I believe that by default, the gcc compilers use a set of generic software floating point code as part of libgcc (
https://gcc.gnu.org/onlinedocs/gccint/Soft-float-library-routines.html ), and higher level math functions as part of gcc libc (
http://www.gnu.org/software/libc/ ) All nice and portable, but not particularly fast or small.
Technically, these are separate from the compiler, and in fact are one of the things that a value-added compiler vendor might provide as "improved" versions. For example, avr-gcc has its own complete set of floating point routines. However, coide expects you to download the ARM compiler from launchpad.net, which claims to be using newlib or newlib-nano, so you can find code there, ie:
https://github.com/32bitmicro/newlib-nano-1.0/tree/master/newlib/libm/mathIt takes a brave (or desperate) vendor or engineer to implement new floating point math code...
Different libs for chips with HW floating point, of course. And cmsis-dsp has some specially optimized functions (apparently not direct replacements for libm functions, though.) CooCox does seem to have a bunch of peripheral libraries that replace the usual vendor libraries, but I don't see alternate floating point functions.