// 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;

};