[Rafael-SOWNet]

The second half of the follow-up to Happypig375's comment on #2327, after #2329.

Before this PR, b ^ e mod m and n! mod m, for whole numbers, wrote out the whole power or factorial and then divided. Now they are reduced modulo m as they are built:

• a power uses modular exponentiation;
• a factorial is multiplied out factor by factor, in machine words when |m| < 2^31;
• n! mod m is 0 outright once n >= |m|, since |m| then divides it.

The remainder is the floored one, as for the operator.

	master	this PR
2^(10^8) mod 1000	29 s, 13.9 GB allocated	2 ms, 0.8 MB
2^(10^7) mod 1000	0.68 s, 772 MB	44 ms, 0.8 MB
10^(10^9) mod 7	no answer in 60 s	35 ms
(10^5)! mod 1000003	21 s, 13.7 GB	4 ms, 0.8 MB

0 ^ 0, a negative or symbolic exponent, and a divisor that is not a whole number go to the evaluation as before. No answer changes, apart from the ones that never finished.

Tests: ARemainderOfALargeWholeTest checks 16 remainders against Python's pow and math.factorial, including negative bases and divisors, 0 ^ 0 and a reciprocal. It also asserts that 2 ^ (10 ^ 7) mod 1000 allocates under 20 MB; that fails on master, at 810 MB.

🤖 Generated with Claude Code

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 86.75%. Comparing base (93a52f0) to head (d3d8f70).
⚠️ Report is 1 commits behind head on master.

Additional details and impacted files

@@           Coverage Diff           @@
##           master    #2330   +/-   ##
=======================================
  Coverage   86.75%   86.75%           
=======================================
  Files         312      312           
  Lines       68447    68477   +30     
  Branches    19909    19921   +12     
=======================================
+ Hits        59379    59406   +27     
- Misses       4908     4913    +5     
+ Partials     4160     4158    -2     

Flag	Coverage Δ
cpp	37.77% <ø> (ø)
csharp	87.29% <100.00%> (+<0.01%)	⬆️
fsharp	32.97% <ø> (ø)
interactive	40.72% <ø> (ø)

Flags with carried forward coverage won't be shown. Click here to find out more.

Files with missing lines	Coverage Δ
...nuous/Evaluation.Continuous.Arithmetics.Classes.cs	87.98% <100.00%> (+0.41%)	⬆️

... and 5 files with indirect coverage changes

🚀 New features to boost your workflow:

• ❄️ Test Analytics: Detect flaky tests, report on failures, and find test suite problems.

[Happypig375]

This shows the importance of separating numerical evaluation from all symbolic operations in v3, there are a lot of special forms that we can take advantage of that would result in huge numbers if evaluated directly

[Rafael-SOWNet]

Agreed. Here it's a shortcut in Modf's own evaluation, which spots the shape before the children are evaluated. In v3 it belongs in the evaluator, which would see b^e mod m as one operation instead of building b^e first.