--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/tweetcast/client/lib/gimite-web-socket-js-55ae639/flash-src/third-party/com/hurlant/math/BigInteger.as Thu Oct 06 11:56:48 2011 +0200
@@ -0,0 +1,1543 @@
+/**
+ * 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);
+ }
+ }
+
+ }
+}