Performance comparison: 64-bit versus 32-bit multiplication
I'm using an Intel i5-4200U with an Intel (R) Core 1.60GHz processor and wondering why the multiplication of 64-bit numbers is slower than 32-bit numbers. I did a test run in C and it turns out it takes twice as long.
I expected it to take the same amount of time because the processor operates on its own 64-bit registers, and it doesn't matter how wide the numbers are (as long as they fit into a 64-bit register).
Can someone explain this?
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There are special instructions in the x86-64 instruction set to express that you only want to multiply two quantities 32-bit
. One instruction may look like it is IMUL %EBX, %ECX
in a specific dialect for x86-64 assembly, as opposed to 64-bit multiplication IMUL %RBX, %RCX
.
So the processor knows that you only want to multiply 32-bit values. This happens often enough that the processor designers have made sure that the internal circuitry will be optimized to provide a faster response in this easier case, just as you can multiply 3-digit numbers more easily than 6-digit numbers. The difference can be seen in the timings as measured by Agner Fog and documented in his comprehensive build optimization resources .
If your compiler targets the older 32-bit IA-32 instruction set, the difference between 32-bit and 64-bit multiplication is even wider. The compiler must implement 64-bit multiplication with instructions for 32-bit multiplication, using four of them (three if only the least significant 64 bits of the result are computed). In this case, 64-bit multiplication can be about three to four times slower than 32-bit multiplication.
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I can think of a problem here due to 64 bit multiplication.
Actually, for multiplying two 32-bit numbers, the result will be no more than 64 bits. But in the case of multiplying two 64-bit numbers, the product can be 128 bits, and in all cases it will be more than 64 bits!
As a similar example in the 8086 microprocessor, if you do the same with 8-bit numbers and 16-bit numbers, you will run into a situation where the CPU registers have to store them from the AX register and DX register as well (if you know assembly language abbreviations).
So, I believe that it is possible to increase the computation time !!! I feel like this is what makes your 64 bit multiplication slow!
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