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Joined 2026-09-21 Message
Incoming links: AAPCS32
ARM architecture family 2026-10-24
A family of processor architectures with several execution states and instruction encodings. The 32-bit instruction sets include the compact Thumb instruction set; the 32-bit AAPCS32 calling convention specifies interoperation at subroutine boundaries.
Null pointer 2026-10-24
A null pointer is a distinguished pointer value that designates no object or function. Pointer-linked binary trees commonly use it to represent an absent child. Dereferencing it is invalid; its representation is target dependent, although AAPCS32 specifies an all-zero null representation.
Use the AAPCS32 convention:
r0 holds the input address, r1 the length, and r0 receives the result. The following Thumb instruction set assembly language uses only scratch processor registers, so no callee-saved registers need saving. Assume the array is valid, halfword-aligned, and has nonnegative length; for the mathematical sum assume it fits a signed 32-bit two's complement integer..syntax unified
.thumb
.thumb_func
sum16:
movs r2, #0 @ accumulated sum
cmp r1, #0
ble .Ldone @ empty array; also returns 0 if n < 0
.Lloop:
movs r3, #0 @ Thumb signed load needs a register offset
ldrsh r3, [r0, r3] @ signed halfword at a; offset read before r3 changes
adds r2, r2, r3 @ include this signed value
adds r0, r0, #2 @ advance by one short, not one byte
subs r1, r1, #1 @ one fewer element remains
bne .Lloop
.Ldone:
movs r0, r2 @ result register
bx lr @ leaf routine: lr was not overwrittenAfter iterations, the loop invariant is that
r2 contains the first elements' sum, r0 points to element , and r1 is . The sign extension in ldrsh supplies the correct signed addend. One iteration preserves this loop invariant, and the decreasing remaining length proves algorithm termination. For the seven-element calls, the sum lies between and , so it fits. For longer arrays that overflow, these instructions compute the sum modulo ; that is not a claim about defined signed C programming language overflow behavior. The operand forms are those of the paper's reference sheet.[ref]Thumb 16-bit instruction set quick reference by Arm. Load: signed halfword; Add/Subtract; Branch
Keep
total in the callee-saved register r4, and the first returned sum in the callee-saved register r5. Suppose the surrounding function has made an aligned stack frame with the local seven-halfword array at the current sp, occupying fourteen bytes in a sixteen-byte slot. One possible frame setup is push {r4,r5,r6,lr} followed by sub sp,sp,#16; the earlier code initializes total, regular, and special before this fragment. ldr r0, =regular @ assembler literal load of the global array address
movs r1, #7
bl sum16
movs r5, r0 @ first sum must survive the next call
add r0, sp, #0 @ current frame's local special array
movs r1, #7
bl sum16
muls r0, r5, r0 @ second sum times first sum
adds r4, r4, r0 @ update totalThe AAPCS32 permits each call to overwrite
r0–r3, r12, and condition flags, but requires preservation of r4–r8, r10, r11, and sp. Thus both r4 and r5 remain valid even if sum16 is replaced by another conforming implementation. bl changes the link processor register lr, so the enclosing function saves its own return address in its prologue. Its epilogue can use add sp,sp,#16 and pop {r4,r5,r6,pc}. The frame uses thirty-two bytes in total, preserving the required eight-byte stack pointer alignment at both calls.[ref]The two calls may be evaluated in this order. Assume the product and final addition fit the signed 32-bit result expected by the source program; unlike each individual seven-element sum, their product need not fit. The assembly language operations retain their low 32 bits if this assumption fails, whereas signed integer overflow in the C programming language has different semantics.
Solutions to all eight questions of the 7 September 2022 resit. Released Oxford examination archive, member
2021/L/a10101w1.pdf. The dated cover establishes the year despite the undated held filename and misleading archive directory. The Thumb instruction set listings assume the 32-bit AAPCS32 data layout; the timer calculation in Question 2 corrects a numerical slip in the paper. Pointer (computer programming) 2026-10-24
A pointer is a value designating a location in a program's memory model, or a special value such as a null pointer that designates no object. A node in a pointer-linked binary tree stores pointers to its two children. Representation, size, alignment and the validity of dereferencing depend on the programming language and target; 32-bit AAPCS32 data pointers occupy four bytes.
Stack alignment 2026-10-24
Stack alignment constrains the stack pointer to a multiple of a specified byte boundary. AAPCS32 requires word alignment generally and eight-byte alignment at public interfaces. Saving four 32-bit words preserves eight-byte alignment; saving three would change it by four bytes and may require padding before another call. Frame size and the alignment of local objects must be considered together.[ref]
Procedure Call Standard for the Arm Architecture by ARM Limited. Base standard, universal and public-interface stack constraints