Is this the most optimal way to shift?

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I have the following code for a filter:

// Shift array to the left
memmove(&Fifo[0], &Fifo[1], 12 * 4);

// Add new value
Fifo[12] = NewValue;

int Result = Factor[0] * Fifo[6];

Result += Factor[1] * (Fifo[5] + Fifo[7]);
Result += Factor[2] * (Fifo[4] + Fifo[8]);
Result += Factor[3] * (Fifo[3] + Fifo[9]);
Result += Factor[4] * (Fifo[2] + Fifo[10]);
Result += Factor[5] * (Fifo[1] + Fifo[11]);
Result += Factor[6] * (Fifo[0] + Fifo[12]);

Is there any way I could rewrite this so that I dont have to copy so much memory each call, to increase performance? I thought about circular buffers and linked lists, but it would require much extra code and complexity, that it seems the above is the best option.

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Scott Hunter On BEST ANSWER

You could implement a circular buffer by simply keeping an extra variable w/ the index of, say, the start of the buffer, and make all references to Fifo relative to that (modulo 13 -- thanks, Ingo!); that way, shifting is just bumping that index.