refactor(avm): replace range and cmp with gadgets (#8164)

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barretenberg/cpp/pil/avm/gadgets/range_check.pil

@@ -1,7 +1,10 @@
 include "../main.pil";
+include "../mem.pil";
 include "../fixed/powers.pil";
 
 namespace range_check(256);
+    // TODO: We should look to rename this to something like rng_idx 
+    // Increasingly this is less likely to be associated directly with a subtrace's clk
     pol commit clk;
 
     // Range check selector
@@ -11,7 +14,7 @@ namespace range_check(256);
     // Witnesses 
     // Value to range check
     pol commit value;
-    // Number of bits to check against
+    // Number of bits to check against (this number must be <=128)
     pol commit rng_chk_bits;
 
     // Bit Size Columns
@@ -188,3 +191,30 @@ namespace range_check(256);
     #[LOOKUP_RNG_CHK_7]
     sel_rng_chk { u16_r7 } in main.sel_rng_16 { main.clk };
 
+    // ===== MEM TRACE RANGE CHECKS =====
+    pol commit mem_rng_chk;
+    // We range check 40 bits in the mem trace
+    mem_rng_chk * (rng_chk_bits - 40) = 0;
+
+    #[PERM_RNG_MEM]
+    mem_rng_chk {clk, value}
+    is
+    mem.sel_rng_chk {mem.tsp, mem.diff};
+
+    // ===== GAS TRACE RANGE CHECKS =====
+    pol commit gas_l2_rng_chk;
+    pol commit gas_da_rng_chk;
+    // We range check 32 bits in the gas trace
+    gas_l2_rng_chk * (rng_chk_bits  - 32) = 0;
+    gas_da_rng_chk * (rng_chk_bits  - 32) = 0;
+
+    #[PERM_RNG_GAS_L2]
+    gas_l2_rng_chk {clk, value}
+    is
+    main.sel_execution_row {main.clk, main.abs_l2_rem_gas };
+
+    #[PERM_RNG_GAS_DA]
+    gas_da_rng_chk {clk, value}
+    is
+    main.sel_execution_row {main.clk, main.abs_da_rem_gas };
+

barretenberg/cpp/pil/avm/gas.pil

@@ -74,16 +74,3 @@ namespace main(256);
     sel_execution_row {opcode_val, base_l2_gas_op_cost, base_da_gas_op_cost, dyn_l2_gas_op_cost, dyn_da_gas_op_cost}
     in
     gas.sel_gas_cost {clk, gas.base_l2_gas_fixed_table, gas.base_da_gas_fixed_table, gas.dyn_l2_gas_fixed_table, gas.dyn_da_gas_fixed_table};
-
-    // ========= Initialize Range Check Gadget ===============================
-    // We range check that the absolute value of the differences between each row of l2 and da gas are 32 bits.
-    #[PERM_RNG_GAS_L2]
-    range_check.gas_l2_rng_chk {range_check.clk, range_check.value}
-    is
-    main.sel_execution_row {main.clk, main.abs_l2_rem_gas };
-
-    #[PERM_RNG_GAS_DA]
-    range_check.gas_da_rng_chk {range_check.clk, range_check.value}
-    is
-    main.sel_execution_row {main.clk, main.abs_da_rem_gas };
-

barretenberg/cpp/pil/avm/mem.pil

@@ -66,6 +66,7 @@ namespace mem(256);
 
     // Helper columns
     pol commit one_min_inv; // Extra value to prove r_in_tag != tag with error handling
+    // pol DIFF: 
     pol commit diff; // 40-bit difference between two consecutive timestamps or two consecutive addresses
 
     // Type constraints

barretenberg/cpp/src/barretenberg/vm/avm/generated/circuit_builder.cpp

@@ -600,6 +600,8 @@ AvmCircuitBuilder::ProverPolynomials AvmCircuitBuilder::compute_polynomials() co
         polys.range_check_dyn_diff[i] = rows[i].range_check_dyn_diff;
         polys.range_check_dyn_rng_chk_bits[i] = rows[i].range_check_dyn_rng_chk_bits;
         polys.range_check_dyn_rng_chk_pow_2[i] = rows[i].range_check_dyn_rng_chk_pow_2;
+        polys.range_check_gas_da_rng_chk[i] = rows[i].range_check_gas_da_rng_chk;
+        polys.range_check_gas_l2_rng_chk[i] = rows[i].range_check_gas_l2_rng_chk;
         polys.range_check_is_lte_u112[i] = rows[i].range_check_is_lte_u112;
         polys.range_check_is_lte_u128[i] = rows[i].range_check_is_lte_u128;
         polys.range_check_is_lte_u16[i] = rows[i].range_check_is_lte_u16;
@@ -608,6 +610,7 @@ AvmCircuitBuilder::ProverPolynomials AvmCircuitBuilder::compute_polynomials() co
         polys.range_check_is_lte_u64[i] = rows[i].range_check_is_lte_u64;
         polys.range_check_is_lte_u80[i] = rows[i].range_check_is_lte_u80;
         polys.range_check_is_lte_u96[i] = rows[i].range_check_is_lte_u96;
+        polys.range_check_mem_rng_chk[i] = rows[i].range_check_mem_rng_chk;
         polys.range_check_rng_chk_bits[i] = rows[i].range_check_rng_chk_bits;
         polys.range_check_sel_lookup_0[i] = rows[i].range_check_sel_lookup_0;
         polys.range_check_sel_lookup_1[i] = rows[i].range_check_sel_lookup_1;