constraints.lookup2_12

Lookup2_12 AIR constraint evaluation.

Lookup2_12 logup terms (from gsum_debug_data hints): 1. Lookup assumes, busid=4, sel=1, cols=[a1, b1] – used in gsum direct_denom 2. Lookup proves, busid=4, mul=1, cols=[c1, d1] – stored_num = +1 3. Lookup assumes, busid=5, sel=1, cols=[a2, b2] – stored_num = -1 4. Lookup assumes, busid=6, sel=sel1, cols=[a3, b3] – stored_num = -sel1 5. Lookup proves, busid=6, mul=mul, cols=[c2, d2] – stored_num = +mul 6. Lookup assumes, busid=7, sel=sel2, cols=[a4, b4] – stored_num = -sel2

Intermediate columns clustering (from expressionsinfo constraint lines): - im_cluster[0]: busid=4 proves [c1,d1] + busid=5 assumes [a2,b2] - im_cluster[1]: busid=6 assumes [a3,b3] + busid=6 proves [c2,d2] - im_single: busid=7 assumes [a4,b4]

Convention: stored_num = -selector for assumes, +multiplicity for proves. This is because im_single*denom = stored_num, and im represents the negated contribution to the logup sum.

5 constraints combined with std_vc powers.

Classes

Lookup2_12Constraints

Constraint evaluation for Lookup2_12 AIR.

Module Contents

class constraints.lookup2_12.Lookup2_12Constraints

Bases: constraints.base.ConstraintModule

Constraint evaluation for Lookup2_12 AIR.

Lookup2_12 has 4096 rows (nBits=12) and exercises FRI folding.

The 5 constraints (from expressionsinfo): - C0: im_cluster[0] verification: im*D1*D2 - (D2 - D1) = 0

D1 = compress(4, [c1, d1]), D2 = compress(5, [a2, b2])

• C1: im_cluster[1] verification: im*D1*D2 - ((-sel1)*D2 + mul*D1) = 0

  D1 = compress(6, [a3, b3]), D2 = compress(6, [c2, d2])

• C2: im_single verification: im*D - (-sel2) = 0

  D = compress(7, [a4, b4])

• C3: gsum recurrence: (gsum - gsum’*(1-L1) - sum_ims) * direct_den + 1 = 0

  direct_den = compress(4, [a1, b1])

• C4: boundary constraint: L1’ * (gsum_result - gsum) = 0

constraint_polynomial(ctx: constraints.base.ConstraintContext) → primitives.field.FF3Poly | primitives.field.FF3

Evaluate combined constraint polynomial.