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This is the safest thing to do to ensure my software is free while
avoiding legal trouble ... hopefully, I'm not a lawyer!
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go1.21, the previous requirement, was released a few months ago, so not
all systems have adopted it. go1.18 is old enough that most systems
should support it, but it introduces generics, which my testing code is
highly dependent on, so I can't easily go any earlier.
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factors.Type now supports all numbers; I have used lookup arrays instead
of determining whether a number is SAN or not. There are only 117
elements to store, and this makes the algorithm Θ(1), so it's an
improvement.
Also, I have changed the size of some integer values to correspond to
this change - they now indicate the size of numbers they can accept.
The only outputs that are hidden for large radices are:
- The digit map, which goes up to 36 because I don't have any more
digits beyond that point
- The multiplication table complexity, which is estimated above 2^16
(for performance), and can optionally be extended to 2^32 (above this,
the output could overflow a uint64).
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The backing constants of NumberType and TotativeType have been changed
so that they can be compared (based on how desirable they are, more
desirable categories are given higher values), and so that I can add new
values in between without changing the constants.
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This is not in the output yet, but it will be soon - printing it is
another task since I want colours in my output.
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This type measures which kind of classes each radix is a part of:
- Colossally Abundant (OEIS: A004490; factor score better than every
other number if you account for size be dividing by a certain power of
the number)
- Superabundant (OEIS: A004394; factor score better than every smaller
number)
- Ordered-Exponent (OEIS: A025487; exponents in prime factorization go
down as you get to bigger primes, and no prime is skipped)
- Practical (OEIS: A005153; factors can sum to any number below the
original number without duplication)
Each of these groups is a subset of the next, so only the most specific
label is reported.
The purpose of this program is to give you useful info to help you
determine which radices are the best, and these categories give a rough,
quantitative measure of how useful a radix's factors are:
- Practical is approximately the minimum requirement for a worthwhile
radix. Non-practical radices above ~16 are probably terrible to use.
- Ordered-Exponent radices act like local maxima - you can't get any
better (smaller) without changing the "shape" (exponents) of your prime
factorization.
- Superabundant radices are the best radices below the next
superabundant number (e.g. 12 is the best radix below 24).
- Colossally abundant radices are, in some sense, the best radices out of
all numbers.
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