You need to have a sliding windows on top of it: when reading a new chunk, you keep a number of bytes from the previous chunk at least as large as the maximal length of the pattern match. So you would process:
Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam nonu
+my eirmod tempor invidunt ut labore et dolore magna aliquyam erat, se
+d diam voluptua. At vero eos et accusam et justo duo dolores et ea re
+bum. Stet clita kasd guber
keep, for example, the
lita kasd guber from this chunk and append the next chunk to get:
lita kasd gubergren, no sea takimata sanctus est Lorem ipsum dolor sit
+ amet.
And now you have your match on the second chunk.
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