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fft.c
1546 lines (1453 loc) · 63 KB
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fft.c
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/* Initialization of all FFT for matrix-vector products; and FFT procedures themselves; not used in sparse mode
* TODO: A lot of indirect indexing used - way to optimize.
*
* Copyright (C) ADDA contributors
* This file is part of ADDA.
*
* ADDA is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as
* published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.
*
* ADDA is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty
* of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License along with ADDA. If not, see
* <http://www.gnu.org/licenses/>.
*/
#include "const.h" // keep this first
#include "fft.h" // corresponding header
// project headers
#include "cmplx.h"
#include "comm.h"
#include "debug.h"
#include "function.h"
#include "io.h"
#include "interaction.h"
#include "memory.h"
#include "oclcore.h"
#include "prec_time.h"
#include "vars.h"
// system headers
#include <math.h>
#include <stdlib.h>
#include <string.h>
#ifdef CLFFT
IGNORE_WARNING(-Wstrict-prototypes) // no way to change the library header (tested with v.2.12.2)
# include <clFFT.h> //external library
STOP_IGNORE
// Defines precision of clFFT transforms.
// CLFFT_DOUBLE_FAST should be tested when becomes operational - in v.2.12.2 it is identical to CLFFT_DOUBLE
# define PRECISION_CLFFT CLFFT_DOUBLE
#elif defined(CLFFT_APPLE)
# include "cpp/clFFT.h" //nearly unmodified APPLE FFT header file
# ifdef NO_CPP
# error "Apple clFFT relies on C++ sources, hence is incompatible with NO_CPP option"
# endif
#endif
/* standard FFT routines (FFTW3 of FFT_TEMPERTON) are required even when OpenCL is used, since they are used for Fourier
* transform of the D-matrix
*/
#ifdef FFTW3
# include <fftw3.h> // types.h or cmplx.h should be defined before (to match C99 complex type)
/* define level of planning for usual and Dmatrix (DM) FFT: FFTW_ESTIMATE (heuristics), FFTW_MEASURE (default),
* FFTW_PATIENT, or FFTW_EXHAUSTIVE
*/
# define PLAN_FFTW FFTW_MEASURE
# define PLAN_FFTW_DM FFTW_ESTIMATE
# define ONLY_FOR_FFTW3 // this is used in function argument declarations
#else
# define ONLY_FOR_FFTW3 ATT_UNUSED
#endif
#ifdef FFT_TEMPERTON
# define ONLY_FOR_TEMPERTON // this is used in function argument declarations
#else
# define ONLY_FOR_TEMPERTON ATT_UNUSED
#endif
// SEMI-GLOBAL VARIABLES
// defined and initialized in interaction.c
extern const int local_Nz_Rm;
// defined and initialized in timing.c
extern TIME_TYPE Timing_FFT_Init,Timing_Dm_Init;
// used in comm.c
double * restrict BT_buffer, * restrict BT_rbuffer; // buffers for BlockTranspose
// used in matvec.c; in OpenCL mode some of those are not used at all, others - only locally
doublecomplex * restrict Dmatrix; // holds FFT of the interaction matrix
doublecomplex * restrict Rmatrix; // holds FFT of the reflection matrix
#ifndef OPENCL
// holds input vector (on expanded grid) to matvec, also used as storage space in iterative.c
doublecomplex * restrict Xmatrix;
doublecomplex * restrict slices; // used in inner cycle of matvec - holds 3 components (for fixed x)
doublecomplex * restrict slices_tr; // additional storage space for slices to accelerate transpose
doublecomplex * restrict slicesR,* restrict slicesR_tr; // same as above, but for reflected interaction
#endif
size_t DsizeY,DsizeZ,DsizeYZ; // size of the 'matrix' D
size_t RsizeY; // size of the 'matrix' R; in OpenCL mode it is used in oclmatvec.c
// used in oclmatvec.c
#ifdef OPENCL
/* clxslices is the number of slices required in MatVec,
* so that more GPU memory is used and kernels can run over larger arrays
*/
size_t clxslices;
size_t local_gridX; // 'thickness' in x direction of a slice*
size_t slicesize; // total number of doublecomplex values per slice
#endif
// LOCAL VARIABLES
// D2 matrix and its two slices; used only temporary for InitDmatrix
static doublecomplex * restrict slice,* restrict slice_tr,* restrict D2matrix;
static doublecomplex * restrict R2matrix; // same for surface (slice and slice_tr are reused from Dmatrix)
static size_t D2sizeY; // size of the 'matrix' D2 (x-size is gridX), Z size is not used
static size_t R2sizeY; // size of the 'matrix' R2 (x- and z-sizes are corresponding grids)
static size_t lz_Dm,lz_Rm; // local sizes along z for D(2) and R(2) matrices
// the following two lines are defined in InitDmatrix but used in InitRmatrix, they are analogous to Dm values
static size_t Rsize,R2sizeTot; // sizes of R and R2 matrices
static int jstartR; // starting index for y
static bool weird_nprocs; // whether weird number of processors is used
#ifdef OPENCL
// clFFT plans
# ifdef CLFFT
static clfftPlanHandle clplanX,clplanY,clplanZ;
static size_t clfftBufSize=0;
# elif defined(CLFFT_APPLE)
static clFFT_Plan clplanX,clplanY,clplanZ;
# endif
#endif
#ifdef FFTW3
// FFTW3 plans: f - FFT_FORWARD; b - FFT_BACKWARD
static fftw_plan planXf_Dm,planYf_slice,planZf_slice,planXf_Rm;
# ifndef OPENCL // these plans are used only if OpenCL is not used
static fftw_plan planXf,planXb,planYf,planYb,planZf,planZb,planYRf,planZRf; // last two for reflected interaction
# endif
#elif defined(FFT_TEMPERTON)
# ifdef NO_FORTRAN
# error "Tempertron FFT is implemented in Fortran, hence incompatible with NO_FORTRAN option"
# endif
# define IFAX_SIZE 20
// arrays for Temperton FFT
static double * restrict trigsX,* restrict trigsY,* restrict trigsZ,* restrict work;
static int ifaxX[IFAX_SIZE],ifaxY[IFAX_SIZE],ifaxZ[IFAX_SIZE];
// Fortran routines from cfft99D.f
void cftfax_(const int *nn,int * restrict ifax,double * restrict trigs);
void cfft99_(double * restrict data,double * restrict _work,const double * restrict trigs,const int * restrict ifax,
const int *inc,const int *jump,const int *nn,const int *lot,const int *isign);
#endif
#ifdef CLFFT
// Test clFFT version
# define CLFFT_VER_REQ 2
# define CLFFT_SUBVER_REQ 12
# if !GREATER_EQ2(clfftVersionMajor,clfftVersionMinor,CLFFT_VER_REQ,CLFFT_SUBVER_REQ)
# error "clFFT version is too old"
# endif
// Error-checking functionality for clFFT
# define CLFFT_CH_ERR(a) Check_clFFT_Err(a,ALL_POS)
//======================================================================================================================
static const char *Print_clFFT_Errstring(clfftStatus err)
// produces meaningful error message from the clFFT-specific error code, based on clFFT.h v.2.12.2 (NULL if not found)
{
switch (err) {
case CLFFT_BUGCHECK: return "Bugcheck";
case CLFFT_NOTIMPLEMENTED: return "Functionality not implemented";
case CLFFT_TRANSPOSED_NOTIMPLEMENTED: return "Transposed functionality not implemented";
case CLFFT_FILE_NOT_FOUND: return "File not found";
case CLFFT_FILE_CREATE_FAILURE: return "File creation failure";
case CLFFT_VERSION_MISMATCH: return "Version conflict between client and library";
case CLFFT_INVALID_PLAN: return "Invalid plan";
case CLFFT_DEVICE_NO_DOUBLE: return "Device does not support double precision";
case CLFFT_DEVICE_MISMATCH: return "Mismatch of plan and device";
default: return NULL;
}
}
//======================================================================================================================
static void Check_clFFT_Err(const clfftStatus err,ERR_LOC_DECL)
/* Checks error code for clFFT calls and prints error if necessary. First searches among clFFT specific errors. If not
* found, uses general error processing for CL calls (since clFFT error codes can take standard cl values as well).
*/
{
if (err != CLFFT_SUCCESS) {
const char *str=Print_clFFT_Errstring(err);
if (str!=NULL) LogError(ERR_LOC_CALL,"clFFT error code %d: %s\n",err,str);
else PrintCLErr((cl_int)err,ERR_LOC_CALL,NULL);
}
}
#endif
//======================================================================================================================
static inline size_t IndexDmatrix(const size_t x,size_t y,size_t z)
// index D matrix to store final result (symmetric with respect to center for y and z)
{
if (y>=DsizeY) y=gridY-y;
if (z>=DsizeZ) z=gridZ-z;
return(NDCOMP*((x*DsizeZ+z)*DsizeY+y));
}
//======================================================================================================================
static inline size_t IndexGarbledD(const size_t x,int y,int z)
// index D2 matrix after BlockTranspose (periodic over y and z)
{
if (y<0) y+=gridY;
if (z<0) z+=gridZ;
#ifdef PARALLEL
return(((z%lz_Dm)*D2sizeY+y)*gridX+(z/lz_Dm)*local_Nx+x%local_Nx);
#else
return((z*D2sizeY+y)*gridX+x);
#endif
}
//======================================================================================================================
static inline size_t IndexSliceD2matrix(int y,int z)
// index slice of D2 matrix (periodic over y and z)
{
if (y<0) y+=gridY;
if (z<0) z+=gridZ;
return(y*gridZ+z);
}
//======================================================================================================================
static inline size_t Index2matrix(int x,int y,const int z,const int sizeY)
// index D2 or R2 matrix to store calculated elements (periodic over x and y), z should already be shifted
{
if (x<0) x+=gridX;
if (y<0) y+=gridY;
return((z*sizeY+y)*gridX+x);
}
//======================================================================================================================
static inline size_t IndexSlice_zy(const size_t y,const size_t z)
// index transposed slice of D2 (or R2) matrix
{
return (z*gridY+y);
}
//======================================================================================================================
static inline size_t IndexRmatrix(const size_t x,size_t y,const size_t z)
// index R matrix to store final result (symmetric with respect to center for y)
{
if (y>=RsizeY) y=gridY-y;
return(NDCOMP*((x*gridZ+z)*RsizeY+y));
}
//======================================================================================================================
static inline size_t IndexGarbledR(const size_t x,int y,const int z)
// index R2 matrix after BlockTranspose (periodic over y)
{
if (y<0) y+=gridY;
#ifdef PARALLEL
return(((z%lz_Rm)*R2sizeY+y)*gridX+(z/lz_Rm)*local_Nx+x%local_Nx);
#else
return((z*R2sizeY+y)*gridX+x);
#endif
}
//======================================================================================================================
static inline size_t IndexSliceR2matrix(int y,const int z)
// index slice of R2 matrix (periodic over y)
{
if (y<0) y+=gridY;
return(y*gridZ+z);
}
//======================================================================================================================
static void transpose(const doublecomplex * restrict data,doublecomplex * restrict trans,const size_t Y,const size_t Z)
// optimized routine to transpose complex matrix with dimensions YxZ: data -> trans
{
size_t y,z,y1,y2,z1,z2,i,j,y0,z0;
doublecomplex *t1,*t2,*t3,*t4;
const doublecomplex *w1,*w2,*w3;
const size_t blockTr=64; // block size
/* Intel compiler 11.1 seems to produce broken code for this function whenever blockTr>1, at least when the function
* is called in row of three from TransposeYZ(). So maybe the bug is due to incorrect inlining. This bug appears
* only for -O3 compilation, but not for -O2. Moreover, the bug is not present for icc 13.0.
* We have no idea what can be done on our side.
*/
y1=Y/blockTr;
y2=Y%blockTr;
z1=Z/blockTr;
z2=Z%blockTr;
w1=data;
t1=trans-Y;
for(i=0;i<=y1;i++) {
if (i==y1) y0=y2;
else y0=blockTr;
w2=w1;
t2=t1;
for(j=0;j<=z1;j++) {
if (j==z1) z0=z2;
else z0=blockTr;
w3=w2;
t3=t2;
for (y=0;y<y0;y++) {
t4=t3+y;
for (z=0;z<z0;z++) *(t4+=Y)=w3[z];
w3+=Z;
}
w2+=blockTr;
t2+=blockTr*Y;
}
w1+=blockTr*Z;
t1+=blockTr;
}
}
//======================================================================================================================
void TransposeYZ(const int direction)
/* optimized routine to transpose y and z; forward: slices->slices_tr; backward: slices_tr->slices; direction can be
* made boolean but this contradicts with existing definitions of FFT_FORWARD and FFT_BACKWARD, which themselves are
* determined by FFT routines invocation format
*/
{
#ifdef OPENCL
const size_t blocksize=16; //this corresponds to BLOCK_DIM in oclkernels.cl
const size_t tblock[3]={blocksize,blocksize,1};
size_t enqtglobalzy[3]={gridZ,gridY,3*local_gridX};
size_t enqtglobalyz[3]={gridY,gridZ,3*local_gridX};
//if the grid is not dividable by blocksize, extend it. Kernel takes care of borders
size_t tgridZ = (gridZ%blocksize==0) ? gridZ : (gridZ/blocksize+1)*blocksize;
size_t tgridY = (gridY%blocksize==0) ? gridY : (gridY/blocksize+1)*blocksize;
enqtglobalzy[0]=tgridZ;
enqtglobalzy[1]=tgridY;
enqtglobalyz[0]=tgridY;
enqtglobalyz[1]=tgridZ;
if (direction==FFT_FORWARD) {
CL_CH_ERR(clEnqueueNDRangeKernel(command_queue,cltransposeof,3,NULL,enqtglobalzy,tblock,0,NULL,NULL));
if (surface)
CL_CH_ERR(clEnqueueNDRangeKernel(command_queue,cltransposeofR,3,NULL,enqtglobalzy,tblock,0,NULL,NULL));
}
else CL_CH_ERR(clEnqueueNDRangeKernel(command_queue,cltransposeob,3,NULL,enqtglobalyz,tblock,0,NULL,NULL));
#else
size_t Xcomp,ind;
if (direction==FFT_FORWARD) for (Xcomp=0;Xcomp<3;Xcomp++) {
ind=Xcomp*gridYZ;
transpose(slices+ind,slices_tr+ind,gridY,gridZ);
if (surface) transpose(slicesR+ind,slicesR_tr+ind,gridY,gridZ);
}
else for (Xcomp=0;Xcomp<3;Xcomp++) { // direction==FFT_BACKWARD
ind=Xcomp*gridYZ;
transpose(slices_tr+ind,slices+ind,gridZ,gridY);
}
#endif
}
//======================================================================================================================
void fftX(const int isign)
// FFT three components of (buf)Xmatrix(x) for all y,z; called from matvec
{
#ifdef OPENCL
# ifdef CLFFT
CLFFT_CH_ERR(clfftEnqueueTransform(clplanX,(clfftDirection)isign,1,&command_queue,0,NULL,NULL,&bufXmatrix,NULL,
NULL));
# elif defined(CLFFT_APPLE)
CL_CH_ERR(clFFT_ExecuteInterleaved(command_queue,clplanX,(int)3*local_Nz*smallY,(clFFT_Direction)isign,bufXmatrix,
bufXmatrix,0,NULL,NULL));
# endif
#elif defined(FFTW3)
if (isign==FFT_FORWARD) fftw_execute(planXf);
else fftw_execute(planXb);
#elif defined(FFT_TEMPERTON)
int nn=gridX,inc=1,jump=nn,lot=boxY;
size_t z;
/* Calls to Temperton FFT cause warnings for translation from doublecomplex to double pointers. However, such a cast
* is perfectly valid in C99. So we set pragmas to remove these warnings.
*
* !!! TODO: Another (ultimate) solution is to remove this routine altogether, since FFTW is perfect in all
* respects. This is also reasonable considering future switch to tgmath.h
*/
IGNORE_WARNING(-Wstrict-aliasing);
for (z=0;z<3*local_Nz;z++) cfft99_((double *)(Xmatrix+z*gridX*smallY),work,trigsX,ifaxX,&inc,&jump,&nn,&lot,&isign);
STOP_IGNORE;
#endif
}
//======================================================================================================================
void fftY(const int isign)
// FFT three components of slices_tr(y) for all z; called from matvec
{
#ifdef OPENCL
# ifdef CLFFT
CLFFT_CH_ERR(clfftEnqueueTransform(clplanY,(clfftDirection)isign,1,&command_queue,0,NULL,NULL,&bufslices_tr,NULL,
NULL));
if (surface && isign==FFT_FORWARD)
CLFFT_CH_ERR(clfftEnqueueTransform(clplanY,(clfftDirection)isign,1,&command_queue,0,NULL,NULL,&bufslicesR_tr,
NULL,NULL));
# elif defined(CLFFT_APPLE)
CL_CH_ERR(clFFT_ExecuteInterleaved(command_queue,clplanY,(int)3*gridZ*local_gridX,(clFFT_Direction)isign,
bufslices_tr,bufslices_tr,0,NULL,NULL));
if (surface && isign==FFT_FORWARD)
CL_CH_ERR(clFFT_ExecuteInterleaved(command_queue,clplanY,(int)3*gridZ*local_gridX,(clFFT_Direction)isign,
bufslicesR_tr,bufslicesR_tr,0,NULL,NULL));
# endif
#elif defined(FFTW3)
if (isign==FFT_FORWARD) {
fftw_execute(planYf);
if (surface) fftw_execute(planYRf);
}
else fftw_execute(planYb);
#elif defined(FFT_TEMPERTON)
int nn=gridY,inc=1,jump=nn,lot=3*gridZ;
IGNORE_WARNING(-Wstrict-aliasing);
cfft99_((double *)(slices_tr),work,trigsY,ifaxY,&inc,&jump,&nn,&lot,&isign);
// the same operation is applied to sliceR_tr, when required
if (surface && isign==FFT_FORWARD) cfft99_((double *)(slicesR_tr),work,trigsY,ifaxY,&inc,&jump,&nn,&lot,&isign);
STOP_IGNORE;
#endif
}
//======================================================================================================================
void fftZ(const int isign)
// FFT three components of slices(z) for all y; called from matvec
{
#ifdef OPENCL
# ifdef CLFFT
CLFFT_CH_ERR(clfftEnqueueTransform(clplanZ,(clfftDirection)isign,1,&command_queue,0,NULL,NULL,&bufslices,NULL,
NULL));
if (surface && isign==FFT_FORWARD) // the same operation is applied to bufslicesR, but with inverse transform
CLFFT_CH_ERR(clfftEnqueueTransform(clplanZ,(clfftDirection)FFT_BACKWARD,1,&command_queue,0,NULL,NULL,
&bufslicesR,NULL,NULL));
# elif defined(CLFFT_APPLE)
CL_CH_ERR(clFFT_ExecuteInterleaved(command_queue,clplanZ,(int)3*gridY*local_gridX,(clFFT_Direction)isign,bufslices,
bufslices,0,NULL,NULL));
if (surface && isign==FFT_FORWARD) // the same operation is applied to bufslicesR, but with inverse transform
CL_CH_ERR(clFFT_ExecuteInterleaved(command_queue,clplanZ,(int)3*gridY*local_gridX,(clFFT_Direction)FFT_BACKWARD,
bufslicesR,bufslicesR,0,NULL,NULL));
# endif
#elif defined(FFTW3)
if (isign==FFT_FORWARD) {
fftw_execute(planZf);
if (surface) fftw_execute(planZRf);
}
else fftw_execute(planZb);
#elif defined(FFT_TEMPERTON)
int nn=gridZ,inc=1,jump=nn,lot=boxY,Xcomp;
IGNORE_WARNING(-Wstrict-aliasing);
for (Xcomp=0;Xcomp<3;Xcomp++) cfft99_((double *)(slices+gridYZ*Xcomp),work,trigsZ,ifaxZ,&inc,&jump,&nn,&lot,&isign);
if (surface && isign==FFT_FORWARD) { // the same operation is applied to slicesR, but with inverse transform
const int invSign=FFT_BACKWARD;
for (Xcomp=0;Xcomp<3;Xcomp++)
cfft99_((double *)(slicesR+gridYZ*Xcomp),work,trigsZ,ifaxZ,&inc,&jump,&nn,&lot,&invSign);
}
STOP_IGNORE;
#endif
}
//======================================================================================================================
static void fftX_Dm(void)
// FFT(forward) D2matrix(x) for all y,z; used for Dmatrix calculation
{
#ifdef FFTW3
fftw_execute(planXf_Dm);
#elif defined(FFT_TEMPERTON)
int nn=gridX,inc=1,jump=nn,lot=D2sizeY,isign=FFT_FORWARD;
size_t z;
IGNORE_WARNING(-Wstrict-aliasing);
for (z=0;z<lz_Dm;z++) cfft99_((double *)(D2matrix+z*gridX*D2sizeY),work,trigsX,ifaxX,&inc,&jump,&nn,&lot,&isign);
STOP_IGNORE;
#endif
}
//======================================================================================================================
static void fftX_Rm(void)
// FFT(forward) D2matrix(x) for all y,z; used for Rmatrix calculation
{
#ifdef FFTW3
fftw_execute(planXf_Rm);
#elif defined(FFT_TEMPERTON)
int nn=gridX,inc=1,jump=nn,lot=R2sizeY,isign=FFT_FORWARD;
size_t z;
const size_t zlim=local_Nz_Rm; // can be smaller by 1 than lz_Rm
IGNORE_WARNING(-Wstrict-aliasing);
for (z=0;z<zlim;z++) cfft99_((double *)(R2matrix+z*gridX*R2sizeY),work,trigsX,ifaxX,&inc,&jump,&nn,&lot,&isign);
STOP_IGNORE;
#endif
}
//======================================================================================================================
static void fftY_slice(void)
// FFT(forward) slice_tr(y) for all z; used for Dmatrix and Rmatrix calculation
{
#ifdef FFTW3
fftw_execute(planYf_slice);
#elif defined(FFT_TEMPERTON)
int nn=gridY,inc=1,jump=nn,lot=gridZ,isign=FFT_FORWARD;
IGNORE_WARNING(-Wstrict-aliasing);
cfft99_((double *)slice_tr,work,trigsY,ifaxY,&inc,&jump,&nn,&lot,&isign);
STOP_IGNORE;
#endif
}
//======================================================================================================================
static void fftZ_slice(void)
// FFT(forward) slice(z) for all y; used for Dmatrix and Rmatrix calculation
{
#ifdef FFTW3
fftw_execute(planZf_slice);
#elif defined(FFT_TEMPERTON)
int nn=gridZ,inc=1,jump=nn,lot=gridY,isign=FFT_FORWARD;
IGNORE_WARNING(-Wstrict-aliasing);
cfft99_((double *)slice,work,trigsZ,ifaxZ,&inc,&jump,&nn,&lot,&isign);
STOP_IGNORE;
#endif
}
//======================================================================================================================
void CheckNprocs(void)
// checks for consistency the specified number of processors; called in the beginning from InitComm
{
int y=nprocs;
// initialize weird_nprocs
weird_nprocs=false;
// remove simple prime divisors of y
while (y%2==0) y/=2;
#ifdef CLFFT_APPLE
// this is redundant (and CLFTT below), since OpenCL is not currently intended to run in parallel
if (y!=1) PrintError("Specified number of processors (%d) is incompatible with Apple clFFT, since the latter "
"supports only FFTs with size 2^n. Revise the number of processors or recompile with clFFT support.",nprocs);
#else
while (y%3==0) y/=3;
while (y%5==0) y/=5;
# ifdef FFT_TEMPERTON
if (y!=1) PrintError("Specified number of processors (%d) is weird (has prime divisors larger than 5). That is "
"incompatible with Temperton FFT. Revise the number of processors (recommended) or recompile with FFTW 3 "
"support.",nprocs);
# else
while (y%7==0) y/=7;
// one multiplier of either 11 or 13 is allowed
if (y%11==0) y/=11;
else if (y%13==0) y/=13;
if (y!=1) {
LogWarning(EC_WARN,ONE_POS,"Specified number of processors (%d) is weird (has prime divisors larger than 13 or "
"more than one divisor of either 11 or 13). FFTW3 will work less efficiently. It is strongly recommended "
"to revise the number of processors.",nprocs);
weird_nprocs=true;
}
# ifdef CLFFT // it allows more factors of 11 and 13, but fails completely otherwise
while (y%11==0) y/=11;
while (y%13==0) y/=13;
if (y!=1) PrintError("Specified number of processors (%d) is weird (has prime divisors larger than 13). That is "
"incompatible with clFFT. Revise the number of processors",nprocs);
# endif
# endif
#endif
}
//======================================================================================================================
int fftFit(int x,int divis)
/* find the first number >=x divisible by 2 only (Apple clFFT) or 2,3,5 only (Temperton FFT) or also
* allowing 7 and one of 11 or 13 (FFTW3) or any number of 11 and 13 factors (clFFT), and also divisible by 2 and divis.
* If weird_nprocs is used, only the latter condition is required.
* In OpenCL mode both CPU and GPU FFT routines are tested (since both are used), otherwise - only CPU ones
*/
{
int y;
if (weird_nprocs) {
if (IS_ODD(divis)) divis*=2;
return (divis*((x+divis-1)/divis));
}
else while (true) { // not very efficient but robust way
if (IS_EVEN(x) && x%divis==0) {
y=x;
while (y%2==0) y/=2; // here Apple clFFT ends
#ifndef CLFFT_APPLE // we assume that it is defined only in OpenCL mode
while (y%3==0) y/=3;
while (y%5==0) y/=5; // here Temperton FFT ends
# ifndef FFT_TEMPERTON
// the following is for FFTW3 and clFFT
while (y%7==0) y/=7;
// one multiplier of either 11 or 13 is allowed - limited by FFTW3
if (y%11==0) y/=11;
else if (y%13==0) y/=13;
# endif
#endif
if (y==1) return(x);
}
x++;
}
}
//======================================================================================================================
static void fftInitBeforeD(void)
// initialize fft before initialization of Dmatrix
{
#ifdef FFTW3
int grXint=gridX,grYint=gridY,grZint=gridZ; // this is needed to provide 'int *' to grids
/* For some reason, the following FFTW strings cannot be found by Visual Studio linker. They are not present in .def
* file for the corresponding library (in v. 3.3.5), while the default way to produce .lib file for linking with this
* linker is through the .def file (http://www.fftw.org/install/windows.html). Potentially, this can be solved by using
* 'dumpbin /exports ...' on the provided DLL, but it will probably require some manual editing.
*/
#ifndef _MSC_VER
D("FFTW library version: %s\n compiler: %s\n codelet optimizations: %s",fftw_version,fftw_cc,
fftw_codelet_optim);
#endif
planYf_slice=fftw_plan_many_dft(1,&grYint,gridZ,slice_tr,NULL,1,gridY,slice_tr,NULL,1,gridY,FFT_FORWARD,
PLAN_FFTW_DM);
planZf_slice=fftw_plan_many_dft(1,&grZint,gridY,slice,NULL,1,gridZ,slice,NULL,1,gridZ,FFT_FORWARD,PLAN_FFTW_DM);
planXf_Dm=fftw_plan_many_dft(1,&grXint,lz_Dm*D2sizeY,D2matrix,NULL,1,gridX,D2matrix,NULL,1,gridX,FFT_FORWARD,
PLAN_FFTW_DM);
// very similar to Dm, but local_Nz_Rm can be smaller by 1 than lz_Rm
if (surface) planXf_Rm=fftw_plan_many_dft(1,&grXint,local_Nz_Rm*R2sizeY,R2matrix,NULL,1,gridX,R2matrix,NULL,1,gridX,
FFT_FORWARD,PLAN_FFTW_DM);
#elif defined(FFT_TEMPERTON)
int nn;
size_t size;
// allocate memory
MALLOC_VECTOR(trigsX,double,2*gridX,ALL);
MALLOC_VECTOR(trigsY,double,2*gridY,ALL);
MALLOC_VECTOR(trigsZ,double,2*gridZ,ALL);
size=MAX(gridX*D2sizeY,3*gridYZ);
if (surface) size=MAX(size,gridX*R2sizeY);
MALLOC_VECTOR(work,double,2*size,ALL);
// initialize ifax and trigs
nn=gridX;
cftfax_(&nn,ifaxX,trigsX);
nn=gridY;
cftfax_(&nn,ifaxY,trigsY);
nn=gridZ;
cftfax_(&nn,ifaxZ,trigsZ);
#endif
}
//======================================================================================================================
static void fftInitAfterD(void)
/* second part of fft initialization
* completely separate code is used for OpenCL and FFTW3, because even precise-timing output is significantly different.
* In particular, FFTW3 uses separate plans for forward and backward, while clFFT uses one plan for both directions.
*
* clFft access the OpenCL buffers directly, so they are not anyhow affected by the definition of complex numbers in the
* main part of the code (although, it is consistent with it)
*/
{
#ifdef OPENCL
# ifdef CLFFT_APPLE
cl_int err; // error code
# else
size_t bufsize;
# endif
# ifdef PRECISE_TIMING
SYSTEM_TIME tvp[4];
# endif
if (IFROOT) PRINTFB("Initializing clFFT\n");
# ifdef PRECISE_TIMING
GET_SYSTEM_TIME(tvp);
# endif
# ifdef CLFFT
// test library version at runtime
cl_uint major,minor,patch;
CLFFT_CH_ERR(clfftGetVersion(&major,&minor,&patch));
if (!GREATER_EQ2(major,minor,CLFFT_VER_REQ,CLFFT_SUBVER_REQ)) LogError(ONE_POS,
"clFFT library version (%u.%u) is too old. Version %d.%d or newer is required",
major,minor,CLFFT_VER_REQ,CLFFT_SUBVER_REQ);
D("clFFT library version - %u.%u.%u",major,minor,patch);
// initialize library
CLFFT_CH_ERR(clfftSetup(NULL));
/* Here and further we explicitly set all plan parameters for clFFT, even those that are equal to the default
* values (as recommended in clFFT manual)
*/
/* Unfortunately, clFFT (and Apple clFFT as well) currently supports only simple regular batches of transforms
* (similar to fftw_plan_many_dft) but not fully flexible configurations, like offered by fftw_plan_guru_dft.
* Basically the problem is due to lack of multi-dimensional (non-tightly packed) batches. So to make X transform as
* a single plan we have have to cycle over the whole smallY instead of (possibly smaller) boxY. This incurs a small
* performance hit for "non-standard" values of boxY, but should be overall faster than making an explicit loop over
* smaller kernels (like is now done with Temperton FFT).
*/
CLFFT_CH_ERR(clfftCreateDefaultPlan(&clplanX,context,CLFFT_1D,&gridX));
CLFFT_CH_ERR(clfftSetPlanBatchSize(clplanX,3*local_Nz*smallY));
CLFFT_CH_ERR(clfftSetPlanPrecision(clplanX,PRECISION_CLFFT));
CLFFT_CH_ERR(clfftSetResultLocation(clplanX,CLFFT_INPLACE));
CLFFT_CH_ERR(clfftSetLayout(clplanX,CLFFT_COMPLEX_INTERLEAVED,CLFFT_COMPLEX_INTERLEAVED));
// more robust to use clfftDirection(FFT_FORWARD) instead of CLFFT_FORWARD, but here the scale is symmetric
CLFFT_CH_ERR(clfftSetPlanScale(clplanX,CLFFT_FORWARD,1));
CLFFT_CH_ERR(clfftSetPlanScale(clplanX,CLFFT_BACKWARD,1)); // override the default 1/N scale for backward direction
CLFFT_CH_ERR(clfftBakePlan(clplanX,1,&command_queue,NULL,NULL));
CLFFT_CH_ERR(clfftGetTmpBufSize(clplanX,&bufsize));
clfftBufSize+=bufsize;
# elif defined(CLFFT_APPLE)
clFFT_Dim3 xdimen;
xdimen.x=(unsigned int)gridX;
xdimen.y=1;
xdimen.z=1;
clplanX=clFFT_CreatePlan(context,xdimen,clFFT_2D,clFFT_InterleavedComplexFormat,&err);
CL_CH_ERR(err);
# endif
# ifdef PRECISE_TIMING
GET_SYSTEM_TIME(tvp+1);
# endif
# ifdef CLFFT
CLFFT_CH_ERR(clfftCreateDefaultPlan(&clplanY,context,CLFFT_1D,&gridY));
CLFFT_CH_ERR(clfftSetPlanBatchSize(clplanY,3*gridZ*local_gridX));
CLFFT_CH_ERR(clfftSetPlanPrecision(clplanY,PRECISION_CLFFT));
CLFFT_CH_ERR(clfftSetResultLocation(clplanY,CLFFT_INPLACE));
CLFFT_CH_ERR(clfftSetLayout(clplanY,CLFFT_COMPLEX_INTERLEAVED,CLFFT_COMPLEX_INTERLEAVED));
CLFFT_CH_ERR(clfftSetPlanScale(clplanY,CLFFT_FORWARD,1));
CLFFT_CH_ERR(clfftSetPlanScale(clplanY,CLFFT_BACKWARD,1)); // override the default 1/N scale for backward direction
CLFFT_CH_ERR(clfftBakePlan(clplanY,1,&command_queue,NULL,NULL));
CLFFT_CH_ERR(clfftGetTmpBufSize(clplanY,&bufsize));
clfftBufSize+=bufsize;
# elif defined(CLFFT_APPLE)
clFFT_Dim3 ydimen;
ydimen.x=(unsigned int)gridY;
ydimen.y=1;
ydimen.z=1;
clplanY=clFFT_CreatePlan(context,ydimen,clFFT_1D,clFFT_InterleavedComplexFormat,&err);
CL_CH_ERR(err);
# endif
# ifdef PRECISE_TIMING
GET_SYSTEM_TIME(tvp+2);
# endif
# ifdef CLFFT
/* Here the issue is similar to clplanX described above. However, we are using full gridY instead of boxY, which
* incurs at least a-factor-of-two performance hit. To solve this problem one need to execute separate plans for 3
* components of vectors. Unfortunately, this cannot be simply done using 3-element loop (like in Temperton FFT),
* because a part of cl_mem object can't be addressed independently (as can be done with simple C arrays). The only
* way to address this issue is to either create three separate cl_mem objects or to change the indexing of levels
* inside the array, so that 3 components are stored together.
*/
CLFFT_CH_ERR(clfftCreateDefaultPlan(&clplanZ,context,CLFFT_1D,&gridZ));
/* TODO: last slices can be very slightly thinner than the previous ones, but since the batchsize is part of the
* plan, another plan would be needed to address this. However, we ignore this currently and assume that every
* slice has a thickness of local_gridX.
* This issue also applies to clplanY.
*/
CLFFT_CH_ERR(clfftSetPlanBatchSize(clplanZ,3*gridY*local_gridX));
CLFFT_CH_ERR(clfftSetPlanPrecision(clplanZ,PRECISION_CLFFT));
CLFFT_CH_ERR(clfftSetResultLocation(clplanZ,CLFFT_INPLACE));
CLFFT_CH_ERR(clfftSetLayout(clplanZ,CLFFT_COMPLEX_INTERLEAVED,CLFFT_COMPLEX_INTERLEAVED));
CLFFT_CH_ERR(clfftSetPlanScale(clplanZ,CLFFT_FORWARD,1));
CLFFT_CH_ERR(clfftSetPlanScale(clplanZ,CLFFT_BACKWARD,1)); // override the default 1/N scale for backward direction
CLFFT_CH_ERR(clfftBakePlan(clplanZ,1,&command_queue,NULL,NULL));
CLFFT_CH_ERR(clfftGetTmpBufSize(clplanZ,&bufsize));
clfftBufSize+=bufsize;
/* In most cases clfftBufSize is zero, except some weird grid sizes like 2x2x60000. Still, we rigorously account
* for this memory. However, we do not update oclMemMaxObj, since even single plan is not guaranteed to allocate a
* single object. So we assume that clFFT will either handle maximum object size itself or produce a meaningful
* error.
*/
oclMem+=clfftBufSize;
MAXIMIZE(oclMemPeak,oclMem);
# elif defined(CLFFT_APPLE)
clFFT_Dim3 zdimen;
zdimen.x=(unsigned int)gridZ;
zdimen.y=1;
zdimen.z=1;
clplanZ=clFFT_CreatePlan(context,zdimen,clFFT_1D,clFFT_InterleavedComplexFormat,&err);
CL_CH_ERR(err);
# endif
# ifdef PRECISE_TIMING
GET_SYSTEM_TIME(tvp+3);
// print precise timing of FFT planning
if (IFROOT) PrintBoth(logfile,
"~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n"
" clFFT planning \n"
"~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n"
"X = "FFORMPT" Total = "FFORMPT"\n"
"Y = "FFORMPT"\n"
"Z = "FFORMPT"\n\n",
DiffSystemTime(tvp,tvp+1),DiffSystemTime(tvp,tvp+3),DiffSystemTime(tvp+1,tvp+2),DiffSystemTime(tvp+2,tvp+3));
# endif
#elif defined(FFTW3) // this is not needed when OpenCL is used
int lot;
fftw_iodim dims,howmany_dims[2];
int grYint=gridY; // this is needed to provide 'int *' to gridY
# ifdef PRECISE_TIMING
SYSTEM_TIME tvp[7];
# endif
if (IFROOT) PRINTFB("Initializing FFTW3\n");
# ifdef PRECISE_TIMING
GET_SYSTEM_TIME(tvp);
# endif
lot=3*gridZ;
planYf=fftw_plan_many_dft(1,&grYint,lot,slices_tr,NULL,1,gridY,slices_tr,NULL,1,gridY,FFT_FORWARD,PLAN_FFTW);
if (surface) // same operation, but applied to slicesR_tr
planYRf=fftw_plan_many_dft(1,&grYint,lot,slicesR_tr,NULL,1,gridY,slicesR_tr,NULL,1,gridY,FFT_FORWARD,PLAN_FFTW);
# ifdef PRECISE_TIMING
GET_SYSTEM_TIME(tvp+1);
# endif
planYb=fftw_plan_many_dft(1,&grYint,lot,slices_tr,NULL,1,gridY,slices_tr,NULL,1,gridY,FFT_BACKWARD,PLAN_FFTW);
# ifdef PRECISE_TIMING
GET_SYSTEM_TIME(tvp+2);
# endif
dims.n=gridZ;
dims.is=dims.os=1;
howmany_dims[0].n=3;
howmany_dims[0].is=howmany_dims[0].os=gridZ*gridY;
howmany_dims[1].n=boxY;
howmany_dims[1].is=howmany_dims[1].os=gridZ;
planZf=fftw_plan_guru_dft(1,&dims,2,howmany_dims,slices,slices,FFT_FORWARD,PLAN_FFTW);
// same operation but for slicesR and inverse transform (since correlation is computed instead of convolution)
if (surface) planZRf=fftw_plan_guru_dft(1,&dims,2,howmany_dims,slicesR,slicesR,FFT_BACKWARD,PLAN_FFTW);
# ifdef PRECISE_TIMING
GET_SYSTEM_TIME(tvp+3);
# endif
planZb=fftw_plan_guru_dft(1,&dims,2,howmany_dims,slices,slices,FFT_BACKWARD,PLAN_FFTW);
# ifdef PRECISE_TIMING
GET_SYSTEM_TIME(tvp+4);
# endif
dims.n=gridX;
dims.is=dims.os=1;
howmany_dims[0].n=3*local_Nz;
howmany_dims[0].is=howmany_dims[0].os=smallY*gridX;
howmany_dims[1].n=boxY;
howmany_dims[1].is=howmany_dims[1].os=gridX;
planXf=fftw_plan_guru_dft(1,&dims,2,howmany_dims,Xmatrix,Xmatrix,FFT_FORWARD,PLAN_FFTW);
# ifdef PRECISE_TIMING
GET_SYSTEM_TIME(tvp+5);
# endif
planXb=fftw_plan_guru_dft(1,&dims,2,howmany_dims,Xmatrix,Xmatrix,FFT_BACKWARD,PLAN_FFTW);
# ifdef PRECISE_TIMING
GET_SYSTEM_TIME(tvp+6);
// print precise timing of FFT planning
if (IFROOT) PrintBoth(logfile,
"~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n"
" FFTW3 planning \n"
"~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n"
"Yf = "FFORMPT" Total = "FFORMPT"\n"
"Yb = "FFORMPT"\n"
"Zf = "FFORMPT"\n"
"Zb = "FFORMPT"\n"
"Xf = "FFORMPT"\n"
"Xb = "FFORMPT"\n\n",
DiffSystemTime(tvp,tvp+1),DiffSystemTime(tvp,tvp+6),DiffSystemTime(tvp+1,tvp+2),DiffSystemTime(tvp+2,tvp+3),
DiffSystemTime(tvp+3,tvp+4),DiffSystemTime(tvp+4,tvp+5),DiffSystemTime(tvp+5,tvp+6));
# endif
#endif
#ifdef FFTW3
// destroy old (D,R-matrix) plans; also in OpenCL mode
fftw_destroy_plan(planXf_Dm);
fftw_destroy_plan(planYf_slice);
fftw_destroy_plan(planZf_slice);
if (surface) fftw_destroy_plan(planXf_Rm);
# ifdef OPENCL // in this case, FFTW ends here
fftw_cleanup();
# endif
#endif
}
//======================================================================================================================
static void InitRmatrix(const double invNgrid)
/* Initializes the matrix R. R[i][j][k]=GR[i1-i2][j1-j2][k1+k2]. Actually R=-FFT(GR)/Ngrid. Then -GR.x=invFFT(R*FFT(x))
* for practical implementation of FFT such that invFFT(FFT(x))=Ngrid*x. GR is exactly reflected Green's tensor. The
* routine is very similar to the corresponding part of InitDmatrix. Moreover, some initialization is delegated to the
* latter function.
*/
{
int i,j,k,Rcomp;
size_t x,y,z,indexfrom,indexto,ind,index;
// allocate memory for Rmatrix (R2matrix is allocated earlier in InitDmatrix)
MALLOC_VECTOR(Rmatrix,complex,Rsize,ALL);
#ifdef PARALLEL
// allocate buffer for BlockTranspose_DRm
size_t bufsize = 2*lz_Rm*R2sizeY*local_Nx;
MALLOC_VECTOR(BT_buffer,double,bufsize,ALL);
MALLOC_VECTOR(BT_rbuffer,double,bufsize,ALL);
#endif
if (IFROOT) PRINTFB("Calculating reflected Green's function (Rmatrix)\n");
/* Interaction matrix values are calculated all at once for performance reasons. They are stored in Rmatrix with
* indexing corresponding to R2matrix (to facilitate copying) but NDCOMP elements instead of one. Afterwards they
* are replaced by Fourier transforms (with different indexing) component-wise (in cycle over NDCOMP)
*/
/* fill Rmatrix with 0, this if to fill the possible gap between e.g. boxY and gridY/2; (and for R=0) probably
* faster than using a lot of conditionals
*/
for (ind=0;ind<Rsize;ind++) Rmatrix[ind]=0;
// fill Rmatrix with values of reflected Green's tensor
for(k=0;k<local_Nz_Rm;k++) for (j=jstartR;j<boxY;j++) for (i=1-boxX;i<boxX;i++) {
index=NDCOMP*Index2matrix(i,j,k,R2sizeY);
(*ReflTerm_int)(i,j,k,Rmatrix+index);
} // end of i,j,k loop
if (IFROOT) PRINTFB("Fourier transform of Rmatrix\n");
for(Rcomp=0;Rcomp<NDCOMP;Rcomp++) { // main cycle over components of Rmatrix
// fill R2matrix with precomputed values from Rmatrix
for (ind=0;ind<R2sizeTot;ind++) R2matrix[ind]=Rmatrix[NDCOMP*ind+Rcomp];
fftX_Rm(); // fftX R2matrix
BlockTranspose_DRm(R2matrix,R2sizeY,lz_Rm);
for(x=local_x0;x<local_x1;x++) {
for (ind=0;ind<gridYZ;ind++) slice[ind]=0.0; // fill slice with 0.0
for(j=jstartR;j<boxY;j++) for(k=0;k<2*boxZ-1;k++) {
indexfrom=IndexGarbledR(x,j,k);
indexto=IndexSliceR2matrix(j,k);
slice[indexto]=R2matrix[indexfrom];
}
/* here a specific symmetry is used, that elements of R depend on direction y/|rho| either as even order
* (0 or 2) or as odd (1) - the latter are elements 1 and 4 (see GetSomIntegral in interaction.c)
*/
if (reduced_FFT) for(j=1;j<boxY;j++) for(k=0;k<2*boxZ-1;k++) {
// mirror along y
indexfrom=IndexSliceR2matrix(j,k);
indexto=IndexSliceR2matrix(-j,k);
if (Rcomp==1 || Rcomp==4) slice[indexto]=-slice[indexfrom];
else slice[indexto]=slice[indexfrom];
}
fftZ_slice(); // fftZ slice
transpose(slice,slice_tr,gridY,gridZ);
fftY_slice(); // fftY slice_tr
for(z=0;z<gridZ;z++) for(y=0;y<RsizeY;y++) {
indexto=IndexRmatrix(x-local_x0,y,z)+Rcomp;
indexfrom=IndexSlice_zy(y,z);
Rmatrix[indexto]=-invNgrid*slice_tr[indexfrom];
}
} // end slice X
} // end of Rcomp
#ifdef PARALLEL
// deallocate buffers for BlockTranspose_DRm
Free_general(BT_buffer);
Free_general(BT_rbuffer);
#endif
#ifdef OPENCL
// Setting kernel arguments which are always the same
// for arith3_surface
CL_CH_ERR(clSetKernelArg(clarith3_surface,0,sizeof(cl_mem),&bufslices_tr));
CL_CH_ERR(clSetKernelArg(clarith3_surface,1,sizeof(cl_mem),&bufDmatrix));
CL_CH_ERR(clSetKernelArg(clarith3_surface,2,sizeof(size_t),&smallY));
CL_CH_ERR(clSetKernelArg(clarith3_surface,3,sizeof(size_t),&smallZ));
CL_CH_ERR(clSetKernelArg(clarith3_surface,4,sizeof(size_t),&gridX));
CL_CH_ERR(clSetKernelArg(clarith3_surface,5,sizeof(size_t),&DsizeY));
CL_CH_ERR(clSetKernelArg(clarith3_surface,6,sizeof(size_t),&DsizeZ));
CL_CH_ERR(clSetKernelArg(clarith3_surface,11,sizeof(cl_mem),&bufslicesR_tr));
CL_CH_ERR(clSetKernelArg(clarith3_surface,12,sizeof(cl_mem),&bufRmatrix));
// for transpose forward (backward are not needed for surface)
CL_CH_ERR(clSetKernelArg(cltransposeofR,0,sizeof(cl_mem),&bufslicesR));
CL_CH_ERR(clSetKernelArg(cltransposeofR,1,sizeof(cl_mem),&bufslicesR_tr));
CL_CH_ERR(clSetKernelArg(cltransposeofR,2,sizeof(size_t),&gridZ));
CL_CH_ERR(clSetKernelArg(cltransposeofR,3,sizeof(size_t),&gridY));
CL_CH_ERR(clSetKernelArg(cltransposeofR,4,17*16*sizeof(doublecomplex),NULL));
// copy Rmatrix to OpenCL buffer, blocking to ensure completion before function end
CL_CH_ERR(clEnqueueWriteBuffer(command_queue,bufRmatrix,CL_TRUE,0,Rsize*sizeof(*Rmatrix),Rmatrix,0,NULL,NULL));
Free_cVector(Rmatrix);
#endif
}
//======================================================================================================================
void InitDmatrix(void)
/* Initializes the matrix D. D[i][j][k]=A[i1-i2][j1-j2][k1-k2]. Actually D=-FFT(G)/Ngrid. Then -G.x=invFFT(D*FFT(x)) for
* practical implementation of FFT such that invFFT(FFT(x))=Ngrid*x. G is exactly Green's tensor. The routine is called
* only once, so does not need to be very fast, however we tried to optimize it.
*/
{
int i,j,k,kcor,Dcomp;
size_t x,y,z,indexfrom,indexto,ind,index,Dsize,D2sizeTot;
double invNgrid;
int nnn; // multiplier used for reduced_FFT or not reduced; 1 or 2
int jstart,kstart;
TIME_TYPE start,time1;
#ifdef PRECISE_TIMING
// precise timing of the Dmatrix computation
SYSTEM_TIME tvp[15];
SYSTEM_TIME Timing_fftX,Timing_fftY,Timing_fftZ,Timing_Gcalc,Timing_ar1,Timing_ar2,Timing_ar3,Timing_BT,Timing_TYZ,
Timing_beg,Timing_InitMV;
double t_fftX,t_fftY,t_fftZ,t_ar1,t_ar2,t_ar3,t_TYZ,t_beg,t_Gcalc,t_Arithm,t_FFT,t_BT,t_InitMV,t_Rm,t_Tot;
// This should be the first occurrence of PRECISE_TIMING in the program
SetTimerFreq();
t_Rm=0; // redundant initialization to remove warnings
InitTime(&Timing_fftX);
InitTime(&Timing_fftY);
InitTime(&Timing_fftZ);
InitTime(&Timing_ar1);
InitTime(&Timing_ar2);
InitTime(&Timing_ar3);