"x /^ y" is x/y rounded up, i.e. the least n such that x <= y*n.
"x %^ y" is the least k such that x+k is a multiple of y.
For comparison,
"x / y" is x/y rounded down, i.e. the greatest n such that x >= y*n.
"x % y" is the least k such that x-k is a multiple of y.
The new syntax is much more suggestive of the relation to "/" and "%".
The width table in CryptolTC.z3 wasn't large enough to solve constraints
about the width of 64-bit words. This change is a bit of a band-aid, as
larger words will expose the same problem. Longer-term, we should try to
solve these constraints after the SMT-based phase, using some other
approach.
The constraints in CryptoBox were too permissive, and when adjusted to
represent the true intent (that values fit within 64-bits), and the
width table was updated, the example will type-check again.
Thanks to @tommd for tracking both of these down.
Cryptol 2.3-alpha couldn't math, but thanks to @yav's hard work, Cryptol 2.3 and
later can math! So with our new found powers comes great simplification. Not
all is perfect, much like Dori-Mic's situation, but things are much better.
See the width constraints in SCrypt.cry for areas that could be improved with
some semi-obvious statements (forall x. 1 + width x >= width (x - 1)).
