chore(avm): make fixed tables use constant polys (#7744)

The witnesses are gone but these columns are still NOT correctly loaded
from the pk/vk.

barretenberg/cpp/pil/avm/binary.pil

@@ -1,7 +1,6 @@
 include "fixed/byte_lookup.pil";
 
 namespace binary(256);
-
     pol commit clk;
 
     // Selector for Binary Operation

barretenberg/cpp/pil/avm/fixed/byte_lookup.pil

@@ -1,15 +1,13 @@
 namespace byte_lookup(256);
-    // These columns are commited for now, but will be migrated to constant/fixed when
-    // we support more *exotic* code generation options
-    pol commit table_op_id; // identifies if operation is AND/OR/XOR
-    pol commit table_input_a; // column of all 8-bit numbers
-    pol commit table_input_b; // column of all 8-bit numbers
-    pol commit table_output; // output = a AND/OR/XOR b
+    pol constant table_op_id; // identifies if operation is AND/OR/XOR
+    pol constant table_input_a; // column of all 8-bit numbers
+    pol constant table_input_b; // column of all 8-bit numbers
+    pol constant table_output; // output = a AND/OR/XOR b
     // Selector to indicate when to utilise the lookup table
     // TODO: Support for 1-sided lookups may make this redundant.
-    pol commit sel_bin;
+    pol constant sel_bin;
 
     // These two columns are a mapping between instruction tags and their byte lengths
     // {U8: 1, U16: 2, ... , U128: 16}
-    pol commit table_in_tags; // Column of U8,U16,...,U128
-    pol commit table_byte_lengths; // Columns of byte lengths 1,2,...,16;
+    pol constant table_in_tags; // Column of U8,U16,...,U128
+    pol constant table_byte_lengths; // Columns of byte lengths 1,2,...,16;

barretenberg/cpp/pil/avm/fixed/gas.pil

@@ -1,13 +1,6 @@
 namespace gas(256);
-    // TODO: WILL BE FIXED - we should be able to have this be a fixed column / the lookup tables are fixed so require no selectors
-    // TODO: All the columns here will have to be constant (when supported by our powdr fork and proving system)
-    pol commit sel_gas_cost;
+    pol constant sel_gas_cost;
 
     // TODO(ISSUE_NUMBER): Constrain variable gas costs
-    pol commit l2_gas_fixed_table;
-    pol commit da_gas_fixed_table;
-
-    // DUMMY RELATIONS to force creation of hpp.
-    sel_gas_cost - sel_gas_cost = 0;
-    l2_gas_fixed_table - l2_gas_fixed_table = 0;
-    da_gas_fixed_table - da_gas_fixed_table = 0;
+    pol constant l2_gas_fixed_table;
+    pol constant da_gas_fixed_table;

barretenberg/cpp/pil/avm/fixed/powers.pil

@@ -3,7 +3,4 @@
 // power_of_2 = 1 << clk;
 namespace powers(256);
     // clk will be the implicit power.
-    pol commit power_of_2;
-
-    // DUMMY RELATION to force creation of hpp.
-    power_of_2 - power_of_2 = 0;
+    pol constant power_of_2;

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

@@ -24,9 +24,20 @@ AvmCircuitBuilder::ProverPolynomials AvmCircuitBuilder::compute_polynomials() co
     }
 
     for (size_t i = 0; i < rows.size(); i++) {
+        polys.byte_lookup_sel_bin[i] = rows[i].byte_lookup_sel_bin;
+        polys.byte_lookup_table_byte_lengths[i] = rows[i].byte_lookup_table_byte_lengths;
+        polys.byte_lookup_table_in_tags[i] = rows[i].byte_lookup_table_in_tags;
+        polys.byte_lookup_table_input_a[i] = rows[i].byte_lookup_table_input_a;
+        polys.byte_lookup_table_input_b[i] = rows[i].byte_lookup_table_input_b;
+        polys.byte_lookup_table_op_id[i] = rows[i].byte_lookup_table_op_id;
+        polys.byte_lookup_table_output[i] = rows[i].byte_lookup_table_output;
+        polys.gas_da_gas_fixed_table[i] = rows[i].gas_da_gas_fixed_table;
+        polys.gas_l2_gas_fixed_table[i] = rows[i].gas_l2_gas_fixed_table;
+        polys.gas_sel_gas_cost[i] = rows[i].gas_sel_gas_cost;
         polys.main_clk[i] = rows[i].main_clk;
         polys.main_sel_first[i] = rows[i].main_sel_first;
         polys.main_zeroes[i] = rows[i].main_zeroes;
+        polys.powers_power_of_2[i] = rows[i].powers_power_of_2;
         polys.kernel_kernel_inputs[i] = rows[i].kernel_kernel_inputs;
         polys.kernel_kernel_value_out[i] = rows[i].kernel_kernel_value_out;
         polys.kernel_kernel_side_effect_out[i] = rows[i].kernel_kernel_side_effect_out;
@@ -129,21 +140,11 @@ AvmCircuitBuilder::ProverPolynomials AvmCircuitBuilder::compute_polynomials() co
         polys.binary_op_id[i] = rows[i].binary_op_id;
         polys.binary_sel_bin[i] = rows[i].binary_sel_bin;
         polys.binary_start[i] = rows[i].binary_start;
-        polys.byte_lookup_sel_bin[i] = rows[i].byte_lookup_sel_bin;
-        polys.byte_lookup_table_byte_lengths[i] = rows[i].byte_lookup_table_byte_lengths;
-        polys.byte_lookup_table_in_tags[i] = rows[i].byte_lookup_table_in_tags;
-        polys.byte_lookup_table_input_a[i] = rows[i].byte_lookup_table_input_a;
-        polys.byte_lookup_table_input_b[i] = rows[i].byte_lookup_table_input_b;
-        polys.byte_lookup_table_op_id[i] = rows[i].byte_lookup_table_op_id;
-        polys.byte_lookup_table_output[i] = rows[i].byte_lookup_table_output;
         polys.conversion_clk[i] = rows[i].conversion_clk;
         polys.conversion_input[i] = rows[i].conversion_input;
         polys.conversion_num_limbs[i] = rows[i].conversion_num_limbs;
         polys.conversion_radix[i] = rows[i].conversion_radix;
         polys.conversion_sel_to_radix_le[i] = rows[i].conversion_sel_to_radix_le;
-        polys.gas_da_gas_fixed_table[i] = rows[i].gas_da_gas_fixed_table;
-        polys.gas_l2_gas_fixed_table[i] = rows[i].gas_l2_gas_fixed_table;
-        polys.gas_sel_gas_cost[i] = rows[i].gas_sel_gas_cost;
         polys.keccakf1600_clk[i] = rows[i].keccakf1600_clk;
         polys.keccakf1600_input[i] = rows[i].keccakf1600_input;
         polys.keccakf1600_output[i] = rows[i].keccakf1600_output;
@@ -602,7 +603,6 @@ AvmCircuitBuilder::ProverPolynomials AvmCircuitBuilder::compute_polynomials() co
         polys.poseidon2_mem_addr_write_d[i] = rows[i].poseidon2_mem_addr_write_d;
         polys.poseidon2_output_addr[i] = rows[i].poseidon2_output_addr;
         polys.poseidon2_sel_poseidon_perm[i] = rows[i].poseidon2_sel_poseidon_perm;
-        polys.powers_power_of_2[i] = rows[i].powers_power_of_2;
         polys.sha256_clk[i] = rows[i].sha256_clk;
         polys.sha256_input[i] = rows[i].sha256_input;
         polys.sha256_output[i] = rows[i].sha256_output;