Is `asprintf` thread-safe?
Yes, it's thread safe except when it reads the locale.
Function: int asprintf (char **ptr, const char *template, …)
Preliminary: | MT-Safe locale | AS-Unsafe heap | AC-Unsafe mem
About the 'locale' exception, in particular:
Functions annotated with locale as an MT-Safety issue read from the locale object without any form of synchronization. Functions annotated with locale called concurrently with locale changes may behave in ways that do not correspond to any of the locales active during their execution, but an unpredictable mix thereof.
These kinds of functions are known as "conditionally" multithread safe because, in some contexts, they turn out not to be, so the programmer needs to take care of that.
glibc is free software and is probably the only (or the most important) library implementing asprintf.
So you can study (and even contribute to improve) its source code. See its stdio-common/asprintf.c & libio/vasprintf.c source files.
It looks like indeed, it is calling in a thread safe manner malloc and related things.