## 8.6. Recursion

Recursive functions are a special class of functions that call themselves (also known as self-referential functions) to compute a value. Like their nonrecursive counterparts, recursive functions create new stack frames for each function call. Unlike standard functions, recursive functions contain function calls to themselves.

Let’s revisit the problem of summing up the set of positive integers from 1 to n. In previous sections, we discussed the `sumUp` function to achieve this task. Table 1 shows a related function called `sumDown`, which adds the numbers in reverse (n to 1), and its recursive equivalent `sumr`:

Table 1. Iterative version (sumDown) and recursive version (sumr)
Iterative Recursive
``````int sumDown(int n) {
int total = 0;
int i = n;
while (i > 0) {
total += i;
i--;
}
}``````
``````int sumr(int n) {
if (n <= 0) {
return 0;
}
return n + sumr(n-1);
}``````

The base case in the recursive function `sumr` accounts for any values of n that are less than one, and the recursive step adds the current value of n to the result of the function call to `sumr` with the value n-1. Compiling `sumr` with the `-m32` flag and disassembling it with GDB yields the following assembly code:

```0x0804841d <+0>:  push  %ebp                  # save ebp
0x0804841e <+1>:  mov   %esp,%ebp             # update ebp (new stack frame)
0x08048420 <+3>:  sub   \$0x8,%esp             # add 8 bytes to stack frame
0x08048423 <+6>:  cmp   \$0x0,0x8(%ebp)        # compare ebp+8 (n) with 0
0x08048427 <+10>: jg    0x8048430 <sumr+19>   # if (n > 0), goto <sumr+19>
0x08048429 <+12>: mov   \$0x0,%eax             # copy 0 to eax (result)
0x0804842e <+17>: jmp   0x8048443 <sumr+38>   # goto <sumr+38>
0x08048430 <+19>: mov   0x8(%ebp),%eax        # copy n to eax (result)
0x08048433 <+22>: sub   \$0x1,%eax             # subtract 1 from n (result--)
0x08048436 <+25>: mov   %eax,(%esp)           # copy n-1 to top of stack
0x08048439 <+28>: call  0x804841d <sumr>      # call sumr() function
0x0804843e <+33>: mov   0x8(%ebp),%edx        # copy n to edx
0x08048443 <+38>: leave                       # prepare to leave the function
0x08048444 <+39>: ret                         # return result```

Each line in the preceding assembly code is annotated with its English translation. Table 2 shows the corresponding `goto` form and C program without `goto` statements:

Table 2. C goto form and translation of sumr assembly code
C goto form C version without goto statements
``````int sumr(int n) {
int result;
if (n > 0) {
goto body;
}
result = 0;
goto done;
body:
result = n;
result -= 1;
result = sumr(result);
result += n;
done:
return result;
}``````
``````int sumr(int n) {
int result;
if (n <= 0) {
return 0;
}
result = sumr(n-1);
result += n;
return result;
}``````

Although this translation may not initially appear to be identical to the original `sumr` function, close inspection reveals that the two functions are indeed equivalent.

### 8.6.1. Animation: Observing How the Call Stack Changes

As an exercise, we encourage you to draw out the stack and see how the values change. The animation below depicts how the stack is updated when we run this function with the value 3. 