Which is faster — sorting or multiplying a small array of elements?

Question

Reading through Cactus Kev's Poker Hand Evaluator, I noticed the following statements:

At first, I thought that I could always simply sort the hand first before passing it to the evaluator; but sorting takes time, and I didn't want to waste any CPU cycles sorting hands. I needed a method that didn't care what order the five cards were given as.
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After a lot of thought, I had a brainstorm to use prime numbers. I would assign a prime number value to each of the thirteen card ranks... The beauty of this system is that if you multiply the prime values of the rank of each card in your hand, you get a unique product, regardless of the order of the five cards.
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Since multiplication is one of the fastest calculations a computer can make, we have shaved hundreds of milliseconds off our time had we been forced to sort each hand before evaluation.

I have a hard time believing this.

Cactus Kev represents each card as a 4-byte integer, and evaluates hands by calling eval_5cards( int c1, int c2, int c3, int c4, int c5 ). We could represent cards as one byte, and a poker hand as a 5-byte array. Sorting this 5-byte array to get a unique hand must be pretty fast. Is it faster than his approach?

What if we keep his representation (cards as 4-byte integers)? Can sorting an array of 5 integers be faster than multiplying them? If not, what sort of low-level optimizations can be done to make sorting a small number of elements faster?

Thanks!

Good answers everyone; I'm working on benchmarking the performance of sorting vs multiplication, to get some hard performance statistics.

Answer 1

Of course it depends a lot on the CPU of your computer, but a typical Intel CPU (e.g. Core 2 Duo) can multiply two 32 Bit numbers within 3 CPU clock cycles. For a sort algorithm to beat that, the algorithm needs to be faster than 3 * 4 = 12 CPU cycles, which is a very tight constraint. None of the standard sorting algorithms can do it in less than 12 cycles for sure. Alone the comparison of two numbers will take one CPU cycle, the conditional branch on the result will also take one CPU cycle and whatever you do then will at least take one CPU cycle (swapping two cards will actually take at least 4 CPU cycles). So multiplying wins.

Of course this is not taking the latency into account to fetch the card value from either 1st or 2nd level cache or maybe even memory; however, this latency applies to either case, multiplying and sorting.

Answer 2

Without testing, I'm sympathetic to his argument. You can do it in 4 multiplications, as compared to sorting, which is n log n. Specifically, the optimal sorting network requires 9 comparisons. The evaluator then has to at least look at every element of the sorted array, which is another 5 operations.