diff --git a/build/websnark.js b/build/websnark.js index 4cbfd61..48fab7f 100644 --- a/build/websnark.js +++ b/build/websnark.js @@ -28,16 +28,30 @@ /* globals window */ -const buildGroth16 = require("./src/groth16.js"); +const buildGroth16 = require("./src/groth16"); +const utils = require("./src/utils"); -buildGroth16().then( (groth16) => { +buildGroth16().then((groth16) => { window.groth16 = groth16; - window.genZKSnarkProof = function(witness, provingKey, cb) { - - const p = groth16.proof(witness, provingKey); + window.zkSnarkProofToSolidityInput = utils.toSolidityInput; + window.genZKSnarkProofAndWitness = function (input, circuitJson, provingKey, cb) { + const p = utils.genWitnessAndProve(groth16, input, circuitJson, provingKey); if (cb) { - p.then( (proof) => { + p.then((proof) => { + cb(null, proof); + }, (err) => { + cb(err); + }); + } else { + return p; + } + }; + + window.genZKSnarkProof = function (witness, provingKey, cb) { + const p = groth16.proof(witness, provingKey); + if (cb) { + p.then((proof) => { cb(null, proof); }, (err) => { cb(err); @@ -47,10 +61,7 @@ buildGroth16().then( (groth16) => { } }; }); - - - -},{"./src/groth16.js":13}],3:[function(require,module,exports){ +},{"./src/groth16":17,"./src/utils":18}],3:[function(require,module,exports){ (function (global){ 'use strict'; @@ -1336,1454 +1347,1454 @@ function fromByteArray (uint8) { } },{}],8:[function(require,module,exports){ -var bigInt = (function (undefined) { - "use strict"; - - var BASE = 1e7, - LOG_BASE = 7, - MAX_INT = 9007199254740992, - MAX_INT_ARR = smallToArray(MAX_INT), - DEFAULT_ALPHABET = "0123456789abcdefghijklmnopqrstuvwxyz"; - - var supportsNativeBigInt = typeof BigInt === "function"; - - function Integer(v, radix, alphabet, caseSensitive) { - if (typeof v === "undefined") return Integer[0]; - if (typeof radix !== "undefined") return +radix === 10 && !alphabet ? parseValue(v) : parseBase(v, radix, alphabet, caseSensitive); - return parseValue(v); - } - - function BigInteger(value, sign) { - this.value = value; - this.sign = sign; - this.isSmall = false; - } - BigInteger.prototype = Object.create(Integer.prototype); - - function SmallInteger(value) { - this.value = value; - this.sign = value < 0; - this.isSmall = true; - } - SmallInteger.prototype = Object.create(Integer.prototype); - - function NativeBigInt(value) { - this.value = value; - } - NativeBigInt.prototype = Object.create(Integer.prototype); - - function isPrecise(n) { - return -MAX_INT < n && n < MAX_INT; - } - - function smallToArray(n) { // For performance reasons doesn't reference BASE, need to change this function if BASE changes - if (n < 1e7) - return [n]; - if (n < 1e14) - return [n % 1e7, Math.floor(n / 1e7)]; - return [n % 1e7, Math.floor(n / 1e7) % 1e7, Math.floor(n / 1e14)]; - } - - function arrayToSmall(arr) { // If BASE changes this function may need to change - trim(arr); - var length = arr.length; - if (length < 4 && compareAbs(arr, MAX_INT_ARR) < 0) { - switch (length) { - case 0: return 0; - case 1: return arr[0]; - case 2: return arr[0] + arr[1] * BASE; - default: return arr[0] + (arr[1] + arr[2] * BASE) * BASE; - } - } - return arr; - } - - function trim(v) { - var i = v.length; - while (v[--i] === 0); - v.length = i + 1; - } - - function createArray(length) { // function shamelessly stolen from Yaffle's library https://github.com/Yaffle/BigInteger - var x = new Array(length); - var i = -1; - while (++i < length) { - x[i] = 0; - } - return x; - } - - function truncate(n) { - if (n > 0) return Math.floor(n); - return Math.ceil(n); - } - - function add(a, b) { // assumes a and b are arrays with a.length >= b.length - var l_a = a.length, - l_b = b.length, - r = new Array(l_a), - carry = 0, - base = BASE, - sum, i; - for (i = 0; i < l_b; i++) { - sum = a[i] + b[i] + carry; - carry = sum >= base ? 1 : 0; - r[i] = sum - carry * base; - } - while (i < l_a) { - sum = a[i] + carry; - carry = sum === base ? 1 : 0; - r[i++] = sum - carry * base; - } - if (carry > 0) r.push(carry); - return r; - } - - function addAny(a, b) { - if (a.length >= b.length) return add(a, b); - return add(b, a); - } - - function addSmall(a, carry) { // assumes a is array, carry is number with 0 <= carry < MAX_INT - var l = a.length, - r = new Array(l), - base = BASE, - sum, i; - for (i = 0; i < l; i++) { - sum = a[i] - base + carry; - carry = Math.floor(sum / base); - r[i] = sum - carry * base; - carry += 1; - } - while (carry > 0) { - r[i++] = carry % base; - carry = Math.floor(carry / base); - } - return r; - } - - BigInteger.prototype.add = function (v) { - var n = parseValue(v); - if (this.sign !== n.sign) { - return this.subtract(n.negate()); - } - var a = this.value, b = n.value; - if (n.isSmall) { - return new BigInteger(addSmall(a, Math.abs(b)), this.sign); - } - return new BigInteger(addAny(a, b), this.sign); - }; - BigInteger.prototype.plus = BigInteger.prototype.add; - - SmallInteger.prototype.add = function (v) { - var n = parseValue(v); - var a = this.value; - if (a < 0 !== n.sign) { - return this.subtract(n.negate()); - } - var b = n.value; - if (n.isSmall) { - if (isPrecise(a + b)) return new SmallInteger(a + b); - b = smallToArray(Math.abs(b)); - } - return new BigInteger(addSmall(b, Math.abs(a)), a < 0); - }; - SmallInteger.prototype.plus = SmallInteger.prototype.add; - - NativeBigInt.prototype.add = function (v) { - return new NativeBigInt(this.value + parseValue(v).value); - } - NativeBigInt.prototype.plus = NativeBigInt.prototype.add; - - function subtract(a, b) { // assumes a and b are arrays with a >= b - var a_l = a.length, - b_l = b.length, - r = new Array(a_l), - borrow = 0, - base = BASE, - i, difference; - for (i = 0; i < b_l; i++) { - difference = a[i] - borrow - b[i]; - if (difference < 0) { - difference += base; - borrow = 1; - } else borrow = 0; - r[i] = difference; - } - for (i = b_l; i < a_l; i++) { - difference = a[i] - borrow; - if (difference < 0) difference += base; - else { - r[i++] = difference; - break; - } - r[i] = difference; - } - for (; i < a_l; i++) { - r[i] = a[i]; - } - trim(r); - return r; - } - - function subtractAny(a, b, sign) { - var value; - if (compareAbs(a, b) >= 0) { - value = subtract(a, b); - } else { - value = subtract(b, a); - sign = !sign; - } - value = arrayToSmall(value); - if (typeof value === "number") { - if (sign) value = -value; - return new SmallInteger(value); - } - return new BigInteger(value, sign); - } - - function subtractSmall(a, b, sign) { // assumes a is array, b is number with 0 <= b < MAX_INT - var l = a.length, - r = new Array(l), - carry = -b, - base = BASE, - i, difference; - for (i = 0; i < l; i++) { - difference = a[i] + carry; - carry = Math.floor(difference / base); - difference %= base; - r[i] = difference < 0 ? difference + base : difference; - } - r = arrayToSmall(r); - if (typeof r === "number") { - if (sign) r = -r; - return new SmallInteger(r); - } return new BigInteger(r, sign); - } - - BigInteger.prototype.subtract = function (v) { - var n = parseValue(v); - if (this.sign !== n.sign) { - return this.add(n.negate()); - } - var a = this.value, b = n.value; - if (n.isSmall) - return subtractSmall(a, Math.abs(b), this.sign); - return subtractAny(a, b, this.sign); - }; - BigInteger.prototype.minus = BigInteger.prototype.subtract; - - SmallInteger.prototype.subtract = function (v) { - var n = parseValue(v); - var a = this.value; - if (a < 0 !== n.sign) { - return this.add(n.negate()); - } - var b = n.value; - if (n.isSmall) { - return new SmallInteger(a - b); - } - return subtractSmall(b, Math.abs(a), a >= 0); - }; - SmallInteger.prototype.minus = SmallInteger.prototype.subtract; - - NativeBigInt.prototype.subtract = function (v) { - return new NativeBigInt(this.value - parseValue(v).value); - } - NativeBigInt.prototype.minus = NativeBigInt.prototype.subtract; - - BigInteger.prototype.negate = function () { - return new BigInteger(this.value, !this.sign); - }; - SmallInteger.prototype.negate = function () { - var sign = this.sign; - var small = new SmallInteger(-this.value); - small.sign = !sign; - return small; - }; - NativeBigInt.prototype.negate = function () { - return new NativeBigInt(-this.value); - } - - BigInteger.prototype.abs = function () { - return new BigInteger(this.value, false); - }; - SmallInteger.prototype.abs = function () { - return new SmallInteger(Math.abs(this.value)); - }; - NativeBigInt.prototype.abs = function () { - return new NativeBigInt(this.value >= 0 ? this.value : -this.value); - } - - - function multiplyLong(a, b) { - var a_l = a.length, - b_l = b.length, - l = a_l + b_l, - r = createArray(l), - base = BASE, - product, carry, i, a_i, b_j; - for (i = 0; i < a_l; ++i) { - a_i = a[i]; - for (var j = 0; j < b_l; ++j) { - b_j = b[j]; - product = a_i * b_j + r[i + j]; - carry = Math.floor(product / base); - r[i + j] = product - carry * base; - r[i + j + 1] += carry; - } - } - trim(r); - return r; - } - - function multiplySmall(a, b) { // assumes a is array, b is number with |b| < BASE - var l = a.length, - r = new Array(l), - base = BASE, - carry = 0, - product, i; - for (i = 0; i < l; i++) { - product = a[i] * b + carry; - carry = Math.floor(product / base); - r[i] = product - carry * base; - } - while (carry > 0) { - r[i++] = carry % base; - carry = Math.floor(carry / base); - } - return r; - } - - function shiftLeft(x, n) { - var r = []; - while (n-- > 0) r.push(0); - return r.concat(x); - } - - function multiplyKaratsuba(x, y) { - var n = Math.max(x.length, y.length); - - if (n <= 30) return multiplyLong(x, y); - n = Math.ceil(n / 2); - - var b = x.slice(n), - a = x.slice(0, n), - d = y.slice(n), - c = y.slice(0, n); - - var ac = multiplyKaratsuba(a, c), - bd = multiplyKaratsuba(b, d), - abcd = multiplyKaratsuba(addAny(a, b), addAny(c, d)); - - var product = addAny(addAny(ac, shiftLeft(subtract(subtract(abcd, ac), bd), n)), shiftLeft(bd, 2 * n)); - trim(product); - return product; - } - - // The following function is derived from a surface fit of a graph plotting the performance difference - // between long multiplication and karatsuba multiplication versus the lengths of the two arrays. - function useKaratsuba(l1, l2) { - return -0.012 * l1 - 0.012 * l2 + 0.000015 * l1 * l2 > 0; - } - - BigInteger.prototype.multiply = function (v) { - var n = parseValue(v), - a = this.value, b = n.value, - sign = this.sign !== n.sign, - abs; - if (n.isSmall) { - if (b === 0) return Integer[0]; - if (b === 1) return this; - if (b === -1) return this.negate(); - abs = Math.abs(b); - if (abs < BASE) { - return new BigInteger(multiplySmall(a, abs), sign); - } - b = smallToArray(abs); - } - if (useKaratsuba(a.length, b.length)) // Karatsuba is only faster for certain array sizes - return new BigInteger(multiplyKaratsuba(a, b), sign); - return new BigInteger(multiplyLong(a, b), sign); - }; - - BigInteger.prototype.times = BigInteger.prototype.multiply; - - function multiplySmallAndArray(a, b, sign) { // a >= 0 - if (a < BASE) { - return new BigInteger(multiplySmall(b, a), sign); - } - return new BigInteger(multiplyLong(b, smallToArray(a)), sign); - } - SmallInteger.prototype._multiplyBySmall = function (a) { - if (isPrecise(a.value * this.value)) { - return new SmallInteger(a.value * this.value); - } - return multiplySmallAndArray(Math.abs(a.value), smallToArray(Math.abs(this.value)), this.sign !== a.sign); - }; - BigInteger.prototype._multiplyBySmall = function (a) { - if (a.value === 0) return Integer[0]; - if (a.value === 1) return this; - if (a.value === -1) return this.negate(); - return multiplySmallAndArray(Math.abs(a.value), this.value, this.sign !== a.sign); - }; - SmallInteger.prototype.multiply = function (v) { - return parseValue(v)._multiplyBySmall(this); - }; - SmallInteger.prototype.times = SmallInteger.prototype.multiply; - - NativeBigInt.prototype.multiply = function (v) { - return new NativeBigInt(this.value * parseValue(v).value); - } - NativeBigInt.prototype.times = NativeBigInt.prototype.multiply; - - function square(a) { - //console.assert(2 * BASE * BASE < MAX_INT); - var l = a.length, - r = createArray(l + l), - base = BASE, - product, carry, i, a_i, a_j; - for (i = 0; i < l; i++) { - a_i = a[i]; - carry = 0 - a_i * a_i; - for (var j = i; j < l; j++) { - a_j = a[j]; - product = 2 * (a_i * a_j) + r[i + j] + carry; - carry = Math.floor(product / base); - r[i + j] = product - carry * base; - } - r[i + l] = carry; - } - trim(r); - return r; - } - - BigInteger.prototype.square = function () { - return new BigInteger(square(this.value), false); - }; - - SmallInteger.prototype.square = function () { - var value = this.value * this.value; - if (isPrecise(value)) return new SmallInteger(value); - return new BigInteger(square(smallToArray(Math.abs(this.value))), false); - }; - - NativeBigInt.prototype.square = function (v) { - return new NativeBigInt(this.value * this.value); - } - - function divMod1(a, b) { // Left over from previous version. Performs faster than divMod2 on smaller input sizes. - var a_l = a.length, - b_l = b.length, - base = BASE, - result = createArray(b.length), - divisorMostSignificantDigit = b[b_l - 1], - // normalization - lambda = Math.ceil(base / (2 * divisorMostSignificantDigit)), - remainder = multiplySmall(a, lambda), - divisor = multiplySmall(b, lambda), - quotientDigit, shift, carry, borrow, i, l, q; - if (remainder.length <= a_l) remainder.push(0); - divisor.push(0); - divisorMostSignificantDigit = divisor[b_l - 1]; - for (shift = a_l - b_l; shift >= 0; shift--) { - quotientDigit = base - 1; - if (remainder[shift + b_l] !== divisorMostSignificantDigit) { - quotientDigit = Math.floor((remainder[shift + b_l] * base + remainder[shift + b_l - 1]) / divisorMostSignificantDigit); - } - // quotientDigit <= base - 1 - carry = 0; - borrow = 0; - l = divisor.length; - for (i = 0; i < l; i++) { - carry += quotientDigit * divisor[i]; - q = Math.floor(carry / base); - borrow += remainder[shift + i] - (carry - q * base); - carry = q; - if (borrow < 0) { - remainder[shift + i] = borrow + base; - borrow = -1; - } else { - remainder[shift + i] = borrow; - borrow = 0; - } - } - while (borrow !== 0) { - quotientDigit -= 1; - carry = 0; - for (i = 0; i < l; i++) { - carry += remainder[shift + i] - base + divisor[i]; - if (carry < 0) { - remainder[shift + i] = carry + base; - carry = 0; - } else { - remainder[shift + i] = carry; - carry = 1; - } - } - borrow += carry; - } - result[shift] = quotientDigit; - } - // denormalization - remainder = divModSmall(remainder, lambda)[0]; - return [arrayToSmall(result), arrayToSmall(remainder)]; - } - - function divMod2(a, b) { // Implementation idea shamelessly stolen from Silent Matt's library http://silentmatt.com/biginteger/ - // Performs faster than divMod1 on larger input sizes. - var a_l = a.length, - b_l = b.length, - result = [], - part = [], - base = BASE, - guess, xlen, highx, highy, check; - while (a_l) { - part.unshift(a[--a_l]); - trim(part); - if (compareAbs(part, b) < 0) { - result.push(0); - continue; - } - xlen = part.length; - highx = part[xlen - 1] * base + part[xlen - 2]; - highy = b[b_l - 1] * base + b[b_l - 2]; - if (xlen > b_l) { - highx = (highx + 1) * base; - } - guess = Math.ceil(highx / highy); - do { - check = multiplySmall(b, guess); - if (compareAbs(check, part) <= 0) break; - guess--; - } while (guess); - result.push(guess); - part = subtract(part, check); - } - result.reverse(); - return [arrayToSmall(result), arrayToSmall(part)]; - } - - function divModSmall(value, lambda) { - var length = value.length, - quotient = createArray(length), - base = BASE, - i, q, remainder, divisor; - remainder = 0; - for (i = length - 1; i >= 0; --i) { - divisor = remainder * base + value[i]; - q = truncate(divisor / lambda); - remainder = divisor - q * lambda; - quotient[i] = q | 0; - } - return [quotient, remainder | 0]; - } - - function divModAny(self, v) { - var value, n = parseValue(v); - if (supportsNativeBigInt) { - return [new NativeBigInt(self.value / n.value), new NativeBigInt(self.value % n.value)]; - } - var a = self.value, b = n.value; - var quotient; - if (b === 0) throw new Error("Cannot divide by zero"); - if (self.isSmall) { - if (n.isSmall) { - return [new SmallInteger(truncate(a / b)), new SmallInteger(a % b)]; - } - return [Integer[0], self]; - } - if (n.isSmall) { - if (b === 1) return [self, Integer[0]]; - if (b == -1) return [self.negate(), Integer[0]]; - var abs = Math.abs(b); - if (abs < BASE) { - value = divModSmall(a, abs); - quotient = arrayToSmall(value[0]); - var remainder = value[1]; - if (self.sign) remainder = -remainder; - if (typeof quotient === "number") { - if (self.sign !== n.sign) quotient = -quotient; - return [new SmallInteger(quotient), new SmallInteger(remainder)]; - } - return [new BigInteger(quotient, self.sign !== n.sign), new SmallInteger(remainder)]; - } - b = smallToArray(abs); - } - var comparison = compareAbs(a, b); - if (comparison === -1) return [Integer[0], self]; - if (comparison === 0) return [Integer[self.sign === n.sign ? 1 : -1], Integer[0]]; - - // divMod1 is faster on smaller input sizes - if (a.length + b.length <= 200) - value = divMod1(a, b); - else value = divMod2(a, b); - - quotient = value[0]; - var qSign = self.sign !== n.sign, - mod = value[1], - mSign = self.sign; - if (typeof quotient === "number") { - if (qSign) quotient = -quotient; - quotient = new SmallInteger(quotient); - } else quotient = new BigInteger(quotient, qSign); - if (typeof mod === "number") { - if (mSign) mod = -mod; - mod = new SmallInteger(mod); - } else mod = new BigInteger(mod, mSign); - return [quotient, mod]; - } - - BigInteger.prototype.divmod = function (v) { - var result = divModAny(this, v); - return { - quotient: result[0], - remainder: result[1] - }; - }; - NativeBigInt.prototype.divmod = SmallInteger.prototype.divmod = BigInteger.prototype.divmod; - - - BigInteger.prototype.divide = function (v) { - return divModAny(this, v)[0]; - }; - NativeBigInt.prototype.over = NativeBigInt.prototype.divide = function (v) { - return new NativeBigInt(this.value / parseValue(v).value); - }; - SmallInteger.prototype.over = SmallInteger.prototype.divide = BigInteger.prototype.over = BigInteger.prototype.divide; - - BigInteger.prototype.mod = function (v) { - return divModAny(this, v)[1]; - }; - NativeBigInt.prototype.mod = NativeBigInt.prototype.remainder = function (v) { - return new NativeBigInt(this.value % parseValue(v).value); - }; - SmallInteger.prototype.remainder = SmallInteger.prototype.mod = BigInteger.prototype.remainder = BigInteger.prototype.mod; - - BigInteger.prototype.pow = function (v) { - var n = parseValue(v), - a = this.value, - b = n.value, - value, x, y; - if (b === 0) return Integer[1]; - if (a === 0) return Integer[0]; - if (a === 1) return Integer[1]; - if (a === -1) return n.isEven() ? Integer[1] : Integer[-1]; - if (n.sign) { - return Integer[0]; - } - if (!n.isSmall) throw new Error("The exponent " + n.toString() + " is too large."); - if (this.isSmall) { - if (isPrecise(value = Math.pow(a, b))) - return new SmallInteger(truncate(value)); - } - x = this; - y = Integer[1]; - while (true) { - if (b & 1 === 1) { - y = y.times(x); - --b; - } - if (b === 0) break; - b /= 2; - x = x.square(); - } - return y; - }; - SmallInteger.prototype.pow = BigInteger.prototype.pow; - - NativeBigInt.prototype.pow = function (v) { - var n = parseValue(v); - var a = this.value, b = n.value; - var _0 = BigInt(0), _1 = BigInt(1), _2 = BigInt(2); - if (b === _0) return Integer[1]; - if (a === _0) return Integer[0]; - if (a === _1) return Integer[1]; - if (a === BigInt(-1)) return n.isEven() ? Integer[1] : Integer[-1]; - if (n.isNegative()) return new NativeBigInt(_0); - var x = this; - var y = Integer[1]; - while (true) { - if ((b & _1) === _1) { - y = y.times(x); - --b; - } - if (b === _0) break; - b /= _2; - x = x.square(); - } - return y; - } - - BigInteger.prototype.modPow = function (exp, mod) { - exp = parseValue(exp); - mod = parseValue(mod); - if (mod.isZero()) throw new Error("Cannot take modPow with modulus 0"); - var r = Integer[1], - base = this.mod(mod); - while (exp.isPositive()) { - if (base.isZero()) return Integer[0]; - if (exp.isOdd()) r = r.multiply(base).mod(mod); - exp = exp.divide(2); - base = base.square().mod(mod); - } - return r; - }; - NativeBigInt.prototype.modPow = SmallInteger.prototype.modPow = BigInteger.prototype.modPow; - - function compareAbs(a, b) { - if (a.length !== b.length) { - return a.length > b.length ? 1 : -1; - } - for (var i = a.length - 1; i >= 0; i--) { - if (a[i] !== b[i]) return a[i] > b[i] ? 1 : -1; - } - return 0; - } - - BigInteger.prototype.compareAbs = function (v) { - var n = parseValue(v), - a = this.value, - b = n.value; - if (n.isSmall) return 1; - return compareAbs(a, b); - }; - SmallInteger.prototype.compareAbs = function (v) { - var n = parseValue(v), - a = Math.abs(this.value), - b = n.value; - if (n.isSmall) { - b = Math.abs(b); - return a === b ? 0 : a > b ? 1 : -1; - } - return -1; - }; - NativeBigInt.prototype.compareAbs = function (v) { - var a = this.value; - var b = parseValue(v).value; - a = a >= 0 ? a : -a; - b = b >= 0 ? b : -b; - return a === b ? 0 : a > b ? 1 : -1; - } - - BigInteger.prototype.compare = function (v) { - // See discussion about comparison with Infinity: - // https://github.com/peterolson/BigInteger.js/issues/61 - if (v === Infinity) { - return -1; - } - if (v === -Infinity) { - return 1; - } - - var n = parseValue(v), - a = this.value, - b = n.value; - if (this.sign !== n.sign) { - return n.sign ? 1 : -1; - } - if (n.isSmall) { - return this.sign ? -1 : 1; - } - return compareAbs(a, b) * (this.sign ? -1 : 1); - }; - BigInteger.prototype.compareTo = BigInteger.prototype.compare; - - SmallInteger.prototype.compare = function (v) { - if (v === Infinity) { - return -1; - } - if (v === -Infinity) { - return 1; - } - - var n = parseValue(v), - a = this.value, - b = n.value; - if (n.isSmall) { - return a == b ? 0 : a > b ? 1 : -1; - } - if (a < 0 !== n.sign) { - return a < 0 ? -1 : 1; - } - return a < 0 ? 1 : -1; - }; - SmallInteger.prototype.compareTo = SmallInteger.prototype.compare; - - NativeBigInt.prototype.compare = function (v) { - if (v === Infinity) { - return -1; - } - if (v === -Infinity) { - return 1; - } - var a = this.value; - var b = parseValue(v).value; - return a === b ? 0 : a > b ? 1 : -1; - } - NativeBigInt.prototype.compareTo = NativeBigInt.prototype.compare; - - BigInteger.prototype.equals = function (v) { - return this.compare(v) === 0; - }; - NativeBigInt.prototype.eq = NativeBigInt.prototype.equals = SmallInteger.prototype.eq = SmallInteger.prototype.equals = BigInteger.prototype.eq = BigInteger.prototype.equals; - - BigInteger.prototype.notEquals = function (v) { - return this.compare(v) !== 0; - }; - NativeBigInt.prototype.neq = NativeBigInt.prototype.notEquals = SmallInteger.prototype.neq = SmallInteger.prototype.notEquals = BigInteger.prototype.neq = BigInteger.prototype.notEquals; - - BigInteger.prototype.greater = function (v) { - return this.compare(v) > 0; - }; - NativeBigInt.prototype.gt = NativeBigInt.prototype.greater = SmallInteger.prototype.gt = SmallInteger.prototype.greater = BigInteger.prototype.gt = BigInteger.prototype.greater; - - BigInteger.prototype.lesser = function (v) { - return this.compare(v) < 0; - }; - NativeBigInt.prototype.lt = NativeBigInt.prototype.lesser = SmallInteger.prototype.lt = SmallInteger.prototype.lesser = BigInteger.prototype.lt = BigInteger.prototype.lesser; - - BigInteger.prototype.greaterOrEquals = function (v) { - return this.compare(v) >= 0; - }; - NativeBigInt.prototype.geq = NativeBigInt.prototype.greaterOrEquals = SmallInteger.prototype.geq = SmallInteger.prototype.greaterOrEquals = BigInteger.prototype.geq = BigInteger.prototype.greaterOrEquals; - - BigInteger.prototype.lesserOrEquals = function (v) { - return this.compare(v) <= 0; - }; - NativeBigInt.prototype.leq = NativeBigInt.prototype.lesserOrEquals = SmallInteger.prototype.leq = SmallInteger.prototype.lesserOrEquals = BigInteger.prototype.leq = BigInteger.prototype.lesserOrEquals; - - BigInteger.prototype.isEven = function () { - return (this.value[0] & 1) === 0; - }; - SmallInteger.prototype.isEven = function () { - return (this.value & 1) === 0; - }; - NativeBigInt.prototype.isEven = function () { - return (this.value & BigInt(1)) === BigInt(0); - } - - BigInteger.prototype.isOdd = function () { - return (this.value[0] & 1) === 1; - }; - SmallInteger.prototype.isOdd = function () { - return (this.value & 1) === 1; - }; - NativeBigInt.prototype.isOdd = function () { - return (this.value & BigInt(1)) === BigInt(1); - } - - BigInteger.prototype.isPositive = function () { - return !this.sign; - }; - SmallInteger.prototype.isPositive = function () { - return this.value > 0; - }; - NativeBigInt.prototype.isPositive = SmallInteger.prototype.isPositive; - - BigInteger.prototype.isNegative = function () { - return this.sign; - }; - SmallInteger.prototype.isNegative = function () { - return this.value < 0; - }; - NativeBigInt.prototype.isNegative = SmallInteger.prototype.isNegative; - - BigInteger.prototype.isUnit = function () { - return false; - }; - SmallInteger.prototype.isUnit = function () { - return Math.abs(this.value) === 1; - }; - NativeBigInt.prototype.isUnit = function () { - return this.abs().value === BigInt(1); - } - - BigInteger.prototype.isZero = function () { - return false; - }; - SmallInteger.prototype.isZero = function () { - return this.value === 0; - }; - NativeBigInt.prototype.isZero = function () { - return this.value === BigInt(0); - } - - BigInteger.prototype.isDivisibleBy = function (v) { - var n = parseValue(v); - if (n.isZero()) return false; - if (n.isUnit()) return true; - if (n.compareAbs(2) === 0) return this.isEven(); - return this.mod(n).isZero(); - }; - NativeBigInt.prototype.isDivisibleBy = SmallInteger.prototype.isDivisibleBy = BigInteger.prototype.isDivisibleBy; - - function isBasicPrime(v) { - var n = v.abs(); - if (n.isUnit()) return false; - if (n.equals(2) || n.equals(3) || n.equals(5)) return true; - if (n.isEven() || n.isDivisibleBy(3) || n.isDivisibleBy(5)) return false; - if (n.lesser(49)) return true; - // we don't know if it's prime: let the other functions figure it out - } - - function millerRabinTest(n, a) { - var nPrev = n.prev(), - b = nPrev, - r = 0, - d, t, i, x; - while (b.isEven()) b = b.divide(2), r++; - next: for (i = 0; i < a.length; i++) { - if (n.lesser(a[i])) continue; - x = bigInt(a[i]).modPow(b, n); - if (x.isUnit() || x.equals(nPrev)) continue; - for (d = r - 1; d != 0; d--) { - x = x.square().mod(n); - if (x.isUnit()) return false; - if (x.equals(nPrev)) continue next; - } - return false; - } - return true; - } - - // Set "strict" to true to force GRH-supported lower bound of 2*log(N)^2 - BigInteger.prototype.isPrime = function (strict) { - var isPrime = isBasicPrime(this); - if (isPrime !== undefined) return isPrime; - var n = this.abs(); - var bits = n.bitLength(); - if (bits <= 64) - return millerRabinTest(n, [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37]); - var logN = Math.log(2) * bits.toJSNumber(); - var t = Math.ceil((strict === true) ? (2 * Math.pow(logN, 2)) : logN); - for (var a = [], i = 0; i < t; i++) { - a.push(bigInt(i + 2)); - } - return millerRabinTest(n, a); - }; - NativeBigInt.prototype.isPrime = SmallInteger.prototype.isPrime = BigInteger.prototype.isPrime; - - BigInteger.prototype.isProbablePrime = function (iterations) { - var isPrime = isBasicPrime(this); - if (isPrime !== undefined) return isPrime; - var n = this.abs(); - var t = iterations === undefined ? 5 : iterations; - for (var a = [], i = 0; i < t; i++) { - a.push(bigInt.randBetween(2, n.minus(2))); - } - return millerRabinTest(n, a); - }; - NativeBigInt.prototype.isProbablePrime = SmallInteger.prototype.isProbablePrime = BigInteger.prototype.isProbablePrime; - - BigInteger.prototype.modInv = function (n) { - var t = bigInt.zero, newT = bigInt.one, r = parseValue(n), newR = this.abs(), q, lastT, lastR; - while (!newR.isZero()) { - q = r.divide(newR); - lastT = t; - lastR = r; - t = newT; - r = newR; - newT = lastT.subtract(q.multiply(newT)); - newR = lastR.subtract(q.multiply(newR)); - } - if (!r.isUnit()) throw new Error(this.toString() + " and " + n.toString() + " are not co-prime"); - if (t.compare(0) === -1) { - t = t.add(n); - } - if (this.isNegative()) { - return t.negate(); - } - return t; - }; - - NativeBigInt.prototype.modInv = SmallInteger.prototype.modInv = BigInteger.prototype.modInv; - - BigInteger.prototype.next = function () { - var value = this.value; - if (this.sign) { - return subtractSmall(value, 1, this.sign); - } - return new BigInteger(addSmall(value, 1), this.sign); - }; - SmallInteger.prototype.next = function () { - var value = this.value; - if (value + 1 < MAX_INT) return new SmallInteger(value + 1); - return new BigInteger(MAX_INT_ARR, false); - }; - NativeBigInt.prototype.next = function () { - return new NativeBigInt(this.value + BigInt(1)); - } - - BigInteger.prototype.prev = function () { - var value = this.value; - if (this.sign) { - return new BigInteger(addSmall(value, 1), true); - } - return subtractSmall(value, 1, this.sign); - }; - SmallInteger.prototype.prev = function () { - var value = this.value; - if (value - 1 > -MAX_INT) return new SmallInteger(value - 1); - return new BigInteger(MAX_INT_ARR, true); - }; - NativeBigInt.prototype.prev = function () { - return new NativeBigInt(this.value - BigInt(1)); - } - - var powersOfTwo = [1]; - while (2 * powersOfTwo[powersOfTwo.length - 1] <= BASE) powersOfTwo.push(2 * powersOfTwo[powersOfTwo.length - 1]); - var powers2Length = powersOfTwo.length, highestPower2 = powersOfTwo[powers2Length - 1]; - - function shift_isSmall(n) { - return Math.abs(n) <= BASE; - } - - BigInteger.prototype.shiftLeft = function (v) { - var n = parseValue(v).toJSNumber(); - if (!shift_isSmall(n)) { - throw new Error(String(n) + " is too large for shifting."); - } - if (n < 0) return this.shiftRight(-n); - var result = this; - if (result.isZero()) return result; - while (n >= powers2Length) { - result = result.multiply(highestPower2); - n -= powers2Length - 1; - } - return result.multiply(powersOfTwo[n]); - }; - NativeBigInt.prototype.shiftLeft = SmallInteger.prototype.shiftLeft = BigInteger.prototype.shiftLeft; - - BigInteger.prototype.shiftRight = function (v) { - var remQuo; - var n = parseValue(v).toJSNumber(); - if (!shift_isSmall(n)) { - throw new Error(String(n) + " is too large for shifting."); - } - if (n < 0) return this.shiftLeft(-n); - var result = this; - while (n >= powers2Length) { - if (result.isZero() || (result.isNegative() && result.isUnit())) return result; - remQuo = divModAny(result, highestPower2); - result = remQuo[1].isNegative() ? remQuo[0].prev() : remQuo[0]; - n -= powers2Length - 1; - } - remQuo = divModAny(result, powersOfTwo[n]); - return remQuo[1].isNegative() ? remQuo[0].prev() : remQuo[0]; - }; - NativeBigInt.prototype.shiftRight = SmallInteger.prototype.shiftRight = BigInteger.prototype.shiftRight; - - function bitwise(x, y, fn) { - y = parseValue(y); - var xSign = x.isNegative(), ySign = y.isNegative(); - var xRem = xSign ? x.not() : x, - yRem = ySign ? y.not() : y; - var xDigit = 0, yDigit = 0; - var xDivMod = null, yDivMod = null; - var result = []; - while (!xRem.isZero() || !yRem.isZero()) { - xDivMod = divModAny(xRem, highestPower2); - xDigit = xDivMod[1].toJSNumber(); - if (xSign) { - xDigit = highestPower2 - 1 - xDigit; // two's complement for negative numbers - } - - yDivMod = divModAny(yRem, highestPower2); - yDigit = yDivMod[1].toJSNumber(); - if (ySign) { - yDigit = highestPower2 - 1 - yDigit; // two's complement for negative numbers - } - - xRem = xDivMod[0]; - yRem = yDivMod[0]; - result.push(fn(xDigit, yDigit)); - } - var sum = fn(xSign ? 1 : 0, ySign ? 1 : 0) !== 0 ? bigInt(-1) : bigInt(0); - for (var i = result.length - 1; i >= 0; i -= 1) { - sum = sum.multiply(highestPower2).add(bigInt(result[i])); - } - return sum; - } - - BigInteger.prototype.not = function () { - return this.negate().prev(); - }; - NativeBigInt.prototype.not = SmallInteger.prototype.not = BigInteger.prototype.not; - - BigInteger.prototype.and = function (n) { - return bitwise(this, n, function (a, b) { return a & b; }); - }; - NativeBigInt.prototype.and = SmallInteger.prototype.and = BigInteger.prototype.and; - - BigInteger.prototype.or = function (n) { - return bitwise(this, n, function (a, b) { return a | b; }); - }; - NativeBigInt.prototype.or = SmallInteger.prototype.or = BigInteger.prototype.or; - - BigInteger.prototype.xor = function (n) { - return bitwise(this, n, function (a, b) { return a ^ b; }); - }; - NativeBigInt.prototype.xor = SmallInteger.prototype.xor = BigInteger.prototype.xor; - - var LOBMASK_I = 1 << 30, LOBMASK_BI = (BASE & -BASE) * (BASE & -BASE) | LOBMASK_I; - function roughLOB(n) { // get lowestOneBit (rough) - // SmallInteger: return Min(lowestOneBit(n), 1 << 30) - // BigInteger: return Min(lowestOneBit(n), 1 << 14) [BASE=1e7] - var v = n.value, - x = typeof v === "number" ? v | LOBMASK_I : - typeof v === "bigint" ? v | BigInt(LOBMASK_I) : - v[0] + v[1] * BASE | LOBMASK_BI; - return x & -x; - } - - function integerLogarithm(value, base) { - if (base.compareTo(value) <= 0) { - var tmp = integerLogarithm(value, base.square(base)); - var p = tmp.p; - var e = tmp.e; - var t = p.multiply(base); - return t.compareTo(value) <= 0 ? { p: t, e: e * 2 + 1 } : { p: p, e: e * 2 }; - } - return { p: bigInt(1), e: 0 }; - } - - BigInteger.prototype.bitLength = function () { - var n = this; - if (n.compareTo(bigInt(0)) < 0) { - n = n.negate().subtract(bigInt(1)); - } - if (n.compareTo(bigInt(0)) === 0) { - return bigInt(0); - } - return bigInt(integerLogarithm(n, bigInt(2)).e).add(bigInt(1)); - } - NativeBigInt.prototype.bitLength = SmallInteger.prototype.bitLength = BigInteger.prototype.bitLength; - - function max(a, b) { - a = parseValue(a); - b = parseValue(b); - return a.greater(b) ? a : b; - } - function min(a, b) { - a = parseValue(a); - b = parseValue(b); - return a.lesser(b) ? a : b; - } - function gcd(a, b) { - a = parseValue(a).abs(); - b = parseValue(b).abs(); - if (a.equals(b)) return a; - if (a.isZero()) return b; - if (b.isZero()) return a; - var c = Integer[1], d, t; - while (a.isEven() && b.isEven()) { - d = min(roughLOB(a), roughLOB(b)); - a = a.divide(d); - b = b.divide(d); - c = c.multiply(d); - } - while (a.isEven()) { - a = a.divide(roughLOB(a)); - } - do { - while (b.isEven()) { - b = b.divide(roughLOB(b)); - } - if (a.greater(b)) { - t = b; b = a; a = t; - } - b = b.subtract(a); - } while (!b.isZero()); - return c.isUnit() ? a : a.multiply(c); - } - function lcm(a, b) { - a = parseValue(a).abs(); - b = parseValue(b).abs(); - return a.divide(gcd(a, b)).multiply(b); - } - function randBetween(a, b) { - a = parseValue(a); - b = parseValue(b); - var low = min(a, b), high = max(a, b); - var range = high.subtract(low).add(1); - if (range.isSmall) return low.add(Math.floor(Math.random() * range)); - var digits = toBase(range, BASE).value; - var result = [], restricted = true; - for (var i = 0; i < digits.length; i++) { - var top = restricted ? digits[i] : BASE; - var digit = truncate(Math.random() * top); - result.push(digit); - if (digit < top) restricted = false; - } - return low.add(Integer.fromArray(result, BASE, false)); - } - - var parseBase = function (text, base, alphabet, caseSensitive) { - alphabet = alphabet || DEFAULT_ALPHABET; - text = String(text); - if (!caseSensitive) { - text = text.toLowerCase(); - alphabet = alphabet.toLowerCase(); - } - var length = text.length; - var i; - var absBase = Math.abs(base); - var alphabetValues = {}; - for (i = 0; i < alphabet.length; i++) { - alphabetValues[alphabet[i]] = i; - } - for (i = 0; i < length; i++) { - var c = text[i]; - if (c === "-") continue; - if (c in alphabetValues) { - if (alphabetValues[c] >= absBase) { - if (c === "1" && absBase === 1) continue; - throw new Error(c + " is not a valid digit in base " + base + "."); - } - } - } - base = parseValue(base); - var digits = []; - var isNegative = text[0] === "-"; - for (i = isNegative ? 1 : 0; i < text.length; i++) { - var c = text[i]; - if (c in alphabetValues) digits.push(parseValue(alphabetValues[c])); - else if (c === "<") { - var start = i; - do { i++; } while (text[i] !== ">" && i < text.length); - digits.push(parseValue(text.slice(start + 1, i))); - } - else throw new Error(c + " is not a valid character"); - } - return parseBaseFromArray(digits, base, isNegative); - }; - - function parseBaseFromArray(digits, base, isNegative) { - var val = Integer[0], pow = Integer[1], i; - for (i = digits.length - 1; i >= 0; i--) { - val = val.add(digits[i].times(pow)); - pow = pow.times(base); - } - return isNegative ? val.negate() : val; - } - - function stringify(digit, alphabet) { - alphabet = alphabet || DEFAULT_ALPHABET; - if (digit < alphabet.length) { - return alphabet[digit]; - } - return "<" + digit + ">"; - } - - function toBase(n, base) { - base = bigInt(base); - if (base.isZero()) { - if (n.isZero()) return { value: [0], isNegative: false }; - throw new Error("Cannot convert nonzero numbers to base 0."); - } - if (base.equals(-1)) { - if (n.isZero()) return { value: [0], isNegative: false }; - if (n.isNegative()) - return { - value: [].concat.apply([], Array.apply(null, Array(-n.toJSNumber())) - .map(Array.prototype.valueOf, [1, 0]) - ), - isNegative: false - }; - - var arr = Array.apply(null, Array(n.toJSNumber() - 1)) - .map(Array.prototype.valueOf, [0, 1]); - arr.unshift([1]); - return { - value: [].concat.apply([], arr), - isNegative: false - }; - } - - var neg = false; - if (n.isNegative() && base.isPositive()) { - neg = true; - n = n.abs(); - } - if (base.isUnit()) { - if (n.isZero()) return { value: [0], isNegative: false }; - - return { - value: Array.apply(null, Array(n.toJSNumber())) - .map(Number.prototype.valueOf, 1), - isNegative: neg - }; - } - var out = []; - var left = n, divmod; - while (left.isNegative() || left.compareAbs(base) >= 0) { - divmod = left.divmod(base); - left = divmod.quotient; - var digit = divmod.remainder; - if (digit.isNegative()) { - digit = base.minus(digit).abs(); - left = left.next(); - } - out.push(digit.toJSNumber()); - } - out.push(left.toJSNumber()); - return { value: out.reverse(), isNegative: neg }; - } - - function toBaseString(n, base, alphabet) { - var arr = toBase(n, base); - return (arr.isNegative ? "-" : "") + arr.value.map(function (x) { - return stringify(x, alphabet); - }).join(''); - } - - BigInteger.prototype.toArray = function (radix) { - return toBase(this, radix); - }; - - SmallInteger.prototype.toArray = function (radix) { - return toBase(this, radix); - }; - - NativeBigInt.prototype.toArray = function (radix) { - return toBase(this, radix); - }; - - BigInteger.prototype.toString = function (radix, alphabet) { - if (radix === undefined) radix = 10; - if (radix !== 10) return toBaseString(this, radix, alphabet); - var v = this.value, l = v.length, str = String(v[--l]), zeros = "0000000", digit; - while (--l >= 0) { - digit = String(v[l]); - str += zeros.slice(digit.length) + digit; - } - var sign = this.sign ? "-" : ""; - return sign + str; - }; - - SmallInteger.prototype.toString = function (radix, alphabet) { - if (radix === undefined) radix = 10; - if (radix != 10) return toBaseString(this, radix, alphabet); - return String(this.value); - }; - - NativeBigInt.prototype.toString = SmallInteger.prototype.toString; - - NativeBigInt.prototype.toJSON = BigInteger.prototype.toJSON = SmallInteger.prototype.toJSON = function () { return this.toString(); } - - BigInteger.prototype.valueOf = function () { - return parseInt(this.toString(), 10); - }; - BigInteger.prototype.toJSNumber = BigInteger.prototype.valueOf; - - SmallInteger.prototype.valueOf = function () { - return this.value; - }; - SmallInteger.prototype.toJSNumber = SmallInteger.prototype.valueOf; - NativeBigInt.prototype.valueOf = NativeBigInt.prototype.toJSNumber = function () { - return parseInt(this.toString(), 10); - } - - function parseStringValue(v) { - if (isPrecise(+v)) { - var x = +v; - if (x === truncate(x)) - return supportsNativeBigInt ? new NativeBigInt(BigInt(x)) : new SmallInteger(x); - throw new Error("Invalid integer: " + v); - } - var sign = v[0] === "-"; - if (sign) v = v.slice(1); - var split = v.split(/e/i); - if (split.length > 2) throw new Error("Invalid integer: " + split.join("e")); - if (split.length === 2) { - var exp = split[1]; - if (exp[0] === "+") exp = exp.slice(1); - exp = +exp; - if (exp !== truncate(exp) || !isPrecise(exp)) throw new Error("Invalid integer: " + exp + " is not a valid exponent."); - var text = split[0]; - var decimalPlace = text.indexOf("."); - if (decimalPlace >= 0) { - exp -= text.length - decimalPlace - 1; - text = text.slice(0, decimalPlace) + text.slice(decimalPlace + 1); - } - if (exp < 0) throw new Error("Cannot include negative exponent part for integers"); - text += (new Array(exp + 1)).join("0"); - v = text; - } - var isValid = /^([0-9][0-9]*)$/.test(v); - if (!isValid) throw new Error("Invalid integer: " + v); - if (supportsNativeBigInt) { - return new NativeBigInt(BigInt(sign ? "-" + v : v)); - } - var r = [], max = v.length, l = LOG_BASE, min = max - l; - while (max > 0) { - r.push(+v.slice(min, max)); - min -= l; - if (min < 0) min = 0; - max -= l; - } - trim(r); - return new BigInteger(r, sign); - } - - function parseNumberValue(v) { - if (supportsNativeBigInt) { - return new NativeBigInt(BigInt(v)); - } - if (isPrecise(v)) { - if (v !== truncate(v)) throw new Error(v + " is not an integer."); - return new SmallInteger(v); - } - return parseStringValue(v.toString()); - } - - function parseValue(v) { - if (typeof v === "number") { - return parseNumberValue(v); - } - if (typeof v === "string") { - return parseStringValue(v); - } - if (typeof v === "bigint") { - return new NativeBigInt(v); - } - return v; - } - // Pre-define numbers in range [-999,999] - for (var i = 0; i < 1000; i++) { - Integer[i] = parseValue(i); - if (i > 0) Integer[-i] = parseValue(-i); - } - // Backwards compatibility - Integer.one = Integer[1]; - Integer.zero = Integer[0]; - Integer.minusOne = Integer[-1]; - Integer.max = max; - Integer.min = min; - Integer.gcd = gcd; - Integer.lcm = lcm; - Integer.isInstance = function (x) { return x instanceof BigInteger || x instanceof SmallInteger || x instanceof NativeBigInt; }; - Integer.randBetween = randBetween; - - Integer.fromArray = function (digits, base, isNegative) { - return parseBaseFromArray(digits.map(parseValue), parseValue(base || 10), isNegative); - }; - - return Integer; -})(); - -// Node.js check -if (typeof module !== "undefined" && module.hasOwnProperty("exports")) { - module.exports = bigInt; -} - -//amd check -if (typeof define === "function" && define.amd) { - define("big-integer", [], function () { - return bigInt; - }); -} +var bigInt = (function (undefined) { + "use strict"; + + var BASE = 1e7, + LOG_BASE = 7, + MAX_INT = 9007199254740992, + MAX_INT_ARR = smallToArray(MAX_INT), + DEFAULT_ALPHABET = "0123456789abcdefghijklmnopqrstuvwxyz"; + + var supportsNativeBigInt = typeof BigInt === "function"; + + function Integer(v, radix, alphabet, caseSensitive) { + if (typeof v === "undefined") return Integer[0]; + if (typeof radix !== "undefined") return +radix === 10 && !alphabet ? parseValue(v) : parseBase(v, radix, alphabet, caseSensitive); + return parseValue(v); + } + + function BigInteger(value, sign) { + this.value = value; + this.sign = sign; + this.isSmall = false; + } + BigInteger.prototype = Object.create(Integer.prototype); + + function SmallInteger(value) { + this.value = value; + this.sign = value < 0; + this.isSmall = true; + } + SmallInteger.prototype = Object.create(Integer.prototype); + + function NativeBigInt(value) { + this.value = value; + } + NativeBigInt.prototype = Object.create(Integer.prototype); + + function isPrecise(n) { + return -MAX_INT < n && n < MAX_INT; + } + + function smallToArray(n) { // For performance reasons doesn't reference BASE, need to change this function if BASE changes + if (n < 1e7) + return [n]; + if (n < 1e14) + return [n % 1e7, Math.floor(n / 1e7)]; + return [n % 1e7, Math.floor(n / 1e7) % 1e7, Math.floor(n / 1e14)]; + } + + function arrayToSmall(arr) { // If BASE changes this function may need to change + trim(arr); + var length = arr.length; + if (length < 4 && compareAbs(arr, MAX_INT_ARR) < 0) { + switch (length) { + case 0: return 0; + case 1: return arr[0]; + case 2: return arr[0] + arr[1] * BASE; + default: return arr[0] + (arr[1] + arr[2] * BASE) * BASE; + } + } + return arr; + } + + function trim(v) { + var i = v.length; + while (v[--i] === 0); + v.length = i + 1; + } + + function createArray(length) { // function shamelessly stolen from Yaffle's library https://github.com/Yaffle/BigInteger + var x = new Array(length); + var i = -1; + while (++i < length) { + x[i] = 0; + } + return x; + } + + function truncate(n) { + if (n > 0) return Math.floor(n); + return Math.ceil(n); + } + + function add(a, b) { // assumes a and b are arrays with a.length >= b.length + var l_a = a.length, + l_b = b.length, + r = new Array(l_a), + carry = 0, + base = BASE, + sum, i; + for (i = 0; i < l_b; i++) { + sum = a[i] + b[i] + carry; + carry = sum >= base ? 1 : 0; + r[i] = sum - carry * base; + } + while (i < l_a) { + sum = a[i] + carry; + carry = sum === base ? 1 : 0; + r[i++] = sum - carry * base; + } + if (carry > 0) r.push(carry); + return r; + } + + function addAny(a, b) { + if (a.length >= b.length) return add(a, b); + return add(b, a); + } + + function addSmall(a, carry) { // assumes a is array, carry is number with 0 <= carry < MAX_INT + var l = a.length, + r = new Array(l), + base = BASE, + sum, i; + for (i = 0; i < l; i++) { + sum = a[i] - base + carry; + carry = Math.floor(sum / base); + r[i] = sum - carry * base; + carry += 1; + } + while (carry > 0) { + r[i++] = carry % base; + carry = Math.floor(carry / base); + } + return r; + } + + BigInteger.prototype.add = function (v) { + var n = parseValue(v); + if (this.sign !== n.sign) { + return this.subtract(n.negate()); + } + var a = this.value, b = n.value; + if (n.isSmall) { + return new BigInteger(addSmall(a, Math.abs(b)), this.sign); + } + return new BigInteger(addAny(a, b), this.sign); + }; + BigInteger.prototype.plus = BigInteger.prototype.add; + + SmallInteger.prototype.add = function (v) { + var n = parseValue(v); + var a = this.value; + if (a < 0 !== n.sign) { + return this.subtract(n.negate()); + } + var b = n.value; + if (n.isSmall) { + if (isPrecise(a + b)) return new SmallInteger(a + b); + b = smallToArray(Math.abs(b)); + } + return new BigInteger(addSmall(b, Math.abs(a)), a < 0); + }; + SmallInteger.prototype.plus = SmallInteger.prototype.add; + + NativeBigInt.prototype.add = function (v) { + return new NativeBigInt(this.value + parseValue(v).value); + } + NativeBigInt.prototype.plus = NativeBigInt.prototype.add; + + function subtract(a, b) { // assumes a and b are arrays with a >= b + var a_l = a.length, + b_l = b.length, + r = new Array(a_l), + borrow = 0, + base = BASE, + i, difference; + for (i = 0; i < b_l; i++) { + difference = a[i] - borrow - b[i]; + if (difference < 0) { + difference += base; + borrow = 1; + } else borrow = 0; + r[i] = difference; + } + for (i = b_l; i < a_l; i++) { + difference = a[i] - borrow; + if (difference < 0) difference += base; + else { + r[i++] = difference; + break; + } + r[i] = difference; + } + for (; i < a_l; i++) { + r[i] = a[i]; + } + trim(r); + return r; + } + + function subtractAny(a, b, sign) { + var value; + if (compareAbs(a, b) >= 0) { + value = subtract(a, b); + } else { + value = subtract(b, a); + sign = !sign; + } + value = arrayToSmall(value); + if (typeof value === "number") { + if (sign) value = -value; + return new SmallInteger(value); + } + return new BigInteger(value, sign); + } + + function subtractSmall(a, b, sign) { // assumes a is array, b is number with 0 <= b < MAX_INT + var l = a.length, + r = new Array(l), + carry = -b, + base = BASE, + i, difference; + for (i = 0; i < l; i++) { + difference = a[i] + carry; + carry = Math.floor(difference / base); + difference %= base; + r[i] = difference < 0 ? difference + base : difference; + } + r = arrayToSmall(r); + if (typeof r === "number") { + if (sign) r = -r; + return new SmallInteger(r); + } return new BigInteger(r, sign); + } + + BigInteger.prototype.subtract = function (v) { + var n = parseValue(v); + if (this.sign !== n.sign) { + return this.add(n.negate()); + } + var a = this.value, b = n.value; + if (n.isSmall) + return subtractSmall(a, Math.abs(b), this.sign); + return subtractAny(a, b, this.sign); + }; + BigInteger.prototype.minus = BigInteger.prototype.subtract; + + SmallInteger.prototype.subtract = function (v) { + var n = parseValue(v); + var a = this.value; + if (a < 0 !== n.sign) { + return this.add(n.negate()); + } + var b = n.value; + if (n.isSmall) { + return new SmallInteger(a - b); + } + return subtractSmall(b, Math.abs(a), a >= 0); + }; + SmallInteger.prototype.minus = SmallInteger.prototype.subtract; + + NativeBigInt.prototype.subtract = function (v) { + return new NativeBigInt(this.value - parseValue(v).value); + } + NativeBigInt.prototype.minus = NativeBigInt.prototype.subtract; + + BigInteger.prototype.negate = function () { + return new BigInteger(this.value, !this.sign); + }; + SmallInteger.prototype.negate = function () { + var sign = this.sign; + var small = new SmallInteger(-this.value); + small.sign = !sign; + return small; + }; + NativeBigInt.prototype.negate = function () { + return new NativeBigInt(-this.value); + } + + BigInteger.prototype.abs = function () { + return new BigInteger(this.value, false); + }; + SmallInteger.prototype.abs = function () { + return new SmallInteger(Math.abs(this.value)); + }; + NativeBigInt.prototype.abs = function () { + return new NativeBigInt(this.value >= 0 ? this.value : -this.value); + } + + + function multiplyLong(a, b) { + var a_l = a.length, + b_l = b.length, + l = a_l + b_l, + r = createArray(l), + base = BASE, + product, carry, i, a_i, b_j; + for (i = 0; i < a_l; ++i) { + a_i = a[i]; + for (var j = 0; j < b_l; ++j) { + b_j = b[j]; + product = a_i * b_j + r[i + j]; + carry = Math.floor(product / base); + r[i + j] = product - carry * base; + r[i + j + 1] += carry; + } + } + trim(r); + return r; + } + + function multiplySmall(a, b) { // assumes a is array, b is number with |b| < BASE + var l = a.length, + r = new Array(l), + base = BASE, + carry = 0, + product, i; + for (i = 0; i < l; i++) { + product = a[i] * b + carry; + carry = Math.floor(product / base); + r[i] = product - carry * base; + } + while (carry > 0) { + r[i++] = carry % base; + carry = Math.floor(carry / base); + } + return r; + } + + function shiftLeft(x, n) { + var r = []; + while (n-- > 0) r.push(0); + return r.concat(x); + } + + function multiplyKaratsuba(x, y) { + var n = Math.max(x.length, y.length); + + if (n <= 30) return multiplyLong(x, y); + n = Math.ceil(n / 2); + + var b = x.slice(n), + a = x.slice(0, n), + d = y.slice(n), + c = y.slice(0, n); + + var ac = multiplyKaratsuba(a, c), + bd = multiplyKaratsuba(b, d), + abcd = multiplyKaratsuba(addAny(a, b), addAny(c, d)); + + var product = addAny(addAny(ac, shiftLeft(subtract(subtract(abcd, ac), bd), n)), shiftLeft(bd, 2 * n)); + trim(product); + return product; + } + + // The following function is derived from a surface fit of a graph plotting the performance difference + // between long multiplication and karatsuba multiplication versus the lengths of the two arrays. + function useKaratsuba(l1, l2) { + return -0.012 * l1 - 0.012 * l2 + 0.000015 * l1 * l2 > 0; + } + + BigInteger.prototype.multiply = function (v) { + var n = parseValue(v), + a = this.value, b = n.value, + sign = this.sign !== n.sign, + abs; + if (n.isSmall) { + if (b === 0) return Integer[0]; + if (b === 1) return this; + if (b === -1) return this.negate(); + abs = Math.abs(b); + if (abs < BASE) { + return new BigInteger(multiplySmall(a, abs), sign); + } + b = smallToArray(abs); + } + if (useKaratsuba(a.length, b.length)) // Karatsuba is only faster for certain array sizes + return new BigInteger(multiplyKaratsuba(a, b), sign); + return new BigInteger(multiplyLong(a, b), sign); + }; + + BigInteger.prototype.times = BigInteger.prototype.multiply; + + function multiplySmallAndArray(a, b, sign) { // a >= 0 + if (a < BASE) { + return new BigInteger(multiplySmall(b, a), sign); + } + return new BigInteger(multiplyLong(b, smallToArray(a)), sign); + } + SmallInteger.prototype._multiplyBySmall = function (a) { + if (isPrecise(a.value * this.value)) { + return new SmallInteger(a.value * this.value); + } + return multiplySmallAndArray(Math.abs(a.value), smallToArray(Math.abs(this.value)), this.sign !== a.sign); + }; + BigInteger.prototype._multiplyBySmall = function (a) { + if (a.value === 0) return Integer[0]; + if (a.value === 1) return this; + if (a.value === -1) return this.negate(); + return multiplySmallAndArray(Math.abs(a.value), this.value, this.sign !== a.sign); + }; + SmallInteger.prototype.multiply = function (v) { + return parseValue(v)._multiplyBySmall(this); + }; + SmallInteger.prototype.times = SmallInteger.prototype.multiply; + + NativeBigInt.prototype.multiply = function (v) { + return new NativeBigInt(this.value * parseValue(v).value); + } + NativeBigInt.prototype.times = NativeBigInt.prototype.multiply; + + function square(a) { + //console.assert(2 * BASE * BASE < MAX_INT); + var l = a.length, + r = createArray(l + l), + base = BASE, + product, carry, i, a_i, a_j; + for (i = 0; i < l; i++) { + a_i = a[i]; + carry = 0 - a_i * a_i; + for (var j = i; j < l; j++) { + a_j = a[j]; + product = 2 * (a_i * a_j) + r[i + j] + carry; + carry = Math.floor(product / base); + r[i + j] = product - carry * base; + } + r[i + l] = carry; + } + trim(r); + return r; + } + + BigInteger.prototype.square = function () { + return new BigInteger(square(this.value), false); + }; + + SmallInteger.prototype.square = function () { + var value = this.value * this.value; + if (isPrecise(value)) return new SmallInteger(value); + return new BigInteger(square(smallToArray(Math.abs(this.value))), false); + }; + + NativeBigInt.prototype.square = function (v) { + return new NativeBigInt(this.value * this.value); + } + + function divMod1(a, b) { // Left over from previous version. Performs faster than divMod2 on smaller input sizes. + var a_l = a.length, + b_l = b.length, + base = BASE, + result = createArray(b.length), + divisorMostSignificantDigit = b[b_l - 1], + // normalization + lambda = Math.ceil(base / (2 * divisorMostSignificantDigit)), + remainder = multiplySmall(a, lambda), + divisor = multiplySmall(b, lambda), + quotientDigit, shift, carry, borrow, i, l, q; + if (remainder.length <= a_l) remainder.push(0); + divisor.push(0); + divisorMostSignificantDigit = divisor[b_l - 1]; + for (shift = a_l - b_l; shift >= 0; shift--) { + quotientDigit = base - 1; + if (remainder[shift + b_l] !== divisorMostSignificantDigit) { + quotientDigit = Math.floor((remainder[shift + b_l] * base + remainder[shift + b_l - 1]) / divisorMostSignificantDigit); + } + // quotientDigit <= base - 1 + carry = 0; + borrow = 0; + l = divisor.length; + for (i = 0; i < l; i++) { + carry += quotientDigit * divisor[i]; + q = Math.floor(carry / base); + borrow += remainder[shift + i] - (carry - q * base); + carry = q; + if (borrow < 0) { + remainder[shift + i] = borrow + base; + borrow = -1; + } else { + remainder[shift + i] = borrow; + borrow = 0; + } + } + while (borrow !== 0) { + quotientDigit -= 1; + carry = 0; + for (i = 0; i < l; i++) { + carry += remainder[shift + i] - base + divisor[i]; + if (carry < 0) { + remainder[shift + i] = carry + base; + carry = 0; + } else { + remainder[shift + i] = carry; + carry = 1; + } + } + borrow += carry; + } + result[shift] = quotientDigit; + } + // denormalization + remainder = divModSmall(remainder, lambda)[0]; + return [arrayToSmall(result), arrayToSmall(remainder)]; + } + + function divMod2(a, b) { // Implementation idea shamelessly stolen from Silent Matt's library http://silentmatt.com/biginteger/ + // Performs faster than divMod1 on larger input sizes. + var a_l = a.length, + b_l = b.length, + result = [], + part = [], + base = BASE, + guess, xlen, highx, highy, check; + while (a_l) { + part.unshift(a[--a_l]); + trim(part); + if (compareAbs(part, b) < 0) { + result.push(0); + continue; + } + xlen = part.length; + highx = part[xlen - 1] * base + part[xlen - 2]; + highy = b[b_l - 1] * base + b[b_l - 2]; + if (xlen > b_l) { + highx = (highx + 1) * base; + } + guess = Math.ceil(highx / highy); + do { + check = multiplySmall(b, guess); + if (compareAbs(check, part) <= 0) break; + guess--; + } while (guess); + result.push(guess); + part = subtract(part, check); + } + result.reverse(); + return [arrayToSmall(result), arrayToSmall(part)]; + } + + function divModSmall(value, lambda) { + var length = value.length, + quotient = createArray(length), + base = BASE, + i, q, remainder, divisor; + remainder = 0; + for (i = length - 1; i >= 0; --i) { + divisor = remainder * base + value[i]; + q = truncate(divisor / lambda); + remainder = divisor - q * lambda; + quotient[i] = q | 0; + } + return [quotient, remainder | 0]; + } + + function divModAny(self, v) { + var value, n = parseValue(v); + if (supportsNativeBigInt) { + return [new NativeBigInt(self.value / n.value), new NativeBigInt(self.value % n.value)]; + } + var a = self.value, b = n.value; + var quotient; + if (b === 0) throw new Error("Cannot divide by zero"); + if (self.isSmall) { + if (n.isSmall) { + return [new SmallInteger(truncate(a / b)), new SmallInteger(a % b)]; + } + return [Integer[0], self]; + } + if (n.isSmall) { + if (b === 1) return [self, Integer[0]]; + if (b == -1) return [self.negate(), Integer[0]]; + var abs = Math.abs(b); + if (abs < BASE) { + value = divModSmall(a, abs); + quotient = arrayToSmall(value[0]); + var remainder = value[1]; + if (self.sign) remainder = -remainder; + if (typeof quotient === "number") { + if (self.sign !== n.sign) quotient = -quotient; + return [new SmallInteger(quotient), new SmallInteger(remainder)]; + } + return [new BigInteger(quotient, self.sign !== n.sign), new SmallInteger(remainder)]; + } + b = smallToArray(abs); + } + var comparison = compareAbs(a, b); + if (comparison === -1) return [Integer[0], self]; + if (comparison === 0) return [Integer[self.sign === n.sign ? 1 : -1], Integer[0]]; + + // divMod1 is faster on smaller input sizes + if (a.length + b.length <= 200) + value = divMod1(a, b); + else value = divMod2(a, b); + + quotient = value[0]; + var qSign = self.sign !== n.sign, + mod = value[1], + mSign = self.sign; + if (typeof quotient === "number") { + if (qSign) quotient = -quotient; + quotient = new SmallInteger(quotient); + } else quotient = new BigInteger(quotient, qSign); + if (typeof mod === "number") { + if (mSign) mod = -mod; + mod = new SmallInteger(mod); + } else mod = new BigInteger(mod, mSign); + return [quotient, mod]; + } + + BigInteger.prototype.divmod = function (v) { + var result = divModAny(this, v); + return { + quotient: result[0], + remainder: result[1] + }; + }; + NativeBigInt.prototype.divmod = SmallInteger.prototype.divmod = BigInteger.prototype.divmod; + + + BigInteger.prototype.divide = function (v) { + return divModAny(this, v)[0]; + }; + NativeBigInt.prototype.over = NativeBigInt.prototype.divide = function (v) { + return new NativeBigInt(this.value / parseValue(v).value); + }; + SmallInteger.prototype.over = SmallInteger.prototype.divide = BigInteger.prototype.over = BigInteger.prototype.divide; + + BigInteger.prototype.mod = function (v) { + return divModAny(this, v)[1]; + }; + NativeBigInt.prototype.mod = NativeBigInt.prototype.remainder = function (v) { + return new NativeBigInt(this.value % parseValue(v).value); + }; + SmallInteger.prototype.remainder = SmallInteger.prototype.mod = BigInteger.prototype.remainder = BigInteger.prototype.mod; + + BigInteger.prototype.pow = function (v) { + var n = parseValue(v), + a = this.value, + b = n.value, + value, x, y; + if (b === 0) return Integer[1]; + if (a === 0) return Integer[0]; + if (a === 1) return Integer[1]; + if (a === -1) return n.isEven() ? Integer[1] : Integer[-1]; + if (n.sign) { + return Integer[0]; + } + if (!n.isSmall) throw new Error("The exponent " + n.toString() + " is too large."); + if (this.isSmall) { + if (isPrecise(value = Math.pow(a, b))) + return new SmallInteger(truncate(value)); + } + x = this; + y = Integer[1]; + while (true) { + if (b & 1 === 1) { + y = y.times(x); + --b; + } + if (b === 0) break; + b /= 2; + x = x.square(); + } + return y; + }; + SmallInteger.prototype.pow = BigInteger.prototype.pow; + + NativeBigInt.prototype.pow = function (v) { + var n = parseValue(v); + var a = this.value, b = n.value; + var _0 = BigInt(0), _1 = BigInt(1), _2 = BigInt(2); + if (b === _0) return Integer[1]; + if (a === _0) return Integer[0]; + if (a === _1) return Integer[1]; + if (a === BigInt(-1)) return n.isEven() ? Integer[1] : Integer[-1]; + if (n.isNegative()) return new NativeBigInt(_0); + var x = this; + var y = Integer[1]; + while (true) { + if ((b & _1) === _1) { + y = y.times(x); + --b; + } + if (b === _0) break; + b /= _2; + x = x.square(); + } + return y; + } + + BigInteger.prototype.modPow = function (exp, mod) { + exp = parseValue(exp); + mod = parseValue(mod); + if (mod.isZero()) throw new Error("Cannot take modPow with modulus 0"); + var r = Integer[1], + base = this.mod(mod); + while (exp.isPositive()) { + if (base.isZero()) return Integer[0]; + if (exp.isOdd()) r = r.multiply(base).mod(mod); + exp = exp.divide(2); + base = base.square().mod(mod); + } + return r; + }; + NativeBigInt.prototype.modPow = SmallInteger.prototype.modPow = BigInteger.prototype.modPow; + + function compareAbs(a, b) { + if (a.length !== b.length) { + return a.length > b.length ? 1 : -1; + } + for (var i = a.length - 1; i >= 0; i--) { + if (a[i] !== b[i]) return a[i] > b[i] ? 1 : -1; + } + return 0; + } + + BigInteger.prototype.compareAbs = function (v) { + var n = parseValue(v), + a = this.value, + b = n.value; + if (n.isSmall) return 1; + return compareAbs(a, b); + }; + SmallInteger.prototype.compareAbs = function (v) { + var n = parseValue(v), + a = Math.abs(this.value), + b = n.value; + if (n.isSmall) { + b = Math.abs(b); + return a === b ? 0 : a > b ? 1 : -1; + } + return -1; + }; + NativeBigInt.prototype.compareAbs = function (v) { + var a = this.value; + var b = parseValue(v).value; + a = a >= 0 ? a : -a; + b = b >= 0 ? b : -b; + return a === b ? 0 : a > b ? 1 : -1; + } + + BigInteger.prototype.compare = function (v) { + // See discussion about comparison with Infinity: + // https://github.com/peterolson/BigInteger.js/issues/61 + if (v === Infinity) { + return -1; + } + if (v === -Infinity) { + return 1; + } + + var n = parseValue(v), + a = this.value, + b = n.value; + if (this.sign !== n.sign) { + return n.sign ? 1 : -1; + } + if (n.isSmall) { + return this.sign ? -1 : 1; + } + return compareAbs(a, b) * (this.sign ? -1 : 1); + }; + BigInteger.prototype.compareTo = BigInteger.prototype.compare; + + SmallInteger.prototype.compare = function (v) { + if (v === Infinity) { + return -1; + } + if (v === -Infinity) { + return 1; + } + + var n = parseValue(v), + a = this.value, + b = n.value; + if (n.isSmall) { + return a == b ? 0 : a > b ? 1 : -1; + } + if (a < 0 !== n.sign) { + return a < 0 ? -1 : 1; + } + return a < 0 ? 1 : -1; + }; + SmallInteger.prototype.compareTo = SmallInteger.prototype.compare; + + NativeBigInt.prototype.compare = function (v) { + if (v === Infinity) { + return -1; + } + if (v === -Infinity) { + return 1; + } + var a = this.value; + var b = parseValue(v).value; + return a === b ? 0 : a > b ? 1 : -1; + } + NativeBigInt.prototype.compareTo = NativeBigInt.prototype.compare; + + BigInteger.prototype.equals = function (v) { + return this.compare(v) === 0; + }; + NativeBigInt.prototype.eq = NativeBigInt.prototype.equals = SmallInteger.prototype.eq = SmallInteger.prototype.equals = BigInteger.prototype.eq = BigInteger.prototype.equals; + + BigInteger.prototype.notEquals = function (v) { + return this.compare(v) !== 0; + }; + NativeBigInt.prototype.neq = NativeBigInt.prototype.notEquals = SmallInteger.prototype.neq = SmallInteger.prototype.notEquals = BigInteger.prototype.neq = BigInteger.prototype.notEquals; + + BigInteger.prototype.greater = function (v) { + return this.compare(v) > 0; + }; + NativeBigInt.prototype.gt = NativeBigInt.prototype.greater = SmallInteger.prototype.gt = SmallInteger.prototype.greater = BigInteger.prototype.gt = BigInteger.prototype.greater; + + BigInteger.prototype.lesser = function (v) { + return this.compare(v) < 0; + }; + NativeBigInt.prototype.lt = NativeBigInt.prototype.lesser = SmallInteger.prototype.lt = SmallInteger.prototype.lesser = BigInteger.prototype.lt = BigInteger.prototype.lesser; + + BigInteger.prototype.greaterOrEquals = function (v) { + return this.compare(v) >= 0; + }; + NativeBigInt.prototype.geq = NativeBigInt.prototype.greaterOrEquals = SmallInteger.prototype.geq = SmallInteger.prototype.greaterOrEquals = BigInteger.prototype.geq = BigInteger.prototype.greaterOrEquals; + + BigInteger.prototype.lesserOrEquals = function (v) { + return this.compare(v) <= 0; + }; + NativeBigInt.prototype.leq = NativeBigInt.prototype.lesserOrEquals = SmallInteger.prototype.leq = SmallInteger.prototype.lesserOrEquals = BigInteger.prototype.leq = BigInteger.prototype.lesserOrEquals; + + BigInteger.prototype.isEven = function () { + return (this.value[0] & 1) === 0; + }; + SmallInteger.prototype.isEven = function () { + return (this.value & 1) === 0; + }; + NativeBigInt.prototype.isEven = function () { + return (this.value & BigInt(1)) === BigInt(0); + } + + BigInteger.prototype.isOdd = function () { + return (this.value[0] & 1) === 1; + }; + SmallInteger.prototype.isOdd = function () { + return (this.value & 1) === 1; + }; + NativeBigInt.prototype.isOdd = function () { + return (this.value & BigInt(1)) === BigInt(1); + } + + BigInteger.prototype.isPositive = function () { + return !this.sign; + }; + SmallInteger.prototype.isPositive = function () { + return this.value > 0; + }; + NativeBigInt.prototype.isPositive = SmallInteger.prototype.isPositive; + + BigInteger.prototype.isNegative = function () { + return this.sign; + }; + SmallInteger.prototype.isNegative = function () { + return this.value < 0; + }; + NativeBigInt.prototype.isNegative = SmallInteger.prototype.isNegative; + + BigInteger.prototype.isUnit = function () { + return false; + }; + SmallInteger.prototype.isUnit = function () { + return Math.abs(this.value) === 1; + }; + NativeBigInt.prototype.isUnit = function () { + return this.abs().value === BigInt(1); + } + + BigInteger.prototype.isZero = function () { + return false; + }; + SmallInteger.prototype.isZero = function () { + return this.value === 0; + }; + NativeBigInt.prototype.isZero = function () { + return this.value === BigInt(0); + } + + BigInteger.prototype.isDivisibleBy = function (v) { + var n = parseValue(v); + if (n.isZero()) return false; + if (n.isUnit()) return true; + if (n.compareAbs(2) === 0) return this.isEven(); + return this.mod(n).isZero(); + }; + NativeBigInt.prototype.isDivisibleBy = SmallInteger.prototype.isDivisibleBy = BigInteger.prototype.isDivisibleBy; + + function isBasicPrime(v) { + var n = v.abs(); + if (n.isUnit()) return false; + if (n.equals(2) || n.equals(3) || n.equals(5)) return true; + if (n.isEven() || n.isDivisibleBy(3) || n.isDivisibleBy(5)) return false; + if (n.lesser(49)) return true; + // we don't know if it's prime: let the other functions figure it out + } + + function millerRabinTest(n, a) { + var nPrev = n.prev(), + b = nPrev, + r = 0, + d, t, i, x; + while (b.isEven()) b = b.divide(2), r++; + next: for (i = 0; i < a.length; i++) { + if (n.lesser(a[i])) continue; + x = bigInt(a[i]).modPow(b, n); + if (x.isUnit() || x.equals(nPrev)) continue; + for (d = r - 1; d != 0; d--) { + x = x.square().mod(n); + if (x.isUnit()) return false; + if (x.equals(nPrev)) continue next; + } + return false; + } + return true; + } + + // Set "strict" to true to force GRH-supported lower bound of 2*log(N)^2 + BigInteger.prototype.isPrime = function (strict) { + var isPrime = isBasicPrime(this); + if (isPrime !== undefined) return isPrime; + var n = this.abs(); + var bits = n.bitLength(); + if (bits <= 64) + return millerRabinTest(n, [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37]); + var logN = Math.log(2) * bits.toJSNumber(); + var t = Math.ceil((strict === true) ? (2 * Math.pow(logN, 2)) : logN); + for (var a = [], i = 0; i < t; i++) { + a.push(bigInt(i + 2)); + } + return millerRabinTest(n, a); + }; + NativeBigInt.prototype.isPrime = SmallInteger.prototype.isPrime = BigInteger.prototype.isPrime; + + BigInteger.prototype.isProbablePrime = function (iterations) { + var isPrime = isBasicPrime(this); + if (isPrime !== undefined) return isPrime; + var n = this.abs(); + var t = iterations === undefined ? 5 : iterations; + for (var a = [], i = 0; i < t; i++) { + a.push(bigInt.randBetween(2, n.minus(2))); + } + return millerRabinTest(n, a); + }; + NativeBigInt.prototype.isProbablePrime = SmallInteger.prototype.isProbablePrime = BigInteger.prototype.isProbablePrime; + + BigInteger.prototype.modInv = function (n) { + var t = bigInt.zero, newT = bigInt.one, r = parseValue(n), newR = this.abs(), q, lastT, lastR; + while (!newR.isZero()) { + q = r.divide(newR); + lastT = t; + lastR = r; + t = newT; + r = newR; + newT = lastT.subtract(q.multiply(newT)); + newR = lastR.subtract(q.multiply(newR)); + } + if (!r.isUnit()) throw new Error(this.toString() + " and " + n.toString() + " are not co-prime"); + if (t.compare(0) === -1) { + t = t.add(n); + } + if (this.isNegative()) { + return t.negate(); + } + return t; + }; + + NativeBigInt.prototype.modInv = SmallInteger.prototype.modInv = BigInteger.prototype.modInv; + + BigInteger.prototype.next = function () { + var value = this.value; + if (this.sign) { + return subtractSmall(value, 1, this.sign); + } + return new BigInteger(addSmall(value, 1), this.sign); + }; + SmallInteger.prototype.next = function () { + var value = this.value; + if (value + 1 < MAX_INT) return new SmallInteger(value + 1); + return new BigInteger(MAX_INT_ARR, false); + }; + NativeBigInt.prototype.next = function () { + return new NativeBigInt(this.value + BigInt(1)); + } + + BigInteger.prototype.prev = function () { + var value = this.value; + if (this.sign) { + return new BigInteger(addSmall(value, 1), true); + } + return subtractSmall(value, 1, this.sign); + }; + SmallInteger.prototype.prev = function () { + var value = this.value; + if (value - 1 > -MAX_INT) return new SmallInteger(value - 1); + return new BigInteger(MAX_INT_ARR, true); + }; + NativeBigInt.prototype.prev = function () { + return new NativeBigInt(this.value - BigInt(1)); + } + + var powersOfTwo = [1]; + while (2 * powersOfTwo[powersOfTwo.length - 1] <= BASE) powersOfTwo.push(2 * powersOfTwo[powersOfTwo.length - 1]); + var powers2Length = powersOfTwo.length, highestPower2 = powersOfTwo[powers2Length - 1]; + + function shift_isSmall(n) { + return Math.abs(n) <= BASE; + } + + BigInteger.prototype.shiftLeft = function (v) { + var n = parseValue(v).toJSNumber(); + if (!shift_isSmall(n)) { + throw new Error(String(n) + " is too large for shifting."); + } + if (n < 0) return this.shiftRight(-n); + var result = this; + if (result.isZero()) return result; + while (n >= powers2Length) { + result = result.multiply(highestPower2); + n -= powers2Length - 1; + } + return result.multiply(powersOfTwo[n]); + }; + NativeBigInt.prototype.shiftLeft = SmallInteger.prototype.shiftLeft = BigInteger.prototype.shiftLeft; + + BigInteger.prototype.shiftRight = function (v) { + var remQuo; + var n = parseValue(v).toJSNumber(); + if (!shift_isSmall(n)) { + throw new Error(String(n) + " is too large for shifting."); + } + if (n < 0) return this.shiftLeft(-n); + var result = this; + while (n >= powers2Length) { + if (result.isZero() || (result.isNegative() && result.isUnit())) return result; + remQuo = divModAny(result, highestPower2); + result = remQuo[1].isNegative() ? remQuo[0].prev() : remQuo[0]; + n -= powers2Length - 1; + } + remQuo = divModAny(result, powersOfTwo[n]); + return remQuo[1].isNegative() ? remQuo[0].prev() : remQuo[0]; + }; + NativeBigInt.prototype.shiftRight = SmallInteger.prototype.shiftRight = BigInteger.prototype.shiftRight; + + function bitwise(x, y, fn) { + y = parseValue(y); + var xSign = x.isNegative(), ySign = y.isNegative(); + var xRem = xSign ? x.not() : x, + yRem = ySign ? y.not() : y; + var xDigit = 0, yDigit = 0; + var xDivMod = null, yDivMod = null; + var result = []; + while (!xRem.isZero() || !yRem.isZero()) { + xDivMod = divModAny(xRem, highestPower2); + xDigit = xDivMod[1].toJSNumber(); + if (xSign) { + xDigit = highestPower2 - 1 - xDigit; // two's complement for negative numbers + } + + yDivMod = divModAny(yRem, highestPower2); + yDigit = yDivMod[1].toJSNumber(); + if (ySign) { + yDigit = highestPower2 - 1 - yDigit; // two's complement for negative numbers + } + + xRem = xDivMod[0]; + yRem = yDivMod[0]; + result.push(fn(xDigit, yDigit)); + } + var sum = fn(xSign ? 1 : 0, ySign ? 1 : 0) !== 0 ? bigInt(-1) : bigInt(0); + for (var i = result.length - 1; i >= 0; i -= 1) { + sum = sum.multiply(highestPower2).add(bigInt(result[i])); + } + return sum; + } + + BigInteger.prototype.not = function () { + return this.negate().prev(); + }; + NativeBigInt.prototype.not = SmallInteger.prototype.not = BigInteger.prototype.not; + + BigInteger.prototype.and = function (n) { + return bitwise(this, n, function (a, b) { return a & b; }); + }; + NativeBigInt.prototype.and = SmallInteger.prototype.and = BigInteger.prototype.and; + + BigInteger.prototype.or = function (n) { + return bitwise(this, n, function (a, b) { return a | b; }); + }; + NativeBigInt.prototype.or = SmallInteger.prototype.or = BigInteger.prototype.or; + + BigInteger.prototype.xor = function (n) { + return bitwise(this, n, function (a, b) { return a ^ b; }); + }; + NativeBigInt.prototype.xor = SmallInteger.prototype.xor = BigInteger.prototype.xor; + + var LOBMASK_I = 1 << 30, LOBMASK_BI = (BASE & -BASE) * (BASE & -BASE) | LOBMASK_I; + function roughLOB(n) { // get lowestOneBit (rough) + // SmallInteger: return Min(lowestOneBit(n), 1 << 30) + // BigInteger: return Min(lowestOneBit(n), 1 << 14) [BASE=1e7] + var v = n.value, + x = typeof v === "number" ? v | LOBMASK_I : + typeof v === "bigint" ? v | BigInt(LOBMASK_I) : + v[0] + v[1] * BASE | LOBMASK_BI; + return x & -x; + } + + function integerLogarithm(value, base) { + if (base.compareTo(value) <= 0) { + var tmp = integerLogarithm(value, base.square(base)); + var p = tmp.p; + var e = tmp.e; + var t = p.multiply(base); + return t.compareTo(value) <= 0 ? { p: t, e: e * 2 + 1 } : { p: p, e: e * 2 }; + } + return { p: bigInt(1), e: 0 }; + } + + BigInteger.prototype.bitLength = function () { + var n = this; + if (n.compareTo(bigInt(0)) < 0) { + n = n.negate().subtract(bigInt(1)); + } + if (n.compareTo(bigInt(0)) === 0) { + return bigInt(0); + } + return bigInt(integerLogarithm(n, bigInt(2)).e).add(bigInt(1)); + } + NativeBigInt.prototype.bitLength = SmallInteger.prototype.bitLength = BigInteger.prototype.bitLength; + + function max(a, b) { + a = parseValue(a); + b = parseValue(b); + return a.greater(b) ? a : b; + } + function min(a, b) { + a = parseValue(a); + b = parseValue(b); + return a.lesser(b) ? a : b; + } + function gcd(a, b) { + a = parseValue(a).abs(); + b = parseValue(b).abs(); + if (a.equals(b)) return a; + if (a.isZero()) return b; + if (b.isZero()) return a; + var c = Integer[1], d, t; + while (a.isEven() && b.isEven()) { + d = min(roughLOB(a), roughLOB(b)); + a = a.divide(d); + b = b.divide(d); + c = c.multiply(d); + } + while (a.isEven()) { + a = a.divide(roughLOB(a)); + } + do { + while (b.isEven()) { + b = b.divide(roughLOB(b)); + } + if (a.greater(b)) { + t = b; b = a; a = t; + } + b = b.subtract(a); + } while (!b.isZero()); + return c.isUnit() ? a : a.multiply(c); + } + function lcm(a, b) { + a = parseValue(a).abs(); + b = parseValue(b).abs(); + return a.divide(gcd(a, b)).multiply(b); + } + function randBetween(a, b) { + a = parseValue(a); + b = parseValue(b); + var low = min(a, b), high = max(a, b); + var range = high.subtract(low).add(1); + if (range.isSmall) return low.add(Math.floor(Math.random() * range)); + var digits = toBase(range, BASE).value; + var result = [], restricted = true; + for (var i = 0; i < digits.length; i++) { + var top = restricted ? digits[i] : BASE; + var digit = truncate(Math.random() * top); + result.push(digit); + if (digit < top) restricted = false; + } + return low.add(Integer.fromArray(result, BASE, false)); + } + + var parseBase = function (text, base, alphabet, caseSensitive) { + alphabet = alphabet || DEFAULT_ALPHABET; + text = String(text); + if (!caseSensitive) { + text = text.toLowerCase(); + alphabet = alphabet.toLowerCase(); + } + var length = text.length; + var i; + var absBase = Math.abs(base); + var alphabetValues = {}; + for (i = 0; i < alphabet.length; i++) { + alphabetValues[alphabet[i]] = i; + } + for (i = 0; i < length; i++) { + var c = text[i]; + if (c === "-") continue; + if (c in alphabetValues) { + if (alphabetValues[c] >= absBase) { + if (c === "1" && absBase === 1) continue; + throw new Error(c + " is not a valid digit in base " + base + "."); + } + } + } + base = parseValue(base); + var digits = []; + var isNegative = text[0] === "-"; + for (i = isNegative ? 1 : 0; i < text.length; i++) { + var c = text[i]; + if (c in alphabetValues) digits.push(parseValue(alphabetValues[c])); + else if (c === "<") { + var start = i; + do { i++; } while (text[i] !== ">" && i < text.length); + digits.push(parseValue(text.slice(start + 1, i))); + } + else throw new Error(c + " is not a valid character"); + } + return parseBaseFromArray(digits, base, isNegative); + }; + + function parseBaseFromArray(digits, base, isNegative) { + var val = Integer[0], pow = Integer[1], i; + for (i = digits.length - 1; i >= 0; i--) { + val = val.add(digits[i].times(pow)); + pow = pow.times(base); + } + return isNegative ? val.negate() : val; + } + + function stringify(digit, alphabet) { + alphabet = alphabet || DEFAULT_ALPHABET; + if (digit < alphabet.length) { + return alphabet[digit]; + } + return "<" + digit + ">"; + } + + function toBase(n, base) { + base = bigInt(base); + if (base.isZero()) { + if (n.isZero()) return { value: [0], isNegative: false }; + throw new Error("Cannot convert nonzero numbers to base 0."); + } + if (base.equals(-1)) { + if (n.isZero()) return { value: [0], isNegative: false }; + if (n.isNegative()) + return { + value: [].concat.apply([], Array.apply(null, Array(-n.toJSNumber())) + .map(Array.prototype.valueOf, [1, 0]) + ), + isNegative: false + }; + + var arr = Array.apply(null, Array(n.toJSNumber() - 1)) + .map(Array.prototype.valueOf, [0, 1]); + arr.unshift([1]); + return { + value: [].concat.apply([], arr), + isNegative: false + }; + } + + var neg = false; + if (n.isNegative() && base.isPositive()) { + neg = true; + n = n.abs(); + } + if (base.isUnit()) { + if (n.isZero()) return { value: [0], isNegative: false }; + + return { + value: Array.apply(null, Array(n.toJSNumber())) + .map(Number.prototype.valueOf, 1), + isNegative: neg + }; + } + var out = []; + var left = n, divmod; + while (left.isNegative() || left.compareAbs(base) >= 0) { + divmod = left.divmod(base); + left = divmod.quotient; + var digit = divmod.remainder; + if (digit.isNegative()) { + digit = base.minus(digit).abs(); + left = left.next(); + } + out.push(digit.toJSNumber()); + } + out.push(left.toJSNumber()); + return { value: out.reverse(), isNegative: neg }; + } + + function toBaseString(n, base, alphabet) { + var arr = toBase(n, base); + return (arr.isNegative ? "-" : "") + arr.value.map(function (x) { + return stringify(x, alphabet); + }).join(''); + } + + BigInteger.prototype.toArray = function (radix) { + return toBase(this, radix); + }; + + SmallInteger.prototype.toArray = function (radix) { + return toBase(this, radix); + }; + + NativeBigInt.prototype.toArray = function (radix) { + return toBase(this, radix); + }; + + BigInteger.prototype.toString = function (radix, alphabet) { + if (radix === undefined) radix = 10; + if (radix !== 10) return toBaseString(this, radix, alphabet); + var v = this.value, l = v.length, str = String(v[--l]), zeros = "0000000", digit; + while (--l >= 0) { + digit = String(v[l]); + str += zeros.slice(digit.length) + digit; + } + var sign = this.sign ? "-" : ""; + return sign + str; + }; + + SmallInteger.prototype.toString = function (radix, alphabet) { + if (radix === undefined) radix = 10; + if (radix != 10) return toBaseString(this, radix, alphabet); + return String(this.value); + }; + + NativeBigInt.prototype.toString = SmallInteger.prototype.toString; + + NativeBigInt.prototype.toJSON = BigInteger.prototype.toJSON = SmallInteger.prototype.toJSON = function () { return this.toString(); } + + BigInteger.prototype.valueOf = function () { + return parseInt(this.toString(), 10); + }; + BigInteger.prototype.toJSNumber = BigInteger.prototype.valueOf; + + SmallInteger.prototype.valueOf = function () { + return this.value; + }; + SmallInteger.prototype.toJSNumber = SmallInteger.prototype.valueOf; + NativeBigInt.prototype.valueOf = NativeBigInt.prototype.toJSNumber = function () { + return parseInt(this.toString(), 10); + } + + function parseStringValue(v) { + if (isPrecise(+v)) { + var x = +v; + if (x === truncate(x)) + return supportsNativeBigInt ? new NativeBigInt(BigInt(x)) : new SmallInteger(x); + throw new Error("Invalid integer: " + v); + } + var sign = v[0] === "-"; + if (sign) v = v.slice(1); + var split = v.split(/e/i); + if (split.length > 2) throw new Error("Invalid integer: " + split.join("e")); + if (split.length === 2) { + var exp = split[1]; + if (exp[0] === "+") exp = exp.slice(1); + exp = +exp; + if (exp !== truncate(exp) || !isPrecise(exp)) throw new Error("Invalid integer: " + exp + " is not a valid exponent."); + var text = split[0]; + var decimalPlace = text.indexOf("."); + if (decimalPlace >= 0) { + exp -= text.length - decimalPlace - 1; + text = text.slice(0, decimalPlace) + text.slice(decimalPlace + 1); + } + if (exp < 0) throw new Error("Cannot include negative exponent part for integers"); + text += (new Array(exp + 1)).join("0"); + v = text; + } + var isValid = /^([0-9][0-9]*)$/.test(v); + if (!isValid) throw new Error("Invalid integer: " + v); + if (supportsNativeBigInt) { + return new NativeBigInt(BigInt(sign ? "-" + v : v)); + } + var r = [], max = v.length, l = LOG_BASE, min = max - l; + while (max > 0) { + r.push(+v.slice(min, max)); + min -= l; + if (min < 0) min = 0; + max -= l; + } + trim(r); + return new BigInteger(r, sign); + } + + function parseNumberValue(v) { + if (supportsNativeBigInt) { + return new NativeBigInt(BigInt(v)); + } + if (isPrecise(v)) { + if (v !== truncate(v)) throw new Error(v + " is not an integer."); + return new SmallInteger(v); + } + return parseStringValue(v.toString()); + } + + function parseValue(v) { + if (typeof v === "number") { + return parseNumberValue(v); + } + if (typeof v === "string") { + return parseStringValue(v); + } + if (typeof v === "bigint") { + return new NativeBigInt(v); + } + return v; + } + // Pre-define numbers in range [-999,999] + for (var i = 0; i < 1000; i++) { + Integer[i] = parseValue(i); + if (i > 0) Integer[-i] = parseValue(-i); + } + // Backwards compatibility + Integer.one = Integer[1]; + Integer.zero = Integer[0]; + Integer.minusOne = Integer[-1]; + Integer.max = max; + Integer.min = min; + Integer.gcd = gcd; + Integer.lcm = lcm; + Integer.isInstance = function (x) { return x instanceof BigInteger || x instanceof SmallInteger || x instanceof NativeBigInt; }; + Integer.randBetween = randBetween; + + Integer.fromArray = function (digits, base, isNegative) { + return parseBaseFromArray(digits.map(parseValue), parseValue(base || 10), isNegative); + }; + + return Integer; +})(); + +// Node.js check +if (typeof module !== "undefined" && module.hasOwnProperty("exports")) { + module.exports = bigInt; +} + +//amd check +if (typeof define === "function" && define.amd) { + define("big-integer", [], function () { + return bigInt; + }); +} },{}],9:[function(require,module,exports){ (function (Buffer){ @@ -4931,6 +4942,976 @@ process.chdir = function (dir) { process.umask = function() { return 0; }; },{}],13:[function(require,module,exports){ +(function (Buffer){ +/* + Copyright 2018 0kims association. + + This file is part of snarkjs. + + snarkjs is a free software: you can redistribute it and/or + modify it under the terms of the GNU General Public License as published by the + Free Software Foundation, either version 3 of the License, or (at your option) + any later version. + + snarkjs is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY + or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for + more details. + + You should have received a copy of the GNU General Public License along with + snarkjs. If not, see . +*/ + +/* global BigInt */ +const bigInt = require("big-integer"); + +let wBigInt; + +if (typeof(BigInt) != "undefined") { + wBigInt = BigInt; + wBigInt.one = wBigInt(1); + wBigInt.zero = wBigInt(0); + + // Affine + wBigInt.genAffine = (q) => { + const nq = -q; + return (a) => { + let aux = a; + if (aux < 0) { + if (aux <= nq) { + aux = aux % q; + } + if (aux < wBigInt.zero) { + aux = aux + q; + } + } else { + if (aux >= q) { + aux = aux % q; + } + } + return aux.valueOf(); + }; + }; + + + // Inverse + wBigInt.genInverse = (q) => { + return (a) => { + let t = wBigInt.zero; + let r = q; + let newt = wBigInt.one; + let newr = wBigInt.affine(a, q); + while (newr!=wBigInt.zero) { + let q = r/newr; + [t, newt] = [newt, t-q*newt]; + [r, newr] = [newr, r-q*newr]; + } + if (t { + if (q) { + return (a,b) => (a+b) % q; + } else { + return (a,b) => a+b; + } + }; + + // Sub + wBigInt.genSub = (q) => { + if (q) { + return (a,b) => (a-b) % q; + } else { + return (a,b) => a-b; + } + }; + + + // Neg + wBigInt.genNeg = (q) => { + if (q) { + return (a) => (-a) % q; + } else { + return (a) => -a; + } + }; + + // Mul + wBigInt.genMul = (q) => { + if (q) { + return (a,b) => (a*b) % q; + } else { + return (a,b) => a*b; + } + }; + + // Shr + wBigInt.genShr = () => { + return (a,b) => a >> wBigInt(b); + }; + + // Shl + wBigInt.genShl = (q) => { + if (q) { + return (a,b) => (a << wBigInt(b)) % q; + } else { + return (a,b) => a << wBigInt(b); + } + }; + + // Equals + wBigInt.genEquals = (q) => { + if (q) { + return (a,b) => (a.affine(q) == b.affine(q)); + } else { + return (a,b) => a == b; + } + }; + + // Square + wBigInt.genSquare = (q) => { + if (q) { + return (a) => (a*a) %q; + } else { + return (a) => a*a; + } + }; + + + // Double + wBigInt.genDouble = (q) => { + if (q) { + return (a) => (a+a) %q; + } else { + return (a) => a+a; + } + }; + + // IsZero + wBigInt.genIsZero = (q) => { + if (q) { + return (a) => (a.affine(q) == wBigInt.zero); + } else { + return (a) => a == wBigInt.zero; + } + }; + + + // Other minor functions + wBigInt.prototype.isOdd = function() { + return (this & wBigInt.one) == wBigInt(1); + }; + + wBigInt.prototype.isNegative = function() { + return this < wBigInt.zero; + }; + + wBigInt.prototype.and = function(m) { + return this & m; + }; + + wBigInt.prototype.div = function(c) { + return this / c; + }; + + wBigInt.prototype.mod = function(c) { + return this % c; + }; + + wBigInt.prototype.modPow = function(e, m) { + let acc = wBigInt.one; + let exp = this; + let rem = e; + while (rem) { + if (rem & wBigInt.one) { + acc = (acc * exp) %m; + } + exp = (exp * exp) % m; + rem = rem >> wBigInt.one; + } + return acc; + }; + + wBigInt.prototype.greaterOrEquals = function(b) { + return this >= b; + }; + + wBigInt.prototype.greater = function(b) { + return this > b; + }; + wBigInt.prototype.gt = wBigInt.prototype.greater; + + wBigInt.prototype.lesserOrEquals = function(b) { + return this <= b; + }; + + wBigInt.prototype.lesser = function(b) { + return this < b; + }; + wBigInt.prototype.lt = wBigInt.prototype.lesser; + + wBigInt.prototype.equals = function(b) { + return this == b; + }; + wBigInt.prototype.eq = wBigInt.prototype.equals; + + wBigInt.prototype.neq = function(b) { + return this != b; + }; + +} else { + + var oldProto = bigInt.prototype; + wBigInt = function(a) { + if ((typeof a == "string") && (a.slice(0,2) == "0x")) { + return bigInt(a.slice(2), 16); + } else { + return bigInt(a); + } + }; + wBigInt.one = bigInt.one; + wBigInt.zero = bigInt.zero; + wBigInt.prototype = oldProto; + + wBigInt.prototype.div = function(c) { + return this.divide(c); + }; + + // Affine + wBigInt.genAffine = (q) => { + const nq = wBigInt.zero.minus(q); + return (a) => { + let aux = a; + if (aux.isNegative()) { + if (aux.lesserOrEquals(nq)) { + aux = aux.mod(q); + } + if (aux.isNegative()) { + aux = aux.add(q); + } + } else { + if (aux.greaterOrEquals(q)) { + aux = aux.mod(q); + } + } + return aux; + }; + }; + + + // Inverse + wBigInt.genInverse = (q) => { + return (a) => a.affine(q).modInv(q); + }; + + // Add + wBigInt.genAdd = (q) => { + if (q) { + return (a,b) => { + const r = a.add(b); + return r.greaterOrEquals(q) ? r.minus(q) : r; + }; + } else { + return (a,b) => a.add(b); + } + }; + + // Sub + wBigInt.genSub = (q) => { + if (q) { + return (a,b) => a.greaterOrEquals(b) ? a.minus(b) : a.minus(b).add(q); + } else { + return (a,b) => a.minus(b); + } + }; + + wBigInt.genNeg = (q) => { + if (q) { + return (a) => a.isZero() ? a : q.minus(a); + } else { + return (a) => wBigInt.zero.minus(a); + } + }; + + // Mul + wBigInt.genMul = (q) => { + if (q) { + return (a,b) => a.times(b).mod(q); + } else { + return (a,b) => a.times(b); + } + }; + + // Shr + wBigInt.genShr = () => { + return (a,b) => a.shiftRight(wBigInt(b).value); + }; + + // Shr + wBigInt.genShl = (q) => { + if (q) { + return (a,b) => a.shiftLeft(wBigInt(b).value).mod(q); + } else { + return (a,b) => a.shiftLeft(wBigInt(b).value); + } + }; + + // Square + wBigInt.genSquare = (q) => { + if (q) { + return (a) => a.square().mod(q); + } else { + return (a) => a.square(); + } + }; + + // Double + wBigInt.genDouble = (q) => { + if (q) { + return (a) => a.add(a).mod(q); + } else { + return (a) => a.add(a); + } + }; + + // Equals + wBigInt.genEquals = (q) => { + if (q) { + return (a,b) => a.affine(q).equals(b.affine(q)); + } else { + return (a,b) => a.equals(b); + } + }; + + // IsZero + wBigInt.genIsZero = (q) => { + if (q) { + return (a) => (a.affine(q).isZero()); + } else { + return (a) => a.isZero(); + } + }; +} + + + +wBigInt.affine = function(a, q) { + return wBigInt.genAffine(q)(a); +}; + +wBigInt.prototype.affine = function (q) { + return wBigInt.affine(this, q); +}; + +wBigInt.inverse = function(a, q) { + return wBigInt.genInverse(q)(a); +}; + +wBigInt.prototype.inverse = function (q) { + return wBigInt.genInverse(q)(this); +}; + +wBigInt.add = function(a, b, q) { + return wBigInt.genAdd(q)(a,b); +}; + +wBigInt.prototype.add = function (a, q) { + return wBigInt.genAdd(q)(this, a); +}; + +wBigInt.sub = function(a, b, q) { + return wBigInt.genSub(q)(a,b); +}; + +wBigInt.prototype.sub = function (a, q) { + return wBigInt.genSub(q)(this, a); +}; + +wBigInt.neg = function(a, q) { + return wBigInt.genNeg(q)(a); +}; + +wBigInt.prototype.neg = function (q) { + return wBigInt.genNeg(q)(this); +}; + +wBigInt.mul = function(a, b, q) { + return wBigInt.genMul(q)(a,b); +}; + +wBigInt.prototype.mul = function (a, q) { + return wBigInt.genMul(q)(this, a); +}; + +wBigInt.shr = function(a, b, q) { + return wBigInt.genShr(q)(a,b); +}; + +wBigInt.prototype.shr = function (a, q) { + return wBigInt.genShr(q)(this, a); +}; + +wBigInt.shl = function(a, b, q) { + return wBigInt.genShl(q)(a,b); +}; + +wBigInt.prototype.shl = function (a, q) { + return wBigInt.genShl(q)(this, a); +}; + +wBigInt.equals = function(a, b, q) { + return wBigInt.genEquals(q)(a,b); +}; + +wBigInt.prototype.equals = function (a, q) { + return wBigInt.genEquals(q)(this, a); +}; + +wBigInt.square = function(a, q) { + return wBigInt.genSquare(q)(a); +}; + +wBigInt.prototype.square = function (q) { + return wBigInt.genSquare(q)(this); +}; + +wBigInt.double = function(a, q) { + return wBigInt.genDouble(q)(a); +}; + +wBigInt.prototype.double = function (q) { + return wBigInt.genDouble(q)(this); +}; + +wBigInt.isZero = function(a, q) { + return wBigInt.genIsZero(q)(a); +}; + +wBigInt.prototype.isZero = function (q) { + return wBigInt.genIsZero(q)(this); +}; + +wBigInt.leBuff2int = function(buff) { + let res = wBigInt.zero; + for (let i=0; i. +*/ + +const bigInt = require("./bigint"); + +module.exports = calculateWitness; + +function calculateWitness(circuit, inputSignals, log) { + log = log || (() => {}); + const ctx = new RTCtx(circuit, log); + + function iterateSelector(values, sels, cb) { + if (!Array.isArray(values)) { + return cb(sels, values); + } + for (let i=0; i " + ctx.witness[i].toString()); + } + return ctx.witness.slice(0, circuit.nVars); +// return ctx.witness; +} + +class RTCtx { + constructor(circuit, log) { + this.log = log || function() {}; + this.scopes = []; + this.circuit = circuit; + this.witness = new Array(circuit.nSignals); + this.notInitSignals = {}; + for (let c in this.circuit.components) { + this.notInitSignals[c] = this.circuit.components[c].inputSignals; + } + } + + _sels2str(sels) { + let res = ""; + for (let i=0; i { + if (this.notInitSignals[c] == 0) this.triggerComponent(c); + }); + return this.witness[sId]; + } + + setVar(name, sels, value) { + function setVarArray(a, sels2, value) { + if (sels2.length == 1) { + a[sels2[0]] = value; + } else { + if (typeof(a[sels2[0]]) == "undefined") a[sels2[0]] = []; + setVarArray(a[sels2[0]], sels2.slice(1), value); + } + } + const scope = this.scopes[this.scopes.length-1]; + if (sels.length == 0) { + scope[name] = value; + } else { + if (typeof(scope[name]) == "undefined") scope[name] = []; + setVarArray(scope[name], sels, value); + } + return value; + } + + getVar(name, sels) { + function select(a, sels2) { + return (sels2.length == 0) ? a : select(a[sels2[0]], sels2.slice(1)); + } + for (let i=this.scopes.length-1; i>=0; i--) { + if (typeof(this.scopes[i][name]) != "undefined") return select(this.scopes[i][name], sels); + } + throw new Error("Variable not defined: " + name); + } + + getSignal(name, sels) { + let fullName = name=="one" ? "one" : this.currentComponent + "." + name; + fullName += this._sels2str(sels); + return this.getSignalFullName(fullName); + } + + + getPin(componentName, componentSels, signalName, signalSels) { + let fullName = componentName=="one" ? "one" : this.currentComponent + "." + componentName; + fullName += this._sels2str(componentSels) + + "."+ + signalName+ + this._sels2str(signalSels); + return this.getSignalFullName(fullName); + } + + getSignalFullName(fullName) { + const sId = this.circuit.getSignalIdx(fullName); + if (typeof(this.witness[sId]) == "undefined") { + throw new Error("Signal not initialized: "+fullName); + } + this.log("get --->" + fullName + " = " + this.witness[sId].toString() ); + return this.witness[sId]; + } + + assert(a,b) { + const ba = bigInt(a); + const bb = bigInt(b); + if (!ba.equals(bb)) { + throw new Error("Constraint doesn't match: " + ba.toString() + " != " + bb.toString()); + } + } +} + +},{"./bigint":13}],15:[function(require,module,exports){ +/* + Copyright 2018 0kims association. + + This file is part of snarkjs. + + snarkjs is a free software: you can redistribute it and/or + modify it under the terms of the GNU General Public License as published by the + Free Software Foundation, either version 3 of the License, or (at your option) + any later version. + + snarkjs is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY + or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for + more details. + + You should have received a copy of the GNU General Public License along with + snarkjs. If not, see . +*/ + +const bigInt = require("./bigint.js"); + +const __P__ = bigInt("21888242871839275222246405745257275088548364400416034343698204186575808495617"); +const __MASK__ = bigInt("28948022309329048855892746252171976963317496166410141009864396001978282409983"); // 0x3FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF +const calculateWitness = require("./calculateWitness.js"); + +module.exports = class Circuit { + constructor(circuitDef) { + this.nPubInputs = circuitDef.nPubInputs; + this.nPrvInputs = circuitDef.nPrvInputs; + this.nInputs = circuitDef.nInputs; + this.nOutputs = circuitDef.nOutputs; + this.nVars = circuitDef.nVars; + this.nSignals = circuitDef.nSignals; + this.nConstants = circuitDef.nConstants; + + this.nConstraints = circuitDef.constraints.length; + + this.signalName2Idx = circuitDef.signalName2Idx; + this.components = circuitDef.components; + this.componentName2Idx = circuitDef.componentName2Idx; + this.signals = circuitDef.signals; + this.constraints = circuitDef.constraints; + + this.templates = {}; + for (let t in circuitDef.templates) { + this.templates[t] = eval(" const __f= " +circuitDef.templates[t] + "\n__f"); + } + + this.functions = {}; + for (let f in circuitDef.functions) { + this.functions[f] = { + params: circuitDef.functions[f].params, + func: eval(" const __f= " +circuitDef.functions[f].func + "\n__f;") + }; + } + } + + calculateWitness(input, log) { + return calculateWitness(this, input, log); + } + + checkWitness(w) { + const evalLC = (lc, w) => { + let acc = bigInt(0); + for (let k in lc) { + acc= acc.add(bigInt(w[k]).mul(bigInt(lc[k]))).mod(__P__); + } + return acc; + } + + const checkConstraint = (ct, w) => { + const a=evalLC(ct[0],w); + const b=evalLC(ct[1],w); + const c=evalLC(ct[2],w); + const res = (a.mul(b).sub(c)).affine(__P__); + if (!res.isZero()) return false; + return true; + } + + + for (let i=0; i { + let S = ""; + for (let k in lc) { + let name = this.signals[k].names[0]; + if (name == "one") name = ""; + let v = bigInt(lc[k]); + let vs; + if (!v.lesserOrEquals(__P__.shr(bigInt(1)))) { + v = __P__.sub(v); + vs = "-"+v.toString(); + } else { + if (S!="") { + vs = "+"+v.toString(); + } else { + vs = ""; + } + if (vs!="1") { + vs = vs + v.toString();; + } + } + + S= S + " " + vs + name; + } + return S; + }; + const S = `[ ${lc2str(c[0])} ] * [ ${lc2str(c[1])} ] - [ ${lc2str(c[2])} ] = 0`; + console.log(S); + } + + printConstraints() { + for (let i=0; i=this.nOutputs) throw new Error("Accessing an invalid output: "+i); + return i+1; + } + + // returns the index of the i'th input + inputIdx(i) { + if (i>=this.nInputs) throw new Error("Accessing an invalid input: "+i); + return this.nOutputs + 1 + i; + } + + // returns the index of the i'th public input + pubInputIdx(i) { + if (i>=this.nPubInputs) throw new Error("Accessing an invalid pubInput: "+i); + return this.inputIdx(i); + } + + // returns the index of the i'th private input + prvInputIdx(i) { + if (i>=this.nPrvInputs) throw new Error("Accessing an invalid prvInput: "+i); + return this.inputIdx(this.nPubInputs + i); + } + + // returns the index of the i'th variable + varIdx(i) { + if (i>=this.nVars) throw new Error("Accessing an invalid variable: "+i); + return i; + } + + // returns the index of the i'th constant + constantIdx(i) { + if (i>=this.nConstants) throw new Error("Accessing an invalid constant: "+i); + return this.nVars + i; + } + + // returns the index of the i'th signal + signalIdx(i) { + if (i>=this.nSignls) throw new Error("Accessing an invalid signal: "+i); + return i; + } + + signalNames(i) { + return this.signals[ this.getSignalIdx(i) ].names.join(", "); + } + + a(constraint, signalIdx) { + return bigInt(this.constraints[constraint][0][signalIdx] || 0 ); + } + + b(constraint, signalIdx) { + return bigInt(this.constraints[constraint][1][signalIdx] || 0); + } + + c(constraint, signalIdx) { + return bigInt(this.constraints[constraint][2][signalIdx] || 0); + } +}; + +},{"./bigint.js":13,"./calculateWitness.js":14}],16:[function(require,module,exports){ +/* + Copyright 2018 0kims association. + + This file is part of snarkjs. + + snarkjs is a free software: you can redistribute it and/or + modify it under the terms of the GNU General Public License as published by the + Free Software Foundation, either version 3 of the License, or (at your option) + any later version. + + snarkjs is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY + or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for + more details. + + You should have received a copy of the GNU General Public License along with + snarkjs. If not, see . +*/ + +const bigInt = require("./bigint.js"); + +module.exports.stringifyBigInts = stringifyBigInts; +module.exports.unstringifyBigInts = unstringifyBigInts; + +function stringifyBigInts(o) { + if ((typeof(o) == "bigint") || (o instanceof bigInt)) { + return o.toString(10); + } else if (Array.isArray(o)) { + return o.map(stringifyBigInts); + } else if (typeof o == "object") { + const res = {}; + for (let k in o) { + res[k] = stringifyBigInts(o[k]); + } + return res; + } else { + return o; + } +} + +function unstringifyBigInts(o) { + if ((typeof(o) == "string") && (/^[0-9]+$/.test(o) )) { + return bigInt(o); + } else if (Array.isArray(o)) { + return o.map(unstringifyBigInts); + } else if (typeof o == "object") { + const res = {}; + for (let k in o) { + res[k] = unstringifyBigInts(o[k]); + } + return res; + } else { + return o; + } +} + +},{"./bigint.js":13}],17:[function(require,module,exports){ (function (process){ /* Copyright 2019 0KIMS association. @@ -5542,4 +6523,175 @@ class Groth16 { module.exports = build; }).call(this,require('_process')) -},{"../build/groth16_wasm.js":1,"_process":12,"assert":3,"big-integer":8,"crypto":undefined,"worker_threads":undefined}]},{},[2]); +},{"../build/groth16_wasm.js":1,"_process":12,"assert":3,"big-integer":8,"crypto":undefined,"worker_threads":undefined}],18:[function(require,module,exports){ +/* + Copyright 2019 0KIMS association. + + This file is part of websnark (Web Assembly zkSnark Prover). + + websnark is a free software: you can redistribute it and/or modify it + under the terms of the GNU General Public License as published by + the Free Software Foundation, either version 3 of the License, or + (at your option) any later version. + + websnark is distributed in the hope that it will be useful, but WITHOUT + ANY WARRANTY; without even the implied warranty of MERCHANTABILITY + or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public + License for more details. + + You should have received a copy of the GNU General Public License + along with websnark. If not, see . +*/ + +const bigInt = require("big-integer"); +const Circuit = require("snarkjs/src/circuit"); +const bigInt2 = require("snarkjs/src/bigint"); +const hexifyBigInts = require("../tools/stringifybigint").hexifyBigInts; +const unstringifyBigInts = require("../tools/stringifybigint").unstringifyBigInts; +const stringifyBigInts2 = require("snarkjs/src/stringifybigint").stringifyBigInts; +const unstringifyBigInts2 = require("snarkjs/src/stringifybigint").unstringifyBigInts; + +function bigInt2BytesLE(_a, len) { + const b = Array(len); + let v = bigInt(_a); + for (let i=0; i. +*/ + +const bigInt = require("big-integer"); + +module.exports.stringifyBigInts = stringifyBigInts; +module.exports.unstringifyBigInts = unstringifyBigInts; +module.exports.hexifyBigInts = hexifyBigInts; + +function stringifyBigInts(o) { + if ((typeof(o) == "bigint") || (o instanceof bigInt)) { + return o.toString(10); + } else if (Array.isArray(o)) { + return o.map(stringifyBigInts); + } else if (typeof o == "object") { + const res = {}; + for (let k in o) { + res[k] = stringifyBigInts(o[k]); + } + return res; + } else { + return o; + } +} + +function unstringifyBigInts(o) { + if ((typeof(o) == "string") && (/^[0-9]+$/.test(o) )) { + return bigInt(o); + } else if (Array.isArray(o)) { + return o.map(unstringifyBigInts); + } else if (typeof o == "object" && !(o instanceof bigInt)) { + const res = {}; + for (let k in o) { + res[k] = unstringifyBigInts(o[k]); + } + return res; + } else { + return o; + } +} + +function hexifyBigInts(o) { + if (typeof (o) === "bigInt" || (o instanceof bigInt)) { + let str = o.toString(16); + while (str.length < 64) str = "0" + str; + str = "0x" + str; + return str; + } else if (Array.isArray(o)) { + return o.map(hexifyBigInts); + } else if (typeof o == "object") { + const res = {}; + for (let k in o) { + res[k] = hexifyBigInts(o[k]); + } + return res; + } else { + return o; + } +} + +},{"big-integer":8}]},{},[2]); diff --git a/example/websnark.js b/example/websnark.js index 4cbfd61..48fab7f 100644 --- a/example/websnark.js +++ b/example/websnark.js @@ -28,16 +28,30 @@ /* globals window */ -const buildGroth16 = require("./src/groth16.js"); +const buildGroth16 = require("./src/groth16"); +const utils = require("./src/utils"); -buildGroth16().then( (groth16) => { +buildGroth16().then((groth16) => { window.groth16 = groth16; - window.genZKSnarkProof = function(witness, provingKey, cb) { - - const p = groth16.proof(witness, provingKey); + window.zkSnarkProofToSolidityInput = utils.toSolidityInput; + window.genZKSnarkProofAndWitness = function (input, circuitJson, provingKey, cb) { + const p = utils.genWitnessAndProve(groth16, input, circuitJson, provingKey); if (cb) { - p.then( (proof) => { + p.then((proof) => { + cb(null, proof); + }, (err) => { + cb(err); + }); + } else { + return p; + } + }; + + window.genZKSnarkProof = function (witness, provingKey, cb) { + const p = groth16.proof(witness, provingKey); + if (cb) { + p.then((proof) => { cb(null, proof); }, (err) => { cb(err); @@ -47,10 +61,7 @@ buildGroth16().then( (groth16) => { } }; }); - - - -},{"./src/groth16.js":13}],3:[function(require,module,exports){ +},{"./src/groth16":17,"./src/utils":18}],3:[function(require,module,exports){ (function (global){ 'use strict'; @@ -1336,1454 +1347,1454 @@ function fromByteArray (uint8) { } },{}],8:[function(require,module,exports){ -var bigInt = (function (undefined) { - "use strict"; - - var BASE = 1e7, - LOG_BASE = 7, - MAX_INT = 9007199254740992, - MAX_INT_ARR = smallToArray(MAX_INT), - DEFAULT_ALPHABET = "0123456789abcdefghijklmnopqrstuvwxyz"; - - var supportsNativeBigInt = typeof BigInt === "function"; - - function Integer(v, radix, alphabet, caseSensitive) { - if (typeof v === "undefined") return Integer[0]; - if (typeof radix !== "undefined") return +radix === 10 && !alphabet ? parseValue(v) : parseBase(v, radix, alphabet, caseSensitive); - return parseValue(v); - } - - function BigInteger(value, sign) { - this.value = value; - this.sign = sign; - this.isSmall = false; - } - BigInteger.prototype = Object.create(Integer.prototype); - - function SmallInteger(value) { - this.value = value; - this.sign = value < 0; - this.isSmall = true; - } - SmallInteger.prototype = Object.create(Integer.prototype); - - function NativeBigInt(value) { - this.value = value; - } - NativeBigInt.prototype = Object.create(Integer.prototype); - - function isPrecise(n) { - return -MAX_INT < n && n < MAX_INT; - } - - function smallToArray(n) { // For performance reasons doesn't reference BASE, need to change this function if BASE changes - if (n < 1e7) - return [n]; - if (n < 1e14) - return [n % 1e7, Math.floor(n / 1e7)]; - return [n % 1e7, Math.floor(n / 1e7) % 1e7, Math.floor(n / 1e14)]; - } - - function arrayToSmall(arr) { // If BASE changes this function may need to change - trim(arr); - var length = arr.length; - if (length < 4 && compareAbs(arr, MAX_INT_ARR) < 0) { - switch (length) { - case 0: return 0; - case 1: return arr[0]; - case 2: return arr[0] + arr[1] * BASE; - default: return arr[0] + (arr[1] + arr[2] * BASE) * BASE; - } - } - return arr; - } - - function trim(v) { - var i = v.length; - while (v[--i] === 0); - v.length = i + 1; - } - - function createArray(length) { // function shamelessly stolen from Yaffle's library https://github.com/Yaffle/BigInteger - var x = new Array(length); - var i = -1; - while (++i < length) { - x[i] = 0; - } - return x; - } - - function truncate(n) { - if (n > 0) return Math.floor(n); - return Math.ceil(n); - } - - function add(a, b) { // assumes a and b are arrays with a.length >= b.length - var l_a = a.length, - l_b = b.length, - r = new Array(l_a), - carry = 0, - base = BASE, - sum, i; - for (i = 0; i < l_b; i++) { - sum = a[i] + b[i] + carry; - carry = sum >= base ? 1 : 0; - r[i] = sum - carry * base; - } - while (i < l_a) { - sum = a[i] + carry; - carry = sum === base ? 1 : 0; - r[i++] = sum - carry * base; - } - if (carry > 0) r.push(carry); - return r; - } - - function addAny(a, b) { - if (a.length >= b.length) return add(a, b); - return add(b, a); - } - - function addSmall(a, carry) { // assumes a is array, carry is number with 0 <= carry < MAX_INT - var l = a.length, - r = new Array(l), - base = BASE, - sum, i; - for (i = 0; i < l; i++) { - sum = a[i] - base + carry; - carry = Math.floor(sum / base); - r[i] = sum - carry * base; - carry += 1; - } - while (carry > 0) { - r[i++] = carry % base; - carry = Math.floor(carry / base); - } - return r; - } - - BigInteger.prototype.add = function (v) { - var n = parseValue(v); - if (this.sign !== n.sign) { - return this.subtract(n.negate()); - } - var a = this.value, b = n.value; - if (n.isSmall) { - return new BigInteger(addSmall(a, Math.abs(b)), this.sign); - } - return new BigInteger(addAny(a, b), this.sign); - }; - BigInteger.prototype.plus = BigInteger.prototype.add; - - SmallInteger.prototype.add = function (v) { - var n = parseValue(v); - var a = this.value; - if (a < 0 !== n.sign) { - return this.subtract(n.negate()); - } - var b = n.value; - if (n.isSmall) { - if (isPrecise(a + b)) return new SmallInteger(a + b); - b = smallToArray(Math.abs(b)); - } - return new BigInteger(addSmall(b, Math.abs(a)), a < 0); - }; - SmallInteger.prototype.plus = SmallInteger.prototype.add; - - NativeBigInt.prototype.add = function (v) { - return new NativeBigInt(this.value + parseValue(v).value); - } - NativeBigInt.prototype.plus = NativeBigInt.prototype.add; - - function subtract(a, b) { // assumes a and b are arrays with a >= b - var a_l = a.length, - b_l = b.length, - r = new Array(a_l), - borrow = 0, - base = BASE, - i, difference; - for (i = 0; i < b_l; i++) { - difference = a[i] - borrow - b[i]; - if (difference < 0) { - difference += base; - borrow = 1; - } else borrow = 0; - r[i] = difference; - } - for (i = b_l; i < a_l; i++) { - difference = a[i] - borrow; - if (difference < 0) difference += base; - else { - r[i++] = difference; - break; - } - r[i] = difference; - } - for (; i < a_l; i++) { - r[i] = a[i]; - } - trim(r); - return r; - } - - function subtractAny(a, b, sign) { - var value; - if (compareAbs(a, b) >= 0) { - value = subtract(a, b); - } else { - value = subtract(b, a); - sign = !sign; - } - value = arrayToSmall(value); - if (typeof value === "number") { - if (sign) value = -value; - return new SmallInteger(value); - } - return new BigInteger(value, sign); - } - - function subtractSmall(a, b, sign) { // assumes a is array, b is number with 0 <= b < MAX_INT - var l = a.length, - r = new Array(l), - carry = -b, - base = BASE, - i, difference; - for (i = 0; i < l; i++) { - difference = a[i] + carry; - carry = Math.floor(difference / base); - difference %= base; - r[i] = difference < 0 ? difference + base : difference; - } - r = arrayToSmall(r); - if (typeof r === "number") { - if (sign) r = -r; - return new SmallInteger(r); - } return new BigInteger(r, sign); - } - - BigInteger.prototype.subtract = function (v) { - var n = parseValue(v); - if (this.sign !== n.sign) { - return this.add(n.negate()); - } - var a = this.value, b = n.value; - if (n.isSmall) - return subtractSmall(a, Math.abs(b), this.sign); - return subtractAny(a, b, this.sign); - }; - BigInteger.prototype.minus = BigInteger.prototype.subtract; - - SmallInteger.prototype.subtract = function (v) { - var n = parseValue(v); - var a = this.value; - if (a < 0 !== n.sign) { - return this.add(n.negate()); - } - var b = n.value; - if (n.isSmall) { - return new SmallInteger(a - b); - } - return subtractSmall(b, Math.abs(a), a >= 0); - }; - SmallInteger.prototype.minus = SmallInteger.prototype.subtract; - - NativeBigInt.prototype.subtract = function (v) { - return new NativeBigInt(this.value - parseValue(v).value); - } - NativeBigInt.prototype.minus = NativeBigInt.prototype.subtract; - - BigInteger.prototype.negate = function () { - return new BigInteger(this.value, !this.sign); - }; - SmallInteger.prototype.negate = function () { - var sign = this.sign; - var small = new SmallInteger(-this.value); - small.sign = !sign; - return small; - }; - NativeBigInt.prototype.negate = function () { - return new NativeBigInt(-this.value); - } - - BigInteger.prototype.abs = function () { - return new BigInteger(this.value, false); - }; - SmallInteger.prototype.abs = function () { - return new SmallInteger(Math.abs(this.value)); - }; - NativeBigInt.prototype.abs = function () { - return new NativeBigInt(this.value >= 0 ? this.value : -this.value); - } - - - function multiplyLong(a, b) { - var a_l = a.length, - b_l = b.length, - l = a_l + b_l, - r = createArray(l), - base = BASE, - product, carry, i, a_i, b_j; - for (i = 0; i < a_l; ++i) { - a_i = a[i]; - for (var j = 0; j < b_l; ++j) { - b_j = b[j]; - product = a_i * b_j + r[i + j]; - carry = Math.floor(product / base); - r[i + j] = product - carry * base; - r[i + j + 1] += carry; - } - } - trim(r); - return r; - } - - function multiplySmall(a, b) { // assumes a is array, b is number with |b| < BASE - var l = a.length, - r = new Array(l), - base = BASE, - carry = 0, - product, i; - for (i = 0; i < l; i++) { - product = a[i] * b + carry; - carry = Math.floor(product / base); - r[i] = product - carry * base; - } - while (carry > 0) { - r[i++] = carry % base; - carry = Math.floor(carry / base); - } - return r; - } - - function shiftLeft(x, n) { - var r = []; - while (n-- > 0) r.push(0); - return r.concat(x); - } - - function multiplyKaratsuba(x, y) { - var n = Math.max(x.length, y.length); - - if (n <= 30) return multiplyLong(x, y); - n = Math.ceil(n / 2); - - var b = x.slice(n), - a = x.slice(0, n), - d = y.slice(n), - c = y.slice(0, n); - - var ac = multiplyKaratsuba(a, c), - bd = multiplyKaratsuba(b, d), - abcd = multiplyKaratsuba(addAny(a, b), addAny(c, d)); - - var product = addAny(addAny(ac, shiftLeft(subtract(subtract(abcd, ac), bd), n)), shiftLeft(bd, 2 * n)); - trim(product); - return product; - } - - // The following function is derived from a surface fit of a graph plotting the performance difference - // between long multiplication and karatsuba multiplication versus the lengths of the two arrays. - function useKaratsuba(l1, l2) { - return -0.012 * l1 - 0.012 * l2 + 0.000015 * l1 * l2 > 0; - } - - BigInteger.prototype.multiply = function (v) { - var n = parseValue(v), - a = this.value, b = n.value, - sign = this.sign !== n.sign, - abs; - if (n.isSmall) { - if (b === 0) return Integer[0]; - if (b === 1) return this; - if (b === -1) return this.negate(); - abs = Math.abs(b); - if (abs < BASE) { - return new BigInteger(multiplySmall(a, abs), sign); - } - b = smallToArray(abs); - } - if (useKaratsuba(a.length, b.length)) // Karatsuba is only faster for certain array sizes - return new BigInteger(multiplyKaratsuba(a, b), sign); - return new BigInteger(multiplyLong(a, b), sign); - }; - - BigInteger.prototype.times = BigInteger.prototype.multiply; - - function multiplySmallAndArray(a, b, sign) { // a >= 0 - if (a < BASE) { - return new BigInteger(multiplySmall(b, a), sign); - } - return new BigInteger(multiplyLong(b, smallToArray(a)), sign); - } - SmallInteger.prototype._multiplyBySmall = function (a) { - if (isPrecise(a.value * this.value)) { - return new SmallInteger(a.value * this.value); - } - return multiplySmallAndArray(Math.abs(a.value), smallToArray(Math.abs(this.value)), this.sign !== a.sign); - }; - BigInteger.prototype._multiplyBySmall = function (a) { - if (a.value === 0) return Integer[0]; - if (a.value === 1) return this; - if (a.value === -1) return this.negate(); - return multiplySmallAndArray(Math.abs(a.value), this.value, this.sign !== a.sign); - }; - SmallInteger.prototype.multiply = function (v) { - return parseValue(v)._multiplyBySmall(this); - }; - SmallInteger.prototype.times = SmallInteger.prototype.multiply; - - NativeBigInt.prototype.multiply = function (v) { - return new NativeBigInt(this.value * parseValue(v).value); - } - NativeBigInt.prototype.times = NativeBigInt.prototype.multiply; - - function square(a) { - //console.assert(2 * BASE * BASE < MAX_INT); - var l = a.length, - r = createArray(l + l), - base = BASE, - product, carry, i, a_i, a_j; - for (i = 0; i < l; i++) { - a_i = a[i]; - carry = 0 - a_i * a_i; - for (var j = i; j < l; j++) { - a_j = a[j]; - product = 2 * (a_i * a_j) + r[i + j] + carry; - carry = Math.floor(product / base); - r[i + j] = product - carry * base; - } - r[i + l] = carry; - } - trim(r); - return r; - } - - BigInteger.prototype.square = function () { - return new BigInteger(square(this.value), false); - }; - - SmallInteger.prototype.square = function () { - var value = this.value * this.value; - if (isPrecise(value)) return new SmallInteger(value); - return new BigInteger(square(smallToArray(Math.abs(this.value))), false); - }; - - NativeBigInt.prototype.square = function (v) { - return new NativeBigInt(this.value * this.value); - } - - function divMod1(a, b) { // Left over from previous version. Performs faster than divMod2 on smaller input sizes. - var a_l = a.length, - b_l = b.length, - base = BASE, - result = createArray(b.length), - divisorMostSignificantDigit = b[b_l - 1], - // normalization - lambda = Math.ceil(base / (2 * divisorMostSignificantDigit)), - remainder = multiplySmall(a, lambda), - divisor = multiplySmall(b, lambda), - quotientDigit, shift, carry, borrow, i, l, q; - if (remainder.length <= a_l) remainder.push(0); - divisor.push(0); - divisorMostSignificantDigit = divisor[b_l - 1]; - for (shift = a_l - b_l; shift >= 0; shift--) { - quotientDigit = base - 1; - if (remainder[shift + b_l] !== divisorMostSignificantDigit) { - quotientDigit = Math.floor((remainder[shift + b_l] * base + remainder[shift + b_l - 1]) / divisorMostSignificantDigit); - } - // quotientDigit <= base - 1 - carry = 0; - borrow = 0; - l = divisor.length; - for (i = 0; i < l; i++) { - carry += quotientDigit * divisor[i]; - q = Math.floor(carry / base); - borrow += remainder[shift + i] - (carry - q * base); - carry = q; - if (borrow < 0) { - remainder[shift + i] = borrow + base; - borrow = -1; - } else { - remainder[shift + i] = borrow; - borrow = 0; - } - } - while (borrow !== 0) { - quotientDigit -= 1; - carry = 0; - for (i = 0; i < l; i++) { - carry += remainder[shift + i] - base + divisor[i]; - if (carry < 0) { - remainder[shift + i] = carry + base; - carry = 0; - } else { - remainder[shift + i] = carry; - carry = 1; - } - } - borrow += carry; - } - result[shift] = quotientDigit; - } - // denormalization - remainder = divModSmall(remainder, lambda)[0]; - return [arrayToSmall(result), arrayToSmall(remainder)]; - } - - function divMod2(a, b) { // Implementation idea shamelessly stolen from Silent Matt's library http://silentmatt.com/biginteger/ - // Performs faster than divMod1 on larger input sizes. - var a_l = a.length, - b_l = b.length, - result = [], - part = [], - base = BASE, - guess, xlen, highx, highy, check; - while (a_l) { - part.unshift(a[--a_l]); - trim(part); - if (compareAbs(part, b) < 0) { - result.push(0); - continue; - } - xlen = part.length; - highx = part[xlen - 1] * base + part[xlen - 2]; - highy = b[b_l - 1] * base + b[b_l - 2]; - if (xlen > b_l) { - highx = (highx + 1) * base; - } - guess = Math.ceil(highx / highy); - do { - check = multiplySmall(b, guess); - if (compareAbs(check, part) <= 0) break; - guess--; - } while (guess); - result.push(guess); - part = subtract(part, check); - } - result.reverse(); - return [arrayToSmall(result), arrayToSmall(part)]; - } - - function divModSmall(value, lambda) { - var length = value.length, - quotient = createArray(length), - base = BASE, - i, q, remainder, divisor; - remainder = 0; - for (i = length - 1; i >= 0; --i) { - divisor = remainder * base + value[i]; - q = truncate(divisor / lambda); - remainder = divisor - q * lambda; - quotient[i] = q | 0; - } - return [quotient, remainder | 0]; - } - - function divModAny(self, v) { - var value, n = parseValue(v); - if (supportsNativeBigInt) { - return [new NativeBigInt(self.value / n.value), new NativeBigInt(self.value % n.value)]; - } - var a = self.value, b = n.value; - var quotient; - if (b === 0) throw new Error("Cannot divide by zero"); - if (self.isSmall) { - if (n.isSmall) { - return [new SmallInteger(truncate(a / b)), new SmallInteger(a % b)]; - } - return [Integer[0], self]; - } - if (n.isSmall) { - if (b === 1) return [self, Integer[0]]; - if (b == -1) return [self.negate(), Integer[0]]; - var abs = Math.abs(b); - if (abs < BASE) { - value = divModSmall(a, abs); - quotient = arrayToSmall(value[0]); - var remainder = value[1]; - if (self.sign) remainder = -remainder; - if (typeof quotient === "number") { - if (self.sign !== n.sign) quotient = -quotient; - return [new SmallInteger(quotient), new SmallInteger(remainder)]; - } - return [new BigInteger(quotient, self.sign !== n.sign), new SmallInteger(remainder)]; - } - b = smallToArray(abs); - } - var comparison = compareAbs(a, b); - if (comparison === -1) return [Integer[0], self]; - if (comparison === 0) return [Integer[self.sign === n.sign ? 1 : -1], Integer[0]]; - - // divMod1 is faster on smaller input sizes - if (a.length + b.length <= 200) - value = divMod1(a, b); - else value = divMod2(a, b); - - quotient = value[0]; - var qSign = self.sign !== n.sign, - mod = value[1], - mSign = self.sign; - if (typeof quotient === "number") { - if (qSign) quotient = -quotient; - quotient = new SmallInteger(quotient); - } else quotient = new BigInteger(quotient, qSign); - if (typeof mod === "number") { - if (mSign) mod = -mod; - mod = new SmallInteger(mod); - } else mod = new BigInteger(mod, mSign); - return [quotient, mod]; - } - - BigInteger.prototype.divmod = function (v) { - var result = divModAny(this, v); - return { - quotient: result[0], - remainder: result[1] - }; - }; - NativeBigInt.prototype.divmod = SmallInteger.prototype.divmod = BigInteger.prototype.divmod; - - - BigInteger.prototype.divide = function (v) { - return divModAny(this, v)[0]; - }; - NativeBigInt.prototype.over = NativeBigInt.prototype.divide = function (v) { - return new NativeBigInt(this.value / parseValue(v).value); - }; - SmallInteger.prototype.over = SmallInteger.prototype.divide = BigInteger.prototype.over = BigInteger.prototype.divide; - - BigInteger.prototype.mod = function (v) { - return divModAny(this, v)[1]; - }; - NativeBigInt.prototype.mod = NativeBigInt.prototype.remainder = function (v) { - return new NativeBigInt(this.value % parseValue(v).value); - }; - SmallInteger.prototype.remainder = SmallInteger.prototype.mod = BigInteger.prototype.remainder = BigInteger.prototype.mod; - - BigInteger.prototype.pow = function (v) { - var n = parseValue(v), - a = this.value, - b = n.value, - value, x, y; - if (b === 0) return Integer[1]; - if (a === 0) return Integer[0]; - if (a === 1) return Integer[1]; - if (a === -1) return n.isEven() ? Integer[1] : Integer[-1]; - if (n.sign) { - return Integer[0]; - } - if (!n.isSmall) throw new Error("The exponent " + n.toString() + " is too large."); - if (this.isSmall) { - if (isPrecise(value = Math.pow(a, b))) - return new SmallInteger(truncate(value)); - } - x = this; - y = Integer[1]; - while (true) { - if (b & 1 === 1) { - y = y.times(x); - --b; - } - if (b === 0) break; - b /= 2; - x = x.square(); - } - return y; - }; - SmallInteger.prototype.pow = BigInteger.prototype.pow; - - NativeBigInt.prototype.pow = function (v) { - var n = parseValue(v); - var a = this.value, b = n.value; - var _0 = BigInt(0), _1 = BigInt(1), _2 = BigInt(2); - if (b === _0) return Integer[1]; - if (a === _0) return Integer[0]; - if (a === _1) return Integer[1]; - if (a === BigInt(-1)) return n.isEven() ? Integer[1] : Integer[-1]; - if (n.isNegative()) return new NativeBigInt(_0); - var x = this; - var y = Integer[1]; - while (true) { - if ((b & _1) === _1) { - y = y.times(x); - --b; - } - if (b === _0) break; - b /= _2; - x = x.square(); - } - return y; - } - - BigInteger.prototype.modPow = function (exp, mod) { - exp = parseValue(exp); - mod = parseValue(mod); - if (mod.isZero()) throw new Error("Cannot take modPow with modulus 0"); - var r = Integer[1], - base = this.mod(mod); - while (exp.isPositive()) { - if (base.isZero()) return Integer[0]; - if (exp.isOdd()) r = r.multiply(base).mod(mod); - exp = exp.divide(2); - base = base.square().mod(mod); - } - return r; - }; - NativeBigInt.prototype.modPow = SmallInteger.prototype.modPow = BigInteger.prototype.modPow; - - function compareAbs(a, b) { - if (a.length !== b.length) { - return a.length > b.length ? 1 : -1; - } - for (var i = a.length - 1; i >= 0; i--) { - if (a[i] !== b[i]) return a[i] > b[i] ? 1 : -1; - } - return 0; - } - - BigInteger.prototype.compareAbs = function (v) { - var n = parseValue(v), - a = this.value, - b = n.value; - if (n.isSmall) return 1; - return compareAbs(a, b); - }; - SmallInteger.prototype.compareAbs = function (v) { - var n = parseValue(v), - a = Math.abs(this.value), - b = n.value; - if (n.isSmall) { - b = Math.abs(b); - return a === b ? 0 : a > b ? 1 : -1; - } - return -1; - }; - NativeBigInt.prototype.compareAbs = function (v) { - var a = this.value; - var b = parseValue(v).value; - a = a >= 0 ? a : -a; - b = b >= 0 ? b : -b; - return a === b ? 0 : a > b ? 1 : -1; - } - - BigInteger.prototype.compare = function (v) { - // See discussion about comparison with Infinity: - // https://github.com/peterolson/BigInteger.js/issues/61 - if (v === Infinity) { - return -1; - } - if (v === -Infinity) { - return 1; - } - - var n = parseValue(v), - a = this.value, - b = n.value; - if (this.sign !== n.sign) { - return n.sign ? 1 : -1; - } - if (n.isSmall) { - return this.sign ? -1 : 1; - } - return compareAbs(a, b) * (this.sign ? -1 : 1); - }; - BigInteger.prototype.compareTo = BigInteger.prototype.compare; - - SmallInteger.prototype.compare = function (v) { - if (v === Infinity) { - return -1; - } - if (v === -Infinity) { - return 1; - } - - var n = parseValue(v), - a = this.value, - b = n.value; - if (n.isSmall) { - return a == b ? 0 : a > b ? 1 : -1; - } - if (a < 0 !== n.sign) { - return a < 0 ? -1 : 1; - } - return a < 0 ? 1 : -1; - }; - SmallInteger.prototype.compareTo = SmallInteger.prototype.compare; - - NativeBigInt.prototype.compare = function (v) { - if (v === Infinity) { - return -1; - } - if (v === -Infinity) { - return 1; - } - var a = this.value; - var b = parseValue(v).value; - return a === b ? 0 : a > b ? 1 : -1; - } - NativeBigInt.prototype.compareTo = NativeBigInt.prototype.compare; - - BigInteger.prototype.equals = function (v) { - return this.compare(v) === 0; - }; - NativeBigInt.prototype.eq = NativeBigInt.prototype.equals = SmallInteger.prototype.eq = SmallInteger.prototype.equals = BigInteger.prototype.eq = BigInteger.prototype.equals; - - BigInteger.prototype.notEquals = function (v) { - return this.compare(v) !== 0; - }; - NativeBigInt.prototype.neq = NativeBigInt.prototype.notEquals = SmallInteger.prototype.neq = SmallInteger.prototype.notEquals = BigInteger.prototype.neq = BigInteger.prototype.notEquals; - - BigInteger.prototype.greater = function (v) { - return this.compare(v) > 0; - }; - NativeBigInt.prototype.gt = NativeBigInt.prototype.greater = SmallInteger.prototype.gt = SmallInteger.prototype.greater = BigInteger.prototype.gt = BigInteger.prototype.greater; - - BigInteger.prototype.lesser = function (v) { - return this.compare(v) < 0; - }; - NativeBigInt.prototype.lt = NativeBigInt.prototype.lesser = SmallInteger.prototype.lt = SmallInteger.prototype.lesser = BigInteger.prototype.lt = BigInteger.prototype.lesser; - - BigInteger.prototype.greaterOrEquals = function (v) { - return this.compare(v) >= 0; - }; - NativeBigInt.prototype.geq = NativeBigInt.prototype.greaterOrEquals = SmallInteger.prototype.geq = SmallInteger.prototype.greaterOrEquals = BigInteger.prototype.geq = BigInteger.prototype.greaterOrEquals; - - BigInteger.prototype.lesserOrEquals = function (v) { - return this.compare(v) <= 0; - }; - NativeBigInt.prototype.leq = NativeBigInt.prototype.lesserOrEquals = SmallInteger.prototype.leq = SmallInteger.prototype.lesserOrEquals = BigInteger.prototype.leq = BigInteger.prototype.lesserOrEquals; - - BigInteger.prototype.isEven = function () { - return (this.value[0] & 1) === 0; - }; - SmallInteger.prototype.isEven = function () { - return (this.value & 1) === 0; - }; - NativeBigInt.prototype.isEven = function () { - return (this.value & BigInt(1)) === BigInt(0); - } - - BigInteger.prototype.isOdd = function () { - return (this.value[0] & 1) === 1; - }; - SmallInteger.prototype.isOdd = function () { - return (this.value & 1) === 1; - }; - NativeBigInt.prototype.isOdd = function () { - return (this.value & BigInt(1)) === BigInt(1); - } - - BigInteger.prototype.isPositive = function () { - return !this.sign; - }; - SmallInteger.prototype.isPositive = function () { - return this.value > 0; - }; - NativeBigInt.prototype.isPositive = SmallInteger.prototype.isPositive; - - BigInteger.prototype.isNegative = function () { - return this.sign; - }; - SmallInteger.prototype.isNegative = function () { - return this.value < 0; - }; - NativeBigInt.prototype.isNegative = SmallInteger.prototype.isNegative; - - BigInteger.prototype.isUnit = function () { - return false; - }; - SmallInteger.prototype.isUnit = function () { - return Math.abs(this.value) === 1; - }; - NativeBigInt.prototype.isUnit = function () { - return this.abs().value === BigInt(1); - } - - BigInteger.prototype.isZero = function () { - return false; - }; - SmallInteger.prototype.isZero = function () { - return this.value === 0; - }; - NativeBigInt.prototype.isZero = function () { - return this.value === BigInt(0); - } - - BigInteger.prototype.isDivisibleBy = function (v) { - var n = parseValue(v); - if (n.isZero()) return false; - if (n.isUnit()) return true; - if (n.compareAbs(2) === 0) return this.isEven(); - return this.mod(n).isZero(); - }; - NativeBigInt.prototype.isDivisibleBy = SmallInteger.prototype.isDivisibleBy = BigInteger.prototype.isDivisibleBy; - - function isBasicPrime(v) { - var n = v.abs(); - if (n.isUnit()) return false; - if (n.equals(2) || n.equals(3) || n.equals(5)) return true; - if (n.isEven() || n.isDivisibleBy(3) || n.isDivisibleBy(5)) return false; - if (n.lesser(49)) return true; - // we don't know if it's prime: let the other functions figure it out - } - - function millerRabinTest(n, a) { - var nPrev = n.prev(), - b = nPrev, - r = 0, - d, t, i, x; - while (b.isEven()) b = b.divide(2), r++; - next: for (i = 0; i < a.length; i++) { - if (n.lesser(a[i])) continue; - x = bigInt(a[i]).modPow(b, n); - if (x.isUnit() || x.equals(nPrev)) continue; - for (d = r - 1; d != 0; d--) { - x = x.square().mod(n); - if (x.isUnit()) return false; - if (x.equals(nPrev)) continue next; - } - return false; - } - return true; - } - - // Set "strict" to true to force GRH-supported lower bound of 2*log(N)^2 - BigInteger.prototype.isPrime = function (strict) { - var isPrime = isBasicPrime(this); - if (isPrime !== undefined) return isPrime; - var n = this.abs(); - var bits = n.bitLength(); - if (bits <= 64) - return millerRabinTest(n, [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37]); - var logN = Math.log(2) * bits.toJSNumber(); - var t = Math.ceil((strict === true) ? (2 * Math.pow(logN, 2)) : logN); - for (var a = [], i = 0; i < t; i++) { - a.push(bigInt(i + 2)); - } - return millerRabinTest(n, a); - }; - NativeBigInt.prototype.isPrime = SmallInteger.prototype.isPrime = BigInteger.prototype.isPrime; - - BigInteger.prototype.isProbablePrime = function (iterations) { - var isPrime = isBasicPrime(this); - if (isPrime !== undefined) return isPrime; - var n = this.abs(); - var t = iterations === undefined ? 5 : iterations; - for (var a = [], i = 0; i < t; i++) { - a.push(bigInt.randBetween(2, n.minus(2))); - } - return millerRabinTest(n, a); - }; - NativeBigInt.prototype.isProbablePrime = SmallInteger.prototype.isProbablePrime = BigInteger.prototype.isProbablePrime; - - BigInteger.prototype.modInv = function (n) { - var t = bigInt.zero, newT = bigInt.one, r = parseValue(n), newR = this.abs(), q, lastT, lastR; - while (!newR.isZero()) { - q = r.divide(newR); - lastT = t; - lastR = r; - t = newT; - r = newR; - newT = lastT.subtract(q.multiply(newT)); - newR = lastR.subtract(q.multiply(newR)); - } - if (!r.isUnit()) throw new Error(this.toString() + " and " + n.toString() + " are not co-prime"); - if (t.compare(0) === -1) { - t = t.add(n); - } - if (this.isNegative()) { - return t.negate(); - } - return t; - }; - - NativeBigInt.prototype.modInv = SmallInteger.prototype.modInv = BigInteger.prototype.modInv; - - BigInteger.prototype.next = function () { - var value = this.value; - if (this.sign) { - return subtractSmall(value, 1, this.sign); - } - return new BigInteger(addSmall(value, 1), this.sign); - }; - SmallInteger.prototype.next = function () { - var value = this.value; - if (value + 1 < MAX_INT) return new SmallInteger(value + 1); - return new BigInteger(MAX_INT_ARR, false); - }; - NativeBigInt.prototype.next = function () { - return new NativeBigInt(this.value + BigInt(1)); - } - - BigInteger.prototype.prev = function () { - var value = this.value; - if (this.sign) { - return new BigInteger(addSmall(value, 1), true); - } - return subtractSmall(value, 1, this.sign); - }; - SmallInteger.prototype.prev = function () { - var value = this.value; - if (value - 1 > -MAX_INT) return new SmallInteger(value - 1); - return new BigInteger(MAX_INT_ARR, true); - }; - NativeBigInt.prototype.prev = function () { - return new NativeBigInt(this.value - BigInt(1)); - } - - var powersOfTwo = [1]; - while (2 * powersOfTwo[powersOfTwo.length - 1] <= BASE) powersOfTwo.push(2 * powersOfTwo[powersOfTwo.length - 1]); - var powers2Length = powersOfTwo.length, highestPower2 = powersOfTwo[powers2Length - 1]; - - function shift_isSmall(n) { - return Math.abs(n) <= BASE; - } - - BigInteger.prototype.shiftLeft = function (v) { - var n = parseValue(v).toJSNumber(); - if (!shift_isSmall(n)) { - throw new Error(String(n) + " is too large for shifting."); - } - if (n < 0) return this.shiftRight(-n); - var result = this; - if (result.isZero()) return result; - while (n >= powers2Length) { - result = result.multiply(highestPower2); - n -= powers2Length - 1; - } - return result.multiply(powersOfTwo[n]); - }; - NativeBigInt.prototype.shiftLeft = SmallInteger.prototype.shiftLeft = BigInteger.prototype.shiftLeft; - - BigInteger.prototype.shiftRight = function (v) { - var remQuo; - var n = parseValue(v).toJSNumber(); - if (!shift_isSmall(n)) { - throw new Error(String(n) + " is too large for shifting."); - } - if (n < 0) return this.shiftLeft(-n); - var result = this; - while (n >= powers2Length) { - if (result.isZero() || (result.isNegative() && result.isUnit())) return result; - remQuo = divModAny(result, highestPower2); - result = remQuo[1].isNegative() ? remQuo[0].prev() : remQuo[0]; - n -= powers2Length - 1; - } - remQuo = divModAny(result, powersOfTwo[n]); - return remQuo[1].isNegative() ? remQuo[0].prev() : remQuo[0]; - }; - NativeBigInt.prototype.shiftRight = SmallInteger.prototype.shiftRight = BigInteger.prototype.shiftRight; - - function bitwise(x, y, fn) { - y = parseValue(y); - var xSign = x.isNegative(), ySign = y.isNegative(); - var xRem = xSign ? x.not() : x, - yRem = ySign ? y.not() : y; - var xDigit = 0, yDigit = 0; - var xDivMod = null, yDivMod = null; - var result = []; - while (!xRem.isZero() || !yRem.isZero()) { - xDivMod = divModAny(xRem, highestPower2); - xDigit = xDivMod[1].toJSNumber(); - if (xSign) { - xDigit = highestPower2 - 1 - xDigit; // two's complement for negative numbers - } - - yDivMod = divModAny(yRem, highestPower2); - yDigit = yDivMod[1].toJSNumber(); - if (ySign) { - yDigit = highestPower2 - 1 - yDigit; // two's complement for negative numbers - } - - xRem = xDivMod[0]; - yRem = yDivMod[0]; - result.push(fn(xDigit, yDigit)); - } - var sum = fn(xSign ? 1 : 0, ySign ? 1 : 0) !== 0 ? bigInt(-1) : bigInt(0); - for (var i = result.length - 1; i >= 0; i -= 1) { - sum = sum.multiply(highestPower2).add(bigInt(result[i])); - } - return sum; - } - - BigInteger.prototype.not = function () { - return this.negate().prev(); - }; - NativeBigInt.prototype.not = SmallInteger.prototype.not = BigInteger.prototype.not; - - BigInteger.prototype.and = function (n) { - return bitwise(this, n, function (a, b) { return a & b; }); - }; - NativeBigInt.prototype.and = SmallInteger.prototype.and = BigInteger.prototype.and; - - BigInteger.prototype.or = function (n) { - return bitwise(this, n, function (a, b) { return a | b; }); - }; - NativeBigInt.prototype.or = SmallInteger.prototype.or = BigInteger.prototype.or; - - BigInteger.prototype.xor = function (n) { - return bitwise(this, n, function (a, b) { return a ^ b; }); - }; - NativeBigInt.prototype.xor = SmallInteger.prototype.xor = BigInteger.prototype.xor; - - var LOBMASK_I = 1 << 30, LOBMASK_BI = (BASE & -BASE) * (BASE & -BASE) | LOBMASK_I; - function roughLOB(n) { // get lowestOneBit (rough) - // SmallInteger: return Min(lowestOneBit(n), 1 << 30) - // BigInteger: return Min(lowestOneBit(n), 1 << 14) [BASE=1e7] - var v = n.value, - x = typeof v === "number" ? v | LOBMASK_I : - typeof v === "bigint" ? v | BigInt(LOBMASK_I) : - v[0] + v[1] * BASE | LOBMASK_BI; - return x & -x; - } - - function integerLogarithm(value, base) { - if (base.compareTo(value) <= 0) { - var tmp = integerLogarithm(value, base.square(base)); - var p = tmp.p; - var e = tmp.e; - var t = p.multiply(base); - return t.compareTo(value) <= 0 ? { p: t, e: e * 2 + 1 } : { p: p, e: e * 2 }; - } - return { p: bigInt(1), e: 0 }; - } - - BigInteger.prototype.bitLength = function () { - var n = this; - if (n.compareTo(bigInt(0)) < 0) { - n = n.negate().subtract(bigInt(1)); - } - if (n.compareTo(bigInt(0)) === 0) { - return bigInt(0); - } - return bigInt(integerLogarithm(n, bigInt(2)).e).add(bigInt(1)); - } - NativeBigInt.prototype.bitLength = SmallInteger.prototype.bitLength = BigInteger.prototype.bitLength; - - function max(a, b) { - a = parseValue(a); - b = parseValue(b); - return a.greater(b) ? a : b; - } - function min(a, b) { - a = parseValue(a); - b = parseValue(b); - return a.lesser(b) ? a : b; - } - function gcd(a, b) { - a = parseValue(a).abs(); - b = parseValue(b).abs(); - if (a.equals(b)) return a; - if (a.isZero()) return b; - if (b.isZero()) return a; - var c = Integer[1], d, t; - while (a.isEven() && b.isEven()) { - d = min(roughLOB(a), roughLOB(b)); - a = a.divide(d); - b = b.divide(d); - c = c.multiply(d); - } - while (a.isEven()) { - a = a.divide(roughLOB(a)); - } - do { - while (b.isEven()) { - b = b.divide(roughLOB(b)); - } - if (a.greater(b)) { - t = b; b = a; a = t; - } - b = b.subtract(a); - } while (!b.isZero()); - return c.isUnit() ? a : a.multiply(c); - } - function lcm(a, b) { - a = parseValue(a).abs(); - b = parseValue(b).abs(); - return a.divide(gcd(a, b)).multiply(b); - } - function randBetween(a, b) { - a = parseValue(a); - b = parseValue(b); - var low = min(a, b), high = max(a, b); - var range = high.subtract(low).add(1); - if (range.isSmall) return low.add(Math.floor(Math.random() * range)); - var digits = toBase(range, BASE).value; - var result = [], restricted = true; - for (var i = 0; i < digits.length; i++) { - var top = restricted ? digits[i] : BASE; - var digit = truncate(Math.random() * top); - result.push(digit); - if (digit < top) restricted = false; - } - return low.add(Integer.fromArray(result, BASE, false)); - } - - var parseBase = function (text, base, alphabet, caseSensitive) { - alphabet = alphabet || DEFAULT_ALPHABET; - text = String(text); - if (!caseSensitive) { - text = text.toLowerCase(); - alphabet = alphabet.toLowerCase(); - } - var length = text.length; - var i; - var absBase = Math.abs(base); - var alphabetValues = {}; - for (i = 0; i < alphabet.length; i++) { - alphabetValues[alphabet[i]] = i; - } - for (i = 0; i < length; i++) { - var c = text[i]; - if (c === "-") continue; - if (c in alphabetValues) { - if (alphabetValues[c] >= absBase) { - if (c === "1" && absBase === 1) continue; - throw new Error(c + " is not a valid digit in base " + base + "."); - } - } - } - base = parseValue(base); - var digits = []; - var isNegative = text[0] === "-"; - for (i = isNegative ? 1 : 0; i < text.length; i++) { - var c = text[i]; - if (c in alphabetValues) digits.push(parseValue(alphabetValues[c])); - else if (c === "<") { - var start = i; - do { i++; } while (text[i] !== ">" && i < text.length); - digits.push(parseValue(text.slice(start + 1, i))); - } - else throw new Error(c + " is not a valid character"); - } - return parseBaseFromArray(digits, base, isNegative); - }; - - function parseBaseFromArray(digits, base, isNegative) { - var val = Integer[0], pow = Integer[1], i; - for (i = digits.length - 1; i >= 0; i--) { - val = val.add(digits[i].times(pow)); - pow = pow.times(base); - } - return isNegative ? val.negate() : val; - } - - function stringify(digit, alphabet) { - alphabet = alphabet || DEFAULT_ALPHABET; - if (digit < alphabet.length) { - return alphabet[digit]; - } - return "<" + digit + ">"; - } - - function toBase(n, base) { - base = bigInt(base); - if (base.isZero()) { - if (n.isZero()) return { value: [0], isNegative: false }; - throw new Error("Cannot convert nonzero numbers to base 0."); - } - if (base.equals(-1)) { - if (n.isZero()) return { value: [0], isNegative: false }; - if (n.isNegative()) - return { - value: [].concat.apply([], Array.apply(null, Array(-n.toJSNumber())) - .map(Array.prototype.valueOf, [1, 0]) - ), - isNegative: false - }; - - var arr = Array.apply(null, Array(n.toJSNumber() - 1)) - .map(Array.prototype.valueOf, [0, 1]); - arr.unshift([1]); - return { - value: [].concat.apply([], arr), - isNegative: false - }; - } - - var neg = false; - if (n.isNegative() && base.isPositive()) { - neg = true; - n = n.abs(); - } - if (base.isUnit()) { - if (n.isZero()) return { value: [0], isNegative: false }; - - return { - value: Array.apply(null, Array(n.toJSNumber())) - .map(Number.prototype.valueOf, 1), - isNegative: neg - }; - } - var out = []; - var left = n, divmod; - while (left.isNegative() || left.compareAbs(base) >= 0) { - divmod = left.divmod(base); - left = divmod.quotient; - var digit = divmod.remainder; - if (digit.isNegative()) { - digit = base.minus(digit).abs(); - left = left.next(); - } - out.push(digit.toJSNumber()); - } - out.push(left.toJSNumber()); - return { value: out.reverse(), isNegative: neg }; - } - - function toBaseString(n, base, alphabet) { - var arr = toBase(n, base); - return (arr.isNegative ? "-" : "") + arr.value.map(function (x) { - return stringify(x, alphabet); - }).join(''); - } - - BigInteger.prototype.toArray = function (radix) { - return toBase(this, radix); - }; - - SmallInteger.prototype.toArray = function (radix) { - return toBase(this, radix); - }; - - NativeBigInt.prototype.toArray = function (radix) { - return toBase(this, radix); - }; - - BigInteger.prototype.toString = function (radix, alphabet) { - if (radix === undefined) radix = 10; - if (radix !== 10) return toBaseString(this, radix, alphabet); - var v = this.value, l = v.length, str = String(v[--l]), zeros = "0000000", digit; - while (--l >= 0) { - digit = String(v[l]); - str += zeros.slice(digit.length) + digit; - } - var sign = this.sign ? "-" : ""; - return sign + str; - }; - - SmallInteger.prototype.toString = function (radix, alphabet) { - if (radix === undefined) radix = 10; - if (radix != 10) return toBaseString(this, radix, alphabet); - return String(this.value); - }; - - NativeBigInt.prototype.toString = SmallInteger.prototype.toString; - - NativeBigInt.prototype.toJSON = BigInteger.prototype.toJSON = SmallInteger.prototype.toJSON = function () { return this.toString(); } - - BigInteger.prototype.valueOf = function () { - return parseInt(this.toString(), 10); - }; - BigInteger.prototype.toJSNumber = BigInteger.prototype.valueOf; - - SmallInteger.prototype.valueOf = function () { - return this.value; - }; - SmallInteger.prototype.toJSNumber = SmallInteger.prototype.valueOf; - NativeBigInt.prototype.valueOf = NativeBigInt.prototype.toJSNumber = function () { - return parseInt(this.toString(), 10); - } - - function parseStringValue(v) { - if (isPrecise(+v)) { - var x = +v; - if (x === truncate(x)) - return supportsNativeBigInt ? new NativeBigInt(BigInt(x)) : new SmallInteger(x); - throw new Error("Invalid integer: " + v); - } - var sign = v[0] === "-"; - if (sign) v = v.slice(1); - var split = v.split(/e/i); - if (split.length > 2) throw new Error("Invalid integer: " + split.join("e")); - if (split.length === 2) { - var exp = split[1]; - if (exp[0] === "+") exp = exp.slice(1); - exp = +exp; - if (exp !== truncate(exp) || !isPrecise(exp)) throw new Error("Invalid integer: " + exp + " is not a valid exponent."); - var text = split[0]; - var decimalPlace = text.indexOf("."); - if (decimalPlace >= 0) { - exp -= text.length - decimalPlace - 1; - text = text.slice(0, decimalPlace) + text.slice(decimalPlace + 1); - } - if (exp < 0) throw new Error("Cannot include negative exponent part for integers"); - text += (new Array(exp + 1)).join("0"); - v = text; - } - var isValid = /^([0-9][0-9]*)$/.test(v); - if (!isValid) throw new Error("Invalid integer: " + v); - if (supportsNativeBigInt) { - return new NativeBigInt(BigInt(sign ? "-" + v : v)); - } - var r = [], max = v.length, l = LOG_BASE, min = max - l; - while (max > 0) { - r.push(+v.slice(min, max)); - min -= l; - if (min < 0) min = 0; - max -= l; - } - trim(r); - return new BigInteger(r, sign); - } - - function parseNumberValue(v) { - if (supportsNativeBigInt) { - return new NativeBigInt(BigInt(v)); - } - if (isPrecise(v)) { - if (v !== truncate(v)) throw new Error(v + " is not an integer."); - return new SmallInteger(v); - } - return parseStringValue(v.toString()); - } - - function parseValue(v) { - if (typeof v === "number") { - return parseNumberValue(v); - } - if (typeof v === "string") { - return parseStringValue(v); - } - if (typeof v === "bigint") { - return new NativeBigInt(v); - } - return v; - } - // Pre-define numbers in range [-999,999] - for (var i = 0; i < 1000; i++) { - Integer[i] = parseValue(i); - if (i > 0) Integer[-i] = parseValue(-i); - } - // Backwards compatibility - Integer.one = Integer[1]; - Integer.zero = Integer[0]; - Integer.minusOne = Integer[-1]; - Integer.max = max; - Integer.min = min; - Integer.gcd = gcd; - Integer.lcm = lcm; - Integer.isInstance = function (x) { return x instanceof BigInteger || x instanceof SmallInteger || x instanceof NativeBigInt; }; - Integer.randBetween = randBetween; - - Integer.fromArray = function (digits, base, isNegative) { - return parseBaseFromArray(digits.map(parseValue), parseValue(base || 10), isNegative); - }; - - return Integer; -})(); - -// Node.js check -if (typeof module !== "undefined" && module.hasOwnProperty("exports")) { - module.exports = bigInt; -} - -//amd check -if (typeof define === "function" && define.amd) { - define("big-integer", [], function () { - return bigInt; - }); -} +var bigInt = (function (undefined) { + "use strict"; + + var BASE = 1e7, + LOG_BASE = 7, + MAX_INT = 9007199254740992, + MAX_INT_ARR = smallToArray(MAX_INT), + DEFAULT_ALPHABET = "0123456789abcdefghijklmnopqrstuvwxyz"; + + var supportsNativeBigInt = typeof BigInt === "function"; + + function Integer(v, radix, alphabet, caseSensitive) { + if (typeof v === "undefined") return Integer[0]; + if (typeof radix !== "undefined") return +radix === 10 && !alphabet ? parseValue(v) : parseBase(v, radix, alphabet, caseSensitive); + return parseValue(v); + } + + function BigInteger(value, sign) { + this.value = value; + this.sign = sign; + this.isSmall = false; + } + BigInteger.prototype = Object.create(Integer.prototype); + + function SmallInteger(value) { + this.value = value; + this.sign = value < 0; + this.isSmall = true; + } + SmallInteger.prototype = Object.create(Integer.prototype); + + function NativeBigInt(value) { + this.value = value; + } + NativeBigInt.prototype = Object.create(Integer.prototype); + + function isPrecise(n) { + return -MAX_INT < n && n < MAX_INT; + } + + function smallToArray(n) { // For performance reasons doesn't reference BASE, need to change this function if BASE changes + if (n < 1e7) + return [n]; + if (n < 1e14) + return [n % 1e7, Math.floor(n / 1e7)]; + return [n % 1e7, Math.floor(n / 1e7) % 1e7, Math.floor(n / 1e14)]; + } + + function arrayToSmall(arr) { // If BASE changes this function may need to change + trim(arr); + var length = arr.length; + if (length < 4 && compareAbs(arr, MAX_INT_ARR) < 0) { + switch (length) { + case 0: return 0; + case 1: return arr[0]; + case 2: return arr[0] + arr[1] * BASE; + default: return arr[0] + (arr[1] + arr[2] * BASE) * BASE; + } + } + return arr; + } + + function trim(v) { + var i = v.length; + while (v[--i] === 0); + v.length = i + 1; + } + + function createArray(length) { // function shamelessly stolen from Yaffle's library https://github.com/Yaffle/BigInteger + var x = new Array(length); + var i = -1; + while (++i < length) { + x[i] = 0; + } + return x; + } + + function truncate(n) { + if (n > 0) return Math.floor(n); + return Math.ceil(n); + } + + function add(a, b) { // assumes a and b are arrays with a.length >= b.length + var l_a = a.length, + l_b = b.length, + r = new Array(l_a), + carry = 0, + base = BASE, + sum, i; + for (i = 0; i < l_b; i++) { + sum = a[i] + b[i] + carry; + carry = sum >= base ? 1 : 0; + r[i] = sum - carry * base; + } + while (i < l_a) { + sum = a[i] + carry; + carry = sum === base ? 1 : 0; + r[i++] = sum - carry * base; + } + if (carry > 0) r.push(carry); + return r; + } + + function addAny(a, b) { + if (a.length >= b.length) return add(a, b); + return add(b, a); + } + + function addSmall(a, carry) { // assumes a is array, carry is number with 0 <= carry < MAX_INT + var l = a.length, + r = new Array(l), + base = BASE, + sum, i; + for (i = 0; i < l; i++) { + sum = a[i] - base + carry; + carry = Math.floor(sum / base); + r[i] = sum - carry * base; + carry += 1; + } + while (carry > 0) { + r[i++] = carry % base; + carry = Math.floor(carry / base); + } + return r; + } + + BigInteger.prototype.add = function (v) { + var n = parseValue(v); + if (this.sign !== n.sign) { + return this.subtract(n.negate()); + } + var a = this.value, b = n.value; + if (n.isSmall) { + return new BigInteger(addSmall(a, Math.abs(b)), this.sign); + } + return new BigInteger(addAny(a, b), this.sign); + }; + BigInteger.prototype.plus = BigInteger.prototype.add; + + SmallInteger.prototype.add = function (v) { + var n = parseValue(v); + var a = this.value; + if (a < 0 !== n.sign) { + return this.subtract(n.negate()); + } + var b = n.value; + if (n.isSmall) { + if (isPrecise(a + b)) return new SmallInteger(a + b); + b = smallToArray(Math.abs(b)); + } + return new BigInteger(addSmall(b, Math.abs(a)), a < 0); + }; + SmallInteger.prototype.plus = SmallInteger.prototype.add; + + NativeBigInt.prototype.add = function (v) { + return new NativeBigInt(this.value + parseValue(v).value); + } + NativeBigInt.prototype.plus = NativeBigInt.prototype.add; + + function subtract(a, b) { // assumes a and b are arrays with a >= b + var a_l = a.length, + b_l = b.length, + r = new Array(a_l), + borrow = 0, + base = BASE, + i, difference; + for (i = 0; i < b_l; i++) { + difference = a[i] - borrow - b[i]; + if (difference < 0) { + difference += base; + borrow = 1; + } else borrow = 0; + r[i] = difference; + } + for (i = b_l; i < a_l; i++) { + difference = a[i] - borrow; + if (difference < 0) difference += base; + else { + r[i++] = difference; + break; + } + r[i] = difference; + } + for (; i < a_l; i++) { + r[i] = a[i]; + } + trim(r); + return r; + } + + function subtractAny(a, b, sign) { + var value; + if (compareAbs(a, b) >= 0) { + value = subtract(a, b); + } else { + value = subtract(b, a); + sign = !sign; + } + value = arrayToSmall(value); + if (typeof value === "number") { + if (sign) value = -value; + return new SmallInteger(value); + } + return new BigInteger(value, sign); + } + + function subtractSmall(a, b, sign) { // assumes a is array, b is number with 0 <= b < MAX_INT + var l = a.length, + r = new Array(l), + carry = -b, + base = BASE, + i, difference; + for (i = 0; i < l; i++) { + difference = a[i] + carry; + carry = Math.floor(difference / base); + difference %= base; + r[i] = difference < 0 ? difference + base : difference; + } + r = arrayToSmall(r); + if (typeof r === "number") { + if (sign) r = -r; + return new SmallInteger(r); + } return new BigInteger(r, sign); + } + + BigInteger.prototype.subtract = function (v) { + var n = parseValue(v); + if (this.sign !== n.sign) { + return this.add(n.negate()); + } + var a = this.value, b = n.value; + if (n.isSmall) + return subtractSmall(a, Math.abs(b), this.sign); + return subtractAny(a, b, this.sign); + }; + BigInteger.prototype.minus = BigInteger.prototype.subtract; + + SmallInteger.prototype.subtract = function (v) { + var n = parseValue(v); + var a = this.value; + if (a < 0 !== n.sign) { + return this.add(n.negate()); + } + var b = n.value; + if (n.isSmall) { + return new SmallInteger(a - b); + } + return subtractSmall(b, Math.abs(a), a >= 0); + }; + SmallInteger.prototype.minus = SmallInteger.prototype.subtract; + + NativeBigInt.prototype.subtract = function (v) { + return new NativeBigInt(this.value - parseValue(v).value); + } + NativeBigInt.prototype.minus = NativeBigInt.prototype.subtract; + + BigInteger.prototype.negate = function () { + return new BigInteger(this.value, !this.sign); + }; + SmallInteger.prototype.negate = function () { + var sign = this.sign; + var small = new SmallInteger(-this.value); + small.sign = !sign; + return small; + }; + NativeBigInt.prototype.negate = function () { + return new NativeBigInt(-this.value); + } + + BigInteger.prototype.abs = function () { + return new BigInteger(this.value, false); + }; + SmallInteger.prototype.abs = function () { + return new SmallInteger(Math.abs(this.value)); + }; + NativeBigInt.prototype.abs = function () { + return new NativeBigInt(this.value >= 0 ? this.value : -this.value); + } + + + function multiplyLong(a, b) { + var a_l = a.length, + b_l = b.length, + l = a_l + b_l, + r = createArray(l), + base = BASE, + product, carry, i, a_i, b_j; + for (i = 0; i < a_l; ++i) { + a_i = a[i]; + for (var j = 0; j < b_l; ++j) { + b_j = b[j]; + product = a_i * b_j + r[i + j]; + carry = Math.floor(product / base); + r[i + j] = product - carry * base; + r[i + j + 1] += carry; + } + } + trim(r); + return r; + } + + function multiplySmall(a, b) { // assumes a is array, b is number with |b| < BASE + var l = a.length, + r = new Array(l), + base = BASE, + carry = 0, + product, i; + for (i = 0; i < l; i++) { + product = a[i] * b + carry; + carry = Math.floor(product / base); + r[i] = product - carry * base; + } + while (carry > 0) { + r[i++] = carry % base; + carry = Math.floor(carry / base); + } + return r; + } + + function shiftLeft(x, n) { + var r = []; + while (n-- > 0) r.push(0); + return r.concat(x); + } + + function multiplyKaratsuba(x, y) { + var n = Math.max(x.length, y.length); + + if (n <= 30) return multiplyLong(x, y); + n = Math.ceil(n / 2); + + var b = x.slice(n), + a = x.slice(0, n), + d = y.slice(n), + c = y.slice(0, n); + + var ac = multiplyKaratsuba(a, c), + bd = multiplyKaratsuba(b, d), + abcd = multiplyKaratsuba(addAny(a, b), addAny(c, d)); + + var product = addAny(addAny(ac, shiftLeft(subtract(subtract(abcd, ac), bd), n)), shiftLeft(bd, 2 * n)); + trim(product); + return product; + } + + // The following function is derived from a surface fit of a graph plotting the performance difference + // between long multiplication and karatsuba multiplication versus the lengths of the two arrays. + function useKaratsuba(l1, l2) { + return -0.012 * l1 - 0.012 * l2 + 0.000015 * l1 * l2 > 0; + } + + BigInteger.prototype.multiply = function (v) { + var n = parseValue(v), + a = this.value, b = n.value, + sign = this.sign !== n.sign, + abs; + if (n.isSmall) { + if (b === 0) return Integer[0]; + if (b === 1) return this; + if (b === -1) return this.negate(); + abs = Math.abs(b); + if (abs < BASE) { + return new BigInteger(multiplySmall(a, abs), sign); + } + b = smallToArray(abs); + } + if (useKaratsuba(a.length, b.length)) // Karatsuba is only faster for certain array sizes + return new BigInteger(multiplyKaratsuba(a, b), sign); + return new BigInteger(multiplyLong(a, b), sign); + }; + + BigInteger.prototype.times = BigInteger.prototype.multiply; + + function multiplySmallAndArray(a, b, sign) { // a >= 0 + if (a < BASE) { + return new BigInteger(multiplySmall(b, a), sign); + } + return new BigInteger(multiplyLong(b, smallToArray(a)), sign); + } + SmallInteger.prototype._multiplyBySmall = function (a) { + if (isPrecise(a.value * this.value)) { + return new SmallInteger(a.value * this.value); + } + return multiplySmallAndArray(Math.abs(a.value), smallToArray(Math.abs(this.value)), this.sign !== a.sign); + }; + BigInteger.prototype._multiplyBySmall = function (a) { + if (a.value === 0) return Integer[0]; + if (a.value === 1) return this; + if (a.value === -1) return this.negate(); + return multiplySmallAndArray(Math.abs(a.value), this.value, this.sign !== a.sign); + }; + SmallInteger.prototype.multiply = function (v) { + return parseValue(v)._multiplyBySmall(this); + }; + SmallInteger.prototype.times = SmallInteger.prototype.multiply; + + NativeBigInt.prototype.multiply = function (v) { + return new NativeBigInt(this.value * parseValue(v).value); + } + NativeBigInt.prototype.times = NativeBigInt.prototype.multiply; + + function square(a) { + //console.assert(2 * BASE * BASE < MAX_INT); + var l = a.length, + r = createArray(l + l), + base = BASE, + product, carry, i, a_i, a_j; + for (i = 0; i < l; i++) { + a_i = a[i]; + carry = 0 - a_i * a_i; + for (var j = i; j < l; j++) { + a_j = a[j]; + product = 2 * (a_i * a_j) + r[i + j] + carry; + carry = Math.floor(product / base); + r[i + j] = product - carry * base; + } + r[i + l] = carry; + } + trim(r); + return r; + } + + BigInteger.prototype.square = function () { + return new BigInteger(square(this.value), false); + }; + + SmallInteger.prototype.square = function () { + var value = this.value * this.value; + if (isPrecise(value)) return new SmallInteger(value); + return new BigInteger(square(smallToArray(Math.abs(this.value))), false); + }; + + NativeBigInt.prototype.square = function (v) { + return new NativeBigInt(this.value * this.value); + } + + function divMod1(a, b) { // Left over from previous version. Performs faster than divMod2 on smaller input sizes. + var a_l = a.length, + b_l = b.length, + base = BASE, + result = createArray(b.length), + divisorMostSignificantDigit = b[b_l - 1], + // normalization + lambda = Math.ceil(base / (2 * divisorMostSignificantDigit)), + remainder = multiplySmall(a, lambda), + divisor = multiplySmall(b, lambda), + quotientDigit, shift, carry, borrow, i, l, q; + if (remainder.length <= a_l) remainder.push(0); + divisor.push(0); + divisorMostSignificantDigit = divisor[b_l - 1]; + for (shift = a_l - b_l; shift >= 0; shift--) { + quotientDigit = base - 1; + if (remainder[shift + b_l] !== divisorMostSignificantDigit) { + quotientDigit = Math.floor((remainder[shift + b_l] * base + remainder[shift + b_l - 1]) / divisorMostSignificantDigit); + } + // quotientDigit <= base - 1 + carry = 0; + borrow = 0; + l = divisor.length; + for (i = 0; i < l; i++) { + carry += quotientDigit * divisor[i]; + q = Math.floor(carry / base); + borrow += remainder[shift + i] - (carry - q * base); + carry = q; + if (borrow < 0) { + remainder[shift + i] = borrow + base; + borrow = -1; + } else { + remainder[shift + i] = borrow; + borrow = 0; + } + } + while (borrow !== 0) { + quotientDigit -= 1; + carry = 0; + for (i = 0; i < l; i++) { + carry += remainder[shift + i] - base + divisor[i]; + if (carry < 0) { + remainder[shift + i] = carry + base; + carry = 0; + } else { + remainder[shift + i] = carry; + carry = 1; + } + } + borrow += carry; + } + result[shift] = quotientDigit; + } + // denormalization + remainder = divModSmall(remainder, lambda)[0]; + return [arrayToSmall(result), arrayToSmall(remainder)]; + } + + function divMod2(a, b) { // Implementation idea shamelessly stolen from Silent Matt's library http://silentmatt.com/biginteger/ + // Performs faster than divMod1 on larger input sizes. + var a_l = a.length, + b_l = b.length, + result = [], + part = [], + base = BASE, + guess, xlen, highx, highy, check; + while (a_l) { + part.unshift(a[--a_l]); + trim(part); + if (compareAbs(part, b) < 0) { + result.push(0); + continue; + } + xlen = part.length; + highx = part[xlen - 1] * base + part[xlen - 2]; + highy = b[b_l - 1] * base + b[b_l - 2]; + if (xlen > b_l) { + highx = (highx + 1) * base; + } + guess = Math.ceil(highx / highy); + do { + check = multiplySmall(b, guess); + if (compareAbs(check, part) <= 0) break; + guess--; + } while (guess); + result.push(guess); + part = subtract(part, check); + } + result.reverse(); + return [arrayToSmall(result), arrayToSmall(part)]; + } + + function divModSmall(value, lambda) { + var length = value.length, + quotient = createArray(length), + base = BASE, + i, q, remainder, divisor; + remainder = 0; + for (i = length - 1; i >= 0; --i) { + divisor = remainder * base + value[i]; + q = truncate(divisor / lambda); + remainder = divisor - q * lambda; + quotient[i] = q | 0; + } + return [quotient, remainder | 0]; + } + + function divModAny(self, v) { + var value, n = parseValue(v); + if (supportsNativeBigInt) { + return [new NativeBigInt(self.value / n.value), new NativeBigInt(self.value % n.value)]; + } + var a = self.value, b = n.value; + var quotient; + if (b === 0) throw new Error("Cannot divide by zero"); + if (self.isSmall) { + if (n.isSmall) { + return [new SmallInteger(truncate(a / b)), new SmallInteger(a % b)]; + } + return [Integer[0], self]; + } + if (n.isSmall) { + if (b === 1) return [self, Integer[0]]; + if (b == -1) return [self.negate(), Integer[0]]; + var abs = Math.abs(b); + if (abs < BASE) { + value = divModSmall(a, abs); + quotient = arrayToSmall(value[0]); + var remainder = value[1]; + if (self.sign) remainder = -remainder; + if (typeof quotient === "number") { + if (self.sign !== n.sign) quotient = -quotient; + return [new SmallInteger(quotient), new SmallInteger(remainder)]; + } + return [new BigInteger(quotient, self.sign !== n.sign), new SmallInteger(remainder)]; + } + b = smallToArray(abs); + } + var comparison = compareAbs(a, b); + if (comparison === -1) return [Integer[0], self]; + if (comparison === 0) return [Integer[self.sign === n.sign ? 1 : -1], Integer[0]]; + + // divMod1 is faster on smaller input sizes + if (a.length + b.length <= 200) + value = divMod1(a, b); + else value = divMod2(a, b); + + quotient = value[0]; + var qSign = self.sign !== n.sign, + mod = value[1], + mSign = self.sign; + if (typeof quotient === "number") { + if (qSign) quotient = -quotient; + quotient = new SmallInteger(quotient); + } else quotient = new BigInteger(quotient, qSign); + if (typeof mod === "number") { + if (mSign) mod = -mod; + mod = new SmallInteger(mod); + } else mod = new BigInteger(mod, mSign); + return [quotient, mod]; + } + + BigInteger.prototype.divmod = function (v) { + var result = divModAny(this, v); + return { + quotient: result[0], + remainder: result[1] + }; + }; + NativeBigInt.prototype.divmod = SmallInteger.prototype.divmod = BigInteger.prototype.divmod; + + + BigInteger.prototype.divide = function (v) { + return divModAny(this, v)[0]; + }; + NativeBigInt.prototype.over = NativeBigInt.prototype.divide = function (v) { + return new NativeBigInt(this.value / parseValue(v).value); + }; + SmallInteger.prototype.over = SmallInteger.prototype.divide = BigInteger.prototype.over = BigInteger.prototype.divide; + + BigInteger.prototype.mod = function (v) { + return divModAny(this, v)[1]; + }; + NativeBigInt.prototype.mod = NativeBigInt.prototype.remainder = function (v) { + return new NativeBigInt(this.value % parseValue(v).value); + }; + SmallInteger.prototype.remainder = SmallInteger.prototype.mod = BigInteger.prototype.remainder = BigInteger.prototype.mod; + + BigInteger.prototype.pow = function (v) { + var n = parseValue(v), + a = this.value, + b = n.value, + value, x, y; + if (b === 0) return Integer[1]; + if (a === 0) return Integer[0]; + if (a === 1) return Integer[1]; + if (a === -1) return n.isEven() ? Integer[1] : Integer[-1]; + if (n.sign) { + return Integer[0]; + } + if (!n.isSmall) throw new Error("The exponent " + n.toString() + " is too large."); + if (this.isSmall) { + if (isPrecise(value = Math.pow(a, b))) + return new SmallInteger(truncate(value)); + } + x = this; + y = Integer[1]; + while (true) { + if (b & 1 === 1) { + y = y.times(x); + --b; + } + if (b === 0) break; + b /= 2; + x = x.square(); + } + return y; + }; + SmallInteger.prototype.pow = BigInteger.prototype.pow; + + NativeBigInt.prototype.pow = function (v) { + var n = parseValue(v); + var a = this.value, b = n.value; + var _0 = BigInt(0), _1 = BigInt(1), _2 = BigInt(2); + if (b === _0) return Integer[1]; + if (a === _0) return Integer[0]; + if (a === _1) return Integer[1]; + if (a === BigInt(-1)) return n.isEven() ? Integer[1] : Integer[-1]; + if (n.isNegative()) return new NativeBigInt(_0); + var x = this; + var y = Integer[1]; + while (true) { + if ((b & _1) === _1) { + y = y.times(x); + --b; + } + if (b === _0) break; + b /= _2; + x = x.square(); + } + return y; + } + + BigInteger.prototype.modPow = function (exp, mod) { + exp = parseValue(exp); + mod = parseValue(mod); + if (mod.isZero()) throw new Error("Cannot take modPow with modulus 0"); + var r = Integer[1], + base = this.mod(mod); + while (exp.isPositive()) { + if (base.isZero()) return Integer[0]; + if (exp.isOdd()) r = r.multiply(base).mod(mod); + exp = exp.divide(2); + base = base.square().mod(mod); + } + return r; + }; + NativeBigInt.prototype.modPow = SmallInteger.prototype.modPow = BigInteger.prototype.modPow; + + function compareAbs(a, b) { + if (a.length !== b.length) { + return a.length > b.length ? 1 : -1; + } + for (var i = a.length - 1; i >= 0; i--) { + if (a[i] !== b[i]) return a[i] > b[i] ? 1 : -1; + } + return 0; + } + + BigInteger.prototype.compareAbs = function (v) { + var n = parseValue(v), + a = this.value, + b = n.value; + if (n.isSmall) return 1; + return compareAbs(a, b); + }; + SmallInteger.prototype.compareAbs = function (v) { + var n = parseValue(v), + a = Math.abs(this.value), + b = n.value; + if (n.isSmall) { + b = Math.abs(b); + return a === b ? 0 : a > b ? 1 : -1; + } + return -1; + }; + NativeBigInt.prototype.compareAbs = function (v) { + var a = this.value; + var b = parseValue(v).value; + a = a >= 0 ? a : -a; + b = b >= 0 ? b : -b; + return a === b ? 0 : a > b ? 1 : -1; + } + + BigInteger.prototype.compare = function (v) { + // See discussion about comparison with Infinity: + // https://github.com/peterolson/BigInteger.js/issues/61 + if (v === Infinity) { + return -1; + } + if (v === -Infinity) { + return 1; + } + + var n = parseValue(v), + a = this.value, + b = n.value; + if (this.sign !== n.sign) { + return n.sign ? 1 : -1; + } + if (n.isSmall) { + return this.sign ? -1 : 1; + } + return compareAbs(a, b) * (this.sign ? -1 : 1); + }; + BigInteger.prototype.compareTo = BigInteger.prototype.compare; + + SmallInteger.prototype.compare = function (v) { + if (v === Infinity) { + return -1; + } + if (v === -Infinity) { + return 1; + } + + var n = parseValue(v), + a = this.value, + b = n.value; + if (n.isSmall) { + return a == b ? 0 : a > b ? 1 : -1; + } + if (a < 0 !== n.sign) { + return a < 0 ? -1 : 1; + } + return a < 0 ? 1 : -1; + }; + SmallInteger.prototype.compareTo = SmallInteger.prototype.compare; + + NativeBigInt.prototype.compare = function (v) { + if (v === Infinity) { + return -1; + } + if (v === -Infinity) { + return 1; + } + var a = this.value; + var b = parseValue(v).value; + return a === b ? 0 : a > b ? 1 : -1; + } + NativeBigInt.prototype.compareTo = NativeBigInt.prototype.compare; + + BigInteger.prototype.equals = function (v) { + return this.compare(v) === 0; + }; + NativeBigInt.prototype.eq = NativeBigInt.prototype.equals = SmallInteger.prototype.eq = SmallInteger.prototype.equals = BigInteger.prototype.eq = BigInteger.prototype.equals; + + BigInteger.prototype.notEquals = function (v) { + return this.compare(v) !== 0; + }; + NativeBigInt.prototype.neq = NativeBigInt.prototype.notEquals = SmallInteger.prototype.neq = SmallInteger.prototype.notEquals = BigInteger.prototype.neq = BigInteger.prototype.notEquals; + + BigInteger.prototype.greater = function (v) { + return this.compare(v) > 0; + }; + NativeBigInt.prototype.gt = NativeBigInt.prototype.greater = SmallInteger.prototype.gt = SmallInteger.prototype.greater = BigInteger.prototype.gt = BigInteger.prototype.greater; + + BigInteger.prototype.lesser = function (v) { + return this.compare(v) < 0; + }; + NativeBigInt.prototype.lt = NativeBigInt.prototype.lesser = SmallInteger.prototype.lt = SmallInteger.prototype.lesser = BigInteger.prototype.lt = BigInteger.prototype.lesser; + + BigInteger.prototype.greaterOrEquals = function (v) { + return this.compare(v) >= 0; + }; + NativeBigInt.prototype.geq = NativeBigInt.prototype.greaterOrEquals = SmallInteger.prototype.geq = SmallInteger.prototype.greaterOrEquals = BigInteger.prototype.geq = BigInteger.prototype.greaterOrEquals; + + BigInteger.prototype.lesserOrEquals = function (v) { + return this.compare(v) <= 0; + }; + NativeBigInt.prototype.leq = NativeBigInt.prototype.lesserOrEquals = SmallInteger.prototype.leq = SmallInteger.prototype.lesserOrEquals = BigInteger.prototype.leq = BigInteger.prototype.lesserOrEquals; + + BigInteger.prototype.isEven = function () { + return (this.value[0] & 1) === 0; + }; + SmallInteger.prototype.isEven = function () { + return (this.value & 1) === 0; + }; + NativeBigInt.prototype.isEven = function () { + return (this.value & BigInt(1)) === BigInt(0); + } + + BigInteger.prototype.isOdd = function () { + return (this.value[0] & 1) === 1; + }; + SmallInteger.prototype.isOdd = function () { + return (this.value & 1) === 1; + }; + NativeBigInt.prototype.isOdd = function () { + return (this.value & BigInt(1)) === BigInt(1); + } + + BigInteger.prototype.isPositive = function () { + return !this.sign; + }; + SmallInteger.prototype.isPositive = function () { + return this.value > 0; + }; + NativeBigInt.prototype.isPositive = SmallInteger.prototype.isPositive; + + BigInteger.prototype.isNegative = function () { + return this.sign; + }; + SmallInteger.prototype.isNegative = function () { + return this.value < 0; + }; + NativeBigInt.prototype.isNegative = SmallInteger.prototype.isNegative; + + BigInteger.prototype.isUnit = function () { + return false; + }; + SmallInteger.prototype.isUnit = function () { + return Math.abs(this.value) === 1; + }; + NativeBigInt.prototype.isUnit = function () { + return this.abs().value === BigInt(1); + } + + BigInteger.prototype.isZero = function () { + return false; + }; + SmallInteger.prototype.isZero = function () { + return this.value === 0; + }; + NativeBigInt.prototype.isZero = function () { + return this.value === BigInt(0); + } + + BigInteger.prototype.isDivisibleBy = function (v) { + var n = parseValue(v); + if (n.isZero()) return false; + if (n.isUnit()) return true; + if (n.compareAbs(2) === 0) return this.isEven(); + return this.mod(n).isZero(); + }; + NativeBigInt.prototype.isDivisibleBy = SmallInteger.prototype.isDivisibleBy = BigInteger.prototype.isDivisibleBy; + + function isBasicPrime(v) { + var n = v.abs(); + if (n.isUnit()) return false; + if (n.equals(2) || n.equals(3) || n.equals(5)) return true; + if (n.isEven() || n.isDivisibleBy(3) || n.isDivisibleBy(5)) return false; + if (n.lesser(49)) return true; + // we don't know if it's prime: let the other functions figure it out + } + + function millerRabinTest(n, a) { + var nPrev = n.prev(), + b = nPrev, + r = 0, + d, t, i, x; + while (b.isEven()) b = b.divide(2), r++; + next: for (i = 0; i < a.length; i++) { + if (n.lesser(a[i])) continue; + x = bigInt(a[i]).modPow(b, n); + if (x.isUnit() || x.equals(nPrev)) continue; + for (d = r - 1; d != 0; d--) { + x = x.square().mod(n); + if (x.isUnit()) return false; + if (x.equals(nPrev)) continue next; + } + return false; + } + return true; + } + + // Set "strict" to true to force GRH-supported lower bound of 2*log(N)^2 + BigInteger.prototype.isPrime = function (strict) { + var isPrime = isBasicPrime(this); + if (isPrime !== undefined) return isPrime; + var n = this.abs(); + var bits = n.bitLength(); + if (bits <= 64) + return millerRabinTest(n, [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37]); + var logN = Math.log(2) * bits.toJSNumber(); + var t = Math.ceil((strict === true) ? (2 * Math.pow(logN, 2)) : logN); + for (var a = [], i = 0; i < t; i++) { + a.push(bigInt(i + 2)); + } + return millerRabinTest(n, a); + }; + NativeBigInt.prototype.isPrime = SmallInteger.prototype.isPrime = BigInteger.prototype.isPrime; + + BigInteger.prototype.isProbablePrime = function (iterations) { + var isPrime = isBasicPrime(this); + if (isPrime !== undefined) return isPrime; + var n = this.abs(); + var t = iterations === undefined ? 5 : iterations; + for (var a = [], i = 0; i < t; i++) { + a.push(bigInt.randBetween(2, n.minus(2))); + } + return millerRabinTest(n, a); + }; + NativeBigInt.prototype.isProbablePrime = SmallInteger.prototype.isProbablePrime = BigInteger.prototype.isProbablePrime; + + BigInteger.prototype.modInv = function (n) { + var t = bigInt.zero, newT = bigInt.one, r = parseValue(n), newR = this.abs(), q, lastT, lastR; + while (!newR.isZero()) { + q = r.divide(newR); + lastT = t; + lastR = r; + t = newT; + r = newR; + newT = lastT.subtract(q.multiply(newT)); + newR = lastR.subtract(q.multiply(newR)); + } + if (!r.isUnit()) throw new Error(this.toString() + " and " + n.toString() + " are not co-prime"); + if (t.compare(0) === -1) { + t = t.add(n); + } + if (this.isNegative()) { + return t.negate(); + } + return t; + }; + + NativeBigInt.prototype.modInv = SmallInteger.prototype.modInv = BigInteger.prototype.modInv; + + BigInteger.prototype.next = function () { + var value = this.value; + if (this.sign) { + return subtractSmall(value, 1, this.sign); + } + return new BigInteger(addSmall(value, 1), this.sign); + }; + SmallInteger.prototype.next = function () { + var value = this.value; + if (value + 1 < MAX_INT) return new SmallInteger(value + 1); + return new BigInteger(MAX_INT_ARR, false); + }; + NativeBigInt.prototype.next = function () { + return new NativeBigInt(this.value + BigInt(1)); + } + + BigInteger.prototype.prev = function () { + var value = this.value; + if (this.sign) { + return new BigInteger(addSmall(value, 1), true); + } + return subtractSmall(value, 1, this.sign); + }; + SmallInteger.prototype.prev = function () { + var value = this.value; + if (value - 1 > -MAX_INT) return new SmallInteger(value - 1); + return new BigInteger(MAX_INT_ARR, true); + }; + NativeBigInt.prototype.prev = function () { + return new NativeBigInt(this.value - BigInt(1)); + } + + var powersOfTwo = [1]; + while (2 * powersOfTwo[powersOfTwo.length - 1] <= BASE) powersOfTwo.push(2 * powersOfTwo[powersOfTwo.length - 1]); + var powers2Length = powersOfTwo.length, highestPower2 = powersOfTwo[powers2Length - 1]; + + function shift_isSmall(n) { + return Math.abs(n) <= BASE; + } + + BigInteger.prototype.shiftLeft = function (v) { + var n = parseValue(v).toJSNumber(); + if (!shift_isSmall(n)) { + throw new Error(String(n) + " is too large for shifting."); + } + if (n < 0) return this.shiftRight(-n); + var result = this; + if (result.isZero()) return result; + while (n >= powers2Length) { + result = result.multiply(highestPower2); + n -= powers2Length - 1; + } + return result.multiply(powersOfTwo[n]); + }; + NativeBigInt.prototype.shiftLeft = SmallInteger.prototype.shiftLeft = BigInteger.prototype.shiftLeft; + + BigInteger.prototype.shiftRight = function (v) { + var remQuo; + var n = parseValue(v).toJSNumber(); + if (!shift_isSmall(n)) { + throw new Error(String(n) + " is too large for shifting."); + } + if (n < 0) return this.shiftLeft(-n); + var result = this; + while (n >= powers2Length) { + if (result.isZero() || (result.isNegative() && result.isUnit())) return result; + remQuo = divModAny(result, highestPower2); + result = remQuo[1].isNegative() ? remQuo[0].prev() : remQuo[0]; + n -= powers2Length - 1; + } + remQuo = divModAny(result, powersOfTwo[n]); + return remQuo[1].isNegative() ? remQuo[0].prev() : remQuo[0]; + }; + NativeBigInt.prototype.shiftRight = SmallInteger.prototype.shiftRight = BigInteger.prototype.shiftRight; + + function bitwise(x, y, fn) { + y = parseValue(y); + var xSign = x.isNegative(), ySign = y.isNegative(); + var xRem = xSign ? x.not() : x, + yRem = ySign ? y.not() : y; + var xDigit = 0, yDigit = 0; + var xDivMod = null, yDivMod = null; + var result = []; + while (!xRem.isZero() || !yRem.isZero()) { + xDivMod = divModAny(xRem, highestPower2); + xDigit = xDivMod[1].toJSNumber(); + if (xSign) { + xDigit = highestPower2 - 1 - xDigit; // two's complement for negative numbers + } + + yDivMod = divModAny(yRem, highestPower2); + yDigit = yDivMod[1].toJSNumber(); + if (ySign) { + yDigit = highestPower2 - 1 - yDigit; // two's complement for negative numbers + } + + xRem = xDivMod[0]; + yRem = yDivMod[0]; + result.push(fn(xDigit, yDigit)); + } + var sum = fn(xSign ? 1 : 0, ySign ? 1 : 0) !== 0 ? bigInt(-1) : bigInt(0); + for (var i = result.length - 1; i >= 0; i -= 1) { + sum = sum.multiply(highestPower2).add(bigInt(result[i])); + } + return sum; + } + + BigInteger.prototype.not = function () { + return this.negate().prev(); + }; + NativeBigInt.prototype.not = SmallInteger.prototype.not = BigInteger.prototype.not; + + BigInteger.prototype.and = function (n) { + return bitwise(this, n, function (a, b) { return a & b; }); + }; + NativeBigInt.prototype.and = SmallInteger.prototype.and = BigInteger.prototype.and; + + BigInteger.prototype.or = function (n) { + return bitwise(this, n, function (a, b) { return a | b; }); + }; + NativeBigInt.prototype.or = SmallInteger.prototype.or = BigInteger.prototype.or; + + BigInteger.prototype.xor = function (n) { + return bitwise(this, n, function (a, b) { return a ^ b; }); + }; + NativeBigInt.prototype.xor = SmallInteger.prototype.xor = BigInteger.prototype.xor; + + var LOBMASK_I = 1 << 30, LOBMASK_BI = (BASE & -BASE) * (BASE & -BASE) | LOBMASK_I; + function roughLOB(n) { // get lowestOneBit (rough) + // SmallInteger: return Min(lowestOneBit(n), 1 << 30) + // BigInteger: return Min(lowestOneBit(n), 1 << 14) [BASE=1e7] + var v = n.value, + x = typeof v === "number" ? v | LOBMASK_I : + typeof v === "bigint" ? v | BigInt(LOBMASK_I) : + v[0] + v[1] * BASE | LOBMASK_BI; + return x & -x; + } + + function integerLogarithm(value, base) { + if (base.compareTo(value) <= 0) { + var tmp = integerLogarithm(value, base.square(base)); + var p = tmp.p; + var e = tmp.e; + var t = p.multiply(base); + return t.compareTo(value) <= 0 ? { p: t, e: e * 2 + 1 } : { p: p, e: e * 2 }; + } + return { p: bigInt(1), e: 0 }; + } + + BigInteger.prototype.bitLength = function () { + var n = this; + if (n.compareTo(bigInt(0)) < 0) { + n = n.negate().subtract(bigInt(1)); + } + if (n.compareTo(bigInt(0)) === 0) { + return bigInt(0); + } + return bigInt(integerLogarithm(n, bigInt(2)).e).add(bigInt(1)); + } + NativeBigInt.prototype.bitLength = SmallInteger.prototype.bitLength = BigInteger.prototype.bitLength; + + function max(a, b) { + a = parseValue(a); + b = parseValue(b); + return a.greater(b) ? a : b; + } + function min(a, b) { + a = parseValue(a); + b = parseValue(b); + return a.lesser(b) ? a : b; + } + function gcd(a, b) { + a = parseValue(a).abs(); + b = parseValue(b).abs(); + if (a.equals(b)) return a; + if (a.isZero()) return b; + if (b.isZero()) return a; + var c = Integer[1], d, t; + while (a.isEven() && b.isEven()) { + d = min(roughLOB(a), roughLOB(b)); + a = a.divide(d); + b = b.divide(d); + c = c.multiply(d); + } + while (a.isEven()) { + a = a.divide(roughLOB(a)); + } + do { + while (b.isEven()) { + b = b.divide(roughLOB(b)); + } + if (a.greater(b)) { + t = b; b = a; a = t; + } + b = b.subtract(a); + } while (!b.isZero()); + return c.isUnit() ? a : a.multiply(c); + } + function lcm(a, b) { + a = parseValue(a).abs(); + b = parseValue(b).abs(); + return a.divide(gcd(a, b)).multiply(b); + } + function randBetween(a, b) { + a = parseValue(a); + b = parseValue(b); + var low = min(a, b), high = max(a, b); + var range = high.subtract(low).add(1); + if (range.isSmall) return low.add(Math.floor(Math.random() * range)); + var digits = toBase(range, BASE).value; + var result = [], restricted = true; + for (var i = 0; i < digits.length; i++) { + var top = restricted ? digits[i] : BASE; + var digit = truncate(Math.random() * top); + result.push(digit); + if (digit < top) restricted = false; + } + return low.add(Integer.fromArray(result, BASE, false)); + } + + var parseBase = function (text, base, alphabet, caseSensitive) { + alphabet = alphabet || DEFAULT_ALPHABET; + text = String(text); + if (!caseSensitive) { + text = text.toLowerCase(); + alphabet = alphabet.toLowerCase(); + } + var length = text.length; + var i; + var absBase = Math.abs(base); + var alphabetValues = {}; + for (i = 0; i < alphabet.length; i++) { + alphabetValues[alphabet[i]] = i; + } + for (i = 0; i < length; i++) { + var c = text[i]; + if (c === "-") continue; + if (c in alphabetValues) { + if (alphabetValues[c] >= absBase) { + if (c === "1" && absBase === 1) continue; + throw new Error(c + " is not a valid digit in base " + base + "."); + } + } + } + base = parseValue(base); + var digits = []; + var isNegative = text[0] === "-"; + for (i = isNegative ? 1 : 0; i < text.length; i++) { + var c = text[i]; + if (c in alphabetValues) digits.push(parseValue(alphabetValues[c])); + else if (c === "<") { + var start = i; + do { i++; } while (text[i] !== ">" && i < text.length); + digits.push(parseValue(text.slice(start + 1, i))); + } + else throw new Error(c + " is not a valid character"); + } + return parseBaseFromArray(digits, base, isNegative); + }; + + function parseBaseFromArray(digits, base, isNegative) { + var val = Integer[0], pow = Integer[1], i; + for (i = digits.length - 1; i >= 0; i--) { + val = val.add(digits[i].times(pow)); + pow = pow.times(base); + } + return isNegative ? val.negate() : val; + } + + function stringify(digit, alphabet) { + alphabet = alphabet || DEFAULT_ALPHABET; + if (digit < alphabet.length) { + return alphabet[digit]; + } + return "<" + digit + ">"; + } + + function toBase(n, base) { + base = bigInt(base); + if (base.isZero()) { + if (n.isZero()) return { value: [0], isNegative: false }; + throw new Error("Cannot convert nonzero numbers to base 0."); + } + if (base.equals(-1)) { + if (n.isZero()) return { value: [0], isNegative: false }; + if (n.isNegative()) + return { + value: [].concat.apply([], Array.apply(null, Array(-n.toJSNumber())) + .map(Array.prototype.valueOf, [1, 0]) + ), + isNegative: false + }; + + var arr = Array.apply(null, Array(n.toJSNumber() - 1)) + .map(Array.prototype.valueOf, [0, 1]); + arr.unshift([1]); + return { + value: [].concat.apply([], arr), + isNegative: false + }; + } + + var neg = false; + if (n.isNegative() && base.isPositive()) { + neg = true; + n = n.abs(); + } + if (base.isUnit()) { + if (n.isZero()) return { value: [0], isNegative: false }; + + return { + value: Array.apply(null, Array(n.toJSNumber())) + .map(Number.prototype.valueOf, 1), + isNegative: neg + }; + } + var out = []; + var left = n, divmod; + while (left.isNegative() || left.compareAbs(base) >= 0) { + divmod = left.divmod(base); + left = divmod.quotient; + var digit = divmod.remainder; + if (digit.isNegative()) { + digit = base.minus(digit).abs(); + left = left.next(); + } + out.push(digit.toJSNumber()); + } + out.push(left.toJSNumber()); + return { value: out.reverse(), isNegative: neg }; + } + + function toBaseString(n, base, alphabet) { + var arr = toBase(n, base); + return (arr.isNegative ? "-" : "") + arr.value.map(function (x) { + return stringify(x, alphabet); + }).join(''); + } + + BigInteger.prototype.toArray = function (radix) { + return toBase(this, radix); + }; + + SmallInteger.prototype.toArray = function (radix) { + return toBase(this, radix); + }; + + NativeBigInt.prototype.toArray = function (radix) { + return toBase(this, radix); + }; + + BigInteger.prototype.toString = function (radix, alphabet) { + if (radix === undefined) radix = 10; + if (radix !== 10) return toBaseString(this, radix, alphabet); + var v = this.value, l = v.length, str = String(v[--l]), zeros = "0000000", digit; + while (--l >= 0) { + digit = String(v[l]); + str += zeros.slice(digit.length) + digit; + } + var sign = this.sign ? "-" : ""; + return sign + str; + }; + + SmallInteger.prototype.toString = function (radix, alphabet) { + if (radix === undefined) radix = 10; + if (radix != 10) return toBaseString(this, radix, alphabet); + return String(this.value); + }; + + NativeBigInt.prototype.toString = SmallInteger.prototype.toString; + + NativeBigInt.prototype.toJSON = BigInteger.prototype.toJSON = SmallInteger.prototype.toJSON = function () { return this.toString(); } + + BigInteger.prototype.valueOf = function () { + return parseInt(this.toString(), 10); + }; + BigInteger.prototype.toJSNumber = BigInteger.prototype.valueOf; + + SmallInteger.prototype.valueOf = function () { + return this.value; + }; + SmallInteger.prototype.toJSNumber = SmallInteger.prototype.valueOf; + NativeBigInt.prototype.valueOf = NativeBigInt.prototype.toJSNumber = function () { + return parseInt(this.toString(), 10); + } + + function parseStringValue(v) { + if (isPrecise(+v)) { + var x = +v; + if (x === truncate(x)) + return supportsNativeBigInt ? new NativeBigInt(BigInt(x)) : new SmallInteger(x); + throw new Error("Invalid integer: " + v); + } + var sign = v[0] === "-"; + if (sign) v = v.slice(1); + var split = v.split(/e/i); + if (split.length > 2) throw new Error("Invalid integer: " + split.join("e")); + if (split.length === 2) { + var exp = split[1]; + if (exp[0] === "+") exp = exp.slice(1); + exp = +exp; + if (exp !== truncate(exp) || !isPrecise(exp)) throw new Error("Invalid integer: " + exp + " is not a valid exponent."); + var text = split[0]; + var decimalPlace = text.indexOf("."); + if (decimalPlace >= 0) { + exp -= text.length - decimalPlace - 1; + text = text.slice(0, decimalPlace) + text.slice(decimalPlace + 1); + } + if (exp < 0) throw new Error("Cannot include negative exponent part for integers"); + text += (new Array(exp + 1)).join("0"); + v = text; + } + var isValid = /^([0-9][0-9]*)$/.test(v); + if (!isValid) throw new Error("Invalid integer: " + v); + if (supportsNativeBigInt) { + return new NativeBigInt(BigInt(sign ? "-" + v : v)); + } + var r = [], max = v.length, l = LOG_BASE, min = max - l; + while (max > 0) { + r.push(+v.slice(min, max)); + min -= l; + if (min < 0) min = 0; + max -= l; + } + trim(r); + return new BigInteger(r, sign); + } + + function parseNumberValue(v) { + if (supportsNativeBigInt) { + return new NativeBigInt(BigInt(v)); + } + if (isPrecise(v)) { + if (v !== truncate(v)) throw new Error(v + " is not an integer."); + return new SmallInteger(v); + } + return parseStringValue(v.toString()); + } + + function parseValue(v) { + if (typeof v === "number") { + return parseNumberValue(v); + } + if (typeof v === "string") { + return parseStringValue(v); + } + if (typeof v === "bigint") { + return new NativeBigInt(v); + } + return v; + } + // Pre-define numbers in range [-999,999] + for (var i = 0; i < 1000; i++) { + Integer[i] = parseValue(i); + if (i > 0) Integer[-i] = parseValue(-i); + } + // Backwards compatibility + Integer.one = Integer[1]; + Integer.zero = Integer[0]; + Integer.minusOne = Integer[-1]; + Integer.max = max; + Integer.min = min; + Integer.gcd = gcd; + Integer.lcm = lcm; + Integer.isInstance = function (x) { return x instanceof BigInteger || x instanceof SmallInteger || x instanceof NativeBigInt; }; + Integer.randBetween = randBetween; + + Integer.fromArray = function (digits, base, isNegative) { + return parseBaseFromArray(digits.map(parseValue), parseValue(base || 10), isNegative); + }; + + return Integer; +})(); + +// Node.js check +if (typeof module !== "undefined" && module.hasOwnProperty("exports")) { + module.exports = bigInt; +} + +//amd check +if (typeof define === "function" && define.amd) { + define("big-integer", [], function () { + return bigInt; + }); +} },{}],9:[function(require,module,exports){ (function (Buffer){ @@ -4931,6 +4942,976 @@ process.chdir = function (dir) { process.umask = function() { return 0; }; },{}],13:[function(require,module,exports){ +(function (Buffer){ +/* + Copyright 2018 0kims association. + + This file is part of snarkjs. + + snarkjs is a free software: you can redistribute it and/or + modify it under the terms of the GNU General Public License as published by the + Free Software Foundation, either version 3 of the License, or (at your option) + any later version. + + snarkjs is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY + or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for + more details. + + You should have received a copy of the GNU General Public License along with + snarkjs. If not, see . +*/ + +/* global BigInt */ +const bigInt = require("big-integer"); + +let wBigInt; + +if (typeof(BigInt) != "undefined") { + wBigInt = BigInt; + wBigInt.one = wBigInt(1); + wBigInt.zero = wBigInt(0); + + // Affine + wBigInt.genAffine = (q) => { + const nq = -q; + return (a) => { + let aux = a; + if (aux < 0) { + if (aux <= nq) { + aux = aux % q; + } + if (aux < wBigInt.zero) { + aux = aux + q; + } + } else { + if (aux >= q) { + aux = aux % q; + } + } + return aux.valueOf(); + }; + }; + + + // Inverse + wBigInt.genInverse = (q) => { + return (a) => { + let t = wBigInt.zero; + let r = q; + let newt = wBigInt.one; + let newr = wBigInt.affine(a, q); + while (newr!=wBigInt.zero) { + let q = r/newr; + [t, newt] = [newt, t-q*newt]; + [r, newr] = [newr, r-q*newr]; + } + if (t { + if (q) { + return (a,b) => (a+b) % q; + } else { + return (a,b) => a+b; + } + }; + + // Sub + wBigInt.genSub = (q) => { + if (q) { + return (a,b) => (a-b) % q; + } else { + return (a,b) => a-b; + } + }; + + + // Neg + wBigInt.genNeg = (q) => { + if (q) { + return (a) => (-a) % q; + } else { + return (a) => -a; + } + }; + + // Mul + wBigInt.genMul = (q) => { + if (q) { + return (a,b) => (a*b) % q; + } else { + return (a,b) => a*b; + } + }; + + // Shr + wBigInt.genShr = () => { + return (a,b) => a >> wBigInt(b); + }; + + // Shl + wBigInt.genShl = (q) => { + if (q) { + return (a,b) => (a << wBigInt(b)) % q; + } else { + return (a,b) => a << wBigInt(b); + } + }; + + // Equals + wBigInt.genEquals = (q) => { + if (q) { + return (a,b) => (a.affine(q) == b.affine(q)); + } else { + return (a,b) => a == b; + } + }; + + // Square + wBigInt.genSquare = (q) => { + if (q) { + return (a) => (a*a) %q; + } else { + return (a) => a*a; + } + }; + + + // Double + wBigInt.genDouble = (q) => { + if (q) { + return (a) => (a+a) %q; + } else { + return (a) => a+a; + } + }; + + // IsZero + wBigInt.genIsZero = (q) => { + if (q) { + return (a) => (a.affine(q) == wBigInt.zero); + } else { + return (a) => a == wBigInt.zero; + } + }; + + + // Other minor functions + wBigInt.prototype.isOdd = function() { + return (this & wBigInt.one) == wBigInt(1); + }; + + wBigInt.prototype.isNegative = function() { + return this < wBigInt.zero; + }; + + wBigInt.prototype.and = function(m) { + return this & m; + }; + + wBigInt.prototype.div = function(c) { + return this / c; + }; + + wBigInt.prototype.mod = function(c) { + return this % c; + }; + + wBigInt.prototype.modPow = function(e, m) { + let acc = wBigInt.one; + let exp = this; + let rem = e; + while (rem) { + if (rem & wBigInt.one) { + acc = (acc * exp) %m; + } + exp = (exp * exp) % m; + rem = rem >> wBigInt.one; + } + return acc; + }; + + wBigInt.prototype.greaterOrEquals = function(b) { + return this >= b; + }; + + wBigInt.prototype.greater = function(b) { + return this > b; + }; + wBigInt.prototype.gt = wBigInt.prototype.greater; + + wBigInt.prototype.lesserOrEquals = function(b) { + return this <= b; + }; + + wBigInt.prototype.lesser = function(b) { + return this < b; + }; + wBigInt.prototype.lt = wBigInt.prototype.lesser; + + wBigInt.prototype.equals = function(b) { + return this == b; + }; + wBigInt.prototype.eq = wBigInt.prototype.equals; + + wBigInt.prototype.neq = function(b) { + return this != b; + }; + +} else { + + var oldProto = bigInt.prototype; + wBigInt = function(a) { + if ((typeof a == "string") && (a.slice(0,2) == "0x")) { + return bigInt(a.slice(2), 16); + } else { + return bigInt(a); + } + }; + wBigInt.one = bigInt.one; + wBigInt.zero = bigInt.zero; + wBigInt.prototype = oldProto; + + wBigInt.prototype.div = function(c) { + return this.divide(c); + }; + + // Affine + wBigInt.genAffine = (q) => { + const nq = wBigInt.zero.minus(q); + return (a) => { + let aux = a; + if (aux.isNegative()) { + if (aux.lesserOrEquals(nq)) { + aux = aux.mod(q); + } + if (aux.isNegative()) { + aux = aux.add(q); + } + } else { + if (aux.greaterOrEquals(q)) { + aux = aux.mod(q); + } + } + return aux; + }; + }; + + + // Inverse + wBigInt.genInverse = (q) => { + return (a) => a.affine(q).modInv(q); + }; + + // Add + wBigInt.genAdd = (q) => { + if (q) { + return (a,b) => { + const r = a.add(b); + return r.greaterOrEquals(q) ? r.minus(q) : r; + }; + } else { + return (a,b) => a.add(b); + } + }; + + // Sub + wBigInt.genSub = (q) => { + if (q) { + return (a,b) => a.greaterOrEquals(b) ? a.minus(b) : a.minus(b).add(q); + } else { + return (a,b) => a.minus(b); + } + }; + + wBigInt.genNeg = (q) => { + if (q) { + return (a) => a.isZero() ? a : q.minus(a); + } else { + return (a) => wBigInt.zero.minus(a); + } + }; + + // Mul + wBigInt.genMul = (q) => { + if (q) { + return (a,b) => a.times(b).mod(q); + } else { + return (a,b) => a.times(b); + } + }; + + // Shr + wBigInt.genShr = () => { + return (a,b) => a.shiftRight(wBigInt(b).value); + }; + + // Shr + wBigInt.genShl = (q) => { + if (q) { + return (a,b) => a.shiftLeft(wBigInt(b).value).mod(q); + } else { + return (a,b) => a.shiftLeft(wBigInt(b).value); + } + }; + + // Square + wBigInt.genSquare = (q) => { + if (q) { + return (a) => a.square().mod(q); + } else { + return (a) => a.square(); + } + }; + + // Double + wBigInt.genDouble = (q) => { + if (q) { + return (a) => a.add(a).mod(q); + } else { + return (a) => a.add(a); + } + }; + + // Equals + wBigInt.genEquals = (q) => { + if (q) { + return (a,b) => a.affine(q).equals(b.affine(q)); + } else { + return (a,b) => a.equals(b); + } + }; + + // IsZero + wBigInt.genIsZero = (q) => { + if (q) { + return (a) => (a.affine(q).isZero()); + } else { + return (a) => a.isZero(); + } + }; +} + + + +wBigInt.affine = function(a, q) { + return wBigInt.genAffine(q)(a); +}; + +wBigInt.prototype.affine = function (q) { + return wBigInt.affine(this, q); +}; + +wBigInt.inverse = function(a, q) { + return wBigInt.genInverse(q)(a); +}; + +wBigInt.prototype.inverse = function (q) { + return wBigInt.genInverse(q)(this); +}; + +wBigInt.add = function(a, b, q) { + return wBigInt.genAdd(q)(a,b); +}; + +wBigInt.prototype.add = function (a, q) { + return wBigInt.genAdd(q)(this, a); +}; + +wBigInt.sub = function(a, b, q) { + return wBigInt.genSub(q)(a,b); +}; + +wBigInt.prototype.sub = function (a, q) { + return wBigInt.genSub(q)(this, a); +}; + +wBigInt.neg = function(a, q) { + return wBigInt.genNeg(q)(a); +}; + +wBigInt.prototype.neg = function (q) { + return wBigInt.genNeg(q)(this); +}; + +wBigInt.mul = function(a, b, q) { + return wBigInt.genMul(q)(a,b); +}; + +wBigInt.prototype.mul = function (a, q) { + return wBigInt.genMul(q)(this, a); +}; + +wBigInt.shr = function(a, b, q) { + return wBigInt.genShr(q)(a,b); +}; + +wBigInt.prototype.shr = function (a, q) { + return wBigInt.genShr(q)(this, a); +}; + +wBigInt.shl = function(a, b, q) { + return wBigInt.genShl(q)(a,b); +}; + +wBigInt.prototype.shl = function (a, q) { + return wBigInt.genShl(q)(this, a); +}; + +wBigInt.equals = function(a, b, q) { + return wBigInt.genEquals(q)(a,b); +}; + +wBigInt.prototype.equals = function (a, q) { + return wBigInt.genEquals(q)(this, a); +}; + +wBigInt.square = function(a, q) { + return wBigInt.genSquare(q)(a); +}; + +wBigInt.prototype.square = function (q) { + return wBigInt.genSquare(q)(this); +}; + +wBigInt.double = function(a, q) { + return wBigInt.genDouble(q)(a); +}; + +wBigInt.prototype.double = function (q) { + return wBigInt.genDouble(q)(this); +}; + +wBigInt.isZero = function(a, q) { + return wBigInt.genIsZero(q)(a); +}; + +wBigInt.prototype.isZero = function (q) { + return wBigInt.genIsZero(q)(this); +}; + +wBigInt.leBuff2int = function(buff) { + let res = wBigInt.zero; + for (let i=0; i. +*/ + +const bigInt = require("./bigint"); + +module.exports = calculateWitness; + +function calculateWitness(circuit, inputSignals, log) { + log = log || (() => {}); + const ctx = new RTCtx(circuit, log); + + function iterateSelector(values, sels, cb) { + if (!Array.isArray(values)) { + return cb(sels, values); + } + for (let i=0; i " + ctx.witness[i].toString()); + } + return ctx.witness.slice(0, circuit.nVars); +// return ctx.witness; +} + +class RTCtx { + constructor(circuit, log) { + this.log = log || function() {}; + this.scopes = []; + this.circuit = circuit; + this.witness = new Array(circuit.nSignals); + this.notInitSignals = {}; + for (let c in this.circuit.components) { + this.notInitSignals[c] = this.circuit.components[c].inputSignals; + } + } + + _sels2str(sels) { + let res = ""; + for (let i=0; i { + if (this.notInitSignals[c] == 0) this.triggerComponent(c); + }); + return this.witness[sId]; + } + + setVar(name, sels, value) { + function setVarArray(a, sels2, value) { + if (sels2.length == 1) { + a[sels2[0]] = value; + } else { + if (typeof(a[sels2[0]]) == "undefined") a[sels2[0]] = []; + setVarArray(a[sels2[0]], sels2.slice(1), value); + } + } + const scope = this.scopes[this.scopes.length-1]; + if (sels.length == 0) { + scope[name] = value; + } else { + if (typeof(scope[name]) == "undefined") scope[name] = []; + setVarArray(scope[name], sels, value); + } + return value; + } + + getVar(name, sels) { + function select(a, sels2) { + return (sels2.length == 0) ? a : select(a[sels2[0]], sels2.slice(1)); + } + for (let i=this.scopes.length-1; i>=0; i--) { + if (typeof(this.scopes[i][name]) != "undefined") return select(this.scopes[i][name], sels); + } + throw new Error("Variable not defined: " + name); + } + + getSignal(name, sels) { + let fullName = name=="one" ? "one" : this.currentComponent + "." + name; + fullName += this._sels2str(sels); + return this.getSignalFullName(fullName); + } + + + getPin(componentName, componentSels, signalName, signalSels) { + let fullName = componentName=="one" ? "one" : this.currentComponent + "." + componentName; + fullName += this._sels2str(componentSels) + + "."+ + signalName+ + this._sels2str(signalSels); + return this.getSignalFullName(fullName); + } + + getSignalFullName(fullName) { + const sId = this.circuit.getSignalIdx(fullName); + if (typeof(this.witness[sId]) == "undefined") { + throw new Error("Signal not initialized: "+fullName); + } + this.log("get --->" + fullName + " = " + this.witness[sId].toString() ); + return this.witness[sId]; + } + + assert(a,b) { + const ba = bigInt(a); + const bb = bigInt(b); + if (!ba.equals(bb)) { + throw new Error("Constraint doesn't match: " + ba.toString() + " != " + bb.toString()); + } + } +} + +},{"./bigint":13}],15:[function(require,module,exports){ +/* + Copyright 2018 0kims association. + + This file is part of snarkjs. + + snarkjs is a free software: you can redistribute it and/or + modify it under the terms of the GNU General Public License as published by the + Free Software Foundation, either version 3 of the License, or (at your option) + any later version. + + snarkjs is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY + or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for + more details. + + You should have received a copy of the GNU General Public License along with + snarkjs. If not, see . +*/ + +const bigInt = require("./bigint.js"); + +const __P__ = bigInt("21888242871839275222246405745257275088548364400416034343698204186575808495617"); +const __MASK__ = bigInt("28948022309329048855892746252171976963317496166410141009864396001978282409983"); // 0x3FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF +const calculateWitness = require("./calculateWitness.js"); + +module.exports = class Circuit { + constructor(circuitDef) { + this.nPubInputs = circuitDef.nPubInputs; + this.nPrvInputs = circuitDef.nPrvInputs; + this.nInputs = circuitDef.nInputs; + this.nOutputs = circuitDef.nOutputs; + this.nVars = circuitDef.nVars; + this.nSignals = circuitDef.nSignals; + this.nConstants = circuitDef.nConstants; + + this.nConstraints = circuitDef.constraints.length; + + this.signalName2Idx = circuitDef.signalName2Idx; + this.components = circuitDef.components; + this.componentName2Idx = circuitDef.componentName2Idx; + this.signals = circuitDef.signals; + this.constraints = circuitDef.constraints; + + this.templates = {}; + for (let t in circuitDef.templates) { + this.templates[t] = eval(" const __f= " +circuitDef.templates[t] + "\n__f"); + } + + this.functions = {}; + for (let f in circuitDef.functions) { + this.functions[f] = { + params: circuitDef.functions[f].params, + func: eval(" const __f= " +circuitDef.functions[f].func + "\n__f;") + }; + } + } + + calculateWitness(input, log) { + return calculateWitness(this, input, log); + } + + checkWitness(w) { + const evalLC = (lc, w) => { + let acc = bigInt(0); + for (let k in lc) { + acc= acc.add(bigInt(w[k]).mul(bigInt(lc[k]))).mod(__P__); + } + return acc; + } + + const checkConstraint = (ct, w) => { + const a=evalLC(ct[0],w); + const b=evalLC(ct[1],w); + const c=evalLC(ct[2],w); + const res = (a.mul(b).sub(c)).affine(__P__); + if (!res.isZero()) return false; + return true; + } + + + for (let i=0; i { + let S = ""; + for (let k in lc) { + let name = this.signals[k].names[0]; + if (name == "one") name = ""; + let v = bigInt(lc[k]); + let vs; + if (!v.lesserOrEquals(__P__.shr(bigInt(1)))) { + v = __P__.sub(v); + vs = "-"+v.toString(); + } else { + if (S!="") { + vs = "+"+v.toString(); + } else { + vs = ""; + } + if (vs!="1") { + vs = vs + v.toString();; + } + } + + S= S + " " + vs + name; + } + return S; + }; + const S = `[ ${lc2str(c[0])} ] * [ ${lc2str(c[1])} ] - [ ${lc2str(c[2])} ] = 0`; + console.log(S); + } + + printConstraints() { + for (let i=0; i=this.nOutputs) throw new Error("Accessing an invalid output: "+i); + return i+1; + } + + // returns the index of the i'th input + inputIdx(i) { + if (i>=this.nInputs) throw new Error("Accessing an invalid input: "+i); + return this.nOutputs + 1 + i; + } + + // returns the index of the i'th public input + pubInputIdx(i) { + if (i>=this.nPubInputs) throw new Error("Accessing an invalid pubInput: "+i); + return this.inputIdx(i); + } + + // returns the index of the i'th private input + prvInputIdx(i) { + if (i>=this.nPrvInputs) throw new Error("Accessing an invalid prvInput: "+i); + return this.inputIdx(this.nPubInputs + i); + } + + // returns the index of the i'th variable + varIdx(i) { + if (i>=this.nVars) throw new Error("Accessing an invalid variable: "+i); + return i; + } + + // returns the index of the i'th constant + constantIdx(i) { + if (i>=this.nConstants) throw new Error("Accessing an invalid constant: "+i); + return this.nVars + i; + } + + // returns the index of the i'th signal + signalIdx(i) { + if (i>=this.nSignls) throw new Error("Accessing an invalid signal: "+i); + return i; + } + + signalNames(i) { + return this.signals[ this.getSignalIdx(i) ].names.join(", "); + } + + a(constraint, signalIdx) { + return bigInt(this.constraints[constraint][0][signalIdx] || 0 ); + } + + b(constraint, signalIdx) { + return bigInt(this.constraints[constraint][1][signalIdx] || 0); + } + + c(constraint, signalIdx) { + return bigInt(this.constraints[constraint][2][signalIdx] || 0); + } +}; + +},{"./bigint.js":13,"./calculateWitness.js":14}],16:[function(require,module,exports){ +/* + Copyright 2018 0kims association. + + This file is part of snarkjs. + + snarkjs is a free software: you can redistribute it and/or + modify it under the terms of the GNU General Public License as published by the + Free Software Foundation, either version 3 of the License, or (at your option) + any later version. + + snarkjs is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY + or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for + more details. + + You should have received a copy of the GNU General Public License along with + snarkjs. If not, see . +*/ + +const bigInt = require("./bigint.js"); + +module.exports.stringifyBigInts = stringifyBigInts; +module.exports.unstringifyBigInts = unstringifyBigInts; + +function stringifyBigInts(o) { + if ((typeof(o) == "bigint") || (o instanceof bigInt)) { + return o.toString(10); + } else if (Array.isArray(o)) { + return o.map(stringifyBigInts); + } else if (typeof o == "object") { + const res = {}; + for (let k in o) { + res[k] = stringifyBigInts(o[k]); + } + return res; + } else { + return o; + } +} + +function unstringifyBigInts(o) { + if ((typeof(o) == "string") && (/^[0-9]+$/.test(o) )) { + return bigInt(o); + } else if (Array.isArray(o)) { + return o.map(unstringifyBigInts); + } else if (typeof o == "object") { + const res = {}; + for (let k in o) { + res[k] = unstringifyBigInts(o[k]); + } + return res; + } else { + return o; + } +} + +},{"./bigint.js":13}],17:[function(require,module,exports){ (function (process){ /* Copyright 2019 0KIMS association. @@ -5542,4 +6523,175 @@ class Groth16 { module.exports = build; }).call(this,require('_process')) -},{"../build/groth16_wasm.js":1,"_process":12,"assert":3,"big-integer":8,"crypto":undefined,"worker_threads":undefined}]},{},[2]); +},{"../build/groth16_wasm.js":1,"_process":12,"assert":3,"big-integer":8,"crypto":undefined,"worker_threads":undefined}],18:[function(require,module,exports){ +/* + Copyright 2019 0KIMS association. + + This file is part of websnark (Web Assembly zkSnark Prover). + + websnark is a free software: you can redistribute it and/or modify it + under the terms of the GNU General Public License as published by + the Free Software Foundation, either version 3 of the License, or + (at your option) any later version. + + websnark is distributed in the hope that it will be useful, but WITHOUT + ANY WARRANTY; without even the implied warranty of MERCHANTABILITY + or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public + License for more details. + + You should have received a copy of the GNU General Public License + along with websnark. If not, see . +*/ + +const bigInt = require("big-integer"); +const Circuit = require("snarkjs/src/circuit"); +const bigInt2 = require("snarkjs/src/bigint"); +const hexifyBigInts = require("../tools/stringifybigint").hexifyBigInts; +const unstringifyBigInts = require("../tools/stringifybigint").unstringifyBigInts; +const stringifyBigInts2 = require("snarkjs/src/stringifybigint").stringifyBigInts; +const unstringifyBigInts2 = require("snarkjs/src/stringifybigint").unstringifyBigInts; + +function bigInt2BytesLE(_a, len) { + const b = Array(len); + let v = bigInt(_a); + for (let i=0; i. +*/ + +const bigInt = require("big-integer"); + +module.exports.stringifyBigInts = stringifyBigInts; +module.exports.unstringifyBigInts = unstringifyBigInts; +module.exports.hexifyBigInts = hexifyBigInts; + +function stringifyBigInts(o) { + if ((typeof(o) == "bigint") || (o instanceof bigInt)) { + return o.toString(10); + } else if (Array.isArray(o)) { + return o.map(stringifyBigInts); + } else if (typeof o == "object") { + const res = {}; + for (let k in o) { + res[k] = stringifyBigInts(o[k]); + } + return res; + } else { + return o; + } +} + +function unstringifyBigInts(o) { + if ((typeof(o) == "string") && (/^[0-9]+$/.test(o) )) { + return bigInt(o); + } else if (Array.isArray(o)) { + return o.map(unstringifyBigInts); + } else if (typeof o == "object" && !(o instanceof bigInt)) { + const res = {}; + for (let k in o) { + res[k] = unstringifyBigInts(o[k]); + } + return res; + } else { + return o; + } +} + +function hexifyBigInts(o) { + if (typeof (o) === "bigInt" || (o instanceof bigInt)) { + let str = o.toString(16); + while (str.length < 64) str = "0" + str; + str = "0x" + str; + return str; + } else if (Array.isArray(o)) { + return o.map(hexifyBigInts); + } else if (typeof o == "object") { + const res = {}; + for (let k in o) { + res[k] = hexifyBigInts(o[k]); + } + return res; + } else { + return o; + } +} + +},{"big-integer":8}]},{},[2]); diff --git a/main.js b/main.js index 042a1d7..6239270 100644 --- a/main.js +++ b/main.js @@ -19,16 +19,17 @@ /* globals window */ -const buildGroth16 = require("./src/groth16.js"); +const buildGroth16 = require("./src/groth16"); +const utils = require("./src/utils"); -buildGroth16().then( (groth16) => { +buildGroth16().then((groth16) => { window.groth16 = groth16; - window.genZKSnarkProof = function(witness, provingKey, cb) { - - const p = groth16.proof(witness, provingKey); + window.zkSnarkProofToSolidityInput = utils.toSolidityInput; + window.genZKSnarkProofAndWitness = function (input, circuitJson, provingKey, cb) { + const p = utils.genWitnessAndProve(groth16, input, circuitJson, provingKey); if (cb) { - p.then( (proof) => { + p.then((proof) => { cb(null, proof); }, (err) => { cb(err); @@ -37,6 +38,17 @@ buildGroth16().then( (groth16) => { return p; } }; -}); - + window.genZKSnarkProof = function (witness, provingKey, cb) { + const p = groth16.proof(witness, provingKey); + if (cb) { + p.then((proof) => { + cb(null, proof); + }, (err) => { + cb(err); + }); + } else { + return p; + } + }; +}); \ No newline at end of file diff --git a/src/utils.js b/src/utils.js index b5701ba..bd1338e 100644 --- a/src/utils.js +++ b/src/utils.js @@ -18,8 +18,14 @@ */ const bigInt = require("big-integer"); +const Circuit = require("snarkjs/src/circuit"); +const bigInt2 = require("snarkjs/src/bigint"); +const hexifyBigInts = require("../tools/stringifybigint").hexifyBigInts; +const unstringifyBigInts = require("../tools/stringifybigint").unstringifyBigInts; +const stringifyBigInts2 = require("snarkjs/src/stringifybigint").stringifyBigInts; +const unstringifyBigInts2 = require("snarkjs/src/stringifybigint").unstringifyBigInts; -exports.bigInt2BytesLE = function bigInt2BytesLE(_a, len) { +function bigInt2BytesLE(_a, len) { const b = Array(len); let v = bigInt(_a); for (let i=0; i