refactor: split implementation files and add more inline / constexpr / noexcept qualifiers

[XuehaiPan]

Description

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Motivation and Context

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If it fixes an open issue, please link to the issue here.
You can use the syntax close #15213 if this solves the issue #15213

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• My change requires a change to the documentation.
• I have updated the tests accordingly. (required for a bug fix or a new feature)
• I have updated the documentation accordingly.
• I have reformatted the code using make format. (required)
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[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 100.00%. Comparing base (3d78747) to head (fc96a61).
Report is 1 commits behind head on main.

Additional details and impacted files

@@            Coverage Diff            @@
##              main      #159   +/-   ##
=========================================
  Coverage   100.00%   100.00%           
=========================================
  Files           12        12           
  Lines         1267      1267           
=========================================
  Hits          1267      1267           

Flag	Coverage Δ
unittests	100.00% <ø> (ø)

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