[ { "api_error_status": null, "duration_api_ms": 67526, "duration_ms": 67576, "fast_mode_disabled_reason": "sdk_opt_in_required", "fast_mode_state": "off", "first_content_frame_ms": 1236, "is_error": false, "modelUsage": { "claude-opus-5": { "cacheCreationInputTokens": 5037, "cacheReadInputTokens": 0, "canonicalModel": "claude-opus-5", "contextWindow": 1000000, "costBasis": "list", "costUSD": 0.18843000000000001, "inputTokens": 2, "maxOutputTokens": 64000, "outputTokens": 5522, "provider": "firstParty", "thinkingTokens": 1611, "webSearchRequests": 0 } }, "num_turns": 1, "permission_denials": [], "queued_turn_count": 0, "result": "## Preconditions\n\n1. Every emitted program is a single MLIR module body consisting of an optional top-level callable declaration/definition followed by one or more `dataflow.thread` symbol definitions, with no other top-level entities.\n2. Each `dataflow.thread` is declared `private`, carries a symbol name of the form `@t`, and is annotated with `domain(#dataflow.thread_domain)`.\n3. Each thread's entry signature is fixed to exactly four data block arguments \u2014 `%scratch: memref<8xindex>`, `%memory: memref<8xindex>`, `%grid: memref<4x4xindex>`, `%n: index` \u2014 plus a separate control argument `ctrl (%ctrl: none)`.\n4. Each thread body is terminated by `dataflow.thread.yield` with no operands.\n5. Each thread body contains exactly one `loom.spatial_region`; spatial regions are never nested, never absent from a thread, and never appear more than once per thread.\n6. The `loom.spatial_region` is always written in generic (quoted) operation form with an explicit inherent-attribute dictionary rather than any custom assembly syntax.\n7. The spatial region op takes exactly three operands \u2014 the `index` value `%n`, the `memref<8xindex>` value `%memory`, and the `memref<4x4xindex>` value `%grid` \u2014 and produces no results, as declared by its function type `(index, memref<8xindex>, memref<4x4xindex>) -> ()`.\n8. The operand grouping is declared by `operandSegmentSizes = array` and the (empty) result grouping by `resultSegmentSizes = array`, and these segment sizes are consistent with the actual operand and result lists.\n9. The spatial region carries exactly one region with exactly one block `^bb0`, whose three arguments `%limit: index`, `%target: memref<8xindex>`, `%tile: memref<4x4xindex>` correspond positionally and type-wise to the three operands.\n10. Values defined outside the spatial region (`%scratch`, `%memory`, `%grid`, `%n`) are never referenced inside the region body; all uses inside the region go through the block arguments `%limit`, `%target`, `%tile`.\n11. The region is terminated by `\"loom.spatial_yield\"()` in generic form with `operandSegmentSizes = array` and type `() -> ()`, yielding no values, consistent with the region-holding op having no results.\n12. The spatial region op carries a `graph_name` string attribute and a `source_maps` attribute; `graph_name` is derived from the owning thread's index so that distinct regions in the module carry distinct graph names.\n13. All index constants used inside the region (`%c0`, `%c1`, `%cw`, `%kv`) are defined by `arith.constant ... : index` operations at the top of the region block, before any control-flow construct that uses them.\n14. Every emitted program satisfies SSA dominance: each value is defined textually before use and within a region that dominates the use, including loop induction variables, iteration arguments, and `while` \"do\"-block arguments.\n15. Inside the spatial region, exactly one graph-owned parallel operation is present on every path: either an `scf.forall` or an `scf.parallel` (possibly a `scf.parallel` immediately nested in another `scf.parallel`).\n16. The parallel operation's iteration domain is fixed at compile time: `scf.forall` uses a literal integer upper bound, and `scf.parallel` uses constant lower bound `%c0`, constant upper bound `%cw`, and constant step `%c1`, so no parallel bound depends on a runtime value such as `%limit`.\n17. Parallel operations are always one-dimensional per op (a single induction variable in each `scf.parallel`/`scf.forall` header); multi-dimensional parallelism is expressed only by nesting two one-dimensional `scf.parallel` ops.\n18. Every `scf.parallel` region is terminated by `scf.reduce` with no reduction operands, and every `scf.parallel` produces no results; `scf.forall` bodies carry no `shared_outs`, no mapping attribute, and rely on the implicit terminator.\n19. Memory writes performed by the parallel body are lane-disjoint: stores into `%target: memref<8xindex>` are always indexed by the parallel induction variable `%lane`, and stores into `%tile: memref<4x4xindex>` are always indexed by the pair of induction variables `(%pi, %pj)` of the enclosing nested parallel loops.\n20. No load operations, no cross-lane data movement, and no reduction or accumulation across lanes occur inside the parallel region; the only memory effects there are stores.\n21. Sequential control flow that encloses the parallel op (`scf.if` / `scf.for`) is value-free: the `scf.if` has no results and no `else` region, and the `scf.for` has no `iter_args` and no results, so no implicit `scf.yield` operands are required.\n22. Sequential control flow inside the parallel body may carry values: `scf.for` with `iter_args` yields exactly one `index` value per iteration via `scf.yield`, and `scf.while` carries a single `index` loop-carried value with `scf.condition(%cond) %v : index` in the \"before\" region and `scf.yield` of a single `index` in the \"after\" region, with matching `(index) -> index` typing.\n23. All predicates used by `scf.if` and `scf.while` are `i1` values produced by `arith.cmpi slt` on `index` operands.\n24. Runtime-dependent trip counts appear only in sequential constructs, where the bound is the region block argument `%limit`.\n25. Code placed in the thread body outside the spatial region is self-contained: it defines its own constants and only touches `%scratch`, never values defined inside the region.\n26. All memref accesses are type-consistent with the declared shapes `memref<8xindex>` (one index) and `memref<4x4xindex>` (two indices), and all stored values are of type `index`.\n27. The optional top-level callable, when present, is a well-formed declaration or definition (`llvm.func` declaration with no body, or `func.func` with a body terminated by `return` of a matching type) and is never called from any thread; threads contain no call operations at all.\n28. The `%ctrl: none` control argument is declared but never used in any emitted body.\n\n## Sampling conventions\n\n1. The module contains either one or two `dataflow.thread` definitions; zero threads and three or more threads are never emitted.\n2. Thread symbols are named by a counter starting at zero, yielding `@t0` and, when a second thread exists, `@t1`.\n3. The top-level preamble is one of exactly three forms: nothing, the fixed declaration `llvm.func @imported_kernel(i64)`, or the fixed definition `func.func @native_helper(%arg0: index) -> index` whose body is `return %arg0 : index`; no other callable signatures, dialects, or multiple preamble entities are emitted.\n4. The preamble choice is made once for the whole module rather than per thread, and the preamble is always separated from the threads by a blank line.\n5. Thread entry argument names and types are a fixed skeleton (`%scratch`, `%memory`, `%grid`, `%n`, `%ctrl`), with memref shapes hard-coded to `8xindex` and `4x4xindex`; sizes are never varied and no other argument counts or element types occur.\n6. The thread domain attribute is always `#dataflow.thread_domain`; no other domain kind is emitted.\n7. Pre-region resident code is either omitted entirely or is one fixed three-line block defining `%rzero = arith.constant 0 : index`, `%rval = arith.constant 3 : index`, and a single `memref.store %rval, %scratch[%rzero]`; no other resident code shapes, lengths, or targets occur.\n8. The in-region constant preamble is always the same four constants in the same order: `%c0 = 0`, `%c1 = 1`, `%cw = `, `%kv = 7`.\n9. The parallel width constant `%cw` (and the `scf.forall` literal bound) is drawn from exactly `{1, 2, 4}`; other widths, non-power-of-two widths, and widths larger than the `memref<8xindex>` extent are never emitted, and the same width is reused for both `%cw` and any `scf.forall` bound within a thread.\n10. The stored payload constant is always `7` and the resident payload constant is always `3`.\n11. The `graph_name` attribute always follows the scheme `\"g_t_0\"`, with a trailing `_0` suffix implying at most one region per thread; `source_maps` is always the empty list `[]`.\n12. Sequential nesting around the parallel op is limited to three alternatives: no wrapper, exactly one `scf.if` guarded by `%ocond = arith.cmpi slt, %c0, %limit`, or exactly one `scf.for %oi = %c0 to %limit step %c1`; wrappers are never stacked, never use `else`, and `scf.while` is never used at this outer level.\n13. The wrapper induction variable `%oi` and the wrapper predicate `%ocond` are defined but never used inside the parallel body.\n14. The graph-owned parallel form is one of exactly three shapes: a single `scf.forall` with a literal bound, a single `scf.parallel` with constant bounds, or two perfectly nested `scf.parallel` ops; deeper nests, `scf.forall` with `scf.parallel` mixing, and reduction-carrying parallel ops are never emitted.\n15. In the two-level nested `scf.parallel` shape, the body is a fixed single `memref.store %kv, %tile[%pi, %pj]`, and the separately chosen inner-body shape is not emitted at all in that case.\n16. The inner (lane-disjoint) body is one of exactly four fixed shapes: a bare store, a store guarded by `scf.if` on `arith.cmpi slt, %lane, %cw`, an `scf.for` with one `index` `iter_args` accumulator initialized to `%lane` and incremented by `%c1` whose result is stored, or an `scf.while` counting `%wi` from `%c0` while `slt %limit`, incrementing by `%c1`, whose result is stored.\n17. Each inner control-flow shape is at most one level deep; `if`/`for`/`while` are never combined or nested within one another inside the parallel body.\n18. All SSA value names are fixed mnemonics (`%c0`, `%c1`, `%cw`, `%kv`, `%lane`, `%pi`, `%pj`, `%oi`, `%ocond`, `%bcond`, `%bi`, `%bacc`, `%bnext`, `%bsum`, `%wi`, `%wc`, `%wb`, `%wn`, `%wres`, `%rzero`, `%rval`), reused identically across threads since each thread is a separate symbol scope.\n19. The four per-thread shape decisions (resident code presence, width, parallel form, outer wrapper, inner body) are made independently for each thread, so two threads in one module may differ in every dimension.\n20. Comparison predicates are always `slt`, arithmetic is always `arith.addi` by `%c1`, and no other `arith` opcodes or predicates appear.\n21. 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