[WIP] Add variant of fingerprint() that yields intermediate columns

[georgwiese]

This test (simulating folding a size-200 tuple) now works:

use std::math::fp2::from_base;
use std::math::fp2::Fp2;
use std::math::fp2::constrain_eq_ext;
use std::prover::challenge;
use std::protocols::fingerprint::fingerprint;
use std::protocols::fingerprint::fingerprint_inter;
use std::array;

machine Main with degree: 8 {

    col witness x;
    // let alpha = from_base(challenge(0, 0));
    let alpha = Fp2::Fp2(challenge(0, 0), challenge(0, 1));

    let n = 200;
    // Because all elements except the first are 0, the fingerprint
    // is going to be alpha^{n - 1} * x.
    let tuple = array::new(n, |i| if i == 0 { x } else { 1 });

    constrain_eq_ext(fingerprint_inter(tuple, alpha), from_base(0));
}

All generated expressions are constant-length.

A few observations:

• Yielding intermediate columns means that we have to turn everything into constr functions. Because fingerprint() is also used in a hint, we need to implement to variants, one that yields intermediate columns and one that computes the result as a pure function. Maybe that can be fixed by passing an expr (involving intermediate columns) to the hint...
• We store all inputs to square_ext_inter, so a single invocation of pow_ext_inter should generate $log(n)$ intermediate columns of constant size.
• fingerprint_inter then calls pow_ext_inter $n$ times. So, overall, $O(n \cdot log(n))$ constant-size expressions are generated. No computation is shared between the $n$ calls to pow_ext_inter!