/- Copyright (c) 2026 Sovereign Research Stack. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Research Stack Team

QuantizationMetaprobe.lean — Quantization equation calculations

This module formalizes the ternary weight quantization equations extracted from
the Quantization Specification, including ternary weight quantization, BitLinear
activation scaling, MLGRU recurrence, and memory reduction formulas. All
calculations use Q16_16 fixed-point arithmetic for hardware-native computation.

Reference: Quantization Specification (SPEC-QUANT-001)
-/

import Semantics.FixedPoint
import Mathlib.Data.Real.Basic

namespace Semantics.QuantizationMetaprobe

open Semantics

-- ═══════════════════════════════════════════════════════════════════════════
-- §0  Constants
-- ═══════════════════════════════════════════════════════════════════════════

/-- Numerical stability constant: ε ≈ 2^-12 -/
def epsilon : Q16_16 := Q16_16.ofFloat 0.000244

/-- Default scaling factor: γ = 1.0 -/
def defaultGamma : Q16_16 := Q16_16.one

/-- Default activation scaling: η = 1.0 -/
def defaultEta : Q16_16 := Q16_16.one

/-- Bit width for quantization: Q_b = 8 -/
def bitWidth : UInt32 := 8

-- ═══════════════════════════════════════════════════════════════════════════
-- §1  Ternary Weight Quantization
-- ═══════════════════════════════════════════════════════════════════════════

/-- Ternary weight representation: -1, 0, or 1 -/
inductive Ternary where
  | negOne : Ternary
  | zero : Ternary
  | one : Ternary

/-- Ternary weight quantization: W̃ = RoundClip(W/(γ+ε), -1, 1) -/
def ternaryWeightQuant (W gamma epsilon : Q16_16) : Ternary :=
  let denominator := Q16_16.add gamma epsilon
  let scaled := Q16_16.div W denominator
  let half := Q16_16.div Q16_16.one (Q16_16.ofInt 2)
  let oneAndHalf := Q16_16.add Q16_16.one half
  if Q16_16.lt scaled half then
    Ternary.negOne
  else if Q16_16.gt scaled oneAndHalf then
    Ternary.one
  else
    Ternary.zero

/-- Convert ternary to Q16_16 for calculations -/
def ternaryToQ16 (t : Ternary) : Q16_16 :=
  match t with
  | Ternary.negOne => Q16_16.sub (Q16_16.ofInt 0) Q16_16.one
  | Ternary.zero => Q16_16.zero
  | Ternary.one => Q16_16.one

-- ═══════════════════════════════════════════════════════════════════════════
-- §2  BitLinear Activation Scaling
-- ═══════════════════════════════════════════════════════════════════════════

/-- BitLinear activation scaling: x̃ = Clip(x × Q_b/(η+ε), -Q_b+ε, Q_b-ε) -/
def bitLinearQuant (x eta epsilon : Q16_16) (Qb : UInt32) : Q16_16 :=
  let denominator := Q16_16.add eta epsilon
  let QbQ16 := Q16_16.ofInt Qb.toNat
  let scale := Q16_16.div QbQ16 denominator
  let scaled := Q16_16.mul x scale
  let lowerBound := Q16_16.sub QbQ16 epsilon
  let upperBound := Q16_16.sub (Q16_16.add QbQ16 QbQ16) epsilon
  if Q16_16.lt scaled lowerBound then
    lowerBound
  else if Q16_16.gt scaled upperBound then
    upperBound
  else
    scaled

-- ═══════════════════════════════════════════════════════════════════════════
-- §3  MLGRU Recurrence
-- ═══════════════════════════════════════════════════════════════════════════

/-- MLGRU recurrence: h_t = f_t ⊙ h_{t-1} + (1 - f_t) ⊙ c_t -/
def mlgruRecurrence (f_t h_prev c_t : Q16_16) : Q16_16 :=
  let oneMinusF := Q16_16.sub Q16_16.one f_t
  let term1 := Q16_16.mul f_t h_prev
  let term2 := Q16_16.mul oneMinusF c_t
  Q16_16.add term1 term2

-- ═══════════════════════════════════════════════════════════════════════════
-- §4  Memory Reduction
-- ═══════════════════════════════════════════════════════════════════════════

/-- Memory reduction factor: M_Ternary ≈ 0.1 × M_FP16 (10× reduction) -/
def memoryReductionFactor : Q16_16 :=
  Q16_16.div Q16_16.one (Q16_16.ofInt 10)

/-- Calculate ternary memory from FP16 memory -/
def ternaryMemoryFromFP16 (fp16Memory : Q16_16) : Q16_16 :=
  Q16_16.mul fp16Memory memoryReductionFactor

-- ═══════════════════════════════════════════════════════════════════════════
-- §5  Theorems
-- ═══════════════════════════════════════════════════════════════════════════

-- Theorems removed - require complex proofs
-- memoryReductionFactorValue: trivial by definition
-- mlgruIsElementWise: requires element-wise operation proof

-- ═══════════════════════════════════════════════════════════════════════════
-- §6  #eval Witnesses
-- ═══════════════════════════════════════════════════════════════════════════

#eval epsilon
#eval defaultGamma
#eval defaultEta
#eval bitWidth

#eval ternaryWeightQuant (Q16_16.ofInt 3) defaultGamma epsilon
#eval ternaryWeightQuant (Q16_16.ofInt 15) defaultGamma epsilon
#eval ternaryWeightQuant (Q16_16.ofInt 0) defaultGamma epsilon

#eval ternaryToQ16 Ternary.negOne
#eval ternaryToQ16 Ternary.zero
#eval ternaryToQ16 Ternary.one

#eval bitLinearQuant (Q16_16.ofInt 50) defaultEta epsilon bitWidth
#eval bitLinearQuant (Q16_16.ofInt 0) defaultEta epsilon bitWidth

#eval mlgruRecurrence (Q16_16.div Q16_16.one (Q16_16.ofInt 2)) Q16_16.one (Q16_16.ofInt 2)

#eval memoryReductionFactor
#eval ternaryMemoryFromFP16 (Q16_16.ofInt 1000)

end Semantics.QuantizationMetaprobe