diff --git a/src/Type/Php/GmpOperatorTypeSpecifyingExtension.php b/src/Type/Php/GmpOperatorTypeSpecifyingExtension.php
new file mode 100644
index 0000000000..ef0a45a956
--- /dev/null
+++ b/src/Type/Php/GmpOperatorTypeSpecifyingExtension.php
@@ -0,0 +1,62 @@
+<?php declare(strict_types = 1);
+
+namespace PHPStan\Type\Php;
+
+use PHPStan\DependencyInjection\AutowiredService;
+use PHPStan\Type\BooleanType;
+use PHPStan\Type\ErrorType;
+use PHPStan\Type\IntegerRangeType;
+use PHPStan\Type\NeverType;
+use PHPStan\Type\ObjectType;
+use PHPStan\Type\OperatorTypeSpecifyingExtension;
+use PHPStan\Type\Type;
+use function in_array;
+
+#[AutowiredService]
+final class GmpOperatorTypeSpecifyingExtension implements OperatorTypeSpecifyingExtension
+{
+
+	public function isOperatorSupported(string $operatorSigil, Type $leftSide, Type $rightSide): bool
+	{
+		if ($leftSide instanceof NeverType || $rightSide instanceof NeverType) {
+			return false;
+		}
+
+		$gmpType = new ObjectType('GMP');
+
+		return in_array($operatorSigil, ['+', '-', '*', '/', '**', '%', '&', '|', '^', '<<', '>>', '<', '<=', '>', '>=', '==', '!=', '<=>'], true)
+			&& (
+				$gmpType->isSuperTypeOf($leftSide)->yes()
+				|| $gmpType->isSuperTypeOf($rightSide)->yes()
+			);
+	}
+
+	public function specifyType(string $operatorSigil, Type $leftSide, Type $rightSide): Type
+	{
+		$gmpType = new ObjectType('GMP');
+		$otherSide = $gmpType->isSuperTypeOf($leftSide)->yes()
+			? $rightSide
+			: $leftSide;
+
+		// Comparison operators return bool or int (for spaceship)
+		if (in_array($operatorSigil, ['<', '<=', '>', '>=', '==', '!='], true)) {
+			return new BooleanType();
+		}
+
+		if ($operatorSigil === '<=>') {
+			return IntegerRangeType::fromInterval(-1, 1);
+		}
+
+		// GMP can operate with: GMP, int, or numeric-string
+		if (
+			$otherSide->isInteger()->yes()
+			|| $otherSide->isNumericString()->yes()
+			|| $gmpType->isSuperTypeOf($otherSide)->yes()
+		) {
+			return $gmpType;
+		}
+
+		return new ErrorType();
+	}
+
+}
diff --git a/src/Type/Php/GmpUnaryOperatorTypeSpecifyingExtension.php b/src/Type/Php/GmpUnaryOperatorTypeSpecifyingExtension.php
new file mode 100644
index 0000000000..4aaa3de4d8
--- /dev/null
+++ b/src/Type/Php/GmpUnaryOperatorTypeSpecifyingExtension.php
@@ -0,0 +1,35 @@
+<?php declare(strict_types = 1);
+
+namespace PHPStan\Type\Php;
+
+use PHPStan\DependencyInjection\AutowiredService;
+use PHPStan\Type\NeverType;
+use PHPStan\Type\ObjectType;
+use PHPStan\Type\Type;
+use PHPStan\Type\UnaryOperatorTypeSpecifyingExtension;
+use function in_array;
+
+#[AutowiredService]
+final class GmpUnaryOperatorTypeSpecifyingExtension implements UnaryOperatorTypeSpecifyingExtension
+{
+
+	public function isOperatorSupported(string $operatorSigil, Type $operand): bool
+	{
+		if ($operand instanceof NeverType) {
+			return false;
+		}
+
+		if (!in_array($operatorSigil, ['-', '+', '~'], true)) {
+			return false;
+		}
+
+		$gmpType = new ObjectType('GMP');
+		return $gmpType->isSuperTypeOf($operand)->yes();
+	}
+
+	public function specifyType(string $operatorSigil, Type $operand): Type
+	{
+		return new ObjectType('GMP');
+	}
+
+}
diff --git a/tests/PHPStan/Analyser/nsrt/gmp-operators.php b/tests/PHPStan/Analyser/nsrt/gmp-operators.php
new file mode 100644
index 0000000000..ae708b560e
--- /dev/null
+++ b/tests/PHPStan/Analyser/nsrt/gmp-operators.php
@@ -0,0 +1,206 @@
+<?php
+
+namespace GmpOperatorsTest;
+
+use function PHPStan\Testing\assertType;
+
+// =============================================================================
+// Operator overloads
+// =============================================================================
+
+function gmpArithmeticOperators(\GMP $a, \GMP $b): void
+{
+	assertType('GMP', $a + $b);
+	assertType('GMP', $a - $b);
+	assertType('GMP', $a * $b);
+	assertType('GMP', $a / $b);
+	assertType('GMP', $a % $b);
+	assertType('GMP', $a ** $b);
+	assertType('GMP', -$a);
+}
+
+function gmpWithIntOperators(\GMP $a, int $i): void
+{
+	// GMP on left
+	assertType('GMP', $a + $i);
+	assertType('GMP', $a - $i);
+	assertType('GMP', $a * $i);
+	assertType('GMP', $a / $i);
+	assertType('GMP', $a % $i);
+	assertType('GMP', $a ** $i);
+
+	// int on left (GMP on right)
+	assertType('GMP', $i + $a);
+	assertType('GMP', $i - $a);
+	assertType('GMP', $i * $a);
+	assertType('GMP', $i / $a);
+	assertType('GMP', $i % $a);
+	// Note: $i ** $a is not supported by GMP - exponent must be int
+}
+
+function gmpBitwiseOperators(\GMP $a, \GMP $b, int $i): void
+{
+	// GMP bitwise with GMP
+	assertType('GMP', $a & $b);
+	assertType('GMP', $a | $b);
+	assertType('GMP', $a ^ $b);
+	assertType('GMP', ~$a);
+	assertType('GMP', $a << $b);
+	assertType('GMP', $a >> $b);
+
+	// GMP on left, int on right
+	assertType('GMP', $a & $i);
+	assertType('GMP', $a | $i);
+	assertType('GMP', $a ^ $i);
+	assertType('GMP', $a << $i);
+	assertType('GMP', $a >> $i);
+
+	// int on left, GMP on right
+	assertType('GMP', $i & $a);
+	assertType('GMP', $i | $a);
+	assertType('GMP', $i ^ $a);
+}
+
+function gmpComparisonOperators(\GMP $a, \GMP $b, int $i): void
+{
+	// GMP compared with GMP
+	assertType('bool', $a < $b);
+	assertType('bool', $a <= $b);
+	assertType('bool', $a > $b);
+	assertType('bool', $a >= $b);
+	assertType('bool', $a == $b);
+	assertType('bool', $a != $b);
+	assertType('int<-1, 1>', $a <=> $b);
+
+	// GMP on left, int on right
+	assertType('bool', $a < $i);
+	assertType('bool', $a <= $i);
+	assertType('bool', $a > $i);
+	assertType('bool', $a >= $i);
+	assertType('bool', $a == $i);
+	assertType('bool', $a != $i);
+	assertType('int<-1, 1>', $a <=> $i);
+
+	// int on left, GMP on right
+	assertType('bool', $i < $a);
+	assertType('bool', $i <= $a);
+	assertType('bool', $i > $a);
+	assertType('bool', $i >= $a);
+	assertType('bool', $i == $a);
+	assertType('bool', $i != $a);
+	assertType('int<-1, 1>', $i <=> $a);
+}
+
+function gmpAssignmentOperators(\GMP $a, int $i): void
+{
+	$x = $a;
+	$x += $i;
+	assertType('GMP', $x);
+
+	$y = $a;
+	$y -= $i;
+	assertType('GMP', $y);
+
+	$z = $a;
+	$z *= $i;
+	assertType('GMP', $z);
+}
+
+// =============================================================================
+// gmp_* functions (corresponding to operator overloads)
+// =============================================================================
+
+function gmpArithmeticFunctions(\GMP $a, \GMP $b, int $i): void
+{
+	// gmp_add corresponds to +
+	assertType('GMP', gmp_add($a, $b));
+	assertType('GMP', gmp_add($a, $i));
+	assertType('GMP', gmp_add($i, $a));
+
+	// gmp_sub corresponds to -
+	assertType('GMP', gmp_sub($a, $b));
+	assertType('GMP', gmp_sub($a, $i));
+	assertType('GMP', gmp_sub($i, $a));
+
+	// gmp_mul corresponds to *
+	assertType('GMP', gmp_mul($a, $b));
+	assertType('GMP', gmp_mul($a, $i));
+	assertType('GMP', gmp_mul($i, $a));
+
+	// gmp_div_q corresponds to /
+	assertType('GMP', gmp_div_q($a, $b));
+	assertType('GMP', gmp_div_q($a, $i));
+
+	// gmp_div is alias of gmp_div_q
+	assertType('GMP', gmp_div($a, $b));
+
+	// gmp_mod corresponds to %
+	assertType('GMP', gmp_mod($a, $b));
+	assertType('GMP', gmp_mod($a, $i));
+
+	// gmp_pow corresponds to **
+	assertType('GMP', gmp_pow($a, 2));
+	assertType('GMP', gmp_pow($a, $i));
+
+	// gmp_neg corresponds to unary -
+	assertType('GMP', gmp_neg($a));
+
+	// gmp_abs (no direct operator)
+	assertType('GMP', gmp_abs($a));
+}
+
+function gmpBitwiseFunctions(\GMP $a, \GMP $b): void
+{
+	// gmp_and corresponds to &
+	assertType('GMP', gmp_and($a, $b));
+
+	// gmp_or corresponds to |
+	assertType('GMP', gmp_or($a, $b));
+
+	// gmp_xor corresponds to ^
+	assertType('GMP', gmp_xor($a, $b));
+
+	// gmp_com corresponds to ~
+	assertType('GMP', gmp_com($a));
+}
+
+function gmpComparisonFunctions(\GMP $a, \GMP $b, int $i): void
+{
+	// gmp_cmp returns -1, 0, or 1 in practice, but stubs say int
+	// TODO: Could be improved to int<-1, 1> like the <=> operator
+	assertType('int', gmp_cmp($a, $b));
+	assertType('int', gmp_cmp($a, $i));
+}
+
+function gmpFromInit(): void
+{
+	$x = gmp_init('1');
+	assertType('GMP', $x);
+
+	// Operator with gmp_init result
+	$y = $x * 2;
+	assertType('GMP', $y);
+
+	$z = $x + gmp_init('5');
+	assertType('GMP', $z);
+}
+
+function gmpWithNumericString(\GMP $a, string $s): void
+{
+	// GMP functions accept numeric strings
+	assertType('GMP', gmp_add($a, '123'));
+	assertType('GMP', gmp_mul($a, '456'));
+}
+
+/**
+ * @param object $obj
+ */
+function nonGmpObjectsDoNotGetGmpTreatment($obj, int $i): void
+{
+	// Generic object should NOT be treated as GMP - the extension should not activate
+	// (object is a supertype of GMP, but GMP is not a supertype of object)
+	/** @phpstan-ignore binaryOp.invalid */
+	assertType('*ERROR*', $obj + $i);
+	/** @phpstan-ignore binaryOp.invalid */
+	assertType('*ERROR*', $i + $obj);
+}
diff --git a/tests/PHPStan/Analyser/nsrt/pow.php b/tests/PHPStan/Analyser/nsrt/pow.php
index 3ca27690db..69a7a3c222 100644
--- a/tests/PHPStan/Analyser/nsrt/pow.php
+++ b/tests/PHPStan/Analyser/nsrt/pow.php
@@ -20,11 +20,12 @@ function (\GMP $a, \GMP $b): void {
 };
 
 function (\stdClass $a, \GMP $b): void {
-	assertType('GMP|stdClass', pow($a, $b));
-	assertType('GMP|stdClass', $a ** $b);
+	// stdClass is not a valid GMP operand, these should error
+	assertType('*ERROR*', pow($a, $b));
+	assertType('*ERROR*', $a ** $b);
 
-	assertType('GMP|stdClass', pow($b, $a));
-	assertType('GMP|stdClass', $b ** $a);
+	assertType('*ERROR*', pow($b, $a));
+	assertType('*ERROR*', $b ** $a);
 };
 
 function (): void {
diff --git a/tests/PHPStan/Type/Php/GmpOperatorTypeSpecifyingExtensionTest.php b/tests/PHPStan/Type/Php/GmpOperatorTypeSpecifyingExtensionTest.php
new file mode 100644
index 0000000000..1ced2596a3
--- /dev/null
+++ b/tests/PHPStan/Type/Php/GmpOperatorTypeSpecifyingExtensionTest.php
@@ -0,0 +1,136 @@
+<?php declare(strict_types = 1);
+
+namespace PHPStan\Type\Php;
+
+use InvalidArgumentException;
+use Override;
+use PHPStan\Testing\PHPStanTestCase;
+use PHPStan\Type\ErrorType;
+use PHPStan\Type\FloatType;
+use PHPStan\Type\IntegerType;
+use PHPStan\Type\ObjectType;
+use PHPStan\Type\Type;
+use PHPStan\Type\UnionType;
+use PHPUnit\Framework\Attributes\DataProvider;
+use function sprintf;
+
+class GmpOperatorTypeSpecifyingExtensionTest extends PHPStanTestCase
+{
+
+	private GmpOperatorTypeSpecifyingExtension $extension;
+
+	#[Override]
+	protected function setUp(): void
+	{
+		$this->extension = new GmpOperatorTypeSpecifyingExtension();
+	}
+
+	#[DataProvider('dataSupportedOperations')]
+	public function testSupportsValidGmpOperations(string $sigil, string $leftType, string $rightType): void
+	{
+		$left = $this->createType($leftType);
+		$right = $this->createType($rightType);
+
+		self::assertTrue($this->extension->isOperatorSupported($sigil, $left, $right));
+	}
+
+	public static function dataSupportedOperations(): iterable
+	{
+		// GMP + GMP
+		yield 'GMP + GMP' => ['+', 'GMP', 'GMP'];
+		yield 'GMP - GMP' => ['-', 'GMP', 'GMP'];
+		yield 'GMP * GMP' => ['*', 'GMP', 'GMP'];
+
+		// GMP + int (activates, specifyType handles compatibility)
+		yield 'GMP + int' => ['+', 'GMP', 'int'];
+		yield 'int + GMP' => ['+', 'int', 'GMP'];
+
+		// GMP + incompatible (activates, specifyType returns ErrorType)
+		yield 'GMP + stdClass' => ['+', 'GMP', 'stdClass'];
+		yield 'stdClass + GMP' => ['+', 'stdClass', 'GMP'];
+
+		// Comparison
+		yield 'GMP < GMP' => ['<', 'GMP', 'GMP'];
+		yield 'GMP <=> int' => ['<=>', 'GMP', 'int'];
+	}
+
+	#[DataProvider('dataUnsupportedOperations')]
+	public function testDoesNotSupportInvalidOperations(string $sigil, string $leftType, string $rightType): void
+	{
+		$left = $this->createType($leftType);
+		$right = $this->createType($rightType);
+
+		self::assertFalse($this->extension->isOperatorSupported($sigil, $left, $right));
+	}
+
+	public static function dataUnsupportedOperations(): iterable
+	{
+		// Neither side is GMP
+		yield 'int + int' => ['+', 'int', 'int'];
+
+		// object is a supertype of GMP, but is not GMP itself
+		// This catches mutations that swap isSuperTypeOf callee/argument
+		yield 'object + int' => ['+', 'object', 'int'];
+		yield 'int + object' => ['+', 'int', 'object'];
+
+		// GMP|int union should not be treated as definitely GMP
+		// This catches mutations that change .yes() to !.no()
+		yield 'GMP|int + int' => ['+', 'GMP|int', 'int'];
+		yield 'int + GMP|int' => ['+', 'int', 'GMP|int'];
+	}
+
+	#[DataProvider('dataSpecifyTypeReturnsError')]
+	public function testSpecifyTypeReturnsErrorForIncompatibleTypes(string $sigil, string $leftType, string $rightType): void
+	{
+		$left = $this->createType($leftType);
+		$right = $this->createType($rightType);
+
+		self::assertInstanceOf(ErrorType::class, $this->extension->specifyType($sigil, $left, $right));
+	}
+
+	public static function dataSpecifyTypeReturnsError(): iterable
+	{
+		yield 'GMP + stdClass' => ['+', 'GMP', 'stdClass'];
+		yield 'stdClass + GMP' => ['+', 'stdClass', 'GMP'];
+		yield 'GMP + float' => ['+', 'GMP', 'float'];
+	}
+
+	#[DataProvider('dataSpecifyTypeReturnsGmp')]
+	public function testSpecifyTypeReturnsGmpForCompatibleTypes(string $sigil, string $leftType, string $rightType): void
+	{
+		$left = $this->createType($leftType);
+		$right = $this->createType($rightType);
+
+		$result = $this->extension->specifyType($sigil, $left, $right);
+		self::assertInstanceOf(ObjectType::class, $result);
+		self::assertSame('GMP', $result->getClassName());
+	}
+
+	public static function dataSpecifyTypeReturnsGmp(): iterable
+	{
+		yield 'GMP + GMP' => ['+', 'GMP', 'GMP'];
+		yield 'GMP + int' => ['+', 'GMP', 'int'];
+		yield 'int + GMP' => ['+', 'int', 'GMP'];
+	}
+
+	private function createType(string $type): Type
+	{
+		switch ($type) {
+			case 'GMP':
+				return new ObjectType('GMP');
+			case 'int':
+				return new IntegerType();
+			case 'float':
+				return new FloatType();
+			case 'object':
+				return new ObjectType('object');
+			case 'stdClass':
+				return new ObjectType('stdClass');
+			case 'GMP|int':
+				return new UnionType([new ObjectType('GMP'), new IntegerType()]);
+			default:
+				throw new InvalidArgumentException(sprintf('Unknown type: %s', $type));
+		}
+	}
+
+}