AI 计算基础设施全景：HBM 内存危机、GPU 集群架构与算力供应链深度解读

"""
HBM 带宽与 GPU 算力利用率分析
计算在不同 HBM 配置下，GPU 算力的实际利用率
"""
import numpy as np
from dataclasses import dataclass

@dataclass
class GPUConfig:
    name: str
    peak_tflops: float  # FP8 峰值算力
    hbm_stacks: int     # HBM 栈数
    hbm_bandwidth_tbs: float  # 每栈带宽 (TB/s)
    hbm_capacity_gb: float    # 每栈容量 (GB)

@dataclass
class ModelConfig:
    name: str
    params_billion: float  # 参数量（十亿）
    bytes_per_param: float  # 每参数字节数 (FP16=2, FP8=1)
    activation_memory_gb: float  # 激活内存

def compute_memory_bandwidth_utilization(gpu: GPUConfig, model: ModelConfig, batch_size: int) -> dict:
    """计算 GPU 在不同场景下的内存带宽利用率"""
    
    total_hbm_bandwidth = gpu.hbm_stacks * gpu.hbm_bandwidth_tbs  # TB/s
    total_hbm_capacity = gpu.hbm_stacks * gpu.hbm_capacity_gb      # GB
    
    # 模型权重内存需求
    weight_memory = model.params_billion * 1e9 * model.bytes_per_param / 1e9  # GB
    
    # 总内存需求（权重 + 激活 × batch_size）
    total_memory = weight_memory + model.activation_memory_gb * batch_size
    
    # 每 token 前向传播需要的内存访问量（近似）
    # 每个参数需要读取一次，加上激活的读写
    bytes_per_token = model.params_billion * 1e9 * model.bytes_per_param  # bytes
    
    # 理论最大吞吐量（受限于内存带宽）
    max_tokens_per_sec_bw = (total_hbm_bandwidth * 1e12) / bytes_per_token  # tokens/s
    
    # 理论最大吞吐量（受限于算力）
    ops_per_token = 2 * model.params_billion * 1e9  # MACs per token (approx)
    max_tokens_per_sec_compute = (gpu.peak_tflops * 1e12) / ops_per_token  # tokens/s
    
    # 实际吞吐量取两者较小值
    actual_tokens_per_sec = min(max_tokens_per_sec_bw, max_tokens_per_sec_compute)
    
    # 计算力利用率
    compute_utilization = actual_tokens_per_sec / max_tokens_per_sec_compute * 100
    
    return {
        "gpu": gpu.name,
        "model": model.name,
        "total_hbm_bandwidth_tbps": total_hbm_bandwidth,
        "total_hbm_capacity_gb": total_hbm_capacity,
        "model_memory_gb": total_memory,
        "fits_in_memory": total_memory <= total_hbm_capacity,
        "bw_limited_max_tokens_s": max_tokens_per_sec_bw,
        "compute_limited_max_tokens_s": max_tokens_per_sec_compute,
        "actual_tokens_s": actual_tokens_per_sec,
        "compute_utilization_pct": round(compute_utilization, 1),
        "bottleneck": "memory_bandwidth" if max_tokens_per_sec_bw < max_tokens_per_sec_compute else "compute",
    }

# 对比 H100 + HBM3 vs B200 + HBM3E
h100 = GPUConfig("H100", 3958, 6, 1.5, 24)   # 6 栈 HBM3, 每栈 1.5TB/s
b200 = GPUConfig("B200", 4500, 8, 1.5, 48)   # 8 栈 HBM3E, 每栈 1.5TB/s

llama_70b = ModelConfig("Llama-70B", 70, 2, 8)  # FP16, 激活约 8GB/batch

print("=" * 80)
print("GPU 内存带宽利用率对比分析")
print("=" * 80)

for gpu in [h100, b200]:
    for bs in [1, 4, 16]:
        result = compute_memory_bandwidth_utilization(gpu, llama_70b, bs)
        print(f"\n{gpu.name} + {llama_70b.name} (batch={bs})")
        print(f"  HBM 带宽: {result['total_hbm_bandwidth_tbps']:.1f} TB/s")
        print(f"  HBM 容量: {result['total_hbm_capacity_gb']:.0f} GB")
        print(f"  模型内存: {result['model_memory_gb']:.0f} GB {'✓' if result['fits_in_memory'] else '✗ 超出!'}")
        print(f"  瓶颈: {result['bottleneck']}")
        print(f"  算力利用率: {result['compute_utilization_pct']}%")
        print(f"  实际吞吐量: {result['actual_tokens_s']:.0f} tokens/s")

"""
HBM 供应链产能模拟
从 DRAM 晶圆到 AI 服务器的完整产能转换模型
"""
from dataclasses import dataclass, field

@dataclass
class HBMProductionLine:
    """HBM 生产线配置"""
    name: str
    monthly_wafer_capacity: int    # 月产能（晶圆数）
    dies_per_wafer: int            # 每晶圆芯片数
    tsv_yield: float               # TSV 良率
    stacking_yield: float          # 堆叠良率（每层独立）
    layers_per_stack: int          # 每栈层数
    testing_yield: float           # 测试良率
    monthly_cowos_capacity: int    # 月 CoWoS 封装产能
    
    def calculate_monthly_stacks(self) -> dict:
        """计算月产 HBM 栈数"""
        raw_dies = self.monthly_wafer_capacity * self.dies_per_wafer
        
        # TSV 良率：每个 TSV 都必须正常
        tsv_pass = raw_dies * self.tsv_yield
        
        # 堆叠良率：N 层堆叠，每层独立良率
        stack_yield = self.stacking_yield ** self.layers_per_stack
        stacked_dies = tsv_pass * stack_yield
        
        # 测试良率
        final_stacks = int(stacked_dies * self.testing_yield)
        
        # CoWoS 封装限制
        cowos_limited = min(final_stacks, self.monthly_cowos_capacity)
        
        bottleneck = "CoWoS 封装" if cowos_limited < final_stacks else "HBM 制造"
        
        return {
            "raw_dies": raw_dies,
            "tsv_pass": int(tsv_pass),
            "after_stacking": int(stacked_dies),
            "final_stacks": final_stacks,
            "cowos_limited_output": cowos_limited,
            "bottleneck": bottleneck,
            "overall_yield": round(cowos_limited / raw_dies * 100, 2),
        }

# 模拟 SK 海力士 2026 年 HBM3E 生产线
sk_hynix_2026 = HBMProductionLine(
    name="SK 海力士 HBM3E (2026)",
    monthly_wafer_capacity=80000,      # 8 万片/月
    dies_per_wafer=600,                # 12 英寸晶圆约 600 颗
    tsv_yield=0.98,                    # TSV 良率 98%
    stacking_yield=0.97,               # 单层堆叠良率 97%
    layers_per_stack=12,               # HBM3E 12 层
    testing_yield=0.95,                # 测试良率 95%
    monthly_cowos_capacity=35000000,   # CoWoS 月产能 3500 万
)

# 模拟三星 2026 年 HBM3E 生产线
samsung_2026 = HBMProductionLine(
    name="三星 HBM3E (2026)",
    monthly_wafer_capacity=100000,     # 10 万片/月（产能更大）
    dies_per_wafer=600,
    tsv_yield=0.95,                    # TSV 良率略低
    stacking_yield=0.94,               # 堆叠良率更低
    layers_per_stack=12,
    testing_yield=0.92,                # 测试良率更低
    monthly_cowos_capacity=35000000,
)

print("=" * 80)
print("HBM3E 供应链产能模拟（2026）")
print("=" * 80)

for line in [sk_hynix_2026, samsung_2026]:
    result = line.calculate_monthly_stacks()
    print(f"\n{line.name}")
    print(f"  原始芯片数: {result['raw_dies']:,}")
    print(f"  TSV 通过: {result['tsv_pass']:,}")
    print(f"  堆叠后: {result['after_stacking']:,}")
    print(f"  最终 HBM 栈: {result['final_stacks']:,}")
    print(f"  CoWoS 限制后: {result['cowos_limited_output']:,}")
    print(f"  瓶颈: {result['bottleneck']}")
    print(f"  总良率: {result['overall_yield']}%")
    
    # 计算可以支持的 GPU 数量（每 GPU 8 栈 HBM）
    gpu_count = result['cowos_limited_output'] // 8
    print(f"  可支持 GPU 数量: {gpu_count:,}（每 GPU 8 栈）")

"""
GPU 集群 MFU 分析与优化
计算不同集群规模下的 Model FLOPs Utilization
"""
import numpy as np

class GPUClusterAnalyzer:
    """分析 GPU 集群效率和瓶颈"""
    
    def __init__(self, gpu_count: int, tflops_per_gpu: float, 
                 nvlink_bandwidth_gbps: float, network_bandwidth_gbps: float):
        self.gpu_count = gpu_count
        self.tflops_per_gpu = tflops_per_gpu
        self.nvlink_bw = nvlink_bandwidth_gbps
        self.network_bw = network_bandwidth_gbps
        
    def analyze_training_efficiency(self, model_params_b: float, 
                                     batch_size_per_gpu: int,
                                     sequence_length: int = 4096) -> dict:
        """分析训练效率"""
        
        # 总计算能力
        total_tflops = self.gpu_count * self.tflops_per_gpu
        
        # 假设通信开销模型
        # All-Reduce 通信量 ≈ 2 × 参数量 × (1 - 1/N) per step
        params_bytes = model_params_b * 1e9 * 2  # FP16
        
        # 每 step 的通信量（简化模型）
        comm_volume = 2 * params_bytes * (1 - 1/self.gpu_count)
        comm_volume_gb = comm_volume / 1e9
        
        # 节点内通信（NVLink）vs 节点间通信（InfiniBand）
        gpus_per_node = 8
        num_nodes = self.gpu_count // gpus_per_node
        
        # 节点内通信比例（取决于模型并行策略）
        intra_node_ratio = 0.7  # 70% 通信在节点内
        intra_node_time = (comm_volume_gb * intra_node_ratio) / (self.nvlink_bw * 1e3)  # ms
        inter_node_time = (comm_volume_gb * (1 - intra_node_ratio)) / (self.network_bw * 1e3)  # ms
        
        total_comm_time = intra_node_time + inter_node_time
        
        # 计算时间（每 step）
        ops_per_step = 6 * model_params_b * 1e9 * batch_size_per_gpu * sequence_length
        compute_time = ops_per_step / (total_tflops * 1e12) * 1000  # ms
        
        # MFU = 计算时间 / (计算时间 + 通信时间)
        step_time = compute_time + total_comm_time
        mfu = compute_time / step_time * 100
        
        return {
            "cluster_size": self.gpu_count,
            "total_tflops": total_tflops,
            "num_nodes": num_nodes,
            "comm_per_step_gb": round(comm_volume_gb, 2),
            "intra_node_comm_ms": round(intra_node_time, 2),
            "inter_node_comm_ms": round(inter_node_time, 2),
            "total_comm_ms": round(total_comm_time, 2),
            "compute_time_ms": round(compute_time, 2),
            "step_time_ms": round(step_time, 2),
            "mfu_pct": round(mfu, 1),
            "bottleneck": "communication" if total_comm_time > compute_time * 0.2 else "compute",
        }

print("=" * 80)
print("GPU 集群训练效率分析")
print("=" * 80)

# 对比不同规模集群
configs = [
    (8, 3958, 900, 400),     # 单节点 H100
    (64, 3958, 900, 400),    # 8 节点 H100
    (512, 3958, 900, 400),   # 64 节点 H100
    (4096, 3958, 900, 400),  # 512 节点 H100
]

for gpus, tflops, nvlink, network in configs:
    analyzer = GPUClusterAnalyzer(gpus, tflops, nvlink, network)
    result = analyzer.analyze_training_efficiency(
        model_params_b=70, batch_size_per_gpu=4
    )
    print(f"\n{gpus} GPU 集群 (H100 × {gpus})")
    print(f"  总算力: {result['total_tflops']:,.0f} TFLOPS")
    print(f"  节点数: {result['num_nodes']}")
    print(f"  每 step 通信量: {result['comm_per_step_gb']} GB")
    print(f"  节点内通信: {result['intra_node_comm_ms']} ms")
    print(f"  节点间通信: {result['inter_node_comm_ms']} ms")
    print(f"  计算时间: {result['compute_time_ms']} ms")
    print(f"  MFU: {result['mfu_pct']}%")
    print(f"  瓶颈: {result['bottleneck']}")