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$index .= pack 'd', tell FILE while <FILE>;

my @index = ( pack 'd', 0 );
push @index, pack 'd', tell FILE while <FILE>;
pop @index;
my $index = join '', @index;

Indexing mine : time   1 s, size   19949431, lines  136126
Indexing mine : time   2 s, size   40308893, lines  258457
...
Indexing yours: time   6 s, size   40308893, lines  258458
Indexing yours: time  31 s, size   95227350, lines  634393
Indexing yours: time 809 s, size  527423877, lines 3441912