I am looking for the different functions available in the yocto just like do_compile_append()? Also, when is the do_compile_append() is invoked by the yocto. I am looking into the in depth manual documentation on such functions. Are there any examples available?
Yocto has extensive documentation. Tasks and dependencies in general as well as the standard tasks like do_compile() are defined in the Reference Manual. The function override style ("_append" and "_prepend") is explained in the Bitbake Manual. What exactly happens during a do_compile depends on the specific recipe of course.
The Mega Manual contains all of the Yocto documentation in a single html file -- very useful for quick searches but it's already far longer than most novels so not suitable for reading front-to-back.