Yeah, they are rounding errors. Rearranging the calculation fixes it (at least, on my platform):

sub ranges_javafan {
  my ($M, $N) = @_;
  return [ map {[int($_/$N*($M+1))
                 , int((($_+1)/$N)*($M+1))-1]
              } 0..$N - 1];
}
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The most important is the final ($_+1)/$N*($M+1) - that should return $M+1 for $_ == $N-1. The impact of other rounding errors is that a range is 1 shorter than expected (but making the next one one larger - it shouldn't skip numbers).