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FpDbl revisited #144
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FpDbl revisited #144
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This was referenced Feb 6, 2021
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For fast Fp2, Fp4, Fp12, implementations we should take advantage of lazy reductions, see #15 (comment)
However this was put on hold due to an unexplained 50 cycles difference between the theory and practice as mentioned here:
constantine/constantine/tower_field_extensions/quadratic_extensions.nim
Lines 129 to 139 in d12d5fa
Since we do 2 reductions, and my CPU is now running at 3.9GHz compared 4.1, we have now found out the source of the differences between theoretical cycle count and practice.
The origin is due to nim-lang/Nim#16887 which made reduction 20 cycles slower than necessary and reduction is used twice in Fp2 multiplication.
This PR:
Assembly squaring is as fast as ADX multiplication so we can expected ADX squaring to have an extra conservative 15% performance boost (up to 40% as you almost halves the number of operations).
constantine/constantine/arithmetic/finite_fields.nim
Lines 164 to 166 in d12d5fa