Prevent recursion in Calculator::gcd()

Author: BenMorel

src/Internal/Calculator.php

@@ -232,15 +232,11 @@ abstract public function modPow(string $base, string $exp, string $mod): string;
      */
     public function gcd(string $a, string $b): string
     {
-        if ($a === '0') {
-            return $this->abs($b);
+        while ($b !== '0') {
+            [$a, $b] = [$b, $this->divR($a, $b)];
         }
 
-        if ($b === '0') {
-            return $this->abs($a);
-        }
-
-        return $this->gcd($b, $this->divR($a, $b));
+        return $this->abs($a);
     }
 
     /**
@@ -610,16 +606,23 @@ final protected function init(string $a, string $b): array
      */
     private function gcdExtended(string $a, string $b): array
     {
-        if ($a === '0') {
-            return [$b, '0', '1'];
+        // Iterative extended Euclidean algorithm (recursion would exhaust memory on large
+        // inputs, see gcd()), maintaining the invariants:
+        //   $a * $x0 + $b * $y0 = $r0
+        //   $a * $x1 + $b * $y1 = $r1
+        [$r0, $r1] = [$a, $b];
+        [$x0, $x1] = ['1', '0'];
+        [$y0, $y1] = ['0', '1'];
+
+        while ($r1 !== '0') {
+            [$q, $r] = $this->divQR($r0, $r1);
+
+            [$r0, $r1] = [$r1, $r];
+            [$x0, $x1] = [$x1, $this->sub($x0, $this->mul($q, $x1))];
+            [$y0, $y1] = [$y1, $this->sub($y0, $this->mul($q, $y1))];
         }
 
-        [$gcd, $x1, $y1] = $this->gcdExtended($this->mod($b, $a), $a);
-
-        $x = $this->sub($y1, $this->mul($this->divQ($b, $a), $x1));
-        $y = $x1;
-
-        return [$gcd, $x, $y];
+        return [$r0, $x0, $y0];
     }
 
     /**