Questions regarding RSADigestSigner and DSAsigner

I am new to Bouncy castle. I have some questions regarding signers package in bouncy castle. For RSADigestSigner, is our message hashed internally or do we have to hash it on our own? Another similiar question is for DSASigner, it does not have a built-in digest, so do we have to pre-hash our message before using DSASigner?

Here are two of my codes:

 // RSADigestSigner

        // Pick the hash, SHA512 in this case
        SHA512Digest digest = new SHA512Digest();

        // Create a RSADigestSigner to sign
        RSADigestSigner sign = new RSADigestSigner(digest);

        // Initialize for signing
        sign.init(true, privKey);

        // Pass data to sign
        sign.update(bytes, 0, bytes.length);

        // Generate the signature
        try {
            signature = sign.generateSignature();
        } catch (DataLengthException | CryptoException e) {
            e.printStackTrace();
        }

// Create a DSASigner to sign 
		DSASigner sign = new DSASigner();
		
		// Initialize DSASigner
		sign.init(true, privKey);
		
		// Hash the message
		
		
		// Generate the signature
		signature = sign.generateSignature(input);

For DSASigner you must compute the hash yourself, whereas for RSADigestSigner the hash is computed internally to the class. This is possible because the constructor for RSADigestSigner takes a Digest argument. But the parallel to RSADigestSigner is DSADigestSigner, not DSASigner, so you probably want to use DSADigestSigner.