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The following test fails with an AssertionError('a' != 'b') on the first read.
import codecs
FILENAME = 'test'
with open(FILENAME, 'wb') as f:
 f.write('abcd'.encode('utf-8'))
with codecs.open(FILENAME, 'r+', encoding='utf-8') as f:
 f.write("1")
 pos = f.writer.tell()
 assert pos == 1, "writer pos: %s != 1" % pos
 pos = f.reader.tell()
 assert pos == 1, "reader pos: %s != 1" % pos
 pos = f.stream.tell()
 assert pos == 1, "stream pos: %s != 1" % pos
 # read() must call writer.flush()
 char = f.read(1)
 assert char == 'b', "%r != 'b'" % (char,)
 # write() must rewind the raw stream
 f.write('3')
 tail = f.read()
 assert tail == 'd', "%r != 'd'" % (tail,)
 f.flush()
 with open(FILENAME, 'rb') as f:
 assert f.read() == b'1b3d'
I suppose that readline(), readlines() and __next__() have also issues.
See also issue #12215: similar issue with io.TextIOWrapper.