I found information that general purpose registers r1-r23 and r26-r28 are used by the compiler to store local variables, but do they have any other purpose? Also which memory are this registers part of(cache/RAM)? Finally what does global pointer gp in register r26 points to?
Also which memory are this registers part of(cache/RAM)?
Register are on-processors storage allowing a fast data transfer (2 reads/1 write per cycle). They store variables that can represent memory addresses, but, besides that, are completely unrelated to memory or cache.
I found information that general purpose registers r1-r23 and r26-r28 are used by the compiler to store local variables, but do they have any other purpose?
Registers are use with respect to hardware or software conventions. Hardware conventions are related to the instruction set architecture. For instance, the call instruction transfers control to a subroutine and stores return address in register r31 (ra). Very nasty things are likely to happen if you overwrite r31 register by any mean without precautions. Software conventions are supposed to insure a proper behavior if used consistently within software. They indicate which register have special use, which need to be saved when context switching, etc. These conventions can be changed without hardware modifications, but doing so will probably require changes in several software tools (compiler, linker, loader, OS, ...).
general purpose registers r1-r23 and r26-r28 are used by the compiler to store local variables
Actually, some registers are reserved.
r1 is used by asm for macro expansion. (sw)
r2-r7 are used by the compiler to pass arguments to functions or get return values. (sw)
r24-r25 can only be used by exception handlers. (sw)
r26-r28 hold different pointers (global, stack, frame) that are set either by the runtime or the compiler and cannot be modified by the programmer.(sw)
r29-r31 are hw coded returns addresses for subprograms or interrupts/exceptions. (hw)
So only r8-r23 can used by the compiler.
but do they have any other purpose?
No, and that's why they can be freely used by the compiler or programmer.
Finally what does global pointer in register r26 points to?
Accessing memory with load or stores have a based memory addressing. Effective address for ldx or stx (where 'x' is is b, bu, h, etc depending on data characteristics) is computed by adding a register and a 16 bits immediate. This only allows to go an an address within +/-32k of the content of register.
If the processor has the address of a var in a register (for instance the value returned by a malloc) the immediate allows to do a displacement to access fields in a struct, next array value, etc.
If the address is local or global, it must be computed by the program. Pointers registers are used to that purpose. Local vars addresses are computed by adding an immediate to the stack pointer (r27or sp).
Addresses of global or static vars are computed by adding an integer to the global pointer (r26 or gp). Content of gp corresponds to the start of the memory data segment and is initialized by the loader just before program execution and must not be modified. The immediate displacement with respect to the start of data segment is computed by the linker when it defines memory layout.
Note that this only allows to access 64k memory because of the 16 bits immediate width. If the size of global/static variables exceeds this value and a var is not within this range, a couple of instructions are required to enter the 32 bits of the address of the var before the data transfer. With gp this is not required and it is a way to provide a faster access to global variables.