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 overwritten
After 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]

Ancestors (12)

  1. a
  2. 2
  3. Digital systems, linear algebra, introduction to formal proof
  4. 2022
  5. Past exam of the year 1 of the computer science course of the University of Oxford
  6. Year 1 of the computer science course of the University of Oxford
  7. Computer science course of the University of Oxford
  8. Undergraduate course of the University of Oxford
  9. Course of the University of Oxford
  10. University of Oxford
  11. List of universities
  12. Home

View article source

Discussion (0)

New discussion

There are no discussions about this article yet.

Articles by others on the same topic (0)

There are currently no matching articles.
See all articles in the same topic Create my own version