[API, Feature] Support response prefill for openai API (#1490)

python/sglang/srt/openai_api/adapter.py

@@ -858,11 +858,18 @@ def v1_chat_generate_request(
                                 openai_compatible_messages.append(
                                     {"role": message.role, "content": content["text"]}
                                 )
+                if openai_compatible_messages[-1]["role"] == "assistant":
+                    assistant_prefix = openai_compatible_messages[-1]["content"]
+                    openai_compatible_messages = openai_compatible_messages[:-1]
+                else:
+                    assistant_prefix = None
                 prompt_ids = tokenizer_manager.tokenizer.apply_chat_template(
                     openai_compatible_messages,
                     tokenize=True,
                     add_generation_prompt=True,
                 )
+                if assistant_prefix:
+                    prompt_ids += tokenizer_manager.tokenizer.encode(assistant_prefix)
                 stop = request.stop
                 image_data = None
                 modalities = []