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I've always thought that floats should be accompanied with a precision value specifying the number of significant digits. Ideally updated by hardware in the same operation. All floating point code has subtle bugs if you don't track error accumulation.
Earlier quoted context omitted.
I hate these text-on-picture-with-music videos. Even the robot-voice videos are better. I know it's using the Super Mario music, but still. It's like a blog post where you can't copy or paste anything, can't scroll back and forth, can't be cached or indexed, etc.
He has some videos that are commentated by voice, but for some reason he finds doing the recordings very stressful, so most of his content is unfortunately on his 'uncommentated' channel. I agree it would be nice to have the voice-overs
https://www.crcpress.com/The-End-of-Error-Unum-Computing/Gus...
It is an amazing compendium of the many ways in which floats fail to give any guarantees in practice. In some cases, due to the format itself, and also because many subtle issues are indicated via internal processor values and flags that are simply not accessible in high-level languages. In addition, the book presents Unums, an alternative number format with several extremely interesting properties that make computations much less error-prone.
Prof. Gustafson has since also presented several additional formats with much stronger guarantees than IEEE floats:
Real world example: 1.09 - 1.09375
Double: 0.00374999999999992
Decimal: 0.00375
Related: A fun video that illustrates floating-point precision by way of Super Mario 64: https://youtu.be/9hdFG2GcNuA
I hate these text-on-picture-with-music videos. Even the robot-voice videos are better. I know it's using the Super Mario music, but still. It's like a blog post where you can't copy or paste anything, can't scroll back and forth, can't be cached or indexed, etc.
And I absolutely disagree with the "Robot voice would be better." That's horrific.
Related: A fun video that illustrates floating-point precision by way of Super Mario 64: https://youtu.be/9hdFG2GcNuA
Speaking of floats, I highly recommend John Gustafson's book, The End of Error: Unum Computing : https://www.crcpress.com/The-End-of-Error-Unum-Computing/Gus... It is an amazing compendium of the many ways in which floats fail to give any guarantees in practice. In some cases, due to the format itself, and also because many subtle issues are indicated via internal processor values and flags that are simply not access…
I try to avoid using floats when doing business calculations. Base 2 doesn't work well with our base 10 currency. Real world example: 1.09 - 1.09375 Double: 0.00374999999999992 Decimal: 0.00375
http://www-users.math.umn.edu/~arnold/disasters/patriot.html
I've always thought that floats should be accompanied with a precision value specifying the number of significant digits. Ideally updated by hardware in the same operation. All floating point code has subtle bugs if you don't track error accumulation.
This sounds like unums, a proposed alternative to IEEE floats, where roughly speaking the significand can have variable size thus only boasting as much precision as the accuracy warrants.
If so that makes them much more interesting to me. Floating point bugs manifest themselves at non linear parts such as equality and comparison operators.
Earlier quoted context omitted.
He has some videos that are commentated by voice, but for some reason he finds doing the recordings very stressful, so most of his content is unfortunately on his 'uncommentated' channel. I agree it would be nice to have the voice-overs
He could be writing blog posts and making videos to supplement. His writing isn't bad.