source: Dev/trunk/src/client/dojox/math/BigInteger.js @ 529

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

        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 && (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;

        return dojox.math.BigInteger;
});