Fts5Table *pTab = (Fts5Table*)(pCsr->base.pVtab);
  int rc = SQLITE_OK;

  if( CsrFlagTest(pCsr, FTS5CSR_REQUIRE_DOCSIZE) ){
    i64 iRowid = fts5CursorRowid(pCsr);
    rc = sqlite3Fts5StorageDocsize(pTab->pStorage, iRowid, pCsr->aColumnSize);
  }






  if( iCol>=0 && iCol<pTab->pConfig->nCol ){
    *pnToken = pCsr->aColumnSize[iCol];
  }else{
    *pnToken = 0;

  }
  return rc;
}

static int fts5ApiPoslist(
  Fts5Context *pCtx, 
  int iPhrase, 

  Fts5Table *pTab = (Fts5Table*)(pCsr->base.pVtab);
  int rc = SQLITE_OK;

  if( CsrFlagTest(pCsr, FTS5CSR_REQUIRE_DOCSIZE) ){
    i64 iRowid = fts5CursorRowid(pCsr);
    rc = sqlite3Fts5StorageDocsize(pTab->pStorage, iRowid, pCsr->aColumnSize);
  }
  if( iCol<0 ){
    int i;
    *pnToken = 0;
    for(i=0; i<pTab->pConfig->nCol; i++){
      *pnToken += pCsr->aColumnSize[i];
    }
  }else if( iCol<pTab->pConfig->nCol ){
    *pnToken = pCsr->aColumnSize[iCol];
  }else{
    *pnToken = 0;
    rc = SQLITE_RANGE;
  }
  return rc;
}

static int fts5ApiPoslist(
  Fts5Context *pCtx, 
  int iPhrase, 

/*
** EXTENSION API FUNCTIONS
**
** xUserData(pFts):
**   Return a copy of the context pointer the extension function was 
**   registered with.
**
**
** xColumnTotalSize(pFts, iCol, pnToken):



**   Returns the total number of tokens in column iCol, considering all
**   rows in the FTS5 table.
**




**
** xColumnCount:
**   Returns the number of columns in the FTS5 table.
**
** xColumnSize:
**   Reports the size in tokens of a column value from the current row.
**

/*
** EXTENSION API FUNCTIONS
**
** xUserData(pFts):
**   Return a copy of the context pointer the extension function was 
**   registered with.
**

** xColumnTotalSize(pFts, iCol, pnToken):
**   If parameter iCol is less than zero, set output variable *pnToken
**   to the total number of tokens in the FTS5 table. Or, if iCol is
**   non-negative but less than the number of columns in the table, return
**   the total number of tokens in column iCol, considering all rows in 
**   the FTS5 table.
**
**   If parameter iCol is greater than or equal to the number of columns
**   in the table, SQLITE_RANGE is returned. Or, if an error occurs (e.g.
**   an OOM condition or IO error), an appropriate SQLite error code is 
**   returned.
**
** xColumnCount:
**   Returns the number of columns in the FTS5 table.
**
** xColumnSize:
**   Reports the size in tokens of a column value from the current row.
**

/*************************************************************************
** Start of highlight() implementation.
*/
typedef struct HighlightContext HighlightContext;
struct HighlightContext {
  CInstIter iter;                 /* Coalesced Instance Iterator */
  int iRangeStart;
  int iRangeEnd;
  const char *zOpen;              /* Opening highlight */
  const char *zClose;             /* Closing highlight */
  const char *zIn;                /* Input text */
  int nIn;                        /* Size of input text in bytes */
  int iOff;                       /* Current offset within zIn[] */
  char *zOut;                     /* Output value */
};
................................................................................
  int iPos                        /* Position offset of token */
){
  HighlightContext *p = (HighlightContext*)pContext;
  int rc = SQLITE_OK;

  if( p->iRangeEnd>0 ){
    if( iPos<p->iRangeStart || iPos>p->iRangeEnd ) return SQLITE_OK;
    if( iPos==p->iRangeStart ) p->iOff = iStartOff;
  }

  if( iPos==p->iter.iStart ){
    fts5HighlightAppend(&rc, p, &p->zIn[p->iOff], iStartOff - p->iOff);
    fts5HighlightAppend(&rc, p, p->zOpen, -1);
    p->iOff = iStartOff;
  }
................................................................................
    sqlite3_result_text(pCtx, (const char*)ctx.zOut, -1, SQLITE_TRANSIENT);
  }else{
    sqlite3_result_error_code(pCtx, rc);
  }
  sqlite3_free(ctx.zOut);
}
/*

**************************************************************************/





static void fts5SnippetFunction(
  const Fts5ExtensionApi *pApi,   /* API offered by current FTS version */
  Fts5Context *pFts,              /* First arg to pass to pApi functions */
  sqlite3_context *pCtx,          /* Context for returning result/error */
  int nVal,                       /* Number of values in apVal[] array */
  sqlite3_value **apVal           /* Array of trailing arguments */
){
................................................................................
  int nToken;                     /* 5th argument to snippet() */
  int nInst;                      /* Number of instance matches this row */
  int i;                          /* Used to iterate through instances */
  int nPhrase;                    /* Number of phrases in query */
  unsigned char *aSeen;           /* Array of "seen instance" flags */
  int iBestCol;                   /* Column containing best snippet */
  int iBestStart = 0;             /* First token of best snippet */
  int iBestLast = nToken;         /* Last token of best snippet */
  int nBestScore = 0;             /* Score of best snippet */
  int nColSize;                   /* Total size of iBestCol in tokens */

  if( nVal!=5 ){
    const char *zErr = "wrong number of arguments to function snippet()";
    sqlite3_result_error(pCtx, zErr, -1);
    return;
  }

  memset(&ctx, 0, sizeof(HighlightContext));
  rc = pApi->xColumnText(pFts, iCol, &ctx.zIn, &ctx.nIn);

  iCol = sqlite3_value_int(apVal[0]);

  ctx.zOpen = (const char*)sqlite3_value_text(apVal[1]);
  ctx.zClose = (const char*)sqlite3_value_text(apVal[2]);
  zEllips = (const char*)sqlite3_value_text(apVal[3]);
  nToken = sqlite3_value_int(apVal[4]);


  iBestCol = (iCol>=0 ? iCol : 0);
  nPhrase = pApi->xPhraseCount(pFts);
  aSeen = sqlite3_malloc(nPhrase);
  if( aSeen==0 ){
    rc = SQLITE_NOMEM;
  }
................................................................................
  }
  sqlite3_free(ctx.zOut);
  sqlite3_free(aSeen);
}

/************************************************************************/


/*

** Context object passed by fts5GatherTotals() to xQueryPhrase callback
** fts5GatherCallback().
*/

struct Fts5GatherCtx {
  int nCol;                       /* Number of columns in FTS table */
  int iPhrase;                    /* Phrase currently under investigation */
  int *anVal;                     /* Array to populate */

};

/*
** Callback used by fts5GatherTotals() with the xQueryPhrase() API.

*/
static int fts5GatherCallback(
  const Fts5ExtensionApi *pApi, 
  Fts5Context *pFts,
  void *pUserData                 /* Pointer to Fts5GatherCtx object */
){
  struct Fts5GatherCtx *p = (struct Fts5GatherCtx*)pUserData;
  int i = 0;
  int iPrev = -1;
  i64 iPos = 0;

  while( 0==pApi->xPoslist(pFts, 0, &i, &iPos) ){
    int iCol = FTS5_POS2COLUMN(iPos);
    if( iCol!=iPrev ){
      p->anVal[p->iPhrase * p->nCol + iCol]++;
      iPrev = iCol;
    }
  }

  return SQLITE_OK;
}

/*
** This function returns a pointer to an array of integers containing entries
** indicating the number of rows in the table for which each phrase features 
** at least once in each column.


**
** If nCol is the number of matchable columns in the table, and nPhrase is
** the number of phrases in the query, the array contains a total of
** (nPhrase*nCol) entries.
**
** For phrase iPhrase and column iCol:
**
**   anVal[iPhrase * nCol + iCol]
**
** is set to the number of rows in the table for which column iCol contains 
** at least one instance of phrase iPhrase.
*/
static int fts5GatherTotals(
  const Fts5ExtensionApi *pApi,   /* API offered by current FTS version */
  Fts5Context *pFts,              /* First arg to pass to pApi functions */
  int **panVal
){
  int rc = SQLITE_OK;
  int *anVal = 0;
  int i;                          /* For iterating through expression phrases */
  int nPhrase = pApi->xPhraseCount(pFts);
  int nCol = pApi->xColumnCount(pFts);
  int nByte = nCol * nPhrase * sizeof(int);
  struct Fts5GatherCtx sCtx;

  sCtx.nCol = nCol;
  anVal = sCtx.anVal = (int*)sqlite3_malloc(nByte);
  if( anVal==0 ){
    rc = SQLITE_NOMEM;
  }else{
    memset(anVal, 0, nByte);
  }

  for(i=0; i<nPhrase && rc==SQLITE_OK; i++){
    sCtx.iPhrase = i;
    rc = pApi->xQueryPhrase(pFts, i, (void*)&sCtx, fts5GatherCallback);
  }

  if( rc!=SQLITE_OK ){
    sqlite3_free(anVal);
    anVal = 0;
  }

  *panVal = anVal;
  return rc;
}

typedef struct Fts5Bm25Context Fts5Bm25Context;
struct Fts5Bm25Context {
  int nPhrase;                    /* Number of phrases in query */
  int nCol;                       /* Number of columns in FTS table */
  double *aIDF;                   /* Array of IDF values */
  double *aAvg;                   /* Average size of each column in tokens */
};

static int fts5Bm25GetContext(
  const Fts5ExtensionApi *pApi,   /* API offered by current FTS version */
  Fts5Context *pFts,              /* First arg to pass to pApi functions */
  Fts5Bm25Context **pp            /* OUT: Context object */

){
  Fts5Bm25Context *p;
  int rc = SQLITE_OK;


  p = pApi->xGetAuxdata(pFts, 0);
  if( p==0 ){
    int *anVal = 0;
    int ic;                       /* For iterating through columns */
    int ip;                       /* For iterating through phrases */

    i64 nRow;                     /* Total number of rows in table */





    int nPhrase = pApi->xPhraseCount(pFts);
    int nCol = pApi->xColumnCount(pFts);
    int nByte = sizeof(Fts5Bm25Context) 
              + sizeof(double) * nPhrase * nCol       /* aIDF[] */
              + sizeof(double) * nCol;                /* aAvg[] */

    p = (Fts5Bm25Context*)sqlite3_malloc(nByte);
    if( p==0 ){
      rc = SQLITE_NOMEM;
    }else{
      memset(p, 0, nByte);
      p->aAvg = (double*)&p[1];
      p->aIDF = (double*)&p->aAvg[nCol];
      p->nCol = nCol;
      p->nPhrase = nPhrase;
    }

    if( rc==SQLITE_OK ){

      rc = pApi->xRowCount(pFts, &nRow); 

      assert( nRow>0 || rc!=SQLITE_OK );
      if( nRow<2 ) nRow = 2;
    }


    for(ic=0; rc==SQLITE_OK && ic<nCol; ic++){

      i64 nToken = 0;
      rc = pApi->xColumnTotalSize(pFts, ic, &nToken);
      p->aAvg[ic] = (double)nToken / (double)nRow;
    }

    if( rc==SQLITE_OK ){
      rc = fts5GatherTotals(pApi, pFts, &anVal);
    }
    for(ic=0; ic<nCol; ic++){
      for(ip=0; rc==SQLITE_OK && ip<nPhrase; ip++){
        /* Calculate the IDF (Inverse Document Frequency) for phrase ip
        ** in column ic. This is done using the standard BM25 formula as
        ** found on wikipedia:
        **
        **   IDF = log( (N - nHit + 0.5) / (nHit + 0.5) )
        **
        ** where "N" is the total number of documents in the set and nHit
        ** is the number that contain at least one instance of the phrase
        ** under consideration.
        **
        ** The problem with this is that if (N < 2*nHit), the IDF is 
        ** negative. Which is undesirable. So the mimimum allowable IDF is
        ** (1e-6) - roughly the same as a term that appears in just over
        ** half of set of 5,000,000 documents.  */
        int idx = ip * nCol + ic; /* Index in aIDF[] and anVal[] arrays */
        int nHit = anVal[idx];    /* Number of docs matching "ic: ip" */

        p->aIDF[idx] = log( (0.5 + nRow - nHit) / (0.5 + nHit) );
        if( p->aIDF[idx]<=0.0 ) p->aIDF[idx] = 1e-6;
        assert( p->aIDF[idx]>=0.0 );
      }
    }


    sqlite3_free(anVal);
    if( rc==SQLITE_OK ){

      rc = pApi->xSetAuxdata(pFts, p, sqlite3_free);
    }
    if( rc!=SQLITE_OK ){
      sqlite3_free(p);
      p = 0;
    }
  }

  *pp = p;
  return rc;
}

static void fts5Bm25DebugContext(
  int *pRc,                       /* IN/OUT: Return code */
  Fts5Buffer *pBuf,               /* Buffer to populate */
  Fts5Bm25Context *p              /* Context object to decode */
){
  int ip;
  int ic;

  sqlite3Fts5BufferAppendString(pRc, pBuf, "idf ");
  if( p->nPhrase>1 || p->nCol>1 ){
    sqlite3Fts5BufferAppendString(pRc, pBuf, "{");
  }
  for(ip=0; ip<p->nPhrase; ip++){
    if( ip>0 ) sqlite3Fts5BufferAppendString(pRc, pBuf, " ");
    if( p->nCol>1 ) sqlite3Fts5BufferAppendString(pRc, pBuf, "{");
    for(ic=0; ic<p->nCol; ic++){
      if( ic>0 ) sqlite3Fts5BufferAppendString(pRc, pBuf, " ");
      sqlite3Fts5BufferAppendPrintf(pRc, pBuf, "%f", p->aIDF[ip*p->nCol+ic]);
    }
    if( p->nCol>1 ) sqlite3Fts5BufferAppendString(pRc, pBuf, "}");
  }
  if( p->nPhrase>1 || p->nCol>1 ){
    sqlite3Fts5BufferAppendString(pRc, pBuf, "}");
  }

  sqlite3Fts5BufferAppendString(pRc, pBuf, " avgdl ");
  if( p->nCol>1 ) sqlite3Fts5BufferAppendString(pRc, pBuf, "{");
  for(ic=0; ic<p->nCol; ic++){
    if( ic>0 ) sqlite3Fts5BufferAppendString(pRc, pBuf, " ");
    sqlite3Fts5BufferAppendPrintf(pRc, pBuf, "%f", p->aAvg[ic]);
  }
  if( p->nCol>1 ) sqlite3Fts5BufferAppendString(pRc, pBuf, "}");
}

static void fts5Bm25DebugRow(
  int *pRc, 
  Fts5Buffer *pBuf, 
  Fts5Bm25Context *p, 
  const Fts5ExtensionApi *pApi, 
  Fts5Context *pFts
){
}




static void fts5Bm25Function(
  const Fts5ExtensionApi *pApi,   /* API offered by current FTS version */
  Fts5Context *pFts,              /* First arg to pass to pApi functions */
  sqlite3_context *pCtx,          /* Context for returning result/error */
  int nVal,                       /* Number of values in apVal[] array */
  sqlite3_value **apVal           /* Array of trailing arguments */
){
  const double k1 = 1.2;
  const double B = 0.75;

  int rc = SQLITE_OK;
  Fts5Bm25Context *p;









  rc = fts5Bm25GetContext(pApi, pFts, &p);

  if( rc==SQLITE_OK ){
    /* If the bDebug flag is set, instead of returning a numeric rank, this
    ** function returns a text value showing how the rank is calculated. */
    Fts5Buffer debug;
    int bDebug = (pApi->xUserData(pFts)!=0);
    memset(&debug, 0, sizeof(Fts5Buffer));





    int ip;
    double score = 0.0;





    if( bDebug ){
      fts5Bm25DebugContext(&rc, &debug, p);
      fts5Bm25DebugRow(&rc, &debug, p, pApi, pFts);
    }

    for(ip=0; rc==SQLITE_OK && ip<p->nPhrase; ip++){
      int iPrev = 0;
      int nHit = 0;
      int i = 0;
      i64 iPos = 0;


      while( rc==SQLITE_OK ){
        int bDone = pApi->xPoslist(pFts, ip, &i, &iPos);
        int iCol = FTS5_POS2COLUMN(iPos);
        if( (iCol!=iPrev || bDone) && nHit>0 ){
          int sz = 0;
          int idx = ip * p->nCol + iPrev;
          double bm25;
          rc = pApi->xColumnSize(pFts, iPrev, &sz);


          bm25 = (p->aIDF[idx] * nHit * (k1+1.0)) /
            (nHit + k1 * (1.0 - B + B * sz / p->aAvg[iPrev]));








          score = score + bm25;
          nHit = 0;
        }
        if( bDone ) break;
        nHit++;
        iPrev = iCol;
      }
    }



    if( rc==SQLITE_OK ){
      if( bDebug ){
        sqlite3_result_text(pCtx, (const char*)debug.p, -1, SQLITE_TRANSIENT);
      }else{
        sqlite3_result_double(pCtx, score);
      }
    }
    sqlite3_free(debug.p);
  }

  if( rc!=SQLITE_OK ){

    sqlite3_result_error_code(pCtx, rc);
  }
}

int sqlite3Fts5AuxInit(fts5_api *pApi){
  struct Builtin {
    const char *zFunc;            /* Function name (nul-terminated) */
    void *pUserData;              /* User-data pointer */
    fts5_extension_function xFunc;/* Callback function */
    void (*xDestroy)(void*);      /* Destructor function */
  } aBuiltin [] = {
    { "bm25debug", (void*)1, fts5Bm25Function,    0 },
    { "snippet",   0, fts5SnippetFunction, 0 },
    { "highlight", 0, fts5HighlightFunction, 0 },
    { "bm25",      0, fts5Bm25Function,    0 },
  };

  int rc = SQLITE_OK;             /* Return code */
  int i;                          /* To iterate through builtin functions */

  for(i=0; rc==SQLITE_OK && i<sizeof(aBuiltin)/sizeof(aBuiltin[0]); i++){
    rc = pApi->xCreateFunction(pApi,
        aBuiltin[i].zFunc,
        aBuiltin[i].pUserData,

/*************************************************************************
** Start of highlight() implementation.
*/
typedef struct HighlightContext HighlightContext;
struct HighlightContext {
  CInstIter iter;                 /* Coalesced Instance Iterator */
  int iRangeStart;                /* First token to include */
  int iRangeEnd;                  /* If non-zero, last token to include */
  const char *zOpen;              /* Opening highlight */
  const char *zClose;             /* Closing highlight */
  const char *zIn;                /* Input text */
  int nIn;                        /* Size of input text in bytes */
  int iOff;                       /* Current offset within zIn[] */
  char *zOut;                     /* Output value */
};
................................................................................
  int iPos                        /* Position offset of token */
){
  HighlightContext *p = (HighlightContext*)pContext;
  int rc = SQLITE_OK;

  if( p->iRangeEnd>0 ){
    if( iPos<p->iRangeStart || iPos>p->iRangeEnd ) return SQLITE_OK;
    if( p->iRangeStart && iPos==p->iRangeStart ) p->iOff = iStartOff;
  }

  if( iPos==p->iter.iStart ){
    fts5HighlightAppend(&rc, p, &p->zIn[p->iOff], iStartOff - p->iOff);
    fts5HighlightAppend(&rc, p, p->zOpen, -1);
    p->iOff = iStartOff;
  }
................................................................................
    sqlite3_result_text(pCtx, (const char*)ctx.zOut, -1, SQLITE_TRANSIENT);
  }else{
    sqlite3_result_error_code(pCtx, rc);
  }
  sqlite3_free(ctx.zOut);
}
/*
** End of highlight() implementation.
**************************************************************************/


/*
** Implementation of snippet() function.
*/
static void fts5SnippetFunction(
  const Fts5ExtensionApi *pApi,   /* API offered by current FTS version */
  Fts5Context *pFts,              /* First arg to pass to pApi functions */
  sqlite3_context *pCtx,          /* Context for returning result/error */
  int nVal,                       /* Number of values in apVal[] array */
  sqlite3_value **apVal           /* Array of trailing arguments */
){
................................................................................
  int nToken;                     /* 5th argument to snippet() */
  int nInst;                      /* Number of instance matches this row */
  int i;                          /* Used to iterate through instances */
  int nPhrase;                    /* Number of phrases in query */
  unsigned char *aSeen;           /* Array of "seen instance" flags */
  int iBestCol;                   /* Column containing best snippet */
  int iBestStart = 0;             /* First token of best snippet */
  int iBestLast;                  /* Last token of best snippet */
  int nBestScore = 0;             /* Score of best snippet */
  int nColSize;                   /* Total size of iBestCol in tokens */

  if( nVal!=5 ){
    const char *zErr = "wrong number of arguments to function snippet()";
    sqlite3_result_error(pCtx, zErr, -1);
    return;
  }

  memset(&ctx, 0, sizeof(HighlightContext));


  iCol = sqlite3_value_int(apVal[0]);
  rc = pApi->xColumnText(pFts, iCol, &ctx.zIn, &ctx.nIn);
  ctx.zOpen = (const char*)sqlite3_value_text(apVal[1]);
  ctx.zClose = (const char*)sqlite3_value_text(apVal[2]);
  zEllips = (const char*)sqlite3_value_text(apVal[3]);
  nToken = sqlite3_value_int(apVal[4]);
  iBestLast = nToken-1;

  iBestCol = (iCol>=0 ? iCol : 0);
  nPhrase = pApi->xPhraseCount(pFts);
  aSeen = sqlite3_malloc(nPhrase);
  if( aSeen==0 ){
    rc = SQLITE_NOMEM;
  }
................................................................................
  }
  sqlite3_free(ctx.zOut);
  sqlite3_free(aSeen);
}

/************************************************************************/


/*
** The first time the bm25() function is called for a query, an instance
** of the following structure is allocated and populated.

*/
typedef struct Fts5Bm25Data Fts5Bm25Data;
struct Fts5Bm25Data {
  int nPhrase;                    /* Number of phrases in query */
  double avgdl;                   /* Average number of tokens in each row */
  double *aIDF;                   /* IDF for each phrase */
  double *aFreq;                  /* Array used to calculate phrase freq. */
};

/*
** Callback used by fts5Bm25GetData() to count the number of rows in the
** table matched by each individual phrase within the query.
*/
static int fts5CountCb(
  const Fts5ExtensionApi *pApi, 
  Fts5Context *pFts,
  void *pUserData                 /* Pointer to sqlite3_int64 variable */
){

  sqlite3_int64 *pn = (sqlite3_int64*)pUserData;
  (*pn)++;










  return SQLITE_OK;
}

/*



** Set *ppData to point to the Fts5Bm25Data object for the current query. 
** If the object has not already been allocated, allocate and populate it
** now.










*/











































static int fts5Bm25GetData(
  const Fts5ExtensionApi *pApi, 
  Fts5Context *pFts,

  Fts5Bm25Data **ppData           /* OUT: bm25-data object for this query */
){

  int rc = SQLITE_OK;             /* Return code */
  Fts5Bm25Data *p;                /* Object to return */

  p = pApi->xGetAuxdata(pFts, 0);
  if( p==0 ){



    int nPhrase;                  /* Number of phrases in query */
    sqlite3_int64 nRow;           /* Number of rows in table */
    sqlite3_int64 nToken;         /* Number of tokens in table */
    int nByte;                    /* Bytes of space to allocate */
    int i;

    /* Allocate the Fts5Bm25Data object */
    nPhrase = pApi->xPhraseCount(pFts);

    nByte = sizeof(Fts5Bm25Data) + nPhrase*2*sizeof(double);



    p = (Fts5Bm25Data*)sqlite3_malloc(nByte);
    if( p==0 ){
      rc = SQLITE_NOMEM;
    }else{
      memset(p, 0, nByte);
      p->nPhrase = nPhrase;
      p->aIDF = (double*)&p[1];
      p->aFreq = &p->aIDF[nPhrase];

    }


    /* Calculate the average document length for this FTS5 table */
    if( rc==SQLITE_OK ) rc = pApi->xRowCount(pFts, &nRow);
    if( rc==SQLITE_OK ) rc = pApi->xColumnTotalSize(pFts, -1, &nToken);
    if( rc==SQLITE_OK ) p->avgdl = (double)nToken  / (double)nRow;



    /* Calculate an IDF for each phrase in the query */
    for(i=0; rc==SQLITE_OK && i<nPhrase; i++){
      sqlite3_int64 nHit = 0;
      rc = pApi->xQueryPhrase(pFts, i, (void*)&nHit, fts5CountCb);




      if( rc==SQLITE_OK ){




        /* Calculate the IDF (Inverse Document Frequency) for phrase i.
        ** This is done using the standard BM25 formula as found on wikipedia:

        **
        **   IDF = log( (N - nHit + 0.5) / (nHit + 0.5) )
        **
        ** where "N" is the total number of documents in the set and nHit
        ** is the number that contain at least one instance of the phrase
        ** under consideration.
        **
        ** The problem with this is that if (N < 2*nHit), the IDF is 
        ** negative. Which is undesirable. So the mimimum allowable IDF is
        ** (1e-6) - roughly the same as a term that appears in just over
        ** half of set of 5,000,000 documents.  */
        double idf = log( (nRow - nHit + 0.5) / (nHit + 0.5) );
        if( idf<=0.0 ) idf = 1e-6;



        p->aIDF[i] = idf;
      }
    }

    if( rc!=SQLITE_OK ){
      sqlite3_free(p);

    }else{
      rc = pApi->xSetAuxdata(pFts, p, sqlite3_free);
    }
    if( rc!=SQLITE_OK ) p = 0;


  }


  *ppData = p;
  return rc;
}












































/*
** Implementation of bm25() function.
*/
static void fts5Bm25Function(
  const Fts5ExtensionApi *pApi,   /* API offered by current FTS version */
  Fts5Context *pFts,              /* First arg to pass to pApi functions */
  sqlite3_context *pCtx,          /* Context for returning result/error */
  int nVal,                       /* Number of values in apVal[] array */
  sqlite3_value **apVal           /* Array of trailing arguments */
){
  const double k1 = 1.2;          /* Constant "k1" from BM25 formula */

  const double b = 0.75;          /* Constant "b" from BM25 formula */
  int rc = SQLITE_OK;             /* Error code */

  double score = 0.0;             /* SQL function return value */
  Fts5Bm25Data *pData;            /* Values allocated/calculated once only */
  int i;                          /* Iterator variable */
  int nInst;                      /* Value returned by xInstCount() */
  double D;                       /* Total number of tokens in row */
  double *aFreq;                  /* Array of phrase freq. for current row */

  /* Calculate the phrase frequency (symbol "f(qi,D)" in the documentation)
  ** for each phrase in the query for the current row. */
  rc = fts5Bm25GetData(pApi, pFts, &pData);

  if( rc==SQLITE_OK ){





    aFreq = pData->aFreq;
    memset(aFreq, 0, sizeof(double) * pData->nPhrase);
    rc = pApi->xInstCount(pFts, &nInst);
  }
  for(i=0; rc==SQLITE_OK && i<nInst; i++){
    int ip; int ic; int io;

    rc = pApi->xInst(pFts, i, &ip, &ic, &io);
    if( rc==SQLITE_OK ){
      double w = (nVal > ic) ? sqlite3_value_double(apVal[ic]) : 1.0;
      aFreq[ip] += w;
    }



  }







  /* Figure out the total size of the current row in tokens. */
  if( rc==SQLITE_OK ){



    int nTok;


    rc = pApi->xColumnSize(pFts, -1, &nTok);
    D = (double)nTok;
  }



  /* Determine the BM25 score for the current row. */
  for(i=0; rc==SQLITE_OK && i<pData->nPhrase; i++){
    score += pData->aIDF[i] * (
      ( aFreq[i] * (k1 + 1.0) ) / 
      ( aFreq[i] + k1 * (1 - b + b * D / pData->avgdl) )
    );
  }


  






  /* If no error has occurred, return the calculated score. Otherwise,
  ** throw an SQL exception.  */
  if( rc==SQLITE_OK ){



    sqlite3_result_double(pCtx, score);






  }else{
    sqlite3_result_error_code(pCtx, rc);
  }
}

int sqlite3Fts5AuxInit(fts5_api *pApi){
  struct Builtin {
    const char *zFunc;            /* Function name (nul-terminated) */
    void *pUserData;              /* User-data pointer */
    fts5_extension_function xFunc;/* Callback function */
    void (*xDestroy)(void*);      /* Destructor function */
  } aBuiltin [] = {

    { "snippet",   0, fts5SnippetFunction, 0 },
    { "highlight", 0, fts5HighlightFunction, 0 },
    { "bm25",      0, fts5Bm25Function,    0 },
  };

  int rc = SQLITE_OK;             /* Return code */
  int i;                          /* To iterate through builtin functions */

  for(i=0; rc==SQLITE_OK && i<sizeof(aBuiltin)/sizeof(aBuiltin[0]); i++){
    rc = pApi->xCreateFunction(pApi,
        aBuiltin[i].zFunc,
        aBuiltin[i].pUserData,

  }
  return rc;
}

int sqlite3Fts5StorageSize(Fts5Storage *p, int iCol, i64 *pnToken){
  int rc = fts5StorageLoadTotals(p, 0);
  if( rc==SQLITE_OK ){







    *pnToken = p->aTotalSize[iCol];



  }
  return rc;
}

int sqlite3Fts5StorageRowCount(Fts5Storage *p, i64 *pnRow){
  int rc = fts5StorageLoadTotals(p, 0);
  if( rc==SQLITE_OK ){

  }
  return rc;
}

int sqlite3Fts5StorageSize(Fts5Storage *p, int iCol, i64 *pnToken){
  int rc = fts5StorageLoadTotals(p, 0);
  if( rc==SQLITE_OK ){
    *pnToken = 0;
    if( iCol<0 ){
      int i;
      for(i=0; i<p->pConfig->nCol; i++){
        *pnToken += p->aTotalSize[i];
      }
    }else if( iCol<p->pConfig->nCol ){
      *pnToken = p->aTotalSize[iCol];
    }else{
      rc = SQLITE_RANGE;
    }
  }
  return rc;
}

int sqlite3Fts5StorageRowCount(Fts5Storage *p, i64 *pnRow){
  int rc = fts5StorageLoadTotals(p, 0);
  if( rc==SQLITE_OK ){