If your file doesn't have any \n delimiters and you want to read it all in one slurp, tell Perl not to stop when reading:

undef $/;
$file_data = <FILE>;     # That pulled it all in
close FILE;
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BTW, This statement: while (<FILE>) {is reading the (single) line from your file and assiging it to $_. The body of the while tries to read from the file a second time. Remember that the <> operator reads data in addition to checking for EOF.

HTH