/*
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"]){ //_hasResource checks added by build. Do not use _hasResource directly in your code.
dojo._hasResource["dojox.math.BigInteger"] = true;
dojo.provide("dojox.math.BigInteger");
dojo.getObject("math.BigInteger", true, dojox);
dojo.experimental("dojox.math.BigInteger");
// Contributed under CLA by Tom Wu <tjw@cs.Stanford.EDU>
// See http://www-cs-students.stanford.edu/~tjw/jsbn/ for details.
// Basic JavaScript BN library - subset useful for RSA encryption.
// The API for dojox.math.BigInteger closely resembles that of the java.math.BigInteger class in Java.
(function(){
// Bits per digit
var dbits;
// JavaScript engine analysis
var canary = 0xdeadbeefcafe;
var j_lm = ((canary&0xffffff)==0xefcafe);
// (public) Constructor
function BigInteger(a,b,c) {
if(a != null)
if("number" == typeof a) this._fromNumber(a,b,c);
else if(!b && "string" != typeof a) this._fromString(a,256);
else this._fromString(a,b);
}
// return new, unset BigInteger
function nbi() { return new BigInteger(null); }
// am: Compute w_j += (x*this_i), propagate carries,
// c is initial carry, returns final carry.
// c < 3*dvalue, x < 2*dvalue, this_i < dvalue
// We need to select the fastest one that works in this environment.
// am1: use a single mult and divide to get the high bits,
// max digit bits should be 26 because
// max internal value = 2*dvalue^2-2*dvalue (< 2^53)
function am1(i,x,w,j,c,n) {
while(--n >= 0) {
var v = x*this[i++]+w[j]+c;
c = Math.floor(v/0x4000000);
w[j++] = v&0x3ffffff;
}
return c;
}
// am2 avoids a big mult-and-extract completely.
// Max digit bits should be <= 30 because we do bitwise ops
// on values up to 2*hdvalue^2-hdvalue-1 (< 2^31)
function am2(i,x,w,j,c,n) {
var xl = x&0x7fff, xh = x>>15;
while(--n >= 0) {
var l = this[i]&0x7fff;
var h = this[i++]>>15;
var m = xh*l+h*xl;
l = xl*l+((m&0x7fff)<<15)+w[j]+(c&0x3fffffff);
c = (l>>>30)+(m>>>15)+xh*h+(c>>>30);
w[j++] = l&0x3fffffff;
}
return c;
}
// Alternately, set max digit bits to 28 since some
// browsers slow down when dealing with 32-bit numbers.
function am3(i,x,w,j,c,n) {
var xl = x&0x3fff, xh = x>>14;
while(--n >= 0) {
var l = this[i]&0x3fff;
var h = this[i++]>>14;
var m = xh*l+h*xl;
l = xl*l+((m&0x3fff)<<14)+w[j]+c;
c = (l>>28)+(m>>14)+xh*h;
w[j++] = l&0xfffffff;
}
return c;
}
if(j_lm && (navigator.appName == "Microsoft Internet Explorer")) {
BigInteger.prototype.am = am2;
dbits = 30;
}
else if(j_lm && (navigator.appName != "Netscape")) {
BigInteger.prototype.am = am1;
dbits = 26;
}
else { // Mozilla/Netscape seems to prefer am3
BigInteger.prototype.am = am3;
dbits = 28;
}
var BI_FP = 52;
// Digit conversions
var BI_RM = "0123456789abcdefghijklmnopqrstuvwxyz";
var BI_RC = [];
var rr,vv;
rr = "0".charCodeAt(0);
for(vv = 0; vv <= 9; ++vv) BI_RC[rr++] = vv;
rr = "a".charCodeAt(0);
for(vv = 10; vv < 36; ++vv) BI_RC[rr++] = vv;
rr = "A".charCodeAt(0);
for(vv = 10; vv < 36; ++vv) BI_RC[rr++] = vv;
function int2char(n) { return BI_RM.charAt(n); }
function intAt(s,i) {
var c = BI_RC[s.charCodeAt(i)];
return (c==null)?-1:c;
}
// (protected) copy this to r
function bnpCopyTo(r) {
for(var i = this.t-1; i >= 0; --i) r[i] = this[i];
r.t = this.t;
r.s = this.s;
}
// (protected) set from integer value x, -DV <= x < DV
function bnpFromInt(x) {
this.t = 1;
this.s = (x<0)?-1:0;
if(x > 0) this[0] = x;
else if(x < -1) this[0] = x+_DV;
else this.t = 0;
}
// return bigint initialized to value
function nbv(i) { var r = nbi(); r._fromInt(i); return r; }
// (protected) set from string and radix
function bnpFromString(s,b) {
var k;
if(b == 16) k = 4;
else if(b == 8) k = 3;
else if(b == 256) k = 8; // byte array
else if(b == 2) k = 1;
else if(b == 32) k = 5;
else if(b == 4) k = 2;
else { this.fromRadix(s,b); return; }
this.t = 0;
this.s = 0;
var i = s.length, mi = false, sh = 0;
while(--i >= 0) {
var x = (k==8)?s[i]&0xff:intAt(s,i);
if(x < 0) {
if(s.charAt(i) == "-") mi = true;
continue;
}
mi = false;
if(sh == 0)
this[this.t++] = x;
else if(sh+k > this._DB) {
this[this.t-1] |= (x&((1<<(this._DB-sh))-1))<<sh;
this[this.t++] = (x>>(this._DB-sh));
}
else
this[this.t-1] |= x<<sh;
sh += k;
if(sh >= this._DB) sh -= this._DB;
}
if(k == 8 && (s[0]&0x80) != 0) {
this.s = -1;
if(sh > 0) this[this.t-1] |= ((1<<(this._DB-sh))-1)<<sh;
}
this._clamp();
if(mi) BigInteger.ZERO._subTo(this,this);
}
// (protected) clamp off excess high words
function bnpClamp() {
var c = this.s&this._DM;
while(this.t > 0 && this[this.t-1] == c) --this.t;
}
// (public) return string representation in given radix
function bnToString(b) {
if(this.s < 0) return "-"+this.negate().toString(b);
var k;
if(b == 16) k = 4;
else if(b == 8) k = 3;
else if(b == 2) k = 1;
else if(b == 32) k = 5;
else if(b == 4) k = 2;
else return this._toRadix(b);
var km = (1<<k)-1, d, m = false, r = "", i = this.t;
var p = this._DB-(i*this._DB)%k;
if(i-- > 0) {
if(p < this._DB && (d = this[i]>>p) > 0) { m = true; r = int2char(d); }
while(i >= 0) {
if(p < k) {
d = (this[i]&((1<<p)-1))<<(k-p);
d |= this[--i]>>(p+=this._DB-k);
}
else {
d = (this[i]>>(p-=k))&km;
if(p <= 0) { p += this._DB; --i; }
}
if(d > 0) m = true;
if(m) r += int2char(d);
}
}
return m?r:"0";
}
// (public) -this
function bnNegate() { var r = nbi(); BigInteger.ZERO._subTo(this,r); return r; }
// (public) |this|
function bnAbs() { return (this.s<0)?this.negate():this; }
// (public) return + if this > a, - if this < a, 0 if equal
function bnCompareTo(a) {
var r = this.s-a.s;
if(r) return r;
var i = this.t;
r = i-a.t;
if(r) return r;
while(--i >= 0) if((r = this[i] - a[i])) return r;
return 0;
}
// returns bit length of the integer x
function nbits(x) {
var r = 1, t;
if((t=x>>>16)) { x = t; r += 16; }
if((t=x>>8)) { x = t; r += 8; }
if((t=x>>4)) { x = t; r += 4; }
if((t=x>>2)) { x = t; r += 2; }
if((t=x>>1)) { x = t; r += 1; }
return r;
}
// (public) return the number of bits in "this"
function bnBitLength() {
if(this.t <= 0) return 0;
return this._DB*(this.t-1)+nbits(this[this.t-1]^(this.s&this._DM));
}
// (protected) r = this << n*DB
function bnpDLShiftTo(n,r) {
var i;
for(i = this.t-1; i >= 0; --i) r[i+n] = this[i];
for(i = n-1; i >= 0; --i) r[i] = 0;
r.t = this.t+n;
r.s = this.s;
}
// (protected) r = this >> n*DB
function bnpDRShiftTo(n,r) {
for(var i = n; i < this.t; ++i) r[i-n] = this[i];
r.t = Math.max(this.t-n,0);
r.s = this.s;
}
// (protected) r = this << n
function bnpLShiftTo(n,r) {
var bs = n%this._DB;
var cbs = this._DB-bs;
var bm = (1<<cbs)-1;
var ds = Math.floor(n/this._DB), c = (this.s<<bs)&this._DM, i;
for(i = this.t-1; i >= 0; --i) {
r[i+ds+1] = (this[i]>>cbs)|c;
c = (this[i]&bm)<<bs;
}
for(i = ds-1; i >= 0; --i) r[i] = 0;
r[ds] = c;
r.t = this.t+ds+1;
r.s = this.s;
r._clamp();
}
// (protected) r = this >> n
function bnpRShiftTo(n,r) {
r.s = this.s;
var ds = Math.floor(n/this._DB);
if(ds >= this.t) { r.t = 0; return; }
var bs = n%this._DB;
var cbs = this._DB-bs;
var bm = (1<<bs)-1;
r[0] = this[ds]>>bs;
for(var i = ds+1; i < this.t; ++i) {
r[i-ds-1] |= (this[i]&bm)<<cbs;
r[i-ds] = this[i]>>bs;
}
if(bs > 0) r[this.t-ds-1] |= (this.s&bm)<<cbs;
r.t = this.t-ds;
r._clamp();
}
// (protected) r = this - a
function bnpSubTo(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 < -1) r[i++] = this._DV+c;
else if(c > 0) r[i++] = c;
r.t = i;
r._clamp();
}
// (protected) r = this * a, r != this,a (HAC 14.12)
// "this" should be the larger one if appropriate.
function bnpMultiplyTo(a,r) {
var x = this.abs(), y = a.abs();
var i = x.t;
r.t = i+y.t;
while(--i >= 0) r[i] = 0;
for(i = 0; i < y.t; ++i) r[i+x.t] = x.am(0,y[i],r,i,0,x.t);
r.s = 0;
r._clamp();
if(this.s != a.s) BigInteger.ZERO._subTo(r,r);
}
// (protected) r = this^2, r != this (HAC 14.16)
function bnpSquareTo(r) {
var x = this.abs();
var i = r.t = 2*x.t;
while(--i >= 0) r[i] = 0;
for(i = 0; i < x.t-1; ++i) {
var c = x.am(i,x[i],r,2*i,0,1);
if((r[i+x.t]+=x.am(i+1,2*x[i],r,2*i+1,c,x.t-i-1)) >= x._DV) {
r[i+x.t] -= x._DV;
r[i+x.t+1] = 1;
}
}
if(r.t > 0) r[r.t-1] += x.am(i,x[i],r,2*i,0,1);
r.s = 0;
r._clamp();
}
// (protected) divide this by m, quotient and remainder to q, r (HAC 14.20)
// r != q, this != m. q or r may be null.
function bnpDivRemTo(m,q,r) {
var pm = m.abs();
if(pm.t <= 0) return;
var pt = this.abs();
if(pt.t < pm.t) {
if(q != null) q._fromInt(0);
if(r != null) this._copyTo(r);
return;
}
if(r == null) r = nbi();
var y = nbi(), ts = this.s, ms = m.s;
var nsh = this._DB-nbits(pm[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 = y.t;
var y0 = y[ys-1];
if(y0 == 0) return;
var yt = y0*(1<<this._F1)+((ys>1)?y[ys-2]>>this._F2:0);
var d1 = this._FV/yt, d2 = (1<<this._F1)/yt, e = 1<<this._F2;
var i = r.t, j = i-ys, t = (q==null)?nbi():q;
y._dlShiftTo(j,t);
if(r.compareTo(t) >= 0) {
r[r.t++] = 1;
r._subTo(t,r);
}
BigInteger.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 = (r[--i]==y0)?this._DM:Math.floor(r[i]*d1+(r[i-1]+e)*d2);
if((r[i]+=y.am(0,qd,r,j,0,ys)) < qd) { // Try it out
y._dlShiftTo(j,t);
r._subTo(t,r);
while(r[i] < --qd) r._subTo(t,r);
}
}
if(q != null) {
r._drShiftTo(ys,q);
if(ts != ms) BigInteger.ZERO._subTo(q,q);
}
r.t = ys;
r._clamp();
if(nsh > 0) r._rShiftTo(nsh,r); // Denormalize remainder
if(ts < 0) BigInteger.ZERO._subTo(r,r);
}
// (public) this mod a
function bnMod(a) {
var r = nbi();
this.abs()._divRemTo(a,null,r);
if(this.s < 0 && r.compareTo(BigInteger.ZERO) > 0) a._subTo(r,r);
return r;
}
// Modular reduction using "classic" algorithm
function Classic(m) { this.m = m; }
function cConvert(x) {
if(x.s < 0 || x.compareTo(this.m) >= 0) return x.mod(this.m);
else return x;
}
function cRevert(x) { return x; }
function cReduce(x) { x._divRemTo(this.m,null,x); }
function cMulTo(x,y,r) { x._multiplyTo(y,r); this.reduce(r); }
function cSqrTo(x,r) { x._squareTo(r); this.reduce(r); }
dojo.extend(Classic, {
convert: cConvert,
revert: cRevert,
reduce: cReduce,
mulTo: cMulTo,
sqrTo: cSqrTo
});
// (protected) return "-1/this % 2^DB"; useful for Mont. reduction
// justification:
// xy == 1 (mod m)
// xy = 1+km
// xy(2-xy) = (1+km)(1-km)
// x[y(2-xy)] = 1-k^2m^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.
// JS multiply "overflows" differently from C/C++, so care is needed here.
function bnpInvDigit() {
if(this.t < 1) return 0;
var x = this[0];
if((x&1) == 0) return 0;
var y = 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
y = (y*(2-x*y%this._DV))%this._DV; // y == 1/x mod 2^dbits
// we really want the negative inverse, and -DV < y < DV
return (y>0)?this._DV-y:-y;
}
// Montgomery reduction
function Montgomery(m) {
this.m = m;
this.mp = m._invDigit();
this.mpl = this.mp&0x7fff;
this.mph = this.mp>>15;
this.um = (1<<(m._DB-15))-1;
this.mt2 = 2*m.t;
}
// xR mod m
function montConvert(x) {
var r = nbi();
x.abs()._dlShiftTo(this.m.t,r);
r._divRemTo(this.m,null,r);
if(x.s < 0 && r.compareTo(BigInteger.ZERO) > 0) this.m._subTo(r,r);
return r;
}
// x/R mod m
function montRevert(x) {
var r = nbi();
x._copyTo(r);
this.reduce(r);
return r;
}
// x = x/R mod m (HAC 14.32)
function montReduce(x) {
while(x.t <= this.mt2) // pad x so am has enough room later
x[x.t++] = 0;
for(var i = 0; i < this.m.t; ++i) {
// faster way of calculating u0 = x[i]*mp mod DV
var j = x[i]&0x7fff;
var u0 = (j*this.mpl+(((j*this.mph+(x[i]>>15)*this.mpl)&this.um)<<15))&x._DM;
// use am to combine the multiply-shift-add into one call
j = i+this.m.t;
x[j] += this.m.am(0,u0,x,i,0,this.m.t);
// propagate carry
while(x[j] >= x._DV) { x[j] -= x._DV; x[++j]++; }
}
x._clamp();
x._drShiftTo(this.m.t,x);
if(x.compareTo(this.m) >= 0) x._subTo(this.m,x);
}
// r = "x^2/R mod m"; x != r
function montSqrTo(x,r) { x._squareTo(r); this.reduce(r); }
// r = "xy/R mod m"; x,y != r
function montMulTo(x,y,r) { x._multiplyTo(y,r); this.reduce(r); }
dojo.extend(Montgomery, {
convert: montConvert,
revert: montRevert,
reduce: montReduce,
mulTo: montMulTo,
sqrTo: montSqrTo
});
// (protected) true iff this is even
function bnpIsEven() { return ((this.t>0)?(this[0]&1):this.s) == 0; }
// (protected) this^e, e < 2^32, doing sqr and mul with "r" (HAC 14.79)
function bnpExp(e,z) {
if(e > 0xffffffff || e < 1) return BigInteger.ONE;
var r = nbi(), r2 = nbi(), g = z.convert(this), i = 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 = r; r = r2; r2 = t; }
}
return z.revert(r);
}
// (public) this^e % m, 0 <= e < 2^32
function bnModPowInt(e,m) {
var z;
if(e < 256 || m._isEven()) z = new Classic(m); else z = new Montgomery(m);
return this._exp(e,z);
}
dojo.extend(BigInteger, {
// protected, not part of the official API
_DB: dbits,
_DM: (1 << dbits) - 1,
_DV: 1 << dbits,
_FV: Math.pow(2, BI_FP),
_F1: BI_FP - dbits,
_F2: 2 * dbits-BI_FP,
// protected
_copyTo: bnpCopyTo,
_fromInt: bnpFromInt,
_fromString: bnpFromString,
_clamp: bnpClamp,
_dlShiftTo: bnpDLShiftTo,
_drShiftTo: bnpDRShiftTo,
_lShiftTo: bnpLShiftTo,
_rShiftTo: bnpRShiftTo,
_subTo: bnpSubTo,
_multiplyTo: bnpMultiplyTo,
_squareTo: bnpSquareTo,
_divRemTo: bnpDivRemTo,
_invDigit: bnpInvDigit,
_isEven: bnpIsEven,
_exp: bnpExp,
// public
toString: bnToString,
negate: bnNegate,
abs: bnAbs,
compareTo: bnCompareTo,
bitLength: bnBitLength,
mod: bnMod,
modPowInt: bnModPowInt
});
dojo._mixin(BigInteger, {
// "constants"
ZERO: nbv(0),
ONE: nbv(1),
// internal functions
_nbi: nbi,
_nbv: nbv,
_nbits: nbits,
// internal classes
_Montgomery: Montgomery
});
// export to DojoX
dojox.math.BigInteger = BigInteger;
})();
}