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1940 lines
53 KiB
1940 lines
53 KiB
(function () { |
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// Copyright (c) 2005 Tom Wu |
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// All Rights Reserved. |
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// See "LICENSE" for details. |
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|
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// Basic JavaScript BN library - subset useful for RSA encryption. |
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|
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// Bits per digit |
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var dbits; |
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|
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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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|
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// (public) Constructor |
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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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|
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// return new, unset BigInteger |
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function nbi() { |
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return new BigInteger(null); |
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} |
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|
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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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|
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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, |
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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, |
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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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var inBrowser = typeof navigator !== 'undefined'; |
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if (inBrowser && 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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} else if (inBrowser && j_lm && navigator.appName != 'Netscape') { |
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BigInteger.prototype.am = am1; |
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dbits = 26; |
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} else { |
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// 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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|
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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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|
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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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|
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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) { |
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return BI_RM.charAt(n); |
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} |
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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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|
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// (protected) copy this to r |
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function bnpCopyTo(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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function bnpFromInt(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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// return bigint initialized to value |
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function nbv(i) { |
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var r = nbi(); |
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r.fromInt(i); |
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return r; |
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} |
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// (protected) set from string and radix |
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function bnpFromString(s, b) { |
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// Auto-detect string notations |
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if (!b && s.length >= 2 && s[0] === '0') { |
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var isDetected = true; |
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switch (s[1]) { |
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case 'x': // Hexadecimal notation |
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b = 16; |
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break; |
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case 'b': // Binary notation |
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b = 2; |
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break; |
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case 'o': // Octal notation |
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b = 8; |
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break; |
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default: |
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isDetected = false; |
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} |
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// Remove the notation string if any has been detected |
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if (isDetected) { |
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s = s.substr(2); |
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} |
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} |
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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; |
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// 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 { |
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this.fromRadix(s, b); |
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return; |
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} |
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this.t = 0; |
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this.s = 0; |
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var i = s.length, |
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mi = false, |
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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) 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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} else 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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function bnpClamp() { |
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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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// (public) return string representation in given radix |
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function bnToString(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, |
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d, |
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m = false, |
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r = '', |
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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) { |
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m = true; |
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r = int2char(d); |
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} |
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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); |
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} else { |
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d = (this[i] >> (p -= k)) & km; |
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if (p <= 0) { |
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p += this.DB; |
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--i; |
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} |
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} |
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if (d > 0) m = true; |
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if (m) r += int2char(d); |
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} |
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} |
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return m ? r : '0'; |
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} |
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// (public) -this |
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function bnNegate() { |
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var r = nbi(); |
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BigInteger.ZERO.subTo(this, r); |
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return r; |
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} |
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// (public) |this| |
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function bnAbs() { |
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return this.s < 0 ? this.negate() : this; |
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} |
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// (public) return + if this > a, - if this < a, 0 if equal |
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function bnCompareTo(a) { |
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var r = this.s - a.s; |
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if (r != 0) return r; |
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var i = this.t; |
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r = i - a.t; |
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if (r != 0) return this.s < 0 ? -r : r; |
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while (--i >= 0) if ((r = this[i] - a[i]) != 0) return r; |
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return 0; |
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} |
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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, |
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t; |
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if ((t = x >>> 16) != 0) { |
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x = t; |
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r += 16; |
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} |
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if ((t = x >> 8) != 0) { |
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x = t; |
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r += 8; |
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} |
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if ((t = x >> 4) != 0) { |
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x = t; |
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r += 4; |
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} |
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if ((t = x >> 2) != 0) { |
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x = t; |
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r += 2; |
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} |
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if ((t = x >> 1) != 0) { |
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x = t; |
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r += 1; |
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} |
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return r; |
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} |
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// (public) return the number of bits in "this" |
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function bnBitLength() { |
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if (this.t <= 0) return 0; |
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return ( |
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this.DB * (this.t - 1) + nbits(this[this.t - 1] ^ (this.s & this.DM)) |
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); |
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} |
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// (protected) r = this << n*DB |
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function bnpDLShiftTo(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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function bnpDRShiftTo(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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function bnpLShiftTo(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), |
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c = (this.s << bs) & this.DM, |
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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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function bnpRShiftTo(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) { |
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r.t = 0; |
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return; |
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} |
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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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function bnpSubTo(a, r) { |
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var i = 0, |
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c = 0, |
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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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} 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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function bnpMultiplyTo(a, r) { |
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var x = this.abs(), |
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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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function bnpSquareTo(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 ( |
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(r[i + x.t] += x.am(i + 1, 2 * x[i], r, 2 * i + 1, c, x.t - i - 1)) >= |
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x.DV |
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) { |
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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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|
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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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function bnpDivRemTo(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(), |
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ts = this.s, |
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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) { |
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pm.lShiftTo(nsh, y); |
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pt.lShiftTo(nsh, r); |
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} else { |
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pm.copyTo(y); |
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pt.copyTo(r); |
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} |
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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, |
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d2 = (1 << this.F1) / yt, |
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e = 1 << this.F2; |
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var i = r.t, |
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j = i - ys, |
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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 = |
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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) { |
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// 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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|
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// (public) this mod a |
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function bnMod(a) { |
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var r = nbi(); |
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this.abs().divRemTo(a, null, r); |
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if (this.s < 0 && r.compareTo(BigInteger.ZERO) > 0) a.subTo(r, r); |
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return r; |
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} |
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|
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// Modular reduction using "classic" algorithm |
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function Classic(m) { |
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this.m = m; |
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} |
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function cConvert(x) { |
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if (x.s < 0 || x.compareTo(this.m) >= 0) return x.mod(this.m); |
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else return x; |
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} |
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function cRevert(x) { |
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return x; |
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} |
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function cReduce(x) { |
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x.divRemTo(this.m, null, x); |
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} |
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function cMulTo(x, y, r) { |
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x.multiplyTo(y, r); |
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this.reduce(r); |
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} |
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function cSqrTo(x, r) { |
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x.squareTo(r); |
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this.reduce(r); |
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} |
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|
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Classic.prototype.convert = cConvert; |
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Classic.prototype.revert = cRevert; |
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Classic.prototype.reduce = cReduce; |
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Classic.prototype.mulTo = cMulTo; |
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Classic.prototype.sqrTo = cSqrTo; |
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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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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); |
|
} |
|
|
|
Montgomery.prototype.convert = montConvert; |
|
Montgomery.prototype.revert = montRevert; |
|
Montgomery.prototype.reduce = montReduce; |
|
Montgomery.prototype.mulTo = montMulTo; |
|
Montgomery.prototype.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); |
|
} |
|
|
|
// protected |
|
BigInteger.prototype.copyTo = bnpCopyTo; |
|
BigInteger.prototype.fromInt = bnpFromInt; |
|
BigInteger.prototype.fromString = bnpFromString; |
|
BigInteger.prototype.clamp = bnpClamp; |
|
BigInteger.prototype.dlShiftTo = bnpDLShiftTo; |
|
BigInteger.prototype.drShiftTo = bnpDRShiftTo; |
|
BigInteger.prototype.lShiftTo = bnpLShiftTo; |
|
BigInteger.prototype.rShiftTo = bnpRShiftTo; |
|
BigInteger.prototype.subTo = bnpSubTo; |
|
BigInteger.prototype.multiplyTo = bnpMultiplyTo; |
|
BigInteger.prototype.squareTo = bnpSquareTo; |
|
BigInteger.prototype.divRemTo = bnpDivRemTo; |
|
BigInteger.prototype.invDigit = bnpInvDigit; |
|
BigInteger.prototype.isEven = bnpIsEven; |
|
BigInteger.prototype.exp = bnpExp; |
|
|
|
// public |
|
BigInteger.prototype.toString = bnToString; |
|
BigInteger.prototype.negate = bnNegate; |
|
BigInteger.prototype.abs = bnAbs; |
|
BigInteger.prototype.compareTo = bnCompareTo; |
|
BigInteger.prototype.bitLength = bnBitLength; |
|
BigInteger.prototype.mod = bnMod; |
|
BigInteger.prototype.modPowInt = bnModPowInt; |
|
|
|
// "constants" |
|
BigInteger.ZERO = nbv(0); |
|
BigInteger.ONE = nbv(1); |
|
BigInteger.valueOf = nbv; |
|
|
|
// 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 |
|
|
|
// (public) |
|
function bnClone() { |
|
var r = nbi(); |
|
this.copyTo(r); |
|
return r; |
|
} |
|
|
|
// (public) return value as integer |
|
function bnIntValue() { |
|
if (this.s < 0) { |
|
if (this.t == 1) return this[0] - this.DV; |
|
else if (this.t == 0) return -1; |
|
} else if (this.t == 1) return this[0]; |
|
else if (this.t == 0) return 0; |
|
// assumes 16 < DB < 32 |
|
return ((this[1] & ((1 << (32 - this.DB)) - 1)) << this.DB) | this[0]; |
|
} |
|
|
|
// (public) return value as byte |
|
function bnByteValue() { |
|
return this.t == 0 ? this.s : (this[0] << 24) >> 24; |
|
} |
|
|
|
// (public) return value as short (assumes DB>=16) |
|
function bnShortValue() { |
|
return this.t == 0 ? this.s : (this[0] << 16) >> 16; |
|
} |
|
|
|
// (protected) return x s.t. r^x < DV |
|
function bnpChunkSize(r) { |
|
return Math.floor((Math.LN2 * this.DB) / Math.log(r)); |
|
} |
|
|
|
// (public) 0 if this == 0, 1 if this > 0 |
|
function bnSigNum() { |
|
if (this.s < 0) return -1; |
|
else if (this.t <= 0 || (this.t == 1 && this[0] <= 0)) return 0; |
|
else return 1; |
|
} |
|
|
|
// (protected) convert to radix string |
|
function bnpToRadix(b) { |
|
if (b == null) b = 10; |
|
if (this.signum() == 0 || b < 2 || b > 36) return '0'; |
|
var cs = this.chunkSize(b); |
|
var a = Math.pow(b, cs); |
|
var d = nbv(a), |
|
y = nbi(), |
|
z = nbi(), |
|
r = ''; |
|
this.divRemTo(d, y, z); |
|
while (y.signum() > 0) { |
|
r = (a + z.intValue()).toString(b).substr(1) + r; |
|
y.divRemTo(d, y, z); |
|
} |
|
return z.intValue().toString(b) + r; |
|
} |
|
|
|
// (protected) convert from radix string |
|
function bnpFromRadix(s, b) { |
|
this.fromInt(0); |
|
if (b == null) b = 10; |
|
var cs = this.chunkSize(b); |
|
var d = Math.pow(b, cs), |
|
mi = false, |
|
j = 0, |
|
w = 0; |
|
for (var i = 0; i < s.length; ++i) { |
|
var x = intAt(s, i); |
|
if (x < 0) { |
|
if (s.charAt(i) == '-' && this.signum() == 0) mi = true; |
|
continue; |
|
} |
|
w = b * w + x; |
|
if (++j >= cs) { |
|
this.dMultiply(d); |
|
this.dAddOffset(w, 0); |
|
j = 0; |
|
w = 0; |
|
} |
|
} |
|
if (j > 0) { |
|
this.dMultiply(Math.pow(b, j)); |
|
this.dAddOffset(w, 0); |
|
} |
|
if (mi) BigInteger.ZERO.subTo(this, this); |
|
} |
|
|
|
// (protected) alternate constructor |
|
function bnpFromNumber(a, b, c) { |
|
if ('number' == typeof b) { |
|
// new BigInteger(int,int,RNG) |
|
if (a < 2) this.fromInt(1); |
|
else { |
|
this.fromNumber(a, c); |
|
if (!this.testBit(a - 1)) |
|
// force MSB set |
|
this.bitwiseTo(BigInteger.ONE.shiftLeft(a - 1), op_or, this); |
|
if (this.isEven()) this.dAddOffset(1, 0); // force odd |
|
while (!this.isProbablePrime(b)) { |
|
this.dAddOffset(2, 0); |
|
if (this.bitLength() > a) |
|
this.subTo(BigInteger.ONE.shiftLeft(a - 1), this); |
|
} |
|
} |
|
} else { |
|
// new BigInteger(int,RNG) |
|
var x = 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); |
|
} |
|
} |
|
|
|
// (public) convert to bigendian byte array |
|
function bnToByteArray() { |
|
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; |
|
} |
|
|
|
function bnEquals(a) { |
|
return this.compareTo(a) == 0; |
|
} |
|
function bnMin(a) { |
|
return this.compareTo(a) < 0 ? this : a; |
|
} |
|
function bnMax(a) { |
|
return this.compareTo(a) > 0 ? this : a; |
|
} |
|
|
|
// (protected) r = this op a (bitwise) |
|
function bnpBitwiseTo(a, op, r) { |
|
var i, |
|
f, |
|
m = Math.min(a.t, this.t); |
|
for (i = 0; i < m; ++i) r[i] = op(this[i], a[i]); |
|
if (a.t < this.t) { |
|
f = a.s & this.DM; |
|
for (i = m; i < this.t; ++i) r[i] = op(this[i], f); |
|
r.t = this.t; |
|
} else { |
|
f = this.s & this.DM; |
|
for (i = m; i < a.t; ++i) r[i] = op(f, a[i]); |
|
r.t = a.t; |
|
} |
|
r.s = op(this.s, a.s); |
|
r.clamp(); |
|
} |
|
|
|
// (public) this & a |
|
function op_and(x, y) { |
|
return x & y; |
|
} |
|
function bnAnd(a) { |
|
var r = nbi(); |
|
this.bitwiseTo(a, op_and, r); |
|
return r; |
|
} |
|
|
|
// (public) this | a |
|
function op_or(x, y) { |
|
return x | y; |
|
} |
|
function bnOr(a) { |
|
var r = nbi(); |
|
this.bitwiseTo(a, op_or, r); |
|
return r; |
|
} |
|
|
|
// (public) this ^ a |
|
function op_xor(x, y) { |
|
return x ^ y; |
|
} |
|
function bnXor(a) { |
|
var r = nbi(); |
|
this.bitwiseTo(a, op_xor, r); |
|
return r; |
|
} |
|
|
|
// (public) this & ~a |
|
function op_andnot(x, y) { |
|
return x & ~y; |
|
} |
|
function bnAndNot(a) { |
|
var r = nbi(); |
|
this.bitwiseTo(a, op_andnot, r); |
|
return r; |
|
} |
|
|
|
// (public) ~this |
|
function bnNot() { |
|
var r = nbi(); |
|
for (var i = 0; i < this.t; ++i) r[i] = this.DM & ~this[i]; |
|
r.t = this.t; |
|
r.s = ~this.s; |
|
return r; |
|
} |
|
|
|
// (public) this << n |
|
function bnShiftLeft(n) { |
|
var r = nbi(); |
|
if (n < 0) this.rShiftTo(-n, r); |
|
else this.lShiftTo(n, r); |
|
return r; |
|
} |
|
|
|
// (public) this >> n |
|
function bnShiftRight(n) { |
|
var r = nbi(); |
|
if (n < 0) this.lShiftTo(-n, r); |
|
else this.rShiftTo(n, r); |
|
return r; |
|
} |
|
|
|
// return index of lowest 1-bit in x, x < 2^31 |
|
function lbit(x) { |
|
if (x == 0) return -1; |
|
var r = 0; |
|
if ((x & 0xffff) == 0) { |
|
x >>= 16; |
|
r += 16; |
|
} |
|
if ((x & 0xff) == 0) { |
|
x >>= 8; |
|
r += 8; |
|
} |
|
if ((x & 0xf) == 0) { |
|
x >>= 4; |
|
r += 4; |
|
} |
|
if ((x & 3) == 0) { |
|
x >>= 2; |
|
r += 2; |
|
} |
|
if ((x & 1) == 0) ++r; |
|
return r; |
|
} |
|
|
|
// (public) returns index of lowest 1-bit (or -1 if none) |
|
function bnGetLowestSetBit() { |
|
for (var i = 0; i < this.t; ++i) |
|
if (this[i] != 0) return i * this.DB + lbit(this[i]); |
|
if (this.s < 0) return this.t * this.DB; |
|
return -1; |
|
} |
|
|
|
// return number of 1 bits in x |
|
function cbit(x) { |
|
var r = 0; |
|
while (x != 0) { |
|
x &= x - 1; |
|
++r; |
|
} |
|
return r; |
|
} |
|
|
|
// (public) return number of set bits |
|
function bnBitCount() { |
|
var r = 0, |
|
x = this.s & this.DM; |
|
for (var i = 0; i < this.t; ++i) r += cbit(this[i] ^ x); |
|
return r; |
|
} |
|
|
|
// (public) true iff nth bit is set |
|
function bnTestBit(n) { |
|
var j = Math.floor(n / this.DB); |
|
if (j >= this.t) return this.s != 0; |
|
return (this[j] & (1 << n % this.DB)) != 0; |
|
} |
|
|
|
// (protected) this op (1<<n) |
|
function bnpChangeBit(n, op) { |
|
var r = BigInteger.ONE.shiftLeft(n); |
|
this.bitwiseTo(r, op, r); |
|
return r; |
|
} |
|
|
|
// (public) this | (1<<n) |
|
function bnSetBit(n) { |
|
return this.changeBit(n, op_or); |
|
} |
|
|
|
// (public) this & ~(1<<n) |
|
function bnClearBit(n) { |
|
return this.changeBit(n, op_andnot); |
|
} |
|
|
|
// (public) this ^ (1<<n) |
|
function bnFlipBit(n) { |
|
return this.changeBit(n, op_xor); |
|
} |
|
|
|
// (protected) r = this + a |
|
function bnpAddTo(a, r) { |
|
var i = 0, |
|
c = 0, |
|
m = Math.min(a.t, this.t); |
|
while (i < m) { |
|
c += this[i] + a[i]; |
|
r[i++] = c & this.DM; |
|
c >>= this.DB; |
|
} |
|
if (a.t < this.t) { |
|
c += a.s; |
|
while (i < this.t) { |
|
c += this[i]; |
|
r[i++] = c & this.DM; |
|
c >>= this.DB; |
|
} |
|
c += this.s; |
|
} else { |
|
c += this.s; |
|
while (i < a.t) { |
|
c += a[i]; |
|
r[i++] = c & this.DM; |
|
c >>= this.DB; |
|
} |
|
c += a.s; |
|
} |
|
r.s = c < 0 ? -1 : 0; |
|
if (c > 0) r[i++] = c; |
|
else if (c < -1) r[i++] = this.DV + c; |
|
r.t = i; |
|
r.clamp(); |
|
} |
|
|
|
// (public) this + a |
|
function bnAdd(a) { |
|
var r = nbi(); |
|
this.addTo(a, r); |
|
return r; |
|
} |
|
|
|
// (public) this - a |
|
function bnSubtract(a) { |
|
var r = nbi(); |
|
this.subTo(a, r); |
|
return r; |
|
} |
|
|
|
// (public) this * a |
|
function bnMultiply(a) { |
|
var r = nbi(); |
|
this.multiplyTo(a, r); |
|
return r; |
|
} |
|
|
|
// (public) this^2 |
|
function bnSquare() { |
|
var r = nbi(); |
|
this.squareTo(r); |
|
return r; |
|
} |
|
|
|
// (public) this / a |
|
function bnDivide(a) { |
|
var r = nbi(); |
|
this.divRemTo(a, r, null); |
|
return r; |
|
} |
|
|
|
// (public) this % a |
|
function bnRemainder(a) { |
|
var r = nbi(); |
|
this.divRemTo(a, null, r); |
|
return r; |
|
} |
|
|
|
// (public) [this/a,this%a] |
|
function bnDivideAndRemainder(a) { |
|
var q = nbi(), |
|
r = nbi(); |
|
this.divRemTo(a, q, r); |
|
return new Array(q, r); |
|
} |
|
|
|
// (protected) this *= n, this >= 0, 1 < n < DV |
|
function bnpDMultiply(n) { |
|
this[this.t] = this.am(0, n - 1, this, 0, 0, this.t); |
|
++this.t; |
|
this.clamp(); |
|
} |
|
|
|
// (protected) this += n << w words, this >= 0 |
|
function bnpDAddOffset(n, w) { |
|
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]; |
|
} |
|
} |
|
|
|
// A "null" reducer |
|
function NullExp() { } |
|
function nNop(x) { |
|
return x; |
|
} |
|
function nMulTo(x, y, r) { |
|
x.multiplyTo(y, r); |
|
} |
|
function nSqrTo(x, r) { |
|
x.squareTo(r); |
|
} |
|
|
|
NullExp.prototype.convert = nNop; |
|
NullExp.prototype.revert = nNop; |
|
NullExp.prototype.mulTo = nMulTo; |
|
NullExp.prototype.sqrTo = nSqrTo; |
|
|
|
// (public) this^e |
|
function bnPow(e) { |
|
return this.exp(e, new NullExp()); |
|
} |
|
|
|
// (protected) r = lower n words of "this * a", a.t <= n |
|
// "this" should be the larger one if appropriate. |
|
function bnpMultiplyLowerTo(a, n, r) { |
|
var i = Math.min(this.t + a.t, n); |
|
r.s = 0; // assumes a,this >= 0 |
|
r.t = i; |
|
while (i > 0) r[--i] = 0; |
|
var j; |
|
for (j = r.t - this.t; i < j; ++i) |
|
r[i + this.t] = this.am(0, a[i], r, i, 0, this.t); |
|
for (j = Math.min(a.t, n); i < j; ++i) this.am(0, a[i], r, i, 0, n - i); |
|
r.clamp(); |
|
} |
|
|
|
// (protected) r = "this * a" without lower n words, n > 0 |
|
// "this" should be the larger one if appropriate. |
|
function bnpMultiplyUpperTo(a, n, r) { |
|
--n; |
|
var i = (r.t = this.t + a.t - n); |
|
r.s = 0; // assumes a,this >= 0 |
|
while (--i >= 0) r[i] = 0; |
|
for (i = Math.max(n - this.t, 0); i < a.t; ++i) |
|
r[this.t + i - n] = this.am(n - i, a[i], r, 0, 0, this.t + i - n); |
|
r.clamp(); |
|
r.drShiftTo(1, r); |
|
} |
|
|
|
// Barrett modular reduction |
|
function Barrett(m) { |
|
// setup Barrett |
|
this.r2 = nbi(); |
|
this.q3 = nbi(); |
|
BigInteger.ONE.dlShiftTo(2 * m.t, this.r2); |
|
this.mu = this.r2.divide(m); |
|
this.m = m; |
|
} |
|
|
|
function barrettConvert(x) { |
|
if (x.s < 0 || x.t > 2 * this.m.t) return x.mod(this.m); |
|
else if (x.compareTo(this.m) < 0) return x; |
|
else { |
|
var r = nbi(); |
|
x.copyTo(r); |
|
this.reduce(r); |
|
return r; |
|
} |
|
} |
|
|
|
function barrettRevert(x) { |
|
return x; |
|
} |
|
|
|
// x = x mod m (HAC 14.42) |
|
function barrettReduce(x) { |
|
x.drShiftTo(this.m.t - 1, this.r2); |
|
if (x.t > this.m.t + 1) { |
|
x.t = this.m.t + 1; |
|
x.clamp(); |
|
} |
|
this.mu.multiplyUpperTo(this.r2, this.m.t + 1, this.q3); |
|
this.m.multiplyLowerTo(this.q3, this.m.t + 1, this.r2); |
|
while (x.compareTo(this.r2) < 0) x.dAddOffset(1, this.m.t + 1); |
|
x.subTo(this.r2, x); |
|
while (x.compareTo(this.m) >= 0) x.subTo(this.m, x); |
|
} |
|
|
|
// r = x^2 mod m; x != r |
|
function barrettSqrTo(x, r) { |
|
x.squareTo(r); |
|
this.reduce(r); |
|
} |
|
|
|
// r = x*y mod m; x,y != r |
|
function barrettMulTo(x, y, r) { |
|
x.multiplyTo(y, r); |
|
this.reduce(r); |
|
} |
|
|
|
Barrett.prototype.convert = barrettConvert; |
|
Barrett.prototype.revert = barrettRevert; |
|
Barrett.prototype.reduce = barrettReduce; |
|
Barrett.prototype.mulTo = barrettMulTo; |
|
Barrett.prototype.sqrTo = barrettSqrTo; |
|
|
|
// (public) this^e % m (HAC 14.85) |
|
function bnModPow(e, m) { |
|
var i = e.bitLength(), |
|
k, |
|
r = nbv(1), |
|
z; |
|
if (i <= 0) return r; |
|
else if (i < 18) k = 1; |
|
else if (i < 48) k = 3; |
|
else if (i < 144) k = 4; |
|
else if (i < 768) k = 5; |
|
else k = 6; |
|
if (i < 8) z = new Classic(m); |
|
else if (m.isEven()) z = new Barrett(m); |
|
else z = new Montgomery(m); |
|
|
|
// precomputation |
|
var g = 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) gcd(this,a) (HAC 14.54) |
|
function bnGCD(a) { |
|
var x = this.s < 0 ? this.negate() : this.clone(); |
|
var y = a.s < 0 ? a.negate() : a.clone(); |
|
if (x.compareTo(y) < 0) { |
|
var t = x; |
|
x = y; |
|
y = t; |
|
} |
|
var i = x.getLowestSetBit(), |
|
g = y.getLowestSetBit(); |
|
if (g < 0) return x; |
|
if (i < g) g = i; |
|
if (g > 0) { |
|
x.rShiftTo(g, x); |
|
y.rShiftTo(g, y); |
|
} |
|
while (x.signum() > 0) { |
|
if ((i = x.getLowestSetBit()) > 0) x.rShiftTo(i, x); |
|
if ((i = y.getLowestSetBit()) > 0) y.rShiftTo(i, y); |
|
if (x.compareTo(y) >= 0) { |
|
x.subTo(y, x); |
|
x.rShiftTo(1, x); |
|
} else { |
|
y.subTo(x, y); |
|
y.rShiftTo(1, y); |
|
} |
|
} |
|
if (g > 0) y.lShiftTo(g, y); |
|
return y; |
|
} |
|
|
|
// (protected) this % n, n < 2^26 |
|
function bnpModInt(n) { |
|
if (n <= 0) return 0; |
|
var d = this.DV % n, |
|
r = this.s < 0 ? n - 1 : 0; |
|
if (this.t > 0) |
|
if (d == 0) r = this[0] % n; |
|
else for (var i = this.t - 1; i >= 0; --i) r = (d * r + this[i]) % n; |
|
return r; |
|
} |
|
|
|
// (public) 1/this % m (HAC 14.61) |
|
function bnModInverse(m) { |
|
var ac = m.isEven(); |
|
if ((this.isEven() && ac) || m.signum() == 0) return BigInteger.ZERO; |
|
var u = m.clone(), |
|
v = this.clone(); |
|
var a = nbv(1), |
|
b = nbv(0), |
|
c = nbv(0), |
|
d = nbv(1); |
|
while (u.signum() != 0) { |
|
while (u.isEven()) { |
|
u.rShiftTo(1, u); |
|
if (ac) { |
|
if (!a.isEven() || !b.isEven()) { |
|
a.addTo(this, a); |
|
b.subTo(m, b); |
|
} |
|
a.rShiftTo(1, a); |
|
} else if (!b.isEven()) b.subTo(m, b); |
|
b.rShiftTo(1, b); |
|
} |
|
while (v.isEven()) { |
|
v.rShiftTo(1, v); |
|
if (ac) { |
|
if (!c.isEven() || !d.isEven()) { |
|
c.addTo(this, c); |
|
d.subTo(m, d); |
|
} |
|
c.rShiftTo(1, c); |
|
} else if (!d.isEven()) d.subTo(m, d); |
|
d.rShiftTo(1, d); |
|
} |
|
if (u.compareTo(v) >= 0) { |
|
u.subTo(v, u); |
|
if (ac) a.subTo(c, a); |
|
b.subTo(d, b); |
|
} else { |
|
v.subTo(u, v); |
|
if (ac) c.subTo(a, c); |
|
d.subTo(b, d); |
|
} |
|
} |
|
if (v.compareTo(BigInteger.ONE) != 0) return BigInteger.ZERO; |
|
if (d.compareTo(m) >= 0) return d.subtract(m); |
|
if (d.signum() < 0) d.addTo(m, d); |
|
else return d; |
|
if (d.signum() < 0) return d.add(m); |
|
else return d; |
|
} |
|
|
|
var lowprimes = [ |
|
2, |
|
3, |
|
5, |
|
7, |
|
11, |
|
13, |
|
17, |
|
19, |
|
23, |
|
29, |
|
31, |
|
37, |
|
41, |
|
43, |
|
47, |
|
53, |
|
59, |
|
61, |
|
67, |
|
71, |
|
73, |
|
79, |
|
83, |
|
89, |
|
97, |
|
101, |
|
103, |
|
107, |
|
109, |
|
113, |
|
127, |
|
131, |
|
137, |
|
139, |
|
149, |
|
151, |
|
157, |
|
163, |
|
167, |
|
173, |
|
179, |
|
181, |
|
191, |
|
193, |
|
197, |
|
199, |
|
211, |
|
223, |
|
227, |
|
229, |
|
233, |
|
239, |
|
241, |
|
251, |
|
257, |
|
263, |
|
269, |
|
271, |
|
277, |
|
281, |
|
283, |
|
293, |
|
307, |
|
311, |
|
313, |
|
317, |
|
331, |
|
337, |
|
347, |
|
349, |
|
353, |
|
359, |
|
367, |
|
373, |
|
379, |
|
383, |
|
389, |
|
397, |
|
401, |
|
409, |
|
419, |
|
421, |
|
431, |
|
433, |
|
439, |
|
443, |
|
449, |
|
457, |
|
461, |
|
463, |
|
467, |
|
479, |
|
487, |
|
491, |
|
499, |
|
503, |
|
509, |
|
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]; |
|
|
|
// (public) test primality with certainty >= 1-.5^t |
|
function bnIsProbablePrime(t) { |
|
var i, |
|
x = this.abs(); |
|
if (x.t == 1 && x[0] <= lowprimes[lowprimes.length - 1]) { |
|
for (i = 0; i < lowprimes.length; ++i) |
|
if (x[0] == lowprimes[i]) return true; |
|
return false; |
|
} |
|
if (x.isEven()) return false; |
|
i = 1; |
|
while (i < lowprimes.length) { |
|
var m = lowprimes[i], |
|
j = i + 1; |
|
while (j < lowprimes.length && m < lplim) m *= lowprimes[j++]; |
|
m = x.modInt(m); |
|
while (i < j) if (m % lowprimes[i++] == 0) return false; |
|
} |
|
return x.millerRabin(t); |
|
} |
|
|
|
// (protected) true if probably prime (HAC 4.24, Miller-Rabin) |
|
function bnpMillerRabin(t) { |
|
var n1 = this.subtract(BigInteger.ONE); |
|
var k = n1.getLowestSetBit(); |
|
if (k <= 0) return false; |
|
var r = n1.shiftRight(k); |
|
t = (t + 1) >> 1; |
|
if (t > lowprimes.length) t = lowprimes.length; |
|
var a = nbi(); |
|
for (var i = 0; i < t; ++i) { |
|
//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; |
|
} |
|
|
|
// protected |
|
BigInteger.prototype.chunkSize = bnpChunkSize; |
|
BigInteger.prototype.toRadix = bnpToRadix; |
|
BigInteger.prototype.fromRadix = bnpFromRadix; |
|
BigInteger.prototype.fromNumber = bnpFromNumber; |
|
BigInteger.prototype.bitwiseTo = bnpBitwiseTo; |
|
BigInteger.prototype.changeBit = bnpChangeBit; |
|
BigInteger.prototype.addTo = bnpAddTo; |
|
BigInteger.prototype.dMultiply = bnpDMultiply; |
|
BigInteger.prototype.dAddOffset = bnpDAddOffset; |
|
BigInteger.prototype.multiplyLowerTo = bnpMultiplyLowerTo; |
|
BigInteger.prototype.multiplyUpperTo = bnpMultiplyUpperTo; |
|
BigInteger.prototype.modInt = bnpModInt; |
|
BigInteger.prototype.millerRabin = bnpMillerRabin; |
|
|
|
// public |
|
BigInteger.prototype.clone = bnClone; |
|
BigInteger.prototype.intValue = bnIntValue; |
|
BigInteger.prototype.byteValue = bnByteValue; |
|
BigInteger.prototype.shortValue = bnShortValue; |
|
BigInteger.prototype.signum = bnSigNum; |
|
BigInteger.prototype.toByteArray = bnToByteArray; |
|
BigInteger.prototype.equals = bnEquals; |
|
BigInteger.prototype.min = bnMin; |
|
BigInteger.prototype.max = bnMax; |
|
BigInteger.prototype.and = bnAnd; |
|
BigInteger.prototype.or = bnOr; |
|
BigInteger.prototype.xor = bnXor; |
|
BigInteger.prototype.andNot = bnAndNot; |
|
BigInteger.prototype.not = bnNot; |
|
BigInteger.prototype.shiftLeft = bnShiftLeft; |
|
BigInteger.prototype.shiftRight = bnShiftRight; |
|
BigInteger.prototype.getLowestSetBit = bnGetLowestSetBit; |
|
BigInteger.prototype.bitCount = bnBitCount; |
|
BigInteger.prototype.testBit = bnTestBit; |
|
BigInteger.prototype.setBit = bnSetBit; |
|
BigInteger.prototype.clearBit = bnClearBit; |
|
BigInteger.prototype.flipBit = bnFlipBit; |
|
BigInteger.prototype.add = bnAdd; |
|
BigInteger.prototype.subtract = bnSubtract; |
|
BigInteger.prototype.multiply = bnMultiply; |
|
BigInteger.prototype.divide = bnDivide; |
|
BigInteger.prototype.remainder = bnRemainder; |
|
BigInteger.prototype.divideAndRemainder = bnDivideAndRemainder; |
|
BigInteger.prototype.modPow = bnModPow; |
|
BigInteger.prototype.modInverse = bnModInverse; |
|
BigInteger.prototype.pow = bnPow; |
|
BigInteger.prototype.gcd = bnGCD; |
|
BigInteger.prototype.isProbablePrime = bnIsProbablePrime; |
|
|
|
// JSBN-specific extension |
|
BigInteger.prototype.square = bnSquare; |
|
|
|
// Expose the Barrett function |
|
BigInteger.prototype.Barrett = Barrett; |
|
|
|
// BigInteger interfaces not implemented in jsbn: |
|
|
|
// BigInteger(int signum, byte[] magnitude) |
|
// double doubleValue() |
|
// float floatValue() |
|
// int hashCode() |
|
// long longValue() |
|
// static BigInteger valueOf(long val) |
|
|
|
// Imported from bitcoinjs-lib |
|
|
|
/** |
|
* 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 new BigInteger.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); |
|
} |
|
}; |
|
|
|
/** |
|
* 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); |
|
} |
|
}; |
|
|
|
/** |
|
* 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(); |
|
|
|
// Empty array, nothing to do |
|
if (!ba.length) { |
|
return ba; |
|
} |
|
|
|
// remove leading 0 |
|
if (ba[0] === 0) { |
|
ba = ba.slice(1); |
|
} |
|
|
|
// all values must be positive |
|
for (var i = 0; i < ba.length; ++i) { |
|
ba[i] = (ba[i] < 0) ? ba[i] + 256 : ba[i]; |
|
} |
|
|
|
return ba; |
|
}; |
|
|
|
/* |
|
* Converts big integer to signed byte representation. |
|
* |
|
* The format for this value uses 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.toByteArrayUnsigned(); |
|
var neg = this.s < 0; |
|
|
|
// if the first bit is set, we always unshift |
|
// either unshift 0x80 or 0x00 |
|
if (val[0] & 0x80) { |
|
val.unshift((neg) ? 0x80 : 0x00); |
|
} |
|
// if the first bit isn't set, set it if negative |
|
else if (neg) { |
|
val[0] |= 0x80; |
|
} |
|
|
|
return val; |
|
}; |
|
|
|
// Random number generator - requires a PRNG backend, e.g. prng4.js |
|
|
|
// For best results, put code like |
|
// <body onClick='rng_seed_time();' onKeyPress='rng_seed_time();'> |
|
// in your main HTML document. |
|
|
|
var rng_state; |
|
var rng_pool; |
|
var rng_pptr; |
|
|
|
// Mix in a 32-bit integer into the pool |
|
function rng_seed_int(x) { |
|
rng_pool[rng_pptr++] ^= x & 255; |
|
rng_pool[rng_pptr++] ^= (x >> 8) & 255; |
|
rng_pool[rng_pptr++] ^= (x >> 16) & 255; |
|
rng_pool[rng_pptr++] ^= (x >> 24) & 255; |
|
if (rng_pptr >= rng_psize) rng_pptr -= rng_psize; |
|
} |
|
|
|
// Mix in the current time (w/milliseconds) into the pool |
|
function rng_seed_time() { |
|
rng_seed_int(new Date().getTime()); |
|
} |
|
|
|
// Initialize the pool with junk if needed. |
|
if (rng_pool == null) { |
|
rng_pool = new Array(); |
|
rng_pptr = 0; |
|
var t; |
|
if (typeof window !== 'undefined' && window.crypto) { |
|
if (window.crypto.getRandomValues) { |
|
// Use webcrypto if available |
|
var ua = new Uint8Array(32); |
|
window.crypto.getRandomValues(ua); |
|
for (t = 0; t < 32; ++t) rng_pool[rng_pptr++] = ua[t]; |
|
} else if ( |
|
navigator.appName == 'Netscape' && |
|
navigator.appVersion < '5' |
|
) { |
|
// Extract entropy (256 bits) from NS4 RNG if available |
|
var z = window.crypto.random(32); |
|
for (t = 0; t < z.length; ++t) |
|
rng_pool[rng_pptr++] = z.charCodeAt(t) & 255; |
|
} |
|
} |
|
while (rng_pptr < rng_psize) { |
|
// extract some randomness from Math.random() |
|
t = Math.floor(65536 * Math.random()); |
|
rng_pool[rng_pptr++] = t >>> 8; |
|
rng_pool[rng_pptr++] = t & 255; |
|
} |
|
rng_pptr = 0; |
|
rng_seed_time(); |
|
//rng_seed_int(window.screenX); |
|
//rng_seed_int(window.screenY); |
|
} |
|
|
|
function rng_get_byte() { |
|
if (rng_state == null) { |
|
rng_seed_time(); |
|
rng_state = prng_newstate(); |
|
rng_state.init(rng_pool); |
|
for (rng_pptr = 0; rng_pptr < rng_pool.length; ++rng_pptr) |
|
rng_pool[rng_pptr] = 0; |
|
rng_pptr = 0; |
|
//rng_pool = null; |
|
} |
|
// TODO: allow reseeding after first request |
|
return rng_state.next(); |
|
} |
|
|
|
function rng_get_bytes(ba) { |
|
var i; |
|
for (i = 0; i < ba.length; ++i) ba[i] = rng_get_byte(); |
|
} |
|
|
|
function SecureRandom() { } |
|
|
|
SecureRandom.prototype.nextBytes = rng_get_bytes; |
|
|
|
// prng4.js - uses Arcfour as a PRNG |
|
|
|
function Arcfour() { |
|
this.i = 0; |
|
this.j = 0; |
|
this.S = new Array(); |
|
} |
|
|
|
// Initialize arcfour context from key, an array of ints, each from [0..255] |
|
function ARC4init(key) { |
|
var i, j, t; |
|
for (i = 0; i < 256; ++i) this.S[i] = i; |
|
j = 0; |
|
for (i = 0; i < 256; ++i) { |
|
j = (j + this.S[i] + key[i % key.length]) & 255; |
|
t = this.S[i]; |
|
this.S[i] = this.S[j]; |
|
this.S[j] = t; |
|
} |
|
this.i = 0; |
|
this.j = 0; |
|
} |
|
|
|
function ARC4next() { |
|
var t; |
|
this.i = (this.i + 1) & 255; |
|
this.j = (this.j + this.S[this.i]) & 255; |
|
t = this.S[this.i]; |
|
this.S[this.i] = this.S[this.j]; |
|
this.S[this.j] = t; |
|
return this.S[(t + this.S[this.i]) & 255]; |
|
} |
|
|
|
Arcfour.prototype.init = ARC4init; |
|
Arcfour.prototype.next = ARC4next; |
|
|
|
// Plug in your RNG constructor here |
|
function prng_newstate() { |
|
return new Arcfour(); |
|
} |
|
|
|
// Pool size must be a multiple of 4 and greater than 32. |
|
// An array of bytes the size of the pool will be passed to init() |
|
var rng_psize = 256; |
|
|
|
if (typeof exports !== 'undefined') { |
|
exports = module.exports = { |
|
default: BigInteger, |
|
BigInteger: BigInteger, |
|
SecureRandom: SecureRandom, |
|
}; |
|
} else { |
|
this.jsbn = { |
|
BigInteger: BigInteger, |
|
SecureRandom: SecureRandom, |
|
}; |
|
} |
|
}.call(this)); |