On 10 Jul 99, at 14:57, Peter Foster wrote:
> When doing an LL test we are always calculating the
> same series of numbers. The modulus is different, so
> we can't use the result of one test to help with
> another. I'm wondering why we don't do the following:
>
> Take 2 Mersenne numbers, m1 and m2 (m1 < m2).
> Do the usual LL series, but use as the modulus m1*m2.
> At the appropriate step, check if the remainder is
> divisible by m1. If so, then m1 is prime.
> At the end, check if the remainder is divisible by
> m2. If so, then m2 is prime.
>
> This allows us to do two (or more) tests for the price
> of one. What is the obvious reason we don't do this?
I suggested something similar (doing 3 or more tests at once) about 6
months ago. My motivation was to improve the efficiency of testing
using programs which have only power-of-two FFT code. There is a
small decrease in efficiency in the FFT as the size goes up, but this
could be more than offset by the gross saving in being able to do
e.g. 3 tests in parallel in a 1024K FFT instead of 3 tests in series
each using a 512K FFT.
The killer is doing the reduction modulo (2^p-1)(2^q-1)(2^r-1). The
point is that the "standard" DWT does the reduction modulo 2^p-1 for
free. Unless someone can come up with a clever method of doing the
reduction for "general" cases, it looks as though it's going to be a
lot more productive to write code for transform sizes which are not
powers of 2.
Regards
Brian Beesley
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