public void GetFractionAsDecimalString(long numerator, int denominator, string expectedResult)
{
var fraction = new BigFraction(numerator, denominator);
Assert.AreEqual(expectedResult, fraction.GetValueDecimalString());
}
private void txtBase64_TextChanged(object sender, EventArgs e)
{
// For every 4 characters in the Base64 text, there's 3 UTF-8 characters encoded.
var plaintextLength = 3 * (txtBase64.Text.Length / 4);
// If the Base64 text ends with '=' (the Base64 padding character), the plaintext length is one less.
// There can be up to 2 '=' at the end of a Base64-encoded string.
if (txtBase64.Text.EndsWith("=="))
{
plaintextLength -= 2;
}
else if (txtBase64.Text.EndsWith("="))
{
plaintextLength -= 1;
}
var numerator = TextEncoder.GetNumeratorFromBase64(txtBase64.Text);
var denominator = BigInteger.Pow(2, plaintextLength * 8);
txtBigNumerator.Text = numerator.ToString();
txtBigDenominator.Text = denominator.ToString();
// This is sufficient for encoding a full message with no data loss (numerator and either the denominator OR plaintext message length).
// To encode (to turn this long numerator into chess moves, assuming each player has one of 30 moves to make):
// Create a new variable that represents N/D of the original message. (This can be done with BigInteger for numerator and denominator.)
// Then, if we want to pull an integer value in the range [0,30),
// we can multiply the numerator by 30, and divide without remainder.
// Let's do an example with real numbers.
// Encoded N/D: 16705/(2^16)) (the denominator will always be a power of 256.)
// Get first encoded digit (from 0 to 30, but not 30):
// Multiply the N/D by 30. (Shortcut: Multiply N by 15, divide D by 2.)
// (16705*15)/(2^15)
// Now, figure out the first digit. (Do the division.)
// 250575/32768
// .. which is the same as: 7 + 21199/32768
// First digit: 7 (this is the first chess move)
// Repeat process for next digits.
// Multiply the N/D by 30. (Shortcut: Multiply N by 15, divide D by 2.)
// (21199*15)/(2^14)
// Figure out next digit. (Do the division.)
// 317985/16384
// .. which is the same as: 19 + 6689/16384
// Next digit: 19 (this is the 2nd chess move)
// Multiply the N/D by 30. (Shortcut: Multiply N by 15, divide D by 2.)
// (6689*15)/(2^13)
// Division:
// ....
// Tools needed to make this happen:
// New class: BigFraction (has 2 parts: Numerator (BigInteger) and Denominator (BigInteger).)
// To decode:
// For simplicity, let's assume we're seeing moves on a chess board.
// Each player, in turn, has X possible moves (in an ordered list), then chooses 1 of those moves.
// We can build up a running 'numerator' and 'denominator' to approximate the original message.
// Numerator (N) starts at 0, denominator (D) starts at 1.
// For move X out of Y:
// N = (N * Y) + X;
// D *= Y;
// We can derive the complete message when D >= PlaintextMessageLength.
// We can derive partial messages for any (N, D) because we'll have a Range of actual N we can use.
// ^ Possible, in theory. But difficult. Let's find an easier way.
// This is a tricky problem. We don't have infinite precision. (We don't Need infinite precision.)
// One ultimate goal is to get back to the original BigInteger; then we'd know the original message Exactly.
// We know the plaintext length (given to us in the chessgame header).
// Subgoal (nice-to-have): Decode the message one byte (move?) at a time. (eg. move 'a4' is move 0 out of 20 for white, so ...
// ... the decimal is between 0.00 and 0.05 (dividing the search space into 20 chunks, and taking the first chunk.)
// If the next move is 'a6' (move 0 out of 20 for black), then we'd divide that space into another 20 chunks, and take the first one,
// which is 0.000 through 0.004. So we know the first two digits in the decimal are '00'. Not sure if this helps us.
// OR: Instead of using an infinite-precision decimal, let's use a big integer. That makes more sense. As we get each digit,
// we learn more about the moves. And we can turn each move into a range (just like before), because we know the total range
// of the encoded text-integer (it's 2^[messagelength]). So we can keep track of a 'min' and 'max', and narrowing it down until we get
// to the final plaintext.
// ^ Won't work because we'd have fractional parts. If, for example, the final number is somewhere in [0,10), and we find out that
// it's in chunk 2 of 6, we can't easily divide the search space.
// Maybe revisit the infinite decimal [0-1)? I don't want to have to make a calculation across ALL digits in the number each time we want
// to pop a digit. (It would be O(n^2), and that's just terrible. We want O(n).)
// GetValueString
if (chkAutoUpdate.Checked)
{
/*
* var f = new BaseTwoFraction(numerator, plaintextLength * 8);
* txtDecimal.Text = f.GetValueDecimalString();
*/
var f = new BigFraction(numerator, denominator);
txtDecimal.Text = f.GetValueDecimalString();
}
else
{
txtDecimal.Text = "";
}
}