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Earlier quoted context omitted.
.125 + .375 == .5 You should be using == for floats when they're actually equal. 0.1 just isn't an actual number.
> 0.1 just isn't an actual number. A finitist computer scientists only accepts those numbers as real that can be expressed exactly in finite base-two floating point?
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
Can you elaborate a little on what 1 is supposed to mean?
So many of us spend so much time getting enamoured with technical solutions to problems that no one cares about.
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
Can you elaborate a little on what 1 is supposed to mean?
(From "An Essay on Numerical Methods" p 3 of the mentioned text; emphasis authors)
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.
Fixed point gave rise to the old programmers meme 'if you need floating point you don't understand your problem'. It's of course partially in jest but there is a grain of truth in it as well.
Earlier quoted context omitted.
> 0.1 just isn't an actual number. A finitist computer scientists only accepts those numbers as real that can be expressed exactly in finite base-two floating point?
0.1 is of course a real number, but let A \in R the set of actual numbers... (/s)
> 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.
> they (might) have a float, and are using the `==` operator, they're doing something wrong. Storage, retrieval, transmission, and serialization/deserialization systems should be able to transmit and round-trip floats without losing any bits at all.
Earlier quoted context omitted.
> 0.1 just isn't an actual number. A finitist computer scientists only accepts those numbers as real that can be expressed exactly in finite base-two floating point?
0.1 is of course a real number, but let A \in R the set of actual numbers... (/s)
Earlier quoted context omitted.
> 0.1 just isn't an actual number. A finitist computer scientists only accepts those numbers as real that can be expressed exactly in finite base-two floating point?
0.1 is of course a real number, but let A \in R the set of actual numbers... (/s)
I worked through what fp6 (e3m2) would look like, doing manual additions and multiplications, showing cases where the operations are non-associative, etc. and then I wanted something more rigorous to read.
For anyone interested in floating point numbers, I highly recommend working through fp6 as an activity! Felt like I truly came away with a much deeper understanding of floats. Anything less than fp6 felt too simple/constrained, and anything more than fp6 felt like too much to write out by hand. For fp6 you can enumerate all 64 possible values on a small sheet of paper.
For anyone not (yet) interested in floating point numbers, I’d still recommend giving it a shot.