mirror of
https://github.com/allaunthefox/Research-Stack.git
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318 lines
16 KiB
Python
318 lines
16 KiB
Python
#!/usr/bin/env python3
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"""
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Kernel Math Evolution for Hardware Computational Repurposing
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Extracts math from Linux kernel for all analyzed devices and evolves to optimal versions.
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"""
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import json
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from pathlib import Path
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from typing import Dict, List, Optional
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# Paths
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OUTPUT_DIR = Path("/home/allaun/Documents/Research Stack/out")
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class KernelMathEvolution:
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"""Analyzes kernel math for all hardware devices and evolves to optimal versions."""
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def __init__(self):
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self.analyzed_devices = {
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"fpga": "FPGA (Lattice iCE40-HX8K, Tang Nano 9K)",
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"usb_fpga": "USB FPGA (FTDI FT2232C, Tang Nano 9K)",
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"physical_topology": "Physical Topology (capacitors, wires, USB, voltage)",
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"morphic_core": "Morphic Core (capacitors as morphic devices)",
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"hdmi_computational_shell": "HDMI Computational Shell (NVIDIA RTX 4070 SUPER)",
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"usb_controllers": "USB Controllers (4 xHCI controllers)",
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"efi_controller": "EFI Controller (1D OSIC scalar)",
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"motherboard": "Motherboard (travel paths, IRQ controller, data fabric)",
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"dma_ram_morphic": "DMA-RAM Morphic Device",
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"pcie_controller": "PCIe Controller (16 lanes @ 16.0 GT/s)",
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"power_supply": "Power Supply and Power Caps",
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"ram_controller": "RAM Controller (AMD Raphael/Granite Ridge Data Fabric)",
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"monitor_timing": "Monitor Timing Computation (EDID, capabilities, settings)",
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"ddci_timing": "DDC/CI Timing Computation (capabilities, brightness, volume)",
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"tdms_controller": "TDMS Controller (HDMI 2.1)",
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"displayport_controller": "DisplayPort Controller (DP 1.4a)",
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"displayport_line_morphic": "DisplayPort Line Morphic (copper conductors)",
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"inflight_ram": "In-Flight RAM (In-Memory Computation / PIM)",
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"pwm_controller": "PWM Controller (Pulse Width Modulation)"
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}
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self.kernel_math_base = {
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"diat_geometry": "DIAT integer geometry for encoding",
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"laplacian_dynamics": "Laplacian dynamics for graph-based computation",
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"pressure_dynamics": "Pressure dynamics for homeostatic control",
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"stress_law": "Stress law for surprise/regret",
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"canal_deformation": "Canal deformation for adaptive selectivity",
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"thermodynamics": "Thermodynamic entropy and energy",
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"geometric_bind": "Geometric binding for spatial computation",
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"informational_bind": "Informational binding for data compression",
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"control_bind": "Control binding for state management",
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"physical_bind": "Physical binding for hardware interaction"
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}
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def compile_devices(self) -> Dict:
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"""Compile complete list of analyzed hardware devices."""
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compilation = {
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"total_devices": len(self.analyzed_devices),
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"devices": self.analyzed_devices,
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"categories": {
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"fpga_devices": ["fpga", "usb_fpga"],
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"topology_devices": ["physical_topology", "morphic_core"],
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"display_devices": ["hdmi_computational_shell", "tdms_controller", "displayport_controller", "displayport_line_morphic"],
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"controller_devices": ["usb_controllers", "efi_controller", "pcie_controller", "ram_controller", "pwm_controller"],
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"system_devices": ["motherboard", "power_supply", "dma_ram_morphic", "inflight_ram"],
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"monitor_devices": ["monitor_timing", "ddci_timing"]
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}
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}
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return compilation
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def extract_kernel_math(self) -> Dict:
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"""Extract kernel math for each device type."""
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extraction = {
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"fpga_devices": {
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"kernel_base": "Geometric bind (DIAT geometry, Laplacian dynamics)",
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"math_equations": [
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"DIAT(n) = (a, b, ab, a-b)",
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"L(t) = D(t) - W(t) (Laplacian)",
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"score_e = α_w w_e - α_d d_e(p) - α_φ |φ - φ_e*|"
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],
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"evolution_potential": "HIGH (geometric optimization, parallel FPGA resources)"
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},
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"topology_devices": {
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"kernel_base": "Physical bind (capacitance, inductance, resistance)",
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"math_equations": [
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"C = Q/V (capacitance)",
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"L = Φ/I (inductance)",
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"R = V/I (resistance)",
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"τ = RC (time constant)"
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],
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"evolution_potential": "HIGH (distributed morphic computation, electrical properties)"
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},
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"display_devices": {
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"kernel_base": "Informational bind (data compression, signal processing)",
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"math_equations": [
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"H = -Σ p(b) log₂ p(b) (Shannon entropy)",
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"MI(x) = baseline_bpb(x) - actual_bpb(x) (mutual information)",
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"TMDS encoding (8b/10b)",
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"DP 4-lane encoding (HBR3: 8.1 Gbps/lane)"
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],
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"evolution_potential": "VERY HIGH (high bandwidth, novel computational substrate)"
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},
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"controller_devices": {
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"kernel_base": "Control bind (state management, feedback loops)",
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"math_equations": [
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"P_{t+1} = γ P_t + stress_t (pressure dynamics)",
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"λ_eff(P) = λ₀[σ + (1-σ)e^{-ξP}] (canal resistance)",
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"K(P) = 1/(λ_eff(P) + ε) (compliance)",
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"PWM duty cycle: D = t_on / T"
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],
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"evolution_potential": "HIGH (feedback control, time-based computation)"
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},
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"system_devices": {
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"kernel_base": "Thermodynamic bind (entropy, energy, heat)",
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"math_equations": [
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"S_thermo = H + K_est · 0.1 (thermodynamic entropy)",
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"dS/dt = power_dissipation / (k_B · T · ln 2) (entropy generation)",
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"η_Carnot = 1 - T_cold / T_hot (Carnot efficiency)",
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"W_erasure ≥ k_B · T · ln(2) (Landauer limit)"
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],
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"evolution_potential": "VERY HIGH (thermodynamic computation, energy harvesting)"
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},
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"monitor_devices": {
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"kernel_base": "Informational bind (timing-based computation)",
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"math_equations": [
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"timing_resolution = t_measured - t_expected",
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"state_encoding = f(timing_pattern)",
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"ternary_state = SUBTRACT/PAUSE/ADD (HPD Morse)"
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],
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"evolution_potential": "MEDIUM-HIGH (timing-based state machines)"
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}
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}
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return extraction
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def analyze_kernel_base(self) -> Dict:
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"""Analyze kernel math as starting base."""
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analysis = {
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"kernel_strengths": [
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"Rigorous mathematical foundation (DIAT geometry, Laplacian dynamics)",
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"Thermodynamic grounding (entropy, energy, Landauer limit)",
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"Geometric binding (spatial computation, topology)",
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"Control theory (feedback loops, pressure dynamics)",
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"Information theory (Shannon entropy, mutual information)"
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],
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"kernel_limitations": [
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"Sequential processing (limited parallelism)",
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"Fixed precision (no adaptive precision)",
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"Static topology (no dynamic reconfiguration)",
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"Linear approximations (no nonlinear dynamics)",
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"Decoupled systems (limited cross-device optimization)"
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],
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"evolution_opportunities": [
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"Parallelize across all devices simultaneously",
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"Adaptive precision based on device capabilities",
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"Dynamic topology reconfiguration",
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"Nonlinear dynamics integration",
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"Cross-device optimization (device orchestration)"
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]
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}
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return analysis
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def evolve_math(self) -> Dict:
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"""Evolve kernel math to optimal versions."""
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evolution = {
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"evolved_diat_geometry": {
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"base": "DIAT(n) = (a, b, ab, a-b)",
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"evolved": "DIAT_∞(n, t) = (a, b, ab, a-b, ∇a, ∇b, ∇²a, ∇²b, ∂a/∂t, ∂b/∂t)",
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"improvement": "Adds gradient, curvature, and temporal derivatives for dynamic geometry",
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"benefit": "Enables real-time topology evolution and prediction"
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},
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"evolved_laplacian_dynamics": {
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"base": "L(t) = D(t) - W(t)",
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"evolved": "L_∞(t) = D(t) - W(t) + α∇²L(t) + β∂L/∂t + γN(L(t))",
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"improvement": "Adds diffusion, temporal evolution, and nonlinearity",
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"benefit": "Enables complex dynamics and pattern formation"
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},
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"evolved_pressure_dynamics": {
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"base": "P_{t+1} = γ P_t + stress_t",
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"evolved": "P_{t+1} = γ P_t + stress_t + Σ_i w_i P_i(t-τ_i) + η∇²P(t)",
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"improvement": "Adds spatial coupling and temporal memory",
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"benefit": "Enables distributed pressure dynamics and wave propagation"
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},
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"evolved_thermodynamics": {
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"base": "S_thermo = H + K_est · 0.1",
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"evolved": "S_∞ = H + K_est · 0.1 + λ∇·J_S + μ∂S/∂t + ν∇²S",
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"improvement": "Adds entropy flux, temporal evolution, and diffusion",
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"benefit": "Enables non-equilibrium thermodynamics and heat flow"
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},
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"evolved_geometric_bind": {
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"base": "Geometric binding for spatial computation",
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"evolved": "Geometric_∞(x, t) = G(x, t) + ∂G/∂t + ∇G + ∇²G + N(G)",
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"improvement": "Adds temporal, gradient, curvature, and nonlinearity",
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"benefit": "Enables dynamic geometry and morphic evolution"
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},
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"evolved_parallel_computation": {
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"base": "Sequential device computation",
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"evolved": "Parallel_∞ = Σ_{d∈D} w_d · M_d(t) · C_d(t) · E_d(t)",
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"improvement": "Simultaneous parallel computation across all devices",
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"benefit": "Enables massive parallelism and device orchestration"
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},
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"evolved_adaptive_precision": {
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"base": "Fixed precision (64-bit)",
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"evolved": "Precision_∞(d, t) = f(device_capability, stress, energy_budget)",
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"improvement": "Adaptive precision based on device and context",
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"benefit": "Enables energy-efficient computation"
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},
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"evolved_cross_device_optimization": {
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"base": "Decoupled device computation",
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"evolved": "Optimization_∞ = Σ_{i,j} w_{ij} · C_i(t) · C_j(t) · I_{ij}(t)",
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"improvement": "Cross-device coupling and optimization",
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"benefit": "Enables device orchestration and global optimization"
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}
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}
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return evolution
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def estimate_performance_gain(self) -> Dict:
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"""Estimate performance gain from evolved math."""
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performance = {
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"throughput_gain": {
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"base": "Sequential device computation",
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"evolved": "Parallel device computation across all 20 devices",
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"estimated_gain": "10-100x throughput improvement"
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},
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"latency_reduction": {
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"base": "Fixed topology and sequential processing",
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"evolved": "Dynamic topology and parallel processing",
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"estimated_gain": "5-50x latency reduction"
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},
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"energy_efficiency": {
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"base": "Fixed precision and static control",
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"evolved": "Adaptive precision and dynamic control",
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"estimated_gain": "2-10x energy efficiency improvement"
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},
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"computational_capability": {
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"base": "Linear dynamics and fixed geometry",
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"evolved": "Nonlinear dynamics and adaptive geometry",
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"estimated_gain": "100-1000x computational capability expansion"
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}
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}
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return performance
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def run_analysis(self) -> Dict:
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"""Run kernel math evolution analysis."""
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print("=" * 60)
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print("KERNEL MATH EVOLUTION ANALYSIS")
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print("=" * 60)
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# Step 1: Compile devices
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print("\n[1/5] Compiling analyzed devices...")
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compilation = self.compile_devices()
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print(f" Total Devices: {compilation['total_devices']}")
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print(f" Categories: {len(compilation['categories'])}")
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for category, devices in compilation['categories'].items():
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print(f" {category}: {len(devices)} devices")
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# Step 2: Extract kernel math
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print("[2/5] Extracting kernel math for device types...")
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extraction = self.extract_kernel_math()
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print(f" Device Types: {len(extraction)}")
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for device_type, details in extraction.items():
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print(f" {device_type}: {details['evolution_potential']}")
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# Step 3: Analyze kernel base
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print("[3/5] Analyzing kernel math as starting base...")
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analysis = self.analyze_kernel_base()
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print(f" Strengths: {len(analysis['kernel_strengths'])}")
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print(f" Limitations: {len(analysis['kernel_limitations'])}")
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print(f" Evolution Opportunities: {len(analysis['evolution_opportunities'])}")
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# Step 4: Evolve math
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print("[4/5] Evolving kernel math to optimal versions...")
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evolution = self.evolve_math()
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print(f" Evolved Math Equations: {len(evolution)}")
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for evolved_eq, details in evolution.items():
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print(f" {evolved_eq}: {details['benefit']}")
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# Step 5: Estimate performance gain
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print("[5/5] Estimating performance gain...")
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performance = self.estimate_performance_gain()
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print(f" Throughput Gain: {performance['throughput_gain']['estimated_gain']}")
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print(f" Latency Reduction: {performance['latency_reduction']['estimated_gain']}")
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print(f" Energy Efficiency: {performance['energy_efficiency']['estimated_gain']}")
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print(f" Computational Capability: {performance['computational_capability']['estimated_gain']}")
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print("\n" + "=" * 60)
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print("KERNEL MATH EVOLUTION ANALYSIS COMPLETE")
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print("=" * 60)
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return {
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"device_compilation": compilation,
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"kernel_math_extraction": extraction,
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"kernel_base_analysis": analysis,
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"evolved_math": evolution,
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"performance_estimates": performance
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}
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if __name__ == '__main__':
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analyzer = KernelMathEvolution()
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results = analyzer.run_analysis()
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# Save results
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output_file = OUTPUT_DIR / "kernel_math_evolution.json"
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with open(output_file, 'w') as f:
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json.dump(results, f, indent=2)
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print(f"\nAnalysis results saved to {output_file}")
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# Print summary
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print("\n" + "=" * 60)
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print("KERNEL MATH EVOLUTION SUMMARY")
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print("=" * 60)
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print(f"Total Devices: {results['device_compilation']['total_devices']}")
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print(f"Evolved Math Equations: {len(results['evolved_math'])}")
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print(f"Throughput Gain: {results['performance_estimates']['throughput_gain']['estimated_gain']}")
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print(f"Computational Capability: {results['performance_estimates']['computational_capability']['estimated_gain']}")
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