Improve documentation for BN curve parameter ATE_LOOP_COUNT

[weikengchen]

Description

This PR is to clarify that ATE_LOOP_COUNT is 6 X + 2 instead of |6 X + 2|, a possible confusion.

This is related to #274 and arkworks-rs/curves#54.

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N/A:

• Wrote unit tests
• Added a relevant changelog entry to the Pending section in CHANGELOG.md

[daira]

Isn't 6X + 2 negative exactly when X is negative? (Because X is an integer and 2 < 6.) That implies that this field should probably just be removed and X_IS_NEGATIVE used instead.

[daira]

Also I'm confused because this doc appears to contradict the following sentence in the PR description:

This PR is to clarify that ATE_LOOP_COUNT is 6 X + 2 instead of |6 X + 2|, a possible confusion.

[weikengchen]

You are right.

Let me clarify this PR's documentation as well as the documentation in the code (you are right, 2 < 6 so X must be negative).

I think there are two possible future plans:

1. Not too breaking, which can be done now:

• Use X_IS_NEGATIVE to decide whatever ATE_LOOP_COUNT_IS_NEGATIVE is deciding, since they should be equivalent for BN curves.

2. Breaking:

• Remove ATE_LOOP_COUNT_IS_NEGATIVE and update the BN254 implementation accordingly.