Eq[Polynomial[C]] throws ArrayIndexOutOfBoundsException for negative exponents

[LukaJCB]

Reproduce:

scala> def x: Polynomial[Int] = PolySparse(List(Term(-1642198702, -1)))
x: spire.math.Polynomial[Int]
scala> x === x
java.lang.ArrayIndexOutOfBoundsException: -1
  at scala.runtime.ScalaRunTime$.array_update(ScalaRunTime.scala:76)
  at spire.math.poly.PolySparse.coeffsArray(PolySparse.scala:54)
  at spire.math.PolynomialEq.eqv(Polynomial.scala:556)
  at spire.math.PolynomialEq.eqv$(Polynomial.scala:555)
  at spire.math.PolynomialInstances0$$anon$14.eqv(Polynomial.scala:568)
  ... 36 elided

[denisrosset]

I'm not sure polynomials were designed to accept negative exponents. For example, the parse method on the companion object does not support negative exponents (see the termRe regexp).

@tixxit: can you comment on this?

[tixxit]

They were not - I think it is probably a bug that we don't throw an exception during construction in this case and we should fix that bug.

[LukaJCB]

Then we must also fix this line right here, which generates random exponents that could all be negative :)
https://github.com/non/spire/blob/master/laws/src/main/scala/spire/laws/gen.scala#L100

[tixxit]

😬

[LukaJCB]

Submitted a quick fix for that particular problem.

[kschwarz1116]

If polynomials aren't supposed to have negative exponents, should Term have UInt for exponent instead of Int?

[armanbilge]

@kschwarz1116 that's a good question. I wonder if UInt interacts poorly with specialization, and so would be boxed, which is why Int is preferable for performance. But I'm not sure about that without looking at bytecode.