Optimized Reed-Solomon code recovery based on danksharding

[qizhou]

The major optimization is that given the sample size = 16, we can reduce the recovery problem from size 8192 to 16 problems with size 512 (=8192/512) with proper pre-processing. This means that the cost such as Z(x) and Q2(x) can be amortized over 16 recoveries with size 512.

Some benchmark numbers on my MacBook (8192 recovery):

• Original: 1.07s
• Optimized zpoly: 0.500s
• Optimized RS: 0.4019s

[dankrad]

Shall we make a new folder for this stuff? mimc_stark does not seem appropriate. (There is also polynomial_reconstruction which is my own implementation of this stuff, so putting your version somewhere there would make sense)

[qizhou]

Shall we make a new folder for this stuff? mimc_stark does not seem appropriate. (There is also polynomial_reconstruction which is my own implementation of this stuff, so putting your version somewhere there would make sense)

Great suggestion! I will migrate the code there. Thanks!

[qizhou]

Shall we make a new folder for this stuff? mimc_stark does not seem appropriate. (There is also polynomial_reconstruction which is my own implementation of this stuff, so putting your version somewhere there would make sense)

I have moved to code to polynomial_reconstruction based on reconstruct_polynomial_from_samples() function. The performance number of 8192 data points with sample size 16 is now (on my MacBook):

• Original: total 1.4794s with 0.79s for zpoly
• Optimized zpoly: total 0.7755s with 0.06s for zpoly
• Optimized recovery: total 0.3202 with 0.04s for preparation of zpoly/shifted_zpoly/etc

Please know if you have any questions. Thank you!