3 ms·

> IEEE 754 is like democracy in a sense that it is the worst, except for all the others. I can't see what would be worse. The entire raison d'etre for computer

by bigstrat2003 2y ago

> IEEE 754 is like democracy in a sense that it is the worst, except for all the others. I can't see what would be worse. The entire raison d'etre for computers is to give accurate results. Introducing a math system which is inherently inaccurate to computers cuts against the whole reason they exist! Literally any other math solution seems like it would be better, so long as it produces accurate results.

raverbashing 2y ago
There's no "accurate results" most of the time You can only have a result that's exact enough in your desired precision
aoeusnth1 2y ago
Sometimes you need a number system which is 1. approximate 2. compact and fast 3. high dynamic range You’re going to have a hard time doing better than floats with those constraints.
meindnoch 2y ago
Define "accurate"!
recursive 2y ago
> so long as it produces accurate results That's doing a lot of work. IEE-754 does very in terms of error vs representation size. What system has accurate results? I don't know any number system at all in usage that 1) represents numbers with a fixed size 2) Can represent 1/n accurately for reasonable integers 3) can do exponents accurately
foxglacier 2y ago
It's ideal for engineering calculations which is a common use of computers. There, nobody cares if 1-1=0 exactly or not because you could never have measured those values exactly in the first place. Single precision is good enough for just about any real-world measurement or result while double precision is good for intermediate results without losing accuracy that's visible in the single precision input/output as long as you're not using a numerically unstable algorithm.
dan-robertson 2y ago
Electronic computers were created to be faster and cheaper than a pool of human computers (who may have had slide rules or mechanical adding machines). Human computers were basically doing decimal floating point with limited precision.
bazoom42 2y ago
Given a computer have finite memory but there are infinitely many real numbers in any range, any system using real numbers will have to use rounding.

raverbashing 2y ago

There's no "accurate results" most of the time You can only have a result that's exact enough in your desired precision

aoeusnth1 2y ago

Sometimes you need a number system which is 1. approximate 2. compact and fast 3. high dynamic range You’re going to have a hard time doing better than floats with those constraints.

meindnoch 2y ago

Define "accurate"!

recursive 2y ago

> so long as it produces accurate results That's doing a lot of work. IEE-754 does very in terms of error vs representation size. What system has accurate results? I don't know any number system at all in usage that 1) represents numbers with a fixed size 2) Can represent 1/n accurately for reasonable integers 3) can do exponents accurately

foxglacier 2y ago

It's ideal for engineering calculations which is a common use of computers. There, nobody cares if 1-1=0 exactly or not because you could never have measured those values exactly in the first place. Single precision is good enough for just about any real-world measurement or result while double precision is good for intermediate results without losing accuracy that's visible in the single precision input/output as long as you're not using a numerically unstable algorithm.

dan-robertson 2y ago

Electronic computers were created to be faster and cheaper than a pool of human computers (who may have had slide rules or mechanical adding machines). Human computers were basically doing decimal floating point with limited precision.

bazoom42 2y ago

Given a computer have finite memory but there are infinitely many real numbers in any range, any system using real numbers will have to use rounding.