Possibility of magnitude restrictions on group element field values

[peterdettman]

The group operations seem to generally assume input x,y,z can be multiplied directly i.e. there is an implicit mag 8 requirement, which could be worth adding verification for. In some group operations (broadly speaking those where special z values are in play, either gej_add_ge or coz) the input field values are normalized, usually to ensure that they are mag 6 or so (I am presupposing zero tests for h/i replacing u?/s? equality checks), but it varies. In practice the group ops don't produce higher than 6 mag anyway, so there's some waste here (and some performance-neutral jiggling might lower the output mags).

So I'm proposing to i) add pre/post verification for the current mag 8 assumptions, then ii) explore whether tightening the requirements can improve performance. At this stage, I'm only envisaging a simple global requirement, not op-specific bounds.

Thoughts?

[peterdettman]

I should add that of course the mag 8 requirement is enforced by the field, but part ii) will be confusing if it is not explicit in the group code.

[sipa]

I'm fine with adding a requirement that all field elements inside _ge, _gej or _coz structs have a stronger normalization requirements than strictly necessary for field, if that means we can get rid of some explicit normalization steps.

[peterdettman]

Great, I'll put something together once #159 goes through.