maybe I dont understand, but is this article only trying to suggest exhaustive testing for single precision, single input functions? obviously this approach is not practical as soon as there are multiple inputs or wider precision.
Yes, the article says "Exhaustive testing works brilliantly for functions that take a single float as input. I used this to great effect when rewriting all of the CRT math functions for a game console some years ago. On the other hand, if you have a function that takes multiple floats or a double as input then the search space is too big. In that case a mixture of test cases for suspected problem areas and random testing should work."
I think the point is that exhaustive testing is feasible in more situations than you might at first think, and than floating-point arithmetic is a particularly fertile source of edge conditions and corner cases, so it's a good place to go for exhaustive testing where you can.
In many cases it is practical but people wrongly assume it isn't. In cases where its not practical exhausting a subset can still be very powerful.
E.g. for a function that takes two floats (x,y) test every value of x input with y={0,-0,1,nan,inf,-1,x,-x,2x,x/2,FLT_EPSILON,FLT_MIN,FLT_MAX,random,random,random...}, and then repeat with x,y swapped.
A little knowledge of the domain can help pick better special values, but there is a trade-off in introducing the same blind-spots that permitted bugs in the first place. Still: testing just one argument on all values because that's all you can afford is still a lot better than only testing a couple special values for both arguments.
Exhaustive testing, like randomized testing catches errors you weren't even thinking about-- but unlike random testing exhaustion can reliably catch bugs which are extremely rare. "Partial exhaustion" can have some of the same benefits.
mmm, disagree based on my experience. oh also I think people on this thread may be misusing the concept of float epsilon. keep in mind that is not the smallest value of a float.
Testing all of the doubles may actually be possible [1]. Even if that estimate is optimistic, testing all doubles for order $10k would be feasible for some problems.
