]>
git.immae.eu Git - perso/Immae/Projets/Cryptomonnaies/BIP39.git/blob - src/js/entropy.js
2 * Detects entropy from a string.
11 * Automatically uses lowest entropy to avoid issues such as interpretting 0101
12 * as hexadecimal which would be 16 bits when really it's only 4 bits of binary
16 window
.Entropy
= new (function() {
18 // matchers returns an array of the matched events for each type of entropy.
20 // matchers.binary("010") returns ["0", "1", "0"]
21 // matchers.binary("a10") returns ["1", "0"]
22 // matchers.hex("a10") returns ["a", "1", "0"]
24 binary: function(str
) {
25 return str
.match(/[0-1]/gi) || [];
27 base6: function(str
) {
28 return str
.match(/[0-5]/gi) || [];
31 return str
.match(/[1-6]/gi) || []; // ie dice numbers
33 base10: function(str
) {
34 return str
.match(/[0-9]/gi) || [];
37 return str
.match(/[0-9A-F]/gi) || [];
40 // Format is NumberSuit, eg
47 return str
.match(/([A2-9TJQK][CDHS])/gi) || [];
51 // Convert array of cards from ["ac", "4d", "ks"]
52 // to numbers between 0 and 51 [0, 16, 51]
53 function convertCardsToInts(cards
) {
55 var values
= "a23456789tjqk";
57 for (var i
=0; i
<cards
.length
; i
++) {
58 var card
= cards
[i
].toLowerCase();
61 var asInt
= 13 * suits
.indexOf(suit
) + values
.indexOf(value
);
67 this.fromString = function(rawEntropyStr
) {
68 // Find type of entropy being used (binary, hex, dice etc)
69 var base
= getBase(rawEntropyStr
);
70 // Convert dice to base6 entropy (ie 1-6 to 0-5)
71 if (base
.str
== "dice") {
72 var newRawEntropyStr
= "";
73 for (var i
=0; i
<rawEntropyStr
.length
; i
++) {
74 var c
= rawEntropyStr
[i
];
75 if ("123456".indexOf(c
) > -1) {
76 newRawEntropyStr
+= (parseInt(c
) - 1).toString();
82 rawEntropyStr
= newRawEntropyStr
;
83 base
.str
= "base 6 (dice)";
84 base
.parts
= matchers
.base6(rawEntropyStr
);
85 base
.matcher
= matchers
.base6
;
87 // Detect empty entropy
88 if (base
.parts
.length
== 0) {
95 // Pull leading zeros off
96 var leadingZeros
= [];
97 while (base
.ints
[0] == "0") {
98 leadingZeros
.push("0");
101 // Convert leading zeros to binary equivalent
102 var numBinLeadingZeros
= Math
.floor(Math
.log2(base
.asInt
) * leadingZeros
.length
);
103 var binLeadingZeros
= "";
104 for (var i
=0; i
<numBinLeadingZeros
; i
++) {
105 binLeadingZeros
+= "0";
107 // Handle entropy of zero
108 if (base
.ints
.length
== 0) {
110 binaryStr: binLeadingZeros
,
111 cleanStr: leadingZeros
,
115 // If the first integer is small, it must be padded with zeros.
116 // Otherwise the chance of the first bit being 1 is 100%, which is
117 // obviously incorrect.
118 // This is not perfect for unusual bases, eg base 6 has 2.6 bits, so is
119 // slightly biased toward having leading zeros, but it's still better
120 // than ignoring it completely.
121 // TODO: revise this, it seems very fishy. For example, in base 10, there are
122 // 8 opportunities to start with 0 but only 2 to start with 1
123 var firstInt
= base
.ints
[0];
124 var firstIntBits
= Math
.floor(Math
.log2(firstInt
))+1;
125 var maxFirstIntBits
= Math
.floor(Math
.log2(base
.asInt
-1))+1;
126 var missingFirstIntBits
= maxFirstIntBits
- firstIntBits
;
127 var firstIntLeadingZeros
= "";
128 for (var i
=0; i
<missingFirstIntBits
; i
++) {
129 binLeadingZeros
+= "0";
131 // Convert base.ints to BigInteger.
132 // Due to using unusual bases, eg cards of base52, this is not as simple as
133 // using BigInteger.parse()
134 var entropyInt
= BigInteger
.ZERO
;
135 for (var i
=base
.ints
.length
-1; i
>=0; i
--) {
136 var thisInt
= BigInteger
.parse(base
.ints
[i
]);
137 var power
= (base
.ints
.length
- 1) - i
;
138 var additionalEntropy
= BigInteger
.parse(base
.asInt
).pow(power
).multiply(thisInt
);
139 entropyInt
= entropyInt
.add(additionalEntropy
);
141 // Convert entropy to different formats
142 var entropyBin
= binLeadingZeros
+ entropyInt
.toString(2);
143 var entropyClean
= base
.parts
.join("");
145 binaryStr: entropyBin
,
146 cleanStr: entropyClean
,
152 function getBase(str
) {
153 // Need to get the lowest base for the supplied entropy.
154 // This prevents interpreting, say, dice rolls as hexadecimal.
155 var binaryMatches
= matchers
.binary(str
);
156 var hexMatches
= matchers
.hex(str
);
157 // Find the lowest base that can be used, whilst ignoring any irrelevant chars
158 if (binaryMatches
.length
== hexMatches
.length
&& hexMatches
.length
> 0) {
159 var ints
= binaryMatches
.map(function(i
) { return parseInt(i
, 2) });
162 parts: binaryMatches
,
163 matcher: matchers
.binary
,
168 var cardMatches
= matchers
.card(str
);
169 if (cardMatches
.length
>= hexMatches
.length
/ 2) {
170 var ints
= convertCardsToInts(cardMatches
);
174 matcher: matchers
.card
,
179 var diceMatches
= matchers
.dice(str
);
180 if (diceMatches
.length
== hexMatches
.length
&& hexMatches
.length
> 0) {
181 var ints
= diceMatches
.map(function(i
) { return parseInt(i
) });
185 matcher: matchers
.dice
,
190 var base6Matches
= matchers
.base6(str
);
191 if (base6Matches
.length
== hexMatches
.length
&& hexMatches
.length
> 0) {
192 var ints
= base6Matches
.map(function(i
) { return parseInt(i
) });
196 matcher: matchers
.base6
,
201 var base10Matches
= matchers
.base10(str
);
202 if (base10Matches
.length
== hexMatches
.length
&& hexMatches
.length
> 0) {
203 var ints
= base10Matches
.map(function(i
) { return parseInt(i
) });
206 parts: base10Matches
,
207 matcher: matchers
.base10
,
212 var ints
= hexMatches
.map(function(i
) { return parseInt(i
, 16) });
216 matcher: matchers
.hex
,
222 // Polyfill for Math.log2
223 // See https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Math/log2#Polyfill
224 Math
.log2
= Math
.log2
|| function(x
) {
225 // The polyfill isn't good enough because of the poor accuracy of
227 // log2(8) gave 2.9999999999999996 which when floored causes issues.
228 // So instead use the BigInteger library to get it right.
229 return BigInteger
.log(x
) / BigInteger
.log(2);
235 // BigInteger library included here because
236 // only the entropy library depends on it
237 // so if entropy detection is removed so is the dependency
241 JavaScript BigInteger library version 0.9.1
242 http://silentmatt.com/biginteger/
244 Copyright (c) 2009 Matthew Crumley <email@matthewcrumley.com>
245 Copyright (c) 2010,2011 by John Tobey <John.Tobey@gmail.com>
246 Licensed under the MIT license.
248 Support for arbitrary internal representation base was added by
263 An arbitrarily-large integer.
265 <BigInteger> objects should be considered immutable. None of the "built-in"
266 methods modify *this* or their arguments. All properties should be
269 All the methods of <BigInteger> instances can be called "statically". The
270 static versions are convenient if you don't already have a <BigInteger>
273 As an example, these calls are equivalent.
275 > BigInteger(4).multiply(5); // returns BigInteger(20);
276 > BigInteger.multiply(4, 5); // returns BigInteger(20);
279 > var a = BigInteger.toJSValue("0b101010"); // Not completely useless...
282 var CONSTRUCT
= {}; // Unique token to call "private" version of constructor
285 Constructor: BigInteger()
286 Convert a value to a <BigInteger>.
288 Although <BigInteger()> is the constructor for <BigInteger> objects, it is
289 best not to call it as a constructor. If *n* is a <BigInteger> object, it is
290 simply returned as-is. Otherwise, <BigInteger()> is equivalent to <parse>
291 without a radix argument.
293 > var n0 = BigInteger(); // Same as <BigInteger.ZERO>
294 > var n1 = BigInteger("123"); // Create a new <BigInteger> with value 123
295 > var n2 = BigInteger(123); // Create a new <BigInteger> with value 123
296 > var n3 = BigInteger(n2); // Return n2, unchanged
298 The constructor form only takes an array and a sign. *n* must be an
299 array of numbers in little-endian order, where each digit is between 0
300 and BigInteger.base. The second parameter sets the sign: -1 for
301 negative, +1 for positive, or 0 for zero. The array is *not copied and
302 may be modified*. If the array contains only zeros, the sign parameter
303 is ignored and is forced to zero.
305 > new BigInteger([5], -1): create a new BigInteger with value -5
309 n - Value to convert to a <BigInteger>.
313 A <BigInteger> value.
317 <parse>, <BigInteger>
319 function BigInteger(n
, s
, token
) {
320 if (token
!== CONSTRUCT
) {
321 if (n
instanceof BigInteger
) {
324 else if (typeof n
=== "undefined") {
327 return BigInteger
.parse(n
);
330 n
= n
|| []; // Provide the nullary constructor for subclasses.
331 while (n
.length
&& !n
[n
.length
- 1]) {
335 this._s
= n
.length
? (s
|| 1) : 0;
338 BigInteger
._construct = function(n
, s
) {
339 return new BigInteger(n
, s
, CONSTRUCT
);
342 // Base-10 speedup hacks in parse, toString, exp10 and log functions
343 // require base to be a power of 10. 10^7 is the largest such power
344 // that won't cause a precision loss when digits are multiplied.
345 var BigInteger_base
= 10000000;
346 var BigInteger_base_log10
= 7;
348 BigInteger
.base
= BigInteger_base
;
349 BigInteger
.base_log10
= BigInteger_base_log10
;
351 var ZERO
= new BigInteger([], 0, CONSTRUCT
);
354 BigInteger
.ZERO
= ZERO
;
356 var ONE
= new BigInteger([1], 1, CONSTRUCT
);
359 BigInteger
.ONE
= ONE
;
361 var M_ONE
= new BigInteger(ONE
._d
, -1, CONSTRUCT
);
364 BigInteger
.M_ONE
= M_ONE
;
367 // Shortcut for <ZERO>.
368 BigInteger
._0
= ZERO
;
371 // Shortcut for <ONE>.
376 Array of <BigIntegers> from 0 to 36.
378 These are used internally for parsing, but useful when you need a "small"
383 <ZERO>, <ONE>, <_0>, <_1>
388 /* Assuming BigInteger_base > 36 */
389 new BigInteger( [2], 1, CONSTRUCT
),
390 new BigInteger( [3], 1, CONSTRUCT
),
391 new BigInteger( [4], 1, CONSTRUCT
),
392 new BigInteger( [5], 1, CONSTRUCT
),
393 new BigInteger( [6], 1, CONSTRUCT
),
394 new BigInteger( [7], 1, CONSTRUCT
),
395 new BigInteger( [8], 1, CONSTRUCT
),
396 new BigInteger( [9], 1, CONSTRUCT
),
397 new BigInteger([10], 1, CONSTRUCT
),
398 new BigInteger([11], 1, CONSTRUCT
),
399 new BigInteger([12], 1, CONSTRUCT
),
400 new BigInteger([13], 1, CONSTRUCT
),
401 new BigInteger([14], 1, CONSTRUCT
),
402 new BigInteger([15], 1, CONSTRUCT
),
403 new BigInteger([16], 1, CONSTRUCT
),
404 new BigInteger([17], 1, CONSTRUCT
),
405 new BigInteger([18], 1, CONSTRUCT
),
406 new BigInteger([19], 1, CONSTRUCT
),
407 new BigInteger([20], 1, CONSTRUCT
),
408 new BigInteger([21], 1, CONSTRUCT
),
409 new BigInteger([22], 1, CONSTRUCT
),
410 new BigInteger([23], 1, CONSTRUCT
),
411 new BigInteger([24], 1, CONSTRUCT
),
412 new BigInteger([25], 1, CONSTRUCT
),
413 new BigInteger([26], 1, CONSTRUCT
),
414 new BigInteger([27], 1, CONSTRUCT
),
415 new BigInteger([28], 1, CONSTRUCT
),
416 new BigInteger([29], 1, CONSTRUCT
),
417 new BigInteger([30], 1, CONSTRUCT
),
418 new BigInteger([31], 1, CONSTRUCT
),
419 new BigInteger([32], 1, CONSTRUCT
),
420 new BigInteger([33], 1, CONSTRUCT
),
421 new BigInteger([34], 1, CONSTRUCT
),
422 new BigInteger([35], 1, CONSTRUCT
),
423 new BigInteger([36], 1, CONSTRUCT
)
426 // Used for parsing/radix conversion
427 BigInteger
.digits
= "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ".split("");
431 Convert a <BigInteger> to a string.
433 When *base* is greater than 10, letters are upper case.
437 base - Optional base to represent the number in (default is base 10).
438 Must be between 2 and 36 inclusive, or an Error will be thrown.
442 The string representation of the <BigInteger>.
444 BigInteger
.prototype.toString = function(base
) {
446 if (base
< 2 || base
> 36) {
447 throw new Error("illegal radix " + base
+ ".");
453 var str
= this._s
< 0 ? "-" : "";
454 str
+= this._d
[this._d
.length
- 1].toString();
455 for (var i
= this._d
.length
- 2; i
>= 0; i
--) {
456 var group
= this._d
[i
].toString();
457 while (group
.length
< BigInteger_base_log10
) group
= '0' + group
;
463 var numerals
= BigInteger
.digits
;
464 base
= BigInteger
.small
[base
];
472 var divmod
= n
.divRem(base
);
475 // TODO: This could be changed to unshift instead of reversing at the end.
476 // Benchmark both to compare speeds.
477 digits
.push(numerals
[digit
.valueOf()]);
479 return (sign
< 0 ? "-" : "") + digits
.reverse().join("");
483 // Verify strings for parsing
484 BigInteger
.radixRegex
= [
526 Parse a string into a <BigInteger>.
528 *base* is optional but, if provided, must be from 2 to 36 inclusive. If
529 *base* is not provided, it will be guessed based on the leading characters
532 - "0x" or "0X": *base* = 16
533 - "0c" or "0C": *base* = 8
534 - "0b" or "0B": *base* = 2
537 If no base is provided, or *base* is 10, the number can be in exponential
538 form. For example, these are all valid:
540 > BigInteger.parse("1e9"); // Same as "1000000000"
541 > BigInteger.parse("1.234*10^3"); // Same as 1234
542 > BigInteger.parse("56789 * 10 ** -2"); // Same as 567
544 If any characters fall outside the range defined by the radix, an exception
549 s - The string to parse.
550 base - Optional radix (default is to guess based on *s*).
554 a <BigInteger> instance.
556 BigInteger
.parse = function(s
, base
) {
557 // Expands a number in exponential form to decimal form.
558 // expandExponential("-13.441*10^5") === "1344100";
559 // expandExponential("1.12300e-1") === "0.112300";
560 // expandExponential(1000000000000000000000000000000) === "1000000000000000000000000000000";
561 function expandExponential(str
) {
562 str
= str
.replace(/\s*[*xX]\s*10\s*(\^|\*\*)\s*/, "e");
564 return str
.replace(/^([+\-])?(\d+)\.?(\d*)[eE]([+\-]?\d+)$/, function(x
, s
, n
, f
, c
) {
567 var i
= n
.length
+ c
;
568 x
= (l
? n : f
).length
;
569 c
= ((c
= Math
.abs(c
)) >= x
? c
- x
+ l : 0);
570 var z
= (new Array(c
+ 1)).join("0");
572 return (s
|| "") + (l
? r
= z
+ r : r
+= z
).substr(0, i
+= l
? z
.length : 0) + (i
< r
.length
? "." + r
.substr(i
) : "");
577 if (typeof base
=== "undefined" || +base
=== 10) {
578 s
= expandExponential(s
);
582 if (typeof base
=== "undefined") {
585 else if (base
== 16) {
588 else if (base
== 8) {
591 else if (base
== 2) {
597 var parts
= new RegExp('^([+\\-]?)(' + prefixRE
+ ')?([0-9a-z]*)(?:\\.\\d*)?$', 'i').exec(s
);
599 var sign
= parts
[1] || "+";
600 var baseSection
= parts
[2] || "";
601 var digits
= parts
[3] || "";
603 if (typeof base
=== "undefined") {
605 if (baseSection
=== "0x" || baseSection
=== "0X") { // Hex
608 else if (baseSection
=== "0c" || baseSection
=== "0C") { // Octal
611 else if (baseSection
=== "0b" || baseSection
=== "0B") { // Binary
618 else if (base
< 2 || base
> 36) {
619 throw new Error("Illegal radix " + base
+ ".");
624 // Check for digits outside the range
625 if (!(BigInteger
.radixRegex
[base
].test(digits
))) {
626 throw new Error("Bad digit for radix " + base
);
629 // Strip leading zeros, and convert to array
630 digits
= digits
.replace(/^0+/, "").split("");
631 if (digits
.length
=== 0) {
635 // Get the sign (we know it's not zero)
636 sign
= (sign
=== "-") ? -1 : 1;
641 while (digits
.length
>= BigInteger_base_log10
) {
642 d
.push(parseInt(digits
.splice(digits
.length
-BigInteger
.base_log10
, BigInteger
.base_log10
).join(''), 10));
644 d
.push(parseInt(digits
.join(''), 10));
645 return new BigInteger(d
, sign
, CONSTRUCT
);
650 base
= BigInteger
.small
[base
];
651 var small
= BigInteger
.small
;
652 for (var i
= 0; i
< digits
.length
; i
++) {
653 d
= d
.multiply(base
).add(small
[parseInt(digits
[i
], 36)]);
655 return new BigInteger(d
._d
, sign
, CONSTRUCT
);
658 throw new Error("Invalid BigInteger format: " + s
);
664 Add two <BigIntegers>.
668 n - The number to add to *this*. Will be converted to a <BigInteger>.
672 The numbers added together.
676 <subtract>, <multiply>, <quotient>, <next>
678 BigInteger
.prototype.add = function(n
) {
680 return BigInteger(n
);
687 if (this._s
!== n
._s
) {
689 return this.subtract(n
);
696 var sum
= new Array(Math
.max(al
, bl
) + 1);
697 var size
= Math
.min(al
, bl
);
701 for (var i
= 0; i
< size
; i
++) {
702 digit
= a
[i
] + b
[i
] + carry
;
703 sum
[i
] = digit
% BigInteger_base
;
704 carry
= (digit
/ BigInteger_base
) | 0;
710 for (i
= size
; carry
&& i
< al
; i
++) {
711 digit
= a
[i
] + carry
;
712 sum
[i
] = digit
% BigInteger_base
;
713 carry
= (digit
/ BigInteger_base
) | 0;
719 for ( ; i
< al
; i
++) {
723 return new BigInteger(sum
, this._s
, CONSTRUCT
);
728 Get the additive inverse of a <BigInteger>.
732 A <BigInteger> with the same magnatude, but with the opposite sign.
738 BigInteger
.prototype.negate = function() {
739 return new BigInteger(this._d
, (-this._s
) | 0, CONSTRUCT
);
744 Get the absolute value of a <BigInteger>.
748 A <BigInteger> with the same magnatude, but always positive (or zero).
754 BigInteger
.prototype.abs = function() {
755 return (this._s
< 0) ? this.negate() : this;
760 Subtract two <BigIntegers>.
764 n - The number to subtract from *this*. Will be converted to a <BigInteger>.
768 The *n* subtracted from *this*.
772 <add>, <multiply>, <quotient>, <prev>
774 BigInteger
.prototype.subtract = function(n
) {
776 return BigInteger(n
).negate();
783 if (this._s
!== n
._s
) {
789 // negative - negative => -|a| - -|b| => -|a| + |b| => |b| - |a|
791 m
= new BigInteger(n
._d
, 1, CONSTRUCT
);
792 n
= new BigInteger(this._d
, 1, CONSTRUCT
);
795 // Both are positive => a - b
796 var sign
= m
.compareAbs(n
);
812 var diff
= new Array(al
); // al >= bl since a > b
817 for (i
= 0; i
< bl
; i
++) {
818 digit
= a
[i
] - borrow
- b
[i
];
820 digit
+= BigInteger_base
;
828 for (i
= bl
; i
< al
; i
++) {
829 digit
= a
[i
] - borrow
;
831 digit
+= BigInteger_base
;
839 for ( ; i
< al
; i
++) {
843 return new BigInteger(diff
, sign
, CONSTRUCT
);
847 function addOne(n
, sign
) {
854 var digit
= (a
[i
] || 0) + 1;
855 sum
[i
] = digit
% BigInteger_base
;
856 if (digit
<= BigInteger_base
- 1) {
862 return new BigInteger(sum
, sign
, CONSTRUCT
);
865 function subtractOne(n
, sign
) {
872 var digit
= (a
[i
] || 0) - 1;
874 sum
[i
] = digit
+ BigInteger_base
;
883 return new BigInteger(sum
, sign
, CONSTRUCT
);
888 Get the next <BigInteger> (add one).
898 BigInteger
.prototype.next = function() {
903 return subtractOne(this, -1);
906 return addOne(this, 1);
912 Get the previous <BigInteger> (subtract one).
922 BigInteger
.prototype.prev = function() {
927 return addOne(this, -1);
930 return subtractOne(this, 1);
937 Compare the absolute value of two <BigIntegers>.
939 Calling <compareAbs> is faster than calling <abs> twice, then <compare>.
943 n - The number to compare to *this*. Will be converted to a <BigInteger>.
947 -1, 0, or +1 if *|this|* is less than, equal to, or greater than *|n|*.
953 BigInteger
.prototype.compareAbs = function(n
) {
958 if (!(n
instanceof BigInteger
)) {
960 return(isNaN(n
) ? n : -1);
966 return (n
._s
!== 0) ? -1 : 0;
972 var l
= this._d
.length
;
973 var nl
= n
._d
.length
;
983 for (var i
= l
-1; i
>= 0; i
--) {
985 return a
[i
] < b
[i
] ? -1 : 1;
994 Compare two <BigIntegers>.
998 n - The number to compare to *this*. Will be converted to a <BigInteger>.
1002 -1, 0, or +1 if *this* is less than, equal to, or greater than *n*.
1006 <compareAbs>, <isPositive>, <isNegative>, <isUnit>
1008 BigInteger
.prototype.compare = function(n
) {
1015 if (this._s
=== 0) {
1019 if (this._s
=== n
._s
) { // both positive or both negative
1020 var cmp
= this.compareAbs(n
);
1021 return cmp
* this._s
;
1030 Return true iff *this* is either 1 or -1.
1034 true if *this* compares equal to <BigInteger.ONE> or <BigInteger.M_ONE>.
1038 <isZero>, <isNegative>, <isPositive>, <compareAbs>, <compare>,
1039 <BigInteger.ONE>, <BigInteger.M_ONE>
1041 BigInteger
.prototype.isUnit = function() {
1042 return this === ONE
||
1044 (this._d
.length
=== 1 && this._d
[0] === 1);
1049 Multiply two <BigIntegers>.
1053 n - The number to multiply *this* by. Will be converted to a
1058 The numbers multiplied together.
1062 <add>, <subtract>, <quotient>, <square>
1064 BigInteger
.prototype.multiply = function(n
) {
1065 // TODO: Consider adding Karatsuba multiplication for large numbers
1066 if (this._s
=== 0) {
1074 if (this.isUnit()) {
1082 return this.negate();
1087 return this.square();
1090 var r
= (this._d
.length
>= n
._d
.length
);
1091 var a
= (r
? this : n
)._d
; // a will be longer than b
1092 var b
= (r
? n : this)._d
;
1097 var partial
= new Array(pl
);
1099 for (i
= 0; i
< pl
; i
++) {
1103 for (i
= 0; i
< bl
; i
++) {
1106 var jlimit
= al
+ i
;
1108 for (var j
= i
; j
< jlimit
; j
++) {
1109 digit
= partial
[j
] + bi
* a
[j
- i
] + carry
;
1110 carry
= (digit
/ BigInteger_base
) | 0;
1111 partial
[j
] = (digit
% BigInteger_base
) | 0;
1114 digit
= partial
[j
] + carry
;
1115 carry
= (digit
/ BigInteger_base
) | 0;
1116 partial
[j
] = digit
% BigInteger_base
;
1119 return new BigInteger(partial
, this._s
* n
._s
, CONSTRUCT
);
1122 // Multiply a BigInteger by a single-digit native number
1123 // Assumes that this and n are >= 0
1124 // This is not really intended to be used outside the library itself
1125 BigInteger
.prototype.multiplySingleDigit = function(n
) {
1126 if (n
=== 0 || this._s
=== 0) {
1134 if (this._d
.length
=== 1) {
1135 digit
= this._d
[0] * n
;
1136 if (digit
>= BigInteger_base
) {
1137 return new BigInteger([(digit
% BigInteger_base
)|0,
1138 (digit
/ BigInteger_base
)|0], 1, CONSTRUCT
);
1140 return new BigInteger([digit
], 1, CONSTRUCT
);
1144 return this.add(this);
1146 if (this.isUnit()) {
1147 return new BigInteger([n
], 1, CONSTRUCT
);
1154 var partial
= new Array(pl
);
1155 for (var i
= 0; i
< pl
; i
++) {
1160 for (var j
= 0; j
< al
; j
++) {
1161 digit
= n
* a
[j
] + carry
;
1162 carry
= (digit
/ BigInteger_base
) | 0;
1163 partial
[j
] = (digit
% BigInteger_base
) | 0;
1169 return new BigInteger(partial
, 1, CONSTRUCT
);
1174 Multiply a <BigInteger> by itself.
1176 This is slightly faster than regular multiplication, since it removes the
1177 duplicated multiplcations.
1181 > this.multiply(this)
1186 BigInteger
.prototype.square = function() {
1187 // Normally, squaring a 10-digit number would take 100 multiplications.
1188 // Of these 10 are unique diagonals, of the remaining 90 (100-10), 45 are repeated.
1189 // This procedure saves (N*(N-1))/2 multiplications, (e.g., 45 of 100 multiplies).
1190 // Based on code by Gary Darby, Intellitech Systems Inc., www.DelphiForFun.org
1192 if (this._s
=== 0) {
1195 if (this.isUnit()) {
1199 var digits
= this._d
;
1200 var length
= digits
.length
;
1201 var imult1
= new Array(length
+ length
+ 1);
1202 var product
, carry
, k
;
1205 // Calculate diagonal
1206 for (i
= 0; i
< length
; i
++) {
1208 product
= digits
[i
] * digits
[i
];
1209 carry
= (product
/ BigInteger_base
) | 0;
1210 imult1
[k
] = product
% BigInteger_base
;
1211 imult1
[k
+ 1] = carry
;
1214 // Calculate repeating part
1215 for (i
= 0; i
< length
; i
++) {
1218 for (var j
= i
+ 1; j
< length
; j
++, k
++) {
1219 product
= digits
[j
] * digits
[i
] * 2 + imult1
[k
] + carry
;
1220 carry
= (product
/ BigInteger_base
) | 0;
1221 imult1
[k
] = product
% BigInteger_base
;
1224 var digit
= carry
+ imult1
[k
];
1225 carry
= (digit
/ BigInteger_base
) | 0;
1226 imult1
[k
] = digit
% BigInteger_base
;
1227 imult1
[k
+ 1] += carry
;
1230 return new BigInteger(imult1
, 1, CONSTRUCT
);
1235 Divide two <BigIntegers> and truncate towards zero.
1237 <quotient> throws an exception if *n* is zero.
1241 n - The number to divide *this* by. Will be converted to a <BigInteger>.
1245 The *this* / *n*, truncated to an integer.
1249 <add>, <subtract>, <multiply>, <divRem>, <remainder>
1251 BigInteger
.prototype.quotient = function(n
) {
1252 return this.divRem(n
)[0];
1257 Deprecated synonym for <quotient>.
1259 BigInteger
.prototype.divide
= BigInteger
.prototype.quotient
;
1263 Calculate the remainder of two <BigIntegers>.
1265 <remainder> throws an exception if *n* is zero.
1269 n - The remainder after *this* is divided *this* by *n*. Will be
1270 converted to a <BigInteger>.
1278 <divRem>, <quotient>
1280 BigInteger
.prototype.remainder = function(n
) {
1281 return this.divRem(n
)[1];
1286 Calculate the integer quotient and remainder of two <BigIntegers>.
1288 <divRem> throws an exception if *n* is zero.
1292 n - The number to divide *this* by. Will be converted to a <BigInteger>.
1296 A two-element array containing the quotient and the remainder.
1300 is exactly equivalent to
1302 > [a.quotient(b), a.remainder(b)]
1304 except it is faster, because they are calculated at the same time.
1308 <quotient>, <remainder>
1310 BigInteger
.prototype.divRem = function(n
) {
1313 throw new Error("Divide by zero");
1315 if (this._s
=== 0) {
1316 return [ZERO
, ZERO
];
1318 if (n
._d
.length
=== 1) {
1319 return this.divRemSmall(n
._s
* n
._d
[0]);
1322 // Test for easy cases -- |n1| <= |n2|
1323 switch (this.compareAbs(n
)) {
1325 return [this._s
=== n
._s
? ONE : M_ONE
, ZERO
];
1326 case -1: // |n1| < |n2|
1327 return [ZERO
, this];
1330 var sign
= this._s
* n
._s
;
1332 var b_digits
= this._d
;
1333 var b_index
= b_digits
.length
;
1334 var digits
= n
._d
.length
;
1338 var part
= new BigInteger([], 0, CONSTRUCT
);
1341 part
._d
.unshift(b_digits
[--b_index
]);
1342 part
= new BigInteger(part
._d
, 1, CONSTRUCT
);
1344 if (part
.compareAbs(n
) < 0) {
1348 if (part
._s
=== 0) {
1352 var xlen
= part
._d
.length
, ylen
= a
._d
.length
;
1353 var highx
= part
._d
[xlen
-1]*BigInteger_base
+ part
._d
[xlen
-2];
1354 var highy
= a
._d
[ylen
-1]*BigInteger_base
+ a
._d
[ylen
-2];
1355 if (part
._d
.length
> a
._d
.length
) {
1356 // The length of part._d can either match a._d length,
1357 // or exceed it by one.
1358 highx
= (highx
+1)*BigInteger_base
;
1360 guess
= Math
.ceil(highx
/highy
);
1363 var check
= a
.multiplySingleDigit(guess
);
1364 if (check
.compareAbs(part
) <= 0) {
1374 var diff
= part
.subtract(check
);
1375 part
._d
= diff
._d
.slice();
1378 return [new BigInteger(quot
.reverse(), sign
, CONSTRUCT
),
1379 new BigInteger(part
._d
, this._s
, CONSTRUCT
)];
1382 // Throws an exception if n is outside of (-BigInteger.base, -1] or
1383 // [1, BigInteger.base). It's not necessary to call this, since the
1384 // other division functions will call it if they are able to.
1385 BigInteger
.prototype.divRemSmall = function(n
) {
1389 throw new Error("Divide by zero");
1392 var n_s
= n
< 0 ? -1 : 1;
1393 var sign
= this._s
* n_s
;
1396 if (n
< 1 || n
>= BigInteger_base
) {
1397 throw new Error("Argument out of range");
1400 if (this._s
=== 0) {
1401 return [ZERO
, ZERO
];
1404 if (n
=== 1 || n
=== -1) {
1405 return [(sign
=== 1) ? this.abs() : new BigInteger(this._d
, sign
, CONSTRUCT
), ZERO
];
1408 // 2 <= n < BigInteger_base
1410 // divide a single digit by a single digit
1411 if (this._d
.length
=== 1) {
1412 var q
= new BigInteger([(this._d
[0] / n
) | 0], 1, CONSTRUCT
);
1413 r
= new BigInteger([(this._d
[0] % n
) | 0], 1, CONSTRUCT
);
1423 var digits
= this._d
.slice();
1424 var quot
= new Array(digits
.length
);
1430 while (digits
.length
) {
1431 part
= part
* BigInteger_base
+ digits
[digits
.length
- 1];
1435 diff
= BigInteger_base
* diff
+ part
;
1442 guess
= (part
/ n
) | 0;
1445 var check
= n
* guess
;
1446 diff
= part
- check
;
1457 r
= new BigInteger([diff
], 1, CONSTRUCT
);
1461 return [new BigInteger(quot
.reverse(), sign
, CONSTRUCT
), r
];
1466 Return true iff *this* is divisible by two.
1468 Note that <BigInteger.ZERO> is even.
1472 true if *this* is even, false otherwise.
1478 BigInteger
.prototype.isEven = function() {
1479 var digits
= this._d
;
1480 return this._s
=== 0 || digits
.length
=== 0 || (digits
[0] % 2) === 0;
1485 Return true iff *this* is not divisible by two.
1489 true if *this* is odd, false otherwise.
1495 BigInteger
.prototype.isOdd = function() {
1496 return !this.isEven();
1501 Get the sign of a <BigInteger>.
1511 <isZero>, <isPositive>, <isNegative>, <compare>, <BigInteger.ZERO>
1513 BigInteger
.prototype.sign = function() {
1518 Function: isPositive
1519 Return true iff *this* > 0.
1523 true if *this*.compare(<BigInteger.ZERO>) == 1.
1527 <sign>, <isZero>, <isNegative>, <isUnit>, <compare>, <BigInteger.ZERO>
1529 BigInteger
.prototype.isPositive = function() {
1534 Function: isNegative
1535 Return true iff *this* < 0.
1539 true if *this*.compare(<BigInteger.ZERO>) == -1.
1543 <sign>, <isPositive>, <isZero>, <isUnit>, <compare>, <BigInteger.ZERO>
1545 BigInteger
.prototype.isNegative = function() {
1551 Return true iff *this* == 0.
1555 true if *this*.compare(<BigInteger.ZERO>) == 0.
1559 <sign>, <isPositive>, <isNegative>, <isUnit>, <BigInteger.ZERO>
1561 BigInteger
.prototype.isZero = function() {
1562 return this._s
=== 0;
1567 Multiply a <BigInteger> by a power of 10.
1569 This is equivalent to, but faster than
1572 > return this.multiply(BigInteger("1e" + n));
1575 > return this.quotient(BigInteger("1e" + -n));
1580 n - The power of 10 to multiply *this* by. *n* is converted to a
1581 javascipt number and must be no greater than <BigInteger.MAX_EXP>
1582 (0x7FFFFFFF), or an exception will be thrown.
1586 *this* * (10 ** *n*), truncated to an integer if necessary.
1592 BigInteger
.prototype.exp10 = function(n
) {
1597 if (Math
.abs(n
) > Number(MAX_EXP
)) {
1598 throw new Error("exponent too large in BigInteger.exp10");
1600 // Optimization for this == 0. This also keeps us from having to trim zeros in the positive n case
1601 if (this._s
=== 0) {
1605 var k
= new BigInteger(this._d
.slice(), this._s
, CONSTRUCT
);
1607 for (; n
>= BigInteger_base_log10
; n
-= BigInteger_base_log10
) {
1613 k
= k
.multiplySingleDigit(Math
.pow(10, n
));
1614 return (this._s
< 0 ? k
.negate() : k
);
1615 } else if (-n
>= this._d
.length
*BigInteger_base_log10
) {
1618 var k
= new BigInteger(this._d
.slice(), this._s
, CONSTRUCT
);
1620 for (n
= -n
; n
>= BigInteger_base_log10
; n
-= BigInteger_base_log10
) {
1623 return (n
== 0) ? k : k
.divRemSmall(Math
.pow(10, n
))[0];
1629 Raise a <BigInteger> to a power.
1631 In this implementation, 0**0 is 1.
1635 n - The exponent to raise *this* by. *n* must be no greater than
1636 <BigInteger.MAX_EXP> (0x7FFFFFFF), or an exception will be thrown.
1640 *this* raised to the *nth* power.
1646 BigInteger
.prototype.pow = function(n
) {
1647 if (this.isUnit()) {
1652 return BigInteger(n
).isOdd() ? this : this.negate();
1660 else if (n
._s
< 0) {
1661 if (this._s
=== 0) {
1662 throw new Error("Divide by zero");
1668 if (this._s
=== 0) {
1675 if (n
.compareAbs(MAX_EXP
) > 0) {
1676 throw new Error("exponent too large in BigInteger.pow");
1680 var two
= BigInteger
.small
[2];
1682 while (n
.isPositive()) {
1684 aux
= aux
.multiply(x
);
1690 n
= n
.quotient(two
);
1698 Raise a <BigInteger> to a power (mod m).
1700 Because it is reduced by a modulus, <modPow> is not limited by
1701 <BigInteger.MAX_EXP> like <pow>.
1705 exponent - The exponent to raise *this* by. Must be positive.
1706 modulus - The modulus.
1710 *this* ^ *exponent* (mod *modulus*).
1716 BigInteger
.prototype.modPow = function(exponent
, modulus
) {
1720 while (exponent
.isPositive()) {
1721 if (exponent
.isOdd()) {
1722 result
= result
.multiply(base
).remainder(modulus
);
1725 exponent
= exponent
.quotient(BigInteger
.small
[2]);
1726 if (exponent
.isPositive()) {
1727 base
= base
.square().remainder(modulus
);
1736 Get the natural logarithm of a <BigInteger> as a native JavaScript number.
1738 This is equivalent to
1740 > Math.log(this.toJSValue())
1742 but handles values outside of the native number range.
1752 BigInteger
.prototype.log = function() {
1754 case 0: return -Infinity
;
1755 case -1: return NaN
;
1756 default: // Fall through.
1759 var l
= this._d
.length
;
1761 if (l
*BigInteger_base_log10
< 30) {
1762 return Math
.log(this.valueOf());
1765 var N
= Math
.ceil(30/BigInteger_base_log10
);
1766 var firstNdigits
= this._d
.slice(l
- N
);
1767 return Math
.log((new BigInteger(firstNdigits
, 1, CONSTRUCT
)).valueOf()) + (l
- N
) * Math
.log(BigInteger_base
);
1772 Convert a <BigInteger> to a native JavaScript integer.
1774 This is called automatically by JavaScipt to convert a <BigInteger> to a
1779 > parseInt(this.toString(), 10)
1783 <toString>, <toJSValue>
1785 BigInteger
.prototype.valueOf = function() {
1786 return parseInt(this.toString(), 10);
1791 Convert a <BigInteger> to a native JavaScript integer.
1793 This is the same as valueOf, but more explicitly named.
1797 > parseInt(this.toString(), 10)
1801 <toString>, <valueOf>
1803 BigInteger
.prototype.toJSValue = function() {
1804 return parseInt(this.toString(), 10);
1807 var MAX_EXP
= BigInteger(0x7FFFFFFF);
1808 // Constant: MAX_EXP
1809 // The largest exponent allowed in <pow> and <exp10> (0x7FFFFFFF or 2147483647).
1810 BigInteger
.MAX_EXP
= MAX_EXP
;
1813 function makeUnary(fn
) {
1814 return function(a
) {
1815 return fn
.call(BigInteger(a
));
1819 function makeBinary(fn
) {
1820 return function(a
, b
) {
1821 return fn
.call(BigInteger(a
), BigInteger(b
));
1825 function makeTrinary(fn
) {
1826 return function(a
, b
, c
) {
1827 return fn
.call(BigInteger(a
), BigInteger(b
), BigInteger(c
));
1833 var unary
= "toJSValue,isEven,isOdd,sign,isZero,isNegative,abs,isUnit,square,negate,isPositive,toString,next,prev,log".split(",");
1834 var binary
= "compare,remainder,divRem,subtract,add,quotient,divide,multiply,pow,compareAbs".split(",");
1835 var trinary
= ["modPow"];
1837 for (i
= 0; i
< unary
.length
; i
++) {
1839 BigInteger
[fn
] = makeUnary(BigInteger
.prototype[fn
]);
1842 for (i
= 0; i
< binary
.length
; i
++) {
1844 BigInteger
[fn
] = makeBinary(BigInteger
.prototype[fn
]);
1847 for (i
= 0; i
< trinary
.length
; i
++) {
1849 BigInteger
[fn
] = makeTrinary(BigInteger
.prototype[fn
]);
1852 BigInteger
.exp10 = function(x
, n
) {
1853 return BigInteger(x
).exp10(n
);
1858 exports
.BigInteger
= BigInteger
;
1859 })(typeof exports
!== 'undefined' ? exports : this);