(-1).Pow(2E308) throws OverflowException "The result is too small to represent." instead of returning 1

[matt-edmondson]

What happens

Pow special-cases a base of One (SignificantNumber/SignificantNumber.cs:599) but not NegativeOne. When the base is -1 and the integer power is beyond the range of a double, PowByLogarithm computes:

• Math.Log(1) * power.To<double>(), which is 0 · ∞ = NaN (line 643).
• It then falls back to Log10OfMagnitude(-1) * ∞, which is NaN again.
• FromLog10OfMagnitude (around lines 713-718) sees a non-finite value and throws. The message says "too small" only because NaN > 0 is false.

S("-1").Pow(S("2E308"))   // throws OverflowException: The result is too small to represent.  expected 1
S("-1").Pow(S("-1E400"))  // throws the same                                                  expected 1
S("-1").Pow(S("2" + new string('0', 310) + "1")) // throws                                    expected -1
S("-1").Pow(S("1E308"))   // 1 (correct, still inside double range)

Why it matters

The README documents -1, 0 and 1 as exact values. (-1)^n for an integer n always has an exact answer (±1), whatever the size of n. Callers get an exception with a misleading message instead. Impact is limited to very large exponents, but the fix is a two-liner.

Suggested fix

Next to the Equal(this, One) check:

else if (Equal(this, NegativeOne) && PreciseNumber.IsInteger(power))
{
	return PreciseNumber.IsEvenInteger(power) ? One : NegativeOne;
}

IsInteger and IsEvenInteger work on the PreciseNumber directly, without going through a double.

Acceptance criteria

• (-1)^(2E308) == 1, (-1)^(-1E400) == 1, and (-1)^(odd integer beyond 1E308) == -1.
• A non-integer power of -1 keeps its current behaviour.

[matt-edmondson]

Triage

• Category: Bug
• Priority: Low. It only triggers for integer exponents beyond double range. The failure is a loud exception, not a wrong value, and the fix is two lines.
• Area / suggested assignment: Pow special cases in SignificantNumber/SignificantNumber.cs, next to the Equal(this, One) check.
• Duplicates: none. It touches the same PowByLogarithm / FromLog10OfMagnitude path as Pow of a base near 1 is wrong from the 3rd digit but reports 15 significant digits: 1.00000000000001^1E14 = 2.71611… (true 2.71828…), and x^1025 == x^1024 #116 and Pow and Exp report 15–17 significant digits when only 12–13 are correct for large |power·ln x| #113, but it is independent: the special case returns before that path runs. It's a good quick win to bundle into whichever PR lands Pow of a base near 1 is wrong from the 3rd digit but reports 15 significant digits: 1.00000000000001^1E14 = 2.71611… (true 2.71828…), and x^1025 == x^1024 #116/Pow and Exp report 15–17 significant digits when only 12–13 are correct for large |power·ln x| #113.
• In progress: no matching open PR.

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