sbv-8.7: SMT Based Verification: Symbolic Haskell theorem prover using SMT solving.

Copyright (c) Levent Erkok BSD3 erkokl@gmail.com experimental None Haskell2010

Description

An SBV solution to the bit-precise puzzle of shuffling the bits in a 64-bit word in a custom order. The idea is to take a 64-bit value:

1.......2.......3.......4.......5.......6.......7.......8.......

And turn it into another 64-bit value, that looks like this:

12345678........................................................

We do not care what happens to the bits that are represented by dots. The problem is to do this with one mask and one multiplication.

Apparently this operation has several applications, including in programs that play chess of all things. We use SBV to find the appropriate mask and the multiplier.

Note that this is an instance of the program synthesis problem, where we "fill in the blanks" given a certain skeleton that satisfy a certain property, using quantified formulas.

Synopsis

# Documentation

Find the multiplier and the mask as described. We have:

>>> maskAndMult
Satisfiable. Model:
mask = 0x8080808080808080 :: Word64
mult = 0x0002040810204081 :: Word64


That is, any 64 bit value masked by the first and multipled by the second value above will have its bits at positions [7,15,23,31,39,47,55,63] moved to positions [56,57,58,59,60,61,62,63] respectively.

NB. Depending on your z3 version, you might also get the following multiplier as the result: 0x8202040810204081. That value works just fine as well!

Note that we have to use a custom SAT command for this problem, as otherwise it takes too long. See https://github.com/Z3Prover/z3/issues/2587 for details.