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88 lines
2.6 KiB
Text
88 lines
2.6 KiB
Text
/-
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CacheSieve.lean - L0 Local Sorter Cache Verification
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Migrates legacy f64 penalty evaluations and raw limits.
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-/
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import Semantics.Bind
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import Semantics.SLUQ
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namespace Semantics.CacheSieve
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open SLUQ (SLUQState)
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inductive CouplingBucket
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| None
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| Low
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| Medium
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| High
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deriving Repr, DecidableEq, Inhabited
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def edgeBand (bucket : CouplingBucket) : UInt16 :=
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match bucket with
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| .None => 0x0200
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| .Low => 0x0400
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| .Medium => 0x0800
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| .High => 0x1000
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def isEdgeBand (value threshold band : UInt16) : Bool :=
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let diff := if value > threshold then value - threshold else threshold - value
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diff <= band
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structure SieveNode where
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acc : UInt16
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state : SLUQState
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previousState : SLUQState
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bucket : CouplingBucket
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deriving Repr, DecidableEq, Inhabited
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def stateToUInt8 (s : SLUQState) : UInt8 :=
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match s with
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| .Stable => 0
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| .Rising => 1
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| .Unstable => 2
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| .Reset => 3
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def advanceNode (node : SieveNode) (val : UInt8) (phi : UInt8) : SieveNode :=
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let product := val.toUInt16 * phi.toUInt16
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let newAcc := node.acc + product
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let band := edgeBand node.bucket
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let edge0 := isEdgeBand newAcc 0x4000 band
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let edge1 := isEdgeBand newAcc 0x8000 band
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let edge2 := isEdgeBand newAcc 0xC000 band
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let inEdgeBand := edge0 || edge1 || edge2
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let newState := if inEdgeBand then node.previousState else
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if newAcc.toNat < 0x4000 then SLUQState.Stable
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else if newAcc.toNat < 0x8000 then SLUQState.Rising
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else if newAcc.toNat < 0xC000 then SLUQState.Unstable
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else SLUQState.Reset
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{ node with acc := newAcc, state := newState, previousState := node.state }
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/-- Compute raw survivor base ratio bounded as a fixed Q16.16 mapped index -/
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def triageSurvivorValue (maxState : UInt8) : UInt32 :=
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-- Base Score (1.0 - max_state/3.0) represented in Q16.16 mathematically (1.0 == 65536)
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if maxState == 0 then 65536
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else if maxState == 1 then 43690 -- 2/3
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else if maxState == 2 then 21845 -- 1/3
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else 0
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/-- Informational invariant binding the mathematical evaluation. -/
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def sieveCost (nodesA _nodesB : Array SieveNode) (_metric : Metric) : UInt32 :=
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if nodesA.size > 0 then
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let maxSt := Array.foldl (fun (acc : UInt8) (n : SieveNode) =>
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if stateToUInt8 n.state > acc then stateToUInt8 n.state else acc
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) 0 nodesA
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triageSurvivorValue maxSt
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else 0
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def sieveInvariant (nodes : Array SieveNode) : String := s!"sieve[{nodes.size}]"
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def sieveBind (nodesA _nodesB : Array SieveNode) (metric : Metric) : Bind (Array SieveNode) (Array SieveNode) :=
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controlBind nodesA _nodesB metric sieveCost sieveInvariant sieveInvariant
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-- Evaluate structural completion.
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#eval triageSurvivorValue 1
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end Semantics.CacheSieve
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