797 lines
28 KiB
Python
797 lines
28 KiB
Python
import os
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import sys
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import uuid
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import time
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import math
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import multiprocessing
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from typing import List, Optional, Union, Generator, Sequence, Iterator
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from collections import deque
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from . import llama_cpp
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from .llama_types import *
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class Llama:
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"""High-level Python wrapper for a llama.cpp model."""
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def __init__(
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self,
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model_path: str,
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# NOTE: These parameters are likely to change in the future.
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n_ctx: int = 512,
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n_parts: int = -1,
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seed: int = 1337,
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f16_kv: bool = False,
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logits_all: bool = False,
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vocab_only: bool = False,
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use_mmap: bool = True,
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use_mlock: bool = False,
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embedding: bool = False,
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n_threads: Optional[int] = None,
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n_batch: int = 8,
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last_n_tokens_size: int = 64,
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verbose: bool = True,
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):
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"""Load a llama.cpp model from `model_path`.
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Args:
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model_path: Path to the model.
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n_ctx: Maximum context size.
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n_parts: Number of parts to split the model into. If -1, the number of parts is automatically determined.
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seed: Random seed. 0 for random.
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f16_kv: Use half-precision for key/value cache.
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logits_all: Return logits for all tokens, not just the last token.
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vocab_only: Only load the vocabulary no weights.
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use_mmap: Use mmap if possible.
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use_mlock: Force the system to keep the model in RAM.
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embedding: Embedding mode only.
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n_threads: Number of threads to use. If None, the number of threads is automatically determined.
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n_batch: Maximum number of prompt tokens to batch together when calling llama_eval.
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last_n_tokens_size: Maximum number of tokens to keep in the last_n_tokens deque.
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verbose: Print verbose output to stderr.
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Raises:
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ValueError: If the model path does not exist.
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Returns:
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A Llama instance.
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"""
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self.verbose = verbose
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self.model_path = model_path
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self.params = llama_cpp.llama_context_default_params()
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self.params.n_ctx = n_ctx
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self.params.n_parts = n_parts
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self.params.seed = seed
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self.params.f16_kv = f16_kv
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self.params.logits_all = logits_all
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self.params.vocab_only = vocab_only
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self.params.use_mmap = use_mmap
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self.params.use_mlock = use_mlock
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self.params.embedding = embedding
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self.last_n_tokens_size = last_n_tokens_size
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self.last_n_tokens_data = deque(
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[llama_cpp.llama_token(0)] * self.last_n_tokens_size,
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maxlen=self.last_n_tokens_size,
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)
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self.tokens_consumed = 0
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self.n_batch = min(n_ctx, n_batch)
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self.n_tokens = 0
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self.n_past = 0
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self.all_logits: List[List[float]] = [] # TODO: Use an array instead of a list.
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self.n_threads = n_threads or max(multiprocessing.cpu_count() // 2, 1)
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if not os.path.exists(model_path):
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raise ValueError(f"Model path does not exist: {model_path}")
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self.ctx = llama_cpp.llama_init_from_file(
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self.model_path.encode("utf-8"), self.params
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)
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if self.verbose:
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print(llama_cpp.llama_print_system_info().decode("utf-8"), file=sys.stderr)
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def tokenize(self, text: bytes) -> List[llama_cpp.llama_token]:
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"""Tokenize a string.
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Args:
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text: The utf-8 encoded string to tokenize.
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Raises:
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RuntimeError: If the tokenization failed.
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Returns:
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A list of tokens.
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"""
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assert self.ctx is not None
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n_ctx = llama_cpp.llama_n_ctx(self.ctx)
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tokens = (llama_cpp.llama_token * int(n_ctx))()
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n_tokens = llama_cpp.llama_tokenize(
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self.ctx,
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text,
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tokens,
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n_ctx,
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llama_cpp.c_bool(True),
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)
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if int(n_tokens) < 0:
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raise RuntimeError(f'Failed to tokenize: text="{text}" n_tokens={n_tokens}')
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return list(tokens[:n_tokens])
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def detokenize(self, tokens: List[llama_cpp.llama_token]) -> bytes:
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"""Detokenize a list of tokens.
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Args:
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tokens: The list of tokens to detokenize.
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Returns:
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The detokenized string.
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"""
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assert self.ctx is not None
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output = b""
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for token in tokens:
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output += llama_cpp.llama_token_to_str(self.ctx, token)
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return output
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def reset(self):
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"""Reset the model state."""
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self.last_n_tokens_data.extend(
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[llama_cpp.llama_token(0)] * self.last_n_tokens_size
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)
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self.tokens_consumed = 0
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self.n_tokens = 0
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self.n_past = 0
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self.all_logits = []
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def eval(self, tokens: Sequence[llama_cpp.llama_token]):
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"""Evaluate a list of tokens.
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Args:
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tokens: The list of tokens to evaluate.
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"""
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assert self.ctx is not None
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n_ctx = int(llama_cpp.llama_n_ctx(self.ctx))
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for i in range(0, len(tokens), self.n_batch):
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batch = tokens[i : min(len(tokens), i + self.n_batch)]
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self.n_past = min(n_ctx - len(batch), self.tokens_consumed)
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self.n_tokens = len(batch)
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return_code = llama_cpp.llama_eval(
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ctx=self.ctx,
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tokens=(llama_cpp.llama_token * len(batch))(*batch),
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n_tokens=llama_cpp.c_int(self.n_tokens),
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n_past=llama_cpp.c_int(self.n_past),
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n_threads=llama_cpp.c_int(self.n_threads),
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)
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if int(return_code) != 0:
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raise RuntimeError(f"llama_eval returned {return_code}")
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self.last_n_tokens_data.extend(batch)
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self.tokens_consumed += len(batch)
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if self.params.logits_all:
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self.all_logits.extend(self._logits())
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def _logits(self) -> List[List[float]]:
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"""Return the logits from the last call to llama_eval."""
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assert self.ctx is not None
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n_vocab = llama_cpp.llama_n_vocab(self.ctx)
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cols = int(n_vocab)
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rows = self.n_tokens if self.params.logits_all else 1
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logits_view = llama_cpp.llama_get_logits(self.ctx)
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logits = [[logits_view[i * cols + j] for j in range(cols)] for i in range(rows)]
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return logits
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def sample(
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self,
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top_k: int,
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top_p: float,
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temp: float,
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repeat_penalty: float,
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):
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"""Sample a token from the model.
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Args:
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top_k: The top-k sampling parameter.
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top_p: The top-p sampling parameter.
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temp: The temperature parameter.
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repeat_penalty: The repeat penalty parameter.
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Returns:
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The sampled token.
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"""
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assert self.ctx is not None
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return llama_cpp.llama_sample_top_p_top_k(
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ctx=self.ctx,
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last_n_tokens_data=(llama_cpp.llama_token * self.last_n_tokens_size)(
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*self.last_n_tokens_data
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),
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last_n_tokens_size=llama_cpp.c_int(self.last_n_tokens_size),
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top_k=llama_cpp.c_int(top_k),
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top_p=llama_cpp.c_float(top_p),
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temp=llama_cpp.c_float(temp),
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repeat_penalty=llama_cpp.c_float(repeat_penalty),
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)
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def generate(
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self,
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tokens: Sequence[llama_cpp.llama_token],
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top_k: int,
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top_p: float,
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temp: float,
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repeat_penalty: float,
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reset: bool = True,
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) -> Generator[
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llama_cpp.llama_token, Optional[Sequence[llama_cpp.llama_token]], None
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]:
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"""Create a generator of tokens from a prompt.
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Examples:
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>>> llama = Llama("models/ggml-7b.bin")
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>>> tokens = llama.tokenize(b"Hello, world!")
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>>> for token in llama.generate(tokens, top_k=40, top_p=0.95, temp=1.0, repeat_penalty=1.1):
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... print(llama.detokenize([token]))
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Args:
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tokens: The prompt tokens.
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top_k: The top-k sampling parameter.
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top_p: The top-p sampling parameter.
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temp: The temperature parameter.
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repeat_penalty: The repeat penalty parameter.
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reset: Whether to reset the model state.
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Yields:
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The generated tokens.
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"""
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assert self.ctx is not None
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if reset:
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self.reset()
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while True:
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self.eval(tokens)
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token = self.sample(
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top_k=top_k,
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top_p=top_p,
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temp=temp,
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repeat_penalty=repeat_penalty,
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)
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tokens_or_none = yield token
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tokens = [token]
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if tokens_or_none is not None:
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tokens.extend(tokens_or_none)
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def create_embedding(self, input: str) -> Embedding:
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"""Embed a string.
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Args:
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input: The utf-8 encoded string to embed.
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Returns:
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An embedding object.
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"""
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assert self.ctx is not None
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if self.params.embedding == False:
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raise RuntimeError(
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"Llama model must be created with embedding=True to call this method"
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)
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if self.verbose:
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llama_cpp.llama_reset_timings(self.ctx)
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tokens = self.tokenize(input.encode("utf-8"))
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self.reset()
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self.eval(tokens)
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n_tokens = len(tokens)
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embedding = llama_cpp.llama_get_embeddings(self.ctx)[
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: llama_cpp.llama_n_embd(self.ctx)
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]
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if self.verbose:
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llama_cpp.llama_print_timings(self.ctx)
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return {
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"object": "list",
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"data": [
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{
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"object": "embedding",
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"embedding": embedding,
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"index": 0,
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}
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],
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"model": self.model_path,
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"usage": {
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"prompt_tokens": n_tokens,
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"total_tokens": n_tokens,
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},
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}
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def embed(self, input: str) -> List[float]:
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"""Embed a string.
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Args:
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input: The utf-8 encoded string to embed.
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Returns:
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A list of embeddings
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"""
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return list(map(float, self.create_embedding(input)["data"][0]["embedding"]))
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def _create_completion(
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self,
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prompt: str,
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suffix: Optional[str] = None,
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max_tokens: int = 16,
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temperature: float = 0.8,
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top_p: float = 0.95,
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logprobs: Optional[int] = None,
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echo: bool = False,
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stop: List[str] = [],
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repeat_penalty: float = 1.1,
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top_k: int = 40,
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stream: bool = False,
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) -> Union[Iterator[Completion], Iterator[CompletionChunk]]:
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assert self.ctx is not None
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completion_id = f"cmpl-{str(uuid.uuid4())}"
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created = int(time.time())
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completion_tokens: List[llama_cpp.llama_token] = []
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# Add blank space to start of prompt to match OG llama tokenizer
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prompt_tokens = self.tokenize(b" " + prompt.encode("utf-8"))
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text = b""
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returned_characters = 0
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if self.verbose:
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llama_cpp.llama_reset_timings(self.ctx)
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if len(prompt_tokens) + max_tokens > int(llama_cpp.llama_n_ctx(self.ctx)):
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raise ValueError(
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f"Requested tokens exceed context window of {llama_cpp.llama_n_ctx(self.ctx)}"
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)
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if stop != []:
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stop_sequences = [s.encode("utf-8") for s in stop]
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else:
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stop_sequences = []
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text_offset = 0
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text_offsets: List[int] = []
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token_logprobs: List[float] = []
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tokens: List[str] = []
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top_logprobs: List[Dict[str, float]] = []
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self.reset()
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self.eval(prompt_tokens)
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if logprobs is not None and self.params.logits_all is False:
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raise ValueError(
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"logprobs is not supported for models created with logits_all=False"
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)
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if logprobs is not None:
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token_strs = [
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self.detokenize([token]).decode("utf-8") for token in prompt_tokens
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]
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logprobs_all = [
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[Llama.logit_to_logprob(logit) for logit in row]
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for row in self.all_logits
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]
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for token, token_str, logprobs_token in zip(
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prompt_tokens, token_strs, logprobs_all
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):
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text_offsets.append(text_offset)
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text_offset += len(token_str)
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tokens.append(token_str)
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sorted_logprobs = list(
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sorted(
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zip(logprobs_token, range(len(logprobs_token))), reverse=True
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)
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)
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token_logprobs.append(sorted_logprobs[int(token)][0])
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top_logprob = {
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self.detokenize([llama_cpp.llama_token(i)]).decode("utf-8"): logprob
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for logprob, i in sorted_logprobs[:logprobs]
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}
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top_logprob.update({token_str: sorted_logprobs[int(token)][0]})
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top_logprobs.append(top_logprob)
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finish_reason = "length"
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while True:
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token = self.sample(
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top_k=top_k,
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top_p=top_p,
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temp=temperature,
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repeat_penalty=repeat_penalty,
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)
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if token == llama_cpp.llama_token_eos():
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text = self.detokenize(completion_tokens)
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finish_reason = "stop"
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break
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completion_tokens.append(token)
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all_text = self.detokenize(completion_tokens)
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any_stop = [s for s in stop_sequences if s in all_text]
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if len(any_stop) > 0:
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first_stop = any_stop[0]
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text = all_text[: all_text.index(first_stop)]
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finish_reason = "stop"
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break
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if stream:
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start = returned_characters
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longest = 0
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# We want to avoid yielding any characters from
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# the generated text if they are part of a stop
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# sequence.
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for s in stop_sequences:
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for i in range(len(s), 0, -1):
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if all_text.endswith(s[:i]):
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if i > longest:
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longest = i
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break
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text = all_text[: len(all_text) - longest]
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returned_characters += len(text[start:])
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yield {
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"id": completion_id,
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"object": "text_completion",
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"created": created,
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"model": self.model_path,
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"choices": [
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{
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"text": text[start:].decode("utf-8"),
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"index": 0,
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"logprobs": None,
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"finish_reason": None,
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}
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],
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}
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if logprobs is not None:
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# TODO: Confirm wether this should happen before or after
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# next eval.
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token_str = self.detokenize([token]).decode("utf-8")
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text_offsets.append(text_offset)
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text_offset += len(token_str)
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tokens.append(token_str)
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logprobs_token = [
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Llama.logit_to_logprob(logit) for logit in self.all_logits[-1]
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]
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sorted_logprobs = list(
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sorted(
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zip(logprobs_token, range(len(logprobs_token))), reverse=True
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)
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)
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token_logprobs.append(sorted_logprobs[int(token)][0])
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top_logprob = {
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self.detokenize([llama_cpp.llama_token(i)]).decode("utf-8"): logprob
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for logprob, i in sorted_logprobs[:logprobs]
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}
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top_logprob.update({token_str: logprobs_token[int(token)]})
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top_logprobs.append(top_logprob)
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if len(completion_tokens) >= max_tokens:
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text = self.detokenize(completion_tokens)
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finish_reason = "length"
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break
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self.eval([token])
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if stream:
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yield {
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"id": completion_id,
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"object": "text_completion",
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"created": created,
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"model": self.model_path,
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"choices": [
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{
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"text": text[returned_characters:].decode("utf-8"),
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"index": 0,
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"logprobs": None,
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"finish_reason": finish_reason,
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}
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],
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}
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return
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text = text.decode("utf-8")
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if echo:
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text = prompt + text
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if suffix is not None:
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text = text + suffix
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logprobs_or_none: Optional[CompletionLogprobs] = None
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if logprobs is not None:
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logprobs_or_none = {
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"tokens": tokens,
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"text_offset": text_offsets,
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"token_logprobs": token_logprobs,
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"top_logprobs": top_logprobs,
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}
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if self.verbose:
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llama_cpp.llama_print_timings(self.ctx)
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yield {
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"id": completion_id,
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"object": "text_completion",
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"created": created,
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"model": self.model_path,
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"choices": [
|
|
{
|
|
"text": text,
|
|
"index": 0,
|
|
"logprobs": logprobs_or_none,
|
|
"finish_reason": finish_reason,
|
|
}
|
|
],
|
|
"usage": {
|
|
"prompt_tokens": len(prompt_tokens),
|
|
"completion_tokens": len(completion_tokens),
|
|
"total_tokens": len(prompt_tokens) + len(completion_tokens),
|
|
},
|
|
}
|
|
|
|
def create_completion(
|
|
self,
|
|
prompt: str,
|
|
suffix: Optional[str] = None,
|
|
max_tokens: int = 128,
|
|
temperature: float = 0.8,
|
|
top_p: float = 0.95,
|
|
logprobs: Optional[int] = None,
|
|
echo: bool = False,
|
|
stop: List[str] = [],
|
|
repeat_penalty: float = 1.1,
|
|
top_k: int = 40,
|
|
stream: bool = False,
|
|
) -> Union[Completion, Iterator[CompletionChunk]]:
|
|
"""Generate text from a prompt.
|
|
|
|
Args:
|
|
prompt: The prompt to generate text from.
|
|
suffix: A suffix to append to the generated text. If None, no suffix is appended.
|
|
max_tokens: The maximum number of tokens to generate.
|
|
temperature: The temperature to use for sampling.
|
|
top_p: The top-p value to use for sampling.
|
|
logprobs: The number of logprobs to return. If None, no logprobs are returned.
|
|
echo: Whether to echo the prompt.
|
|
stop: A list of strings to stop generation when encountered.
|
|
repeat_penalty: The penalty to apply to repeated tokens.
|
|
top_k: The top-k value to use for sampling.
|
|
stream: Whether to stream the results.
|
|
|
|
Raises:
|
|
ValueError: If the requested tokens exceed the context window.
|
|
RuntimeError: If the prompt fails to tokenize or the model fails to evaluate the prompt.
|
|
|
|
Returns:
|
|
Response object containing the generated text.
|
|
"""
|
|
completion_or_chunks = self._create_completion(
|
|
prompt=prompt,
|
|
suffix=suffix,
|
|
max_tokens=max_tokens,
|
|
temperature=temperature,
|
|
top_p=top_p,
|
|
logprobs=logprobs,
|
|
echo=echo,
|
|
stop=stop,
|
|
repeat_penalty=repeat_penalty,
|
|
top_k=top_k,
|
|
stream=stream,
|
|
)
|
|
if stream:
|
|
chunks: Iterator[CompletionChunk] = completion_or_chunks
|
|
return chunks
|
|
completion: Completion = next(completion_or_chunks) # type: ignore
|
|
return completion
|
|
|
|
def __call__(
|
|
self,
|
|
prompt: str,
|
|
suffix: Optional[str] = None,
|
|
max_tokens: int = 128,
|
|
temperature: float = 0.8,
|
|
top_p: float = 0.95,
|
|
logprobs: Optional[int] = None,
|
|
echo: bool = False,
|
|
stop: List[str] = [],
|
|
repeat_penalty: float = 1.1,
|
|
top_k: int = 40,
|
|
stream: bool = False,
|
|
) -> Union[Completion, Iterator[CompletionChunk]]:
|
|
"""Generate text from a prompt.
|
|
|
|
Args:
|
|
prompt: The prompt to generate text from.
|
|
suffix: A suffix to append to the generated text. If None, no suffix is appended.
|
|
max_tokens: The maximum number of tokens to generate.
|
|
temperature: The temperature to use for sampling.
|
|
top_p: The top-p value to use for sampling.
|
|
logprobs: The number of logprobs to return. If None, no logprobs are returned.
|
|
echo: Whether to echo the prompt.
|
|
stop: A list of strings to stop generation when encountered.
|
|
repeat_penalty: The penalty to apply to repeated tokens.
|
|
top_k: The top-k value to use for sampling.
|
|
stream: Whether to stream the results.
|
|
|
|
Raises:
|
|
ValueError: If the requested tokens exceed the context window.
|
|
RuntimeError: If the prompt fails to tokenize or the model fails to evaluate the prompt.
|
|
|
|
Returns:
|
|
Response object containing the generated text.
|
|
"""
|
|
return self.create_completion(
|
|
prompt=prompt,
|
|
suffix=suffix,
|
|
max_tokens=max_tokens,
|
|
temperature=temperature,
|
|
top_p=top_p,
|
|
logprobs=logprobs,
|
|
echo=echo,
|
|
stop=stop,
|
|
repeat_penalty=repeat_penalty,
|
|
top_k=top_k,
|
|
stream=stream,
|
|
)
|
|
|
|
def _convert_text_completion_to_chat(
|
|
self, completion: Completion
|
|
) -> ChatCompletion:
|
|
return {
|
|
"id": "chat" + completion["id"],
|
|
"object": "chat.completion",
|
|
"created": completion["created"],
|
|
"model": completion["model"],
|
|
"choices": [
|
|
{
|
|
"index": 0,
|
|
"message": {
|
|
"role": "assistant",
|
|
"content": completion["choices"][0]["text"],
|
|
},
|
|
"finish_reason": completion["choices"][0]["finish_reason"],
|
|
}
|
|
],
|
|
"usage": completion["usage"],
|
|
}
|
|
|
|
def _convert_text_completion_chunks_to_chat(
|
|
self,
|
|
chunks: Iterator[CompletionChunk],
|
|
) -> Iterator[ChatCompletionChunk]:
|
|
for i, chunk in enumerate(chunks):
|
|
if i == 0:
|
|
yield {
|
|
"id": "chat" + chunk["id"],
|
|
"model": chunk["model"],
|
|
"created": chunk["created"],
|
|
"object": "chat.completion.chunk",
|
|
"choices": [
|
|
{
|
|
"index": 0,
|
|
"delta": {
|
|
"role": "assistant",
|
|
},
|
|
"finish_reason": None,
|
|
}
|
|
],
|
|
}
|
|
yield {
|
|
"id": "chat" + chunk["id"],
|
|
"model": chunk["model"],
|
|
"created": chunk["created"],
|
|
"object": "chat.completion.chunk",
|
|
"choices": [
|
|
{
|
|
"index": 0,
|
|
"delta": {
|
|
"content": chunk["choices"][0]["text"],
|
|
},
|
|
"finish_reason": chunk["choices"][0]["finish_reason"],
|
|
}
|
|
],
|
|
}
|
|
|
|
def create_chat_completion(
|
|
self,
|
|
messages: List[ChatCompletionMessage],
|
|
temperature: float = 0.8,
|
|
top_p: float = 0.95,
|
|
top_k: int = 40,
|
|
stream: bool = False,
|
|
stop: List[str] = [],
|
|
max_tokens: int = 128,
|
|
repeat_penalty: float = 1.1,
|
|
) -> Union[ChatCompletion, Iterator[ChatCompletionChunk]]:
|
|
"""Generate a chat completion from a list of messages.
|
|
|
|
Args:
|
|
messages: A list of messages to generate a response for.
|
|
temperature: The temperature to use for sampling.
|
|
top_p: The top-p value to use for sampling.
|
|
top_k: The top-k value to use for sampling.
|
|
stream: Whether to stream the results.
|
|
stop: A list of strings to stop generation when encountered.
|
|
max_tokens: The maximum number of tokens to generate.
|
|
repeat_penalty: The penalty to apply to repeated tokens.
|
|
|
|
Returns:
|
|
Generated chat completion or a stream of chat completion chunks.
|
|
"""
|
|
instructions = """Complete the following chat conversation between the user and the assistant. System messages should be strictly followed as additional instructions."""
|
|
chat_history = "\n".join(
|
|
f'{message["role"]} {message.get("user", "")}: {message["content"]}'
|
|
for message in messages
|
|
)
|
|
PROMPT = f" \n\n### Instructions:{instructions}\n\n### Inputs:{chat_history}\n\n### Response:\nassistant: "
|
|
PROMPT_STOP = ["###", "\nuser: ", "\nassistant: ", "\nsystem: "]
|
|
completion_or_chunks = self(
|
|
prompt=PROMPT,
|
|
stop=PROMPT_STOP + stop,
|
|
temperature=temperature,
|
|
top_p=top_p,
|
|
top_k=top_k,
|
|
stream=stream,
|
|
max_tokens=max_tokens,
|
|
repeat_penalty=repeat_penalty,
|
|
)
|
|
if stream:
|
|
chunks: Iterator[CompletionChunk] = completion_or_chunks # type: ignore
|
|
return self._convert_text_completion_chunks_to_chat(chunks)
|
|
else:
|
|
completion: Completion = completion_or_chunks # type: ignore
|
|
return self._convert_text_completion_to_chat(completion)
|
|
|
|
def __del__(self):
|
|
if self.ctx is not None:
|
|
llama_cpp.llama_free(self.ctx)
|
|
self.ctx = None
|
|
|
|
def __getstate__(self):
|
|
return dict(
|
|
verbose=self.verbose,
|
|
model_path=self.model_path,
|
|
n_ctx=self.params.n_ctx,
|
|
n_parts=self.params.n_parts,
|
|
seed=self.params.seed,
|
|
f16_kv=self.params.f16_kv,
|
|
logits_all=self.params.logits_all,
|
|
vocab_only=self.params.vocab_only,
|
|
use_mmap=self.params.use_mmap,
|
|
use_mlock=self.params.use_mlock,
|
|
embedding=self.params.embedding,
|
|
last_n_tokens_size=self.last_n_tokens_size,
|
|
n_batch=self.n_batch,
|
|
n_threads=self.n_threads,
|
|
)
|
|
|
|
def __setstate__(self, state):
|
|
self.__init__(
|
|
model_path=state["model_path"],
|
|
n_ctx=state["n_ctx"],
|
|
n_parts=state["n_parts"],
|
|
seed=state["seed"],
|
|
f16_kv=state["f16_kv"],
|
|
logits_all=state["logits_all"],
|
|
vocab_only=state["vocab_only"],
|
|
use_mmap=state["use_mmap"],
|
|
use_mlock=state["use_mlock"],
|
|
embedding=state["embedding"],
|
|
n_threads=state["n_threads"],
|
|
n_batch=state["n_batch"],
|
|
last_n_tokens_size=state["last_n_tokens_size"],
|
|
verbose=state["verbose"],
|
|
)
|
|
|
|
@staticmethod
|
|
def token_eos() -> llama_cpp.llama_token:
|
|
"""Return the end-of-sequence token."""
|
|
return llama_cpp.llama_token_eos()
|
|
|
|
@staticmethod
|
|
def token_bos() -> llama_cpp.llama_token:
|
|
"""Return the beginning-of-sequence token."""
|
|
return llama_cpp.llama_token_bos()
|
|
|
|
@staticmethod
|
|
def logit_to_logprob(x: float) -> float:
|
|
return math.log(1.0 + math.exp(x))
|