[Rafael-SOWNet]

Part of #1448.

Since #2347, an exact power too large to build (past 2^24 bits) evaluated as a decimal. 2^(10^9) became +oo, and 2^(-(10^9)) became 0. 2.6.0 hung on these. A guard kept Simplify from collapsing the bare power to +oo, but differences, products and comparisons took the decimal, so they answered NaN or the wrong truth value for numbers that exist.

Now:

• The power stays written, in Evaled as in Simplify, and so for rational exponents: 8^(10^9/3) was +oo too. Subtraction, 0 * a and 2^m / 2^n then come out right from the existing rules.

• Comparisons with such a power are decided in three ways, and otherwise left undecided:

  • exactly by the exponents, for two powers of one positive base;
  • by the signs, using the exponent's parity for a negative base;
  • by the logarithms of the magnitudes at 120 digits, only where they differ by more than 1e-90 of their size.

  Two magnitudes that may be equal are never told apart, so 2^(10^9) = 4^(5*10^8) stays written. It was True on master only because +oo = +oo.

#1448's thread asked for a decimal approximation from Evaled, and measured that today's decimals overflow to +oo. That approximation needs the v3 numerics, so #1448 stays open for it.

Expression	2.6.0	master	this branch	true
eval 2^(10^9)	hangs	+oo	2 ^ 1000000000	(as written)
eval 2^(-(10^9))	hangs	0	2 ^ (-1000000000)	(as written)
simplify 2^(10^9) - 2^(10^9)	hangs	NaN	0	0
simplify 2^(10^9)/2^(10^9 - 1)	hangs	NaN	2	2
simplify 2^(10^9) * 2^(-(10^9))	hangs	NaN	1	1
eval 0 * 2^(10^9)	hangs	NaN	0	0
eval 2^(10^9) > 2^(10^9 - 1)	hangs	False	True	True
simplify 2^(-(10^9)) > 0	hangs	False	True	True
eval 2^(10^9) = 2^(10^9 - 1)	hangs	True	False	False
eval 3^(10^9) > 2^(10^9)	hangs	False	True	True
eval 2^(10^9) = 4^(5*10^8)	hangs	True	undecided	True
eval 46655^(10^20)	hangs	+oo	written	finite
eval forall n in ZZ* : 3^(n+1) divides 2^(3^n)+1	hangs	as written	as written	unsettled

All of #2347's former hang cases finish in 175–291 ms, among them simplify (x^x - 1)^(e^(e^x)), simplify 2^(10^10) and simplify 46655^(10^20) + 1. #2347's unshipped BREAKING-CHANGES.md entry is replaced by "An exact power too large to build is left written", measured from 2.6.0 to now.

Not changed, because both come from the decimal context's exponent range, which the v3 numerics own:

• 2^(10^7 + 0.5), whose exponent is a decimal;
• (3+4i)^2000, which is +oo + +ooi on master and NaN on 2.6.0.

Checked on this branch:

• Tests: UnitTests 19441 passed, plus the MCP, Terminal, InteractiveWrapper and F# wrapper suites, and the AOT smoke test. The rewritten AnExactPowerTooLargeToBuildTest has 42 cases, 21 of which fail on master.
• Harnesses: BoundCheck, RootCheck, CasBench, PropCheck, SimpSweep, RuleCheck, CanonCheck and Confluence all pass.

🤖 Generated with Claude Code

[codecov]

Codecov Report

❌ Patch coverage is 95.74468% with 2 lines in your changes missing coverage. Please review.
✅ Project coverage is 86.86%. Comparing base (4949e4c) to head (ebca5ff).

Files with missing lines	Patch %	Lines
...Evaluation.Discrete/Evaluation.Discrete.Classes.cs	94.73%	0 Missing and 2 partials ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #2437      +/-   ##
==========================================
- Coverage   86.87%   86.86%   -0.01%     
==========================================
  Files         312      312              
  Lines       69724    69771      +47     
  Branches    20385    20403      +18     
==========================================
+ Hits        60570    60609      +39     
- Misses       4913     4918       +5     
- Partials     4241     4244       +3     

Flag	Coverage Δ
cpp	37.77% <ø> (ø)
csharp	87.41% <95.74%> (-0.01%)	⬇️
fsharp	32.97% <ø> (ø)
interactive	39.81% <ø> (ø)

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

Files with missing lines	Coverage Δ
...uriMath/Core/Entity/Continuous/Number/Operators.cs	90.07% <ø> (-0.80%)	⬇️
...nuous/Evaluation.Continuous.Arithmetics.Classes.cs	88.22% <100.00%> (+0.11%)	⬆️
...Evaluation.Discrete/Evaluation.Discrete.Classes.cs	90.04% <94.73%> (+0.45%)	⬆️

... and 3 files with indirect coverage changes

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