[stephencanon]

With floating-point math libraries especially, it's frequently the case that it's relatively easy to compute the desired result accurately by using higher precision for internal computations; e.g. you might compare against the same function evaluated in double and then rounded to float.

This sounds pretty sketchy at first, but it turns out that almost all of the difficulty (and hence almost all of the bugs) are in getting the last few bits right, and the last few bits of a much-higher precision result don't matter when you're testing a lower-precision implementation, so combined with some basic sanity checks this is actually a very reasonable testing strategy (and widely used in industry).