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@proton/ccxt

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A JavaScript / TypeScript / Python / C# / PHP cryptocurrency trading library with support for 130+ exchanges

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// ---------------------------------------------------------------------------- // PLEASE DO NOT EDIT THIS FILE, IT IS GENERATED AND WILL BE OVERWRITTEN: // https://github.com/ccxt/ccxt/blob/master/CONTRIBUTING.md#how-to-contribute-code // EDIT THE CORRESPONDENT .ts FILE INSTEAD // Copyright (c) 2005 Tom Wu // All Rights Reserved. // See "LICENSE" for details. // Basic JavaScript BN library - subset useful for RSA encryption. import { cbit, int2char, lbit, op_and, op_andnot, op_or, op_xor } from "./util.js"; // Bits per digit let dbits; // JavaScript engine analysis const canary = 0xdeadbeefcafe; const j_lm = ((canary & 0xffffff) == 0xefcafe); //#region const 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]; const lplim = (1 << 26) / lowprimes[lowprimes.length - 1]; //#endregion // (public) Constructor /** * @type Class */ export class BigInteger { constructor(a, b, c) { if (a != null) { if ("number" == typeof a) { this.fromNumber(a, b, c); } else if (b == null && "string" != typeof a) { this.fromString(a, 256); } else { this.fromString(a, b); } } } //#region PUBLIC // BigInteger.prototype.toString = bnToString; // (public) return string representation in given radix toString(b) { if (this.s < 0) { return "-" + this.negate().toString(b); } let k; if (b == 16) { k = 4; } else if (b == 8) { k = 3; } else if (b == 2) { k = 1; } else if (b == 32) { k = 5; } else if (b == 4) { k = 2; } else { return this.toRadix(b); } const km = (1 << k) - 1; let d; let m = false; let r = ""; let i = this.t; let p = this.DB - (i * this.DB) % k; if (i-- > 0) { if (p < this.DB && (d = this[i] >> p) > 0) { m = true; r = int2char(d); } while (i >= 0) { if (p < k) { d = (this[i] & ((1 << p) - 1)) << (k - p); d |= this[--i] >> (p += this.DB - k); } else { d = (this[i] >> (p -= k)) & km; if (p <= 0) { p += this.DB; --i; } } if (d > 0) { m = true; } if (m) { r += int2char(d); } } } return m ? r : "0"; } // BigInteger.prototype.negate = bnNegate; // (public) -this negate() { const r = nbi(); BigInteger.ZERO.subTo(this, r); return r; } // BigInteger.prototype.abs = bnAbs; // (public) |this| abs() { return (this.s < 0) ? this.negate() : this; } // BigInteger.prototype.compareTo = bnCompareTo; // (public) return + if this > a, - if this < a, 0 if equal compareTo(a) { let r = this.s - a.s; if (r != 0) { return r; } let 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; } // BigInteger.prototype.bitLength = bnBitLength; // (public) return the number of bits in "this" bitLength() { if (this.t <= 0) { return 0; } return this.DB * (this.t - 1) + nbits(this[this.t - 1] ^ (this.s & this.DM)); } // BigInteger.prototype.mod = bnMod; // (public) this mod a mod(a) { const r = nbi(); this.abs().divRemTo(a, null, r); if (this.s < 0 && r.compareTo(BigInteger.ZERO) > 0) { a.subTo(r, r); } return r; } // BigInteger.prototype.modPowInt = bnModPowInt; // (public) this^e % m, 0 <= e < 2^32 modPowInt(e, m) { let z; if (e < 256 || m.isEven()) { z = new Classic(m); } else { z = new Montgomery(m); } return this.exp(e, z); } // BigInteger.prototype.clone = bnClone; // (public) clone() { const r = nbi(); this.copyTo(r); return r; } // BigInteger.prototype.intValue = bnIntValue; // (public) return value as integer intValue() { 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]; } // BigInteger.prototype.byteValue = bnByteValue; // (public) return value as byte byteValue() { return (this.t == 0) ? this.s : (this[0] << 24) >> 24; } // BigInteger.prototype.shortValue = bnShortValue; // (public) return value as short (assumes DB>=16) shortValue() { return (this.t == 0) ? this.s : (this[0] << 16) >> 16; } // BigInteger.prototype.signum = bnSigNum; // (public) 0 if this == 0, 1 if this > 0 signum() { if (this.s < 0) { return -1; } else if (this.t <= 0 || (this.t == 1 && this[0] <= 0)) { return 0; } else { return 1; } } // BigInteger.prototype.toByteArray = bnToByteArray; // (public) convert to bigendian byte array toByteArray() { let i = this.t; const r = []; r[0] = this.s; let p = this.DB - (i * this.DB) % 8; let d; let 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 = bnEquals; equals(a) { return (this.compareTo(a) == 0); } // BigInteger.prototype.min = bnMin; min(a) { return (this.compareTo(a) < 0) ? this : a; } // BigInteger.prototype.max = bnMax; max(a) { return (this.compareTo(a) > 0) ? this : a; } // BigInteger.prototype.and = bnAnd; and(a) { const r = nbi(); this.bitwiseTo(a, op_and, r); return r; } // BigInteger.prototype.or = bnOr; or(a) { const r = nbi(); this.bitwiseTo(a, op_or, r); return r; } // BigInteger.prototype.xor = bnXor; xor(a) { const r = nbi(); this.bitwiseTo(a, op_xor, r); return r; } // BigInteger.prototype.andNot = bnAndNot; andNot(a) { const r = nbi(); this.bitwiseTo(a, op_andnot, r); return r; } // BigInteger.prototype.not = bnNot; // (public) ~this not() { const r = nbi(); for (let i = 0; i < this.t; ++i) { r[i] = this.DM & ~this[i]; } r.t = this.t; r.s = ~this.s; return r; } // BigInteger.prototype.shiftLeft = bnShiftLeft; // (public) this << n shiftLeft(n) { const r = nbi(); if (n < 0) { this.rShiftTo(-n, r); } else { this.lShiftTo(n, r); } return r; } // BigInteger.prototype.shiftRight = bnShiftRight; // (public) this >> n shiftRight(n) { const r = nbi(); if (n < 0) { this.lShiftTo(-n, r); } else { this.rShiftTo(n, r); } return r; } // BigInteger.prototype.getLowestSetBit = bnGetLowestSetBit; // (public) returns index of lowest 1-bit (or -1 if none) getLowestSetBit() { for (let 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; } // BigInteger.prototype.bitCount = bnBitCount; // (public) return number of set bits bitCount() { let r = 0; const x = this.s & this.DM; for (let i = 0; i < this.t; ++i) { r += cbit(this[i] ^ x); } return r; } // BigInteger.prototype.testBit = bnTestBit; // (public) true iff nth bit is set testBit(n) { const j = Math.floor(n / this.DB); if (j >= this.t) { return (this.s != 0); } return ((this[j] & (1 << (n % this.DB))) != 0); } // BigInteger.prototype.setBit = bnSetBit; // (public) this | (1<<n) setBit(n) { return this.changeBit(n, op_or); } // BigInteger.prototype.clearBit = bnClearBit; // (public) this & ~(1<<n) clearBit(n) { return this.changeBit(n, op_andnot); } // BigInteger.prototype.flipBit = bnFlipBit; // (public) this ^ (1<<n) flipBit(n) { return this.changeBit(n, op_xor); } // BigInteger.prototype.add = bnAdd; // (public) this + a add(a) { const r = nbi(); this.addTo(a, r); return r; } // BigInteger.prototype.subtract = bnSubtract; // (public) this - a subtract(a) { const r = nbi(); this.subTo(a, r); return r; } // BigInteger.prototype.multiply = bnMultiply; // (public) this * a multiply(a) { const r = nbi(); this.multiplyTo(a, r); return r; } // BigInteger.prototype.divide = bnDivide; // (public) this / a divide(a) { const r = nbi(); this.divRemTo(a, r, null); return r; } // BigInteger.prototype.remainder = bnRemainder; // (public) this % a remainder(a) { const r = nbi(); this.divRemTo(a, null, r); return r; } // BigInteger.prototype.divideAndRemainder = bnDivideAndRemainder; // (public) [this/a,this%a] divideAndRemainder(a) { const q = nbi(); const r = nbi(); this.divRemTo(a, q, r); return [q, r]; } // BigInteger.prototype.modPow = bnModPow; // (public) this^e % m (HAC 14.85) modPow(e, m) { let i = e.bitLength(); let k; let r = nbv(1); let 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 const g = []; let n = 3; const k1 = k - 1; const km = (1 << k) - 1; g[1] = z.convert(this); if (k > 1) { const g2 = nbi(); z.sqrTo(g[1], g2); while (n <= km) { g[n] = nbi(); z.mulTo(g2, g[n - 2], g[n]); n += 2; } } let j = e.t - 1; let w; let is1 = true; let r2 = nbi(); let 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); } // BigInteger.prototype.modInverse = bnModInverse; // (public) 1/this % m (HAC 14.61) modInverse(m) { const ac = m.isEven(); if ((this.isEven() && ac) || m.signum() == 0) { return BigInteger.ZERO; } const u = m.clone(); const v = this.clone(); const a = nbv(1); const b = nbv(0); const c = nbv(0); const 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; } } // BigInteger.prototype.pow = bnPow; // (public) this^e pow(e) { return this.exp(e, new NullExp()); } // BigInteger.prototype.gcd = bnGCD; // (public) gcd(this,a) (HAC 14.54) gcd(a) { let x = (this.s < 0) ? this.negate() : this.clone(); let y = (a.s < 0) ? a.negate() : a.clone(); if (x.compareTo(y) < 0) { const t = x; x = y; y = t; } let i = x.getLowestSetBit(); let 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; } // BigInteger.prototype.isProbablePrime = bnIsProbablePrime; // (public) test primality with certainty >= 1-.5^t isProbablePrime(t) { let i; const 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) { let m = lowprimes[i]; let 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); } //#endregion PUBLIC //#region PROTECTED // BigInteger.prototype.copyTo = bnpCopyTo; // (protected) copy this to r copyTo(r) { for (let i = this.t - 1; i >= 0; --i) { r[i] = this[i]; } r.t = this.t; r.s = this.s; } // BigInteger.prototype.fromInt = bnpFromInt; // (protected) set from integer value x, -DV <= x < DV fromInt(x) { this.t = 1; this.s = (x < 0) ? -1 : 0; if (x > 0) { this[0] = x; } else if (x < -1) { this[0] = x + this.DV; } else { this.t = 0; } } // BigInteger.prototype.fromString = bnpFromString; // (protected) set from string and radix fromString(s, b) { let k; if (b == 16) { k = 4; } else if (b == 8) { k = 3; } else if (b == 256) { k = 8; /* byte array */ } else if (b == 2) { k = 1; } else if (b == 32) { k = 5; } else if (b == 4) { k = 2; } else { this.fromRadix(s, b); return; } this.t = 0; this.s = 0; let i = s.length; let mi = false; let sh = 0; while (--i >= 0) { const x = (k == 8) ? (+s[i]) & 0xff : intAt(s, i); if (x < 0) { if (s.charAt(i) == "-") { mi = true; } continue; } mi = false; if (sh == 0) { this[this.t++] = x; } else if (sh + k > this.DB) { this[this.t - 1] |= (x & ((1 << (this.DB - sh)) - 1)) << sh; this[this.t++] = (x >> (this.DB - sh)); } else { this[this.t - 1] |= x << sh; } sh += k; if (sh >= this.DB) { sh -= this.DB; } } if (k == 8 && ((+s[0]) & 0x80) != 0) { this.s = -1; if (sh > 0) { this[this.t - 1] |= ((1 << (this.DB - sh)) - 1) << sh; } } this.clamp(); if (mi) { BigInteger.ZERO.subTo(this, this); } } // BigInteger.prototype.clamp = bnpClamp; // (protected) clamp off excess high words clamp() { const c = this.s & this.DM; while (this.t > 0 && this[this.t - 1] == c) { --this.t; } } // BigInteger.prototype.dlShiftTo = bnpDLShiftTo; // (protected) r = this << n*DB dlShiftTo(n, r) { let i; for (i = this.t - 1; i >= 0; --i) { r[i + n] = this[i]; } for (i = n - 1; i >= 0; --i) { r[i] = 0; } r.t = this.t + n; r.s = this.s; } // BigInteger.prototype.drShiftTo = bnpDRShiftTo; // (protected) r = this >> n*DB drShiftTo(n, r) { for (let i = n; i < this.t; ++i) { r[i - n] = this[i]; } r.t = Math.max(this.t - n, 0); r.s = this.s; } // BigInteger.prototype.lShiftTo = bnpLShiftTo; // (protected) r = this << n lShiftTo(n, r) { const bs = n % this.DB; const cbs = this.DB - bs; const bm = (1 << cbs) - 1; const ds = Math.floor(n / this.DB); let c = (this.s << bs) & this.DM; for (let i = this.t - 1; i >= 0; --i) { r[i + ds + 1] = (this[i] >> cbs) | c; c = (this[i] & bm) << bs; } for (let i = ds - 1; i >= 0; --i) { r[i] = 0; } r[ds] = c; r.t = this.t + ds + 1; r.s = this.s; r.clamp(); } // BigInteger.prototype.rShiftTo = bnpRShiftTo; // (protected) r = this >> n rShiftTo(n, r) { r.s = this.s; const ds = Math.floor(n / this.DB); if (ds >= this.t) { r.t = 0; return; } const bs = n % this.DB; const cbs = this.DB - bs; const bm = (1 << bs) - 1; r[0] = this[ds] >> bs; for (let i = ds + 1; i < this.t; ++i) { r[i - ds - 1] |= (this[i] & bm) << cbs; r[i - ds] = this[i] >> bs; } if (bs > 0) { r[this.t - ds - 1] |= (this.s & bm) << cbs; } r.t = this.t - ds; r.clamp(); } // BigInteger.prototype.subTo = bnpSubTo; // (protected) r = this - a subTo(a, r) { let i = 0; let c = 0; const m = Math.min(a.t, this.t); while (i < m) { c += this[i] - a[i]; r[i++] = c & this.DM; c >>= this.DB; } if (a.t < this.t) { c -= a.s; while (i < this.t) { c += this[i]; r[i++] = c & this.DM; c >>= this.DB; } c += this.s; } else { c += this.s; while (i < a.t) { c -= a[i]; r[i++] = c & this.DM; c >>= this.DB; } c -= a.s; } r.s = (c < 0) ? -1 : 0; if (c < -1) { r[i++] = this.DV + c; } else if (c > 0) { r[i++] = c; } r.t = i; r.clamp(); } // BigInteger.prototype.multiplyTo = bnpMultiplyTo; // (protected) r = this * a, r != this,a (HAC 14.12) // "this" should be the larger one if appropriate. multiplyTo(a, r) { const x = this.abs(); const y = a.abs(); let i = x.t; r.t = i + y.t; while (--i >= 0) { r[i] = 0; } for (i = 0; i < y.t; ++i) { r[i + x.t] = x.am(0, y[i], r, i, 0, x.t); } r.s = 0; r.clamp(); if (this.s != a.s) { BigInteger.ZERO.subTo(r, r); } } // BigInteger.prototype.squareTo = bnpSquareTo; // (protected) r = this^2, r != this (HAC 14.16) squareTo(r) { const x = this.abs(); let i = r.t = 2 * x.t; while (--i >= 0) { r[i] = 0; } for (i = 0; i < x.t - 1; ++i) { const c = x.am(i, x[i], r, 2 * i, 0, 1); if ((r[i + x.t] += x.am(i + 1, 2 * x[i], r, 2 * i + 1, c, x.t - i - 1)) >= x.DV) { r[i + x.t] -= x.DV; r[i + x.t + 1] = 1; } } if (r.t > 0) { r[r.t - 1] += x.am(i, x[i], r, 2 * i, 0, 1); } r.s = 0; r.clamp(); } // BigInteger.prototype.divRemTo = bnpDivRemTo; // (protected) divide this by m, quotient and remainder to q, r (HAC 14.20) // r != q, this != m. q or r may be null. divRemTo(m, q, r) { const pm = m.abs(); if (pm.t <= 0) { return; } const pt = this.abs(); if (pt.t < pm.t) { if (q != null) { q.fromInt(0); } if (r != null) { this.copyTo(r); } return; } if (r == null) { r = nbi(); } const y = nbi(); const ts = this.s; const ms = m.s; const nsh = this.DB - nbits(pm[pm.t - 1]); // normalize modulus if (nsh > 0) { pm.lShiftTo(nsh, y); pt.lShiftTo(nsh, r); } else { pm.copyTo(y); pt.copyTo(r); } const ys = y.t; const y0 = y[ys - 1]; if (y0 == 0) { return; } const yt = y0 * (1 << this.F1) + ((ys > 1) ? y[ys - 2] >> this.F2 : 0); const d1 = this.FV / yt; const d2 = (1 << this.F1) / yt; const e = 1 << this.F2; let i = r.t; let j = i - ys; const t = (q == null) ? nbi() : q; y.dlShiftTo(j, t); if (r.compareTo(t) >= 0) { r[r.t++] = 1; r.subTo(t, r); } BigInteger.ONE.dlShiftTo(ys, t); t.subTo(y, y); // "negative" y so we can replace sub with am later while (y.t < ys) { y[y.t++] = 0; } while (--j >= 0) { // Estimate quotient digit let qd = (r[--i] == y0) ? this.DM : Math.floor(r[i] * d1 + (r[i - 1] + e) * d2); if ((r[i] += y.am(0, qd, r, j, 0, ys)) < qd) { // Try it out y.dlShiftTo(j, t); r.subTo(t, r); while (r[i] < --qd) { r.subTo(t, r); } } } if (q != null) { r.drShiftTo(ys, q); if (ts != ms) { BigInteger.ZERO.subTo(q, q); } } r.t = ys; r.clamp(); if (nsh > 0) { r.rShiftTo(nsh, r); } // Denormalize remainder if (ts < 0) { BigInteger.ZERO.subTo(r, r); } } // BigInteger.prototype.invDigit = bnpInvDigit; // (protected) return "-1/this % 2^DB"; useful for Mont. reduction // justification: // xy == 1 (mod m) // xy = 1+km // xy(2-xy) = (1+km)(1-km) // x[y(2-xy)] = 1-k^2m^2 // x[y(2-xy)] == 1 (mod m^2) // if y is 1/x mod m, then y(2-xy) is 1/x mod m^2 // should reduce x and y(2-xy) by m^2 at each step to keep size bounded. // JS multiply "overflows" differently from C/C++, so care is needed here. invDigit() { if (this.t < 1) { return 0; } const x = this[0]; if ((x & 1) == 0) { return 0; } let 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; } // BigInteger.prototype.isEven = bnpIsEven; // (protected) true iff this is even isEven() { return ((this.t > 0) ? (this[0] & 1) : this.s) == 0; } // BigInteger.prototype.exp = bnpExp; // (protected) this^e, e < 2^32, doing sqr and mul with "r" (HAC 14.79) exp(e, z) { if (e > 0xffffffff || e < 1) { return BigInteger.ONE; } let r = nbi(); let r2 = nbi(); const g = z.convert(this); let 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 { const t = r; r = r2; r2 = t; } } return z.revert(r); } // BigInteger.prototype.chunkSize = bnpChunkSize; // (protected) return x s.t. r^x < DV chunkSize(r) { return Math.floor(Math.LN2 * this.DB / Math.log(r)); } // BigInteger.prototype.toRadix = bnpToRadix; // (protected) convert to radix string toRadix(b) { if (b == null) { b = 10; } if (this.signum() == 0 || b < 2 || b > 36) { return "0"; } const cs = this.chunkSize(b); const a = Math.pow(b, cs); const d = nbv(a); const y = nbi(); const z = nbi(); let 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; } // BigInteger.prototype.fromRadix = bnpFromRadix; // (protected) convert from radix string fromRadix(s, b) { this.fromInt(0); if (b == null) { b = 10; } const cs = this.chunkSize(b); const d = Math.pow(b, cs); let mi = false; let j = 0; let w = 0; for (let i = 0; i < s.length; ++i) { const 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); } } // BigInteger.prototype.fromNumber = bnpFromNumber; // (protected) alternate constructor fromNumber(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) const x = []; const 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); } } // BigInteger.prototype.bitwiseTo = bnpBitwiseTo; // (protected) r = this op a (bitwise) bitwiseTo(a, op, r) { let i; let f; const 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(); } // BigInteger.prototype.changeBit = bnpChangeBit; // (protected) this op (1<<n) changeBit(n, op) { const r = BigInteger.ONE.shiftLeft(n); this.bitwiseTo(r, op, r); return r; } // BigInteger.prototype.addTo = bnpAddTo; // (protected) r = this + a addTo(a, r) { let i = 0; let c = 0; const 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(); } // BigInteger.prototype.dMultiply = bnpDMultiply; // (protected) this *= n, this >= 0, 1 < n < DV dMultiply(n) { this[this.t] = this.am(0, n - 1, this, 0, 0, this.t); ++this.t; this.clamp(); } // BigInteger.prototype.dAddOffset = bnpDAddOffset; // (protected) this += n << w words, this >= 0 dAddOffset(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]; } } // BigInteger.prototype.multiplyLowerTo = bnpMultiplyLowerTo; // (protected) r = lower n words of "this * a", a.t <= n // "this" should be the larger one if appropriate. multiplyLowerTo(a, n, r) { let i = Math.min(this.t + a.t, n); r.s = 0; // assumes a,this >= 0 r.t = i; while (i > 0) { r[--i] = 0; } for (const j = r.t - this.t; i < j; ++i) { r[i + this.t] = this.am(0, a[i], r, i, 0, this.t); } for (const j = Math.min(a.t, n); i < j; ++i) { this.am(0, a[i], r, i, 0, n - i); } r.clamp(); } // BigInteger.prototype.multiplyUpperTo = bnpMultiplyUpperTo; // (protected) r = "this * a" without lower n words, n > 0 // "this" should be the larger one if appropriate. multiplyUpperTo(a, n, r) { --n; let 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); } // BigInteger.prototype.modInt = bnpModInt; // (protected) this % n, n < 2^26 modInt(n) { if (n <= 0) { return 0; } const d = this.DV % n; let r = (this.s < 0) ? n - 1 : 0; if (this.t > 0) { if (d == 0) { r = this[0] % n; } else { for (let i = this.t - 1; i >= 0; --i) { r = (d * r + this[i]) % n; } } } return r; } // BigInteger.prototype.millerRabin = bnpMillerRabin; // (protected) true if probably prime (HAC 4.24, Miller-Rabin) millerRabin(t) { const n1 = this.subtract(BigInteger.ONE); const k = n1.getLowestSetBit(); if (k <= 0) { return false; } const r = n1.shiftRight(k); t = (t + 1) >> 1; if (t > lowprimes.length) { t = lowprimes.length; } const a = nbi(); for (let i = 0; i < t; ++i) { // Pick bases at random, instead of starting at 2 a.fromInt(lowprimes[Math.floor(Math.random() * lowprimes.length)]); let y = a.modPow(r, this); if (y.compareTo(BigInteger.ONE) != 0 && y.compareTo(n1) != 0) { let 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; } // BigInteger.prototype.square = bnSquare; // (public) this^2 square() { const r = nbi(); this.squareTo(r); return r; } //#region ASYNC // Public API method gcda(a, callback) { let x = (this.s < 0) ? this.negate() : this.clone(); let y = (a.s < 0) ? a.negate() : a.clone(); if (x.compareTo(y) < 0) { const t = x; x = y; y = t; } let i = x.getLowestSetBit(); let g = y.getLowestSetBit(); if (g < 0) { callback(x); return; } if (i < g) { g = i; } if (g > 0) { x.rShiftTo(g, x); y.rShiftTo(g, y); } // Workhorse of the algorithm, gets called 200 - 800 times per 512 bit keygen. const gcda1 = function () { 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 (!(x.signum() > 0)) { if (g > 0) { y.lShiftTo(g, y); } setTimeout(function () { callback(y); }, 0); // escape } else { setTimeout(gcda1, 0); } }; setTimeout(gcda1, 10); } // (protected) alternate constructor fromNumberAsync(a, b, c, callback) { if ("number" == typeof b) { if (a < 2) { this.fromInt(1); } else { this.fromNumber(a, c); if (!this.testBit(a - 1)) { this.bitwiseTo(BigInteger.ONE.shiftLeft(a - 1), op_or, this); } if (this.isEven()) { this.dAddOffset(1, 0); } const bnp = this; const bnpfn1 = function () { bnp.dAddOffset(2, 0); if (bnp.bitLength() > a) { bnp.subTo(BigInteger.ONE.shiftLeft(a - 1), bnp); } if (bnp.isProbablePrime(b)) { setTimeout(function () { callback(); }, 0); // escape } else { setTimeout(bnpfn1, 0); } }; setTimeout(bnpfn1, 0); } } else { const x = []; const 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); } } } //#region REDUCERS //#region NullExp class NullExp { constructor() { } // NullExp.prototype.convert = nNop; convert(x) { return x; } // NullExp.prototype.revert = nNop; revert(x) { return x; } // NullExp.prototype.mulTo = nMulTo; mulTo(x, y, r) { x.multiplyTo(y, r); } // NullExp.prototype.sqrTo = nSqrTo; sqrTo(x, r) { x.squareTo(r); } } // Modular reduction using "classic" algorithm class Classic { constructor(m) { this.m = m; } // Classic.prototype.convert = cConvert; convert(x) { if (x.s < 0 || x.compareTo(this.m) >= 0) { return x.mod(this.m); } else { return x; } } // Classic.prototype.revert = cRevert; revert(x) { return x; } // Classic.prototype.reduce = cReduce; reduce(x) { x.divRemTo(this.m, null, x); } // Classic.prototype.mulTo = cMulTo; mulTo(x, y, r) { x.multiplyTo(y, r); this.reduce(r); } // Classic.prototype.sqrTo = cSqrTo; sqrTo(x, r) { x.squareTo(r); this.reduce(r); } } //#endregion //#region Montgomery // Montgomery reduction class Montgomery { constructor(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; } // Montgomery.prototype.convert = montConvert; // xR mod m convert(x) { const 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; } // Montgomery.prototype.revert = montRevert; // x/R mod m revert(x) { const r = nbi(); x.copyTo(r); this.reduce(r); return r; } // Montgomery.prototype.reduce = montReduce; // x = x/R mod m (HAC 14.32) reduce(x) { while (x.t <= this.mt2) { // pad x so am has enough room later x[x.t++] = 0; } for (let i = 0; i < this.m.t; ++i) { // faster way of calculating u0 = x[i]*mp mod DV let j = x[i] & 0x7fff; const 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); } } // Montgomery.prototype.mulTo = montMulTo; // r = "xy/R mod m"; x,y != r mulTo(x, y, r) { x.multiplyTo(y, r); this.reduce(r); } // Montgomery.prototype.sqrTo = montSqrTo; // r = "x^2/R mod m"; x != r sqrTo(x, r) { x.squareTo(r); this.reduce(r); } } //#endregion Montgomery //#region Barrett // Barrett modular reduction class Barrett { constructor(m) { this.m = m; // setup Barrett this.r2 = nbi(); this.q3 = nbi(); BigInteger.ONE.dlShiftTo(2 * m.t, this.r2); this.mu = this.r2.divide(m); } // Barrett.prototype.convert = barrettConvert; convert(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 { const r = nbi(); x.copyTo(r); this.reduce(r); return r; } } // Barrett.prototype.revert = barrettRevert; revert(x) { return x; } // Barrett.prototype.reduce = barrettReduce; // x = x mod m (HAC 14.42) reduce(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); } } // Barrett.prototype.mulTo = barrettMulTo; // r = x*y mod m; x,y != r mulTo(x, y, r) { x.multiplyTo(y, r); this.reduce(r); } // Barrett.prototype.sqrTo = barrettSqrTo; // r = x^2 mod m; x != r sqrTo(x, r) { x.squareTo(r); this.reduce(r); } } //#endregion //#endregion REDUCERS // return new, unset BigInteger export function nbi() { return new BigInteger(null); } export function parseBigInt(str, r) { return new BigInteger(str, r); } // am: Compute w_j += (x*this_i), propagate carries, // c is initial carry, returns final carry. // c < 3*dvalue, x < 2*dvalue, this_i < dvalue // We need to select the fastest one that works in this environment. const inBrowser = typeof navigator !== "undefined"; if (inBrowser && j_lm && (navigator.appName == "Microsoft Internet Explorer")) { // am2 avoids a big mult-and-extract completely. // Max digit bits should be <= 30 because we do bitwise ops // on values up to 2*hdvalue^2-hdvalue-1 (< 2^31) BigInteger.prototype.am = function am2(i, x, w, j, c, n) { const xl = x & 0x7fff; const xh = x >> 15; while (--n >= 0) { let l = this[i] & 0x7fff; const h = this[i++] >> 15; const m = xh * l + h * xl; l = xl * l + ((m & 0x7fff) << 15) + w[j] + (c & 0x3fffffff); c = (l >>> 30) + (m >>> 15) + xh * h + (c >>> 30); w[j++] = l & 0x3fffffff; } return c; }; dbits = 30; } else if (inBrowser && j_lm && (navigator.appName != "Netscape")) { // am1: use a single mult and divide to get the high bits, // max digit bits should be 26 because // max internal value = 2*dvalue^2-2*dvalue (< 2^53) BigInteger.prototype.am = function am1(i, x, w, j, c, n) { while (--n >= 0) { const v = x * this[i++] + w[j] + c; c = Math.floor(v / 0x4000000); w[j++] = v & 0x3ffffff; } return c; }; dbits = 26; } else { // Mozilla/Netscape seems to prefer am3 // Alternately, set max digit bits to 28 since some // browsers slow down when dealing with 32-bit numbers. BigInteger.prototype.am = function am3(i, x, w, j, c, n) { const xl = x & 0x3fff; const xh = x >> 14; while (--n >= 0) { let l = this[i] & 0x3fff; const h = this[i++] >> 14; const m = xh * l + h * xl; l = xl * l + ((m & 0x3fff) << 14) + w[j] + c; c = (l >> 28) + (m >> 14) + xh * h; w[j++] = l & 0xfffffff; } return c; }; dbits = 28; } BigInteger.prototype.DB = dbits; BigInteger.prototype.DM = ((1 << dbits) - 1); BigInteger.prototype.DV = (1 << dbits); const BI_FP = 52; BigInteger.prototype.FV = Math.pow(2, BI_FP); BigInteger.prototype.F1 = BI_FP - dbits; BigInteger.prototype.F2 = 2 * dbits - BI_FP; // Digit conversions const BI_RC = []; let rr; let vv; rr = "0".charCodeAt(0); for (vv = 0; vv <= 9; ++vv) { BI_RC[rr++] = vv; } rr = "a".charCodeAt(0); for (vv = 10; vv < 36; ++vv) { BI_RC[rr++] = vv; } rr = "A".charCodeAt(0); for (vv = 10; vv < 36; ++vv) { BI_RC[rr++] = vv; } export function intAt(s, i) { const c = BI_RC[s.charCodeAt(i)]; return (c == null) ? -1 : c; } // return bigint initialized to value export function nbv(i) { const r = nbi(); r.fromInt(i); return r; } // returns bit length of the integer x export function nbits(x) { let r = 1; let t; if ((t = x >>> 16) != 0) { x = t; r += 16; } if ((t = x >> 8) != 0) { x = t; r += 8; } if ((t = x >> 4) != 0) { x = t; r += 4; } if ((t = x >> 2) != 0) { x = t; r += 2; } if ((t = x >> 1) != 0) { x = t; r += 1; } return r; } // "constants" BigInteger.ZERO = nbv(0); BigInteger.ONE = nbv(1);