There are multiple implementations, the one often found on linux is glibc, you can find the source code for that online. printf is going to be a small wrapper for vfprintf though, so that is where you will probably find what you are looking for
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Check out GLIBC, the standard libc implementation for GNU/Linux, or the easier to read, minimalist, alternative libc MUSL.
Bootlin, runs the Elixir Code Cross Referencer that lets you easily hop between files. For instance, Here is the code for printf in GLIBC.
if you want to see how you can write your own: https://linux-is-best.pckt.blog/writing-your-own-print-function-16xt8wv
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