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<script src="js/wordlist_italian.js"></script>
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+ <script src="js/biginteger.js"></script>
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--- /dev/null
+/*
+ JavaScript BigInteger library version 0.9.1
+ http://silentmatt.com/biginteger/
+
+ Copyright (c) 2009 Matthew Crumley <email@matthewcrumley.com>
+ Copyright (c) 2010,2011 by John Tobey <John.Tobey@gmail.com>
+ Licensed under the MIT license.
+
+ Support for arbitrary internal representation base was added by
+ Vitaly Magerya.
+*/
+
+/*
+ File: biginteger.js
+
+ Exports:
+
+ <BigInteger>
+*/
+(function(exports) {
+"use strict";
+/*
+ Class: BigInteger
+ An arbitrarily-large integer.
+
+ <BigInteger> objects should be considered immutable. None of the "built-in"
+ methods modify *this* or their arguments. All properties should be
+ considered private.
+
+ All the methods of <BigInteger> instances can be called "statically". The
+ static versions are convenient if you don't already have a <BigInteger>
+ object.
+
+ As an example, these calls are equivalent.
+
+ > BigInteger(4).multiply(5); // returns BigInteger(20);
+ > BigInteger.multiply(4, 5); // returns BigInteger(20);
+
+ > var a = 42;
+ > var a = BigInteger.toJSValue("0b101010"); // Not completely useless...
+*/
+
+var CONSTRUCT = {}; // Unique token to call "private" version of constructor
+
+/*
+ Constructor: BigInteger()
+ Convert a value to a <BigInteger>.
+
+ Although <BigInteger()> is the constructor for <BigInteger> objects, it is
+ best not to call it as a constructor. If *n* is a <BigInteger> object, it is
+ simply returned as-is. Otherwise, <BigInteger()> is equivalent to <parse>
+ without a radix argument.
+
+ > var n0 = BigInteger(); // Same as <BigInteger.ZERO>
+ > var n1 = BigInteger("123"); // Create a new <BigInteger> with value 123
+ > var n2 = BigInteger(123); // Create a new <BigInteger> with value 123
+ > var n3 = BigInteger(n2); // Return n2, unchanged
+
+ The constructor form only takes an array and a sign. *n* must be an
+ array of numbers in little-endian order, where each digit is between 0
+ and BigInteger.base. The second parameter sets the sign: -1 for
+ negative, +1 for positive, or 0 for zero. The array is *not copied and
+ may be modified*. If the array contains only zeros, the sign parameter
+ is ignored and is forced to zero.
+
+ > new BigInteger([5], -1): create a new BigInteger with value -5
+
+ Parameters:
+
+ n - Value to convert to a <BigInteger>.
+
+ Returns:
+
+ A <BigInteger> value.
+
+ See Also:
+
+ <parse>, <BigInteger>
+*/
+function BigInteger(n, s, token) {
+ if (token !== CONSTRUCT) {
+ if (n instanceof BigInteger) {
+ return n;
+ }
+ else if (typeof n === "undefined") {
+ return ZERO;
+ }
+ return BigInteger.parse(n);
+ }
+
+ n = n || []; // Provide the nullary constructor for subclasses.
+ while (n.length && !n[n.length - 1]) {
+ --n.length;
+ }
+ this._d = n;
+ this._s = n.length ? (s || 1) : 0;
+}
+
+BigInteger._construct = function(n, s) {
+ return new BigInteger(n, s, CONSTRUCT);
+};
+
+// Base-10 speedup hacks in parse, toString, exp10 and log functions
+// require base to be a power of 10. 10^7 is the largest such power
+// that won't cause a precision loss when digits are multiplied.
+var BigInteger_base = 10000000;
+var BigInteger_base_log10 = 7;
+
+BigInteger.base = BigInteger_base;
+BigInteger.base_log10 = BigInteger_base_log10;
+
+var ZERO = new BigInteger([], 0, CONSTRUCT);
+// Constant: ZERO
+// <BigInteger> 0.
+BigInteger.ZERO = ZERO;
+
+var ONE = new BigInteger([1], 1, CONSTRUCT);
+// Constant: ONE
+// <BigInteger> 1.
+BigInteger.ONE = ONE;
+
+var M_ONE = new BigInteger(ONE._d, -1, CONSTRUCT);
+// Constant: M_ONE
+// <BigInteger> -1.
+BigInteger.M_ONE = M_ONE;
+
+// Constant: _0
+// Shortcut for <ZERO>.
+BigInteger._0 = ZERO;
+
+// Constant: _1
+// Shortcut for <ONE>.
+BigInteger._1 = ONE;
+
+/*
+ Constant: small
+ Array of <BigIntegers> from 0 to 36.
+
+ These are used internally for parsing, but useful when you need a "small"
+ <BigInteger>.
+
+ See Also:
+
+ <ZERO>, <ONE>, <_0>, <_1>
+*/
+BigInteger.small = [
+ ZERO,
+ ONE,
+ /* Assuming BigInteger_base > 36 */
+ new BigInteger( [2], 1, CONSTRUCT),
+ new BigInteger( [3], 1, CONSTRUCT),
+ new BigInteger( [4], 1, CONSTRUCT),
+ new BigInteger( [5], 1, CONSTRUCT),
+ new BigInteger( [6], 1, CONSTRUCT),
+ new BigInteger( [7], 1, CONSTRUCT),
+ new BigInteger( [8], 1, CONSTRUCT),
+ new BigInteger( [9], 1, CONSTRUCT),
+ new BigInteger([10], 1, CONSTRUCT),
+ new BigInteger([11], 1, CONSTRUCT),
+ new BigInteger([12], 1, CONSTRUCT),
+ new BigInteger([13], 1, CONSTRUCT),
+ new BigInteger([14], 1, CONSTRUCT),
+ new BigInteger([15], 1, CONSTRUCT),
+ new BigInteger([16], 1, CONSTRUCT),
+ new BigInteger([17], 1, CONSTRUCT),
+ new BigInteger([18], 1, CONSTRUCT),
+ new BigInteger([19], 1, CONSTRUCT),
+ new BigInteger([20], 1, CONSTRUCT),
+ new BigInteger([21], 1, CONSTRUCT),
+ new BigInteger([22], 1, CONSTRUCT),
+ new BigInteger([23], 1, CONSTRUCT),
+ new BigInteger([24], 1, CONSTRUCT),
+ new BigInteger([25], 1, CONSTRUCT),
+ new BigInteger([26], 1, CONSTRUCT),
+ new BigInteger([27], 1, CONSTRUCT),
+ new BigInteger([28], 1, CONSTRUCT),
+ new BigInteger([29], 1, CONSTRUCT),
+ new BigInteger([30], 1, CONSTRUCT),
+ new BigInteger([31], 1, CONSTRUCT),
+ new BigInteger([32], 1, CONSTRUCT),
+ new BigInteger([33], 1, CONSTRUCT),
+ new BigInteger([34], 1, CONSTRUCT),
+ new BigInteger([35], 1, CONSTRUCT),
+ new BigInteger([36], 1, CONSTRUCT)
+];
+
+// Used for parsing/radix conversion
+BigInteger.digits = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ".split("");
+
+/*
+ Method: toString
+ Convert a <BigInteger> to a string.
+
+ When *base* is greater than 10, letters are upper case.
+
+ Parameters:
+
+ base - Optional base to represent the number in (default is base 10).
+ Must be between 2 and 36 inclusive, or an Error will be thrown.
+
+ Returns:
+
+ The string representation of the <BigInteger>.
+*/
+BigInteger.prototype.toString = function(base) {
+ base = +base || 10;
+ if (base < 2 || base > 36) {
+ throw new Error("illegal radix " + base + ".");
+ }
+ if (this._s === 0) {
+ return "0";
+ }
+ if (base === 10) {
+ var str = this._s < 0 ? "-" : "";
+ str += this._d[this._d.length - 1].toString();
+ for (var i = this._d.length - 2; i >= 0; i--) {
+ var group = this._d[i].toString();
+ while (group.length < BigInteger_base_log10) group = '0' + group;
+ str += group;
+ }
+ return str;
+ }
+ else {
+ var numerals = BigInteger.digits;
+ base = BigInteger.small[base];
+ var sign = this._s;
+
+ var n = this.abs();
+ var digits = [];
+ var digit;
+
+ while (n._s !== 0) {
+ var divmod = n.divRem(base);
+ n = divmod[0];
+ digit = divmod[1];
+ // TODO: This could be changed to unshift instead of reversing at the end.
+ // Benchmark both to compare speeds.
+ digits.push(numerals[digit.valueOf()]);
+ }
+ return (sign < 0 ? "-" : "") + digits.reverse().join("");
+ }
+};
+
+// Verify strings for parsing
+BigInteger.radixRegex = [
+ /^$/,
+ /^$/,
+ /^[01]*$/,
+ /^[012]*$/,
+ /^[0-3]*$/,
+ /^[0-4]*$/,
+ /^[0-5]*$/,
+ /^[0-6]*$/,
+ /^[0-7]*$/,
+ /^[0-8]*$/,
+ /^[0-9]*$/,
+ /^[0-9aA]*$/,
+ /^[0-9abAB]*$/,
+ /^[0-9abcABC]*$/,
+ /^[0-9a-dA-D]*$/,
+ /^[0-9a-eA-E]*$/,
+ /^[0-9a-fA-F]*$/,
+ /^[0-9a-gA-G]*$/,
+ /^[0-9a-hA-H]*$/,
+ /^[0-9a-iA-I]*$/,
+ /^[0-9a-jA-J]*$/,
+ /^[0-9a-kA-K]*$/,
+ /^[0-9a-lA-L]*$/,
+ /^[0-9a-mA-M]*$/,
+ /^[0-9a-nA-N]*$/,
+ /^[0-9a-oA-O]*$/,
+ /^[0-9a-pA-P]*$/,
+ /^[0-9a-qA-Q]*$/,
+ /^[0-9a-rA-R]*$/,
+ /^[0-9a-sA-S]*$/,
+ /^[0-9a-tA-T]*$/,
+ /^[0-9a-uA-U]*$/,
+ /^[0-9a-vA-V]*$/,
+ /^[0-9a-wA-W]*$/,
+ /^[0-9a-xA-X]*$/,
+ /^[0-9a-yA-Y]*$/,
+ /^[0-9a-zA-Z]*$/
+];
+
+/*
+ Function: parse
+ Parse a string into a <BigInteger>.
+
+ *base* is optional but, if provided, must be from 2 to 36 inclusive. If
+ *base* is not provided, it will be guessed based on the leading characters
+ of *s* as follows:
+
+ - "0x" or "0X": *base* = 16
+ - "0c" or "0C": *base* = 8
+ - "0b" or "0B": *base* = 2
+ - else: *base* = 10
+
+ If no base is provided, or *base* is 10, the number can be in exponential
+ form. For example, these are all valid:
+
+ > BigInteger.parse("1e9"); // Same as "1000000000"
+ > BigInteger.parse("1.234*10^3"); // Same as 1234
+ > BigInteger.parse("56789 * 10 ** -2"); // Same as 567
+
+ If any characters fall outside the range defined by the radix, an exception
+ will be thrown.
+
+ Parameters:
+
+ s - The string to parse.
+ base - Optional radix (default is to guess based on *s*).
+
+ Returns:
+
+ a <BigInteger> instance.
+*/
+BigInteger.parse = function(s, base) {
+ // Expands a number in exponential form to decimal form.
+ // expandExponential("-13.441*10^5") === "1344100";
+ // expandExponential("1.12300e-1") === "0.112300";
+ // expandExponential(1000000000000000000000000000000) === "1000000000000000000000000000000";
+ function expandExponential(str) {
+ str = str.replace(/\s*[*xX]\s*10\s*(\^|\*\*)\s*/, "e");
+
+ return str.replace(/^([+\-])?(\d+)\.?(\d*)[eE]([+\-]?\d+)$/, function(x, s, n, f, c) {
+ c = +c;
+ var l = c < 0;
+ var i = n.length + c;
+ x = (l ? n : f).length;
+ c = ((c = Math.abs(c)) >= x ? c - x + l : 0);
+ var z = (new Array(c + 1)).join("0");
+ var r = n + f;
+ return (s || "") + (l ? r = z + r : r += z).substr(0, i += l ? z.length : 0) + (i < r.length ? "." + r.substr(i) : "");
+ });
+ }
+
+ s = s.toString();
+ if (typeof base === "undefined" || +base === 10) {
+ s = expandExponential(s);
+ }
+
+ var prefixRE;
+ if (typeof base === "undefined") {
+ prefixRE = '0[xcb]';
+ }
+ else if (base == 16) {
+ prefixRE = '0x';
+ }
+ else if (base == 8) {
+ prefixRE = '0c';
+ }
+ else if (base == 2) {
+ prefixRE = '0b';
+ }
+ else {
+ prefixRE = '';
+ }
+ var parts = new RegExp('^([+\\-]?)(' + prefixRE + ')?([0-9a-z]*)(?:\\.\\d*)?$', 'i').exec(s);
+ if (parts) {
+ var sign = parts[1] || "+";
+ var baseSection = parts[2] || "";
+ var digits = parts[3] || "";
+
+ if (typeof base === "undefined") {
+ // Guess base
+ if (baseSection === "0x" || baseSection === "0X") { // Hex
+ base = 16;
+ }
+ else if (baseSection === "0c" || baseSection === "0C") { // Octal
+ base = 8;
+ }
+ else if (baseSection === "0b" || baseSection === "0B") { // Binary
+ base = 2;
+ }
+ else {
+ base = 10;
+ }
+ }
+ else if (base < 2 || base > 36) {
+ throw new Error("Illegal radix " + base + ".");
+ }
+
+ base = +base;
+
+ // Check for digits outside the range
+ if (!(BigInteger.radixRegex[base].test(digits))) {
+ throw new Error("Bad digit for radix " + base);
+ }
+
+ // Strip leading zeros, and convert to array
+ digits = digits.replace(/^0+/, "").split("");
+ if (digits.length === 0) {
+ return ZERO;
+ }
+
+ // Get the sign (we know it's not zero)
+ sign = (sign === "-") ? -1 : 1;
+
+ // Optimize 10
+ if (base == 10) {
+ var d = [];
+ while (digits.length >= BigInteger_base_log10) {
+ d.push(parseInt(digits.splice(digits.length-BigInteger.base_log10, BigInteger.base_log10).join(''), 10));
+ }
+ d.push(parseInt(digits.join(''), 10));
+ return new BigInteger(d, sign, CONSTRUCT);
+ }
+
+ // Do the conversion
+ var d = ZERO;
+ base = BigInteger.small[base];
+ var small = BigInteger.small;
+ for (var i = 0; i < digits.length; i++) {
+ d = d.multiply(base).add(small[parseInt(digits[i], 36)]);
+ }
+ return new BigInteger(d._d, sign, CONSTRUCT);
+ }
+ else {
+ throw new Error("Invalid BigInteger format: " + s);
+ }
+};
+
+/*
+ Function: add
+ Add two <BigIntegers>.
+
+ Parameters:
+
+ n - The number to add to *this*. Will be converted to a <BigInteger>.
+
+ Returns:
+
+ The numbers added together.
+
+ See Also:
+
+ <subtract>, <multiply>, <quotient>, <next>
+*/
+BigInteger.prototype.add = function(n) {
+ if (this._s === 0) {
+ return BigInteger(n);
+ }
+
+ n = BigInteger(n);
+ if (n._s === 0) {
+ return this;
+ }
+ if (this._s !== n._s) {
+ n = n.negate();
+ return this.subtract(n);
+ }
+
+ var a = this._d;
+ var b = n._d;
+ var al = a.length;
+ var bl = b.length;
+ var sum = new Array(Math.max(al, bl) + 1);
+ var size = Math.min(al, bl);
+ var carry = 0;
+ var digit;
+
+ for (var i = 0; i < size; i++) {
+ digit = a[i] + b[i] + carry;
+ sum[i] = digit % BigInteger_base;
+ carry = (digit / BigInteger_base) | 0;
+ }
+ if (bl > al) {
+ a = b;
+ al = bl;
+ }
+ for (i = size; carry && i < al; i++) {
+ digit = a[i] + carry;
+ sum[i] = digit % BigInteger_base;
+ carry = (digit / BigInteger_base) | 0;
+ }
+ if (carry) {
+ sum[i] = carry;
+ }
+
+ for ( ; i < al; i++) {
+ sum[i] = a[i];
+ }
+
+ return new BigInteger(sum, this._s, CONSTRUCT);
+};
+
+/*
+ Function: negate
+ Get the additive inverse of a <BigInteger>.
+
+ Returns:
+
+ A <BigInteger> with the same magnatude, but with the opposite sign.
+
+ See Also:
+
+ <abs>
+*/
+BigInteger.prototype.negate = function() {
+ return new BigInteger(this._d, (-this._s) | 0, CONSTRUCT);
+};
+
+/*
+ Function: abs
+ Get the absolute value of a <BigInteger>.
+
+ Returns:
+
+ A <BigInteger> with the same magnatude, but always positive (or zero).
+
+ See Also:
+
+ <negate>
+*/
+BigInteger.prototype.abs = function() {
+ return (this._s < 0) ? this.negate() : this;
+};
+
+/*
+ Function: subtract
+ Subtract two <BigIntegers>.
+
+ Parameters:
+
+ n - The number to subtract from *this*. Will be converted to a <BigInteger>.
+
+ Returns:
+
+ The *n* subtracted from *this*.
+
+ See Also:
+
+ <add>, <multiply>, <quotient>, <prev>
+*/
+BigInteger.prototype.subtract = function(n) {
+ if (this._s === 0) {
+ return BigInteger(n).negate();
+ }
+
+ n = BigInteger(n);
+ if (n._s === 0) {
+ return this;
+ }
+ if (this._s !== n._s) {
+ n = n.negate();
+ return this.add(n);
+ }
+
+ var m = this;
+ // negative - negative => -|a| - -|b| => -|a| + |b| => |b| - |a|
+ if (this._s < 0) {
+ m = new BigInteger(n._d, 1, CONSTRUCT);
+ n = new BigInteger(this._d, 1, CONSTRUCT);
+ }
+
+ // Both are positive => a - b
+ var sign = m.compareAbs(n);
+ if (sign === 0) {
+ return ZERO;
+ }
+ else if (sign < 0) {
+ // swap m and n
+ var t = n;
+ n = m;
+ m = t;
+ }
+
+ // a > b
+ var a = m._d;
+ var b = n._d;
+ var al = a.length;
+ var bl = b.length;
+ var diff = new Array(al); // al >= bl since a > b
+ var borrow = 0;
+ var i;
+ var digit;
+
+ for (i = 0; i < bl; i++) {
+ digit = a[i] - borrow - b[i];
+ if (digit < 0) {
+ digit += BigInteger_base;
+ borrow = 1;
+ }
+ else {
+ borrow = 0;
+ }
+ diff[i] = digit;
+ }
+ for (i = bl; i < al; i++) {
+ digit = a[i] - borrow;
+ if (digit < 0) {
+ digit += BigInteger_base;
+ }
+ else {
+ diff[i++] = digit;
+ break;
+ }
+ diff[i] = digit;
+ }
+ for ( ; i < al; i++) {
+ diff[i] = a[i];
+ }
+
+ return new BigInteger(diff, sign, CONSTRUCT);
+};
+
+(function() {
+ function addOne(n, sign) {
+ var a = n._d;
+ var sum = a.slice();
+ var carry = true;
+ var i = 0;
+
+ while (true) {
+ var digit = (a[i] || 0) + 1;
+ sum[i] = digit % BigInteger_base;
+ if (digit <= BigInteger_base - 1) {
+ break;
+ }
+ ++i;
+ }
+
+ return new BigInteger(sum, sign, CONSTRUCT);
+ }
+
+ function subtractOne(n, sign) {
+ var a = n._d;
+ var sum = a.slice();
+ var borrow = true;
+ var i = 0;
+
+ while (true) {
+ var digit = (a[i] || 0) - 1;
+ if (digit < 0) {
+ sum[i] = digit + BigInteger_base;
+ }
+ else {
+ sum[i] = digit;
+ break;
+ }
+ ++i;
+ }
+
+ return new BigInteger(sum, sign, CONSTRUCT);
+ }
+
+ /*
+ Function: next
+ Get the next <BigInteger> (add one).
+
+ Returns:
+
+ *this* + 1.
+
+ See Also:
+
+ <add>, <prev>
+ */
+ BigInteger.prototype.next = function() {
+ switch (this._s) {
+ case 0:
+ return ONE;
+ case -1:
+ return subtractOne(this, -1);
+ // case 1:
+ default:
+ return addOne(this, 1);
+ }
+ };
+
+ /*
+ Function: prev
+ Get the previous <BigInteger> (subtract one).
+
+ Returns:
+
+ *this* - 1.
+
+ See Also:
+
+ <next>, <subtract>
+ */
+ BigInteger.prototype.prev = function() {
+ switch (this._s) {
+ case 0:
+ return M_ONE;
+ case -1:
+ return addOne(this, -1);
+ // case 1:
+ default:
+ return subtractOne(this, 1);
+ }
+ };
+})();
+
+/*
+ Function: compareAbs
+ Compare the absolute value of two <BigIntegers>.
+
+ Calling <compareAbs> is faster than calling <abs> twice, then <compare>.
+
+ Parameters:
+
+ n - The number to compare to *this*. Will be converted to a <BigInteger>.
+
+ Returns:
+
+ -1, 0, or +1 if *|this|* is less than, equal to, or greater than *|n|*.
+
+ See Also:
+
+ <compare>, <abs>
+*/
+BigInteger.prototype.compareAbs = function(n) {
+ if (this === n) {
+ return 0;
+ }
+
+ if (!(n instanceof BigInteger)) {
+ if (!isFinite(n)) {
+ return(isNaN(n) ? n : -1);
+ }
+ n = BigInteger(n);
+ }
+
+ if (this._s === 0) {
+ return (n._s !== 0) ? -1 : 0;
+ }
+ if (n._s === 0) {
+ return 1;
+ }
+
+ var l = this._d.length;
+ var nl = n._d.length;
+ if (l < nl) {
+ return -1;
+ }
+ else if (l > nl) {
+ return 1;
+ }
+
+ var a = this._d;
+ var b = n._d;
+ for (var i = l-1; i >= 0; i--) {
+ if (a[i] !== b[i]) {
+ return a[i] < b[i] ? -1 : 1;
+ }
+ }
+
+ return 0;
+};
+
+/*
+ Function: compare
+ Compare two <BigIntegers>.
+
+ Parameters:
+
+ n - The number to compare to *this*. Will be converted to a <BigInteger>.
+
+ Returns:
+
+ -1, 0, or +1 if *this* is less than, equal to, or greater than *n*.
+
+ See Also:
+
+ <compareAbs>, <isPositive>, <isNegative>, <isUnit>
+*/
+BigInteger.prototype.compare = function(n) {
+ if (this === n) {
+ return 0;
+ }
+
+ n = BigInteger(n);
+
+ if (this._s === 0) {
+ return -n._s;
+ }
+
+ if (this._s === n._s) { // both positive or both negative
+ var cmp = this.compareAbs(n);
+ return cmp * this._s;
+ }
+ else {
+ return this._s;
+ }
+};
+
+/*
+ Function: isUnit
+ Return true iff *this* is either 1 or -1.
+
+ Returns:
+
+ true if *this* compares equal to <BigInteger.ONE> or <BigInteger.M_ONE>.
+
+ See Also:
+
+ <isZero>, <isNegative>, <isPositive>, <compareAbs>, <compare>,
+ <BigInteger.ONE>, <BigInteger.M_ONE>
+*/
+BigInteger.prototype.isUnit = function() {
+ return this === ONE ||
+ this === M_ONE ||
+ (this._d.length === 1 && this._d[0] === 1);
+};
+
+/*
+ Function: multiply
+ Multiply two <BigIntegers>.
+
+ Parameters:
+
+ n - The number to multiply *this* by. Will be converted to a
+ <BigInteger>.
+
+ Returns:
+
+ The numbers multiplied together.
+
+ See Also:
+
+ <add>, <subtract>, <quotient>, <square>
+*/
+BigInteger.prototype.multiply = function(n) {
+ // TODO: Consider adding Karatsuba multiplication for large numbers
+ if (this._s === 0) {
+ return ZERO;
+ }
+
+ n = BigInteger(n);
+ if (n._s === 0) {
+ return ZERO;
+ }
+ if (this.isUnit()) {
+ if (this._s < 0) {
+ return n.negate();
+ }
+ return n;
+ }
+ if (n.isUnit()) {
+ if (n._s < 0) {
+ return this.negate();
+ }
+ return this;
+ }
+ if (this === n) {
+ return this.square();
+ }
+
+ var r = (this._d.length >= n._d.length);
+ var a = (r ? this : n)._d; // a will be longer than b
+ var b = (r ? n : this)._d;
+ var al = a.length;
+ var bl = b.length;
+
+ var pl = al + bl;
+ var partial = new Array(pl);
+ var i;
+ for (i = 0; i < pl; i++) {
+ partial[i] = 0;
+ }
+
+ for (i = 0; i < bl; i++) {
+ var carry = 0;
+ var bi = b[i];
+ var jlimit = al + i;
+ var digit;
+ for (var j = i; j < jlimit; j++) {
+ digit = partial[j] + bi * a[j - i] + carry;
+ carry = (digit / BigInteger_base) | 0;
+ partial[j] = (digit % BigInteger_base) | 0;
+ }
+ if (carry) {
+ digit = partial[j] + carry;
+ carry = (digit / BigInteger_base) | 0;
+ partial[j] = digit % BigInteger_base;
+ }
+ }
+ return new BigInteger(partial, this._s * n._s, CONSTRUCT);
+};
+
+// Multiply a BigInteger by a single-digit native number
+// Assumes that this and n are >= 0
+// This is not really intended to be used outside the library itself
+BigInteger.prototype.multiplySingleDigit = function(n) {
+ if (n === 0 || this._s === 0) {
+ return ZERO;
+ }
+ if (n === 1) {
+ return this;
+ }
+
+ var digit;
+ if (this._d.length === 1) {
+ digit = this._d[0] * n;
+ if (digit >= BigInteger_base) {
+ return new BigInteger([(digit % BigInteger_base)|0,
+ (digit / BigInteger_base)|0], 1, CONSTRUCT);
+ }
+ return new BigInteger([digit], 1, CONSTRUCT);
+ }
+
+ if (n === 2) {
+ return this.add(this);
+ }
+ if (this.isUnit()) {
+ return new BigInteger([n], 1, CONSTRUCT);
+ }
+
+ var a = this._d;
+ var al = a.length;
+
+ var pl = al + 1;
+ var partial = new Array(pl);
+ for (var i = 0; i < pl; i++) {
+ partial[i] = 0;
+ }
+
+ var carry = 0;
+ for (var j = 0; j < al; j++) {
+ digit = n * a[j] + carry;
+ carry = (digit / BigInteger_base) | 0;
+ partial[j] = (digit % BigInteger_base) | 0;
+ }
+ if (carry) {
+ partial[j] = carry;
+ }
+
+ return new BigInteger(partial, 1, CONSTRUCT);
+};
+
+/*
+ Function: square
+ Multiply a <BigInteger> by itself.
+
+ This is slightly faster than regular multiplication, since it removes the
+ duplicated multiplcations.
+
+ Returns:
+
+ > this.multiply(this)
+
+ See Also:
+ <multiply>
+*/
+BigInteger.prototype.square = function() {
+ // Normally, squaring a 10-digit number would take 100 multiplications.
+ // Of these 10 are unique diagonals, of the remaining 90 (100-10), 45 are repeated.
+ // This procedure saves (N*(N-1))/2 multiplications, (e.g., 45 of 100 multiplies).
+ // Based on code by Gary Darby, Intellitech Systems Inc., www.DelphiForFun.org
+
+ if (this._s === 0) {
+ return ZERO;
+ }
+ if (this.isUnit()) {
+ return ONE;
+ }
+
+ var digits = this._d;
+ var length = digits.length;
+ var imult1 = new Array(length + length + 1);
+ var product, carry, k;
+ var i;
+
+ // Calculate diagonal
+ for (i = 0; i < length; i++) {
+ k = i * 2;
+ product = digits[i] * digits[i];
+ carry = (product / BigInteger_base) | 0;
+ imult1[k] = product % BigInteger_base;
+ imult1[k + 1] = carry;
+ }
+
+ // Calculate repeating part
+ for (i = 0; i < length; i++) {
+ carry = 0;
+ k = i * 2 + 1;
+ for (var j = i + 1; j < length; j++, k++) {
+ product = digits[j] * digits[i] * 2 + imult1[k] + carry;
+ carry = (product / BigInteger_base) | 0;
+ imult1[k] = product % BigInteger_base;
+ }
+ k = length + i;
+ var digit = carry + imult1[k];
+ carry = (digit / BigInteger_base) | 0;
+ imult1[k] = digit % BigInteger_base;
+ imult1[k + 1] += carry;
+ }
+
+ return new BigInteger(imult1, 1, CONSTRUCT);
+};
+
+/*
+ Function: quotient
+ Divide two <BigIntegers> and truncate towards zero.
+
+ <quotient> throws an exception if *n* is zero.
+
+ Parameters:
+
+ n - The number to divide *this* by. Will be converted to a <BigInteger>.
+
+ Returns:
+
+ The *this* / *n*, truncated to an integer.
+
+ See Also:
+
+ <add>, <subtract>, <multiply>, <divRem>, <remainder>
+*/
+BigInteger.prototype.quotient = function(n) {
+ return this.divRem(n)[0];
+};
+
+/*
+ Function: divide
+ Deprecated synonym for <quotient>.
+*/
+BigInteger.prototype.divide = BigInteger.prototype.quotient;
+
+/*
+ Function: remainder
+ Calculate the remainder of two <BigIntegers>.
+
+ <remainder> throws an exception if *n* is zero.
+
+ Parameters:
+
+ n - The remainder after *this* is divided *this* by *n*. Will be
+ converted to a <BigInteger>.
+
+ Returns:
+
+ *this* % *n*.
+
+ See Also:
+
+ <divRem>, <quotient>
+*/
+BigInteger.prototype.remainder = function(n) {
+ return this.divRem(n)[1];
+};
+
+/*
+ Function: divRem
+ Calculate the integer quotient and remainder of two <BigIntegers>.
+
+ <divRem> throws an exception if *n* is zero.
+
+ Parameters:
+
+ n - The number to divide *this* by. Will be converted to a <BigInteger>.
+
+ Returns:
+
+ A two-element array containing the quotient and the remainder.
+
+ > a.divRem(b)
+
+ is exactly equivalent to
+
+ > [a.quotient(b), a.remainder(b)]
+
+ except it is faster, because they are calculated at the same time.
+
+ See Also:
+
+ <quotient>, <remainder>
+*/
+BigInteger.prototype.divRem = function(n) {
+ n = BigInteger(n);
+ if (n._s === 0) {
+ throw new Error("Divide by zero");
+ }
+ if (this._s === 0) {
+ return [ZERO, ZERO];
+ }
+ if (n._d.length === 1) {
+ return this.divRemSmall(n._s * n._d[0]);
+ }
+
+ // Test for easy cases -- |n1| <= |n2|
+ switch (this.compareAbs(n)) {
+ case 0: // n1 == n2
+ return [this._s === n._s ? ONE : M_ONE, ZERO];
+ case -1: // |n1| < |n2|
+ return [ZERO, this];
+ }
+
+ var sign = this._s * n._s;
+ var a = n.abs();
+ var b_digits = this._d;
+ var b_index = b_digits.length;
+ var digits = n._d.length;
+ var quot = [];
+ var guess;
+
+ var part = new BigInteger([], 0, CONSTRUCT);
+
+ while (b_index) {
+ part._d.unshift(b_digits[--b_index]);
+ part = new BigInteger(part._d, 1, CONSTRUCT);
+
+ if (part.compareAbs(n) < 0) {
+ quot.push(0);
+ continue;
+ }
+ if (part._s === 0) {
+ guess = 0;
+ }
+ else {
+ var xlen = part._d.length, ylen = a._d.length;
+ var highx = part._d[xlen-1]*BigInteger_base + part._d[xlen-2];
+ var highy = a._d[ylen-1]*BigInteger_base + a._d[ylen-2];
+ if (part._d.length > a._d.length) {
+ // The length of part._d can either match a._d length,
+ // or exceed it by one.
+ highx = (highx+1)*BigInteger_base;
+ }
+ guess = Math.ceil(highx/highy);
+ }
+ do {
+ var check = a.multiplySingleDigit(guess);
+ if (check.compareAbs(part) <= 0) {
+ break;
+ }
+ guess--;
+ } while (guess);
+
+ quot.push(guess);
+ if (!guess) {
+ continue;
+ }
+ var diff = part.subtract(check);
+ part._d = diff._d.slice();
+ }
+
+ return [new BigInteger(quot.reverse(), sign, CONSTRUCT),
+ new BigInteger(part._d, this._s, CONSTRUCT)];
+};
+
+// Throws an exception if n is outside of (-BigInteger.base, -1] or
+// [1, BigInteger.base). It's not necessary to call this, since the
+// other division functions will call it if they are able to.
+BigInteger.prototype.divRemSmall = function(n) {
+ var r;
+ n = +n;
+ if (n === 0) {
+ throw new Error("Divide by zero");
+ }
+
+ var n_s = n < 0 ? -1 : 1;
+ var sign = this._s * n_s;
+ n = Math.abs(n);
+
+ if (n < 1 || n >= BigInteger_base) {
+ throw new Error("Argument out of range");
+ }
+
+ if (this._s === 0) {
+ return [ZERO, ZERO];
+ }
+
+ if (n === 1 || n === -1) {
+ return [(sign === 1) ? this.abs() : new BigInteger(this._d, sign, CONSTRUCT), ZERO];
+ }
+
+ // 2 <= n < BigInteger_base
+
+ // divide a single digit by a single digit
+ if (this._d.length === 1) {
+ var q = new BigInteger([(this._d[0] / n) | 0], 1, CONSTRUCT);
+ r = new BigInteger([(this._d[0] % n) | 0], 1, CONSTRUCT);
+ if (sign < 0) {
+ q = q.negate();
+ }
+ if (this._s < 0) {
+ r = r.negate();
+ }
+ return [q, r];
+ }
+
+ var digits = this._d.slice();
+ var quot = new Array(digits.length);
+ var part = 0;
+ var diff = 0;
+ var i = 0;
+ var guess;
+
+ while (digits.length) {
+ part = part * BigInteger_base + digits[digits.length - 1];
+ if (part < n) {
+ quot[i++] = 0;
+ digits.pop();
+ diff = BigInteger_base * diff + part;
+ continue;
+ }
+ if (part === 0) {
+ guess = 0;
+ }
+ else {
+ guess = (part / n) | 0;
+ }
+
+ var check = n * guess;
+ diff = part - check;
+ quot[i++] = guess;
+ if (!guess) {
+ digits.pop();
+ continue;
+ }
+
+ digits.pop();
+ part = diff;
+ }
+
+ r = new BigInteger([diff], 1, CONSTRUCT);
+ if (this._s < 0) {
+ r = r.negate();
+ }
+ return [new BigInteger(quot.reverse(), sign, CONSTRUCT), r];
+};
+
+/*
+ Function: isEven
+ Return true iff *this* is divisible by two.
+
+ Note that <BigInteger.ZERO> is even.
+
+ Returns:
+
+ true if *this* is even, false otherwise.
+
+ See Also:
+
+ <isOdd>
+*/
+BigInteger.prototype.isEven = function() {
+ var digits = this._d;
+ return this._s === 0 || digits.length === 0 || (digits[0] % 2) === 0;
+};
+
+/*
+ Function: isOdd
+ Return true iff *this* is not divisible by two.
+
+ Returns:
+
+ true if *this* is odd, false otherwise.
+
+ See Also:
+
+ <isEven>
+*/
+BigInteger.prototype.isOdd = function() {
+ return !this.isEven();
+};
+
+/*
+ Function: sign
+ Get the sign of a <BigInteger>.
+
+ Returns:
+
+ * -1 if *this* < 0
+ * 0 if *this* == 0
+ * +1 if *this* > 0
+
+ See Also:
+
+ <isZero>, <isPositive>, <isNegative>, <compare>, <BigInteger.ZERO>
+*/
+BigInteger.prototype.sign = function() {
+ return this._s;
+};
+
+/*
+ Function: isPositive
+ Return true iff *this* > 0.
+
+ Returns:
+
+ true if *this*.compare(<BigInteger.ZERO>) == 1.
+
+ See Also:
+
+ <sign>, <isZero>, <isNegative>, <isUnit>, <compare>, <BigInteger.ZERO>
+*/
+BigInteger.prototype.isPositive = function() {
+ return this._s > 0;
+};
+
+/*
+ Function: isNegative
+ Return true iff *this* < 0.
+
+ Returns:
+
+ true if *this*.compare(<BigInteger.ZERO>) == -1.
+
+ See Also:
+
+ <sign>, <isPositive>, <isZero>, <isUnit>, <compare>, <BigInteger.ZERO>
+*/
+BigInteger.prototype.isNegative = function() {
+ return this._s < 0;
+};
+
+/*
+ Function: isZero
+ Return true iff *this* == 0.
+
+ Returns:
+
+ true if *this*.compare(<BigInteger.ZERO>) == 0.
+
+ See Also:
+
+ <sign>, <isPositive>, <isNegative>, <isUnit>, <BigInteger.ZERO>
+*/
+BigInteger.prototype.isZero = function() {
+ return this._s === 0;
+};
+
+/*
+ Function: exp10
+ Multiply a <BigInteger> by a power of 10.
+
+ This is equivalent to, but faster than
+
+ > if (n >= 0) {
+ > return this.multiply(BigInteger("1e" + n));
+ > }
+ > else { // n <= 0
+ > return this.quotient(BigInteger("1e" + -n));
+ > }
+
+ Parameters:
+
+ n - The power of 10 to multiply *this* by. *n* is converted to a
+ javascipt number and must be no greater than <BigInteger.MAX_EXP>
+ (0x7FFFFFFF), or an exception will be thrown.
+
+ Returns:
+
+ *this* * (10 ** *n*), truncated to an integer if necessary.
+
+ See Also:
+
+ <pow>, <multiply>
+*/
+BigInteger.prototype.exp10 = function(n) {
+ n = +n;
+ if (n === 0) {
+ return this;
+ }
+ if (Math.abs(n) > Number(MAX_EXP)) {
+ throw new Error("exponent too large in BigInteger.exp10");
+ }
+ // Optimization for this == 0. This also keeps us from having to trim zeros in the positive n case
+ if (this._s === 0) {
+ return ZERO;
+ }
+ if (n > 0) {
+ var k = new BigInteger(this._d.slice(), this._s, CONSTRUCT);
+
+ for (; n >= BigInteger_base_log10; n -= BigInteger_base_log10) {
+ k._d.unshift(0);
+ }
+ if (n == 0)
+ return k;
+ k._s = 1;
+ k = k.multiplySingleDigit(Math.pow(10, n));
+ return (this._s < 0 ? k.negate() : k);
+ } else if (-n >= this._d.length*BigInteger_base_log10) {
+ return ZERO;
+ } else {
+ var k = new BigInteger(this._d.slice(), this._s, CONSTRUCT);
+
+ for (n = -n; n >= BigInteger_base_log10; n -= BigInteger_base_log10) {
+ k._d.shift();
+ }
+ return (n == 0) ? k : k.divRemSmall(Math.pow(10, n))[0];
+ }
+};
+
+/*
+ Function: pow
+ Raise a <BigInteger> to a power.
+
+ In this implementation, 0**0 is 1.
+
+ Parameters:
+
+ n - The exponent to raise *this* by. *n* must be no greater than
+ <BigInteger.MAX_EXP> (0x7FFFFFFF), or an exception will be thrown.
+
+ Returns:
+
+ *this* raised to the *nth* power.
+
+ See Also:
+
+ <modPow>
+*/
+BigInteger.prototype.pow = function(n) {
+ if (this.isUnit()) {
+ if (this._s > 0) {
+ return this;
+ }
+ else {
+ return BigInteger(n).isOdd() ? this : this.negate();
+ }
+ }
+
+ n = BigInteger(n);
+ if (n._s === 0) {
+ return ONE;
+ }
+ else if (n._s < 0) {
+ if (this._s === 0) {
+ throw new Error("Divide by zero");
+ }
+ else {
+ return ZERO;
+ }
+ }
+ if (this._s === 0) {
+ return ZERO;
+ }
+ if (n.isUnit()) {
+ return this;
+ }
+
+ if (n.compareAbs(MAX_EXP) > 0) {
+ throw new Error("exponent too large in BigInteger.pow");
+ }
+ var x = this;
+ var aux = ONE;
+ var two = BigInteger.small[2];
+
+ while (n.isPositive()) {
+ if (n.isOdd()) {
+ aux = aux.multiply(x);
+ if (n.isUnit()) {
+ return aux;
+ }
+ }
+ x = x.square();
+ n = n.quotient(two);
+ }
+
+ return aux;
+};
+
+/*
+ Function: modPow
+ Raise a <BigInteger> to a power (mod m).
+
+ Because it is reduced by a modulus, <modPow> is not limited by
+ <BigInteger.MAX_EXP> like <pow>.
+
+ Parameters:
+
+ exponent - The exponent to raise *this* by. Must be positive.
+ modulus - The modulus.
+
+ Returns:
+
+ *this* ^ *exponent* (mod *modulus*).
+
+ See Also:
+
+ <pow>, <mod>
+*/
+BigInteger.prototype.modPow = function(exponent, modulus) {
+ var result = ONE;
+ var base = this;
+
+ while (exponent.isPositive()) {
+ if (exponent.isOdd()) {
+ result = result.multiply(base).remainder(modulus);
+ }
+
+ exponent = exponent.quotient(BigInteger.small[2]);
+ if (exponent.isPositive()) {
+ base = base.square().remainder(modulus);
+ }
+ }
+
+ return result;
+};
+
+/*
+ Function: log
+ Get the natural logarithm of a <BigInteger> as a native JavaScript number.
+
+ This is equivalent to
+
+ > Math.log(this.toJSValue())
+
+ but handles values outside of the native number range.
+
+ Returns:
+
+ log( *this* )
+
+ See Also:
+
+ <toJSValue>
+*/
+BigInteger.prototype.log = function() {
+ switch (this._s) {
+ case 0: return -Infinity;
+ case -1: return NaN;
+ default: // Fall through.
+ }
+
+ var l = this._d.length;
+
+ if (l*BigInteger_base_log10 < 30) {
+ return Math.log(this.valueOf());
+ }
+
+ var N = Math.ceil(30/BigInteger_base_log10);
+ var firstNdigits = this._d.slice(l - N);
+ return Math.log((new BigInteger(firstNdigits, 1, CONSTRUCT)).valueOf()) + (l - N) * Math.log(BigInteger_base);
+};
+
+/*
+ Function: valueOf
+ Convert a <BigInteger> to a native JavaScript integer.
+
+ This is called automatically by JavaScipt to convert a <BigInteger> to a
+ native value.
+
+ Returns:
+
+ > parseInt(this.toString(), 10)
+
+ See Also:
+
+ <toString>, <toJSValue>
+*/
+BigInteger.prototype.valueOf = function() {
+ return parseInt(this.toString(), 10);
+};
+
+/*
+ Function: toJSValue
+ Convert a <BigInteger> to a native JavaScript integer.
+
+ This is the same as valueOf, but more explicitly named.
+
+ Returns:
+
+ > parseInt(this.toString(), 10)
+
+ See Also:
+
+ <toString>, <valueOf>
+*/
+BigInteger.prototype.toJSValue = function() {
+ return parseInt(this.toString(), 10);
+};
+
+var MAX_EXP = BigInteger(0x7FFFFFFF);
+// Constant: MAX_EXP
+// The largest exponent allowed in <pow> and <exp10> (0x7FFFFFFF or 2147483647).
+BigInteger.MAX_EXP = MAX_EXP;
+
+(function() {
+ function makeUnary(fn) {
+ return function(a) {
+ return fn.call(BigInteger(a));
+ };
+ }
+
+ function makeBinary(fn) {
+ return function(a, b) {
+ return fn.call(BigInteger(a), BigInteger(b));
+ };
+ }
+
+ function makeTrinary(fn) {
+ return function(a, b, c) {
+ return fn.call(BigInteger(a), BigInteger(b), BigInteger(c));
+ };
+ }
+
+ (function() {
+ var i, fn;
+ var unary = "toJSValue,isEven,isOdd,sign,isZero,isNegative,abs,isUnit,square,negate,isPositive,toString,next,prev,log".split(",");
+ var binary = "compare,remainder,divRem,subtract,add,quotient,divide,multiply,pow,compareAbs".split(",");
+ var trinary = ["modPow"];
+
+ for (i = 0; i < unary.length; i++) {
+ fn = unary[i];
+ BigInteger[fn] = makeUnary(BigInteger.prototype[fn]);
+ }
+
+ for (i = 0; i < binary.length; i++) {
+ fn = binary[i];
+ BigInteger[fn] = makeBinary(BigInteger.prototype[fn]);
+ }
+
+ for (i = 0; i < trinary.length; i++) {
+ fn = trinary[i];
+ BigInteger[fn] = makeTrinary(BigInteger.prototype[fn]);
+ }
+
+ BigInteger.exp10 = function(x, n) {
+ return BigInteger(x).exp10(n);
+ };
+ })();
+})();
+
+exports.BigInteger = BigInteger;
+})(typeof exports !== 'undefined' ? exports : this);
};
})();
-
-
-// BigInteger library included here because
-// only the entropy library depends on it
-// so if entropy detection is removed so is the dependency
-
-
-/*
- JavaScript BigInteger library version 0.9.1
- http://silentmatt.com/biginteger/
-
- Copyright (c) 2009 Matthew Crumley <email@matthewcrumley.com>
- Copyright (c) 2010,2011 by John Tobey <John.Tobey@gmail.com>
- Licensed under the MIT license.
-
- Support for arbitrary internal representation base was added by
- Vitaly Magerya.
-*/
-
-/*
- File: biginteger.js
-
- Exports:
-
- <BigInteger>
-*/
-(function(exports) {
-"use strict";
-/*
- Class: BigInteger
- An arbitrarily-large integer.
-
- <BigInteger> objects should be considered immutable. None of the "built-in"
- methods modify *this* or their arguments. All properties should be
- considered private.
-
- All the methods of <BigInteger> instances can be called "statically". The
- static versions are convenient if you don't already have a <BigInteger>
- object.
-
- As an example, these calls are equivalent.
-
- > BigInteger(4).multiply(5); // returns BigInteger(20);
- > BigInteger.multiply(4, 5); // returns BigInteger(20);
-
- > var a = 42;
- > var a = BigInteger.toJSValue("0b101010"); // Not completely useless...
-*/
-
-var CONSTRUCT = {}; // Unique token to call "private" version of constructor
-
-/*
- Constructor: BigInteger()
- Convert a value to a <BigInteger>.
-
- Although <BigInteger()> is the constructor for <BigInteger> objects, it is
- best not to call it as a constructor. If *n* is a <BigInteger> object, it is
- simply returned as-is. Otherwise, <BigInteger()> is equivalent to <parse>
- without a radix argument.
-
- > var n0 = BigInteger(); // Same as <BigInteger.ZERO>
- > var n1 = BigInteger("123"); // Create a new <BigInteger> with value 123
- > var n2 = BigInteger(123); // Create a new <BigInteger> with value 123
- > var n3 = BigInteger(n2); // Return n2, unchanged
-
- The constructor form only takes an array and a sign. *n* must be an
- array of numbers in little-endian order, where each digit is between 0
- and BigInteger.base. The second parameter sets the sign: -1 for
- negative, +1 for positive, or 0 for zero. The array is *not copied and
- may be modified*. If the array contains only zeros, the sign parameter
- is ignored and is forced to zero.
-
- > new BigInteger([5], -1): create a new BigInteger with value -5
-
- Parameters:
-
- n - Value to convert to a <BigInteger>.
-
- Returns:
-
- A <BigInteger> value.
-
- See Also:
-
- <parse>, <BigInteger>
-*/
-function BigInteger(n, s, token) {
- if (token !== CONSTRUCT) {
- if (n instanceof BigInteger) {
- return n;
- }
- else if (typeof n === "undefined") {
- return ZERO;
- }
- return BigInteger.parse(n);
- }
-
- n = n || []; // Provide the nullary constructor for subclasses.
- while (n.length && !n[n.length - 1]) {
- --n.length;
- }
- this._d = n;
- this._s = n.length ? (s || 1) : 0;
-}
-
-BigInteger._construct = function(n, s) {
- return new BigInteger(n, s, CONSTRUCT);
-};
-
-// Base-10 speedup hacks in parse, toString, exp10 and log functions
-// require base to be a power of 10. 10^7 is the largest such power
-// that won't cause a precision loss when digits are multiplied.
-var BigInteger_base = 10000000;
-var BigInteger_base_log10 = 7;
-
-BigInteger.base = BigInteger_base;
-BigInteger.base_log10 = BigInteger_base_log10;
-
-var ZERO = new BigInteger([], 0, CONSTRUCT);
-// Constant: ZERO
-// <BigInteger> 0.
-BigInteger.ZERO = ZERO;
-
-var ONE = new BigInteger([1], 1, CONSTRUCT);
-// Constant: ONE
-// <BigInteger> 1.
-BigInteger.ONE = ONE;
-
-var M_ONE = new BigInteger(ONE._d, -1, CONSTRUCT);
-// Constant: M_ONE
-// <BigInteger> -1.
-BigInteger.M_ONE = M_ONE;
-
-// Constant: _0
-// Shortcut for <ZERO>.
-BigInteger._0 = ZERO;
-
-// Constant: _1
-// Shortcut for <ONE>.
-BigInteger._1 = ONE;
-
-/*
- Constant: small
- Array of <BigIntegers> from 0 to 36.
-
- These are used internally for parsing, but useful when you need a "small"
- <BigInteger>.
-
- See Also:
-
- <ZERO>, <ONE>, <_0>, <_1>
-*/
-BigInteger.small = [
- ZERO,
- ONE,
- /* Assuming BigInteger_base > 36 */
- new BigInteger( [2], 1, CONSTRUCT),
- new BigInteger( [3], 1, CONSTRUCT),
- new BigInteger( [4], 1, CONSTRUCT),
- new BigInteger( [5], 1, CONSTRUCT),
- new BigInteger( [6], 1, CONSTRUCT),
- new BigInteger( [7], 1, CONSTRUCT),
- new BigInteger( [8], 1, CONSTRUCT),
- new BigInteger( [9], 1, CONSTRUCT),
- new BigInteger([10], 1, CONSTRUCT),
- new BigInteger([11], 1, CONSTRUCT),
- new BigInteger([12], 1, CONSTRUCT),
- new BigInteger([13], 1, CONSTRUCT),
- new BigInteger([14], 1, CONSTRUCT),
- new BigInteger([15], 1, CONSTRUCT),
- new BigInteger([16], 1, CONSTRUCT),
- new BigInteger([17], 1, CONSTRUCT),
- new BigInteger([18], 1, CONSTRUCT),
- new BigInteger([19], 1, CONSTRUCT),
- new BigInteger([20], 1, CONSTRUCT),
- new BigInteger([21], 1, CONSTRUCT),
- new BigInteger([22], 1, CONSTRUCT),
- new BigInteger([23], 1, CONSTRUCT),
- new BigInteger([24], 1, CONSTRUCT),
- new BigInteger([25], 1, CONSTRUCT),
- new BigInteger([26], 1, CONSTRUCT),
- new BigInteger([27], 1, CONSTRUCT),
- new BigInteger([28], 1, CONSTRUCT),
- new BigInteger([29], 1, CONSTRUCT),
- new BigInteger([30], 1, CONSTRUCT),
- new BigInteger([31], 1, CONSTRUCT),
- new BigInteger([32], 1, CONSTRUCT),
- new BigInteger([33], 1, CONSTRUCT),
- new BigInteger([34], 1, CONSTRUCT),
- new BigInteger([35], 1, CONSTRUCT),
- new BigInteger([36], 1, CONSTRUCT)
-];
-
-// Used for parsing/radix conversion
-BigInteger.digits = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ".split("");
-
-/*
- Method: toString
- Convert a <BigInteger> to a string.
-
- When *base* is greater than 10, letters are upper case.
-
- Parameters:
-
- base - Optional base to represent the number in (default is base 10).
- Must be between 2 and 36 inclusive, or an Error will be thrown.
-
- Returns:
-
- The string representation of the <BigInteger>.
-*/
-BigInteger.prototype.toString = function(base) {
- base = +base || 10;
- if (base < 2 || base > 36) {
- throw new Error("illegal radix " + base + ".");
- }
- if (this._s === 0) {
- return "0";
- }
- if (base === 10) {
- var str = this._s < 0 ? "-" : "";
- str += this._d[this._d.length - 1].toString();
- for (var i = this._d.length - 2; i >= 0; i--) {
- var group = this._d[i].toString();
- while (group.length < BigInteger_base_log10) group = '0' + group;
- str += group;
- }
- return str;
- }
- else {
- var numerals = BigInteger.digits;
- base = BigInteger.small[base];
- var sign = this._s;
-
- var n = this.abs();
- var digits = [];
- var digit;
-
- while (n._s !== 0) {
- var divmod = n.divRem(base);
- n = divmod[0];
- digit = divmod[1];
- // TODO: This could be changed to unshift instead of reversing at the end.
- // Benchmark both to compare speeds.
- digits.push(numerals[digit.valueOf()]);
- }
- return (sign < 0 ? "-" : "") + digits.reverse().join("");
- }
-};
-
-// Verify strings for parsing
-BigInteger.radixRegex = [
- /^$/,
- /^$/,
- /^[01]*$/,
- /^[012]*$/,
- /^[0-3]*$/,
- /^[0-4]*$/,
- /^[0-5]*$/,
- /^[0-6]*$/,
- /^[0-7]*$/,
- /^[0-8]*$/,
- /^[0-9]*$/,
- /^[0-9aA]*$/,
- /^[0-9abAB]*$/,
- /^[0-9abcABC]*$/,
- /^[0-9a-dA-D]*$/,
- /^[0-9a-eA-E]*$/,
- /^[0-9a-fA-F]*$/,
- /^[0-9a-gA-G]*$/,
- /^[0-9a-hA-H]*$/,
- /^[0-9a-iA-I]*$/,
- /^[0-9a-jA-J]*$/,
- /^[0-9a-kA-K]*$/,
- /^[0-9a-lA-L]*$/,
- /^[0-9a-mA-M]*$/,
- /^[0-9a-nA-N]*$/,
- /^[0-9a-oA-O]*$/,
- /^[0-9a-pA-P]*$/,
- /^[0-9a-qA-Q]*$/,
- /^[0-9a-rA-R]*$/,
- /^[0-9a-sA-S]*$/,
- /^[0-9a-tA-T]*$/,
- /^[0-9a-uA-U]*$/,
- /^[0-9a-vA-V]*$/,
- /^[0-9a-wA-W]*$/,
- /^[0-9a-xA-X]*$/,
- /^[0-9a-yA-Y]*$/,
- /^[0-9a-zA-Z]*$/
-];
-
-/*
- Function: parse
- Parse a string into a <BigInteger>.
-
- *base* is optional but, if provided, must be from 2 to 36 inclusive. If
- *base* is not provided, it will be guessed based on the leading characters
- of *s* as follows:
-
- - "0x" or "0X": *base* = 16
- - "0c" or "0C": *base* = 8
- - "0b" or "0B": *base* = 2
- - else: *base* = 10
-
- If no base is provided, or *base* is 10, the number can be in exponential
- form. For example, these are all valid:
-
- > BigInteger.parse("1e9"); // Same as "1000000000"
- > BigInteger.parse("1.234*10^3"); // Same as 1234
- > BigInteger.parse("56789 * 10 ** -2"); // Same as 567
-
- If any characters fall outside the range defined by the radix, an exception
- will be thrown.
-
- Parameters:
-
- s - The string to parse.
- base - Optional radix (default is to guess based on *s*).
-
- Returns:
-
- a <BigInteger> instance.
-*/
-BigInteger.parse = function(s, base) {
- // Expands a number in exponential form to decimal form.
- // expandExponential("-13.441*10^5") === "1344100";
- // expandExponential("1.12300e-1") === "0.112300";
- // expandExponential(1000000000000000000000000000000) === "1000000000000000000000000000000";
- function expandExponential(str) {
- str = str.replace(/\s*[*xX]\s*10\s*(\^|\*\*)\s*/, "e");
-
- return str.replace(/^([+\-])?(\d+)\.?(\d*)[eE]([+\-]?\d+)$/, function(x, s, n, f, c) {
- c = +c;
- var l = c < 0;
- var i = n.length + c;
- x = (l ? n : f).length;
- c = ((c = Math.abs(c)) >= x ? c - x + l : 0);
- var z = (new Array(c + 1)).join("0");
- var r = n + f;
- return (s || "") + (l ? r = z + r : r += z).substr(0, i += l ? z.length : 0) + (i < r.length ? "." + r.substr(i) : "");
- });
- }
-
- s = s.toString();
- if (typeof base === "undefined" || +base === 10) {
- s = expandExponential(s);
- }
-
- var prefixRE;
- if (typeof base === "undefined") {
- prefixRE = '0[xcb]';
- }
- else if (base == 16) {
- prefixRE = '0x';
- }
- else if (base == 8) {
- prefixRE = '0c';
- }
- else if (base == 2) {
- prefixRE = '0b';
- }
- else {
- prefixRE = '';
- }
- var parts = new RegExp('^([+\\-]?)(' + prefixRE + ')?([0-9a-z]*)(?:\\.\\d*)?$', 'i').exec(s);
- if (parts) {
- var sign = parts[1] || "+";
- var baseSection = parts[2] || "";
- var digits = parts[3] || "";
-
- if (typeof base === "undefined") {
- // Guess base
- if (baseSection === "0x" || baseSection === "0X") { // Hex
- base = 16;
- }
- else if (baseSection === "0c" || baseSection === "0C") { // Octal
- base = 8;
- }
- else if (baseSection === "0b" || baseSection === "0B") { // Binary
- base = 2;
- }
- else {
- base = 10;
- }
- }
- else if (base < 2 || base > 36) {
- throw new Error("Illegal radix " + base + ".");
- }
-
- base = +base;
-
- // Check for digits outside the range
- if (!(BigInteger.radixRegex[base].test(digits))) {
- throw new Error("Bad digit for radix " + base);
- }
-
- // Strip leading zeros, and convert to array
- digits = digits.replace(/^0+/, "").split("");
- if (digits.length === 0) {
- return ZERO;
- }
-
- // Get the sign (we know it's not zero)
- sign = (sign === "-") ? -1 : 1;
-
- // Optimize 10
- if (base == 10) {
- var d = [];
- while (digits.length >= BigInteger_base_log10) {
- d.push(parseInt(digits.splice(digits.length-BigInteger.base_log10, BigInteger.base_log10).join(''), 10));
- }
- d.push(parseInt(digits.join(''), 10));
- return new BigInteger(d, sign, CONSTRUCT);
- }
-
- // Do the conversion
- var d = ZERO;
- base = BigInteger.small[base];
- var small = BigInteger.small;
- for (var i = 0; i < digits.length; i++) {
- d = d.multiply(base).add(small[parseInt(digits[i], 36)]);
- }
- return new BigInteger(d._d, sign, CONSTRUCT);
- }
- else {
- throw new Error("Invalid BigInteger format: " + s);
- }
-};
-
-/*
- Function: add
- Add two <BigIntegers>.
-
- Parameters:
-
- n - The number to add to *this*. Will be converted to a <BigInteger>.
-
- Returns:
-
- The numbers added together.
-
- See Also:
-
- <subtract>, <multiply>, <quotient>, <next>
-*/
-BigInteger.prototype.add = function(n) {
- if (this._s === 0) {
- return BigInteger(n);
- }
-
- n = BigInteger(n);
- if (n._s === 0) {
- return this;
- }
- if (this._s !== n._s) {
- n = n.negate();
- return this.subtract(n);
- }
-
- var a = this._d;
- var b = n._d;
- var al = a.length;
- var bl = b.length;
- var sum = new Array(Math.max(al, bl) + 1);
- var size = Math.min(al, bl);
- var carry = 0;
- var digit;
-
- for (var i = 0; i < size; i++) {
- digit = a[i] + b[i] + carry;
- sum[i] = digit % BigInteger_base;
- carry = (digit / BigInteger_base) | 0;
- }
- if (bl > al) {
- a = b;
- al = bl;
- }
- for (i = size; carry && i < al; i++) {
- digit = a[i] + carry;
- sum[i] = digit % BigInteger_base;
- carry = (digit / BigInteger_base) | 0;
- }
- if (carry) {
- sum[i] = carry;
- }
-
- for ( ; i < al; i++) {
- sum[i] = a[i];
- }
-
- return new BigInteger(sum, this._s, CONSTRUCT);
-};
-
-/*
- Function: negate
- Get the additive inverse of a <BigInteger>.
-
- Returns:
-
- A <BigInteger> with the same magnatude, but with the opposite sign.
-
- See Also:
-
- <abs>
-*/
-BigInteger.prototype.negate = function() {
- return new BigInteger(this._d, (-this._s) | 0, CONSTRUCT);
-};
-
-/*
- Function: abs
- Get the absolute value of a <BigInteger>.
-
- Returns:
-
- A <BigInteger> with the same magnatude, but always positive (or zero).
-
- See Also:
-
- <negate>
-*/
-BigInteger.prototype.abs = function() {
- return (this._s < 0) ? this.negate() : this;
-};
-
-/*
- Function: subtract
- Subtract two <BigIntegers>.
-
- Parameters:
-
- n - The number to subtract from *this*. Will be converted to a <BigInteger>.
-
- Returns:
-
- The *n* subtracted from *this*.
-
- See Also:
-
- <add>, <multiply>, <quotient>, <prev>
-*/
-BigInteger.prototype.subtract = function(n) {
- if (this._s === 0) {
- return BigInteger(n).negate();
- }
-
- n = BigInteger(n);
- if (n._s === 0) {
- return this;
- }
- if (this._s !== n._s) {
- n = n.negate();
- return this.add(n);
- }
-
- var m = this;
- // negative - negative => -|a| - -|b| => -|a| + |b| => |b| - |a|
- if (this._s < 0) {
- m = new BigInteger(n._d, 1, CONSTRUCT);
- n = new BigInteger(this._d, 1, CONSTRUCT);
- }
-
- // Both are positive => a - b
- var sign = m.compareAbs(n);
- if (sign === 0) {
- return ZERO;
- }
- else if (sign < 0) {
- // swap m and n
- var t = n;
- n = m;
- m = t;
- }
-
- // a > b
- var a = m._d;
- var b = n._d;
- var al = a.length;
- var bl = b.length;
- var diff = new Array(al); // al >= bl since a > b
- var borrow = 0;
- var i;
- var digit;
-
- for (i = 0; i < bl; i++) {
- digit = a[i] - borrow - b[i];
- if (digit < 0) {
- digit += BigInteger_base;
- borrow = 1;
- }
- else {
- borrow = 0;
- }
- diff[i] = digit;
- }
- for (i = bl; i < al; i++) {
- digit = a[i] - borrow;
- if (digit < 0) {
- digit += BigInteger_base;
- }
- else {
- diff[i++] = digit;
- break;
- }
- diff[i] = digit;
- }
- for ( ; i < al; i++) {
- diff[i] = a[i];
- }
-
- return new BigInteger(diff, sign, CONSTRUCT);
-};
-
-(function() {
- function addOne(n, sign) {
- var a = n._d;
- var sum = a.slice();
- var carry = true;
- var i = 0;
-
- while (true) {
- var digit = (a[i] || 0) + 1;
- sum[i] = digit % BigInteger_base;
- if (digit <= BigInteger_base - 1) {
- break;
- }
- ++i;
- }
-
- return new BigInteger(sum, sign, CONSTRUCT);
- }
-
- function subtractOne(n, sign) {
- var a = n._d;
- var sum = a.slice();
- var borrow = true;
- var i = 0;
-
- while (true) {
- var digit = (a[i] || 0) - 1;
- if (digit < 0) {
- sum[i] = digit + BigInteger_base;
- }
- else {
- sum[i] = digit;
- break;
- }
- ++i;
- }
-
- return new BigInteger(sum, sign, CONSTRUCT);
- }
-
- /*
- Function: next
- Get the next <BigInteger> (add one).
-
- Returns:
-
- *this* + 1.
-
- See Also:
-
- <add>, <prev>
- */
- BigInteger.prototype.next = function() {
- switch (this._s) {
- case 0:
- return ONE;
- case -1:
- return subtractOne(this, -1);
- // case 1:
- default:
- return addOne(this, 1);
- }
- };
-
- /*
- Function: prev
- Get the previous <BigInteger> (subtract one).
-
- Returns:
-
- *this* - 1.
-
- See Also:
-
- <next>, <subtract>
- */
- BigInteger.prototype.prev = function() {
- switch (this._s) {
- case 0:
- return M_ONE;
- case -1:
- return addOne(this, -1);
- // case 1:
- default:
- return subtractOne(this, 1);
- }
- };
-})();
-
-/*
- Function: compareAbs
- Compare the absolute value of two <BigIntegers>.
-
- Calling <compareAbs> is faster than calling <abs> twice, then <compare>.
-
- Parameters:
-
- n - The number to compare to *this*. Will be converted to a <BigInteger>.
-
- Returns:
-
- -1, 0, or +1 if *|this|* is less than, equal to, or greater than *|n|*.
-
- See Also:
-
- <compare>, <abs>
-*/
-BigInteger.prototype.compareAbs = function(n) {
- if (this === n) {
- return 0;
- }
-
- if (!(n instanceof BigInteger)) {
- if (!isFinite(n)) {
- return(isNaN(n) ? n : -1);
- }
- n = BigInteger(n);
- }
-
- if (this._s === 0) {
- return (n._s !== 0) ? -1 : 0;
- }
- if (n._s === 0) {
- return 1;
- }
-
- var l = this._d.length;
- var nl = n._d.length;
- if (l < nl) {
- return -1;
- }
- else if (l > nl) {
- return 1;
- }
-
- var a = this._d;
- var b = n._d;
- for (var i = l-1; i >= 0; i--) {
- if (a[i] !== b[i]) {
- return a[i] < b[i] ? -1 : 1;
- }
- }
-
- return 0;
-};
-
-/*
- Function: compare
- Compare two <BigIntegers>.
-
- Parameters:
-
- n - The number to compare to *this*. Will be converted to a <BigInteger>.
-
- Returns:
-
- -1, 0, or +1 if *this* is less than, equal to, or greater than *n*.
-
- See Also:
-
- <compareAbs>, <isPositive>, <isNegative>, <isUnit>
-*/
-BigInteger.prototype.compare = function(n) {
- if (this === n) {
- return 0;
- }
-
- n = BigInteger(n);
-
- if (this._s === 0) {
- return -n._s;
- }
-
- if (this._s === n._s) { // both positive or both negative
- var cmp = this.compareAbs(n);
- return cmp * this._s;
- }
- else {
- return this._s;
- }
-};
-
-/*
- Function: isUnit
- Return true iff *this* is either 1 or -1.
-
- Returns:
-
- true if *this* compares equal to <BigInteger.ONE> or <BigInteger.M_ONE>.
-
- See Also:
-
- <isZero>, <isNegative>, <isPositive>, <compareAbs>, <compare>,
- <BigInteger.ONE>, <BigInteger.M_ONE>
-*/
-BigInteger.prototype.isUnit = function() {
- return this === ONE ||
- this === M_ONE ||
- (this._d.length === 1 && this._d[0] === 1);
-};
-
-/*
- Function: multiply
- Multiply two <BigIntegers>.
-
- Parameters:
-
- n - The number to multiply *this* by. Will be converted to a
- <BigInteger>.
-
- Returns:
-
- The numbers multiplied together.
-
- See Also:
-
- <add>, <subtract>, <quotient>, <square>
-*/
-BigInteger.prototype.multiply = function(n) {
- // TODO: Consider adding Karatsuba multiplication for large numbers
- if (this._s === 0) {
- return ZERO;
- }
-
- n = BigInteger(n);
- if (n._s === 0) {
- return ZERO;
- }
- if (this.isUnit()) {
- if (this._s < 0) {
- return n.negate();
- }
- return n;
- }
- if (n.isUnit()) {
- if (n._s < 0) {
- return this.negate();
- }
- return this;
- }
- if (this === n) {
- return this.square();
- }
-
- var r = (this._d.length >= n._d.length);
- var a = (r ? this : n)._d; // a will be longer than b
- var b = (r ? n : this)._d;
- var al = a.length;
- var bl = b.length;
-
- var pl = al + bl;
- var partial = new Array(pl);
- var i;
- for (i = 0; i < pl; i++) {
- partial[i] = 0;
- }
-
- for (i = 0; i < bl; i++) {
- var carry = 0;
- var bi = b[i];
- var jlimit = al + i;
- var digit;
- for (var j = i; j < jlimit; j++) {
- digit = partial[j] + bi * a[j - i] + carry;
- carry = (digit / BigInteger_base) | 0;
- partial[j] = (digit % BigInteger_base) | 0;
- }
- if (carry) {
- digit = partial[j] + carry;
- carry = (digit / BigInteger_base) | 0;
- partial[j] = digit % BigInteger_base;
- }
- }
- return new BigInteger(partial, this._s * n._s, CONSTRUCT);
-};
-
-// Multiply a BigInteger by a single-digit native number
-// Assumes that this and n are >= 0
-// This is not really intended to be used outside the library itself
-BigInteger.prototype.multiplySingleDigit = function(n) {
- if (n === 0 || this._s === 0) {
- return ZERO;
- }
- if (n === 1) {
- return this;
- }
-
- var digit;
- if (this._d.length === 1) {
- digit = this._d[0] * n;
- if (digit >= BigInteger_base) {
- return new BigInteger([(digit % BigInteger_base)|0,
- (digit / BigInteger_base)|0], 1, CONSTRUCT);
- }
- return new BigInteger([digit], 1, CONSTRUCT);
- }
-
- if (n === 2) {
- return this.add(this);
- }
- if (this.isUnit()) {
- return new BigInteger([n], 1, CONSTRUCT);
- }
-
- var a = this._d;
- var al = a.length;
-
- var pl = al + 1;
- var partial = new Array(pl);
- for (var i = 0; i < pl; i++) {
- partial[i] = 0;
- }
-
- var carry = 0;
- for (var j = 0; j < al; j++) {
- digit = n * a[j] + carry;
- carry = (digit / BigInteger_base) | 0;
- partial[j] = (digit % BigInteger_base) | 0;
- }
- if (carry) {
- partial[j] = carry;
- }
-
- return new BigInteger(partial, 1, CONSTRUCT);
-};
-
-/*
- Function: square
- Multiply a <BigInteger> by itself.
-
- This is slightly faster than regular multiplication, since it removes the
- duplicated multiplcations.
-
- Returns:
-
- > this.multiply(this)
-
- See Also:
- <multiply>
-*/
-BigInteger.prototype.square = function() {
- // Normally, squaring a 10-digit number would take 100 multiplications.
- // Of these 10 are unique diagonals, of the remaining 90 (100-10), 45 are repeated.
- // This procedure saves (N*(N-1))/2 multiplications, (e.g., 45 of 100 multiplies).
- // Based on code by Gary Darby, Intellitech Systems Inc., www.DelphiForFun.org
-
- if (this._s === 0) {
- return ZERO;
- }
- if (this.isUnit()) {
- return ONE;
- }
-
- var digits = this._d;
- var length = digits.length;
- var imult1 = new Array(length + length + 1);
- var product, carry, k;
- var i;
-
- // Calculate diagonal
- for (i = 0; i < length; i++) {
- k = i * 2;
- product = digits[i] * digits[i];
- carry = (product / BigInteger_base) | 0;
- imult1[k] = product % BigInteger_base;
- imult1[k + 1] = carry;
- }
-
- // Calculate repeating part
- for (i = 0; i < length; i++) {
- carry = 0;
- k = i * 2 + 1;
- for (var j = i + 1; j < length; j++, k++) {
- product = digits[j] * digits[i] * 2 + imult1[k] + carry;
- carry = (product / BigInteger_base) | 0;
- imult1[k] = product % BigInteger_base;
- }
- k = length + i;
- var digit = carry + imult1[k];
- carry = (digit / BigInteger_base) | 0;
- imult1[k] = digit % BigInteger_base;
- imult1[k + 1] += carry;
- }
-
- return new BigInteger(imult1, 1, CONSTRUCT);
-};
-
-/*
- Function: quotient
- Divide two <BigIntegers> and truncate towards zero.
-
- <quotient> throws an exception if *n* is zero.
-
- Parameters:
-
- n - The number to divide *this* by. Will be converted to a <BigInteger>.
-
- Returns:
-
- The *this* / *n*, truncated to an integer.
-
- See Also:
-
- <add>, <subtract>, <multiply>, <divRem>, <remainder>
-*/
-BigInteger.prototype.quotient = function(n) {
- return this.divRem(n)[0];
-};
-
-/*
- Function: divide
- Deprecated synonym for <quotient>.
-*/
-BigInteger.prototype.divide = BigInteger.prototype.quotient;
-
-/*
- Function: remainder
- Calculate the remainder of two <BigIntegers>.
-
- <remainder> throws an exception if *n* is zero.
-
- Parameters:
-
- n - The remainder after *this* is divided *this* by *n*. Will be
- converted to a <BigInteger>.
-
- Returns:
-
- *this* % *n*.
-
- See Also:
-
- <divRem>, <quotient>
-*/
-BigInteger.prototype.remainder = function(n) {
- return this.divRem(n)[1];
-};
-
-/*
- Function: divRem
- Calculate the integer quotient and remainder of two <BigIntegers>.
-
- <divRem> throws an exception if *n* is zero.
-
- Parameters:
-
- n - The number to divide *this* by. Will be converted to a <BigInteger>.
-
- Returns:
-
- A two-element array containing the quotient and the remainder.
-
- > a.divRem(b)
-
- is exactly equivalent to
-
- > [a.quotient(b), a.remainder(b)]
-
- except it is faster, because they are calculated at the same time.
-
- See Also:
-
- <quotient>, <remainder>
-*/
-BigInteger.prototype.divRem = function(n) {
- n = BigInteger(n);
- if (n._s === 0) {
- throw new Error("Divide by zero");
- }
- if (this._s === 0) {
- return [ZERO, ZERO];
- }
- if (n._d.length === 1) {
- return this.divRemSmall(n._s * n._d[0]);
- }
-
- // Test for easy cases -- |n1| <= |n2|
- switch (this.compareAbs(n)) {
- case 0: // n1 == n2
- return [this._s === n._s ? ONE : M_ONE, ZERO];
- case -1: // |n1| < |n2|
- return [ZERO, this];
- }
-
- var sign = this._s * n._s;
- var a = n.abs();
- var b_digits = this._d;
- var b_index = b_digits.length;
- var digits = n._d.length;
- var quot = [];
- var guess;
-
- var part = new BigInteger([], 0, CONSTRUCT);
-
- while (b_index) {
- part._d.unshift(b_digits[--b_index]);
- part = new BigInteger(part._d, 1, CONSTRUCT);
-
- if (part.compareAbs(n) < 0) {
- quot.push(0);
- continue;
- }
- if (part._s === 0) {
- guess = 0;
- }
- else {
- var xlen = part._d.length, ylen = a._d.length;
- var highx = part._d[xlen-1]*BigInteger_base + part._d[xlen-2];
- var highy = a._d[ylen-1]*BigInteger_base + a._d[ylen-2];
- if (part._d.length > a._d.length) {
- // The length of part._d can either match a._d length,
- // or exceed it by one.
- highx = (highx+1)*BigInteger_base;
- }
- guess = Math.ceil(highx/highy);
- }
- do {
- var check = a.multiplySingleDigit(guess);
- if (check.compareAbs(part) <= 0) {
- break;
- }
- guess--;
- } while (guess);
-
- quot.push(guess);
- if (!guess) {
- continue;
- }
- var diff = part.subtract(check);
- part._d = diff._d.slice();
- }
-
- return [new BigInteger(quot.reverse(), sign, CONSTRUCT),
- new BigInteger(part._d, this._s, CONSTRUCT)];
-};
-
-// Throws an exception if n is outside of (-BigInteger.base, -1] or
-// [1, BigInteger.base). It's not necessary to call this, since the
-// other division functions will call it if they are able to.
-BigInteger.prototype.divRemSmall = function(n) {
- var r;
- n = +n;
- if (n === 0) {
- throw new Error("Divide by zero");
- }
-
- var n_s = n < 0 ? -1 : 1;
- var sign = this._s * n_s;
- n = Math.abs(n);
-
- if (n < 1 || n >= BigInteger_base) {
- throw new Error("Argument out of range");
- }
-
- if (this._s === 0) {
- return [ZERO, ZERO];
- }
-
- if (n === 1 || n === -1) {
- return [(sign === 1) ? this.abs() : new BigInteger(this._d, sign, CONSTRUCT), ZERO];
- }
-
- // 2 <= n < BigInteger_base
-
- // divide a single digit by a single digit
- if (this._d.length === 1) {
- var q = new BigInteger([(this._d[0] / n) | 0], 1, CONSTRUCT);
- r = new BigInteger([(this._d[0] % n) | 0], 1, CONSTRUCT);
- if (sign < 0) {
- q = q.negate();
- }
- if (this._s < 0) {
- r = r.negate();
- }
- return [q, r];
- }
-
- var digits = this._d.slice();
- var quot = new Array(digits.length);
- var part = 0;
- var diff = 0;
- var i = 0;
- var guess;
-
- while (digits.length) {
- part = part * BigInteger_base + digits[digits.length - 1];
- if (part < n) {
- quot[i++] = 0;
- digits.pop();
- diff = BigInteger_base * diff + part;
- continue;
- }
- if (part === 0) {
- guess = 0;
- }
- else {
- guess = (part / n) | 0;
- }
-
- var check = n * guess;
- diff = part - check;
- quot[i++] = guess;
- if (!guess) {
- digits.pop();
- continue;
- }
-
- digits.pop();
- part = diff;
- }
-
- r = new BigInteger([diff], 1, CONSTRUCT);
- if (this._s < 0) {
- r = r.negate();
- }
- return [new BigInteger(quot.reverse(), sign, CONSTRUCT), r];
-};
-
-/*
- Function: isEven
- Return true iff *this* is divisible by two.
-
- Note that <BigInteger.ZERO> is even.
-
- Returns:
-
- true if *this* is even, false otherwise.
-
- See Also:
-
- <isOdd>
-*/
-BigInteger.prototype.isEven = function() {
- var digits = this._d;
- return this._s === 0 || digits.length === 0 || (digits[0] % 2) === 0;
-};
-
-/*
- Function: isOdd
- Return true iff *this* is not divisible by two.
-
- Returns:
-
- true if *this* is odd, false otherwise.
-
- See Also:
-
- <isEven>
-*/
-BigInteger.prototype.isOdd = function() {
- return !this.isEven();
-};
-
-/*
- Function: sign
- Get the sign of a <BigInteger>.
-
- Returns:
-
- * -1 if *this* < 0
- * 0 if *this* == 0
- * +1 if *this* > 0
-
- See Also:
-
- <isZero>, <isPositive>, <isNegative>, <compare>, <BigInteger.ZERO>
-*/
-BigInteger.prototype.sign = function() {
- return this._s;
-};
-
-/*
- Function: isPositive
- Return true iff *this* > 0.
-
- Returns:
-
- true if *this*.compare(<BigInteger.ZERO>) == 1.
-
- See Also:
-
- <sign>, <isZero>, <isNegative>, <isUnit>, <compare>, <BigInteger.ZERO>
-*/
-BigInteger.prototype.isPositive = function() {
- return this._s > 0;
-};
-
-/*
- Function: isNegative
- Return true iff *this* < 0.
-
- Returns:
-
- true if *this*.compare(<BigInteger.ZERO>) == -1.
-
- See Also:
-
- <sign>, <isPositive>, <isZero>, <isUnit>, <compare>, <BigInteger.ZERO>
-*/
-BigInteger.prototype.isNegative = function() {
- return this._s < 0;
-};
-
-/*
- Function: isZero
- Return true iff *this* == 0.
-
- Returns:
-
- true if *this*.compare(<BigInteger.ZERO>) == 0.
-
- See Also:
-
- <sign>, <isPositive>, <isNegative>, <isUnit>, <BigInteger.ZERO>
-*/
-BigInteger.prototype.isZero = function() {
- return this._s === 0;
-};
-
-/*
- Function: exp10
- Multiply a <BigInteger> by a power of 10.
-
- This is equivalent to, but faster than
-
- > if (n >= 0) {
- > return this.multiply(BigInteger("1e" + n));
- > }
- > else { // n <= 0
- > return this.quotient(BigInteger("1e" + -n));
- > }
-
- Parameters:
-
- n - The power of 10 to multiply *this* by. *n* is converted to a
- javascipt number and must be no greater than <BigInteger.MAX_EXP>
- (0x7FFFFFFF), or an exception will be thrown.
-
- Returns:
-
- *this* * (10 ** *n*), truncated to an integer if necessary.
-
- See Also:
-
- <pow>, <multiply>
-*/
-BigInteger.prototype.exp10 = function(n) {
- n = +n;
- if (n === 0) {
- return this;
- }
- if (Math.abs(n) > Number(MAX_EXP)) {
- throw new Error("exponent too large in BigInteger.exp10");
- }
- // Optimization for this == 0. This also keeps us from having to trim zeros in the positive n case
- if (this._s === 0) {
- return ZERO;
- }
- if (n > 0) {
- var k = new BigInteger(this._d.slice(), this._s, CONSTRUCT);
-
- for (; n >= BigInteger_base_log10; n -= BigInteger_base_log10) {
- k._d.unshift(0);
- }
- if (n == 0)
- return k;
- k._s = 1;
- k = k.multiplySingleDigit(Math.pow(10, n));
- return (this._s < 0 ? k.negate() : k);
- } else if (-n >= this._d.length*BigInteger_base_log10) {
- return ZERO;
- } else {
- var k = new BigInteger(this._d.slice(), this._s, CONSTRUCT);
-
- for (n = -n; n >= BigInteger_base_log10; n -= BigInteger_base_log10) {
- k._d.shift();
- }
- return (n == 0) ? k : k.divRemSmall(Math.pow(10, n))[0];
- }
-};
-
-/*
- Function: pow
- Raise a <BigInteger> to a power.
-
- In this implementation, 0**0 is 1.
-
- Parameters:
-
- n - The exponent to raise *this* by. *n* must be no greater than
- <BigInteger.MAX_EXP> (0x7FFFFFFF), or an exception will be thrown.
-
- Returns:
-
- *this* raised to the *nth* power.
-
- See Also:
-
- <modPow>
-*/
-BigInteger.prototype.pow = function(n) {
- if (this.isUnit()) {
- if (this._s > 0) {
- return this;
- }
- else {
- return BigInteger(n).isOdd() ? this : this.negate();
- }
- }
-
- n = BigInteger(n);
- if (n._s === 0) {
- return ONE;
- }
- else if (n._s < 0) {
- if (this._s === 0) {
- throw new Error("Divide by zero");
- }
- else {
- return ZERO;
- }
- }
- if (this._s === 0) {
- return ZERO;
- }
- if (n.isUnit()) {
- return this;
- }
-
- if (n.compareAbs(MAX_EXP) > 0) {
- throw new Error("exponent too large in BigInteger.pow");
- }
- var x = this;
- var aux = ONE;
- var two = BigInteger.small[2];
-
- while (n.isPositive()) {
- if (n.isOdd()) {
- aux = aux.multiply(x);
- if (n.isUnit()) {
- return aux;
- }
- }
- x = x.square();
- n = n.quotient(two);
- }
-
- return aux;
-};
-
-/*
- Function: modPow
- Raise a <BigInteger> to a power (mod m).
-
- Because it is reduced by a modulus, <modPow> is not limited by
- <BigInteger.MAX_EXP> like <pow>.
-
- Parameters:
-
- exponent - The exponent to raise *this* by. Must be positive.
- modulus - The modulus.
-
- Returns:
-
- *this* ^ *exponent* (mod *modulus*).
-
- See Also:
-
- <pow>, <mod>
-*/
-BigInteger.prototype.modPow = function(exponent, modulus) {
- var result = ONE;
- var base = this;
-
- while (exponent.isPositive()) {
- if (exponent.isOdd()) {
- result = result.multiply(base).remainder(modulus);
- }
-
- exponent = exponent.quotient(BigInteger.small[2]);
- if (exponent.isPositive()) {
- base = base.square().remainder(modulus);
- }
- }
-
- return result;
-};
-
-/*
- Function: log
- Get the natural logarithm of a <BigInteger> as a native JavaScript number.
-
- This is equivalent to
-
- > Math.log(this.toJSValue())
-
- but handles values outside of the native number range.
-
- Returns:
-
- log( *this* )
-
- See Also:
-
- <toJSValue>
-*/
-BigInteger.prototype.log = function() {
- switch (this._s) {
- case 0: return -Infinity;
- case -1: return NaN;
- default: // Fall through.
- }
-
- var l = this._d.length;
-
- if (l*BigInteger_base_log10 < 30) {
- return Math.log(this.valueOf());
- }
-
- var N = Math.ceil(30/BigInteger_base_log10);
- var firstNdigits = this._d.slice(l - N);
- return Math.log((new BigInteger(firstNdigits, 1, CONSTRUCT)).valueOf()) + (l - N) * Math.log(BigInteger_base);
-};
-
-/*
- Function: valueOf
- Convert a <BigInteger> to a native JavaScript integer.
-
- This is called automatically by JavaScipt to convert a <BigInteger> to a
- native value.
-
- Returns:
-
- > parseInt(this.toString(), 10)
-
- See Also:
-
- <toString>, <toJSValue>
-*/
-BigInteger.prototype.valueOf = function() {
- return parseInt(this.toString(), 10);
-};
-
-/*
- Function: toJSValue
- Convert a <BigInteger> to a native JavaScript integer.
-
- This is the same as valueOf, but more explicitly named.
-
- Returns:
-
- > parseInt(this.toString(), 10)
-
- See Also:
-
- <toString>, <valueOf>
-*/
-BigInteger.prototype.toJSValue = function() {
- return parseInt(this.toString(), 10);
-};
-
-var MAX_EXP = BigInteger(0x7FFFFFFF);
-// Constant: MAX_EXP
-// The largest exponent allowed in <pow> and <exp10> (0x7FFFFFFF or 2147483647).
-BigInteger.MAX_EXP = MAX_EXP;
-
-(function() {
- function makeUnary(fn) {
- return function(a) {
- return fn.call(BigInteger(a));
- };
- }
-
- function makeBinary(fn) {
- return function(a, b) {
- return fn.call(BigInteger(a), BigInteger(b));
- };
- }
-
- function makeTrinary(fn) {
- return function(a, b, c) {
- return fn.call(BigInteger(a), BigInteger(b), BigInteger(c));
- };
- }
-
- (function() {
- var i, fn;
- var unary = "toJSValue,isEven,isOdd,sign,isZero,isNegative,abs,isUnit,square,negate,isPositive,toString,next,prev,log".split(",");
- var binary = "compare,remainder,divRem,subtract,add,quotient,divide,multiply,pow,compareAbs".split(",");
- var trinary = ["modPow"];
-
- for (i = 0; i < unary.length; i++) {
- fn = unary[i];
- BigInteger[fn] = makeUnary(BigInteger.prototype[fn]);
- }
-
- for (i = 0; i < binary.length; i++) {
- fn = binary[i];
- BigInteger[fn] = makeBinary(BigInteger.prototype[fn]);
- }
-
- for (i = 0; i < trinary.length; i++) {
- fn = trinary[i];
- BigInteger[fn] = makeTrinary(BigInteger.prototype[fn]);
- }
-
- BigInteger.exp10 = function(x, n) {
- return BigInteger(x).exp10(n);
- };
- })();
-})();
-
-exports.BigInteger = BigInteger;
-})(typeof exports !== 'undefined' ? exports : this);
projects / perso / Immae / Projets / Cryptomonnaies / BIP39.git / commitdiff
