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my @index;
while (<BIGLOG>){
...
        : Mktime( unpack 'A4xA2xA2xA2xA2xA2', $_  );
    push @index, pack 'NN', $epoch, $offset;
}

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my( $offset, @index ) = 0; ## The first lines offset is zero
while (<BIGLOG>){
...
    push @index, pack 'NN', $epoch, $offset; ## Pair with previous off
+set
    $offset = tell BIGLOG;   ## and now get the start of the next line
+ 
}