dojo_app/js/library/dojox/math/BigInteger.js

// AMD-ID "dojox/math/BigInteger"
define(["dojo", "dojox", "dojo/has"], function(dojo, dojox, has) {

	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.

	// 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 && has("ie")) {
		BigInteger.prototype.am = am2;
		dbits = 30;
	}
	// had another guard navigator.appName != "Netscape"
	// this was removed since
	// https://stackoverflow.com/questions/14573881/why-does-javascript-navigator-appname-return-netscape-for-safari-firefox-and-ch
	else if(j_lm) {
		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;
		this.t = (this.t === 0) ? 1 : 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 +1 if this > a, -1 if this < a, 0 if equal
	function bnCompareTo(a) {
		if(this.s !== a.s) return this.s > a.s ? 1 : -1; // check sign
		if(this.t !== a.t) return (this.s === 0) ? (this.t > a.t ? 1 : -1) : (this.t < a.t ? 1 : -1); // check size
		var i = this.t;
		while(--i >= 0) if(this[i] !== a[i]) return (this.s === 0) ? (this[i] > a[i] ? 1 : -1) : (this[i] > a[i] ? 1 : -1); // check indivitual bytes
		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,
		_intAt:  intAt,

		// 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;

	return dojox.math.BigInteger;
});