# Parallel Programing Homework #1
Author: 312551015 Sean Wei
Spec: https://pp-f23.github.io/assignments/HW1/
Due date: Thu, Oct 26, 23:59

## Question 1-1
> Does the vector utilization increase, decrease or stay the same as VECTOR_WIDTH changes? Why?
>
> Run ./myexp -s 10000 and sweep the vector width from 2, 4, 8, to 16. Record the resulting vector utilization. You can do this by changing the #define VECTOR_WIDTH value in def.h.

In my experiment, when size is set to 10,000:
| `VECTOR_WIDTH` | Approx. utilization |
| :--: | :--: |
| 2 | 82% |
| 4 | 78% |
| 8 | 76% |
| 16 | 75% |

The **utilization decreases** as `VECTOR_WIDTH` increases.
This is because the definition of vector utilization is the percentage of lanes used, which will be higher if we use `maskAll`.
In my program, it will only multiply for those with positive exponents and decrease exponents as it progresses. So when `VECTOR_WIDTH` increases, more lanes with relatively small exponents have to wait for those with large exponents.

## Question 2-1
> Fix the code to make sure it uses aligned moves for the best performance.
>
> Hint: we want to see vmovaps rather than vmovups.

In my local environment, the three assembly code is exactly identical.

$ g++ -v
Apple clang version 14.0.3 (clang-1403.0.22.14.1)
Target: arm64-apple-darwin22.6.0
Thread model: posix
InstalledDir: /Library/Developer/CommandLineTools/usr/bin

But I noticed that there is a warning message:

clang: warning: argument unused during compilation:
       '-mavx2' [-Wunused-command-line-argument]

## Question 2-2
> Q2-2: What speedup does the vectorized code achieve over the unvectorized code?
> What additional speedup does using -mavx2 give (AVX2=1 in the Makefile)?
> You may wish to run this experiment several times and take median elapsed times; you can report answers to the nearest 100% (e.g., 2×, 3×, etc).
> What can you infer about the bit width of the default vector registers on the PP machines?
> What about the bit width of the AVX2 vector registers.
>
> Hint: Aside from speedup and the vectorization report, the most relevant information is that the data type for each array is float.

## Question 2-3
> Provide a theory for why the compiler is generating dramatically different assembly.