chore: resolve field_t issues from external audit (#16210)

### `field_t` Issues and Resolutions Tracker

For more details, see the comments below.

| ID | Title | Status |
| --- |
--------------------------------------------------------------------------------------------
| ------ |
| 17 | `test_slice_random` not covering the entire input space | `slice`
is replaced with a simpler method `split_at` |
| 16 | Unexpected random value in `test_slice_random` | `slice` is
replaced with a simpler method `split_at` |
| 15 | \[opt] Duplicate constraint in `invert` | ✅ |
| 14 | `set_public` on constant `field_t` passes `IS_CONSTANT` as a wire
index | added the assertion that the input is not constant |
| 13 | \[opt] Multiplication by zero in `field_t` not canonicalized to
constant | ❌ (breaks bigfield assertions + no efficiency gains in real
circuits) |
| 12 | \[opt] `decompose_into_bits` with `num_bits = 253` does
unnecessary aliasing check | deleted |
| 11 | \[doc] Incorrect documentation of `slice` method | `slice` is
replaced with a simpler method `split_at` |
| 10 | Missing builder context validation in field operations | ✅ |
| 9 | \[doc] Confusing comment in `accumulate` | ✅ |
| 8 | \[opt] `assert_equal` optimization | ✅ |
| 7 | Unnecessary witness multiplied by 0 in `normalize` | ✅ |
| 6 | \[opt] `madd` could be optimized when 2 inputs are constant | ✅ |
| 5 | Inconsistent naming of PLONK gate terms | Made the comments
consistent with the naming in gate-related structs |
| 4 | `bool_t` has a constructor that takes context and value | ✅ |
| 3 | Use `get_value` to get a boolean value | ✅ |
| 2 | No restriction on `num_bits` in `ranged_less_than` | ✅ |
| 1 | \[doc] Assumption over `ranged_less_than` is overly restrictive,
method comment has mistakes | ✅ |

Author: iakovenkos

barretenberg/cpp/scripts/test_civc_standalone_vks_havent_changed.sh

@@ -11,7 +11,7 @@ cd ..
 # - Generate a hash for versioning: sha256sum bb-civc-inputs.tar.gz
 # - Upload the compressed results: aws s3 cp bb-civc-inputs.tar.gz s3://aztec-ci-artifacts/protocol/bb-civc-inputs-[hash(0:8)].tar.gz
 # Note: In case of the "Test suite failed to run ... Unexpected token 'with' " error, need to run: docker pull aztecprotocol/build:3.0
-pinned_short_hash="42c72e0d"
+pinned_short_hash="ca12eef6"
 pinned_civc_inputs_url="https://aztec-ci-artifacts.s3.us-east-2.amazonaws.com/protocol/bb-civc-inputs-${pinned_short_hash}.tar.gz"
 
 function compress_and_upload {

barretenberg/cpp/src/barretenberg/stdlib/honk_verifier/ultra_recursive_verifier.test.cpp

@@ -291,7 +291,7 @@ template <typename RecursiveFlavor> class RecursiveVerifierTest : public testing
         }
         // Check the size of the recursive verifier
         if constexpr (std::same_as<RecursiveFlavor, MegaZKRecursiveFlavor_<UltraCircuitBuilder>>) {
-            uint32_t NUM_GATES_EXPECTED = 873673;
+            uint32_t NUM_GATES_EXPECTED = 873519;
             ASSERT_EQ(static_cast<uint32_t>(outer_circuit.get_num_finalized_gates()), NUM_GATES_EXPECTED)
                 << "MegaZKHonk Recursive verifier changed in Ultra gate count! Update this value if you "
                    "are sure this is expected.";