# pragma pylint: disable=missing-docstring, W0212, too-many-arguments """ This module contains the backtesting logic """ import logging from collections import defaultdict from copy import deepcopy from datetime import datetime, timedelta, timezone from typing import Any, Dict, List, Optional, Tuple from pandas import DataFrame from freqtrade.configuration import TimeRange, validate_config_consistency from freqtrade.constants import DATETIME_PRINT_FORMAT from freqtrade.data import history from freqtrade.data.btanalysis import trade_list_to_dataframe from freqtrade.data.converter import trim_dataframe, trim_dataframes from freqtrade.data.dataprovider import DataProvider from freqtrade.enums import BacktestState, SellType from freqtrade.exceptions import DependencyException, OperationalException from freqtrade.exchange import timeframe_to_minutes, timeframe_to_seconds from freqtrade.mixins import LoggingMixin from freqtrade.optimize.bt_progress import BTProgress from freqtrade.optimize.optimize_reports import (generate_backtest_stats, show_backtest_results, store_backtest_stats) from freqtrade.persistence import LocalTrade, PairLocks, Trade from freqtrade.plugins.pairlistmanager import PairListManager from freqtrade.plugins.protectionmanager import ProtectionManager from freqtrade.resolvers import ExchangeResolver, StrategyResolver from freqtrade.strategy.interface import IStrategy, SellCheckTuple from freqtrade.strategy.strategy_wrapper import strategy_safe_wrapper from freqtrade.wallets import Wallets logger = logging.getLogger(__name__) # Indexes for backtest tuples DATE_IDX = 0 BUY_IDX = 1 OPEN_IDX = 2 CLOSE_IDX = 3 SELL_IDX = 4 LOW_IDX = 5 HIGH_IDX = 6 BUY_TAG_IDX = 7 EXIT_TAG_IDX = 8 class Backtesting: """ Backtesting class, this class contains all the logic to run a backtest To run a backtest: backtesting = Backtesting(config) backtesting.start() """ def __init__(self, config: Dict[str, Any]) -> None: LoggingMixin.show_output = False self.config = config self.results: Optional[Dict[str, Any]] = None config['dry_run'] = True self.strategylist: List[IStrategy] = [] self.all_results: Dict[str, Dict] = {} self.exchange = ExchangeResolver.load_exchange(self.config['exchange']['name'], self.config) self.dataprovider = DataProvider(self.config, self.exchange) if self.config.get('strategy_list', None): for strat in list(self.config['strategy_list']): stratconf = deepcopy(self.config) stratconf['strategy'] = strat self.strategylist.append(StrategyResolver.load_strategy(stratconf)) validate_config_consistency(stratconf) else: # No strategy list specified, only one strategy self.strategylist.append(StrategyResolver.load_strategy(self.config)) validate_config_consistency(self.config) if "timeframe" not in self.config: raise OperationalException("Timeframe (ticker interval) needs to be set in either " "configuration or as cli argument `--timeframe 5m`") self.timeframe = str(self.config.get('timeframe')) self.timeframe_min = timeframe_to_minutes(self.timeframe) self.init_backtest_detail() self.pairlists = PairListManager(self.exchange, self.config) if 'VolumePairList' in self.pairlists.name_list: raise OperationalException("VolumePairList not allowed for backtesting. " "Please use StaticPairlist instead.") if 'PerformanceFilter' in self.pairlists.name_list: raise OperationalException("PerformanceFilter not allowed for backtesting.") if len(self.strategylist) > 1 and 'PrecisionFilter' in self.pairlists.name_list: raise OperationalException( "PrecisionFilter not allowed for backtesting multiple strategies." ) self.dataprovider.add_pairlisthandler(self.pairlists) self.pairlists.refresh_pairlist() if len(self.pairlists.whitelist) == 0: raise OperationalException("No pair in whitelist.") if config.get('fee', None) is not None: self.fee = config['fee'] else: self.fee = self.exchange.get_fee(symbol=self.pairlists.whitelist[0]) self.timerange = TimeRange.parse_timerange( None if self.config.get('timerange') is None else str(self.config.get('timerange'))) # Get maximum required startup period self.required_startup = max([strat.startup_candle_count for strat in self.strategylist]) # Add maximum startup candle count to configuration for informative pairs support self.config['startup_candle_count'] = self.required_startup self.exchange.validate_required_startup_candles(self.required_startup, self.timeframe) self.init_backtest() def __del__(self): self.cleanup() def cleanup(self): LoggingMixin.show_output = True PairLocks.use_db = True Trade.use_db = True def init_backtest_detail(self): # Load detail timeframe if specified self.timeframe_detail = str(self.config.get('timeframe_detail', '')) if self.timeframe_detail: self.timeframe_detail_min = timeframe_to_minutes(self.timeframe_detail) if self.timeframe_min <= self.timeframe_detail_min: raise OperationalException( "Detail timeframe must be smaller than strategy timeframe.") else: self.timeframe_detail_min = 0 self.detail_data: Dict[str, DataFrame] = {} def init_backtest(self): self.prepare_backtest(False) self.wallets = Wallets(self.config, self.exchange, log=False) self.progress = BTProgress() self.abort = False def _set_strategy(self, strategy: IStrategy): """ Load strategy into backtesting """ self.strategy: IStrategy = strategy strategy.dp = self.dataprovider # Attach Wallets to Strategy baseclass strategy.wallets = self.wallets # Set stoploss_on_exchange to false for backtesting, # since a "perfect" stoploss-sell is assumed anyway # And the regular "stoploss" function would not apply to that case self.strategy.order_types['stoploss_on_exchange'] = False def _load_protections(self, strategy: IStrategy): if self.config.get('enable_protections', False): conf = self.config if hasattr(strategy, 'protections'): conf = deepcopy(conf) conf['protections'] = strategy.protections self.protections = ProtectionManager(self.config, strategy.protections) def load_bt_data(self) -> Tuple[Dict[str, DataFrame], TimeRange]: """ Loads backtest data and returns the data combined with the timerange as tuple. """ self.progress.init_step(BacktestState.DATALOAD, 1) data = history.load_data( datadir=self.config['datadir'], pairs=self.pairlists.whitelist, timeframe=self.timeframe, timerange=self.timerange, startup_candles=self.required_startup, fail_without_data=True, data_format=self.config.get('dataformat_ohlcv', 'json'), ) min_date, max_date = history.get_timerange(data) logger.info(f'Loading data from {min_date.strftime(DATETIME_PRINT_FORMAT)} ' f'up to {max_date.strftime(DATETIME_PRINT_FORMAT)} ' f'({(max_date - min_date).days} days).') # Adjust startts forward if not enough data is available self.timerange.adjust_start_if_necessary(timeframe_to_seconds(self.timeframe), self.required_startup, min_date) self.progress.set_new_value(1) return data, self.timerange def load_bt_data_detail(self) -> None: """ Loads backtest detail data (smaller timeframe) if necessary. """ if self.timeframe_detail: self.detail_data = history.load_data( datadir=self.config['datadir'], pairs=self.pairlists.whitelist, timeframe=self.timeframe_detail, timerange=self.timerange, startup_candles=0, fail_without_data=True, data_format=self.config.get('dataformat_ohlcv', 'json'), ) else: self.detail_data = {} def prepare_backtest(self, enable_protections): """ Backtesting setup method - called once for every call to "backtest()". """ PairLocks.use_db = False PairLocks.timeframe = self.config['timeframe'] Trade.use_db = False PairLocks.reset_locks() Trade.reset_trades() self.rejected_trades = 0 self.dataprovider.clear_cache() if enable_protections: self._load_protections(self.strategy) def check_abort(self): """ Check if abort was requested, raise DependencyException if that's the case Only applies to Interactive backtest mode (webserver mode) """ if self.abort: self.abort = False raise DependencyException("Stop requested") def _get_ohlcv_as_lists(self, processed: Dict[str, DataFrame]) -> Dict[str, Tuple]: """ Helper function to convert a processed dataframes into lists for performance reasons. Used by backtest() - so keep this optimized for performance. """ # Every change to this headers list must evaluate further usages of the resulting tuple # and eventually change the constants for indexes at the top headers = ['date', 'buy', 'open', 'close', 'sell', 'low', 'high', 'buy_tag', 'exit_tag'] data: Dict = {} self.progress.init_step(BacktestState.CONVERT, len(processed)) # Create dict with data for pair, pair_data in processed.items(): self.check_abort() self.progress.increment() if not pair_data.empty: pair_data.loc[:, 'buy'] = 0 # cleanup if buy_signal is exist pair_data.loc[:, 'sell'] = 0 # cleanup if sell_signal is exist pair_data.loc[:, 'buy_tag'] = None # cleanup if buy_tag is exist pair_data.loc[:, 'exit_tag'] = None # cleanup if exit_tag is exist df_analyzed = self.strategy.advise_sell( self.strategy.advise_buy(pair_data, {'pair': pair}), {'pair': pair}).copy() # Trim startup period from analyzed dataframe df_analyzed = trim_dataframe(df_analyzed, self.timerange, startup_candles=self.required_startup) # To avoid using data from future, we use buy/sell signals shifted # from the previous candle df_analyzed.loc[:, 'buy'] = df_analyzed.loc[:, 'buy'].shift(1) df_analyzed.loc[:, 'sell'] = df_analyzed.loc[:, 'sell'].shift(1) df_analyzed.loc[:, 'buy_tag'] = df_analyzed.loc[:, 'buy_tag'].shift(1) df_analyzed.loc[:, 'exit_tag'] = df_analyzed.loc[:, 'exit_tag'].shift(1) # Update dataprovider cache self.dataprovider._set_cached_df(pair, self.timeframe, df_analyzed) df_analyzed = df_analyzed.drop(df_analyzed.head(1).index) # Convert from Pandas to list for performance reasons # (Looping Pandas is slow.) data[pair] = df_analyzed[headers].values.tolist() return data def _get_close_rate(self, sell_row: Tuple, trade: LocalTrade, sell: SellCheckTuple, trade_dur: int) -> float: """ Get close rate for backtesting result """ # Special handling if high or low hit STOP_LOSS or ROI if sell.sell_type in (SellType.STOP_LOSS, SellType.TRAILING_STOP_LOSS): if trade.stop_loss > sell_row[HIGH_IDX]: # our stoploss was already higher than candle high, # possibly due to a cancelled trade exit. # sell at open price. return sell_row[OPEN_IDX] # Special case: trailing triggers within same candle as trade opened. Assume most # pessimistic price movement, which is moving just enough to arm stoploss and # immediately going down to stop price. if sell.sell_type == SellType.TRAILING_STOP_LOSS and trade_dur == 0: if ( not self.strategy.use_custom_stoploss and self.strategy.trailing_stop and self.strategy.trailing_only_offset_is_reached and self.strategy.trailing_stop_positive_offset is not None and self.strategy.trailing_stop_positive ): # Worst case: price reaches stop_positive_offset and dives down. stop_rate = (sell_row[OPEN_IDX] * (1 + abs(self.strategy.trailing_stop_positive_offset) - abs(self.strategy.trailing_stop_positive))) else: # Worst case: price ticks tiny bit above open and dives down. stop_rate = sell_row[OPEN_IDX] * (1 - abs(trade.stop_loss_pct)) assert stop_rate < sell_row[HIGH_IDX] # Limit lower-end to candle low to avoid sells below the low. # This still remains "worst case" - but "worst realistic case". return max(sell_row[LOW_IDX], stop_rate) # Set close_rate to stoploss return trade.stop_loss elif sell.sell_type == (SellType.ROI): roi_entry, roi = self.strategy.min_roi_reached_entry(trade_dur) if roi is not None and roi_entry is not None: if roi == -1 and roi_entry % self.timeframe_min == 0: # When forceselling with ROI=-1, the roi time will always be equal to trade_dur. # If that entry is a multiple of the timeframe (so on candle open) # - we'll use open instead of close return sell_row[OPEN_IDX] # - (Expected abs profit + open_rate + open_fee) / (fee_close -1) close_rate = - (trade.open_rate * roi + trade.open_rate * (1 + trade.fee_open)) / (trade.fee_close - 1) if (trade_dur > 0 and trade_dur == roi_entry and roi_entry % self.timeframe_min == 0 and sell_row[OPEN_IDX] > close_rate): # new ROI entry came into effect. # use Open rate if open_rate > calculated sell rate return sell_row[OPEN_IDX] return close_rate else: # This should not be reached... return sell_row[OPEN_IDX] else: return sell_row[OPEN_IDX] def _get_sell_trade_entry_for_candle(self, trade: LocalTrade, sell_row: Tuple) -> Optional[LocalTrade]: sell_candle_time = sell_row[DATE_IDX].to_pydatetime() sell = self.strategy.should_sell(trade, sell_row[OPEN_IDX], # type: ignore sell_candle_time, sell_row[BUY_IDX], sell_row[SELL_IDX], low=sell_row[LOW_IDX], high=sell_row[HIGH_IDX]) if sell.sell_flag: trade.close_date = sell_candle_time trade_dur = int((trade.close_date_utc - trade.open_date_utc).total_seconds() // 60) closerate = self._get_close_rate(sell_row, trade, sell, trade_dur) # call the custom exit price,with default value as previous closerate current_profit = trade.calc_profit_ratio(closerate) if sell.sell_type in (SellType.SELL_SIGNAL, SellType.CUSTOM_SELL): # Custom exit pricing only for sell-signals closerate = strategy_safe_wrapper(self.strategy.custom_exit_price, default_retval=closerate)( pair=trade.pair, trade=trade, current_time=sell_row[DATE_IDX], proposed_rate=closerate, current_profit=current_profit) # Use the maximum between close_rate and low as we cannot sell outside of a candle. # Applies when a new ROI setting comes in place and the whole candle is above that. closerate = min(max(closerate, sell_row[LOW_IDX]), sell_row[HIGH_IDX]) # Confirm trade exit: time_in_force = self.strategy.order_time_in_force['sell'] if not strategy_safe_wrapper(self.strategy.confirm_trade_exit, default_retval=True)( pair=trade.pair, trade=trade, order_type='limit', amount=trade.amount, rate=closerate, time_in_force=time_in_force, sell_reason=sell.sell_reason, current_time=sell_candle_time): return None trade.sell_reason = sell.sell_reason # Checks and adds an exit tag, after checking that the length of the # sell_row has the length for an exit tag column if( len(sell_row) > EXIT_TAG_IDX and sell_row[EXIT_TAG_IDX] is not None and len(sell_row[EXIT_TAG_IDX]) > 0 ): trade.sell_reason = sell_row[EXIT_TAG_IDX] trade.close(closerate, show_msg=False) return trade return None def _get_sell_trade_entry(self, trade: LocalTrade, sell_row: Tuple) -> Optional[LocalTrade]: if self.timeframe_detail and trade.pair in self.detail_data: sell_candle_time = sell_row[DATE_IDX].to_pydatetime() sell_candle_end = sell_candle_time + timedelta(minutes=self.timeframe_min) detail_data = self.detail_data[trade.pair] detail_data = detail_data.loc[ (detail_data['date'] >= sell_candle_time) & (detail_data['date'] < sell_candle_end) ].copy() if len(detail_data) == 0: # Fall back to "regular" data if no detail data was found for this candle return self._get_sell_trade_entry_for_candle(trade, sell_row) detail_data.loc[:, 'buy'] = sell_row[BUY_IDX] detail_data.loc[:, 'sell'] = sell_row[SELL_IDX] headers = ['date', 'buy', 'open', 'close', 'sell', 'low', 'high'] for det_row in detail_data[headers].values.tolist(): res = self._get_sell_trade_entry_for_candle(trade, det_row) if res: return res return None else: return self._get_sell_trade_entry_for_candle(trade, sell_row) def _enter_trade(self, pair: str, row: List) -> Optional[LocalTrade]: try: stake_amount = self.wallets.get_trade_stake_amount(pair, None) except DependencyException: return None # let's call the custom entry price, using the open price as default price propose_rate = strategy_safe_wrapper(self.strategy.custom_entry_price, default_retval=row[OPEN_IDX])( pair=pair, current_time=row[DATE_IDX].to_pydatetime(), proposed_rate=row[OPEN_IDX]) # default value is the open rate # Move rate to within the candle's low/high rate propose_rate = min(max(propose_rate, row[LOW_IDX]), row[HIGH_IDX]) min_stake_amount = self.exchange.get_min_pair_stake_amount(pair, propose_rate, -0.05) or 0 max_stake_amount = self.wallets.get_available_stake_amount() stake_amount = strategy_safe_wrapper(self.strategy.custom_stake_amount, default_retval=stake_amount)( pair=pair, current_time=row[DATE_IDX].to_pydatetime(), current_rate=propose_rate, proposed_stake=stake_amount, min_stake=min_stake_amount, max_stake=max_stake_amount) stake_amount = self.wallets.validate_stake_amount(pair, stake_amount, min_stake_amount) if not stake_amount: return None order_type = self.strategy.order_types['buy'] time_in_force = self.strategy.order_time_in_force['sell'] # Confirm trade entry: if not strategy_safe_wrapper(self.strategy.confirm_trade_entry, default_retval=True)( pair=pair, order_type=order_type, amount=stake_amount, rate=propose_rate, time_in_force=time_in_force, current_time=row[DATE_IDX].to_pydatetime()): return None if stake_amount and (not min_stake_amount or stake_amount > min_stake_amount): # Enter trade has_buy_tag = len(row) >= BUY_TAG_IDX + 1 trade = LocalTrade( pair=pair, open_rate=propose_rate, open_date=row[DATE_IDX].to_pydatetime(), stake_amount=stake_amount, amount=round(stake_amount / propose_rate, 8), fee_open=self.fee, fee_close=self.fee, is_open=True, buy_tag=row[BUY_TAG_IDX] if has_buy_tag else None, exchange='backtesting', ) return trade return None def handle_left_open(self, open_trades: Dict[str, List[LocalTrade]], data: Dict[str, List[Tuple]]) -> List[LocalTrade]: """ Handling of left open trades at the end of backtesting """ trades = [] for pair in open_trades.keys(): if len(open_trades[pair]) > 0: for trade in open_trades[pair]: sell_row = data[pair][-1] trade.close_date = sell_row[DATE_IDX].to_pydatetime() trade.sell_reason = SellType.FORCE_SELL.value trade.close(sell_row[OPEN_IDX], show_msg=False) LocalTrade.close_bt_trade(trade) # Deepcopy object to have wallets update correctly trade1 = deepcopy(trade) trade1.is_open = True trades.append(trade1) return trades def trade_slot_available(self, max_open_trades: int, open_trade_count: int) -> bool: # Always allow trades when max_open_trades is enabled. if max_open_trades <= 0 or open_trade_count < max_open_trades: return True # Rejected trade self.rejected_trades += 1 return False def backtest(self, processed: Dict, start_date: datetime, end_date: datetime, max_open_trades: int = 0, position_stacking: bool = False, enable_protections: bool = False) -> Dict[str, Any]: """ Implement backtesting functionality NOTE: This method is used by Hyperopt at each iteration. Please keep it optimized. Of course try to not have ugly code. By some accessor are sometime slower than functions. Avoid extensive logging in this method and functions it calls. :param processed: a processed dictionary with format {pair, data} :param start_date: backtesting timerange start datetime :param end_date: backtesting timerange end datetime :param max_open_trades: maximum number of concurrent trades, <= 0 means unlimited :param position_stacking: do we allow position stacking? :param enable_protections: Should protections be enabled? :return: DataFrame with trades (results of backtesting) """ trades: List[LocalTrade] = [] self.prepare_backtest(enable_protections) # Use dict of lists with data for performance # (looping lists is a lot faster than pandas DataFrames) data: Dict = self._get_ohlcv_as_lists(processed) # Indexes per pair, so some pairs are allowed to have a missing start. indexes: Dict = defaultdict(int) tmp = start_date + timedelta(minutes=self.timeframe_min) open_trades: Dict[str, List[LocalTrade]] = defaultdict(list) open_trade_count = 0 self.progress.init_step(BacktestState.BACKTEST, int( (end_date - start_date) / timedelta(minutes=self.timeframe_min))) # Loop timerange and get candle for each pair at that point in time while tmp <= end_date: open_trade_count_start = open_trade_count self.check_abort() for i, pair in enumerate(data): row_index = indexes[pair] try: # Row is treated as "current incomplete candle". # Buy / sell signals are shifted by 1 to compensate for this. row = data[pair][row_index] except IndexError: # missing Data for one pair at the end. # Warnings for this are shown during data loading continue # Waits until the time-counter reaches the start of the data for this pair. if row[DATE_IDX] > tmp: continue row_index += 1 indexes[pair] = row_index self.dataprovider._set_dataframe_max_index(row_index) # without positionstacking, we can only have one open trade per pair. # max_open_trades must be respected # don't open on the last row if ( (position_stacking or len(open_trades[pair]) == 0) and self.trade_slot_available(max_open_trades, open_trade_count_start) and tmp != end_date and row[BUY_IDX] == 1 and row[SELL_IDX] != 1 and not PairLocks.is_pair_locked(pair, row[DATE_IDX]) ): trade = self._enter_trade(pair, row) if trade: # TODO: hacky workaround to avoid opening > max_open_trades # This emulates previous behaviour - not sure if this is correct # Prevents buying if the trade-slot was freed in this candle open_trade_count_start += 1 open_trade_count += 1 # logger.debug(f"{pair} - Emulate creation of new trade: {trade}.") open_trades[pair].append(trade) LocalTrade.add_bt_trade(trade) for trade in list(open_trades[pair]): # also check the buying candle for sell conditions. trade_entry = self._get_sell_trade_entry(trade, row) # Sell occurred if trade_entry: # logger.debug(f"{pair} - Backtesting sell {trade}") open_trade_count -= 1 open_trades[pair].remove(trade) LocalTrade.close_bt_trade(trade) trades.append(trade_entry) if enable_protections: self.protections.stop_per_pair(pair, row[DATE_IDX]) self.protections.global_stop(tmp) # Move time one configured time_interval ahead. self.progress.increment() tmp += timedelta(minutes=self.timeframe_min) trades += self.handle_left_open(open_trades, data=data) self.wallets.update() results = trade_list_to_dataframe(trades) return { 'results': results, 'config': self.strategy.config, 'locks': PairLocks.get_all_locks(), 'rejected_signals': self.rejected_trades, 'final_balance': self.wallets.get_total(self.strategy.config['stake_currency']), } def backtest_one_strategy(self, strat: IStrategy, data: Dict[str, DataFrame], timerange: TimeRange): self.progress.init_step(BacktestState.ANALYZE, 0) logger.info("Running backtesting for Strategy %s", strat.get_strategy_name()) backtest_start_time = datetime.now(timezone.utc) self._set_strategy(strat) strategy_safe_wrapper(self.strategy.bot_loop_start, supress_error=True)() # Use max_open_trades in backtesting, except --disable-max-market-positions is set if self.config.get('use_max_market_positions', True): # Must come from strategy config, as the strategy may modify this setting. max_open_trades = self.strategy.config['max_open_trades'] else: logger.info( 'Ignoring max_open_trades (--disable-max-market-positions was used) ...') max_open_trades = 0 # need to reprocess data every time to populate signals preprocessed = self.strategy.advise_all_indicators(data) # Trim startup period from analyzed dataframe preprocessed_tmp = trim_dataframes(preprocessed, timerange, self.required_startup) if not preprocessed_tmp: raise OperationalException( "No data left after adjusting for startup candles.") # Use preprocessed_tmp for date generation (the trimmed dataframe). # Backtesting will re-trim the dataframes after buy/sell signal generation. min_date, max_date = history.get_timerange(preprocessed_tmp) logger.info(f'Backtesting with data from {min_date.strftime(DATETIME_PRINT_FORMAT)} ' f'up to {max_date.strftime(DATETIME_PRINT_FORMAT)} ' f'({(max_date - min_date).days} days).') # Execute backtest and store results results = self.backtest( processed=preprocessed, start_date=min_date, end_date=max_date, max_open_trades=max_open_trades, position_stacking=self.config.get('position_stacking', False), enable_protections=self.config.get('enable_protections', False), ) backtest_end_time = datetime.now(timezone.utc) results.update({ 'backtest_start_time': int(backtest_start_time.timestamp()), 'backtest_end_time': int(backtest_end_time.timestamp()), }) self.all_results[self.strategy.get_strategy_name()] = results return min_date, max_date def start(self) -> None: """ Run backtesting end-to-end :return: None """ data: Dict[str, Any] = {} data, timerange = self.load_bt_data() self.load_bt_data_detail() logger.info("Dataload complete. Calculating indicators") for strat in self.strategylist: min_date, max_date = self.backtest_one_strategy(strat, data, timerange) if len(self.strategylist) > 0: self.results = generate_backtest_stats(data, self.all_results, min_date=min_date, max_date=max_date) if self.config.get('export', 'none') == 'trades': store_backtest_stats(self.config['exportfilename'], self.results) # Show backtest results show_backtest_results(self.config, self.results)