diff --git a/src/Reflection/InitializerExprTypeResolver.php b/src/Reflection/InitializerExprTypeResolver.php
index 384b945d17..c76661d6d2 100644
--- a/src/Reflection/InitializerExprTypeResolver.php
+++ b/src/Reflection/InitializerExprTypeResolver.php
@@ -1008,9 +1008,21 @@ public function getBitwiseAndTypeFromTypes(Type $leftType, Type $rightType): Typ
 			$rightType = $this->optimizeScalarType($rightType);
 		}
 
-		if ($leftType->isString()->yes() && $rightType->isString()->yes()) {
+		if ($leftType instanceof MixedType && $rightType instanceof MixedType) {
+			return new BenevolentUnionType([new IntegerType(), new StringType()]);
+		}
+
+		$leftIsString = $leftType->isString();
+		$rightIsString = $rightType->isString();
+		if (
+			($leftIsString->yes() || $leftType instanceof MixedType)
+			&& ($rightIsString->yes() || $rightType instanceof MixedType)
+		) {
 			return new StringType();
 		}
+		if ($leftIsString->maybe() && $rightIsString->maybe()) {
+			return new ErrorType();
+		}
 
 		$leftNumberType = $leftType->toNumber();
 		$rightNumberType = $rightType->toNumber();
@@ -1082,9 +1094,21 @@ public function getBitwiseOrTypeFromTypes(Type $leftType, Type $rightType): Type
 			$rightType = $this->optimizeScalarType($rightType);
 		}
 
-		if ($leftType->isString()->yes() && $rightType->isString()->yes()) {
+		if ($leftType instanceof MixedType && $rightType instanceof MixedType) {
+			return new BenevolentUnionType([new IntegerType(), new StringType()]);
+		}
+
+		$leftIsString = $leftType->isString();
+		$rightIsString = $rightType->isString();
+		if (
+			($leftIsString->yes() || $leftType instanceof MixedType)
+			&& ($rightIsString->yes() || $rightType instanceof MixedType)
+		) {
 			return new StringType();
 		}
+		if ($leftIsString->maybe() && $rightIsString->maybe()) {
+			return new ErrorType();
+		}
 
 		if (TypeCombinator::union($leftType->toNumber(), $rightType->toNumber()) instanceof ErrorType) {
 			return new ErrorType();
@@ -1146,9 +1170,21 @@ public function getBitwiseXorTypeFromTypes(Type $leftType, Type $rightType): Typ
 			$rightType = $this->optimizeScalarType($rightType);
 		}
 
-		if ($leftType->isString()->yes() && $rightType->isString()->yes()) {
+		if ($leftType instanceof MixedType && $rightType instanceof MixedType) {
+			return new BenevolentUnionType([new IntegerType(), new StringType()]);
+		}
+
+		$leftIsString = $leftType->isString();
+		$rightIsString = $rightType->isString();
+		if (
+			($leftIsString->yes() || $leftType instanceof MixedType)
+			&& ($rightIsString->yes() || $rightType instanceof MixedType)
+		) {
 			return new StringType();
 		}
+		if ($leftIsString->maybe() && $rightIsString->maybe()) {
+			return new ErrorType();
+		}
 
 		if (TypeCombinator::union($leftType->toNumber(), $rightType->toNumber()) instanceof ErrorType) {
 			return new ErrorType();
diff --git a/tests/PHPStan/Analyser/Generator/data/gnsr.php b/tests/PHPStan/Analyser/Generator/data/gnsr.php
index c6bddf33ff..a5324af90c 100644
--- a/tests/PHPStan/Analyser/Generator/data/gnsr.php
+++ b/tests/PHPStan/Analyser/Generator/data/gnsr.php
@@ -110,7 +110,7 @@ public function doBitwiseNot($a, int $b): void
 	public function doBitwiseAnd($a, $b, int $c, int $d): void
 	{
 		assertType('int', $a & $b);
-		assertNativeType('int', $a & $b);
+		assertNativeType('(int|string)', $a & $b);
 		assertType('1', 1 & 1);
 		assertNativeType('1', 1 & 1);
 		assertType('int', $c & $d);
@@ -125,7 +125,7 @@ public function doBitwiseAnd($a, $b, int $c, int $d): void
 	public function doBitwiseOr($a, $b, int $c, int $d): void
 	{
 		assertType('int', $a | $b);
-		assertNativeType('int', $a | $b);
+		assertNativeType('(int|string)', $a | $b);
 		assertType('1', 1 | 1);
 		assertNativeType('1', 1 | 1);
 		assertType('int', $c | $d);
@@ -140,7 +140,7 @@ public function doBitwiseOr($a, $b, int $c, int $d): void
 	public function doBitwiseXor($a, $b, int $c, int $d): void
 	{
 		assertType('int', $a ^ $b);
-		assertNativeType('int', $a ^ $b);
+		assertNativeType('(int|string)', $a ^ $b);
 		assertType('0', 1 ^ 1);
 		assertNativeType('0', 1 ^ 1);
 		assertType('int', $c ^ $d);
diff --git a/tests/PHPStan/Analyser/nsrt/bitwise.php b/tests/PHPStan/Analyser/nsrt/bitwise.php
new file mode 100644
index 0000000000..6acac4237c
--- /dev/null
+++ b/tests/PHPStan/Analyser/nsrt/bitwise.php
@@ -0,0 +1,63 @@
+<?php
+
+namespace Bitwise;
+
+use function PHPStan\Testing\assertType;
+
+/**
+ * @param string|int $stringOrInt
+ * @param mixed $mixed
+ */
+function test(int $int, string $string, $stringOrInt, $mixed) : void
+{
+	assertType('int', $int & $int);
+	assertType('*ERROR*', $int & $string);
+	assertType('*ERROR*', $int & $stringOrInt);
+	assertType('int', $int & $mixed);
+	assertType('*ERROR*', $string & $int);
+	assertType('string', $string & $string);
+	assertType('*ERROR*', $string & $stringOrInt);
+	assertType('string', $string & $mixed);
+	assertType('*ERROR*', $stringOrInt & $int);
+	assertType('*ERROR*', $stringOrInt & $string);
+	assertType('*ERROR*', $stringOrInt & $stringOrInt);
+	assertType('*ERROR*', $stringOrInt & $mixed);
+	assertType('int', $mixed & $int);
+	assertType('string', $mixed & $string);
+	assertType('*ERROR*', $mixed & $stringOrInt);
+	assertType('(int|string)', $mixed & $mixed);
+
+	assertType('int', $int | $int);
+	assertType('*ERROR*', $int | $string);
+	assertType('*ERROR*', $int | $stringOrInt);
+	assertType('int', $int | $mixed);
+	assertType('*ERROR*', $string | $int);
+	assertType('string', $string | $string);
+	assertType('*ERROR*', $string | $stringOrInt);
+	assertType('string', $string | $mixed);
+	assertType('*ERROR*', $stringOrInt | $int);
+	assertType('*ERROR*', $stringOrInt | $string);
+	assertType('*ERROR*', $stringOrInt | $stringOrInt);
+	assertType('*ERROR*', $stringOrInt | $mixed);
+	assertType('int', $mixed | $int);
+	assertType('string', $mixed | $string);
+	assertType('*ERROR*', $mixed | $stringOrInt);
+	assertType('(int|string)', $mixed | $mixed);
+
+	assertType('int', $int ^ $int);
+	assertType('*ERROR*', $int ^ $string);
+	assertType('*ERROR*', $int ^ $stringOrInt);
+	assertType('int', $int ^ $mixed);
+	assertType('*ERROR*', $string ^ $int);
+	assertType('string', $string ^ $string);
+	assertType('*ERROR*', $string ^ $stringOrInt);
+	assertType('string', $string ^ $mixed);
+	assertType('*ERROR*', $stringOrInt ^ $int);
+	assertType('*ERROR*', $stringOrInt ^ $string);
+	assertType('*ERROR*', $stringOrInt ^ $stringOrInt);
+	assertType('*ERROR*', $stringOrInt ^ $mixed);
+	assertType('int', $mixed ^ $int);
+	assertType('string', $mixed ^ $string);
+	assertType('*ERROR*', $mixed ^ $stringOrInt);
+	assertType('(int|string)', $mixed ^ $mixed);
+}
diff --git a/tests/PHPStan/Rules/Functions/CallToFunctionParametersRuleTest.php b/tests/PHPStan/Rules/Functions/CallToFunctionParametersRuleTest.php
index 53ddb13625..5d098ec163 100644
--- a/tests/PHPStan/Rules/Functions/CallToFunctionParametersRuleTest.php
+++ b/tests/PHPStan/Rules/Functions/CallToFunctionParametersRuleTest.php
@@ -2404,6 +2404,11 @@ public function testBug13784(): void
 		$this->analyse([__DIR__ . '/data/bug-13784.php'], []);
 	}
 
+	public function testBug8094(): void
+	{
+		$this->analyse([__DIR__ . '/data/bug-8094.php'], []);
+	}
+
 	public function testBug13556(): void
 	{
 		$this->checkExplicitMixed = true;
diff --git a/tests/PHPStan/Rules/Functions/data/bug-8094.php b/tests/PHPStan/Rules/Functions/data/bug-8094.php
new file mode 100644
index 0000000000..620ffd0597
--- /dev/null
+++ b/tests/PHPStan/Rules/Functions/data/bug-8094.php
@@ -0,0 +1,10 @@
+<?php
+
+namespace Bug8094;
+
+function mask_encode($data, $mask)
+{
+	$mask = substr($mask, 0, strlen($data));
+	$data ^= $mask;
+	return(base64_encode($data));
+}