Pow(0, y) returns 0 for negative y, but 1/0 and RootN(0, -n) throw DivideByZeroException

[matt-edmondson]

What's wrong

In the instance Pow (PreciseNumber/PreciseNumber.cs ~L1755), the zero-base branch runs before the sign of power is checked:

if (power.Significand.IsZero) return One;
else if (Significand.IsZero) return Zero;   // runs for negative power as well

The static Pow (PreciseNumber.Exponentials.cs) forwards to this method, so it has the same bug.

0^-y is 1/0^y, which is a division by zero. PreciseNumber has no infinity, and everywhere else it handles this case by throwing:

• One / Zero throws DivideByZeroException
• RootN(0, -2) explicitly throws DivideByZeroException (Roots.cs ~L159)

Failure scenario (reproduced)

• PreciseNumber.Pow(0, -1) returns 0, where the mathematical answer is unbounded and Math.Pow(0, -1) gives +∞
• PreciseNumber.Pow(0, -0.5) returns 0
• 1 / 0 throws DivideByZeroException
• RootN(0, -2) throws DivideByZeroException

Generic-math code such as T.Pow(x, -1) that runs over PreciseNumber gets a finite, wrong answer without any error.

Suggested fix

In the zero-base branch, return Zero only when power > 0, and throw DivideByZeroException when power < 0. Document the exception with an <exception> tag, as RootN does.

Acceptance criteria

• Pow(0, -1) and Pow(0, -0.5) throw DivideByZeroException.
• Pow(0, 2) still returns 0 and Pow(0, 0) still returns 1.

[matt-edmondson]

Triage

• Category: Bug
• Priority: Medium. Pow(0, y) with negative y returns a finite, wrong answer, and generic-math callers get no error. It is an edge case, the fix is one line, and it brings Pow in line with / and RootN.
• Area / suggested assignee: the zero-base branch of Pow in PreciseNumber/PreciseNumber.cs, @matt-edmondson.
• Duplicates: None. It is related to Multiply/Divide wrap the exponent on int overflow: 1e2000000000 squared returns 1e-294967296 instead of throwing #109 in spirit: both are cases where Pow's documented or consistent exception behaviour doesn't happen.
• In progress: No open PR covers this. Open PRs Count trailing zeros in IsEvenInteger and IsOddInteger #107 and Round to negative decimal places correctly for integers #108 address IsEvenInteger(10) returns false and IsOddInteger(10) returns true for any integer with a trailing zero #104, Round with negative decimalDigits returns 0.12 for 1234 (and 0 for 1500) when the value has no fractional part #105 and Count trailing zeros in IsEvenInteger and IsOddInteger #107.

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