diff --git a/src/Type/Constant/ConstantFloatType.php b/src/Type/Constant/ConstantFloatType.php
index 229bf6696f..3468ab5de8 100644
--- a/src/Type/Constant/ConstantFloatType.php
+++ b/src/Type/Constant/ConstantFloatType.php
@@ -5,8 +5,6 @@
 use PHPStan\PhpDocParser\Ast\ConstExpr\ConstExprFloatNode;
 use PHPStan\PhpDocParser\Ast\Type\ConstTypeNode;
 use PHPStan\PhpDocParser\Ast\Type\TypeNode;
-use PHPStan\TrinaryLogic;
-use PHPStan\Type\CompoundType;
 use PHPStan\Type\ConstantScalarType;
 use PHPStan\Type\FloatType;
 use PHPStan\Type\GeneralizePrecision;
@@ -14,12 +12,11 @@
 use PHPStan\Type\Traits\ConstantScalarTypeTrait;
 use PHPStan\Type\Type;
 use PHPStan\Type\VerbosityLevel;
-use function abs;
 use function ini_get;
 use function ini_set;
 use function is_finite;
+use function is_nan;
 use function str_contains;
-use const PHP_FLOAT_EPSILON;
 
 /** @api */
 class ConstantFloatType extends FloatType implements ConstantScalarType
@@ -42,7 +39,7 @@ public function getValue(): float
 
 	public function equals(Type $type): bool
 	{
-		return $type instanceof self && abs($this->value - $type->value) < PHP_FLOAT_EPSILON;
+		return $type instanceof self && ($this->value === $type->value || is_nan($this->value) && is_nan($type->value));
 	}
 
 	private function castFloatToString(float $value): string
@@ -69,31 +66,6 @@ public function describe(VerbosityLevel $level): string
 		);
 	}
 
-	public function isSuperTypeOf(Type $type): TrinaryLogic
-	{
-		if ($type instanceof self) {
-			if (!$this->equals($type)) {
-				if (abs($this->value - $type->value) < PHP_FLOAT_EPSILON) {
-					return TrinaryLogic::createMaybe();
-				}
-
-				return TrinaryLogic::createNo();
-			}
-
-			return TrinaryLogic::createYes();
-		}
-
-		if ($type instanceof parent) {
-			return TrinaryLogic::createMaybe();
-		}
-
-		if ($type instanceof CompoundType) {
-			return $type->isSubTypeOf($this);
-		}
-
-		return TrinaryLogic::createNo();
-	}
-
 	public function toString(): Type
 	{
 		return new ConstantStringType((string) $this->value);
diff --git a/src/Type/Traits/ConstantScalarTypeTrait.php b/src/Type/Traits/ConstantScalarTypeTrait.php
index cca9b12008..5a8d6dcfc5 100644
--- a/src/Type/Traits/ConstantScalarTypeTrait.php
+++ b/src/Type/Traits/ConstantScalarTypeTrait.php
@@ -24,7 +24,7 @@ public function accepts(Type $type, bool $strictTypes): TrinaryLogic
 	public function acceptsWithReason(Type $type, bool $strictTypes): AcceptsResult
 	{
 		if ($type instanceof self) {
-			return AcceptsResult::createFromBoolean($this->value === $type->value);
+			return AcceptsResult::createFromBoolean($this->equals($type));
 		}
 
 		if ($type instanceof CompoundType) {
@@ -37,7 +37,7 @@ public function acceptsWithReason(Type $type, bool $strictTypes): AcceptsResult
 	public function isSuperTypeOf(Type $type): TrinaryLogic
 	{
 		if ($type instanceof self) {
-			return $this->value === $type->value ? TrinaryLogic::createYes() : TrinaryLogic::createNo();
+			return TrinaryLogic::createFromBoolean($this->equals($type));
 		}
 
 		if ($type instanceof parent) {
diff --git a/tests/PHPStan/Rules/Functions/CallToFunctionParametersRuleTest.php b/tests/PHPStan/Rules/Functions/CallToFunctionParametersRuleTest.php
index 28cd5caa9d..1a8770dd05 100644
--- a/tests/PHPStan/Rules/Functions/CallToFunctionParametersRuleTest.php
+++ b/tests/PHPStan/Rules/Functions/CallToFunctionParametersRuleTest.php
@@ -1664,4 +1664,9 @@ public function testParamClosureThis(): void
 		]);
 	}
 
+	public function testBug10297(): void
+	{
+		$this->analyse([__DIR__ . '/data/bug-10297.php'], []);
+	}
+
 }
diff --git a/tests/PHPStan/Rules/Functions/data/bug-10297.php b/tests/PHPStan/Rules/Functions/data/bug-10297.php
new file mode 100644
index 0000000000..ed3a8cf3dd
--- /dev/null
+++ b/tests/PHPStan/Rules/Functions/data/bug-10297.php
@@ -0,0 +1,86 @@
+<?php declare(strict_types = 1);
+
+namespace Bug10297;
+
+use Generator;
+use TypeError;
+use UnexpectedValueException;
+
+/**
+ * @template K
+ * @template T
+ * @template L
+ * @template U
+ *
+ * @param iterable<K, T> $stream
+ * @param callable(T, K): iterable<L, U> $fn
+ *
+ * @return Generator<L, U>
+ */
+function scollect(iterable $stream, callable $fn): Generator
+{
+    foreach ($stream as $key => $value) {
+        yield from $fn($value, $key);
+    }
+}
+
+/**
+ * @template K of array-key
+ * @template T
+ * @template L of array-key
+ * @template U
+ *
+ * @param array<K, T> $array
+ * @param callable(T, K): iterable<L, U> $fn
+ *
+ * @return array<L, U>
+ */
+function collectWithKeys(array $array, callable $fn): array
+{
+    $map = [];
+    $counter = 0;
+
+    try {
+        foreach (scollect($array, $fn) as $key => $value) {
+            $map[$key] = $value;
+            ++$counter;
+        }
+    } catch (TypeError) {
+        throw new UnexpectedValueException('The key yielded in the callable is not compatible with the type "array-key".');
+    }
+
+    if ($counter !== count($map)) {
+        throw new UnexpectedValueException(
+            'Data loss occurred because of duplicated keys. Use `collect()` if you do not care about ' .
+            'the yielded keys, or use `scollect()` if you need to support duplicated keys (as arrays cannot).',
+        );
+    }
+
+    return $map;
+}
+
+class SomeUnitTest
+{
+	/**
+	 * @return iterable<mixed>
+	 */
+	public static function someProvider(): iterable
+	{
+		$unsupportedTypes = [
+			// this one does not work:
+            'Not a Number' => NAN,
+			// these work:
+            'Infinity' => INF,
+            stdClass::class => new stdClass(),
+            self::class => self::class,
+            'hello there' => 'hello there',
+            'array' => [[42]],
+        ];
+
+        yield from collectWithKeys($unsupportedTypes, static function (mixed $value, string $type): iterable {
+            $error = sprintf('Some %s error message', $type);
+
+            yield sprintf('"%s" something something', $type) => [$value, [$error, $error, $error]];
+        });
+	}
+}
diff --git a/tests/PHPStan/Rules/Methods/IncompatibleDefaultParameterTypeRuleTest.php b/tests/PHPStan/Rules/Methods/IncompatibleDefaultParameterTypeRuleTest.php
index 0061758036..e55eb6eede 100644
--- a/tests/PHPStan/Rules/Methods/IncompatibleDefaultParameterTypeRuleTest.php
+++ b/tests/PHPStan/Rules/Methods/IncompatibleDefaultParameterTypeRuleTest.php
@@ -73,4 +73,9 @@ public function testDefaultValueForPromotedProperty(): void
 		]);
 	}
 
+	public function testBug10956(): void
+	{
+		$this->analyse([__DIR__ . '/data/bug-10956.php'], []);
+	}
+
 }
diff --git a/tests/PHPStan/Rules/Methods/data/bug-10956.php b/tests/PHPStan/Rules/Methods/data/bug-10956.php
new file mode 100644
index 0000000000..459d5bd6c2
--- /dev/null
+++ b/tests/PHPStan/Rules/Methods/data/bug-10956.php
@@ -0,0 +1,19 @@
+<?php declare(strict_types = 1);
+
+namespace Bug10956;
+
+class HelloWorld
+{
+	const DEFAULT_VALUE = [NAN]; // unique value, distinct from anything, but equal to itself
+
+	/**
+	 * @param int|self::DEFAULT_VALUE $value
+	 */
+	public function test (mixed $value = self::DEFAULT_VALUE) {
+		if ($value === self::DEFAULT_VALUE) {
+			echo 'default';
+		} else {
+			echo (int) $value;
+		}
+	}
+}