Pow(-1, n) throws OverflowException for any integer |n| ≥ 2^31, although the result is ±1

[matt-edmondson]

What's wrong

The integer-power path in Pow (PreciseNumber/PreciseNumber.cs:1818) loops over power.Abs().To<int>(), so an exponent that doesn't fit in an int throws. IsUnit already short-circuits a base of +1, but a base of −1 gets no such shortcut, even though (−1)^n is always ±1.

Repro

Parse("-1").Pow(Parse("2147483648"));   // OverflowException, expected 1
Parse("-1").Pow(Parse("-2147483648"));  // OverflowException, expected 1
Parse("-1").Pow(Parse("1e20"));         // OverflowException, expected 1
Parse("-1").Pow(Parse("2147483647"));   // -1 (correct)
Parse("1").Pow(Parse("1e20"));          // 1 (correct, short-circuited)

For comparison, double.Pow(-1, 1e20) returns 1.

Suggested fix / acceptance criteria

• Before the loop, when the base is −1, return IsEvenInteger(power) ? One : NegativeOne.
• For any other base, an exponent that large really does overflow the result's exponent, so the current exception is fine there.
• Add tests for the three failing calls above.

[matt-edmondson]

Triage

• Category: Bug
• Priority: Low. It is an edge case (base −1 with an exponent of at least 2^31) and fails loudly with OverflowException rather than returning a wrong value.
• Area / suggested owner: Integer-power path in PreciseNumber.Pow
• Duplicates / in progress: None found. Open PRs Report zero as not normal, and nothing as subnormal [patch] #129 and Reject a precision below one in ReduceSignificance [patch] #130 fix IsNormal(Zero) returns true, unlike int/decimal/BigInteger, so generic math treats PreciseNumber zero as a normal number #122 and ReduceSignificance(0) returns 10 and ReduceSignificance(-1) returns 0 instead of rejecting the argument #126 and don't touch Pow.
• Notes: A one-line shortcut next to the existing IsUnit check. A fix for Pow with a fractional exponent misrounds the last digit: Pow(19, 1.5) ends in …417 instead of …416 (double rounding without guard digits) #127 (also in Pow) could carry it, as long as both keep their own tests.

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