test_collective_api_base.py 23.4 KB
Newer Older
1
# Copyright (c) 2020 PaddlePaddle Authors. All Rights Reserved.
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
#     http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.

import numpy as np
import unittest
import os
import sys
import subprocess
import pickle
21
import tempfile
22
from contextlib import closing
23
import paddle
24 25 26 27
import paddle.fluid as fluid
from paddle.fluid import core


28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59
def create_bool_test_data(shape=None, seed=None):
    if seed:
        np.random.seed(seed)
    data = np.random.choice([True, False], size=shape)
    return data


def create_float_test_data(shape=None, dtype=None, seed=None):
    if seed:
        np.random.seed(seed)
    data = np.random.random(shape).astype(dtype)
    return data


def create_int_test_data(shape=None, dtype=None, seed=None):
    if seed:
        np.random.seed(seed)
    data = np.random.randint(0, high=100, size=shape).astype(dtype)
    return data


def create_complex_test_data(shape=None, dtype=None, seed=None):
    if seed:
        np.random.seed(seed)
    data = np.random.random(shape).astype(dtype)
    data.imag = np.random.random(shape)
    return data


def create_pylist_test_data(shape=None, seed=None):
    if seed:
        np.random.seed(seed)
60 61
    # Generate random shape test case for xxx_object api
    shape = np.random.randint(0, high=100, size=(2)).tolist()
62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92
    data = np.random.random(shape).tolist()
    return data


def create_pydict_test_data(shape=None, seed=None):
    if seed:
        np.random.seed(seed)
    key = [i for i in range(0, shape[0])]
    value = np.random.random(shape).tolist()
    data = dict(zip(key, value))
    return data


def create_test_data(shape=None, dtype=None, seed=None):
    assert shape, "Shape should be specified"
    if dtype == "float32" or dtype == "float16" or dtype == "float64":
        return create_float_test_data(shape=shape, dtype=dtype, seed=seed)
    elif dtype == "bool":
        return create_bool_test_data(shape=shape, seed=seed)
    elif dtype == "int32" or dtype == "int64" or dtype == "int8" or dtype == "uint8":
        return create_int_test_data(shape=shape, dtype=dtype, seed=seed)
    elif dtype == "complex64" or dtype == "complex128":
        return create_complex_test_data(shape=shape, dtype=dtype, seed=seed)
    elif dtype == "pylist":
        return create_pylist_test_data(shape=shape, seed=seed)
    elif dtype == "pydict":
        return create_pydict_test_data(shape=shape, seed=seed)
    else:
        raise NotImplementedError("Unsupported dtype for creating test data.")


93
class TestCollectiveAPIRunnerBase(object):
94

95 96 97 98 99 100
    def get_model(self,
                  train_prog,
                  startup_prog,
                  rank,
                  indata=None,
                  dtype=None):
101 102 103 104 105 106 107 108 109 110
        raise NotImplementedError(
            "get model should be implemented by child class.")

    def run_trainer(self, args):
        train_prog = fluid.Program()
        startup_prog = fluid.Program()
        endpoints = args["endpoints"].split(",")
        rank = args["trainerid"]
        current_endpoint = args["currentendpoint"]
        nranks = 2
111
        paddle.distributed.init_parallel_env()
112 113 114 115
        if args['backend'] == 'nccl':
            device_id = int(os.getenv("FLAGS_selected_gpus", "0"))
            place = fluid.CUDAPlace(
                device_id)  #if args.use_gpu else fluid.CPUPlace()
116 117 118
        elif args['backend'] == 'bkcl':
            device_id = int(os.getenv("FLAGS_selected_xpus", "0"))
            place = fluid.XPUPlace(device_id)
119 120
        else:
            place = fluid.CPUPlace()
121 122 123
        indata = create_test_data(shape=(10, 1000),
                                  dtype=args["dtype"],
                                  seed=os.getpid())
L
lilong12 已提交
124 125 126 127 128 129 130 131 132 133 134 135 136
        if args['static_mode']:
            result = self.get_model(train_prog, startup_prog, rank)
            exe = fluid.Executor(place)
            exe.run(startup_prog)
            fetch_list = []
            for elem in result:
                fetch_list.append(elem.name)
            out = exe.run(train_prog,
                          feed={'tindata': indata},
                          fetch_list=fetch_list)
        else:
            out = self.get_model(train_prog, startup_prog, rank, indata)
            #print(out, sys.stderr)
T
tianshuo78520a 已提交
137
        sys.stdout.buffer.write(pickle.dumps(out))
138 139 140 141 142 143 144 145 146 147 148 149


def runtime_main(test_class, col_type):
    args = {}
    model = test_class()
    args["trainerid"] = int(os.getenv("PADDLE_TRAINER_ID"))
    args["trainernum"] = int(os.getenv("PADDLE_TRAINERS_NUM"))
    args["endpoints"] = os.getenv('PADDLE_TRAINER_ENDPOINTS')
    args["currentendpoint"] = os.getenv("PADDLE_CURRENT_ENDPOINT")
    args["col_type"] = col_type
    args["backend"] = os.getenv("BACKEND")
    args["path_id"] = int(os.getenv("PATH_ID"))
L
lilong12 已提交
150
    args["static_mode"] = int(os.getenv("STATIC_MODE"))
151
    args["dtype"] = os.getenv("DTYPE")
152 153 154 155 156 157 158 159
    model.run_trainer(args)


import socket
from contextlib import closing


class TestDistBase(unittest.TestCase):
160

161 162 163 164 165 166 167
    def setUp(self):
        self._port_set = set()
        self._trainers = 2
        self._ps_endpoints = "127.0.0.1:%s,127.0.0.1:%s" % (
            self._find_free_port(), self._find_free_port())
        self._python_interp = sys.executable

168 169 170 171 172
        self.temp_dir = tempfile.TemporaryDirectory()

    def tearDown(self):
        self.temp_dir.cleanup()

173
    def _find_free_port(self):
174

175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190
        def __free_port():
            with closing(socket.socket(socket.AF_INET,
                                       socket.SOCK_STREAM)) as s:
                s.bind(('', 0))
                return s.getsockname()[1]

        while True:
            port = __free_port()
            if port not in self._port_set:
                self._port_set.add(port)
                return port

    def _run_cluster(self, model_file, envs):
        worker_endpoints = self._ps_endpoints.split(",")
        w0_ep, w1_ep = worker_endpoints
        #print("w0_ep:",w0_ep," w1_ep:",w1_ep)
191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222
        if core.is_compiled_with_cuda():
            env0 = {
                "FLAGS_selected_gpus": "0",
                "PADDLE_TRAINER_ID": "0",
                "PADDLE_TRAINERS_NUM": "2",
                "PADDLE_TRAINER_ENDPOINTS": self._ps_endpoints,
                "PADDLE_CURRENT_ENDPOINT": w0_ep
            }

            env1 = {
                "FLAGS_selected_gpus": "1",
                "PADDLE_TRAINER_ID": "1",
                "PADDLE_TRAINERS_NUM": "2",
                "PADDLE_TRAINER_ENDPOINTS": self._ps_endpoints,
                "PADDLE_CURRENT_ENDPOINT": w1_ep
            }
        elif core.is_compiled_with_xpu():
            env0 = {
                "FLAGS_selected_xpus": "0",
                "PADDLE_TRAINER_ID": "0",
                "PADDLE_TRAINERS_NUM": "2",
                "PADDLE_TRAINER_ENDPOINTS": self._ps_endpoints,
                "PADDLE_CURRENT_ENDPOINT": w0_ep
            }

            env1 = {
                "FLAGS_selected_xpus": "1",
                "PADDLE_TRAINER_ID": "1",
                "PADDLE_TRAINERS_NUM": "2",
                "PADDLE_TRAINER_ENDPOINTS": self._ps_endpoints,
                "PADDLE_CURRENT_ENDPOINT": w1_ep
            }
223 224 225
        #update environment
        env0.update(envs)
        env1.update(envs)
226 227 228 229
        if os.getenv('WITH_COVERAGE', 'OFF') == 'ON':
            tr_cmd = "%s -m coverage run --branch -p %s"
        else:
            tr_cmd = "%s %s"
230 231
        tr0_cmd = tr_cmd % (self._python_interp, model_file)
        tr1_cmd = tr_cmd % (self._python_interp, model_file)
232 233 234 235 236 237
        path0 = os.path.join(self.temp_dir.name,
                             "/tmp/tr0_err_%d.log" % os.getpid())
        path1 = os.path.join(self.temp_dir.name,
                             "/tmp/tr1_err_%d.log" % os.getpid())
        tr0_pipe = open(path0, "w")
        tr1_pipe = open(path1, "w")
238 239 240 241 242 243 244 245 246 247
        #print(tr0_cmd)
        tr0_proc = subprocess.Popen(tr0_cmd.strip().split(),
                                    stdout=subprocess.PIPE,
                                    stderr=tr0_pipe,
                                    env=env0)

        tr1_proc = subprocess.Popen(tr0_cmd.strip().split(),
                                    stdout=subprocess.PIPE,
                                    stderr=tr1_pipe,
                                    env=env1)
248 249 250 251 252 253 254 255

        tr0_out, tr0_err = tr0_proc.communicate()
        tr1_out, tr1_err = tr1_proc.communicate()
        sys.stderr.write('trainer 0 stderr: %s\n' % tr0_err)
        sys.stderr.write('trainer 1 stderr: %s\n' % tr1_err)
        # close trainer file
        tr0_pipe.close()
        tr1_pipe.close()
256
        with open(path0, "r") as f:
257
            sys.stderr.write('trainer 0 stderr file: %s\n' % f.read())
258
        with open(path1, "r") as f:
259
            sys.stderr.write('trainer 1 stderr file: %s\n' % f.read())
260 261 262 263 264 265 266 267
        return pickle.loads(tr0_out), pickle.loads(
            tr1_out), tr0_proc.pid, tr1_proc.pid

    def check_with_place(self,
                         model_file,
                         col_type,
                         backend="nccl",
                         path_id="0",
L
lilong12 已提交
268
                         static_mode="1",
269
                         check_error_log=False,
270
                         need_envs={},
271 272
                         eager_mode=True,
                         dtype=None):
273 274 275 276
        if backend == "nccl" or backend == "bkcl":
            with_gloo = '0'
        else:
            with_gloo = '1'
277
        required_envs = os.environ.copy()
278
        dtype = "float32" if dtype is None else dtype
279
        additional_envs = {
280
            "NCCL_P2P_DISABLE": "1",
L
lilong12 已提交
281
            "STATIC_MODE": static_mode,
L
lilong12 已提交
282
            "PADDLE_WITH_GLOO": with_gloo,
283
            "PADDLE_DISTRI_BACKEND": backend,
284
            "BACKEND": backend,
285 286
            "PATH_ID": path_id,
            "DTYPE": dtype
287
        }
288
        required_envs.update(additional_envs)
289 290 291 292
        required_envs.update(need_envs)
        if check_error_log:
            required_envs["GLOG_v"] = "3"
            required_envs["GLOG_logtostderr"] = "1"
293
            required_envs["GLOO_LOG_LEVEL"] = "TRACE"
294

295 296 297 298
        if os.getenv('NVIDIA_TF32_OVERRIDE', '') is not None:
            required_envs['NVIDIA_TF32_OVERRIDE'] = os.getenv(
                'NVIDIA_TF32_OVERRIDE', '')

299 300
        if eager_mode:
            required_envs["FLAGS_enable_eager_mode"] = "%d" % 1
301 302
        else:
            required_envs["FLAGS_enable_eager_mode"] = "%d" % 0
303

304 305
        tr0_out, tr1_out, pid0, pid1 = self._run_cluster(
            model_file, required_envs)
306 307
        input1 = create_test_data(shape=(10, 1000), dtype=dtype, seed=pid0)
        input2 = create_test_data(shape=(10, 1000), dtype=dtype, seed=pid1)
308 309 310 311
        if col_type == "allgather":
            need_result = np.vstack((input1, input2))
            tr_out0 = np.vstack((tr0_out[0], tr0_out[1]))
            tr_out1 = np.vstack((tr1_out[0], tr1_out[1]))
312 313
            np.testing.assert_allclose(tr_out0, need_result, rtol=1e-05)
            np.testing.assert_allclose(tr_out1, need_result, rtol=1e-05)
314 315 316 317
        if col_type == "allgather_object":
            need_result = [input1, input2]
            self.assertEqual(need_result, tr0_out)
            self.assertEqual(need_result, tr1_out)
318 319
        elif col_type == "broadcast":
            need_result = input2
320 321
            np.testing.assert_allclose(tr0_out[0], need_result, rtol=1e-05)
            np.testing.assert_allclose(tr1_out[0], need_result, rtol=1e-05)
322 323
        elif col_type == "reduce":
            need_result = input1 + input2
324
            np.testing.assert_allclose(tr0_out[0], need_result, rtol=1e-05)
325 326 327 328
        elif col_type == "scatter":
            need_result = input2
            need_result1 = need_result[0:need_result.shape[0] // 2]
            need_result2 = need_result[need_result.shape[0] // 2:]
329 330
            np.testing.assert_allclose(tr0_out[0], need_result1, rtol=1e-05)
            np.testing.assert_allclose(tr1_out[0], need_result2, rtol=1e-05)
331 332 333 334 335 336
        elif col_type == "reduce_scatter":
            need_result = input1 + input2
            need_result1 = need_result[0:need_result.shape[0] // 2]
            need_result2 = need_result[need_result.shape[0] // 2:]
            np.testing.assert_allclose(tr0_out[0], need_result1, rtol=1e-05)
            np.testing.assert_allclose(tr1_out[0], need_result2, rtol=1e-05)
337 338
        elif col_type == "allreduce":
            need_result = input1 + input2
339 340 341 342 343 344 345 346
            np.testing.assert_allclose(tr0_out[0],
                                       need_result,
                                       rtol=1e-05,
                                       atol=1e-05)
            np.testing.assert_allclose(tr1_out[0],
                                       need_result,
                                       rtol=1e-05,
                                       atol=1e-05)
347 348 349
        elif col_type == "parallel_embedding":
            result_data = tr0_out[0]
            np.random.seed(2020)
350
            need_result = np.random.rand(12, 8)
351 352 353
            for i in range(result_data.shape[0]):
                for j in range(result_data.shape[1]):
                    data = result_data[i][j]
354 355 356
                    assert np.allclose(tr0_out[1][i][j],
                                       need_result[data],
                                       atol=1e-08)
357 358 359 360 361
        elif col_type == "row_parallel_linear":
            result_data = tr0_out[0]
            np.random.seed(2020)
            weight = np.random.rand(1000, 16)
            need_result = np.matmul(input1, weight)
362 363 364 365
            np.testing.assert_allclose(result_data,
                                       need_result,
                                       rtol=1e-05,
                                       atol=1e-05)
366 367 368 369 370
        elif col_type == "column_parallel_linear":
            result_data = tr0_out[0]
            np.random.seed(2020)
            weight = np.random.rand(1000, 16)
            need_result = np.matmul(input1, weight)
371 372 373 374
            np.testing.assert_allclose(result_data,
                                       need_result,
                                       rtol=1e-05,
                                       atol=1e-05)
L
lilong12 已提交
375 376 377 378 379 380 381
        elif col_type == "alltoall":
            need_result1 = np.vstack((input1[0:input1.shape[0] // 2, :],
                                      input2[0:input2.shape[0] // 2, :]))
            need_result2 = np.vstack((input1[input1.shape[0] // 2:, :],
                                      input2[input2.shape[0] // 2:, :]))
            tr0_out = np.vstack(tr0_out)
            tr1_out = np.vstack(tr1_out)
382 383 384 385 386 387 388 389
            np.testing.assert_allclose(tr0_out,
                                       need_result1,
                                       rtol=1e-05,
                                       atol=1e-05)
            np.testing.assert_allclose(tr1_out,
                                       need_result2,
                                       rtol=1e-05,
                                       atol=1e-05)
L
lilong12 已提交
390 391
        elif col_type == "sendrecv":
            result_data = tr1_out[0]
392 393 394 395
            np.testing.assert_allclose(input1,
                                       result_data,
                                       rtol=1e-05,
                                       atol=1e-05)
396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471
        elif col_type == "global_gather":
            in_feat = 2
            n_expert = 2
            world_size = 2
            tot_expert = n_expert * world_size

            np.random.seed(pid0)
            local_expert_count1 = np.random.randint(
                1, 4, size=tot_expert).astype("int")
            expert_ptr1 = np.ones(tot_expert, dtype=np.int32)
            expert_ptr1[0] = 0
            for i in range(1, tot_expert):
                expert_ptr1[i] = expert_ptr1[i - 1] + local_expert_count1[i - 1]

            np.random.seed(pid1)
            local_expert_count2 = np.random.randint(
                1, 4, size=tot_expert).astype("int")
            expert_ptr2 = np.ones(tot_expert, dtype=np.int32)
            expert_ptr2[0] = 0
            for i in range(1, tot_expert):
                expert_ptr2[i] = expert_ptr2[i - 1] + local_expert_count2[i - 1]

            global_expert_count1 = np.zeros(tot_expert).astype("int")
            global_expert_count2 = np.zeros(tot_expert).astype("int")
            global_expert_count1[0:n_expert] = local_expert_count1[0:n_expert]
            global_expert_count1[n_expert:] = local_expert_count2[0:n_expert]
            global_expert_count2[0:n_expert] = local_expert_count1[n_expert:]
            global_expert_count2[n_expert:] = local_expert_count2[n_expert:]

            np.random.seed(pid0)
            fwd_expert_count = sum(global_expert_count1).astype("int")
            local_input_buf1 = np.random.rand(fwd_expert_count,
                                              in_feat).astype("float32")
            np.random.seed(pid1)
            fwd_expert_count = sum(global_expert_count2).astype("int")
            local_input_buf2 = np.random.rand(fwd_expert_count,
                                              in_feat).astype("float32")
            output1 = [[], [], [], []]
            output2 = [[], [], [], []]
            send_ptr1 = 0
            send_ptr2 = 0

            for i in range(n_expert):
                for j in range(world_size):
                    idx = j * n_expert + i
                    if j == 0:
                        output1_part1 = local_input_buf1[send_ptr1: \
                            send_ptr1 + global_expert_count1[idx], :]
                        output1_part2 = local_input_buf2[send_ptr2: \
                            send_ptr2 + global_expert_count2[idx], :]
                        output1[i].extend(output1_part1)
                        output1[i + n_expert].extend(output1_part2)
                    else:
                        output2_part1 = local_input_buf1[send_ptr1: \
                            send_ptr1 + global_expert_count1[idx]]
                        output2_part2 = local_input_buf2[send_ptr2: \
                            send_ptr2 + global_expert_count2[idx]]
                        output2[i].extend(output2_part1)
                        output2[i + n_expert].extend(output2_part2)
                    send_ptr1 = send_ptr1 + global_expert_count1[idx]
                    send_ptr2 = send_ptr2 + global_expert_count2[idx]
            result1 = []
            result2 = []
            for i in range(tot_expert):
                for arr in output1[i]:
                    if arr == []:
                        continue
                    result1.append(arr)
            for i in range(tot_expert):
                for arr in output2[i]:
                    if arr == []:
                        continue
                    result2.append(arr)
            if result1 == []:
                output1 = np.array([])
            else:
472 473
                output1 = np.concatenate(result1, axis=0).reshape(
                    sum(local_expert_count1), in_feat)
474 475 476
            if result2 == []:
                output2 = np.array([])
            else:
477 478
                output2 = np.concatenate(result2, axis=0).reshape(
                    sum(local_expert_count2), in_feat)
479 480 481 482 483 484 485

            if tr0_out[0] is None or tr0_out[0].shape[0] == 0:
                tr0_out[0] = np.array([])

            if tr1_out[0] is None or tr1_out[0].shape[0] == 0:
                tr1_out[0] = np.array([])

486 487 488 489 490 491 492 493
            np.testing.assert_allclose(tr0_out[0],
                                       output1,
                                       rtol=1e-05,
                                       atol=1e-05)
            np.testing.assert_allclose(tr1_out[0],
                                       output2,
                                       rtol=1e-05,
                                       atol=1e-05)
494
            if static_mode == 0:
495 496 497 498 499 500 501 502
                np.testing.assert_allclose(tr0_out[1],
                                           2 * local_input_buf1,
                                           rtol=1e-05,
                                           atol=1e-05)
                np.testing.assert_allclose(tr1_out[1],
                                           2 * local_input_buf2,
                                           rtol=1e-05,
                                           atol=1e-05)
503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554

        elif col_type == "global_scatter":
            np.random.seed(pid0)
            local_expert_count1 = np.random.randint(1, 4, size=4).astype("int")
            fwd_expert_count = sum(local_expert_count1)
            local_input_buf1 = np.random.rand(fwd_expert_count,
                                              2).astype("float32")
            expert_ptr1 = np.ones(4, dtype=np.int32)
            expert_ptr1[0] = 0
            for i in range(1, 4):
                expert_ptr1[i] = expert_ptr1[i - 1] + local_expert_count1[i - 1]
            np.random.seed(pid1)
            local_expert_count2 = np.random.randint(1, 4, size=4).astype("int")
            fwd_expert_count = sum(local_expert_count2)
            local_input_buf2 = np.random.rand(fwd_expert_count,
                                              2).astype("float32")
            expert_ptr2 = np.ones(4, dtype=np.int32)
            expert_ptr2[0] = 0
            for i in range(1, 4):
                expert_ptr2[i] = expert_ptr2[i - 1] + local_expert_count2[i - 1]

            output1 = []
            output2 = []
            for i in range(2):
                for j in range(2):
                    idx = j * 2 + i
                    if j == 0:
                        # send data to 0 card
                        output1.append(local_input_buf1[expert_ptr1[idx]: \
                            expert_ptr1[idx]+local_expert_count1[idx]])
                        output1.append(local_input_buf2[expert_ptr2[idx]:\
                            expert_ptr2[idx]+local_expert_count2[idx]])
                    else:
                        output2.append(local_input_buf1[expert_ptr1[idx]: \
                            expert_ptr1[idx]+local_expert_count1[idx]])
                        output2.append(local_input_buf2[expert_ptr2[idx]:\
                            expert_ptr2[idx]+local_expert_count2[idx]])
            if output1 == []:
                output1 = np.array([])
            else:
                output1 = np.concatenate(output1)
            if output2 == []:
                output2 = np.array([])
            else:
                output2 = np.concatenate(output2)

            if tr0_out[0] is None or tr0_out[0].shape[0] == 0:
                tr0_out[0] = np.array([])

            if tr1_out[0] is None or tr1_out[0].shape[0] == 0:
                tr1_out[0] = np.array([])

555 556 557 558 559 560 561 562
            np.testing.assert_allclose(tr0_out[0],
                                       output1,
                                       rtol=1e-05,
                                       atol=1e-05)
            np.testing.assert_allclose(tr1_out[0],
                                       output2,
                                       rtol=1e-05,
                                       atol=1e-05)
563
            if static_mode == 0:
564 565 566 567 568 569 570 571
                np.testing.assert_allclose(tr0_out[1],
                                           2 * local_input_buf1,
                                           rtol=1e-05,
                                           atol=1e-05)
                np.testing.assert_allclose(tr1_out[1],
                                           2 * local_input_buf2,
                                           rtol=1e-05,
                                           atol=1e-05)
572 573
        else:
            pass