To form the compound verbs we only conjugate the auxiliary verb, while the main verb is always in the participle.
You compound times are the auxiliary verbs having and having linked to a main verb in the participle, which results in a verbal phrase.
See below how all compound tenses are formed, remembering that the main verb is always in the participle and that these paradigms are followed in the 1st, 2nd and 3rd conjugations.
Formation of the Indicative Compounds
The indicatively compounded times are: Past Perfect, Past perfect past tense, future of the present and Past Future.
Past Perfect
The auxiliary verb to have or to have is conjugated in the present tense.
Example:
I've been playing, you've been playing, you've been playing, we've been playing, you've been playing, we've been playing.
Past perfect past tense
The auxiliary verb to have or to have is conjugated in the past tense imperfect of the callsign.
Example:
had played, had played, had played, had played, had played, had played.
future of the present
The auxiliary verb to have or to have is conjugated in the present tense tense.
Example:
will have played, will have played, will have played, will have played, will have played, will have played.
Past Future
The auxiliary verb to have or to have is conjugated in the past tense.
Example:
I would have played, you would have played, you would have played, we would have played, you would have played, you would have played.
Compound Times of the Subjunctive
The tenses composed of the subjunctive mode are: Past Perfect, Past More-than-Perfect and Future.
Past Perfect
The auxiliary verb to have or to have is conjugated in the subjunctive present.
Example:
have played, have played, have played, have played, have played, have played.
Past perfect past tense
The auxiliary verb to have or to have is conjugated in the imperfect subjunctive.
Example:
had played, had played, had played, had we played, had played, had played.
Future
The auxiliary verb to have or to have is conjugated in the future subjunctive.
Examples:
have played, have played, have played, have played, have played, have played.
Nominal Forms
Personal infinitive
The auxiliary verb to have or to have is conjugated in the personal infinitive.
Example:
have played, have played, have played, have played, have played, have played.
impersonal infinitive
The auxiliary verb to have or to have is conjugated in the impersonal infinitive.
Example:
have played.
Learn more at Personal Infinitive and Impersonal Infinitive.
Gerund
The auxiliary verb to have or to have is conjugated in the gerund.
Example:
having played.
Read more about the Auxiliary verbs.