3 ms·
That's handwaving the "OKness of dividing by zero" – yeah, computers can only do limited-precision arithmetic performantly. But by allowing overflow to infinity
by GolDDranks 6y ago
That's handwaving the "OKness of dividing by zero" – yeah, computers can only do limited-precision arithmetic performantly. But by allowing overflow to infinity, we are essentially making the relative error infinite instead of bounded. After reading about Posit arithmetic ( https://www.posithub.org/docs/Posits4.pdf https://www.posithub.org/docs/Posits4.pdf ) I think that IEEE 754 under- and overflows and multiple representations of zero are a design mistake.
- nwallin 6y agoWhat do posits do when you run out of bits? 32 is ... not very many bits.
- GolDDranks 6y agoThey round to non-infinite values (the maximum and minimum representable finite values). This is not ideal, of course, but the relative error stays bounded, unlike with rounding to infinity. Additionally, they have a neat encoding that makes the size of the mantissa and exponent fields variable. (The whole bitsize of the number is fixed at 32 or 64 bits though.) This allows to have "tapered" accuracy at super large and extra tiny numbers, which allows for more gradual under- and overflow, and buys more accuracy where most of the calculations tend to be done, around 1.