#else
        /* It makes more sense to use 0.5 */
        for(idx=precision, rounder=0.5; idx>0; idx--, rounder*=0.1){}
#endif
        if( xtype==etFLOAT ) realvalue += rounder;
        /* Normalize realvalue to within 10.0 > realvalue >= 1.0 */
        exp = 0;
        if( sqlite3_isnan(realvalue) ){
          bufpt = "NaN";
          length = 3;
          break;
        }
        if( realvalue>0.0 ){
          while( realvalue>=1e32 && exp<=350 ){ realvalue *= 1e-32; exp+=32; }
          while( realvalue>=1e8 && exp<=350 ){ realvalue *= 1e-8; exp+=8; }

#else
        /* It makes more sense to use 0.5 */
        for(idx=precision, rounder=0.5; idx>0; idx--, rounder*=0.1){}
#endif
        if( xtype==etFLOAT ) realvalue += rounder;
        /* Normalize realvalue to within 10.0 > realvalue >= 1.0 */
        exp = 0;
        if( sqlite3IsNaN(realvalue) ){
          bufpt = "NaN";
          length = 3;
          break;
        }
        if( realvalue>0.0 ){
          while( realvalue>=1e32 && exp<=350 ){ realvalue *= 1e-32; exp+=32; }
          while( realvalue>=1e8 && exp<=350 ){ realvalue *= 1e-8; exp+=8; }

**    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.
**
*************************************************************************
** Internal interface definitions for SQLite.
**
** @(#) $Id: sqliteInt.h,v 1.697 2008/04/28 12:54:15 drh Exp $
*/
#ifndef _SQLITEINT_H_
#define _SQLITEINT_H_

/*
** Include the configuration header output by 'configure' if it was run
** (otherwise we get an empty default).
................................................................................
#include "parse.h"
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <assert.h>
#include <stddef.h>

#define sqlite3_isnan(X)  ((X)!=(X))

/*
** If compiling for a processor that lacks floating point support,
** substitute integer for floating-point
*/
#ifdef SQLITE_OMIT_FLOATING_POINT
# define double sqlite_int64
# define LONGDOUBLE_TYPE sqlite_int64
................................................................................
char *sqlite3StrDup(const char*);
char *sqlite3StrNDup(const char*, int);
char *sqlite3DbStrDup(sqlite3*,const char*);
char *sqlite3DbStrNDup(sqlite3*,const char*, int);
void *sqlite3DbReallocOrFree(sqlite3 *, void *, int);
void *sqlite3DbRealloc(sqlite3 *, void *, int);
int sqlite3MallocSize(void *);



char *sqlite3MPrintf(sqlite3*,const char*, ...);
char *sqlite3VMPrintf(sqlite3*,const char*, va_list);
#if defined(SQLITE_TEST) || defined(SQLITE_DEBUG)
  void sqlite3DebugPrintf(const char*, ...);
#endif
#if defined(SQLITE_TEST)

**    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.
**
*************************************************************************
** Internal interface definitions for SQLite.
**
** @(#) $Id: sqliteInt.h,v 1.698 2008/04/28 16:55:26 drh Exp $
*/
#ifndef _SQLITEINT_H_
#define _SQLITEINT_H_

/*
** Include the configuration header output by 'configure' if it was run
** (otherwise we get an empty default).
................................................................................
#include "parse.h"
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <assert.h>
#include <stddef.h>



/*
** If compiling for a processor that lacks floating point support,
** substitute integer for floating-point
*/
#ifdef SQLITE_OMIT_FLOATING_POINT
# define double sqlite_int64
# define LONGDOUBLE_TYPE sqlite_int64
................................................................................
char *sqlite3StrDup(const char*);
char *sqlite3StrNDup(const char*, int);
char *sqlite3DbStrDup(sqlite3*,const char*);
char *sqlite3DbStrNDup(sqlite3*,const char*, int);
void *sqlite3DbReallocOrFree(sqlite3 *, void *, int);
void *sqlite3DbRealloc(sqlite3 *, void *, int);
int sqlite3MallocSize(void *);

int sqlite3IsNaN(double);

char *sqlite3MPrintf(sqlite3*,const char*, ...);
char *sqlite3VMPrintf(sqlite3*,const char*, va_list);
#if defined(SQLITE_TEST) || defined(SQLITE_DEBUG)
  void sqlite3DebugPrintf(const char*, ...);
#endif
#if defined(SQLITE_TEST)

**
*************************************************************************
** Utility functions used throughout sqlite.
**
** This file contains functions for allocating memory, comparing
** strings, and stuff like that.
**
** $Id: util.c,v 1.222 2008/04/16 00:49:12 drh Exp $
*/
#include "sqliteInt.h"
#include <stdarg.h>
#include <ctype.h>










/*
** Set the most recent error code and error string for the sqlite
** handle "db". The error code is set to "err_code".
**
** If it is not NULL, string zFormat specifies the format of the
** error string in the style of the printf functions: The following

**
*************************************************************************
** Utility functions used throughout sqlite.
**
** This file contains functions for allocating memory, comparing
** strings, and stuff like that.
**
** $Id: util.c,v 1.223 2008/04/28 16:55:26 drh Exp $
*/
#include "sqliteInt.h"
#include <stdarg.h>
#include <ctype.h>


/*
** Return true if the floating point value is Not a Number.
*/
int sqlite3IsNaN(double x){
  volatile double y = x;
  return x!=y;
}

/*
** Set the most recent error code and error string for the sqlite
** handle "db". The error code is set to "err_code".
**
** If it is not NULL, string zFormat specifies the format of the
** error string in the style of the printf functions: The following

**
** Various scripts scan this source file in order to generate HTML
** documentation, headers files, or other derived files.  The formatting
** of the code in this file is, therefore, important.  See other comments
** in this file for details.  If in doubt, do not deviate from existing
** commenting and indentation practices when changing or adding code.
**
** $Id: vdbe.c,v 1.735 2008/04/25 12:25:42 drh Exp $
*/
#include "sqliteInt.h"
#include <ctype.h>
#include "vdbeInt.h"

/*
** The following global variable is incremented every time a cursor
................................................................................
        i64 ib = (i64)b;
        if( ia==0 ) goto arithmetic_result_is_null;
        if( ia==-1 ) ia = 1;
        b = ib % ia;
        break;
      }
    }
    if( sqlite3_isnan(b) ){
      goto arithmetic_result_is_null;
    }
    pOut->r = b;
    MemSetTypeFlag(pOut, MEM_Real);
    if( (flags & MEM_Real)==0 ){
      sqlite3VdbeIntegerAffinity(pOut);
    }

**
** Various scripts scan this source file in order to generate HTML
** documentation, headers files, or other derived files.  The formatting
** of the code in this file is, therefore, important.  See other comments
** in this file for details.  If in doubt, do not deviate from existing
** commenting and indentation practices when changing or adding code.
**
** $Id: vdbe.c,v 1.736 2008/04/28 16:55:26 drh Exp $
*/
#include "sqliteInt.h"
#include <ctype.h>
#include "vdbeInt.h"

/*
** The following global variable is incremented every time a cursor
................................................................................
        i64 ib = (i64)b;
        if( ia==0 ) goto arithmetic_result_is_null;
        if( ia==-1 ) ia = 1;
        b = ib % ia;
        break;
      }
    }
    if( sqlite3IsNaN(b) ){
      goto arithmetic_result_is_null;
    }
    pOut->r = b;
    MemSetTypeFlag(pOut, MEM_Real);
    if( (flags & MEM_Real)==0 ){
      sqlite3VdbeIntegerAffinity(pOut);
    }

}

/*
** Delete any previous value and set the value stored in *pMem to val,
** manifest type REAL.
*/
void sqlite3VdbeMemSetDouble(Mem *pMem, double val){
  if( sqlite3_isnan(val) ){
    sqlite3VdbeMemSetNull(pMem);
  }else{
    sqlite3VdbeMemRelease(pMem);
    pMem->r = val;
    pMem->flags = MEM_Real;
    pMem->type = SQLITE_FLOAT;
  }

}

/*
** Delete any previous value and set the value stored in *pMem to val,
** manifest type REAL.
*/
void sqlite3VdbeMemSetDouble(Mem *pMem, double val){
  if( sqlite3IsNaN(val) ){
    sqlite3VdbeMemSetNull(pMem);
  }else{
    sqlite3VdbeMemRelease(pMem);
    pMem->r = val;
    pMem->flags = MEM_Real;
    pMem->type = SQLITE_FLOAT;
  }