[ { "api_error_status": null, "duration_api_ms": 50108, "duration_ms": 50147, "fast_mode_disabled_reason": "sdk_opt_in_required", "fast_mode_state": "off", "first_content_frame_ms": 1816, "is_error": false, "modelUsage": { "claude-opus-5": { "cacheCreationInputTokens": 5149, "cacheReadInputTokens": 0, "canonicalModel": "claude-opus-5", "contextWindow": 1000000, "costBasis": "list", "costUSD": 0.14404999999999998, "inputTokens": 2, "maxOutputTokens": 64000, "outputTokens": 3702, "provider": "firstParty", "thinkingTokens": 659, "webSearchRequests": 0 } }, "num_turns": 1, "permission_denials": [], "queued_turn_count": 0, "result": "## Preconditions\n\n1. Every emitted program is a single MLIR module whose body consists only of `dataflow.graph` definitions and nothing else.\n2. Each `dataflow.graph` is declared `private`, carries a symbol name, and is given the attribute dictionary `input_segments = array` together with `result_segments = array`, i.e. one control-typed input, no second-class inputs, two memory inputs, and no results of any kind.\n3. Each graph's signature is `(%start: none, %limit: i32, %input: memref, %output: memref) -> ()`, so the graph produces no results and its memory operands are dynamically shaped one-dimensional `i32` memrefs that are block arguments of the graph region (canonical, unaliased roots).\n4. Each graph body is terminated by `dataflow.graph.return %start : none`, returning the incoming control token and no data values, consistent with the empty result list.\n5. Each graph body contains exactly one `scf.while` operation, and that loop is at the top level of the graph body \u2014 loops are never nested inside one another and never appear inside the before or after region of another loop.\n6. The `scf.while` is written in its explicit two-region form: a before region ending in `scf.condition`, and a `do` region whose entry block `^bb0` is explicitly labelled and whose body ends in `scf.yield`.\n7. The loop's result arity, its initializer list, its operand type list, its result type list, the arity of the `^bb0` block-argument list, the operand count of `scf.condition` after the condition value, and the operand count of `scf.yield` are all equal and all of type `i32`; the whole loop state is a homogeneous `i32` tuple.\n8. All loop-carried initializers are values defined before the loop in the same graph body (the `arith.constant` values `%zero` and `%one`), never loop-internal or region-local values.\n9. Every memory access is a scalar `memref.load` or `memref.store` on a dynamically shaped `memref` graph argument with exactly one index operand; no multi-dimensional, vector, strided, or aggregate accesses occur.\n10. Every index operand of a load or store is produced by an `arith.index_cast ... : i32 to index` applied to an `i32` SSA value available at that point; index values are never computed by `arith` index arithmetic, by `affine.apply`, or by constants of type `index` directly.\n11. Loads read only from `%input` and stores write only to `%output`; the two memrefs are never swapped, so no load\u2013store pair within a graph targets the same memref.\n12. Every SSA value is defined before its uses in the enclosing region, and values defined in the before region are never referenced in the after region or after the loop \u2014 cross-region communication happens exclusively through `scf.condition` operands and `^bb0` block arguments.\n13. The before region reads memory, computes the next loop state, optionally writes memory, computes an `i1` predicate with `arith.cmpi slt` on `i32` operands, and forwards exactly the computed next-state values through `scf.condition`; the value compared against the bound is the first (index-like) state lane.\n14. The loop-exit condition's bound operand is an `i32` value defined outside the loop \u2014 either a graph block argument or an `arith.constant` in the graph body \u2014 so the trip bound is loop-invariant.\n15. The after region yields exactly one value per loop lane, each of which is either an unmodified `^bb0` block argument or a value computed from block arguments within that same region; it never yields values captured from the before region.\n16. Any store performed in the after region indexes memory through an `arith.index_cast` of an after-region block argument, not through an index produced in the before region.\n17. Every result of the `scf.while` is consumed after the loop by at least one operation in the graph body, so no loop-exit lane is dead.\n18. Each post-loop consumption is a `memref.store` of the result into `%output` at a constant index obtained by `arith.index_cast` of an `i32` constant, so all exit values become observable memory effects.\n19. Within one graph body all SSA names are distinct, and the naming of values defined under a mode-dependent alternative never collides with names defined unconditionally.\n20. The program contains no function definitions, no calls, no branches other than the structured `scf.while`, no `if`/`for` constructs, no floating-point or non-`i32` scalar types, no allocations, deallocations, copies, subviews, casts of memrefs, or aliasing operations of any kind.\n21. Distinct graphs in one module have distinct symbol names and are mutually independent: no graph calls, references, or shares SSA values with another.\n\n## Sampling conventions\n\n1. The module holds either one or two graph definitions and never zero, three, or more.\n2. Graph symbols are named `@while_case` followed by the graph's zero-based position in the module, giving `@while_case0` and optionally `@while_case1`.\n3. Every graph uses the identical fixed signature and identical argument names `%start`, `%limit`, `%input`, `%output`; no other argument counts, orders, element types, or memref ranks are ever emitted.\n4. The attribute dictionary is emitted verbatim on every graph and is never varied or omitted.\n5. Every graph body opens with the same three-instruction constant preamble: `%zero = arith.constant 0 : i32`, `%one = arith.constant 1 : i32`, and `%bound = arith.constant : i32`.\n6. The literal bound constant `LIMIT` is an integer chosen from 2 through 6 inclusive; no other magnitudes, negative values, or zero are emitted.\n7. The loop state width is either 2 or 3 lanes; one-lane and four-or-more-lane loops are never generated.\n8. Loop-state initializers are `%zero` for lanes 0 and 1, and `%one` for lane 2 when present; no other initializer combination is used.\n9. Loop state, loop results, block arguments, and yields are named with the fixed schemes `%s0/%s1/%s2` (initializers), `%b0/%b1/%b2` (after-region block arguments), `%n0/%n1/%n2` (next-state values), and `%res` for the loop result tuple.\n10. The before region always begins with the same fixed skeleton: index-cast of lane 0 (`%idx0`), a load `%v0` from `%input[%idx0]`, and an increment `%n0 = arith.addi %s0, %one`, so lane 0 is always an unit-stride counter.\n11. An optional second load is emitted or omitted; when emitted it index-casts `%n0` into `%idx1`, loads `%v1` from `%input[%idx1]`, and sums the two loaded values into `%vsum`, thereby producing two loads from the same memref at adjacent offsets in one iteration.\n12. Lane 1 is always updated as `%n1 = arith.addi %s1, X` where `X` is `%vsum` when the second load is present and `%v0` otherwise; no other accumulation expression is used.\n13. When the loop has three lanes, lane 2 is always updated as `%n2 = arith.addi %s2, %n0`, coupling the third lane to the freshly computed counter.\n14. An optional in-loop store is emitted or omitted; when emitted it is exactly `memref.store %n1, %output[%idx0]`, reusing the index already computed for the load, and it is placed after all state computation and before the comparison.\n15. The comparison is always `arith.cmpi slt` with `%n0` on the left; the right operand is either the graph argument `%limit` or the local constant `%bound`, chosen per graph, and no other predicate or operand order is emitted.\n16. The after region takes exactly one of three fixed shapes: a pure forwarding of all block arguments; a recomputation `%d1 = arith.addi %b1, %b0` whose result replaces lane 1 in the yield; or a store `memref.store %b1, %output[%bidx]` where `%bidx = arith.index_cast %b0`, with the yield still forwarding the unmodified block arguments.\n17. In the after region, lanes 0 and 2 are always forwarded unchanged; only lane 1 is ever recomputed.\n18. The post-loop epilogue is a fixed skeleton that stores result 0 at index 0 via `arith.index_cast %zero` and result 1 at index 1 via `arith.index_cast %one`; when a third lane exists, an extra `%otwo = arith.constant 2` is materialized and result 2 is stored at index 2.\n19. All per-graph shape decisions \u2014 lane count, bound magnitude, presence of the second load, presence of the in-loop store, choice of bound operand, and after-region mode \u2014 are drawn independently for each graph, so the two graphs in a module may differ in every respect except signature and naming scheme.\n20. Indentation is fixed: graph-body operations use two spaces and region-body operations use four, with the module braces and region delimiters laid out in a single fixed textual skeleton.\n21. 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