Update MEMW and MEMW_A to match spec

prover/src/tables/memw.rs

@@ -11,12 +11,12 @@
 //! - `timestamp`: DWordWL (64-bit timestamp, 2 cols)
 //! - `write2/4/8`: Bit (access width flags)
 //! - `old[8]`: BaseField[8] (previous values at address)
-//! - `add_limb_overflow[7]`: Bit[7] (carry flags for base_address + i)
+//! - `carry[7]`: Bit[7] (carry flags for base_address + i)
 //! - `old_timestamp[8]`: DWordWL[8] (previous timestamps, 16 cols)
 //! - `mu_read`, `mu_write`: multiplicity columns
 //!
 //! ## Virtual (computed inline)
-//! - `address_add[i]` = (base_address_0 + i+1 - 2^32 * overflow[i], base_address_1 + overflow[i])
+//! - `address_add[i]` = (base_address_0 + i+1 - 2^32 * carry[i], base_address_1 + carry[i])
 //! - `w2`: write2 + write4 + write8 (writing at least 2 bytes)
 //! - `w4`: write4 + write8 (writing at least 4 bytes)
 //! - `μ_sum`: μ_read + μ_write
@@ -25,6 +25,8 @@
 //! - 8 LT timestamp checks (old_timestamp[i] < timestamp)
 //! - 16 Memory bus tokens (read old + write new, per byte)
 //! - 2 MEMW output interactions (read + write, from CPU)
+//!
+//! ## Constraints (11 total: 2 custom + 2 IS_BIT for multiplicities + 7 IS_BIT for carry)
 
 use math::field::element::FieldElement;
 use math::field::traits::{IsField, IsSubFieldOf};
@@ -72,8 +74,8 @@ pub mod cols {
     pub const OLD: [usize; 8] = [16, 17, 18, 19, 20, 21, 22, 23];
 
     // Auxiliary columns
-    /// add_limb_overflow[7]: Bit columns indicating carry when adding i+1 to base_address_0
-    pub const ADD_LIMB_OVERFLOW: [usize; 7] = [24, 25, 26, 27, 28, 29, 30];
+    /// carry[7]: Bit columns indicating carry when adding i+1 to base_address_0
+    pub const CARRY: [usize; 7] = [24, 25, 26, 27, 28, 29, 30];
 
     /// old_timestamp[8]: each is DWordWL (2 words = 2 columns)
     /// Total: 8 * 2 = 16 columns
@@ -206,11 +208,11 @@ pub fn generate_memw_trace(
             data[base + cols::OLD[i]] = FE::from(op.old[i]);
         }
 
-        // Auxiliary: add_limb_overflow[7]
-        // overflow[i] = 1 if (base_address_lo + i+1) >= 2^32
+        // Auxiliary: carry[7]
+        // carry[i] = 1 if (base_address_lo + i+1) >= 2^32
         for i in 0..7 {
             let overflows = base_addr_lo + (i as u64 + 1) >= (1u64 << 32);
-            data[base + cols::ADD_LIMB_OVERFLOW[i]] = FE::from(overflows as u64);
+            data[base + cols::CARRY[i]] = FE::from(overflows as u64);
         }
 
         // Auxiliary: old_timestamp[8] - each as DWordWL (2 words)
@@ -245,18 +247,17 @@ pub fn bus_interactions() -> Vec<BusInteraction> {
     // Memory bus interactions (16 total)
     // -------------------------------------------------------------------------
     // address_add[i] is VIRTUAL:
-    //   lo = base_address_0 + (i+1) - 2^32 * add_limb_overflow[i]
-    //   hi = base_address_1 + add_limb_overflow[i]
+    //   lo = base_address_0 + (i+1) - 2^32 * carry[i]
+    //   hi = base_address_1 + carry[i]
     //
     // Safety: `hi` is at most `base_address_1 + 1`. This never reaches 2^32
     // because the CPU table splits addresses into (lo, hi) with both halves
     // in [0, 2^32), and the Memw bus ties MEMW's base_address to the CPU's
     // value. MEMW only receives accesses where base_address_1 <= 0xFFFF_FFFE
     // (addresses near u64::MAX are rejected by the executor before proving).
-    // Consequently, `add_limb_overflow[i]` is implicitly correct: a wrong
-    // carry bit produces a memory token at a wrong address that has no
-    // matching PAGE/REGISTER token, causing multiset imbalance and an
-    // invalid proof.
+    // Consequently, `carry[i]` is implicitly correct: a wrong carry bit
+    // produces a memory token at a wrong address that has no matching
+    // PAGE/REGISTER token, causing multiset imbalance and an invalid proof.
 
     // CM8: memory[is_register, base_address, old_timestamp[0], old[0]] with +μ_sum
     interactions.push(BusInteraction::sender(
@@ -323,8 +324,8 @@ pub fn bus_interactions() -> Vec<BusInteraction> {
     ));
 
     // CM10/11: byte 1, multiplicity w2 = write2 + write4 + write8
-    // address_add[0] is virtual: lo = base_address_0 + 1 - 2^32 * overflow[0]
-    //                            hi = base_address_1 + overflow[0]
+    // address_add[0] is virtual: lo = base_address_0 + 1 - 2^32 * carry[0]
+    //                            hi = base_address_1 + carry[0]
     let addr_add_0_lo = BusValue::linear(vec![
         LinearTerm::Column {
             coefficient: 1,
@@ -333,7 +334,7 @@ pub fn bus_interactions() -> Vec<BusInteraction> {
         LinearTerm::Constant(1),
         LinearTerm::Column {
             coefficient: -(1i64 << 32),
-            column: cols::ADD_LIMB_OVERFLOW[0],
+            column: cols::CARRY[0],
         },
     ]);
     let addr_add_0_hi = BusValue::linear(vec![
@@ -343,7 +344,7 @@ pub fn bus_interactions() -> Vec<BusInteraction> {
         },
         LinearTerm::Column {
             coefficient: 1,
-            column: cols::ADD_LIMB_OVERFLOW[0],
+            column: cols::CARRY[0],
         },
     ]);
 
@@ -401,7 +402,7 @@ pub fn bus_interactions() -> Vec<BusInteraction> {
 
     // CM12/13: bytes 2-3 with multiplicity w4 = write4 + write8
     for i in 2..=3 {
-        let overflow_col = cols::ADD_LIMB_OVERFLOW[i - 1];
+        let overflow_col = cols::CARRY[i - 1];
         let addr_add_lo = BusValue::linear(vec![
             LinearTerm::Column {
                 coefficient: 1,
@@ -479,7 +480,7 @@ pub fn bus_interactions() -> Vec<BusInteraction> {
 
     // CM14/15: bytes 4-7 with multiplicity write8
     for i in 4..=7 {
-        let overflow_col = cols::ADD_LIMB_OVERFLOW[i - 1];
+        let overflow_col = cols::CARRY[i - 1];
         let addr_add_lo = BusValue::linear(vec![
             LinearTerm::Column {
                 coefficient: 1,
@@ -857,7 +858,7 @@ where
 }
 
 // =========================================================================
-// Constraints (9 total: 2 custom + 7 IS_BIT)
+// Constraints (11 total: 2 custom + 2 IS_BIT for multiplicities + 7 IS_BIT for carry)
 // =========================================================================
 
 /// MEMW table constraint kinds.
@@ -946,10 +947,12 @@ impl TransitionConstraint<GoldilocksField, GoldilocksExtension> for MemwConstrai
 
 /// Creates all constraints for the MEMW table.
 ///
-/// 9 constraints total:
+/// 11 constraints total:
 /// - IS_BIT<μ_sum> (1)
 /// - w2 => μ_sum (1)
-/// - IS_BIT for add_limb_overflow[0..6] (7)
+/// - IS_BIT<μ_read> (1)
+/// - IS_BIT<μ_write> (1)
+/// - IS_BIT for carry[0..6] (7)
 pub fn constraints() -> Vec<Box<dyn TransitionConstraint<GoldilocksField, GoldilocksExtension>>> {
     let mut constraints: Vec<Box<dyn TransitionConstraint<GoldilocksField, GoldilocksExtension>>> =
         Vec::new();
@@ -970,8 +973,19 @@ pub fn constraints() -> Vec<Box<dyn TransitionConstraint<GoldilocksField, Goldil
     )));
     idx += 1;
 
-    // IS_BIT for add_limb_overflow[0..6]
-    for &col in &cols::ADD_LIMB_OVERFLOW {
+    // IS_BIT<μ_read>
+    constraints.push(Box::new(IsBitConstraint::unconditional(cols::MU_READ, idx)));
+    idx += 1;
+
+    // IS_BIT<μ_write>
+    constraints.push(Box::new(IsBitConstraint::unconditional(
+        cols::MU_WRITE,
+        idx,
+    )));
+    idx += 1;
+
+    // IS_BIT for carry[0..6]
+    for &col in &cols::CARRY {
         constraints.push(Box::new(IsBitConstraint::unconditional(col, idx)));
         idx += 1;
     }
@@ -1013,45 +1027,45 @@ mod tests {
     }
 
     #[test]
-    fn test_add_limb_overflow() {
-        // Address 0xFFFF_FFFF should overflow when adding 1
+    fn test_carry_flags() {
+        // Address 0xFFFF_FFFF should carry when adding 1
         let op =
             MemwOperation::new(false, 0xFFFF_FFFF, [0; 8], 100, 8, false).with_old([0; 8], [50; 8]);
         let trace = generate_memw_trace(&[op]);
 
-        // All 7 overflow flags should be 1 since 0xFFFF_FFFF + i >= 2^32 for i >= 1
+        // All 7 carry flags should be 1 since 0xFFFF_FFFF + i >= 2^32 for i >= 1
         for i in 0..7 {
-            let val = trace.get_main(0, cols::ADD_LIMB_OVERFLOW[i]);
-            assert_eq!(*val, FE::one(), "overflow[{i}] should be 1");
+            let val = trace.get_main(0, cols::CARRY[i]);
+            assert_eq!(*val, FE::one(), "carry[{i}] should be 1");
         }
 
-        // Address 0x0000_0000 should not overflow
+        // Address 0x0000_0000 should not carry
         let op2 =
             MemwOperation::new(false, 0x0000_0000, [0; 8], 100, 8, false).with_old([0; 8], [50; 8]);
         let trace2 = generate_memw_trace(&[op2]);
         for i in 0..7 {
-            let val = trace2.get_main(0, cols::ADD_LIMB_OVERFLOW[i]);
-            assert_eq!(*val, FE::zero(), "overflow[{i}] should be 0");
+            let val = trace2.get_main(0, cols::CARRY[i]);
+            assert_eq!(*val, FE::zero(), "carry[{i}] should be 0");
         }
 
         // Address 0xFFFF_FFFE with width=8 exercises mixed per-byte carry bits:
-        // overflow[0]=0 (0xFFFF_FFFE+1 = 0xFFFF_FFFF < 2^32)
-        // overflow[1..6]=1 (0xFFFF_FFFE+2..8 >= 2^32)
+        // carry[0]=0 (0xFFFF_FFFE+1 = 0xFFFF_FFFF < 2^32)
+        // carry[1..6]=1 (0xFFFF_FFFE+2..8 >= 2^32)
         let op3 =
             MemwOperation::new(false, 0xFFFF_FFFE, [0; 8], 100, 8, false).with_old([0; 8], [50; 8]);
         let trace3 = generate_memw_trace(&[op3]);
-        let val0 = trace3.get_main(0, cols::ADD_LIMB_OVERFLOW[0]);
+        let val0 = trace3.get_main(0, cols::CARRY[0]);
         assert_eq!(
             *val0,
             FE::zero(),
-            "overflow[0] should be 0 for base 0xFFFF_FFFE"
+            "carry[0] should be 0 for base 0xFFFF_FFFE"
         );
         for i in 1..7 {
-            let val = trace3.get_main(0, cols::ADD_LIMB_OVERFLOW[i]);
+            let val = trace3.get_main(0, cols::CARRY[i]);
             assert_eq!(
                 *val,
                 FE::one(),
-                "overflow[{i}] should be 1 for base 0xFFFF_FFFE"
+                "carry[{i}] should be 1 for base 0xFFFF_FFFE"
             );
         }
     }