forked from lix-project/lix-website
1454 lines
51 KiB
JavaScript
1454 lines
51 KiB
JavaScript
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);
|
|
if (exp.isNegative()) {
|
|
exp = exp.multiply(Integer[-1]);
|
|
base = base.modInv(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, rng) {
|
|
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), rng));
|
|
}
|
|
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, rng) {
|
|
a = parseValue(a);
|
|
b = parseValue(b);
|
|
var usedRNG = rng || Math.random;
|
|
var low = min(a, b), high = max(a, b);
|
|
var range = high.subtract(low).add(1);
|
|
if (range.isSmall) return low.add(Math.floor(usedRNG() * range));
|
|
var digits = toBase(range, BASE).value;
|
|
var result = [], restricted = true;
|
|
for (var i = 0; i < digits.length; i++) {
|
|
var top = restricted ? digits[i] + (i + 1 < digits.length ? digits[i + 1] / BASE : 0) : BASE;
|
|
var digit = truncate(usedRNG() * top);
|
|
result.push(digit);
|
|
if (digit < digits[i]) 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 || alphabet) 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 || alphabet) 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( function () {
|
|
return bigInt;
|
|
});
|
|
}
|