The table below shows all 70 primitives and which rules they implement. Note that a rule might be missing because it was just not added yet, or because it does not apply for a specific primitive.
| Name | StableHLO | Backward |
|---|---|---|
| abs | ✓ | ✓ |
| add | ✓ | ✓ |
| and | ✓ | ✓ |
| atan2 | ✓ | ✓ |
| bitcast_convert | ✓ | ✓ |
| broadcast_in_dim | ✓ | ✓ |
| cbrt | ✓ | ✓ |
| ceil | ✓ | ✓ |
| clamp | ✓ | ✓ |
| concatenate | ✓ | ✓ |
| convert | ✓ | ✓ |
| cosine | ✓ | ✓ |
| divide | ✓ | ✓ |
| dot_general | ✓ | ✓ |
| dynamic_slice | ✓ | ✓ |
| dynamic_update_slice | ✓ | ✓ |
| equal | ✓ | ✓ |
| exp | ✓ | ✓ |
| expm1 | ✓ | ✓ |
| fill | ✓ | ✗ |
| floor | ✓ | ✓ |
| gather | ✓ | ✓ |
| greater | ✓ | ✓ |
| greater_equal | ✓ | ✓ |
| if | ✓ | ✓ |
| iota | ✓ | ✗ |
| is_finite | ✓ | ✓ |
| less | ✓ | ✓ |
| less_equal | ✓ | ✓ |
| log | ✓ | ✓ |
| log1p | ✓ | ✓ |
| logistic | ✓ | ✓ |
| maximum | ✓ | ✓ |
| minimum | ✓ | ✓ |
| mul | ✓ | ✓ |
| negate | ✓ | ✓ |
| not | ✓ | ✓ |
| not_equal | ✓ | ✓ |
| or | ✓ | ✓ |
| pad | ✓ | ✓ |
| popcnt | ✓ | ✓ |
| power | ✓ | ✓ |
| ✓ | ✗ | |
| reduce_all | ✓ | ✓ |
| reduce_any | ✓ | ✓ |
| reduce_max | ✓ | ✓ |
| reduce_min | ✓ | ✓ |
| reduce_prod | ✓ | ✓ |
| reduce_sum | ✓ | ✓ |
| remainder | ✓ | ✓ |
| reshape | ✓ | ✓ |
| reverse | ✓ | ✓ |
| rng_bit_generator | ✓ | ✗ |
| round | ✓ | ✓ |
| rsqrt | ✓ | ✓ |
| scatter | ✓ | ✓ |
| select | ✓ | ✓ |
| shift_left | ✓ | ✓ |
| shift_right_arithmetic | ✓ | ✓ |
| shift_right_logical | ✓ | ✓ |
| sign | ✓ | ✓ |
| sine | ✓ | ✓ |
| sqrt | ✓ | ✓ |
| static_slice | ✓ | ✓ |
| sub | ✓ | ✓ |
| tan | ✓ | ✓ |
| tanh | ✓ | ✓ |
| transpose | ✓ | ✓ |
| while | ✓ | ✗ |
| xor | ✓ | ✓ |