This may or may not be appropriate; you haven't really given enough information about how this would be used.
(Are you looking for integers or floating point? Is the range going to be in the hundreds or billions? etc.)
sub distinct_random_int {
my ($num, $start, $end) = @_;
my @rand;
my @avail = $start..$end;
push @rand, splice(@avail, rand(@avail), 1) for 1..$num;
@rand;
}
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