Fibonacci Sequence

Fibonacci Sequence

The Fibonacci sequence is defined as:

fib(0) = 0
fib(1) = 1
fib(n) = fib(n-1) + fib(n-2)

The first few values: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, ...

Iterative Approach

While recursion is elegant, the iterative approach is much more efficient -- it uses just two registers instead of a deep call stack:

MOV X0, #0          // prev = fib(0)
MOV X1, #1          // curr = fib(1)
MOV X2, #10         // n = 10
MOV X3, #0          // i = 0

fib_loop:
    CMP X3, X2
    B.GE fib_done
    ADD X4, X0, X1  // next = prev + curr
    MOV X0, X1      // prev = curr
    MOV X1, X4      // curr = next
    ADD X3, X3, #1
    B fib_loop

fib_done:
// X0 = fib(10) = 55

Register Allocation

This is a great exercise in register management:

• X0 = previous value
• X1 = current value
• X2 = target n
• X3 = loop counter
• X4 = temporary for the sum

Printing the Result

Since fib(10) = 55 is a two-digit number, you'll need to convert it to ASCII. Divide by 10 to get each digit:

MOV X5, #10
UDIV X6, X0, X5        // tens digit
MUL X7, X6, X5
SUB X7, X0, X7         // ones digit
ADD X6, X6, #48        // to ASCII
ADD X7, X7, #48        // to ASCII

Your Task

Compute fib(10) iteratively and print the result (55) followed by a newline.