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46 lines
1.5 KiB
Text
46 lines
1.5 KiB
Text
-- M002: Entropy Encoding Kernel Module
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-- Source: shannon_entropy_v1 (3-Mathematical-Models)
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-- Kernel Function: DeltaCompressor
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--
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-- Shannon entropy H(X) = -Σ p(x) log₂ p(x)
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-- Used for adaptive compression ratio estimation.
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-- Truth Seal: [ SSS-ENE-ENTROPY-2026-05-03 ]
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module M002_EntropyEncoding where
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import BaseTypes
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import Semantics.Q0_16 (Q0_16)
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structure SymbolDistribution where
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symbols : Array UInt8
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counts : Array Nat
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total : Nat
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def shannonEntropy (dist : SymbolDistribution) : Q0_16 :=
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let entropy := dist.counts.foldl (\acc count =>
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if count == 0 then acc
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else
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let p := count.toFloat / dist.total.toFloat
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acc - p * log₂ p
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) 0.0
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Q0_16.ofFloat (entropy / 8.0) -- Normalize to [0,1] (max entropy = 8 bits)
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-- Kernel interface: estimate compression ratio from entropy
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def estimateCompressionRatio (data : Array UInt8) : IO CompressionEstimate := do
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let freqTable := frequencyTable data
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let entropy := shannonEntropy freqTable
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-- Theoretical minimum size = entropy × original_size
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-- Actual compression depends on model overhead
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let theoreticalRatio := entropy -- Q0_16 [0,1]
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let modelOverhead := Q0_16.ofFloat 0.05 -- 5% for codon tables
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let predictedRatio := add theoreticalRatio modelOverhead
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return {
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entropy := entropy
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theoreticalRatio := theoreticalRatio
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predictedCompressedSize := (data.size.toFloat * predictedRatio.toFloat).toNat
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confidence := Q0_16.sub Q0_16.one (abs (Q0_16.sub entropy Q0_16.half))
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}
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end M002_EntropyEncoding
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