/// <summary>
/// A common feature of the above techniques—indeed, the key technique that
/// allows us to track the decayed weights efficiently—is that they maintain
/// counts and other quantities based on g(ti − L), and only scale by g(t − L)
/// at query time. But while g(ti −L)/g(t−L) is guaranteed to lie between zero
/// and one, the intermediate values of g(ti − L) could become very large. For
/// polynomial functions, these values should not grow too large, and should be
/// effectively represented in practice by floating point values without loss of
/// precision. For exponential functions, these values could grow quite large as
/// new values of (ti − L) become large, and potentially exceed the capacity of
/// common floating point types. However, since the values stored by the
/// algorithms are linear combinations of g values (scaled sums), they can be
/// rescaled relative to a new landmark. That is, by the analysis of exponential
/// decay in Section III-A, the choice of L does not affect the final result. We
/// can therefore multiply each value based on L by a factor of exp(−α(L′ − L)),
/// and obtain the correct value as if we had instead computed relative to a new
/// landmark L′ (and then use this new L′ at query time). This can be done with
/// a linear pass over whatever data structure is being used."
/// </summary>
private void Rescale()
{
var lockTaken = false;
try
{
_lock.Enter(ref lockTaken);
var oldStartTime = _startTime.GetValue();
_startTime.SetValue(_clock.Seconds);
var scalingFactor = Math.Exp(-_alpha * (_startTime.GetValue() - oldStartTime));
var keys = new List<double>(_values.Keys);
foreach (var key in keys)
{
var sample = _values[key];
_values.Remove(key);
var newKey = key * Math.Exp(-_alpha * (_startTime.GetValue() - oldStartTime));
var newSample = new WeightedSample(sample.Value, sample.UserValue, sample.Weight * scalingFactor);
_values[newKey] = newSample;
}
// make sure the counter is in sync with the number of stored samples.
_count.SetValue(_values.Count);
}
finally
{
if (lockTaken)
{
_lock.Exit();
}
}
}
private void Update(long value, string userValue, long timestamp)
{
var lockTaken = false;
try
{
_lock.Enter(ref lockTaken);
var itemWeight = Math.Exp(_alpha * (timestamp - _startTime.GetValue()));
var sample = new WeightedSample(value, userValue, itemWeight);
var random = 0.0;
// Prevent division by 0
while (random.Equals(.0))
{
random = ThreadLocalRandom.NextDouble();
}
var priority = itemWeight / random;
var newCount = _count.GetValue();
newCount++;
_count.SetValue(newCount);
if (newCount <= _sampleSize)
{
_values[priority] = sample;
}
else
{
var first = _values.Keys[_values.Count - 1];
if (first < priority)
{
_values.Remove(first);
_values[priority] = sample;
}
}
}
finally
{
if (lockTaken)
{
_lock.Exit();
}
}
}
