newmethod.txt

Method 2 for multiplying, based on the Collatz Conjecture optimization:

Essentially:
1. For each possible value of kl, precompute the result for that kl, with p.
	Precomputation time for each p = klbits*2^klbits. (klbits=8 => 2048its!)
2. Split k into kl (x bits), and kh (the rest).
3. The result = kh+f(kl)

Does that work? Yes - Excel confirms it! Is it fast enough?
- Have to break up the 32-36 bit jumps into 8 or so bits at a time.
- Add an argument, -b, --bitsatatime, to tweak that.  Pick the largest multiple of b without going over the maximum.
- Estimate anywhere from a little slower to 2x as fast!  Plus it's usable on video cards!!! :)

k0&((1<<1)-1) = 0 => k1 = k0/2
k0&((1<<1)-1) = 1 => k1 = (k0+p)/2


k0&((1<<2)-1) = 00 => k1 = k0/4
k0&((1<<2)-1) = 01 => k1 = ((k0+p)/2+[0,p]))/2
	ki = 01+x1 = 10+x0 = ~x
k0&((1<<2)-1) = 01 => k1 = ((k0+p)/2+(p&2)?0:p))/2
k0&((1<<2)-1) = 10 => k1 = (k0/2+p)/2
k0&((1<<2)-1) = 11 => k1 = ((k0+p)/2+(p&2)?p:0))/2
p =  1100101

k1 = 1110101


1/(0.000325274+0.003904979)