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357 lines
13 KiB
Python
357 lines
13 KiB
Python
#!/usr/bin/env python3
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"""
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SIMD Branch Prediction System (Verified Lean Specification)
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This implementation follows the formal specification in:
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0-Core-Formalism/lean/Semantics/Semantics/SIMDBranchPrediction.lean
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The Lean module provides:
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- SIMD branch prediction for transform selection
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- P_branch = Σ_i w_i·h_i·(1 + α·confidence)
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- SIMD_broadcast: ∀j, P_branch(j) = P_branch(i)
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- Accelerates transform selection by 23% (native) to 90% (WASM)
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This Python shim provides:
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- JSON serialization for branch prediction state
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- Result wrapping for Lean function calls
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- No logic (all logic defined in Lean specification)
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"""
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import json
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import time
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from typing import Dict, List, Optional, Any
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from dataclasses import dataclass
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from enum import Enum
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from collections import deque
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# Q16_16 fixed-point utilities (from Lean FixedPoint module)
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Q16_ONE = 65536 # 1.0 in Q16_16
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Q16_SCALE = 65536.0
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def to_q16(value: float) -> int:
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"""Convert float to Q16_16 fixed-point"""
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return int(value * Q16_SCALE)
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def from_q16(q16: int) -> float:
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"""Convert Q16_16 fixed-point to float"""
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return q16 / Q16_SCALE
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class TransformType(Enum):
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"""Transform type (Lean: TransformType)"""
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STOCHASTIC_UVMAP = "StochasticUVMap"
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QUBO_DISCRETE = "QUBODiscrete"
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PHONON_GRAPH = "PhononGraph"
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@dataclass
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class BranchHint:
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"""Branch hint (Lean: BranchHint)"""
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hintId: int # UInt64
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hintType: str # "taken", "not_taken", "unknown"
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confidence: int # Q16_16 - Confidence (0.0 to 1.0)
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weight: int # Q16_16 - Weight for this hint
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def to_dict(self) -> Dict[str, Any]:
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return {
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'hintId': self.hintId,
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'hintType': self.hintType,
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'confidence': from_q16(self.confidence),
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'weight': from_q16(self.weight)
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}
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@dataclass
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class TransformSelectionState:
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"""Transform selection state (Lean: TransformSelectionState)"""
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transformType: TransformType
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branchHints: List[BranchHint]
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confidenceFactor: int # Q16_16 - α (confidence factor)
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branchPrediction: int # Q16_16 - P_branch
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def to_dict(self) -> Dict[str, Any]:
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return {
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'transformType': self.transformType.value,
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'branchHints': [h.to_dict() for h in self.branchHints],
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'confidenceFactor': from_q16(self.confidenceFactor),
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'branchPrediction': from_q16(self.branchPrediction)
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}
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@dataclass
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class SIMDBranchAction:
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"""SIMD branch prediction action (Lean: SIMDBranchAction)"""
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transformType: TransformType
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hintId: int # Hint to add or update
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hintType: str
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confidence: int # Q16_16
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weight: int # Q16_16
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def to_dict(self) -> Dict[str, Any]:
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return {
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'transformType': self.transformType.value,
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'hintId': self.hintId,
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'hintType': self.hintType,
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'confidence': from_q16(self.confidence),
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'weight': from_q16(self.weight)
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}
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@dataclass
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class SIMDBranchBind:
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"""SIMD branch bind result (Lean: SIMDBranchBind)"""
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lawful: bool
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predictionBefore: int # Q16_16
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predictionAfter: int # Q16_16
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selectedTransform: TransformType
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simdLanes: int # Number of SIMD lanes
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invariant: str
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def to_dict(self) -> Dict[str, Any]:
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return {
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'lawful': self.lawful,
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'predictionBefore': from_q16(self.predictionBefore),
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'predictionAfter': from_q16(self.predictionAfter),
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'selectedTransform': self.selectedTransform.value,
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'simdLanes': self.simdLanes,
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'invariant': self.invariant
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}
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# ═══════════════════════════════════════════════════════════════════════════
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# Lean Function Implementations (verified by specification)
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# ═══════════════════════════════════════════════════════════════════════════
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def branchPrediction(state: TransformSelectionState) -> int:
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"""Calculate branch prediction: P_branch = Σ_i w_i·h_i·(1 + α·confidence) (Lean: branchPrediction)"""
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predictionSum = 0
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for hint in state.branchHints:
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h = Q16_ONE if hint.hintType == "taken" else 0
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confidenceBoost = Q16_ONE + (state.confidenceFactor * hint.confidence) // Q16_ONE
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contribution = hint.weight * h * confidenceBoost // (Q16_ONE * Q16_ONE)
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predictionSum += contribution
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return predictionSum
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def simdBroadcast(prediction: int, numLanes: int) -> List[int]:
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"""SIMD broadcast: ∀j, P_branch(j) = P_branch(i) (Lean: simdBroadcast)"""
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return [prediction] * numLanes
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def selectTransform(state: TransformSelectionState) -> TransformType:
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"""Select transform based on branch prediction (Lean: selectTransform)"""
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if state.branchPrediction > (Q16_ONE // 2):
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return state.transformType
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else:
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return TransformType.STOCHASTIC_UVMAP # Default fallback
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def addBranchHint(state: TransformSelectionState, hint: BranchHint) -> TransformSelectionState:
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"""Add branch hint to state (Lean: addBranchHint)"""
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newHints = state.branchHints + [hint]
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tempState = TransformSelectionState(
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transformType=state.transformType,
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branchHints=newHints,
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confidenceFactor=state.confidenceFactor,
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branchPrediction=0
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)
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newPrediction = branchPrediction(tempState)
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return TransformSelectionState(
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transformType=state.transformType,
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branchHints=newHints,
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confidenceFactor=state.confidenceFactor,
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branchPrediction=newPrediction
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)
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def isSIMDBranchActionLawful(action: SIMDBranchAction) -> bool:
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"""Check if SIMD branch action is lawful (Lean: isSIMDBranchActionLawful)"""
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return (action.confidence >= 0 and action.confidence <= Q16_ONE and
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action.weight >= 0 and action.weight <= Q16_ONE)
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def simdBranchedBind(state: TransformSelectionState, action: SIMDBranchAction, numLanes: int = 4) -> SIMDBranchBind:
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"""Bind primitive for SIMD branch prediction (Lean: simdBranchedBind)"""
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lawful = isSIMDBranchActionLawful(action)
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predictionBefore = state.branchPrediction
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if lawful:
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hint = BranchHint(
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hintId=action.hintId,
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hintType=action.hintType,
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confidence=action.confidence,
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weight=action.weight
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)
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updatedState = TransformSelectionState(
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transformType=action.transformType,
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branchHints=state.branchHints,
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confidenceFactor=state.confidenceFactor,
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branchPrediction=0
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)
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newState = addBranchHint(updatedState, hint)
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else:
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newState = state
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predictionAfter = newState.branchPrediction
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selectedTransform = selectTransform(newState)
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return SIMDBranchBind(
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lawful=lawful,
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predictionBefore=predictionBefore,
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predictionAfter=predictionAfter,
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selectedTransform=selectedTransform,
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simdLanes=numLanes,
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invariant="simd_branch_prediction_satisfied" if lawful else "simd_constraint_violated"
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)
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class SIMDBranchPredictionSystem:
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"""
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SIMD branch prediction system (Python shim wrapping Lean specification).
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All core logic is defined in 0-Core-Formalism/lean/Semantics/Semantics/SIMDBranchPrediction.lean
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"""
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def __init__(self):
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self.selectionState: Optional[TransformSelectionState] = None
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self.actionHistory: List[Dict[str, Any]] = []
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print("[SIMDBranchPrediction] Initialized (Lean specification)")
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def initializeSelection(self, transformType: TransformType = TransformType.STOCHASTIC_UVMAP,
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confidenceFactor: float = 0.5) -> Dict[str, Any]:
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"""Initialize transform selection state"""
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state = TransformSelectionState(
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transformType=transformType,
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branchHints=[],
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confidenceFactor=to_q16(confidenceFactor),
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branchPrediction=0
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)
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self.selectionState = state
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return {
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'transformType': transformType.value,
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'confidenceFactor': confidenceFactor,
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'state': state.to_dict()
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}
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def addBranchHint(self, hintId: int, hintType: str, confidence: float, weight: float) -> Dict[str, Any]:
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"""Add a branch hint"""
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if self.selectionState is None:
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self.initializeSelection()
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hint = BranchHint(
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hintId=hintId,
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hintType=hintType,
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confidence=to_q16(confidence),
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weight=to_q16(weight)
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)
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self.selectionState = addBranchHint(self.selectionState, hint)
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return {
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'hintId': hintId,
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'hint': hint.to_dict(),
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'state': self.selectionState.to_dict()
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}
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def submitSIMDBranchAction(self, action: SIMDBranchAction, numLanes: int = 4) -> Dict[str, Any]:
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"""Submit SIMD branch action for processing (Lean specification)"""
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if self.selectionState is None:
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return {'error': 'Selection not initialized'}
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bindResult = simdBranchedBind(self.selectionState, action, numLanes)
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if bindResult.lawful:
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self.selectionState.branchPrediction = bindResult.predictionAfter
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self.selectionState.transformType = bindResult.selectedTransform
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# Record action history
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self.actionHistory.append({
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'action': action.to_dict(),
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'bindResult': bindResult.to_dict(),
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'timestamp': time.time()
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})
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return {
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'success': bindResult.lawful,
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'bindResult': bindResult.to_dict(),
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'state': self.selectionState.to_dict()
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}
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def getSelectionState(self) -> Optional[Dict[str, Any]]:
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"""Get current selection state"""
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if self.selectionState:
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return self.selectionState.to_dict()
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return None
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def getActionHistory(self, limit: int = 10) -> List[Dict[str, Any]]:
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"""Get action history"""
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return self.actionHistory[-limit:]
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def printSystemState(self):
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"""Print system state"""
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print("\n" + "="*60)
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print("SIMD BRANCH PREDICTION STATE")
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print("="*60)
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if self.selectionState:
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print(f"\n📊 Selection Metrics:")
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print(f" Transform Type: {self.selectionState.transformType.value}")
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print(f" Confidence Factor: {from_q16(self.selectionState.confidenceFactor):.3f}")
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print(f" Branch Prediction: {from_q16(self.selectionState.branchPrediction):.3f}")
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print(f"\n📍 Branch Hints: {len(self.selectionState.branchHints)}")
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for hint in self.selectionState.branchHints:
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print(f" Hint {hint.hintId}:")
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print(f" Type: {hint.hintType}")
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print(f" Confidence: {from_q16(hint.confidence):.3f}")
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print(f" Weight: {from_q16(hint.weight):.3f}")
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print(f"\n📜 Action History: {len(self.actionHistory)} entries")
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print("\n" + "="*60)
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def main():
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"""Test SIMD branch prediction system"""
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system = SIMDBranchPredictionSystem()
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print("[Test 1] Initialize transform selection...")
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result1 = system.initializeSelection(TransformType.STOCHASTIC_UVMAP, confidenceFactor=0.5)
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print(f" Selection initialized: {result1['transformType']}")
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print("\n[Test 2] Add branch hint (taken, high confidence)...")
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result2 = system.addBranchHint(hintId=1, hintType="taken", confidence=0.9, weight=0.8)
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print(f" Hint 1 added")
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print("\n[Test 3] Add branch hint (not_taken, medium confidence)...")
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result3 = system.addBranchHint(hintId=2, hintType="not_taken", confidence=0.7, weight=0.6)
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print(f" Hint 2 added")
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print("\n[Test 4] Submit SIMD branch action (add taken hint)...")
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action1 = SIMDBranchAction(
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transformType=TransformType.QUBO_DISCRETE,
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hintId=3,
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hintType="taken",
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confidence=to_q16(0.85),
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weight=to_q16(0.75)
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)
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result4 = system.submitSIMDBranchAction(action1, numLanes=4)
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print(f" Result: Success={result4['success']}")
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if result4['success']:
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print(f" Prediction before: {result4['bindResult']['predictionBefore']:.3f}")
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print(f" Prediction after: {result4['bindResult']['predictionAfter']:.3f}")
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print(f" Selected Transform: {result4['bindResult']['selectedTransform']}")
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print(f" SIMD Lanes: {result4['bindResult']['simdLanes']}")
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print("\n[System State]")
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system.printSystemState()
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if __name__ == '__main__':
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main()
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