Refactor and document complexity calculation

[ulvgard]

Hello,

In trying to derive and understand how complexity is calculated I found that the algorithm is made less readable with the factors sigma_gn_squared and sigma_time_gn which can be cancelled in expression. Also, the link to the description of the Least-Square calculation is dead. The author has a similarly named repository (https://github.com/ismaelJimenez/cpp.leastsq) that provides a description for the least-square derivation which in my opinion is difficult to follow and arrives in an less familiar expression.

This pull request provides a hand-waving argument on how complexity is calculated. It is derived similarly with least-square minimization and the description detail the conceptual approach in text.

[googlebot]

We found a Contributor License Agreement for you (the sender of this pull request), but were unable to find agreements for all the commit author(s) or Co-authors. If you authored these, maybe you used a different email address in the git commits than was used to sign the CLA (login here to double check)? If these were authored by someone else, then they will need to sign a CLA as well, and confirm that they're okay with these being contributed to Google.
In order to pass this check, please resolve this problem and have the pull request author add another comment and the bot will run again. If the bot doesn't comment, it means it doesn't think anything has changed.

[ulvgard]

googlebot please try again

[coveralls]

Coverage remained the same at 89.288% when pulling 5d4ad0a on ulvgard:refactor_complexity into 56f5cd6 on google:master.

[AppVeyorBot]

✅ Build benchmark 1569 completed (commit cbf1e47d9c by @)

[googlebot]

So there's good news and bad news.

👍 The good news is that everyone that needs to sign a CLA (the pull request submitter and all commit authors) have done so. Everything is all good there.

😕 The bad news is that it appears that one or more commits were authored or co-authored by someone other than the pull request submitter. We need to confirm that all authors are ok with their commits being contributed to this project. Please have them confirm that here in the pull request.

Note to project maintainer: This is a terminal state, meaning the cla/google commit status will not change from this state. It's up to you to confirm consent of all the commit author(s), set the cla label to yes (if enabled on your project), and then merge this pull request when appropriate.

[AppVeyorBot]

✅ Build benchmark 1570 completed (commit ea1180937f by @)

[AppVeyorBot]

✅ Build benchmark 1571 completed (commit 7ccf229f3a by @)

[ulvgard]

Are any actions required by me to move forward?

[LebedevRI]

Looks like CLA bot is still unhappy?

[ulvgard]

Looks like CLA bot is still unhappy?

Is it because the initial commit was made with another Author and Email? I squshed that and rewrote the auther to my CLA signed user.

[LebedevRI]

https://github.com/google/benchmark/commit/5d4ad0a277e1761463a227cf50d7748fcf5f1ef4.patch

From: Tobias Ulvgard <tobias@ulvgard.se>

^ i guess it is checking this email. Is that the one with signed CLA?

[ulvgard]

https://github.com/google/benchmark/commit/5d4ad0a277e1761463a227cf50d7748fcf5f1ef4.patch

From: Tobias Ulvgard <tobias@ulvgard.se>

^ i guess it is checking this email. Is that the one with signed CLA?

It is yes.

[ulvgard]

Is is possible to merge this? From what I understand googlebot is confused because the initial commit was made by me but with another author signature.

[ulvgard]

ping @LebedevRI ?

[LebedevRI]

cc @dominichamon

[dmah42]

LGTM