/* Loop through the elements that will make up the record to figure
  ** out how much space is required for the new record.
  */
  pRec = pLast;
  do{
    assert( memIsValid(pRec) );
    serial_type = sqlite3VdbeSerialType(pRec, file_format, &len);
    if( pRec->flags & MEM_Zero ){
      if( serial_type==0 ){
        /* Values with MEM_Null and MEM_Zero are created by xColumn virtual
        ** table methods that never invoke sqlite3_result_xxxxx() while
        ** computing an unchanging column value in an UPDATE statement.
        ** Give such values a special internal-use-only serial-type of 10
        ** so that they can be passed through to xUpdate and have
        ** a true sqlite3_value_nochange(). */
        assert( pOp->p5==OPFLAG_NOCHNG_MAGIC || CORRUPT_DB );




























































        serial_type = 10;
      }else if( nData ){
        if( sqlite3VdbeMemExpandBlob(pRec) ) goto no_mem;

      }else{
        nZero += pRec->u.nZero;
        len -= pRec->u.nZero;
      }
    }
    nData += len;
    testcase( serial_type==127 );
    testcase( serial_type==128 );
    nHdr += serial_type<=127 ? 1 : sqlite3VarintLen(serial_type);
    pRec->uTemp = serial_type;

    if( pRec==pData0 ) break;
    pRec--;
  }while(1);

  /* EVIDENCE-OF: R-22564-11647 The header begins with a single varint
  ** which determines the total number of bytes in the header. The varint
  ** value is the size of the header in bytes including the size varint

  /* Loop through the elements that will make up the record to figure
  ** out how much space is required for the new record.
  */
  pRec = pLast;
  do{
    assert( memIsValid(pRec) );
    if( pRec->flags & MEM_Null ){
      if( pRec->flags & MEM_Zero ){

        /* Values with MEM_Null and MEM_Zero are created by xColumn virtual
        ** table methods that never invoke sqlite3_result_xxxxx() while
        ** computing an unchanging column value in an UPDATE statement.
        ** Give such values a special internal-use-only serial-type of 10
        ** so that they can be passed through to xUpdate and have
        ** a true sqlite3_value_nochange(). */
        assert( pOp->p5==OPFLAG_NOCHNG_MAGIC || CORRUPT_DB );
        pRec->uTemp = 10;
      }else{
        pRec->uTemp = 0;  /* Serial-type 0 means NULL */
      }
      nHdr++;
    }else if( pRec->flags & (MEM_Int|MEM_IntReal) ){
      /* Figure out whether to use 1, 2, 4, 6 or 8 bytes. */
      i64 i = pRec->u.i;
      u64 u;
      testcase( pRec->flags & MEM_Int );
      testcase( pRec->flags & MEM_IntReal );
      if( i<0 ){
        u = ~i;
      }else{
        u = i;
      }
      nHdr++;
      if( u<=127 ){
        if( (i&1)==i && file_format>=4 ){
          pRec->uTemp = 8+(u32)u;
        }else{
          nData++;
          pRec->uTemp = 1;
        }
      }else if( u<=32767 ){
        nData += 2;
        pRec->uTemp = 2;
      }else if( u<=8388607 ){
        nData += 3;
        pRec->uTemp = 3;
      }else if( u<=2147483647 ){
        nData += 4;
        pRec->uTemp = 4;
      }else if( u<=140737488355327LL ){
        nData += 6;
        pRec->uTemp = 5;
      }else{
        nData += 8;
        if( pRec->flags & MEM_IntReal ){
          /* If the value is IntReal and is going to take up 8 bytes to store
          ** as an integer, then we might as well make it an 8-byte floating
          ** point value */
          pRec->u.r = (double)pRec->u.i;
          pRec->flags &= ~MEM_IntReal;
          pRec->flags |= MEM_Real;
          pRec->uTemp = 7;
        }else{
          pRec->uTemp = 6;
        }
      }
    }else if( pRec->flags & MEM_Real ){
      nHdr++;
      nData += 8;
      pRec->uTemp = 7;
    }else{
      assert( db->mallocFailed || pRec->flags&(MEM_Str|MEM_Blob) );
      assert( pRec->n>=0 );
      len = (u32)pRec->n;
      serial_type = (len*2) + 12 + ((pRec->flags & MEM_Str)!=0);
      if( pRec->flags & MEM_Zero ){
        serial_type += pRec->u.nZero*2;
        if( nData ){
          if( sqlite3VdbeMemExpandBlob(pRec) ) goto no_mem;
          len += pRec->u.nZero;
        }else{
          nZero += pRec->u.nZero;

        }
      }
      nData += len;


      nHdr += sqlite3VarintLen(serial_type);
      pRec->uTemp = serial_type;
    }
    if( pRec==pData0 ) break;
    pRec--;
  }while(1);

  /* EVIDENCE-OF: R-22564-11647 The header begins with a single varint
  ** which determines the total number of bytes in the header. The varint
  ** value is the size of the header in bytes including the size varint

void sqlite3VdbeError(Vdbe*, const char *, ...);
void sqlite3VdbeFreeCursor(Vdbe *, VdbeCursor*);
void sqliteVdbePopStack(Vdbe*,int);
int sqlite3VdbeCursorMoveto(VdbeCursor**, int*);
int sqlite3VdbeCursorRestore(VdbeCursor*);
u32 sqlite3VdbeSerialTypeLen(u32);
u8 sqlite3VdbeOneByteSerialTypeLen(u8);

u32 sqlite3VdbeSerialType(Mem*, int, u32*);

u32 sqlite3VdbeSerialPut(unsigned char*, Mem*, u32);
u32 sqlite3VdbeSerialGet(const unsigned char*, u32, Mem*);
void sqlite3VdbeDeleteAuxData(sqlite3*, AuxData**, int, int);

int sqlite2BtreeKeyCompare(BtCursor *, const void *, int, int, int *);
int sqlite3VdbeIdxKeyCompare(sqlite3*,VdbeCursor*,UnpackedRecord*,int*);
int sqlite3VdbeIdxRowid(sqlite3*, BtCursor*, i64*);

void sqlite3VdbeError(Vdbe*, const char *, ...);
void sqlite3VdbeFreeCursor(Vdbe *, VdbeCursor*);
void sqliteVdbePopStack(Vdbe*,int);
int sqlite3VdbeCursorMoveto(VdbeCursor**, int*);
int sqlite3VdbeCursorRestore(VdbeCursor*);
u32 sqlite3VdbeSerialTypeLen(u32);
u8 sqlite3VdbeOneByteSerialTypeLen(u8);
#ifdef SQLITE_ENABLE_STAT3_OR_STAT4
u32 sqlite3VdbeSerialType(Mem*, int, u32*);
#endif
u32 sqlite3VdbeSerialPut(unsigned char*, Mem*, u32);
u32 sqlite3VdbeSerialGet(const unsigned char*, u32, Mem*);
void sqlite3VdbeDeleteAuxData(sqlite3*, AuxData**, int, int);

int sqlite2BtreeKeyCompare(BtCursor *, const void *, int, int, int *);
int sqlite3VdbeIdxKeyCompare(sqlite3*,VdbeCursor*,UnpackedRecord*,int*);
int sqlite3VdbeIdxRowid(sqlite3*, BtCursor*, i64*);

**    N>=12 and even       (N-12)/2        BLOB
**    N>=13 and odd        (N-13)/2        text
**
** The 8 and 9 types were added in 3.3.0, file format 4.  Prior versions
** of SQLite will not understand those serial types.
*/


/*
** Return the serial-type for the value stored in pMem.
**
** This routine might convert a large MEM_IntReal value into MEM_Real.





*/
u32 sqlite3VdbeSerialType(Mem *pMem, int file_format, u32 *pLen){
  int flags = pMem->flags;
  u32 n;

  assert( pLen!=0 );
  if( flags&MEM_Null ){
................................................................................
  n = (u32)pMem->n;
  if( flags & MEM_Zero ){
    n += pMem->u.nZero;
  }
  *pLen = n;
  return ((n*2) + 12 + ((flags&MEM_Str)!=0));
}


/*
** The sizes for serial types less than 128
*/
static const u8 sqlite3SmallTypeSizes[] = {
        /*  0   1   2   3   4   5   6   7   8   9 */   
/*   0 */   0,  1,  2,  3,  4,  6,  8,  8,  0,  0,

**    N>=12 and even       (N-12)/2        BLOB
**    N>=13 and odd        (N-13)/2        text
**
** The 8 and 9 types were added in 3.3.0, file format 4.  Prior versions
** of SQLite will not understand those serial types.
*/

#ifdef SQLITE_ENABLE_STAT3_OR_STAT4
/*
** Return the serial-type for the value stored in pMem.
**
** This routine might convert a large MEM_IntReal value into MEM_Real.
**
** 2019-07-11:  The primary user of this subroutine was the OP_MakeRecord
** opcode in the byte-code engine.  But by moving this routine in-line, we
** can omit some redundant tests and make that opcode a lot faster.  So
** this routine is now only used by the STAT3/4 logic.
*/
u32 sqlite3VdbeSerialType(Mem *pMem, int file_format, u32 *pLen){
  int flags = pMem->flags;
  u32 n;

  assert( pLen!=0 );
  if( flags&MEM_Null ){
................................................................................
  n = (u32)pMem->n;
  if( flags & MEM_Zero ){
    n += pMem->u.nZero;
  }
  *pLen = n;
  return ((n*2) + 12 + ((flags&MEM_Str)!=0));
}
#endif /* SQLITE_ENABLE_STAT3_OR_STAT4 */

/*
** The sizes for serial types less than 128
*/
static const u8 sqlite3SmallTypeSizes[] = {
        /*  0   1   2   3   4   5   6   7   8   9 */   
/*   0 */   0,  1,  2,  3,  4,  6,  8,  8,  0,  0,