algorithm - Avoiding Possible Precision Loss with a Simple Moving Average -

suppose had basic moving average function keeping track of sum. example:

queue values; double sum;  double calcsma(double next) {     values.push(next);     sum -= values.pop();     sum += next;     return sum / sma_length; } 

one example of how break down if our window 5 wide fed like: 2, 2, 2, 2, 2, 2, 2, 1e100, 2, 2, 2, 2, 2, 2, 2, 2. output 2, 2, 2, 2e99, 2e99, 2e99, 2e99, 2e99, 0, 0, 0.

even if sum isn't quite dramatically off, there still quite reasonable instances small loss in precision make sum artificially increase tiny amount. on long period of time, add , become issue.

does have ideas of how work around loss in precision?

edit: note function designed work o(1). necessary. so, recalculating each time won't work: window large.

you recalculate fresh sum on every sma_length values stop errors accumulating:

queue values; double sum = 0.0; double freshsum = 0.0; int count = 0;  double calcsma(double next) {     values.push(next);     sum -= values.pop();     sum += next;     freshsum += next;     if(++count == sma_length)     {         sum = freshsum;         freshsum = 0.0;         count = 0;     }      return sum / sma_length; }