10-01-2022, 04:44 PM
Speaking of 78 years...
I got to thinking last night about how much faster factoring is when you can go from 500 binomial iterations where the numbers get hundreds of digits long to just 5 iterations by 10 root 8 = x 10 root x = x 5 root x = answer. Now the problem is large PRIME numbers. You can't factor those down. When you get like or higher than 503 root whatever, you are back to going away the morning to wait for you result.
I don't know if there are any other equation manipulations that could be made to always reduce the radicand under 500 and preserve the answer. Anyone know of a method?
As far as the log method. I did try out that function I posted with some very large string numbers. It did return values that did not fall apart, but I have not found a high precision log calculator to check them for accuracy. I know next to nothing about log functions. I think natural logs is base 10, so it is surprising to me a base 10 operation in computer math isn't noticeably falling apart. I need to do more research.
Mark, the significant figures rabbit hole can be avoided with long division nth root routines, but speed is still an issue with radicands in the hundreds+. Lookup tables are the way around that, but to what limit? 1000? 10,000? Could you imagine having to fill up a program with 90,000 indexed strings, many hundreds of digits long?
Pete
I got to thinking last night about how much faster factoring is when you can go from 500 binomial iterations where the numbers get hundreds of digits long to just 5 iterations by 10 root 8 = x 10 root x = x 5 root x = answer. Now the problem is large PRIME numbers. You can't factor those down. When you get like or higher than 503 root whatever, you are back to going away the morning to wait for you result.
I don't know if there are any other equation manipulations that could be made to always reduce the radicand under 500 and preserve the answer. Anyone know of a method?
As far as the log method. I did try out that function I posted with some very large string numbers. It did return values that did not fall apart, but I have not found a high precision log calculator to check them for accuracy. I know next to nothing about log functions. I think natural logs is base 10, so it is surprising to me a base 10 operation in computer math isn't noticeably falling apart. I need to do more research.
Mark, the significant figures rabbit hole can be avoided with long division nth root routines, but speed is still an issue with radicands in the hundreds+. Lookup tables are the way around that, but to what limit? 1000? 10,000? Could you imagine having to fill up a program with 90,000 indexed strings, many hundreds of digits long?
Pete