I have just installed LibreOffice 3.5.4 and yes, there is a drastic performance improvement. Documents and application do load much much faster (I am on Windows 7). A real improvement here, but I am not sure 'accurate' figures can be reported. I am impressed by the boost.

It could mean it's 100% faster for some tasks. So it could be 100% faster in loading docx or whatever, and only 20% faster in loading .doc. Are you looking for something like an average speed improvement? That probably wouldn't be very accurate, either. But they could say the new LibreOffice is 20%-100% faster, I suppose.

How can it be 100% faster at anything? This is mathematically impossible. If a task used to take 100 seconds, 1 second (an unlikely improvement!) is just 99% faster.

Throughput can be 100% faster. Eg if it could previously decode docx at 100kb/s and now can do it 200kb/s then it would be 100% faster.

Or wouldn't you say that a car that goes 100 mph is 100% faster than a car that goes 50 mph?

No, I'd say it goes twice as fast.

That's the same thing. "Twice as fast" = "Two times as fast" = "200% as fast" = "100% faster"

Making a 100 sec task taking 1 sec is a 9900% improvement, because in the same amount of time, you can do that task 99 more times.

Surely, a 1 second improvement would mean it is 1% faster. (Put another way, no change would mean a 0% change in speed, right?)

Since somethings are bound to have not changed at all in terms of speed it would probably have to be 0%-100% (Or, well, up to 100%.)

Or if they've used some kind of tradeoff, certain things could be much slower (or use more memory, etc.)

I've always had a problem with this too. If a product is 80% off, you pay 20% of the original price; 100% off and it's free. If a product is 80% faster, it runs in 20% of the original time. If it's 100% faster, it runs in zero time.

Generally 100% is used in terms of an increase, where 50% would be used in terms of the same decrease. Since it's twice as fast, it's 100% faster. Which also means it takes 50% less time to do the same task. If it had gotten slower, it would be 50% slower, which means it takes 100% more time to do the same task.

It's all in how it's worded. Instead of being worded as "100% improvement", it could have been worded "50% decrease in how long it takes to complete the operation". One of these rolls off the tongue nicer, but both are valid and mean the same thing.

In your example, both the sales prices are worded as a negative value. "50% off" could be worded as a positive value as "100% more". In this case, LibreOffice has 100% more than the original amount of speed. Twice as fast.

Your right, they should give more details on how they came to this conclusion.

I rather use average improvement rather than best case improvement - that way users don't feel duped.