https://www.sciencenews.org/article/mathematicians-may-have-found-fastest-way-multiply-huge-numbers

In the new study, the researchers considered only numbers with more than roughly 10^^214857091104455251940635045059417341952 digits when written in binary, in which numbers are encoded with a sequence of 0s and 1s. But the scientists didn’t actually perform any of these massive multiplications, because that’s vastly more digits than the number of atoms in the universe.

 

In my slide rule days it was 2-3 significant digits and carry the decimal place in your head...

 

https://www.sciencenews.org/article/mathematicians-may-have-found-fastest-way-multiply-huge-numbers

Kind of funny when, near the end, the author seems decided to stop flying high, giving us, mere mortals, some hope.

There’s still a possibility that the method could be shown to work for smaller, but still large, numbers.

 

In my slide rule days it was 2-3 significant digits and carry the decimal place in your head...

I used it for few years and then the calculators showed up.

I had the chance to watch an hydraulic engineer running a long calculation, standing leaning his elbow on the drawing board and doing fast calculations while taking quick notes on a paper to support subsequent revision of the process. Impresive.

Not sure how to translate, he called them "la marcha del cálculo".

 

https://www.sciencenews.org/article/mathematicians-may-have-found-fastest-way-multiply-huge-numbers

In the new study, the researchers considered only numbers with more than roughly 10^^214857091104455251940635045059417341952 digits when written in binary, in which numbers are encoded with a sequence of 0s and 1s. But the scientists didn’t actually perform any of these massive multiplications, because that’s vastly more digits than the number of atoms in the universe.

Given that there are only about 10^80 atoms in the known universe, that's more than a bit of an understatement.

I'd like to know where they came up with that particular value of an exponent.

I have no problem with the notion that the algorithm is likely important from a theoretical sense and may well have practical implications for other things someday (perhaps someday soon).

It also underscore the asymptotic nature of complexity analysis. An O(n·log(n)) algorithm is not necessarily faster than a O(n²) algorithm. This is only the case for problem sizes larger than some limit. If that limit is large enough, then the "slower" algorithm may well be much faster than the "faster" algorithm for any problem of actual interest.

 

In my slide rule days it was 2-3 significant digits and carry the decimal place in your head...

For many applications, of course, that is more than sufficient; but for many others it is not. We all use something nearly every day that requires working with numbers that have hundreds of digits -- namely public key cryptography, the backbone of securing e-commerce and many other things.

Here we routinely calculate a^b Mod N where all three numbers have as many as 4096 bits. These number have about 1200 decimal digits in them and the math operations performed must be exact down to the least significant bit. If done blindly, a^b with such numbers would result in values with over 16 million bits in them before being reduced Mod N. Because we know that we will eventually be reducing them, though, we can keep intermediate results to 8192 bits (under ~2500 decimal digits).

Because of the large numbers involved, asymmetric algorithms are typically thousands of times slower than their symmetric brethren, which greatly limits the range of practical application for them. If this new multiplication algorithm opens up the doors to algorithms that are faster at this scale of number, that would be a huge practical win. But the span between the two scales is so enormous, that it may well never be crossed.

 

Given that there are only about 10^80 atoms in the known universe, that's more than a bit of an understatement.

I'd like to know where they came up with that particular value of an exponent.

I have no problem with the notion that the algorithm is likely important from a theoretical sense and may well have practical implications for other things someday (perhaps someday soon).

It also underscore the asymptotic nature of complexity analysis. An O(n·log(n)) algorithm is not necessarily faster than a O(n²) algorithm. This is only the case for problem sizes larger than some limit. If that limit is large enough, then the "slower" algorithm may well be much faster than the "faster" algorithm for any problem of actual interest.

Hi,

That number:
10^^214857091104455251940635045059417341952 digits

is actually wrong, it is really:
10^^214857091104455251940635045059417341952 +1 digits

 

https://www.sciencenews.org/article/mathematicians-may-have-found-fastest-way-multiply-huge-numbers

Hi,

Cute article especially for me because in the past i had to design number crunchers that had to do huge numbers with huge exponents.

Also, back in the early days algorithms were classified as to how many multiplications they had to perform ignoring the additions because multiplications took so much longer. That changed when numerical processors came about so that multiply and add take almost the ame time now. But when we get to big numbers that changes back again to the old standard so any advance in this area is more than welcome.

The sad part like so many other 'articles' on the web is that they go on and on and on yet do not hint at the new method. I had a feeling this was going to happen because it quickly started to read like the typical bs advertisement article were we get constantly told how great it is yet we never seem to get to the heart of the matter. Still nice to know they are working on this.

The other interesting part is that quantum computers if they ever becomes a reality for real life complicated problems will be able to solve a large number of problems in one fell swoop. Unfortunately this might be after my time.

 

The other interesting part is that quantum computers if they ever becomes a reality for real life complicated problems will be able to solve a large number of problems in one fell swoop. Unfortunately this might be after my time.

Some of us believe it will be a very long time before we have true quantum computing supremacy beyond a very narrow set of problems that involve inherently low level but detectable patterns in a vast sea of numbers.

A lot of sweet vaporous aromas but still not much substance and bite.
https://www.nextplatform.com/2019/04/17/why-hpe-has-abandoned-quantum-computing-research/

HPE == Hewlett Packard Enterprise

 

I think all numbers must be small, since they would go on forever

 

I think all numbers must be small, since they would go on forever

Not one of the cognoscenti I suppose

 

I'm saying all numbers we ever think of or could imagine are small. So there are no big numbers

 

Look up Pi... And try to get to the end of it.

 

I'm saying all numbers we ever think of or could imagine are small. So there are no big numbers

No member of the cognoscenti would presume to draw a true conclusion from a false premise. What you are saying sounds facile.

 

I'm saying all numbers we ever think of or could imagine are small. So there are no big numbers

Please elaborate.

 

Look up Pi... And try to get to the end of it.

My password is the last four digits of pi.

 

My password is the last four digits of pi.

Wow amazing mine is all the digits of pi but backwards
I chose that because it's so easy to remember.

 

Please elaborate.

I just mean all finite numbers are small, so there's only small numbers, and then the concept of infinity. And thats without considering different sizes of infinity.

 

I just mean all finite numbers are small, so there's only small numbers, and then the concept of infinity. And thats without considering different sizes of infinity.

Hello again,

Well you are saying a lot but not really explaining what you mean.
Maybe give a couple examples?

 

10^^21485

What the double caret means? Never seen that before. Exponent?