It's clear enough to plainly see that you are adding something to the number, then rounding it, which means that in any thing close to 0.49e-${p}, you'll force a round-up, so often wrong, in the other direction.

Being 9.0e-5 + 0.5e-5 is 9.5e-5 -- So, you are forcing it to always add "up".

Just adding a single 0.00009 at the end of your code, shows how bad this can be. However, the same problem also happens (with a smaller error area) if you try a higher exponent -- it simply intentionally inserts an error, which is a really dangerous way to try to correct a problem. 

sub rnd{
        my( $p, $n ) = @_;
            return sprintf "%.${p}f", $n + "0.5e-$p"
};;

print $_, ': ', rnd( 5, $_ ), qq{\n} for
    0.000005, 0.000015, 0.000025, 0.000035, 0.000045,
    0.000055, 0.000065, 0.000075, 0.000085, 0.000095,
    0.00009;;
__DATA__
5e-06: 0.00001
1.5e-05: 0.00002
2.5e-05: 0.00003
3.5e-05: 0.00004
4.5e-05: 0.00005
5.5e-05: 0.00006
6.5e-05: 0.00007
7.5e-05: 0.00008
8.5e-05: 0.00009
9.5e-05: 0.00010
9e-05: 0.00010

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In reply to Re^10: RFC: Large Floating Point Numbers - Rounding Errors by GAVollink
in thread RFC: Large Floating Point Numbers - Rounding Errors by GAVollink

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