feat: Implement u32_less_than comparison primitive for Aiur#319
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feat: Implement u32_less_than comparison primitive for Aiur#319arthurpaulino wants to merge 1 commit intomainfrom
u32_less_than comparison primitive for Aiur#319arthurpaulino wants to merge 1 commit intomainfrom
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less_than for full Goldilocks field elements
Add a constrained comparison operation for 32-bit unsigned integers, returning 1 if x < y and 0 otherwise. The algorithm byte-decomposes both operands into 4 little-endian bytes, then computes y - x - 1 via a borrow chain of 8 u8_sub lookups (2 per byte). The final borrow determines the result: no borrow means x < y, borrow means x >= y. No canonicality enforcement is needed since u32 values are below 2^32, which is well within the Goldilocks prime (p = 2^64 - 2^32 + 1), so the 4-byte decomposition is unique. Resources per operation: 24 auxiliaries, 8 Bytes2 lookups, 2 polynomial constraints (one decomposition sum per operand). Changes span Lean (Term, Meta, Check, Bytecode, Compile) and Rust (bytecode, FFI, execute, trace, constraints), plus end-to-end tests.
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u32_less_than comparison primitive for Aiur
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Add a constrained comparison operation for 32-bit unsigned integers, returning 1 if x < y and 0 otherwise. The algorithm byte-decomposes both operands into 4 little-endian bytes, then computes y - x - 1 via a borrow chain of 8 u8_sub lookups (2 per byte). The final borrow determines the result: no borrow means x < y, borrow means x >= y.
No canonicality enforcement is needed since u32 values are below 2^32, which is well within the Goldilocks prime (p = 2^64 - 2^32 + 1), so the 4-byte decomposition is unique.
Resources per operation: 24 auxiliaries, 8 Bytes2 lookups, 2 polynomial constraints (one decomposition sum per operand).
Changes span Lean (Term, Meta, Check, Bytecode, Compile) and Rust (bytecode, FFI, execute, trace, constraints), plus end-to-end tests.