`(1e10 - 1e-10i) sqrt` does not work

[SergeStinckwich]

I try to compute: (1e10 - 1e-10i) sqrt and I got a division by zero error.

I'm wondering if this is not the same bug than in Math.js: josdejong/mathjs#208
Any comments on that @nicolas-cellier-aka-nice ?

[olekscode]

The problem comes from PMComplex >> abs and it can be boiled down to this:

superBig := 1e10 * 1e10.
superSmall := 1e-10 * 1e-10.

superSmall = 0. "false"

superBig + superSmall = superBig. "true"
superBig - superSmall = superBig. "true"

I think this is an awesome bug 😃

[olekscode]

Which is why in this method:

sqrt
	"Return the square root of the receiver with a positive imaginary part."

	| u v |
	(imaginary = 0 and: [real >= 0])
		ifTrue:	[^self class real: real sqrt imaginary: 0].
	v := (self abs - real / 2) sqrt.
	u := imaginary / 2 / v.
	^self class real: u imaginary: v

when we check if imaginary = 0, the answer is false
But inside PMComplex >> abs this happens:

abs
	"Answer the distance of the receiver from zero (0 + 0 i)."

	^ ((real * real) + (imaginary * imaginary)) sqrt

So superBig + superSmall = superBig
And therefore self.abs = real
And self.abs - real = 0

Hence a zero divide

[olekscode]

I have opened an issue in Pharo: pharo-project/pharo#11152
We will discuss it there and if it is possible to fix it, the problem will be gone.
Otherwise, we will adapt the PolyMath code to deal with this limitation of Pharo

[nicolas-cellier-aka-nice]

Good find, implementation of Complex sqrt is too naive.