- // 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;
- }
- // Assume cards are NOT replaced.
- // Additional entropy decreases as more cards are used. This means
- // total possible entropy is measured using n!, not base^n.
- // eg the second last card can be only one of two, not one of fifty two
- // so the added entropy for that card is only one bit at most
- if (base.asInt == 52) {
- var totalDecks = Math.ceil(base.parts.length / 52);
- var totalCards = totalDecks * 52;
- var totalCombos = factorial(52).pow(totalDecks);
- var totalRemainingCards = totalCards - base.parts.length;
- var remainingDecks = Math.floor(totalRemainingCards / 52);
- var remainingCards = totalRemainingCards % 52;
- var remainingCombos = factorial(52).pow(remainingDecks).multiply(factorial(remainingCards));
- var currentCombos = totalCombos.divide(remainingCombos);
- var numberOfBits = Math.log2(currentCombos);
- var maxWithoutReplace = BigInteger.pow(2, numberOfBits);
- // Use a bunch of sorted decks to measure entropy from, populated
- // as needed.
- var sortedDecks = [];
- // Initialize the final entropy value for these cards
- var entropyInt = BigInteger.ZERO;
- // Track how many instances of each card have been used, and thus
- // how many decks are in use.
- var cardCounts = {};
- // Track the total bits of entropy that remain, which diminishes as
- // each card is drawn.
- var totalBitsLeft = numberOfBits;
- // Work out entropy contribution of each card drawn
- for (var i=0; i<base.parts.length; i++) {
- // Get the card that was drawn
- var cardLower = base.parts[i];
- var card = cardLower.toUpperCase();
- // Initialize the deck for this card if needed, to track how
- // much entropy it adds.
- if (!(card in cardCounts)) {
- cardCounts[card] = 0;
- }
- // Get the deck this card is from
- var deckIndex = cardCounts[card];
- while (deckIndex > sortedDecks.length-1) {
- sortedDecks.push(getSortedDeck());
- }
- // See how many bits this card contributes (depends on how many
- // are left in the deck it's from)
- var deckForCard = sortedDecks[deckIndex];
- var cardsLeftInDeck = deckForCard.length;
- var additionalBits = Math.log2(cardsLeftInDeck);
- // Work out the min and max value for this card
- var nextTotalBitsLeft = totalBitsLeft - additionalBits;
- var minPossibleNewEntropy = TWO.pow(nextTotalBitsLeft).subtract(1);
- var maxPossibleNewEntropy = TWO.pow(totalBitsLeft).subtract(1);
- var diff = maxPossibleNewEntropy.subtract(minPossibleNewEntropy);
- // BigInteger aggresively floors numbers which greatly affects
- // the small numbers. In that case, use native Math library
- var useBigInt = totalBitsLeft >= 32;
- if (!useBigInt) {
- minPossibleNewEntropy = Math.round(Math.pow(2, nextTotalBitsLeft)-1);
- maxPossibleNewEntropy = Math.round(Math.pow(2, totalBitsLeft)-1);
- diff = maxPossibleNewEntropy - minPossibleNewEntropy;
- }
- // Scale the value between possible min and max depending on
- // this card value
- var thisCardIndex = deckForCard.indexOf(card);
- var toAdd = BigInteger.ZERO;
- if (cardsLeftInDeck > 1) {
- if (useBigInt) {
- toAdd = diff.multiply(thisCardIndex)
- .divide(deckForCard.length - 1)
- .add(minPossibleNewEntropy);
- }
- else {
- var ratio = thisCardIndex / (deckForCard.length -1);
- var f = diff * ratio;
- toAdd = new BigInteger(f).add(minPossibleNewEntropy);
- }
- }
- // Add this card entropy to existing entropy
- entropyInt = entropyInt.add(toAdd);
- // Remove this card from the deck it comes from
- deckForCard.splice(thisCardIndex,1);
- // Ensure the next insance of this card uses the next deck
- cardCounts[card] = cardCounts[card] + 1;
- // Next card drawn has less total remaining bits to work with
- totalBitsLeft = nextTotalBitsLeft;
- }
- // Convert to binary
- var entropyBin = entropyInt.toString(2);
- var numberOfBitsInt = Math.floor(numberOfBits);
- while (entropyBin.length < numberOfBitsInt) {
- entropyBin = "0" + entropyBin;
- }
- }