You should never test for equality numbers which are known only approximately, which is the case for most FP numbers.
There are nonetheless cases when certain FP values are known exactly and it is OK to test them for equality.
In general the rule does not depend on number representation, it applies equally to floating-point numbers, fixed-point numbers, rational numbers and even large integers in some cases.
What counts is whether a number is known exactly or only approximately.
But the type of barycentric interpolation formula that leads to Inf/Inf at an interpolation point isn't one of those exceptions - it's an example which shows why the rule should be borne in mind.
When the input is very close to one of the interpolation points, the calculation becomes ill-conditioned, unsurprisingly as two values are diverging towards Inf, so the result can become incorrect as the input approaches the interpolation point, until it becomes Inf/Inf = Nan at some even closer, but non-zero, distance. Before reaching Nan it can also have an interval where the result is +/-Inf.
It depends on the interpolation points. But under some circumstances, it is necessary to recognise when the input is close to an interpolation point, and adjust the formula appropriately.
You should never test for equality numbers which are known only approximately, which is the case for most FP numbers.
There are nonetheless cases when certain FP values are known exactly and it is OK to test them for equality.
In general the rule does not depend on number representation, it applies equally to floating-point numbers, fixed-point numbers, rational numbers and even large integers in some cases.
What counts is whether a number is known exactly or only approximately.