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Commit | Line | Data |
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6606c50f IC |
1 | /* |
2 | * Detects entropy from a string. | |
3 | * | |
4 | * Formats include: | |
5 | * binary [0-1] | |
6 | * base 6 [0-5] | |
7 | * dice 6 [1-6] | |
8 | * decimal [0-9] | |
9 | * hexadecimal [0-9A-F] | |
10 | * | |
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 | |
13 | * entropy. | |
14 | */ | |
15 | ||
c6624d51 IC |
16 | window.Entropy = new (function() { |
17 | ||
6606c50f IC |
18 | // matchers returns an array of the matched events for each type of entropy. |
19 | // eg | |
20 | // matchers.binary("010") returns ["0", "1", "0"] | |
21 | // matchers.binary("a10") returns ["1", "0"] | |
22 | // matchers.hex("a10") returns ["a", "1", "0"] | |
c6624d51 | 23 | var matchers = { |
6606c50f IC |
24 | binary: function(str) { |
25 | return str.match(/[0-1]/gi) || []; | |
26 | }, | |
27 | base6: function(str) { | |
28 | return str.match(/[0-5]/gi) || []; | |
29 | }, | |
30 | dice: function(str) { | |
31 | return str.match(/[1-6]/gi) || []; // ie dice numbers | |
32 | }, | |
33 | base10: function(str) { | |
34 | return str.match(/[0-9]/gi) || []; | |
35 | }, | |
36 | hex: function(str) { | |
37 | return str.match(/[0-9A-F]/gi) || []; | |
38 | }, | |
adc8ce12 IC |
39 | card: function(str) { |
40 | // Format is NumberSuit, eg | |
41 | // AH ace of hearts | |
42 | // 8C eight of clubs | |
43 | // TD ten of diamonds | |
44 | // JS jack of spades | |
45 | // QH queen of hearts | |
46 | // KC king of clubs | |
47 | return str.match(/([A2-9TJQK][CDHS])/gi) || []; | |
48 | } | |
49 | } | |
50 | ||
51 | // Convert array of cards from ["ac", "4d", "ks"] | |
52 | // to numbers between 0 and 51 [0, 16, 51] | |
53 | function convertCardsToInts(cards) { | |
54 | var ints = []; | |
55 | var values = "a23456789tjqk"; | |
56 | var suits = "cdhs"; | |
57 | for (var i=0; i<cards.length; i++) { | |
58 | var card = cards[i].toLowerCase(); | |
59 | var value = card[0]; | |
60 | var suit = card[1]; | |
61 | var asInt = 13 * suits.indexOf(suit) + values.indexOf(value); | |
62 | ints.push(asInt); | |
63 | } | |
64 | return ints; | |
c6624d51 IC |
65 | } |
66 | ||
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) | |
425b75a9 | 71 | // This is done by changing all 6s to 0s |
c6624d51 IC |
72 | if (base.str == "dice") { |
73 | var newRawEntropyStr = ""; | |
74 | for (var i=0; i<rawEntropyStr.length; i++) { | |
75 | var c = rawEntropyStr[i]; | |
425b75a9 IC |
76 | if ("12345".indexOf(c) > -1) { |
77 | newRawEntropyStr += c; | |
c6624d51 IC |
78 | } |
79 | else { | |
425b75a9 | 80 | newRawEntropyStr += "0"; |
c6624d51 IC |
81 | } |
82 | } | |
83 | rawEntropyStr = newRawEntropyStr; | |
84 | base.str = "base 6 (dice)"; | |
6606c50f | 85 | base.parts = matchers.base6(rawEntropyStr); |
c6624d51 IC |
86 | base.matcher = matchers.base6; |
87 | } | |
c6624d51 | 88 | // Detect empty entropy |
6606c50f | 89 | if (base.parts.length == 0) { |
c6624d51 IC |
90 | return { |
91 | binaryStr: "", | |
c6624d51 IC |
92 | cleanStr: "", |
93 | base: base, | |
94 | }; | |
95 | } | |
96 | // Pull leading zeros off | |
6606c50f | 97 | var leadingZeros = []; |
adc8ce12 | 98 | while (base.ints[0] == "0") { |
6606c50f | 99 | leadingZeros.push("0"); |
adc8ce12 | 100 | base.ints.shift(); |
c6624d51 IC |
101 | } |
102 | // Convert leading zeros to binary equivalent | |
adc8ce12 | 103 | var numBinLeadingZeros = Math.floor(Math.log2(base.asInt) * leadingZeros.length); |
c6624d51 IC |
104 | var binLeadingZeros = ""; |
105 | for (var i=0; i<numBinLeadingZeros; i++) { | |
106 | binLeadingZeros += "0"; | |
107 | } | |
c6624d51 | 108 | // Handle entropy of zero |
adc8ce12 | 109 | if (base.ints.length == 0) { |
c6624d51 IC |
110 | return { |
111 | binaryStr: binLeadingZeros, | |
c6624d51 IC |
112 | cleanStr: leadingZeros, |
113 | base: base, | |
114 | } | |
115 | } | |
adc8ce12 IC |
116 | // If the first integer is small, it must be padded with zeros. |
117 | // Otherwise the chance of the first bit being 1 is 100%, which is | |
118 | // obviously incorrect. | |
119 | // This is not perfect for unusual bases, eg base 6 has 2.6 bits, so is | |
120 | // slightly biased toward having leading zeros, but it's still better | |
121 | // than ignoring it completely. | |
122 | // TODO: revise this, it seems very fishy. For example, in base 10, there are | |
123 | // 8 opportunities to start with 0 but only 2 to start with 1 | |
124 | var firstInt = base.ints[0]; | |
125 | var firstIntBits = Math.floor(Math.log2(firstInt))+1; | |
126 | var maxFirstIntBits = Math.floor(Math.log2(base.asInt-1))+1; | |
127 | var missingFirstIntBits = maxFirstIntBits - firstIntBits; | |
128 | var firstIntLeadingZeros = ""; | |
129 | for (var i=0; i<missingFirstIntBits; i++) { | |
130 | binLeadingZeros += "0"; | |
131 | } | |
132 | // Convert base.ints to BigInteger. | |
133 | // Due to using unusual bases, eg cards of base52, this is not as simple as | |
134 | // using BigInteger.parse() | |
135 | var entropyInt = BigInteger.ZERO; | |
136 | for (var i=base.ints.length-1; i>=0; i--) { | |
137 | var thisInt = BigInteger.parse(base.ints[i]); | |
138 | var power = (base.ints.length - 1) - i; | |
139 | var additionalEntropy = BigInteger.parse(base.asInt).pow(power).multiply(thisInt); | |
140 | entropyInt = entropyInt.add(additionalEntropy); | |
c6624d51 | 141 | } |
adc8ce12 | 142 | // Convert entropy to different formats |
c6624d51 | 143 | var entropyBin = binLeadingZeros + entropyInt.toString(2); |
adc8ce12 | 144 | var entropyClean = base.parts.join(""); |
c6624d51 IC |
145 | var e = { |
146 | binaryStr: entropyBin, | |
c6624d51 IC |
147 | cleanStr: entropyClean, |
148 | base: base, | |
149 | } | |
150 | return e; | |
151 | } | |
152 | ||
153 | function getBase(str) { | |
154 | // Need to get the lowest base for the supplied entropy. | |
155 | // This prevents interpreting, say, dice rolls as hexadecimal. | |
6606c50f IC |
156 | var binaryMatches = matchers.binary(str); |
157 | var hexMatches = matchers.hex(str); | |
c6624d51 | 158 | // Find the lowest base that can be used, whilst ignoring any irrelevant chars |
adc8ce12 IC |
159 | if (binaryMatches.length == hexMatches.length && hexMatches.length > 0) { |
160 | var ints = binaryMatches.map(function(i) { return parseInt(i, 2) }); | |
c6624d51 | 161 | return { |
adc8ce12 | 162 | ints: ints, |
6606c50f | 163 | parts: binaryMatches, |
c6624d51 IC |
164 | matcher: matchers.binary, |
165 | asInt: 2, | |
166 | str: "binary", | |
167 | } | |
168 | } | |
adc8ce12 IC |
169 | var cardMatches = matchers.card(str); |
170 | if (cardMatches.length >= hexMatches.length / 2) { | |
171 | var ints = convertCardsToInts(cardMatches); | |
172 | return { | |
173 | ints: ints, | |
174 | parts: cardMatches, | |
175 | matcher: matchers.card, | |
176 | asInt: 52, | |
177 | str: "card", | |
178 | } | |
179 | } | |
6606c50f | 180 | var diceMatches = matchers.dice(str); |
adc8ce12 IC |
181 | if (diceMatches.length == hexMatches.length && hexMatches.length > 0) { |
182 | var ints = diceMatches.map(function(i) { return parseInt(i) }); | |
c6624d51 | 183 | return { |
adc8ce12 | 184 | ints: ints, |
6606c50f | 185 | parts: diceMatches, |
c6624d51 IC |
186 | matcher: matchers.dice, |
187 | asInt: 6, | |
188 | str: "dice", | |
189 | } | |
190 | } | |
6606c50f | 191 | var base6Matches = matchers.base6(str); |
adc8ce12 IC |
192 | if (base6Matches.length == hexMatches.length && hexMatches.length > 0) { |
193 | var ints = base6Matches.map(function(i) { return parseInt(i) }); | |
c6624d51 | 194 | return { |
adc8ce12 | 195 | ints: ints, |
6606c50f | 196 | parts: base6Matches, |
c6624d51 IC |
197 | matcher: matchers.base6, |
198 | asInt: 6, | |
199 | str: "base 6", | |
200 | } | |
201 | } | |
6606c50f | 202 | var base10Matches = matchers.base10(str); |
adc8ce12 IC |
203 | if (base10Matches.length == hexMatches.length && hexMatches.length > 0) { |
204 | var ints = base10Matches.map(function(i) { return parseInt(i) }); | |
c6624d51 | 205 | return { |
adc8ce12 | 206 | ints: ints, |
6606c50f | 207 | parts: base10Matches, |
c6624d51 IC |
208 | matcher: matchers.base10, |
209 | asInt: 10, | |
210 | str: "base 10", | |
211 | } | |
212 | } | |
adc8ce12 | 213 | var ints = hexMatches.map(function(i) { return parseInt(i, 16) }); |
c6624d51 | 214 | return { |
adc8ce12 | 215 | ints: ints, |
6606c50f | 216 | parts: hexMatches, |
c6624d51 IC |
217 | matcher: matchers.hex, |
218 | asInt: 16, | |
219 | str: "hexadecimal", | |
220 | } | |
221 | } | |
222 | ||
223 | // Polyfill for Math.log2 | |
224 | // See https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Math/log2#Polyfill | |
225 | Math.log2 = Math.log2 || function(x) { | |
adc8ce12 IC |
226 | // The polyfill isn't good enough because of the poor accuracy of |
227 | // Math.LOG2E | |
228 | // log2(8) gave 2.9999999999999996 which when floored causes issues. | |
229 | // So instead use the BigInteger library to get it right. | |
230 | return BigInteger.log(x) / BigInteger.log(2); | |
c6624d51 IC |
231 | }; |
232 | ||
233 | })(); | |
234 | ||
235 | ||
236 | // BigInteger library included here because | |
237 | // only the entropy library depends on it | |
238 | // so if entropy detection is removed so is the dependency | |
239 | ||
240 | ||
241 | /* | |
242 | JavaScript BigInteger library version 0.9.1 | |
243 | http://silentmatt.com/biginteger/ | |
244 | ||
245 | Copyright (c) 2009 Matthew Crumley <email@matthewcrumley.com> | |
246 | Copyright (c) 2010,2011 by John Tobey <John.Tobey@gmail.com> | |
247 | Licensed under the MIT license. | |
248 | ||
249 | Support for arbitrary internal representation base was added by | |
250 | Vitaly Magerya. | |
251 | */ | |
252 | ||
253 | /* | |
254 | File: biginteger.js | |
255 | ||
256 | Exports: | |
257 | ||
258 | <BigInteger> | |
259 | */ | |
260 | (function(exports) { | |
261 | "use strict"; | |
262 | /* | |
263 | Class: BigInteger | |
264 | An arbitrarily-large integer. | |
265 | ||
266 | <BigInteger> objects should be considered immutable. None of the "built-in" | |
267 | methods modify *this* or their arguments. All properties should be | |
268 | considered private. | |
269 | ||
270 | All the methods of <BigInteger> instances can be called "statically". The | |
271 | static versions are convenient if you don't already have a <BigInteger> | |
272 | object. | |
273 | ||
274 | As an example, these calls are equivalent. | |
275 | ||
276 | > BigInteger(4).multiply(5); // returns BigInteger(20); | |
277 | > BigInteger.multiply(4, 5); // returns BigInteger(20); | |
278 | ||
279 | > var a = 42; | |
280 | > var a = BigInteger.toJSValue("0b101010"); // Not completely useless... | |
281 | */ | |
282 | ||
283 | var CONSTRUCT = {}; // Unique token to call "private" version of constructor | |
284 | ||
285 | /* | |
286 | Constructor: BigInteger() | |
287 | Convert a value to a <BigInteger>. | |
288 | ||
289 | Although <BigInteger()> is the constructor for <BigInteger> objects, it is | |
290 | best not to call it as a constructor. If *n* is a <BigInteger> object, it is | |
291 | simply returned as-is. Otherwise, <BigInteger()> is equivalent to <parse> | |
292 | without a radix argument. | |
293 | ||
294 | > var n0 = BigInteger(); // Same as <BigInteger.ZERO> | |
295 | > var n1 = BigInteger("123"); // Create a new <BigInteger> with value 123 | |
296 | > var n2 = BigInteger(123); // Create a new <BigInteger> with value 123 | |
297 | > var n3 = BigInteger(n2); // Return n2, unchanged | |
298 | ||
299 | The constructor form only takes an array and a sign. *n* must be an | |
300 | array of numbers in little-endian order, where each digit is between 0 | |
301 | and BigInteger.base. The second parameter sets the sign: -1 for | |
302 | negative, +1 for positive, or 0 for zero. The array is *not copied and | |
303 | may be modified*. If the array contains only zeros, the sign parameter | |
304 | is ignored and is forced to zero. | |
305 | ||
306 | > new BigInteger([5], -1): create a new BigInteger with value -5 | |
307 | ||
308 | Parameters: | |
309 | ||
310 | n - Value to convert to a <BigInteger>. | |
311 | ||
312 | Returns: | |
313 | ||
314 | A <BigInteger> value. | |
315 | ||
316 | See Also: | |
317 | ||
318 | <parse>, <BigInteger> | |
319 | */ | |
320 | function BigInteger(n, s, token) { | |
321 | if (token !== CONSTRUCT) { | |
322 | if (n instanceof BigInteger) { | |
323 | return n; | |
324 | } | |
325 | else if (typeof n === "undefined") { | |
326 | return ZERO; | |
327 | } | |
328 | return BigInteger.parse(n); | |
329 | } | |
330 | ||
331 | n = n || []; // Provide the nullary constructor for subclasses. | |
332 | while (n.length && !n[n.length - 1]) { | |
333 | --n.length; | |
334 | } | |
335 | this._d = n; | |
336 | this._s = n.length ? (s || 1) : 0; | |
337 | } | |
338 | ||
339 | BigInteger._construct = function(n, s) { | |
340 | return new BigInteger(n, s, CONSTRUCT); | |
341 | }; | |
342 | ||
343 | // Base-10 speedup hacks in parse, toString, exp10 and log functions | |
344 | // require base to be a power of 10. 10^7 is the largest such power | |
345 | // that won't cause a precision loss when digits are multiplied. | |
346 | var BigInteger_base = 10000000; | |
347 | var BigInteger_base_log10 = 7; | |
348 | ||
349 | BigInteger.base = BigInteger_base; | |
350 | BigInteger.base_log10 = BigInteger_base_log10; | |
351 | ||
352 | var ZERO = new BigInteger([], 0, CONSTRUCT); | |
353 | // Constant: ZERO | |
354 | // <BigInteger> 0. | |
355 | BigInteger.ZERO = ZERO; | |
356 | ||
357 | var ONE = new BigInteger([1], 1, CONSTRUCT); | |
358 | // Constant: ONE | |
359 | // <BigInteger> 1. | |
360 | BigInteger.ONE = ONE; | |
361 | ||
362 | var M_ONE = new BigInteger(ONE._d, -1, CONSTRUCT); | |
363 | // Constant: M_ONE | |
364 | // <BigInteger> -1. | |
365 | BigInteger.M_ONE = M_ONE; | |
366 | ||
367 | // Constant: _0 | |
368 | // Shortcut for <ZERO>. | |
369 | BigInteger._0 = ZERO; | |
370 | ||
371 | // Constant: _1 | |
372 | // Shortcut for <ONE>. | |
373 | BigInteger._1 = ONE; | |
374 | ||
375 | /* | |
376 | Constant: small | |
377 | Array of <BigIntegers> from 0 to 36. | |
378 | ||
379 | These are used internally for parsing, but useful when you need a "small" | |
380 | <BigInteger>. | |
381 | ||
382 | See Also: | |
383 | ||
384 | <ZERO>, <ONE>, <_0>, <_1> | |
385 | */ | |
386 | BigInteger.small = [ | |
387 | ZERO, | |
388 | ONE, | |
389 | /* Assuming BigInteger_base > 36 */ | |
390 | new BigInteger( [2], 1, CONSTRUCT), | |
391 | new BigInteger( [3], 1, CONSTRUCT), | |
392 | new BigInteger( [4], 1, CONSTRUCT), | |
393 | new BigInteger( [5], 1, CONSTRUCT), | |
394 | new BigInteger( [6], 1, CONSTRUCT), | |
395 | new BigInteger( [7], 1, CONSTRUCT), | |
396 | new BigInteger( [8], 1, CONSTRUCT), | |
397 | new BigInteger( [9], 1, CONSTRUCT), | |
398 | new BigInteger([10], 1, CONSTRUCT), | |
399 | new BigInteger([11], 1, CONSTRUCT), | |
400 | new BigInteger([12], 1, CONSTRUCT), | |
401 | new BigInteger([13], 1, CONSTRUCT), | |
402 | new BigInteger([14], 1, CONSTRUCT), | |
403 | new BigInteger([15], 1, CONSTRUCT), | |
404 | new BigInteger([16], 1, CONSTRUCT), | |
405 | new BigInteger([17], 1, CONSTRUCT), | |
406 | new BigInteger([18], 1, CONSTRUCT), | |
407 | new BigInteger([19], 1, CONSTRUCT), | |
408 | new BigInteger([20], 1, CONSTRUCT), | |
409 | new BigInteger([21], 1, CONSTRUCT), | |
410 | new BigInteger([22], 1, CONSTRUCT), | |
411 | new BigInteger([23], 1, CONSTRUCT), | |
412 | new BigInteger([24], 1, CONSTRUCT), | |
413 | new BigInteger([25], 1, CONSTRUCT), | |
414 | new BigInteger([26], 1, CONSTRUCT), | |
415 | new BigInteger([27], 1, CONSTRUCT), | |
416 | new BigInteger([28], 1, CONSTRUCT), | |
417 | new BigInteger([29], 1, CONSTRUCT), | |
418 | new BigInteger([30], 1, CONSTRUCT), | |
419 | new BigInteger([31], 1, CONSTRUCT), | |
420 | new BigInteger([32], 1, CONSTRUCT), | |
421 | new BigInteger([33], 1, CONSTRUCT), | |
422 | new BigInteger([34], 1, CONSTRUCT), | |
423 | new BigInteger([35], 1, CONSTRUCT), | |
424 | new BigInteger([36], 1, CONSTRUCT) | |
425 | ]; | |
426 | ||
427 | // Used for parsing/radix conversion | |
428 | BigInteger.digits = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ".split(""); | |
429 | ||
430 | /* | |
431 | Method: toString | |
432 | Convert a <BigInteger> to a string. | |
433 | ||
434 | When *base* is greater than 10, letters are upper case. | |
435 | ||
436 | Parameters: | |
437 | ||
438 | base - Optional base to represent the number in (default is base 10). | |
439 | Must be between 2 and 36 inclusive, or an Error will be thrown. | |
440 | ||
441 | Returns: | |
442 | ||
443 | The string representation of the <BigInteger>. | |
444 | */ | |
445 | BigInteger.prototype.toString = function(base) { | |
446 | base = +base || 10; | |
447 | if (base < 2 || base > 36) { | |
448 | throw new Error("illegal radix " + base + "."); | |
449 | } | |
450 | if (this._s === 0) { | |
451 | return "0"; | |
452 | } | |
453 | if (base === 10) { | |
454 | var str = this._s < 0 ? "-" : ""; | |
455 | str += this._d[this._d.length - 1].toString(); | |
456 | for (var i = this._d.length - 2; i >= 0; i--) { | |
457 | var group = this._d[i].toString(); | |
458 | while (group.length < BigInteger_base_log10) group = '0' + group; | |
459 | str += group; | |
460 | } | |
461 | return str; | |
462 | } | |
463 | else { | |
464 | var numerals = BigInteger.digits; | |
465 | base = BigInteger.small[base]; | |
466 | var sign = this._s; | |
467 | ||
468 | var n = this.abs(); | |
469 | var digits = []; | |
470 | var digit; | |
471 | ||
472 | while (n._s !== 0) { | |
473 | var divmod = n.divRem(base); | |
474 | n = divmod[0]; | |
475 | digit = divmod[1]; | |
476 | // TODO: This could be changed to unshift instead of reversing at the end. | |
477 | // Benchmark both to compare speeds. | |
478 | digits.push(numerals[digit.valueOf()]); | |
479 | } | |
480 | return (sign < 0 ? "-" : "") + digits.reverse().join(""); | |
481 | } | |
482 | }; | |
483 | ||
484 | // Verify strings for parsing | |
485 | BigInteger.radixRegex = [ | |
486 | /^$/, | |
487 | /^$/, | |
488 | /^[01]*$/, | |
489 | /^[012]*$/, | |
490 | /^[0-3]*$/, | |
491 | /^[0-4]*$/, | |
492 | /^[0-5]*$/, | |
493 | /^[0-6]*$/, | |
494 | /^[0-7]*$/, | |
495 | /^[0-8]*$/, | |
496 | /^[0-9]*$/, | |
497 | /^[0-9aA]*$/, | |
498 | /^[0-9abAB]*$/, | |
499 | /^[0-9abcABC]*$/, | |
500 | /^[0-9a-dA-D]*$/, | |
501 | /^[0-9a-eA-E]*$/, | |
502 | /^[0-9a-fA-F]*$/, | |
503 | /^[0-9a-gA-G]*$/, | |
504 | /^[0-9a-hA-H]*$/, | |
505 | /^[0-9a-iA-I]*$/, | |
506 | /^[0-9a-jA-J]*$/, | |
507 | /^[0-9a-kA-K]*$/, | |
508 | /^[0-9a-lA-L]*$/, | |
509 | /^[0-9a-mA-M]*$/, | |
510 | /^[0-9a-nA-N]*$/, | |
511 | /^[0-9a-oA-O]*$/, | |
512 | /^[0-9a-pA-P]*$/, | |
513 | /^[0-9a-qA-Q]*$/, | |
514 | /^[0-9a-rA-R]*$/, | |
515 | /^[0-9a-sA-S]*$/, | |
516 | /^[0-9a-tA-T]*$/, | |
517 | /^[0-9a-uA-U]*$/, | |
518 | /^[0-9a-vA-V]*$/, | |
519 | /^[0-9a-wA-W]*$/, | |
520 | /^[0-9a-xA-X]*$/, | |
521 | /^[0-9a-yA-Y]*$/, | |
522 | /^[0-9a-zA-Z]*$/ | |
523 | ]; | |
524 | ||
525 | /* | |
526 | Function: parse | |
527 | Parse a string into a <BigInteger>. | |
528 | ||
529 | *base* is optional but, if provided, must be from 2 to 36 inclusive. If | |
530 | *base* is not provided, it will be guessed based on the leading characters | |
531 | of *s* as follows: | |
532 | ||
533 | - "0x" or "0X": *base* = 16 | |
534 | - "0c" or "0C": *base* = 8 | |
535 | - "0b" or "0B": *base* = 2 | |
536 | - else: *base* = 10 | |
537 | ||
538 | If no base is provided, or *base* is 10, the number can be in exponential | |
539 | form. For example, these are all valid: | |
540 | ||
541 | > BigInteger.parse("1e9"); // Same as "1000000000" | |
542 | > BigInteger.parse("1.234*10^3"); // Same as 1234 | |
543 | > BigInteger.parse("56789 * 10 ** -2"); // Same as 567 | |
544 | ||
545 | If any characters fall outside the range defined by the radix, an exception | |
546 | will be thrown. | |
547 | ||
548 | Parameters: | |
549 | ||
550 | s - The string to parse. | |
551 | base - Optional radix (default is to guess based on *s*). | |
552 | ||
553 | Returns: | |
554 | ||
555 | a <BigInteger> instance. | |
556 | */ | |
557 | BigInteger.parse = function(s, base) { | |
558 | // Expands a number in exponential form to decimal form. | |
559 | // expandExponential("-13.441*10^5") === "1344100"; | |
560 | // expandExponential("1.12300e-1") === "0.112300"; | |
561 | // expandExponential(1000000000000000000000000000000) === "1000000000000000000000000000000"; | |
562 | function expandExponential(str) { | |
563 | str = str.replace(/\s*[*xX]\s*10\s*(\^|\*\*)\s*/, "e"); | |
564 | ||
565 | return str.replace(/^([+\-])?(\d+)\.?(\d*)[eE]([+\-]?\d+)$/, function(x, s, n, f, c) { | |
566 | c = +c; | |
567 | var l = c < 0; | |
568 | var i = n.length + c; | |
569 | x = (l ? n : f).length; | |
570 | c = ((c = Math.abs(c)) >= x ? c - x + l : 0); | |
571 | var z = (new Array(c + 1)).join("0"); | |
572 | var r = n + f; | |
573 | return (s || "") + (l ? r = z + r : r += z).substr(0, i += l ? z.length : 0) + (i < r.length ? "." + r.substr(i) : ""); | |
574 | }); | |
575 | } | |
576 | ||
577 | s = s.toString(); | |
578 | if (typeof base === "undefined" || +base === 10) { | |
579 | s = expandExponential(s); | |
580 | } | |
581 | ||
582 | var prefixRE; | |
583 | if (typeof base === "undefined") { | |
584 | prefixRE = '0[xcb]'; | |
585 | } | |
586 | else if (base == 16) { | |
587 | prefixRE = '0x'; | |
588 | } | |
589 | else if (base == 8) { | |
590 | prefixRE = '0c'; | |
591 | } | |
592 | else if (base == 2) { | |
593 | prefixRE = '0b'; | |
594 | } | |
595 | else { | |
596 | prefixRE = ''; | |
597 | } | |
598 | var parts = new RegExp('^([+\\-]?)(' + prefixRE + ')?([0-9a-z]*)(?:\\.\\d*)?$', 'i').exec(s); | |
599 | if (parts) { | |
600 | var sign = parts[1] || "+"; | |
601 | var baseSection = parts[2] || ""; | |
602 | var digits = parts[3] || ""; | |
603 | ||
604 | if (typeof base === "undefined") { | |
605 | // Guess base | |
606 | if (baseSection === "0x" || baseSection === "0X") { // Hex | |
607 | base = 16; | |
608 | } | |
609 | else if (baseSection === "0c" || baseSection === "0C") { // Octal | |
610 | base = 8; | |
611 | } | |
612 | else if (baseSection === "0b" || baseSection === "0B") { // Binary | |
613 | base = 2; | |
614 | } | |
615 | else { | |
616 | base = 10; | |
617 | } | |
618 | } | |
619 | else if (base < 2 || base > 36) { | |
620 | throw new Error("Illegal radix " + base + "."); | |
621 | } | |
622 | ||
623 | base = +base; | |
624 | ||
625 | // Check for digits outside the range | |
626 | if (!(BigInteger.radixRegex[base].test(digits))) { | |
627 | throw new Error("Bad digit for radix " + base); | |
628 | } | |
629 | ||
630 | // Strip leading zeros, and convert to array | |
631 | digits = digits.replace(/^0+/, "").split(""); | |
632 | if (digits.length === 0) { | |
633 | return ZERO; | |
634 | } | |
635 | ||
636 | // Get the sign (we know it's not zero) | |
637 | sign = (sign === "-") ? -1 : 1; | |
638 | ||
639 | // Optimize 10 | |
640 | if (base == 10) { | |
641 | var d = []; | |
642 | while (digits.length >= BigInteger_base_log10) { | |
643 | d.push(parseInt(digits.splice(digits.length-BigInteger.base_log10, BigInteger.base_log10).join(''), 10)); | |
644 | } | |
645 | d.push(parseInt(digits.join(''), 10)); | |
646 | return new BigInteger(d, sign, CONSTRUCT); | |
647 | } | |
648 | ||
649 | // Do the conversion | |
650 | var d = ZERO; | |
651 | base = BigInteger.small[base]; | |
652 | var small = BigInteger.small; | |
653 | for (var i = 0; i < digits.length; i++) { | |
654 | d = d.multiply(base).add(small[parseInt(digits[i], 36)]); | |
655 | } | |
656 | return new BigInteger(d._d, sign, CONSTRUCT); | |
657 | } | |
658 | else { | |
659 | throw new Error("Invalid BigInteger format: " + s); | |
660 | } | |
661 | }; | |
662 | ||
663 | /* | |
664 | Function: add | |
665 | Add two <BigIntegers>. | |
666 | ||
667 | Parameters: | |
668 | ||
669 | n - The number to add to *this*. Will be converted to a <BigInteger>. | |
670 | ||
671 | Returns: | |
672 | ||
673 | The numbers added together. | |
674 | ||
675 | See Also: | |
676 | ||
677 | <subtract>, <multiply>, <quotient>, <next> | |
678 | */ | |
679 | BigInteger.prototype.add = function(n) { | |
680 | if (this._s === 0) { | |
681 | return BigInteger(n); | |
682 | } | |
683 | ||
684 | n = BigInteger(n); | |
685 | if (n._s === 0) { | |
686 | return this; | |
687 | } | |
688 | if (this._s !== n._s) { | |
689 | n = n.negate(); | |
690 | return this.subtract(n); | |
691 | } | |
692 | ||
693 | var a = this._d; | |
694 | var b = n._d; | |
695 | var al = a.length; | |
696 | var bl = b.length; | |
697 | var sum = new Array(Math.max(al, bl) + 1); | |
698 | var size = Math.min(al, bl); | |
699 | var carry = 0; | |
700 | var digit; | |
701 | ||
702 | for (var i = 0; i < size; i++) { | |
703 | digit = a[i] + b[i] + carry; | |
704 | sum[i] = digit % BigInteger_base; | |
705 | carry = (digit / BigInteger_base) | 0; | |
706 | } | |
707 | if (bl > al) { | |
708 | a = b; | |
709 | al = bl; | |
710 | } | |
711 | for (i = size; carry && i < al; i++) { | |
712 | digit = a[i] + carry; | |
713 | sum[i] = digit % BigInteger_base; | |
714 | carry = (digit / BigInteger_base) | 0; | |
715 | } | |
716 | if (carry) { | |
717 | sum[i] = carry; | |
718 | } | |
719 | ||
720 | for ( ; i < al; i++) { | |
721 | sum[i] = a[i]; | |
722 | } | |
723 | ||
724 | return new BigInteger(sum, this._s, CONSTRUCT); | |
725 | }; | |
726 | ||
727 | /* | |
728 | Function: negate | |
729 | Get the additive inverse of a <BigInteger>. | |
730 | ||
731 | Returns: | |
732 | ||
733 | A <BigInteger> with the same magnatude, but with the opposite sign. | |
734 | ||
735 | See Also: | |
736 | ||
737 | <abs> | |
738 | */ | |
739 | BigInteger.prototype.negate = function() { | |
740 | return new BigInteger(this._d, (-this._s) | 0, CONSTRUCT); | |
741 | }; | |
742 | ||
743 | /* | |
744 | Function: abs | |
745 | Get the absolute value of a <BigInteger>. | |
746 | ||
747 | Returns: | |
748 | ||
749 | A <BigInteger> with the same magnatude, but always positive (or zero). | |
750 | ||
751 | See Also: | |
752 | ||
753 | <negate> | |
754 | */ | |
755 | BigInteger.prototype.abs = function() { | |
756 | return (this._s < 0) ? this.negate() : this; | |
757 | }; | |
758 | ||
759 | /* | |
760 | Function: subtract | |
761 | Subtract two <BigIntegers>. | |
762 | ||
763 | Parameters: | |
764 | ||
765 | n - The number to subtract from *this*. Will be converted to a <BigInteger>. | |
766 | ||
767 | Returns: | |
768 | ||
769 | The *n* subtracted from *this*. | |
770 | ||
771 | See Also: | |
772 | ||
773 | <add>, <multiply>, <quotient>, <prev> | |
774 | */ | |
775 | BigInteger.prototype.subtract = function(n) { | |
776 | if (this._s === 0) { | |
777 | return BigInteger(n).negate(); | |
778 | } | |
779 | ||
780 | n = BigInteger(n); | |
781 | if (n._s === 0) { | |
782 | return this; | |
783 | } | |
784 | if (this._s !== n._s) { | |
785 | n = n.negate(); | |
786 | return this.add(n); | |
787 | } | |
788 | ||
789 | var m = this; | |
790 | // negative - negative => -|a| - -|b| => -|a| + |b| => |b| - |a| | |
791 | if (this._s < 0) { | |
792 | m = new BigInteger(n._d, 1, CONSTRUCT); | |
793 | n = new BigInteger(this._d, 1, CONSTRUCT); | |
794 | } | |
795 | ||
796 | // Both are positive => a - b | |
797 | var sign = m.compareAbs(n); | |
798 | if (sign === 0) { | |
799 | return ZERO; | |
800 | } | |
801 | else if (sign < 0) { | |
802 | // swap m and n | |
803 | var t = n; | |
804 | n = m; | |
805 | m = t; | |
806 | } | |
807 | ||
808 | // a > b | |
809 | var a = m._d; | |
810 | var b = n._d; | |
811 | var al = a.length; | |
812 | var bl = b.length; | |
813 | var diff = new Array(al); // al >= bl since a > b | |
814 | var borrow = 0; | |
815 | var i; | |
816 | var digit; | |
817 | ||
818 | for (i = 0; i < bl; i++) { | |
819 | digit = a[i] - borrow - b[i]; | |
820 | if (digit < 0) { | |
821 | digit += BigInteger_base; | |
822 | borrow = 1; | |
823 | } | |
824 | else { | |
825 | borrow = 0; | |
826 | } | |
827 | diff[i] = digit; | |
828 | } | |
829 | for (i = bl; i < al; i++) { | |
830 | digit = a[i] - borrow; | |
831 | if (digit < 0) { | |
832 | digit += BigInteger_base; | |
833 | } | |
834 | else { | |
835 | diff[i++] = digit; | |
836 | break; | |
837 | } | |
838 | diff[i] = digit; | |
839 | } | |
840 | for ( ; i < al; i++) { | |
841 | diff[i] = a[i]; | |
842 | } | |
843 | ||
844 | return new BigInteger(diff, sign, CONSTRUCT); | |
845 | }; | |
846 | ||
847 | (function() { | |
848 | function addOne(n, sign) { | |
849 | var a = n._d; | |
850 | var sum = a.slice(); | |
851 | var carry = true; | |
852 | var i = 0; | |
853 | ||
854 | while (true) { | |
855 | var digit = (a[i] || 0) + 1; | |
856 | sum[i] = digit % BigInteger_base; | |
857 | if (digit <= BigInteger_base - 1) { | |
858 | break; | |
859 | } | |
860 | ++i; | |
861 | } | |
862 | ||
863 | return new BigInteger(sum, sign, CONSTRUCT); | |
864 | } | |
865 | ||
866 | function subtractOne(n, sign) { | |
867 | var a = n._d; | |
868 | var sum = a.slice(); | |
869 | var borrow = true; | |
870 | var i = 0; | |
871 | ||
872 | while (true) { | |
873 | var digit = (a[i] || 0) - 1; | |
874 | if (digit < 0) { | |
875 | sum[i] = digit + BigInteger_base; | |
876 | } | |
877 | else { | |
878 | sum[i] = digit; | |
879 | break; | |
880 | } | |
881 | ++i; | |
882 | } | |
883 | ||
884 | return new BigInteger(sum, sign, CONSTRUCT); | |
885 | } | |
886 | ||
887 | /* | |
888 | Function: next | |
889 | Get the next <BigInteger> (add one). | |
890 | ||
891 | Returns: | |
892 | ||
893 | *this* + 1. | |
894 | ||
895 | See Also: | |
896 | ||
897 | <add>, <prev> | |
898 | */ | |
899 | BigInteger.prototype.next = function() { | |
900 | switch (this._s) { | |
901 | case 0: | |
902 | return ONE; | |
903 | case -1: | |
904 | return subtractOne(this, -1); | |
905 | // case 1: | |
906 | default: | |
907 | return addOne(this, 1); | |
908 | } | |
909 | }; | |
910 | ||
911 | /* | |
912 | Function: prev | |
913 | Get the previous <BigInteger> (subtract one). | |
914 | ||
915 | Returns: | |
916 | ||
917 | *this* - 1. | |
918 | ||
919 | See Also: | |
920 | ||
921 | <next>, <subtract> | |
922 | */ | |
923 | BigInteger.prototype.prev = function() { | |
924 | switch (this._s) { | |
925 | case 0: | |
926 | return M_ONE; | |
927 | case -1: | |
928 | return addOne(this, -1); | |
929 | // case 1: | |
930 | default: | |
931 | return subtractOne(this, 1); | |
932 | } | |
933 | }; | |
934 | })(); | |
935 | ||
936 | /* | |
937 | Function: compareAbs | |
938 | Compare the absolute value of two <BigIntegers>. | |
939 | ||
940 | Calling <compareAbs> is faster than calling <abs> twice, then <compare>. | |
941 | ||
942 | Parameters: | |
943 | ||
944 | n - The number to compare to *this*. Will be converted to a <BigInteger>. | |
945 | ||
946 | Returns: | |
947 | ||
948 | -1, 0, or +1 if *|this|* is less than, equal to, or greater than *|n|*. | |
949 | ||
950 | See Also: | |
951 | ||
952 | <compare>, <abs> | |
953 | */ | |
954 | BigInteger.prototype.compareAbs = function(n) { | |
955 | if (this === n) { | |
956 | return 0; | |
957 | } | |
958 | ||
959 | if (!(n instanceof BigInteger)) { | |
960 | if (!isFinite(n)) { | |
961 | return(isNaN(n) ? n : -1); | |
962 | } | |
963 | n = BigInteger(n); | |
964 | } | |
965 | ||
966 | if (this._s === 0) { | |
967 | return (n._s !== 0) ? -1 : 0; | |
968 | } | |
969 | if (n._s === 0) { | |
970 | return 1; | |
971 | } | |
972 | ||
973 | var l = this._d.length; | |
974 | var nl = n._d.length; | |
975 | if (l < nl) { | |
976 | return -1; | |
977 | } | |
978 | else if (l > nl) { | |
979 | return 1; | |
980 | } | |
981 | ||
982 | var a = this._d; | |
983 | var b = n._d; | |
984 | for (var i = l-1; i >= 0; i--) { | |
985 | if (a[i] !== b[i]) { | |
986 | return a[i] < b[i] ? -1 : 1; | |
987 | } | |
988 | } | |
989 | ||
990 | return 0; | |
991 | }; | |
992 | ||
993 | /* | |
994 | Function: compare | |
995 | Compare two <BigIntegers>. | |
996 | ||
997 | Parameters: | |
998 | ||
999 | n - The number to compare to *this*. Will be converted to a <BigInteger>. | |
1000 | ||
1001 | Returns: | |
1002 | ||
1003 | -1, 0, or +1 if *this* is less than, equal to, or greater than *n*. | |
1004 | ||
1005 | See Also: | |
1006 | ||
1007 | <compareAbs>, <isPositive>, <isNegative>, <isUnit> | |
1008 | */ | |
1009 | BigInteger.prototype.compare = function(n) { | |
1010 | if (this === n) { | |
1011 | return 0; | |
1012 | } | |
1013 | ||
1014 | n = BigInteger(n); | |
1015 | ||
1016 | if (this._s === 0) { | |
1017 | return -n._s; | |
1018 | } | |
1019 | ||
1020 | if (this._s === n._s) { // both positive or both negative | |
1021 | var cmp = this.compareAbs(n); | |
1022 | return cmp * this._s; | |
1023 | } | |
1024 | else { | |
1025 | return this._s; | |
1026 | } | |
1027 | }; | |
1028 | ||
1029 | /* | |
1030 | Function: isUnit | |
1031 | Return true iff *this* is either 1 or -1. | |
1032 | ||
1033 | Returns: | |
1034 | ||
1035 | true if *this* compares equal to <BigInteger.ONE> or <BigInteger.M_ONE>. | |
1036 | ||
1037 | See Also: | |
1038 | ||
1039 | <isZero>, <isNegative>, <isPositive>, <compareAbs>, <compare>, | |
1040 | <BigInteger.ONE>, <BigInteger.M_ONE> | |
1041 | */ | |
1042 | BigInteger.prototype.isUnit = function() { | |
1043 | return this === ONE || | |
1044 | this === M_ONE || | |
1045 | (this._d.length === 1 && this._d[0] === 1); | |
1046 | }; | |
1047 | ||
1048 | /* | |
1049 | Function: multiply | |
1050 | Multiply two <BigIntegers>. | |
1051 | ||
1052 | Parameters: | |
1053 | ||
1054 | n - The number to multiply *this* by. Will be converted to a | |
1055 | <BigInteger>. | |
1056 | ||
1057 | Returns: | |
1058 | ||
1059 | The numbers multiplied together. | |
1060 | ||
1061 | See Also: | |
1062 | ||
1063 | <add>, <subtract>, <quotient>, <square> | |
1064 | */ | |
1065 | BigInteger.prototype.multiply = function(n) { | |
1066 | // TODO: Consider adding Karatsuba multiplication for large numbers | |
1067 | if (this._s === 0) { | |
1068 | return ZERO; | |
1069 | } | |
1070 | ||
1071 | n = BigInteger(n); | |
1072 | if (n._s === 0) { | |
1073 | return ZERO; | |
1074 | } | |
1075 | if (this.isUnit()) { | |
1076 | if (this._s < 0) { | |
1077 | return n.negate(); | |
1078 | } | |
1079 | return n; | |
1080 | } | |
1081 | if (n.isUnit()) { | |
1082 | if (n._s < 0) { | |
1083 | return this.negate(); | |
1084 | } | |
1085 | return this; | |
1086 | } | |
1087 | if (this === n) { | |
1088 | return this.square(); | |
1089 | } | |
1090 | ||
1091 | var r = (this._d.length >= n._d.length); | |
1092 | var a = (r ? this : n)._d; // a will be longer than b | |
1093 | var b = (r ? n : this)._d; | |
1094 | var al = a.length; | |
1095 | var bl = b.length; | |
1096 | ||
1097 | var pl = al + bl; | |
1098 | var partial = new Array(pl); | |
1099 | var i; | |
1100 | for (i = 0; i < pl; i++) { | |
1101 | partial[i] = 0; | |
1102 | } | |
1103 | ||
1104 | for (i = 0; i < bl; i++) { | |
1105 | var carry = 0; | |
1106 | var bi = b[i]; | |
1107 | var jlimit = al + i; | |
1108 | var digit; | |
1109 | for (var j = i; j < jlimit; j++) { | |
1110 | digit = partial[j] + bi * a[j - i] + carry; | |
1111 | carry = (digit / BigInteger_base) | 0; | |
1112 | partial[j] = (digit % BigInteger_base) | 0; | |
1113 | } | |
1114 | if (carry) { | |
1115 | digit = partial[j] + carry; | |
1116 | carry = (digit / BigInteger_base) | 0; | |
1117 | partial[j] = digit % BigInteger_base; | |
1118 | } | |
1119 | } | |
1120 | return new BigInteger(partial, this._s * n._s, CONSTRUCT); | |
1121 | }; | |
1122 | ||
1123 | // Multiply a BigInteger by a single-digit native number | |
1124 | // Assumes that this and n are >= 0 | |
1125 | // This is not really intended to be used outside the library itself | |
1126 | BigInteger.prototype.multiplySingleDigit = function(n) { | |
1127 | if (n === 0 || this._s === 0) { | |
1128 | return ZERO; | |
1129 | } | |
1130 | if (n === 1) { | |
1131 | return this; | |
1132 | } | |
1133 | ||
1134 | var digit; | |
1135 | if (this._d.length === 1) { | |
1136 | digit = this._d[0] * n; | |
1137 | if (digit >= BigInteger_base) { | |
1138 | return new BigInteger([(digit % BigInteger_base)|0, | |
1139 | (digit / BigInteger_base)|0], 1, CONSTRUCT); | |
1140 | } | |
1141 | return new BigInteger([digit], 1, CONSTRUCT); | |
1142 | } | |
1143 | ||
1144 | if (n === 2) { | |
1145 | return this.add(this); | |
1146 | } | |
1147 | if (this.isUnit()) { | |
1148 | return new BigInteger([n], 1, CONSTRUCT); | |
1149 | } | |
1150 | ||
1151 | var a = this._d; | |
1152 | var al = a.length; | |
1153 | ||
1154 | var pl = al + 1; | |
1155 | var partial = new Array(pl); | |
1156 | for (var i = 0; i < pl; i++) { | |
1157 | partial[i] = 0; | |
1158 | } | |
1159 | ||
1160 | var carry = 0; | |
1161 | for (var j = 0; j < al; j++) { | |
1162 | digit = n * a[j] + carry; | |
1163 | carry = (digit / BigInteger_base) | 0; | |
1164 | partial[j] = (digit % BigInteger_base) | 0; | |
1165 | } | |
1166 | if (carry) { | |
1167 | partial[j] = carry; | |
1168 | } | |
1169 | ||
1170 | return new BigInteger(partial, 1, CONSTRUCT); | |
1171 | }; | |
1172 | ||
1173 | /* | |
1174 | Function: square | |
1175 | Multiply a <BigInteger> by itself. | |
1176 | ||
1177 | This is slightly faster than regular multiplication, since it removes the | |
1178 | duplicated multiplcations. | |
1179 | ||
1180 | Returns: | |
1181 | ||
1182 | > this.multiply(this) | |
1183 | ||
1184 | See Also: | |
1185 | <multiply> | |
1186 | */ | |
1187 | BigInteger.prototype.square = function() { | |
1188 | // Normally, squaring a 10-digit number would take 100 multiplications. | |
1189 | // Of these 10 are unique diagonals, of the remaining 90 (100-10), 45 are repeated. | |
1190 | // This procedure saves (N*(N-1))/2 multiplications, (e.g., 45 of 100 multiplies). | |
1191 | // Based on code by Gary Darby, Intellitech Systems Inc., www.DelphiForFun.org | |
1192 | ||
1193 | if (this._s === 0) { | |
1194 | return ZERO; | |
1195 | } | |
1196 | if (this.isUnit()) { | |
1197 | return ONE; | |
1198 | } | |
1199 | ||
1200 | var digits = this._d; | |
1201 | var length = digits.length; | |
1202 | var imult1 = new Array(length + length + 1); | |
1203 | var product, carry, k; | |
1204 | var i; | |
1205 | ||
1206 | // Calculate diagonal | |
1207 | for (i = 0; i < length; i++) { | |
1208 | k = i * 2; | |
1209 | product = digits[i] * digits[i]; | |
1210 | carry = (product / BigInteger_base) | 0; | |
1211 | imult1[k] = product % BigInteger_base; | |
1212 | imult1[k + 1] = carry; | |
1213 | } | |
1214 | ||
1215 | // Calculate repeating part | |
1216 | for (i = 0; i < length; i++) { | |
1217 | carry = 0; | |
1218 | k = i * 2 + 1; | |
1219 | for (var j = i + 1; j < length; j++, k++) { | |
1220 | product = digits[j] * digits[i] * 2 + imult1[k] + carry; | |
1221 | carry = (product / BigInteger_base) | 0; | |
1222 | imult1[k] = product % BigInteger_base; | |
1223 | } | |
1224 | k = length + i; | |
1225 | var digit = carry + imult1[k]; | |
1226 | carry = (digit / BigInteger_base) | 0; | |
1227 | imult1[k] = digit % BigInteger_base; | |
1228 | imult1[k + 1] += carry; | |
1229 | } | |
1230 | ||
1231 | return new BigInteger(imult1, 1, CONSTRUCT); | |
1232 | }; | |
1233 | ||
1234 | /* | |
1235 | Function: quotient | |
1236 | Divide two <BigIntegers> and truncate towards zero. | |
1237 | ||
1238 | <quotient> throws an exception if *n* is zero. | |
1239 | ||
1240 | Parameters: | |
1241 | ||
1242 | n - The number to divide *this* by. Will be converted to a <BigInteger>. | |
1243 | ||
1244 | Returns: | |
1245 | ||
1246 | The *this* / *n*, truncated to an integer. | |
1247 | ||
1248 | See Also: | |
1249 | ||
1250 | <add>, <subtract>, <multiply>, <divRem>, <remainder> | |
1251 | */ | |
1252 | BigInteger.prototype.quotient = function(n) { | |
1253 | return this.divRem(n)[0]; | |
1254 | }; | |
1255 | ||
1256 | /* | |
1257 | Function: divide | |
1258 | Deprecated synonym for <quotient>. | |
1259 | */ | |
1260 | BigInteger.prototype.divide = BigInteger.prototype.quotient; | |
1261 | ||
1262 | /* | |
1263 | Function: remainder | |
1264 | Calculate the remainder of two <BigIntegers>. | |
1265 | ||
1266 | <remainder> throws an exception if *n* is zero. | |
1267 | ||
1268 | Parameters: | |
1269 | ||
1270 | n - The remainder after *this* is divided *this* by *n*. Will be | |
1271 | converted to a <BigInteger>. | |
1272 | ||
1273 | Returns: | |
1274 | ||
1275 | *this* % *n*. | |
1276 | ||
1277 | See Also: | |
1278 | ||
1279 | <divRem>, <quotient> | |
1280 | */ | |
1281 | BigInteger.prototype.remainder = function(n) { | |
1282 | return this.divRem(n)[1]; | |
1283 | }; | |
1284 | ||
1285 | /* | |
1286 | Function: divRem | |
1287 | Calculate the integer quotient and remainder of two <BigIntegers>. | |
1288 | ||
1289 | <divRem> throws an exception if *n* is zero. | |
1290 | ||
1291 | Parameters: | |
1292 | ||
1293 | n - The number to divide *this* by. Will be converted to a <BigInteger>. | |
1294 | ||
1295 | Returns: | |
1296 | ||
1297 | A two-element array containing the quotient and the remainder. | |
1298 | ||
1299 | > a.divRem(b) | |
1300 | ||
1301 | is exactly equivalent to | |
1302 | ||
1303 | > [a.quotient(b), a.remainder(b)] | |
1304 | ||
1305 | except it is faster, because they are calculated at the same time. | |
1306 | ||
1307 | See Also: | |
1308 | ||
1309 | <quotient>, <remainder> | |
1310 | */ | |
1311 | BigInteger.prototype.divRem = function(n) { | |
1312 | n = BigInteger(n); | |
1313 | if (n._s === 0) { | |
1314 | throw new Error("Divide by zero"); | |
1315 | } | |
1316 | if (this._s === 0) { | |
1317 | return [ZERO, ZERO]; | |
1318 | } | |
1319 | if (n._d.length === 1) { | |
1320 | return this.divRemSmall(n._s * n._d[0]); | |
1321 | } | |
1322 | ||
1323 | // Test for easy cases -- |n1| <= |n2| | |
1324 | switch (this.compareAbs(n)) { | |
1325 | case 0: // n1 == n2 | |
1326 | return [this._s === n._s ? ONE : M_ONE, ZERO]; | |
1327 | case -1: // |n1| < |n2| | |
1328 | return [ZERO, this]; | |
1329 | } | |
1330 | ||
1331 | var sign = this._s * n._s; | |
1332 | var a = n.abs(); | |
1333 | var b_digits = this._d; | |
1334 | var b_index = b_digits.length; | |
1335 | var digits = n._d.length; | |
1336 | var quot = []; | |
1337 | var guess; | |
1338 | ||
1339 | var part = new BigInteger([], 0, CONSTRUCT); | |
1340 | ||
1341 | while (b_index) { | |
1342 | part._d.unshift(b_digits[--b_index]); | |
1343 | part = new BigInteger(part._d, 1, CONSTRUCT); | |
1344 | ||
1345 | if (part.compareAbs(n) < 0) { | |
1346 | quot.push(0); | |
1347 | continue; | |
1348 | } | |
1349 | if (part._s === 0) { | |
1350 | guess = 0; | |
1351 | } | |
1352 | else { | |
1353 | var xlen = part._d.length, ylen = a._d.length; | |
1354 | var highx = part._d[xlen-1]*BigInteger_base + part._d[xlen-2]; | |
1355 | var highy = a._d[ylen-1]*BigInteger_base + a._d[ylen-2]; | |
1356 | if (part._d.length > a._d.length) { | |
1357 | // The length of part._d can either match a._d length, | |
1358 | // or exceed it by one. | |
1359 | highx = (highx+1)*BigInteger_base; | |
1360 | } | |
1361 | guess = Math.ceil(highx/highy); | |
1362 | } | |
1363 | do { | |
1364 | var check = a.multiplySingleDigit(guess); | |
1365 | if (check.compareAbs(part) <= 0) { | |
1366 | break; | |
1367 | } | |
1368 | guess--; | |
1369 | } while (guess); | |
1370 | ||
1371 | quot.push(guess); | |
1372 | if (!guess) { | |
1373 | continue; | |
1374 | } | |
1375 | var diff = part.subtract(check); | |
1376 | part._d = diff._d.slice(); | |
1377 | } | |
1378 | ||
1379 | return [new BigInteger(quot.reverse(), sign, CONSTRUCT), | |
1380 | new BigInteger(part._d, this._s, CONSTRUCT)]; | |
1381 | }; | |
1382 | ||
1383 | // Throws an exception if n is outside of (-BigInteger.base, -1] or | |
1384 | // [1, BigInteger.base). It's not necessary to call this, since the | |
1385 | // other division functions will call it if they are able to. | |
1386 | BigInteger.prototype.divRemSmall = function(n) { | |
1387 | var r; | |
1388 | n = +n; | |
1389 | if (n === 0) { | |
1390 | throw new Error("Divide by zero"); | |
1391 | } | |
1392 | ||
1393 | var n_s = n < 0 ? -1 : 1; | |
1394 | var sign = this._s * n_s; | |
1395 | n = Math.abs(n); | |
1396 | ||
1397 | if (n < 1 || n >= BigInteger_base) { | |
1398 | throw new Error("Argument out of range"); | |
1399 | } | |
1400 | ||
1401 | if (this._s === 0) { | |
1402 | return [ZERO, ZERO]; | |
1403 | } | |
1404 | ||
1405 | if (n === 1 || n === -1) { | |
1406 | return [(sign === 1) ? this.abs() : new BigInteger(this._d, sign, CONSTRUCT), ZERO]; | |
1407 | } | |
1408 | ||
1409 | // 2 <= n < BigInteger_base | |
1410 | ||
1411 | // divide a single digit by a single digit | |
1412 | if (this._d.length === 1) { | |
1413 | var q = new BigInteger([(this._d[0] / n) | 0], 1, CONSTRUCT); | |
1414 | r = new BigInteger([(this._d[0] % n) | 0], 1, CONSTRUCT); | |
1415 | if (sign < 0) { | |
1416 | q = q.negate(); | |
1417 | } | |
1418 | if (this._s < 0) { | |
1419 | r = r.negate(); | |
1420 | } | |
1421 | return [q, r]; | |
1422 | } | |
1423 | ||
1424 | var digits = this._d.slice(); | |
1425 | var quot = new Array(digits.length); | |
1426 | var part = 0; | |
1427 | var diff = 0; | |
1428 | var i = 0; | |
1429 | var guess; | |
1430 | ||
1431 | while (digits.length) { | |
1432 | part = part * BigInteger_base + digits[digits.length - 1]; | |
1433 | if (part < n) { | |
1434 | quot[i++] = 0; | |
1435 | digits.pop(); | |
1436 | diff = BigInteger_base * diff + part; | |
1437 | continue; | |
1438 | } | |
1439 | if (part === 0) { | |
1440 | guess = 0; | |
1441 | } | |
1442 | else { | |
1443 | guess = (part / n) | 0; | |
1444 | } | |
1445 | ||
1446 | var check = n * guess; | |
1447 | diff = part - check; | |
1448 | quot[i++] = guess; | |
1449 | if (!guess) { | |
1450 | digits.pop(); | |
1451 | continue; | |
1452 | } | |
1453 | ||
1454 | digits.pop(); | |
1455 | part = diff; | |
1456 | } | |
1457 | ||
1458 | r = new BigInteger([diff], 1, CONSTRUCT); | |
1459 | if (this._s < 0) { | |
1460 | r = r.negate(); | |
1461 | } | |
1462 | return [new BigInteger(quot.reverse(), sign, CONSTRUCT), r]; | |
1463 | }; | |
1464 | ||
1465 | /* | |
1466 | Function: isEven | |
1467 | Return true iff *this* is divisible by two. | |
1468 | ||
1469 | Note that <BigInteger.ZERO> is even. | |
1470 | ||
1471 | Returns: | |
1472 | ||
1473 | true if *this* is even, false otherwise. | |
1474 | ||
1475 | See Also: | |
1476 | ||
1477 | <isOdd> | |
1478 | */ | |
1479 | BigInteger.prototype.isEven = function() { | |
1480 | var digits = this._d; | |
1481 | return this._s === 0 || digits.length === 0 || (digits[0] % 2) === 0; | |
1482 | }; | |
1483 | ||
1484 | /* | |
1485 | Function: isOdd | |
1486 | Return true iff *this* is not divisible by two. | |
1487 | ||
1488 | Returns: | |
1489 | ||
1490 | true if *this* is odd, false otherwise. | |
1491 | ||
1492 | See Also: | |
1493 | ||
1494 | <isEven> | |
1495 | */ | |
1496 | BigInteger.prototype.isOdd = function() { | |
1497 | return !this.isEven(); | |
1498 | }; | |
1499 | ||
1500 | /* | |
1501 | Function: sign | |
1502 | Get the sign of a <BigInteger>. | |
1503 | ||
1504 | Returns: | |
1505 | ||
1506 | * -1 if *this* < 0 | |
1507 | * 0 if *this* == 0 | |
1508 | * +1 if *this* > 0 | |
1509 | ||
1510 | See Also: | |
1511 | ||
1512 | <isZero>, <isPositive>, <isNegative>, <compare>, <BigInteger.ZERO> | |
1513 | */ | |
1514 | BigInteger.prototype.sign = function() { | |
1515 | return this._s; | |
1516 | }; | |
1517 | ||
1518 | /* | |
1519 | Function: isPositive | |
1520 | Return true iff *this* > 0. | |
1521 | ||
1522 | Returns: | |
1523 | ||
1524 | true if *this*.compare(<BigInteger.ZERO>) == 1. | |
1525 | ||
1526 | See Also: | |
1527 | ||
1528 | <sign>, <isZero>, <isNegative>, <isUnit>, <compare>, <BigInteger.ZERO> | |
1529 | */ | |
1530 | BigInteger.prototype.isPositive = function() { | |
1531 | return this._s > 0; | |
1532 | }; | |
1533 | ||
1534 | /* | |
1535 | Function: isNegative | |
1536 | Return true iff *this* < 0. | |
1537 | ||
1538 | Returns: | |
1539 | ||
1540 | true if *this*.compare(<BigInteger.ZERO>) == -1. | |
1541 | ||
1542 | See Also: | |
1543 | ||
1544 | <sign>, <isPositive>, <isZero>, <isUnit>, <compare>, <BigInteger.ZERO> | |
1545 | */ | |
1546 | BigInteger.prototype.isNegative = function() { | |
1547 | return this._s < 0; | |
1548 | }; | |
1549 | ||
1550 | /* | |
1551 | Function: isZero | |
1552 | Return true iff *this* == 0. | |
1553 | ||
1554 | Returns: | |
1555 | ||
1556 | true if *this*.compare(<BigInteger.ZERO>) == 0. | |
1557 | ||
1558 | See Also: | |
1559 | ||
1560 | <sign>, <isPositive>, <isNegative>, <isUnit>, <BigInteger.ZERO> | |
1561 | */ | |
1562 | BigInteger.prototype.isZero = function() { | |
1563 | return this._s === 0; | |
1564 | }; | |
1565 | ||
1566 | /* | |
1567 | Function: exp10 | |
1568 | Multiply a <BigInteger> by a power of 10. | |
1569 | ||
1570 | This is equivalent to, but faster than | |
1571 | ||
1572 | > if (n >= 0) { | |
1573 | > return this.multiply(BigInteger("1e" + n)); | |
1574 | > } | |
1575 | > else { // n <= 0 | |
1576 | > return this.quotient(BigInteger("1e" + -n)); | |
1577 | > } | |
1578 | ||
1579 | Parameters: | |
1580 | ||
1581 | n - The power of 10 to multiply *this* by. *n* is converted to a | |
1582 | javascipt number and must be no greater than <BigInteger.MAX_EXP> | |
1583 | (0x7FFFFFFF), or an exception will be thrown. | |
1584 | ||
1585 | Returns: | |
1586 | ||
1587 | *this* * (10 ** *n*), truncated to an integer if necessary. | |
1588 | ||
1589 | See Also: | |
1590 | ||
1591 | <pow>, <multiply> | |
1592 | */ | |
1593 | BigInteger.prototype.exp10 = function(n) { | |
1594 | n = +n; | |
1595 | if (n === 0) { | |
1596 | return this; | |
1597 | } | |
1598 | if (Math.abs(n) > Number(MAX_EXP)) { | |
1599 | throw new Error("exponent too large in BigInteger.exp10"); | |
1600 | } | |
1601 | // Optimization for this == 0. This also keeps us from having to trim zeros in the positive n case | |
1602 | if (this._s === 0) { | |
1603 | return ZERO; | |
1604 | } | |
1605 | if (n > 0) { | |
1606 | var k = new BigInteger(this._d.slice(), this._s, CONSTRUCT); | |
1607 | ||
1608 | for (; n >= BigInteger_base_log10; n -= BigInteger_base_log10) { | |
1609 | k._d.unshift(0); | |
1610 | } | |
1611 | if (n == 0) | |
1612 | return k; | |
1613 | k._s = 1; | |
1614 | k = k.multiplySingleDigit(Math.pow(10, n)); | |
1615 | return (this._s < 0 ? k.negate() : k); | |
1616 | } else if (-n >= this._d.length*BigInteger_base_log10) { | |
1617 | return ZERO; | |
1618 | } else { | |
1619 | var k = new BigInteger(this._d.slice(), this._s, CONSTRUCT); | |
1620 | ||
1621 | for (n = -n; n >= BigInteger_base_log10; n -= BigInteger_base_log10) { | |
1622 | k._d.shift(); | |
1623 | } | |
1624 | return (n == 0) ? k : k.divRemSmall(Math.pow(10, n))[0]; | |
1625 | } | |
1626 | }; | |
1627 | ||
1628 | /* | |
1629 | Function: pow | |
1630 | Raise a <BigInteger> to a power. | |
1631 | ||
1632 | In this implementation, 0**0 is 1. | |
1633 | ||
1634 | Parameters: | |
1635 | ||
1636 | n - The exponent to raise *this* by. *n* must be no greater than | |
1637 | <BigInteger.MAX_EXP> (0x7FFFFFFF), or an exception will be thrown. | |
1638 | ||
1639 | Returns: | |
1640 | ||
1641 | *this* raised to the *nth* power. | |
1642 | ||
1643 | See Also: | |
1644 | ||
1645 | <modPow> | |
1646 | */ | |
1647 | BigInteger.prototype.pow = function(n) { | |
1648 | if (this.isUnit()) { | |
1649 | if (this._s > 0) { | |
1650 | return this; | |
1651 | } | |
1652 | else { | |
1653 | return BigInteger(n).isOdd() ? this : this.negate(); | |
1654 | } | |
1655 | } | |
1656 | ||
1657 | n = BigInteger(n); | |
1658 | if (n._s === 0) { | |
1659 | return ONE; | |
1660 | } | |
1661 | else if (n._s < 0) { | |
1662 | if (this._s === 0) { | |
1663 | throw new Error("Divide by zero"); | |
1664 | } | |
1665 | else { | |
1666 | return ZERO; | |
1667 | } | |
1668 | } | |
1669 | if (this._s === 0) { | |
1670 | return ZERO; | |
1671 | } | |
1672 | if (n.isUnit()) { | |
1673 | return this; | |
1674 | } | |
1675 | ||
1676 | if (n.compareAbs(MAX_EXP) > 0) { | |
1677 | throw new Error("exponent too large in BigInteger.pow"); | |
1678 | } | |
1679 | var x = this; | |
1680 | var aux = ONE; | |
1681 | var two = BigInteger.small[2]; | |
1682 | ||
1683 | while (n.isPositive()) { | |
1684 | if (n.isOdd()) { | |
1685 | aux = aux.multiply(x); | |
1686 | if (n.isUnit()) { | |
1687 | return aux; | |
1688 | } | |
1689 | } | |
1690 | x = x.square(); | |
1691 | n = n.quotient(two); | |
1692 | } | |
1693 | ||
1694 | return aux; | |
1695 | }; | |
1696 | ||
1697 | /* | |
1698 | Function: modPow | |
1699 | Raise a <BigInteger> to a power (mod m). | |
1700 | ||
1701 | Because it is reduced by a modulus, <modPow> is not limited by | |
1702 | <BigInteger.MAX_EXP> like <pow>. | |
1703 | ||
1704 | Parameters: | |
1705 | ||
1706 | exponent - The exponent to raise *this* by. Must be positive. | |
1707 | modulus - The modulus. | |
1708 | ||
1709 | Returns: | |
1710 | ||
1711 | *this* ^ *exponent* (mod *modulus*). | |
1712 | ||
1713 | See Also: | |
1714 | ||
1715 | <pow>, <mod> | |
1716 | */ | |
1717 | BigInteger.prototype.modPow = function(exponent, modulus) { | |
1718 | var result = ONE; | |
1719 | var base = this; | |
1720 | ||
1721 | while (exponent.isPositive()) { | |
1722 | if (exponent.isOdd()) { | |
1723 | result = result.multiply(base).remainder(modulus); | |
1724 | } | |
1725 | ||
1726 | exponent = exponent.quotient(BigInteger.small[2]); | |
1727 | if (exponent.isPositive()) { | |
1728 | base = base.square().remainder(modulus); | |
1729 | } | |
1730 | } | |
1731 | ||
1732 | return result; | |
1733 | }; | |
1734 | ||
1735 | /* | |
1736 | Function: log | |
1737 | Get the natural logarithm of a <BigInteger> as a native JavaScript number. | |
1738 | ||
1739 | This is equivalent to | |
1740 | ||
1741 | > Math.log(this.toJSValue()) | |
1742 | ||
1743 | but handles values outside of the native number range. | |
1744 | ||
1745 | Returns: | |
1746 | ||
1747 | log( *this* ) | |
1748 | ||
1749 | See Also: | |
1750 | ||
1751 | <toJSValue> | |
1752 | */ | |
1753 | BigInteger.prototype.log = function() { | |
1754 | switch (this._s) { | |
1755 | case 0: return -Infinity; | |
1756 | case -1: return NaN; | |
1757 | default: // Fall through. | |
1758 | } | |
1759 | ||
1760 | var l = this._d.length; | |
1761 | ||
1762 | if (l*BigInteger_base_log10 < 30) { | |
1763 | return Math.log(this.valueOf()); | |
1764 | } | |
1765 | ||
1766 | var N = Math.ceil(30/BigInteger_base_log10); | |
1767 | var firstNdigits = this._d.slice(l - N); | |
1768 | return Math.log((new BigInteger(firstNdigits, 1, CONSTRUCT)).valueOf()) + (l - N) * Math.log(BigInteger_base); | |
1769 | }; | |
1770 | ||
1771 | /* | |
1772 | Function: valueOf | |
1773 | Convert a <BigInteger> to a native JavaScript integer. | |
1774 | ||
1775 | This is called automatically by JavaScipt to convert a <BigInteger> to a | |
1776 | native value. | |
1777 | ||
1778 | Returns: | |
1779 | ||
1780 | > parseInt(this.toString(), 10) | |
1781 | ||
1782 | See Also: | |
1783 | ||
1784 | <toString>, <toJSValue> | |
1785 | */ | |
1786 | BigInteger.prototype.valueOf = function() { | |
1787 | return parseInt(this.toString(), 10); | |
1788 | }; | |
1789 | ||
1790 | /* | |
1791 | Function: toJSValue | |
1792 | Convert a <BigInteger> to a native JavaScript integer. | |
1793 | ||
1794 | This is the same as valueOf, but more explicitly named. | |
1795 | ||
1796 | Returns: | |
1797 | ||
1798 | > parseInt(this.toString(), 10) | |
1799 | ||
1800 | See Also: | |
1801 | ||
1802 | <toString>, <valueOf> | |
1803 | */ | |
1804 | BigInteger.prototype.toJSValue = function() { | |
1805 | return parseInt(this.toString(), 10); | |
1806 | }; | |
1807 | ||
1808 | var MAX_EXP = BigInteger(0x7FFFFFFF); | |
1809 | // Constant: MAX_EXP | |
1810 | // The largest exponent allowed in <pow> and <exp10> (0x7FFFFFFF or 2147483647). | |
1811 | BigInteger.MAX_EXP = MAX_EXP; | |
1812 | ||
1813 | (function() { | |
1814 | function makeUnary(fn) { | |
1815 | return function(a) { | |
1816 | return fn.call(BigInteger(a)); | |
1817 | }; | |
1818 | } | |
1819 | ||
1820 | function makeBinary(fn) { | |
1821 | return function(a, b) { | |
1822 | return fn.call(BigInteger(a), BigInteger(b)); | |
1823 | }; | |
1824 | } | |
1825 | ||
1826 | function makeTrinary(fn) { | |
1827 | return function(a, b, c) { | |
1828 | return fn.call(BigInteger(a), BigInteger(b), BigInteger(c)); | |
1829 | }; | |
1830 | } | |
1831 | ||
1832 | (function() { | |
1833 | var i, fn; | |
1834 | var unary = "toJSValue,isEven,isOdd,sign,isZero,isNegative,abs,isUnit,square,negate,isPositive,toString,next,prev,log".split(","); | |
1835 | var binary = "compare,remainder,divRem,subtract,add,quotient,divide,multiply,pow,compareAbs".split(","); | |
1836 | var trinary = ["modPow"]; | |
1837 | ||
1838 | for (i = 0; i < unary.length; i++) { | |
1839 | fn = unary[i]; | |
1840 | BigInteger[fn] = makeUnary(BigInteger.prototype[fn]); | |
1841 | } | |
1842 | ||
1843 | for (i = 0; i < binary.length; i++) { | |
1844 | fn = binary[i]; | |
1845 | BigInteger[fn] = makeBinary(BigInteger.prototype[fn]); | |
1846 | } | |
1847 | ||
1848 | for (i = 0; i < trinary.length; i++) { | |
1849 | fn = trinary[i]; | |
1850 | BigInteger[fn] = makeTrinary(BigInteger.prototype[fn]); | |
1851 | } | |
1852 | ||
1853 | BigInteger.exp10 = function(x, n) { | |
1854 | return BigInteger(x).exp10(n); | |
1855 | }; | |
1856 | })(); | |
1857 | })(); | |
1858 | ||
1859 | exports.BigInteger = BigInteger; | |
1860 | })(typeof exports !== 'undefined' ? exports : this); |