Fix "alloc" feature for tests

[moCello]

Also add an example for creating a circuit.

Resolves #346

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Comparison is base (780bbf9) 85.71% compared to head (70447ac) 85.71%.

Additional details and impacted files

@@           Coverage Diff           @@
##           master     #808   +/-   ##
=======================================
  Coverage   85.71%   85.71%           
=======================================
  Files          57       57           
  Lines        4095     4095           
=======================================
  Hits         3510     3510           
  Misses        585      585           

Files	Coverage Δ
src/fft/domain.rs	71.42% <ø> (ø)
tests/common/mod.rs	81.81% <ø> (ø)

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[xevisalle]

I remember that you explained me the reason for that, but I can't remember it now. As such, maybe would be a good moment to fix this? Probably more people will have the same doubt...

[moCello]

The range component can only operate with even numbers. This is why we give it half of the number we want to operate on, see here.

I was trying to convey this by introducing the constant and naming it HALF_* where * is the value that we are checking on. As much as I can see that this is far from ideal, I'm also not sure how to make this better.
Do you have a suggestion?

[moCello]

How about this:

        // 1) a < 2^6
        composer.component_range::<3>(a); // 3 BIT_PAIRS = 6 bits

        // 2) b < 2^4
        composer.component_range::<2>(b); // 2 BIT_PAIRS = 4 bits

[xevisalle]

is there a way to do a compile time check on the provided value? otherwise, we could also throw an error at runtime. e.g., if the provided number is not even, throw NotEvenError: provided constant not even.

EDIT: I saw that time ago, the function had this check:

plonk/src/composer.rs

Line 913 in 65db5f0

debug_assert_eq!(num_bits % 2, 0);

[moCello]

Actually we introduced BIT_PAIRS to get rid of this debug_assert (see the discussion in #764 ).

In any case, any change in the range or logic components is not in the scope of this PR.

If you want we can open another issue on this to have the discussion.

[xevisalle]

LGTM, just consider the comment I added.