diff --git a/conf/config.neon b/conf/config.neon
index b7e91bd3d9..54f4ff3186 100644
--- a/conf/config.neon
+++ b/conf/config.neon
@@ -1053,6 +1053,10 @@ services:
 		arguments:
 			reportMagicProperties: %reportMagicProperties%
 			checkDynamicProperties: %checkDynamicProperties%
+	-
+		class: PHPStan\Type\Php\BcMathNumberOperatorTypeSpecifyingExtension
+		tags:
+			- phpstan.broker.operatorTypeSpecifyingExtension
 
 	-
 		class: PHPStan\Rules\Properties\UninitializedPropertyRule
diff --git a/src/Php/PhpVersion.php b/src/Php/PhpVersion.php
index 6f55bdda15..5215a30606 100644
--- a/src/Php/PhpVersion.php
+++ b/src/Php/PhpVersion.php
@@ -400,4 +400,9 @@ public function substrReturnFalseInsteadOfEmptyString(): bool
 		return $this->versionId < 80000;
 	}
 
+	public function supportsBcMathNumberOperatorOverloading(): bool
+	{
+		return $this->versionId >= 80400;
+	}
+
 }
diff --git a/src/Reflection/InitializerExprTypeResolver.php b/src/Reflection/InitializerExprTypeResolver.php
index 9fef24a587..fb935ac630 100644
--- a/src/Reflection/InitializerExprTypeResolver.php
+++ b/src/Reflection/InitializerExprTypeResolver.php
@@ -872,6 +872,11 @@ public function getModType(Expr $left, Expr $right, callable $getTypeCallback):
 			return $this->getNeverType($leftType, $rightType);
 		}
 
+		$extensionSpecified = $this->callOperatorTypeSpecifyingExtensions(new BinaryOp\Mod($left, $right), $leftType, $rightType);
+		if ($extensionSpecified !== null) {
+			return $extensionSpecified;
+		}
+
 		if ($leftType->toNumber() instanceof ErrorType || $rightType->toNumber() instanceof ErrorType) {
 			return new ErrorType();
 		}
@@ -1234,16 +1239,16 @@ public function getPowType(Expr $left, Expr $right, callable $getTypeCallback):
 		$leftType = $getTypeCallback($left);
 		$rightType = $getTypeCallback($right);
 
-		$exponentiatedTyped = $leftType->exponentiate($rightType);
-		if (!$exponentiatedTyped instanceof ErrorType) {
-			return $exponentiatedTyped;
-		}
-
 		$extensionSpecified = $this->callOperatorTypeSpecifyingExtensions(new BinaryOp\Pow($left, $right), $leftType, $rightType);
 		if ($extensionSpecified !== null) {
 			return $extensionSpecified;
 		}
 
+		$exponentiatedTyped = $leftType->exponentiate($rightType);
+		if (!$exponentiatedTyped instanceof ErrorType) {
+			return $exponentiatedTyped;
+		}
+
 		return new ErrorType();
 	}
 
diff --git a/src/Type/ObjectType.php b/src/Type/ObjectType.php
index 0ad78520f2..5a05575059 100644
--- a/src/Type/ObjectType.php
+++ b/src/Type/ObjectType.php
@@ -31,6 +31,8 @@
 use PHPStan\Reflection\Type\UnresolvedPropertyPrototypeReflection;
 use PHPStan\ShouldNotHappenException;
 use PHPStan\TrinaryLogic;
+use PHPStan\Type\Accessory\AccessoryNonEmptyStringType;
+use PHPStan\Type\Accessory\AccessoryNumericStringType;
 use PHPStan\Type\Constant\ConstantArrayType;
 use PHPStan\Type\Constant\ConstantBooleanType;
 use PHPStan\Type\Constant\ConstantStringType;
@@ -593,6 +595,14 @@ public function toFloat(): Type
 
 	public function toString(): Type
 	{
+		if ($this->isInstanceOf('BcMath\Number')->yes()) {
+			return new IntersectionType([
+				new StringType(),
+				new AccessoryNumericStringType(),
+				new AccessoryNonEmptyStringType(),
+			]);
+		}
+
 		$classReflection = $this->getClassReflection();
 		if ($classReflection === null) {
 			return new ErrorType();
@@ -678,7 +688,10 @@ public function toCoercedArgumentType(bool $strictTypes): Type
 
 	public function toBoolean(): BooleanType
 	{
-		if ($this->isInstanceOf('SimpleXMLElement')->yes()) {
+		if (
+			$this->isInstanceOf('SimpleXMLElement')->yes()
+			|| $this->isInstanceOf('BcMath\Number')->yes()
+		) {
 			return new BooleanType();
 		}
 
diff --git a/src/Type/Php/BcMathNumberOperatorTypeSpecifyingExtension.php b/src/Type/Php/BcMathNumberOperatorTypeSpecifyingExtension.php
new file mode 100644
index 0000000000..3e0d793052
--- /dev/null
+++ b/src/Type/Php/BcMathNumberOperatorTypeSpecifyingExtension.php
@@ -0,0 +1,53 @@
+<?php declare(strict_types = 1);
+
+namespace PHPStan\Type\Php;
+
+use PHPStan\Php\PhpVersion;
+use PHPStan\Type\ErrorType;
+use PHPStan\Type\NeverType;
+use PHPStan\Type\ObjectType;
+use PHPStan\Type\OperatorTypeSpecifyingExtension;
+use PHPStan\Type\Type;
+use function in_array;
+
+final class BcMathNumberOperatorTypeSpecifyingExtension implements OperatorTypeSpecifyingExtension
+{
+
+	public function __construct(private PhpVersion $phpVersion)
+	{
+	}
+
+	public function isOperatorSupported(string $operatorSigil, Type $leftSide, Type $rightSide): bool
+	{
+		if (!$this->phpVersion->supportsBcMathNumberOperatorOverloading() || $leftSide instanceof NeverType || $rightSide instanceof NeverType) {
+			return false;
+		}
+
+		$bcMathNumberType = new ObjectType('BcMath\Number');
+
+		return in_array($operatorSigil, ['-', '+', '*', '/', '**', '%'], true)
+			&& (
+				$bcMathNumberType->isSuperTypeOf($leftSide)->yes()
+				|| $bcMathNumberType->isSuperTypeOf($rightSide)->yes()
+			);
+	}
+
+	public function specifyType(string $operatorSigil, Type $leftSide, Type $rightSide): Type
+	{
+		$bcMathNumberType = new ObjectType('BcMath\Number');
+		$otherSide = $bcMathNumberType->isSuperTypeOf($leftSide)->yes()
+			? $rightSide
+			: $leftSide;
+
+		if (
+			$otherSide->isInteger()->yes()
+			|| $otherSide->isNumericString()->yes()
+			|| $bcMathNumberType->isSuperTypeOf($otherSide)->yes()
+		) {
+			return $bcMathNumberType;
+		}
+
+		return new ErrorType();
+	}
+
+}
diff --git a/tests/PHPStan/Analyser/nsrt/bcmath-number.php b/tests/PHPStan/Analyser/nsrt/bcmath-number.php
new file mode 100644
index 0000000000..2bdd9611b4
--- /dev/null
+++ b/tests/PHPStan/Analyser/nsrt/bcmath-number.php
@@ -0,0 +1,408 @@
+<?php // lint >= 8.4
+
+declare(strict_types = 1);
+
+namespace BcMathNumber;
+
+use BcMath\Number;
+use function PHPStan\Testing\assertType;
+
+class Foo
+{
+	public function bcVsBc(Number $a, Number $b): void
+	{
+		assertType('BcMath\Number', $a + $b);
+		assertType('BcMath\Number', $a - $b);
+		assertType('BcMath\Number', $a * $b);
+		assertType('BcMath\Number', $a / $b);
+		assertType('BcMath\Number', $a % $b);
+		assertType('non-falsy-string', $a . $b);
+		assertType('BcMath\Number', $a ** $b);
+		assertType('*ERROR*', $a << $b);
+		assertType('*ERROR*', $a >> $b);
+		assertType('bool', $a < $b);
+		assertType('bool', $a <= $b);
+		assertType('bool', $a > $b);
+		assertType('bool', $a >= $b);
+		assertType('int<-1, 1>', $a <=> $b);
+		assertType('bool', $a == $b);
+		assertType('bool', $a != $b);
+		assertType('*ERROR*', $a & $b);
+		assertType('*ERROR*', $a ^ $b);
+		assertType('*ERROR*', $a | $b);
+		assertType('bool', $a && $b);
+		assertType('bool', $a || $b);
+		assertType('bool', $a and $b);
+		assertType('bool', $a xor $b);
+		assertType('bool', $a or $b);
+	}
+
+	public function bcVsInt(Number $a, int $b): void
+	{
+		assertType('BcMath\Number', $a + $b);
+		assertType('BcMath\Number', $a - $b);
+		assertType('BcMath\Number', $a * $b);
+		assertType('BcMath\Number', $a / $b);
+		assertType('BcMath\Number', $a % $b);
+		assertType('non-falsy-string', $a . $b);
+		assertType('BcMath\Number', $a ** $b);
+		assertType('*ERROR*', $a << $b);
+		assertType('*ERROR*', $a >> $b);
+		assertType('bool', $a < $b);
+		assertType('bool', $a <= $b);
+		assertType('bool', $a > $b);
+		assertType('bool', $a >= $b);
+		assertType('int<-1, 1>', $a <=> $b);
+		assertType('bool', $a == $b);
+		assertType('bool', $a != $b);
+		assertType('*ERROR*', $a & $b);
+		assertType('*ERROR*', $a ^ $b);
+		assertType('*ERROR*', $a | $b);
+		assertType('bool', $a && $b);
+		assertType('bool', $a || $b);
+		assertType('bool', $a and $b);
+		assertType('bool', $a xor $b);
+		assertType('bool', $a or $b);
+	}
+
+	public function bcVsFloat(Number $a, float $b): void
+	{
+		assertType('*ERROR*', $a + $b);
+		assertType('*ERROR*', $a - $b);
+		assertType('*ERROR*', $a * $b);
+		assertType('*ERROR*', $a / $b);
+		assertType('*ERROR*', $a % $b);
+		assertType('non-falsy-string', $a . $b);
+		assertType('*ERROR*', $a ** $b);
+		assertType('*ERROR*', $a << $b);
+		assertType('*ERROR*', $a >> $b);
+		assertType('bool', $a < $b);
+		assertType('bool', $a <= $b);
+		assertType('bool', $a > $b);
+		assertType('bool', $a >= $b);
+		assertType('int<-1, 1>', $a <=> $b);
+		assertType('bool', $a == $b);
+		assertType('bool', $a != $b);
+		assertType('*ERROR*', $a & $b);
+		assertType('*ERROR*', $a ^ $b);
+		assertType('*ERROR*', $a | $b);
+		assertType('bool', $a && $b);
+		assertType('bool', $a || $b);
+		assertType('bool', $a and $b);
+		assertType('bool', $a xor $b);
+		assertType('bool', $a or $b);
+	}
+
+	/** @param numeric-string $b */
+	public function bcVsNumericString(Number $a, string $b): void
+	{
+		assertType('BcMath\Number', $a + $b);
+		assertType('BcMath\Number', $a - $b);
+		assertType('BcMath\Number', $a * $b);
+		assertType('BcMath\Number', $a / $b);
+		assertType('BcMath\Number', $a % $b);
+		assertType('non-falsy-string', $a . $b);
+		assertType('BcMath\Number', $a ** $b);
+		assertType('*ERROR*', $a << $b);
+		assertType('*ERROR*', $a >> $b);
+		assertType('bool', $a < $b);
+		assertType('bool', $a <= $b);
+		assertType('bool', $a > $b);
+		assertType('bool', $a >= $b);
+		assertType('int<-1, 1>', $a <=> $b);
+		assertType('bool', $a == $b);
+		assertType('bool', $a != $b);
+		assertType('*ERROR*', $a & $b);
+		assertType('*ERROR*', $a ^ $b);
+		assertType('*ERROR*', $a | $b);
+		assertType('bool', $a && $b);
+		assertType('bool', $a || $b);
+		assertType('bool', $a and $b);
+		assertType('bool', $a xor $b);
+		assertType('bool', $a or $b);
+	}
+
+	public function bcVsNonNumericString(Number $a, string $b): void
+	{
+		assertType('*ERROR*', $a + $b);
+		assertType('*ERROR*', $a - $b);
+		assertType('*ERROR*', $a * $b);
+		assertType('*ERROR*', $a / $b);
+		assertType('*ERROR*', $a % $b);
+		assertType('non-empty-string', $a . $b);
+		assertType('*ERROR*', $a ** $b);
+		assertType('*ERROR*', $a << $b);
+		assertType('*ERROR*', $a >> $b);
+		assertType('bool', $a < $b);
+		assertType('bool', $a <= $b);
+		assertType('bool', $a > $b);
+		assertType('bool', $a >= $b);
+		assertType('int<-1, 1>', $a <=> $b);
+		assertType('bool', $a == $b);
+		assertType('bool', $a != $b);
+		assertType('*ERROR*', $a & $b);
+		assertType('*ERROR*', $a ^ $b);
+		assertType('*ERROR*', $a | $b);
+		assertType('bool', $a && $b);
+		assertType('bool', $a || $b);
+		assertType('bool', $a and $b);
+		assertType('bool', $a xor $b);
+		assertType('bool', $a or $b);
+	}
+
+	public function bcVsBool(Number $a, bool $b): void
+	{
+		assertType('*ERROR*', $a + $b);
+		assertType('*ERROR*', $a - $b);
+		assertType('*ERROR*', $a * $b);
+		assertType('*ERROR*', $a / $b);
+		assertType('*ERROR*', $a % $b);
+		assertType('non-empty-string&numeric-string', $a . $b);
+		assertType('*ERROR*', $a ** $b);
+		assertType('*ERROR*', $a << $b);
+		assertType('*ERROR*', $a >> $b);
+		assertType('bool', $a < $b);
+		assertType('bool', $a <= $b);
+		assertType('bool', $a > $b);
+		assertType('bool', $a >= $b);
+		assertType('int<-1, 1>', $a <=> $b);
+		assertType('bool', $a == $b);
+		assertType('bool', $a != $b);
+		assertType('*ERROR*', $a & $b);
+		assertType('*ERROR*', $a ^ $b);
+		assertType('*ERROR*', $a | $b);
+		assertType('bool', $a && $b);
+		assertType('bool', $a || $b);
+		assertType('bool', $a and $b);
+		assertType('bool', $a xor $b);
+		assertType('bool', $a or $b);
+	}
+
+	public function bcVsNull(Number $a): void
+	{
+		$b = null;
+		assertType('*ERROR*', $a + $b);
+		assertType('*ERROR*', $a - $b);
+		assertType('0', $a * $b); // BUG: This throws type error, but getMulType assumes that since null (mostly) behaves like zero, it will be zero.
+		assertType('*ERROR*', $a / $b);
+		assertType('*ERROR*', $a % $b);
+		assertType('non-empty-string&numeric-string', $a . $b);
+		assertType('*ERROR*', $a ** $b);
+		assertType('*ERROR*', $a << $b);
+		assertType('*ERROR*', $a >> $b);
+		assertType('bool', $a < $b);
+		assertType('bool', $a <= $b);
+		assertType('bool', $a > $b);
+		assertType('bool', $a >= $b);
+		assertType('int<-1, 1>', $a <=> $b);
+		assertType('bool', $a == $b);
+		assertType('bool', $a != $b);
+		assertType('*ERROR*', $a & $b);
+		assertType('*ERROR*', $a ^ $b);
+		assertType('*ERROR*', $a | $b);
+		assertType('false', $a && $b);
+		assertType('bool', $a || $b);
+		assertType('false', $a and $b);
+		assertType('bool', $a xor $b);
+		assertType('bool', $a or $b);
+	}
+
+	public function bcVsArray(Number $a, array $b): void
+	{
+		assertType('*ERROR*', $a + $b);
+		assertType('*ERROR*', $a - $b);
+		assertType('*ERROR*', $a * $b);
+		assertType('*ERROR*', $a / $b);
+		assertType('*ERROR*', $a % $b);
+		assertType('*ERROR*', $a . $b);
+		assertType('*ERROR*', $a ** $b);
+		assertType('*ERROR*', $a << $b);
+		assertType('*ERROR*', $a >> $b);
+		assertType('bool', $a < $b);
+		assertType('bool', $a <= $b);
+		assertType('bool', $a > $b);
+		assertType('bool', $a >= $b);
+		assertType('int<-1, 1>', $a <=> $b);
+		assertType('bool', $a == $b);
+		assertType('bool', $a != $b);
+		assertType('*ERROR*', $a & $b);
+		assertType('*ERROR*', $a ^ $b);
+		assertType('*ERROR*', $a | $b);
+		assertType('bool', $a && $b);
+		assertType('bool', $a || $b);
+		assertType('bool', $a and $b);
+		assertType('bool', $a xor $b);
+		assertType('bool', $a or $b);
+	}
+
+	public function bcVsObject(Number $a, object $b): void
+	{
+		assertType('*ERROR*', $a + $b);
+		assertType('*ERROR*', $a - $b);
+		assertType('*ERROR*', $a * $b);
+		assertType('*ERROR*', $a / $b);
+		assertType('*ERROR*', $a % $b);
+		assertType('*ERROR*', $a . $b);
+		assertType('*ERROR*', $a ** $b);
+		assertType('*ERROR*', $a << $b);
+		assertType('*ERROR*', $a >> $b);
+		assertType('bool', $a < $b);
+		assertType('bool', $a <= $b);
+		assertType('bool', $a > $b);
+		assertType('bool', $a >= $b);
+		assertType('int<-1, 1>', $a <=> $b);
+		assertType('bool', $a == $b);
+		assertType('bool', $a != $b);
+		assertType('*ERROR*', $a & $b);
+		assertType('*ERROR*', $a ^ $b);
+		assertType('*ERROR*', $a | $b);
+		assertType('bool', $a && $b);
+		assertType('true', $a || $b);
+		assertType('bool', $a and $b);
+		assertType('bool', $a xor $b);
+		assertType('true', $a or $b);
+	}
+
+	/** @param resource $b */
+	public function bcVsResource(Number $a, $b): void
+	{
+		assertType('*ERROR*', $a + $b);
+		assertType('*ERROR*', $a - $b);
+		assertType('*ERROR*', $a * $b);
+		assertType('*ERROR*', $a / $b);
+		assertType('*ERROR*', $a % $b);
+		assertType('non-empty-string', $a . $b);
+		assertType('*ERROR*', $a ** $b);
+		assertType('*ERROR*', $a << $b);
+		assertType('*ERROR*', $a >> $b);
+		assertType('bool', $a < $b);
+		assertType('bool', $a <= $b);
+		assertType('bool', $a > $b);
+		assertType('bool', $a >= $b);
+		assertType('int<-1, 1>', $a <=> $b);
+		assertType('bool', $a == $b);
+		assertType('bool', $a != $b);
+		assertType('*ERROR*', $a & $b);
+		assertType('*ERROR*', $a ^ $b);
+		assertType('*ERROR*', $a | $b);
+		assertType('bool', $a && $b);
+		assertType('true', $a || $b);
+		assertType('bool', $a and $b);
+		assertType('bool', $a xor $b);
+		assertType('true', $a or $b);
+	}
+
+	public function bcVsCallable(Number $a, callable $b): void
+	{
+		assertType('*ERROR*', $a + $b);
+		assertType('*ERROR*', $a - $b);
+		assertType('*ERROR*', $a * $b);
+		assertType('*ERROR*', $a / $b);
+		assertType('*ERROR*', $a % $b);
+		assertType('*ERROR*', $a . $b);
+		assertType('*ERROR*', $a ** $b);
+		assertType('*ERROR*', $a << $b);
+		assertType('*ERROR*', $a >> $b);
+		assertType('bool', $a < $b);
+		assertType('bool', $a <= $b);
+		assertType('bool', $a > $b);
+		assertType('bool', $a >= $b);
+		assertType('int<-1, 1>', $a <=> $b);
+		assertType('bool', $a == $b);
+		assertType('bool', $a != $b);
+		assertType('*ERROR*', $a & $b);
+		assertType('*ERROR*', $a ^ $b);
+		assertType('*ERROR*', $a | $b);
+		assertType('bool', $a && $b);
+		assertType('true', $a || $b);
+		assertType('bool', $a and $b);
+		assertType('bool', $a xor $b);
+		assertType('true', $a or $b);
+	}
+
+	public function bcVsIterable(Number $a, iterable $b): void
+	{
+		assertType('*ERROR*', $a + $b);
+		assertType('*ERROR*', $a - $b);
+		assertType('*ERROR*', $a * $b);
+		assertType('*ERROR*', $a / $b);
+		assertType('*ERROR*', $a % $b);
+		assertType('*ERROR*', $a . $b);
+		assertType('*ERROR*', $a ** $b);
+		assertType('*ERROR*', $a << $b);
+		assertType('*ERROR*', $a >> $b);
+		assertType('bool', $a < $b);
+		assertType('bool', $a <= $b);
+		assertType('bool', $a > $b);
+		assertType('bool', $a >= $b);
+		assertType('int<-1, 1>', $a <=> $b);
+		assertType('bool', $a == $b);
+		assertType('bool', $a != $b);
+		assertType('*ERROR*', $a & $b);
+		assertType('*ERROR*', $a ^ $b);
+		assertType('*ERROR*', $a | $b);
+		assertType('bool', $a && $b);
+		assertType('bool', $a || $b);
+		assertType('bool', $a and $b);
+		assertType('bool', $a xor $b);
+		assertType('bool', $a or $b);
+	}
+
+	public function bcVsStringable(Number $a, \Stringable $b): void
+	{
+		assertType('*ERROR*', $a + $b);
+		assertType('*ERROR*', $a - $b);
+		assertType('*ERROR*', $a * $b);
+		assertType('*ERROR*', $a / $b);
+		assertType('*ERROR*', $a % $b);
+		assertType('non-empty-string', $a . $b);
+		assertType('*ERROR*', $a ** $b);
+		assertType('*ERROR*', $a << $b);
+		assertType('*ERROR*', $a >> $b);
+		assertType('bool', $a < $b);
+		assertType('bool', $a <= $b);
+		assertType('bool', $a > $b);
+		assertType('bool', $a >= $b);
+		assertType('int<-1, 1>', $a <=> $b);
+		assertType('bool', $a == $b);
+		assertType('bool', $a != $b);
+		assertType('*ERROR*', $a & $b);
+		assertType('*ERROR*', $a ^ $b);
+		assertType('*ERROR*', $a | $b);
+		assertType('bool', $a && $b);
+		assertType('true', $a || $b);
+		assertType('bool', $a and $b);
+		assertType('bool', $a xor $b);
+		assertType('true', $a or $b);
+	}
+
+	public function bcVsNever(Number $a): void
+	{
+		for ($b = 1; $b < count([]); $b++) {
+			assertType('*NEVER*', $a + $b);
+			assertType('*ERROR*', $a - $b); // Inconsistency: getPlusType handles never types right at the beginning, getMinusType doesn't.
+			assertType('*ERROR*', $a * $b);
+			assertType('*ERROR*', $a / $b);
+			assertType('*NEVER*', $a % $b);
+			assertType('non-empty-string&numeric-string', $a . $b);
+			assertType('*ERROR*', $a ** $b);
+			assertType('*NEVER*', $a << $b);
+			assertType('*NEVER*', $a >> $b);
+			assertType('bool', $a < $b);
+			assertType('bool', $a <= $b);
+			assertType('bool', $a > $b);
+			assertType('bool', $a >= $b);
+			assertType('*NEVER*', $a <=> $b);
+			assertType('bool', $a == $b);
+			assertType('bool', $a != $b);
+			assertType('*NEVER*', $a & $b);
+			assertType('*NEVER*', $a ^ $b);
+			assertType('*NEVER*', $a | $b);
+			assertType('bool', $a && $b);
+			assertType('bool', $a || $b);
+			assertType('bool', $a and $b);
+			assertType('bool', $a xor $b);
+			assertType('bool', $a or $b);
+		}
+	}
+}