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68 lines
2.4 KiB
Text
68 lines
2.4 KiB
Text
-- M007: FAMM Nanofield Kernel Module
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-- Source: famm_frustration_v2 (2-Search-Space/FAMM)
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-- Kernel Function: ResourceBalancer
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--
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-- Frustrated Antiferromagnetic Manifold for resource allocation.
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-- Frustration field guides load balancing decisions.
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-- Truth Seal: [ SSS-ENE-FAMM-2026-05-03 ]
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module M007_FAMMNanofield where
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import BaseTypes
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import Semantics.Q16_16
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structure FAMMSite where
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id : SiteID
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position : Vec3
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spin : Q16_16 -- -1 to 1 (antiferromagnetic)
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energy : Q16_16 -- Local field energy
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resources : ResourceState -- CPU, memory, IO capacity
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structure FAMMBond where
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source : SiteID
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target : SiteID
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coupling : Q16_16 -- Bond strength J
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distance : Q16_16
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def frustrationEnergy (sites : Array FAMMSite) (bonds : Array FAMMBond) : Q16_16 :=
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bonds.foldl (\acc bond =>
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let s_i := sites.find (\s => s.id == bond.source)
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let s_j := sites.find (\s => s.id == bond.target)
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let J := bond.coupling
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-- E = -J * s_i * s_j (antiferromagnetic: J > 0, spins anti-align for min energy)
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acc - J * s_i.spin * s_j.spin
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) Q16_16.zero
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-- Monte Carlo step: flip spins to minimize frustration
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def mcStep (sites : Array FAMMSite) (bonds : Array FAMMBond) (temperature : Q16_16) : Array FAMMSite :=
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sites.map (\site =>
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let E_before := localEnergy site bonds
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let spin_flipped := { site with spin := Q16_16.neg site.spin }
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let E_after := localEnergy spin_flipped bonds
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let deltaE := E_after - E_before
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if deltaE < Q16_16.zero then
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spin_flipped -- Accept: lowers energy
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else if randomQ16_16 < exp (Q16_16.neg deltaE / temperature) then
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spin_flipped -- Accept with Boltzmann probability
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else
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site -- Reject
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)
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-- Kernel interface: balance load via FAMM relaxation
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def syscallBalanceLoad (requests : Array ResourceRequest) : IO LoadBalance := do
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let sites ← getCurrentFAMMSites
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let bonds ← getCurrentFAMMBonds
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-- Relax FAMM to low-frustration state
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let relaxed := iterate 100 (\s => mcStep s bonds TEMPERATURE) sites
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-- Assign requests to sites with lowest energy (most available resources)
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let assignments := requests.map (\req =>
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let bestSite := relaxed.minBy (\s => s.energy)
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{ request := req, site := bestSite.id, expectedLatency := s.energy }
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)
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return { assignments := assignments, finalFrustration := frustrationEnergy relaxed bonds }
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end M007_FAMMNanofield
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