Quote from: botnet on August 23, 2013, 04:51:08 PM

Quote from: jlcooke on August 22, 2013, 06:57:07 PM

Any updates?

Memory is the big issue right now, trying to run simulations to determine how much ram will be needed.
I did runs with 4, 6, 7, and 8 symbolic input bits to see the peak working set of the mathematica kernel. I picked bits from nonce to be symbolic, and the fixed bits came from a previously solved blockheader.

4 bits: 79,312 K
6 bits: 84,720 K
7 bits: 89,372 K
8 bits: 850,800 K

What's odd is it looked very linear until 8 bits were reached; It's running now with 9 bits across 4 cores, I'll have those results in about 30 hours.

I also computed the equation length after PolynomialReduce at each node in the tree; I trust all the data except for '7 bits' where I maybe have recorded it wrong:

4 bits: median: 25, max: 62
6 bits: median: 170, max:222
7 bits: median: 379, max:495
8 bits: median: 919, max:1218

There the growth does appear linear.

For 8 bits I also computed the number of nodes that contained two leaf node children. This is essentially the number of equations that can be simplified in parallel (before any potential adjustments to the tree.) Is there a word for this type of node?

median: 17, max:96

I can post the output equations if anyone is interested.

Lastly, I would be open to try any other symbolic computation engines that support modulus->2 to compare speed and memory consumption. Any suggestions?

Cool. How are you generating the formulas? Iterating through each input possibility?

The 8th bit "explosion" is probably due to triggering the use of a 2nd path of 32bit addition.

The formulas for 32bit add (64 in, 32 out) get very large very quickly (http://jlcooke.ca/btc/sha256_logred_formulas.html) due to carry bits. Result r_31 depends on a_31 .. a_0 and b_31 .. b_0.