feat(avm): Mov opcode with direct memory (#5204)

Resolves #5159

barretenberg/cpp/pil/avm/avm_main.pil

@@ -21,6 +21,9 @@ namespace avm_main(256);
 
     // Halt program execution
     pol commit sel_halt;
+
+    //===== MEMORY OPCODES ==========================================================
+    pol commit sel_mov;
 
     //===== TABLE SUBOP-TR ========================================================
     // Boolean selectors for (sub-)operations. Only one operation is activated at
@@ -94,6 +97,9 @@ namespace avm_main(256);
     sel_jump * (1 - sel_jump) = 0;
     sel_halt * (1 - sel_halt) = 0;
 
+    // Might be removed if derived from opcode based on a lookup of constants
+    sel_mov * ( 1 - sel_mov) = 0;
+
     op_err * (1 - op_err) = 0;
     tag_err * (1 - tag_err) = 0; // Potential optimization (boolean constraint derivation from equivalence check to avm_mem)?
 
@@ -188,11 +194,17 @@ namespace avm_main(256);
 
     // TODO: we want to set an initial number for the reserved memory of the jump pointer
 
-    // Inter-table Constraints
+    //====== MEMORY OPCODES CONSTRAINTS =========================================
+    #[MOV_SAME_VALUE]
+    sel_mov * (ia - ic) = 0; // Ensure that the correct value is moved/copied.
 
+    //====== Inter-table Constraints ============================================
     #[INCL_MAIN_TAG_ERR]
     avm_mem.m_tag_err {avm_mem.m_clk} in tag_err {clk};
 
+    #[INCL_MEM_TAG_ERR]
+    tag_err {clk} in avm_mem.m_tag_err {avm_mem.m_clk};
+
     // Predicate to activate the copy of intermediate registers to ALU table. If tag_err == 1,
     // the operation is not copied to the ALU table.
     // TODO: when division is moved to the alu, we will need to add the selector in the list below:
@@ -208,9 +220,9 @@ namespace avm_main(256);
                      avm_alu.alu_op_not, avm_alu.alu_in_tag};
 
     #[PERM_MAIN_MEM_A]
-    mem_op_a {clk, mem_idx_a, ia, rwa, in_tag}
+    mem_op_a {clk, mem_idx_a, ia, rwa, in_tag, sel_mov}
     is
-    avm_mem.m_op_a {avm_mem.m_clk, avm_mem.m_addr, avm_mem.m_val, avm_mem.m_rw, avm_mem.m_in_tag};
+    avm_mem.m_op_a {avm_mem.m_clk, avm_mem.m_addr, avm_mem.m_val, avm_mem.m_rw, avm_mem.m_in_tag, avm_mem.m_sel_mov};
 
     #[PERM_MAIN_MEM_B]
     mem_op_b {clk, mem_idx_b, ib, rwb, in_tag}

barretenberg/cpp/pil/avm/avm_mem.pil

@@ -20,6 +20,10 @@ namespace avm_mem(256);
     pol commit m_op_b;
     pol commit m_op_c;
 
+    // Selector for MOV opcode (copied from main trace for loading operation on intermediated register ia)
+    // Boolean constraint is performed in main trace.
+    pol commit m_sel_mov;
+
     // Error columns
     pol commit m_tag_err; // Boolean (1 if m_in_tag != m_tag is detected)
 
@@ -111,4 +115,15 @@ namespace avm_mem(256);
 
     // Correctness of two above checks MEM_IN_TAG_CONSISTENCY_1/2:
     // m_in_tag == m_tag ==> m_tag_err == 0 (first relation)
-    // m_tag_err == 0 ==> m_one_min_inv == 0 by second relation. First relation ==> m_in_tag - m_tag == 0
+    // m_tag_err == 0 ==> m_one_min_inv == 0 by second relation. First relation ==> m_in_tag - m_tag == 0
+
+    //====== MOV Opcode in_tag Constraint =====================================
+    // The following constraint ensures that the m_in_tag is set to m_tag for
+    // the load operation pertaining to Ia.
+    // The permutation check #[PERM_MAIN_MEM_A] guarantees that the m_in_tag
+    // value load operation for Ia is copied back in the main trace. Then,
+    // #[PERM_MAIN_MEM_C] copies back m_in_tag for store operation from Ic.
+    // Finally, the following constraint guarantees that m_tag is correct for
+    // the output.
+    #[MOV_SAME_TAG]
+    m_sel_mov * m_tag_err = 0; // Equivalent to m_sel_mov * (m_in_tag - m_tag) = 0