2ee9278fec
Add TAJ design Add Lanadesign Add ARC design add Tajcoin add aquariuscoin, lanacoin and nevacoin remove trailing white spaces remove trailing white spaces Wrong AquariusCoin logo New AquariusCoin ARCO logo Partial Slovenian translation "si" Update si.js Slovenian translation -SI Update README Update README
1271 lines
36 KiB
JavaScript
1271 lines
36 KiB
JavaScript
/*!
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* Basic JavaScript BN library - subset useful for RSA encryption. v1.3
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*
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* Copyright (c) 2005 Tom Wu
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* All Rights Reserved.
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* BSD License
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* http://www-cs-students.stanford.edu/~tjw/jsbn/LICENSE
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*
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* Copyright Stephan Thomas
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* Copyright bitaddress.org
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*/
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(function () {
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// (public) Constructor function of Global BigInteger object
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var BigInteger = window.BigInteger = function BigInteger(a, b, c) {
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if (a != null)
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if ("number" == typeof a) this.fromNumber(a, b, c);
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else if (b == null && "string" != typeof a) this.fromString(a, 256);
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else this.fromString(a, b);
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};
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// Bits per digit
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var dbits;
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// JavaScript engine analysis
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var canary = 0xdeadbeefcafe;
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var j_lm = ((canary & 0xffffff) == 0xefcafe);
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// return new, unset BigInteger
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function nbi() { return new BigInteger(null); }
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// am: Compute w_j += (x*this_i), propagate carries,
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// c is initial carry, returns final carry.
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// c < 3*dvalue, x < 2*dvalue, this_i < dvalue
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// We need to select the fastest one that works in this environment.
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// am1: use a single mult and divide to get the high bits,
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// max digit bits should be 26 because
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// max internal value = 2*dvalue^2-2*dvalue (< 2^53)
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function am1(i, x, w, j, c, n) {
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while (--n >= 0) {
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var v = x * this[i++] + w[j] + c;
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c = Math.floor(v / 0x4000000);
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w[j++] = v & 0x3ffffff;
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}
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return c;
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}
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// am2 avoids a big mult-and-extract completely.
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// Max digit bits should be <= 30 because we do bitwise ops
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// on values up to 2*hdvalue^2-hdvalue-1 (< 2^31)
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function am2(i, x, w, j, c, n) {
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var xl = x & 0x7fff, xh = x >> 15;
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while (--n >= 0) {
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var l = this[i] & 0x7fff;
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var h = this[i++] >> 15;
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var m = xh * l + h * xl;
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l = xl * l + ((m & 0x7fff) << 15) + w[j] + (c & 0x3fffffff);
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c = (l >>> 30) + (m >>> 15) + xh * h + (c >>> 30);
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w[j++] = l & 0x3fffffff;
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}
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return c;
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}
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// Alternately, set max digit bits to 28 since some
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// browsers slow down when dealing with 32-bit numbers.
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function am3(i, x, w, j, c, n) {
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var xl = x & 0x3fff, xh = x >> 14;
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while (--n >= 0) {
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var l = this[i] & 0x3fff;
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var h = this[i++] >> 14;
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var m = xh * l + h * xl;
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l = xl * l + ((m & 0x3fff) << 14) + w[j] + c;
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c = (l >> 28) + (m >> 14) + xh * h;
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w[j++] = l & 0xfffffff;
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}
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return c;
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}
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if (j_lm && (navigator.appName == "Microsoft Internet Explorer")) {
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BigInteger.prototype.am = am2;
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dbits = 30;
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}
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else if (j_lm && (navigator.appName != "Netscape")) {
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BigInteger.prototype.am = am1;
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dbits = 26;
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}
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else { // Mozilla/Netscape seems to prefer am3
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BigInteger.prototype.am = am3;
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dbits = 28;
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}
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BigInteger.prototype.DB = dbits;
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BigInteger.prototype.DM = ((1 << dbits) - 1);
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BigInteger.prototype.DV = (1 << dbits);
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var BI_FP = 52;
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BigInteger.prototype.FV = Math.pow(2, BI_FP);
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BigInteger.prototype.F1 = BI_FP - dbits;
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BigInteger.prototype.F2 = 2 * dbits - BI_FP;
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// Digit conversions
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var BI_RM = "0123456789abcdefghijklmnopqrstuvwxyz";
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var BI_RC = new Array();
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var rr, vv;
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rr = "0".charCodeAt(0);
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for (vv = 0; vv <= 9; ++vv) BI_RC[rr++] = vv;
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rr = "a".charCodeAt(0);
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for (vv = 10; vv < 36; ++vv) BI_RC[rr++] = vv;
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rr = "A".charCodeAt(0);
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for (vv = 10; vv < 36; ++vv) BI_RC[rr++] = vv;
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function int2char(n) { return BI_RM.charAt(n); }
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function intAt(s, i) {
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var c = BI_RC[s.charCodeAt(i)];
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return (c == null) ? -1 : c;
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}
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// return bigint initialized to value
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function nbv(i) { var r = nbi(); r.fromInt(i); return r; }
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// returns bit length of the integer x
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function nbits(x) {
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var r = 1, t;
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if ((t = x >>> 16) != 0) { x = t; r += 16; }
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if ((t = x >> 8) != 0) { x = t; r += 8; }
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if ((t = x >> 4) != 0) { x = t; r += 4; }
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if ((t = x >> 2) != 0) { x = t; r += 2; }
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if ((t = x >> 1) != 0) { x = t; r += 1; }
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return r;
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}
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// (protected) copy this to r
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BigInteger.prototype.copyTo = function (r) {
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for (var i = this.t - 1; i >= 0; --i) r[i] = this[i];
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r.t = this.t;
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r.s = this.s;
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};
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// (protected) set from integer value x, -DV <= x < DV
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BigInteger.prototype.fromInt = function (x) {
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this.t = 1;
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this.s = (x < 0) ? -1 : 0;
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if (x > 0) this[0] = x;
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else if (x < -1) this[0] = x + this.DV;
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else this.t = 0;
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};
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// (protected) set from string and radix
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BigInteger.prototype.fromString = function (s, b) {
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var k;
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if (b == 16) k = 4;
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else if (b == 8) k = 3;
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else if (b == 256) k = 8; // byte array
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else if (b == 2) k = 1;
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else if (b == 32) k = 5;
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else if (b == 4) k = 2;
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else { this.fromRadix(s, b); return; }
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this.t = 0;
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this.s = 0;
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var i = s.length, mi = false, sh = 0;
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while (--i >= 0) {
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var x = (k == 8) ? s[i] & 0xff : intAt(s, i);
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if (x < 0) {
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if (s.charAt(i) == "-") mi = true;
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continue;
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}
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mi = false;
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if (sh == 0)
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this[this.t++] = x;
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else if (sh + k > this.DB) {
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this[this.t - 1] |= (x & ((1 << (this.DB - sh)) - 1)) << sh;
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this[this.t++] = (x >> (this.DB - sh));
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}
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else
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this[this.t - 1] |= x << sh;
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sh += k;
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if (sh >= this.DB) sh -= this.DB;
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}
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if (k == 8 && (s[0] & 0x80) != 0) {
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this.s = -1;
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if (sh > 0) this[this.t - 1] |= ((1 << (this.DB - sh)) - 1) << sh;
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}
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this.clamp();
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if (mi) BigInteger.ZERO.subTo(this, this);
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};
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// (protected) clamp off excess high words
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BigInteger.prototype.clamp = function () {
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var c = this.s & this.DM;
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while (this.t > 0 && this[this.t - 1] == c) --this.t;
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};
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// (protected) r = this << n*DB
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BigInteger.prototype.dlShiftTo = function (n, r) {
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var i;
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for (i = this.t - 1; i >= 0; --i) r[i + n] = this[i];
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for (i = n - 1; i >= 0; --i) r[i] = 0;
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r.t = this.t + n;
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r.s = this.s;
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};
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// (protected) r = this >> n*DB
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BigInteger.prototype.drShiftTo = function (n, r) {
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for (var i = n; i < this.t; ++i) r[i - n] = this[i];
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r.t = Math.max(this.t - n, 0);
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r.s = this.s;
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};
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// (protected) r = this << n
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BigInteger.prototype.lShiftTo = function (n, r) {
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var bs = n % this.DB;
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var cbs = this.DB - bs;
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var bm = (1 << cbs) - 1;
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var ds = Math.floor(n / this.DB), c = (this.s << bs) & this.DM, i;
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for (i = this.t - 1; i >= 0; --i) {
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r[i + ds + 1] = (this[i] >> cbs) | c;
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c = (this[i] & bm) << bs;
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}
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for (i = ds - 1; i >= 0; --i) r[i] = 0;
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r[ds] = c;
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r.t = this.t + ds + 1;
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r.s = this.s;
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r.clamp();
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};
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// (protected) r = this >> n
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BigInteger.prototype.rShiftTo = function (n, r) {
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r.s = this.s;
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var ds = Math.floor(n / this.DB);
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if (ds >= this.t) { r.t = 0; return; }
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var bs = n % this.DB;
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var cbs = this.DB - bs;
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var bm = (1 << bs) - 1;
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r[0] = this[ds] >> bs;
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for (var i = ds + 1; i < this.t; ++i) {
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r[i - ds - 1] |= (this[i] & bm) << cbs;
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r[i - ds] = this[i] >> bs;
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}
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if (bs > 0) r[this.t - ds - 1] |= (this.s & bm) << cbs;
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r.t = this.t - ds;
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r.clamp();
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};
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// (protected) r = this - a
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BigInteger.prototype.subTo = function (a, r) {
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var i = 0, c = 0, m = Math.min(a.t, this.t);
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while (i < m) {
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c += this[i] - a[i];
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r[i++] = c & this.DM;
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c >>= this.DB;
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}
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if (a.t < this.t) {
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c -= a.s;
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while (i < this.t) {
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c += this[i];
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r[i++] = c & this.DM;
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c >>= this.DB;
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}
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c += this.s;
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}
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else {
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c += this.s;
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while (i < a.t) {
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c -= a[i];
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r[i++] = c & this.DM;
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c >>= this.DB;
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}
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c -= a.s;
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}
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r.s = (c < 0) ? -1 : 0;
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if (c < -1) r[i++] = this.DV + c;
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else if (c > 0) r[i++] = c;
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r.t = i;
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r.clamp();
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};
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// (protected) r = this * a, r != this,a (HAC 14.12)
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// "this" should be the larger one if appropriate.
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BigInteger.prototype.multiplyTo = function (a, r) {
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var x = this.abs(), y = a.abs();
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var i = x.t;
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r.t = i + y.t;
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while (--i >= 0) r[i] = 0;
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for (i = 0; i < y.t; ++i) r[i + x.t] = x.am(0, y[i], r, i, 0, x.t);
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r.s = 0;
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r.clamp();
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if (this.s != a.s) BigInteger.ZERO.subTo(r, r);
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};
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// (protected) r = this^2, r != this (HAC 14.16)
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BigInteger.prototype.squareTo = function (r) {
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var x = this.abs();
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var i = r.t = 2 * x.t;
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while (--i >= 0) r[i] = 0;
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for (i = 0; i < x.t - 1; ++i) {
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var c = x.am(i, x[i], r, 2 * i, 0, 1);
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if ((r[i + x.t] += x.am(i + 1, 2 * x[i], r, 2 * i + 1, c, x.t - i - 1)) >= x.DV) {
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r[i + x.t] -= x.DV;
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r[i + x.t + 1] = 1;
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}
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}
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if (r.t > 0) r[r.t - 1] += x.am(i, x[i], r, 2 * i, 0, 1);
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r.s = 0;
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r.clamp();
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};
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// (protected) divide this by m, quotient and remainder to q, r (HAC 14.20)
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// r != q, this != m. q or r may be null.
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BigInteger.prototype.divRemTo = function (m, q, r) {
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var pm = m.abs();
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if (pm.t <= 0) return;
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var pt = this.abs();
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if (pt.t < pm.t) {
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if (q != null) q.fromInt(0);
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if (r != null) this.copyTo(r);
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return;
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}
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if (r == null) r = nbi();
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var y = nbi(), ts = this.s, ms = m.s;
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var nsh = this.DB - nbits(pm[pm.t - 1]); // normalize modulus
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if (nsh > 0) { pm.lShiftTo(nsh, y); pt.lShiftTo(nsh, r); }
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else { pm.copyTo(y); pt.copyTo(r); }
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var ys = y.t;
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var y0 = y[ys - 1];
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if (y0 == 0) return;
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var yt = y0 * (1 << this.F1) + ((ys > 1) ? y[ys - 2] >> this.F2 : 0);
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var d1 = this.FV / yt, d2 = (1 << this.F1) / yt, e = 1 << this.F2;
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var i = r.t, j = i - ys, t = (q == null) ? nbi() : q;
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y.dlShiftTo(j, t);
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if (r.compareTo(t) >= 0) {
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r[r.t++] = 1;
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r.subTo(t, r);
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}
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BigInteger.ONE.dlShiftTo(ys, t);
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t.subTo(y, y); // "negative" y so we can replace sub with am later
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while (y.t < ys) y[y.t++] = 0;
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while (--j >= 0) {
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// Estimate quotient digit
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var qd = (r[--i] == y0) ? this.DM : Math.floor(r[i] * d1 + (r[i - 1] + e) * d2);
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if ((r[i] += y.am(0, qd, r, j, 0, ys)) < qd) { // Try it out
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y.dlShiftTo(j, t);
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r.subTo(t, r);
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while (r[i] < --qd) r.subTo(t, r);
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}
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}
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if (q != null) {
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r.drShiftTo(ys, q);
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if (ts != ms) BigInteger.ZERO.subTo(q, q);
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}
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r.t = ys;
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r.clamp();
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if (nsh > 0) r.rShiftTo(nsh, r); // Denormalize remainder
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if (ts < 0) BigInteger.ZERO.subTo(r, r);
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};
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// (protected) return "-1/this % 2^DB"; useful for Mont. reduction
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// justification:
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// xy == 1 (mod m)
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// xy = 1+km
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// xy(2-xy) = (1+km)(1-km)
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// x[y(2-xy)] = 1-k^2m^2
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// x[y(2-xy)] == 1 (mod m^2)
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// if y is 1/x mod m, then y(2-xy) is 1/x mod m^2
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// should reduce x and y(2-xy) by m^2 at each step to keep size bounded.
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// JS multiply "overflows" differently from C/C++, so care is needed here.
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BigInteger.prototype.invDigit = function () {
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if (this.t < 1) return 0;
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var x = this[0];
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if ((x & 1) == 0) return 0;
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var y = x & 3; // y == 1/x mod 2^2
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y = (y * (2 - (x & 0xf) * y)) & 0xf; // y == 1/x mod 2^4
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y = (y * (2 - (x & 0xff) * y)) & 0xff; // y == 1/x mod 2^8
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y = (y * (2 - (((x & 0xffff) * y) & 0xffff))) & 0xffff; // y == 1/x mod 2^16
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// last step - calculate inverse mod DV directly;
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// assumes 16 < DB <= 32 and assumes ability to handle 48-bit ints
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y = (y * (2 - x * y % this.DV)) % this.DV; // y == 1/x mod 2^dbits
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// we really want the negative inverse, and -DV < y < DV
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return (y > 0) ? this.DV - y : -y;
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};
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// (protected) true iff this is even
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BigInteger.prototype.isEven = function () { return ((this.t > 0) ? (this[0] & 1) : this.s) == 0; };
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// (protected) this^e, e < 2^32, doing sqr and mul with "r" (HAC 14.79)
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BigInteger.prototype.exp = function (e, z) {
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if (e > 0xffffffff || e < 1) return BigInteger.ONE;
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var r = nbi(), r2 = nbi(), g = z.convert(this), i = nbits(e) - 1;
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g.copyTo(r);
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while (--i >= 0) {
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z.sqrTo(r, r2);
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if ((e & (1 << i)) > 0) z.mulTo(r2, g, r);
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else { var t = r; r = r2; r2 = t; }
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}
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return z.revert(r);
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};
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// (public) return string representation in given radix
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BigInteger.prototype.toString = function (b) {
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if (this.s < 0) return "-" + this.negate().toString(b);
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var k;
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if (b == 16) k = 4;
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else if (b == 8) k = 3;
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else if (b == 2) k = 1;
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else if (b == 32) k = 5;
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else if (b == 4) k = 2;
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else return this.toRadix(b);
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var km = (1 << k) - 1, d, m = false, r = "", i = this.t;
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var p = this.DB - (i * this.DB) % k;
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if (i-- > 0) {
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if (p < this.DB && (d = this[i] >> p) > 0) { m = true; r = int2char(d); }
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while (i >= 0) {
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if (p < k) {
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d = (this[i] & ((1 << p) - 1)) << (k - p);
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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
|
|
BigInteger.prototype.negate = function () { var r = nbi(); BigInteger.ZERO.subTo(this, r); return r; };
|
|
|
|
// (public) |this|
|
|
BigInteger.prototype.abs = function () { return (this.s < 0) ? this.negate() : this; };
|
|
|
|
// (public) return + if this > a, - if this < a, 0 if equal
|
|
BigInteger.prototype.compareTo = function (a) {
|
|
var r = this.s - a.s;
|
|
if (r != 0) return r;
|
|
var i = this.t;
|
|
r = i - a.t;
|
|
if (r != 0) return (this.s < 0) ? -r : r;
|
|
while (--i >= 0) if ((r = this[i] - a[i]) != 0) return r;
|
|
return 0;
|
|
}
|
|
|
|
// (public) return the number of bits in "this"
|
|
BigInteger.prototype.bitLength = function () {
|
|
if (this.t <= 0) return 0;
|
|
return this.DB * (this.t - 1) + nbits(this[this.t - 1] ^ (this.s & this.DM));
|
|
};
|
|
|
|
// (public) this mod a
|
|
BigInteger.prototype.mod = function (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;
|
|
}
|
|
|
|
// (public) this^e % m, 0 <= e < 2^32
|
|
BigInteger.prototype.modPowInt = function (e, m) {
|
|
var z;
|
|
if (e < 256 || m.isEven()) z = new Classic(m); else z = new Montgomery(m);
|
|
return this.exp(e, z);
|
|
};
|
|
|
|
// "constants"
|
|
BigInteger.ZERO = nbv(0);
|
|
BigInteger.ONE = nbv(1);
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
// Copyright (c) 2005-2009 Tom Wu
|
|
// All Rights Reserved.
|
|
// See "LICENSE" for details.
|
|
// Extended JavaScript BN functions, required for RSA private ops.
|
|
// Version 1.1: new BigInteger("0", 10) returns "proper" zero
|
|
// Version 1.2: square() API, isProbablePrime fix
|
|
|
|
|
|
// 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;
|
|
}
|
|
|
|
// return number of 1 bits in x
|
|
function cbit(x) {
|
|
var r = 0;
|
|
while (x != 0) { x &= x - 1; ++r; }
|
|
return r;
|
|
}
|
|
|
|
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, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997];
|
|
var lplim = (1 << 26) / lowprimes[lowprimes.length - 1];
|
|
|
|
|
|
|
|
// (protected) return x s.t. r^x < DV
|
|
BigInteger.prototype.chunkSize = function (r) { return Math.floor(Math.LN2 * this.DB / Math.log(r)); };
|
|
|
|
// (protected) convert to radix string
|
|
BigInteger.prototype.toRadix = function (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
|
|
BigInteger.prototype.fromRadix = function (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
|
|
BigInteger.prototype.fromNumber = function (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 = new Array(), 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);
|
|
}
|
|
};
|
|
|
|
// (protected) r = this op a (bitwise)
|
|
BigInteger.prototype.bitwiseTo = function (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();
|
|
};
|
|
|
|
// (protected) this op (1<<n)
|
|
BigInteger.prototype.changeBit = function (n, op) {
|
|
var r = BigInteger.ONE.shiftLeft(n);
|
|
this.bitwiseTo(r, op, r);
|
|
return r;
|
|
};
|
|
|
|
// (protected) r = this + a
|
|
BigInteger.prototype.addTo = function (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();
|
|
};
|
|
|
|
// (protected) this *= n, this >= 0, 1 < n < DV
|
|
BigInteger.prototype.dMultiply = function (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
|
|
BigInteger.prototype.dAddOffset = function (n, w) {
|
|
if (n == 0) return;
|
|
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];
|
|
}
|
|
};
|
|
|
|
// (protected) r = lower n words of "this * a", a.t <= n
|
|
// "this" should be the larger one if appropriate.
|
|
BigInteger.prototype.multiplyLowerTo = function (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.
|
|
BigInteger.prototype.multiplyUpperTo = function (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);
|
|
};
|
|
|
|
// (protected) this % n, n < 2^26
|
|
BigInteger.prototype.modInt = function (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;
|
|
};
|
|
|
|
|
|
// (protected) true if probably prime (HAC 4.24, Miller-Rabin)
|
|
BigInteger.prototype.millerRabin = function (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) {
|
|
//Pick bases at random, instead of starting at 2
|
|
a.fromInt(lowprimes[Math.floor(Math.random() * lowprimes.length)]);
|
|
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;
|
|
};
|
|
|
|
|
|
|
|
// (public)
|
|
BigInteger.prototype.clone = function () { var r = nbi(); this.copyTo(r); return r; };
|
|
|
|
// (public) return value as integer
|
|
BigInteger.prototype.intValue = function () {
|
|
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
|
|
BigInteger.prototype.byteValue = function () { return (this.t == 0) ? this.s : (this[0] << 24) >> 24; };
|
|
|
|
// (public) return value as short (assumes DB>=16)
|
|
BigInteger.prototype.shortValue = function () { return (this.t == 0) ? this.s : (this[0] << 16) >> 16; };
|
|
|
|
// (public) 0 if this == 0, 1 if this > 0
|
|
BigInteger.prototype.signum = function () {
|
|
if (this.s < 0) return -1;
|
|
else if (this.t <= 0 || (this.t == 1 && this[0] <= 0)) return 0;
|
|
else return 1;
|
|
};
|
|
|
|
|
|
// (public) convert to bigendian byte array
|
|
BigInteger.prototype.toByteArray = function () {
|
|
var i = this.t, r = new Array();
|
|
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;
|
|
};
|
|
|
|
BigInteger.prototype.equals = function (a) { return (this.compareTo(a) == 0); };
|
|
BigInteger.prototype.min = function (a) { return (this.compareTo(a) < 0) ? this : a; };
|
|
BigInteger.prototype.max = function (a) { return (this.compareTo(a) > 0) ? this : a; };
|
|
|
|
// (public) this & a
|
|
function op_and(x, y) { return x & y; }
|
|
BigInteger.prototype.and = function (a) { var r = nbi(); this.bitwiseTo(a, op_and, r); return r; };
|
|
|
|
// (public) this | a
|
|
function op_or(x, y) { return x | y; }
|
|
BigInteger.prototype.or = function (a) { var r = nbi(); this.bitwiseTo(a, op_or, r); return r; };
|
|
|
|
// (public) this ^ a
|
|
function op_xor(x, y) { return x ^ y; }
|
|
BigInteger.prototype.xor = function (a) { var r = nbi(); this.bitwiseTo(a, op_xor, r); return r; };
|
|
|
|
// (public) this & ~a
|
|
function op_andnot(x, y) { return x & ~y; }
|
|
BigInteger.prototype.andNot = function (a) { var r = nbi(); this.bitwiseTo(a, op_andnot, r); return r; };
|
|
|
|
// (public) ~this
|
|
BigInteger.prototype.not = function () {
|
|
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
|
|
BigInteger.prototype.shiftLeft = function (n) {
|
|
var r = nbi();
|
|
if (n < 0) this.rShiftTo(-n, r); else this.lShiftTo(n, r);
|
|
return r;
|
|
};
|
|
|
|
// (public) this >> n
|
|
BigInteger.prototype.shiftRight = function (n) {
|
|
var r = nbi();
|
|
if (n < 0) this.lShiftTo(-n, r); else this.rShiftTo(n, r);
|
|
return r;
|
|
};
|
|
|
|
// (public) returns index of lowest 1-bit (or -1 if none)
|
|
BigInteger.prototype.getLowestSetBit = function () {
|
|
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;
|
|
};
|
|
|
|
// (public) return number of set bits
|
|
BigInteger.prototype.bitCount = function () {
|
|
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
|
|
BigInteger.prototype.testBit = function (n) {
|
|
var j = Math.floor(n / this.DB);
|
|
if (j >= this.t) return (this.s != 0);
|
|
return ((this[j] & (1 << (n % this.DB))) != 0);
|
|
};
|
|
|
|
// (public) this | (1<<n)
|
|
BigInteger.prototype.setBit = function (n) { return this.changeBit(n, op_or); };
|
|
// (public) this & ~(1<<n)
|
|
BigInteger.prototype.clearBit = function (n) { return this.changeBit(n, op_andnot); };
|
|
// (public) this ^ (1<<n)
|
|
BigInteger.prototype.flipBit = function (n) { return this.changeBit(n, op_xor); };
|
|
// (public) this + a
|
|
BigInteger.prototype.add = function (a) { var r = nbi(); this.addTo(a, r); return r; };
|
|
// (public) this - a
|
|
BigInteger.prototype.subtract = function (a) { var r = nbi(); this.subTo(a, r); return r; };
|
|
// (public) this * a
|
|
BigInteger.prototype.multiply = function (a) { var r = nbi(); this.multiplyTo(a, r); return r; };
|
|
// (public) this / a
|
|
BigInteger.prototype.divide = function (a) { var r = nbi(); this.divRemTo(a, r, null); return r; };
|
|
// (public) this % a
|
|
BigInteger.prototype.remainder = function (a) { var r = nbi(); this.divRemTo(a, null, r); return r; };
|
|
// (public) [this/a,this%a]
|
|
BigInteger.prototype.divideAndRemainder = function (a) {
|
|
var q = nbi(), r = nbi();
|
|
this.divRemTo(a, q, r);
|
|
return new Array(q, r);
|
|
};
|
|
|
|
// (public) this^e % m (HAC 14.85)
|
|
BigInteger.prototype.modPow = function (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 = new Array(), 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) 1/this % m (HAC 14.61)
|
|
BigInteger.prototype.modInverse = function (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;
|
|
};
|
|
|
|
|
|
// (public) this^e
|
|
BigInteger.prototype.pow = function (e) { return this.exp(e, new NullExp()); };
|
|
|
|
// (public) gcd(this,a) (HAC 14.54)
|
|
BigInteger.prototype.gcd = function (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;
|
|
};
|
|
|
|
// (public) test primality with certainty >= 1-.5^t
|
|
BigInteger.prototype.isProbablePrime = function (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);
|
|
};
|
|
|
|
|
|
// JSBN-specific extension
|
|
|
|
// (public) this^2
|
|
BigInteger.prototype.square = function () { var r = nbi(); this.squareTo(r); return r; };
|
|
|
|
|
|
// NOTE: BigInteger interfaces not implemented in jsbn:
|
|
// BigInteger(int signum, byte[] magnitude)
|
|
// double doubleValue()
|
|
// float floatValue()
|
|
// int hashCode()
|
|
// long longValue()
|
|
// static BigInteger valueOf(long val)
|
|
|
|
|
|
|
|
// Copyright Stephan Thomas (start) --- //
|
|
// https://raw.github.com/bitcoinjs/bitcoinjs-lib/07f9d55ccb6abd962efb6befdd37671f85ea4ff9/src/util.js
|
|
// BigInteger monkey patching
|
|
BigInteger.valueOf = nbv;
|
|
|
|
/**
|
|
* Returns a byte array representation of the big integer.
|
|
*
|
|
* This returns the absolute of the contained value in big endian
|
|
* form. A value of zero results in an empty array.
|
|
*/
|
|
BigInteger.prototype.toByteArrayUnsigned = function () {
|
|
var ba = this.abs().toByteArray();
|
|
if (ba.length) {
|
|
if (ba[0] == 0) {
|
|
ba = ba.slice(1);
|
|
}
|
|
return ba.map(function (v) {
|
|
return (v < 0) ? v + 256 : v;
|
|
});
|
|
} else {
|
|
// Empty array, nothing to do
|
|
return ba;
|
|
}
|
|
};
|
|
|
|
/**
|
|
* Turns a byte array into a big integer.
|
|
*
|
|
* This function will interpret a byte array as a big integer in big
|
|
* endian notation and ignore leading zeros.
|
|
*/
|
|
BigInteger.fromByteArrayUnsigned = function (ba) {
|
|
if (!ba.length) {
|
|
return ba.valueOf(0);
|
|
} else if (ba[0] & 0x80) {
|
|
// Prepend a zero so the BigInteger class doesn't mistake this
|
|
// for a negative integer.
|
|
return new BigInteger([0].concat(ba));
|
|
} else {
|
|
return new BigInteger(ba);
|
|
}
|
|
};
|
|
|
|
/**
|
|
* Converts big integer to signed byte representation.
|
|
*
|
|
* The format for this value uses a the most significant bit as a sign
|
|
* bit. If the most significant bit is already occupied by the
|
|
* absolute value, an extra byte is prepended and the sign bit is set
|
|
* there.
|
|
*
|
|
* Examples:
|
|
*
|
|
* 0 => 0x00
|
|
* 1 => 0x01
|
|
* -1 => 0x81
|
|
* 127 => 0x7f
|
|
* -127 => 0xff
|
|
* 128 => 0x0080
|
|
* -128 => 0x8080
|
|
* 255 => 0x00ff
|
|
* -255 => 0x80ff
|
|
* 16300 => 0x3fac
|
|
* -16300 => 0xbfac
|
|
* 62300 => 0x00f35c
|
|
* -62300 => 0x80f35c
|
|
*/
|
|
BigInteger.prototype.toByteArraySigned = function () {
|
|
var val = this.abs().toByteArrayUnsigned();
|
|
var neg = this.compareTo(BigInteger.ZERO) < 0;
|
|
|
|
if (neg) {
|
|
if (val[0] & 0x80) {
|
|
val.unshift(0x80);
|
|
} else {
|
|
val[0] |= 0x80;
|
|
}
|
|
} else {
|
|
if (val[0] & 0x80) {
|
|
val.unshift(0x00);
|
|
}
|
|
}
|
|
|
|
return val;
|
|
};
|
|
|
|
/**
|
|
* Parse a signed big integer byte representation.
|
|
*
|
|
* For details on the format please see BigInteger.toByteArraySigned.
|
|
*/
|
|
BigInteger.fromByteArraySigned = function (ba) {
|
|
// Check for negative value
|
|
if (ba[0] & 0x80) {
|
|
// Remove sign bit
|
|
ba[0] &= 0x7f;
|
|
|
|
return BigInteger.fromByteArrayUnsigned(ba).negate();
|
|
} else {
|
|
return BigInteger.fromByteArrayUnsigned(ba);
|
|
}
|
|
};
|
|
// Copyright Stephan Thomas (end) --- //
|
|
|
|
|
|
|
|
|
|
// ****** REDUCTION ******* //
|
|
|
|
// Modular reduction using "classic" algorithm
|
|
var Classic = window.Classic = function Classic(m) { this.m = m; }
|
|
Classic.prototype.convert = function (x) {
|
|
if (x.s < 0 || x.compareTo(this.m) >= 0) return x.mod(this.m);
|
|
else return x;
|
|
};
|
|
Classic.prototype.revert = function (x) { return x; };
|
|
Classic.prototype.reduce = function (x) { x.divRemTo(this.m, null, x); };
|
|
Classic.prototype.mulTo = function (x, y, r) { x.multiplyTo(y, r); this.reduce(r); };
|
|
Classic.prototype.sqrTo = function (x, r) { x.squareTo(r); this.reduce(r); };
|
|
|
|
|
|
|
|
|
|
|
|
// Montgomery reduction
|
|
var Montgomery = window.Montgomery = 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
|
|
Montgomery.prototype.convert = function (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
|
|
Montgomery.prototype.revert = function (x) {
|
|
var r = nbi();
|
|
x.copyTo(r);
|
|
this.reduce(r);
|
|
return r;
|
|
};
|
|
// x = x/R mod m (HAC 14.32)
|
|
Montgomery.prototype.reduce = function (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 = "xy/R mod m"; x,y != r
|
|
Montgomery.prototype.mulTo = function (x, y, r) { x.multiplyTo(y, r); this.reduce(r); };
|
|
// r = "x^2/R mod m"; x != r
|
|
Montgomery.prototype.sqrTo = function (x, r) { x.squareTo(r); this.reduce(r); };
|
|
|
|
|
|
|
|
|
|
|
|
// A "null" reducer
|
|
var NullExp = window.NullExp = function NullExp() { }
|
|
NullExp.prototype.convert = function (x) { return x; };
|
|
NullExp.prototype.revert = function (x) { return x; };
|
|
NullExp.prototype.mulTo = function (x, y, r) { x.multiplyTo(y, r); };
|
|
NullExp.prototype.sqrTo = function (x, r) { x.squareTo(r); };
|
|
|
|
|
|
|
|
|
|
|
|
// Barrett modular reduction
|
|
var Barrett = window.Barrett = 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;
|
|
}
|
|
Barrett.prototype.convert = function (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; }
|
|
};
|
|
Barrett.prototype.revert = function (x) { return x; };
|
|
// x = x mod m (HAC 14.42)
|
|
Barrett.prototype.reduce = function (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*y mod m; x,y != r
|
|
Barrett.prototype.mulTo = function (x, y, r) { x.multiplyTo(y, r); this.reduce(r); };
|
|
// r = x^2 mod m; x != r
|
|
Barrett.prototype.sqrTo = function (x, r) { x.squareTo(r); this.reduce(r); };
|
|
|
|
})();
|