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import numpy as np
import matplotlib.pyplot as plt
def kv_cache_size_bytes(bs, seq):
"""计算 Qwen2ForCausalLM 模型的 KV cache 大小（字节）"""
n_layers = 28
n_kv_heads = 2
hidden_size = 1536
num_attention_heads = 12
head_dim = hidden_size // num_attention_heads
bytes_per_elem = 2 # bfloat16
return bs * seq * n_kv_heads * head_dim * 2 * n_layers * bytes_per_elem
# ===== Prefill 数据 =====
# seq=640
avg_ns_prefill_640 = np.array([
1418534991, 1033939782, 494241378, 252646178, 135127951,
69450854, 42089250, 35031755, 28423503, 22718985, 15558545
], dtype=np.float64)
bs_prefill_640 = np.array([1024, 512, 256, 128, 64, 32, 16, 8, 4, 2, 1])
seq_prefill_640 = 640
throughput_prefill_640 = bs_prefill_640 * seq_prefill_640 / (avg_ns_prefill_640 * 1e-9)
norm_prefill_640 = throughput_prefill_640 / throughput_prefill_640.max()
kv_prefill_640 = kv_cache_size_bytes(bs_prefill_640, seq_prefill_640) / 1024**3 # 改成 GB
# seq=1152
# avg_ns_prefill_1152 = np.array([
# 2423366261, 1417657581, 1040325509, 389808438, 200051514,
# 110723882, 61663721, 39934013, 30382401, 21185162, 15818426
# ], dtype=np.float64)
# bs_prefill_1152 = np.array([1024, 512, 256, 128, 64, 32, 16, 8, 4, 2, 1])
avg_ns_prefill_1152 = np.array([
1417657581, 1040325509, 389808438, 200051514,
110723882, 61663721, 39934013, 30382401, 21185162, 15818426
], dtype=np.float64)
bs_prefill_1152 = np.array([ 512, 256, 128, 64, 32, 16, 8, 4, 2, 1])
seq_prefill_1152 = 1152
throughput_prefill_1152 = bs_prefill_1152 * seq_prefill_1152 / (avg_ns_prefill_1152 * 1e-9)
norm_prefill_1152 = throughput_prefill_1152 / throughput_prefill_1152.max()
kv_prefill_1152 = kv_cache_size_bytes(bs_prefill_1152, seq_prefill_1152) / 1024**3 # 改成 GB
# ===== Decoding 数据 =====
# seq=512
avg_ns_decoding_512 = np.array([
25285906551, 12679311252, 7440608085, 4841914697, 4272889441,
3997075015, 3825710172, 3726603655, 3648294896, 3635960724, 3319210677
], dtype=np.float64)
bs_decoding_512 = np.array([1024, 512, 256, 128, 64, 32, 16, 8, 2, 4, 1])
seq_decoding_512 = 512
throughput_decoding_512 = bs_decoding_512 * seq_decoding_512 / (avg_ns_decoding_512 * 1e-9)
norm_decoding_512 = throughput_decoding_512 / throughput_decoding_512.max()
kv_decoding_512 = kv_cache_size_bytes(bs_decoding_512, seq_decoding_512) / 1024**3 # 改成 GB
# seq=1024
# avg_ns_decoding_1024 = np.array([
# 65019709544, 30598009745, 16552100314, 11165129518, 8835508288,
# 8037503827, 8020861613, 7502439278, 7275415153, 7204870191, 6423331403
# ], dtype=np.float64)
# bs_decoding_1024 = np.array([1024, 512, 256, 128, 64, 32, 16, 8, 4, 2, 1])
avg_ns_decoding_1024 = np.array([
30598009745, 16552100314, 11165129518, 8835508288,
8037503827, 8020861613, 7502439278, 7275415153, 7204870191, 6423331403
], dtype=np.float64)
bs_decoding_1024 = np.array([ 512, 256, 128, 64, 32, 16, 8, 4, 2, 1])
seq_decoding_1024 = 1024
throughput_decoding_1024 = bs_decoding_1024 * seq_decoding_1024 / (avg_ns_decoding_1024 * 1e-9)
norm_decoding_1024 = throughput_decoding_1024 / throughput_decoding_1024.max()
kv_decoding_1024 = kv_cache_size_bytes(bs_decoding_1024, seq_decoding_1024) / 1024**3 # 改成 GB
# ===== 绘图 =====
fig, axes = plt.subplots(1, 2, figsize=(14, 5))
# Prefill 子图
axes[0].plot(kv_prefill_640, norm_prefill_640, marker='o', label="seq=640")
axes[0].plot(kv_prefill_1152, norm_prefill_1152, marker='s', label="seq=1152")
axes[0].set_xscale('log')
axes[0].set_xlabel("KV Cache Size (GB, log scale)")
axes[0].set_ylabel("Normalized GPU Utilization")
axes[0].set_title("Prefill")
axes[0].grid(True, which="both", ls="--", alpha=0.5)
axes[0].legend()
# Decoding 子图
axes[1].plot(kv_decoding_512, norm_decoding_512, marker='o', label="seq=512")
axes[1].plot(kv_decoding_1024, norm_decoding_1024, marker='s', label="seq=1024")
axes[1].set_xscale('log')
axes[1].set_xlabel("KV Cache Size (GB, log scale)")
axes[1].set_ylabel("Normalized GPU Utilization")
axes[1].set_title("Decoding")
axes[1].grid(True, which="both", ls="--", alpha=0.5)
axes[1].legend()
plt.suptitle("Normalized GPU Utilization vs KV Cache Size")
plt.savefig("kv_cache_vs_util_gb.png", dpi=300, bbox_inches='tight')
plt.savefig("kv_cache_vs_util_gb.pdf", dpi=300, bbox_inches='tight')
plt.show()
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