Algorithm to match IBAN to BIC

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I'm trying to find a solution to convert IBANs to BICs.

In theory, all I need is to have a db with national bank codes and their BICs to compare these national codes with corresponding ones in IBANs (based on IBAN format for that country described in https://www.swift.com/sites/default/files/resources/swift_standards_ibanregistry.pdf). But the problem is, that I can only find limited and not accurate sources of national bank codes (or can't find at all, even for big ones).

Is there a way to find a BIC number for a given IBAN in another way? I also thought about first 4 letters in a BIC code, which represents financial institution - but I did not find if it's possible to convert them to "national" codes or vise versa).

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