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@kilic kilic commented Dec 26, 2025

Currently we combine stir variables in very straight forward way sum(pow(z_i) * alpha^i).
However, as #303 suggests special structure of stir variables z_i = w^(idx_i) allows us to compute the combination with FFT. Concretely truncate(fft(sparse), 1<<num_variables)) == sum(pow(z_i) * alpha^i) where we set sparse[idx_i] = alpha^i.

However as it is implemented it does not bring performance gain since domain size where we sample stir indexes is larger than running sumcheck polynomial. But it seems like with a pruned fft implementation it would be slightly faster than straight forward combination.

@kilic kilic marked this pull request as draft December 26, 2025 13:18
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