config_number_of_transforms.c

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!*****************************************************************************
! Content:
! An example of using DFTI_NUMBER_OF_TRANSFORMS configuration parameter.
! The parameter defines how many identical transforms are computed by one call
! of DftiComputeForward or DftiComputeBackward function.
!
! Values:
! A positive integer (default 1)
!
!****************************************************************************/

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

static void init(MKL_Complex16 *x, MKL_LONG M,
                 MKL_LONG N1, MKL_LONG N2, MKL_LONG N3,
                 MKL_LONG H1, MKL_LONG H2, MKL_LONG H3);
static int verify(MKL_Complex16 *x, MKL_LONG M,
                  MKL_LONG N1, MKL_LONG N2, MKL_LONG N3,
                  MKL_LONG H1, MKL_LONG H2, MKL_LONG H3);

/* 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 3D transform */
    MKL_LONG N[3] = { 7, 13, 5 };

    /* Number of transforms */
    MKL_LONG M = 4;

    /* Arbitrary harmonic used to verify FFT */
    MKL_LONG H[3] = { 1, -1, -2 };

    /* Execution status */
    MKL_LONG status = 0;

    /* Pointer to input/output data */
    MKL_Complex16 *x = 0;

    DFTI_DESCRIPTOR_HANDLE hand = 0;

    /* Distance between first elements for multiple transforms */
    MKL_LONG dist;

    char version[DFTI_VERSION_LENGTH];


    DftiGetValue(0, DFTI_VERSION, version);
    printf("%s\n", version);
    printf("Example config_number_of_transforms\n");
    printf("Multiple in-place 3D FFT\n");
    printf("Configuration parameters:\n");
    printf(" DFTI_PRECISION      = DFTI_DOUBLE\n");
    printf(" DFTI_FORWARD_DOMAIN = DFTI_COMPLEX\n");
    printf(" DFTI_DIMENSION      = 3\n");
    printf(" DFTI_LENGTHS        = { "LI", "LI", "LI" }\n", N[0], N[1], N[2]);
    printf(" DFTI_NUMBER_OF_TRANSFORMS = "LI"\n", M);

    printf("Create DFTI descriptor for double-precision 3D transform\n");
    status = DftiCreateDescriptor(&hand, DFTI_DOUBLE, DFTI_COMPLEX, 3, N);
    if (0 != status) goto failed;

    printf("Set configuration: DFTI_NUMBER_OF_TRANSFORMS\n");
    status = DftiSetValue(hand, DFTI_NUMBER_OF_TRANSFORMS, M);
    if (0 != status) goto failed;

    dist = N[0]*N[1]*N[2];

    printf("Set configuration: DFTI_INPUT_DISTANCE = "LI"\n",dist);
    status = DftiSetValue(hand, DFTI_INPUT_DISTANCE, dist);
    if (0 != status) goto failed;

    /*
     * Output distance is ignored for in-place complex transforms.
     *
     * status = DftiSetValue(hand, DFTI_INPUT_DISTANCE, dist);
     * if (0 != status) goto failed;
     */

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

    /* Allocate input array */
    x = (MKL_Complex16*)malloc( M * N[0]*N[1]*N[2] * sizeof(MKL_Complex16));
    if (0 == x) goto failed;

    printf("Initialize input for forward transform\n");
    init(x, M, N[0], N[1], N[2], H[0], H[1], H[2]);

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

    printf("Verify the result\n");
    status = verify(x, M, N[0], N[1], N[2], H[0], H[1], H[2]);
    if (0 != status) goto failed;

    printf("Initialize input for backward transform\n");
    init(x, M, N[0], N[1], N[2], -H[0], -H[1], -H[2]);

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

    printf("Verify the result\n");
    status = verify(x, M, N[0], N[1], N[2], H[0], H[1], H[2]);
    if (0 != status) goto failed;

 cleanup:

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

    printf("Free data array\n");
    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 double moda(MKL_LONG K, MKL_LONG L, MKL_LONG M)
{
    return (double)(((long long)K * L) % M);
}

/* Initialize array with harmonic {H1, H2, H3} */
static void init(MKL_Complex16 *x, MKL_LONG M,
                 MKL_LONG N1, MKL_LONG N2, MKL_LONG N3,
                 MKL_LONG H1, MKL_LONG H2, MKL_LONG H3)
{
    double TWOPI = 6.2831853071795864769, phase;
    MKL_LONG m, n1, n2, n3, index;

    /* Generalized strides for row-major addressing of x */
    MKL_LONG SM = N1*N2*N3, S1 = N2*N3, S2 = N3, S3 = 1;

    for (m = 0; m < M; m++)
    {
        for (n1 = 0; n1 < N1; n1++)
        {
            for (n2 = 0; n2 < N2; n2++)
            {
                for (n3 = 0; n3 < N3; n3++)
                {
                    phase =  moda(n1,H1,N1) / N1;
                    phase += moda(n2,H2,N2) / N2;
                    phase += moda(n3,H3,N3) / N3;
                    index = m*SM + n1*S1 + n2*S2 + n3*S3;
                    x[index].real = cos( TWOPI * phase ) / (N1*N2*N3);
                    x[index].imag = sin( TWOPI * phase ) / (N1*N2*N3);
                }
            }
        }
    }
}


/* Verify that x(n1,n2,n3,m) are unit peaks at H1,H2,H3 */
static int verify(MKL_Complex16 *x, MKL_LONG M,
                  MKL_LONG N1, MKL_LONG N2, MKL_LONG N3,
                  MKL_LONG H1, MKL_LONG H2, MKL_LONG H3)
{
    double err, errthr, maxerr;
    MKL_LONG m, n1, n2, n3, index;

    /* Generalized strides for row-major addressing of x */
    MKL_LONG SM = N1*N2*N3, S1 = N2*N3, S2 = N3, S3 = 1;

    /*
     * Note, this simple error bound doesn't take into account error of
     * input data
     */
    errthr = 5.0 * log( (double)N1*N2*N3 ) / log(2.0) * DBL_EPSILON;
    printf(" Verify the result, errthr = %.3lg\n", errthr);

    maxerr = 0;
    for (m = 0; m < M; m++)
    {
        for (n1 = 0; n1 < N1; n1++)
        {
            for (n2 = 0; n2 < N2; n2++)
            {
                for (n3 = 0; n3 < N3; n3++)
                {
                    double re_exp = 0.0, im_exp = 0.0, re_got, im_got;

                    if ((n1-H1)%N1==0 && (n2-H2)%N2==0 && (n3-H3)%N3==0)
                    {
                        re_exp = 1;
                    }

                    index = m*SM + n1*S1 + n2*S2 + n3*S3;
                    re_got = x[index].real;
                    im_got = x[index].imag;
                    err  = fabs(re_got - re_exp) + fabs(im_got - im_exp);
                    if (err > maxerr) maxerr = err;
                    if (!(err < errthr))
                    {
                        printf(" x["LI"]["LI"]["LI"]["LI"]: ",m,n1,n2,n3);
                        printf(" expected (%.17lg,%.17lg), ",re_exp,im_exp);
                        printf(" got (%.17lg,%.17lg), ",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;
}
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