floating-point
4 free lessons tagged floating-point across Computer Science. Each one is a short sequence of focused steps with narration and a five-question quiz at the end — take them in any order, no signup required.
Conditioning and Stability: Whose Fault Is the Error
Two different things can make a numerical answer inaccurate: the problem may amplify any input perturbation, or the algorithm may introduce its own. They are separate quantities, one belongs to the problem and one to the code, and only the second is fixable. This lesson separates them and shows what follows.
Comparing Floats, and Testing Code That Uses Them
Equality fails on floats, and both standard replacements fail too: absolute tolerance breaks at scale, relative tolerance breaks near zero. This lesson works through why each fails, what the combined form actually does, and how to choose a tolerance from the problem rather than copying a magic constant.
Cancellation: Where the Digits Actually Go
Every operation is correctly rounded, yet results can be wrong in the first digit. The reason is that subtracting nearly equal numbers is exact and still catastrophic: it does not create error, it promotes error that was already there. This lesson builds that mechanism and the summation techniques that recover the lost accuracy.
How a Float Is Stored, and What That Rules Out
Floating point is not a slightly inaccurate version of real numbers. It is a finite set of values, spaced logarithmically, with exact rules. This lesson builds the IEEE 754 layout, shows why 0.1 cannot be represented, and derives the one error bound that every later result depends on.