Curiously, Freek Wiedijk implemented a fixed point combinator in pure portable C99 in his 2014 IOCCC entry [1] that computes 10 factorial with no loops, as explained in [2].

[1] https://www.ioccc.org/2014/wiedijk/prog.c

[2] https://www.ioccc.org/2014/wiedijk/hint.html