/*******************************************************************************
* Copyright 2011-2018 Intel Corporation.
*
* This software and the related documents are Intel copyrighted materials, and
* your use of them is governed by the express license under which they were
* provided to you (License). Unless the License provides otherwise, you may not
* use, modify, copy, publish, distribute, disclose or transmit this software or
* the related documents without Intel's prior written permission.
*
* This software and the related documents are provided as is, with no express
* or implied warranties, other than those that are expressly stated in the
* License.
*******************************************************************************/
/*
! Content:
! An example of using Intel(R) MKL DFTI configuration parameter DFTI_PLACEMENT.
! The parameter defines if the result overwrites the input data or not.
!
! Values:
! DFTI_INPLACE (default) - result overwrites input data
! DFTI_NOT_INPLACE - result is placed in a separate array
!
! Note: When storage data types of forward and backward domains are
! the same, the configuration parameters for the layout of input are
! also used for the layout of output (e.g. output strides are
! ignored). Otherwise, both input and output layout shall be defined
! (for example real transform with conjugate even storage
! set to DFTI_COMPLEX_COMPLEX).
!
! This example computes an in-place and an out-of-place 2D real transform.
!
!****************************************************************************/
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <float.h>
#include "mkl_service.h"
#include "mkl_dfti.h"
static void init_r(double *x, MKL_LONG *N, MKL_LONG *S, MKL_LONG *H);
static int verify_c(MKL_Complex16 *x, MKL_LONG *N, MKL_LONG *S, MKL_LONG *H);
/* 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 */
MKL_LONG N[2] = { 128, 256 };
/* Arbitrary harmonic used to verify FFT */
MKL_LONG H[2] = { -1, 2 };
/* Execution status */
MKL_LONG status = 0;
/* Pointers to input and output data */
double *r = 0;
MKL_Complex16 *c = 0;
/* Strides define data layout in forward and backward domains */
MKL_LONG rs[3];
MKL_LONG cs[3];
DFTI_DESCRIPTOR_HANDLE hand = 0;
char version[DFTI_VERSION_LENGTH];
DftiGetValue(0, DFTI_VERSION, version);
printf("%s\n", version);
printf("Example config_placement\n");
printf("In-place and out-of-place 2D real FFT\n");
printf(" Configuration parameters:\n");
printf(" DFTI_PRECISION = DFTI_DOUBLE\n");
printf(" DFTI_FORWARD_DOMAIN = DFTI_REAL\n");
printf(" DFTI_DIMENSION = 2\n");
printf(" DFTI_LENGTHS = { "LI", "LI" }\n", N[0], N[1]);
printf("======= In-place 2D real FFT =======\n");
printf("Allocate array for input/output data\n");
r = mkl_malloc(sizeof(double) * N[0]*(N[1]/2+1)*2, 64);
if (r == NULL) goto failed;
printf("Create DFTI descriptor\n");
status = DftiCreateDescriptor(&hand, DFTI_DOUBLE, DFTI_REAL, 2, N);
if (status != DFTI_NO_ERROR) goto failed;
/*
* In-place is default configuration, no need to set it.
*
* status = DftiSetValue(hand, DFTI_PLACEMENT, DFTI_INPLACE);
* if (status != DFTI_NO_ERROR) goto failed;
*/
printf("Set CCE storage\n");
status = DftiSetValue(hand, DFTI_CONJUGATE_EVEN_STORAGE,
DFTI_COMPLEX_COMPLEX);
if (status != DFTI_NO_ERROR) goto failed;
rs[2] = 1; cs[2] = 1;
rs[1] = (N[1]/2+1)*2; cs[1] = (N[1]/2+1);
rs[0] = 0; cs[0] = 0;
printf("Set input strides = "LI", "LI", "LI"\n", rs[0], rs[1], rs[2]);
status = DftiSetValue(hand, DFTI_INPUT_STRIDES, rs);
if (status != DFTI_NO_ERROR) goto failed;
printf("Set output strides = "LI", "LI", "LI"\n", cs[0], cs[1], cs[2]);
status = DftiSetValue(hand, DFTI_OUTPUT_STRIDES, cs);
if (status != DFTI_NO_ERROR) goto failed;
printf("Commit descriptor\n");
status = DftiCommitDescriptor(hand);
if (status != DFTI_NO_ERROR) goto failed;
printf("Inititalize input for 2D real in-place transform\n");
init_r(r, N, rs, H);
printf("Compute real-to-complex in-place transform\n");
status = DftiComputeForward(hand, r);
if (status != DFTI_NO_ERROR) goto failed;
printf("Verify 2D real in-place transform\n");
status = verify_c((MKL_Complex16*)r, N, cs, H);
if (status != 0) goto failed;
printf("======= Reconfigure for out-of-place 2D real FFT =======\n");
printf("Allocate array for output data\n");
c = mkl_malloc(sizeof(MKL_Complex16) * N[0]*(N[1]/2+1), 64);
if (c == NULL) goto failed;
printf("Set out-of-place configuration\n");
status = DftiSetValue(hand, DFTI_PLACEMENT, DFTI_NOT_INPLACE);
if (status != DFTI_NO_ERROR) goto failed;
rs[2] = 1; cs[2] = 1;
rs[1] = N[1]; cs[1] = (N[1]/2+1);
rs[0] = 0; cs[0] = 0;
printf("Set input strides = "LI", "LI", "LI"\n", rs[0], rs[1], rs[2]);
status = DftiSetValue(hand, DFTI_INPUT_STRIDES, rs);
if (status != DFTI_NO_ERROR) goto failed;
printf("Set output strides = "LI", "LI", "LI"\n", cs[0], cs[1], cs[2]);
status = DftiSetValue(hand, DFTI_OUTPUT_STRIDES, cs);
if (status != DFTI_NO_ERROR) goto failed;
printf("Commit descriptor\n");
status = DftiCommitDescriptor(hand);
if (status != DFTI_NO_ERROR) goto failed;
printf("Inititalize input for 2D real out-of-place transform\n");
init_r(r, N, rs, H);
printf("Compute real-to-complex out-of-place transform\n");
status = DftiComputeForward(hand, r, c);
if (status != DFTI_NO_ERROR) goto failed;
printf("Verify 2D real in-place transform\n");
status = verify_c(c, N, cs, H);
if (status != 0) goto failed;
cleanup:
printf("Free DFTI descriptor\n");
DftiFreeDescriptor(&hand);
printf("Free data arrays\n");
mkl_free(r);
mkl_free(c);
printf("TEST %s\n", (status == 0) ? "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 x(N) to produce unit peaks at x(H) and x(N-H) */
static void init_r(double *x, MKL_LONG *N, MKL_LONG *S, MKL_LONG *H)
{
double TWOPI = 6.2831853071795864769, phase, factor;
MKL_LONG n1, n2, N1, N2, S1, S2, H1, H2, index;
N1 = N[0]; S1 = S[1]; H1 = H[0];
N2 = N[1]; S2 = S[2]; H2 = H[1];
factor = (2*(N1-H1)%N1==0 && 2*(N2-H2)%N2==0) ? 1.0 : 2.0;
for (n1 = 0; n1 < N1; n1++)
{
for (n2 = 0; n2 < N2; n2++)
{
phase = moda(n1,H1,N1) / N1;
phase += moda(n2,H2,N2) / N2;
index = n1*S1 + n2*S2;
x[index] = factor * cos( TWOPI * phase ) / (N1*N2);
}
}
}
/* Verify that x has unit peak at H */
static int verify_c(MKL_Complex16 *x, MKL_LONG *N, MKL_LONG *S, MKL_LONG *H)
{
double err, errthr, maxerr;
MKL_LONG n1, n2, N1, N2, S1, S2, H1, H2, index;
N1 = N[0]; S1 = S[1]; H1 = H[0];
N2 = N[1]; S2 = S[2]; H2 = H[1];
/*
* Note, this simple error bound doesn't take into account error of
* input data
*/
errthr = 2.5 * log( (double)N1*N2 ) / log(2.0) * DBL_EPSILON;
printf(" Check if err is below errthr %.3lg\n", errthr);
maxerr = 0;
for (n1 = 0; n1 < N1; n1++)
{
for (n2 = 0; n2 < N2/2+1; n2++)
{
double re_exp = 0.0, im_exp = 0.0, re_got, im_got;
if ((( n1-H1)%N1==0 && ( n2-H2)%N2==0) ||
((-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 = fabs(re_got - re_exp) + fabs(im_got - im_exp);
if (err > maxerr) maxerr = err;
if (!(err < errthr))
{
printf(" x["LI"]["LI"]: ",n1,n2);
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;
}