Remove recursion from Base.:^

[wheeheee]

Prevents stack overflow, in the admittedly unlikely case that -e == e, for e == typemin(Int8) etc.
Also moves some definitions around for readability.

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 97.97%. Comparing base (1f70965) to head (0276bc6).
Report is 1 commits behind head on master.

Additional details and impacted files

@@           Coverage Diff           @@
##           master     #618   +/-   ##
=======================================
  Coverage   97.96%   97.97%           
=======================================
  Files          19       19           
  Lines        3251     3254    +3     
=======================================
+ Hits         3185     3188    +3     
  Misses         66       66           

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[wheeheee]

Using Int8 in the tests, otherwise with Int these might trigger OutOfMemoryError, or in the case of PolynomialRatio, we get ArgumentError: filter must have non-zero leading denominator coefficient because it rounds to zero.

[martinholters]

Haven't verified the code movement in detail, but the rest LGTM. Maybe the one additional test. Apart from that, good to go from my side.

[wheeheee]

Another unfortunate case of arithmetic overflow, as inv(3)^128 != inv(3^128). Should we try to convert g to typeof(inv(g)) first before exponentiation or just change the test?

[martinholters]

Would this fix the overflow in computing k in the test?

Suggested change

	res = ZeroPoleGain{D}(repeat(f.z, ae), repeat(f.p, ae), f.k^ae)
	return e < 0 ? inv(res) : res
	if e < 0
	return ZeroPoleGain{D}(repeat(f.p, ae), repeat(f.z, ae), inv(f.k)^ae)
	else
	return ZeroPoleGain{D}(repeat(f.z, ae), repeat(f.p, ae), f.k^ae)
	end

[wheeheee]

That works too.