C++ requires that the math functions be part of the basic runtime while C allows them to be in a library. The GCC implementation achieved this by automatically linking libm in a C++ build.

There are many other differences in the link phase; C++ linking will consistently fail if a C linker is used.

For a C link, use the C linker and specify -lm to make libm available.

It is documented at: https://gcc.gnu.org/onlinedocs/gcc-11.1.0/gcc/Overall-Options.html#Overall-Options

It is a file containing switches to override standard defaults for various build components such as the compiler, assembler and linker. For example it can be used to replace the default C library.

I have never seen it used; typically bare-metal embedded system builds explicitly specify --nostdlib then explicitly link the required library. It could be used for environment specific build environments to link other default code such as an RTOS I guess. Personally I'd rather make all that explicit on the command line that hiding it in a file somewhere.

Essentially it applies the switches specified in the file as if they were defaults, so can be used to define defaults for specific build and execution environments.

The format of the specs file is documented at https://gcc.gnu.org/onlinedocs/gcc-11.1.0/gcc/Spec-Files.html#Spec-Files

Without seeing both the linker errors and the content of the nosys.specs file in this case it is difficult to say how or why it solved your linker problem. The alternative solution of course would be to apply whatever switches are in the specs file directly.

First you create your library objects. Let us say that you have a foo function written in foo.c, then you do:

arm-none-eabi-gcc -c foo.c

The -c options tells the compiler to stop after assembling and no go further.

Then you need to create the .a file

arm-none-eabi-ar -rc libfoo.a foo.o

this command creates a static library called libfoo.a

At the end you compile your main with:

arm-none-eabi-gcc -L. -lfoo main.c -o main

Note that in -l flag we don put "lib" and ".a", those are automagically added. The -L. flag tells gcc to look into the current folder for library files.