Why is division more expensive than multiplication?

Question

I am not really trying to optimize anything, but I remember hearing this from programmers all the time, that I took it as a truth. After all they are supposed to know this stuff.

But I wonder why is division actually slower than multiplication? Isn't division just a glorified subtraction, and multiplication is a glorified addition? So mathematically I don't see why going one way or the other has computationally very different costs.

Can anyone please clarify the reason/cause of this so I know, instead of what I heard from other programmer's that I asked before which is: "because".

Answer 1

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 effectively (though more transistors are required).

Division algorithms can't be parallelized as efficiently. The most efficient division algorithms are quite complex (The Pentium FDIV bug demonstrates the level of complexity). Generally, they requires more clock cycles per bit. If you're after more technical details, here is a nice explanation from Intel. Intel actually patented their division algorithm.