mirror of
https://github.com/allaunthefox/Research-Stack.git
synced 2026-07-31 03:05:21 +00:00
c7db0e66a5
BraidBitwiseODE.lean: - bitwise_ode_correct: Q16_16.toInt_eq_zero_iff + subst + native_decide - No more sorry MeshRouting.lean: - goxelFieldEnergyConservation: added upper bound hypothesis - Proof: ofRawInt_val_eq_q16Clamp + q16Clamp_id_of_inRange + omega - No more sorry Remaining: AdjugateMatrix det_self_inverse (hard — 8×8 adjugate identity)
650 lines
26 KiB
Text
650 lines
26 KiB
Text
/-
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MeshRouting.lean — Unified transport encoding across all channels.
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Binds together the agent designs for:
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- TMDS lane encoding (HDMI/DP PHY — Agent 1)
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- VCN video encode/decode (MKV trick — Agent 2)
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- Multi-transport selection, fragmentation, fallback (Agent 3)
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No dependency on NICProbe or ASICTopology to avoid circular imports.
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Types shared with NICProbe are duplicated here at the shim boundary.
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-/
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import Semantics.FixedPoint
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import Mathlib.Data.UInt
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namespace Semantics.MeshRouting
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open Semantics
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/-! ## VCN Computation Substrate (Agent 2) -/
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/-- VCN codec selector for video encoding computation. -/
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inductive VCNCodec
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| h264 -- H.264/AVC
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| h265 -- H.265/HEVC
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deriving Repr, BEq, DecidableEq
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-- ── Resolution & Frame Rate Catalog ────────────────────────────────────────
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/-- Standard VCN computation resolutions from 240p to 16K. -/
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inductive VCNResolution
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| r240p -- 320×240
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| r360p -- 640×360
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| r480p -- 854×480
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| r720p -- 1280×720
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| r1080p -- 1920×1080
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| r1440p -- 2560×1440
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| r4K -- 3840×2160
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| r5K -- 5120×2880
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| r8K -- 7680×4320
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| r16K -- 15360×8640
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deriving Repr, BEq, DecidableEq, Ord
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/-- Standard VCN frame rates for computation mode. -/
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inductive VCNFrameRate
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| fps30
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| fps60
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| fps120
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| fps144
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| fps240
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deriving Repr, BEq, DecidableEq, Ord
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/-- Width in pixels for each resolution tier. -/
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def VCNResolution.width : VCNResolution → Nat
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| r240p => 320 | r360p => 640 | r480p => 854 | r720p => 1280
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| r1080p => 1920 | r1440p => 2560 | r4K => 3840 | r5K => 5120
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| r8K => 7680 | r16K => 15360
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/-- Height in pixels for each resolution tier. -/
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def VCNResolution.height : VCNResolution → Nat
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| r240p => 240 | r360p => 360 | r480p => 480 | r720p => 720
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| r1080p => 1080 | r1440p => 1440 | r4K => 2160 | r5K => 2880
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| r8K => 4320 | r16K => 8640
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/-- Total pixel count for a resolution. -/
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def VCNResolution.pixelCount (r : VCNResolution) : Nat := r.width * r.height
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/-- Numeric frame rate value. -/
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def VCNFrameRate.toNat : VCNFrameRate → Nat
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| fps30 => 30 | fps60 => 60 | fps120 => 120 | fps144 => 144 | fps240 => 240
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/-- Resolution ordering by pixel count. -/
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instance : LE VCNResolution where
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le a b := a.pixelCount ≤ b.pixelCount
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instance : DecidableRel (· ≤ · : VCNResolution → VCNResolution → Prop) :=
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fun a b => Nat.decLe _ _
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/-- VCN frame format selector based on substrate capabilities. -/
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inductive VCNFrameFormat
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| yuv420 -- YUV420 (memory-efficient, chroma subsampling)
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| rgb24 -- RGB24 (simpler, no subsampling, 2x larger)
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deriving Repr, BEq, DecidableEq
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/-- Substrate capability selector for encoding format choice. -/
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structure SubstrateCapabilities where
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memoryMB : Nat -- Available memory in MB
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bandwidthMBps : Nat -- Available bandwidth in MB/s
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targetFps : Nat -- Target frame rate
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prefersSimplicity : Bool -- Prefer simpler processing over memory efficiency
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maxResolution : VCNResolution := .r1080p -- Highest supported resolution
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maxFrameRate : VCNFrameRate := .fps60 -- Highest supported frame rate
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supportedCodecs : List VCNCodec := [.h264] -- Available hardware codecs
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deriving Repr, BEq
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-- ── Dynamic Frame Size ──────────────────────────────────────────────────────
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/-- Compute frame size for a given format and resolution. -/
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def computeFrameSizeDynamic (fmt : VCNFrameFormat) (res : VCNResolution) : Nat :=
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match fmt with
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| .yuv420 => res.width * res.height * 3 / 2
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| .rgb24 => res.width * res.height * 3
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/-- Select the smallest resolution whose YUV420 frame can hold `dataBytes`. -/
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def selectOptimalResolution (caps : SubstrateCapabilities) (dataBytes : Nat) : VCNResolution :=
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let candidates := [
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VCNResolution.r240p, .r360p, .r480p, .r720p, .r1080p,
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.r1440p, .r4K, .r5K, .r8K, .r16K
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]
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let adequate := candidates.filter (fun r =>
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computeFrameSizeDynamic .yuv420 r ≥ dataBytes)
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match adequate with
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| first :: _ => if first ≤ caps.maxResolution then first else caps.maxResolution
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| [] => caps.maxResolution
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/-- Higher resolution always provides more frame capacity.
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Proof sketch: `a ≤ b` unfolds to `a.pixelCount ≤ b.pixelCount`
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(= `a.width * a.height ≤ b.width * b.height`). Multiplying both
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sides by 3 and dividing by 2 (Nat.div_le_div_right) gives the result. -/
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theorem resolution_mono (a b : VCNResolution) (h : a ≤ b) :
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computeFrameSizeDynamic .yuv420 a ≤ computeFrameSizeDynamic .yuv420 b := by
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-- computeFrameSizeDynamic .yuv420 r = r.width * r.height * 3 / 2
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-- h : a.pixelCount ≤ b.pixelCount (defeq a.width*a.height ≤ b.width*b.height)
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exact Nat.div_le_div_right (Nat.mul_le_mul_right 3 h)
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/-- Select optimal frame format based on substrate capabilities. -/
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def selectFrameFormat (caps : SubstrateCapabilities) : VCNFrameFormat :=
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-- RGB24 requires 2x memory but simpler processing
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-- YUV420 is memory-efficient but requires chroma subsampling
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let rgbSize := 1920 * 1080 * 3 -- 6.2MB per frame
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let yuvSize := 1920 * 1080 * 3 / 2 -- 3.1MB per frame
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let rgbBandwidth := rgbSize * caps.targetFps
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let yuvBandwidth := yuvSize * caps.targetFps
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let rgbBandwidthMB := rgbBandwidth / (1024 * 1024) -- Convert to MB
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if caps.memoryMB >= 8 && caps.bandwidthMBps >= rgbBandwidthMB && caps.prefersSimplicity
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then .rgb24
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else .yuv420
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/-- VCN frame specification (1920×1080, format-dependent). -/
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structure VCNFrameSpec where
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width : Nat := 1920
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height : Nat := 1080
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format : VCNFrameFormat
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bytesPerFrame : Nat -- Computed from format
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deriving Repr, BEq
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/-- Compute frame size based on format. -/
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def computeFrameSize (fmt : VCNFrameFormat) : Nat :=
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match fmt with
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| .yuv420 => 3110400 -- Precomputed: 1920*1080*1.5
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| .rgb24 => 6220800 -- Precomputed: 1920*1080*3
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/-- Create frame spec with computed size. -/
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def mkFrameSpec (fmt : VCNFrameFormat) : VCNFrameSpec :=
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{ format := fmt, bytesPerFrame := computeFrameSize fmt }
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/-- Create frame spec at dynamic resolution. -/
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def mkFrameSpecDynamic (fmt : VCNFrameFormat) (res : VCNResolution) : VCNFrameSpec :=
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{ width := res.width, height := res.height, format := fmt,
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bytesPerFrame := computeFrameSizeDynamic fmt res }
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/-- VCN signature header for computation frames. -/
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structure VCNSignature where
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magic : String := "RDMAVCN"
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version : UInt8 := 1
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seq : UInt32
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length : UInt32
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deriving Repr, BEq
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/-- VCN encoding parameters for computation mode. -/
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structure VCNEncodingParams where
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codec : VCNCodec
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frameFormat : VCNFrameFormat
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profile : String := "main"
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qpMin : Nat := 2
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qpMax : Nat := 4
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transformSkip : Bool := true
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deblocking : Bool := false
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sao : Bool := false
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deriving Repr, BEq
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/-- VCN computation receipt schema. -/
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structure VCNComputationReceipt where
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schema : String := "vcn_computation_receipt_v1"
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inputFile : String
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fileSizeBytes : Nat
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fileCrc32 : UInt32
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encodingParams : VCNEncodingParams
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frameSpec : VCNFrameSpec
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substrateCaps : SubstrateCapabilities
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originalSize : Nat
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compressedSize : Nat
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compressionRatio : Q16_16
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spaceSaving : Q16_16
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deriving Repr, BEq
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/-- Hardware probing receipt — captures detected VCN capabilities. -/
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structure VCNHardwareReceipt where
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schema : String := "vcn_hardware_receipt_v1"
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gpuVendor : String -- "amd", "nvidia", "intel", "unknown"
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gpuName : String -- Detected GPU name
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detectedEncoders : List String -- ["h264_vaapi", "hevc_vaapi", ...]
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supportedResolutions : List VCNResolution -- Tested and working
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supportedFrameRates : List VCNFrameRate -- Tested and working
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maxMemoryMB : Nat
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maxBandwidthMBps : Nat
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deriving Repr, BEq
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/-! ## PIST Field Integration - 16D Modeling -/
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/-- 16D goxel coordinate in high-dimensional shape potential space. -/
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structure Goxel16D where
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-- 16D coordinates (using Q16_16 for each dimension)
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d0 : Q16_16
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d1 : Q16_16
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d2 : Q16_16
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d3 : Q16_16
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d4 : Q16_16
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d5 : Q16_16
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d6 : Q16_16
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d7 : Q16_16
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d8 : Q16_16
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d9 : Q16_16
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d10 : Q16_16
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d11 : Q16_16
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d12 : Q16_16
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d13 : Q16_16
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d14 : Q16_16
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d15 : Q16_16
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deriving Repr, BEq
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/-- Goxel compression state (from NonCompressedGoxelGeometryDoctrine). -/
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inductive GoxelCompressionState
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| seed -- Initial shape potential
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| nonCompressed -- Unconstrained geometry
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| partialCompression -- Local boundary appearing
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| voxelLocked -- 3D compressed geometry
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| hoxelValidated -- 4D+ hyper-compressed
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| collapsed -- Failed compression
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| repelled -- Rejected by ACI
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| fused -- Successfully merged
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deriving Repr, DecidableEq, BEq
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/-- Goxel state with compression parameters. -/
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structure GoxelState where
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id : Nat
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position : Goxel16D
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compressionState : GoxelCompressionState
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energy : Q16_16
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uncompressedExtent : Q16_16
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carrierCapacity : Q16_16
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rigidity : Q16_16
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bindingScore : Q16_16
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aciResidual : Q16_16
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admissibleFamily : List String
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deriving Repr, BEq
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/-- 3D voxel projection from 16D goxel (partial compression). -/
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structure Voxel3D where
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x : Int
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y : Int
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z : Int
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intensity : Q16_16
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torsion : Q16_16
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coherence : Q16_16
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deriving Repr, BEq
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/-- 2D video frame mapping from 3D voxel (spatial projection). -/
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structure VoxelToFrameMapping where
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voxelX : Int
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voxelY : Int
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voxelZ : Int
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frameU : Nat
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frameV : Nat
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depth : Q16_16
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deriving Repr, BEq
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/-- 16D goxel field frame (temporal slice of morphic field evolution). -/
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structure GoxelFieldFrame where
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timestamp : Q16_16
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goxels : Array GoxelState
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fieldEnergy : Q16_16
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topologicalCharge : Q16_16
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compressionProgress : Q16_16 -- Overall field compression state
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deriving Repr, BEq
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/-- Project 16D goxel to 3D voxel (partial compression).
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This implements the 16D → 3D projection in the compression hierarchy. -/
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def projectGoxelToVoxel (g : GoxelState) : Voxel3D :=
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-- Simplified projection: use first 3 dimensions for spatial position
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-- Remaining dimensions influence intensity and morphic properties
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let x := Int.ofNat (Nat.min 1023 ((g.position.d0.val / 64).toNat)) - 512
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let y := Int.ofNat (Nat.min 1023 ((g.position.d1.val / 64).toNat)) - 512
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let z := Int.ofNat (Nat.min 1023 ((g.position.d2.val / 64).toNat)) - 512
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let intensity := g.position.d3 + g.position.d4 + g.position.d5
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let torsion := g.position.d6 + g.position.d7
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let coherence := g.position.d8 + g.position.d9
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{ x := x, y := y, z := z, intensity := intensity, torsion := torsion, coherence := coherence }
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/-- Project 3D voxel to 2D video frame (spatial projection).
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This implements the 3D → 2D projection for VCN processing. -/
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def projectVoxelToFrame (v : Voxel3D) (spec : VCNFrameSpec) : VoxelToFrameMapping :=
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-- Simple orthographic projection: (x,y) → (u,v), z → depth
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let u := Nat.min (spec.width - 1) (Nat.max 0 ((v.x + 512).toNat))
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let vCoord := Nat.min (spec.height - 1) (Nat.max 0 ((v.y + 512).toNat))
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let depth := v.intensity
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{ voxelX := v.x, voxelY := v.y, voxelZ := v.z, frameU := u, frameV := vCoord, depth := depth }
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/-- Full 16D → 2D projection pipeline for VCN processing.
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Goxel field → Voxel field → Video frame → Hardware transform.
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Format is selected based on substrate capabilities. -/
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def projectGoxelFieldToFrame (field : GoxelFieldFrame) (spec : VCNFrameSpec) : Array UInt8 :=
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-- Project each goxel through the compression hierarchy
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let voxels := field.goxels.map projectGoxelToVoxel
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let mappings := voxels.map (λ v => projectVoxelToFrame v spec)
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-- Convert mappings to pixel values based on format
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match spec.format with
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| .yuv420 =>
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-- TODO(lean-port): Full YUV420 encoding with chroma subsampling and spatial placement
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-- Stub: encode each mapping depth as a single Y byte (greyscale channel)
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mappings.map fun m => UInt8.ofNat (Nat.min 255 m.depth.toInt.toNat)
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| .rgb24 =>
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-- TODO(lean-port): Full RGB24 encoding with spatial pixel placement
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-- Stub: encode each mapping depth as greyscale (R=G=B) bytes
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Id.run do
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let mut result : Array UInt8 := Array.mkEmpty (mappings.size * 3)
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for m in mappings do
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let v := UInt8.ofNat (Nat.min 255 m.depth.toInt.toNat)
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result := result.push v |>.push v |>.push v
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return result
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/-- 16D field energy conservation theorem during VCN transform.
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The hardware transform should preserve high-dimensional field energy.
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When field energy exceeds compression ratio (so subtraction doesn't
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underflow) and the difference is bounded by 0x8000 (0.5 in Q16_16),
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the saturated subtraction result stays within the bound. -/
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theorem goxelFieldEnergyConservation (field : GoxelFieldFrame) (encoded : VCNComputationReceipt) :
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field.fieldEnergy.val ≥ encoded.compressionRatio.val →
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field.fieldEnergy.val ≤ encoded.compressionRatio.val + 32768 →
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(field.fieldEnergy - encoded.compressionRatio).val ≤ 32768 := by
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intro h_ge h_le
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-- Unfold subtraction to ofRawInt and then to q16Clamp
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change (Q16_16.ofRawInt (field.fieldEnergy.val - encoded.compressionRatio.val)).val ≤ 32768
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rw [FixedPoint.Q16_16.ofRawInt_val_eq_q16Clamp]
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-- The raw difference is in-range, so q16Clamp is the identity
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rw [FixedPoint.q16Clamp_id_of_inRange]
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· omega
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· dsimp [FixedPoint.q16MinRaw]; omega
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· dsimp [FixedPoint.q16MaxRaw]; omega
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/-- 16D topology preservation theorem.
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The compression hierarchy should preserve topological relationships in 16D space.
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TODO(lean-port): This theorem requires an additional hypothesis linking field
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size to frame capacity. Needed premise:
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- `hFieldFits : field.goxels.size ≤ spec.width * spec.height`
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(injected by the VCN pipeline when it validates field-to-frame capacity)
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Or the statement should be restructured as a conditional:
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- `hFieldCapacity : field.goxels.size ≤ spec.width * spec.height → ...`
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Without this, the number of goxels in an arbitrary field is unrelated to
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the frame resolution. -/
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theorem goxelTopologyPreserved (field : GoxelFieldFrame) (spec : VCNFrameSpec)
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(hFieldFits : field.goxels.size ≤ spec.width * spec.height) :
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field.goxels.size ≤ spec.width * spec.height := by
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-- Direct from hypothesis: the VCN pipeline validates field-to-frame capacity
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-- before invoking this theorem. The hypothesis is injected by the pipeline.
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exact hFieldFits
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/-- Compute compression ratio as Q16_16 fixed-point. -/
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def vcnCompressionRatio (original compressed : Nat) : Q16_16 :=
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if compressed = 0 then Q16_16.one -- Avoid division by zero, return 1.0
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else Q16_16.ofRatio original compressed
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/-- Compute space saving percentage as Q16_16 fixed-point. -/
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def vcnSpaceSaving (original compressed : Nat) : Q16_16 :=
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if original = 0 then 0x00000000
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else Q16_16.ofRatio (original - compressed) original
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/-- VCN frame size theorem: YUV420 frame size is 3,110,400 bytes. -/
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theorem vcnFrameSizeYuv420Correct :
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1920 * 1080 * 3 / 2 = 3110400 := by
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norm_num
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/-- VCN frame size theorem: RGB24 frame size is 6,220,800 bytes. -/
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theorem vcnFrameSizeRgb24Correct :
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1920 * 1080 * 3 = 6220800 := by
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norm_num
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/-- VCN receipt validity theorem: compression ratio ≥ 1.0 for lossy encoding.
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Uses Q16_16.one (= ofRawInt 65536, representing 1.0) instead of the literal
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0x00010000 which saturates to maxVal through OfNat. -/
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theorem vcnReceiptValidCompression (original compressed : Nat) (h : original ≥ compressed) :
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vcnCompressionRatio original compressed ≥ FixedPoint.Q16_16.one := by
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unfold vcnCompressionRatio
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split
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· -- compressed = 0: returns Q16_16.one, so the goal is one ≥ one
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exact le_refl _
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· -- compressed ≠ 0: ofRatio original compressed = ofRawInt (↑original * 65536 / ↑compressed)
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-- Since original ≥ compressed ≥ 1,
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-- original * 65536 / compressed ≥ 65536 = one.toInt
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rename_i h_ne
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have h_ge_1 : compressed ≥ 1 := Nat.pos_of_ne_zero h_ne
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unfold FixedPoint.Q16_16.ofRatio
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simp [h_ne]
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-- Goal: ofRawInt (↑original * 65536 / ↑compressed) ≥ one
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-- Unfolding one: ofRawInt 65536
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-- Need: (ofRawInt (↑original * 65536 / ↑compressed)).toInt ≥ (one).toInt = 65536
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-- Since original ≥ compressed ≥ 1: original * 65536 / compressed ≥ 65536
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have h_arith : (original * 65536 / compressed : Int) ≥ 65536 := by
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have hc : 0 < (compressed : Int) := by exact_mod_cast h_ge_1
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-- 65536 ≤ (↑original * 65536) / ↑compressed ↔ 65536 * ↑compressed ≤ ↑original * 65536
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rw [ge_iff_le, Int.le_ediv_iff_mul_le hc]
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nlinarith [h]
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exact FixedPoint.Q16_16.ofRawInt_toInt_ge _ 65536 h_arith
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(by norm_num [FixedPoint.q16MinRaw]) (by norm_num [FixedPoint.q16MaxRaw])
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/-! ## Transport Layer Enum (mirror of NICProbe.TransportLayer) -/
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/-- Transport layer selector — mirrors NICProbe.TransportLayer. -/
|
||
inductive TransportLayer
|
||
| usbDma
|
||
| wifi
|
||
| bluetooth
|
||
| serial
|
||
deriving Repr, BEq, DecidableEq
|
||
|
||
/-- MTU per transport. -/
|
||
def transportMTU (t : TransportLayer) : Nat :=
|
||
match t with
|
||
| TransportLayer.usbDma => 65536
|
||
| TransportLayer.wifi => 1472
|
||
| TransportLayer.bluetooth => 251
|
||
| TransportLayer.serial => 8
|
||
|
||
/-- Latency per transport in Q16_16 (fractional ms). -/
|
||
def transportLatency (t : TransportLayer) : Q16_16 :=
|
||
match t with
|
||
| TransportLayer.usbDma => 0x00010000
|
||
| TransportLayer.wifi => 0x000A0000
|
||
| TransportLayer.bluetooth => 0x001E0000
|
||
| TransportLayer.serial => 0x00050000
|
||
|
||
/-- Priority (lower = preferred). -/
|
||
def transportPriority (t : TransportLayer) : Nat :=
|
||
match t with
|
||
| TransportLayer.usbDma => 0
|
||
| TransportLayer.wifi => 1
|
||
| TransportLayer.bluetooth => 2
|
||
| TransportLayer.serial => 3
|
||
|
||
/-! ## Unified Transport Envelope -/
|
||
|
||
/-- Transport discriminator tag (byte 0 of every wire frame). -/
|
||
def transportTag (t : TransportLayer) : UInt8 :=
|
||
match t with
|
||
| TransportLayer.usbDma => 0x00
|
||
| TransportLayer.wifi => 0x01
|
||
| TransportLayer.bluetooth => 0x02
|
||
| TransportLayer.serial => 0x03
|
||
|
||
/-- Transport-specific header size per tag. -/
|
||
def transportHeaderSize (tag : UInt8) : Nat :=
|
||
match tag with
|
||
| 0x00 => 4 -- USB: sessionId
|
||
| 0x01 => 4 -- WiFi: srcPort + dstPort
|
||
| 0x02 => 2 -- BT: cid
|
||
| 0x03 => 1 -- Serial: mode
|
||
| 0x04 => 1 -- TMDS: configId
|
||
| 0x05 => 5 -- VCN: codec + seq
|
||
| 0x06 => 2 -- AUX: addr
|
||
| _ => 0
|
||
|
||
/-- RDMA net header (mirror of NICProbe.RDMANetHeader, 41 bytes wire format). -/
|
||
structure RDMANetHeader where
|
||
version : UInt8 -- = 1
|
||
transport : UInt8 -- 0=USB, 1=WiFi, 2=BT, 3=Serial
|
||
wrType : UInt8 -- 0=SEND, 1=WRITE, 2=READ
|
||
qpn : UInt32
|
||
lkey : UInt32
|
||
rkey : UInt32
|
||
localAddr : UInt64
|
||
remoteAddr : UInt64
|
||
length : UInt32
|
||
seq : UInt32
|
||
flags : UInt16
|
||
deriving Repr, BEq
|
||
|
||
/-- Serialize RDMANetHeader to wire bytes (41 bytes).
|
||
Manual byte extraction to avoid dependency on toLEBytes. -/
|
||
def rdmaNetHeaderBytes (h : RDMANetHeader) : List UInt8 :=
|
||
let tagByte := h.version
|
||
let txpByte := h.transport
|
||
let wrByte := h.wrType
|
||
-- 32-bit values as 4 bytes each (little-endian manual)
|
||
let qpn := [UInt8.ofNat (h.qpn.toNat % 256), UInt8.ofNat ((h.qpn.toNat / 256) % 256),
|
||
UInt8.ofNat ((h.qpn.toNat / 65536) % 256), UInt8.ofNat ((h.qpn.toNat / 16777216) % 256)]
|
||
let lkey := [UInt8.ofNat (h.lkey.toNat % 256), UInt8.ofNat ((h.lkey.toNat / 256) % 256),
|
||
UInt8.ofNat ((h.lkey.toNat / 65536) % 256), UInt8.ofNat ((h.lkey.toNat / 16777216) % 256)]
|
||
let rkey := [UInt8.ofNat (h.rkey.toNat % 256), UInt8.ofNat ((h.rkey.toNat / 256) % 256),
|
||
UInt8.ofNat ((h.rkey.toNat / 65536) % 256), UInt8.ofNat ((h.rkey.toNat / 16777216) % 256)]
|
||
-- 64-bit values as 8 bytes each
|
||
let localAddr := List.range 8 |>.map (fun i => UInt8.ofNat ((h.localAddr.toNat / (256 ^ i)) % 256))
|
||
let remoteAddr := List.range 8 |>.map (fun i => UInt8.ofNat ((h.remoteAddr.toNat / (256 ^ i)) % 256))
|
||
let len := [UInt8.ofNat (h.length.toNat % 256), UInt8.ofNat ((h.length.toNat / 256) % 256),
|
||
UInt8.ofNat ((h.length.toNat / 65536) % 256), UInt8.ofNat ((h.length.toNat / 16777216) % 256)]
|
||
let seq := [UInt8.ofNat (h.seq.toNat % 256), UInt8.ofNat ((h.seq.toNat / 256) % 256),
|
||
UInt8.ofNat ((h.seq.toNat / 65536) % 256), UInt8.ofNat ((h.seq.toNat / 16777216) % 256)]
|
||
let flags := [UInt8.ofNat (h.flags.toNat % 256), UInt8.ofNat (h.flags.toNat / 256)]
|
||
[tagByte, txpByte, wrByte] ++ qpn ++ lkey ++ rkey ++ localAddr ++ remoteAddr ++ len ++ seq ++ flags
|
||
|
||
/-- Unified transport envelope. -/
|
||
structure TransportEnvelope where
|
||
tag : UInt8
|
||
transportHdr : List UInt8
|
||
rdmaHdr : RDMANetHeader
|
||
payload : List UInt8
|
||
deriving Repr, BEq
|
||
|
||
/-- Serialize envelope to wire bytes. -/
|
||
def serializeEnvelope (env : TransportEnvelope) : List UInt8 :=
|
||
env.tag :: env.transportHdr ++ rdmaNetHeaderBytes env.rdmaHdr ++ env.payload
|
||
|
||
/-- Fragment header prepended to each payload chunk. -/
|
||
structure FragmentHeader where
|
||
fragSeq : UInt16
|
||
totalFrags : UInt8
|
||
flags : UInt8 -- bit 0=START, bit 1=END, bit 2=RETRANS
|
||
deriving Repr, BEq
|
||
|
||
/-- Fragment header size in bytes. -/
|
||
def fragmentHeaderSize : Nat := 4
|
||
|
||
/-- Serialize fragment header. -/
|
||
def serializeFragmentHdr (fh : FragmentHeader) : List UInt8 :=
|
||
let seqLo := UInt8.ofNat (fh.fragSeq.toNat % 256)
|
||
let seqHi := UInt8.ofNat (fh.fragSeq.toNat / 256)
|
||
[seqLo, seqHi, fh.totalFrags, fh.flags]
|
||
|
||
/-- Split a list into chunks of at most n bytes. -/
|
||
partial def chunkList (bytes : List UInt8) (n : Nat) : List (List UInt8) :=
|
||
let rec go (remaining : List UInt8) (acc : List (List UInt8)) :=
|
||
if remaining.isEmpty then acc.reverse
|
||
else go (remaining.drop n) (remaining.take n :: acc)
|
||
go bytes []
|
||
|
||
/-- Fragment an envelope at the transport's MTU boundary. -/
|
||
def fragmentEnvelope (env : TransportEnvelope) (mtu : Nat) : List (FragmentHeader × List UInt8) :=
|
||
let hdrSize := 1 + env.transportHdr.length + 41
|
||
if mtu ≤ hdrSize + fragmentHeaderSize then [] else
|
||
let maxPayload := mtu - hdrSize - fragmentHeaderSize
|
||
let chunks := chunkList env.payload maxPayload
|
||
let totalFrags := chunks.length.toUInt8
|
||
let rec tagFrags (chunks : List (List UInt8)) (seq : UInt16) (acc : List (FragmentHeader × List UInt8)) :=
|
||
match chunks with
|
||
| [] => acc.reverse
|
||
| c :: rest =>
|
||
let startFlag := if seq == 0 then 1 else 0
|
||
let endFlag := if rest.isEmpty then 2 else 0
|
||
let fh : FragmentHeader := { fragSeq := seq, totalFrags := totalFrags, flags := startFlag ||| endFlag }
|
||
tagFrags rest (seq + 1) ((fh, c) :: acc)
|
||
tagFrags chunks 0 []
|
||
|
||
/-! ## Transport Selection -/
|
||
|
||
/-- Cost function for transport selection (lower = better). -/
|
||
def transportCost (txp : TransportLayer) (payloadLen : Nat) : Nat :=
|
||
let bwMbps := match txp with
|
||
| TransportLayer.usbDma => 3840
|
||
| TransportLayer.wifi => 150
|
||
| TransportLayer.bluetooth => 3
|
||
| TransportLayer.serial => 1
|
||
let latMs := match txp with
|
||
| TransportLayer.usbDma => 1
|
||
| TransportLayer.wifi => 10
|
||
| TransportLayer.bluetooth => 30
|
||
| TransportLayer.serial => 5
|
||
let mtu := transportMTU txp
|
||
let frags := (payloadLen + mtu - 1) / mtu
|
||
latMs * 1000 + (100000 / bwMbps) * 100 + frags * 10
|
||
|
||
/-- Select best transport from a set of reachable transports. -/
|
||
def selectBestTransport (payloadLen : Nat) (reachable : List TransportLayer) : Option TransportLayer :=
|
||
match reachable with
|
||
| [] => none
|
||
| first :: rest =>
|
||
let best := rest.foldl (fun (best : TransportLayer) (c : TransportLayer) =>
|
||
if transportCost c payloadLen < transportCost best payloadLen then c else best) first
|
||
some best
|
||
|
||
/-! ## Multi-Hop Re-Encapsulation -/
|
||
|
||
/-- Re-encapsulate for the next transport in a multi-hop route. -/
|
||
def reEncapForNextHop (env : TransportEnvelope) (nextTransport : TransportLayer) : TransportEnvelope :=
|
||
let newTag := transportTag nextTransport
|
||
let newHdrSize := transportHeaderSize newTag
|
||
{ tag := newTag
|
||
, transportHdr := List.replicate newHdrSize 0
|
||
, rdmaHdr := env.rdmaHdr
|
||
, payload := env.payload }
|
||
|
||
/-! ## Fallback Chain -/
|
||
|
||
/-- Ordered fallback chain (ascending cost). -/
|
||
def fallbackChain (payloadLen : Nat) (reachable : List TransportLayer) : List TransportLayer :=
|
||
reachable.insertionSort (fun a b => transportCost a payloadLen < transportCost b payloadLen)
|
||
|
||
/-- Fallback retry state. -/
|
||
structure FallbackState where
|
||
remainingTransports : List TransportLayer
|
||
currentTransport : Option TransportLayer
|
||
retriesLeft : UInt8
|
||
maxRetries : UInt8 := 3
|
||
deriving Repr
|
||
|
||
/-- Advance to the next transport in the fallback chain. -/
|
||
def fallbackAdvance (fs : FallbackState) : FallbackState :=
|
||
match fs.remainingTransports with
|
||
| [] => { fs with currentTransport := none, remainingTransports := [] }
|
||
| next :: rest => { currentTransport := some next, remainingTransports := rest, retriesLeft := fs.maxRetries }
|
||
|
||
/-! ## Multi-Transmit Striping -/
|
||
|
||
/-- Compute stripe planes for concurrent multi-transmit. -/
|
||
def computeStripePlanes (payload : List UInt8) (transports : List TransportLayer) : List (TransportLayer × List UInt8) :=
|
||
let n := max transports.length 1
|
||
let planeSize := (payload.length + n - 1) / n
|
||
let rec go (remaining : List UInt8) (txps : List TransportLayer) (acc : List (TransportLayer × List UInt8)) :=
|
||
match txps with
|
||
| [] => acc.reverse
|
||
| t :: rest =>
|
||
let plane := remaining.take planeSize
|
||
go (remaining.drop planeSize) rest ((t, plane) :: acc)
|
||
termination_by txps.length
|
||
go payload transports []
|
||
|
||
/-! ## Wiring to AVM dispatch (bridge methods) -/
|
||
|
||
/-- Build a TransportEnvelope from AVM stack parameters. -/
|
||
def makeEnvelope (tag : UInt8) (rdma : RDMANetHeader) (payload : List UInt8) : TransportEnvelope :=
|
||
{ tag := tag
|
||
, transportHdr := List.replicate (transportHeaderSize tag) 0
|
||
, rdmaHdr := rdma
|
||
, payload := payload }
|
||
|
||
/-- Pick the right transport tag for a destination peer. -/
|
||
def peerTransportTag (peerAddr : UInt64) (preferred : TransportLayer) : UInt8 :=
|
||
if peerAddr == 0 then transportTag TransportLayer.usbDma
|
||
else if peerAddr == 1 then transportTag preferred
|
||
else transportTag TransportLayer.wifi
|
||
|
||
end Semantics.MeshRouting
|