Author: Emily Conover / Source: Science News
Multiplying 2 x 2 is easy. But multiplying two numbers with more than a billion digits each — that takes some serious computation.
The multiplication technique taught in grade school may be simple, but for really big numbers, it’s too slow to be useful. Now, two mathematicians say that they’ve found the fastest way yet to multiply extremely large figures.
The duo claim to have achieved an ultimate speed limit for multiplication, first suggested nearly 50 years ago. That feat, described online March 18 at the document archive HAL, has not yet passed the gauntlet of peer review. But if the technique holds up to scrutiny, it could prove to be the fastest possible way of multiplying whole numbers, or integers.
If you ask an average person what mathematicians do, “they say, ‘Oh, they sit in their office multiplying big numbers together,’” jokes study coauthor David Harvey of the University of New South Wales in Sydney. “For me, it’s actually true.”
When making calculations with exorbitantly large numbers, the most important measure of speed is how quickly the number of operations needed — and hence the time required to do the calculation — grows as you multiply longer and longer strings of digits.
That growth is expressed in terms of n, defined as the number of digits in the numbers being multiplied. For the new technique, the number of operations required is proportional to n times the logarithm of n, expressed as O(n log n) in mathematical lingo. That means that, if you double the number of digits, the number…
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