/**
 * BigInteger
 * 
 * An ActionScript 3 implementation of BigInteger (light version)
 * Copyright (c) 2007 Henri Torgemane
 * 
 * Derived from:
 *         The jsbn library, Copyright (c) 2003-2005 Tom Wu
 * 
 * See LICENSE.txt for full license information.
 */
package com.hurlant.math
{

    import com.hurlant.crypto.prng.Random;
    import com.hurlant.util.Hex;
    import com.hurlant.util.Memory;
    
    import flash.utils.ByteArray;
    use namespace bi_internal;

    public class BigInteger
    {
        public static const DB:int = 30; // number of significant bits per chunk
        public static const DV:int = (1<<DB);
        public static const DM:int = (DV-1); // Max value in a chunk
        
        public static const BI_FP:int = 52;
        public static const FV:Number = Math.pow(2, BI_FP);
        public static const F1:int = BI_FP - DB;
        public static const F2:int = 2*DB - BI_FP;
        
        public static const ZERO:BigInteger = nbv(0);
        public static const ONE:BigInteger  = nbv(1);
        
        /*bi_internal */public var t:int; // number of chunks.
        bi_internal var s:int; // sign
        bi_internal var a:Array; // chunks
        
        /**
         * 
         * @param value
         * @param radix  WARNING: If value is ByteArray, this holds the number of bytes to use.
         * @param unsigned
         * 
         */
        public function BigInteger(value:* = null, radix:int = 0, unsigned:Boolean = false) {
            a = new Array;
            if (value is String) {
                if (radix&&radix!=16) throw new Error("BigInteger construction with radix!=16 is not supported.");
                value = Hex.toArray(value);
                radix=0;
            }
            if (value is ByteArray) {
                var array:ByteArray = value as ByteArray;
                var length:int = radix || (array.length - array.position);
                fromArray(array, length, unsigned);
            }
        }
        public function dispose():void {
            var r:Random = new Random;
            for (var i:uint=0;i<a.length;i++) {
                a[i] = r.nextByte();
                delete a[i];
            }
            a=null;
            t=0;
            s=0;
            Memory.gc();
        }
        
        public function toString(radix:Number=16):String {
            if (s<0) return "-"+negate().toString(radix);
            var k:int;
            switch (radix) {
                case 2:   k=1; break;
                case 4:   k=2; break;
                case 8:   k=3; break;
                case 16:  k=4; break;
                case 32:  k=5; break;
                default:
//                    return toRadix(radix);
            }
            var km:int = (1<<k)-1;
            var d:int = 0;
            var m:Boolean = false;
            var r:String = "";
            var i:int = t;
            var p:int = DB-(i*DB)%k;
            if (i-->0) {
                if (p<DB && (d=a[i]>>p)>0) {
                    m = true;
                    r = d.toString(36);
                }
                while (i >= 0) {
                    if (p<k) {
                        d = (a[i]&((1<<p)-1))<<(k-p);
                        d|= a[--i]>>(p+=DB-k);
                    } else {
                        d = (a[i]>>(p-=k))&km;
                        if (p<=0) {
                            p += DB;
                            --i;
                        }
                    }
                    if (d>0) {
                        m = true;
                    }
                    if (m) {
                        r += d.toString(36);
                    }
                }
            }
            return m?r:"0";
        }
        public function toArray(array:ByteArray):uint {
            const k:int = 8;
            const km:int = (1<<8)-1;
            var d:int = 0;
            var i:int = t;
            var p:int = DB-(i*DB)%k;
            var m:Boolean = false;
            var c:int = 0;
            if (i-->0) {
                if (p<DB && (d=a[i]>>p)>0) {
                    m = true;
                    array.writeByte(d);
                    c++;
                }
                while (i >= 0) {
                    if (p<k) {
                        d = (a[i]&((1<<p)-1))<<(k-p);
                        d|= a[--i]>>(p+=DB-k);
                    } else {
                        d = (a[i]>>(p-=k))&km;
                        if (p<=0) {
                            p += DB;
                            --i;
                        }
                    }
                    if (d>0) {
                        m = true;
                    }
                    if (m) {
                        array.writeByte(d);
                        c++;
                    }
                }
            }
            return c;
        }
        /**
         * best-effort attempt to fit into a Number.
         * precision can be lost if it just can't fit.
         */
        public function valueOf():Number {
            if (s==-1) {
                return -negate().valueOf();
            }
            var coef:Number = 1;
            var value:Number = 0;
            for (var i:uint=0;i<t;i++) {
                value += a[i]*coef;
                coef *= DV;
            }
            return value;
        }
        /**
         * -this
         */
        public function negate():BigInteger {
            var r:BigInteger = nbi();
            ZERO.subTo(this, r);
            return r;
        }
        /**
         * |this|
         */
        public function abs():BigInteger {
            return (s<0)?negate():this;
        }
        /**
         * return + if this > v, - if this < v, 0 if equal
         */
        public function compareTo(v:BigInteger):int {
            var r:int = s - v.s;
            if (r!=0) {
                return r;
            }
            var i:int = t;
            r = i-v.t;
            if (r!=0) {
                return r;
            }
            while (--i >=0) {
                r=a[i]-v.a[i];
                if (r != 0) return r;
            }
            return 0;
        }
        /**
         * returns bit length of the integer x
         */
        bi_internal function nbits(x:int):int {
            var r:int = 1;
            var t:int;
            if ((t=x>>>16) != 0) { x = t; r += 16; }
            if ((t=x>>8) != 0) { x = t; r += 8; }
            if ((t=x>>4) != 0) { x = t; r += 4; }
            if ((t=x>>2) != 0) { x = t; r += 2; }
            if ((t=x>>1) != 0) { x = t; r += 1; }
            return r;
        }
        /**
         * returns the number of bits in this
         */
        public function bitLength():int {
            if (t<=0) return 0;
            return DB*(t-1)+nbits(a[t-1]^(s&DM));
        }
        /**
         * 
         * @param v
         * @return this % v
         * 
         */
        public function mod(v:BigInteger):BigInteger {
            var r:BigInteger = nbi();
            abs().divRemTo(v,null,r);
            if (s<0 && r.compareTo(ZERO)>0) {
                v.subTo(r,r);
            }
            return r;
        }
        /**
         * this^e % m, 0 <= e < 2^32
         */
        public function modPowInt(e:int, m:BigInteger):BigInteger {
            var z:IReduction;
            if (e<256 || m.isEven()) {
                z = new ClassicReduction(m);
            } else {
                z = new MontgomeryReduction(m);
            }
            return exp(e, z);
        }

        /**
         * copy this to r
         */
        bi_internal function copyTo(r:BigInteger):void {
            for (var i:int = t-1; i>=0; --i) {
                r.a[i] = a[i];
            }
            r.t = t;
            r.s = s;
        }
        /**
         * set from integer value "value", -DV <= value < DV
         */
        bi_internal function fromInt(value:int):void {
            t = 1;
            s = (value<0)?-1:0;
            if (value>0) {
                a[0] = value;
            } else if (value<-1) {
                a[0] = value+DV;
            } else {
                t = 0;
            }
        }
        /**
         * set from ByteArray and length,
         * starting a current position
         * If length goes beyond the array, pad with zeroes.
         */
        bi_internal function fromArray(value:ByteArray, length:int, unsigned:Boolean = false):void {
            var p:int = value.position;
            var i:int = p+length;
            var sh:int = 0;
            const k:int = 8;
            t = 0;
            s = 0;
            while (--i >= p) {
                var x:int = i<value.length?value[i]:0;
                if (sh == 0) {
                    a[t++] = x;
                } else if (sh+k > DB) {
                    a[t-1] |= (x&((1<<(DB-sh))-1))<<sh;
                    a[t++] = x>>(DB-sh);
                } else {
                    a[t-1] |= x<<sh;
                }
                sh += k;
                if (sh >= DB) sh -= DB;
            }
            if (!unsigned && (value[0]&0x80)==0x80) {
                s = -1;
                if (sh > 0) {
                    a[t-1] |= ((1<<(DB-sh))-1)<<sh;
                }
            }
            clamp();
            value.position = Math.min(p+length,value.length);
        }
        /**
         * clamp off excess high words
         */
        bi_internal function clamp():void {
            var c:int = s&DM;
            while (t>0 && a[t-1]==c) {
                --t;
            }
        }
        /**
         * r = this << n*DB
         */
        bi_internal function dlShiftTo(n:int, r:BigInteger):void {
            var i:int;
            for (i=t-1; i>=0; --i) {
                r.a[i+n] = a[i];
            }
            for (i=n-1; i>=0; --i) {
                r.a[i] = 0;
            }
            r.t = t+n;
            r.s = s;
        }
        /**
         * r = this >> n*DB
         */
        bi_internal function drShiftTo(n:int, r:BigInteger):void {
            var i:int;
            for (i=n; i<t; ++i) {
                r.a[i-n] = a[i];
            }
            r.t = Math.max(t-n,0);
            r.s = s;
        }
        /**
         * r = this << n
         */
        bi_internal function lShiftTo(n:int, r:BigInteger):void {
            var bs:int = n%DB;
            var cbs:int = DB-bs;
            var bm:int = (1<<cbs)-1;
            var ds:int = n/DB;
            var c:int = (s<<bs)&DM;
            var i:int;
            for (i=t-1; i>=0; --i) {
                r.a[i+ds+1] = (a[i]>>cbs)|c;
                c = (a[i]&bm)<<bs;
            }
            for (i=ds-1; i>=0; --i) {
                r.a[i] = 0;
            }
            r.a[ds] = c;
            r.t = t+ds+1;
            r.s = s;
            r.clamp();
        }
        /**
         * r = this >> n
         */
        bi_internal function rShiftTo(n:int, r:BigInteger):void {
            r.s = s;
            var ds:int = n/DB;
            if (ds >= t) {
                r.t = 0;
                return;
            }
            var bs:int = n%DB;
            var cbs:int = DB-bs;
            var bm:int = (1<<bs)-1;
            r.a[0] = a[ds]>>bs;
            var i:int;
            for (i=ds+1; i<t; ++i) {
                r.a[i-ds-1] |= (a[i]&bm)<<cbs;
                r.a[i-ds] = a[i]>>bs;
            }
            if (bs>0) {
                r.a[t-ds-1] |= (s&bm)<<cbs;
            }
            r.t = t-ds;
            r.clamp();
        }
        /**
         * r = this - v
         */
        bi_internal function subTo(v:BigInteger, r:BigInteger):void {
            var i:int = 0;
            var c:int = 0;
            var m:int = Math.min(v.t, t);
            while (i<m) {
                c += a[i] - v.a[i];
                r.a[i++] = c & DM;
                c >>= DB;
            }
            if (v.t < t) {
                c -= v.s;
                while (i< t) {
                    c+= a[i];
                    r.a[i++] = c&DM;
                    c >>= DB;
                }
                c += s;
            } else {
                c += s;
                while (i < v.t) {
                    c -= v.a[i];
                    r.a[i++] = c&DM;
                    c >>= DB;
                }
                c -= v.s;
            }
            r.s = (c<0)?-1:0;
            if (c<-1) {
                r.a[i++] = DV+c;
            } else if (c>0) {
                r.a[i++] = c;
            }
            r.t = i;
            r.clamp();
        }
        /**
         * am: Compute w_j += (x*this_i), propagates carries,
         * c is initial carry, returns final carry.
         * c < 3*dvalue, x < 2*dvalue, this_i < dvalue
         */
        bi_internal function am(i:int,x:int,w:BigInteger,j:int,c:int,n:int):int {
            var xl:int = x&0x7fff;
            var xh:int = x>>15;
            while(--n >= 0) {
                var l:int = a[i]&0x7fff;
                var h:int = a[i++]>>15;
                var m:int = xh*l + h*xl;
                l = xl*l + ((m&0x7fff)<<15)+w.a[j]+(c&0x3fffffff);
                c = (l>>>30)+(m>>>15)+xh*h+(c>>>30);
                w.a[j++] = l&0x3fffffff;
            }
            return c;
        }
        /**
         * r = this * v, r != this,a (HAC 14.12)
         * "this" should be the larger one if appropriate
         */
        bi_internal function multiplyTo(v:BigInteger, r:BigInteger):void {
            var x:BigInteger = abs();
            var y:BigInteger = v.abs();
            var i:int = x.t;
            r.t = i+y.t;
            while (--i >= 0) {
                r.a[i] = 0;
            }
            for (i=0; i<y.t; ++i) {
                r.a[i+x.t] = x.am(0, y.a[i], r, i, 0, x.t);
            }
            r.s = 0;
            r.clamp();
            if (s!=v.s) {
                ZERO.subTo(r, r);
            }
        }
        /**
         * r = this^2, r != this (HAC 14.16)
         */
        bi_internal function squareTo(r:BigInteger):void {
            var x:BigInteger = abs();
            var i:int = r.t = 2*x.t;
            while (--i>=0) r.a[i] = 0;
            for (i=0; i<x.t-1; ++i) {
                var c:int = x.am(i, x.a[i], r, 2*i, 0, 1);
                if ((r.a[i+x.t] += x.am(i+1, 2*x.a[i], r, 2*i+1, c, x.t-i-1)) >= DV) {
                    r.a[i+x.t] -= DV;
                    r.a[i+x.t+1] = 1;
                }
            }
            if (r.t>0) {
                r.a[r.t-1] += x.am(i, x.a[i], r, 2*i, 0, 1);
            }
            r.s = 0;
            r.clamp();
        }
        /**
         * divide this by m, quotient and remainder to q, r (HAC 14.20)
         * r != q, this != m. q or r may be null.
         */
        bi_internal function divRemTo(m:BigInteger, q:BigInteger = null, r:BigInteger = null):void {
            var pm:BigInteger = m.abs();
            if (pm.t <= 0) return;
            var pt:BigInteger = abs();
            if (pt.t < pm.t) {
                if (q!=null) q.fromInt(0);
                if (r!=null) copyTo(r);
                return;
            }
            if (r==null) r = nbi();
            var y:BigInteger = nbi();
            var ts:int = s;
            var ms:int = m.s;
            var nsh:int = DB-nbits(pm.a[pm.t-1]); // normalize modulus
            if (nsh>0) {
                pm.lShiftTo(nsh, y);
                pt.lShiftTo(nsh, r);
            } else {
                pm.copyTo(y);
                pt.copyTo(r);
            }
            var ys:int = y.t;
            var y0:int = y.a[ys-1];
            if (y0==0) return;
            var yt:Number = y0*(1<<F1)+((ys>1)?y.a[ys-2]>>F2:0);
            var d1:Number = FV/yt;
            var d2:Number = (1<<F1)/yt;
            var e:Number = 1<<F2;
            var i:int = r.t;
            var j:int = i-ys;
            var t:BigInteger = (q==null)?nbi():q;
            y.dlShiftTo(j,t);
            if (r.compareTo(t)>=0) {
                r.a[r.t++] = 1;
                r.subTo(t,r);
            }
            ONE.dlShiftTo(ys,t);
            t.subTo(y,y); // "negative" y so we can replace sub with am later.
            while(y.t<ys) y.(y.t++, 0);
            while(--j >= 0) {
                // Estimate quotient digit
                var qd:int = (r.a[--i]==y0)?DM:Number(r.a[i])*d1+(Number(r.a[i-1])+e)*d2;
                if ((r.a[i]+= y.am(0, qd, r, j, 0, ys))<qd) { // Try it out
                    y.dlShiftTo(j, t);
                    r.subTo(t,r);
                    while (r.a[i]<--qd) {
                        r.subTo(t,r);
                    }
                }
            }
            if (q!=null) {
                r.drShiftTo(ys,q);
                if (ts!=ms) {
                    ZERO.subTo(q,q);
                }
            }
            r.t = ys;
            r.clamp();
            if (nsh>0) {
                r.rShiftTo(nsh, r); // Denormalize remainder
            }
            if (ts<0) {
                ZERO.subTo(r,r);
            }
        }
        /**
         * return "-1/this % 2^DB"; useful for Mont. reduction
         * justification:
         *         xy == 1 (mod n)
         *         xy =  1+km
         *      xy(2-xy) = (1+km)(1-km)
         * x[y(2-xy)] =  1-k^2.m^2
         * x[y(2-xy)] == 1 (mod m^2)
         * if y is 1/x mod m, then y(2-xy) is 1/x mod m^2
         * should reduce x and y(2-xy) by m^2 at each step to keep size bounded
         * [XXX unit test the living shit out of this.]
         */
        bi_internal function invDigit():int {
            if (t<1) return 0;
            var x:int = a[0];
            if ((x&1)==0) return 0;
            var y:int = x&3;                             // y == 1/x mod 2^2
            y = (y*(2-(x&0xf )*y))             &0xf;    // y == 1/x mod 2^4
            y = (y*(2-(x&0xff)*y))             &0xff;    // y == 1/x mod 2^8
            y = (y*(2-(((x&0xffff)*y)&0xffff)))&0xffff;    // y == 1/x mod 2^16
            // last step - calculate inverse mod DV directly;
            // assumes 16 < DB <= 32 and assumes ability to handle 48-bit ints
            // XXX 48 bit ints? Whaaaa? is there an implicit float conversion in here?
            y = (y*(2-x*y%DV))%DV;    // y == 1/x mod 2^dbits
            // we really want the negative inverse, and -DV < y < DV
            return (y>0)?DV-y:-y;
        }
        /**
         * true iff this is even
         */
        bi_internal function isEven():Boolean {
            return ((t>0)?(a[0]&1):s) == 0;
        }
        /**
         * this^e, e < 2^32, doing sqr and mul with "r" (HAC 14.79)
         */
        bi_internal function exp(e:int, z:IReduction):BigInteger {
            if (e > 0xffffffff || e < 1) return ONE;
            var r:BigInteger = nbi();
            var r2:BigInteger = nbi();
            var g:BigInteger = z.convert(this);
            var i:int = nbits(e)-1;
            g.copyTo(r);
            while(--i>=0) {
                z.sqrTo(r, r2);
                if ((e&(1<<i))>0) {
                    z.mulTo(r2,g,r);
                } else {
                    var t:BigInteger = r;
                    r = r2;
                    r2 = t;
                }
                
            }
            return z.revert(r);
        }
        bi_internal function intAt(str:String, index:int):int {
            return parseInt(str.charAt(index), 36);
        }


        protected function nbi():* {
            return new BigInteger;
        }
        /**
         * return bigint initialized to value
         */
        public static function nbv(value:int):BigInteger {
            var bn:BigInteger = new BigInteger;
            bn.fromInt(value);
            return bn;
        }


        // Functions above are sufficient for RSA encryption.
        // The stuff below is useful for decryption and key generation

        public static const lowprimes:Array = [2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,103,107,109,113,127,131,137,139,149,151,157,163,167,173,179,181,191,193,197,199,211,223,227,229,233,239,241,251,257,263,269,271,277,281,283,293,307,311,313,317,331,337,347,349,353,359,367,373,379,383,389,397,401,409,419,421,431,433,439,443,449,457,461,463,467,479,487,491,499,503,509];
        public static const lplim:int = (1<<26)/lowprimes[lowprimes.length-1];


        public function clone():BigInteger {
            var r:BigInteger = new BigInteger;
            this.copyTo(r);
            return r;
        }
        
        /**
         * 
         * @return value as integer
         * 
         */
        public function intValue():int {
            if (s<0) {
                if (t==1) {
                    return a[0]-DV;
                } else if (t==0) {
                    return -1;
                }
            } else if (t==1) {
                return a[0];
            } else if (t==0) {
                return 0;
            }
            // assumes 16 < DB < 32
            return  ((a[1]&((1<<(32-DB))-1))<<DB)|a[0];
        }
        
        /**
         * 
         * @return value as byte
         * 
         */
        public function byteValue():int {
            return (t==0)?s:(a[0]<<24)>>24;
        }
        
        /**
         * 
         * @return value as short (assumes DB>=16)
         * 
         */
        public function shortValue():int {
            return (t==0)?s:(a[0]<<16)>>16;
        }
        
        /**
         * 
         * @param r
         * @return x s.t. r^x < DV
         * 
         */
        protected function chunkSize(r:Number):int {
            return Math.floor(Math.LN2*DB/Math.log(r));
        }
        
        /**
         * 
         * @return 0 if this ==0, 1 if this >0
         * 
         */
        public function sigNum():int {
            if (s<0) {
                return -1;
            } else if (t<=0 || (t==1 && a[0]<=0)) {
                return 0;
            } else{
                return 1;
            }
        }
        
        /**
         * 
         * @param b: radix to use
         * @return a string representing the integer converted to the radix.
         * 
         */
        protected function toRadix(b:uint=10):String {
            if (sigNum()==0 || b<2 || b>32) return "0";
            var cs:int = chunkSize(b);
            var a:Number = Math.pow(b, cs);
            var d:BigInteger = nbv(a);
            var y:BigInteger = nbi();
            var z:BigInteger = nbi();
            var r:String = "";
            divRemTo(d, y, z);
            while (y.sigNum()>0) {
                r = (a+z.intValue()).toString(b).substr(1) + r;
                y.divRemTo(d,y,z);
            }
            return z.intValue().toString(b) + r;
        }
        
        /**
         * 
         * @param s a string to convert from using radix.
         * @param b a radix
         * 
         */
        protected function fromRadix(s:String, b:int = 10):void {
            fromInt(0);
            var cs:int = chunkSize(b);
            var d:Number = Math.pow(b, cs);
            var mi:Boolean = false;
            var j:int = 0;
            var w:int = 0;
            for (var i:int=0;i<s.length;++i) {
                var x:int = intAt(s, i);
                if (x<0) {
                    if (s.charAt(i) == "-" && sigNum() == 0) {
                        mi = true;
                    }
                    continue;
                }
                w = b*w+x;
                if (++j >= cs) {
                    dMultiply(d);
                    dAddOffset(w,0);
                    j=0;
                    w=0;
                }
            }
            if (j>0) {
                dMultiply(Math.pow(b,j));
                dAddOffset(w,0);
            }
            if (mi) {
                BigInteger.ZERO.subTo(this, this);
            }
        }
        
        // XXX function fromNumber not written yet.
        
        /**
         * 
         * @return a byte array.
         * 
         */
        public function toByteArray():ByteArray {
            var i:int = t;
            var r:ByteArray = new ByteArray;
            r[0] = s;
            var p:int = DB-(i*DB)%8;
            var d:int;
            var k:int=0;
            if (i-->0) {
                if (p<DB && (d=a[i]>>p)!=(s&DM)>>p) {
                    r[k++] = d|(s<<(DB-p));
                }
                while (i>=0) {
                    if(p<8) {
                        d = (a[i]&((1<<p)-1))<<(8-p);
                        d|= a[--i]>>(p+=DB-8);
                    } else {
                        d = (a[i]>>(p-=8))&0xff;
                        if (p<=0) {
                            p += DB;
                            --i;
                        }
                    }
                    if ((d&0x80)!=0) d|=-256;
                    if (k==0 && (s&0x80)!=(d&0x80)) ++k;
                    if (k>0 || d!=s) r[k++] = d;
                } 
            }
            return r;
        }

        public function equals(a:BigInteger):Boolean {
            return compareTo(a)==0;
        }
        public function min(a:BigInteger):BigInteger {
            return (compareTo(a)<0)?this:a;
        }
        public function max(a:BigInteger):BigInteger {
            return (compareTo(a)>0)?this:a;
        }
        
        /**
         * 
         * @param a    a BigInteger to perform the operation with
         * @param op a Function implementing the operation
         * @param r a BigInteger to store the result of the operation
         * 
         */
        protected function bitwiseTo(a:BigInteger, op:Function, r:BigInteger):void {
            var i:int;
            var f:int;
            var m:int = Math.min(a.t, t);
            for (i=0; i<m; ++i) {
                r.a[i] = op(this.a[i],a.a[i]);
            }
            if (a.t<t) {
                f = a.s&DM;
                for (i=m;i<t;++i) {
                    r.a[i] = op(this.a[i],f);
                }
                r.t = t;
            } else {
                f = s&DM;
                for (i=m;i<a.t;++i) {
                    r.a[i] = op(f,a.a[i]);
                }
                r.t = a.t;
            }
            r.s = op(s, a.s);
            r.clamp();
        }
        
        private function op_and(x:int, y:int):int {return x&y;}
        public function and(a:BigInteger):BigInteger {
            var r:BigInteger = new BigInteger;
            bitwiseTo(a, op_and, r);
            return r;
        }
        
        private function op_or(x:int, y:int):int {return x|y;}
        public function or(a:BigInteger):BigInteger {
            var r:BigInteger = new BigInteger;
            bitwiseTo(a, op_or, r);
            return r;
        }
        
        private function op_xor(x:int, y:int):int {return x^y;}
        public function xor(a:BigInteger):BigInteger {
            var r:BigInteger = new BigInteger;
            bitwiseTo(a, op_xor, r);
            return r;
        }
        
        private function op_andnot(x:int, y:int):int { return x&~y;}
        public function andNot(a:BigInteger):BigInteger {
            var r:BigInteger = new BigInteger;
            bitwiseTo(a, op_andnot, r);
            return r;
        }
        
        public function not():BigInteger {
            var r:BigInteger = new BigInteger;
            for (var i:int=0;i<t;++i) {
                r[i] = DM&~a[i];
            }
            r.t = t;
            r.s = ~s;
            return r;
        }
        
        public function shiftLeft(n:int):BigInteger {
            var r:BigInteger = new BigInteger;
            if (n<0) {
                rShiftTo(-n, r);
            } else {
                lShiftTo(n, r);
            }
            return r;
        }
        public function shiftRight(n:int):BigInteger {
            var r:BigInteger = new BigInteger;
            if (n<0) {
                lShiftTo(-n, r);
            } else {
                rShiftTo(n, r);
            }
            return r;
        }
        
        /**
         * 
         * @param x
         * @return index of lowet 1-bit in x, x < 2^31
         * 
         */
        private function lbit(x:int):int {
            if (x==0) return -1;
            var r:int = 0;
            if ((x&0xffff)==0) { x>>= 16; r += 16; }
            if ((x&0xff) == 0) { x>>=  8; r +=  8; }
            if ((x&0xf)  == 0) { x>>=  4; r +=  4; }
            if ((x&0x3)  == 0) { x>>=  2; r +=  2; }
            if ((x&0x1)  == 0) ++r;
            return r;
        }
        
        /**
         * 
         * @return index of lowest 1-bit (or -1 if none)
         * 
         */
        public function getLowestSetBit():int {
            for (var i:int=0;i<t;++i) {
                if (a[i]!=0) return i*DB+lbit(a[i]);
            }
            if (s<0) return t*DB;
            return -1;
        }
        
        /**
         * 
         * @param x
         * @return number of 1 bits in x
         * 
         */
        private function cbit(x:int):int {
            var r:uint =0;
            while (x!=0) { x &= x-1; ++r }
            return r;
        }
        
        /**
         * 
         * @return number of set bits
         * 
         */
        public function bitCount():int {
            var r:int=0;
            var x:int = s&DM;
            for (var i:int=0;i<t;++i) {
                r += cbit(a[i]^x);
            }
            return r;
        }
        
        /**
         * 
         * @param n
         * @return true iff nth bit is set
         * 
         */
        public function testBit(n:int):Boolean {
            var j:int = Math.floor(n/DB);
            if (j>=t) {
                return s!=0;
            }
            return ((a[j]&(1<<(n%DB)))!=0);
        }
        
        /**
         * 
         * @param n
         * @param op
         * @return this op (1<<n)
         * 
         */
        protected function changeBit(n:int,op:Function):BigInteger {
            var r:BigInteger = BigInteger.ONE.shiftLeft(n);
            bitwiseTo(r, op, r);
            return r;
        }
        
        /**
         * 
         * @param n
         * @return this | (1<<n)
         * 
         */
        public function setBit(n:int):BigInteger { return changeBit(n, op_or); }

        /**
         * 
         * @param n
         * @return this & ~(1<<n)
         * 
         */
        public function clearBit(n:int):BigInteger { return changeBit(n, op_andnot); }

        /**
         * 
         * @param n
         * @return this ^ (1<<n)
         * 
         */
        public function flipBit(n:int):BigInteger { return changeBit(n, op_xor); }

        /**
         * 
         * @param a
         * @param r = this + a
         * 
         */
        protected function addTo(a:BigInteger, r:BigInteger):void {
            var i:int = 0;
            var c:int = 0;
            var m:int = Math.min(a.t, t);
            while (i<m) {
                c += this.a[i] + a.a[i];
                r.a[i++] = c&DM;
                c>>=DB;
            }
            if (a.t < t) {
                c += a.s;
                while (i<t) {
                    c += this.a[i];
                    r.a[i++] = c&DM;
                    c >>= DB;
                }
                c += s;
            } else {
                c += s;
                while (i<a.t) {
                    c += a.a[i];
                    r.a[i++] = c&DM;
                    c >>= DB;
                }
                c += a.s;
            }
            r.s = (c<0)?-1:0;
            if (c>0) {
                r.a[i++] = c;
            } else if (c<-1) {
                r.a[i++] = DV+c;
            }
            r.t = i;
            r.clamp();
        }
        
        /**
         * 
         * @param a
         * @return this + a
         * 
         */
        public function add(a:BigInteger):BigInteger {
            var r:BigInteger = new BigInteger;
            addTo(a,r);
            return r;
        }

        /**
         * 
         * @param a
         * @return this - a
         * 
         */
        public function subtract(a:BigInteger):BigInteger {
            var r:BigInteger = new BigInteger;
            subTo(a,r);
            return r;
        }
        
        /**
         * 
         * @param a
         * @return this * a
         * 
         */
        public function multiply(a:BigInteger):BigInteger {
            var r:BigInteger = new BigInteger;
            multiplyTo(a,r);
            return r;
        }
        
        /**
         * 
         * @param a
         * @return this / a
         * 
         */
        public function divide(a:BigInteger):BigInteger {
            var r:BigInteger = new BigInteger;
            divRemTo(a, r, null);
            return r;
        }
        
        public function remainder(a:BigInteger):BigInteger {
            var r:BigInteger = new BigInteger;
            divRemTo(a, null, r);
            return r;
        }
        
        /**
         * 
         * @param a
         * @return [this/a, this%a]
         * 
         */
        public function divideAndRemainder(a:BigInteger):Array {
            var q:BigInteger = new BigInteger;
            var r:BigInteger = new BigInteger;
            divRemTo(a, q, r);
            return [q,r];
        }
        
        /**
         * 
         * this *= n, this >=0, 1 < n < DV
         * 
         * @param n
         * 
         */
        bi_internal function dMultiply(n:int):void {
            a[t] = am(0, n-1, this, 0, 0, t);
            ++t;
            clamp();
        }
        
        /**
         * 
         * this += n << w words, this >= 0
         * 
         * @param n
         * @param w
         * 
         */
        bi_internal function dAddOffset(n:int, w:int):void {
            while (t<=w) {
                a[t++] = 0;
            }
            a[w] += n;
            while (a[w] >= DV) {
                a[w] -= DV;
                if (++w >= t) {
                    a[t++] = 0;
                }
                ++a[w];
            }
        }

        /**
         * 
         * @param e
         * @return this^e
         * 
         */
        public function pow(e:int):BigInteger {
            return exp(e, new NullReduction);
        }
        
        /**
         * 
         * @param a
         * @param n
         * @param r = lower n words of "this * a", a.t <= n
         * 
         */
        bi_internal function multiplyLowerTo(a:BigInteger, n:int, r:BigInteger):void {
            var i:int = Math.min(t+a.t, n);
            r.s = 0; // assumes a, this >= 0
            r.t = i;
            while (i>0) {
                r.a[--i]=0;
            }
            var j:int;
            for (j=r.t-t;i<j;++i) {
                r.a[i+t] = am(0, a.a[i], r, i, 0, t);
            }
            for (j=Math.min(a.t,n);i<j;++i) {
                am(0, a.a[i], r, i, 0, n-i);
            }
            r.clamp();
        }
        
        /**
         * 
         * @param a
         * @param n
         * @param r = "this * a" without lower n words, n > 0
         * 
         */
        bi_internal function multiplyUpperTo(a:BigInteger, n:int, r:BigInteger):void {
            --n;
            var i:int = r.t = t+a.t-n;
            r.s = 0; // assumes a,this >= 0
            while (--i>=0) {
                r.a[i] = 0;
            }
            for (i=Math.max(n-t,0);i<a.t;++i) {
                r.a[t+i-n] = am(n-i, a.a[i], r, 0, 0, t+i-n);
            }
            r.clamp();
            r.drShiftTo(1,r);
        }
        
        /**
         * 
         * @param e
         * @param m
         * @return this^e % m (HAC 14.85)
         * 
         */
        public function modPow(e:BigInteger, m:BigInteger):BigInteger {
            var i:int = e.bitLength();
            var k:int;
            var r:BigInteger = nbv(1);
            var z:IReduction;
            
            if (i<=0) {
                return r;
            } else if (i<18) {
                k=1;
            } else if (i<48) {
                k=3;
            } else if (i<144) {
                k=4;
            } else if (i<768) {
                k=5;
            } else {
                k=6;
            }
            if (i<8) {
                z = new ClassicReduction(m);
            } else if (m.isEven()) {
                z = new BarrettReduction(m);
            } else {
                z = new MontgomeryReduction(m);
            }
            // precomputation
            var g:Array = [];
            var n:int = 3;
            var k1:int = k-1;
            var km:int = (1<<k)-1;
            g[1] = z.convert(this);
            if (k > 1) {
                var g2:BigInteger = new BigInteger;
                z.sqrTo(g[1], g2);
                while (n<=km) {
                    g[n] = new BigInteger;
                    z.mulTo(g2, g[n-2], g[n]);
                    n += 2;
                }
            }
            
            var j:int = e.t-1;
            var w:int;
            var is1:Boolean = true;
            var r2:BigInteger = new BigInteger;
            var t:BigInteger;
            i = nbits(e.a[j])-1;
            while (j>=0) {
                if (i>=k1) {
                    w = (e.a[j]>>(i-k1))&km;
                } else {
                    w = (e.a[j]&((1<<(i+1))-1))<<(k1-i);
                    if (j>0) {
                        w |= e.a[j-1]>>(DB+i-k1);
                    }
                }
                n = k;
                while ((w&1)==0) {
                    w >>= 1;
                    --n;
                }
                if ((i -= n) <0) {
                    i += DB;
                    --j;
                }
                if (is1) { // ret == 1, don't bother squaring or multiplying it
                    g[w].copyTo(r);
                    is1 = false;
                } else {
                    while (n>1) {
                        z.sqrTo(r, r2);
                        z.sqrTo(r2, r);
                        n -= 2;
                    }
                    if (n>0) {
                        z.sqrTo(r, r2);
                    } else {
                        t = r;
                        r = r2;
                        r2 = t;
                    }
                    z.mulTo(r2, g[w], r);
                }
                while (j>=0 && (e.a[j]&(1<<i)) == 0) {
                    z.sqrTo(r, r2);
                    t = r;
                    r = r2;
                    r2 = t;
                    if (--i<0) {
                        i = DB-1;
                        --j;
                    }
                    
                }
            }
            return z.revert(r);
        }
        
        /**
         * 
         * @param a
         * @return gcd(this, a) (HAC 14.54)
         * 
         */
        public function gcd(a:BigInteger):BigInteger {
            var x:BigInteger = (s<0)?negate():clone();
            var y:BigInteger = (a.s<0)?a.negate():a.clone();
            if (x.compareTo(y)<0) {
                var t:BigInteger=x;
                x=y;
                y=t;
            }
            var i:int = x.getLowestSetBit();
            var g:int = y.getLowestSetBit();
            if (g<0) return x;
            if (i<g) g= i;
            if (g>0) {
                x.rShiftTo(g, x);
                y.rShiftTo(g, y);
            }
            while (x.sigNum()>0) {
                if ((i = x.getLowestSetBit()) >0) {
                    x.rShiftTo(i, x);
                }
                if ((i = y.getLowestSetBit()) >0) {
                    y.rShiftTo(i, y);
                }
                if (x.compareTo(y) >= 0) {
                    x.subTo(y, x);
                    x.rShiftTo(1, x);
                } else {
                    y.subTo(x, y);
                    y.rShiftTo(1, y);
                }
            }
            if (g>0) {
                y.lShiftTo(g, y);
            }
            return y;
        }

        /**
         * 
         * @param n
         * @return this % n, n < 2^DB
         * 
         */
        protected function modInt(n:int):int {
            if (n<=0) return 0;
            var d:int = DV%n;
            var r:int = (s<0)?n-1:0;
            if (t>0) {
                if (d==0) {
                    r = a[0]%n;
                } else {
                    for (var i:int=t-1;i>=0;--i) {
                        r = (d*r+a[i])%n;
                    }
                }
            }
            return r;
        }
        
        /**
         * 
         * @param m
         * @return 1/this %m (HAC 14.61)
         * 
         */
        public function modInverse(m:BigInteger):BigInteger {
            var ac:Boolean = m.isEven();
            if ((isEven()&&ac) || m.sigNum()==0) {
                return BigInteger.ZERO;
            }
            var u:BigInteger = m.clone();
            var v:BigInteger = clone();
            var a:BigInteger = nbv(1);
            var b:BigInteger = nbv(0);
            var c:BigInteger = nbv(0);
            var d:BigInteger = nbv(1);
            while (u.sigNum()!=0) {
                while (u.isEven()) {
                    u.rShiftTo(1,u);
                    if (ac) {
                        if (!a.isEven() || !b.isEven()) {
                            a.addTo(this,a);
                            b.subTo(m,b);
                        }
                        a.rShiftTo(1,a);
                    } else if (!b.isEven()) {
                        b.subTo(m,b);
                    }
                    b.rShiftTo(1,b);
                }
                while (v.isEven()) {
                    v.rShiftTo(1,v);
                    if (ac) {
                        if (!c.isEven() || !d.isEven()) {
                            c.addTo(this,c);
                            d.subTo(m,d);
                        }
                        c.rShiftTo(1,c);
                    } else if (!d.isEven()) {
                        d.subTo(m,d);
                    }
                    d.rShiftTo(1,d);
                }
                if (u.compareTo(v)>=0) {
                    u.subTo(v,u);
                    if (ac) {
                        a.subTo(c,a);
                    }
                    b.subTo(d,b);
                } else {
                    v.subTo(u,v);
                    if (ac) {
                        c.subTo(a,c);
                    }
                    d.subTo(b,d);
                }
            }
            if (v.compareTo(BigInteger.ONE) != 0) {
                return BigInteger.ZERO;
            }
            if (d.compareTo(m) >= 0) {
                return d.subtract(m);
            }
            if (d.sigNum()<0) {
                d.addTo(m,d);
            } else {
                return d;
            }
            if (d.sigNum()<0) {
                return d.add(m);
            } else {
                return d;
            }
        }

        /**
         * 
         * @param t
         * @return primality with certainty >= 1-.5^t
         * 
         */
        public function isProbablePrime(t:int):Boolean {
            var i:int;
            var x:BigInteger = abs();
            if (x.t == 1 && x.a[0]<=lowprimes[lowprimes.length-1]) {
                for (i=0;i<lowprimes.length;++i) {
                    if (x[0]==lowprimes[i]) return true;
                }
                return false;
            }
            if (x.isEven()) return false;
            i = 1;
            while (i<lowprimes.length) {
                var m:int = lowprimes[i];
                var j:int = i+1;
                while (j<lowprimes.length && m<lplim) {
                    m *= lowprimes[j++];
                }
                m = x.modInt(m);
                while (i<j) {
                    if (m%lowprimes[i++]==0) {
                        return false;
                    }
                }
            }
            return x.millerRabin(t);
        }
        
        /**
         * 
         * @param t
         * @return true if probably prime (HAC 4.24, Miller-Rabin)
         * 
         */
        protected function millerRabin(t:int):Boolean {
            var n1:BigInteger = subtract(BigInteger.ONE);
            var k:int = n1.getLowestSetBit();
            if (k<=0) {
                return false;
            }
            var r:BigInteger = n1.shiftRight(k);
            t = (t+1)>>1;
            if (t>lowprimes.length) {
                t = lowprimes.length;
            }
            var a:BigInteger = new BigInteger;
            for (var i:int=0;i<t;++i) {
                a.fromInt(lowprimes[i]);
                var y:BigInteger = a.modPow(r, this);
                if (y.compareTo(BigInteger.ONE)!=0 && y.compareTo(n1)!=0) {
                    var j:int = 1;
                    while (j++<k && y.compareTo(n1)!=0) {
                        y = y.modPowInt(2, this);
                        if (y.compareTo(BigInteger.ONE)==0) {
                            return false;
                        }
                    }
                    if (y.compareTo(n1)!=0) {
                        return false;
                    }
                }
            }
            return true;
        }

        /**
         * Tweak our BigInteger until it looks prime enough
         * 
         * @param bits
         * @param t
         * 
         */
        public function primify(bits:int, t:int):void {
            if (!testBit(bits-1)) {    // force MSB set
                bitwiseTo(BigInteger.ONE.shiftLeft(bits-1), op_or, this);
            }
            if (isEven()) {
                dAddOffset(1,0);    // force odd
            }
            while (!isProbablePrime(t)) {
                dAddOffset(2,0);
                while(bitLength()>bits) subTo(BigInteger.ONE.shiftLeft(bits-1),this);
            }
        }

    }
}