Comment on Why is division so much more complex than other arithmetic operations?parentComments−pfdietz3yAddition can be performed with circuits of depth O(log n), where n is the number of bits, and with a little more work also of size O(n).−ithkuil3yI'm confused. Since O(log n) is faster than O(n) why would O(n) require a little more work? Did I misread something or did you miswrite?−pfdietz3yI'm talking about constructing boolean circuits. The usual parallel prefix algorithm yields a circuit of depth O(log n) with O(n log n) gates. Using some trickery, however, this can be reduced to O(n) gates, with a constant factor increase in depth.https://en.wikipedia.org/wiki/Prefix_sum https://en.wikipedia.org/wiki/Adder_(electronics)−ithkuil3yConstant depth requires unbounded fan-in, which may not be available in practice−pfdietz3yYes, I was talking about using gates of bounded fan-in.
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Addition can be performed with circuits of depth O(log n), where n is the number of bits, and with a little more work also of size O(n).
I'm confused. Since O(log n) is faster than O(n) why would O(n) require a little more work? Did I misread something or did you miswrite?
I'm talking about constructing boolean circuits. The usual parallel prefix algorithm yields a circuit of depth O(log n) with O(n log n) gates. Using some trickery, however, this can be reduced to O(n) gates, with a constant factor increase in depth.
https://en.wikipedia.org/wiki/Prefix_sum https://en.wikipedia.org/wiki/Adder_(electronics)
Constant depth requires unbounded fan-in, which may not be available in practice
Yes, I was talking about using gates of bounded fan-in.