Best way to make sure a number is an even multiple of another?

demerphq has asked for the wisdom of the Perl Monks concerning the following question:

I need a function (call it 'fix' for lack of a better name) to find the value $N that is an even multiple of $m that is larger than or equal to $n. (See note at bottom for clarification of "even multiple") The best I came up with requires control flow logic and I was wondering if anyone could suggest something better, preferably that doesn't require an 'if'.

sub fix{
    my ($n,$m)=@_;
    my $M = $n % $m;
    $M ? $n + $m - $M : $n
}

print "<table width='80%' align='center' border='1'>\n";
print "<tr><th></th><th colspan='4'>\$m</th></tr>\n";
for my $n (0..20) {
    print "  <tr>".join("", map { "<th>$_</th>" } '$n',2..5),"</tr>\n"
        unless $n;
    print "  <tr>".join("", map { "<td>$_</td>" } $n,map fix($n,$_),2.
+.5),"</tr>\n";
}
print "</table>";
__END__
[download]

(Sample output below:)

	$m
$n	2	3	4	5
0	0	0	0	0
1	2	3	4	5
2	2	3	4	5
3	4	3	4	5
4	4	6	4	5
5	6	6	8	5
6	6	6	8	10
7	8	9	8	10
8	8	9	8	10
9	10	9	12	10
10	10	12	12	10
11	12	12	12	15
12	12	12	12	15
13	14	15	16	15
14	14	15	16	15
15	16	15	16	15
16	16	18	16	20
17	18	18	20	20
18	18	18	20	20
19	20	21	20	20
20	20	21	20	20

Note that $m and $n may be any non negative integer,( and thus be odd, or even prime), so you can't use binary operators like '&'.

---
demerphq

_{First they ignore you, then they laugh at you, then they fight you, then you win.

-- Gandhi

Flux8}

_{• Update:

To clarify the use of 'evenly' in the above I mean the definition X divides Y evenly if and only if Y % X == 0. Or expressed another way, Y is an even multiple of X if and only if Y % X == 0. Sorry, I'm not much of a mathematician so I forget the textbook definitions and terms for these things.}

Comment on Best way to make sure a number is an even multiple of another? Download Code

Replies are listed 'Best First'.
•Re: Best way to make sure a number is an even multiple of another? by merlyn (Sage) on Oct 21, 2004 at 13:08 UTC
`sub fix { my $n = shift; # must be greater or equal to this (assert >= 0) my $m = shift; # must be multiple of this (assert > 0) $m*int(($n+$m-1)/$m); }` [download] -- Randal L. Schwartz, Perl hacker Be sure to read my standard disclaimer if this is a reply.	[reply] [d/l]
Re^2: Best way to make sure a number is an even multiple of another? by demerphq (Chancellor) on Oct 21, 2004 at 13:14 UTC
Yeah, thats it. Thanks and ++ merlyn. I knew it was possible, I just couldn't see past the damn if. :-) --- demerphq _{First they ignore you, then they laugh at you, then they fight you, then you win. -- Gandhi Flux8}	[reply]
Re^3: Best way to make sure a number is an even multiple of another? by Arunbear (Prior) on Oct 21, 2004 at 14:01 UTC
I may have misunderstood this, but with $n = 19 and $m = 3, fix gives 21 which is not an even multiple of 3. Why not just use `$m * $n * 2` ?	[reply] [d/l]
Re^4: Best way to make sure a number is an even multiple of another? by husker (Chaplain) on Oct 21, 2004 at 14:13 UTC
Re^5: Best way to make sure a number is an even multiple of another? by Arunbear (Prior) on Oct 21, 2004 at 14:23 UTC
Some notes below your chosen depth have not been shown here
Re: Best way to make sure a number is an even multiple of another? by castaway (Parson) on Oct 21, 2004 at 12:58 UTC
Cheat, no if(): `sub fix{ my ($n,$m)=@_; my $M = $n % $m; $M && return $n + $m - $M; $n; }` [download] C.	[reply] [d/l]
Re: Best way to make sure a number is an even multiple of another? by itub (Priest) on Oct 21, 2004 at 13:00 UTC
Perhaps something like: `use POSIX qw(ceil); sub fix { my ($n, $m) = @_; ceil($n/$m)*$m; }` [download]	[reply] [d/l]
Re: Best way to make sure a number is an even multiple of another? by Corion (Patriarch) on Oct 21, 2004 at 13:22 UTC
For the fun of it, I wanted to give the thing a closed, whole-integer form. The problem was, that a "close fitting" was wanted, and all I had was the following expression: `my $M; my $n; my $remaining = $n % $M; my $next_multiple = $n + $M - $remaining;` [download] This means, that my calculation always was one multiple too large whenever `$remaining` was zero. So I needed to fudge that a bit, by the idea that, if I made `$n` one smaller in one part, and added that one later on, I could maybe shift the error into the right direction: `for my $n (1..20) { print "$n:\t"; for my $M (2..5) { my $remaining = ($n-1) % $M; # subtract one from the remainder my $next_multiple = $n-1 + $M - $remaining; print "$next_multiple\t"; }; print "\n"; };` [download] or, as my unreadable shell test expression: `perl -e "my $n=20; for(@ARGV){$x=$n-1+($_-($n-1)%$_);print qq($n\[$_] +:$x\n)}" 2 3 4 5 6 7 8 9 10 # resp. $x=$n-1+($M-($n-1)%$M)` [download]	[reply] [d/l] [select]
Re: Best way to make sure a number is an even multiple of another? by bart (Canon) on Oct 21, 2004 at 13:20 UTC
Just for the record: `sub fix { my($n, $m) = @_; $n + ($n*$m - $n)%$m; }` [download]	[reply] [d/l]
Re^2: Best way to make sure a number is an even multiple of another? by Roy Johnson (Monsignor) on Oct 21, 2004 at 14:37 UTC
What's your rationale for the multiplication? It seems to work fine with "$n" deleted. Caution:* Contents may have been coded under pressure.	[reply]
Re^3: Best way to make sure a number is an even multiple of another? by bart (Canon) on Oct 21, 2004 at 14:46 UTC
I don't trust modulo on a negative number. I'm never sure what value `-2 % 5` will have. 3 or -2? I believe it depends on the language. So, I want an easy, reliable way to add a multiple ($i) of $m so that `$i - $n >= 0`. The exact number doesn't matter, as `($r$m + $s) % $m == $s % $m` [download] for any non-negative integers $r and $s, and positive integer $m. `$m$n` is both a multiple of $m, and at least as large as $n.	[reply] [d/l] [select]
Re^4: Best way to make sure a number is an even multiple of another? by Roy Johnson (Monsignor) on Oct 21, 2004 at 16:39 UTC
Re^5: Best way to make sure a number is an even multiple of another? by hv (Prior) on Oct 22, 2004 at 10:44 UTC
Re: Best way to make sure a number is an even multiple of another? by Limbic~Region (Chancellor) on Oct 21, 2004 at 13:04 UTC
demerphq, I am not sure how large your numbers are, so the following approach may not be what you need/want: Perform prime factorization on the number Math::Big::Factors or factors if the numbers are smaller than 2^32 Look through all combinations (multiplying factors) until you find one that meets your criteria If I get a chance, I might even try and implementation. Cheers - L~R	[reply]
Re^2: Best way to make sure a number is an even multiple of another? by demerphq (Chancellor) on Oct 21, 2004 at 13:10 UTC
$n will be small. Assume its a 16 bit integer. --- demerphq _{First they ignore you, then they laugh at you, then they fight you, then you win. -- Gandhi Flux8}	[reply]
Re^3: Best way to make sure a number is an even multiple of another? by Limbic~Region (Chancellor) on Oct 21, 2004 at 14:33 UTC
demerphq, I am guilty. I am guilty of not spending enough time reading your question to see what you were asking for before jumping to conclusions. The conclusion I jumped to is that you wanted the largest factor greater than or equal to a certain number. To that end, here is code that I believe does that. Read more... (2 kB) While I know that this isn't what you asked for, it might be of benefit to someone. Cheers - L~R	[reply] [d/l]
Re: Best way to make sure a number is an even multiple of another? by Roy Johnson (Monsignor) on Oct 21, 2004 at 13:50 UTC
`sub fix2 { my $n = shift; # must be greater or equal to this (assert >= 0) my $m = shift; # must be multiple of this (assert > 0) $n + ($m-$n)%$m; }` [download] Caution: Contents may have been coded under pressure.	[reply] [d/l]
Re: Best way to make sure a number is an even multiple of another? by thospel (Hermit) on Oct 21, 2004 at 16:20 UTC
Assuming $n is any integer and $m is a positive integer (if $m is negative it finds the first equal or below instead of equal or above) `-$n%$m+$n` [download] (don't use this under "use integer")	[reply] [d/l]
Re: Best way to make sure a number is an even multiple of another? by TomDLux (Vicar) on Oct 21, 2004 at 14:55 UTC
M goes into N `int( N/M )` times, with a remainder of `M%N`. So, `M * (1 + int( N/M ))` will be the smallest multiple of M greater then N. -- `TTTATCGGTCGTTATATAGATGTTTGCA`	[reply]
Re^2: Best way to make sure a number is an even multiple of another? by Roy Johnson (Monsignor) on Oct 21, 2004 at 17:00 UTC
The trick is that what the OP wanted was greater than or equal to, without doing an if (or equivalent). Here's one way to modify your suggestion: `$m(($n%$m > 0) + int($n/$m));` [download] Caution:* Contents may have been coded under pressure.	[reply] [d/l]

	$m
$n	2	3	4	5
0	0	0	0	0
1	2	3	4	5
2	2	3	4	5
3	4	3	4	5
4	4	6	4	5
5	6	6	8	5
6	6	6	8	10
7	8	9	8	10
8	8	9	8	10
9	10	9	12	10
10	10	12	12	10
11	12	12	12	15
12	12	12	12	15
13	14	15	16	15
14	14	15	16	15
15	16	15	16	15
16	16	18	16	20
17	18	18	20	20
18	18	18	20	20
19	20	21	20	20
20	20	21	20	20

	$m
$n	2	3	4	5
0	0	0	0	0
1	2	3	4	5
2	2	3	4	5
3	4	3	4	5
4	4	6	4	5
5	6	6	8	5
6	6	6	8	10
7	8	9	8	10
8	8	9	8	10
9	10	9	12	10
10	10	12	12	10
11	12	12	12	15
12	12	12	12	15
13	14	15	16	15
14	14	15	16	15
15	16	15	16	15
16	16	18	16	20
17	18	18	20	20
18	18	18	20	20
19	20	21	20	20
20	20	21	20	20

	$m
$n	2	3	4	5
0	0	0	0	0
1	2	3	4	5
2	2	3	4	5
3	4	3	4	5
4	4	6	4	5
5	6	6	8	5
6	6	6	8	10
7	8	9	8	10
8	8	9	8	10
9	10	9	12	10
10	10	12	12	10
11	12	12	12	15
12	12	12	12	15
13	14	15	16	15
14	14	15	16	15
15	16	15	16	15
16	16	18	16	20
17	18	18	20	20
18	18	18	20	20
19	20	21	20	20
20	20	21	20	20