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Old 2020-02-07, 10:14   #16
Mysticial's Avatar
Sep 2016

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Originally Posted by LaurV View Post
Very nice, congrats!

How do you make the base switch "in place"? I have some ideas how to transform from base 2 to base 10 quite fast and also have some checkpoints, but you would need more storage space (it can't really be done "in place"), and I don't believe this is new, for sure somebody else was thinking to it before. I "invented" it long time ago and used it in my programs in the past, but never for such large inputs.
To answer your actual question of how I do the conversion "in place". The algorithm is the scaled remainder tree. The only operations are multiplications. There are no additions or subtractions at all.

Each multiply is a middle-product FFT that splits a 2N-bit binary input into two N-bit binary outputs which are written back into the same memory - overwriting the 2N-bit input. One of the N-bit outputs is the same as the upper-half of the 2B-bit output. Thus instead of overwriting the entire memory region, the "new" N-bit output overwrites the no-longer-needed portion of the 2N-bit input. This partial write is hard to checkpoint due to problem (2) of the previous post.

Since the in-place multiply is the only operation for the entire radix conversion, these in-place multiplications form a dependency chain/tree that prevents any sort of checkpointing at any step.

Last fiddled with by Mysticial on 2020-02-07 at 10:20
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