Index: src/alter.c
==================================================================
--- src/alter.c
+++ src/alter.c
@@ -296,18 +296,10 @@
   if( sqlite3AuthCheck(pParse, SQLITE_ALTER_TABLE, zDb, pTab->zName, 0) ){
     return;
   }
 #endif
 
-  /* If the default value for the new column was specified with a 
-  ** literal NULL, then set pDflt to 0. This simplifies checking
-  ** for an SQL NULL default below.
-  */
-  assert( pDflt==0 || pDflt->op==TK_SPAN );
-  if( pDflt && pDflt->pLeft->op==TK_NULL ){
-    pDflt = 0;
-  }
 
   /* Check that the new column is not specified as PRIMARY KEY or UNIQUE.
   ** If there is a NOT NULL constraint, then the default value for the
   ** column must not be NULL.
   */
@@ -317,39 +309,53 @@
   }
   if( pNew->pIndex ){
     sqlite3ErrorMsg(pParse, "Cannot add a UNIQUE column");
     return;
   }
-  if( (db->flags&SQLITE_ForeignKeys) && pNew->pFKey && pDflt ){
-    sqlite3ErrorMsg(pParse, 
-        "Cannot add a REFERENCES column with non-NULL default value");
-    return;
-  }
-  if( pCol->notNull && !pDflt ){
-    sqlite3ErrorMsg(pParse, 
-        "Cannot add a NOT NULL column with default value NULL");
-    return;
-  }
-
-  /* Ensure the default expression is something that sqlite3ValueFromExpr()
-  ** can handle (i.e. not CURRENT_TIME etc.)
-  */
-  if( pDflt ){
-    sqlite3_value *pVal = 0;
-    int rc;
-    rc = sqlite3ValueFromExpr(db, pDflt, SQLITE_UTF8, SQLITE_AFF_BLOB, &pVal);
-    assert( rc==SQLITE_OK || rc==SQLITE_NOMEM );
-    if( rc!=SQLITE_OK ){
-      assert( db->mallocFailed == 1 );
-      return;
-    }
-    if( !pVal ){
-      sqlite3ErrorMsg(pParse, "Cannot add a column with non-constant default");
-      return;
-    }
-    sqlite3ValueFree(pVal);
-  }
+  if( (pCol->colFlags & COLFLAG_GENERATED)==0 ){
+    /* If the default value for the new column was specified with a 
+    ** literal NULL, then set pDflt to 0. This simplifies checking
+    ** for an SQL NULL default below.
+    */
+    assert( pDflt==0 || pDflt->op==TK_SPAN );
+    if( pDflt && pDflt->pLeft->op==TK_NULL ){
+      pDflt = 0;
+    }
+    if( (db->flags&SQLITE_ForeignKeys) && pNew->pFKey && pDflt ){
+      sqlite3ErrorMsg(pParse, 
+          "Cannot add a REFERENCES column with non-NULL default value");
+      return;
+    }
+    if( pCol->notNull && !pDflt ){
+      sqlite3ErrorMsg(pParse, 
+          "Cannot add a NOT NULL column with default value NULL");
+      return;
+    }
+
+    /* Ensure the default expression is something that sqlite3ValueFromExpr()
+    ** can handle (i.e. not CURRENT_TIME etc.)
+    */
+    if( pDflt ){
+      sqlite3_value *pVal = 0;
+      int rc;
+      rc = sqlite3ValueFromExpr(db, pDflt, SQLITE_UTF8, SQLITE_AFF_BLOB, &pVal);
+      assert( rc==SQLITE_OK || rc==SQLITE_NOMEM );
+      if( rc!=SQLITE_OK ){
+        assert( db->mallocFailed == 1 );
+        return;
+      }
+      if( !pVal ){
+        sqlite3ErrorMsg(pParse,"Cannot add a column with non-constant default");
+        return;
+      }
+      sqlite3ValueFree(pVal);
+    }
+  }else if( pCol->colFlags & COLFLAG_STORED ){
+    sqlite3ErrorMsg(pParse, "cannot add a STORED column");
+    return;
+  }
+
 
   /* Modify the CREATE TABLE statement. */
   zCol = sqlite3DbStrNDup(db, (char*)pColDef->z, pColDef->n);
   if( zCol ){
     char *zEnd = &zCol[pColDef->n-1];
@@ -1329,10 +1335,15 @@
         }
         for(pIdx=sParse.pNewIndex; pIdx; pIdx=pIdx->pNext){
           sqlite3WalkExprList(&sWalker, pIdx->aColExpr);
         }
       }
+#ifndef SQLITE_OMIT_GENERATED_COLUMNS
+      for(i=0; i<sParse.pNewTable->nCol; i++){
+        sqlite3WalkExpr(&sWalker, sParse.pNewTable->aCol[i].pDflt);
+      }
+#endif
 
       for(pFKey=sParse.pNewTable->pFKey; pFKey; pFKey=pFKey->pNextFrom){
         for(i=0; i<pFKey->nCol; i++){
           if( bFKOnly==0 && pFKey->aCol[i].iFrom==iCol ){
             renameTokenFind(&sParse, &sCtx, (void*)&pFKey->aCol[i]);

Index: src/analyze.c
==================================================================
--- src/analyze.c
+++ src/analyze.c
@@ -1180,11 +1180,11 @@
     }else{
       Index *pPk = sqlite3PrimaryKeyIndex(pIdx->pTable);
       int j, k, regKey;
       regKey = sqlite3GetTempRange(pParse, pPk->nKeyCol);
       for(j=0; j<pPk->nKeyCol; j++){
-        k = sqlite3ColumnOfIndex(pIdx, pPk->aiColumn[j]);
+        k = sqlite3TableColumnToIndex(pIdx, pPk->aiColumn[j]);
         assert( k>=0 && k<pIdx->nColumn );
         sqlite3VdbeAddOp3(v, OP_Column, iIdxCur, k, regKey+j);
         VdbeComment((v, "%s", pTab->aCol[pPk->aiColumn[j]].zName));
       }
       sqlite3VdbeAddOp3(v, OP_MakeRecord, regKey, pPk->nKeyCol, regRowid);

Index: src/build.c
==================================================================
--- src/build.c
+++ src/build.c
@@ -875,20 +875,98 @@
   for(p=pTab->pIndex; p && !IsPrimaryKeyIndex(p); p=p->pNext){}
   return p;
 }
 
 /*
-** Return the column of index pIdx that corresponds to table
-** column iCol.  Return -1 if not found.
+** Convert an table column number into a index column number.  That is,
+** for the column iCol in the table (as defined by the CREATE TABLE statement)
+** find the (first) offset of that column in index pIdx.  Or return -1
+** if column iCol is not used in index pIdx.
 */
-i16 sqlite3ColumnOfIndex(Index *pIdx, i16 iCol){
+i16 sqlite3TableColumnToIndex(Index *pIdx, i16 iCol){
   int i;
   for(i=0; i<pIdx->nColumn; i++){
     if( iCol==pIdx->aiColumn[i] ) return i;
   }
   return -1;
 }
+
+#ifndef SQLITE_OMIT_GENERATED_COLUMNS
+/* Convert a storage column number into a table column number.
+**
+** The storage column number (0,1,2,....) is the index of the value
+** as it appears in the record on disk.  The true column number
+** is the index (0,1,2,...) of the column in the CREATE TABLE statement.
+**
+** The storage column number is less than the table column number if
+** and only there are VIRTUAL columns to the left.
+**
+** If SQLITE_OMIT_GENERATED_COLUMNS, this routine is a no-op macro.
+*/
+i16 sqlite3StorageColumnToTable(Table *pTab, i16 iCol){
+  if( pTab->tabFlags & TF_HasVirtual ){
+    int i;
+    for(i=0; i<=iCol; i++){
+      if( pTab->aCol[i].colFlags & COLFLAG_VIRTUAL ) iCol++;
+    }
+  }
+  return iCol;
+}
+#endif
+
+#ifndef SQLITE_OMIT_GENERATED_COLUMNS
+/* Convert a table column number into a storage column number.
+**
+** The storage column number (0,1,2,....) is the index of the value
+** as it appears in the record on disk.  Or, if the input column is
+** the N-th virtual column (zero-based) then the storage number is
+** the number of non-virtual columns in the table plus N.  
+**
+** The true column number is the index (0,1,2,...) of the column in
+** the CREATE TABLE statement.
+**
+** If the input column is a VIRTUAL column, then it should not appear
+** in storage.  But the value sometimes is cached in registers that
+** follow the range of registers used to construct storage.  This
+** avoids computing the same VIRTUAL column multiple times, and provides
+** values for use by OP_Param opcodes in triggers.  Hence, if the
+** input column is a VIRTUAL table, put it after all the other columns.
+**
+** In the following, N means "normal column", S means STORED, and
+** V means VIRTUAL.  Suppose the CREATE TABLE has columns like this:
+**
+**        CREATE TABLE ex(N,S,V,N,S,V,N,S,V);
+**                     -- 0 1 2 3 4 5 6 7 8
+**
+** Then the mapping from this function is as follows:
+**
+**    INPUTS:     0 1 2 3 4 5 6 7 8
+**    OUTPUTS:    0 1 6 2 3 7 4 5 8
+**
+** So, in other words, this routine shifts all the virtual columns to
+** the end.
+**
+** If SQLITE_OMIT_GENERATED_COLUMNS then there are no virtual columns and
+** this routine is a no-op macro.
+*/
+i16 sqlite3TableColumnToStorage(Table *pTab, i16 iCol){
+  int i;
+  i16 n;
+  assert( iCol<pTab->nCol );
+  if( (pTab->tabFlags & TF_HasVirtual)==0 ) return iCol;
+  for(i=0, n=0; i<iCol; i++){
+    if( (pTab->aCol[i].colFlags & COLFLAG_VIRTUAL)==0 ) n++;
+  }
+  if( pTab->aCol[i].colFlags & COLFLAG_VIRTUAL ){
+    /* iCol is a virtual column itself */
+    return pTab->nNVCol + i - n;
+  }else{
+    /* iCol is a normal or stored column */
+    return n;
+  }
+}
+#endif
 
 /*
 ** Begin constructing a new table representation in memory.  This is
 ** the first of several action routines that get called in response
 ** to a CREATE TABLE statement.  In particular, this routine is called
@@ -1176,10 +1254,11 @@
     sqlite3Dequote(zType);
     pCol->affinity = sqlite3AffinityType(zType, pCol);
     pCol->colFlags |= COLFLAG_HASTYPE;
   }
   p->nCol++;
+  p->nNVCol++;
   pParse->constraintName.n = 0;
 }
 
 /*
 ** This routine is called by the parser while in the middle of
@@ -1324,10 +1403,16 @@
   if( p!=0 ){
     pCol = &(p->aCol[p->nCol-1]);
     if( !sqlite3ExprIsConstantOrFunction(pExpr, db->init.busy) ){
       sqlite3ErrorMsg(pParse, "default value of column [%s] is not constant",
           pCol->zName);
+#ifndef SQLITE_OMIT_GENERATED_COLUMNS
+    }else if( pCol->colFlags & COLFLAG_GENERATED ){
+      testcase( pCol->colFlags & COLFLAG_VIRTUAL );
+      testcase( pCol->colFlags & COLFLAG_STORED );
+      sqlite3ErrorMsg(pParse, "cannot use DEFAULT on a generated column");
+#endif
     }else{
       /* A copy of pExpr is used instead of the original, as pExpr contains
       ** tokens that point to volatile memory.
       */
       Expr x;
@@ -1368,10 +1453,25 @@
     p->op = TK_ID;
   }else if( p->op==TK_COLLATE && p->pLeft->op==TK_STRING ){
     p->pLeft->op = TK_ID;
   }
 }
+
+/*
+** Tag the given column as being part of the PRIMARY KEY
+*/
+static void makeColumnPartOfPrimaryKey(Parse *pParse, Column *pCol){
+  pCol->colFlags |= COLFLAG_PRIMKEY;
+#ifndef SQLITE_OMIT_GENERATED_COLUMNS
+  if( pCol->colFlags & COLFLAG_GENERATED ){
+    testcase( pCol->colFlags & COLFLAG_VIRTUAL );
+    testcase( pCol->colFlags & COLFLAG_STORED );
+    sqlite3ErrorMsg(pParse,
+      "generated columns cannot be part of the PRIMARY KEY");
+  }
+#endif          
+}
 
 /*
 ** Designate the PRIMARY KEY for the table.  pList is a list of names 
 ** of columns that form the primary key.  If pList is NULL, then the
 ** most recently added column of the table is the primary key.
@@ -1408,11 +1508,11 @@
   }
   pTab->tabFlags |= TF_HasPrimaryKey;
   if( pList==0 ){
     iCol = pTab->nCol - 1;
     pCol = &pTab->aCol[iCol];
-    pCol->colFlags |= COLFLAG_PRIMKEY;
+    makeColumnPartOfPrimaryKey(pParse, pCol);
     nTerm = 1;
   }else{
     nTerm = pList->nExpr;
     for(i=0; i<nTerm; i++){
       Expr *pCExpr = sqlite3ExprSkipCollate(pList->a[i].pExpr);
@@ -1421,11 +1521,11 @@
       if( pCExpr->op==TK_ID ){
         const char *zCName = pCExpr->u.zToken;
         for(iCol=0; iCol<pTab->nCol; iCol++){
           if( sqlite3StrICmp(zCName, pTab->aCol[iCol].zName)==0 ){
             pCol = &pTab->aCol[iCol];
-            pCol->colFlags |= COLFLAG_PRIMKEY;
+            makeColumnPartOfPrimaryKey(pParse, pCol);
             break;
           }
         }
       }
     }
@@ -1517,10 +1617,56 @@
     }
   }else{
     sqlite3DbFree(db, zColl);
   }
 }
+
+/* Change the most recently parsed column to be a GENERATED ALWAYS AS
+** column.
+*/
+void sqlite3AddGenerated(Parse *pParse, Expr *pExpr, Token *pType){
+#ifndef SQLITE_OMIT_GENERATED_COLUMNS
+  u8 eType = COLFLAG_VIRTUAL;
+  Table *pTab = pParse->pNewTable;
+  Column *pCol;
+  if( NEVER(pTab==0) ) goto generated_done;
+  pCol = &(pTab->aCol[pTab->nCol-1]);
+  if( IN_DECLARE_VTAB ){
+    sqlite3ErrorMsg(pParse, "virtual tables cannot use computed columns");
+    goto generated_done;
+  }
+  if( pCol->pDflt ) goto generated_error;
+  if( pType ){
+    if( pType->n==7 && sqlite3StrNICmp("virtual",pType->z,7)==0 ){
+      /* no-op */
+    }else if( pType->n==6 && sqlite3StrNICmp("stored",pType->z,6)==0 ){
+      eType = COLFLAG_STORED;
+    }else{
+      goto generated_error;
+    }
+  }
+  if( eType==COLFLAG_VIRTUAL ) pTab->nNVCol--;
+  pCol->colFlags |= eType;
+  assert( TF_HasVirtual==COLFLAG_VIRTUAL );
+  assert( TF_HasStored==COLFLAG_STORED );
+  pTab->tabFlags |= eType;
+  pCol->pDflt = pExpr;
+  pExpr = 0;
+  goto generated_done;
+
+generated_error:
+  sqlite3ErrorMsg(pParse, "error in generated column \"%s\"",
+                  pCol->zName);
+generated_done:
+  sqlite3ExprDelete(pParse->db, pExpr);
+#else
+  /* Throw and error for the GENERATED ALWAYS AS clause if the
+  ** SQLITE_OMIT_GENERATED_COLUMNS compile-time option is used. */
+  sqlite3ErrorMsg(pParse, "generated columns not supported");
+  sqlite3ExprDelete(pParse->db, pExpr);
+#endif
+}
 
 /*
 ** Generate code that will increment the schema cookie.
 **
 ** The schema cookie is used to determine when the schema for the
@@ -1774,20 +1920,29 @@
 **
 ** colNotIdxed is a bitmask that has a 0 bit representing each indexed
 ** columns that are within the first 63 columns of the table.  The
 ** high-order bit of colNotIdxed is always 1.  All unindexed columns
 ** of the table have a 1.
+**
+** 2019-10-24:  For the purpose of this computation, virtual columns are
+** not considered to be covered by the index, even if they are in the
+** index, because we do not trust the logic in whereIndexExprTrans() to be
+** able to find all instances of a reference to the indexed table column
+** and convert them into references to the index.  Hence we always want
+** the actual table at hand in order to recompute the virtual column, if
+** necessary.
 **
 ** The colNotIdxed mask is AND-ed with the SrcList.a[].colUsed mask
 ** to determine if the index is covering index.
 */
 static void recomputeColumnsNotIndexed(Index *pIdx){
   Bitmask m = 0;
   int j;
+  Table *pTab = pIdx->pTable;
   for(j=pIdx->nColumn-1; j>=0; j--){
     int x = pIdx->aiColumn[j];
-    if( x>=0 ){
+    if( x>=0 && (pTab->aCol[x].colFlags & COLFLAG_VIRTUAL)==0 ){
       testcase( x==BMS-1 );
       testcase( x==BMS-2 );
       if( x<BMS-1 ) m |= MASKBIT(x);
     }
   }
@@ -1941,23 +2096,26 @@
 
   /* Add all table columns to the PRIMARY KEY index
   */
   nExtra = 0;
   for(i=0; i<pTab->nCol; i++){
-    if( !hasColumn(pPk->aiColumn, nPk, i) ) nExtra++;
+    if( !hasColumn(pPk->aiColumn, nPk, i)
+     && (pTab->aCol[i].colFlags & COLFLAG_VIRTUAL)==0 ) nExtra++;
   }
   if( resizeIndexObject(db, pPk, nPk+nExtra) ) return;
   for(i=0, j=nPk; i<pTab->nCol; i++){
-    if( !hasColumn(pPk->aiColumn, j, i) ){
+    if( !hasColumn(pPk->aiColumn, j, i)
+     && (pTab->aCol[i].colFlags & COLFLAG_VIRTUAL)==0
+    ){
       assert( j<pPk->nColumn );
       pPk->aiColumn[j] = i;
       pPk->azColl[j] = sqlite3StrBINARY;
       j++;
     }
   }
   assert( pPk->nColumn==j );
-  assert( pTab->nCol<=j );
+  assert( pTab->nNVCol<=j );
   recomputeColumnsNotIndexed(pPk);
 }
 
 #ifndef SQLITE_OMIT_VIRTUALTABLE
 /*
@@ -2062,25 +2220,40 @@
           "AUTOINCREMENT not allowed on WITHOUT ROWID tables");
       return;
     }
     if( (p->tabFlags & TF_HasPrimaryKey)==0 ){
       sqlite3ErrorMsg(pParse, "PRIMARY KEY missing on table %s", p->zName);
-    }else{
-      p->tabFlags |= TF_WithoutRowid | TF_NoVisibleRowid;
-      convertToWithoutRowidTable(pParse, p);
+      return;
     }
+    p->tabFlags |= TF_WithoutRowid | TF_NoVisibleRowid;
+    convertToWithoutRowidTable(pParse, p);
   }
-
   iDb = sqlite3SchemaToIndex(db, p->pSchema);
 
 #ifndef SQLITE_OMIT_CHECK
   /* Resolve names in all CHECK constraint expressions.
   */
   if( p->pCheck ){
     sqlite3ResolveSelfReference(pParse, p, NC_IsCheck, 0, p->pCheck);
   }
 #endif /* !defined(SQLITE_OMIT_CHECK) */
+#ifndef SQLITE_OMIT_GENERATED_COLUMNS
+  if( p->tabFlags & TF_HasGenerated ){
+    int ii;
+    testcase( p->tabFlags & TF_HasVirtual );
+    testcase( p->tabFlags & TF_HasStored );
+    for(ii=0; ii<p->nCol; ii++){
+      u32 colFlags = p->aCol[ii].colFlags;
+      if( (colFlags & COLFLAG_GENERATED)!=0 ){
+        testcase( colFlags & COLFLAG_VIRTUAL );
+        testcase( colFlags & COLFLAG_STORED );
+        sqlite3ResolveSelfReference(pParse, p, NC_GenCol, 
+                                    p->aCol[ii].pDflt, 0);
+      }
+    }
+  }
+#endif
 
   /* Estimate the average row size for the table and for all implied indices */
   estimateTableWidth(p);
   for(pIdx=p->pIndex; pIdx; pIdx=pIdx->pNext){
     estimateIndexWidth(pIdx);
@@ -2153,11 +2326,11 @@
       sqlite3VdbeAddOp3(v, OP_InitCoroutine, regYield, 0, addrTop);
       if( pParse->nErr ) return;
       pSelTab = sqlite3ResultSetOfSelect(pParse, pSelect, SQLITE_AFF_BLOB);
       if( pSelTab==0 ) return;
       assert( p->aCol==0 );
-      p->nCol = pSelTab->nCol;
+      p->nCol = p->nNVCol = pSelTab->nCol;
       p->aCol = pSelTab->aCol;
       pSelTab->nCol = 0;
       pSelTab->aCol = 0;
       sqlite3DeleteTable(db, pSelTab);
       sqlite3SelectDestInit(&dest, SRT_Coroutine, regYield);
@@ -2441,11 +2614,11 @@
     }else if( pSelTab ){
       /* CREATE VIEW name AS...  without an argument list.  Construct
       ** the column names from the SELECT statement that defines the view.
       */
       assert( pTable->aCol==0 );
-      pTable->nCol = pSelTab->nCol;
+      pTable->nCol = pTable->nNVCol = pSelTab->nCol;
       pTable->aCol = pSelTab->aCol;
       pSelTab->nCol = 0;
       pSelTab->aCol = 0;
       assert( sqlite3SchemaMutexHeld(db, 0, pTable->pSchema) );
     }else{
@@ -3451,12 +3624,17 @@
     }else{
       j = pCExpr->iColumn;
       assert( j<=0x7fff );
       if( j<0 ){
         j = pTab->iPKey;
-      }else if( pTab->aCol[j].notNull==0 ){
-        pIndex->uniqNotNull = 0;
+      }else{
+        if( pTab->aCol[j].notNull==0 ){
+          pIndex->uniqNotNull = 0;
+        }
+        if( pTab->aCol[j].colFlags & COLFLAG_VIRTUAL ){
+          pIndex->bHasVCol = 1;
+        }
       }
       pIndex->aiColumn[i] = (i16)j;
     }
     zColl = 0;
     if( pListItem->pExpr->op==TK_COLLATE ){
@@ -3507,17 +3685,17 @@
   if( pParse->pNewTable==0 ) estimateIndexWidth(pIndex);
 
   /* If this index contains every column of its table, then mark
   ** it as a covering index */
   assert( HasRowid(pTab) 
-      || pTab->iPKey<0 || sqlite3ColumnOfIndex(pIndex, pTab->iPKey)>=0 );
+      || pTab->iPKey<0 || sqlite3TableColumnToIndex(pIndex, pTab->iPKey)>=0 );
   recomputeColumnsNotIndexed(pIndex);
   if( pTblName!=0 && pIndex->nColumn>=pTab->nCol ){
     pIndex->isCovering = 1;
     for(j=0; j<pTab->nCol; j++){
       if( j==pTab->iPKey ) continue;
-      if( sqlite3ColumnOfIndex(pIndex,j)>=0 ) continue;
+      if( sqlite3TableColumnToIndex(pIndex,j)>=0 ) continue;
       pIndex->isCovering = 0;
       break;
     }
   }
 

Index: src/expr.c
==================================================================
--- src/expr.c
+++ src/expr.c
@@ -3397,35 +3397,77 @@
     sqlite3ExprCodeGetColumnOfTable(pParse->pVdbe, pIdx->pTable, iTabCur,
                                     iTabCol, regOut);
   }
 }
 
+#ifndef SQLITE_OMIT_GENERATED_COLUMNS
+/*
+** Generate code that will compute the value of generated column pCol
+** and store the result in register regOut
+*/
+void sqlite3ExprCodeGeneratedColumn(
+  Parse *pParse,
+  Column *pCol,
+  int regOut
+){
+  sqlite3ExprCode(pParse, pCol->pDflt, regOut);
+  if( pCol->affinity>=SQLITE_AFF_TEXT ){
+    sqlite3VdbeAddOp4(pParse->pVdbe, OP_Affinity, regOut, 1, 0,
+                      &pCol->affinity, 1);
+  }
+}
+#endif /* SQLITE_OMIT_GENERATED_COLUMNS */
+
 /*
 ** Generate code to extract the value of the iCol-th column of a table.
 */
 void sqlite3ExprCodeGetColumnOfTable(
-  Vdbe *v,        /* The VDBE under construction */
+  Vdbe *v,        /* Parsing context */
   Table *pTab,    /* The table containing the value */
   int iTabCur,    /* The table cursor.  Or the PK cursor for WITHOUT ROWID */
   int iCol,       /* Index of the column to extract */
   int regOut      /* Extract the value into this register */
 ){
+  Column *pCol;
+  assert( v!=0 );
   if( pTab==0 ){
     sqlite3VdbeAddOp3(v, OP_Column, iTabCur, iCol, regOut);
     return;
   }
   if( iCol<0 || iCol==pTab->iPKey ){
     sqlite3VdbeAddOp2(v, OP_Rowid, iTabCur, regOut);
   }else{
-    int op = IsVirtual(pTab) ? OP_VColumn : OP_Column;
-    int x = iCol;
-    if( !HasRowid(pTab) && !IsVirtual(pTab) ){
-      x = sqlite3ColumnOfIndex(sqlite3PrimaryKeyIndex(pTab), iCol);
+    int op;
+    int x;
+    if( IsVirtual(pTab) ){
+      op = OP_VColumn;
+      x = iCol;
+#ifndef SQLITE_OMIT_GENERATED_COLUMNS
+    }else if( (pCol = &pTab->aCol[iCol])->colFlags & COLFLAG_VIRTUAL ){
+      Parse *pParse = sqlite3VdbeParser(v);
+      if( pCol->colFlags & COLFLAG_BUSY ){
+        sqlite3ErrorMsg(pParse, "generated column loop on \"%s\"", pCol->zName);
+      }else{
+        int savedSelfTab = pParse->iSelfTab;
+        pCol->colFlags |= COLFLAG_BUSY;
+        pParse->iSelfTab = iTabCur+1;
+        sqlite3ExprCodeGeneratedColumn(pParse, pCol, regOut);
+        pParse->iSelfTab = savedSelfTab;
+        pCol->colFlags &= ~COLFLAG_BUSY;
+      }
+      return;
+#endif
+    }else if( !HasRowid(pTab) ){
+      testcase( iCol!=sqlite3TableColumnToStorage(pTab, iCol) );
+      x = sqlite3TableColumnToIndex(sqlite3PrimaryKeyIndex(pTab), iCol);
+      op = OP_Column;
+    }else{
+      x = sqlite3TableColumnToStorage(pTab,iCol);
+      testcase( x!=iCol );
+      op = OP_Column;
     }
     sqlite3VdbeAddOp3(v, op, iTabCur, x, regOut);
-  }
-  if( iCol>=0 ){
     sqlite3ColumnDefault(v, pTab, iCol, regOut);
   }
 }
 
 /*
@@ -3441,15 +3483,14 @@
   int iColumn,     /* Index of the table column */
   int iTable,      /* The cursor pointing to the table */
   int iReg,        /* Store results here */
   u8 p5            /* P5 value for OP_Column + FLAGS */
 ){
-  Vdbe *v = pParse->pVdbe;
-  assert( v!=0 );
-  sqlite3ExprCodeGetColumnOfTable(v, pTab, iTable, iColumn, iReg);
+  assert( pParse->pVdbe!=0 );
+  sqlite3ExprCodeGetColumnOfTable(pParse->pVdbe, pTab, iTable, iColumn, iReg);
   if( p5 ){
-    sqlite3VdbeChangeP5(v, p5);
+    sqlite3VdbeChangeP5(pParse->pVdbe, p5);
   }
   return iReg;
 }
 
 /*
@@ -3581,23 +3622,50 @@
         }
         return iReg;
       }
       if( iTab<0 ){
         if( pParse->iSelfTab<0 ){
-          /* Generating CHECK constraints or inserting into partial index */
-          assert( pExpr->y.pTab!=0 );
-          assert( pExpr->iColumn>=XN_ROWID );
-          assert( pExpr->iColumn<pExpr->y.pTab->nCol );
-          if( pExpr->iColumn>=0
-            && pExpr->y.pTab->aCol[pExpr->iColumn].affinity==SQLITE_AFF_REAL
-          ){
-            sqlite3VdbeAddOp2(v, OP_SCopy, pExpr->iColumn - pParse->iSelfTab,
-                              target);
+          /* Other columns in the same row for CHECK constraints or
+          ** generated columns or for inserting into partial index.
+          ** The row is unpacked into registers beginning at
+          ** 0-(pParse->iSelfTab).  The rowid (if any) is in a register
+          ** immediately prior to the first column.
+          */
+          Column *pCol;
+          Table *pTab = pExpr->y.pTab;
+          int iSrc;
+          int iCol = pExpr->iColumn;
+          assert( pTab!=0 );
+          assert( iCol>=XN_ROWID );
+          assert( iCol<pExpr->y.pTab->nCol );
+          if( iCol<0 ){
+            return -1-pParse->iSelfTab;
+          }
+          pCol = pTab->aCol + iCol;
+          testcase( iCol!=sqlite3TableColumnToStorage(pTab,iCol) );
+          iSrc = sqlite3TableColumnToStorage(pTab, iCol) - pParse->iSelfTab;
+#ifndef SQLITE_OMIT_GENERATED_COLUMNS
+          if( pCol->colFlags & COLFLAG_GENERATED ){
+            if( pCol->colFlags & COLFLAG_BUSY ){
+              sqlite3ErrorMsg(pParse, "generated column loop on \"%s\"",
+                              pCol->zName);
+              return 0;
+            }
+            pCol->colFlags |= COLFLAG_BUSY;
+            if( pCol->colFlags & COLFLAG_NOTAVAIL ){
+              sqlite3ExprCodeGeneratedColumn(pParse, pCol, iSrc);
+            }
+            pCol->colFlags &= ~(COLFLAG_BUSY|COLFLAG_NOTAVAIL);
+            return iSrc;
+          }else
+#endif /* SQLITE_OMIT_GENERATED_COLUMNS */
+          if( pCol->affinity==SQLITE_AFF_REAL ){
+            sqlite3VdbeAddOp2(v, OP_SCopy, iSrc, target);
             sqlite3VdbeAddOp1(v, OP_RealAffinity, target);
             return target;
           }else{
-            return pExpr->iColumn - pParse->iSelfTab;
+            return iSrc;
           }
         }else{
           /* Coding an expression that is part of an index where column names
           ** in the index refer to the table to which the index belongs */
           iTab = pParse->iSelfTab - 1;
@@ -4061,32 +4129,32 @@
       **   p1==0   ->    old.rowid     p1==3   ->    new.rowid
       **   p1==1   ->    old.a         p1==4   ->    new.a
       **   p1==2   ->    old.b         p1==5   ->    new.b       
       */
       Table *pTab = pExpr->y.pTab;
-      int p1 = pExpr->iTable * (pTab->nCol+1) + 1 + pExpr->iColumn;
+      int iCol = pExpr->iColumn;
+      int p1 = pExpr->iTable * (pTab->nCol+1) + 1 
+                     + (iCol>=0 ? sqlite3TableColumnToStorage(pTab, iCol) : -1);
 
       assert( pExpr->iTable==0 || pExpr->iTable==1 );
-      assert( pExpr->iColumn>=-1 && pExpr->iColumn<pTab->nCol );
-      assert( pTab->iPKey<0 || pExpr->iColumn!=pTab->iPKey );
+      assert( iCol>=-1 && iCol<pTab->nCol );
+      assert( pTab->iPKey<0 || iCol!=pTab->iPKey );
       assert( p1>=0 && p1<(pTab->nCol*2+2) );
 
       sqlite3VdbeAddOp2(v, OP_Param, p1, target);
       VdbeComment((v, "r[%d]=%s.%s", target,
         (pExpr->iTable ? "new" : "old"),
-        (pExpr->iColumn<0 ? "rowid" : pExpr->y.pTab->aCol[pExpr->iColumn].zName)
+        (pExpr->iColumn<0 ? "rowid" : pExpr->y.pTab->aCol[iCol].zName)
       ));
 
 #ifndef SQLITE_OMIT_FLOATING_POINT
       /* If the column has REAL affinity, it may currently be stored as an
       ** integer. Use OP_RealAffinity to make sure it is really real.
       **
       ** EVIDENCE-OF: R-60985-57662 SQLite will convert the value back to
       ** floating point when extracting it from the record.  */
-      if( pExpr->iColumn>=0 
-       && pTab->aCol[pExpr->iColumn].affinity==SQLITE_AFF_REAL
-      ){
+      if( iCol>=0 && pTab->aCol[iCol].affinity==SQLITE_AFF_REAL ){
         sqlite3VdbeAddOp1(v, OP_RealAffinity, target);
       }
 #endif
       break;
     }
@@ -4315,18 +4383,14 @@
 */
 void sqlite3ExprCode(Parse *pParse, Expr *pExpr, int target){
   int inReg;
 
   assert( target>0 && target<=pParse->nMem );
-  if( pExpr && pExpr->op==TK_REGISTER ){
-    sqlite3VdbeAddOp2(pParse->pVdbe, OP_Copy, pExpr->iTable, target);
-  }else{
-    inReg = sqlite3ExprCodeTarget(pParse, pExpr, target);
-    assert( pParse->pVdbe!=0 || pParse->db->mallocFailed );
-    if( inReg!=target && pParse->pVdbe ){
-      sqlite3VdbeAddOp2(pParse->pVdbe, OP_SCopy, inReg, target);
-    }
+  inReg = sqlite3ExprCodeTarget(pParse, pExpr, target);
+  assert( pParse->pVdbe!=0 || pParse->db->mallocFailed );
+  if( inReg!=target && pParse->pVdbe ){
+    sqlite3VdbeAddOp2(pParse->pVdbe, OP_SCopy, inReg, target);
   }
 }
 
 /*
 ** Make a transient copy of expression pExpr and then code it using
@@ -4352,34 +4416,10 @@
   }else{
     sqlite3ExprCode(pParse, pExpr, target);
   }
 }
 
-/*
-** Generate code that evaluates the given expression and puts the result
-** in register target.
-**
-** Also make a copy of the expression results into another "cache" register
-** and modify the expression so that the next time it is evaluated,
-** the result is a copy of the cache register.
-**
-** This routine is used for expressions that are used multiple 
-** times.  They are evaluated once and the results of the expression
-** are reused.
-*/
-void sqlite3ExprCodeAndCache(Parse *pParse, Expr *pExpr, int target){
-  Vdbe *v = pParse->pVdbe;
-  int iMem;
-
-  assert( target>0 );
-  assert( pExpr->op!=TK_REGISTER );
-  sqlite3ExprCode(pParse, pExpr, target);
-  iMem = ++pParse->nMem;
-  sqlite3VdbeAddOp2(v, OP_Copy, target, iMem);
-  exprToRegister(pExpr, iMem);
-}
-
 /*
 ** Generate code that pushes the value of every element of the given
 ** expression list into a sequence of registers beginning at target.
 **
 ** Return the number of elements evaluated.  The number returned will
@@ -5298,11 +5338,11 @@
 ** pWalker->u.pIdxCover->pIdx.
 */
 static int exprIdxCover(Walker *pWalker, Expr *pExpr){
   if( pExpr->op==TK_COLUMN
    && pExpr->iTable==pWalker->u.pIdxCover->iCur
-   && sqlite3ColumnOfIndex(pWalker->u.pIdxCover->pIdx, pExpr->iColumn)<0
+   && sqlite3TableColumnToIndex(pWalker->u.pIdxCover->pIdx, pExpr->iColumn)<0
   ){
     pWalker->eCode = 1;
     return WRC_Abort;
   }
   return WRC_Continue;

Index: src/fkey.c
==================================================================
--- src/fkey.c
+++ src/fkey.c
@@ -347,11 +347,11 @@
   if( nIncr<0 ){
     sqlite3VdbeAddOp2(v, OP_FkIfZero, pFKey->isDeferred, iOk);
     VdbeCoverage(v);
   }
   for(i=0; i<pFKey->nCol; i++){
-    int iReg = aiCol[i] + regData + 1;
+    int iReg = sqlite3TableColumnToStorage(pFKey->pFrom,aiCol[i]) + regData + 1;
     sqlite3VdbeAddOp2(v, OP_IsNull, iReg, iOk); VdbeCoverage(v);
   }
 
   if( isIgnore==0 ){
     if( pIdx==0 ){
@@ -363,11 +363,12 @@
       /* Invoke MustBeInt to coerce the child key value to an integer (i.e. 
       ** apply the affinity of the parent key). If this fails, then there
       ** is no matching parent key. Before using MustBeInt, make a copy of
       ** the value. Otherwise, the value inserted into the child key column
       ** will have INTEGER affinity applied to it, which may not be correct.  */
-      sqlite3VdbeAddOp2(v, OP_SCopy, aiCol[0]+1+regData, regTemp);
+      sqlite3VdbeAddOp2(v, OP_SCopy, 
+        sqlite3TableColumnToStorage(pFKey->pFrom,aiCol[0])+1+regData, regTemp);
       iMustBeInt = sqlite3VdbeAddOp2(v, OP_MustBeInt, regTemp, 0);
       VdbeCoverage(v);
   
       /* If the parent table is the same as the child table, and we are about
       ** to increment the constraint-counter (i.e. this is an INSERT operation),
@@ -390,11 +391,13 @@
       int regRec = sqlite3GetTempReg(pParse);
   
       sqlite3VdbeAddOp3(v, OP_OpenRead, iCur, pIdx->tnum, iDb);
       sqlite3VdbeSetP4KeyInfo(pParse, pIdx);
       for(i=0; i<nCol; i++){
-        sqlite3VdbeAddOp2(v, OP_Copy, aiCol[i]+1+regData, regTemp+i);
+        sqlite3VdbeAddOp2(v, OP_Copy, 
+               sqlite3TableColumnToStorage(pFKey->pFrom, aiCol[i])+1+regData,
+               regTemp+i);
       }
   
       /* If the parent table is the same as the child table, and we are about
       ** to increment the constraint-counter (i.e. this is an INSERT operation),
       ** then check if the row being inserted matches itself. If so, do not
@@ -406,12 +409,15 @@
       ** none of the child key values are).
       */
       if( pTab==pFKey->pFrom && nIncr==1 ){
         int iJump = sqlite3VdbeCurrentAddr(v) + nCol + 1;
         for(i=0; i<nCol; i++){
-          int iChild = aiCol[i]+1+regData;
-          int iParent = pIdx->aiColumn[i]+1+regData;
+          int iChild = sqlite3TableColumnToStorage(pFKey->pFrom,aiCol[i])
+                              +1+regData;
+          int iParent = 1+regData;
+          iParent += sqlite3TableColumnToStorage(pIdx->pTable,
+                                                 pIdx->aiColumn[i]);
           assert( pIdx->aiColumn[i]>=0 );
           assert( aiCol[i]!=pTab->iPKey );
           if( pIdx->aiColumn[i]==pTab->iPKey ){
             /* The parent key is a composite key that includes the IPK column */
             iParent = regData;

Index: src/insert.c
==================================================================
--- src/insert.c
+++ src/insert.c
@@ -35,11 +35,11 @@
   v = sqlite3GetVdbe(pParse);
   assert( opcode==OP_OpenWrite || opcode==OP_OpenRead );
   sqlite3TableLock(pParse, iDb, pTab->tnum, 
                    (opcode==OP_OpenWrite)?1:0, pTab->zName);
   if( HasRowid(pTab) ){
-    sqlite3VdbeAddOp4Int(v, opcode, iCur, pTab->tnum, iDb, pTab->nCol);
+    sqlite3VdbeAddOp4Int(v, opcode, iCur, pTab->tnum, iDb, pTab->nNVCol);
     VdbeComment((v, "%s", pTab->zName));
   }else{
     Index *pPk = sqlite3PrimaryKeyIndex(pTab);
     assert( pPk!=0 );
     assert( pPk->tnum==pTab->tnum );
@@ -127,27 +127,29 @@
 **  'C'            NUMERIC
 **  'D'            INTEGER
 **  'E'            REAL
 */
 void sqlite3TableAffinity(Vdbe *v, Table *pTab, int iReg){
-  int i;
+  int i, j;
   char *zColAff = pTab->zColAff;
   if( zColAff==0 ){
     sqlite3 *db = sqlite3VdbeDb(v);
     zColAff = (char *)sqlite3DbMallocRaw(0, pTab->nCol+1);
     if( !zColAff ){
       sqlite3OomFault(db);
       return;
     }
 
-    for(i=0; i<pTab->nCol; i++){
+    for(i=j=0; i<pTab->nCol; i++){
       assert( pTab->aCol[i].affinity!=0 );
-      zColAff[i] = pTab->aCol[i].affinity;
+      if( (pTab->aCol[i].colFlags & COLFLAG_VIRTUAL)==0 ){
+        zColAff[j++] = pTab->aCol[i].affinity;
+      }
     }
     do{
-      zColAff[i--] = 0;
-    }while( i>=0 && zColAff[i]<=SQLITE_AFF_BLOB );
+      zColAff[j--] = 0;
+    }while( j>=0 && zColAff[j]<=SQLITE_AFF_BLOB );
     pTab->zColAff = zColAff;
   }
   assert( zColAff!=0 );
   i = sqlite3Strlen30NN(zColAff);
   if( i ){
@@ -196,10 +198,65 @@
     }
 #endif
   }
   return 0;
 }
+
+#ifndef SQLITE_OMIT_GENERATED_COLUMNS
+/*
+** All regular columns for table pTab have been puts into registers
+** starting with iRegStore.  The registers that correspond to STORED
+** or VIRTUAL columns have not yet been initialized.  This routine goes
+** back and computes the values for those columns based on the previously
+** computed normal columns.
+*/
+void sqlite3ComputeGeneratedColumns(
+  Parse *pParse,    /* Parsing context */
+  int iRegStore,    /* Register holding the first column */
+  Table *pTab       /* The table */
+){
+  int i;
+  int nv;
+  /* Because there can be multiple generated columns that refer to one another,
+  ** this is a two-pass algorithm.  On the first pass, mark all generated
+  ** columns as "not available".
+  */
+  for(i=0; i<pTab->nCol; i++){
+    if( pTab->aCol[i].colFlags & COLFLAG_GENERATED ){
+      testcase( pTab->aCol[i].colFlags & COLFLAG_VIRTUAL );
+      testcase( pTab->aCol[i].colFlags & COLFLAG_STORED );
+      pTab->aCol[i].colFlags |= COLFLAG_NOTAVAIL;
+    }
+  }
+  /* On the second pass, compute the value of each NOT-AVAILABLE column.
+  ** Companion code in the TK_COLUMN case of sqlite3ExprCodeTarget() will
+  ** compute dependencies and mark remove the COLSPAN_NOTAVAIL mark, as
+  ** they are needed.
+  */
+  pParse->iSelfTab = -iRegStore;
+  for(i=nv=0; i<pTab->nCol; i++){
+    u32 colFlags = pTab->aCol[i].colFlags;
+    if( (colFlags & COLFLAG_NOTAVAIL)!=0 ){
+      assert( colFlags & COLFLAG_GENERATED );
+      if( colFlags & COLFLAG_VIRTUAL ){
+        /* Virtual columns go at the end */
+        assert( pTab->nNVCol+nv == sqlite3TableColumnToStorage(pTab,i) );
+        sqlite3ExprCodeGeneratedColumn(pParse, &pTab->aCol[i],
+                                       iRegStore+pTab->nNVCol+nv);
+      }else{
+        /* Stored columns go in column order */
+        assert( i-nv == sqlite3TableColumnToStorage(pTab,i) );
+        sqlite3ExprCodeGeneratedColumn(pParse, &pTab->aCol[i], iRegStore+i-nv);
+      }
+      pTab->aCol[i].colFlags &= ~COLFLAG_NOTAVAIL;
+    }
+    if( (colFlags & COLFLAG_VIRTUAL)!=0 ) nv++;
+  }
+  pParse->iSelfTab = 0;
+}
+#endif /* SQLITE_OMIT_GENERATED_COLUMNS */
+
 
 #ifndef SQLITE_OMIT_AUTOINCREMENT
 /*
 ** Locate or create an AutoincInfo structure associated with table pTab
 ** which is in database iDb.  Return the register number for the register
@@ -504,11 +561,11 @@
 */
 void sqlite3Insert(
   Parse *pParse,        /* Parser context */
   SrcList *pTabList,    /* Name of table into which we are inserting */
   Select *pSelect,      /* A SELECT statement to use as the data source */
-  IdList *pColumn,      /* Column names corresponding to IDLIST. */
+  IdList *pColumn,      /* Column names corresponding to IDLIST, or NULL. */
   int onError,          /* How to handle constraint errors */
   Upsert *pUpsert       /* ON CONFLICT clauses for upsert, or NULL */
 ){
   sqlite3 *db;          /* The main database structure */
   Table *pTab;          /* The table to insert into.  aka TABLE */
@@ -529,10 +586,11 @@
   u8 useTempTable = 0;  /* Store SELECT results in intermediate table */
   u8 appendFlag = 0;    /* True if the insert is likely to be an append */
   u8 withoutRowid;      /* 0 for normal table.  1 for WITHOUT ROWID table */
   u8 bIdListInOrder;    /* True if IDLIST is in table order */
   ExprList *pList = 0;  /* List of VALUES() to be inserted  */
+  int iRegStore;        /* Register in which to store next column */
 
   /* Register allocations */
   int regFromSelect = 0;/* Base register for data coming from SELECT */
   int regAutoinc = 0;   /* Register holding the AUTOINCREMENT counter */
   int regRowCount = 0;  /* Memory cell used for the row counter */
@@ -636,12 +694,12 @@
   /* If this is an AUTOINCREMENT table, look up the sequence number in the
   ** sqlite_sequence table and store it in memory cell regAutoinc.
   */
   regAutoinc = autoIncBegin(pParse, iDb, pTab);
 
-  /* Allocate registers for holding the rowid of the new row,
-  ** the content of the new row, and the assembled row record.
+  /* Allocate a block registers to hold the rowid and the values
+  ** for all columns of the new row.
   */
   regRowid = regIns = pParse->nMem+1;
   pParse->nMem += pTab->nCol + 1;
   if( IsVirtual(pTab) ){
     regRowid++;
@@ -656,13 +714,21 @@
   ** If the table has an INTEGER PRIMARY KEY column and that column
   ** is named in the IDLIST, then record in the ipkColumn variable
   ** the index into IDLIST of the primary key column.  ipkColumn is
   ** the index of the primary key as it appears in IDLIST, not as
   ** is appears in the original table.  (The index of the INTEGER
-  ** PRIMARY KEY in the original table is pTab->iPKey.)
+  ** PRIMARY KEY in the original table is pTab->iPKey.)  After this
+  ** loop, if ipkColumn==(-1), that means that integer primary key
+  ** is unspecified, and hence the table is either WITHOUT ROWID or
+  ** it will automatically generated an integer primary key.
+  **
+  ** bIdListInOrder is true if the columns in IDLIST are in storage
+  ** order.  This enables an optimization that avoids shuffling the
+  ** columns into storage order.  False negatives are harmless,
+  ** but false positives will cause database corruption.
   */
-  bIdListInOrder = (pTab->tabFlags & TF_OOOHidden)==0;
+  bIdListInOrder = (pTab->tabFlags & (TF_OOOHidden|TF_HasStored))==0;
   if( pColumn ){
     for(i=0; i<pColumn->nId; i++){
       pColumn->a[i].idx = -1;
     }
     for(i=0; i<pColumn->nId; i++){
@@ -671,10 +737,18 @@
           pColumn->a[i].idx = j;
           if( i!=j ) bIdListInOrder = 0;
           if( j==pTab->iPKey ){
             ipkColumn = i;  assert( !withoutRowid );
           }
+#ifndef SQLITE_OMIT_GENERATED_COLUMNS
+          if( pTab->aCol[j].colFlags & (COLFLAG_STORED|COLFLAG_VIRTUAL) ){
+            sqlite3ErrorMsg(pParse, 
+               "cannot INSERT into generated column \"%s\"",
+               pTab->aCol[j].zName);
+            goto insert_cleanup;
+          }
+#endif
           break;
         }
       }
       if( j>=pTab->nCol ){
         if( sqlite3IsRowid(pColumn->a[i].zName) && !withoutRowid ){
@@ -780,17 +854,30 @@
   ** key, the set the ipkColumn variable to the integer primary key 
   ** column index in the original table definition.
   */
   if( pColumn==0 && nColumn>0 ){
     ipkColumn = pTab->iPKey;
+#ifndef SQLITE_OMIT_GENERATED_COLUMNS
+    if( ipkColumn>=0 && (pTab->tabFlags & TF_HasGenerated)!=0 ){
+      testcase( pTab->tabFlags & TF_HasVirtual );
+      testcase( pTab->tabFlags & TF_HasStored );
+      for(i=ipkColumn-1; i>=0; i--){
+        if( pTab->aCol[i].colFlags & COLFLAG_GENERATED ){
+          testcase( pTab->aCol[i].colFlags & COLFLAG_VIRTUAL );
+          testcase( pTab->aCol[i].colFlags & COLFLAG_STORED );
+          ipkColumn--;
+        }
+      }
+    }
+#endif
   }
 
   /* Make sure the number of columns in the source data matches the number
   ** of columns to be inserted into the table.
   */
   for(i=0; i<pTab->nCol; i++){
-    nHidden += (IsHiddenColumn(&pTab->aCol[i]) ? 1 : 0);
+    if( pTab->aCol[i].colFlags & COLFLAG_NOINSERT ) nHidden++;
   }
   if( pColumn==0 && nColumn && nColumn!=(pTab->nCol-nHidden) ){
     sqlite3ErrorMsg(pParse, 
        "table %S has %d columns but %d values were supplied",
        pTabList, 0, pTab->nCol-nHidden, nColumn);
@@ -871,11 +958,91 @@
     **         goto C
     **      D: ...
     */
     addrInsTop = addrCont = sqlite3VdbeAddOp1(v, OP_Yield, dest.iSDParm);
     VdbeCoverage(v);
+    if( ipkColumn>=0 ){
+      /* tag-20191021-001: If the INTEGER PRIMARY KEY is being generated by the
+      ** SELECT, go ahead and copy the value into the rowid slot now, so that
+      ** the value does not get overwritten by a NULL at tag-20191021-002. */
+      sqlite3VdbeAddOp2(v, OP_Copy, regFromSelect+ipkColumn, regRowid);
+    }
+  }
+
+  /* Compute data for ordinary columns of the new entry.  Values
+  ** are written in storage order into registers starting with regData.
+  ** Only ordinary columns are computed in this loop. The rowid
+  ** (if there is one) is computed later and generated columns are
+  ** computed after the rowid since they might depend on the value
+  ** of the rowid.
+  */
+  nHidden = 0;
+  iRegStore = regData;  assert( regData==regRowid+1 );
+  for(i=0; i<pTab->nCol; i++, iRegStore++){
+    int k;
+    u32 colFlags;
+    assert( i>=nHidden );
+    if( i==pTab->iPKey ){
+      /* tag-20191021-002: References to the INTEGER PRIMARY KEY are filled
+      ** using the rowid. So put a NULL in the IPK slot of the record to avoid
+      ** using excess space.  The file format definition requires this extra
+      ** NULL - we cannot optimize further by skipping the column completely */
+      sqlite3VdbeAddOp1(v, OP_SoftNull, iRegStore);
+      continue;
+    }
+    if( ((colFlags = pTab->aCol[i].colFlags) & COLFLAG_NOINSERT)!=0 ){
+      nHidden++;
+      if( (colFlags & COLFLAG_VIRTUAL)!=0 ){
+        /* Virtual columns do not participate in OP_MakeRecord.  So back up
+        ** iRegStore by one slot to compensate for the iRegStore++ in the
+        ** outer for() loop */
+        iRegStore--;
+        continue;
+      }else if( (colFlags & COLFLAG_STORED)!=0 ){
+        /* Stored columns are computed later.  But if there are BEFORE
+        ** triggers, the slots used for stored columns will be OP_Copy-ed
+        ** to a second block of registers, so the register needs to be
+        ** initialized to NULL to avoid an uninitialized register read */
+        if( tmask & TRIGGER_BEFORE ){
+          sqlite3VdbeAddOp1(v, OP_SoftNull, iRegStore);
+        }
+        continue;
+      }else if( pColumn==0 ){
+        /* Hidden columns that are not explicitly named in the INSERT
+        ** get there default value */
+        sqlite3ExprCodeFactorable(pParse, pTab->aCol[i].pDflt, iRegStore);
+        continue;
+      }
+    }
+    if( pColumn ){
+      for(j=0; j<pColumn->nId && pColumn->a[j].idx!=i; j++){}
+      if( j>=pColumn->nId ){
+        /* A column not named in the insert column list gets its
+        ** default value */
+        sqlite3ExprCodeFactorable(pParse, pTab->aCol[i].pDflt, iRegStore);
+        continue;
+      }
+      k = j;
+    }else if( nColumn==0 ){
+      /* This is INSERT INTO ... DEFAULT VALUES.  Load the default value. */
+      sqlite3ExprCodeFactorable(pParse, pTab->aCol[i].pDflt, iRegStore);
+      continue;
+    }else{
+      k = i - nHidden;
+    }
+
+    if( useTempTable ){
+      sqlite3VdbeAddOp3(v, OP_Column, srcTab, k, iRegStore); 
+    }else if( pSelect ){
+      if( regFromSelect!=regData ){
+        sqlite3VdbeAddOp2(v, OP_SCopy, regFromSelect+k, iRegStore);
+      }
+    }else{
+      sqlite3ExprCode(pParse, pList->a[k].pExpr, iRegStore);
+    }
   }
+
 
   /* Run the BEFORE and INSTEAD OF triggers, if there are any
   */
   endOfLoop = sqlite3VdbeMakeLabel(pParse);
   if( tmask & TRIGGER_BEFORE ){
@@ -907,29 +1074,25 @@
     /* Cannot have triggers on a virtual table. If it were possible,
     ** this block would have to account for hidden column.
     */
     assert( !IsVirtual(pTab) );
 
-    /* Create the new column data
-    */
-    for(i=j=0; i<pTab->nCol; i++){
-      if( pColumn ){
-        for(j=0; j<pColumn->nId; j++){
-          if( pColumn->a[j].idx==i ) break;
-        }
-      }
-      if( (!useTempTable && !pList) || (pColumn && j>=pColumn->nId)
-            || (pColumn==0 && IsOrdinaryHiddenColumn(&pTab->aCol[i])) ){
-        sqlite3ExprCode(pParse, pTab->aCol[i].pDflt, regCols+i+1);
-      }else if( useTempTable ){
-        sqlite3VdbeAddOp3(v, OP_Column, srcTab, j, regCols+i+1); 
-      }else{
-        assert( pSelect==0 ); /* Otherwise useTempTable is true */
-        sqlite3ExprCodeAndCache(pParse, pList->a[j].pExpr, regCols+i+1);
-      }
-      if( pColumn==0 && !IsOrdinaryHiddenColumn(&pTab->aCol[i]) ) j++;
-    }
+    /* Copy the new data already generated. */
+    assert( pTab->nNVCol>0 );
+    sqlite3VdbeAddOp3(v, OP_Copy, regRowid+1, regCols+1, pTab->nNVCol-1);
+
+#ifndef SQLITE_OMIT_GENERATED_COLUMNS
+    /* Compute the new value for generated columns after all other
+    ** columns have already been computed.  This must be done after
+    ** computing the ROWID in case one of the generated columns
+    ** refers to the ROWID. */
+    if( pTab->tabFlags & TF_HasGenerated ){
+      testcase( pTab->tabFlags & TF_HasVirtual );
+      testcase( pTab->tabFlags & TF_HasStored );
+      sqlite3ComputeGeneratedColumns(pParse, regCols+1, pTab);
+    }
+#endif
 
     /* If this is an INSERT on a view with an INSTEAD OF INSERT trigger,
     ** do not attempt any conversions before assembling the record.
     ** If this is a real table, attempt conversions as required by the
     ** table column affinities.
@@ -943,23 +1106,21 @@
         pTab, regCols-pTab->nCol-1, onError, endOfLoop);
 
     sqlite3ReleaseTempRange(pParse, regCols, pTab->nCol+1);
   }
 
-  /* Compute the content of the next row to insert into a range of
-  ** registers beginning at regIns.
-  */
   if( !isView ){
     if( IsVirtual(pTab) ){
       /* The row that the VUpdate opcode will delete: none */
       sqlite3VdbeAddOp2(v, OP_Null, 0, regIns);
     }
     if( ipkColumn>=0 ){
+      /* Compute the new rowid */
       if( useTempTable ){
         sqlite3VdbeAddOp3(v, OP_Column, srcTab, ipkColumn, regRowid);
       }else if( pSelect ){
-        sqlite3VdbeAddOp2(v, OP_Copy, regFromSelect+ipkColumn, regRowid);
+        /* Rowid already initialized at tag-20191021-001 */
       }else{
         Expr *pIpk = pList->a[ipkColumn].pExpr;
         if( pIpk->op==TK_NULL && !IsVirtual(pTab) ){
           sqlite3VdbeAddOp3(v, OP_NewRowid, iDataCur, regRowid, regAutoinc);
           appendFlag = 1;
@@ -988,49 +1149,21 @@
       sqlite3VdbeAddOp3(v, OP_NewRowid, iDataCur, regRowid, regAutoinc);
       appendFlag = 1;
     }
     autoIncStep(pParse, regAutoinc, regRowid);
 
-    /* Compute data for all columns of the new entry, beginning
-    ** with the first column.
-    */
-    nHidden = 0;
-    for(i=0; i<pTab->nCol; i++){
-      int iRegStore = regRowid+1+i;
-      if( i==pTab->iPKey ){
-        /* The value of the INTEGER PRIMARY KEY column is always a NULL.
-        ** Whenever this column is read, the rowid will be substituted
-        ** in its place.  Hence, fill this column with a NULL to avoid
-        ** taking up data space with information that will never be used.
-        ** As there may be shallow copies of this value, make it a soft-NULL */
-        sqlite3VdbeAddOp1(v, OP_SoftNull, iRegStore);
-        continue;
-      }
-      if( pColumn==0 ){
-        if( IsHiddenColumn(&pTab->aCol[i]) ){
-          j = -1;
-          nHidden++;
-        }else{
-          j = i - nHidden;
-        }
-      }else{
-        for(j=0; j<pColumn->nId; j++){
-          if( pColumn->a[j].idx==i ) break;
-        }
-      }
-      if( j<0 || nColumn==0 || (pColumn && j>=pColumn->nId) ){
-        sqlite3ExprCodeFactorable(pParse, pTab->aCol[i].pDflt, iRegStore);
-      }else if( useTempTable ){
-        sqlite3VdbeAddOp3(v, OP_Column, srcTab, j, iRegStore); 
-      }else if( pSelect ){
-        if( regFromSelect!=regData ){
-          sqlite3VdbeAddOp2(v, OP_SCopy, regFromSelect+j, iRegStore);
-        }
-      }else{
-        sqlite3ExprCode(pParse, pList->a[j].pExpr, iRegStore);
-      }
-    }
+#ifndef SQLITE_OMIT_GENERATED_COLUMNS
+    /* Compute the new value for generated columns after all other
+    ** columns have already been computed.  This must be done after
+    ** computing the ROWID in case one of the generated columns
+    ** refers to the ROWID. */
+    if( pTab->tabFlags & TF_HasGenerated ){
+      testcase( pTab->tabFlags & TF_HasVirtual );
+      testcase( pTab->tabFlags & TF_HasStored );
+      sqlite3ComputeGeneratedColumns(pParse, regRowid+1, pTab);
+    }
+#endif
 
     /* Generate code to check constraints and generate index keys and
     ** do the insertion.
     */
 #ifndef SQLITE_OMIT_VIRTUALTABLE
@@ -1344,10 +1477,11 @@
                      iDataCur, iIdxCur, regNewData, regOldData, pkChng));
 
   /* Test all NOT NULL constraints.
   */
   for(i=0; i<nCol; i++){
+    int iReg;
     if( i==pTab->iPKey ){
       continue;        /* ROWID is never NULL */
     }
     if( aiChng && aiChng[i]<0 ){
       /* Don't bother checking for NOT NULL on columns that do not change */
@@ -1364,18 +1498,22 @@
       onError = OE_Abort;
     }
     assert( onError==OE_Rollback || onError==OE_Abort || onError==OE_Fail
         || onError==OE_Ignore || onError==OE_Replace );
     addr1 = 0;
+    testcase( i!=sqlite3TableColumnToStorage(pTab, i) );
+    testcase( pTab->aCol[i].colFlags & COLFLAG_VIRTUAL );
+    testcase( pTab->aCol[i].colFlags & COLFLAG_STORED );
+    iReg = sqlite3TableColumnToStorage(pTab, i) + regNewData + 1;
     switch( onError ){
       case OE_Replace: {
         assert( onError==OE_Replace );
         addr1 = sqlite3VdbeMakeLabel(pParse);
-        sqlite3VdbeAddOp2(v, OP_NotNull, regNewData+1+i, addr1);
+        sqlite3VdbeAddOp2(v, OP_NotNull, iReg, addr1);
           VdbeCoverage(v);
         sqlite3ExprCode(pParse, pTab->aCol[i].pDflt, regNewData+1+i);
-        sqlite3VdbeAddOp2(v, OP_NotNull, regNewData+1+i, addr1);
+        sqlite3VdbeAddOp2(v, OP_NotNull, iReg, addr1);
           VdbeCoverage(v);
         onError = OE_Abort;
         /* Fall through into the OE_Abort case to generate code that runs
         ** if both the input and the default value are NULL */
       }
@@ -1385,20 +1523,20 @@
       case OE_Rollback:
       case OE_Fail: {
         char *zMsg = sqlite3MPrintf(db, "%s.%s", pTab->zName,
                                     pTab->aCol[i].zName);
         sqlite3VdbeAddOp3(v, OP_HaltIfNull, SQLITE_CONSTRAINT_NOTNULL, onError,
-                          regNewData+1+i);
+                          iReg);
         sqlite3VdbeAppendP4(v, zMsg, P4_DYNAMIC);
         sqlite3VdbeChangeP5(v, P5_ConstraintNotNull);
         VdbeCoverage(v);
         if( addr1 ) sqlite3VdbeResolveLabel(v, addr1);
         break;
       }
       default: {
         assert( onError==OE_Ignore );
-        sqlite3VdbeAddOp2(v, OP_IsNull, regNewData+1+i, ignoreDest);
+        sqlite3VdbeAddOp2(v, OP_IsNull, iReg, ignoreDest);
         VdbeCoverage(v);
         break;
       }
     }
   }
@@ -1669,18 +1807,26 @@
       if( iField==XN_EXPR ){
         pParse->iSelfTab = -(regNewData+1);
         sqlite3ExprCodeCopy(pParse, pIdx->aColExpr->a[i].pExpr, regIdx+i);
         pParse->iSelfTab = 0;
         VdbeComment((v, "%s column %d", pIdx->zName, i));
-      }else{
-        if( iField==XN_ROWID || iField==pTab->iPKey ){
-          x = regNewData;
-        }else{
-          x = iField + regNewData + 1;
-        }
-        sqlite3VdbeAddOp2(v, iField<0 ? OP_IntCopy : OP_SCopy, x, regIdx+i);
-        VdbeComment((v, "%s", iField<0 ? "rowid" : pTab->aCol[iField].zName));
+      }else if( iField==XN_ROWID || iField==pTab->iPKey ){
+        x = regNewData;
+        sqlite3VdbeAddOp2(v, OP_IntCopy, x, regIdx+i);
+        VdbeComment((v, "rowid"));
+#ifndef SQLITE_OMIT_GENERATED_COLUMNS
+      }else if( pTab->aCol[iField].colFlags & COLFLAG_VIRTUAL ){
+        pParse->iSelfTab = -(regNewData+1);
+        sqlite3ExprCodeCopy(pParse, pTab->aCol[iField].pDflt, regIdx+i);
+        pParse->iSelfTab = 0;
+        VdbeComment((v, "%s column %d", pIdx->zName, i));
+#endif
+      }else{
+        testcase( sqlite3TableColumnToStorage(pTab, iField)!=iField );
+        x = sqlite3TableColumnToStorage(pTab, iField) + regNewData + 1;
+        sqlite3VdbeAddOp2(v, OP_SCopy, x, regIdx+i);
+        VdbeComment((v, "%s", pTab->aCol[iField].zName));
       }
     }
     sqlite3VdbeAddOp3(v, OP_MakeRecord, regIdx, pIdx->nColumn, aRegIdx[ix]);
     VdbeComment((v, "for %s", pIdx->zName));
 #ifdef SQLITE_ENABLE_NULL_TRIM
@@ -1765,11 +1911,11 @@
         /* Extract the PRIMARY KEY from the end of the index entry and
         ** store it in registers regR..regR+nPk-1 */
         if( pIdx!=pPk ){
           for(i=0; i<pPk->nKeyCol; i++){
             assert( pPk->aiColumn[i]>=0 );
-            x = sqlite3ColumnOfIndex(pIdx, pPk->aiColumn[i]);
+            x = sqlite3TableColumnToIndex(pIdx, pPk->aiColumn[i]);
             sqlite3VdbeAddOp3(v, OP_Column, iThisCur, x, regR+i);
             VdbeComment((v, "%s.%s", pTab->zName,
                          pTab->aCol[pPk->aiColumn[i]].zName));
           }
         }
@@ -1868,11 +2014,11 @@
   }
 
   /* Generate the table record */
   if( HasRowid(pTab) ){
     int regRec = aRegIdx[ix];
-    sqlite3VdbeAddOp3(v, OP_MakeRecord, regNewData+1, pTab->nCol, regRec);
+    sqlite3VdbeAddOp3(v, OP_MakeRecord, regNewData+1, pTab->nNVCol, regRec);
     sqlite3SetMakeRecordP5(v, pTab);
     if( !bAffinityDone ){
       sqlite3TableAffinity(v, pTab, 0);
     }
   }
@@ -2262,10 +2408,43 @@
     if( (db->mDbFlags & DBFLAG_Vacuum)==0 
      && (pDestCol->colFlags | pSrcCol->colFlags) & COLFLAG_HIDDEN 
     ){
       return 0;    /* Neither table may have __hidden__ columns */
     }
+#endif
+#ifndef SQLITE_OMIT_GENERATED_COLUMNS
+    /* Even if tables t1 and t2 have identical schemas, if they contain
+    ** generated columns, then this statement is semantically incorrect:
+    **
+    **     INSERT INTO t2 SELECT * FROM t1;
+    **
+    ** The reason is that generated column values are returned by the
+    ** the SELECT statement on the right but the INSERT statement on the
+    ** left wants them to be omitted.
+    **
+    ** Nevertheless, this is a useful notational shorthand to tell SQLite
+    ** to do a bulk transfer all of the content from t1 over to t2.
+    ** 
+    ** We could, in theory, disable this (except for internal use by the
+    ** VACUUM command where it is actually needed).  But why do that?  It
+    ** seems harmless enough, and provides a useful service.
+    */
+    if( (pDestCol->colFlags & COLFLAG_GENERATED) !=
+        (pSrcCol->colFlags & COLFLAG_GENERATED) ){
+      return 0;    /* Both columns have the same generated-column type */
+    }
+    /* But the transfer is only allowed if both the source and destination
+    ** tables have the exact same expressions for generated columns.
+    ** This requirement could be relaxed for VIRTUAL columns, I suppose.
+    */
+    if( (pDestCol->colFlags & COLFLAG_GENERATED)!=0 ){
+      if( sqlite3ExprCompare(0, pSrcCol->pDflt, pDestCol->pDflt, -1)!=0 ){
+        testcase( pDestCol->colFlags & COLFLAG_VIRTUAL );
+        testcase( pDestCol->colFlags & COLFLAG_STORED );
+        return 0;  /* Different generator expressions */
+      }
+    }
 #endif
     if( pDestCol->affinity!=pSrcCol->affinity ){
       return 0;    /* Affinity must be the same on all columns */
     }
     if( sqlite3_stricmp(pDestCol->zColl, pSrcCol->zColl)!=0 ){
@@ -2273,11 +2452,11 @@
     }
     if( pDestCol->notNull && !pSrcCol->notNull ){
       return 0;    /* tab2 must be NOT NULL if tab1 is */
     }
     /* Default values for second and subsequent columns need to match. */
-    if( i>0 ){
+    if( (pDestCol->colFlags & COLFLAG_GENERATED)==0 && i>0 ){
       assert( pDestCol->pDflt==0 || pDestCol->pDflt->op==TK_SPAN );
       assert( pSrcCol->pDflt==0 || pSrcCol->pDflt->op==TK_SPAN );
       if( (pDestCol->pDflt==0)!=(pSrcCol->pDflt==0) 
        || (pDestCol->pDflt && strcmp(pDestCol->pDflt->u.zToken,
                                        pSrcCol->pDflt->u.zToken)!=0)

Index: src/parse.y
==================================================================
--- src/parse.y
+++ src/parse.y
@@ -345,10 +345,14 @@
 ccons ::= CHECK LP expr(X) RP.   {sqlite3AddCheckConstraint(pParse,X);}
 ccons ::= REFERENCES nm(T) eidlist_opt(TA) refargs(R).
                                  {sqlite3CreateForeignKey(pParse,0,&T,TA,R);}
 ccons ::= defer_subclause(D).    {sqlite3DeferForeignKey(pParse,D);}
 ccons ::= COLLATE ids(C).        {sqlite3AddCollateType(pParse, &C);}
+ccons ::= GENERATED ALWAYS AS generated.
+ccons ::= AS generated.
+generated ::= LP expr(E) RP.          {sqlite3AddGenerated(pParse,E,0);}
+generated ::= LP expr(E) RP ID(TYPE). {sqlite3AddGenerated(pParse,E,&TYPE);}
 
 // The optional AUTOINCREMENT keyword
 %type autoinc {int}
 autoinc(X) ::= .          {X = 0;}
 autoinc(X) ::= AUTOINCR.  {X = 1;}

Index: src/pragma.c
==================================================================
--- src/pragma.c
+++ src/pragma.c
@@ -1098,29 +1098,38 @@
       Index *pPk = sqlite3PrimaryKeyIndex(pTab);
       pParse->nMem = 7;
       sqlite3CodeVerifySchema(pParse, iTabDb);
       sqlite3ViewGetColumnNames(pParse, pTab);
       for(i=0, pCol=pTab->aCol; i<pTab->nCol; i++, pCol++){
-        int isHidden = IsHiddenColumn(pCol);
-        if( isHidden && pPragma->iArg==0 ){
-          nHidden++;
-          continue;
+        int isHidden = 0;
+        if( pCol->colFlags & COLFLAG_NOINSERT ){
+          if( pPragma->iArg==0 ){
+            nHidden++;
+            continue;
+          }
+          if( pCol->colFlags & COLFLAG_VIRTUAL ){
+            isHidden = 2;  /* GENERATED ALWAYS AS ... VIRTUAL */
+          }else if( pCol->colFlags & COLFLAG_STORED ){
+            isHidden = 3;  /* GENERATED ALWAYS AS ... STORED */
+          }else{ assert( pCol->colFlags & COLFLAG_HIDDEN );
+            isHidden = 1;  /* HIDDEN */
+          }
         }
         if( (pCol->colFlags & COLFLAG_PRIMKEY)==0 ){
           k = 0;
         }else if( pPk==0 ){
           k = 1;
         }else{
           for(k=1; k<=pTab->nCol && pPk->aiColumn[k-1]!=i; k++){}
         }
-        assert( pCol->pDflt==0 || pCol->pDflt->op==TK_SPAN );
+        assert( pCol->pDflt==0 || pCol->pDflt->op==TK_SPAN || isHidden>=2 );
         sqlite3VdbeMultiLoad(v, 1, pPragma->iArg ? "issisii" : "issisi",
                i-nHidden,
                pCol->zName,
                sqlite3ColumnType(pCol,""),
                pCol->notNull ? 1 : 0,
-               pCol->pDflt ? pCol->pDflt->u.zToken : 0,
+               pCol->pDflt && isHidden<2 ? pCol->pDflt->u.zToken : 0,
                k,
                isHidden);
       }
     }
   }
@@ -1575,11 +1584,11 @@
         assert( sqlite3NoTempsInRange(pParse,1,7+j) );
         sqlite3VdbeAddOp2(v, OP_Rewind, iDataCur, 0); VdbeCoverage(v);
         loopTop = sqlite3VdbeAddOp2(v, OP_AddImm, 7, 1);
         if( !isQuick ){
           /* Sanity check on record header decoding */
-          sqlite3VdbeAddOp3(v, OP_Column, iDataCur, pTab->nCol-1, 3);
+          sqlite3VdbeAddOp3(v, OP_Column, iDataCur, pTab->nNVCol-1,3);
           sqlite3VdbeChangeP5(v, OPFLAG_TYPEOFARG);
         }
         /* Verify that all NOT NULL columns really are NOT NULL */
         for(j=0; j<pTab->nCol; j++){
           char *zErr;

Index: src/resolve.c
==================================================================
--- src/resolve.c
+++ src/resolve.c
@@ -412,11 +412,11 @@
     ** Perhaps the name is a reference to the ROWID
     */
     if( cnt==0
      && cntTab==1
      && pMatch
-     && (pNC->ncFlags & NC_IdxExpr)==0
+     && (pNC->ncFlags & (NC_IdxExpr|NC_GenCol))==0
      && sqlite3IsRowid(zCol)
      && VisibleRowid(pMatch->pTab)
     ){
       cnt = 1;
       pExpr->iColumn = -1;
@@ -623,17 +623,20 @@
   Parse *pParse,       /* Leave error message here */
   NameContext *pNC,    /* The name context */
   const char *zMsg,    /* Type of error */
   int validMask        /* Set of contexts for which prohibited */
 ){
-  assert( (validMask&~(NC_IsCheck|NC_PartIdx|NC_IdxExpr))==0 );
+  assert( (validMask&~(NC_IsCheck|NC_PartIdx|NC_IdxExpr|NC_GenCol))==0 );
   if( (pNC->ncFlags & validMask)!=0 ){
     const char *zIn = "partial index WHERE clauses";
     if( pNC->ncFlags & NC_IdxExpr )      zIn = "index expressions";
 #ifndef SQLITE_OMIT_CHECK
     else if( pNC->ncFlags & NC_IsCheck ) zIn = "CHECK constraints";
 #endif
+#ifndef SQLITE_OMIT_GENERATED_COLUMNS
+    else if( pNC->ncFlags & NC_GenCol ) zIn = "generated columns";
+#endif
     sqlite3ErrorMsg(pParse, "%s prohibited in %s", zMsg, zIn);
   }
 }
 
 /*
@@ -721,11 +724,11 @@
         zDb = 0;
         zTable = 0;
         zColumn = pExpr->u.zToken;
       }else{
         Expr *pLeft = pExpr->pLeft;
-        notValid(pParse, pNC, "the \".\" operator", NC_IdxExpr);
+        notValid(pParse, pNC, "the \".\" operator", NC_IdxExpr|NC_GenCol);
         pRight = pExpr->pRight;
         if( pRight->op==TK_ID ){
           zDb = 0;
         }else{
           assert( pRight->op==TK_DOT );
@@ -818,11 +821,11 @@
         if( (pDef->funcFlags & SQLITE_FUNC_CONSTANT)==0 ){
           /* Date/time functions that use 'now', and other functions like
           ** sqlite_version() that might change over time cannot be used
           ** in an index. */
           notValid(pParse, pNC, "non-deterministic functions",
-                   NC_IdxExpr|NC_PartIdx);
+                   NC_IdxExpr|NC_PartIdx|NC_GenCol);
         }
         if( (pDef->funcFlags & SQLITE_FUNC_INTERNAL)!=0
          && pParse->nested==0
          && sqlite3Config.bInternalFunctions==0
         ){
@@ -962,11 +965,12 @@
 #endif
     case TK_IN: {
       testcase( pExpr->op==TK_IN );
       if( ExprHasProperty(pExpr, EP_xIsSelect) ){
         int nRef = pNC->nRef;
-        notValid(pParse, pNC, "subqueries", NC_IsCheck|NC_PartIdx|NC_IdxExpr);
+        notValid(pParse, pNC, "subqueries", 
+                 NC_IsCheck|NC_PartIdx|NC_IdxExpr|NC_GenCol);
         sqlite3WalkSelect(pWalker, pExpr->x.pSelect);
         assert( pNC->nRef>=nRef );
         if( nRef!=pNC->nRef ){
           ExprSetProperty(pExpr, EP_VarSelect);
           pNC->ncFlags |= NC_VarSelect;
@@ -973,11 +977,12 @@
         }
       }
       break;
     }
     case TK_VARIABLE: {
-      notValid(pParse, pNC, "parameters", NC_IsCheck|NC_PartIdx|NC_IdxExpr);
+      notValid(pParse, pNC, "parameters",
+               NC_IsCheck|NC_PartIdx|NC_IdxExpr|NC_GenCol);
       break;
     }
     case TK_IS:
     case TK_ISNOT: {
       Expr *pRight = sqlite3ExprSkipCollateAndLikely(pExpr->pRight);
@@ -1786,30 +1791,32 @@
 **
 **    (1)   CHECK constraints
 **    (2)   WHERE clauses on partial indices
 **    (3)   Expressions in indexes on expressions
 **    (4)   Expression arguments to VACUUM INTO.
+**    (5)   GENERATED ALWAYS as expressions
 **
 ** In all cases except (4), the Expr.iTable value for Expr.op==TK_COLUMN
 ** nodes of the expression is set to -1 and the Expr.iColumn value is
 ** set to the column number.  In case (4), TK_COLUMN nodes cause an error.
 **
 ** Any errors cause an error message to be set in pParse.
 */
 int sqlite3ResolveSelfReference(
-  Parse *pParse,      /* Parsing context */
-  Table *pTab,        /* The table being referenced, or NULL */
-  int type,           /* NC_IsCheck or NC_PartIdx or NC_IdxExpr, or 0 */
-  Expr *pExpr,        /* Expression to resolve.  May be NULL. */
-  ExprList *pList     /* Expression list to resolve.  May be NULL. */
+  Parse *pParse,   /* Parsing context */
+  Table *pTab,     /* The table being referenced, or NULL */
+  int type,        /* NC_IsCheck, NC_PartIdx, NC_IdxExpr, NC_GenCol, or 0 */
+  Expr *pExpr,     /* Expression to resolve.  May be NULL. */
+  ExprList *pList  /* Expression list to resolve.  May be NULL. */
 ){
   SrcList sSrc;                   /* Fake SrcList for pParse->pNewTable */
   NameContext sNC;                /* Name context for pParse->pNewTable */
   int rc;
 
   assert( type==0 || pTab!=0 );
-  assert( type==NC_IsCheck || type==NC_PartIdx || type==NC_IdxExpr || pTab==0 );
+  assert( type==NC_IsCheck || type==NC_PartIdx || type==NC_IdxExpr
+          || type==NC_GenCol || pTab==0 );
   memset(&sNC, 0, sizeof(sNC));
   memset(&sSrc, 0, sizeof(sSrc));
   if( pTab ){
     sSrc.nSrc = 1;
     sSrc.a[0].zName = pTab->zName;

Index: src/sqliteInt.h
==================================================================
--- src/sqliteInt.h
+++ src/sqliteInt.h
@@ -1816,30 +1816,49 @@
   void (*xDestroy)(void *);            /* Module destructor function */
   Table *pEpoTab;                      /* Eponymous table for this module */
 };
 
 /*
-** information about each column of an SQL table is held in an instance
-** of this structure.
+** Information about each column of an SQL table is held in an instance
+** of the Column structure, in the Table.aCol[] array.
+**
+** Definitions:
+**
+**   "table column index"     This is the index of the column in the
+**                            Table.aCol[] array, and also the index of
+**                            the column in the original CREATE TABLE stmt.
+**
+**   "storage column index"   This is the index of the column in the
+**                            record BLOB generated by the OP_MakeRecord
+**                            opcode.  The storage column index is less than
+**                            or equal to the table column index.  It is
+**                            equal if and only if there are no VIRTUAL
+**                            columns to the left.
 */
 struct Column {
   char *zName;     /* Name of this column, \000, then the type */
-  Expr *pDflt;     /* Default value of this column */
+  Expr *pDflt;     /* Default value or GENERATED ALWAYS AS value */
   char *zColl;     /* Collating sequence.  If NULL, use the default */
   u8 notNull;      /* An OE_ code for handling a NOT NULL constraint */
   char affinity;   /* One of the SQLITE_AFF_... values */
   u8 szEst;        /* Estimated size of value in this column. sizeof(INT)==1 */
-  u8 colFlags;     /* Boolean properties.  See COLFLAG_ defines below */
+  u16 colFlags;    /* Boolean properties.  See COLFLAG_ defines below */
 };
 
 /* Allowed values for Column.colFlags:
 */
-#define COLFLAG_PRIMKEY  0x0001    /* Column is part of the primary key */
-#define COLFLAG_HIDDEN   0x0002    /* A hidden column in a virtual table */
-#define COLFLAG_HASTYPE  0x0004    /* Type name follows column name */
-#define COLFLAG_UNIQUE   0x0008    /* Column def contains "UNIQUE" or "PK" */
+#define COLFLAG_PRIMKEY   0x0001   /* Column is part of the primary key */
+#define COLFLAG_HIDDEN    0x0002   /* A hidden column in a virtual table */
+#define COLFLAG_HASTYPE   0x0004   /* Type name follows column name */
+#define COLFLAG_UNIQUE    0x0008   /* Column def contains "UNIQUE" or "PK" */
 #define COLFLAG_SORTERREF 0x0010   /* Use sorter-refs with this column */
+#define COLFLAG_VIRTUAL   0x0020   /* GENERATED ALWAYS AS ... VIRTUAL */
+#define COLFLAG_STORED    0x0040   /* GENERATED ALWAYS AS ... STORED */
+#define COLFLAG_BUSY      0x0080   /* Blocks recursion on GENERATED columns */
+#define COLFLAG_NOTAVAIL  0x0100   /* STORED column not yet calculated */
+#define COLFLAG_GENERATED 0x0060   /* Combo: _STORED, _VIRTUAL */
+#define COLFLAG_NOINSERT  0x0062   /* Combo: _HIDDEN, _STORED, _VIRTUAL */
 
 /*
 ** A "Collating Sequence" is defined by an instance of the following
 ** structure. Conceptually, a collating sequence consists of a name and
 ** a comparison routine that defines the order of that sequence.
@@ -1975,10 +1994,11 @@
   int tnum;            /* Root BTree page for this table */
   u32 nTabRef;         /* Number of pointers to this Table */
   u32 tabFlags;        /* Mask of TF_* values */
   i16 iPKey;           /* If not negative, use aCol[iPKey] as the rowid */
   i16 nCol;            /* Number of columns in this table */
+  i16 nNVCol;          /* Number of columns that are not VIRTUAL */
   LogEst nRowLogEst;   /* Estimated rows in table - from sqlite_stat1 table */
   LogEst szTabRow;     /* Estimated size of each table row in bytes */
 #ifdef SQLITE_ENABLE_COSTMULT
   LogEst costMult;     /* Cost multiplier for using this table */
 #endif
@@ -2001,24 +2021,32 @@
 **
 ** TF_OOOHidden applies to tables or view that have hidden columns that are
 ** followed by non-hidden columns.  Example:  "CREATE VIRTUAL TABLE x USING
 ** vtab1(a HIDDEN, b);".  Since "b" is a non-hidden column but "a" is hidden,
 ** the TF_OOOHidden attribute would apply in this case.  Such tables require
-** special handling during INSERT processing.
+** special handling during INSERT processing. The "OOO" means "Out Of Order".
+**
+** Constraints:
+**
+**         TF_HasVirtual == COLFLAG_Virtual
+**         TF_HasStored  == COLFLAG_Stored
 */
 #define TF_Readonly        0x0001    /* Read-only system table */
 #define TF_Ephemeral       0x0002    /* An ephemeral table */
 #define TF_HasPrimaryKey   0x0004    /* Table has a primary key */
 #define TF_Autoincrement   0x0008    /* Integer primary key is autoincrement */
 #define TF_HasStat1        0x0010    /* nRowLogEst set from sqlite_stat1 */
-#define TF_WithoutRowid    0x0020    /* No rowid.  PRIMARY KEY is the key */
-#define TF_NoVisibleRowid  0x0040    /* No user-visible "rowid" column */
-#define TF_OOOHidden       0x0080    /* Out-of-Order hidden columns */
+#define TF_HasVirtual      0x0020    /* Has one or more VIRTUAL columns */
+#define TF_HasStored       0x0040    /* Has one or more STORED columns */
+#define TF_HasGenerated    0x0060    /* Combo: HasVirtual + HasStored */
+#define TF_WithoutRowid    0x0080    /* No rowid.  PRIMARY KEY is the key */
 #define TF_StatsUsed       0x0100    /* Query planner decisions affected by
                                      ** Index.aiRowLogEst[] values */
-#define TF_HasNotNull      0x0200    /* Contains NOT NULL constraints */
-#define TF_Shadow          0x0400    /* True for a shadow table */
+#define TF_NoVisibleRowid  0x0200    /* No user-visible "rowid" column */
+#define TF_OOOHidden       0x0400    /* Out-of-Order hidden columns */
+#define TF_HasNotNull      0x0800    /* Contains NOT NULL constraints */
+#define TF_Shadow          0x1000    /* True for a shadow table */
 
 /*
 ** Test to see whether or not a table is a virtual table.  This is
 ** done as a macro so that it will be optimized out when virtual
 ** table support is omitted from the build.
@@ -2265,10 +2293,11 @@
   unsigned isCovering:1;   /* True if this is a covering index */
   unsigned noSkipScan:1;   /* Do not try to use skip-scan if true */
   unsigned hasStat1:1;     /* aiRowLogEst values come from sqlite_stat1 */
   unsigned bNoQuery:1;     /* Do not use this index to optimize queries */
   unsigned bAscKeyBug:1;   /* True if the bba7b69f9849b5bf bug applies */
+  unsigned bHasVCol:1;     /* Index references one or more VIRTUAL columns */
 #ifdef SQLITE_ENABLE_STAT4
   int nSample;             /* Number of elements in aSample[] */
   int nSampleCol;          /* Size of IndexSample.anEq[] and so on */
   tRowcnt *aAvgEq;         /* Average nEq values for keys not in aSample */
   IndexSample *aSample;    /* Samples of the left-most key */
@@ -2806,25 +2835,26 @@
 **    NC_HasAgg    == SF_HasAgg    == EP_Agg
 **    NC_MinMaxAgg == SF_MinMaxAgg == SQLITE_FUNC_MINMAX
 **    NC_HasWin    == EP_Win
 **
 */
-#define NC_AllowAgg  0x0001  /* Aggregate functions are allowed here */
-#define NC_PartIdx   0x0002  /* True if resolving a partial index WHERE */
-#define NC_IsCheck   0x0004  /* True if resolving names in a CHECK constraint */
-#define NC_InAggFunc 0x0008  /* True if analyzing arguments to an agg func */
-#define NC_HasAgg    0x0010  /* One or more aggregate functions seen */
-#define NC_IdxExpr   0x0020  /* True if resolving columns of CREATE INDEX */
-#define NC_VarSelect 0x0040  /* A correlated subquery has been seen */
-#define NC_UEList    0x0080  /* True if uNC.pEList is used */
-#define NC_UAggInfo  0x0100  /* True if uNC.pAggInfo is used */
-#define NC_UUpsert   0x0200  /* True if uNC.pUpsert is used */
-#define NC_MinMaxAgg 0x1000  /* min/max aggregates seen.  See note above */
-#define NC_Complex   0x2000  /* True if a function or subquery seen */
-#define NC_AllowWin  0x4000  /* Window functions are allowed here */
-#define NC_HasWin    0x8000  /* One or more window functions seen */
-#define NC_IsDDL    0x10000  /* Resolving names in a CREATE statement */
+#define NC_AllowAgg  0x00001  /* Aggregate functions are allowed here */
+#define NC_PartIdx   0x00002  /* True if resolving a partial index WHERE */
+#define NC_IsCheck   0x00004  /* True if resolving a CHECK constraint */
+#define NC_InAggFunc 0x00008  /* True if analyzing arguments to an agg func */
+#define NC_HasAgg    0x00010  /* One or more aggregate functions seen */
+#define NC_IdxExpr   0x00020  /* True if resolving columns of CREATE INDEX */
+#define NC_VarSelect 0x00040  /* A correlated subquery has been seen */
+#define NC_UEList    0x00080  /* True if uNC.pEList is used */
+#define NC_UAggInfo  0x00100  /* True if uNC.pAggInfo is used */
+#define NC_UUpsert   0x00200  /* True if uNC.pUpsert is used */
+#define NC_MinMaxAgg 0x01000  /* min/max aggregates seen.  See note above */
+#define NC_Complex   0x02000  /* True if a function or subquery seen */
+#define NC_AllowWin  0x04000  /* Window functions are allowed here */
+#define NC_HasWin    0x08000  /* One or more window functions seen */
+#define NC_IsDDL     0x10000  /* Resolving names in a CREATE statement */
+#define NC_GenCol    0x20000  /* True for a GENERATED ALWAYS AS clause */
 
 /*
 ** An instance of the following object describes a single ON CONFLICT
 ** clause in an upsert.
 **
@@ -3935,11 +3965,18 @@
 int sqlite3ColumnsFromExprList(Parse*,ExprList*,i16*,Column**);
 void sqlite3SelectAddColumnTypeAndCollation(Parse*,Table*,Select*,char);
 Table *sqlite3ResultSetOfSelect(Parse*,Select*,char);
 void sqlite3OpenMasterTable(Parse *, int);
 Index *sqlite3PrimaryKeyIndex(Table*);
-i16 sqlite3ColumnOfIndex(Index*, i16);
+i16 sqlite3TableColumnToIndex(Index*, i16);
+#ifdef SQLITE_OMIT_GENERATED_COLUMNS
+# define sqlite3TableColumnToStorage(T,X) (X)  /* No-op pass-through */
+# define sqlite3StorageColumnToTable(T,X) (X)  /* No-op pass-through */
+#else
+  i16 sqlite3TableColumnToStorage(Table*, i16);
+  i16 sqlite3StorageColumnToTable(Table*, i16);
+#endif
 void sqlite3StartTable(Parse*,Token*,Token*,int,int,int,int);
 #if SQLITE_ENABLE_HIDDEN_COLUMNS
   void sqlite3ColumnPropertiesFromName(Table*, Column*);
 #else
 # define sqlite3ColumnPropertiesFromName(T,C) /* no-op */
@@ -3948,10 +3985,11 @@
 void sqlite3AddNotNull(Parse*, int);
 void sqlite3AddPrimaryKey(Parse*, ExprList*, int, int, int);
 void sqlite3AddCheckConstraint(Parse*, Expr*);
 void sqlite3AddDefaultValue(Parse*,Expr*,const char*,const char*);
 void sqlite3AddCollateType(Parse*, Token*);
+void sqlite3AddGenerated(Parse*,Expr*,Token*);
 void sqlite3EndTable(Parse*,Token*,Token*,u8,Select*);
 int sqlite3ParseUri(const char*,const char*,unsigned int*,
                     sqlite3_vfs**,char**,char **);
 #ifdef SQLITE_HAS_CODEC
   int sqlite3CodecQueryParameters(sqlite3*,const char*,const char*);
@@ -4005,10 +4043,13 @@
 #else
 # define sqlite3AutoincrementBegin(X)
 # define sqlite3AutoincrementEnd(X)
 #endif
 void sqlite3Insert(Parse*, SrcList*, Select*, IdList*, int, Upsert*);
+#ifndef SQLITE_OMIT_GENERATED_COLUMNS
+  void sqlite3ComputeGeneratedColumns(Parse*, int, Table*);
+#endif
 void *sqlite3ArrayAllocate(sqlite3*,void*,int,int*,int*);
 IdList *sqlite3IdListAppend(Parse*, IdList*, Token*);
 int sqlite3IdListIndex(IdList*,const char*);
 SrcList *sqlite3SrcListEnlarge(Parse*, SrcList*, int, int);
 SrcList *sqlite3SrcListAppend(Parse*, SrcList*, Token*, Token*);
@@ -4054,16 +4095,18 @@
 void sqlite3ExprCodeLoadIndexColumn(Parse*, Index*, int, int, int);
 int sqlite3ExprCodeGetColumn(Parse*, Table*, int, int, int, u8);
 void sqlite3ExprCodeGetColumnOfTable(Vdbe*, Table*, int, int, int);
 void sqlite3ExprCodeMove(Parse*, int, int, int);
 void sqlite3ExprCode(Parse*, Expr*, int);
+#ifndef SQLITE_OMIT_GENERATED_COLUMNS
+void sqlite3ExprCodeGeneratedColumn(Parse*, Column*, int);
+#endif
 void sqlite3ExprCodeCopy(Parse*, Expr*, int);
 void sqlite3ExprCodeFactorable(Parse*, Expr*, int);
 int sqlite3ExprCodeAtInit(Parse*, Expr*, int);
 int sqlite3ExprCodeTemp(Parse*, Expr*, int*);
 int sqlite3ExprCodeTarget(Parse*, Expr*, int);
-void sqlite3ExprCodeAndCache(Parse*, Expr*, int);
 int sqlite3ExprCodeExprList(Parse*, ExprList*, int, int, u8);
 #define SQLITE_ECEL_DUP      0x01  /* Deep, not shallow copies */
 #define SQLITE_ECEL_FACTOR   0x02  /* Factor out constant terms */
 #define SQLITE_ECEL_REF      0x04  /* Use ExprList.u.x.iOrderByCol */
 #define SQLITE_ECEL_OMITREF  0x08  /* Omit if ExprList.u.x.iOrderByCol */

Index: src/update.c
==================================================================
--- src/update.c
+++ src/update.c
@@ -145,11 +145,11 @@
   int onError,           /* How to handle constraint errors */
   ExprList *pOrderBy,    /* ORDER BY clause. May be null */
   Expr *pLimit,          /* LIMIT clause. May be null */
   Upsert *pUpsert        /* ON CONFLICT clause, or null */
 ){
-  int i, j;              /* Loop counters */
+  int i, j, k;           /* Loop counters */
   Table *pTab;           /* The table to be updated */
   int addrTop = 0;       /* VDBE instruction address of the start of the loop */
   WhereInfo *pWInfo;     /* Information about the WHERE clause */
   Vdbe *v;               /* The virtual database engine */
   Index *pIdx;           /* For looping over indices */
@@ -310,10 +310,20 @@
           chngRowid = 1;
           pRowidExpr = pChanges->a[i].pExpr;
         }else if( pPk && (pTab->aCol[j].colFlags & COLFLAG_PRIMKEY)!=0 ){
           chngPk = 1;
         }
+#ifndef SQLITE_OMIT_GENERATED_COLUMNS
+        else if( pTab->aCol[j].colFlags & COLFLAG_GENERATED ){
+          testcase( pTab->aCol[j].colFlags & COLFLAG_VIRTUAL );
+          testcase( pTab->aCol[j].colFlags & COLFLAG_STORED );
+          sqlite3ErrorMsg(pParse, 
+             "cannot UPDATE generated column \"%s\"",
+             pTab->aCol[j].zName);
+          goto update_cleanup;
+        }
+#endif
         aXRef[j] = i;
         break;
       }
     }
     if( j>=pTab->nCol ){
@@ -343,10 +353,37 @@
   }
   assert( (chngRowid & chngPk)==0 );
   assert( chngRowid==0 || chngRowid==1 );
   assert( chngPk==0 || chngPk==1 );
   chngKey = chngRowid + chngPk;
+
+#ifndef SQLITE_OMIT_GENERATED_COLUMNS
+  /* Mark generated columns as changing if their generator expressions
+  ** reference any changing column.  The actual aXRef[] value for 
+  ** generated expressions is not used, other than to check to see that it
+  ** is non-negative, so the value of aXRef[] for generated columns can be
+  ** set to any non-negative number.  We use 99999 so that the value is
+  ** obvious when looking at aXRef[] in a symbolic debugger. 
+  */
+  if( pTab->tabFlags & TF_HasGenerated ){
+    int bProgress;
+    testcase( pTab->tabFlags & TF_HasVirtual );
+    testcase( pTab->tabFlags & TF_HasStored );
+    do{
+      bProgress = 0;
+      for(i=0; i<pTab->nCol; i++){
+        if( aXRef[i]>=0 ) continue;
+        if( (pTab->aCol[i].colFlags & COLFLAG_GENERATED)==0 ) continue;
+        if( sqlite3ExprReferencesUpdatedColumn(pTab->aCol[i].pDflt,
+                                               aXRef, chngRowid) ){
+          aXRef[i] = 99999;
+          bProgress = 1;
+        }
+      }
+    }while( bProgress );
+  }
+#endif
 
   /* The SET expressions are not actually used inside the WHERE loop.  
   ** So reset the colUsed mask. Unless this is a virtual table. In that
   ** case, set all bits of the colUsed mask (to ensure that the virtual
   ** table implementation makes all columns available).
@@ -541,11 +578,12 @@
     ** the ephemeral table. Or, in ONEPASS_SINGLE or MULTI mode, change
     ** the OP_OpenEphemeral instruction to a Noop (the ephemeral table 
     ** is not required) and leave the PK fields in the array of registers.  */
     for(i=0; i<nPk; i++){
       assert( pPk->aiColumn[i]>=0 );
-      sqlite3ExprCodeGetColumnOfTable(v, pTab, iDataCur,pPk->aiColumn[i],iPk+i);
+      sqlite3ExprCodeGetColumnOfTable(v, pTab, iDataCur,
+                                      pPk->aiColumn[i], iPk+i);
     }
     if( eOnePass ){
       if( addrOpen ) sqlite3VdbeChangeToNoop(v, addrOpen);
       nKey = nPk;
       regKey = iPk;
@@ -621,19 +659,24 @@
   if( chngPk || hasFK || pTrigger ){
     u32 oldmask = (hasFK ? sqlite3FkOldmask(pParse, pTab) : 0);
     oldmask |= sqlite3TriggerColmask(pParse, 
         pTrigger, pChanges, 0, TRIGGER_BEFORE|TRIGGER_AFTER, pTab, onError
     );
-    for(i=0; i<pTab->nCol; i++){
+    for(i=0, k=regOld; i<pTab->nCol; i++, k++){
+      u32 colFlags = pTab->aCol[i].colFlags;
+      if( colFlags & COLFLAG_VIRTUAL ){
+        k--;
+        continue;
+      }
       if( oldmask==0xffffffff
        || (i<32 && (oldmask & MASKBIT32(i))!=0)
-       || (pTab->aCol[i].colFlags & COLFLAG_PRIMKEY)!=0
+       || (colFlags & COLFLAG_PRIMKEY)!=0
       ){
         testcase(  oldmask!=0xffffffff && i==31 );
-        sqlite3ExprCodeGetColumnOfTable(v, pTab, iDataCur, i, regOld+i);
+        sqlite3ExprCodeGetColumnOfTable(v, pTab, iDataCur, i, k);
       }else{
-        sqlite3VdbeAddOp2(v, OP_Null, 0, regOld+i);
+        sqlite3VdbeAddOp2(v, OP_Null, 0, k);
       }
     }
     if( chngRowid==0 && pPk==0 ){
       sqlite3VdbeAddOp2(v, OP_Copy, regOldRowid, regNewRowid);
     }
@@ -653,31 +696,40 @@
   ** be used eliminates some redundant opcodes.
   */
   newmask = sqlite3TriggerColmask(
       pParse, pTrigger, pChanges, 1, TRIGGER_BEFORE, pTab, onError
   );
-  for(i=0; i<pTab->nCol; i++){
+  for(i=0, k=regNew; i<pTab->nCol; i++, k++){
     if( i==pTab->iPKey ){
-      sqlite3VdbeAddOp2(v, OP_Null, 0, regNew+i);
+      sqlite3VdbeAddOp2(v, OP_Null, 0, k);
+    }else if( (pTab->aCol[i].colFlags & COLFLAG_GENERATED)!=0 ){
+      if( pTab->aCol[i].colFlags & COLFLAG_VIRTUAL ) k--;
     }else{
       j = aXRef[i];
       if( j>=0 ){
-        sqlite3ExprCode(pParse, pChanges->a[j].pExpr, regNew+i);
+        sqlite3ExprCode(pParse, pChanges->a[j].pExpr, k);
       }else if( 0==(tmask&TRIGGER_BEFORE) || i>31 || (newmask & MASKBIT32(i)) ){
         /* This branch loads the value of a column that will not be changed 
         ** into a register. This is done if there are no BEFORE triggers, or
         ** if there are one or more BEFORE triggers that use this value via
         ** a new.* reference in a trigger program.
         */
         testcase( i==31 );
         testcase( i==32 );
-        sqlite3ExprCodeGetColumnOfTable(v, pTab, iDataCur, i, regNew+i);
+        sqlite3ExprCodeGetColumnOfTable(v, pTab, iDataCur, i, k);
       }else{
-        sqlite3VdbeAddOp2(v, OP_Null, 0, regNew+i);
+        sqlite3VdbeAddOp2(v, OP_Null, 0, k);
       }
     }
   }
+#ifndef SQLITE_OMIT_GENERATED_COLUMNS
+  if( pTab->tabFlags & TF_HasGenerated ){
+    testcase( pTab->tabFlags & TF_HasVirtual );
+    testcase( pTab->tabFlags & TF_HasStored );
+    sqlite3ComputeGeneratedColumns(pParse, regNew, pTab);
+  }
+#endif
 
   /* Fire any BEFORE UPDATE triggers. This happens before constraints are
   ** verified. One could argue that this is wrong.
   */
   if( tmask&TRIGGER_BEFORE ){
@@ -706,15 +758,24 @@
     ** in case this has happened. Only unmodified columns are reloaded.
     ** The values computed for modified columns use the values before the
     ** BEFORE trigger runs.  See test case trigger1-18.0 (added 2018-04-26)
     ** for an example.
     */
-    for(i=0; i<pTab->nCol; i++){
-      if( aXRef[i]<0 && i!=pTab->iPKey ){
-        sqlite3ExprCodeGetColumnOfTable(v, pTab, iDataCur, i, regNew+i);
+    for(i=0, k=regNew; i<pTab->nCol; i++, k++){
+      if( pTab->aCol[i].colFlags & COLFLAG_GENERATED ){
+        if( pTab->aCol[i].colFlags & COLFLAG_VIRTUAL ) k--;
+      }else if( aXRef[i]<0 && i!=pTab->iPKey ){
+        sqlite3ExprCodeGetColumnOfTable(v, pTab, iDataCur, i, k);
       }
     }
+#ifndef SQLITE_OMIT_GENERATED_COLUMNS
+    if( pTab->tabFlags & TF_HasGenerated ){
+      testcase( pTab->tabFlags & TF_HasVirtual );
+      testcase( pTab->tabFlags & TF_HasStored );
+      sqlite3ComputeGeneratedColumns(pParse, regNew, pTab);
+    }
+#endif 
   }
 
   if( !isView ){
     /* Do constraint checks. */
     assert( regOldRowid>0 );
@@ -916,10 +977,11 @@
   pWInfo = sqlite3WhereBegin(pParse, pSrc, pWhere, 0,0,WHERE_ONEPASS_DESIRED,0);
   if( pWInfo==0 ) return;
 
   /* Populate the argument registers. */
   for(i=0; i<pTab->nCol; i++){
+    assert( (pTab->aCol[i].colFlags & COLFLAG_GENERATED)==0 );
     if( aXRef[i]>=0 ){
       sqlite3ExprCode(pParse, pChanges->a[aXRef[i]].pExpr, regArg+2+i);
     }else{
       sqlite3VdbeAddOp3(v, OP_VColumn, iCsr, i, regArg+2+i);
       sqlite3VdbeChangeP5(v, OPFLAG_NOCHNG);/* Enable sqlite3_vtab_nochange() */

Index: src/upsert.c
==================================================================
--- src/upsert.c
+++ src/upsert.c
@@ -224,11 +224,11 @@
       int iPk = pParse->nMem+1;
       pParse->nMem += nPk;
       for(i=0; i<nPk; i++){
         int k;
         assert( pPk->aiColumn[i]>=0 );
-        k = sqlite3ColumnOfIndex(pIdx, pPk->aiColumn[i]);
+        k = sqlite3TableColumnToIndex(pIdx, pPk->aiColumn[i]);
         sqlite3VdbeAddOp3(v, OP_Column, iCur, k, iPk+i);
         VdbeComment((v, "%s.%s", pIdx->zName,
                     pTab->aCol[pPk->aiColumn[i]].zName));
       }
       sqlite3VdbeVerifyAbortable(v, OE_Abort);

Index: src/vdbe.c
==================================================================
--- src/vdbe.c
+++ src/vdbe.c
@@ -3373,11 +3373,10 @@
       p->pc = (int)(pOp - aOp);
       db->autoCommit = (u8)(1-desiredAutoCommit);
       p->rc = rc = SQLITE_BUSY;
       goto vdbe_return;
     }
-    assert( db->nStatement==0 );
     sqlite3CloseSavepoints(db);
     if( p->rc==SQLITE_OK ){
       rc = SQLITE_DONE;
     }else{
       rc = SQLITE_ERROR;

Index: src/vdbe.h
==================================================================
--- src/vdbe.h
+++ src/vdbe.h
@@ -177,10 +177,11 @@
 /*
 ** Prototypes for the VDBE interface.  See comments on the implementation
 ** for a description of what each of these routines does.
 */
 Vdbe *sqlite3VdbeCreate(Parse*);
+Parse *sqlite3VdbeParser(Vdbe*);
 int sqlite3VdbeAddOp0(Vdbe*,int);
 int sqlite3VdbeAddOp1(Vdbe*,int,int);
 int sqlite3VdbeAddOp2(Vdbe*,int,int,int);
 int sqlite3VdbeGoto(Vdbe*,int);
 int sqlite3VdbeLoadString(Vdbe*,int,const char*);

Index: src/vdbeapi.c
==================================================================
--- src/vdbeapi.c
+++ src/vdbeapi.c
@@ -1829,11 +1829,11 @@
   if( !p || p->op==SQLITE_INSERT ){
     rc = SQLITE_MISUSE_BKPT;
     goto preupdate_old_out;
   }
   if( p->pPk ){
-    iIdx = sqlite3ColumnOfIndex(p->pPk, iIdx);
+    iIdx = sqlite3TableColumnToIndex(p->pPk, iIdx);
   }
   if( iIdx>=p->pCsr->nField || iIdx<0 ){
     rc = SQLITE_RANGE;
     goto preupdate_old_out;
   }
@@ -1919,11 +1919,11 @@
   if( !p || p->op==SQLITE_DELETE ){
     rc = SQLITE_MISUSE_BKPT;
     goto preupdate_new_out;
   }
   if( p->pPk && p->op!=SQLITE_UPDATE ){
-    iIdx = sqlite3ColumnOfIndex(p->pPk, iIdx);
+    iIdx = sqlite3TableColumnToIndex(p->pPk, iIdx);
   }
   if( iIdx>=p->pCsr->nField || iIdx<0 ){
     rc = SQLITE_RANGE;
     goto preupdate_new_out;
   }

Index: src/vdbeaux.c
==================================================================
--- src/vdbeaux.c
+++ src/vdbeaux.c
@@ -39,10 +39,17 @@
   assert( p->nOpAlloc==0 );
   assert( pParse->szOpAlloc==0 );
   sqlite3VdbeAddOp2(p, OP_Init, 0, 1);
   return p;
 }
+
+/*
+** Return the Parse object that owns a Vdbe object.
+*/
+Parse *sqlite3VdbeParser(Vdbe *p){
+  return p->pParse;
+}
 
 /*
 ** Change the error string stored in Vdbe.zErrMsg
 */
 void sqlite3VdbeError(Vdbe *p, const char *zFormat, ...){

Index: src/vtab.c
==================================================================
--- src/vtab.c
+++ src/vtab.c
@@ -622,11 +622,11 @@
       *pzErr = sqlite3MPrintf(db, zFormat, pTab->zName);
       sqlite3VtabUnlock(pVTable);
       rc = SQLITE_ERROR;
     }else{
       int iCol;
-      u8 oooHidden = 0;
+      u16 oooHidden = 0;
       /* If everything went according to plan, link the new VTable structure
       ** into the linked list headed by pTab->pVTable. Then loop through the 
       ** columns of the table to see if any of them contain the token "hidden".
       ** If so, set the Column COLFLAG_HIDDEN flag and remove the token from
       ** the type string.  */

Index: src/where.c
==================================================================
--- src/where.c
+++ src/where.c
@@ -5374,12 +5374,15 @@
           assert( pIdx->pTable==pTab );
           if( !HasRowid(pTab) ){
             Index *pPk = sqlite3PrimaryKeyIndex(pTab);
             x = pPk->aiColumn[x];
             assert( x>=0 );
+          }else{
+            testcase( x!=sqlite3StorageColumnToTable(pTab,x) );
+            x = sqlite3StorageColumnToTable(pTab,x);
           }
-          x = sqlite3ColumnOfIndex(pIdx, x);
+          x = sqlite3TableColumnToIndex(pIdx, x);
           if( x>=0 ){
             pOp->p2 = x;
             pOp->p1 = pLevel->iIdxCur;
             OpcodeRewriteTrace(db, k, pOp);
           }

Index: src/wherecode.c
==================================================================
--- src/wherecode.c
+++ src/wherecode.c
@@ -821,11 +821,11 @@
 static int codeCursorHintCheckExpr(Walker *pWalker, Expr *pExpr){
   struct CCurHint *pHint = pWalker->u.pCCurHint;
   assert( pHint->pIdx!=0 );
   if( pExpr->op==TK_COLUMN
    && pExpr->iTable==pHint->iTabCur
-   && sqlite3ColumnOfIndex(pHint->pIdx, pExpr->iColumn)<0
+   && sqlite3TableColumnToIndex(pHint->pIdx, pExpr->iColumn)<0
   ){
     pWalker->eCode = 1;
   }
   return WRC_Continue;
 }
@@ -889,11 +889,11 @@
       sqlite3ExprCode(pWalker->pParse, pExpr, reg);
       pExpr->op = TK_REGISTER;
       pExpr->iTable = reg;
     }else if( pHint->pIdx!=0 ){
       pExpr->iTable = pHint->iIdxCur;
-      pExpr->iColumn = sqlite3ColumnOfIndex(pHint->pIdx, pExpr->iColumn);
+      pExpr->iColumn = sqlite3TableColumnToIndex(pHint->pIdx, pExpr->iColumn);
       assert( pExpr->iColumn>=0 );
     }
   }else if( pExpr->op==TK_AGG_FUNCTION ){
     /* An aggregate function in the WHERE clause of a query means this must
     ** be a correlated sub-query, and expression pExpr is an aggregate from
@@ -1104,10 +1104,11 @@
 typedef struct IdxExprTrans {
   Expr *pIdxExpr;    /* The index expression */
   int iTabCur;       /* The cursor of the corresponding table */
   int iIdxCur;       /* The cursor for the index */
   int iIdxCol;       /* The column for the index */
+  int iTabCol;       /* The column for the table */
 } IdxExprTrans;
 
 /* The walker node callback used to transform matching expressions into
 ** a reference to an index column for an index on an expression.
 **
@@ -1126,37 +1127,73 @@
   }else{
     return WRC_Continue;
   }
 }
 
+#ifndef SQLITE_OMIT_GENERATED_COLUMNS
+/* A walker node callback that translates a column reference to a table
+** into a corresponding column reference of an index.
+*/
+static int whereIndexExprTransColumn(Walker *p, Expr *pExpr){
+  if( pExpr->op==TK_COLUMN ){
+    IdxExprTrans *pX = p->u.pIdxTrans;
+    if( pExpr->iTable==pX->iTabCur && pExpr->iColumn==pX->iTabCol ){
+      pExpr->iTable = pX->iIdxCur;
+      pExpr->iColumn = pX->iIdxCol;
+      pExpr->y.pTab = 0;
+    }
+  }
+  return WRC_Continue;
+}
+#endif /* SQLITE_OMIT_GENERATED_COLUMNS */
+
 /*
 ** For an indexes on expression X, locate every instance of expression X
 ** in pExpr and change that subexpression into a reference to the appropriate
 ** column of the index.
+**
+** 2019-10-24: Updated to also translate references to a VIRTUAL column in
+** the table into references to the corresponding (stored) column of the
+** index.
 */
 static void whereIndexExprTrans(
   Index *pIdx,      /* The Index */
   int iTabCur,      /* Cursor of the table that is being indexed */
   int iIdxCur,      /* Cursor of the index itself */
   WhereInfo *pWInfo /* Transform expressions in this WHERE clause */
 ){
   int iIdxCol;               /* Column number of the index */
   ExprList *aColExpr;        /* Expressions that are indexed */
+  Table *pTab;
   Walker w;
   IdxExprTrans x;
   aColExpr = pIdx->aColExpr;
-  if( aColExpr==0 ) return;  /* Not an index on expressions */
+  if( aColExpr==0 && !pIdx->bHasVCol ){
+    /* The index does not reference any expressions or virtual columns
+    ** so no translations are needed. */
+    return;
+  }
+  pTab = pIdx->pTable;
   memset(&w, 0, sizeof(w));
-  w.xExprCallback = whereIndexExprTransNode;
   w.u.pIdxTrans = &x;
   x.iTabCur = iTabCur;
   x.iIdxCur = iIdxCur;
-  for(iIdxCol=0; iIdxCol<aColExpr->nExpr; iIdxCol++){
-    if( pIdx->aiColumn[iIdxCol]!=XN_EXPR ) continue;
-    assert( aColExpr->a[iIdxCol].pExpr!=0 );
+  for(iIdxCol=0; iIdxCol<pIdx->nColumn; iIdxCol++){
+    i16 iRef = pIdx->aiColumn[iIdxCol];
+    if( iRef==XN_EXPR ){
+      assert( aColExpr->a[iIdxCol].pExpr!=0 );
+      x.pIdxExpr = aColExpr->a[iIdxCol].pExpr;
+      w.xExprCallback = whereIndexExprTransNode;
+#ifndef SQLITE_OMIT_GENERATED_COLUMNS
+    }else if( iRef>=0 && (pTab->aCol[iRef].colFlags & COLFLAG_VIRTUAL)!=0 ){
+      x.iTabCol = iRef;
+      w.xExprCallback = whereIndexExprTransColumn;
+#endif /* SQLITE_OMIT_GENERATED_COLUMNS */
+    }else{
+      continue;
+    }
     x.iIdxCol = iIdxCol;
-    x.pIdxExpr = aColExpr->a[iIdxCol].pExpr;
     sqlite3WalkExpr(&w, pWInfo->pWhere);
     sqlite3WalkExprList(&w, pWInfo->pOrderBy);
     sqlite3WalkExprList(&w, pWInfo->pResultSet);
   }
 }
@@ -1824,20 +1861,22 @@
       }
     }else if( iCur!=iIdxCur ){
       Index *pPk = sqlite3PrimaryKeyIndex(pIdx->pTable);
       iRowidReg = sqlite3GetTempRange(pParse, pPk->nKeyCol);
       for(j=0; j<pPk->nKeyCol; j++){
-        k = sqlite3ColumnOfIndex(pIdx, pPk->aiColumn[j]);
+        k = sqlite3TableColumnToIndex(pIdx, pPk->aiColumn[j]);
         sqlite3VdbeAddOp3(v, OP_Column, iIdxCur, k, iRowidReg+j);
       }
       sqlite3VdbeAddOp4Int(v, OP_NotFound, iCur, addrCont,
                            iRowidReg, pPk->nKeyCol); VdbeCoverage(v);
     }
 
     /* If pIdx is an index on one or more expressions, then look through
     ** all the expressions in pWInfo and try to transform matching expressions
-    ** into reference to index columns.
+    ** into reference to index columns.  Also attempt to translate references
+    ** to virtual columns in the table into references to (stored) columns
+    ** of the index.
     **
     ** Do not do this for the RHS of a LEFT JOIN. This is because the 
     ** expression may be evaluated after OP_NullRow has been executed on
     ** the cursor. In this case it is important to do the full evaluation,
     ** as the result of the expression may not be NULL, even if all table
@@ -2084,11 +2123,11 @@
 
               /* Read the PK into an array of temp registers. */
               r = sqlite3GetTempRange(pParse, nPk);
               for(iPk=0; iPk<nPk; iPk++){
                 int iCol = pPk->aiColumn[iPk];
-                sqlite3ExprCodeGetColumnOfTable(v, pTab, iCur, iCol, r+iPk);
+                sqlite3ExprCodeGetColumnOfTable(v, pTab, iCur, iCol,r+iPk);
               }
 
               /* Check if the temp table already contains this key. If so,
               ** the row has already been included in the result set and
               ** can be ignored (by jumping past the Gosub below). Otherwise,

Index: tool/mkkeywordhash.c
==================================================================
--- tool/mkkeywordhash.c
+++ tool/mkkeywordhash.c
@@ -162,10 +162,11 @@
   { "ACTION",           "TK_ACTION",       FKEY                   },
   { "ADD",              "TK_ADD",          ALTER                  },
   { "AFTER",            "TK_AFTER",        TRIGGER                },
   { "ALL",              "TK_ALL",          ALWAYS                 },
   { "ALTER",            "TK_ALTER",        ALTER                  },
+  { "ALWAYS",           "TK_ALWAYS",       ALWAYS                 },
   { "ANALYZE",          "TK_ANALYZE",      ANALYZE                },
   { "AND",              "TK_AND",          ALWAYS                 },
   { "AS",               "TK_AS",           ALWAYS                 },
   { "ASC",              "TK_ASC",          ALWAYS                 },
   { "ATTACH",           "TK_ATTACH",       ATTACH                 },
@@ -214,10 +215,11 @@
   { "FOLLOWING",        "TK_FOLLOWING",    WINDOWFUNC             },
   { "FOR",              "TK_FOR",          TRIGGER                },
   { "FOREIGN",          "TK_FOREIGN",      FKEY                   },
   { "FROM",             "TK_FROM",         ALWAYS                 },
   { "FULL",             "TK_JOIN_KW",      ALWAYS                 },
+  { "GENERATED",        "TK_GENERATED",    ALWAYS                 },
   { "GLOB",             "TK_LIKE_KW",      ALWAYS                 },
   { "GROUP",            "TK_GROUP",        ALWAYS                 },
   { "GROUPS",           "TK_GROUPS",       WINDOWFUNC             },
   { "HAVING",           "TK_HAVING",       ALWAYS                 },
   { "IF",               "TK_IF",           ALWAYS                 },