r.sign = A.sign ^ B.sign;
  r.approx = A.approx | B.approx;
  if( r.approx==0 && A.m%B.m!=0 ) r.approx = 1;
  r.m = A.m/B.m;
  r.e = A.e - B.e;
  return r;
}

/*
** Test if A is infinite.
*/
int sqlite4_num_isinf(sqlite4_num A){
  return A.e>SQLITE4_MX_EXP && A.m!=0;
}

/*
** Test if A is NaN.
*/
int sqlite4_num_isnan(sqlite4_num A){
  return A.e>SQLITE4_MX_EXP && A.m==0; 
}

/*
** Compare numbers A and B.  Return:
**
**    1     if A<B
**    2     if A==B
**    3     if A>B

    return A.sign ? 1 : 3;
  }
  if( B.e>SQLITE4_MX_EXP ){
    if( B.m==0 ) return 0;
    return B.sign ? 3 : 1;
  }
  if( A.sign!=B.sign ){
    if ( A.m==0 && B.m==0 ) return 2;
    return A.sign ? 1 : 3;
  }
  adjustExponent(&A, &B);
  if( A.sign ){
    sqlite4_num t = A;
    A = B;
    B = t;

    i = incr;
  }else if( zIn[0]=='+' ){
    i = incr;
  }else{
    i = 0;
  }
  if( nIn<=0 ) goto not_a_valid_number;
  if( nIn>=incr*3
   && ((c=zIn[i])=='i' || c=='I')
   && ((c=zIn[i+incr])=='n' || c=='N')
   && ((c=zIn[i+incr*2])=='f' || c=='F')
  ){
    r.e = SQLITE4_MX_EXP+1;
    r.m = nIn<=i+incr*3 || zIn[i+incr*3]==0;
    return r;
  }
  while( i<nIn && (c = zIn[i])!=0 ){
    i += incr;
    if( c>='0' && c<='9' ){
      if( c=='0' && nDigit==0 ){
        if( seenRadix && r.e > -(SQLITE4_MX_EXP+1000) ) r.e--;
        continue;
      }
      nDigit++;
      if( nDigit<=18 ){
        r.m = (r.m*10) + c - '0';
        if( seenRadix ) r.e--;
      }else{
        if( c!='0' ) r.approx = 1;
        if( !seenRadix ) r.e++;
      }
    }else if( c=='.' ){
      seenRadix = 1;




    }else if( c=='e' || c=='E' ){
      int exp = 0;
      int expsign = 0;
      int nEDigit = 0;
      if( zIn[i]=='-' ){
        expsign = 1;
        i += incr;
      }else if( zIn[i]=='+' ){
        i += incr;
      }
      if( i>=nIn ) goto not_a_valid_number;
      while( i<nIn && (c = zIn[i])!=0 ){
        i += incr;
        if( c<'0' || c>'9' ) goto not_a_valid_number;
        if( c=='0' && nEDigit==0 ) continue;
        nEDigit++;
        if( nEDigit>3 ) goto not_a_valid_number;
        exp = exp*10 + c - '0';
      }
      if( expsign ) exp = -exp;
      r.e += exp;
      break;
    }else{
      goto not_a_valid_number;
    }
  }
  return r;
  
not_a_valid_number:
  r.e = SQLITE4_MX_EXP+1;
  r.m = 0;
  return r;  
}

/*
** Convert an sqlite4_int64 to a number and return that number.
*/
sqlite4_num sqlite4_num_from_int64(sqlite4_int64 n){
  sqlite4_num r;
  r.approx = 0;
  r.e = 0;
  r.sign = n < 0;
  if( n>=0 ){
    r.m = n;
  }else if( n!=SMALLEST_INT64 ){
    r.m = -n;
  }else{
    r.m = 1+(u64)LARGEST_INT64;
  }
  return r;
}

/*
** Convert an integer into text in the buffer supplied. The
** text is zero-terminated and right-justified in the buffer.
** A pointer to the first character of text is returned.
**
** The buffer needs to be at least 21 bytes in length.

    zNum += m;
    n -= m;
    removeTrailingZeros(zNum, &n);
    if( n>0 ){
      zOut[0] = '.';
      memcpy(zOut+1, zNum, n);
      nOut += n;

      zOut[n+1] = 0;
    }else{
      zOut[0] = 0;
    }
    return nOut;
  }
  if( x.e<0 && x.e >= -n-5 ){
    /* Values less than 1 and with no more than 5 subsequent zeros prior
    ** to the first significant digit.  Ex:  0.0000012345 */
    int j = -(n + x.e);
    memcpy(zOut, "0.", 2);

** Every number in SQLite is represented in memory by an instance of
** the following object.
*/
typedef struct sqlite4_num sqlite4_num;
struct sqlite4_num {
  unsigned char sign;     /* Sign of the overall value */
  unsigned char approx;   /* True if the value is approximate */
  short e;                /* The exponent. */
  sqlite4_uint64 m;       /* The significant */
};

/*
** CAPI4REF: Operations On SQLite Number Objects
*/
sqlite4_num sqlite4_num_add(sqlite4_num, sqlite4_num);

/*
** Constants for the largest and smallest possible 64-bit signed integers.
** These macros are designed to work correctly on both 32-bit and 64-bit
** compilers.
*/
#define LARGEST_INT64  (0xffffffff|(((i64)0x7fffffff)<<32))
#define SMALLEST_INT64 (((i64)-1) - LARGEST_INT64)
#define LARGEST_UINT64  (0xffffffff|(((u64)0xffffffff)<<32))

/* 
** Round up a number to the next larger multiple of 8.  This is used
** to force 8-byte alignment on 64-bit architectures.
*/
#define ROUND8(x)     (((x)+7)&~7)

# 2001 September 15
#
# 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.
#
#***********************************************************************
# This file implements regression tests for SQLite library.  The
# focus of this file is testing the sqlite_*_printf() interface.
#
# $Id: printf.test,v 1.31 2009/02/01 00:21:10 drh Exp $

set testdir [file dirname $argv0]
source $testdir/tester.tcl

do_test num-1.1.1 {
  sqlite4_num_compare 20 20 
} {equal}
do_test num-1.1.2 {
  sqlite4_num_compare 20 2e1
} {equal}
do_test num-1.1.3 {
  sqlite4_num_compare -00034 -3.4e1
} {equal}
do_test num-1.1.4 {
  sqlite4_num_compare -inf +inf
} {lesser}
do_test num-1.1.5 {
  sqlite4_num_compare -inf 0
} {lesser}
do_test num-1.1.6 {
  sqlite4_num_compare inf 4
} {greater}
do_test num-1.1.7 {
  sqlite4_num_compare nan 7
} {incomparable}
# Is +0 > -0?
#do_test num-equal-1.1.4 {
#  sqlite4_num_compare +0 -0
#} {equal}

do_test num-2.1.1 {
  sqlite4_num_to_text [sqlite4_num_from_text 37]
} {37}
do_test num-2.1.2 {
  sqlite4_num_to_text [sqlite4_num_from_text 37 2]
} {37}
do_test num-2.1.4 {
  sqlite4_num_compare [sqlite4_num_from_text 2.9e2X 5] 290
} {equal}
do_test num-2.1.5 {
  sqlite4_num_isnan [sqlite4_num_from_text inf 2]
} {true}
do_test num-2.1.6 {
  sqlite4_num_isinf [sqlite4_num_from_text inf 3]
} {true}

do_test num-3.1.1 {
  sqlite4_num_to_text [sqlite4_num_add 5 7]
} {12}

do_test num-4.1.1 {
  sqlite4_num_to_text [sqlite4_num_sub 9 3]
} {6}
do_test num-4.1.2 {
  sqlite4_num_to_text [sqlite4_num_sub 5 12]
} {-7}
do_test num-4.2.1 {
  sqlite4_num_compare [sqlite4_num_sub 1 1] [sqlite4_num_sub -1 -1]
} {equal}

do_test num-5.1.1 {
  sqlite4_num_to_text [sqlite4_num_mul 9 8]
} {72}

do_test num-6.1.1 {
  sqlite4_num_to_text [sqlite4_num_div 6 5]
} {1.2}
do_test num-6.1.2 {
  sqlite4_num_compare 2 [sqlite4_num_div 2 1]
} {equal}
do_test num-6.1.3 {
  sqlite4_num_to_text [sqlite4_num_div 2 1]
} {2}
do_test num-6.1.4 {
  sqlite4_num_to_text [sqlite4_num_div 22 10]
} {2.2}
finish_test

      Tcl_AppendResult(interp, " ", aOpt[i].zOptName);
    }
    return TCL_ERROR;
  }
  sqlite4_test_control(SQLITE4_TESTCTRL_OPTIMIZATIONS, db, mask);
  return TCL_OK;
}

#define NUM_FORMAT "sign:%d approx:%d e:%d m:%lld"

/* Append a return value representing a sqlite4_num.
*/
static void append_num_result( Tcl_Interp *interp, sqlite4_num A ){
  char buf[100];
  sprintf( buf, NUM_FORMAT, A.sign, A.approx, A.e, A.m );
  Tcl_AppendResult(interp, buf, 0);
}

/* Convert a string either representing a sqlite4_num (listing its fields as
** returned by append_num_result) or that can be parsed as one. Invalid
** strings become NaN.
*/
static sqlite4_num test_parse_num( char *arg ){
  sqlite4_num A;
  int sign, approx, e;
  if( sscanf( arg, NUM_FORMAT, &sign, &approx, &e, &A.m)==4 ){
    A.sign = sign;
    A.approx = approx;
    A.e = e;
    return A;
  } else {
    return sqlite4_num_from_text(arg, -1, 0);
  }
}

/* Convert return values of sqlite4_num to strings that will be readable in
** the tests.
*/
static char *describe_num_comparison( int code ){
  switch( code ){
    case 0: return "incomparable";
    case 1: return "lesser";
    case 2: return "equal";
    case 3: return "greater";
    default: return "error"; 
  }
}

/* Compare two numbers A and B. Returns "incomparable", "lesser", "equal",
** "greater", or "error".
*/
static int test_num_compare(
  void *NotUsed,
  Tcl_Interp *interp,    /* The TCL interpreter that invoked this command */
  int argc,              /* Number of arguments */
  char **argv            /* Text of each argument */
){
  sqlite4_num A, B;
  int cmp;
  if( argc!=3 ){
    Tcl_AppendResult(interp, "wrong # args: should be \"", argv[0],
       " NUM NUM\"", 0);
    return TCL_ERROR;
  }
  
  A = test_parse_num( argv[1] );
  B = test_parse_num( argv[2] );
  cmp = sqlite4_num_compare(A, B);
  Tcl_AppendResult( interp, describe_num_comparison( cmp ), 0);
  return TCL_OK; 
}

/* Create a sqlite4_num from a string. The optional second argument specifies
** how many bytes may be read.
*/
static int test_num_from_text(
  void *NotUsed,
  Tcl_Interp *interp,    /* The TCL interpreter that invoked this command */
  int argc,              /* Number of arguments */
  char **argv            /* Text of each argument */
){
  sqlite4_num A;
  int len;
  if( argc!=2 && argc!=3 ){
    Tcl_AppendResult(interp, "wrong # args: should be \"", argv[0],
      " STRING\" or \"", argv[0], " STRING INTEGER\"", 0);
    return TCL_ERROR;
  }

  if( argc==3 ){
    if ( Tcl_GetInt(interp, argv[2], &len) ) return TCL_ERROR; 
  }else{
    len = -1;
  }

  A = sqlite4_num_from_text( argv[1], len, 0 );
  append_num_result(interp, A);
  return TCL_OK;
}

static int test_num_to_text(
  void *NotUsed,
  Tcl_Interp *interp,    /* The TCL interpreter that invoked this command */
  int argc,              /* Number of arguments */
  char **argv            /* Text of each argument */
){
  char text[30];
  if( argc!=2 ){
    Tcl_AppendResult(interp, "wrong # args: should be \"", argv[0],
      " NUM\"", 0);
    return TCL_ERROR;
  }
  sqlite4_num_to_text( test_parse_num( argv[1] ), text );
  Tcl_AppendResult( interp, text, 0 );
  return TCL_OK;
}

static int test_num_binary_op(
  Tcl_Interp *interp,    /* The TCL interpreter that invoked this command */
  int argc,              /* Number of arguments */
  char **argv,            /* Text of each argument */
  sqlite4_num (*op) (sqlite4_num, sqlite4_num)
){
  sqlite4_num A, B, R;
  if( argc!=3 ){
    Tcl_AppendResult(interp, "wrong # args: should be \"", argv[0],
      " NUM NUM\"", 0);
    return TCL_ERROR;
  }
  A = test_parse_num(argv[1]);
  B = test_parse_num(argv[2]);
  R = op(A, B);
  append_num_result(interp, R);
  return TCL_OK;
}

static int test_num_add(
  void *NotUsed,
  Tcl_Interp *interp,    /* The TCL interpreter that invoked this command */
  int argc,              /* Number of arguments */
  char **argv            /* Text of each argument */
){
  return test_num_binary_op( interp, argc, argv, sqlite4_num_add );
}

static int test_num_sub(
  void *NotUsed,
  Tcl_Interp *interp,    /* The TCL interpreter that invoked this command */
  int argc,              /* Number of arguments */
  char **argv            /* Text of each argument */
){
  return test_num_binary_op( interp, argc, argv, sqlite4_num_sub );
}

static int test_num_mul(
  void *NotUsed,
  Tcl_Interp *interp,    /* The TCL interpreter that invoked this command */
  int argc,              /* Number of arguments */
  char **argv            /* Text of each argument */
){
  return test_num_binary_op( interp, argc, argv, sqlite4_num_mul );
}

static int test_num_div(
  void *NotUsed,
  Tcl_Interp *interp,    /* The TCL interpreter that invoked this command */
  int argc,              /* Number of arguments */
  char **argv            /* Text of each argument */
){
  return test_num_binary_op( interp, argc, argv, sqlite4_num_div );
}

static int test_num_predicate(
  Tcl_Interp *interp,    /* The TCL interpreter that invoked this command */
  int argc,              /* Number of arguments */
  char **argv,            /* Text of each argument */
  int (*pred) (sqlite4_num)
){
  sqlite4_num A;
  if( argc!=2 ){
    Tcl_AppendResult(interp, "wrong # args: should be \"", argv[0],
      " NUM\"", 0);
    return TCL_ERROR;
  }
  A = test_parse_num(argv[1]);
  Tcl_AppendResult(interp, pred(A) ? "true" : "false", 0);  
  return TCL_OK;
}

static int test_num_isinf(
  void *NotUsed,
  Tcl_Interp *interp,    /* The TCL interpreter that invoked this command */
  int argc,              /* Number of arguments */
  char **argv            /* Text of each argument */
){
  return test_num_predicate( interp, argc, argv, sqlite4_num_isinf );
}

static int test_num_isnan(
  void *NotUsed,
  Tcl_Interp *interp,    /* The TCL interpreter that invoked this command */
  int argc,              /* Number of arguments */
  char **argv            /* Text of each argument */
){
  return test_num_predicate( interp, argc, argv, sqlite4_num_isnan );
}

/*
** Register commands with the TCL interpreter.
*/
int Sqlitetest1_Init(Tcl_Interp *interp){
  extern int sqlite4_search_count;
  extern int sqlite4_found_count;

     { "sqlite_set_magic",              (Tcl_CmdProc*)sqlite_set_magic      },
     { "sqlite4_interrupt",             (Tcl_CmdProc*)test_interrupt        },
     { "sqlite_delete_function",        (Tcl_CmdProc*)delete_function       },
     { "sqlite_delete_collation",       (Tcl_CmdProc*)delete_collation      },
     { "sqlite4_get_autocommit",        (Tcl_CmdProc*)get_autocommit        },
     { "sqlite4_stack_used",            (Tcl_CmdProc*)test_stack_used       },
     { "printf",                        (Tcl_CmdProc*)test_printf           },
     { "sqlite4IoTrace",                (Tcl_CmdProc*)test_io_trace         },
     { "sqlite4_num_compare",           (Tcl_CmdProc*)test_num_compare      }, 
     { "sqlite4_num_from_text",         (Tcl_CmdProc*)test_num_from_text    }, 
     { "sqlite4_num_to_text",           (Tcl_CmdProc*)test_num_to_text      },
     { "sqlite4_num_add",               (Tcl_CmdProc*)test_num_add          },
     { "sqlite4_num_sub",               (Tcl_CmdProc*)test_num_sub          },
     { "sqlite4_num_mul",               (Tcl_CmdProc*)test_num_mul          },
     { "sqlite4_num_div",               (Tcl_CmdProc*)test_num_div          },
     { "sqlite4_num_isinf",             (Tcl_CmdProc*)test_num_isinf        },
     { "sqlite4_num_isnan",             (Tcl_CmdProc*)test_num_isnan        },
  };
  static struct {
     char *zName;
     Tcl_ObjCmdProc *xProc;
     void *clientData;
  } aObjCmd[] = {
     { "sqlite4_connection_pointer",    get_sqlite_pointer, 0 },