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support logup #21

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support logup #21

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mooreland
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instead of lookup, logup is based on logarithmic derivation.
logup scheme can group more inputs which have same table together and save lookup scale

for basic inputs and tables:

                 φ_i(X) = input(X) + α
                 τ(X) = table(X) + α
                 LHS = τ(X) * Π(φ_i(X)) * (ϕ(gX) - ϕ(X))
                 RHS = τ(X) * Π(φ_i(X)) * (∑ 1/(φ_i(X)) - m(X) / τ(X))))

for extra same table's inputs, it only need suffice:

                     φ_i(X) = inputs(X) + α
                     LHS = Π(φ_i(X)) * (ϕ(gX) - ϕ(X))
                     RHS = Π(φ_i(X)) * (∑ 1/(φ_i(X)))

the m(x) make a statistic to all inputs in table
they generate different grand sum z poly and finally the last value of last z poly need be zero.

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