ComputeFstat_Resamp_Generic.c

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//
// Copyright (C) 2009, 2014--2015 Reinhard Prix
// Copyright (C) 2012--2015 Karl Wette
// Copyright (C) 2009 Chris Messenger, Pinkesh Patel, Xavier Siemens, Holger Pletsch
//
// This program 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 2 of the License, or
// (at your option) any later version.
//
// This program 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 with program; see the file COPYING. If not, write to the
// Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston,
// MA  02110-1301  USA
//
 
#include <stdlib.h>
#include <stdio.h>
#include <math.h>
#include <complex.h>
#include <fftw3.h>
 
#include "ComputeFstat_internal.h"
#include "ComputeFstat_Resamp_internal.h"
 
#include <lal/FFTWMutex.h>
#include <lal/Factorial.h>
#include <lal/LFTandTSutils.h>
#include <lal/LogPrintf.h>
#include <lal/SinCosLUT.h>
#include <lal/TimeSeries.h>
#include <lal/Units.h>
 
///
/// \defgroup ComputeFstat_Resamp_Generic_c Module ComputeFstat_Resamp_Generic.c
/// \ingroup ComputeFstat_h
/// \brief Implements a generic version \cite Prix2022 of the \a Resamp FFT-based resampling algorithm for
/// computing the \f$ \mathcal{F} \f$ -statistic \cite JKS98 .
///
 
/// @{
 
// ========== Resamp internals ==========
 
// ----- local constants ----------
 
// ----- local macros ----------
 
// ----- local types ----------
 
// ----- workspace ----------
typedef struct tagResampGenericWorkspace {
  // intermediate quantities to interpolate and operate on SRC-frame timeseries
  COMPLEX8Vector *TStmp1_SRC;   // can hold a single-detector SRC-frame spindown-corrected timeseries [without zero-padding]
  COMPLEX8Vector *TStmp2_SRC;   // can hold a single-detector SRC-frame spindown-corrected timeseries [without zero-padding]
  REAL8Vector *SRCtimes_DET;    // holds uniformly-spaced SRC-frame timesteps translated into detector frame [for interpolation]
 
  // input padded timeseries ts(t) and output Fab(f) of length 'numSamplesFFT'
  UINT4 numSamplesFFTAlloc;     // allocated number of zero-padded SRC-frame time samples (related to dFreq)
  COMPLEX8 *TS_FFT;             // zero-padded, spindown-corr SRC-frame TS
  COMPLEX8 *FabX_Raw;           // raw full-band FFT result Fa,Fb
 
  // arrays of size numFreqBinsOut over frequency bins f_k:
  COMPLEX8 *FaX_k;              // properly normalized F_a^X(f_k) over output bins
  COMPLEX8 *FbX_k;              // properly normalized F_b^X(f_k) over output bins
  COMPLEX8 *Fa_k;               // properly normalized F_a(f_k) over output bins
  COMPLEX8 *Fb_k;               // properly normalized F_b(f_k) over output bins
  UINT4 numFreqBinsAlloc;       // internal: keep track of allocated length of frequency-arrays
 
} ResampGenericWorkspace;
 
typedef struct {
  UINT4 Dterms;                                         // Number of terms to use (on either side) in Windowed-Sinc interpolation kernel
  MultiCOMPLEX8TimeSeries  *multiTimeSeries_DET;        // input SFTs converted into a heterodyned timeseries
  // ----- buffering -----
  PulsarDopplerParams prev_doppler;                     // buffering: previous phase-evolution ("doppler") parameters
  MultiAMCoeffs *multiAMcoef;                           // buffered antenna-pattern functions
  MultiSSBtimes *multiSSBtimes;                         // buffered SSB times, including *only* sky-position corrections, not binary
  MultiSSBtimes *multiBinaryTimes;                      // buffered SRC times, including both sky- and binary corrections [to avoid re-allocating this]
 
  AntennaPatternMatrix Mmunu;                           // combined multi-IFO antenna-pattern coefficients {A,B,C,E}
  AntennaPatternMatrix MmunuX[PULSAR_MAX_DETECTORS];    // per-IFO antenna-pattern coefficients {AX,BX,CX,EX}
 
  MultiCOMPLEX8TimeSeries *multiTimeSeries_SRC_a;       // multi-detector SRC-frame timeseries, multiplied by AM function a(t)
  MultiCOMPLEX8TimeSeries *multiTimeSeries_SRC_b;       // multi-detector SRC-frame timeseries, multiplied by AM function b(t)
 
  UINT4 numSamplesFFT;                                  // length of zero-padded SRC-frame timeseries (related to dFreq)
  UINT4 decimateFFT;                                    // output every n-th frequency bin, with n>1 iff (dFreq > 1/Tspan), and was internally decreased by n
  fftwf_plan fftplan;                                   // FFT plan
 
  // ----- timing -----
  BOOLEAN collectTiming;                                // flag whether or not to collect timing information
  FstatTimingGeneric timingGeneric;                     // measured (generic) F-statistic timing values
  FstatTimingResamp  timingResamp;                      // measured Resamp-specific timing model data
 
} ResampGenericMethodData;
 
 
// ----- local prototypes ----------
 
int XLALSetupFstatResampGeneric( void **method_data, FstatCommon *common, FstatMethodFuncs *funcs, MultiSFTVector *multiSFTs, const FstatOptionalArgs *optArgs );
int XLALExtractResampledTimeseries_ResampGeneric( MultiCOMPLEX8TimeSeries **multiTimeSeries_SRC_a, MultiCOMPLEX8TimeSeries **multiTimeSeries_SRC_b, void *method_data );
int XLALGetFstatTiming_ResampGeneric( const void *method_data, FstatTimingGeneric *timingGeneric, FstatTimingModel *timingModel );
 
static int XLALComputeFstatResampGeneric( FstatResults *Fstats, const FstatCommon *common, void *method_data );
static int XLALApplySpindownAndFreqShiftGeneric( COMPLEX8 *xOut, const COMPLEX8TimeSeries *xIn, const PulsarDopplerParams *doppler, REAL8 freqShift );
static int XLALBarycentricResampleMultiCOMPLEX8TimeSeriesGeneric( ResampGenericMethodData *resamp, const PulsarDopplerParams *thisPoint, const FstatCommon *common );
static int XLALComputeFaFb_ResampGeneric( ResampGenericMethodData *resamp, ResampGenericWorkspace *ws, const PulsarDopplerParams thisPoint, REAL8 dFreq, UINT4 numFreqBins, const COMPLEX8TimeSeries *TimeSeries_SRC_a, const COMPLEX8TimeSeries *TimeSeries_SRC_b );
static void XLALGetFFTPlanHints( int *planMode, double *planGenTimeoutSeconds );
static void XLALDestroyResampGenericWorkspace( void *workspace );
static void XLALDestroyResampGenericMethodData( void *method_data );
 
// ==================== function definitions ====================
 
static void XLALDestroyResampGenericWorkspace( void *workspace )
{
  ResampGenericWorkspace *ws = ( ResampGenericWorkspace * ) workspace;
 
  XLALDestroyCOMPLEX8Vector( ws->TStmp1_SRC );
  XLALDestroyCOMPLEX8Vector( ws->TStmp2_SRC );
  XLALDestroyREAL8Vector( ws->SRCtimes_DET );
 
  fftw_free( ws->FabX_Raw );
  fftw_free( ws->TS_FFT );
 
  XLALFree( ws->FaX_k );
  XLALFree( ws->FbX_k );
  XLALFree( ws->Fa_k );
  XLALFree( ws->Fb_k );
 
  XLALFree( ws );
  return;
 
} // XLALDestroyResampGenericWorkspace()
 
static void XLALDestroyResampGenericMethodData( void *method_data )
{
 
  ResampGenericMethodData *resamp = ( ResampGenericMethodData * ) method_data;
 
  XLALDestroyMultiCOMPLEX8TimeSeries( resamp->multiTimeSeries_DET );
 
  // ----- free buffer
  XLALDestroyMultiCOMPLEX8TimeSeries( resamp->multiTimeSeries_SRC_a );
  XLALDestroyMultiCOMPLEX8TimeSeries( resamp->multiTimeSeries_SRC_b );
  XLALDestroyMultiAMCoeffs( resamp->multiAMcoef );
  XLALDestroyMultiSSBtimes( resamp->multiSSBtimes );
  XLALDestroyMultiSSBtimes( resamp->multiBinaryTimes );
 
  LAL_FFTW_WISDOM_LOCK;
  fftwf_destroy_plan( resamp->fftplan );
  LAL_FFTW_WISDOM_UNLOCK;
 
  XLALFree( resamp );
 
} // XLALDestroyResampGenericMethodData()
 
int
XLALSetupFstatResampGeneric( void **method_data,
                             FstatCommon *common,
                             FstatMethodFuncs *funcs,
                             MultiSFTVector *multiSFTs,
                             const FstatOptionalArgs *optArgs
                           )
{
  // Check input
  XLAL_CHECK( method_data != NULL, XLAL_EFAULT );
  XLAL_CHECK( common != NULL, XLAL_EFAULT );
  XLAL_CHECK( funcs != NULL, XLAL_EFAULT );
  XLAL_CHECK( multiSFTs != NULL, XLAL_EFAULT );
  XLAL_CHECK( optArgs != NULL, XLAL_EFAULT );
 
  // Allocate method data
  ResampGenericMethodData *resamp = *method_data = XLALCalloc( 1, sizeof( *resamp ) );
  XLAL_CHECK( resamp != NULL, XLAL_ENOMEM );
 
  resamp->Dterms = optArgs->Dterms;
 
  // Set method function pointers
  funcs->compute_func = XLALComputeFstatResampGeneric;
  funcs->method_data_destroy_func = XLALDestroyResampGenericMethodData;
  funcs->workspace_destroy_func = XLALDestroyResampGenericWorkspace;
 
  // Extra band needed for resampling: Hamming-windowed sinc used for interpolation has a transition bandwith of
  // TB=(4/L)*fSamp, where L=2*Dterms+1 is the window-length, and here fSamp=Band (i.e. the full SFT frequency band)
  // However, we're only interested in the physical band and we'll be throwing away all bins outside of this.
  // This implies that we're only affected by *half* the transition band TB/2 on either side, as the other half of TB is outside of the band of interest
  // (and will actually get aliased, i.e. the region [-fNy - TB/2, -fNy] overlaps with [fNy-TB/2,fNy] and vice-versa: [fNy,fNy+TB/2] overlaps with [-fNy,-fNy+TB/2])
  // ==> therefore we only need to add an extra TB/2 on each side to be able to safely avoid the transition-band effects
  REAL8 f0 = multiSFTs->data[0]->data[0].f0;
  REAL8 dFreq = multiSFTs->data[0]->data[0].deltaF;
  REAL8 Band = multiSFTs->data[0]->data[0].data->length * dFreq;
  REAL8 extraBand = 2.0  / ( 2 * optArgs->Dterms + 1 ) * Band;
  XLAL_CHECK( XLALMultiSFTVectorResizeBand( multiSFTs, f0 - extraBand, Band + 2 * extraBand ) == XLAL_SUCCESS, XLAL_EFUNC );
  // Convert SFTs into heterodyned complex timeseries [in detector frame]
  XLAL_CHECK( ( resamp->multiTimeSeries_DET = XLALMultiSFTVectorToCOMPLEX8TimeSeries( multiSFTs ) ) != NULL, XLAL_EFUNC );
 
  XLALDestroyMultiSFTVector( multiSFTs );       // don't need them SFTs any more ...
 
  UINT4 numDetectors = resamp->multiTimeSeries_DET->length;
  REAL8 dt_DET       = resamp->multiTimeSeries_DET->data[0]->deltaT;
  REAL8 fHet         = resamp->multiTimeSeries_DET->data[0]->f0;
  REAL8 Tsft         = common->multiTimestamps->data[0]->deltaT;
 
  // determine resampled timeseries parameters
  REAL8 TspanFFT = 1.0 / common->dFreq;
 
  // check that TspanFFT >= TspanX for all detectors X, otherwise increase TspanFFT by an integer factor 'decimateFFT' such that this is true
  REAL8 TspanXMax = 0;
  for ( UINT4 X = 0; X < numDetectors; X ++ ) {
    UINT4 numSamples_DETX = resamp->multiTimeSeries_DET->data[X]->data->length;
    REAL8 TspanX = numSamples_DETX * dt_DET;
    TspanXMax = fmax( TspanXMax, TspanX );
  }
  UINT4 decimateFFT = ( UINT4 )ceil( TspanXMax / TspanFFT );    // larger than 1 means we need to artificially increase dFreqFFT by 'decimateFFT'
  if ( decimateFFT > 1 ) {
    XLALPrintWarning( "WARNING: Frequency spacing larger than 1/Tspan, we'll internally decimate FFT frequency bins by a factor of %" LAL_UINT4_FORMAT "\n", decimateFFT );
  }
  TspanFFT *= decimateFFT;
  resamp->decimateFFT = decimateFFT;
 
  UINT4 numSamplesFFT0 = ( UINT4 ) ceil( TspanFFT / dt_DET );     // we use ceil() so that we artificially widen the band rather than reduce it
  UINT4 numSamplesFFT = 0;
  if ( optArgs->resampFFTPowerOf2 ) {
    numSamplesFFT = ( UINT4 ) pow( 2, ceil( log2( numSamplesFFT0 ) ) );   // round numSamplesFFT up to next power of 2 for most effiecient FFT
  } else {
    numSamplesFFT = ( UINT4 ) 2 * ceil( numSamplesFFT0 / 2 );   // always ensure numSamplesFFT is even
  }
 
  REAL8 dt_SRC = TspanFFT / numSamplesFFT;                      // adjust sampling rate to allow achieving exact requested dFreq=1/TspanFFT !
 
  resamp->numSamplesFFT = numSamplesFFT;
  // ----- allocate buffer Memory ----------
 
  // header for SRC-frame resampled timeseries buffer
  XLAL_CHECK( ( resamp->multiTimeSeries_SRC_a = XLALCalloc( 1, sizeof( MultiCOMPLEX8TimeSeries ) ) ) != NULL, XLAL_ENOMEM );
  XLAL_CHECK( ( resamp->multiTimeSeries_SRC_a->data = XLALCalloc( numDetectors, sizeof( COMPLEX8TimeSeries ) ) ) != NULL, XLAL_ENOMEM );
  resamp->multiTimeSeries_SRC_a->length = numDetectors;
 
  XLAL_CHECK( ( resamp->multiTimeSeries_SRC_b = XLALCalloc( 1, sizeof( MultiCOMPLEX8TimeSeries ) ) ) != NULL, XLAL_ENOMEM );
  XLAL_CHECK( ( resamp->multiTimeSeries_SRC_b->data = XLALCalloc( numDetectors, sizeof( COMPLEX8TimeSeries ) ) ) != NULL, XLAL_ENOMEM );
  resamp->multiTimeSeries_SRC_b->length = numDetectors;
 
  LIGOTimeGPS XLAL_INIT_DECL( epoch0 ); // will be set to corresponding SRC-frame epoch when barycentering
  UINT4 numSamplesMax_SRC = 0;
  for ( UINT4 X = 0; X < numDetectors; X ++ ) {
    // ----- check input consistency ----------
    REAL8 dt_DETX = resamp->multiTimeSeries_DET->data[X]->deltaT;
    XLAL_CHECK( dt_DET == dt_DETX, XLAL_EINVAL, "Input timeseries must have identical 'deltaT(X=%d)' (%.16g != %.16g)\n", X, dt_DET, dt_DETX );
 
    REAL8 fHetX = resamp->multiTimeSeries_DET->data[X]->f0;
    XLAL_CHECK( fabs( fHet - fHetX ) < LAL_REAL8_EPS * fHet, XLAL_EINVAL, "Input timeseries must have identical heterodyning frequency 'f0(X=%d)' (%.16g != %.16g)\n", X, fHet, fHetX );
 
    REAL8 TsftX = common->multiTimestamps->data[X]->deltaT;
    XLAL_CHECK( Tsft == TsftX, XLAL_EINVAL, "Input timestamps must have identical stepsize 'Tsft(X=%d)' (%.16g != %.16g)\n", X, Tsft, TsftX );
 
    // ----- prepare Memory fo SRC-frame timeseries and AM coefficients
    const char *nameX = resamp->multiTimeSeries_DET->data[X]->name;
    UINT4 numSamples_DETX = resamp->multiTimeSeries_DET->data[X]->data->length;
    UINT4 numSamples_SRCX = ( UINT4 )ceil( numSamples_DETX * dt_DET / dt_SRC );
 
    XLAL_CHECK( ( resamp->multiTimeSeries_SRC_a->data[X] = XLALCreateCOMPLEX8TimeSeries( nameX, &epoch0, fHet, dt_SRC, &lalDimensionlessUnit, numSamples_SRCX ) ) != NULL, XLAL_EFUNC );
    XLAL_CHECK( ( resamp->multiTimeSeries_SRC_b->data[X] = XLALCreateCOMPLEX8TimeSeries( nameX, &epoch0, fHet, dt_SRC, &lalDimensionlessUnit, numSamples_SRCX ) ) != NULL, XLAL_EFUNC );
 
    numSamplesMax_SRC = MYMAX( numSamplesMax_SRC, numSamples_SRCX );
  } // for X < numDetectors
 
  XLAL_CHECK( numSamplesFFT >= numSamplesMax_SRC, XLAL_EFAILED, "[numSamplesFFT = %d] < [numSamplesMax_SRC = %d]\n", numSamplesFFT, numSamplesMax_SRC );
 
  // ---- re-use shared workspace, or allocate here ----------
  ResampGenericWorkspace *ws = ( ResampGenericWorkspace * ) common->workspace;
  if ( ws != NULL ) {
    if ( numSamplesFFT > ws->numSamplesFFTAlloc ) {
      fftw_free( ws->FabX_Raw );
      XLAL_CHECK( ( ws->FabX_Raw = fftw_malloc( numSamplesFFT * sizeof( COMPLEX8 ) ) ) != NULL, XLAL_ENOMEM );
      fftw_free( ws->TS_FFT );
      XLAL_CHECK( ( ws->TS_FFT   = fftw_malloc( numSamplesFFT * sizeof( COMPLEX8 ) ) ) != NULL, XLAL_ENOMEM );
 
      ws->numSamplesFFTAlloc = numSamplesFFT;
    }
 
    // adjust maximal SRC-frame timeseries length, if necessary
    if ( numSamplesMax_SRC > ws->TStmp1_SRC->length ) {
      XLAL_CHECK( ( ws->TStmp1_SRC->data = XLALRealloc( ws->TStmp1_SRC->data,   numSamplesMax_SRC * sizeof( COMPLEX8 ) ) ) != NULL, XLAL_ENOMEM );
      ws->TStmp1_SRC->length = numSamplesMax_SRC;
      XLAL_CHECK( ( ws->TStmp2_SRC->data = XLALRealloc( ws->TStmp2_SRC->data,   numSamplesMax_SRC * sizeof( COMPLEX8 ) ) ) != NULL, XLAL_ENOMEM );
      ws->TStmp2_SRC->length = numSamplesMax_SRC;
      XLAL_CHECK( ( ws->SRCtimes_DET->data = XLALRealloc( ws->SRCtimes_DET->data, numSamplesMax_SRC * sizeof( REAL8 ) ) ) != NULL, XLAL_ENOMEM );
      ws->SRCtimes_DET->length = numSamplesMax_SRC;
    }
 
  } // end: if shared workspace given
  else {
    XLAL_CHECK( ( ws = XLALCalloc( 1, sizeof( *ws ) ) ) != NULL, XLAL_ENOMEM );
    XLAL_CHECK( ( ws->TStmp1_SRC   = XLALCreateCOMPLEX8Vector( numSamplesMax_SRC ) ) != NULL, XLAL_EFUNC );
    XLAL_CHECK( ( ws->TStmp2_SRC   = XLALCreateCOMPLEX8Vector( numSamplesMax_SRC ) ) != NULL, XLAL_EFUNC );
    XLAL_CHECK( ( ws->SRCtimes_DET = XLALCreateREAL8Vector( numSamplesMax_SRC ) ) != NULL, XLAL_EFUNC );
 
    XLAL_CHECK( ( ws->FabX_Raw = fftw_malloc( numSamplesFFT * sizeof( COMPLEX8 ) ) ) != NULL, XLAL_ENOMEM );
    XLAL_CHECK( ( ws->TS_FFT   = fftw_malloc( numSamplesFFT * sizeof( COMPLEX8 ) ) ) != NULL, XLAL_ENOMEM );
    ws->numSamplesFFTAlloc = numSamplesFFT;
 
    common->workspace = ws;
  } // end: if we create our own workspace
 
  // ----- compute and buffer FFT plan ----------
  int fft_plan_flags = FFTW_MEASURE;
  double fft_plan_timeout = FFTW_NO_TIMELIMIT ;
  char *wisdom_filename;
  static int tried_wisdom = 0;
 
  LAL_FFTW_WISDOM_LOCK;
  // if FFTWF_WISDOM_FILENAME is set, try to import that wisdom
  wisdom_filename = getenv( "FFTWF_WISDOM_FILENAME" );
  if ( wisdom_filename && !tried_wisdom ) {
    FILE *fp = fopen( wisdom_filename, "r" );
    if ( !fp ) {
      XLALPrintWarning( "WARNING: Couldn't open wisdom file '%s'\n", wisdom_filename );
    } else if ( fftwf_import_wisdom_from_file( fp ) ) {
      XLALPrintInfo( "INFO: imported wisdom from file '%s'\n", wisdom_filename );
      fclose( fp );
    } else {
      XLALPrintWarning( "WARNING: Couldn't import wisdom from file '%s'\n", wisdom_filename );
      fclose( fp );
    }
    tried_wisdom = -1;
  }
  XLALGetFFTPlanHints( & fft_plan_flags, & fft_plan_timeout );
  fftw_set_timelimit( fft_plan_timeout );
  XLAL_CHECK( ( resamp->fftplan = fftwf_plan_dft_1d( resamp->numSamplesFFT, ws->TS_FFT, ws->FabX_Raw, FFTW_FORWARD, fft_plan_flags ) ) != NULL, XLAL_EFAILED, "fftwf_plan_dft_1d() failed\n" );
  LAL_FFTW_WISDOM_UNLOCK;
 
  // turn on timing collection if requested
  resamp->collectTiming = optArgs->collectTiming;
 
  // initialize struct for collecting timing data, store invariant 'meta' quantities about this setup
  if ( resamp->collectTiming ) {
    XLAL_INIT_MEM( resamp->timingGeneric );
    resamp->timingGeneric.Ndet = numDetectors;
 
    XLAL_INIT_MEM( resamp->timingResamp );
    resamp->timingResamp.Resolution = TspanXMax / TspanFFT;
    resamp->timingResamp.NsampFFT0  = numSamplesFFT0;
    resamp->timingResamp.NsampFFT   = numSamplesFFT;
  }
 
  return XLAL_SUCCESS;
 
} // XLALSetupFstatResampGeneric()
 
 
static int
XLALComputeFstatResampGeneric( FstatResults *Fstats,
                               const FstatCommon *common,
                               void *method_data
                             )
{
  // Check input
  XLAL_CHECK( Fstats != NULL, XLAL_EFAULT );
  XLAL_CHECK( common != NULL, XLAL_EFAULT );
  XLAL_CHECK( method_data != NULL, XLAL_EFAULT );
 
  ResampGenericMethodData *resamp = ( ResampGenericMethodData * ) method_data;
 
  const FstatQuantities whatToCompute = Fstats->whatWasComputed;
  XLAL_CHECK( !( whatToCompute & FSTATQ_ATOMS_PER_DET ), XLAL_EINVAL, "Resampling does not currently support atoms per detector" );
 
  ResampGenericWorkspace *ws = ( ResampGenericWorkspace * ) common->workspace;
 
  // ----- handy shortcuts ----------
  PulsarDopplerParams thisPoint = Fstats->doppler;
  const MultiCOMPLEX8TimeSeries *multiTimeSeries_DET = resamp->multiTimeSeries_DET;
  UINT4 numDetectors = multiTimeSeries_DET->length;
 
  // collect internal timing info
  BOOLEAN collectTiming = resamp->collectTiming;
  Timings_t *Tau = &( resamp->timingResamp.Tau );
  XLAL_INIT_MEM( ( *Tau ) );    // these need to be initialized to 0 for each call
 
  REAL8 ticStart = 0, tocEnd = 0;
  REAL8 tic = 0, toc = 0;
  if ( collectTiming ) {
    XLAL_INIT_MEM( ( *Tau ) );  // re-set all timings to 0 at beginning of each Fstat-call
    ticStart = XLALGetCPUTime();
  }
  // Note: all buffering is done within that function
  XLAL_CHECK( XLALBarycentricResampleMultiCOMPLEX8TimeSeriesGeneric( resamp, &thisPoint, common ) == XLAL_SUCCESS, XLAL_EFUNC );
 
  if ( whatToCompute == FSTATQ_NONE ) {
    return XLAL_SUCCESS;
  }
 
  MultiCOMPLEX8TimeSeries *multiTimeSeries_SRC_a = resamp->multiTimeSeries_SRC_a;
  MultiCOMPLEX8TimeSeries *multiTimeSeries_SRC_b = resamp->multiTimeSeries_SRC_b;
 
  // ============================== check workspace is properly allocated and initialized ===========
 
  // ----- workspace that depends on maximal number of output frequency bins 'numFreqBins' ----------
  UINT4 numFreqBins = Fstats->numFreqBins;
 
  if ( collectTiming ) {
    tic = XLALGetCPUTime();
  }
 
  // NOTE: we try to use as much existing memory as possible in FstatResults, so we only
  // allocate local 'workspace' storage in case there's not already a vector allocated in FstatResults for it
  // this also avoid having to copy these results in case the user asked for them to be returned
  if ( whatToCompute & FSTATQ_FAFB ) {
    XLALFree( ws->Fa_k );  // avoid memory leak if allocated in previous call
    ws->Fa_k = Fstats->Fa;
    XLALFree( ws->Fb_k );  // avoid memory leak if allocated in previous call
    ws->Fb_k = Fstats->Fb;
  } // end: if returning FaFb we can use that return-struct as 'workspace'
  else { // otherwise: we (re)allocate it locally
    if ( numFreqBins > ws->numFreqBinsAlloc ) {
      XLAL_CHECK( ( ws->Fa_k = XLALRealloc( ws->Fa_k, numFreqBins * sizeof( COMPLEX8 ) ) ) != NULL, XLAL_ENOMEM );
      XLAL_CHECK( ( ws->Fb_k = XLALRealloc( ws->Fb_k, numFreqBins * sizeof( COMPLEX8 ) ) ) != NULL, XLAL_ENOMEM );
    } // only increase workspace arrays
  }
 
  if ( whatToCompute & FSTATQ_FAFB_PER_DET ) {
    XLALFree( ws->FaX_k );  // avoid memory leak if allocated in previous call
    ws->FaX_k = NULL; // will be set in loop over detectors X
    XLALFree( ws->FbX_k );  // avoid memory leak if allocated in previous call
    ws->FbX_k = NULL; // will be set in loop over detectors X
  } // end: if returning FaFbPerDet we can use that return-struct as 'workspace'
  else { // otherwise: we (re)allocate it locally
    if ( numFreqBins > ws->numFreqBinsAlloc ) {
      XLAL_CHECK( ( ws->FaX_k = XLALRealloc( ws->FaX_k, numFreqBins * sizeof( COMPLEX8 ) ) ) != NULL, XLAL_ENOMEM );
      XLAL_CHECK( ( ws->FbX_k = XLALRealloc( ws->FbX_k, numFreqBins * sizeof( COMPLEX8 ) ) ) != NULL, XLAL_ENOMEM );
    } // only increase workspace arrays
  }
  if ( numFreqBins > ws->numFreqBinsAlloc ) {
    ws->numFreqBinsAlloc = numFreqBins; // keep track of allocated array length
  }
 
  if ( collectTiming ) {
    toc = XLALGetCPUTime();
    Tau->Mem = ( toc - tic );   // this one doesn't scale with number of detector!
  }
  // ====================================================================================================
 
  // loop over detectors
  for ( UINT4 X = 0; X < numDetectors; X++ ) {
    // if return-struct contains memory for holding FaFbPerDet: use that directly instead of local memory
    if ( whatToCompute & FSTATQ_FAFB_PER_DET ) {
      ws->FaX_k = Fstats->FaPerDet[X];
      ws->FbX_k = Fstats->FbPerDet[X];
    }
    const COMPLEX8TimeSeries *TimeSeriesX_SRC_a = multiTimeSeries_SRC_a->data[X];
    const COMPLEX8TimeSeries *TimeSeriesX_SRC_b = multiTimeSeries_SRC_b->data[X];
 
    // compute {Fa^X(f_k), Fb^X(f_k)}: results returned via workspace ws
    XLAL_CHECK( XLALComputeFaFb_ResampGeneric( resamp, ws, thisPoint, common->dFreq, numFreqBins, TimeSeriesX_SRC_a, TimeSeriesX_SRC_b ) == XLAL_SUCCESS, XLAL_EFUNC );
 
    if ( collectTiming ) {
      tic = XLALGetCPUTime();
    }
    if ( X == 0 ) {
      // avoid having to memset this array: for the first detector we *copy* results
      for ( UINT4 k = 0; k < numFreqBins; k++ ) {
        ws->Fa_k[k] = ws->FaX_k[k];
        ws->Fb_k[k] = ws->FbX_k[k];
      }
    } // end: if X==0
    else {
      // for subsequent detectors we *add to* them
      for ( UINT4 k = 0; k < numFreqBins; k++ ) {
        ws->Fa_k[k] += ws->FaX_k[k];
        ws->Fb_k[k] += ws->FbX_k[k];
      }
    } // end:if X>0
 
    if ( collectTiming ) {
      toc = XLALGetCPUTime();
      Tau->SumFabX += ( toc - tic );
      tic = toc;
    }
 
    // ----- if requested: compute per-detector Fstat_X_k
    if ( whatToCompute & FSTATQ_2F_PER_DET ) {
      const REAL4 AdX = resamp->MmunuX[X].Ad;
      const REAL4 BdX = resamp->MmunuX[X].Bd;
      const REAL4 CdX = resamp->MmunuX[X].Cd;
      const REAL4 EdX = resamp->MmunuX[X].Ed;
      const REAL4 DdX_inv = 1.0f / resamp->MmunuX[X].Dd;
      for ( UINT4 k = 0; k < numFreqBins; k ++ ) {
        Fstats->twoFPerDet[X][k] = compute_fstat_from_fa_fb( ws->FaX_k[k], ws->FbX_k[k], AdX, BdX, CdX, EdX, DdX_inv );
      }  // for k < numFreqBins
    } // end: if compute F_X
 
    if ( collectTiming ) {
      toc = XLALGetCPUTime();
      Tau->Fab2F += ( toc - tic );
    }
 
  } // for X < numDetectors
 
  if ( collectTiming ) {
    Tau->SumFabX /= numDetectors;
    Tau->Fab2F /= numDetectors;
    tic = XLALGetCPUTime();
  }
 
  if ( whatToCompute & FSTATQ_2F ) {
    const REAL4 Ad = resamp->Mmunu.Ad;
    const REAL4 Bd = resamp->Mmunu.Bd;
    const REAL4 Cd = resamp->Mmunu.Cd;
    const REAL4 Ed = resamp->Mmunu.Ed;
    const REAL4 Dd_inv = 1.0f / resamp->Mmunu.Dd;
    for ( UINT4 k = 0; k < numFreqBins; k++ ) {
      Fstats->twoF[k] = compute_fstat_from_fa_fb( ws->Fa_k[k], ws->Fb_k[k], Ad, Bd, Cd, Ed, Dd_inv );
    }
  } // if FSTATQ_2F
  if ( whatToCompute & FSTATQ_2F_CUDA ) {
    XLAL_ERROR( XLAL_EINVAL, "Not implemented for FSTATQ_2F_CUDA" );
  }
 
  if ( collectTiming ) {
    toc = XLALGetCPUTime();
    Tau->Fab2F += ( toc - tic );
  }
 
  // Return F-atoms per detector
  if ( whatToCompute & FSTATQ_ATOMS_PER_DET ) {
    XLAL_ERROR( XLAL_EFAILED, "NOT implemented!" );
  }
 
  // Return antenna-pattern matrix
  Fstats->Mmunu = resamp->Mmunu;
 
  // return per-detector antenna-pattern matrices
  for ( UINT4 X = 0; X < numDetectors; X ++ ) {
    Fstats->MmunuX[X] = resamp->MmunuX[X];
  }
 
  // ----- workspace memory management:
  // if we used the return struct directly to store Fa,Fb results,
  // make sure to wipe those pointers to avoid mistakenly considering them as 'local' memory
  // and re-allocing it in another call to this function
  if ( whatToCompute & FSTATQ_FAFB ) {
    ws->Fa_k = NULL;
    ws->Fb_k = NULL;
  }
  if ( whatToCompute & FSTATQ_FAFB_PER_DET ) {
    ws->FaX_k = NULL;
    ws->FbX_k = NULL;
  }
 
  if ( collectTiming ) {
    tocEnd = XLALGetCPUTime();
 
    FstatTimingGeneric *tiGen = &( resamp->timingGeneric );
    FstatTimingResamp  *tiRS  = &( resamp->timingResamp );
    XLAL_CHECK( numDetectors == tiGen->Ndet, XLAL_EINVAL, "Inconsistent number of detectors between XLALCreateSetup() [%d] and XLALComputeFstat() [%d]\n", tiGen->Ndet, numDetectors );
 
    Tau->Total = ( tocEnd - ticStart );
    // rescale all relevant timings to per-detector
    Tau->Total /= numDetectors;
    Tau->Bary  /= numDetectors;
    Tau->Spin  /= numDetectors;
    Tau->FFT   /= numDetectors;
    Tau->Norm  /= numDetectors;
    Tau->Copy  /= numDetectors;
    REAL8 Tau_buffer = Tau->Bary;
    // compute generic F-stat timing model contributions
    UINT4 NFbin      = Fstats->numFreqBins;
    REAL8 tauF_eff   = Tau->Total / NFbin;
    REAL8 tauF_core  = ( Tau->Total - Tau_buffer ) / NFbin;
 
    // compute resampling timing model coefficients
    REAL8 tau0_Fbin  = ( Tau->Copy + Tau->Norm + Tau->SumFabX + Tau->Fab2F ) / NFbin;
    REAL8 tau0_spin  = Tau->Spin / ( tiRS->Resolution * tiRS->NsampFFT );
    REAL8 tau0_FFT   = Tau->FFT / ( 5.0 * tiRS->NsampFFT * log2( tiRS->NsampFFT ) );
 
    // update the averaged timing-model quantities
    tiGen->NCalls ++; // keep track of number of Fstat-calls for timing
#define updateAvgF(q) tiGen->q = ((tiGen->q *(tiGen->NCalls-1) + q)/(tiGen->NCalls))
    updateAvgF( tauF_eff );
    updateAvgF( tauF_core );
    // we also average NFbin, which can be different between different calls to XLALComputeFstat() (contrary to Ndet)
    updateAvgF( NFbin );
 
#define updateAvgRS(q) tiRS->q = ((tiRS->q *(tiGen->NCalls-1) + q)/(tiGen->NCalls))
    updateAvgRS( tau0_Fbin );
    updateAvgRS( tau0_spin );
    updateAvgRS( tau0_FFT );
 
    // buffer-quantities only updated if buffer was actually recomputed
    if ( Tau->BufferRecomputed ) {
      REAL8 tau0_bary   = Tau_buffer / ( tiRS->Resolution * tiRS->NsampFFT );
      REAL8 tauF_buffer = Tau_buffer / NFbin;
 
      updateAvgF( tauF_buffer );
      updateAvgRS( tau0_bary );
    } // if BufferRecomputed
 
  } // if collectTiming
 
  return XLAL_SUCCESS;
 
} // XLALComputeFstatResampGeneric()
 
 
static int
XLALComputeFaFb_ResampGeneric( ResampGenericMethodData *resamp,                        //!< [in,out] buffered resampling data and workspace
                               ResampGenericWorkspace *ws,                             //!< [in,out] resampling workspace (memory-sharing across segments)
                               const PulsarDopplerParams thisPoint,                    //!< [in] Doppler point to compute {FaX,FbX} for
                               REAL8 dFreq,                                            //!< [in] output frequency resolution
                               UINT4 numFreqBins,                                      //!< [in] number of output frequency bins
                               const COMPLEX8TimeSeries *restrict TimeSeries_SRC_a,    //!< [in] SRC-frame single-IFO timeseries * a(t)
                               const COMPLEX8TimeSeries *restrict TimeSeries_SRC_b     //!< [in] SRC-frame single-IFO timeseries * b(t)
                             )
{
  XLAL_CHECK( ( resamp != NULL ) && ( ws != NULL ) && ( TimeSeries_SRC_a != NULL ) && ( TimeSeries_SRC_b != NULL ), XLAL_EINVAL );
  XLAL_CHECK( dFreq > 0, XLAL_EINVAL );
  XLAL_CHECK( numFreqBins <= ws->numFreqBinsAlloc, XLAL_EINVAL );
 
  REAL8 FreqOut0 = thisPoint.fkdot[0];
 
  // compute frequency shift to align heterodyne frequency with output frequency bins
  REAL8 fHet   = TimeSeries_SRC_a->f0;
  REAL8 dt_SRC = TimeSeries_SRC_a->deltaT;
 
  REAL8 dFreqFFT = dFreq / resamp->decimateFFT; // internally may be using higher frequency resolution dFreqFFT than requested
  REAL8 freqShift = remainder( FreqOut0 - fHet, dFreq );  // frequency shift to closest bin
  REAL8 fMinFFT = fHet + freqShift - dFreqFFT * ( resamp->numSamplesFFT / 2 );  // we'll shift DC into the *middle bin* N/2  [N always even!]
  XLAL_CHECK( FreqOut0 >= fMinFFT, XLAL_EDOM, "Lowest output frequency outside the available frequency band: [FreqOut0 = %.16g] < [fMinFFT = %.16g]\n", FreqOut0, fMinFFT );
  UINT4 offset_bins = ( UINT4 ) lround( ( FreqOut0 - fMinFFT ) / dFreqFFT );
  UINT4 maxOutputBin = offset_bins + ( numFreqBins - 1 ) * resamp->decimateFFT;
  XLAL_CHECK( maxOutputBin < resamp->numSamplesFFT, XLAL_EDOM, "Highest output frequency bin outside available band: [maxOutputBin = %d] >= [numSamplesFFT = %d]\n", maxOutputBin, resamp->numSamplesFFT );
 
  FstatTimingResamp *tiRS = &( resamp->timingResamp );
  BOOLEAN collectTiming = resamp->collectTiming;
  REAL8 tic = 0, toc = 0;
 
  XLAL_CHECK( resamp->numSamplesFFT >= TimeSeries_SRC_a->data->length, XLAL_EFAILED, "[numSamplesFFT = %d] < [len(TimeSeries_SRC_a) = %d]\n", resamp->numSamplesFFT, TimeSeries_SRC_a->data->length );
  XLAL_CHECK( resamp->numSamplesFFT >= TimeSeries_SRC_b->data->length, XLAL_EFAILED, "[numSamplesFFT = %d] < [len(TimeSeries_SRC_b) = %d]\n", resamp->numSamplesFFT, TimeSeries_SRC_b->data->length );
 
  if ( collectTiming ) {
    tic = XLALGetCPUTime();
  }
  memset( ws->TS_FFT, 0, resamp->numSamplesFFT * sizeof( ws->TS_FFT[0] ) );
  // ----- compute FaX_k
  // apply spindown phase-factors, store result in zero-padded timeseries for 'FFT'ing
  XLAL_CHECK( XLALApplySpindownAndFreqShiftGeneric( ws->TS_FFT, TimeSeries_SRC_a, &thisPoint, freqShift ) == XLAL_SUCCESS, XLAL_EFUNC );
 
  if ( collectTiming ) {
    toc = XLALGetCPUTime();
    tiRS->Tau.Spin += ( toc - tic );
    tic = toc;
  }
 
  // Fourier transform the resampled Fa(t)
  fftwf_execute_dft( resamp->fftplan, ws->TS_FFT, ws->FabX_Raw );
 
  if ( collectTiming ) {
    toc = XLALGetCPUTime();
    tiRS->Tau.FFT += ( toc - tic );
    tic = toc;
  }
 
  for ( UINT4 k = 0; k < numFreqBins; k++ ) {
    ws->FaX_k[k] = ws->FabX_Raw [ offset_bins + k * resamp->decimateFFT ];
  }
 
  if ( collectTiming ) {
    toc = XLALGetCPUTime();
    tiRS->Tau.Copy += ( toc - tic );
    tic = toc;
  }
 
  // ----- compute FbX_k
  // apply spindown phase-factors, store result in zero-padded timeseries for 'FFT'ing
  XLAL_CHECK( XLALApplySpindownAndFreqShiftGeneric( ws->TS_FFT, TimeSeries_SRC_b, &thisPoint, freqShift ) == XLAL_SUCCESS, XLAL_EFUNC );
 
  if ( collectTiming ) {
    toc = XLALGetCPUTime();
    tiRS->Tau.Spin += ( toc - tic );
    tic = toc;
  }
 
  // Fourier transform the resampled Fa(t)
  fftwf_execute_dft( resamp->fftplan, ws->TS_FFT, ws->FabX_Raw );
 
  if ( collectTiming ) {
    toc = XLALGetCPUTime();
    tiRS->Tau.FFT += ( toc - tic );
    tic = toc;
  }
 
  for ( UINT4 k = 0; k < numFreqBins; k++ ) {
    ws->FbX_k[k] = ws->FabX_Raw [ offset_bins + k * resamp->decimateFFT ];
  }
 
  if ( collectTiming ) {
    toc = XLALGetCPUTime();
    tiRS->Tau.Copy += ( toc - tic );
    tic = toc;
  }
 
  // ----- normalization factors to be applied to Fa and Fb:
  const REAL8 dtauX = GPSDIFF( TimeSeries_SRC_a->epoch, thisPoint.refTime );
  for ( UINT4 k = 0; k < numFreqBins; k++ ) {
    REAL8 f_k = FreqOut0 + k * dFreq;
    REAL8 cycles = - f_k * dtauX;
    REAL4 sinphase, cosphase;
    XLALSinCos2PiLUT( &sinphase, &cosphase, cycles );
    COMPLEX8 normX_k = dt_SRC * crectf( cosphase, sinphase );
    ws->FaX_k[k] *= normX_k;
    ws->FbX_k[k] *= normX_k;
  } // for k < numFreqBinsOut
 
  if ( collectTiming ) {
    toc = XLALGetCPUTime();
    tiRS->Tau.Norm += ( toc - tic );
    tic = toc;
  }
 
  return XLAL_SUCCESS;
 
} // XLALComputeFaFb_ResampGeneric()
 
static int
XLALApplySpindownAndFreqShiftGeneric( COMPLEX8 *restrict xOut,                         ///< [out] the spindown-corrected SRC-frame timeseries
                                      const COMPLEX8TimeSeries *restrict xIn,          ///< [in] the input SRC-frame timeseries
                                      const PulsarDopplerParams *restrict doppler,     ///< [in] containing spindown parameters
                                      REAL8 freqShift                                  ///< [in] frequency-shift to apply, sign is "new - old"
                                    )
{
  // input sanity checks
  XLAL_CHECK( xOut != NULL, XLAL_EINVAL );
  XLAL_CHECK( xIn != NULL, XLAL_EINVAL );
  XLAL_CHECK( doppler != NULL, XLAL_EINVAL );
 
  // determine number of spin downs to include
  UINT4 s_max = PULSAR_MAX_SPINS - 1;
  while ( ( s_max > 0 ) && ( doppler->fkdot[s_max] == 0 ) ) {
    s_max --;
  }
 
  REAL8 dt = xIn->deltaT;
  UINT4 numSamplesIn  = xIn->data->length;
 
  LIGOTimeGPS epoch = xIn->epoch;
  REAL8 Dtau0 = GPSDIFF( epoch, doppler->refTime );
 
  // loop over time samples
  for ( UINT4 j = 0; j < numSamplesIn; j ++ ) {
    REAL8 taup_j = j * dt;
    REAL8 Dtau_alpha_j = Dtau0 + taup_j;
 
    REAL8 cycles = - freqShift * taup_j;
 
    REAL8 Dtau_pow_kp1 = Dtau_alpha_j;
    for ( UINT4 k = 1; k <= s_max; k++ ) {
      Dtau_pow_kp1 *= Dtau_alpha_j;
      cycles += - LAL_FACT_INV[k + 1] * doppler->fkdot[k] * Dtau_pow_kp1;
    } // for k = 1 ... s_max
 
    REAL4 cosphase, sinphase;
    XLAL_CHECK( XLALSinCos2PiLUT( &sinphase, &cosphase, cycles ) == XLAL_SUCCESS, XLAL_EFUNC );
    COMPLEX8 em2piphase = crectf( cosphase, sinphase );
 
    // weight the complex timeseries by the antenna patterns
    xOut[j] = em2piphase * xIn->data->data[j];
 
  } // for j < numSamplesIn
 
  return XLAL_SUCCESS;
 
} // XLALApplySpindownAndFreqShiftGeneric()
 
///
/// Performs barycentric resampling on a multi-detector timeseries, updates resampling buffer with results
///
/// NOTE Buffering: this function does check
/// 1) whether the previously-buffered solution can be completely reused (same sky-position and binary parameters), or
/// 2) if at least sky-dependent quantities can be re-used (antenna-patterns + timings) in case only binary parameters changed
///
static int
XLALBarycentricResampleMultiCOMPLEX8TimeSeriesGeneric(
  ResampGenericMethodData *resamp,        // [in/out] resampling input and buffer (to store resampling TS)
  const PulsarDopplerParams *thisPoint,   // [in] current skypoint and reftime
  const FstatCommon *common               // [in] various input quantities and parameters used here
)
{
  // check input sanity
  XLAL_CHECK( thisPoint != NULL, XLAL_EINVAL );
  XLAL_CHECK( common != NULL, XLAL_EINVAL );
  XLAL_CHECK( resamp != NULL, XLAL_EINVAL );
  XLAL_CHECK( resamp->multiTimeSeries_DET != NULL, XLAL_EINVAL );
  XLAL_CHECK( resamp->multiTimeSeries_SRC_a != NULL, XLAL_EINVAL );
  XLAL_CHECK( resamp->multiTimeSeries_SRC_b != NULL, XLAL_EINVAL );
 
  ResampGenericWorkspace *ws = ( ResampGenericWorkspace * ) common->workspace;
 
  UINT4 numDetectors = resamp->multiTimeSeries_DET->length;
  XLAL_CHECK( resamp->multiTimeSeries_SRC_a->length == numDetectors, XLAL_EINVAL, "Inconsistent number of detectors tsDET(%d) != tsSRC(%d)\n", numDetectors, resamp->multiTimeSeries_SRC_a->length );
  XLAL_CHECK( resamp->multiTimeSeries_SRC_b->length == numDetectors, XLAL_EINVAL, "Inconsistent number of detectors tsDET(%d) != tsSRC(%d)\n", numDetectors, resamp->multiTimeSeries_SRC_b->length );
 
  // ============================== BEGIN: handle buffering =============================
  BOOLEAN same_skypos = ( resamp->prev_doppler.Alpha == thisPoint->Alpha ) && ( resamp->prev_doppler.Delta == thisPoint->Delta );
  BOOLEAN same_refTime = ( GPSDIFF( resamp->prev_doppler.refTime, thisPoint->refTime ) == 0 );
  BOOLEAN same_binary = \
                        ( resamp->prev_doppler.asini == thisPoint->asini ) &&
                        ( resamp->prev_doppler.period == thisPoint->period ) &&
                        ( resamp->prev_doppler.ecc == thisPoint->ecc ) &&
                        ( GPSDIFF( resamp->prev_doppler.tp, thisPoint->tp ) == 0 ) &&
                        ( resamp->prev_doppler.argp == thisPoint->argp );
 
  Timings_t *Tau = &( resamp->timingResamp.Tau );
  REAL8 tic = 0, toc = 0;
  BOOLEAN collectTiming = resamp->collectTiming;
 
  // if same sky-position *and* same binary, we can simply return as there's nothing to be done here
  if ( same_skypos && same_refTime && same_binary ) {
    Tau->BufferRecomputed = 0;
    return XLAL_SUCCESS;
  }
  // else: keep track of 'buffer miss', ie we need to recompute the buffer
  Tau->BufferRecomputed = 1;
  resamp->timingGeneric.NBufferMisses ++;
  if ( collectTiming ) {
    tic = XLALGetCPUTime();
  }
 
  MultiSSBtimes *multiSRCtimes = NULL;
 
  // only if different sky-position: re-compute antenna-patterns and SSB timings, re-use from buffer otherwise
  if ( !( same_skypos && same_refTime ) ) {
    SkyPosition skypos;
    skypos.system = COORDINATESYSTEM_EQUATORIAL;
    skypos.longitude = thisPoint->Alpha;
    skypos.latitude  = thisPoint->Delta;
 
    XLALDestroyMultiAMCoeffs( resamp->multiAMcoef );
    XLAL_CHECK( ( resamp->multiAMcoef = XLALComputeMultiAMCoeffs( common->multiDetectorStates, common->multiNoiseWeights, skypos ) ) != NULL, XLAL_EFUNC );
    resamp->Mmunu = resamp->multiAMcoef->Mmunu;
    for ( UINT4 X = 0; X < numDetectors; X ++ ) {
      resamp->MmunuX[X].Ad = resamp->multiAMcoef->data[X]->A;
      resamp->MmunuX[X].Bd = resamp->multiAMcoef->data[X]->B;
      resamp->MmunuX[X].Cd = resamp->multiAMcoef->data[X]->C;
      resamp->MmunuX[X].Ed = 0;
      resamp->MmunuX[X].Dd = resamp->multiAMcoef->data[X]->D;
    }
 
    XLALDestroyMultiSSBtimes( resamp->multiSSBtimes );
    XLAL_CHECK( ( resamp->multiSSBtimes = XLALGetMultiSSBtimes( common->multiDetectorStates, skypos, thisPoint->refTime, common->SSBprec ) ) != NULL, XLAL_EFUNC );
 
  } // if cannot re-use buffered solution ie if !(same_skypos && same_binary)
 
  if ( thisPoint->asini > 0 ) { // binary case
    XLAL_CHECK( XLALAddMultiBinaryTimes( &resamp->multiBinaryTimes, resamp->multiSSBtimes, thisPoint ) == XLAL_SUCCESS, XLAL_EFUNC );
    multiSRCtimes = resamp->multiBinaryTimes;
  } else { // isolated case
    multiSRCtimes = resamp->multiSSBtimes;
  }
 
  // record barycenter parameters in order to allow re-usal of this result ('buffering')
  resamp->prev_doppler = ( *thisPoint );
 
  // shorthands
  REAL8 fHet = resamp->multiTimeSeries_DET->data[0]->f0;
  REAL8 Tsft = common->multiTimestamps->data[0]->deltaT;
  REAL8 dt_SRC = resamp->multiTimeSeries_SRC_a->data[0]->deltaT;
 
  const REAL4 signumLUT[2] = {1, -1};
 
  // loop over detectors X
  for ( UINT4 X = 0; X < numDetectors; X++ ) {
    // shorthand pointers: input
    const COMPLEX8TimeSeries *TimeSeries_DETX = resamp->multiTimeSeries_DET->data[X];
    const LIGOTimeGPSVector  *Timestamps_DETX = common->multiTimestamps->data[X];
    const SSBtimes *SRCtimesX                 = multiSRCtimes->data[X];
    const AMCoeffs *AMcoefX                   = resamp->multiAMcoef->data[X];
 
    // shorthand pointers: output
    COMPLEX8TimeSeries *TimeSeries_SRCX_a     = resamp->multiTimeSeries_SRC_a->data[X];
    COMPLEX8TimeSeries *TimeSeries_SRCX_b     = resamp->multiTimeSeries_SRC_b->data[X];
    REAL8Vector *ti_DET = ws->SRCtimes_DET;
 
    // useful shorthands
    REAL8 refTime8        = GPSGETREAL8( &SRCtimesX->refTime );
    UINT4 numSFTsX        = Timestamps_DETX->length;
    UINT4 numSamples_DETX = TimeSeries_DETX->data->length;
    UINT4 numSamples_SRCX = TimeSeries_SRCX_a->data->length;
 
    // sanity checks on input data
    XLAL_CHECK( numSamples_SRCX == TimeSeries_SRCX_b->data->length, XLAL_EINVAL );
    XLAL_CHECK( dt_SRC == TimeSeries_SRCX_a->deltaT, XLAL_EINVAL );
    XLAL_CHECK( dt_SRC == TimeSeries_SRCX_b->deltaT, XLAL_EINVAL );
    XLAL_CHECK( numSamples_DETX > 0, XLAL_EINVAL, "Input timeseries for detector X=%d has zero samples. Can't handle that!\n", X );
    XLAL_CHECK( ( SRCtimesX->DeltaT->length == numSFTsX ) && ( SRCtimesX->Tdot->length == numSFTsX ), XLAL_EINVAL );
    REAL8 fHetX = resamp->multiTimeSeries_DET->data[X]->f0;
    XLAL_CHECK( fabs( fHet - fHetX ) < LAL_REAL8_EPS * fHet, XLAL_EINVAL, "Input timeseries must have identical heterodyning frequency 'f0(X=%d)' (%.16g != %.16g)\n", X, fHet, fHetX );
    REAL8 TsftX = common->multiTimestamps->data[X]->deltaT;
    XLAL_CHECK( Tsft == TsftX, XLAL_EINVAL, "Input timestamps must have identical stepsize 'Tsft(X=%d)' (%.16g != %.16g)\n", X, Tsft, TsftX );
 
    TimeSeries_SRCX_a->f0 = fHet;
    TimeSeries_SRCX_b->f0 = fHet;
    // set SRC-frame time-series start-time
    REAL8 tStart_SRC_0 = refTime8 + SRCtimesX->DeltaT->data[0] - ( 0.5 * Tsft ) * SRCtimesX->Tdot->data[0];
    LIGOTimeGPS epoch;
    GPSSETREAL8( epoch, tStart_SRC_0 );
    TimeSeries_SRCX_a->epoch = epoch;
    TimeSeries_SRCX_b->epoch = epoch;
 
    // make sure all output samples are initialized to zero first, in case of gaps
    memset( TimeSeries_SRCX_a->data->data, 0, TimeSeries_SRCX_a->data->length * sizeof( TimeSeries_SRCX_a->data->data[0] ) );
    memset( TimeSeries_SRCX_b->data->data, 0, TimeSeries_SRCX_b->data->length * sizeof( TimeSeries_SRCX_b->data->data[0] ) );
    // make sure detector-frame timesteps to interpolate to are initialized to 0, in case of gaps
    memset( ws->SRCtimes_DET->data, 0, ws->SRCtimes_DET->length * sizeof( ws->SRCtimes_DET->data[0] ) );
 
    memset( ws->TStmp1_SRC->data, 0, ws->TStmp1_SRC->length * sizeof( ws->TStmp1_SRC->data[0] ) );
    memset( ws->TStmp2_SRC->data, 0, ws->TStmp2_SRC->length * sizeof( ws->TStmp2_SRC->data[0] ) );
 
    REAL8 tStart_DET_0 = GPSGETREAL8( &( Timestamps_DETX->data[0] ) ); // START time of the SFT at the detector
 
    // loop over SFT timestamps and compute the detector frame time samples corresponding to uniformly sampled SRC time samples
    for ( UINT4 alpha = 0; alpha < numSFTsX; alpha ++ ) {
      // define some useful shorthands
      REAL8 Tdot_al       = SRCtimesX->Tdot->data [ alpha ];                // the instantaneous time derivitive dt_SRC/dt_DET at the MID-POINT of the SFT
      REAL8 tMid_SRC_al   = refTime8 + SRCtimesX->DeltaT->data[alpha];      // MID-POINT time of the SFT at the SRC
      REAL8 tStart_SRC_al = tMid_SRC_al - 0.5 * Tsft * Tdot_al;             // approximate START time of the SFT at the SRC
      REAL8 tEnd_SRC_al   = tMid_SRC_al + 0.5 * Tsft * Tdot_al;             // approximate END time of the SFT at the SRC
 
      REAL8 tStart_DET_al = GPSGETREAL8( &( Timestamps_DETX->data[alpha] ) ); // START time of the SFT at the detector
      REAL8 tMid_DET_al   = tStart_DET_al + 0.5 * Tsft;                     // MID-POINT time of the SFT at the detector
 
      // indices of first and last SRC-frame sample corresponding to this SFT
      UINT4 iStart_SRC_al = lround( ( tStart_SRC_al - tStart_SRC_0 ) / dt_SRC );    // the index of the resampled timeseries corresponding to the start of the SFT
      UINT4 iEnd_SRC_al   = lround( ( tEnd_SRC_al - tStart_SRC_0 ) / dt_SRC );      // the index of the resampled timeseries corresponding to the end of the SFT
 
      // truncate to actual SRC-frame timeseries
      iStart_SRC_al = MYMIN( iStart_SRC_al, numSamples_SRCX - 1 );
      iEnd_SRC_al   = MYMIN( iEnd_SRC_al, numSamples_SRCX - 1 );
      UINT4 numSamplesSFT_SRC_al = iEnd_SRC_al - iStart_SRC_al + 1;         // the number of samples in the SRC-frame for this SFT
 
      REAL4 a_al = AMcoefX->a->data[alpha];
      REAL4 b_al = AMcoefX->b->data[alpha];
      for ( UINT4 j = 0; j < numSamplesSFT_SRC_al; j++ ) {
        UINT4 iSRC_al_j  = iStart_SRC_al + j;
 
        // for each time sample in the SRC frame, we estimate the corresponding detector time,
        // using a linear approximation expanding around the midpoint of each SFT
        REAL8 t_SRC = tStart_SRC_0 + iSRC_al_j * dt_SRC;
        ti_DET->data [ iSRC_al_j ] = tMid_DET_al + ( t_SRC - tMid_SRC_al ) / Tdot_al;
 
        // pre-compute correction factors due to non-zero heterodyne frequency of input
        REAL8 tDiff = iSRC_al_j * dt_SRC + ( tStart_DET_0 - ti_DET->data [ iSRC_al_j ] ); // tSRC_al_j - tDET(tSRC_al_j)
        REAL8 cycles = fmod( fHet * tDiff, 1.0 );                                 // the accumulated heterodyne cycles
 
        // use a look-up-table for speed to compute real and imaginary phase
        REAL4 cosphase, sinphase;                                   // the real and imaginary parts of the phase correction
        XLAL_CHECK( XLALSinCos2PiLUT( &sinphase, &cosphase, -cycles ) == XLAL_SUCCESS, XLAL_EFUNC );
        COMPLEX8 ei2piphase = crectf( cosphase, sinphase );
 
        // apply AM coefficients a(t), b(t) to SRC frame timeseries [alternate sign to get final FFT return DC in the middle]
        REAL4 signum = signumLUT [( iSRC_al_j % 2 ) ];    // alternating sign, avoid branching
        ei2piphase *= signum;
        ws->TStmp1_SRC->data [ iSRC_al_j ] = ei2piphase * a_al;
        ws->TStmp2_SRC->data [ iSRC_al_j ] = ei2piphase * b_al;
      } // for j < numSamples_SRC_al
 
    } // for  alpha < numSFTsX
 
    XLAL_CHECK( ti_DET->length >= TimeSeries_SRCX_a->data->length, XLAL_EINVAL );
    UINT4 bak_length = ti_DET->length;
    ti_DET->length = TimeSeries_SRCX_a->data->length;
    XLAL_CHECK( XLALSincInterpolateCOMPLEX8TimeSeries( TimeSeries_SRCX_a->data, ti_DET, TimeSeries_DETX, resamp->Dterms ) == XLAL_SUCCESS, XLAL_EFUNC );
    ti_DET->length = bak_length;
 
    // apply heterodyne correction and AM-functions a(t) and b(t) to interpolated timeseries
    for ( UINT4 j = 0; j < numSamples_SRCX; j ++ ) {
      TimeSeries_SRCX_b->data->data[j] = TimeSeries_SRCX_a->data->data[j] * ws->TStmp2_SRC->data[j];
      TimeSeries_SRCX_a->data->data[j] *= ws->TStmp1_SRC->data[j];
    } // for j < numSamples_SRCX
 
  } // for X < numDetectors
 
  if ( collectTiming ) {
    toc = XLALGetCPUTime();
    Tau->Bary = ( toc - tic );
  }
 
  return XLAL_SUCCESS;
 
} // XLALBarycentricResampleMultiCOMPLEX8TimeSeriesGeneric()
 
static void
XLALGetFFTPlanHints( int *planMode,
                     double *planGenTimeoutSeconds
                   )
{
  char *planMode_env = getenv( "LAL_FSTAT_FFT_PLAN_MODE" );
  char *planGenTimeout_env = getenv( "LAL_FSTAT_FFT_PLAN_TIMEOUT" );;
  int fft_plan_flags = FFTW_MEASURE;
  double fft_plan_timeout = FFTW_NO_TIMELIMIT ;
 
  if ( planGenTimeout_env ) {
    char *end;
    fft_plan_timeout = strtod( planGenTimeout_env, & end );
    if ( end[0] != '\0' ) {
      fft_plan_timeout = FFTW_NO_TIMELIMIT;
    }
  }
 
  if ( planMode_env ) {
    if ( strcmp( planMode_env, "ESTIMATE" ) == 0 ) {
      fft_plan_flags = FFTW_ESTIMATE;
    }
 
    if ( strcmp( planMode_env, "MEASURE" ) == 0 ) {
      fft_plan_flags = FFTW_MEASURE;
    }
 
    if ( strcmp( planMode_env, "PATIENT" ) == 0 ) {
      fft_plan_flags = FFTW_PATIENT;
    }
  }
  *planMode = fft_plan_flags;
  *planGenTimeoutSeconds = fft_plan_timeout;
} // XLALGetFFTPlanHints
 
int
XLALExtractResampledTimeseries_ResampGeneric( MultiCOMPLEX8TimeSeries **multiTimeSeries_SRC_a, MultiCOMPLEX8TimeSeries **multiTimeSeries_SRC_b, void *method_data )
{
  XLAL_CHECK( method_data != NULL, XLAL_EINVAL );
  XLAL_CHECK( ( multiTimeSeries_SRC_a != NULL ) && ( multiTimeSeries_SRC_b != NULL ), XLAL_EINVAL );
  XLAL_CHECK( method_data != NULL, XLAL_EINVAL );
 
  ResampGenericMethodData *resamp = ( ResampGenericMethodData * ) method_data;
  *multiTimeSeries_SRC_a = resamp->multiTimeSeries_SRC_a;
  *multiTimeSeries_SRC_b = resamp->multiTimeSeries_SRC_b;
 
  return XLAL_SUCCESS;
 
} // XLALExtractResampledTimeseries_intern()
 
int
XLALGetFstatTiming_ResampGeneric( const void *method_data, FstatTimingGeneric *timingGeneric, FstatTimingModel *timingModel )
{
  XLAL_CHECK( method_data != NULL, XLAL_EINVAL );
  XLAL_CHECK( timingGeneric != NULL, XLAL_EINVAL );
  XLAL_CHECK( timingModel != NULL, XLAL_EINVAL );
 
  const ResampGenericMethodData *resamp = ( const ResampGenericMethodData * ) method_data;
  XLAL_CHECK( resamp != NULL, XLAL_EINVAL );
 
  ( *timingGeneric ) = resamp->timingGeneric; // struct-copy generic timing measurements
 
  XLAL_CHECK( XLALGetFstatTiming_Resamp_intern( &( resamp->timingResamp ), timingModel ) == XLAL_SUCCESS, XLAL_EFUNC );
 
  return XLAL_SUCCESS;
} // XLALGetFstatTiming_ResampGeneric()
 
/// @}