Research-Stack/4-Infrastructure/nano-kernel/gcl-modules/m002-entropy-encoding.gcl

46 lines
1.5 KiB
Text
Raw Blame History

This file contains ambiguous Unicode characters

This file contains Unicode characters that might be confused with other characters. If you think that this is intentional, you can safely ignore this warning. Use the Escape button to reveal them.

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