Initial data commit

Task/Tonelli-Shanks-algorithm/Raku/tonelli-shanks-algorithm.raku

@@ -0,0 +1,52 @@
+#  Legendre operator (𝑛│𝑝)
+sub infix:<│> (Int \𝑛, Int \𝑝 where 𝑝.is-prime && (𝑝 != 2)) {
+    given 𝑛.expmod( (𝑝-1) div 2, 𝑝 ) {
+        when 0  {  0 }
+        when 1  {  1 }
+        default { -1 }
+    }
+}
+
+sub tonelli-shanks ( \𝑛, \𝑝 where (𝑛│𝑝) > 0 ) {
+    my $𝑄 = 𝑝 - 1;
+    my $𝑆 = 0;
+    $𝑄 +>= 1 and $𝑆++ while $𝑄 %% 2;
+    return 𝑛.expmod((𝑝+1) div 4, 𝑝) if $𝑆 == 1;
+    my $𝑐 = ((2..𝑝).first: (*│𝑝) < 0).expmod($𝑄, 𝑝);
+    my $𝑅 = 𝑛.expmod( ($𝑄+1) +> 1, 𝑝 );
+    my $𝑡 = 𝑛.expmod( $𝑄, 𝑝 );
+    while ($𝑡-1) % 𝑝 {
+        my $b;
+        my $𝑡2 = $𝑡² % 𝑝;
+        for 1 .. $𝑆 {
+            if ($𝑡2-1) %% 𝑝 {
+                $b = $𝑐.expmod(1 +< ($𝑆-1-$_), 𝑝);
+                $𝑆 = $_;
+                last;
+            }
+            $𝑡2 = $𝑡2² % 𝑝;
+        }
+        $𝑅 = ($𝑅 * $b) % 𝑝;
+        $𝑐 = $b² % 𝑝;
+        $𝑡 = ($𝑡 * $𝑐) % 𝑝;
+    }
+    $𝑅;
+}
+
+my @tests = (
+    (10, 13),
+    (56, 101),
+    (1030, 10009),
+    (1032, 10009),
+    (44402, 100049),
+    (665820697, 1000000009),
+    (881398088036, 1000000000039),
+    (41660815127637347468140745042827704103445750172002,
+      100000000000000000000000000000000000000000000000577)
+);
+
+ for @tests -> ($n, $p) {
+    try my $t = tonelli-shanks($n, $p);
+    say "No solution for ({$n}, {$p})." and next if !$t or ($t² - $n) % $p;
+    say "Roots of $n are ($t, {$p-$t}) mod $p";
+}