Add convenience function qml.math.ceil_log2

[dwierichs]

Context:
We often want to compute the integer $\lceil \log_2(n)\rceil$ of an integer $n$.
This currently requires three function calls if we want to receive an int as output: out = int(np.ceil(np.log2(n)))
In various places in the codebase, the call to int is actually skipped, so that variables that conceptually describe integers remain float values in code.

Description of the Change:
Add a convenience function qml.math.ceil_log2 that bundles the three function calls into one.

Benefits:
Declutter code base.
Make sure we are using int values where applicable.

Possible Drawbacks:
N/A

Related GitHub Issues:

[github-actions]

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[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 99.44%. Comparing base (31f5441) to head (219bdd5).
⚠️ Report is 6 commits behind head on master.

Additional details and impacted files

@@           Coverage Diff           @@
##           master    #8972   +/-   ##
=======================================
  Coverage   99.44%   99.44%           
=======================================
  Files         601      601           
  Lines       64754    64759    +5     
=======================================
+ Hits        64393    64398    +5     
  Misses        361      361           

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[comp-phys-marc]

This looks great! Only thing is I am still seeing 3 instances of math.ceil(math.log2(...)) in the codebase on your branch. Could you look into them please?

[dwierichs]

This looks great! Only thing is I am still seeing 3 instances of math.ceil(math.log2(...)) in the codebase on your branch. Could you look into them please?

Oh thanks for catching those! The first two I overlooked because they are in tests/
The last one actually needs to stay because we do want the following to be supported:

n = 0
a = np.log2(n) # -np.inf
b = np.ceil(a) # -np.inf
c = 2**b # 0.0

I know, it's a bit of an unconventional computational path, but there actually is a test taking it (which is why I know, heh.)
I think I'll replace this, because we anyways replace 0.0 by 1 3 lines further down :D

[comp-phys-marc]

This looks great! Only thing is I am still seeing 3 instances of math.ceil(math.log2(...)) in the codebase on your branch. Could you look into them please?

Oh thanks for catching those! The first two I overlooked because they are in tests/ The last one actually needs to stay because we do want the following to be supported:

n = 0
a = np.log2(n) # -np.inf
b = np.ceil(a) # -np.inf
c = 2**b # 0.0

I know, it's a bit of an unconventional computational path, but there actually is a test taking it (which is why I know, heh.) I think I'll replace this, because we anyways replace 0.0 by 1 3 lines further down :D

Glad to be of service. Sounds interesting, while I don't understand why we want to do that with the negative infinities etc.

[dwierichs]

Glad to be of service. Sounds interesting, while I don't understand why we want to do that with the negative infinities etc.

Unfortunately I am missing the context here myself, but it seems to be a supported case that opt_width_continuous=0, which is then mapped to a lower bound of opt_width_continuous right after 🤷

[comp-phys-marc]

Looks great! Good QoL improvement.

[andrijapau]

Thanks 🚀 !