What Every Computer Scientist Should Know About Floating-Point Arithmetic (1991) - https://news.ycombinator.com/item?id=23665529 - June 2020 (85 comments)

What Every Computer Scientist Should Know About Floating-Point Arithmetic - https://news.ycombinator.com/item?id=3808168 - April 2012 (3 comments)

What Every Computer Scientist Should Know About Floating-Point Arithmetic - https://news.ycombinator.com/item?id=1982332 - Dec 2010 (14 comments)

What Every Computer Scientist Should Know About Floating-Point Arithmetic - https://news.ycombinator.com/item?id=1746797 - Oct 2010 (2 comments)

Weekend project: What Every Programmer Should Know About FP Arithmetic - https://news.ycombinator.com/item?id=1257610 - April 2010 (9 comments)

What every computer scientist should know about floating-point arithmetic - https://news.ycombinator.com/item?id=687604 - July 2009 (2 comments)

For anyone turned off by this document and its proofs, I recommend Numerical Methods for Scientists and Engineers (Hamming). Still a math text, but more approachable.

The five key ideas from that book, enumerated by the author:

(1) the purpose of computing is insight, not numbers

(2) study families and relationships of methods, not individual algorithms

(3) roundoff error

(4) truncation error

(5) instability

(1991). This article is also available in HTML: https://docs.oracle.com/cd/E19957-01/806-3568/ncg_goldberg.h...

    > 0.1 + 0.1 + 0.1 == 0.3
    
    False

I always tell my students that if they (might) have a float, and are using the `==` operator, they're doing something wrong.

One thing that really did it for me was programming something where you would normally use floats (audio/DSP) on a platform where floats were abysmally slow. This forced me to explore Fixed-Point options which in turn forced me to explore what the differences to floats are.