Tonelli-Shanks algorithm: Difference between revisions
Added Perl example
SqrtNegInf (talk | contribs) (Added Perl example) |
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root2 = 67897014630059379150258016012699961096274733366069
</pre>
=={{header|Perl}}==
{{trans|Perl 6}}
<lang perl>use bigint;
use ntheory qw(is_prime powmod kronecker);
sub tonelli_shanks {
my($n,$p) = @_;
return if kronecker($n,$p) <= 0;
my $Q = $p - 1;
my $S = 0;
$Q >>= 1 and $S++ while 0 == $Q%2;
return powmod($n,int(($p+1)/4), $p) if $S == 1;
my $c;
for $n (2..$p) {
next if kronecker($n,$p) >= 0;
$c = powmod($n, $Q, $p);
last;
}
my $R = powmod($n, ($Q+1) >> 1, $p ); # ?
my $t = powmod($n, $Q, $p );
while (($t-1) % $p) {
my $b;
my $t2 = $t**2 % $p;
for (1 .. $S) {
if (0 == ($t2-1)%$p) {
$b = powmod($c, 1 << ($S-1-$_), $p);
$S = $_;
last;
}
$t2 = $t2**2 % $p;
}
$R = ($R * $b) % $p;
$c = $b**2 % $p;
$t = ($t * $c) % $p;
}
$R;
}
my @tests = (
(10, 13),
(56, 101),
(1030, 10009),
(1032, 10009),
(44402, 100049),
(665820697, 1000000009),
(881398088036, 1000000000039),
);
while (@tests) {
$n = shift @tests;
$p = shift @tests;
my $t = tonelli_shanks($n, $p);
if (!$t or ($t**2 - $n) % $p) {
printf "No solution for (%d, %d)\n", $n, $p;
} else {
printf "Roots of %d are (%d, %d) mod %d\n", $n, $t, $p-$t, $p;
}
}</lang>
{{out}}
<pre>Roots of 10 are (7, 6) mod 13
Roots of 56 are (37, 64) mod 101
Roots of 1030 are (1632, 8377) mod 10009
No solution for (1032, 10009)
Roots of 44402 are (30468, 69581) mod 100049
Roots of 665820697 are (378633312, 621366697) mod 1000000009
Roots of 881398088036 are (791399408049, 208600591990) mod 1000000000039</pre>
=={{header|Perl 6}}==
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