Support Thinking Budget (via custom_logit_processor for OpenAI API) [Fix #6572] (#11416)

Signed-off-by: ybyang <ybyang7@iflytek.com>
Co-authored-by: YorkSu <york_su@qq.com>

docs/basic_usage/deepseek.md

@@ -235,6 +235,44 @@ Important Notes:
 2. To receive more consistent tool call results, it is recommended to use `--chat-template examples/chat_template/tool_chat_template_deepseekv3.jinja`. It provides an improved unified prompt.
 
 
+### Thinking Budget for DeepSeek R1
+
+In SGLang, we can implement thinking budget with `CustomLogitProcessor`.
+
+Launch a server with `--enable-custom-logit-processor` flag on.
+
+```
+python3 -m sglang.launch_server --model deepseek-ai/DeepSeek-R1 --tp 8 --port 30000 --host 0.0.0.0 --mem-fraction-static 0.9 --disable-cuda-graph --reasoning-parser deepseek-r1 --enable-custom-logit-processor
+```
+
+Sample Request:
+
+```python
+import openai
+from rich.pretty import pprint
+from sglang.srt.sampling.custom_logit_processor import DeepSeekR1ThinkingBudgetLogitProcessor
+
+
+client = openai.Client(base_url="http://127.0.0.1:30000/v1", api_key="*")
+response = client.chat.completions.create(
+    model="deepseek-ai/DeepSeek-R1",
+    messages=[
+        {
+            "role": "user",
+            "content": "Question: Is Paris the Capital of France?",
+        }
+    ],
+    max_tokens=1024,
+    extra_body={
+        "custom_logit_processor": DeepSeekR1ThinkingBudgetLogitProcessor().to_str(),
+        "custom_params": {
+            "thinking_budget": 512,
+        },
+    },
+)
+pprint(response)
+```
+
 ## FAQ
 
 **Q: Model loading is taking too long, and I'm encountering an NCCL timeout. What should I do?**

docs/basic_usage/sampling_params.md

@@ -319,3 +319,27 @@ response = requests.post(
 )
 print(response.json())
 ```
+
+Send an OpenAI chat completion request:
+
+```python
+import openai
+from sglang.utils import print_highlight
+
+client = openai.Client(base_url="http://127.0.0.1:30000/v1", api_key="None")
+
+response = client.chat.completions.create(
+    model="meta-llama/Meta-Llama-3-8B-Instruct",
+    messages=[
+        {"role": "user", "content": "List 3 countries and their capitals."},
+    ],
+    temperature=0.0,
+    max_tokens=32,
+    extra_body={
+        "custom_logit_processor": DeterministicLogitProcessor().to_str(),
+        "custom_params": {"token_id": 5},
+    },
+)
+
+print_highlight(f"Response: {response}")
+```