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added to README for strlen and started work on recursion.
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Perry Kivolowitz
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4 changed files with 62 additions and 120 deletions
38
section_1/recursion/README.md
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38
section_1/recursion/README.md
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@ -0,0 +1,38 @@
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# Section 1 - recursion
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Let it be said right from the start:
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*Recursion in assembly language is not the ball of joy that it is in
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higher level languages*.
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## Fibonacci Sequence
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The Fibonacci Sequence is one primary example of recursion. Consider
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this example:
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```c++
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unsigned int FibonacciInC(unsigned int nthNumber) {
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if (nthNumber <= 1) {
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return nthNumber;
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}
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return FibonacciInC(nthNumber - 1) + FibonacciInC(nthNumber - 2);
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}
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```
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The terminal condition is `nthNumber` less than or equal to 1. If the
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parameter is less than or equal to 1, the very same value is returned.
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If the parameter is greater than 1, the result is the sum or the
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results of the Fibonacci value of one less than the parameter plus the
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results of two less than the parameter.
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## Recursion Leverages the Stack
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Notice that recursion is accomplished by simply calling a function
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inside itself. All of the work of implementing recursion is hidden
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behind the scenes by the compiler.
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Specifically, `nthNumber` and the results of
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`FibonacciInC(nthNumber - 1)` is pushed onto (and popped off of) the
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stack. The value of `FibonacciInC(nthNumber - 2)` doesn't go on the
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stack because its results are used right away.
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@ -11,11 +11,11 @@ unsigned int FibonacciInC(unsigned int nthNumber) {
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int main() {
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printf("In C:\n");
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for (unsigned int n = 0; n < 10; n++) {
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for (unsigned int n = 0; n < 14; n++) {
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printf("Fibonacci number %2d is: %d\n", n, FibonacciInC(n));
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}
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printf("In assembly language:\n");
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for (unsigned int n = 0; n < 10; n++) {
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for (unsigned int n = 0; n < 14; n++) {
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printf("Fibonacci number %2d is: %d\n", n, Fib(n));
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}
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return 0;
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@ -1,115 +0,0 @@
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.arch armv8-a
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.file "fib.c"
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.text
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.align 2
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.global FibonacciInC
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.type FibonacciInC, %function
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FibonacciInC:
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.LFB0:
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.cfi_startproc
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stp x29, x30, [sp, -48]!
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.cfi_def_cfa_offset 48
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.cfi_offset 29, -48
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.cfi_offset 30, -40
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mov x29, sp
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str x19, [sp, 16]
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.cfi_offset 19, -32
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str w0, [sp, 44]
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ldr w0, [sp, 44]
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cmp w0, 1
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bhi .L2
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ldr w0, [sp, 44]
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b .L3
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.L2:
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ldr w0, [sp, 44]
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sub w0, w0, #1
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bl FibonacciInC
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mov w19, w0
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ldr w0, [sp, 44]
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sub w0, w0, #2
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bl FibonacciInC
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add w0, w19, w0
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.L3:
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ldr x19, [sp, 16]
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ldp x29, x30, [sp], 48
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.cfi_restore 30
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.cfi_restore 29
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.cfi_restore 19
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.cfi_def_cfa_offset 0
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ret
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.cfi_endproc
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.LFE0:
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.size FibonacciInC, .-FibonacciInC
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.section .rodata
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.align 3
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.LC0:
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.string "In C:"
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.align 3
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.LC1:
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.string "Fibonacci number %2d is: %d\n"
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.align 3
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.LC2:
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.string "In assembly language:"
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.text
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.align 2
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.global main
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.type main, %function
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main:
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.LFB1:
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.cfi_startproc
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stp x29, x30, [sp, -32]!
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.cfi_def_cfa_offset 32
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.cfi_offset 29, -32
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.cfi_offset 30, -24
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mov x29, sp
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adrp x0, .LC0
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add x0, x0, :lo12:.LC0
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bl puts
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str wzr, [sp, 24]
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b .L5
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.L6:
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ldr w0, [sp, 24]
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bl FibonacciInC
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mov w2, w0
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ldr w1, [sp, 24]
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adrp x0, .LC1
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add x0, x0, :lo12:.LC1
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bl printf
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ldr w0, [sp, 24]
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add w0, w0, 1
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str w0, [sp, 24]
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.L5:
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ldr w0, [sp, 24]
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cmp w0, 9
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bls .L6
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adrp x0, .LC2
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add x0, x0, :lo12:.LC2
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bl puts
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str wzr, [sp, 28]
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b .L7
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.L8:
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ldr w0, [sp, 28]
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bl Fib
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mov w2, w0
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ldr w1, [sp, 28]
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adrp x0, .LC1
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add x0, x0, :lo12:.LC1
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bl printf
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ldr w0, [sp, 28]
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add w0, w0, 1
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str w0, [sp, 28]
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.L7:
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ldr w0, [sp, 28]
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cmp w0, 9
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bls .L8
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mov w0, 0
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ldp x29, x30, [sp], 32
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.cfi_restore 30
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.cfi_restore 29
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.cfi_def_cfa_offset 0
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ret
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.cfi_endproc
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.LFE1:
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.size main, .-main
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.ident "GCC: (Ubuntu 9.4.0-1ubuntu1~20.04.1) 9.4.0"
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.section .note.GNU-stack,"",@progbits
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@ -3,19 +3,38 @@
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.align 4
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Fib: str x30, [sp, -16]!
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cmp w0, 1
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// If w0 is 0 or 1, take the branch to return w0.
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cmp w0, 1
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bls 99f
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// If we get here, we need to do the recursion.
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// Save the parameter on the stack so we can
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// get it back between recursions.
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str w0, [sp, -16]!
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// nthNumber to be stored at 16 off sp
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str w0, [sp, -16]! // +1
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// Execute Fib(nthNumber - 1)
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sub w0, w0, 1
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bl Fib
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ldr w0, [sp], 16 // temporary
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// Fib(n-1) stored at 32 of sp
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str w0, [sp, -16]! // +2
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// Execute Fib(nthNumber - 2)
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ldr w0, [sp, 16]
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sub w0, w0, 2
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bl Fib
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// Restore the results of Fib(nthNumber - 1) and also
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// undo the stack change associated with preserving it.
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ldr w1, [sp], 16 // +1
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add w0, w0, w1
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// Undo the stack change due to storing nthNumber
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ldr w1, [sp], 16 // 0
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99: ldr x30, [sp], 16
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ret
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