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fpga: systolic wavefront array spec -- matrix multiply as a schedule (for the ai-accelerator course) - #7719
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fpga: systolic wavefront array spec -- matrix multiply as a schedule (for the ai-accelerator course)#7719gHashTag wants to merge 1 commit into
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…(for the ai-accelerator course) A 4x4 Kung-Leiserson wavefront array for matrix multiply, modeled tick by tick: a[j][q] enters row j's west edge at tick j+q, b[q][k] enters column k's north edge at tick q+k, both walk one cell per tick, and every operand pair of output (j,k) therefore meets inside the cell at tick j+k+q -- N consecutive MACs per output, no gaps, no double booking. Six tests + one invariant, none vacuous (test-report 100%): - pair_meets_inside_the_cell: all 64 (j,k,q) triples meet on one tick - macs_of_one_output_are_consecutive: the pipeline never stalls - every_mac_fires_exactly_once: playing every tick fires exactly N^3 = 64 MACs in 3N-2 = 10 ticks -- a lost MAC or a double firing breaks the count - the_wavefront_takes_three_n_minus_two: 3N-2 = 10 ticks vs the weight-stationary variant's 2N-1 = 7 - the_array_computes_the_product: the schedule equals the plain triple loop, entry by entry, on a matrix with negatives and zeros (Python 3 oracle, constants named in the test) - identity_leaves_the_matrix_alone: the array cannot skip ticks and still lands on A untouched Course use: gHashTag/trinity#1487 module dataflow lesson systolic-arrays. Algorithm truth only -- no board measurement, no frequency claimed. Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com>
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This was referenced Oct 8, 2026
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policy: owner-approved exception for the AX7203 Ethernet beacon wrapper and XDC (Closes #7792)
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This was referenced Oct 8, 2026
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What
specs/fpga/systolic.t27-- a 4x4 Kung-Leiserson wavefront array for matrix multiply, modeled tick by tick. This is the one new specgHashTag/trinity#1487(AI accelerator course, module dataflow, lesson systolic-arrays) asks for; same path as #7626 took for the buses course.The schedule, as the spec states it
a[j][q]enters row j's west edge at tickj+q;b[q][k]enters column k's north edge at tickq+k; both walk one cell per tick.(j,k)meets inside the cell at tickj+k+q-- N consecutive MACs per output, no gaps, no double booking, each cell busy every tick after the wavefront reaches it.3N-2ticks (10 for N=4) forN^3MACs onN^2cells; the weight-stationary variant is2N-1(7) -- the trade the course lesson teaches.Tests (test-report: 6/6 pass, 1 invariant proved, 0 vacuous)
pair_meets_inside_the_cell(j,k,q)triples meet on one tickmacs_of_one_output_are_consecutiveevery_mac_fires_exactly_oncethe_wavefront_takes_three_n_minus_twothe_array_computes_the_productidentity_leaves_the_matrix_aloneVerified locally:
t27c test-report specs/fpga/systolic.t27100%,t27c gen-verilogexit 0 (tests/invariant correctly reported NOT LOWERED by the synthesis backend).Honesty line carried in the header: algorithm truth only -- no board measurement, no frequency claimed.
Closes nothing in this repo; the course issue is gHashTag/trinity#1487.
🤖 Generated with Claude Code