refactor: refactor range checker

[tohrnii]

Describe your changes

Addressing #395. This PR simplifies the range checker and removes the 8-bit section of the range checker. The new design works as follows:

1. The values to be range checked are sorted.
2. The difference between two consecutive values to be range checked can be expressed as a linear combination of powers of 3 less than or equal to $3^7$, i.e.,

$$ \Delta n = \sum_{i=0}^{7} x_i \cdot 3^i $$

3. Then bridge rows are added in between the values to be range checked. For each $3^i$ in the above equation, $x_i$ number of bridge rows are added. However, if the sum of $x_i$ from $i=0$ to $i=7$ is 0 or 1, no bridge rows are required since the next row contains the value to be range checked.
   Hence, the constraint to check the transition between two rows in the range checker becomes:

$$ \Delta v \cdot (\Delta v - 1) \cdot (\Delta v - 3) \cdot (\Delta v - 9) \cdot (\Delta v - 27) \cdot (\Delta v - 81) \cdot (\Delta v - 243) \cdot (\Delta v - 729) \cdot (\Delta v - 2187) = 0 $$

This construction reduces the minimum trace length to 64 from the current 1024 and removes 1 column from the main trace and 1 column from the auxiliary trace.

Integration tests run time reduced by ~42% after this PR.

• remove 8 bit portion of the range checker
• update trace
• update constraints
• update tests
• refactor and cleanup
• update docs
• update images

Edit: I haven't included the excalidraw image zip file for the updated range checker image in this. I'll add that before we merge this.

Checklist before requesting a review

• Repo forked and branch created from next according to naming convention.
• Commit messages and codestyle follow conventions.
• Relevant issues are linked in the PR description.
• Tests added for new functionality.
• Documentation/comments updated according to changes.

[tohrnii]

@bobbinth @grjte I haven't updated the images yet. I'll update them if the rest of the changes looks correct.

[bobbinth]

Looks right! Thank you! This is not a full review yet - but I left a few small comments inline.

[bobbinth]

Looks good! Thank you! I left a few minor comments inline.

[bobbinth]

Looks good! Thank you!