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This is incorrect. Standard radix-4 Booth-2 encoding of an n-bit operand produces ⌈n/2⌉ = 32 signed-digit rows total (for n=64). The sign-correction is a *bit added to the existing rows* (the MSB of the highest digit), not a separate full-width partial product row. A 64-bit radix-4 Booth multiplier has 32 partial products, not 33. This error propagates to the B1 design description, the proposal, and the recommendation.\n\n2. **Booth radix-8 partial-product count is wrong (B2).** Document claims 22 signed-digit rows + 1 sign-correction = 23. For 64-bit radix-8 Booth, the standard count is ⌈n/3⌉ = 22 signed-digit rows. The \"extra sign-correction row\" framing is the same misconception as issue 1. The 11-PP correction (vs. 32-bit) is also misleadingly explained.\n\n3. **MULH/MULHU full-product requirement is misleading.** The document states the multiplier is \"sized to produce the full 128-bit product so that MULH/MULHU selection requires only output muxing.\" A 64×64→128 multiplier is required for MULH/MULHU, but it is not required for MUL; this is a real cost driver. The framing implies the datapath is \"free\" beyond MUL when in fact the upper 64 bits exist specifically to serve MULH*. The document also fails to note that for 32-bit operands (the W-variants) the full 64×64→128 product is overkill, though reusing the same datapath is reasonable.\n\n4. **Newton–Raphson B5 latency claim is inconsistent and likely wrong.** A 64-bit Newton–Raphson divider with a 32-bit initial reciprocal and 2 iterations does **not** produce a 64-bit-accurate quotient. Two iterations of N–R on a 32-bit seed approximately double the bit-accuracy per iteration, so after 2 iterations you have ~32 + 2·(32 − accuracy) bits — for a properly initialized seed this typically gives ~64 bits only with a carefully chosen seed and the right number of iterations (commonly 2–3 iterations from a 16–32 bit seed, depending on the exact variant). The \"6–10 cycles\" budget for two multiplies + two iterations + correction is not obviously wrong but the bit-accuracy argument is not given. The \"4–6 cycle for 32-bit\" prior figure is also not defended.\n\n5. **B6 \"combinational non-restoring array divider\" size claim is uncalibrated.** The document removes the prior \"~50×\" figure as unsupported but offers no replacement order-of-magnitude estimate, only \"very large.\" The comparison table still lists \"very large (unvalidated)\" with no quantitative anchor, which makes the comparison table non-actionable for B6.\n\n6. **B7 per-core effective area math is sloppy.** Cluster of 8 cores sharing one B1 + B4-pipe unit: per-cluster area estimated 8–12× A1, divided by 8 cores gives 1–1.5× A1 per core. But B1 alone is 3–5× A1 and B4-pipe adds more. A cluster containing a full B1 + B4-pipe cannot be \"8–12× A1 total\" — that range would put the B4-pipe contribution at roughly 0×, which contradicts B4-pipe's stated 6–8× to A2 (i.e., ~3–4× to A1 added on top of A2's 3–4× A1). The cluster cost arithmetic does not close.\n\n7. **B5 throughput \"1/6–1/10\" is misleading.** Newton–Raphson is variable-latency; throughput depends on whether a subsequent divide can start before the previous finishes. The document treats throughput as 1/latency without justifying the absence of pipelining.\n\n8. **A3 divider throughput of \"1/16\" is inconsistent with a \"pipelined\" SRT-4 elsewhere.** A3 is explicitly non-pipelined, but the entry still says \"pipelined radix-4/8 Booth multiplier.\" The A3/B4 split is confusing because the document says A3 is the non-pipelined SRT-4 view \"for direct comparison with B4,\" then later notes B4-pipe is a separate point. This is internally confusing even if not strictly wrong.\n\n9. **Area ranges in the comparison table use A1 as the baseline but the A1 baseline is never quantified.** All relative areas are multiples of an undefined \"1×.\" This is acknowledged but undermines the entire comparison; there is no absolute number to anchor \"3–5× of A1\" to.\n\n10. **Power/energy section is non-quantitative and largely vacuous.** \"Energy tends to scale with switching nodes\" is not an analysis. The section does not consider that an iterative divider is the worst case for energy *per divide*, not the best, because 64 cycles of clocked register activity typically dominates the energy budget for a single divide vs. a faster divider that completes in fewer cycles. The framing (\"lower average switching power\") is misleading without an operations-per-second normalization.\n\n11. **Failure to consider that W-variants need only a 32×32→64 (sign-extended) datapath, not 64×64→128.** Reusing the 64-bit datapath for 32-bit operands costs 4× the energy and area of a dedicated 32-bit datapath. The document claims this reuse is \"acceptable\" without comparing against a dedicated W-datapath. The W-extension is a real workload consideration in many RV64 deployments.\n\n12. **128-core scalability claim about voltage/frequency is unsupported.** \"Moderately pipelined MUL/DIV is more resilient to voltage droop\" is asserted without source or reasoning. Voltage-droop resilience depends on the depth of pipelining, clock-tree design, and decoupling — not directly on whether the MUL/DIV is \"moderately pipelined.\" This is a hand-wave.\n\n13. **F/D extension \"out of scope\" but Recommendation 2 implies otherwise.** The document lists F/D as an open question, yet the recommended design's relevance to F extension (FP reciprocal, FP-to-int conversions, Newton–Raphson for FP divide) is a major design driver that is dismissed as out of scope. Given XH-1 is described as balancing general-purpose and HPC-adjacent workloads, excluding F from the MUL/DIV analysis is a significant gap.\n\n14. **Sources section is weak on specificity.** Rocket, BOOM, Ariane are cited by file name but without commit hashes, and the document admits \"specific commit, measured numbers, and PPA data: INSUFFICIENT EVIDENCE.\" Hennessy & Patterson and Parhami are cited without chapter or edition. Per the document's own labeling standard, these citations are not actionable.\n\n15. **MULH/MULHSU \"Booth complicates verification\" claim is overstated.** Radix-4 Booth of a signed operand is the standard recoding; signed/unsigned operand handling at the input is the issue, not Booth itself. The verification complication is the sign-extension/correction logic, which is small. The document overstates this.\n\n16. **\"Signed overflow (DIV of INT64_MIN by −1): quotient = INT64_MIN, remainder = 0\" is correct but the document does not note the verification implication** — that this requires detecting the overflow case explicitly, separate from a generic restore step. Mentioning the rule without mentioning the hardware detector is a gap.\n\n17. **The \"2-cycle MUL matches typical issue-to-use distances\" claim is unsupported.** No pipeline depth or issue-to-use distance is established; `pipeline.md` is TBD. This is a quantitative claim with no anchor.\n\n18. **A5 \"Shared / Clustered MUL/DIV Unit\" is listed under \"Existing Approaches\" but is then analyzed as B7, a new design point.** The boundary between existing and proposed is blurred; the document acknowledges this was not analyzed in the prior revision.\n\n19. **B4-pipe area accounting in the comparison table is wrong.** Row says \"adds ~6–8× to A2 total (unval.)\" but A2's area is 3–4× A1, so 6–8× relative to A2 would be 18–32× A1, which is absurd and contradicts the B1+B4-pipe narrative. The text earlier says ~3–4× of B1's divider, added to B1 → 6–8× of A1 total, but the table column header says \"to A2 total\" and the value is not consistent with either reading. This is a clear internal inconsistency.\n\n20. **The \"previous revision contained an error\" pattern is repeated many times** (32-cycle divider, 11 partial products, \"~50×\" array divider, MULH/Montgomery claim, DIVU-by-zero description). The document is a self-correction of a prior version, which is fine, but the volume of corrections suggests the document is still in flux and not ready for a recommendation-grade verdict.\n\n21. **The \"primary recommendation is conditional on synthesis data that does not yet exist\" disclaimer is repeated in the Status, Proposal, Recommendation, and Confidence sections.** This is honest but means the document's primary deliverable is, by its own admission, not actionable today. The document should be marked as \"research survey\" rather than issuing a conditional recommendation.\n\nREQUIRED FIXES:\n\n- Correct the Booth partial-product counts (radix-4: 32 rows, not 33; radix-8: 22 rows, not 23) and propagate the correction through B1, B2, the Proposal, and the Recommendation. The sign-correction is a bit added to existing rows, not a separate full-width row.\n- Reconcile the B4-pipe / A2 / B1 area math in the comparison table; either restate the units of the \"adds 3–4×\" and \"6–8×\" figures consistently, or drop the relative numbers and label them all \"unvalidated, pending synthesis.\"\n- Quantify the A1 baseline in absolute terms (gate count, NAND2 equivalent, or area in a named process) or remove the relative-area columns and replace with qualitative ranking.\n- Provide an order-of-magnitude estimate for B6 (combinational non-restoring array divider) area, even as a wide range, so the comparison table is non-vacuous for that row.\n- Re-derive B5 (Newton–Raphson) latency and iteration count with the bit-accuracy argument made explicit, including the seed width and the number of correct bits per iteration.\n- Resolve the W-variant question: either justify reusing the 64-bit datapath with a quantitative energy/area comparison, or note that a dedicated 32-bit datapath is an alternative.\n- Address F/D extension implications in the MUL/DIV analysis, or explicitly state the design is integer-only with no plan to add F/D and accept the consequences.\n- Strengthen the Sources section with specific citations (edition, chapter, commit hash) or remove the citation claims entirely.\n- Remove the unsupported voltage-droop-resilience claim or replace it with a sourced statement.\n- Distinguish explicitly, for each numbered claim in the Proposal and Recommendation, whether it is a FACT (spec-defined), an ASSUMPTION (engineering judgment with stated basis), a PROPOSAL (design choice), a RECOMMENDATION (action with trigger), or an OPEN QUESTION. Several items currently mix these categories.\n- Verify the RISC-V spec citation (Document Version 20191213) actually contains the exact ÷0 and INT64_MIN/−1 behavior as stated, and that the document is not relying on memory of the spec text.\n- State the per-core area budget assumption (or lack thereof) explicitly in the Recommendation, not only in the Status section.\n\nCONFIDENCE: HIGH","refusal":null,"reasoning":null}}],"usage":{"prompt_tokens":9375,"completion_tokens":2624,"total_tokens":11999,"cost":0,"is_byok":false,"prompt_tokens_details":{"cached_tokens":134,"cache_write_tokens":0,"audio_tokens":0,"video_tokens":0},"cost_details":{"upstream_inference_cost":0,"upstream_inference_prompt_cost":0,"upstream_inference_completions_cost":0},"completion_tokens_details":{"reasoning_tokens":0,"image_tokens":0,"audio_tokens":0}}}