriptor\n");
    DftiFreeDescriptor(&hand);

    printf("Free data array\n");
    mkl_free(x);

    printf("TEST %s\n",0==status ? "PASSED" : "FAILED");
    return status;

 failed:
    printf(" ERROR, status = "LI"\n", status);
    status = 1;
    goto cleanup;
}

/* Compute (K*L)%M accurately */
static float moda(int K, int L, int M)
{
    return (float)(((long long)K * L) % M);
}

/* Initialize array with harmonic {H1, H2} */
static void init(MKL_Complex8 *x, int N1, int N2, int H1, int H2)
{
    float TWOPI = 6.2831853071795864769f, phase;
    int n1, n2, index;

    /* Generalized strides for row-major addressing of x */
    int S1 = N2, S2 = 1;

    for (n1 = 0; n1 < N1; n1++)
    {
        for (n2 = 0; n2 < N2; n2++)
        {
            phase = TWOPI * ( moda(n1,H1,N1) / N1
                              + moda(n2,H2,N2) / N2 );
            index = n1*S1 + n2*S2;
             x[index].real = cosf(phase) / (N1*N2);
             x[index].imag = sinf(phase) / (N1*N2);
        }
    }
}

/* Verify that x has unit peak at H */
static int verify(MKL_Complex8 *x, int N1, int N2, int H1, int H2)
{
    float err, errthr, maxerr;
    int n1, n2, index;

    /* Generalized strides for row-major addressing of x */
    int S1 = N2, S2 = 1;

    /*
     * Note, this simple error bound doesn't take into account error of
     * input data
     */
    errthr = 5.0f * logf( (float)N1*N2 ) / logf(2.0f) * FLT_EPSILON;
    printf(" Verify the result, errthr = %.3lg\n", errthr);

    maxerr = 0;
    for (n1 = 0; n1 < N1; n1++)
    {
        for (n2 = 0; n2 < N2; n2++)
        {
            float re_exp = 0.0f, im_exp = 0.0f, re_got, im_got;

            if ((n1-H1)%N1==0 && (n2-H2)%N2==0)
            {
                re_exp = 1;
            }

            index = n1*S1 + n2*S2;
            re_got = x[index].real;
            im_got = x[index].imag;
            err  = fabsf(re_got - re_exp) + fabsf(im_got - im_exp);
            if (err > maxerr) maxerr = err;
            if (!(err < errthr))
            {
                printf(" x[%i][%i]: ",n1,n2);
                printf(" expected (%.7g,%.7g), ",re_exp,im_exp);
                printf(" got (%.7g,%.7g), ",re_got,im_got);
                printf(" err %.3lg\n", err);
                printf(" Verification FAILED\n");
                return 1;
            }
        }
    }
    printf(" Verified, maximum error was %.3lg\n", maxerr);
    return 0;
}