/*
* Detects entropy from a string.
*
* Formats include:
* binary [0-1]
* base 6 [0-5]
* dice 6 [1-6]
* decimal [0-9]
* hexadecimal [0-9A-F]
*
* Automatically uses lowest entropy to avoid issues such as interpretting 0101
* as hexadecimal which would be 16 bits when really it's only 4 bits of binary
* entropy.
*/
window.Entropy = new (function() {
// matchers returns an array of the matched events for each type of entropy.
// eg
// matchers.binary("010") returns ["0", "1", "0"]
// matchers.binary("a10") returns ["1", "0"]
// matchers.hex("a10") returns ["a", "1", "0"]
var matchers = {
binary: function(str) {
return str.match(/[0-1]/gi) || [];
},
base6: function(str) {
return str.match(/[0-5]/gi) || [];
},
dice: function(str) {
return str.match(/[1-6]/gi) || []; // ie dice numbers
},
base10: function(str) {
return str.match(/[0-9]/gi) || [];
},
hex: function(str) {
return str.match(/[0-9A-F]/gi) || [];
},
card: function(str) {
// Format is NumberSuit, eg
// AH ace of hearts
// 8C eight of clubs
// TD ten of diamonds
// JS jack of spades
// QH queen of hearts
// KC king of clubs
return str.match(/([A2-9TJQK][CDHS])/gi) || [];
}
}
// Convert array of cards from ["ac", "4d", "ks"]
// to numbers between 0 and 51 [0, 16, 51]
function convertCardsToInts(cards) {
var ints = [];
var values = "a23456789tjqk";
var suits = "cdhs";
for (var i=0; i<cards.length; i++) {
var card = cards[i].toLowerCase();
var value = card[0];
var suit = card[1];
var asInt = 13 * suits.indexOf(suit) + values.indexOf(value);
ints.push(asInt);
}
return ints;
}
this.fromString = function(rawEntropyStr) {
// Find type of entropy being used (binary, hex, dice etc)
var base = getBase(rawEntropyStr);
// Convert dice to base6 entropy (ie 1-6 to 0-5)
// This is done by changing all 6s to 0s
if (base.str == "dice") {
var newParts = [];
var newInts = [];
for (var i=0; i<base.parts.length; i++) {
var c = base.parts[i];
if ("12345".indexOf(c) > -1) {
newParts[i] = base.parts[i];
newInts[i] = base.ints[i];
}
else {
newParts[i] = "0";
newInts[i] = 0;
}
}
base.str = "base 6 (dice)";
base.ints = newInts;
base.parts = newParts;
base.matcher = matchers.base6;
}
// Detect empty entropy
if (base.parts.length == 0) {
return {
binaryStr: "",
cleanStr: "",
cleanHtml: "",
base: base,
};
}
// Convert base.ints to BigInteger.
// Due to using unusual bases, eg cards of base52, this is not as simple as
// using BigInteger.parse()
var entropyInt = BigInteger.ZERO;
for (var i=base.ints.length-1; i>=0; i--) {
var thisInt = BigInteger.parse(base.ints[i]);
var power = (base.ints.length - 1) - i;
var additionalEntropy = BigInteger.parse(base.asInt).pow(power).multiply(thisInt);
entropyInt = entropyInt.add(additionalEntropy);
}
// Convert entropy to binary
var entropyBin = entropyInt.toString(2);
// If the first integer is small, it must be padded with zeros.
// Otherwise the chance of the first bit being 1 is 100%, which is
// obviously incorrect.
// This is not perfect for non-2^n bases.
var expectedBits = Math.floor(base.parts.length * Math.log2(base.asInt));
while (entropyBin.length < expectedBits) {
entropyBin = "0" + entropyBin;
}
// Supply a 'filtered' entropy string for display purposes
var entropyClean = base.parts.join("");
var entropyHtml = base.parts.join("");
if (base.asInt == 52) {
entropyClean = base.parts.join(" ").toUpperCase();
entropyClean = entropyClean.replace(/C/g, "\u2663");
entropyClean = entropyClean.replace(/D/g, "\u2666");
entropyClean = entropyClean.replace(/H/g, "\u2665");
entropyClean = entropyClean.replace(/S/g, "\u2660");
entropyHtml = base.parts.join(" ").toUpperCase();
entropyHtml = entropyHtml.replace(/C/g, "<span class='card-suit club'>\u2663</span>");
entropyHtml = entropyHtml.replace(/D/g, "<span class='card-suit diamond'>\u2666</span>");
entropyHtml = entropyHtml.replace(/H/g, "<span class='card-suit heart'>\u2665</span>");
entropyHtml = entropyHtml.replace(/S/g, "<span class='card-suit spade'>\u2660</span>");
}
var e = {
binaryStr: entropyBin,
cleanStr: entropyClean,
cleanHtml: entropyHtml,
base: base,
}
return e;
}
function getBase(str) {
// Need to get the lowest base for the supplied entropy.
// This prevents interpreting, say, dice rolls as hexadecimal.
var binaryMatches = matchers.binary(str);
var hexMatches = matchers.hex(str);
// Find the lowest base that can be used, whilst ignoring any irrelevant chars
if (binaryMatches.length == hexMatches.length && hexMatches.length > 0) {
var ints = binaryMatches.map(function(i) { return parseInt(i, 2) });
return {
ints: ints,
parts: binaryMatches,
matcher: matchers.binary,
asInt: 2,
str: "binary",
}
}
var cardMatches = matchers.card(str);
if (cardMatches.length >= hexMatches.length / 2) {
var ints = convertCardsToInts(cardMatches);
return {
ints: ints,
parts: cardMatches,
matcher: matchers.card,
asInt: 52,
str: "card",
}
}
var diceMatches = matchers.dice(str);
if (diceMatches.length == hexMatches.length && hexMatches.length > 0) {
var ints = diceMatches.map(function(i) { return parseInt(i) });
return {
ints: ints,
parts: diceMatches,
matcher: matchers.dice,
asInt: 6,
str: "dice",
}
}
var base6Matches = matchers.base6(str);
if (base6Matches.length == hexMatches.length && hexMatches.length > 0) {
var ints = base6Matches.map(function(i) { return parseInt(i) });
return {
ints: ints,
parts: base6Matches,
matcher: matchers.base6,
asInt: 6,
str: "base 6",
}
}
var base10Matches = matchers.base10(str);
if (base10Matches.length == hexMatches.length && hexMatches.length > 0) {
var ints = base10Matches.map(function(i) { return parseInt(i) });
return {
ints: ints,
parts: base10Matches,
matcher: matchers.base10,
asInt: 10,
str: "base 10",
}
}
var ints = hexMatches.map(function(i) { return parseInt(i, 16) });
return {
ints: ints,
parts: hexMatches,
matcher: matchers.hex,
asInt: 16,
str: "hexadecimal",
}
}
// Polyfill for Math.log2
// See https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Math/log2#Polyfill
Math.log2 = Math.log2 || function(x) {
// The polyfill isn't good enough because of the poor accuracy of
// Math.LOG2E
// log2(8) gave 2.9999999999999996 which when floored causes issues.
// So instead use the BigInteger library to get it right.
return BigInteger.log(x) / BigInteger.log(2);
};
})();
// 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);