girm_master:
I can't really tell. But first make it clear so you can debug it. Then when it's running, see if it's too slow. If so, *then* try to figure out how to speed it up.
Normally to speed things up, you'll have to do one or more of:
- Reduce the number of operations per iteration. A million additions will take four times as long as 250,000 additions, so if your formula was something like:
$t = $alpha * $t + $beta + $gamma + $delta; where $t is your only variable, you might instead compute the sum of $beta + $gamma + $delta once before you enter the loop, and use that sum repeatedly.
- Strength reduction: Some operations are more expensive than others--and sometimes you can convert one operation to another to reduce the amount of time taken. (See http://en.wikipedia.org/wiki/Strength_reduction).
- Algorithm changes: You might be able to find a different algorithm to generate the same (or equivalent) results. Usually algorithmic improvements are the source of the most impressive improvements.
- Profiling: By profiling the code, you'll see which parts are actually taking the most time, so you can focus on them. After all, if you miraculously reduce the runtime of a line of code to 0, but that line accounts for only 5% of the runtime, you've saved at best 5%. But if you halve the speed of a line of code that's consumes 50% of your runtime, you knock off 25% of your runtime.
- Cache results: For some problems, you can save a copy of a partial result so you can use it again later.
Putting my "old man" hat on: When I started with computers, additions were cheap (only a handful of cycles), multiplications were expensive (hundreds of cycles), and transcendental functions were *really slow*. Today, however, multiplications are nearly as inexpensive as additions, and transcendental functions aren't terribly slow, either. I have a piece of paper around here somewhere--on it, I would document the range of cycles it took to perform several operations every time I upgraded computers. It was really kind of interesting watching the cycles dropping generation after generation. CPUs are *much* more efficient than when I started, so even if today's computers ran at the same clock speed as my first computer, it would still be 100 times faster.
The reason I'm rambling on like this: For serious optimization, you need to look over the current literature. Each decade seems to have new issues arise, while others go away. I don't work nearly so hard to remove multiplications as I used to. But back then, I didn't worry about memory speed, either. But with the ever-increasing mismatch of CPU cycle speeds and memory I/O speeds, you have to pay more attention to how you're using your cache. I haven't seriously tried to optimize a program for nearly ten years. I'm sure that my assembly-language tuning techniques from back then wouldn't be nearly as useful today. I'd have to learn new ones for the current generation of computers.
</old-man-hat>
...roboticus
When your only tool is a hammer, all problems look like your thumb.
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