/*
Copyright (c) 2004-2011, The Dojo Foundation All Rights Reserved.
Available via Academic Free License >= 2.1 OR the modified BSD license.
see: http://dojotoolkit.org/license for details
*/
if(!dojo._hasResource["dojox.math.BigInteger-ext"]){ //_hasResource checks added by build. Do not use _hasResource directly in your code.
dojo._hasResource["dojox.math.BigInteger-ext"] = true;
dojo.provide("dojox.math.BigInteger-ext");
dojo.require("dojox.math.BigInteger");
dojo.experimental("dojox.math.BigInteger-ext");
// Contributed under CLA by Tom Wu
// Extended JavaScript BN functions, required for RSA private ops.
(function(){
var BigInteger = dojox.math.BigInteger,
nbi = BigInteger._nbi, nbv = BigInteger._nbv,
nbits = BigInteger._nbits,
Montgomery = BigInteger._Montgomery;
// (public)
function bnClone() { var r = nbi(); this._copyTo(r); return r; }
// (public) return value as integer
function bnIntValue() {
if(this.s < 0) {
if(this.t == 1) return this[0]-this._DV;
else if(this.t == 0) return -1;
}
else if(this.t == 1) return this[0];
else if(this.t == 0) return 0;
// assumes 16 < DB < 32
return ((this[1]&((1<<(32-this._DB))-1))<<this._DB)|this[0];
}
// (public) return value as byte
function bnByteValue() { return (this.t==0)?this.s:(this[0]<<24)>>24; }
// (public) return value as short (assumes DB>=16)
function bnShortValue() { return (this.t==0)?this.s:(this[0]<<16)>>16; }
// (protected) return x s.t. r^x < DV
function bnpChunkSize(r) { return Math.floor(Math.LN2*this._DB/Math.log(r)); }
// (public) 0 if this == 0, 1 if this > 0
function bnSigNum() {
if(this.s < 0) return -1;
else if(this.t <= 0 || (this.t == 1 && this[0] <= 0)) return 0;
else return 1;
}
// (protected) convert to radix string
function bnpToRadix(b) {
if(b == null) b = 10;
if(this.signum() == 0 || b < 2 || b > 36) return "0";
var cs = this._chunkSize(b);
var a = Math.pow(b,cs);
var d = nbv(a), y = nbi(), z = nbi(), r = "";
this._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;
}
// (protected) convert from radix string
function bnpFromRadix(s,b) {
this._fromInt(0);
if(b == null) b = 10;
var cs = this._chunkSize(b);
var d = Math.pow(b,cs), mi = false, j = 0, w = 0;
for(var i = 0; i < s.length; ++i) {
var x = intAt(s,i);
if(x < 0) {
if(s.charAt(i) == "-" && this.signum() == 0) mi = true;
continue;
}
w = b*w+x;
if(++j >= cs) {
this._dMultiply(d);
this._dAddOffset(w,0);
j = 0;
w = 0;
}
}
if(j > 0) {
this._dMultiply(Math.pow(b,j));
this._dAddOffset(w,0);
}
if(mi) BigInteger.ZERO._subTo(this,this);
}
// (protected) alternate constructor
function bnpFromNumber(a,b,c) {
if("number" == typeof b) {
// new BigInteger(int,int,RNG)
if(a < 2) this._fromInt(1);
else {
this._fromNumber(a,c);
if(!this.testBit(a-1)) // force MSB set
this._bitwiseTo(BigInteger.ONE.shiftLeft(a-1),op_or,this);
if(this._isEven()) this._dAddOffset(1,0); // force odd
while(!this.isProbablePrime(b)) {
this._dAddOffset(2,0);
if(this.bitLength() > a) this._subTo(BigInteger.ONE.shiftLeft(a-1),this);
}
}
}
else {
// new BigInteger(int,RNG)
var x = [], t = a&7;
x.length = (a>>3)+1;
b.nextBytes(x);
if(t > 0) x[0] &= ((1<<t)-1); else x[0] = 0;
this._fromString(x,256);
}
}
// (public) convert to bigendian byte array
function bnToByteArray() {
var i = this.t, r = [];
r[0] = this.s;
var p = this._DB-(i*this._DB)%8, d, k = 0;
if(i-- > 0) {
if(p < this._DB && (d = this[i]>>p) != (this.s&this._DM)>>p)
r[k++] = d|(this.s<<(this._DB-p));
while(i >= 0) {
if(p < 8) {
d = (this[i]&((1<<p)-1))<<(8-p);
d |= this[--i]>>(p+=this._DB-8);
}
else {
d = (this[i]>>(p-=8))&0xff;
if(p <= 0) { p += this._DB; --i; }
}
if((d&0x80) != 0) d |= -256;
if(k == 0 && (this.s&0x80) != (d&0x80)) ++k;
if(k > 0 || d != this.s) r[k++] = d;
}
}
return r;
}
function bnEquals(a) { return(this.compareTo(a)==0); }
function bnMin(a) { return(this.compareTo(a)<0)?this:a; }
function bnMax(a) { return(this.compareTo(a)>0)?this:a; }
// (protected) r = this op a (bitwise)
function bnpBitwiseTo(a,op,r) {
var i, f, m = Math.min(a.t,this.t);
for(i = 0; i < m; ++i) r[i] = op(this[i],a[i]);
if(a.t < this.t) {
f = a.s&this._DM;
for(i = m; i < this.t; ++i) r[i] = op(this[i],f);
r.t = this.t;
}
else {
f = this.s&this._DM;
for(i = m; i < a.t; ++i) r[i] = op(f,a[i]);
r.t = a.t;
}
r.s = op(this.s,a.s);
r._clamp();
}
// (public) this & a
function op_and(x,y) { return x&y; }
function bnAnd(a) { var r = nbi(); this._bitwiseTo(a,op_and,r); return r; }
// (public) this | a
function op_or(x,y) { return x|y; }
function bnOr(a) { var r = nbi(); this._bitwiseTo(a,op_or,r); return r; }
// (public) this ^ a
function op_xor(x,y) { return x^y; }
function bnXor(a) { var r = nbi(); this._bitwiseTo(a,op_xor,r); return r; }
// (public) this & ~a
function op_andnot(x,y) { return x&~y; }
function bnAndNot(a) { var r = nbi(); this._bitwiseTo(a,op_andnot,r); return r; }
// (public) ~this
function bnNot() {
var r = nbi();
for(var i = 0; i < this.t; ++i) r[i] = this._DM&~this[i];
r.t = this.t;
r.s = ~this.s;
return r;
}
// (public) this << n
function bnShiftLeft(n) {
var r = nbi();
if(n < 0) this._rShiftTo(-n,r); else this._lShiftTo(n,r);
return r;
}
// (public) this >> n
function bnShiftRight(n) {
var r = nbi();
if(n < 0) this._lShiftTo(-n,r); else this._rShiftTo(n,r);
return r;
}
// return index of lowest 1-bit in x, x < 2^31
function lbit(x) {
if(x == 0) return -1;
var r = 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&3) == 0) { x >>= 2; r += 2; }
if((x&1) == 0) ++r;
return r;
}
// (public) returns index of lowest 1-bit (or -1 if none)
function bnGetLowestSetBit() {
for(var i = 0; i < this.t; ++i)
if(this[i] != 0) return i*this._DB+lbit(this[i]);
if(this.s < 0) return this.t*this._DB;
return -1;
}
// return number of 1 bits in x
function cbit(x) {
var r = 0;
while(x != 0) { x &= x-1; ++r; }
return r;
}
// (public) return number of set bits
function bnBitCount() {
var r = 0, x = this.s&this._DM;
for(var i = 0; i < this.t; ++i) r += cbit(this[i]^x);
return r;
}
// (public) true iff nth bit is set
function bnTestBit(n) {
var j = Math.floor(n/this._DB);
if(j >= this.t) return(this.s!=0);
return((this[j]&(1<<(n%this._DB)))!=0);
}
// (protected) this op (1<<n)
function bnpChangeBit(n,op) {
var r = BigInteger.ONE.shiftLeft(n);
this._bitwiseTo(r,op,r);
return r;
}
// (public) this | (1<<n)
function bnSetBit(n) { return this._changeBit(n,op_or); }
// (public) this & ~(1<<n)
function bnClearBit(n) { return this._changeBit(n,op_andnot); }
// (public) this ^ (1<<n)
function bnFlipBit(n) { return this._changeBit(n,op_xor); }
// (protected) r = this + a
function bnpAddTo(a,r) {
var i = 0, c = 0, m = Math.min(a.t,this.t);
while(i < m) {
c += this[i]+a[i];
r[i++] = c&this._DM;
c >>= this._DB;
}
if(a.t < this.t) {
c += a.s;
while(i < this.t) {
c += this[i];
r[i++] = c&this._DM;
c >>= this._DB;
}
c += this.s;
}
else {
c += this.s;
while(i < a.t) {
c += a[i];
r[i++] = c&this._DM;
c >>= this._DB;
}
c += a.s;
}
r.s = (c<0)?-1:0;
if(c > 0) r[i++] = c;
else if(c < -1) r[i++] = this._DV+c;
r.t = i;
r._clamp();
}
// (public) this + a
function bnAdd(a) { var r = nbi(); this._addTo(a,r); return r; }
// (public) this - a
function bnSubtract(a) { var r = nbi(); this._subTo(a,r); return r; }
// (public) this * a
function bnMultiply(a) { var r = nbi(); this._multiplyTo(a,r); return r; }
// (public) this / a
function bnDivide(a) { var r = nbi(); this._divRemTo(a,r,null); return r; }
// (public) this % a
function bnRemainder(a) { var r = nbi(); this._divRemTo(a,null,r); return r; }
// (public) [this/a,this%a]
function bnDivideAndRemainder(a) {
var q = nbi(), r = nbi();
this._divRemTo(a,q,r);
return [q, r];
}
// (protected) this *= n, this >= 0, 1 < n < DV
function bnpDMultiply(n) {
this[this.t] = this.am(0,n-1,this,0,0,this.t);
++this.t;
this._clamp();
}
// (protected) this += n << w words, this >= 0
function bnpDAddOffset(n,w) {
while(this.t <= w) this[this.t++] = 0;
this[w] += n;
while(this[w] >= this._DV) {
this[w] -= this._DV;
if(++w >= this.t) this[this.t++] = 0;
++this[w];
}
}
// A "null" reducer
function NullExp() {}
function nNop(x) { return x; }
function nMulTo(x,y,r) { x._multiplyTo(y,r); }
function nSqrTo(x,r) { x._squareTo(r); }
NullExp.prototype.convert = nNop;
NullExp.prototype.revert = nNop;
NullExp.prototype.mulTo = nMulTo;
NullExp.prototype.sqrTo = nSqrTo;
// (public) this^e
function bnPow(e) { return this._exp(e,new NullExp()); }
// (protected) r = lower n words of "this * a", a.t <= n
// "this" should be the larger one if appropriate.
function bnpMultiplyLowerTo(a,n,r) {
var i = Math.min(this.t+a.t,n);
r.s = 0; // assumes a,this >= 0
r.t = i;
while(i > 0) r[--i] = 0;
var j;
for(j = r.t-this.t; i < j; ++i) r[i+this.t] = this.am(0,a[i],r,i,0,this.t);
for(j = Math.min(a.t,n); i < j; ++i) this.am(0,a[i],r,i,0,n-i);
r._clamp();
}
// (protected) r = "this * a" without lower n words, n > 0
// "this" should be the larger one if appropriate.
function bnpMultiplyUpperTo(a,n,r) {
--n;
var i = r.t = this.t+a.t-n;
r.s = 0; // assumes a,this >= 0
while(--i >= 0) r[i] = 0;
for(i = Math.max(n-this.t,0); i < a.t; ++i)
r[this.t+i-n] = this.am(n-i,a[i],r,0,0,this.t+i-n);
r._clamp();
r._drShiftTo(1,r);
}
// Barrett modular reduction
function Barrett(m) {
// setup Barrett
this.r2 = nbi();
this.q3 = nbi();
BigInteger.ONE._dlShiftTo(2*m.t,this.r2);
this.mu = this.r2.divide(m);
this.m = m;
}
function barrettConvert(x) {
if(x.s < 0 || x.t > 2*this.m.t) return x.mod(this.m);
else if(x.compareTo(this.m) < 0) return x;
else { var r = nbi(); x._copyTo(r); this.reduce(r); return r; }
}
function barrettRevert(x) { return x; }
// x = x mod m (HAC 14.42)
function barrettReduce(x) {
x._drShiftTo(this.m.t-1,this.r2);
if(x.t > this.m.t+1) { x.t = this.m.t+1; x._clamp(); }
this.mu._multiplyUpperTo(this.r2,this.m.t+1,this.q3);
this.m._multiplyLowerTo(this.q3,this.m.t+1,this.r2);
while(x.compareTo(this.r2) < 0) x._dAddOffset(1,this.m.t+1);
x._subTo(this.r2,x);
while(x.compareTo(this.m) >= 0) x._subTo(this.m,x);
}
// r = x^2 mod m; x != r
function barrettSqrTo(x,r) { x._squareTo(r); this.reduce(r); }
// r = x*y mod m; x,y != r
function barrettMulTo(x,y,r) { x._multiplyTo(y,r); this.reduce(r); }
Barrett.prototype.convert = barrettConvert;
Barrett.prototype.revert = barrettRevert;
Barrett.prototype.reduce = barrettReduce;
Barrett.prototype.mulTo = barrettMulTo;
Barrett.prototype.sqrTo = barrettSqrTo;
// (public) this^e % m (HAC 14.85)
function bnModPow(e,m) {
var i = e.bitLength(), k, r = nbv(1), z;
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 Classic(m);
else if(m._isEven())
z = new Barrett(m);
else
z = new Montgomery(m);
// precomputation
var g = [], n = 3, k1 = k-1, km = (1<<k)-1;
g[1] = z.convert(this);
if(k > 1) {
var g2 = nbi();
z.sqrTo(g[1],g2);
while(n <= km) {
g[n] = nbi();
z.mulTo(g2,g[n-2],g[n]);
n += 2;
}
}
var j = e.t-1, w, is1 = true, r2 = nbi(), t;
i = nbits(e[j])-1;
while(j >= 0) {
if(i >= k1) w = (e[j]>>(i-k1))&km;
else {
w = (e[j]&((1<<(i+1))-1))<<(k1-i);
if(j > 0) w |= e[j-1]>>(this._DB+i-k1);
}
n = k;
while((w&1) == 0) { w >>= 1; --n; }
if((i -= n) < 0) { i += this._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[j]&(1<<i)) == 0) {
z.sqrTo(r,r2); t = r; r = r2; r2 = t;
if(--i < 0) { i = this._DB-1; --j; }
}
}
return z.revert(r);
}
// (public) gcd(this,a) (HAC 14.54)
function bnGCD(a) {
var x = (this.s<0)?this.negate():this.clone();
var y = (a.s<0)?a.negate():a.clone();
if(x.compareTo(y) < 0) { var t = x; x = y; y = t; }
var i = x.getLowestSetBit(), g = 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;
}
// (protected) this % n, n < 2^26
function bnpModInt(n) {
if(n <= 0) return 0;
var d = this._DV%n, r = (this.s<0)?n-1:0;
if(this.t > 0)
if(d == 0) r = this[0]%n;
else for(var i = this.t-1; i >= 0; --i) r = (d*r+this[i])%n;
return r;
}
// (public) 1/this % m (HAC 14.61)
function bnModInverse(m) {
var ac = m._isEven();
if((this._isEven() && ac) || m.signum() == 0) return BigInteger.ZERO;
var u = m.clone(), v = this.clone();
var a = nbv(1), b = nbv(0), c = nbv(0), d = 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;
}
var lowprimes = [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];
var lplim = (1<<26)/lowprimes[lowprimes.length-1];
// (public) test primality with certainty >= 1-.5^t
function bnIsProbablePrime(t) {
var i, x = this.abs();
if(x.t == 1 && x[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 = lowprimes[i], j = 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);
}
// (protected) true if probably prime (HAC 4.24, Miller-Rabin)
function bnpMillerRabin(t) {
var n1 = this.subtract(BigInteger.ONE);
var k = n1.getLowestSetBit();
if(k <= 0) return false;
var r = n1.shiftRight(k);
t = (t+1)>>1;
if(t > lowprimes.length) t = lowprimes.length;
var a = nbi();
for(var i = 0; i < t; ++i) {
a._fromInt(lowprimes[i]);
var y = a.modPow(r,this);
if(y.compareTo(BigInteger.ONE) != 0 && y.compareTo(n1) != 0) {
var j = 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;
}
dojo.extend(BigInteger, {
// protected
_chunkSize: bnpChunkSize,
_toRadix: bnpToRadix,
_fromRadix: bnpFromRadix,
_fromNumber: bnpFromNumber,
_bitwiseTo: bnpBitwiseTo,
_changeBit: bnpChangeBit,
_addTo: bnpAddTo,
_dMultiply: bnpDMultiply,
_dAddOffset: bnpDAddOffset,
_multiplyLowerTo: bnpMultiplyLowerTo,
_multiplyUpperTo: bnpMultiplyUpperTo,
_modInt: bnpModInt,
_millerRabin: bnpMillerRabin,
// public
clone: bnClone,
intValue: bnIntValue,
byteValue: bnByteValue,
shortValue: bnShortValue,
signum: bnSigNum,
toByteArray: bnToByteArray,
equals: bnEquals,
min: bnMin,
max: bnMax,
and: bnAnd,
or: bnOr,
xor: bnXor,
andNot: bnAndNot,
not: bnNot,
shiftLeft: bnShiftLeft,
shiftRight: bnShiftRight,
getLowestSetBit: bnGetLowestSetBit,
bitCount: bnBitCount,
testBit: bnTestBit,
setBit: bnSetBit,
clearBit: bnClearBit,
flipBit: bnFlipBit,
add: bnAdd,
subtract: bnSubtract,
multiply: bnMultiply,
divide: bnDivide,
remainder: bnRemainder,
divideAndRemainder: bnDivideAndRemainder,
modPow: bnModPow,
modInverse: bnModInverse,
pow: bnPow,
gcd: bnGCD,
isProbablePrime: bnIsProbablePrime
});
// BigInteger interfaces not implemented in jsbn:
// BigInteger(int signum, byte[] magnitude)
// double doubleValue()
// float floatValue()
// int hashCode()
// long longValue()
// static BigInteger valueOf(long val)
})();
}