// empty line needed here

 Number.prototype.add32 = function(x) { return (this + x) | 0; };

 Number.prototype.sub32 = function(x) { return (this - x) | 0; };

 Number.prototype.mul32 = function(x) { 

     return (((this * (x >> 16)) << 16) + this * (x & 0xFFFF)) | 0;

 };

 Number.prototype.toInt8 = function()  { return (this << 24) >> 24; };

 Number.prototype.toInt16 = function() { return (this << 16) >> 16; };

 Number.prototype.next32 = function(low) {

   if (this === 0) {

     return low;

   }

   var l = new Number(low);

   l.hi = this;

   return l;

 };

 Number.prototype.high32 = function() { 

     return this.hi ? this.hi : (Math.floor(this / 0xFFFFFFFF)) | 0;

 };

 Number.prototype.toInt32 = function() { return this | 0; };

 Number.prototype.toFP = function() {

     return this.hi ? this.hi * 0xFFFFFFFF + this : this;

 };

 Number.prototype.toLong = function() {

     var hi = (this > 0xFFFFFFFF) ? (Math.floor(this / 0xFFFFFFFF)) | 0 : 0;

     return hi.next32(this % 0xFFFFFFFF);

 };

 Number.prototype.toExactString = function() {

     if (this.hi) {

         var res = 0;

         var a = [ 6,9,2,7,6,9,4,9,2,4 ];

         var s = '';

         var digit;

         var hi = this.hi;

         var low = this;

         for (var i = 0; i < a.length; i++) {

             res += hi * a[i];

             var low_digit = low % 10;

             digit = (res % 10) + low_digit;

             low = Math.floor(low / 10);

             res = Math.floor(res / 10);

             if (digit >= 10) {

                 digit -= 10;

                 res++;

             }

             s = String(digit).concat(s);

         }

         return String(res).concat(s);

     }

     return String(this);

 };

 Number.prototype.add64 = function(x) {

     var low = this + x;

     carry = 0;

     if (low > 0xFFFFFFFF) {

         carry = 1;

         low -= 0xFFFFFFFF;  // should not here be also -1?

     }

     var hi = (this.high32() + x.high32() + carry) & 0xFFFFFFFF;

     return hi.next32(low);

 };

 Number.prototype.div64 = function(x) {

     var low = Math.floor(this.toFP() / x.toFP()); // TODO: not exact enough

     if (low > 0xFFFFFFFF) {

         var hi = Math.floor(low / 0xFFFFFFFF) | 0;

         return hi.next32(low % 0xFFFFFFFF);

     }

     return low;

 };

 Number.prototype.shl64 = function(x) {

     if (x > 32) {

         var hi = (this << (x - 32)) & 0xFFFFFFFF;

         return hi.next32(0);

     } else {

         var hi = (this.high32() << x) & 0xFFFFFFFF;

         var low_reminder = this >> x;

         hi |= low_reminder;

         var low = this << x;

         return hi.next32(low);

     }

 };

 Number.prototype.compare64 = function(x) {

     if (this.hi == x.hi) {

         return (this == x) ? 0 : ((this < x) ? -1 : 1);

     }

     return (this.hi < x.hi) ? -1 : 1;

 };