Adding upstream version 3.45.1.upstream/3.45.1

Signed-off-by: Daniel Baumann <daniel.baumann@progress-linux.org>

1 files changed, 3102 insertions, 0 deletions

diff --git a/src/window.c b/src/window.c
new file mode 100644
index 0000000..62df349
--- /dev/null
+++ b/src/window.c
@@ -0,0 +1,3102 @@
+/*
+** 2018 May 08
+**
+** The author disclaims copyright to this source code.  In place of
+** a legal notice, here is a blessing:
+**
+**    May you do good and not evil.
+**    May you find forgiveness for yourself and forgive others.
+**    May you share freely, never taking more than you give.
+**
+*************************************************************************
+*/
+#include "sqliteInt.h"
+
+#ifndef SQLITE_OMIT_WINDOWFUNC
+
+/*
+** SELECT REWRITING
+**
+**   Any SELECT statement that contains one or more window functions in
+**   either the select list or ORDER BY clause (the only two places window
+**   functions may be used) is transformed by function sqlite3WindowRewrite()
+**   in order to support window function processing. For example, with the
+**   schema:
+**
+**     CREATE TABLE t1(a, b, c, d, e, f, g);
+**
+**   the statement:
+**
+**     SELECT a+1, max(b) OVER (PARTITION BY c ORDER BY d) FROM t1 ORDER BY e;
+**
+**   is transformed to:
+**
+**     SELECT a+1, max(b) OVER (PARTITION BY c ORDER BY d) FROM (
+**         SELECT a, e, c, d, b FROM t1 ORDER BY c, d
+**     ) ORDER BY e;
+**
+**   The flattening optimization is disabled when processing this transformed
+**   SELECT statement. This allows the implementation of the window function
+**   (in this case max()) to process rows sorted in order of (c, d), which
+**   makes things easier for obvious reasons. More generally:
+**
+**     * FROM, WHERE, GROUP BY and HAVING clauses are all moved to
+**       the sub-query.
+**
+**     * ORDER BY, LIMIT and OFFSET remain part of the parent query.
+**
+**     * Terminals from each of the expression trees that make up the
+**       select-list and ORDER BY expressions in the parent query are
+**       selected by the sub-query. For the purposes of the transformation,
+**       terminals are column references and aggregate functions.
+**
+**   If there is more than one window function in the SELECT that uses
+**   the same window declaration (the OVER bit), then a single scan may
+**   be used to process more than one window function. For example:
+**
+**     SELECT max(b) OVER (PARTITION BY c ORDER BY d),
+**            min(e) OVER (PARTITION BY c ORDER BY d)
+**     FROM t1;
+**
+**   is transformed in the same way as the example above. However:
+**
+**     SELECT max(b) OVER (PARTITION BY c ORDER BY d),
+**            min(e) OVER (PARTITION BY a ORDER BY b)
+**     FROM t1;
+**
+**   Must be transformed to:
+**
+**     SELECT max(b) OVER (PARTITION BY c ORDER BY d) FROM (
+**         SELECT e, min(e) OVER (PARTITION BY a ORDER BY b), c, d, b FROM
+**           SELECT a, e, c, d, b FROM t1 ORDER BY a, b
+**         ) ORDER BY c, d
+**     ) ORDER BY e;
+**
+**   so that both min() and max() may process rows in the order defined by
+**   their respective window declarations.
+**
+** INTERFACE WITH SELECT.C
+**
+**   When processing the rewritten SELECT statement, code in select.c calls
+**   sqlite3WhereBegin() to begin iterating through the results of the
+**   sub-query, which is always implemented as a co-routine. It then calls
+**   sqlite3WindowCodeStep() to process rows and finish the scan by calling
+**   sqlite3WhereEnd().
+**
+**   sqlite3WindowCodeStep() generates VM code so that, for each row returned
+**   by the sub-query a sub-routine (OP_Gosub) coded by select.c is invoked.
+**   When the sub-routine is invoked:
+**
+**     * The results of all window-functions for the row are stored
+**       in the associated Window.regResult registers.
+**
+**     * The required terminal values are stored in the current row of
+**       temp table Window.iEphCsr.
+**
+**   In some cases, depending on the window frame and the specific window
+**   functions invoked, sqlite3WindowCodeStep() caches each entire partition
+**   in a temp table before returning any rows. In other cases it does not.
+**   This detail is encapsulated within this file, the code generated by
+**   select.c is the same in either case.
+**
+** BUILT-IN WINDOW FUNCTIONS
+**
+**   This implementation features the following built-in window functions:
+**
+**     row_number()
+**     rank()
+**     dense_rank()
+**     percent_rank()
+**     cume_dist()
+**     ntile(N)
+**     lead(expr [, offset [, default]])
+**     lag(expr [, offset [, default]])
+**     first_value(expr)
+**     last_value(expr)
+**     nth_value(expr, N)
+**  
+**   These are the same built-in window functions supported by Postgres.
+**   Although the behaviour of aggregate window functions (functions that
+**   can be used as either aggregates or window functions) allows them to
+**   be implemented using an API, built-in window functions are much more
+**   esoteric. Additionally, some window functions (e.g. nth_value())
+**   may only be implemented by caching the entire partition in memory.
+**   As such, some built-in window functions use the same API as aggregate
+**   window functions and some are implemented directly using VDBE
+**   instructions. Additionally, for those functions that use the API, the
+**   window frame is sometimes modified before the SELECT statement is
+**   rewritten. For example, regardless of the specified window frame, the
+**   row_number() function always uses:
+**
+**     ROWS BETWEEN UNBOUNDED PRECEDING AND CURRENT ROW
+**
+**   See sqlite3WindowUpdate() for details.
+**
+**   As well as some of the built-in window functions, aggregate window
+**   functions min() and max() are implemented using VDBE instructions if
+**   the start of the window frame is declared as anything other than
+**   UNBOUNDED PRECEDING.
+*/
+
+/*
+** Implementation of built-in window function row_number(). Assumes that the
+** window frame has been coerced to:
+**
+**   ROWS BETWEEN UNBOUNDED PRECEDING AND CURRENT ROW
+*/
+static void row_numberStepFunc(
+  sqlite3_context *pCtx,
+  int nArg,
+  sqlite3_value **apArg
+){
+  i64 *p = (i64*)sqlite3_aggregate_context(pCtx, sizeof(*p));
+  if( p ) (*p)++;
+  UNUSED_PARAMETER(nArg);
+  UNUSED_PARAMETER(apArg);
+}
+static void row_numberValueFunc(sqlite3_context *pCtx){
+  i64 *p = (i64*)sqlite3_aggregate_context(pCtx, sizeof(*p));
+  sqlite3_result_int64(pCtx, (p ? *p : 0));
+}
+
+/*
+** Context object type used by rank(), dense_rank(), percent_rank() and
+** cume_dist().
+*/
+struct CallCount {
+  i64 nValue;
+  i64 nStep;
+  i64 nTotal;
+};
+
+/*
+** Implementation of built-in window function dense_rank(). Assumes that
+** the window frame has been set to:
+**
+**   RANGE BETWEEN UNBOUNDED PRECEDING AND CURRENT ROW
+*/
+static void dense_rankStepFunc(
+  sqlite3_context *pCtx,
+  int nArg,
+  sqlite3_value **apArg
+){
+  struct CallCount *p;
+  p = (struct CallCount*)sqlite3_aggregate_context(pCtx, sizeof(*p));
+  if( p ) p->nStep = 1;
+  UNUSED_PARAMETER(nArg);
+  UNUSED_PARAMETER(apArg);
+}
+static void dense_rankValueFunc(sqlite3_context *pCtx){
+  struct CallCount *p;
+  p = (struct CallCount*)sqlite3_aggregate_context(pCtx, sizeof(*p));
+  if( p ){
+    if( p->nStep ){
+      p->nValue++;
+      p->nStep = 0;
+    }
+    sqlite3_result_int64(pCtx, p->nValue);
+  }
+}
+
+/*
+** Implementation of built-in window function nth_value(). This
+** implementation is used in "slow mode" only - when the EXCLUDE clause
+** is not set to the default value "NO OTHERS".
+*/
+struct NthValueCtx {
+  i64 nStep;
+  sqlite3_value *pValue;
+};
+static void nth_valueStepFunc(
+  sqlite3_context *pCtx,
+  int nArg,
+  sqlite3_value **apArg
+){
+  struct NthValueCtx *p;
+  p = (struct NthValueCtx*)sqlite3_aggregate_context(pCtx, sizeof(*p));
+  if( p ){
+    i64 iVal;
+    switch( sqlite3_value_numeric_type(apArg[1]) ){
+      case SQLITE_INTEGER:
+        iVal = sqlite3_value_int64(apArg[1]);
+        break;
+      case SQLITE_FLOAT: {
+        double fVal = sqlite3_value_double(apArg[1]);
+        if( ((i64)fVal)!=fVal ) goto error_out;
+        iVal = (i64)fVal;
+        break;
+      }
+      default:
+        goto error_out;
+    }
+    if( iVal<=0 ) goto error_out;
+
+    p->nStep++;
+    if( iVal==p->nStep ){
+      p->pValue = sqlite3_value_dup(apArg[0]);
+      if( !p->pValue ){
+        sqlite3_result_error_nomem(pCtx);
+      }
+    }
+  }
+  UNUSED_PARAMETER(nArg);
+  UNUSED_PARAMETER(apArg);
+  return;
+
+ error_out:
+  sqlite3_result_error(
+      pCtx, "second argument to nth_value must be a positive integer", -1
+  );
+}
+static void nth_valueFinalizeFunc(sqlite3_context *pCtx){
+  struct NthValueCtx *p;
+  p = (struct NthValueCtx*)sqlite3_aggregate_context(pCtx, 0);
+  if( p && p->pValue ){
+    sqlite3_result_value(pCtx, p->pValue);
+    sqlite3_value_free(p->pValue);
+    p->pValue = 0;
+  }
+}
+#define nth_valueInvFunc noopStepFunc
+#define nth_valueValueFunc noopValueFunc
+
+static void first_valueStepFunc(
+  sqlite3_context *pCtx,
+  int nArg,
+  sqlite3_value **apArg
+){
+  struct NthValueCtx *p;
+  p = (struct NthValueCtx*)sqlite3_aggregate_context(pCtx, sizeof(*p));
+  if( p && p->pValue==0 ){
+    p->pValue = sqlite3_value_dup(apArg[0]);
+    if( !p->pValue ){
+      sqlite3_result_error_nomem(pCtx);
+    }
+  }
+  UNUSED_PARAMETER(nArg);
+  UNUSED_PARAMETER(apArg);
+}
+static void first_valueFinalizeFunc(sqlite3_context *pCtx){
+  struct NthValueCtx *p;
+  p = (struct NthValueCtx*)sqlite3_aggregate_context(pCtx, sizeof(*p));
+  if( p && p->pValue ){
+    sqlite3_result_value(pCtx, p->pValue);
+    sqlite3_value_free(p->pValue);
+    p->pValue = 0;
+  }
+}
+#define first_valueInvFunc noopStepFunc
+#define first_valueValueFunc noopValueFunc
+
+/*
+** Implementation of built-in window function rank(). Assumes that
+** the window frame has been set to:
+**
+**   RANGE BETWEEN UNBOUNDED PRECEDING AND CURRENT ROW
+*/
+static void rankStepFunc(
+  sqlite3_context *pCtx,
+  int nArg,
+  sqlite3_value **apArg
+){
+  struct CallCount *p;
+  p = (struct CallCount*)sqlite3_aggregate_context(pCtx, sizeof(*p));
+  if( p ){
+    p->nStep++;
+    if( p->nValue==0 ){
+      p->nValue = p->nStep;
+    }
+  }
+  UNUSED_PARAMETER(nArg);
+  UNUSED_PARAMETER(apArg);
+}
+static void rankValueFunc(sqlite3_context *pCtx){
+  struct CallCount *p;
+  p = (struct CallCount*)sqlite3_aggregate_context(pCtx, sizeof(*p));
+  if( p ){
+    sqlite3_result_int64(pCtx, p->nValue);
+    p->nValue = 0;
+  }
+}
+
+/*
+** Implementation of built-in window function percent_rank(). Assumes that
+** the window frame has been set to:
+**
+**   GROUPS BETWEEN CURRENT ROW AND UNBOUNDED FOLLOWING
+*/
+static void percent_rankStepFunc(
+  sqlite3_context *pCtx,
+  int nArg,
+  sqlite3_value **apArg
+){
+  struct CallCount *p;
+  UNUSED_PARAMETER(nArg); assert( nArg==0 );
+  UNUSED_PARAMETER(apArg);
+  p = (struct CallCount*)sqlite3_aggregate_context(pCtx, sizeof(*p));
+  if( p ){
+    p->nTotal++;
+  }
+}
+static void percent_rankInvFunc(
+  sqlite3_context *pCtx,
+  int nArg,
+  sqlite3_value **apArg
+){
+  struct CallCount *p;
+  UNUSED_PARAMETER(nArg); assert( nArg==0 );
+  UNUSED_PARAMETER(apArg);
+  p = (struct CallCount*)sqlite3_aggregate_context(pCtx, sizeof(*p));
+  p->nStep++;
+}
+static void percent_rankValueFunc(sqlite3_context *pCtx){
+  struct CallCount *p;
+  p = (struct CallCount*)sqlite3_aggregate_context(pCtx, sizeof(*p));
+  if( p ){
+    p->nValue = p->nStep;
+    if( p->nTotal>1 ){
+      double r = (double)p->nValue / (double)(p->nTotal-1);
+      sqlite3_result_double(pCtx, r);
+    }else{
+      sqlite3_result_double(pCtx, 0.0);
+    }
+  }
+}
+#define percent_rankFinalizeFunc percent_rankValueFunc
+
+/*
+** Implementation of built-in window function cume_dist(). Assumes that
+** the window frame has been set to:
+**
+**   GROUPS BETWEEN 1 FOLLOWING AND UNBOUNDED FOLLOWING
+*/
+static void cume_distStepFunc(
+  sqlite3_context *pCtx,
+  int nArg,
+  sqlite3_value **apArg
+){
+  struct CallCount *p;
+  UNUSED_PARAMETER(nArg); assert( nArg==0 );
+  UNUSED_PARAMETER(apArg);
+  p = (struct CallCount*)sqlite3_aggregate_context(pCtx, sizeof(*p));
+  if( p ){
+    p->nTotal++;
+  }
+}
+static void cume_distInvFunc(
+  sqlite3_context *pCtx,
+  int nArg,
+  sqlite3_value **apArg
+){
+  struct CallCount *p;
+  UNUSED_PARAMETER(nArg); assert( nArg==0 );
+  UNUSED_PARAMETER(apArg);
+  p = (struct CallCount*)sqlite3_aggregate_context(pCtx, sizeof(*p));
+  p->nStep++;
+}
+static void cume_distValueFunc(sqlite3_context *pCtx){
+  struct CallCount *p;
+  p = (struct CallCount*)sqlite3_aggregate_context(pCtx, 0);
+  if( p ){
+    double r = (double)(p->nStep) / (double)(p->nTotal);
+    sqlite3_result_double(pCtx, r);
+  }
+}
+#define cume_distFinalizeFunc cume_distValueFunc
+
+/*
+** Context object for ntile() window function.
+*/
+struct NtileCtx {
+  i64 nTotal;                     /* Total rows in partition */
+  i64 nParam;                     /* Parameter passed to ntile(N) */
+  i64 iRow;                       /* Current row */
+};
+
+/*
+** Implementation of ntile(). This assumes that the window frame has
+** been coerced to:
+**
+**   ROWS CURRENT ROW AND UNBOUNDED FOLLOWING
+*/
+static void ntileStepFunc(
+  sqlite3_context *pCtx,
+  int nArg,
+  sqlite3_value **apArg
+){
+  struct NtileCtx *p;
+  assert( nArg==1 ); UNUSED_PARAMETER(nArg);
+  p = (struct NtileCtx*)sqlite3_aggregate_context(pCtx, sizeof(*p));
+  if( p ){
+    if( p->nTotal==0 ){
+      p->nParam = sqlite3_value_int64(apArg[0]);
+      if( p->nParam<=0 ){
+        sqlite3_result_error(
+            pCtx, "argument of ntile must be a positive integer", -1
+        );
+      }
+    }
+    p->nTotal++;
+  }
+}
+static void ntileInvFunc(
+  sqlite3_context *pCtx,
+  int nArg,
+  sqlite3_value **apArg
+){
+  struct NtileCtx *p;
+  assert( nArg==1 ); UNUSED_PARAMETER(nArg);
+  UNUSED_PARAMETER(apArg);
+  p = (struct NtileCtx*)sqlite3_aggregate_context(pCtx, sizeof(*p));
+  p->iRow++;
+}
+static void ntileValueFunc(sqlite3_context *pCtx){
+  struct NtileCtx *p;
+  p = (struct NtileCtx*)sqlite3_aggregate_context(pCtx, sizeof(*p));
+  if( p && p->nParam>0 ){
+    int nSize = (p->nTotal / p->nParam);
+    if( nSize==0 ){
+      sqlite3_result_int64(pCtx, p->iRow+1);
+    }else{
+      i64 nLarge = p->nTotal - p->nParam*nSize;
+      i64 iSmall = nLarge*(nSize+1);
+      i64 iRow = p->iRow;
+
+      assert( (nLarge*(nSize+1) + (p->nParam-nLarge)*nSize)==p->nTotal );
+
+      if( iRow<iSmall ){
+        sqlite3_result_int64(pCtx, 1 + iRow/(nSize+1));
+      }else{
+        sqlite3_result_int64(pCtx, 1 + nLarge + (iRow-iSmall)/nSize);
+      }
+    }
+  }
+}
+#define ntileFinalizeFunc ntileValueFunc
+
+/*
+** Context object for last_value() window function.
+*/
+struct LastValueCtx {
+  sqlite3_value *pVal;
+  int nVal;
+};
+
+/*
+** Implementation of last_value().
+*/
+static void last_valueStepFunc(
+  sqlite3_context *pCtx,
+  int nArg,
+  sqlite3_value **apArg
+){
+  struct LastValueCtx *p;
+  UNUSED_PARAMETER(nArg);
+  p = (struct LastValueCtx*)sqlite3_aggregate_context(pCtx, sizeof(*p));
+  if( p ){
+    sqlite3_value_free(p->pVal);
+    p->pVal = sqlite3_value_dup(apArg[0]);
+    if( p->pVal==0 ){
+      sqlite3_result_error_nomem(pCtx);
+    }else{
+      p->nVal++;
+    }
+  }
+}
+static void last_valueInvFunc(
+  sqlite3_context *pCtx,
+  int nArg,
+  sqlite3_value **apArg
+){
+  struct LastValueCtx *p;
+  UNUSED_PARAMETER(nArg);
+  UNUSED_PARAMETER(apArg);
+  p = (struct LastValueCtx*)sqlite3_aggregate_context(pCtx, sizeof(*p));
+  if( ALWAYS(p) ){
+    p->nVal--;
+    if( p->nVal==0 ){
+      sqlite3_value_free(p->pVal);
+      p->pVal = 0;
+    }
+  }
+}
+static void last_valueValueFunc(sqlite3_context *pCtx){
+  struct LastValueCtx *p;
+  p = (struct LastValueCtx*)sqlite3_aggregate_context(pCtx, 0);
+  if( p && p->pVal ){
+    sqlite3_result_value(pCtx, p->pVal);
+  }
+}
+static void last_valueFinalizeFunc(sqlite3_context *pCtx){
+  struct LastValueCtx *p;
+  p = (struct LastValueCtx*)sqlite3_aggregate_context(pCtx, sizeof(*p));
+  if( p && p->pVal ){
+    sqlite3_result_value(pCtx, p->pVal);
+    sqlite3_value_free(p->pVal);
+    p->pVal = 0;
+  }
+}
+
+/*
+** Static names for the built-in window function names.  These static
+** names are used, rather than string literals, so that FuncDef objects
+** can be associated with a particular window function by direct
+** comparison of the zName pointer.  Example:
+**
+**       if( pFuncDef->zName==row_valueName ){ ... }
+*/
+static const char row_numberName[] =   "row_number";
+static const char dense_rankName[] =   "dense_rank";
+static const char rankName[] =         "rank";
+static const char percent_rankName[] = "percent_rank";
+static const char cume_distName[] =    "cume_dist";
+static const char ntileName[] =        "ntile";
+static const char last_valueName[] =   "last_value";
+static const char nth_valueName[] =    "nth_value";
+static const char first_valueName[] =  "first_value";
+static const char leadName[] =         "lead";
+static const char lagName[] =          "lag";
+
+/*
+** No-op implementations of xStep() and xFinalize().  Used as place-holders
+** for built-in window functions that never call those interfaces.
+**
+** The noopValueFunc() is called but is expected to do nothing.  The
+** noopStepFunc() is never called, and so it is marked with NO_TEST to
+** let the test coverage routine know not to expect this function to be
+** invoked.
+*/
+static void noopStepFunc(    /*NO_TEST*/
+  sqlite3_context *p,        /*NO_TEST*/
+  int n,                     /*NO_TEST*/
+  sqlite3_value **a          /*NO_TEST*/
+){                           /*NO_TEST*/
+  UNUSED_PARAMETER(p);       /*NO_TEST*/
+  UNUSED_PARAMETER(n);       /*NO_TEST*/
+  UNUSED_PARAMETER(a);       /*NO_TEST*/
+  assert(0);                 /*NO_TEST*/
+}                            /*NO_TEST*/
+static void noopValueFunc(sqlite3_context *p){ UNUSED_PARAMETER(p); /*no-op*/ }
+
+/* Window functions that use all window interfaces: xStep, xFinal,
+** xValue, and xInverse */
+#define WINDOWFUNCALL(name,nArg,extra) {                                   \
+  nArg, (SQLITE_FUNC_BUILTIN|SQLITE_UTF8|SQLITE_FUNC_WINDOW|extra), 0, 0,  \
+  name ## StepFunc, name ## FinalizeFunc, name ## ValueFunc,               \
+  name ## InvFunc, name ## Name, {0}                                       \
+}
+
+/* Window functions that are implemented using bytecode and thus have
+** no-op routines for their methods */
+#define WINDOWFUNCNOOP(name,nArg,extra) {                                  \
+  nArg, (SQLITE_FUNC_BUILTIN|SQLITE_UTF8|SQLITE_FUNC_WINDOW|extra), 0, 0,  \
+  noopStepFunc, noopValueFunc, noopValueFunc,                              \
+  noopStepFunc, name ## Name, {0}                                          \
+}
+
+/* Window functions that use all window interfaces: xStep, the
+** same routine for xFinalize and xValue and which never call
+** xInverse. */
+#define WINDOWFUNCX(name,nArg,extra) {                                     \
+  nArg, (SQLITE_FUNC_BUILTIN|SQLITE_UTF8|SQLITE_FUNC_WINDOW|extra), 0, 0,  \
+  name ## StepFunc, name ## ValueFunc, name ## ValueFunc,                  \
+  noopStepFunc, name ## Name, {0}                                          \
+}
+
+
+/*
+** Register those built-in window functions that are not also aggregates.
+*/
+void sqlite3WindowFunctions(void){
+  static FuncDef aWindowFuncs[] = {
+    WINDOWFUNCX(row_number, 0, 0),
+    WINDOWFUNCX(dense_rank, 0, 0),
+    WINDOWFUNCX(rank, 0, 0),
+    WINDOWFUNCALL(percent_rank, 0, 0),
+    WINDOWFUNCALL(cume_dist, 0, 0),
+    WINDOWFUNCALL(ntile, 1, 0),
+    WINDOWFUNCALL(last_value, 1, 0),
+    WINDOWFUNCALL(nth_value, 2, 0),
+    WINDOWFUNCALL(first_value, 1, 0),
+    WINDOWFUNCNOOP(lead, 1, 0),
+    WINDOWFUNCNOOP(lead, 2, 0),
+    WINDOWFUNCNOOP(lead, 3, 0),
+    WINDOWFUNCNOOP(lag, 1, 0),
+    WINDOWFUNCNOOP(lag, 2, 0),
+    WINDOWFUNCNOOP(lag, 3, 0),
+  };
+  sqlite3InsertBuiltinFuncs(aWindowFuncs, ArraySize(aWindowFuncs));
+}
+
+static Window *windowFind(Parse *pParse, Window *pList, const char *zName){
+  Window *p;
+  for(p=pList; p; p=p->pNextWin){
+    if( sqlite3StrICmp(p->zName, zName)==0 ) break;
+  }
+  if( p==0 ){
+    sqlite3ErrorMsg(pParse, "no such window: %s", zName);
+  }
+  return p;
+}
+
+/*
+** This function is called immediately after resolving the function name
+** for a window function within a SELECT statement. Argument pList is a
+** linked list of WINDOW definitions for the current SELECT statement.
+** Argument pFunc is the function definition just resolved and pWin
+** is the Window object representing the associated OVER clause. This
+** function updates the contents of pWin as follows:
+**
+**   * If the OVER clause referred to a named window (as in "max(x) OVER win"),
+**     search list pList for a matching WINDOW definition, and update pWin
+**     accordingly. If no such WINDOW clause can be found, leave an error
+**     in pParse.
+**
+**   * If the function is a built-in window function that requires the
+**     window to be coerced (see "BUILT-IN WINDOW FUNCTIONS" at the top
+**     of this file), pWin is updated here.
+*/
+void sqlite3WindowUpdate(
+  Parse *pParse,
+  Window *pList,                  /* List of named windows for this SELECT */
+  Window *pWin,                   /* Window frame to update */
+  FuncDef *pFunc                  /* Window function definition */
+){
+  if( pWin->zName && pWin->eFrmType==0 ){
+    Window *p = windowFind(pParse, pList, pWin->zName);
+    if( p==0 ) return;
+    pWin->pPartition = sqlite3ExprListDup(pParse->db, p->pPartition, 0);
+    pWin->pOrderBy = sqlite3ExprListDup(pParse->db, p->pOrderBy, 0);
+    pWin->pStart = sqlite3ExprDup(pParse->db, p->pStart, 0);
+    pWin->pEnd = sqlite3ExprDup(pParse->db, p->pEnd, 0);
+    pWin->eStart = p->eStart;
+    pWin->eEnd = p->eEnd;
+    pWin->eFrmType = p->eFrmType;
+    pWin->eExclude = p->eExclude;
+  }else{
+    sqlite3WindowChain(pParse, pWin, pList);
+  }
+  if( (pWin->eFrmType==TK_RANGE)
+   && (pWin->pStart || pWin->pEnd)
+   && (pWin->pOrderBy==0 || pWin->pOrderBy->nExpr!=1)
+  ){
+    sqlite3ErrorMsg(pParse,
+      "RANGE with offset PRECEDING/FOLLOWING requires one ORDER BY expression"
+    );
+  }else
+  if( pFunc->funcFlags & SQLITE_FUNC_WINDOW ){
+    sqlite3 *db = pParse->db;
+    if( pWin->pFilter ){
+      sqlite3ErrorMsg(pParse,
+          "FILTER clause may only be used with aggregate window functions"
+      );
+    }else{
+      struct WindowUpdate {
+        const char *zFunc;
+        int eFrmType;
+        int eStart;
+        int eEnd;
+      } aUp[] = {
+        { row_numberName,   TK_ROWS,   TK_UNBOUNDED, TK_CURRENT },
+        { dense_rankName,   TK_RANGE,  TK_UNBOUNDED, TK_CURRENT },
+        { rankName,         TK_RANGE,  TK_UNBOUNDED, TK_CURRENT },
+        { percent_rankName, TK_GROUPS, TK_CURRENT,   TK_UNBOUNDED },
+        { cume_distName,    TK_GROUPS, TK_FOLLOWING, TK_UNBOUNDED },
+        { ntileName,        TK_ROWS,   TK_CURRENT,   TK_UNBOUNDED },
+        { leadName,         TK_ROWS,   TK_UNBOUNDED, TK_UNBOUNDED },
+        { lagName,          TK_ROWS,   TK_UNBOUNDED, TK_CURRENT },
+      };
+      int i;
+      for(i=0; i<ArraySize(aUp); i++){
+        if( pFunc->zName==aUp[i].zFunc ){
+          sqlite3ExprDelete(db, pWin->pStart);
+          sqlite3ExprDelete(db, pWin->pEnd);
+          pWin->pEnd = pWin->pStart = 0;
+          pWin->eFrmType = aUp[i].eFrmType;
+          pWin->eStart = aUp[i].eStart;
+          pWin->eEnd = aUp[i].eEnd;
+          pWin->eExclude = 0;
+          if( pWin->eStart==TK_FOLLOWING ){
+            pWin->pStart = sqlite3Expr(db, TK_INTEGER, "1");
+          }
+          break;
+        }
+      }
+    }
+  }
+  pWin->pWFunc = pFunc;
+}
+
+/*
+** Context object passed through sqlite3WalkExprList() to
+** selectWindowRewriteExprCb() by selectWindowRewriteEList().
+*/
+typedef struct WindowRewrite WindowRewrite;
+struct WindowRewrite {
+  Window *pWin;
+  SrcList *pSrc;
+  ExprList *pSub;
+  Table *pTab;
+  Select *pSubSelect;             /* Current sub-select, if any */
+};
+
+/*
+** Callback function used by selectWindowRewriteEList(). If necessary,
+** this function appends to the output expression-list and updates
+** expression (*ppExpr) in place.
+*/
+static int selectWindowRewriteExprCb(Walker *pWalker, Expr *pExpr){
+  struct WindowRewrite *p = pWalker->u.pRewrite;
+  Parse *pParse = pWalker->pParse;
+  assert( p!=0 );
+  assert( p->pWin!=0 );
+
+  /* If this function is being called from within a scalar sub-select
+  ** that used by the SELECT statement being processed, only process
+  ** TK_COLUMN expressions that refer to it (the outer SELECT). Do
+  ** not process aggregates or window functions at all, as they belong
+  ** to the scalar sub-select.  */
+  if( p->pSubSelect ){
+    if( pExpr->op!=TK_COLUMN ){
+      return WRC_Continue;
+    }else{
+      int nSrc = p->pSrc->nSrc;
+      int i;
+      for(i=0; i<nSrc; i++){
+        if( pExpr->iTable==p->pSrc->a[i].iCursor ) break;
+      }
+      if( i==nSrc ) return WRC_Continue;
+    }
+  }
+
+  switch( pExpr->op ){
+
+    case TK_FUNCTION:
+      if( !ExprHasProperty(pExpr, EP_WinFunc) ){
+        break;
+      }else{
+        Window *pWin;
+        for(pWin=p->pWin; pWin; pWin=pWin->pNextWin){
+          if( pExpr->y.pWin==pWin ){
+            assert( pWin->pOwner==pExpr );
+            return WRC_Prune;
+          }
+        }
+      }
+      /* no break */ deliberate_fall_through
+
+    case TK_IF_NULL_ROW:
+    case TK_AGG_FUNCTION:
+    case TK_COLUMN: {
+      int iCol = -1;
+      if( pParse->db->mallocFailed ) return WRC_Abort;
+      if( p->pSub ){
+        int i;
+        for(i=0; i<p->pSub->nExpr; i++){
+          if( 0==sqlite3ExprCompare(0, p->pSub->a[i].pExpr, pExpr, -1) ){
+            iCol = i;
+            break;
+          }
+        }
+      }
+      if( iCol<0 ){
+        Expr *pDup = sqlite3ExprDup(pParse->db, pExpr, 0);
+        if( pDup && pDup->op==TK_AGG_FUNCTION ) pDup->op = TK_FUNCTION;
+        p->pSub = sqlite3ExprListAppend(pParse, p->pSub, pDup);
+      }
+      if( p->pSub ){
+        int f = pExpr->flags & EP_Collate;
+        assert( ExprHasProperty(pExpr, EP_Static)==0 );
+        ExprSetProperty(pExpr, EP_Static);
+        sqlite3ExprDelete(pParse->db, pExpr);
+        ExprClearProperty(pExpr, EP_Static);
+        memset(pExpr, 0, sizeof(Expr));
+
+        pExpr->op = TK_COLUMN;
+        pExpr->iColumn = (iCol<0 ? p->pSub->nExpr-1: iCol);
+        pExpr->iTable = p->pWin->iEphCsr;
+        pExpr->y.pTab = p->pTab;
+        pExpr->flags = f;
+      }
+      if( pParse->db->mallocFailed ) return WRC_Abort;
+      break;
+    }
+
+    default: /* no-op */
+      break;
+  }
+
+  return WRC_Continue;
+}
+static int selectWindowRewriteSelectCb(Walker *pWalker, Select *pSelect){
+  struct WindowRewrite *p = pWalker->u.pRewrite;
+  Select *pSave = p->pSubSelect;
+  if( pSave==pSelect ){
+    return WRC_Continue;
+  }else{
+    p->pSubSelect = pSelect;
+    sqlite3WalkSelect(pWalker, pSelect);
+    p->pSubSelect = pSave;
+  }
+  return WRC_Prune;
+}
+
+
+/*
+** Iterate through each expression in expression-list pEList. For each:
+**
+**   * TK_COLUMN,
+**   * aggregate function, or
+**   * window function with a Window object that is not a member of the
+**     Window list passed as the second argument (pWin).
+**
+** Append the node to output expression-list (*ppSub). And replace it
+** with a TK_COLUMN that reads the (N-1)th element of table
+** pWin->iEphCsr, where N is the number of elements in (*ppSub) after
+** appending the new one.
+*/
+static void selectWindowRewriteEList(
+  Parse *pParse,
+  Window *pWin,
+  SrcList *pSrc,
+  ExprList *pEList,               /* Rewrite expressions in this list */
+  Table *pTab,
+  ExprList **ppSub                /* IN/OUT: Sub-select expression-list */
+){
+  Walker sWalker;
+  WindowRewrite sRewrite;
+
+  assert( pWin!=0 );
+  memset(&sWalker, 0, sizeof(Walker));
+  memset(&sRewrite, 0, sizeof(WindowRewrite));
+
+  sRewrite.pSub = *ppSub;
+  sRewrite.pWin = pWin;
+  sRewrite.pSrc = pSrc;
+  sRewrite.pTab = pTab;
+
+  sWalker.pParse = pParse;
+  sWalker.xExprCallback = selectWindowRewriteExprCb;
+  sWalker.xSelectCallback = selectWindowRewriteSelectCb;
+  sWalker.u.pRewrite = &sRewrite;
+
+  (void)sqlite3WalkExprList(&sWalker, pEList);
+
+  *ppSub = sRewrite.pSub;
+}
+
+/*
+** Append a copy of each expression in expression-list pAppend to
+** expression list pList. Return a pointer to the result list.
+*/
+static ExprList *exprListAppendList(
+  Parse *pParse,          /* Parsing context */
+  ExprList *pList,        /* List to which to append. Might be NULL */
+  ExprList *pAppend,      /* List of values to append. Might be NULL */
+  int bIntToNull
+){
+  if( pAppend ){
+    int i;
+    int nInit = pList ? pList->nExpr : 0;
+    for(i=0; i<pAppend->nExpr; i++){
+      sqlite3 *db = pParse->db;
+      Expr *pDup = sqlite3ExprDup(db, pAppend->a[i].pExpr, 0);
+      if( db->mallocFailed ){
+        sqlite3ExprDelete(db, pDup);
+        break;
+      }
+      if( bIntToNull ){
+        int iDummy;
+        Expr *pSub;
+        pSub = sqlite3ExprSkipCollateAndLikely(pDup);
+        if( sqlite3ExprIsInteger(pSub, &iDummy) ){
+          pSub->op = TK_NULL;
+          pSub->flags &= ~(EP_IntValue|EP_IsTrue|EP_IsFalse);
+          pSub->u.zToken = 0;
+        }
+      }
+      pList = sqlite3ExprListAppend(pParse, pList, pDup);
+      if( pList ) pList->a[nInit+i].fg.sortFlags = pAppend->a[i].fg.sortFlags;
+    }
+  }
+  return pList;
+}
+
+/*
+** When rewriting a query, if the new subquery in the FROM clause
+** contains TK_AGG_FUNCTION nodes that refer to an outer query,
+** then we have to increase the Expr->op2 values of those nodes
+** due to the extra subquery layer that was added.
+**
+** See also the incrAggDepth() routine in resolve.c
+*/
+static int sqlite3WindowExtraAggFuncDepth(Walker *pWalker, Expr *pExpr){
+  if( pExpr->op==TK_AGG_FUNCTION
+   && pExpr->op2>=pWalker->walkerDepth
+  ){
+    pExpr->op2++;
+  }
+  return WRC_Continue;
+}
+
+static int disallowAggregatesInOrderByCb(Walker *pWalker, Expr *pExpr){
+  if( pExpr->op==TK_AGG_FUNCTION && pExpr->pAggInfo==0 ){
+    assert( !ExprHasProperty(pExpr, EP_IntValue) );
+     sqlite3ErrorMsg(pWalker->pParse,
+         "misuse of aggregate: %s()", pExpr->u.zToken);
+  }
+  return WRC_Continue;
+}
+
+/*
+** If the SELECT statement passed as the second argument does not invoke
+** any SQL window functions, this function is a no-op. Otherwise, it
+** rewrites the SELECT statement so that window function xStep functions
+** are invoked in the correct order as described under "SELECT REWRITING"
+** at the top of this file.
+*/
+int sqlite3WindowRewrite(Parse *pParse, Select *p){
+  int rc = SQLITE_OK;
+  if( p->pWin
+   && p->pPrior==0
+   && ALWAYS((p->selFlags & SF_WinRewrite)==0)
+   && ALWAYS(!IN_RENAME_OBJECT)
+  ){
+    Vdbe *v = sqlite3GetVdbe(pParse);
+    sqlite3 *db = pParse->db;
+    Select *pSub = 0;             /* The subquery */
+    SrcList *pSrc = p->pSrc;
+    Expr *pWhere = p->pWhere;
+    ExprList *pGroupBy = p->pGroupBy;
+    Expr *pHaving = p->pHaving;
+    ExprList *pSort = 0;
+
+    ExprList *pSublist = 0;       /* Expression list for sub-query */
+    Window *pMWin = p->pWin;      /* Main window object */
+    Window *pWin;                 /* Window object iterator */
+    Table *pTab;
+    Walker w;
+
+    u32 selFlags = p->selFlags;
+
+    pTab = sqlite3DbMallocZero(db, sizeof(Table));
+    if( pTab==0 ){
+      return sqlite3ErrorToParser(db, SQLITE_NOMEM);
+    }
+    sqlite3AggInfoPersistWalkerInit(&w, pParse);
+    sqlite3WalkSelect(&w, p);
+    if( (p->selFlags & SF_Aggregate)==0 ){
+      w.xExprCallback = disallowAggregatesInOrderByCb;
+      w.xSelectCallback = 0;
+      sqlite3WalkExprList(&w, p->pOrderBy);
+    }
+
+    p->pSrc = 0;
+    p->pWhere = 0;
+    p->pGroupBy = 0;
+    p->pHaving = 0;
+    p->selFlags &= ~SF_Aggregate;
+    p->selFlags |= SF_WinRewrite;
+
+    /* Create the ORDER BY clause for the sub-select. This is the concatenation
+    ** of the window PARTITION and ORDER BY clauses. Then, if this makes it
+    ** redundant, remove the ORDER BY from the parent SELECT.  */
+    pSort = exprListAppendList(pParse, 0, pMWin->pPartition, 1);
+    pSort = exprListAppendList(pParse, pSort, pMWin->pOrderBy, 1);
+    if( pSort && p->pOrderBy && p->pOrderBy->nExpr<=pSort->nExpr ){
+      int nSave = pSort->nExpr;
+      pSort->nExpr = p->pOrderBy->nExpr;
+      if( sqlite3ExprListCompare(pSort, p->pOrderBy, -1)==0 ){
+        sqlite3ExprListDelete(db, p->pOrderBy);
+        p->pOrderBy = 0;
+      }
+      pSort->nExpr = nSave;
+    }
+
+    /* Assign a cursor number for the ephemeral table used to buffer rows.
+    ** The OpenEphemeral instruction is coded later, after it is known how
+    ** many columns the table will have.  */
+    pMWin->iEphCsr = pParse->nTab++;
+    pParse->nTab += 3;
+
+    selectWindowRewriteEList(pParse, pMWin, pSrc, p->pEList, pTab, &pSublist);
+    selectWindowRewriteEList(pParse, pMWin, pSrc, p->pOrderBy, pTab, &pSublist);
+    pMWin->nBufferCol = (pSublist ? pSublist->nExpr : 0);
+
+    /* Append the PARTITION BY and ORDER BY expressions to the to the
+    ** sub-select expression list. They are required to figure out where
+    ** boundaries for partitions and sets of peer rows lie.  */
+    pSublist = exprListAppendList(pParse, pSublist, pMWin->pPartition, 0);
+    pSublist = exprListAppendList(pParse, pSublist, pMWin->pOrderBy, 0);
+
+    /* Append the arguments passed to each window function to the
+    ** sub-select expression list. Also allocate two registers for each
+    ** window function - one for the accumulator, another for interim
+    ** results.  */
+    for(pWin=pMWin; pWin; pWin=pWin->pNextWin){
+      ExprList *pArgs;
+      assert( ExprUseXList(pWin->pOwner) );
+      assert( pWin->pWFunc!=0 );
+      pArgs = pWin->pOwner->x.pList;
+      if( pWin->pWFunc->funcFlags & SQLITE_SUBTYPE ){
+        selectWindowRewriteEList(pParse, pMWin, pSrc, pArgs, pTab, &pSublist);
+        pWin->iArgCol = (pSublist ? pSublist->nExpr : 0);
+        pWin->bExprArgs = 1;
+      }else{
+        pWin->iArgCol = (pSublist ? pSublist->nExpr : 0);
+        pSublist = exprListAppendList(pParse, pSublist, pArgs, 0);
+      }
+      if( pWin->pFilter ){
+        Expr *pFilter = sqlite3ExprDup(db, pWin->pFilter, 0);
+        pSublist = sqlite3ExprListAppend(pParse, pSublist, pFilter);
+      }
+      pWin->regAccum = ++pParse->nMem;
+      pWin->regResult = ++pParse->nMem;
+      sqlite3VdbeAddOp2(v, OP_Null, 0, pWin->regAccum);
+    }
+
+    /* If there is no ORDER BY or PARTITION BY clause, and the window
+    ** function accepts zero arguments, and there are no other columns
+    ** selected (e.g. "SELECT row_number() OVER () FROM t1"), it is possible
+    ** that pSublist is still NULL here. Add a constant expression here to
+    ** keep everything legal in this case.
+    */
+    if( pSublist==0 ){
+      pSublist = sqlite3ExprListAppend(pParse, 0,
+        sqlite3Expr(db, TK_INTEGER, "0")
+      );
+    }
+
+    pSub = sqlite3SelectNew(
+        pParse, pSublist, pSrc, pWhere, pGroupBy, pHaving, pSort, 0, 0
+    );
+    TREETRACE(0x40,pParse,pSub,
+       ("New window-function subquery in FROM clause of (%u/%p)\n",
+       p->selId, p));
+    p->pSrc = sqlite3SrcListAppend(pParse, 0, 0, 0);
+    assert( pSub!=0 || p->pSrc==0 ); /* Due to db->mallocFailed test inside
+                                     ** of sqlite3DbMallocRawNN() called from
+                                     ** sqlite3SrcListAppend() */
+    if( p->pSrc ){
+      Table *pTab2;
+      p->pSrc->a[0].pSelect = pSub;
+      p->pSrc->a[0].fg.isCorrelated = 1;
+      sqlite3SrcListAssignCursors(pParse, p->pSrc);
+      pSub->selFlags |= SF_Expanded|SF_OrderByReqd;
+      pTab2 = sqlite3ResultSetOfSelect(pParse, pSub, SQLITE_AFF_NONE);
+      pSub->selFlags |= (selFlags & SF_Aggregate);
+      if( pTab2==0 ){
+        /* Might actually be some other kind of error, but in that case
+        ** pParse->nErr will be set, so if SQLITE_NOMEM is set, we will get
+        ** the correct error message regardless. */
+        rc = SQLITE_NOMEM;
+      }else{
+        memcpy(pTab, pTab2, sizeof(Table));
+        pTab->tabFlags |= TF_Ephemeral;
+        p->pSrc->a[0].pTab = pTab;
+        pTab = pTab2;
+        memset(&w, 0, sizeof(w));
+        w.xExprCallback = sqlite3WindowExtraAggFuncDepth;
+        w.xSelectCallback = sqlite3WalkerDepthIncrease;
+        w.xSelectCallback2 = sqlite3WalkerDepthDecrease;
+        sqlite3WalkSelect(&w, pSub);
+      }
+    }else{
+      sqlite3SelectDelete(db, pSub);
+    }
+    if( db->mallocFailed ) rc = SQLITE_NOMEM;
+
+    /* Defer deleting the temporary table pTab because if an error occurred,
+    ** there could still be references to that table embedded in the
+    ** result-set or ORDER BY clause of the SELECT statement p.  */
+    sqlite3ParserAddCleanup(pParse, sqlite3DbFree, pTab);
+  }
+
+  assert( rc==SQLITE_OK || pParse->nErr!=0 );
+  return rc;
+}
+
+/*
+** Unlink the Window object from the Select to which it is attached,
+** if it is attached.
+*/
+void sqlite3WindowUnlinkFromSelect(Window *p){
+  if( p->ppThis ){
+    *p->ppThis = p->pNextWin;
+    if( p->pNextWin ) p->pNextWin->ppThis = p->ppThis;
+    p->ppThis = 0;
+  }
+}
+
+/*
+** Free the Window object passed as the second argument.
+*/
+void sqlite3WindowDelete(sqlite3 *db, Window *p){
+  if( p ){
+    sqlite3WindowUnlinkFromSelect(p);
+    sqlite3ExprDelete(db, p->pFilter);
+    sqlite3ExprListDelete(db, p->pPartition);
+    sqlite3ExprListDelete(db, p->pOrderBy);
+    sqlite3ExprDelete(db, p->pEnd);
+    sqlite3ExprDelete(db, p->pStart);
+    sqlite3DbFree(db, p->zName);
+    sqlite3DbFree(db, p->zBase);
+    sqlite3DbFree(db, p);
+  }
+}
+
+/*
+** Free the linked list of Window objects starting at the second argument.
+*/
+void sqlite3WindowListDelete(sqlite3 *db, Window *p){
+  while( p ){
+    Window *pNext = p->pNextWin;
+    sqlite3WindowDelete(db, p);
+    p = pNext;
+  }
+}
+
+/*
+** The argument expression is an PRECEDING or FOLLOWING offset.  The
+** value should be a non-negative integer.  If the value is not a
+** constant, change it to NULL.  The fact that it is then a non-negative
+** integer will be caught later.  But it is important not to leave
+** variable values in the expression tree.
+*/
+static Expr *sqlite3WindowOffsetExpr(Parse *pParse, Expr *pExpr){
+  if( 0==sqlite3ExprIsConstant(pExpr) ){
+    if( IN_RENAME_OBJECT ) sqlite3RenameExprUnmap(pParse, pExpr);
+    sqlite3ExprDelete(pParse->db, pExpr);
+    pExpr = sqlite3ExprAlloc(pParse->db, TK_NULL, 0, 0);
+  }
+  return pExpr;
+}
+
+/*
+** Allocate and return a new Window object describing a Window Definition.
+*/
+Window *sqlite3WindowAlloc(
+  Parse *pParse,    /* Parsing context */
+  int eType,        /* Frame type. TK_RANGE, TK_ROWS, TK_GROUPS, or 0 */
+  int eStart,       /* Start type: CURRENT, PRECEDING, FOLLOWING, UNBOUNDED */
+  Expr *pStart,     /* Start window size if TK_PRECEDING or FOLLOWING */
+  int eEnd,         /* End type: CURRENT, FOLLOWING, TK_UNBOUNDED, PRECEDING */
+  Expr *pEnd,       /* End window size if TK_FOLLOWING or PRECEDING */
+  u8 eExclude       /* EXCLUDE clause */
+){
+  Window *pWin = 0;
+  int bImplicitFrame = 0;
+
+  /* Parser assures the following: */
+  assert( eType==0 || eType==TK_RANGE || eType==TK_ROWS || eType==TK_GROUPS );
+  assert( eStart==TK_CURRENT || eStart==TK_PRECEDING
+           || eStart==TK_UNBOUNDED || eStart==TK_FOLLOWING );
+  assert( eEnd==TK_CURRENT || eEnd==TK_FOLLOWING
+           || eEnd==TK_UNBOUNDED || eEnd==TK_PRECEDING );
+  assert( (eStart==TK_PRECEDING || eStart==TK_FOLLOWING)==(pStart!=0) );
+  assert( (eEnd==TK_FOLLOWING || eEnd==TK_PRECEDING)==(pEnd!=0) );
+
+  if( eType==0 ){
+    bImplicitFrame = 1;
+    eType = TK_RANGE;
+  }
+
+  /* Additionally, the
+  ** starting boundary type may not occur earlier in the following list than
+  ** the ending boundary type:
+  **
+  **   UNBOUNDED PRECEDING
+  **   <expr> PRECEDING
+  **   CURRENT ROW
+  **   <expr> FOLLOWING
+  **   UNBOUNDED FOLLOWING
+  **
+  ** The parser ensures that "UNBOUNDED PRECEDING" cannot be used as an ending
+  ** boundary, and than "UNBOUNDED FOLLOWING" cannot be used as a starting
+  ** frame boundary.
+  */
+  if( (eStart==TK_CURRENT && eEnd==TK_PRECEDING)
+   || (eStart==TK_FOLLOWING && (eEnd==TK_PRECEDING || eEnd==TK_CURRENT))
+  ){
+    sqlite3ErrorMsg(pParse, "unsupported frame specification");
+    goto windowAllocErr;
+  }
+
+  pWin = (Window*)sqlite3DbMallocZero(pParse->db, sizeof(Window));
+  if( pWin==0 ) goto windowAllocErr;
+  pWin->eFrmType = eType;
+  pWin->eStart = eStart;
+  pWin->eEnd = eEnd;
+  if( eExclude==0 && OptimizationDisabled(pParse->db, SQLITE_WindowFunc) ){
+    eExclude = TK_NO;
+  }
+  pWin->eExclude = eExclude;
+  pWin->bImplicitFrame = bImplicitFrame;
+  pWin->pEnd = sqlite3WindowOffsetExpr(pParse, pEnd);
+  pWin->pStart = sqlite3WindowOffsetExpr(pParse, pStart);
+  return pWin;
+
+windowAllocErr:
+  sqlite3ExprDelete(pParse->db, pEnd);
+  sqlite3ExprDelete(pParse->db, pStart);
+  return 0;
+}
+
+/*
+** Attach PARTITION and ORDER BY clauses pPartition and pOrderBy to window
+** pWin. Also, if parameter pBase is not NULL, set pWin->zBase to the
+** equivalent nul-terminated string.
+*/
+Window *sqlite3WindowAssemble(
+  Parse *pParse,
+  Window *pWin,
+  ExprList *pPartition,
+  ExprList *pOrderBy,
+  Token *pBase
+){
+  if( pWin ){
+    pWin->pPartition = pPartition;
+    pWin->pOrderBy = pOrderBy;
+    if( pBase ){
+      pWin->zBase = sqlite3DbStrNDup(pParse->db, pBase->z, pBase->n);
+    }
+  }else{
+    sqlite3ExprListDelete(pParse->db, pPartition);
+    sqlite3ExprListDelete(pParse->db, pOrderBy);
+  }
+  return pWin;
+}
+
+/*
+** Window *pWin has just been created from a WINDOW clause. Token pBase
+** is the base window. Earlier windows from the same WINDOW clause are
+** stored in the linked list starting at pWin->pNextWin. This function
+** either updates *pWin according to the base specification, or else
+** leaves an error in pParse.
+*/
+void sqlite3WindowChain(Parse *pParse, Window *pWin, Window *pList){
+  if( pWin->zBase ){
+    sqlite3 *db = pParse->db;
+    Window *pExist = windowFind(pParse, pList, pWin->zBase);
+    if( pExist ){
+      const char *zErr = 0;
+      /* Check for errors */
+      if( pWin->pPartition ){
+        zErr = "PARTITION clause";
+      }else if( pExist->pOrderBy && pWin->pOrderBy ){
+        zErr = "ORDER BY clause";
+      }else if( pExist->bImplicitFrame==0 ){
+        zErr = "frame specification";
+      }
+      if( zErr ){
+        sqlite3ErrorMsg(pParse,
+            "cannot override %s of window: %s", zErr, pWin->zBase
+        );
+      }else{
+        pWin->pPartition = sqlite3ExprListDup(db, pExist->pPartition, 0);
+        if( pExist->pOrderBy ){
+          assert( pWin->pOrderBy==0 );
+          pWin->pOrderBy = sqlite3ExprListDup(db, pExist->pOrderBy, 0);
+        }
+        sqlite3DbFree(db, pWin->zBase);
+        pWin->zBase = 0;
+      }
+    }
+  }
+}
+
+/*
+** Attach window object pWin to expression p.
+*/
+void sqlite3WindowAttach(Parse *pParse, Expr *p, Window *pWin){
+  if( p ){
+    assert( p->op==TK_FUNCTION );
+    assert( pWin );
+    assert( ExprIsFullSize(p) );
+    p->y.pWin = pWin;
+    ExprSetProperty(p, EP_WinFunc|EP_FullSize);
+    pWin->pOwner = p;
+    if( (p->flags & EP_Distinct) && pWin->eFrmType!=TK_FILTER ){
+      sqlite3ErrorMsg(pParse,
+          "DISTINCT is not supported for window functions"
+      );
+    }
+  }else{
+    sqlite3WindowDelete(pParse->db, pWin);
+  }
+}
+
+/*
+** Possibly link window pWin into the list at pSel->pWin (window functions
+** to be processed as part of SELECT statement pSel). The window is linked
+** in if either (a) there are no other windows already linked to this
+** SELECT, or (b) the windows already linked use a compatible window frame.
+*/
+void sqlite3WindowLink(Select *pSel, Window *pWin){
+  if( pSel ){
+    if( 0==pSel->pWin || 0==sqlite3WindowCompare(0, pSel->pWin, pWin, 0) ){
+      pWin->pNextWin = pSel->pWin;
+      if( pSel->pWin ){
+        pSel->pWin->ppThis = &pWin->pNextWin;
+      }
+      pSel->pWin = pWin;
+      pWin->ppThis = &pSel->pWin;
+    }else{
+      if( sqlite3ExprListCompare(pWin->pPartition, pSel->pWin->pPartition,-1) ){
+        pSel->selFlags |= SF_MultiPart;
+      }
+    }
+  }
+}
+
+/*
+** Return 0 if the two window objects are identical, 1 if they are
+** different, or 2 if it cannot be determined if the objects are identical
+** or not. Identical window objects can be processed in a single scan.
+*/
+int sqlite3WindowCompare(
+  const Parse *pParse,
+  const Window *p1,
+  const Window *p2,
+  int bFilter
+){
+  int res;
+  if( NEVER(p1==0) || NEVER(p2==0) ) return 1;
+  if( p1->eFrmType!=p2->eFrmType ) return 1;
+  if( p1->eStart!=p2->eStart ) return 1;
+  if( p1->eEnd!=p2->eEnd ) return 1;
+  if( p1->eExclude!=p2->eExclude ) return 1;
+  if( sqlite3ExprCompare(pParse, p1->pStart, p2->pStart, -1) ) return 1;
+  if( sqlite3ExprCompare(pParse, p1->pEnd, p2->pEnd, -1) ) return 1;
+  if( (res = sqlite3ExprListCompare(p1->pPartition, p2->pPartition, -1)) ){
+    return res;
+  }
+  if( (res = sqlite3ExprListCompare(p1->pOrderBy, p2->pOrderBy, -1)) ){
+    return res;
+  }
+  if( bFilter ){
+    if( (res = sqlite3ExprCompare(pParse, p1->pFilter, p2->pFilter, -1)) ){
+      return res;
+    }
+  }
+  return 0;
+}
+
+
+/*
+** This is called by code in select.c before it calls sqlite3WhereBegin()
+** to begin iterating through the sub-query results. It is used to allocate
+** and initialize registers and cursors used by sqlite3WindowCodeStep().
+*/
+void sqlite3WindowCodeInit(Parse *pParse, Select *pSelect){
+  int nEphExpr = pSelect->pSrc->a[0].pSelect->pEList->nExpr;
+  Window *pMWin = pSelect->pWin;
+  Window *pWin;
+  Vdbe *v = sqlite3GetVdbe(pParse);
+
+  sqlite3VdbeAddOp2(v, OP_OpenEphemeral, pMWin->iEphCsr, nEphExpr);
+  sqlite3VdbeAddOp2(v, OP_OpenDup, pMWin->iEphCsr+1, pMWin->iEphCsr);
+  sqlite3VdbeAddOp2(v, OP_OpenDup, pMWin->iEphCsr+2, pMWin->iEphCsr);
+  sqlite3VdbeAddOp2(v, OP_OpenDup, pMWin->iEphCsr+3, pMWin->iEphCsr);
+
+  /* Allocate registers to use for PARTITION BY values, if any. Initialize
+  ** said registers to NULL.  */
+  if( pMWin->pPartition ){
+    int nExpr = pMWin->pPartition->nExpr;
+    pMWin->regPart = pParse->nMem+1;
+    pParse->nMem += nExpr;
+    sqlite3VdbeAddOp3(v, OP_Null, 0, pMWin->regPart, pMWin->regPart+nExpr-1);
+  }
+
+  pMWin->regOne = ++pParse->nMem;
+  sqlite3VdbeAddOp2(v, OP_Integer, 1, pMWin->regOne);
+
+  if( pMWin->eExclude ){
+    pMWin->regStartRowid = ++pParse->nMem;
+    pMWin->regEndRowid = ++pParse->nMem;
+    pMWin->csrApp = pParse->nTab++;
+    sqlite3VdbeAddOp2(v, OP_Integer, 1, pMWin->regStartRowid);
+    sqlite3VdbeAddOp2(v, OP_Integer, 0, pMWin->regEndRowid);
+    sqlite3VdbeAddOp2(v, OP_OpenDup, pMWin->csrApp, pMWin->iEphCsr);
+    return;
+  }
+
+  for(pWin=pMWin; pWin; pWin=pWin->pNextWin){
+    FuncDef *p = pWin->pWFunc;
+    if( (p->funcFlags & SQLITE_FUNC_MINMAX) && pWin->eStart!=TK_UNBOUNDED ){
+      /* The inline versions of min() and max() require a single ephemeral
+      ** table and 3 registers. The registers are used as follows:
+      **
+      **   regApp+0: slot to copy min()/max() argument to for MakeRecord
+      **   regApp+1: integer value used to ensure keys are unique
+      **   regApp+2: output of MakeRecord
+      */
+      ExprList *pList;
+      KeyInfo *pKeyInfo;
+      assert( ExprUseXList(pWin->pOwner) );
+      pList = pWin->pOwner->x.pList;
+      pKeyInfo = sqlite3KeyInfoFromExprList(pParse, pList, 0, 0);
+      pWin->csrApp = pParse->nTab++;
+      pWin->regApp = pParse->nMem+1;
+      pParse->nMem += 3;
+      if( pKeyInfo && pWin->pWFunc->zName[1]=='i' ){
+        assert( pKeyInfo->aSortFlags[0]==0 );
+        pKeyInfo->aSortFlags[0] = KEYINFO_ORDER_DESC;
+      }
+      sqlite3VdbeAddOp2(v, OP_OpenEphemeral, pWin->csrApp, 2);
+      sqlite3VdbeAppendP4(v, pKeyInfo, P4_KEYINFO);
+      sqlite3VdbeAddOp2(v, OP_Integer, 0, pWin->regApp+1);
+    }
+    else if( p->zName==nth_valueName || p->zName==first_valueName ){
+      /* Allocate two registers at pWin->regApp. These will be used to
+      ** store the start and end index of the current frame.  */
+      pWin->regApp = pParse->nMem+1;
+      pWin->csrApp = pParse->nTab++;
+      pParse->nMem += 2;
+      sqlite3VdbeAddOp2(v, OP_OpenDup, pWin->csrApp, pMWin->iEphCsr);
+    }
+    else if( p->zName==leadName || p->zName==lagName ){
+      pWin->csrApp = pParse->nTab++;
+      sqlite3VdbeAddOp2(v, OP_OpenDup, pWin->csrApp, pMWin->iEphCsr);
+    }
+  }
+}
+
+#define WINDOW_STARTING_INT  0
+#define WINDOW_ENDING_INT    1
+#define WINDOW_NTH_VALUE_INT 2
+#define WINDOW_STARTING_NUM  3
+#define WINDOW_ENDING_NUM    4
+
+/*
+** A "PRECEDING <expr>" (eCond==0) or "FOLLOWING <expr>" (eCond==1) or the
+** value of the second argument to nth_value() (eCond==2) has just been
+** evaluated and the result left in register reg. This function generates VM
+** code to check that the value is a non-negative integer and throws an
+** exception if it is not.
+*/
+static void windowCheckValue(Parse *pParse, int reg, int eCond){
+  static const char *azErr[] = {
+    "frame starting offset must be a non-negative integer",
+    "frame ending offset must be a non-negative integer",
+    "second argument to nth_value must be a positive integer",
+    "frame starting offset must be a non-negative number",
+    "frame ending offset must be a non-negative number",
+  };
+  static int aOp[] = { OP_Ge, OP_Ge, OP_Gt, OP_Ge, OP_Ge };
+  Vdbe *v = sqlite3GetVdbe(pParse);
+  int regZero = sqlite3GetTempReg(pParse);
+  assert( eCond>=0 && eCond<ArraySize(azErr) );
+  sqlite3VdbeAddOp2(v, OP_Integer, 0, regZero);
+  if( eCond>=WINDOW_STARTING_NUM ){
+    int regString = sqlite3GetTempReg(pParse);
+    sqlite3VdbeAddOp4(v, OP_String8, 0, regString, 0, "", P4_STATIC);
+    sqlite3VdbeAddOp3(v, OP_Ge, regString, sqlite3VdbeCurrentAddr(v)+2, reg);
+    sqlite3VdbeChangeP5(v, SQLITE_AFF_NUMERIC|SQLITE_JUMPIFNULL);
+    VdbeCoverage(v);
+    assert( eCond==3 || eCond==4 );
+    VdbeCoverageIf(v, eCond==3);
+    VdbeCoverageIf(v, eCond==4);
+  }else{
+    sqlite3VdbeAddOp2(v, OP_MustBeInt, reg, sqlite3VdbeCurrentAddr(v)+2);
+    VdbeCoverage(v);
+    assert( eCond==0 || eCond==1 || eCond==2 );
+    VdbeCoverageIf(v, eCond==0);
+    VdbeCoverageIf(v, eCond==1);
+    VdbeCoverageIf(v, eCond==2);
+  }
+  sqlite3VdbeAddOp3(v, aOp[eCond], regZero, sqlite3VdbeCurrentAddr(v)+2, reg);
+  sqlite3VdbeChangeP5(v, SQLITE_AFF_NUMERIC);
+  VdbeCoverageNeverNullIf(v, eCond==0); /* NULL case captured by */
+  VdbeCoverageNeverNullIf(v, eCond==1); /*   the OP_MustBeInt */
+  VdbeCoverageNeverNullIf(v, eCond==2);
+  VdbeCoverageNeverNullIf(v, eCond==3); /* NULL case caught by */
+  VdbeCoverageNeverNullIf(v, eCond==4); /*   the OP_Ge */
+  sqlite3MayAbort(pParse);
+  sqlite3VdbeAddOp2(v, OP_Halt, SQLITE_ERROR, OE_Abort);
+  sqlite3VdbeAppendP4(v, (void*)azErr[eCond], P4_STATIC);
+  sqlite3ReleaseTempReg(pParse, regZero);
+}
+
+/*
+** Return the number of arguments passed to the window-function associated
+** with the object passed as the only argument to this function.
+*/
+static int windowArgCount(Window *pWin){
+  const ExprList *pList;
+  assert( ExprUseXList(pWin->pOwner) );
+  pList = pWin->pOwner->x.pList;
+  return (pList ? pList->nExpr : 0);
+}
+
+typedef struct WindowCodeArg WindowCodeArg;
+typedef struct WindowCsrAndReg WindowCsrAndReg;
+
+/*
+** See comments above struct WindowCodeArg.
+*/
+struct WindowCsrAndReg {
+  int csr;                        /* Cursor number */
+  int reg;                        /* First in array of peer values */
+};
+
+/*
+** A single instance of this structure is allocated on the stack by
+** sqlite3WindowCodeStep() and a pointer to it passed to the various helper
+** routines. This is to reduce the number of arguments required by each
+** helper function.
+**
+** regArg:
+**   Each window function requires an accumulator register (just as an
+**   ordinary aggregate function does). This variable is set to the first
+**   in an array of accumulator registers - one for each window function
+**   in the WindowCodeArg.pMWin list.
+**
+** eDelete:
+**   The window functions implementation sometimes caches the input rows
+**   that it processes in a temporary table. If it is not zero, this
+**   variable indicates when rows may be removed from the temp table (in
+**   order to reduce memory requirements - it would always be safe just
+**   to leave them there). Possible values for eDelete are:
+**
+**      WINDOW_RETURN_ROW:
+**        An input row can be discarded after it is returned to the caller.
+**
+**      WINDOW_AGGINVERSE:
+**        An input row can be discarded after the window functions xInverse()
+**        callbacks have been invoked in it.
+**
+**      WINDOW_AGGSTEP:
+**        An input row can be discarded after the window functions xStep()
+**        callbacks have been invoked in it.
+**
+** start,current,end
+**   Consider a window-frame similar to the following:
+**
+**     (ORDER BY a, b GROUPS BETWEEN 2 PRECEDING AND 2 FOLLOWING)
+**
+**   The windows functions implementation caches the input rows in a temp
+**   table, sorted by "a, b" (it actually populates the cache lazily, and
+**   aggressively removes rows once they are no longer required, but that's
+**   a mere detail). It keeps three cursors open on the temp table. One
+**   (current) that points to the next row to return to the query engine
+**   once its window function values have been calculated. Another (end)
+**   points to the next row to call the xStep() method of each window function
+**   on (so that it is 2 groups ahead of current). And a third (start) that
+**   points to the next row to call the xInverse() method of each window
+**   function on.
+**
+**   Each cursor (start, current and end) consists of a VDBE cursor
+**   (WindowCsrAndReg.csr) and an array of registers (starting at
+**   WindowCodeArg.reg) that always contains a copy of the peer values
+**   read from the corresponding cursor.
+**
+**   Depending on the window-frame in question, all three cursors may not
+**   be required. In this case both WindowCodeArg.csr and reg are set to
+**   0.
+*/
+struct WindowCodeArg {
+  Parse *pParse;             /* Parse context */
+  Window *pMWin;             /* First in list of functions being processed */
+  Vdbe *pVdbe;               /* VDBE object */
+  int addrGosub;             /* OP_Gosub to this address to return one row */
+  int regGosub;              /* Register used with OP_Gosub(addrGosub) */
+  int regArg;                /* First in array of accumulator registers */
+  int eDelete;               /* See above */
+  int regRowid;
+
+  WindowCsrAndReg start;
+  WindowCsrAndReg current;
+  WindowCsrAndReg end;
+};
+
+/*
+** Generate VM code to read the window frames peer values from cursor csr into
+** an array of registers starting at reg.
+*/
+static void windowReadPeerValues(
+  WindowCodeArg *p,
+  int csr,
+  int reg
+){
+  Window *pMWin = p->pMWin;
+  ExprList *pOrderBy = pMWin->pOrderBy;
+  if( pOrderBy ){
+    Vdbe *v = sqlite3GetVdbe(p->pParse);
+    ExprList *pPart = pMWin->pPartition;
+    int iColOff = pMWin->nBufferCol + (pPart ? pPart->nExpr : 0);
+    int i;
+    for(i=0; i<pOrderBy->nExpr; i++){
+      sqlite3VdbeAddOp3(v, OP_Column, csr, iColOff+i, reg+i);
+    }
+  }
+}
+
+/*
+** Generate VM code to invoke either xStep() (if bInverse is 0) or
+** xInverse (if bInverse is non-zero) for each window function in the
+** linked list starting at pMWin. Or, for built-in window functions
+** that do not use the standard function API, generate the required
+** inline VM code.
+**
+** If argument csr is greater than or equal to 0, then argument reg is
+** the first register in an array of registers guaranteed to be large
+** enough to hold the array of arguments for each function. In this case
+** the arguments are extracted from the current row of csr into the
+** array of registers before invoking OP_AggStep or OP_AggInverse
+**
+** Or, if csr is less than zero, then the array of registers at reg is
+** already populated with all columns from the current row of the sub-query.
+**
+** If argument regPartSize is non-zero, then it is a register containing the
+** number of rows in the current partition.
+*/
+static void windowAggStep(
+  WindowCodeArg *p,
+  Window *pMWin,                  /* Linked list of window functions */
+  int csr,                        /* Read arguments from this cursor */
+  int bInverse,                   /* True to invoke xInverse instead of xStep */
+  int reg                         /* Array of registers */
+){
+  Parse *pParse = p->pParse;
+  Vdbe *v = sqlite3GetVdbe(pParse);
+  Window *pWin;
+  for(pWin=pMWin; pWin; pWin=pWin->pNextWin){
+    FuncDef *pFunc = pWin->pWFunc;
+    int regArg;
+    int nArg = pWin->bExprArgs ? 0 : windowArgCount(pWin);
+    int i;
+
+    assert( bInverse==0 || pWin->eStart!=TK_UNBOUNDED );
+
+    /* All OVER clauses in the same window function aggregate step must
+    ** be the same. */
+    assert( pWin==pMWin || sqlite3WindowCompare(pParse,pWin,pMWin,0)!=1 );
+
+    for(i=0; i<nArg; i++){
+      if( i!=1 || pFunc->zName!=nth_valueName ){
+        sqlite3VdbeAddOp3(v, OP_Column, csr, pWin->iArgCol+i, reg+i);
+      }else{
+        sqlite3VdbeAddOp3(v, OP_Column, pMWin->iEphCsr, pWin->iArgCol+i, reg+i);
+      }
+    }
+    regArg = reg;
+
+    if( pMWin->regStartRowid==0
+     && (pFunc->funcFlags & SQLITE_FUNC_MINMAX)
+     && (pWin->eStart!=TK_UNBOUNDED)
+    ){
+      int addrIsNull = sqlite3VdbeAddOp1(v, OP_IsNull, regArg);
+      VdbeCoverage(v);
+      if( bInverse==0 ){
+        sqlite3VdbeAddOp2(v, OP_AddImm, pWin->regApp+1, 1);
+        sqlite3VdbeAddOp2(v, OP_SCopy, regArg, pWin->regApp);
+        sqlite3VdbeAddOp3(v, OP_MakeRecord, pWin->regApp, 2, pWin->regApp+2);
+        sqlite3VdbeAddOp2(v, OP_IdxInsert, pWin->csrApp, pWin->regApp+2);
+      }else{
+        sqlite3VdbeAddOp4Int(v, OP_SeekGE, pWin->csrApp, 0, regArg, 1);
+        VdbeCoverageNeverTaken(v);
+        sqlite3VdbeAddOp1(v, OP_Delete, pWin->csrApp);
+        sqlite3VdbeJumpHere(v, sqlite3VdbeCurrentAddr(v)-2);
+      }
+      sqlite3VdbeJumpHere(v, addrIsNull);
+    }else if( pWin->regApp ){
+      assert( pFunc->zName==nth_valueName
+           || pFunc->zName==first_valueName
+      );
+      assert( bInverse==0 || bInverse==1 );
+      sqlite3VdbeAddOp2(v, OP_AddImm, pWin->regApp+1-bInverse, 1);
+    }else if( pFunc->xSFunc!=noopStepFunc ){
+      int addrIf = 0;
+      if( pWin->pFilter ){
+        int regTmp;
+        assert( ExprUseXList(pWin->pOwner) );
+        assert( pWin->bExprArgs || !nArg ||nArg==pWin->pOwner->x.pList->nExpr );
+        assert( pWin->bExprArgs || nArg  ||pWin->pOwner->x.pList==0 );
+        regTmp = sqlite3GetTempReg(pParse);
+        sqlite3VdbeAddOp3(v, OP_Column, csr, pWin->iArgCol+nArg,regTmp);
+        addrIf = sqlite3VdbeAddOp3(v, OP_IfNot, regTmp, 0, 1);
+        VdbeCoverage(v);
+        sqlite3ReleaseTempReg(pParse, regTmp);
+      }
+     
+      if( pWin->bExprArgs ){
+        int iOp = sqlite3VdbeCurrentAddr(v);
+        int iEnd;
+
+        assert( ExprUseXList(pWin->pOwner) );
+        nArg = pWin->pOwner->x.pList->nExpr;
+        regArg = sqlite3GetTempRange(pParse, nArg);
+        sqlite3ExprCodeExprList(pParse, pWin->pOwner->x.pList, regArg, 0, 0);
+
+        for(iEnd=sqlite3VdbeCurrentAddr(v); iOp<iEnd; iOp++){
+          VdbeOp *pOp = sqlite3VdbeGetOp(v, iOp);
+          if( pOp->opcode==OP_Column && pOp->p1==pMWin->iEphCsr ){
+            pOp->p1 = csr;
+          }
+        }
+      }
+      if( pFunc->funcFlags & SQLITE_FUNC_NEEDCOLL ){
+        CollSeq *pColl;
+        assert( nArg>0 );
+        assert( ExprUseXList(pWin->pOwner) );
+        pColl = sqlite3ExprNNCollSeq(pParse, pWin->pOwner->x.pList->a[0].pExpr);
+        sqlite3VdbeAddOp4(v, OP_CollSeq, 0,0,0, (const char*)pColl, P4_COLLSEQ);
+      }
+      sqlite3VdbeAddOp3(v, bInverse? OP_AggInverse : OP_AggStep,
+                        bInverse, regArg, pWin->regAccum);
+      sqlite3VdbeAppendP4(v, pFunc, P4_FUNCDEF);
+      sqlite3VdbeChangeP5(v, (u8)nArg);
+      if( pWin->bExprArgs ){
+        sqlite3ReleaseTempRange(pParse, regArg, nArg);
+      }
+      if( addrIf ) sqlite3VdbeJumpHere(v, addrIf);
+    }
+  }
+}
+
+/*
+** Values that may be passed as the second argument to windowCodeOp().
+*/
+#define WINDOW_RETURN_ROW 1
+#define WINDOW_AGGINVERSE 2
+#define WINDOW_AGGSTEP    3
+
+/*
+** Generate VM code to invoke either xValue() (bFin==0) or xFinalize()
+** (bFin==1) for each window function in the linked list starting at
+** pMWin. Or, for built-in window-functions that do not use the standard
+** API, generate the equivalent VM code.
+*/
+static void windowAggFinal(WindowCodeArg *p, int bFin){
+  Parse *pParse = p->pParse;
+  Window *pMWin = p->pMWin;
+  Vdbe *v = sqlite3GetVdbe(pParse);
+  Window *pWin;
+
+  for(pWin=pMWin; pWin; pWin=pWin->pNextWin){
+    if( pMWin->regStartRowid==0
+     && (pWin->pWFunc->funcFlags & SQLITE_FUNC_MINMAX)
+     && (pWin->eStart!=TK_UNBOUNDED)
+    ){
+      sqlite3VdbeAddOp2(v, OP_Null, 0, pWin->regResult);
+      sqlite3VdbeAddOp1(v, OP_Last, pWin->csrApp);
+      VdbeCoverage(v);
+      sqlite3VdbeAddOp3(v, OP_Column, pWin->csrApp, 0, pWin->regResult);
+      sqlite3VdbeJumpHere(v, sqlite3VdbeCurrentAddr(v)-2);
+    }else if( pWin->regApp ){
+      assert( pMWin->regStartRowid==0 );
+    }else{
+      int nArg = windowArgCount(pWin);
+      if( bFin ){
+        sqlite3VdbeAddOp2(v, OP_AggFinal, pWin->regAccum, nArg);
+        sqlite3VdbeAppendP4(v, pWin->pWFunc, P4_FUNCDEF);
+        sqlite3VdbeAddOp2(v, OP_Copy, pWin->regAccum, pWin->regResult);
+        sqlite3VdbeAddOp2(v, OP_Null, 0, pWin->regAccum);
+      }else{
+        sqlite3VdbeAddOp3(v, OP_AggValue,pWin->regAccum,nArg,pWin->regResult);
+        sqlite3VdbeAppendP4(v, pWin->pWFunc, P4_FUNCDEF);
+      }
+    }
+  }
+}
+
+/*
+** Generate code to calculate the current values of all window functions in the
+** p->pMWin list by doing a full scan of the current window frame. Store the
+** results in the Window.regResult registers, ready to return the upper
+** layer.
+*/
+static void windowFullScan(WindowCodeArg *p){
+  Window *pWin;
+  Parse *pParse = p->pParse;
+  Window *pMWin = p->pMWin;
+  Vdbe *v = p->pVdbe;
+
+  int regCRowid = 0;              /* Current rowid value */
+  int regCPeer = 0;               /* Current peer values */
+  int regRowid = 0;               /* AggStep rowid value */
+  int regPeer = 0;                /* AggStep peer values */
+
+  int nPeer;
+  int lblNext;
+  int lblBrk;
+  int addrNext;
+  int csr;
+
+  VdbeModuleComment((v, "windowFullScan begin"));
+
+  assert( pMWin!=0 );
+  csr = pMWin->csrApp;
+  nPeer = (pMWin->pOrderBy ? pMWin->pOrderBy->nExpr : 0);
+
+  lblNext = sqlite3VdbeMakeLabel(pParse);
+  lblBrk = sqlite3VdbeMakeLabel(pParse);
+
+  regCRowid = sqlite3GetTempReg(pParse);
+  regRowid = sqlite3GetTempReg(pParse);
+  if( nPeer ){
+    regCPeer = sqlite3GetTempRange(pParse, nPeer);
+    regPeer = sqlite3GetTempRange(pParse, nPeer);
+  }
+
+  sqlite3VdbeAddOp2(v, OP_Rowid, pMWin->iEphCsr, regCRowid);
+  windowReadPeerValues(p, pMWin->iEphCsr, regCPeer);
+
+  for(pWin=pMWin; pWin; pWin=pWin->pNextWin){
+    sqlite3VdbeAddOp2(v, OP_Null, 0, pWin->regAccum);
+  }
+
+  sqlite3VdbeAddOp3(v, OP_SeekGE, csr, lblBrk, pMWin->regStartRowid);
+  VdbeCoverage(v);
+  addrNext = sqlite3VdbeCurrentAddr(v);
+  sqlite3VdbeAddOp2(v, OP_Rowid, csr, regRowid);
+  sqlite3VdbeAddOp3(v, OP_Gt, pMWin->regEndRowid, lblBrk, regRowid);
+  VdbeCoverageNeverNull(v);
+
+  if( pMWin->eExclude==TK_CURRENT ){
+    sqlite3VdbeAddOp3(v, OP_Eq, regCRowid, lblNext, regRowid);
+    VdbeCoverageNeverNull(v);
+  }else if( pMWin->eExclude!=TK_NO ){
+    int addr;
+    int addrEq = 0;
+    KeyInfo *pKeyInfo = 0;
+
+    if( pMWin->pOrderBy ){
+      pKeyInfo = sqlite3KeyInfoFromExprList(pParse, pMWin->pOrderBy, 0, 0);
+    }
+    if( pMWin->eExclude==TK_TIES ){
+      addrEq = sqlite3VdbeAddOp3(v, OP_Eq, regCRowid, 0, regRowid);
+      VdbeCoverageNeverNull(v);
+    }
+    if( pKeyInfo ){
+      windowReadPeerValues(p, csr, regPeer);
+      sqlite3VdbeAddOp3(v, OP_Compare, regPeer, regCPeer, nPeer);
+      sqlite3VdbeAppendP4(v, (void*)pKeyInfo, P4_KEYINFO);
+      addr = sqlite3VdbeCurrentAddr(v)+1;
+      sqlite3VdbeAddOp3(v, OP_Jump, addr, lblNext, addr);
+      VdbeCoverageEqNe(v);
+    }else{
+      sqlite3VdbeAddOp2(v, OP_Goto, 0, lblNext);
+    }
+    if( addrEq ) sqlite3VdbeJumpHere(v, addrEq);
+  }
+
+  windowAggStep(p, pMWin, csr, 0, p->regArg);
+
+  sqlite3VdbeResolveLabel(v, lblNext);
+  sqlite3VdbeAddOp2(v, OP_Next, csr, addrNext);
+  VdbeCoverage(v);
+  sqlite3VdbeJumpHere(v, addrNext-1);
+  sqlite3VdbeJumpHere(v, addrNext+1);
+  sqlite3ReleaseTempReg(pParse, regRowid);
+  sqlite3ReleaseTempReg(pParse, regCRowid);
+  if( nPeer ){
+    sqlite3ReleaseTempRange(pParse, regPeer, nPeer);
+    sqlite3ReleaseTempRange(pParse, regCPeer, nPeer);
+  }
+
+  windowAggFinal(p, 1);
+  VdbeModuleComment((v, "windowFullScan end"));
+}
+
+/*
+** Invoke the sub-routine at regGosub (generated by code in select.c) to
+** return the current row of Window.iEphCsr. If all window functions are
+** aggregate window functions that use the standard API, a single
+** OP_Gosub instruction is all that this routine generates. Extra VM code
+** for per-row processing is only generated for the following built-in window
+** functions:
+**
+**   nth_value()
+**   first_value()
+**   lag()
+**   lead()
+*/
+static void windowReturnOneRow(WindowCodeArg *p){
+  Window *pMWin = p->pMWin;
+  Vdbe *v = p->pVdbe;
+
+  if( pMWin->regStartRowid ){
+    windowFullScan(p);
+  }else{
+    Parse *pParse = p->pParse;
+    Window *pWin;
+
+    for(pWin=pMWin; pWin; pWin=pWin->pNextWin){
+      FuncDef *pFunc = pWin->pWFunc;
+      assert( ExprUseXList(pWin->pOwner) );
+      if( pFunc->zName==nth_valueName
+       || pFunc->zName==first_valueName
+      ){
+        int csr = pWin->csrApp;
+        int lbl = sqlite3VdbeMakeLabel(pParse);
+        int tmpReg = sqlite3GetTempReg(pParse);
+        sqlite3VdbeAddOp2(v, OP_Null, 0, pWin->regResult);
+ 
+        if( pFunc->zName==nth_valueName ){
+          sqlite3VdbeAddOp3(v, OP_Column,pMWin->iEphCsr,pWin->iArgCol+1,tmpReg);
+          windowCheckValue(pParse, tmpReg, 2);
+        }else{
+          sqlite3VdbeAddOp2(v, OP_Integer, 1, tmpReg);
+        }
+        sqlite3VdbeAddOp3(v, OP_Add, tmpReg, pWin->regApp, tmpReg);
+        sqlite3VdbeAddOp3(v, OP_Gt, pWin->regApp+1, lbl, tmpReg);
+        VdbeCoverageNeverNull(v);
+        sqlite3VdbeAddOp3(v, OP_SeekRowid, csr, 0, tmpReg);
+        VdbeCoverageNeverTaken(v);
+        sqlite3VdbeAddOp3(v, OP_Column, csr, pWin->iArgCol, pWin->regResult);
+        sqlite3VdbeResolveLabel(v, lbl);
+        sqlite3ReleaseTempReg(pParse, tmpReg);
+      }
+      else if( pFunc->zName==leadName || pFunc->zName==lagName ){
+        int nArg = pWin->pOwner->x.pList->nExpr;
+        int csr = pWin->csrApp;
+        int lbl = sqlite3VdbeMakeLabel(pParse);
+        int tmpReg = sqlite3GetTempReg(pParse);
+        int iEph = pMWin->iEphCsr;
+ 
+        if( nArg<3 ){
+          sqlite3VdbeAddOp2(v, OP_Null, 0, pWin->regResult);
+        }else{
+          sqlite3VdbeAddOp3(v, OP_Column, iEph,pWin->iArgCol+2,pWin->regResult);
+        }
+        sqlite3VdbeAddOp2(v, OP_Rowid, iEph, tmpReg);
+        if( nArg<2 ){
+          int val = (pFunc->zName==leadName ? 1 : -1);
+          sqlite3VdbeAddOp2(v, OP_AddImm, tmpReg, val);
+        }else{
+          int op = (pFunc->zName==leadName ? OP_Add : OP_Subtract);
+          int tmpReg2 = sqlite3GetTempReg(pParse);
+          sqlite3VdbeAddOp3(v, OP_Column, iEph, pWin->iArgCol+1, tmpReg2);
+          sqlite3VdbeAddOp3(v, op, tmpReg2, tmpReg, tmpReg);
+          sqlite3ReleaseTempReg(pParse, tmpReg2);
+        }
+ 
+        sqlite3VdbeAddOp3(v, OP_SeekRowid, csr, lbl, tmpReg);
+        VdbeCoverage(v);
+        sqlite3VdbeAddOp3(v, OP_Column, csr, pWin->iArgCol, pWin->regResult);
+        sqlite3VdbeResolveLabel(v, lbl);
+        sqlite3ReleaseTempReg(pParse, tmpReg);
+      }
+    }
+  }
+  sqlite3VdbeAddOp2(v, OP_Gosub, p->regGosub, p->addrGosub);
+}
+
+/*
+** Generate code to set the accumulator register for each window function
+** in the linked list passed as the second argument to NULL. And perform
+** any equivalent initialization required by any built-in window functions
+** in the list.
+*/
+static int windowInitAccum(Parse *pParse, Window *pMWin){
+  Vdbe *v = sqlite3GetVdbe(pParse);
+  int regArg;
+  int nArg = 0;
+  Window *pWin;
+  for(pWin=pMWin; pWin; pWin=pWin->pNextWin){
+    FuncDef *pFunc = pWin->pWFunc;
+    assert( pWin->regAccum );
+    sqlite3VdbeAddOp2(v, OP_Null, 0, pWin->regAccum);
+    nArg = MAX(nArg, windowArgCount(pWin));
+    if( pMWin->regStartRowid==0 ){
+      if( pFunc->zName==nth_valueName || pFunc->zName==first_valueName ){
+        sqlite3VdbeAddOp2(v, OP_Integer, 0, pWin->regApp);
+        sqlite3VdbeAddOp2(v, OP_Integer, 0, pWin->regApp+1);
+      }
+
+      if( (pFunc->funcFlags & SQLITE_FUNC_MINMAX) && pWin->csrApp ){
+        assert( pWin->eStart!=TK_UNBOUNDED );
+        sqlite3VdbeAddOp1(v, OP_ResetSorter, pWin->csrApp);
+        sqlite3VdbeAddOp2(v, OP_Integer, 0, pWin->regApp+1);
+      }
+    }
+  }
+  regArg = pParse->nMem+1;
+  pParse->nMem += nArg;
+  return regArg;
+}
+
+/*
+** Return true if the current frame should be cached in the ephemeral table,
+** even if there are no xInverse() calls required.
+*/
+static int windowCacheFrame(Window *pMWin){
+  Window *pWin;
+  if( pMWin->regStartRowid ) return 1;
+  for(pWin=pMWin; pWin; pWin=pWin->pNextWin){
+    FuncDef *pFunc = pWin->pWFunc;
+    if( (pFunc->zName==nth_valueName)
+     || (pFunc->zName==first_valueName)
+     || (pFunc->zName==leadName)
+     || (pFunc->zName==lagName)
+    ){
+      return 1;
+    }
+  }
+  return 0;
+}
+
+/*
+** regOld and regNew are each the first register in an array of size
+** pOrderBy->nExpr. This function generates code to compare the two
+** arrays of registers using the collation sequences and other comparison
+** parameters specified by pOrderBy.
+**
+** If the two arrays are not equal, the contents of regNew is copied to
+** regOld and control falls through. Otherwise, if the contents of the arrays
+** are equal, an OP_Goto is executed. The address of the OP_Goto is returned.
+*/
+static void windowIfNewPeer(
+  Parse *pParse,
+  ExprList *pOrderBy,
+  int regNew,                     /* First in array of new values */
+  int regOld,                     /* First in array of old values */
+  int addr                        /* Jump here */
+){
+  Vdbe *v = sqlite3GetVdbe(pParse);
+  if( pOrderBy ){
+    int nVal = pOrderBy->nExpr;
+    KeyInfo *pKeyInfo = sqlite3KeyInfoFromExprList(pParse, pOrderBy, 0, 0);
+    sqlite3VdbeAddOp3(v, OP_Compare, regOld, regNew, nVal);
+    sqlite3VdbeAppendP4(v, (void*)pKeyInfo, P4_KEYINFO);
+    sqlite3VdbeAddOp3(v, OP_Jump,
+      sqlite3VdbeCurrentAddr(v)+1, addr, sqlite3VdbeCurrentAddr(v)+1
+    );
+    VdbeCoverageEqNe(v);
+    sqlite3VdbeAddOp3(v, OP_Copy, regNew, regOld, nVal-1);
+  }else{
+    sqlite3VdbeAddOp2(v, OP_Goto, 0, addr);
+  }
+}
+
+/*
+** This function is called as part of generating VM programs for RANGE
+** offset PRECEDING/FOLLOWING frame boundaries. Assuming "ASC" order for
+** the ORDER BY term in the window, and that argument op is OP_Ge, it generates
+** code equivalent to:
+**
+**   if( csr1.peerVal + regVal >= csr2.peerVal ) goto lbl;
+**
+** The value of parameter op may also be OP_Gt or OP_Le. In these cases the
+** operator in the above pseudo-code is replaced with ">" or "<=", respectively.
+**
+** If the sort-order for the ORDER BY term in the window is DESC, then the
+** comparison is reversed. Instead of adding regVal to csr1.peerVal, it is
+** subtracted. And the comparison operator is inverted to - ">=" becomes "<=",
+** ">" becomes "<", and so on. So, with DESC sort order, if the argument op
+** is OP_Ge, the generated code is equivalent to:
+**
+**   if( csr1.peerVal - regVal <= csr2.peerVal ) goto lbl;
+**
+** A special type of arithmetic is used such that if csr1.peerVal is not
+** a numeric type (real or integer), then the result of the addition
+** or subtraction is a a copy of csr1.peerVal.
+*/
+static void windowCodeRangeTest(
+  WindowCodeArg *p,
+  int op,                         /* OP_Ge, OP_Gt, or OP_Le */
+  int csr1,                       /* Cursor number for cursor 1 */
+  int regVal,                     /* Register containing non-negative number */
+  int csr2,                       /* Cursor number for cursor 2 */
+  int lbl                         /* Jump destination if condition is true */
+){
+  Parse *pParse = p->pParse;
+  Vdbe *v = sqlite3GetVdbe(pParse);
+  ExprList *pOrderBy = p->pMWin->pOrderBy;  /* ORDER BY clause for window */
+  int reg1 = sqlite3GetTempReg(pParse);     /* Reg. for csr1.peerVal+regVal */
+  int reg2 = sqlite3GetTempReg(pParse);     /* Reg. for csr2.peerVal */
+  int regString = ++pParse->nMem;           /* Reg. for constant value '' */
+  int arith = OP_Add;                       /* OP_Add or OP_Subtract */
+  int addrGe;                               /* Jump destination */
+  int addrDone = sqlite3VdbeMakeLabel(pParse);   /* Address past OP_Ge */
+  CollSeq *pColl;
+
+  /* Read the peer-value from each cursor into a register */
+  windowReadPeerValues(p, csr1, reg1);
+  windowReadPeerValues(p, csr2, reg2);
+
+  assert( op==OP_Ge || op==OP_Gt || op==OP_Le );
+  assert( pOrderBy && pOrderBy->nExpr==1 );
+  if( pOrderBy->a[0].fg.sortFlags & KEYINFO_ORDER_DESC ){
+    switch( op ){
+      case OP_Ge: op = OP_Le; break;
+      case OP_Gt: op = OP_Lt; break;
+      default: assert( op==OP_Le ); op = OP_Ge; break;
+    }
+    arith = OP_Subtract;
+  }
+
+  VdbeModuleComment((v, "CodeRangeTest: if( R%d %s R%d %s R%d ) goto lbl",
+      reg1, (arith==OP_Add ? "+" : "-"), regVal,
+      ((op==OP_Ge) ? ">=" : (op==OP_Le) ? "<=" : (op==OP_Gt) ? ">" : "<"), reg2
+  ));
+
+  /* If the BIGNULL flag is set for the ORDER BY, then it is required to
+  ** consider NULL values to be larger than all other values, instead of
+  ** the usual smaller. The VDBE opcodes OP_Ge and so on do not handle this
+  ** (and adding that capability causes a performance regression), so
+  ** instead if the BIGNULL flag is set then cases where either reg1 or
+  ** reg2 are NULL are handled separately in the following block. The code
+  ** generated is equivalent to:
+  **
+  **   if( reg1 IS NULL ){
+  **     if( op==OP_Ge ) goto lbl;
+  **     if( op==OP_Gt && reg2 IS NOT NULL ) goto lbl;
+  **     if( op==OP_Le && reg2 IS NULL ) goto lbl;
+  **   }else if( reg2 IS NULL ){
+  **     if( op==OP_Le ) goto lbl;
+  **   }
+  **
+  ** Additionally, if either reg1 or reg2 are NULL but the jump to lbl is
+  ** not taken, control jumps over the comparison operator coded below this
+  ** block.  */
+  if( pOrderBy->a[0].fg.sortFlags & KEYINFO_ORDER_BIGNULL ){
+    /* This block runs if reg1 contains a NULL. */
+    int addr = sqlite3VdbeAddOp1(v, OP_NotNull, reg1); VdbeCoverage(v);
+    switch( op ){
+      case OP_Ge:
+        sqlite3VdbeAddOp2(v, OP_Goto, 0, lbl);
+        break;
+      case OP_Gt:
+        sqlite3VdbeAddOp2(v, OP_NotNull, reg2, lbl);
+        VdbeCoverage(v);
+        break;
+      case OP_Le:
+        sqlite3VdbeAddOp2(v, OP_IsNull, reg2, lbl);
+        VdbeCoverage(v);
+        break;
+      default: assert( op==OP_Lt ); /* no-op */ break;
+    }
+    sqlite3VdbeAddOp2(v, OP_Goto, 0, addrDone);
+
+    /* This block runs if reg1 is not NULL, but reg2 is. */
+    sqlite3VdbeJumpHere(v, addr);
+    sqlite3VdbeAddOp2(v, OP_IsNull, reg2,
+                      (op==OP_Gt || op==OP_Ge) ? addrDone : lbl);
+    VdbeCoverage(v);
+  }
+
+  /* Register reg1 currently contains csr1.peerVal (the peer-value from csr1).
+  ** This block adds (or subtracts for DESC) the numeric value in regVal
+  ** from it. Or, if reg1 is not numeric (it is a NULL, a text value or a blob),
+  ** then leave reg1 as it is. In pseudo-code, this is implemented as:
+  **
+  **   if( reg1>='' ) goto addrGe;
+  **   reg1 = reg1 +/- regVal
+  **   addrGe:
+  **
+  ** Since all strings and blobs are greater-than-or-equal-to an empty string,
+  ** the add/subtract is skipped for these, as required. If reg1 is a NULL,
+  ** then the arithmetic is performed, but since adding or subtracting from
+  ** NULL is always NULL anyway, this case is handled as required too.  */
+  sqlite3VdbeAddOp4(v, OP_String8, 0, regString, 0, "", P4_STATIC);
+  addrGe = sqlite3VdbeAddOp3(v, OP_Ge, regString, 0, reg1);
+  VdbeCoverage(v);
+  if( (op==OP_Ge && arith==OP_Add) || (op==OP_Le && arith==OP_Subtract) ){
+    sqlite3VdbeAddOp3(v, op, reg2, lbl, reg1); VdbeCoverage(v);
+  }
+  sqlite3VdbeAddOp3(v, arith, regVal, reg1, reg1);
+  sqlite3VdbeJumpHere(v, addrGe);
+
+  /* Compare registers reg2 and reg1, taking the jump if required. Note that
+  ** control skips over this test if the BIGNULL flag is set and either
+  ** reg1 or reg2 contain a NULL value.  */
+  sqlite3VdbeAddOp3(v, op, reg2, lbl, reg1); VdbeCoverage(v);
+  pColl = sqlite3ExprNNCollSeq(pParse, pOrderBy->a[0].pExpr);
+  sqlite3VdbeAppendP4(v, (void*)pColl, P4_COLLSEQ);
+  sqlite3VdbeChangeP5(v, SQLITE_NULLEQ);
+  sqlite3VdbeResolveLabel(v, addrDone);
+
+  assert( op==OP_Ge || op==OP_Gt || op==OP_Lt || op==OP_Le );
+  testcase(op==OP_Ge); VdbeCoverageIf(v, op==OP_Ge);
+  testcase(op==OP_Lt); VdbeCoverageIf(v, op==OP_Lt);
+  testcase(op==OP_Le); VdbeCoverageIf(v, op==OP_Le);
+  testcase(op==OP_Gt); VdbeCoverageIf(v, op==OP_Gt);
+  sqlite3ReleaseTempReg(pParse, reg1);
+  sqlite3ReleaseTempReg(pParse, reg2);
+
+  VdbeModuleComment((v, "CodeRangeTest: end"));
+}
+
+/*
+** Helper function for sqlite3WindowCodeStep(). Each call to this function
+** generates VM code for a single RETURN_ROW, AGGSTEP or AGGINVERSE
+** operation. Refer to the header comment for sqlite3WindowCodeStep() for
+** details.
+*/
+static int windowCodeOp(
+ WindowCodeArg *p,                /* Context object */
+ int op,                          /* WINDOW_RETURN_ROW, AGGSTEP or AGGINVERSE */
+ int regCountdown,                /* Register for OP_IfPos countdown */
+ int jumpOnEof                    /* Jump here if stepped cursor reaches EOF */
+){
+  int csr, reg;
+  Parse *pParse = p->pParse;
+  Window *pMWin = p->pMWin;
+  int ret = 0;
+  Vdbe *v = p->pVdbe;
+  int addrContinue = 0;
+  int bPeer = (pMWin->eFrmType!=TK_ROWS);
+
+  int lblDone = sqlite3VdbeMakeLabel(pParse);
+  int addrNextRange = 0;
+
+  /* Special case - WINDOW_AGGINVERSE is always a no-op if the frame
+  ** starts with UNBOUNDED PRECEDING. */
+  if( op==WINDOW_AGGINVERSE && pMWin->eStart==TK_UNBOUNDED ){
+    assert( regCountdown==0 && jumpOnEof==0 );
+    return 0;
+  }
+
+  if( regCountdown>0 ){
+    if( pMWin->eFrmType==TK_RANGE ){
+      addrNextRange = sqlite3VdbeCurrentAddr(v);
+      assert( op==WINDOW_AGGINVERSE || op==WINDOW_AGGSTEP );
+      if( op==WINDOW_AGGINVERSE ){
+        if( pMWin->eStart==TK_FOLLOWING ){
+          windowCodeRangeTest(
+              p, OP_Le, p->current.csr, regCountdown, p->start.csr, lblDone
+          );
+        }else{
+          windowCodeRangeTest(
+              p, OP_Ge, p->start.csr, regCountdown, p->current.csr, lblDone
+          );
+        }
+      }else{
+        windowCodeRangeTest(
+            p, OP_Gt, p->end.csr, regCountdown, p->current.csr, lblDone
+        );
+      }
+    }else{
+      sqlite3VdbeAddOp3(v, OP_IfPos, regCountdown, lblDone, 1);
+      VdbeCoverage(v);
+    }
+  }
+
+  if( op==WINDOW_RETURN_ROW && pMWin->regStartRowid==0 ){
+    windowAggFinal(p, 0);
+  }
+  addrContinue = sqlite3VdbeCurrentAddr(v);
+
+  /* If this is a (RANGE BETWEEN a FOLLOWING AND b FOLLOWING) or
+  ** (RANGE BETWEEN b PRECEDING AND a PRECEDING) frame, ensure the
+  ** start cursor does not advance past the end cursor within the
+  ** temporary table. It otherwise might, if (a>b). Also ensure that,
+  ** if the input cursor is still finding new rows, that the end
+  ** cursor does not go past it to EOF. */
+  if( pMWin->eStart==pMWin->eEnd && regCountdown
+   && pMWin->eFrmType==TK_RANGE
+  ){
+    int regRowid1 = sqlite3GetTempReg(pParse);
+    int regRowid2 = sqlite3GetTempReg(pParse);
+    if( op==WINDOW_AGGINVERSE ){
+      sqlite3VdbeAddOp2(v, OP_Rowid, p->start.csr, regRowid1);
+      sqlite3VdbeAddOp2(v, OP_Rowid, p->end.csr, regRowid2);
+      sqlite3VdbeAddOp3(v, OP_Ge, regRowid2, lblDone, regRowid1);
+      VdbeCoverage(v);
+    }else if( p->regRowid ){
+      sqlite3VdbeAddOp2(v, OP_Rowid, p->end.csr, regRowid1);
+      sqlite3VdbeAddOp3(v, OP_Ge, p->regRowid, lblDone, regRowid1);
+      VdbeCoverageNeverNull(v);
+    }
+    sqlite3ReleaseTempReg(pParse, regRowid1);
+    sqlite3ReleaseTempReg(pParse, regRowid2);
+    assert( pMWin->eStart==TK_PRECEDING || pMWin->eStart==TK_FOLLOWING );
+  }
+
+  switch( op ){
+    case WINDOW_RETURN_ROW:
+      csr = p->current.csr;
+      reg = p->current.reg;
+      windowReturnOneRow(p);
+      break;
+
+    case WINDOW_AGGINVERSE:
+      csr = p->start.csr;
+      reg = p->start.reg;
+      if( pMWin->regStartRowid ){
+        assert( pMWin->regEndRowid );
+        sqlite3VdbeAddOp2(v, OP_AddImm, pMWin->regStartRowid, 1);
+      }else{
+        windowAggStep(p, pMWin, csr, 1, p->regArg);
+      }
+      break;
+
+    default:
+      assert( op==WINDOW_AGGSTEP );
+      csr = p->end.csr;
+      reg = p->end.reg;
+      if( pMWin->regStartRowid ){
+        assert( pMWin->regEndRowid );
+        sqlite3VdbeAddOp2(v, OP_AddImm, pMWin->regEndRowid, 1);
+      }else{
+        windowAggStep(p, pMWin, csr, 0, p->regArg);
+      }
+      break;
+  }
+
+  if( op==p->eDelete ){
+    sqlite3VdbeAddOp1(v, OP_Delete, csr);
+    sqlite3VdbeChangeP5(v, OPFLAG_SAVEPOSITION);
+  }
+
+  if( jumpOnEof ){
+    sqlite3VdbeAddOp2(v, OP_Next, csr, sqlite3VdbeCurrentAddr(v)+2);
+    VdbeCoverage(v);
+    ret = sqlite3VdbeAddOp0(v, OP_Goto);
+  }else{
+    sqlite3VdbeAddOp2(v, OP_Next, csr, sqlite3VdbeCurrentAddr(v)+1+bPeer);
+    VdbeCoverage(v);
+    if( bPeer ){
+      sqlite3VdbeAddOp2(v, OP_Goto, 0, lblDone);
+    }
+  }
+
+  if( bPeer ){
+    int nReg = (pMWin->pOrderBy ? pMWin->pOrderBy->nExpr : 0);
+    int regTmp = (nReg ? sqlite3GetTempRange(pParse, nReg) : 0);
+    windowReadPeerValues(p, csr, regTmp);
+    windowIfNewPeer(pParse, pMWin->pOrderBy, regTmp, reg, addrContinue);
+    sqlite3ReleaseTempRange(pParse, regTmp, nReg);
+  }
+
+  if( addrNextRange ){
+    sqlite3VdbeAddOp2(v, OP_Goto, 0, addrNextRange);
+  }
+  sqlite3VdbeResolveLabel(v, lblDone);
+  return ret;
+}
+
+
+/*
+** Allocate and return a duplicate of the Window object indicated by the
+** third argument. Set the Window.pOwner field of the new object to
+** pOwner.
+*/
+Window *sqlite3WindowDup(sqlite3 *db, Expr *pOwner, Window *p){
+  Window *pNew = 0;
+  if( ALWAYS(p) ){
+    pNew = sqlite3DbMallocZero(db, sizeof(Window));
+    if( pNew ){
+      pNew->zName = sqlite3DbStrDup(db, p->zName);
+      pNew->zBase = sqlite3DbStrDup(db, p->zBase);
+      pNew->pFilter = sqlite3ExprDup(db, p->pFilter, 0);
+      pNew->pWFunc = p->pWFunc;
+      pNew->pPartition = sqlite3ExprListDup(db, p->pPartition, 0);
+      pNew->pOrderBy = sqlite3ExprListDup(db, p->pOrderBy, 0);
+      pNew->eFrmType = p->eFrmType;
+      pNew->eEnd = p->eEnd;
+      pNew->eStart = p->eStart;
+      pNew->eExclude = p->eExclude;
+      pNew->regResult = p->regResult;
+      pNew->regAccum = p->regAccum;
+      pNew->iArgCol = p->iArgCol;
+      pNew->iEphCsr = p->iEphCsr;
+      pNew->bExprArgs = p->bExprArgs;
+      pNew->pStart = sqlite3ExprDup(db, p->pStart, 0);
+      pNew->pEnd = sqlite3ExprDup(db, p->pEnd, 0);
+      pNew->pOwner = pOwner;
+      pNew->bImplicitFrame = p->bImplicitFrame;
+    }
+  }
+  return pNew;
+}
+
+/*
+** Return a copy of the linked list of Window objects passed as the
+** second argument.
+*/
+Window *sqlite3WindowListDup(sqlite3 *db, Window *p){
+  Window *pWin;
+  Window *pRet = 0;
+  Window **pp = &pRet;
+
+  for(pWin=p; pWin; pWin=pWin->pNextWin){
+    *pp = sqlite3WindowDup(db, 0, pWin);
+    if( *pp==0 ) break;
+    pp = &((*pp)->pNextWin);
+  }
+
+  return pRet;
+}
+
+/*
+** Return true if it can be determined at compile time that expression
+** pExpr evaluates to a value that, when cast to an integer, is greater
+** than zero. False otherwise.
+**
+** If an OOM error occurs, this function sets the Parse.db.mallocFailed
+** flag and returns zero.
+*/
+static int windowExprGtZero(Parse *pParse, Expr *pExpr){
+  int ret = 0;
+  sqlite3 *db = pParse->db;
+  sqlite3_value *pVal = 0;
+  sqlite3ValueFromExpr(db, pExpr, db->enc, SQLITE_AFF_NUMERIC, &pVal);
+  if( pVal && sqlite3_value_int(pVal)>0 ){
+    ret = 1;
+  }
+  sqlite3ValueFree(pVal);
+  return ret;
+}
+
+/*
+** sqlite3WhereBegin() has already been called for the SELECT statement
+** passed as the second argument when this function is invoked. It generates
+** code to populate the Window.regResult register for each window function
+** and invoke the sub-routine at instruction addrGosub once for each row.
+** sqlite3WhereEnd() is always called before returning.
+**
+** This function handles several different types of window frames, which
+** require slightly different processing. The following pseudo code is
+** used to implement window frames of the form:
+**
+**   ROWS BETWEEN <expr1> PRECEDING AND <expr2> FOLLOWING
+**
+** Other window frame types use variants of the following:
+**
+**     ... loop started by sqlite3WhereBegin() ...
+**       if( new partition ){
+**         Gosub flush
+**       }
+**       Insert new row into eph table.
+**      
+**       if( first row of partition ){
+**         // Rewind three cursors, all open on the eph table.
+**         Rewind(csrEnd);
+**         Rewind(csrStart);
+**         Rewind(csrCurrent);
+**      
+**         regEnd = <expr2>          // FOLLOWING expression
+**         regStart = <expr1>        // PRECEDING expression
+**       }else{
+**         // First time this branch is taken, the eph table contains two
+**         // rows. The first row in the partition, which all three cursors
+**         // currently point to, and the following row.
+**         AGGSTEP
+**         if( (regEnd--)<=0 ){
+**           RETURN_ROW
+**           if( (regStart--)<=0 ){
+**             AGGINVERSE
+**           }
+**         }
+**       }
+**     }
+**     flush:
+**       AGGSTEP
+**       while( 1 ){
+**         RETURN ROW
+**         if( csrCurrent is EOF ) break;
+**         if( (regStart--)<=0 ){
+**           AggInverse(csrStart)
+**           Next(csrStart)
+**         }
+**       }
+**
+** The pseudo-code above uses the following shorthand:
+**
+**   AGGSTEP:    invoke the aggregate xStep() function for each window function
+**               with arguments read from the current row of cursor csrEnd, then
+**               step cursor csrEnd forward one row (i.e. sqlite3BtreeNext()).
+**
+**   RETURN_ROW: return a row to the caller based on the contents of the
+**               current row of csrCurrent and the current state of all
+**               aggregates. Then step cursor csrCurrent forward one row.
+**
+**   AGGINVERSE: invoke the aggregate xInverse() function for each window
+**               functions with arguments read from the current row of cursor
+**               csrStart. Then step csrStart forward one row.
+**
+** There are two other ROWS window frames that are handled significantly
+** differently from the above - "BETWEEN <expr> PRECEDING AND <expr> PRECEDING"
+** and "BETWEEN <expr> FOLLOWING AND <expr> FOLLOWING". These are special
+** cases because they change the order in which the three cursors (csrStart,
+** csrCurrent and csrEnd) iterate through the ephemeral table. Cases that
+** use UNBOUNDED or CURRENT ROW are much simpler variations on one of these
+** three.
+**
+**   ROWS BETWEEN <expr1> PRECEDING AND <expr2> PRECEDING
+**
+**     ... loop started by sqlite3WhereBegin() ...
+**       if( new partition ){
+**         Gosub flush
+**       }
+**       Insert new row into eph table.
+**       if( first row of partition ){
+**         Rewind(csrEnd) ; Rewind(csrStart) ; Rewind(csrCurrent)
+**         regEnd = <expr2>
+**         regStart = <expr1>
+**       }else{
+**         if( (regEnd--)<=0 ){
+**           AGGSTEP
+**         }
+**         RETURN_ROW
+**         if( (regStart--)<=0 ){
+**           AGGINVERSE
+**         }
+**       }
+**     }
+**     flush:
+**       if( (regEnd--)<=0 ){
+**         AGGSTEP
+**       }
+**       RETURN_ROW
+**
+**
+**   ROWS BETWEEN <expr1> FOLLOWING AND <expr2> FOLLOWING
+**
+**     ... loop started by sqlite3WhereBegin() ...
+**     if( new partition ){
+**       Gosub flush
+**     }
+**     Insert new row into eph table.
+**     if( first row of partition ){
+**       Rewind(csrEnd) ; Rewind(csrStart) ; Rewind(csrCurrent)
+**       regEnd = <expr2>
+**       regStart = regEnd - <expr1>
+**     }else{
+**       AGGSTEP
+**       if( (regEnd--)<=0 ){
+**         RETURN_ROW
+**       }
+**       if( (regStart--)<=0 ){
+**         AGGINVERSE
+**       }
+**     }
+**   }
+**   flush:
+**     AGGSTEP
+**     while( 1 ){
+**       if( (regEnd--)<=0 ){
+**         RETURN_ROW
+**         if( eof ) break;
+**       }
+**       if( (regStart--)<=0 ){
+**         AGGINVERSE
+**         if( eof ) break
+**       }
+**     }
+**     while( !eof csrCurrent ){
+**       RETURN_ROW
+**     }
+**
+** For the most part, the patterns above are adapted to support UNBOUNDED by
+** assuming that it is equivalent to "infinity PRECEDING/FOLLOWING" and
+** CURRENT ROW by assuming that it is equivalent to "0 PRECEDING/FOLLOWING".
+** This is optimized of course - branches that will never be taken and
+** conditions that are always true are omitted from the VM code. The only
+** exceptional case is:
+**
+**   ROWS BETWEEN <expr1> FOLLOWING AND UNBOUNDED FOLLOWING
+**
+**     ... loop started by sqlite3WhereBegin() ...
+**     if( new partition ){
+**       Gosub flush
+**     }
+**     Insert new row into eph table.
+**     if( first row of partition ){
+**       Rewind(csrEnd) ; Rewind(csrStart) ; Rewind(csrCurrent)
+**       regStart = <expr1>
+**     }else{
+**       AGGSTEP
+**     }
+**   }
+**   flush:
+**     AGGSTEP
+**     while( 1 ){
+**       if( (regStart--)<=0 ){
+**         AGGINVERSE
+**         if( eof ) break
+**       }
+**       RETURN_ROW
+**     }
+**     while( !eof csrCurrent ){
+**       RETURN_ROW
+**     }
+**
+** Also requiring special handling are the cases:
+**
+**   ROWS BETWEEN <expr1> PRECEDING AND <expr2> PRECEDING
+**   ROWS BETWEEN <expr1> FOLLOWING AND <expr2> FOLLOWING
+**
+** when (expr1 < expr2). This is detected at runtime, not by this function.
+** To handle this case, the pseudo-code programs depicted above are modified
+** slightly to be:
+**
+**     ... loop started by sqlite3WhereBegin() ...
+**     if( new partition ){
+**       Gosub flush
+**     }
+**     Insert new row into eph table.
+**     if( first row of partition ){
+**       Rewind(csrEnd) ; Rewind(csrStart) ; Rewind(csrCurrent)
+**       regEnd = <expr2>
+**       regStart = <expr1>
+**       if( regEnd < regStart ){
+**         RETURN_ROW
+**         delete eph table contents
+**         continue
+**       }
+**     ...
+**
+** The new "continue" statement in the above jumps to the next iteration
+** of the outer loop - the one started by sqlite3WhereBegin().
+**
+** The various GROUPS cases are implemented using the same patterns as
+** ROWS. The VM code is modified slightly so that:
+**
+**   1. The else branch in the main loop is only taken if the row just
+**      added to the ephemeral table is the start of a new group. In
+**      other words, it becomes:
+**
+**         ... loop started by sqlite3WhereBegin() ...
+**         if( new partition ){
+**           Gosub flush
+**         }
+**         Insert new row into eph table.
+**         if( first row of partition ){
+**           Rewind(csrEnd) ; Rewind(csrStart) ; Rewind(csrCurrent)
+**           regEnd = <expr2>
+**           regStart = <expr1>
+**         }else if( new group ){
+**           ...
+**         }
+**       }
+**
+**   2. Instead of processing a single row, each RETURN_ROW, AGGSTEP or
+**      AGGINVERSE step processes the current row of the relevant cursor and
+**      all subsequent rows belonging to the same group.
+**
+** RANGE window frames are a little different again. As for GROUPS, the
+** main loop runs once per group only. And RETURN_ROW, AGGSTEP and AGGINVERSE
+** deal in groups instead of rows. As for ROWS and GROUPS, there are three
+** basic cases:
+**
+**   RANGE BETWEEN <expr1> PRECEDING AND <expr2> FOLLOWING
+**
+**     ... loop started by sqlite3WhereBegin() ...
+**       if( new partition ){
+**         Gosub flush
+**       }
+**       Insert new row into eph table.
+**       if( first row of partition ){
+**         Rewind(csrEnd) ; Rewind(csrStart) ; Rewind(csrCurrent)
+**         regEnd = <expr2>
+**         regStart = <expr1>
+**       }else{
+**         AGGSTEP
+**         while( (csrCurrent.key + regEnd) < csrEnd.key ){
+**           RETURN_ROW
+**           while( csrStart.key + regStart) < csrCurrent.key ){
+**             AGGINVERSE
+**           }
+**         }
+**       }
+**     }
+**     flush:
+**       AGGSTEP
+**       while( 1 ){
+**         RETURN ROW
+**         if( csrCurrent is EOF ) break;
+**           while( csrStart.key + regStart) < csrCurrent.key ){
+**             AGGINVERSE
+**           }
+**         }
+**       }
+**
+** In the above notation, "csr.key" means the current value of the ORDER BY
+** expression (there is only ever 1 for a RANGE that uses an <expr> FOLLOWING
+** or <expr PRECEDING) read from cursor csr.
+**
+**   RANGE BETWEEN <expr1> PRECEDING AND <expr2> PRECEDING
+**
+**     ... loop started by sqlite3WhereBegin() ...
+**       if( new partition ){
+**         Gosub flush
+**       }
+**       Insert new row into eph table.
+**       if( first row of partition ){
+**         Rewind(csrEnd) ; Rewind(csrStart) ; Rewind(csrCurrent)
+**         regEnd = <expr2>
+**         regStart = <expr1>
+**       }else{
+**         while( (csrEnd.key + regEnd) <= csrCurrent.key ){
+**           AGGSTEP
+**         }
+**         while( (csrStart.key + regStart) < csrCurrent.key ){
+**           AGGINVERSE
+**         }
+**         RETURN_ROW
+**       }
+**     }
+**     flush:
+**       while( (csrEnd.key + regEnd) <= csrCurrent.key ){
+**         AGGSTEP
+**       }
+**       while( (csrStart.key + regStart) < csrCurrent.key ){
+**         AGGINVERSE
+**       }
+**       RETURN_ROW
+**
+**   RANGE BETWEEN <expr1> FOLLOWING AND <expr2> FOLLOWING
+**
+**     ... loop started by sqlite3WhereBegin() ...
+**       if( new partition ){
+**         Gosub flush
+**       }
+**       Insert new row into eph table.
+**       if( first row of partition ){
+**         Rewind(csrEnd) ; Rewind(csrStart) ; Rewind(csrCurrent)
+**         regEnd = <expr2>
+**         regStart = <expr1>
+**       }else{
+**         AGGSTEP
+**         while( (csrCurrent.key + regEnd) < csrEnd.key ){
+**           while( (csrCurrent.key + regStart) > csrStart.key ){
+**             AGGINVERSE
+**           }
+**           RETURN_ROW
+**         }
+**       }
+**     }
+**     flush:
+**       AGGSTEP
+**       while( 1 ){
+**         while( (csrCurrent.key + regStart) > csrStart.key ){
+**           AGGINVERSE
+**           if( eof ) break "while( 1 )" loop.
+**         }
+**         RETURN_ROW
+**       }
+**       while( !eof csrCurrent ){
+**         RETURN_ROW
+**       }
+**
+** The text above leaves out many details. Refer to the code and comments
+** below for a more complete picture.
+*/
+void sqlite3WindowCodeStep(
+  Parse *pParse,                  /* Parse context */
+  Select *p,                      /* Rewritten SELECT statement */
+  WhereInfo *pWInfo,              /* Context returned by sqlite3WhereBegin() */
+  int regGosub,                   /* Register for OP_Gosub */
+  int addrGosub                   /* OP_Gosub here to return each row */
+){
+  Window *pMWin = p->pWin;
+  ExprList *pOrderBy = pMWin->pOrderBy;
+  Vdbe *v = sqlite3GetVdbe(pParse);
+  int csrWrite;                   /* Cursor used to write to eph. table */
+  int csrInput = p->pSrc->a[0].iCursor;     /* Cursor of sub-select */
+  int nInput = p->pSrc->a[0].pTab->nCol;    /* Number of cols returned by sub */
+  int iInput;                               /* To iterate through sub cols */
+  int addrNe;                     /* Address of OP_Ne */
+  int addrGosubFlush = 0;         /* Address of OP_Gosub to flush: */
+  int addrInteger = 0;            /* Address of OP_Integer */
+  int addrEmpty;                  /* Address of OP_Rewind in flush: */
+  int regNew;                     /* Array of registers holding new input row */
+  int regRecord;                  /* regNew array in record form */
+  int regNewPeer = 0;             /* Peer values for new row (part of regNew) */
+  int regPeer = 0;                /* Peer values for current row */
+  int regFlushPart = 0;           /* Register for "Gosub flush_partition" */
+  WindowCodeArg s;                /* Context object for sub-routines */
+  int lblWhereEnd;                /* Label just before sqlite3WhereEnd() code */
+  int regStart = 0;               /* Value of <expr> PRECEDING */
+  int regEnd = 0;                 /* Value of <expr> FOLLOWING */
+
+  assert( pMWin->eStart==TK_PRECEDING || pMWin->eStart==TK_CURRENT
+       || pMWin->eStart==TK_FOLLOWING || pMWin->eStart==TK_UNBOUNDED
+  );
+  assert( pMWin->eEnd==TK_FOLLOWING || pMWin->eEnd==TK_CURRENT
+       || pMWin->eEnd==TK_UNBOUNDED || pMWin->eEnd==TK_PRECEDING
+  );
+  assert( pMWin->eExclude==0 || pMWin->eExclude==TK_CURRENT
+       || pMWin->eExclude==TK_GROUP || pMWin->eExclude==TK_TIES
+       || pMWin->eExclude==TK_NO
+  );
+
+  lblWhereEnd = sqlite3VdbeMakeLabel(pParse);
+
+  /* Fill in the context object */
+  memset(&s, 0, sizeof(WindowCodeArg));
+  s.pParse = pParse;
+  s.pMWin = pMWin;
+  s.pVdbe = v;
+  s.regGosub = regGosub;
+  s.addrGosub = addrGosub;
+  s.current.csr = pMWin->iEphCsr;
+  csrWrite = s.current.csr+1;
+  s.start.csr = s.current.csr+2;
+  s.end.csr = s.current.csr+3;
+
+  /* Figure out when rows may be deleted from the ephemeral table. There
+  ** are four options - they may never be deleted (eDelete==0), they may
+  ** be deleted as soon as they are no longer part of the window frame
+  ** (eDelete==WINDOW_AGGINVERSE), they may be deleted as after the row
+  ** has been returned to the caller (WINDOW_RETURN_ROW), or they may
+  ** be deleted after they enter the frame (WINDOW_AGGSTEP). */
+  switch( pMWin->eStart ){
+    case TK_FOLLOWING:
+      if( pMWin->eFrmType!=TK_RANGE
+       && windowExprGtZero(pParse, pMWin->pStart)
+      ){
+        s.eDelete = WINDOW_RETURN_ROW;
+      }
+      break;
+    case TK_UNBOUNDED:
+      if( windowCacheFrame(pMWin)==0 ){
+        if( pMWin->eEnd==TK_PRECEDING ){
+          if( pMWin->eFrmType!=TK_RANGE
+           && windowExprGtZero(pParse, pMWin->pEnd)
+          ){
+            s.eDelete = WINDOW_AGGSTEP;
+          }
+        }else{
+          s.eDelete = WINDOW_RETURN_ROW;
+        }
+      }
+      break;
+    default:
+      s.eDelete = WINDOW_AGGINVERSE;
+      break;
+  }
+
+  /* Allocate registers for the array of values from the sub-query, the
+  ** same values in record form, and the rowid used to insert said record
+  ** into the ephemeral table.  */
+  regNew = pParse->nMem+1;
+  pParse->nMem += nInput;
+  regRecord = ++pParse->nMem;
+  s.regRowid = ++pParse->nMem;
+
+  /* If the window frame contains an "<expr> PRECEDING" or "<expr> FOLLOWING"
+  ** clause, allocate registers to store the results of evaluating each
+  ** <expr>.  */
+  if( pMWin->eStart==TK_PRECEDING || pMWin->eStart==TK_FOLLOWING ){
+    regStart = ++pParse->nMem;
+  }
+  if( pMWin->eEnd==TK_PRECEDING || pMWin->eEnd==TK_FOLLOWING ){
+    regEnd = ++pParse->nMem;
+  }
+
+  /* If this is not a "ROWS BETWEEN ..." frame, then allocate arrays of
+  ** registers to store copies of the ORDER BY expressions (peer values)
+  ** for the main loop, and for each cursor (start, current and end). */
+  if( pMWin->eFrmType!=TK_ROWS ){
+    int nPeer = (pOrderBy ? pOrderBy->nExpr : 0);
+    regNewPeer = regNew + pMWin->nBufferCol;
+    if( pMWin->pPartition ) regNewPeer += pMWin->pPartition->nExpr;
+    regPeer = pParse->nMem+1;       pParse->nMem += nPeer;
+    s.start.reg = pParse->nMem+1;   pParse->nMem += nPeer;
+    s.current.reg = pParse->nMem+1; pParse->nMem += nPeer;
+    s.end.reg = pParse->nMem+1;     pParse->nMem += nPeer;
+  }
+
+  /* Load the column values for the row returned by the sub-select
+  ** into an array of registers starting at regNew. Assemble them into
+  ** a record in register regRecord. */
+  for(iInput=0; iInput<nInput; iInput++){
+    sqlite3VdbeAddOp3(v, OP_Column, csrInput, iInput, regNew+iInput);
+  }
+  sqlite3VdbeAddOp3(v, OP_MakeRecord, regNew, nInput, regRecord);
+
+  /* An input row has just been read into an array of registers starting
+  ** at regNew. If the window has a PARTITION clause, this block generates
+  ** VM code to check if the input row is the start of a new partition.
+  ** If so, it does an OP_Gosub to an address to be filled in later. The
+  ** address of the OP_Gosub is stored in local variable addrGosubFlush. */
+  if( pMWin->pPartition ){
+    int addr;
+    ExprList *pPart = pMWin->pPartition;
+    int nPart = pPart->nExpr;
+    int regNewPart = regNew + pMWin->nBufferCol;
+    KeyInfo *pKeyInfo = sqlite3KeyInfoFromExprList(pParse, pPart, 0, 0);
+
+    regFlushPart = ++pParse->nMem;
+    addr = sqlite3VdbeAddOp3(v, OP_Compare, regNewPart, pMWin->regPart, nPart);
+    sqlite3VdbeAppendP4(v, (void*)pKeyInfo, P4_KEYINFO);
+    sqlite3VdbeAddOp3(v, OP_Jump, addr+2, addr+4, addr+2);
+    VdbeCoverageEqNe(v);
+    addrGosubFlush = sqlite3VdbeAddOp1(v, OP_Gosub, regFlushPart);
+    VdbeComment((v, "call flush_partition"));
+    sqlite3VdbeAddOp3(v, OP_Copy, regNewPart, pMWin->regPart, nPart-1);
+  }
+
+  /* Insert the new row into the ephemeral table */
+  sqlite3VdbeAddOp2(v, OP_NewRowid, csrWrite, s.regRowid);
+  sqlite3VdbeAddOp3(v, OP_Insert, csrWrite, regRecord, s.regRowid);
+  addrNe = sqlite3VdbeAddOp3(v, OP_Ne, pMWin->regOne, 0, s.regRowid);
+  VdbeCoverageNeverNull(v);
+
+  /* This block is run for the first row of each partition */
+  s.regArg = windowInitAccum(pParse, pMWin);
+
+  if( regStart ){
+    sqlite3ExprCode(pParse, pMWin->pStart, regStart);
+    windowCheckValue(pParse, regStart, 0 + (pMWin->eFrmType==TK_RANGE?3:0));
+  }
+  if( regEnd ){
+    sqlite3ExprCode(pParse, pMWin->pEnd, regEnd);
+    windowCheckValue(pParse, regEnd, 1 + (pMWin->eFrmType==TK_RANGE?3:0));
+  }
+
+  if( pMWin->eFrmType!=TK_RANGE && pMWin->eStart==pMWin->eEnd && regStart ){
+    int op = ((pMWin->eStart==TK_FOLLOWING) ? OP_Ge : OP_Le);
+    int addrGe = sqlite3VdbeAddOp3(v, op, regStart, 0, regEnd);
+    VdbeCoverageNeverNullIf(v, op==OP_Ge); /* NeverNull because bound <expr> */
+    VdbeCoverageNeverNullIf(v, op==OP_Le); /*   values previously checked */
+    windowAggFinal(&s, 0);
+    sqlite3VdbeAddOp1(v, OP_Rewind, s.current.csr);
+    windowReturnOneRow(&s);
+    sqlite3VdbeAddOp1(v, OP_ResetSorter, s.current.csr);
+    sqlite3VdbeAddOp2(v, OP_Goto, 0, lblWhereEnd);
+    sqlite3VdbeJumpHere(v, addrGe);
+  }
+  if( pMWin->eStart==TK_FOLLOWING && pMWin->eFrmType!=TK_RANGE && regEnd ){
+    assert( pMWin->eEnd==TK_FOLLOWING );
+    sqlite3VdbeAddOp3(v, OP_Subtract, regStart, regEnd, regStart);
+  }
+
+  if( pMWin->eStart!=TK_UNBOUNDED ){
+    sqlite3VdbeAddOp1(v, OP_Rewind, s.start.csr);
+  }
+  sqlite3VdbeAddOp1(v, OP_Rewind, s.current.csr);
+  sqlite3VdbeAddOp1(v, OP_Rewind, s.end.csr);
+  if( regPeer && pOrderBy ){
+    sqlite3VdbeAddOp3(v, OP_Copy, regNewPeer, regPeer, pOrderBy->nExpr-1);
+    sqlite3VdbeAddOp3(v, OP_Copy, regPeer, s.start.reg, pOrderBy->nExpr-1);
+    sqlite3VdbeAddOp3(v, OP_Copy, regPeer, s.current.reg, pOrderBy->nExpr-1);
+    sqlite3VdbeAddOp3(v, OP_Copy, regPeer, s.end.reg, pOrderBy->nExpr-1);
+  }
+
+  sqlite3VdbeAddOp2(v, OP_Goto, 0, lblWhereEnd);
+
+  sqlite3VdbeJumpHere(v, addrNe);
+
+  /* Beginning of the block executed for the second and subsequent rows. */
+  if( regPeer ){
+    windowIfNewPeer(pParse, pOrderBy, regNewPeer, regPeer, lblWhereEnd);
+  }
+  if( pMWin->eStart==TK_FOLLOWING ){
+    windowCodeOp(&s, WINDOW_AGGSTEP, 0, 0);
+    if( pMWin->eEnd!=TK_UNBOUNDED ){
+      if( pMWin->eFrmType==TK_RANGE ){
+        int lbl = sqlite3VdbeMakeLabel(pParse);
+        int addrNext = sqlite3VdbeCurrentAddr(v);
+        windowCodeRangeTest(&s, OP_Ge, s.current.csr, regEnd, s.end.csr, lbl);
+        windowCodeOp(&s, WINDOW_AGGINVERSE, regStart, 0);
+        windowCodeOp(&s, WINDOW_RETURN_ROW, 0, 0);
+        sqlite3VdbeAddOp2(v, OP_Goto, 0, addrNext);
+        sqlite3VdbeResolveLabel(v, lbl);
+      }else{
+        windowCodeOp(&s, WINDOW_RETURN_ROW, regEnd, 0);
+        windowCodeOp(&s, WINDOW_AGGINVERSE, regStart, 0);
+      }
+    }
+  }else
+  if( pMWin->eEnd==TK_PRECEDING ){
+    int bRPS = (pMWin->eStart==TK_PRECEDING && pMWin->eFrmType==TK_RANGE);
+    windowCodeOp(&s, WINDOW_AGGSTEP, regEnd, 0);
+    if( bRPS ) windowCodeOp(&s, WINDOW_AGGINVERSE, regStart, 0);
+    windowCodeOp(&s, WINDOW_RETURN_ROW, 0, 0);
+    if( !bRPS ) windowCodeOp(&s, WINDOW_AGGINVERSE, regStart, 0);
+  }else{
+    int addr = 0;
+    windowCodeOp(&s, WINDOW_AGGSTEP, 0, 0);
+    if( pMWin->eEnd!=TK_UNBOUNDED ){
+      if( pMWin->eFrmType==TK_RANGE ){
+        int lbl = 0;
+        addr = sqlite3VdbeCurrentAddr(v);
+        if( regEnd ){
+          lbl = sqlite3VdbeMakeLabel(pParse);
+          windowCodeRangeTest(&s, OP_Ge, s.current.csr, regEnd, s.end.csr, lbl);
+        }
+        windowCodeOp(&s, WINDOW_RETURN_ROW, 0, 0);
+        windowCodeOp(&s, WINDOW_AGGINVERSE, regStart, 0);
+        if( regEnd ){
+          sqlite3VdbeAddOp2(v, OP_Goto, 0, addr);
+          sqlite3VdbeResolveLabel(v, lbl);
+        }
+      }else{
+        if( regEnd ){
+          addr = sqlite3VdbeAddOp3(v, OP_IfPos, regEnd, 0, 1);
+          VdbeCoverage(v);
+        }
+        windowCodeOp(&s, WINDOW_RETURN_ROW, 0, 0);
+        windowCodeOp(&s, WINDOW_AGGINVERSE, regStart, 0);
+        if( regEnd ) sqlite3VdbeJumpHere(v, addr);
+      }
+    }
+  }
+
+  /* End of the main input loop */
+  sqlite3VdbeResolveLabel(v, lblWhereEnd);
+  sqlite3WhereEnd(pWInfo);
+
+  /* Fall through */
+  if( pMWin->pPartition ){
+    addrInteger = sqlite3VdbeAddOp2(v, OP_Integer, 0, regFlushPart);
+    sqlite3VdbeJumpHere(v, addrGosubFlush);
+  }
+
+  s.regRowid = 0;
+  addrEmpty = sqlite3VdbeAddOp1(v, OP_Rewind, csrWrite);
+  VdbeCoverage(v);
+  if( pMWin->eEnd==TK_PRECEDING ){
+    int bRPS = (pMWin->eStart==TK_PRECEDING && pMWin->eFrmType==TK_RANGE);
+    windowCodeOp(&s, WINDOW_AGGSTEP, regEnd, 0);
+    if( bRPS ) windowCodeOp(&s, WINDOW_AGGINVERSE, regStart, 0);
+    windowCodeOp(&s, WINDOW_RETURN_ROW, 0, 0);
+  }else if( pMWin->eStart==TK_FOLLOWING ){
+    int addrStart;
+    int addrBreak1;
+    int addrBreak2;
+    int addrBreak3;
+    windowCodeOp(&s, WINDOW_AGGSTEP, 0, 0);
+    if( pMWin->eFrmType==TK_RANGE ){
+      addrStart = sqlite3VdbeCurrentAddr(v);
+      addrBreak2 = windowCodeOp(&s, WINDOW_AGGINVERSE, regStart, 1);
+      addrBreak1 = windowCodeOp(&s, WINDOW_RETURN_ROW, 0, 1);
+    }else
+    if( pMWin->eEnd==TK_UNBOUNDED ){
+      addrStart = sqlite3VdbeCurrentAddr(v);
+      addrBreak1 = windowCodeOp(&s, WINDOW_RETURN_ROW, regStart, 1);
+      addrBreak2 = windowCodeOp(&s, WINDOW_AGGINVERSE, 0, 1);
+    }else{
+      assert( pMWin->eEnd==TK_FOLLOWING );
+      addrStart = sqlite3VdbeCurrentAddr(v);
+      addrBreak1 = windowCodeOp(&s, WINDOW_RETURN_ROW, regEnd, 1);
+      addrBreak2 = windowCodeOp(&s, WINDOW_AGGINVERSE, regStart, 1);
+    }
+    sqlite3VdbeAddOp2(v, OP_Goto, 0, addrStart);
+    sqlite3VdbeJumpHere(v, addrBreak2);
+    addrStart = sqlite3VdbeCurrentAddr(v);
+    addrBreak3 = windowCodeOp(&s, WINDOW_RETURN_ROW, 0, 1);
+    sqlite3VdbeAddOp2(v, OP_Goto, 0, addrStart);
+    sqlite3VdbeJumpHere(v, addrBreak1);
+    sqlite3VdbeJumpHere(v, addrBreak3);
+  }else{
+    int addrBreak;
+    int addrStart;
+    windowCodeOp(&s, WINDOW_AGGSTEP, 0, 0);
+    addrStart = sqlite3VdbeCurrentAddr(v);
+    addrBreak = windowCodeOp(&s, WINDOW_RETURN_ROW, 0, 1);
+    windowCodeOp(&s, WINDOW_AGGINVERSE, regStart, 0);
+    sqlite3VdbeAddOp2(v, OP_Goto, 0, addrStart);
+    sqlite3VdbeJumpHere(v, addrBreak);
+  }
+  sqlite3VdbeJumpHere(v, addrEmpty);
+
+  sqlite3VdbeAddOp1(v, OP_ResetSorter, s.current.csr);
+  if( pMWin->pPartition ){
+    if( pMWin->regStartRowid ){
+      sqlite3VdbeAddOp2(v, OP_Integer, 1, pMWin->regStartRowid);
+      sqlite3VdbeAddOp2(v, OP_Integer, 0, pMWin->regEndRowid);
+    }
+    sqlite3VdbeChangeP1(v, addrInteger, sqlite3VdbeCurrentAddr(v));
+    sqlite3VdbeAddOp1(v, OP_Return, regFlushPart);
+  }
+}
+
+#endif /* SQLITE_OMIT_WINDOWFUNC */