feat(avm): non-field sized cmp circuit ops (#9895)

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barretenberg/cpp/pil/avm/alu.pil

@@ -84,17 +84,21 @@ namespace alu(256);
     pol commit cmp_gadget_input_b;
     pol commit cmp_gadget_result;
     pol commit cmp_gadget_gt;
+    pol commit cmp_gadget_non_ff_gt;
 
     // We use the comparison gadget to test GT for the following operations
-    cmp_gadget_gt = op_lt + op_lte + op_div + op_shr + op_shl;
+    pol CMP_GADGET_GT = op_lt + op_lte + op_div + op_shr + op_shl;
+    cmp_gadget_gt = CMP_GADGET_GT * ff_tag;
+    cmp_gadget_non_ff_gt = CMP_GADGET_GT * (1 - ff_tag);
+
     // The cmp gadget is on when we are either testing GT or EQ
-    cmp_gadget_sel - (cmp_gadget_gt + op_eq) = 0;
+    cmp_gadget_sel - (cmp_gadget_gt + op_eq + cmp_gadget_non_ff_gt) = 0;
 
     // Permutation to the Comparison Gadget
     #[PERM_CMP_ALU]
-    cmp.sel_cmp {cmp.clk, cmp.input_a, cmp.input_b, cmp.result, cmp.op_eq, cmp.op_gt}
+    cmp.sel_cmp {cmp.clk, cmp.input_a, cmp.input_b, cmp.result, cmp.op_eq, cmp.op_gt, cmp.op_non_ff_gt}
     is
-    cmp_gadget_sel {clk, cmp_gadget_input_a, cmp_gadget_input_b, cmp_gadget_result, op_eq, cmp_gadget_gt };
+    cmp_gadget_sel {clk, cmp_gadget_input_a, cmp_gadget_input_b, cmp_gadget_result, op_eq, cmp_gadget_gt, cmp_gadget_non_ff_gt };
 
 
     // =============== HELPER POLYNOMIAL RELATIONS ================================================= 

barretenberg/cpp/pil/avm/gadgets/cmp.pil

@@ -16,6 +16,25 @@ namespace cmp(256);
     pol commit input_b;
     pol commit result;
 
+    // ========= NON FF GT Short-circuit computation ===============================
+    // If this is a non-ff check, we can short circuit (a > b) by checking
+    // 0 < a - b - 1 < 2**128 --> i.e. we just check we dont underlow which for "small" sized 128-bit number is just a 
+    // single 128 bit range check
+    // This will be constrained by the calling function - maybe through instruction decomposition
+    pol commit op_non_ff_gt;
+    // Value of a - b
+    pol commit diff;
+
+    pol A_GT_B = input_a - input_b - 1;
+    pol B_GTE_A = input_b - input_a;
+    op_non_ff_gt * (diff -  (A_GT_B * result) - (B_GTE_A * (1 - result))) = 0; 
+
+    #[PERM_RNG_NON_FF_CMP]
+    range_check.cmp_non_ff_rng_chk {range_check.clk, range_check.value}
+    is
+    op_non_ff_gt {range_chk_clk, diff};
+
+    // ========= FF GT computation ===============================
     // We range check two columns per row of the cmp gadget, the lo and hi bit ranges resp.
     #[PERM_RNG_CMP_LO]
     range_check.cmp_lo_bits_rng_chk {range_check.clk, range_check.value}
@@ -32,7 +51,7 @@ namespace cmp(256);
     pol commit op_eq;
     pol commit op_gt;
 
-    sel_cmp = op_eq + op_gt;
+    sel_cmp = op_eq + op_gt + op_non_ff_gt;
 
     // There are some standardised constraints on this gadget
     // The result is always a boolean

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

@@ -201,6 +201,9 @@ namespace range_check(256);
     // We range check 128 bits in the cmp trace
     cmp_lo_bits_rng_chk * (rng_chk_bits - 128) = 0;
     cmp_hi_bits_rng_chk * (rng_chk_bits - 128) = 0;
+    // For non FF
+    pol commit cmp_non_ff_rng_chk;
+    cmp_non_ff_rng_chk * (rng_chk_bits - 128) = 0;
 
     // ==== ALU TRACE RANGE CHECKS ====
     pol commit alu_rng_chk;

barretenberg/cpp/pil/avm/gas.pil

@@ -96,7 +96,6 @@ namespace main(256);
     // We range check that the absolute value of the differences between each row of l2 and da gas are 32 bits.
     pol commit l2_gas_u16_r0;
     pol commit l2_gas_u16_r1;
-    // Do we need DA?
     main.abs_l2_rem_gas = l2_gas_u16_r0 + l2_gas_u16_r1 * 2**16;
 
     #[LOOKUP_L2_GAS_RNG_CHK_0]

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

@@ -139,6 +139,7 @@ AvmCircuitBuilder::ProverPolynomials AvmCircuitBuilder::compute_polynomials() co
                 polys.alu_cmp_gadget_gt.set_if_valid_index(i, rows[i].alu_cmp_gadget_gt);
                 polys.alu_cmp_gadget_input_a.set_if_valid_index(i, rows[i].alu_cmp_gadget_input_a);
                 polys.alu_cmp_gadget_input_b.set_if_valid_index(i, rows[i].alu_cmp_gadget_input_b);
+                polys.alu_cmp_gadget_non_ff_gt.set_if_valid_index(i, rows[i].alu_cmp_gadget_non_ff_gt);
                 polys.alu_cmp_gadget_result.set_if_valid_index(i, rows[i].alu_cmp_gadget_result);
                 polys.alu_cmp_gadget_sel.set_if_valid_index(i, rows[i].alu_cmp_gadget_sel);
                 polys.alu_ff_tag.set_if_valid_index(i, rows[i].alu_ff_tag);
@@ -218,11 +219,13 @@ AvmCircuitBuilder::ProverPolynomials AvmCircuitBuilder::compute_polynomials() co
                 polys.cmp_borrow.set_if_valid_index(i, rows[i].cmp_borrow);
                 polys.cmp_clk.set_if_valid_index(i, rows[i].cmp_clk);
                 polys.cmp_cmp_rng_ctr.set_if_valid_index(i, rows[i].cmp_cmp_rng_ctr);
+                polys.cmp_diff.set_if_valid_index(i, rows[i].cmp_diff);
                 polys.cmp_input_a.set_if_valid_index(i, rows[i].cmp_input_a);
                 polys.cmp_input_b.set_if_valid_index(i, rows[i].cmp_input_b);
                 polys.cmp_op_eq.set_if_valid_index(i, rows[i].cmp_op_eq);
                 polys.cmp_op_eq_diff_inv.set_if_valid_index(i, rows[i].cmp_op_eq_diff_inv);
                 polys.cmp_op_gt.set_if_valid_index(i, rows[i].cmp_op_gt);
+                polys.cmp_op_non_ff_gt.set_if_valid_index(i, rows[i].cmp_op_non_ff_gt);
                 polys.cmp_p_a_borrow.set_if_valid_index(i, rows[i].cmp_p_a_borrow);
                 polys.cmp_p_b_borrow.set_if_valid_index(i, rows[i].cmp_p_b_borrow);
                 polys.cmp_p_sub_a_hi.set_if_valid_index(i, rows[i].cmp_p_sub_a_hi);
@@ -760,6 +763,7 @@ AvmCircuitBuilder::ProverPolynomials AvmCircuitBuilder::compute_polynomials() co
                 polys.range_check_clk.set_if_valid_index(i, rows[i].range_check_clk);
                 polys.range_check_cmp_hi_bits_rng_chk.set_if_valid_index(i, rows[i].range_check_cmp_hi_bits_rng_chk);
                 polys.range_check_cmp_lo_bits_rng_chk.set_if_valid_index(i, rows[i].range_check_cmp_lo_bits_rng_chk);
+                polys.range_check_cmp_non_ff_rng_chk.set_if_valid_index(i, rows[i].range_check_cmp_non_ff_rng_chk);
                 polys.range_check_dyn_diff.set_if_valid_index(i, rows[i].range_check_dyn_diff);
                 polys.range_check_dyn_rng_chk_bits.set_if_valid_index(i, rows[i].range_check_dyn_rng_chk_bits);
                 polys.range_check_dyn_rng_chk_pow_2.set_if_valid_index(i, rows[i].range_check_dyn_rng_chk_pow_2);