Gruen sumcheck optimization

[moodlezoup]

Implement the sumcheck optimization described in Section 3.2 of Angus Gruen's Some Improvements for the PIOP for ZeroCheck. Should apply to all of the sumchecks in Jolt.

Note that Jolt has already integrated the Dao-Thaler sumcheck optimization (for large EQ polynomial evaluations). That paper has a section describing how the two optimization interact.

[HiddenAndBound]

I'd like to take this up!

[moodlezoup]

All yours @HiddenAndBound !

[protoben]

As mentioned by @jprider63 here, he and I would like to take on implementing Gruen's at the points in the code relevant to Twist and Shout. If I'm understanding correctly, that would be approximately these points in the code:

• the Shout read-checking sumcheck
• the Twist read- and write-checking sumcheck
• the Booleanity sumcheck

Am I right in understanding that we can perform this work directly on top of main, or do we need to work off of feat/twist-shout-integration?

[0xAndoroid]

Out of date as gruen is implemented for most relevant places now.