Understanding Assembly - sorting

Question

I've got some assembly of a sorting algorithm and I want to figure out how exactly it functions.
I'm a little confused on some of the instructions, particularly the cmp and jle instructions, so I'm looking for help. This assembly sorts an array of three elements.
0.00 : 4009f8: 48 8b 07 mov (%rdi),%rax
0.00 : 4009fb: 48 8b 57 08 mov 0x8(%rdi),%rdx
0.00 : 4009ff: 48 8b 4f 10 mov 0x10(%rdi),%rcx
0.00 : 400a03: 48 39 d0 cmp %rdx,%rax
0.00 : 400a06: 7e 2b jle 400a33 <b+0x3b>
0.00 : 400a08: 48 39 c8 cmp %rcx,%rax
0.00 : 400a0b: 7e 1a jle 400a27 <b+0x2f>
0.00 : 400a0d: 48 39 ca cmp %rcx,%rdx
0.00 : 400a10: 7e 0c jle 400a1e <b+0x26>
0.00 : 400a12: 48 89 0f mov %rcx,(%rdi)
0.00 : 400a15: 48 89 57 08 mov %rdx,0x8(%rdi)
0.00 : 400a19: 48 89 47 10 mov %rax,0x10(%rdi)
0.00 : 400a1d: c3 retq
0.00 : 400a1e: 48 89 17 mov %rdx,(%rdi)
0.00 : 400a21: 48 89 4f 08 mov %rcx,0x8(%rdi)
0.00 : 400a25: eb f2 jmp 400a19 <b+0x21>
0.00 : 400a27: 48 89 17 mov %rdx,(%rdi)
0.00 : 400a2a: 48 89 47 08 mov %rax,0x8(%rdi)
0.00 : 400a2e: 48 89 4f 10 mov %rcx,0x10(%rdi)
0.00 : 400a32: c3 retq
0.00 : 400a33: 48 39 ca cmp %rcx,%rdx
0.00 : 400a36: 7e 1d jle 400a55 <b+0x5d>
0.00 : 400a38: 48 39 c8 cmp %rcx,%rax
0.00 : 400a3b: 7e 0c jle 400a49 <b+0x51>
0.00 : 400a3d: 48 89 0f mov %rcx,(%rdi)
0.00 : 400a40: 48 89 47 08 mov %rax,0x8(%rdi)
0.00 : 400a44: 48 89 57 10 mov %rdx,0x10(%rdi)
0.00 : 400a48: c3 retq
0.00 : 400a49: 48 89 07 mov %rax,(%rdi)
0.00 : 400a4c: 48 89 4f 08 mov %rcx,0x8(%rdi)
0.00 : 400a50: 48 89 57 10 mov %rdx,0x10(%rdi)
0.00 : 400a54: c3 retq
0.00 : 400a55: 48 89 07 mov %rax,(%rdi)
0.00 : 400a58: 48 89 57 08 mov %rdx,0x8(%rdi)
0.00 : 400a5c: 48 89 4f 10 mov %rcx,0x10(%rdi)
0.00 : 400a60: c3 retq
0.00 : 400a61: 90 nop
If someone can walk me through it, it'd be very helpful. I kind of get confused around the operands like 0x8(%rdi) and the cmp and jle instructions. Thanks.

Answer 1

Here are what the instructions mean:
mov : move
cmp : compare
jle : jump if less or equal (branch)
ret : return from procedure
nop : no-op
%r** are registers. They are usually %e** (eg: %eax, %edx, ...), but these are 64-bit registers.
As far as de-compiling the whole thing, that will take some more work.
See this: http://www.x86-64.org/documentation/assembly

Answer 2

It helps to replace the register names with proper names to trace the flow of data, and add branch labels for the control flow.
0.00 : 4009f8: 48 8b 07 mov (%argptr),%var1
0.00 : 4009fb: 48 8b 57 08 mov 0x8(%argptr),%var2
0.00 : 4009ff: 48 8b 4f 10 mov 0x10(%argptr),%var3
0.00 : 400a03: 48 39 d0 cmp %var2,%var1
0.00 : 400a06: 7e 2b jle #v2le1
0.00 : 400a08: 48 39 c8 cmp %var3,%var1
0.00 : 400a0b: 7e 1a jle #v3le1
0.00 : 400a0d: 48 39 ca cmp %var3,%var2
0.00 : 400a10: 7e 0c jle #v3le2
# Now we know that 2 > 1 and 3 > 1 and 3 > 2. Write them to memory in order.
etc

Answer 3

0.00 : 4009f8: 48 8b 07 mov (%rdi),%rax
The register RDI contains the address to a location in memory of your array. This line above copy the contents of the RAX register into the first element of your array. Since pointers in x64 are 0x8 bytes, the following two lines:
0.00 : 4009fb: 48 8b 57 08 mov 0x8(%rdi),%rdx
0.00 : 4009ff: 48 8b 4f 10 mov 0x10(%rdi),%rcx
will copy the contents of the RDX and RCX registers into the second and third elements into your array respectively. Now we need to start comparing the values to see where we need to swap.
0.00 : 400a03: 48 39 d0 cmp %rdx,%rax
0.00 : 400a06: 7e 2b jle 400a33 <b+0x3b>
The cmp will compare the value of RDX with the value of RAX (essentially array[1] against array[0]). If RDX is less than or equal to RAX then this will jump program execution directly to line 400a33. You can think of this as if (array[1] > array[0]). And so it continues, comparing the values.
It appears that the code is trying to sort in descending order. Very roughly, the C code will probably look something like this:
array[0] = rax;
array[1] = rdx;
array[2] = rcx;
if (rdx > rax)
{
if (rcx > rax)
{
if (rcx > rdx)
{
rcx = array[0];
rdx = array[1];
LABEL:
rax = array[2];
}
else
{
rdx = array[0];
rcx = array[1];
GOTO LABEL;
}
}
else
{
rdx = array[0];
rax = array[1];
rcx = array[2];
}
}
else
{
if (rcx > rdx)
{
if (rcx > rax)
{
rcx = array[0];
rax = array[1];
rdx = array[2];
}
else
{
rax = array[0];
rdx = array[1];
rcx = array[2];
}
}
else
{
rax = array[0];
rdx = array[1];
rcx = array[2];
}
}