Start by taking $i = 1 + $hash % ($p-1) instead of $i = $hash % $p ?

That just offsets the problem, not fixes it unfortunately:

for( my $i=0; $i<17; ++$i ) { 
    my $j = ( 1 + $i ) % ( 17 - 1 ); 
    printf "%2u: %s\n", $i, join' ', map{ sprintf "%2u", $j = ( $j + $
+i ) % 17 } 0 .. 16; 
};;
 0:  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 <<<<<<<<<<<<<<<
+<<<<<<<<<<<<<<<<<<<<<<
 1:  3  4  5  6  7  8  9 10 11 12 13 14 15 16  0  1  2
 2:  5  7  9 11 13 15  0  2  4  6  8 10 12 14 16  1  3
 3:  7 10 13 16  2  5  8 11 14  0  3  6  9 12 15  1  4
 4:  9 13  0  4  8 12 16  3  7 11 15  2  6 10 14  1  5
 5: 11 16  4  9 14  2  7 12  0  5 10 15  3  8 13  1  6
 6: 13  2  8 14  3  9 15  4 10 16  5 11  0  6 12  1  7
 7: 15  5 12  2  9 16  6 13  3 10  0  7 14  4 11  1  8
 8:  0  8 16  7 15  6 14  5 13  4 12  3 11  2 10  1  9
 9:  2 11  3 12  4 13  5 14  6 15  7 16  8  0  9  1 10
10:  4 14  7  0 10  3 13  6 16  9  2 12  5 15  8  1 11
11:  6  0 11  5 16 10  4 15  9  3 14  8  2 13  7  1 12
12:  8  3 15 10  5  0 12  7  2 14  9  4 16 11  6  1 13
13: 10  6  2 15 11  7  3 16 12  8  4  0 13  9  5  1 14
14: 12  9  6  3  0 14 11  8  5  2 16 13 10  7  4  1 15
15: 15 13 11  9  7  5  3  1 16 14 12 10  8  6  4  2  0
16:  0 16 15 14 13 12 11 10  9  8  7  6  5  4  3  2  1
[download]

---

With the rise and rise of 'Social' network sites: 'Computers are making people easier to use everyday'

Examine what is said, not who speaks -- Silence betokens consent -- Love the truth but pardon error.

"Science is about questioning the status quo. Questioning authority". I'm with torvalds on this

In the absence of evidence, opinion is indistinguishable from prejudice. Agile (and TDD) debunked

$i = 1 + $hash % ($p-1)

my $j = ( 1 + $i ) % ( 17 - 1 );

I'm not sure who you got those extra parens from, but they weren't from me. :)

Or, looking at it another way:

my $i=0;

The point of my suggestion, $i = 1 + $hash % ($p-1), is that it never results in $i == 0 (even if your computed $hash equals 0). So calling out the line that resulted from you doing $i=0 doesn't really have much bearing on the validity of my suggestion.

Does any of that help you see how you misinterpreted my suggestion? I ask because I'm not completely sure were the disconnect is and I'm reluctant to try guess at what I should try to explain.

- tye        

You didn't calculate (n + p) %p -- what you actual did was (n + n%p) % p, and when n%p is zero you get stuck.

You didn't calculate (n + p) %p

But ( 0 + x ) % x is just x % x; and is always 0?

---

With the rise and rise of 'Social' network sites: 'Computers are making people easier to use everyday'

Examine what is said, not who speaks -- Silence betokens consent -- Love the truth but pardon error.

"Science is about questioning the status quo. Questioning authority". I'm with torvalds on this

In the absence of evidence, opinion is indistinguishable from prejudice. Agile (and TDD) debunked

Yes you're right.

So your code does something like this :-

     int r = rand();
     int n = r % p;
     while ( a[n] != 0 ) {
         n = (n + n) % p;
     }
     a[n] = r;
[download]

so you get stuck when n =0. But if you add a value to n that's relatively prime to P then it should work.

for example,

say (($_ + 5) % 11 ) for (0..10);

5
6
7
8
9
10
0
1
2
3
4
[download]

my %hash; # hash of stored values
my $PRIME = some_large_prime(); # random or fixed, your choice
my $PRIME_HALF = int($PRIME/2); # or some other known value or functio
+n
...
my $i = $initial_index; # wherever you get this from
my $failed_tries = $PRIME;
while (defined($hash{$i}) and $failed_tries--) {
    my $offset = $hash{$i} % $PRIME;
    $offset = $PRIME_HALF if ($offset == 0);
    $i = ($i + ($hash{$i}) % $PRIME;
}

if ($failed_tries) {
    $hash{$i} = $value;
} else { 
    warn "Hash full\n";
}
[download]

Update: I'm assuming that the hash values, once written, are read only, and never change.

Use the value at the hash collision to get the offset for the next hash key.

Problem. The value giving the trouble is 0; so the value at the hash collision can be 0; and 0 + 0 == 0 :)

Of course, it won't always be zero. Any multiple of the Prime size will mod to a hash of 0; but is still means that if a true 0 value arises, the thing disappears up it you know where.

Having spent the last 3 days running some long-running, large scale simulations; I'm satisfied that the benefits of the declustering affect of the i⁺¹ = ( i + prime ) % prime scheme are real, and outweigh the need to have an if( !i ) { //take a different path conditional test in the inner loop.

I'm still trying a couple of things for that other path; but adding prime/2 seems as good as any other thing I've thought of.

---

With the rise and rise of 'Social' network sites: 'Computers are making people easier to use everyday'

Examine what is said, not who speaks -- Silence betokens consent -- Love the truth but pardon error.

"Science is about questioning the status quo. Questioning authority". I'm with torvalds on this

In the absence of evidence, opinion is indistinguishable from prejudice. Agile (and TDD) debunked