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9999999999999999.0 – 9999999999999998.0

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Re: 9999999999999999.0 – 9999999999999998.0

#81

Post by baddox »

chrisseaton wrote: post #56
twtw wrote: post #39

I don't understand all the crap that IEEE 754 gets. I appreciate that it may be surprising that 0.1 + 0.2 != 0.3 at first, or that many people are not educated about floating point, but I don't understand the people who "understand" floating point and continue to criticize it for the 0.1 + 0.2 "problem." The fact is that IEEE 754 is an exceptionally good way to approximate the reals in computers with a minimum number…

People get upset that floating point can’t represent all infinite number of real numbers exactly - I can’t understand how they think that’s going to be possible in a finite 64 bits.

Or on any computer at all, even an “infinite” (at least unbounded) computer like a Turing machine, considering that almost all real numbers are not computable.

Re: 9999999999999999.0 – 9999999999999998.0

#82

Post by crankylinuxuser »

So.. Can someone better versed in the ways of system level programming tell me why we still use IEEE 754 exponential notation?

Iv'e seen article after article of how "horrible it is". So, are there default libs to use Binary Coded Decimal (BCD) or something like that?

Re: 9999999999999999.0 – 9999999999999998.0

#83

Post by dkarl »

coddingtonbear wrote: post #70
Gibbon1 wrote: post #67

Earlier quoted context omitted.

> exceptionally good way to approximate You answered your question. 99% of the time being exact is a requirement and calculation speed is utterly unimportant, thus using IEEE 754 results in programs that are fundamentally broken.

Is that really true? In my experience, 99.9% of the time I don't need an exact number; the vanishingly few times when I have such a need (almost entirely calculations involving currency), using a fixed point representation is simple enough.

People do different kinds of work, so there are programmers who experience it both ways, 99% of the time floats are good solution or 99% of the time floats are an incorrect solution. Because of history and language support, classes and other resources for learning to program teach you to use floating-point numbers and don't bother with alternatives. As a result you have a lot of programmers who default to treating every number with a dot in it as floating point number, and they get burned by it, and instead of realizing it's just a gap in their education that they can correct, they treat overuse of floats as a mistaken industry-wide consensus that needs to be overturned.

Re: 9999999999999999.0 – 9999999999999998.0

#84

Post by m0zg »

chrisseaton wrote: post #56
twtw wrote: post #39

I don't understand all the crap that IEEE 754 gets. I appreciate that it may be surprising that 0.1 + 0.2 != 0.3 at first, or that many people are not educated about floating point, but I don't understand the people who "understand" floating point and continue to criticize it for the 0.1 + 0.2 "problem." The fact is that IEEE 754 is an exceptionally good way to approximate the reals in computers with a minimum number…

People get upset that floating point can’t represent all infinite number of real numbers exactly - I can’t understand how they think that’s going to be possible in a finite 64 bits.

To hit the point home a little harder: you can easily iterate through the entire representable set of float32 on a modern machine within seconds. I've encountered many engineers who don't quite get that.

Re: 9999999999999999.0 – 9999999999999998.0

#85

Post by ummonk »

chrisseaton wrote: post #56
twtw wrote: post #39

I don't understand all the crap that IEEE 754 gets. I appreciate that it may be surprising that 0.1 + 0.2 != 0.3 at first, or that many people are not educated about floating point, but I don't understand the people who "understand" floating point and continue to criticize it for the 0.1 + 0.2 "problem." The fact is that IEEE 754 is an exceptionally good way to approximate the reals in computers with a minimum number…

People get upset that floating point can’t represent all infinite number of real numbers exactly - I can’t understand how they think that’s going to be possible in a finite 64 bits.

Well, you don't need to represent all the real numbers. You can get quite far with just rationals or algebraic numbers, although you'll have trouble with exponentials and trignometry. And computable numbers are basically superior to any other number system for computation.

You of course need an unbounded but finite amount of space to store these numbers, which is perfectly fine.

Re: 9999999999999999.0 – 9999999999999998.0

#86

Post by crankylinuxuser »

svat wrote: post #71
twtw wrote: post #39

I don't understand all the crap that IEEE 754 gets. I appreciate that it may be surprising that 0.1 + 0.2 != 0.3 at first, or that many people are not educated about floating point, but I don't understand the people who "understand" floating point and continue to criticize it for the 0.1 + 0.2 "problem." The fact is that IEEE 754 is an exceptionally good way to approximate the reals in computers with a minimum number…

> considering the problem is to fit the reals into 64/32/16 bits and have fast math Floating-point numbers (and IEEE-754 in particular) are a good solution to this problem, but is it the right problem? I think the "minimum of surprises" part isn't true. Many programmers develop incorrect mental models when starting to program, and get no feedback to correct them until much later (when they get surprised). It is true…

When NASA can't even get it right, because of "surprises", there's no chance in hell I'm blaming us mere mortal programmers... or even 10x wizards. (0)

It's time to look at other ways to depict fractional parts of numbers in a computer. I know that one can express any rational number as a integer fraction. And our computers are incapable of expressing a irrational number exactly - it does so to a certain precision... In other words, every number a computer expresses is a rational number.

The exception is if the computer could express irrational numbers as symbolics, then we could work with the symbolic instead. And then as a last pass, the symbolic could convert to a imprecise rational depiction, or express as its native type.

(0) https://itsfoss.com/a-floating-point-error-that-caused-a-dam...

Re: 9999999999999999.0 – 9999999999999998.0

#87

Post by ummonk »

twtw wrote: post #39

I don't understand all the crap that IEEE 754 gets. I appreciate that it may be surprising that 0.1 + 0.2 != 0.3 at first, or that many people are not educated about floating point, but I don't understand the people who "understand" floating point and continue to criticize it for the 0.1 + 0.2 "problem." The fact is that IEEE 754 is an exceptionally good way to approximate the reals in computers with a minimum number…

Presumably we could actually make decimal floating point computation the default and greatly reduce the amount of surprise. I don't think the performance difference would be an issue for most software.

Re: 9999999999999999.0 – 9999999999999998.0

#88

Post by [deleted] »

svat wrote: post #71
twtw wrote: post #39

I don't understand all the crap that IEEE 754 gets. I appreciate that it may be surprising that 0.1 + 0.2 != 0.3 at first, or that many people are not educated about floating point, but I don't understand the people who "understand" floating point and continue to criticize it for the 0.1 + 0.2 "problem." The fact is that IEEE 754 is an exceptionally good way to approximate the reals in computers with a minimum number…

> considering the problem is to fit the reals into 64/32/16 bits and have fast math Floating-point numbers (and IEEE-754 in particular) are a good solution to this problem, but is it the right problem? I think the "minimum of surprises" part isn't true. Many programmers develop incorrect mental models when starting to program, and get no feedback to correct them until much later (when they get surprised). It is true…

[deleted]

Re: 9999999999999999.0 – 9999999999999998.0

#89

Post by ummonk »

seanalltogether wrote: post #13

Are there any mainstream languages that consider a decimal number to be a primitive type? I feel like floating point numbers are far less meaningful in every day programs. Even 2d graphics would be easier with decimal numbers. Unless you're using numbers that scale from very small to very large, like 3d games or scientific calculations, you don't actually want to use floating point.

Do you mean some fixed point decimal number? Cause the normal way to do decimal numbers would still be floating point.
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