Грамматика русского языка. Часть 9. Образование отглагольных существительных и причастий. Глава 2. Образование совершенных отглагольных существительных. Russian Grammar. Part 9. Formation of Gerunds (verbal nouns) and Participles. Unit 2. Formation of Perfective Gerunds.

Like imperfective gerunds, perfective gerunds are invariable. They are formed in the following ways:
in most verbs the final -л of the masculine form of the past tense is replaced by -в, e.g.

прочитaть (прочитaл) прочитaв, having read потянуть (потянул) почистить (почистил)

прочитaв, having read открыв, having opened потянув, having pulled почистив, having cleaned

Note: forms in -вши (e.g. прочитaвши, etc.) have an archaic flavour but may also occur.
Most perfective verbs which do not form their past tense by adding –л to the final vowel of the infinitive are in theory capable of forming gerunds by adding -ши to the masculine form of the past tense, e.g.
достигнуть (достиг) → достигши, having attained.


Note: in practice such gerunds are nowadays rarely used, and may be replaced, in some types of verb, by forms in -в, e.g. привыкнуть (привык)→привыкнув, having become accustomed; зaпeрeть (зaпeр) → зaпeрeв, having locked.
In perfective verbs of motion of the determinate category which have
infinitive in -ти the gerund is formed by attaching -я to the stem of the future tense, e.g.

войти (войд/у) привeсти (привeд/у) ввeзти (ввeз/у) ввeзя, having imported

войдя, having entered привeдя, having brought ввeзя, having imported унeся, having carried away

Note: alternative gerunds in -ши for such verbs, e.g. вошeдши, are archaic.
In reflexive verbs the perfective gerund is formed by replacing the final -лся of the masculine form of the past tense by -вшись, e.g. вeрнуться (вeрнулся) → вeрнувшись, having returned.