Shared libraries and PLT using GCC toolchain

Hi all,

I am trying to understand how shared libraries and PLT works. As per my current understanding linking a shared library should output code that calls a function (function from the shared library) by going through the PLT. And the function itself should not be present in the linked output.

For example.

fun.c (Compiled into a shared library)

unsigned int fun ( unsigned int x )
{
    return(x+3);
}

so.c (main executable)

extern unsigned int fun ( unsigned int x );
unsigned int x;
unsigned int y;
unsigned int z;

void centry ( void )
{
    x=7;
    y=8;
    z=fun(77);
    
    while(1){
        
    }
}

I am compiling using the following steps.

rm -rf boot.o so.o fun.o so.elf so.srec so.list so.bin
arm-none-eabi-as -g -mcpu=cortex-m4 -mthumb --warn  boot.s -o boot.o
arm-none-eabi-gcc -g -Wall -O0 -fpic -mcpu=cortex-m4 -mthumb -c so.c -o so.o
arm-none-eabi-gcc -g -shared -Wall -O0 -fpic -mcpu=cortex-m4 -mthumb -c fun.c -o libfun.so
arm-none-eabi-ld -g -o so.elf -T flash.ld boot.o so.o -shared -L. -lfun
arm-none-eabi-objdump -D so.elf > so.list
arm-none-eabi-objcopy --srec-forceS3 so.elf -O srec so.srec
arm-none-eabi-objcopy so.elf so.bin -O binary

Complete code is at: https://github.com/rgujju/STM32-projects/tree/master/got_plt

question 1) The output of the above code should not have the function <fun> right? But the output elf file <so.elf> has the function <fun> in it. The call to <fun> and <centry> both go through the plt which I think is correct and the dynamic linker will patch these entries. But why does it contain the function <fun>?

question 2) In the disassembly of the PLT there are instructions which contain a register <ip>. As per my understanding there isnt any register called <ip> in cortex M4. see line 9 and 10 below.

Disassembly of section .plt:

08000084 <.plt>:
 8000084:	b500      	push	{lr}
 8000086:	f8df e008 	ldr.w	lr, [pc, #8]	; 8000090 <.plt+0xc>
 800008a:	44fe      	add	lr, pc
 800008c:	f85e ff08 	ldr.w	pc, [lr, #8]!
 8000090:	00000220 	andeq	r0, r0, r0, lsr #4
 8000094:	f240 2c1c 	movw	ip, #540	; 0x21c
 8000098:	f2c0 0c00 	movt	ip, #0
 800009c:	44fc      	add	ip, pc
 800009e:	f8dc f000 	ldr.w	pc, [ip]
 80000a2:	bf00      	nop
 80000a4:	f240 2c10 	movw	ip, #528	; 0x210
 80000a8:	f2c0 0c00 	movt	ip, #0
 80000ac:	44fc      	add	ip, pc
 80000ae:	f8dc f000 	ldr.w	pc, [ip]
 80000b2:	bf00      	nop

Thank you for your help.