do_dft2.c

//////////////////////////////////////////////////////////////////////////////
//                                                                          //
//                  _                _   __  _    ____                      //
//               __| |  ___       __| | / _|| |_ |___ \     ___             //
//              / _` | / _ \     / _` || |_ | __|  __) |   / __|            //
//             | (_| || (_) |   | (_| ||  _|| |_  / __/  _| (__             //
//              \__,_| \___/_____\__,_||_|   \__||_____|(_)\___|            //
//                         |_____|                                          //
//                                                                          //
//////////////////////////////////////////////////////////////////////////////
//                                                                          //
//          Copyright (c) 2013 by S.F.T. Inc. - All rights reserved         //
//      Use, copying, and distribution of this software may be licensed     //
//         using a GPLv2, GPLv3, MIT, or BSD license, as appropriate.       //
//                                                                          //
//     OR - if you prefer - just use/distribute it without ANY license.     //
//   But I'd like some credit for it. A favorable mention is appreciated.   //
//                                                                          //
//////////////////////////////////////////////////////////////////////////////

#define _GNU_SOURCE

#include <stdio.h>
#include <stdlib.h>
#include <pthread.h>
#include <unistd.h>
#include <math.h>
#include <time.h>
#include <sys/time.h>

//**************************************************************************
// build command:  cc -O3 -o do_dft2 do_dft2.c -lm -lpthread
//
// you can add '-D' directives as appropriate (such as '-DUSE_FAST_SINCOS')
//**************************************************************************


// approximate value of pi beyond precision of double
#define _PI_ 3.1415926535897932384626433832795028841971693993751

#define MAX_HARMONIC 4096

//#define USE_FAST_SINCOS  /* define this out to use the fast sin/cos instead of the 'libc' sin/cos */
//#define TEST_FAST_SINCOS /* define this to include the test '-!' for fast sin/cos */

#ifdef __gnu_linux__
#define HAS_SINCOS /* this should work for all GNU-LINUX implementations */
// NOTE:  if this causes build problems, please let me know.
#endif // __gnu_linux__

// NOTE:  FreeBSD's libc does not have 'sincos', nor do any of the ports
//        for gcc, as far as I can tell.  It's a GNU extension.

#ifdef USE_FAST_SINCOS
#define sin fast_sin
#define cos fast_cos
#define sincos fast_sincos

double dDebugY = 0.0;
int wDebugIndex = -1;

void fast_sincos(double dTheta, double *pSin, double *pCos);
double fast_cos(double);
double fast_sin(double);

#ifndef HAS_SINCOS
#define HAS_SINCOS
#endif // HAS_SINCOS

static const float _SIN_VALUES_[];
static const float * const _COS_VALUES_;

#endif // USE_FAST_SINCOS

typedef struct _XY_
{
  double dX;
  double dY;
} XY;

typedef struct _MY_XY_
{
  XY *pData;
  int nItems; // # of items
  int nSize;  //memory block size
} MY_XY;

typedef struct _WORK_UNIT_
{
  double *pdA, *pdB;
  XY *pData;
  int nVal;
  double dC, dX0, dXY;  // for retest and for scaling X(Xnew = X * dXY + dX0, use 0.0 and 1.0 to leave X as - is)
  long lStart, lEnd;
  double dRval;         // NOTE: cannot be 'passed in', initial value will be 0.0
  volatile long lState; // initially zero, non - zero when thread has finished
  pthread_t idThread;   // caller waits on this object; object must be free 'd by caller via pthread_detach
                        // call pthread_join when finished to properly clean up and get err return
} WORK_UNIT;

WORK_UNIT *create_work_unit(double *pdA, double *pdB, double dC, XY * pData, int nVal,
                            double dX0, double dXY, long lStart, long lEnd,
                            void *(*callback) (void *), int iThreadFlag)
{
WORK_UNIT *pRval = (WORK_UNIT *) malloc(sizeof(WORK_UNIT));

  if(!pRval)
  {
    return NULL;
  }

  pRval->pdA = pdA;
  pRval->pdB = pdB;
  pRval->dC = dC;
  pRval->pData = pData;
  pRval->nVal = nVal;
  pRval->dX0 = dX0;
  pRval->dXY = dXY;
  pRval->lStart = lStart;
  pRval->lEnd = lEnd;
  pRval->dRval = 0.0;
  pRval->lState = 0;
  pRval->idThread = 0; // initially

  if(!iThreadFlag) // direct call, useful for first work unit(after spawning others)
  {
    // fprintf(stderr, "TEMPORARY:  call direct\n");
    // fflush(stderr);

    if(callback(pRval))
    {
      free(pRval);
      return NULL;
    }

    return pRval; // so I can get the return info
  }

  // fprintf(stderr, "TEMPORARY:  spawn thread\n");
  // fflush(stderr);

  if(pthread_create(&(pRval->idThread), NULL, callback, (void *)pRval))
  {
    if(pRval->idThread)
    {
      pthread_cancel(pRval->idThread);
      pRval->idThread = 0;
    }

    free(pRval);
    return NULL;
  }

  return pRval;
}

// determining # of cpus (workaround)

#define THREAD_COUNT 16

static unsigned long long MyGetTick(void)
{
static unsigned long long iMyTick = 0;
static unsigned long long lLastTickCount;
static int iFirstTime = 1;
struct timeval tv;
long long lTick;

  gettimeofday(&tv, NULL);
  lTick = (long long)tv.tv_sec * (long long)1000000 + (long long)tv.tv_usec;

  if(iFirstTime)
  {
    lLastTickCount = lTick;
    iMyTick = lTick;
    iFirstTime = 0;
  }
  else
  {
    iMyTick += lTick - lLastTickCount; //TODO:improve this for wraparound?
    lLastTickCount = lTick;
  }

  return (iMyTick);
}

static void *thread_proc(void *pNothing)
{
volatile long *pMe = pNothing ? (volatile long *)pNothing : (volatile long *)&(pMe);
volatile long long l1;
unsigned long long lStart;
int i1;

  usleep(1000);

  if(pNothing)
  {
    while(!*pMe)
    {
      usleep(100);
    }
  }

  lStart = MyGetTick();

  for(i1 = 0; i1 < 1000000; i1++)
  {
    l1 += *pMe;
  }

  if(pNothing)
  {
    *((long *)pNothing) = MyGetTick() - lStart;
    return 0;
  }

  return (void *)(MyGetTick() - lStart);
}

int cpu_count0(void)
{
pthread_t thr[THREAD_COUNT] = {NULL};
static volatile long lResult[THREAD_COUNT] = {0};
long lResult0, lResultTTL;
int i1;

  lResult0 = (long)thread_proc(0);

  usleep(1000);

  for(i1 = 0; i1 < THREAD_COUNT; i1++)
  {
    thr[i1] = NULL; //make sure
    if(pthread_create(&(thr[i1]), NULL, thread_proc, (void *)&(lResult[i1])))
    {
      while(i1 >= 0)
      {
        if(thr[i1])
        {
          pthread_cancel(thr[i1]);
        }

        i1--;
      }

      return -2;
    }
  }

  for(i1 = 0; i1 < THREAD_COUNT; i1++)
  {
    lResult[i1] = 1;
  }

  for(i1 = 0, lResultTTL = 0; i1 < THREAD_COUNT; i1++)
  {
    if(pthread_join(thr[i1], NULL))
    {
      fprintf(stderr, "thread canceled\n");
      pthread_cancel(thr[i1]);
      continue;
    }

    lResultTTL += lResult[i1];
  }

  // printf("%ld %ld\n", lResultTTL, lResult0);

  lResultTTL += lResultTTL / 2; // for round-off, add 75 %
  lResultTTL /= (THREAD_COUNT * lResult0);

  // printf("Total CPU:  %ld\n", lResultTTL);

  return (int)lResultTTL;
}

static int my_int_cmp(const void *p1, const void *p2)
{
int i1 = *((const int *)p1) - *((const int *)p2);

  return i1 > 0 ? 1 : (i1 < 0 ? -1 : 0);
}

int cpu_count(void)
{
int i1, i2[THREAD_COUNT];

  for(i1 = 0; i1 < THREAD_COUNT; i1++)
  {
    i2[i1] = cpu_count0();
  }

  qsort(i2, sizeof(i2[0]), THREAD_COUNT, my_int_cmp);

  return i2[THREAD_COUNT / 2];
}




/////////////////////////////////////////////////////////////////////////////
// FUNCTION: dFourier
//
// on entry 'aVal' is array of XY, 'nVal' is # of entries in aVal,
// nH is # harmonic (sin,cos) coefficients to generate [excluding '0']
// and 'dA' and 'dB' are the sin and cos arrays, and 'dC' is the 'C0' value.
// and 'nWU' is the # of 'work units' (using pthreads)
//
// note:  list must be sorted by X value, no duplicate X values
//
/////////////////////////////////////////////////////////////////////////////

void *dFourier_work(void *pV)
{
WORK_UNIT *pW = (WORK_UNIT *) pV;
int i1, i2, i3;
double dX, dY, dX0, dXY;
XY *aVal;
int nVal;
double dRval, *dA, *dB;


  if(!pV)
  {
    return NULL;
  }

  dRval = 0;

  aVal = pW->pData;
  nVal = pW->nVal;
  dA = pW->pdA;
  dB = pW->pdB;
  dX0 = pW->dX0;
  dXY = pW->dXY;

  for(i1 = pW->lStart, i3 = pW->lEnd; i1 <= i3; i1++)
  {
    for(i2 = 0; i2 < nVal; i2++)
    {
      if(!i1)
      {
        dRval += aVal[i2].dY;

        // printf("temporary:  item %d X=%g\n",i2, (double)(dX0 + aVal[i2].dX * dXY));
      }
      else
      {
        double dS, dC, dXNew = i1 * (dX0 + aVal[i2].dX * dXY);
#ifdef HAS_SINCOS // GNU linux and when I do 'fast sin/cos'
        sincos(dXNew, &dS, &dC); // NOTE:   'sincos' should be slightly faster than individual calls
#else // HAS_SINCOS
        dS = sin(dXNew);
        dC = cos(dXNew);
#endif // HAS_SINCOS
        dA[i1 - 1] += aVal[i2].dY * dC;
        dB[i1 - 1] += aVal[i2].dY * dS;
      }
    }
  }

  pW->dRval = dRval;
  pW->lState = 1;  // to say I 'm done

  return 0;
}

void dFourier(XY * aVal, int nVal, int nH, double *dC, double *dA, double *dB, int nWU, int iAutoScale)
{
int i1, i2, iW;
double dX, dY, dX0, dXY;
WORK_UNIT *aW[THREAD_COUNT] = {0};


  *dC = 0.0;
  // fprintf(stderr, "call to dFourier, %d work units\n", nWU);
  // fflush(stderr);
  // usleep(10000);

  // assume sorted list, calculate X0, XY for x = -PI to PI

  if(!iAutoScale)
  {
    dXY = 1.0;
    dX0 = 0.0;
  }
  else
  {
    dXY = 2.0 * _PI_ / (aVal[nVal - 1].dX + (aVal[nVal - 1].dX - aVal[0].dX) / (nVal - 1));
    dX0 = -dXY * aVal[0].dX - _PI_; // derived from -_PI_ == dX0 + dXY * aVal[0].dX
  }

  if(nH < nWU)
  {
    nWU = nH;
  }
  if(nVal < 1024)
  {
    nWU = 1;
  }

  for(i1 = 0; i1 < nH; i1++)
  {
    dA[i1] = dB[i1] = 0.0; // zero this out
  }

  for(iW = 0, i1 = 0; iW < nWU; iW++)
  {
    i2 = (iW + 1) * nH / nWU; // next i1

    if(i2 <= i1)
    {
      continue; // just in case
    }

    if(i2 >= nH || (iW == (nWU - 1)))
    {
      i2 = nH + 1; // to make sure I capture the last data point in the work unit
    }

    // fprintf(stderr, "temporary:  work unit %d\n", iW);
    // fflush(stderr);
    aW[iW] = create_work_unit(dA, dB, 0.0, aVal, nVal, dX0, dXY, i1, i2 - 1,
                              dFourier_work, iW < (nWU - 1) ? 1 : 0);

    i1 = i2; // "next"
    if(i2 >= nH)
    {
      break; // safety(for now)
    }
  }

        //now we must wait for all of the work units to complete
  for(iW = 0; iW < nWU; iW++)
  {
    if(!aW[iW])
    {
      continue;
    }

    if(aW[iW]->idThread)
    {
      pthread_join(aW[iW]->idThread, NULL); // ignore any error for now
      // pthread_detach(&(aW[iW].idThread);

      *dC += aW[iW]->dRval; // returned C0 value(when applicable) adds into 'dC'
    }
    else // not a thread, keep 'dC' return here also
    {
      *dC += aW[iW]->dRval; // returned C0 value(when applicable) adds into 'dC'
    }

    free(aW[iW]);
    aW[iW] = NULL; // by convention
  }

  // fix up arrays and whatnot

  *dC /= nVal;  // C0 must be half A[0] i.e Y = A[0] / 2 +[sum n = 1 - ?] An *cos(n * X) + Bn * sin(n * X)
  // see http : //en.wikipedia.org / wiki / Fourier_series

  for(i1 = 0; i1 < nH; i1++)
  {
    dA[i1] *= 2.0 / nVal;
    dB[i1] *= 2.0 / nVal;
  }
}




// FUNCTION:xy_comp - sort compare for 'XY' structure

int xy_comp(const void *p1, const void *p2)
{
  int iRval = ((XY *) p1)->dX - ((XY *) p2)->dX;

  if(iRval > 0)
  {
    return 1;
  }

  if(iRval < 0)
  {
    return -1;
  }

  return 0;
}

//FUNCTION:get_xy_data - file input of X and Y values(space delimiter)

MY_XY get_xy_data(FILE * pIn)
{
  char tbuf[512];
  double dX, dY;
  MY_XY xyNULL = {NULL, 0, 0}, xy = {NULL, 0, 0};


  while(fgets(tbuf, sizeof(tbuf), pIn))
  {
    if(!xy.pData ||
        xy.nItems * sizeof(xy.pData[0]) >= xy.nSize)
    {
      if(xy.nItems > 1024)
      {
        xy.nSize = (xy.nItems * 2) * sizeof(xy.pData[0]);
      }
      else
      {
        xy.nSize = 2048 * sizeof(xy.pData[0]);
      }

      if(xy.pData)
      {
        void *p1 = realloc(xy.pData, xy.nSize + 1);

        if(!p1)
        {
          free(xy.pData);
          return xyNULL;
        }

        xy.pData = (XY *) p1;
      }
      else
      {
        xy.pData = (XY *) malloc(xy.nSize);
        if(!xy.pData)
        {
          return xyNULL;
        }
      }
    }

    dX = dY = 0.0;

    sscanf(tbuf, "%lg %lg\n", &dX, &dY);

    // printf("TEMPORARY:  data point %d %g %g   %s\n", xy.nItems, dX, dY, tbuf);

    xy.pData[xy.nItems].dX = dX;
    xy.pData[xy.nItems].dY = dY;
    xy.nItems++;
  }

  // sort data by X

  qsort(xy.pData, xy.nItems, sizeof(xy.pData[0]), xy_comp);

  return xy;
}


void usage(void)
{
  fprintf(stderr,
          "         Copyright (c) 2013 by S.F.T. Inc. - All rights reserved\n"
          "     Use, copying, and distribution of this software may be licensed\n"
          "        using a GPLv2, GPLv3, MIT, or BSD license, as appropriate.\n"
          "\n"
          "    OR - if you prefer - just use/distribute it without ANY license.\n"
          "  But I'd like some credit for it. A favorable mention is appreciated.\n"
          "\n"
          "USAGE:  do_dft -h\n"
          "        do_dft [-a|-s m,n][-t nthrd][input_file [input_file [...]]]\n"
          "where   'input_file' is the name of a file containing rows of sorted X and Y\n"
          "                     values delimited by white-space and terminated with LF\n"
          " and    '-a' indicates 'auto scale X' to 0-2pi\n"
          " and    '-s' specifies a range of 'm to n'\n"
          " and    '-t' indicates how many threads you want to use\n"
          " and    '-h' instructs do_dft to print this information\n"
          "        (if no file or '-h' specified, input is 'stdin')\n");
}


// check_callback - offloads work for multiple threads to check data and calc std dev

void *check_callback(void *pV)
{
  WORK_UNIT *pW = (WORK_UNIT *) pV;
  int i1, i2, i3;
  double dX, dY, dX0, dXY, dC;
  XY *aVal;
  int nHarm;
  double dErr, *pdA, *pdB;


  if(!pV)
  {
    return 0;
  }

   dErr = 0.0;

  aVal = pW->pData;
  nHarm = pW->nVal;
  pdA = pW->pdA;
  pdB = pW->pdB;
  dC = pW->dC;
  dX0 = pW->dX0;
  dXY = pW->dXY;

  for(i1 = pW->lStart; i1 < pW->lEnd; i1++)
  {
    double dCheck = dC;

    for(i2 = 0; i2 < nHarm; i2++)
    {
      dCheck += pdA[i2] * cos((i2 + 1) * (aVal[i1].dX * dXY + dX0))
         + pdB[i2] * sin((i2 + 1) * (aVal[i1].dX * dXY + dX0));
    }

    // printf("  data point %d\t%g\t%g\t%g\n", i1, xy.pData[i1].dX, xy.pData[i1].dY, dCheck);
    dErr += (dCheck - aVal[i1].dY) * (dCheck - aVal[i1].dY);
  }

  pW->dRval = dErr;
  pW->lState = 1;
  return 0;
}


  ////////////////
  //   MAIN
  ///////////////


int main(int argc, char *argv[])
{
double dC, dXY, dX0, *pdA = NULL, *pdB = NULL, dErr;
int i1, i2, iW;
FILE *pIn = stdin;
int nHarm, nThread = 0;
WORK_UNIT *aW[THREAD_COUNT];
double dScale1 = 0.0, dScale2 = 0.0;
int bDoScale = 0;
double dXFactor, dXOffset;
char tbuf[256];



  while(argc > 1)
  {
    const char *p1 = argv[1];
    char *p2;

    if(*p1 != '-')
    {
      break;
    }

    p1++;

#if defined(TEST_FAST_SINCOS) && defined(USE_FAST_SINCOS)

#undef sin /* I need the original versions for this section */
#undef cos /* so I must un-define them, then re-define them */

#define SINCOS_ACCURACY 0.000001

    if(*p1 == '!')
    {
      // this is a special switch that allows self-testing the fast sin/cos functions

      double d1, dS, dC;
      int i2 = 0;
      unsigned long long llTick;

      for(i1=0, d1=-2.0 * _PI_ - 0.1; d1 < 2.0 * _PI_ + 0.1; d1 += 0.00001, i1+=4)
      {
        fast_sincos(d1, &dS, &dC);

        if(fabs(cos(d1) - dC) > SINCOS_ACCURACY)
        {
          fprintf(stderr, "cos(%0.3f) delta = %0.7f  wIndex=%d  y=%0.6f\n", d1,
                  fabs(cos(d1) - dC), wDebugIndex, dDebugY);
        }
        else
        {
          i2++;
        }

        if(fabs(sin(d1) - dS) > SINCOS_ACCURACY)
        {
          fprintf(stderr, "sin(%0.3f) delta = %0.7f  wIndex=%d  y=%0.6f\n", d1,
                  fabs(sin(d1) - dS), wDebugIndex, dDebugY);
        }
        else
        {
          i2++;
        }

        if(fabs(cos(d1) - fast_cos(d1)) > SINCOS_ACCURACY)
        {
          fprintf(stderr, "cos(%0.3f) delta = %0.7f  wIndex=%d  y=%0.6f\n", d1,
                  fabs(cos(d1) - fast_cos(d1)), wDebugIndex, dDebugY);
        }
        else
        {
          i2++;
        }

        if(fabs(sin(d1) - fast_sin(d1)) > SINCOS_ACCURACY)
        {
          fprintf(stderr, "sin(%0.3f) delta = %0.7f  wIndex=%d  y=%0.6f\n", d1,
                  fabs(sin(d1) - fast_sin(d1)), wDebugIndex, dDebugY);
        }
        else
        {
          i2++;
        }
      }

      fprintf(stderr, "Tested %d values, %d in spec\n", i1, i2);

      llTick = MyGetTick();

      for(i1=0, d1=-2.0 * _PI_ - 0.1; d1 < 2.0 * _PI_ + 0.1; d1 += 0.00001, i1+=4)
      {
        fast_sincos(d1, &dS, &dC);
      }

      fprintf(stderr, "fast_sincos took %lld msecs\n", MyGetTick() - llTick);

      llTick = MyGetTick();

      for(i1=0, d1=-2.0 * _PI_ - 0.1; d1 < 2.0 * _PI_ + 0.1; d1 += 0.00001, i1+=4)
      {
        *((volatile double *)&dS) = sin(d1);
        *((volatile double *)&dC) = cos(d1);
      }

      fprintf(stderr, "sin,cos took %lld msecs\n", MyGetTick() - llTick);

      return 0;
    }

#define sin fast_sin
#define cos fast_cos

#endif // USE_FAST_SINCOS, TEST_FAST_SINCOS

    if(!*p1)
    {
      usage();
      return -1;
    }
    while(*p1)
    {
      if(*p1 == 'h')
      {
        usage();
        if(p1[1] || argc > 2)
        {
          return -1;
        }
        else
        {
          return 0;
        }
      }
      else if(*p1 == 'a') // autoscale
      {
        bDoScale = -1;
      }
      else if(*p1 == 's') // set scale
      {
        bDoScale = 1;

        p1++;
        if(!*p1)
        {
          argc--;
          argv++;
          if(argc < 2)
          {
            usage();
            return -1;
          }

          p1 = argv[1];
        }

        p2 = tbuf;

        while(*p1 && *p1 != ',')
        {
          *(p2++) = *(p1++);
        }

        *p2 = 0;
        dScale1 = atof(tbuf);

        if(*p1 != ',' || !p1[1])
        {
          usage();
          return -1;
        }

        p1++;
        p2 = tbuf;

        while(*p1 && *p1 != ',')
        {
          *(p2++) = *(p1++);
        }

        *p2 = 0;
        dScale2 = atof(tbuf);

        break; //the parsing stops here for this term
      }
      else if(*p1 == 't') // # of threads
      {
        p1++;
        if(*p1)
        {
          nThread = atoi(p1);
        }
        else
        {
          argc--;
          argv++;
          if(argc < 2)
          {
            usage();
            return -1;
          }

          nThread = atoi(argv[1]);
        }

        if(nThread <= 0)
        {
          usage();
          return -2;
        }
        break; // the parsing stops here for this term
      }
      // TODO: other options, like cycle count maybe ?
      else
      {
        usage();
        return -2; // unknown option
      }
      p1++;
    }

    argc--; // in anticipation of other options, this is the loop counter for it
    argv++;
  }

  if(!nThread)
  {
    nThread = cpu_count();
    //fprintf(stderr, "TEMPORARY:  %d threads\n");
  }

  while(argc > 1 || pIn == stdin)
  {
MY_XY xy;

    if(argc > 1)
    {
      pIn = fopen(argv[1], "r");

      if(!pIn)
      {
        argv++;
        argc--;

        continue;
      }

      printf("FILE:  %s\n", argv[1]);
      argv++;
      argc--;
    }

    xy = get_xy_data(pIn);

    fclose(pIn);
    pIn = NULL;

    if(!xy.pData || !xy.nItems)
    {
      continue;
    }

    if(bDoScale > 0)
    {
      if(xy.pData[xy.nItems - 1].dX > xy.pData[0].dX)
      {
        //assume data is sorted
        dXFactor = ((dScale2 - dScale1) // the delta scale(normally - pi to pi for autoscale)
                 / (xy.pData[xy.nItems - 1].dX - xy.pData[0].dX)) // the delta X
                 * (double)(xy.nItems - 1)
                 / (double)(xy.nItems);  // last data point represents "not quite 2 * pi"

        dXOffset = dScale1 - xy.pData[0].dX * dXFactor;

        for(i1 = 0; i1 < xy.nItems; i1++)
        {
          xy.pData[i1].dX = xy.pData[i1].dX * dXFactor + dXOffset;
        }
      }

      fprintf(stderr, "TEMPORARY:  scaling factors:  m=%g b=%g\n", dXFactor, dXOffset);
    }
    else if(bDoScale < 0)
    {
      fprintf(stderr, "TEMPORARY:  autoscale -PI to PI\n");
    }


    nHarm = xy.nItems / 2 > MAX_HARMONIC
          ? MAX_HARMONIC : xy.nItems / 2;

    if(xy.nItems < 2 || nHarm < 1)
    {
      continue;
    }

    pdA = (double *)malloc(sizeof(*pdA) * (nHarm + 1) * 2);
    if(!pdA)
    {
      fprintf(stderr, "out of memory for work buffers\n");
      return -3;
    }

    pdB = pdA + nHarm + 1;

    dFourier(xy.pData, xy.nItems, nHarm, &dC, pdA, pdB, nThread, bDoScale < 0 ? 1 : 0);

    printf("harm #\t      magnitude\t    phase (deg)\t  offset (C0)=%g\n", dC);

    for(i1 = 0; i1 < nHarm; i1++)
    {
      printf("  %3d\t"
             // "%7g\t%7g\t"
             "%15.6f\t%15.6f\n",
             i1 + 1,
             //dA[i1],
             //dB[i1],
             sqrt(pdA[i1] * pdA[i1] + pdB[i1] * pdB[i1]),
             atan2(pdB[i1], pdA[i1]) * 180 / _PI_ + 180);
      // NOTE:  atan result for cosine will be - 180, sin - 90
      //        because the analysis is - PI to PI
      //        adding 180 will give you 0, 90
    }

    // figure out relative error (i.e. std deviation) and report it

//  if() TODO - make this optional
//  {
    dXY = 2.0 * _PI_ / (xy.pData[xy.nItems - 1].dX + (xy.pData[xy.nItems - 1].dX - xy.pData[0].dX) / (xy.nItems - 1));
    dX0 = -dXY * xy.pData[0].dX - _PI_; // derived from -_PI_ == dX0 + dXY * aVal[0].dX


    for(i1 = 0, iW = 0; iW < nThread; iW++)
    {
      i2 = (iW + 1) * xy.nItems / nThread;
      if(i2 > xy.nItems)
      {
        i2 = xy.nItems;
      }
      aW[iW] = create_work_unit(pdA, pdB, dC, xy.pData, nHarm, dX0, dXY,
                                i1, i2 - 1, check_callback, iW < (nThread - 1));
      if(!aW[iW])
      {
        fprintf(stderr, "threading error on data check\n");
        return -3;
      }

      i1 = i2; // next group
    }

    for(iW = 0, dErr = 0.0; iW < nThread; iW++)
    {
      if(!aW[iW])
      {
        continue;
      }

      if(aW[iW]->idThread)
      {
        pthread_join(aW[iW]->idThread, NULL); // ignore any error for now
        //pthread_detach(&(aW[iW].idThread);

        dErr += aW[iW]->dRval; // returned C0 value(when applicable) adds into 'dC'
      }
      else // not a thread, keep 'dC' return here also
      {
        dErr += aW[iW]->dRval; // returned C0 value(when applicable) adds into 'dC'
      }

      free(aW[iW]);
      aW[iW] = NULL; // by convention
    }

    printf("relative accuracy:  %g\n", sqrt(dErr / xy.nItems));

//  }

    if(xy.pData)
    {
      free(xy.pData);
    }
    if(pdA)
    {
      free(pdA);
    }
  }

  return 0;
}

#ifdef USE_FAST_SINCOS

// FAST SIN/COS UTILITIES - you can use these as you see fit, by the way (no license restrictions)
// These really are trivial, though, so it's no big deal.  Just has a sin/cos table.
// What makes it faster is a) float precision, b) table lookup, c) shared calcs for 'fast_sincos'
// And the precision tester, if you compile it in, shows that it's a match within 6 digits of precision
// so there should be no problem using it, though your results may differ slightly.

double make_valid_sincos_range(double dTheta)
{
float x0;

  x0 = (float)dTheta;

  if(x0<(float)-(3 * _PI_) || x0>(float)(3 * _PI_))
  {
    x0 -= ( floorf(x0 * (float)(1 / (2 * _PI_))) ) * (float)(2.0 * _PI_);
  }

  /* optimized, hopefully, to minimize multiplications! */

  if(x0<(float)-_PI_)
  {
    x0+= (float)(2 * _PI_);  /* ensure it's between -pi & pi */
  }
  if(x0>(float)_PI_)
  {
    x0-= (float)(2 * _PI_);  /* ensure it's between -pi & pi */
  }

  return(x0);
}

void fast_sincos(double dTheta, double *pSin, double *pCos)
{
unsigned int wIndex;
float x0, y;


  x0 = make_valid_sincos_range(dTheta);             /* x is between -pi and pi */

  y = (float)5000.0 + x0 * (float)(5000.0 / _PI_); /* convert to an 'index' value... */

  wIndex = (unsigned int)floorf(y);
  y -= (float)wIndex;  /* this gives us the index and the 'interpolate' value... */

  dDebugY = y;
  wDebugIndex = wIndex;

  if(y == 0.0) // possible
  {
    *pCos = _COS_VALUES_[wIndex];
    *pSin = _SIN_VALUES_[wIndex];
  }
  else       /* not an 'even' value - interpolate between two entries */
  {
    *pCos = _COS_VALUES_[wIndex] +
            (_COS_VALUES_[wIndex + 1] - _COS_VALUES_[wIndex]) * y;

    *pSin = _SIN_VALUES_[wIndex] +
            (_SIN_VALUES_[wIndex + 1] - _SIN_VALUES_[wIndex]) * y;
  }
}

double fast_cos(double dTheta)
{
unsigned int wIndex;
float x0, y;


  x0 = make_valid_sincos_range(dTheta);             /* x is between -pi and pi */

  y = (float)5000.0 + x0 * (float)(5000.0 / _PI_);
                                       /* convert to an 'index' value... */

  wIndex = (unsigned int)floorf(y);
  y -= (float)wIndex;    /* this gives us the index and the 'interpolate' value... */

  if(!y)
  {
    return(_COS_VALUES_[wIndex]);
  }
  else       /* not an 'even' value - interpolate between two entries */
  {
    return(_COS_VALUES_[wIndex] +
           (_COS_VALUES_[wIndex + 1] - _COS_VALUES_[wIndex]) * y);
  }
}

double fast_sin(double dTheta)
{
unsigned int wIndex;
float x0, y;

  x0 = make_valid_sincos_range(dTheta);            /* x is between -pi and pi */

  y = (float)5000.0 + x0 * (float)(5000.0 / _PI_);
                                       /* convert to an 'index' value... */

  wIndex = (unsigned int)floorf(y);
  y -= (float)wIndex;    /* this gives us the index and the 'interpolate' value... */

  if(!y)
  {
    return(_SIN_VALUES_[wIndex]);
  }
  else       /* not an 'even' value - interpolate between two entries */
  {
    return(_SIN_VALUES_[wIndex] +
           (_SIN_VALUES_[wIndex + 1] - _SIN_VALUES_[wIndex]) * y);
  }
}

static const float _SIN_VALUES_[12501]=
{
   0.00000000,-0.00062831,-0.00125663,-0.00188495,-0.00251327,
   -0.00314158,-0.00376990,-0.00439821,-0.00502652,-0.00565483,
   -0.00628314,-0.00691144,-0.00753975,-0.00816804,-0.00879634,
   -0.00942463,-0.01005292,-0.01068121,-0.01130949,-0.01193776,
   -0.01256603,-0.01319430,-0.01382256,-0.01445082,-0.01507907,
   -0.01570731,-0.01633555,-0.01696378,-0.01759201,-0.01822022,
   -0.01884843,-0.01947664,-0.02010483,-0.02073302,-0.02136120,
   -0.02198937,-0.02261753,-0.02324569,-0.02387383,-0.02450197,
   -0.02513009,-0.02575821,-0.02638631,-0.02701440,-0.02764249,
   -0.02827056,-0.02889862,-0.02952667,-0.03015471,-0.03078274,
   -0.03141075,-0.03203876,-0.03266675,-0.03329472,-0.03392269,
   -0.03455064,-0.03517857,-0.03580650,-0.03643440,-0.03706230,
   -0.03769018,-0.03831804,-0.03894589,-0.03957373,-0.04020154,
   -0.04082935,-0.04145713,-0.04208490,-0.04271266,-0.04334039,
   -0.04396811,-0.04459582,-0.04522350,-0.04585117,-0.04647882,
   -0.04710645,-0.04773406,-0.04836165,-0.04898922,-0.04961678,
   -0.05024431,-0.05087183,-0.05149932,-0.05212680,-0.05275425,
   -0.05338168,-0.05400910,-0.05463649,-0.05526386,-0.05589120,
   -0.05651853,-0.05714583,-0.05777311,-0.05840037,-0.05902760,
   -0.05965482,-0.06028200,-0.06090917,-0.06153631,-0.06216342,
   -0.06279051,-0.06341758,-0.06404462,-0.06467164,-0.06529863,
   -0.06592559,-0.06655253,-0.06717944,-0.06780633,-0.06843319,
   -0.06906002,-0.06968683,-0.07031360,-0.07094035,-0.07156707,
   -0.07219377,-0.07282043,-0.07344707,-0.07407367,-0.07470025,
   -0.07532680,-0.07595332,-0.07657981,-0.07720627,-0.07783269,
   -0.07845909,-0.07908546,-0.07971179,-0.08033809,-0.08096437,
   -0.08159061,-0.08221681,-0.08284299,-0.08346913,-0.08409524,
   -0.08472132,-0.08534736,-0.08597337,-0.08659934,-0.08722528,
   -0.08785119,-0.08847706,-0.08910290,-0.08972870,-0.09035447,
   -0.09098020,-0.09160589,-0.09223155,-0.09285717,-0.09348276,
   -0.09410831,-0.09473382,-0.09535929,-0.09598473,-0.09661013,
   -0.09723549,-0.09786081,-0.09848609,-0.09911134,-0.09973654,
   -0.10036171,-0.10098684,-0.10161192,-0.10223697,-0.10286197,
   -0.10348694,-0.10411186,-0.10473675,-0.10536159,-0.10598639,
   -0.10661115,-0.10723587,-0.10786054,-0.10848517,-0.10910976,
   -0.10973431,-0.11035881,-0.11098327,-0.11160768,-0.11223205,
   -0.11285638,-0.11348066,-0.11410490,-0.11472909,-0.11535324,
   -0.11597734,-0.11660140,-0.11722540,-0.11784937,-0.11847328,
   -0.11909715,-0.11972098,-0.12034475,-0.12096848,-0.12159216,
   -0.12221579,-0.12283938,-0.12346291,-0.12408640,-0.12470984,
   -0.12533323,-0.12595657,-0.12657986,-0.12720310,-0.12782629,
   -0.12844943,-0.12907251,-0.12969555,-0.13031854,-0.13094147,
   -0.13156435,-0.13218718,-0.13280996,-0.13343269,-0.13405536,
   -0.13467798,-0.13530055,-0.13592307,-0.13654553,-0.13716793,
   -0.13779029,-0.13841258,-0.13903483,-0.13965702,-0.14027915,
   -0.14090123,-0.14152325,-0.14214522,-0.14276713,-0.14338898,
   -0.14401078,-0.14463252,-0.14525420,-0.14587583,-0.14649740,
   -0.14711891,-0.14774036,-0.14836175,-0.14898309,-0.14960437,
   -0.15022558,-0.15084674,-0.15146784,-0.15208888,-0.15270986,
   -0.15333078,-0.15395164,-0.15457243,-0.15519317,-0.15581385,
   -0.15643446,-0.15705501,-0.15767550,-0.15829593,-0.15891629,
   -0.15953660,-0.16015684,-0.16077701,-0.16139713,-0.16201717,
   -0.16263716,-0.16325708,-0.16387694,-0.16449673,-0.16511646,
   -0.16573612,-0.16635571,-0.16697524,-0.16759471,-0.16821411,
   -0.16883344,-0.16945270,-0.17007190,-0.17069103,-0.17131010,
   -0.17192910,-0.17254802,-0.17316688,-0.17378568,-0.17440440,
   -0.17502305,-0.17564164,-0.17626016,-0.17687860,-0.17749698,
   -0.17811529,-0.17873352,-0.17935169,-0.17996978,-0.18058781,
   -0.18120576,-0.18182364,-0.18244145,-0.18305919,-0.18367685,
   -0.18429444,-0.18491196,-0.18552941,-0.18614678,-0.18676408,
   -0.18738131,-0.18799846,-0.18861554,-0.18923254,-0.18984947,
   -0.19046633,-0.19108310,-0.19169981,-0.19231644,-0.19293299,
   -0.19354946,-0.19416586,-0.19478218,-0.19539843,-0.19601460,
   -0.19663069,-0.19724670,-0.19786264,-0.19847850,-0.19909427,
   -0.19970998,-0.20032560,-0.20094114,-0.20155660,-0.20217199,
   -0.20278729,-0.20340251,-0.20401766,-0.20463272,-0.20524770,
   -0.20586260,-0.20647742,-0.20709216,-0.20770682,-0.20832139,
   -0.20893589,-0.20955030,-0.21016462,-0.21077887,-0.21139303,
   -0.21200710,-0.21262110,-0.21323501,-0.21384883,-0.21446258,
   -0.21507623,-0.21568980,-0.21630329,-0.21691669,-0.21753001,
   -0.21814324,-0.21875638,-0.21936944,-0.21998241,-0.22059529,
   -0.22120809,-0.22182080,-0.22243342,-0.22304595,-0.22365840,
   -0.22427076,-0.22488302,-0.22549520,-0.22610730,-0.22671930,
   -0.22733121,-0.22794303,-0.22855477,-0.22916641,-0.22977796,
   -0.23038942,-0.23100079,-0.23161207,-0.23222326,-0.23283435,
   -0.23344536,-0.23405627,-0.23466709,-0.23527782,-0.23588845,
   -0.23649899,-0.23710944,-0.23771979,-0.23833005,-0.23894022,
   -0.23955029,-0.24016027,-0.24077015,-0.24137994,-0.24198963,
   -0.24259923,-0.24320873,-0.24381813,-0.24442744,-0.24503665,
   -0.24564577,-0.24625478,-0.24686370,-0.24747253,-0.24808125,
   -0.24868988,-0.24929841,-0.24990684,-0.25051518,-0.25112341,
   -0.25173154,-0.25233958,-0.25294751,-0.25355535,-0.25416309,
   -0.25477072,-0.25537826,-0.25598569,-0.25659302,-0.25720025,
   -0.25780738,-0.25841441,-0.25902134,-0.25962816,-0.26023488,
   -0.26084150,-0.26144802,-0.26205443,-0.26266074,-0.26326694,
   -0.26387304,-0.26447904,-0.26508493,-0.26569072,-0.26629641,
   -0.26690198,-0.26750746,-0.26811282,-0.26871809,-0.26932324,
   -0.26992829,-0.27053323,-0.27113807,-0.27174280,-0.27234742,
   -0.27295193,-0.27355634,-0.27416063,-0.27476482,-0.27536890,
   -0.27597288,-0.27657674,-0.27718050,-0.27778414,-0.27838768,
   -0.27899110,-0.27959442,-0.28019762,-0.28080072,-0.28140370,
   -0.28200657,-0.28260933,-0.28321198,-0.28381452,-0.28441694,
   -0.28501926,-0.28562146,-0.28622355,-0.28682552,-0.28742738,
   -0.28802913,-0.28863077,-0.28923229,-0.28983369,-0.29043498,
   -0.29103616,-0.29163722,-0.29223817,-0.29283900,-0.29343972,
   -0.29404032,-0.29464080,-0.29524117,-0.29584142,-0.29644156,
   -0.29704158,-0.29764148,-0.29824126,-0.29884092,-0.29944047,
   -0.30003990,-0.30063921,-0.30123840,-0.30183748,-0.30243643,
   -0.30303526,-0.30363398,-0.30423257,-0.30483105,-0.30542940,
   -0.30602764,-0.30662575,-0.30722374,-0.30782161,-0.30841936,
   -0.30901699,-0.30961449,-0.31021188,-0.31080914,-0.31140628,
   -0.31200329,-0.31260018,-0.31319695,-0.31379360,-0.31439012,
   -0.31498651,-0.31558279,-0.31617893,-0.31677496,-0.31737086,
   -0.31796663,-0.31856228,-0.31915780,-0.31975319,-0.32034846,
   -0.32094360,-0.32153862,-0.32213351,-0.32272827,-0.32332291,
   -0.32391741,-0.32451179,-0.32510604,-0.32570017,-0.32629416,
   -0.32688802,-0.32748176,-0.32807537,-0.32866884,-0.32926219,
   -0.32985541,-0.33044850,-0.33104145,-0.33163428,-0.33222698,
   -0.33281954,-0.33341197,-0.33400427,-0.33459644,-0.33518848,
   -0.33578038,-0.33637216,-0.33696380,-0.33755530,-0.33814668,
   -0.33873792,-0.33932902,-0.33991999,-0.34051083,-0.34110153,
   -0.34169210,-0.34228254,-0.34287284,-0.34346300,-0.34405303,
   -0.34464292,-0.34523267,-0.34582229,-0.34641178,-0.34700112,
   -0.34759033,-0.34817940,-0.34876834,-0.34935714,-0.34994579,
   -0.35053432,-0.35112270,-0.35171094,-0.35229905,-0.35288701,
   -0.35347484,-0.35406253,-0.35465007,-0.35523748,-0.35582475,
   -0.35641187,-0.35699886,-0.35758570,-0.35817241,-0.35875897,
   -0.35934539,-0.35993167,-0.36051781,-0.36110380,-0.36168965,
   -0.36227536,-0.36286093,-0.36344635,-0.36403163,-0.36461677,
   -0.36520176,-0.36578660,-0.36637131,-0.36695587,-0.36754028,
   -0.36812455,-0.36870867,-0.36929265,-0.36987648,-0.37046017,
   -0.37104371,-0.37162710,-0.37221034,-0.37279344,-0.37337640,
   -0.37395920,-0.37454186,-0.37512437,-0.37570673,-0.37628894,
   -0.37687101,-0.37745292,-0.37803469,-0.37861630,-0.37919777,
   -0.37977909,-0.38036026,-0.38094128,-0.38152214,-0.38210286,
   -0.38268343,-0.38326384,-0.38384411,-0.38442422,-0.38500418,
   -0.38558399,-0.38616364,-0.38674315,-0.38732250,-0.38790170,
   -0.38848074,-0.38905963,-0.38963837,-0.39021696,-0.39079539,
   -0.39137366,-0.39195178,-0.39252975,-0.39310756,-0.39368522,
   -0.39426272,-0.39484006,-0.39541725,-0.39599429,-0.39657116,
   -0.39714789,-0.39772445,-0.39830086,-0.39887711,-0.39945320,
   -0.40002913,-0.40060491,-0.40118053,-0.40175599,-0.40233129,
   -0.40290643,-0.40348141,-0.40405624,-0.40463090,-0.40520541,
   -0.40577975,-0.40635394,-0.40692796,-0.40750183,-0.40807553,
   -0.40864907,-0.40922245,-0.40979567,-0.41036873,-0.41094162,
   -0.41151435,-0.41208692,-0.41265933,-0.41323158,-0.41380366,
   -0.41437558,-0.41494733,-0.41551892,-0.41609035,-0.41666161,
   -0.41723271,-0.41780364,-0.41837441,-0.41894501,-0.41951545,
   -0.42008572,-0.42065583,-0.42122577,-0.42179554,-0.42236515,
   -0.42293459,-0.42350387,-0.42407297,-0.42464191,-0.42521068,
   -0.42577929,-0.42634772,-0.42691599,-0.42748409,-0.42805202,
   -0.42861978,-0.42918737,-0.42975479,-0.43032205,-0.43088913,
   -0.43145604,-0.43202278,-0.43258935,-0.43315576,-0.43372199,
   -0.43428804,-0.43485393,-0.43541965,-0.43598519,-0.43655056,
   -0.43711576,-0.43768079,-0.43824564,-0.43881032,-0.43937483,
   -0.43993916,-0.44050333,-0.44106731,-0.44163112,-0.44219476,
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   -0.99857418,-0.99860752,-0.99864047,-0.99867302,-0.99870519,
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   -0.99916613,-0.99919159,-0.99921665,-0.99924132,-0.99926559,
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   -0.99950656,-0.99952609,-0.99954524,-0.99956399,-0.99958234,
   -0.99960030,-0.99961787,-0.99963504,-0.99965182,-0.99966820,
   -0.99968418,-0.99969978,-0.99971497,-0.99972978,-0.99974419,
   -0.99975820,-0.99977182,-0.99978504,-0.99979787,-0.99981031,
   -0.99982235,-0.99983399,-0.99984524,-0.99985610,-0.99986656,
   -0.99987663,-0.99988630,-0.99989558,-0.99990446,-0.99991295,
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   -0.99995558,-0.99996131,-0.99996664,-0.99997157,-0.99997611,
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   -0.99999506,-0.99999684,-0.99999822,-0.99999921,-0.99999980,
   -1.00000000 // extra element
};

static const float * const _COS_VALUES_ = &(_SIN_VALUES_[2500]);


#endif // USE_FAST_SINCOS