public static UInt[] PySeedGetStateFor(string program)
{
if (program.Length * 2 > MersenneTwister.N)
{
throw new ArgumentException($"Length of {nameof(program)} must be less than or equal to {MersenneTwister.N / 2}", nameof(program));
}
Dictionary <char, double> neededRngs = new Dictionary <char, double>();
const double chancePerChar = 1 / 96D;
const double correction = chancePerChar / 10D;
// Calculate required RNG output for each character
for (char c = (char)0; c < 96; c++)
{
neededRngs[c == 95 ? '\n' : (char)(c + 32)] = chancePerChar * c + correction;
}
UInt[] state = new UInt[MersenneTwister.N];
int i = 0;
foreach (char c in program)
{
if (!neededRngs.TryGetValue(c, out double rng))
{
continue;
}
(UInt a, UInt b)states = MersenneTwister.PyGetPossibleOutputs(rng);
state[i++] = MersenneTwister.GetState(states.a);
state[i++] = MersenneTwister.GetState(states.b);
}
return(state);
}
public static uint GetState(UInt n)
{
n = MersenneTwister.UntemperR(n, MersenneTwister.L);
n = MersenneTwister.UntemperL(n, MersenneTwister.T, MersenneTwister.C);
n = MersenneTwister.UntemperL(n, MersenneTwister.S, MersenneTwister.B);
n = MersenneTwister.UntemperR(n, MersenneTwister.U, MersenneTwister.D);
return(n);
}
public static UInt UntemperR(UInt n, int shift, UInt mask)
{
UInt cur = n;
for (int accuracy = shift; accuracy < UInt.WIDTH; accuracy += shift)
{
cur = n ^ ((cur >> shift) & mask);
}
return(cur);
}
public static (UInt a, UInt b) PyGetPossibleOutputs(double d)
{
const double k = 1UL << 53; // Maximum value of a 53-bit number + 1
const uint bMask = (1U << 26) - 1; // A binary number containing 26 1s, used to extract b from d (the last 26 bits)
ULong n = (ULong)(d * k); // Convert d back into a long by multiplying it by its max value + 1
UInt b = (uint)(n & bMask) << 6; // Use bitwise AND to get b from n, then shift the bits back to the correct locations
UInt a = (uint)(n >> 26) << 5; // The rest of the bits are a, so just use some shifting, then shift the bits back to the correct locations
return(a, b); // Keep in mind that some bits were lost by PyRandom. Those bits don't matter to the algorithm though, so anything can go there and you'd get the same result
}
public double PyRandom()
{
// Why 53-bit numbers..?
UInt a = this.ExtractNumber() >> 5; // Remove 5 bits, 27-bit number
UInt b = this.ExtractNumber() >> 6; // Remove 6 bits, 26-bit number
const double k = 1UL << 53; // Maximum value of a 53-bit number + 1
ULong n = ((ulong)a << 26) + b; // Create a 53-bit number in the form ab
return(n / k); // Turn n into a fraction
}
public uint ExtractNumber()
{
if (this._index >= MersenneTwister.N)
{
if (this._index > MersenneTwister.N)
{
throw new Exception("Generator was never seeded");
}
this.Twist();
}
UInt y = this._mt[this._index++];
y = y ^ ((y >> MersenneTwister.U) & MersenneTwister.D);
y = y ^ ((y << MersenneTwister.S) & MersenneTwister.B);
y = y ^ ((y << MersenneTwister.T) & MersenneTwister.C);
y = y ^ (y >> MersenneTwister.L);
return(y);
}
// Brute force the factor
private static UInt GetFactorFromProduct(UInt product)
{
IEnumerable <BigInteger> Multiples(BigInteger factor, BigInteger maxMultiple)
{
maxMultiple /= factor;
for (BigInteger i = 0; i <= maxMultiple; i++)
{
yield return(factor * i);
}
}
const uint mask = 0xFFFFFFFF;
foreach (BigInteger multiple in Multiples(0x5D588B65U, (ulong)0x5D588B65U * 0xFFFFFFFF).Where(m => (m & mask) == product))
{
return((uint)(multiple / 0x5D588B65U));
}
throw new Exception("Failed to find a factor");
}
private static UInt GetStateFromProduct(UInt product, UInt curState) => product ^ curState;
private static UInt GetProductFromFactor(UInt factor) => factor * 0x5D588B65U;
//////
private static UInt GetFactorFromKey(UInt key) => key ^ (key >> 30);
private static UInt GetKeyFromFactor(UInt factor) => factor ^ (factor >> 30);
//////
private static UInt GetOriginalStateFromProduct(UInt state, UInt product) => state ^ product;
public static UInt Temper(UInt n, int shift, UInt mask) => n ^ ((n << shift) & mask);
public static UInt Temper(UInt n, int shift) => n ^ (n >> shift);
/// <summary>Returns an initKey for the current state. If the first key value is incorrect, try a different <see cref="tryKey"/> to see if that works.</summary>
/// <param name="tryKey">First initKey value</param>
/// <param name="keyWidth">Width of the initKey. Only the first N values matter in it</param>
/// <returns>A (probably working) initKey</returns>
public UInt[] PyGetInitKey(uint tryKey = 0, uint keyWidth = MersenneTwister.N)
{
UInt[] initKey = new UInt[keyWidth];
UInt[] mt = this._mt.ToArray();
uint j = 0;
uint k;
// Emulate setting the state without actually setting it. This can be done mathematically
for (k = Math.Max(MersenneTwister.N, (uint)initKey.Length); k > 0; k--)
{
j++;
if (j >= initKey.Length)
{
j = 0;
}
}
// Reverse the process
// This is the value for mt[0] after the first loop and throughout the second loop
mt[0] = mt[MersenneTwister.N - 1];
// Undo the last 'i++' that occured to set i to the last modified index (1)
uint i = 1;
// Undo second for loop
// Hilariously enough, this looks almost exactly the same as the process used to get the state from the initKey
for (k = 1; k < MersenneTwister.N; k++)
{
mt[i] += i;
mt[i] = mt[i] ^ (mt[i - 1] ^ (mt[i - 1] >> 30)) * 0x5D588B65U;
i--;
if (i == 0)
{
i = MersenneTwister.N - 1;
}
}
// This is the value for mt[0]
mt[0] = mt[MersenneTwister.N - 1];
i = 1;
j--;
if (j > initKey.Length)
{
j = (uint)initKey.Length - 1;
}
// Undo first for loop and grab the initKey
UInt[] origMt = new MersenneTwister(0x12BD6AAU)._mt;
for (k = 1; k < Math.Max(MersenneTwister.N, (uint)initKey.Length); k++)
{
if (k == 1)
{
// initKey[j] is actually a function of initKey[j0]. There is not a single solution for it, but many solutions (finite due to integer restriction).
const uint j2 = 0; // j when the first loop starts
UInt mtPrev = (origMt[i] ^ (origMt[i - 1] ^ origMt[i - 1] >> 30) * 0x19660DU) + tryKey + j2;
initKey[j] = mt[i] - (mtPrev ^ (mt[i - 1] ^ mt[i - 1] >> 30) * 0x19660DU) - j;
mt[i] = mtPrev;
}
else
{
initKey[j] = mt[i] - (origMt[i] ^ (mt[i - 1] ^ mt[i - 1] >> 30) * 0x19660DU) - j;
mt[i] = origMt[i];
}
i--;
j--;
if (i == 0)
{
mt[0] = origMt[0];
i = MersenneTwister.N - 1;
}
if (j == uint.MaxValue)
{
j = (uint)initKey.Length - 1;
}
}
return(initKey);
}