Silicon Die Cross-Section:
┌─────────────────────────┐
│  Active Circuits        │ ← Transistors, logic
├─────────────────────────┤
│  Metal Layers (10-15)   │ ← Interconnects
├─────────────────────────┤
│     TSV Column          │ ← Through-Silicon Via
│      ┃ ┃ ┃ ┃           │    (5-10 μm diameter)
│      ┃ ┃ ┃ ┃           │
└─────────────────────────┘
        ↓ ↓ ↓ ↓
    Micro-bumps to next die

class TSVManufacturing:
    def __init__(self):
        self.steps = [
            "Deep Reactive Ion Etching (DRIE)",
            "Oxide liner deposition",
            "Barrier/seed layer (Ta/Cu)",
            "Copper electroplating",
            "Chemical-mechanical polishing (CMP)",
            "Die thinning (50-100 μm)",
            "Micro-bump formation"
        ]
    
    def calculate_tsv_resistance(self, diameter_um, height_um):
        """Calculate electrical resistance of TSV"""
        # Copper resistivity at room temperature
        rho_cu = 1.68e-8  # Ω⋅m
        
        # Convert to meters
        d = diameter_um * 1e-6
        h = height_um * 1e-6
        
        # Cross-sectional area
        area = np.pi * (d/2)**2
        
        # Resistance
        resistance = rho_cu * h / area
        
        return resistance * 1e3  # Return in mΩ
    
    def thermal_consideration(self, power_w, num_dies=8):
        """Calculate thermal resistance through stack"""
        # Silicon thermal conductivity
        k_si = 150  # W/(m⋅K)
        
        # Die dimensions
        thickness = 50e-6  # 50 μm per die
        area = 100e-6  # 100 mm² die area
        
        # Thermal resistance per die
        r_die = thickness / (k_si * area)
        
        # Total stack resistance
        r_total = r_die * num_dies
        
        # Temperature rise
        delta_t = power_w * r_total
        
        return {
            'resistance_per_die': r_die,
            'total_resistance': r_total,
            'temperature_rise': delta_t
        }

import numpy as np
import matplotlib.pyplot as plt

def plot_hbm_evolution():
    generations = ['HBM', 'HBM2', 'HBM2E', 'HBM3', 'HBM3E', 'HBM4*']
    years = [2013, 2016, 2018, 2022, 2024, 2026]
    bandwidth = [128, 256, 461, 819, 1200, 2000]  # GB/s per stack
    capacity = [4, 8, 16, 24, 36, 64]  # GB per stack
    
    fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(12, 5))
    
    # Bandwidth evolution
    ax1.semilogy(years, bandwidth, 'o-', linewidth=2, markersize=8)
    ax1.set_xlabel('Year')
    ax1.set_ylabel('Bandwidth (GB/s per stack)')
    ax1.set_title('HBM Bandwidth Evolution')
    ax1.grid(True, alpha=0.3)
    
    # Add generation labels
    for i, gen in enumerate(generations):
        ax1.annotate(gen, (years[i], bandwidth[i]), 
                    textcoords="offset points", xytext=(0,10))
    
    # Capacity evolution
    ax2.semilogy(years, capacity, 's-', color='green', linewidth=2, markersize=8)
    ax2.set_xlabel('Year')
    ax2.set_ylabel('Capacity (GB per stack)')
    ax2.set_title('HBM Capacity Evolution')
    ax2.grid(True, alpha=0.3)
    
    plt.tight_layout()
    return fig

# Calculate bandwidth efficiency
def bandwidth_efficiency(generation, actual_bw, theoretical_bw):
    """Calculate how efficiently bandwidth is utilized"""
    efficiency = actual_bw / theoretical_bw
    
    print(f"{generation} Bandwidth Efficiency:")
    print(f"  Theoretical: {theoretical_bw} GB/s")
    print(f"  Achieved: {actual_bw} GB/s")
    print(f"  Efficiency: {efficiency:.1%}")
    
    return efficiency

class GPUMemoryHierarchy:
    def __init__(self):
        self.levels = {
            'Registers': {
                'size': '256 KB/SM',
                'bandwidth': '~20 TB/s/SM',
                'latency': '~1 cycle',
                'scope': 'Thread'
            },
            'L1/Shared': {
                'size': '128 KB/SM',
                'bandwidth': '~10 TB/s/SM',
                'latency': '~30 cycles',
                'scope': 'Block'
            },
            'L2 Cache': {
                'size': '40-60 MB',
                'bandwidth': '~4 TB/s',
                'latency': '~200 cycles',
                'scope': 'Device'
            },
            'HBM': {
                'size': '40-80 GB',
                'bandwidth': '~2-3 TB/s',
                'latency': '~400 cycles',
                'scope': 'Device'
            }
        }
    
    def calculate_bandwidth_requirements(self, flops, arithmetic_intensity):
        """
        Calculate memory bandwidth requirements based on compute
        
        Args:
            flops: Peak FP32 FLOPS (TFLOPS)
            arithmetic_intensity: FLOPS per byte
        
        Returns:
            Required bandwidth in GB/s
        """
        required_bandwidth = (flops * 1e12) / arithmetic_intensity
        return required_bandwidth / 1e9  # Convert to GB/s
    
    def is_memory_bound(self, kernel_flops, kernel_bytes):
        """Determine if kernel is compute or memory bound"""
        intensity = kernel_flops / kernel_bytes
        
        # Example: NVIDIA A100
        peak_flops = 19.5e12  # 19.5 TFLOPS
        peak_bandwidth = 2039e9  # 2039 GB/s HBM2e
        
        ridge_point = peak_flops / peak_bandwidth
        
        return intensity < ridge_point

class SiliconInterposer:
    def __init__(self, hbm_stacks=4, processor_size_mm2=800):
        self.hbm_stacks = hbm_stacks
        self.processor_size = processor_size_mm2
        
        # Physical parameters
        self.trace_width_um = 0.5  # Microns
        self.trace_pitch_um = 1.0  # Microns
        self.via_diameter_um = 10
        
    def calculate_signal_paths(self):
        """Calculate number of signal paths needed"""
        signals_per_stack = {
            'data': 1024,      # 1024-bit wide interface
            'command': 32,     # Command/address
            'clock': 8,        # Differential clocks
            'power': 200,      # Power/ground
            'total': 1264
        }
        
        total_signals = signals_per_stack['total'] * self.hbm_stacks
        
        # Routing density
        traces_per_mm = 1000 / self.trace_pitch_um
        routing_area_mm2 = total_signals / traces_per_mm
        
        return {
            'total_signals': total_signals,
            'routing_density': traces_per_mm,
            'required_area': routing_area_mm2
        }
    
    def power_delivery_network(self, power_per_stack_w=15):
        """Design power delivery for HBM stacks"""
        total_power = power_per_stack_w * self.hbm_stacks
        
        # Current at 1.1V (HBM3)
        current = total_power / 1.1
        
        # Number of power vias needed (assuming 100mA per via)
        power_vias = int(current / 0.1)
        
        return {
            'total_power': total_power,
            'total_current': current,
            'power_vias_needed': power_vias
        }

// CUDA kernel optimized for HBM bandwidth
__global__ void hbm_optimized_gemm(
    float* __restrict__ A,
    float* __restrict__ B,
    float* __restrict__ C,
    int M, int N, int K
) {
    // Tile dimensions optimized for HBM burst length
    const int TILE_M = 128;
    const int TILE_N = 128;
    const int TILE_K = 32;
    
    // Shared memory for tiles
    __shared__ float As[TILE_M][TILE_K];
    __shared__ float Bs[TILE_K][TILE_N];
    
    // Thread and block indices
    int tx = threadIdx.x;
    int ty = threadIdx.y;
    int bx = blockIdx.x;
    int by = blockIdx.y;
    
    // Global indices
    int row = by * TILE_M + ty;
    int col = bx * TILE_N + tx;
    
    float sum = 0.0f;
    
    // Main loop over K dimension
    for (int tile_idx = 0; tile_idx < K; tile_idx += TILE_K) {
        // Collaborative loading with coalesced access
        // Each thread loads one element
        if (row < M && tile_idx + tx < K) {
            As[ty][tx] = A[row * K + tile_idx + tx];
        } else {
            As[ty][tx] = 0.0f;
        }
        
        if (col < N && tile_idx + ty < K) {
            Bs[ty][tx] = B[(tile_idx + ty) * N + col];
        } else {
            Bs[ty][tx] = 0.0f;
        }
        
        __syncthreads();
        
        // Compute on shared memory tile
        #pragma unroll
        for (int k = 0; k < TILE_K; k++) {
            sum += As[ty][k] * Bs[k][tx];
        }
        
        __syncthreads();
    }
    
    // Write result
    if (row < M && col < N) {
        C[row * N + col] = sum;
    }
}

// Host code to maximize HBM utilization
void optimize_hbm_transfer(float* d_data, size_t size) {
    // Enable peer access for multi-GPU
    cudaSetDevice(0);
    cudaDeviceEnablePeerAccess(1, 0);
    
    // Use pinned memory for host-device transfers
    float* h_pinned;
    cudaMallocHost(&h_pinned, size);
    
    // Asynchronous transfers with multiple streams
    const int num_streams = 4;
    cudaStream_t streams[num_streams];
    
    for (int i = 0; i < num_streams; i++) {
        cudaStreamCreate(&streams[i]);
    }
    
    // Overlap computation and data transfer
    size_t chunk_size = size / num_streams;
    for (int i = 0; i < num_streams; i++) {
        size_t offset = i * chunk_size;
        cudaMemcpyAsync(
            d_data + offset,
            h_pinned + offset,
            chunk_size,
            cudaMemcpyHostToDevice,
            streams[i]
        );
    }
}

def benchmark_hbm_bandwidth():
    """Benchmark achievable HBM bandwidth"""
    import cupy as cp
    
    # Test different access patterns
    sizes = [1, 10, 100, 1000, 10000]  # MB
    patterns = ['sequential', 'strided', 'random']
    
    results = {}
    
    for size_mb in sizes:
        size_bytes = size_mb * 1024 * 1024
        n_elements = size_bytes // 4  # float32
        
        for pattern in patterns:
            # Allocate arrays
            a = cp.random.random(n_elements, dtype=cp.float32)
            b = cp.random.random(n_elements, dtype=cp.float32)
            c = cp.zeros(n_elements, dtype=cp.float32)
            
            # Create access pattern
            if pattern == 'sequential':
                indices = cp.arange(n_elements)
            elif pattern == 'strided':
                indices = cp.arange(0, n_elements, 16) % n_elements
            else:  # random
                indices = cp.random.randint(0, n_elements, n_elements)
            
            # Measure bandwidth
            start = cp.cuda.Event()
            end = cp.cuda.Event()
            
            start.record()
            
            # Memory-bound operation
            for _ in range(100):
                c = a[indices] + b[indices]
            
            end.record()
            end.synchronize()
            
            time_ms = cp.cuda.get_elapsed_time(start, end)
            bandwidth = (size_bytes * 2 * 100) / (time_ms * 1e6)  # GB/s
            
            results[f"{size_mb}MB_{pattern}"] = bandwidth
    
    return results

class ThermalAnalysis:
    def __init__(self):
        self.materials = {
            'silicon': {'k': 150, 'rho': 2330, 'cp': 700},  # W/(m⋅K), kg/m³, J/(kg⋅K)
            'copper': {'k': 400, 'rho': 8960, 'cp': 385},
            'tim': {'k': 5, 'rho': 3000, 'cp': 1000},  # Thermal Interface Material
        }
    
    def calculate_junction_temperature(self, 
                                      power_w, 
                                      ambient_c=25,
                                      num_dies=8):
        """Calculate junction temperature in HBM stack"""
        
        # Thermal resistances (K/W)
        r_die = 0.5 * num_dies  # Through silicon
        r_tim = 0.2            # TIM between stack and substrate
        r_substrate = 0.3      # Package substrate
        r_heatsink = 0.1       # Heatsink to ambient
        
        r_total = r_die + r_tim + r_substrate + r_heatsink
        
        # Temperature rise
        delta_t = power_w * r_total
        t_junction = ambient_c + delta_t
        
        # Check thermal throttling
        throttle_temp = 95  # °C
        if t_junction > throttle_temp:
            # Calculate reduced power for safe operation
            safe_power = (throttle_temp - ambient_c) / r_total
            throttle_percent = (1 - safe_power/power_w) * 100
            
            return {
                'junction_temp': t_junction,
                'throttling': True,
                'throttle_percent': throttle_percent,
                'safe_power': safe_power
            }
        
        return {
            'junction_temp': t_junction,
            'throttling': False,
            'thermal_margin': throttle_temp - t_junction
        }

def cost_comparison(capacity_gb, bandwidth_gb_s):
    """Compare cost of different memory solutions"""
    
    # Cost per GB (approximate, relative)
    cost_per_gb = {
        'DDR5': 10,
        'GDDR6X': 30,
        'HBM2E': 100,
        'HBM3': 150,
        'HBM3E': 200
    }
    
    # Bandwidth per module/stack
    bandwidth_per_unit = {
        'DDR5': 38.4,    # Per channel
        'GDDR6X': 84,    # Per chip
        'HBM2E': 461,    # Per stack
        'HBM3': 819,     # Per stack
        'HBM3E': 1200    # Per stack
    }
    
    results = {}
    
    for tech in cost_per_gb.keys():
        units_needed = np.ceil(bandwidth_gb_s / bandwidth_per_unit[tech])
        capacity_per_unit = {
            'DDR5': 32,
            'GDDR6X': 2,
            'HBM2E': 16,
            'HBM3': 24,
            'HBM3E': 36
        }[tech]
        
        total_capacity = units_needed * capacity_per_unit
        total_cost = total_capacity * cost_per_gb[tech]
        
        results[tech] = {
            'units': int(units_needed),
            'total_capacity_gb': total_capacity,
            'total_cost': total_cost,
            'cost_per_gb_bandwidth': total_cost / bandwidth_gb_s
        }
    
    return results

class FutureHBM:
    def __init__(self):
        self.roadmap = {
            'HBM4': {
                'year': 2026,
                'bandwidth': 2000,  # GB/s per stack
                'capacity': 64,     # GB per stack
                'features': [
                    'Advanced error correction',
                    'Lower voltage (1.0V)',
                    'Improved thermal management',
                    'Processing-in-Memory (PIM)'
                ]
            },
            'HBM5': {
                'year': 2028,
                'bandwidth': 4000,  # Projected
                'capacity': 128,
                'features': [
                    'Optical interconnects',
                    'Chiplet integration',
                    'AI acceleration units',
                    'Non-volatile memory layers'
                ]
            }
        }
    
    def calculate_ai_model_requirements(self, model_params_b, year=2024):
        """Project memory requirements for AI models"""
        
        # Model size growth: ~10x every 2 years
        years_from_now = year - 2024
        size_multiplier = 10 ** (years_from_now / 2)
        
        projected_params = model_params_b * size_multiplier
        
        # Memory requirements (rough estimates)
        # Parameters + gradients + optimizer states + activations
        memory_gb = projected_params * 20 / 1e9  # 20 bytes per parameter
        
        # Bandwidth requirements (training)
        # Assuming need to access each parameter 3x per iteration
        # Target: 1 iteration per second
        bandwidth_tb_s = projected_params * 3 * 4 / 1e12  # 4 bytes per param
        
        return {
            'year': year,
            'model_size_b': projected_params,
            'memory_required_gb': memory_gb,
            'bandwidth_required_tb_s': bandwidth_tb_s,
            'hbm_stacks_needed': np.ceil(memory_gb / 64)  # HBM4 capacity
        }

class HBMOptimizationTechniques:
    @staticmethod
    def optimize_data_layout(tensor_shape, hbm_burst_size=256):
        """Optimize tensor layout for HBM access"""
        
        # Align to burst boundaries
        aligned_shape = []
        bytes_per_element = 4  # float32
        elements_per_burst = hbm_burst_size // bytes_per_element
        
        for dim in tensor_shape:
            aligned_dim = ((dim + elements_per_burst - 1) // 
                          elements_per_burst) * elements_per_burst
            aligned_shape.append(aligned_dim)
        
        padding_overhead = (np.prod(aligned_shape) - 
                          np.prod(tensor_shape)) / np.prod(tensor_shape)
        
        return {
            'original_shape': tensor_shape,
            'aligned_shape': aligned_shape,
            'padding_overhead': f"{padding_overhead:.1%}",
            'memory_efficiency': f"{1/(1+padding_overhead):.1%}"
        }