class URHO3D_API BigInt
{
private:
    // If the value can be stored in i32, it is stored here. Otherwise, this field is -1 or +1.
    i32 signOrShortValue_;

public:
    BigInt(i32 value = 0)
        : signOrShortValue_(value)
    {
    }

    BigInt(u32 value)
        : signOrShortValue_(+1)
    {
    }

    String ToString() const
    {
        return String(signOrShortValue_);
    }
};

// BigInt::BigInt(i32 value = 0)
static void BigInt__BigInt_i32(BigInt* _ptr, i32 value)
{
    new(_ptr) BigInt(value);
}
// BigInt::BigInt(u32 value)
static void BigInt__BigInt_u32(BigInt* _ptr, u32 value)
{
    new(_ptr) BigInt(value);
}

    // BigInt::BigInt(i32 value = 0)
    engine->RegisterObjectBehaviour("BigInt", asBEHAVE_CONSTRUCT, "void f(int = 0)", AS_FUNCTION_OBJFIRST(BigInt__BigInt_i32), AS_CALL_CDECL_OBJFIRST);
    
    // BigInt::BigInt(u32 value)
    engine->RegisterObjectBehaviour("BigInt", asBEHAVE_CONSTRUCT, "void f(uint)", AS_FUNCTION_OBJFIRST(BigInt__BigInt_u32), AS_CALL_CDECL_OBJFIRST);

// C++
    {
        BigInt bigInt = -7; // -7 is int
        assert(bigInt.ToString() == "-7");
    }

    {
        BigInt bigInt = 0xFFFFFFFF; // 0xFFFFFFFF is unsigned
        assert(bigInt.ToString() == "1");
    }
    
    {
        BigInt bigInt = 0xFFFFFFF; // 0xFFFFFFF is int
        assert(bigInt.ToString() != "1");
    }

// AngelScript

void Start()
{
    BigInt i1(2147483647); 
    log.Error(i1.ToString()); // print 2147483647 (used int constructor)
    BigInt u1(2147483648);
    log.Error(u1.ToString()); // print -2147483648 (used int constructor)
    BigInt i2(0xFF);
    log.Error(i2.ToString()); // print 1 (used uint constructor)
    BigInt u2(0xFFFFFFFF);
    log.Error(u2.ToString());  // print 1 (used uint constructor)
}

p.s. I known about uint(xxx), but a user can easily forget about it

This version https://github.com/urho3d/Urho3D/blob/master/Source/ThirdParty/AngelScript/Urho3DNotes.txt

Also

typedef int32_t i32;
typedef uint32_t u32;

and C++17 enabled

Thanks!