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Language rule (GpuStack PLAN.md): new host-runtime code lands in .om. PR #139 adds the general matrix multiply omega_gpu_gemm_ex as MIGRATION-PENDING C (src/omega_gpu_gemm_ex.c, build switch CUDAPP_MIGRATION_PENDING_GEMM_EX in mk/gemm-ex.mk, default 1). This issue tracks its Omega successor, src/omega_gpu_gemm_ex.om, named in src/omega_gpu_gemm_ex.h and mk/gemm-ex.mk.
Scope to port (C today, src/omega_gpu_gemm_ex.c at #139 head):
The host orchestration of omega_gpu_gemm_ex: C tiles of at most 4096 x 4096, k parts of at most 16384 (1808 on bf16x3), block-scale k breaks, zero-copy native calls, operand packing into the core type, bf16x3 plane split (9 plane products), double accumulation of the parts, alpha/beta and scales, round-to-nearest-even stores to f32/bf16/f16, the inf/NaN row/column host recompute.
omega_gpu_gemm_ex_fp8_block_rows (the fp8 GEMV and grouped GEMM fallback).
Omega words needed (omega main e5b32567a): f32/f64 arithmetic, compares and conversions exist in seed/omc/omc.om (float section from line 3038). The successor calls the C3 core (omega_gpu_gemm_ld, src/omega_gpu_gemm.c, itself C): check at the then-current pin how a CUDApp .om unit calls into libomega_gpu.a; if no such path exists, file the concrete extension proposal (omega-bridge emits C/Python from .om and lets foreign callers call compiled Omega units, it does not import C).
Acceptance: the .om entry passes tests/gpu_gemm_ex_test.c host (--host-only, 224 checks at fba0384), simulator (--sim) and chip tiers (901 checks at fba0384, evidence/GEMM-GENERAL-fba0384/), with every mutant red, bit for bit equal to the C path on the predeclared sweep; then the C path goes behind the migration-pending switch defaulting OFF and is removed in a separate PR.
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gemm_ex: runtime API 0.6.0 manifest entries, API.md section 9.8, READ…