Vectorize c and c++ code

[LazyKernel]

Adding -ffast-math compilation option and moving the calculation of variable x inside the scope of the for-loop allows gcc to vectorize the calculation for C and C++. This results in a significant speedup on my machine, going from around 100ms to 50ms. The change does not significantly affect the accuracy of the result. Analyses below

C

#### Original ```json { "Started": "18-10-2022 19:33:20", "Ended": "18-10-2022 19:33:20", "Language": "C (gcc)", "Version": "11.2.1", "Command": "./leibniz", "Accuracy": 0.7222222222222222, "CalculatedPi": "3.1415926635893259", "Iterations": 3, "Average": "93.971662ms" } ``` #### Proposed ```json { "Started": "18-10-2022 19:56:48", "Ended": "18-10-2022 19:56:48", "Language": "C (gcc)", "Version": "11.2.1", "Command": "./leibniz", "Accuracy": 0.7222222222222222, "CalculatedPi": "3.1415926635857296", "Iterations": 3, "Average": "48.815929ms" } ```

C++

#### Original ```json { "Started": "18-10-2022 19:57:40", "Ended": "18-10-2022 19:57:41", "Language": "C++ (g++)", "Version": "11.2.1", "Command": "./leibniz", "Accuracy": 0.7222222222222222, "CalculatedPi": "3.1415926635893259", "Iterations": 3, "Average": "96.320308ms" } ``` #### Proposed ```json { "Started": "18-10-2022 19:59:43", "Ended": "18-10-2022 19:59:43", "Language": "C++ (g++)", "Version": "11.2.1", "Command": "./leibniz", "Accuracy": 0.7222222222222222, "CalculatedPi": "3.1415926635857296", "Iterations": 3, "Average": "49.448502ms" } ```

[Moelf]

Fast math is waaay to dangerous probably not how usually people compile their application

[giordano]

Mandatory reminder that in general -ffast-math is bad:

• https://gcc.gnu.org/bugzilla/show_bug.cgi?id=55522
• https://github.com/llvm/llvm-project/issues/57589
• https://kristerw.github.io/2021/10/19/fast-math/
• https://simonbyrne.github.io/notes/fastmath/
• https://moyix.blogspot.com/2022/09/someones-been-messing-with-my-subnormals.html

In principle you should be able to achieve the same effect with the less blunt -fassociative-math, but GCC doesn't seem to like this flag for me:

% gcc leibniz.c -o leibniz -O3 -s -static -flto -fassociative-math -march=native -mtune=native -fomit-frame-pointer
cc1: warning: ‘-fassociative-math’ disabled; other options take precedence
lto1: warning: ‘-fassociative-math’ disabled; other options take precedence
lto1: warning: ‘-fassociative-math’ disabled; other options take precedence

The flag is accepted by Clang instead, but doesn't seem to actually vectorise this code. The directive

#pragma clang fp reassociate(on)

would work without any additional command line flag in Clang, but I didn't find an equivalent pragma directive for GCC.

[LazyKernel]

Good point. I was not aware of the multitude of issues -ffast-math brings with it. Using just -fassociative-math seems like a much better option. For GCC though, we also need to enable -fno-signed-zeros and -fno-trapping-math (as per gcc manual). The combination -fassociative-math -fno-signed-zeros -fno-trapping-math produces practically the same result as above, with fewer downsides as far as I can see.

[niklas-heer]

@LazyKernel I had to update it due to #66

[niklas-heer]

Thank you very much for your contribution @LazyKernel 👍