Why is division more expensive than multiplication?

CPU’s ALU (Arithmetic-Logic Unit) executes algorithms, though they are implemented in hardware. Classic multiplications algorithms includes Wallace tree and Dadda tree. More information is available here. More sophisticated techniques are available in newer processors. Generally, processors strive to parallelize bit-pairs operations in order the minimize the clock cycles required. Multiplication algorithms can be parallelized quite … Read more

Is integer multiplication really done at the same speed as addition on a modern CPU?

Multiplication of two n-bit numbers can in fact be done in O(log n) circuit depth, just like addition. Addition in O(log n) is done by splitting the number in half and (recursively) adding the two parts in parallel, where the upper half is solved for both the “0-carry” and “1-carry” case. Once the lower half … Read more

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