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Cf. https://www.ingonyama.com/blogs/goldilocks-ntt-trick some of the primitive roots of unity can be implemented as powers of 2. This holds for the roots with order 4 to 64 (both inclusive).
With this trick, the new orders of unity become:
static PRIMITIVE_ROOTS: phf::Map<u64, u64> = phf_map! { 2u64 => Q - 1, 4u64 => 1u64 << 48, 8u64 => 1u64 << 24, 16u64 => 1u64 << 12, 32u64 => 1u64 << 6, 64u64 => 1u64 << 3, 128u64 => 2198989700608, 256u64 => 4404853092538523347, 512u64 => 6434636298004421797, 1024u64 => 4255134452441852017, 2048u64 => 9113133275150391358, 4096u64 => 4355325209153869931, 8192u64 => 4308460244895131701, 16384u64 => 7126024226993609386, 32768u64 => 1873558160482552414, 65536u64 => 8167150655112846419, 131072u64 => 5718075921287398682, 262144u64 => 3411401055030829696, 524288u64 => 8982441859486529725, 1048576u64 => 1971462654193939361, 2097152u64 => 6553637399136210105, 4194304u64 => 8124823329697072476, 8388608u64 => 5936499541590631774, 16777216u64 => 2709866199236980323, 33554432u64 => 8877499657461974390, 67108864u64 => 3757607247483852735, 134217728u64 => 4969973714567017225, 268435456u64 => 2147253751702802259, 536870912u64 => 2530564950562219707, 1073741824u64 => 1905180297017055339, 2147483648u64 => 3524815499551269279, 4294967296u64 => 7277203076849721926, };
I think the NTT/INTT is only determined up to a constant so there might be some intermediate NTT results that are no longer valid.
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Cf. https://www.ingonyama.com/blogs/goldilocks-ntt-trick some of the primitive roots of unity can be implemented as powers of 2. This holds for the roots with order 4 to 64 (both inclusive).
With this trick, the new orders of unity become:
I think the NTT/INTT is only determined up to a constant so there might be some intermediate NTT results that are no longer valid.
The text was updated successfully, but these errors were encountered: