Float Exposed

#1

Post by nint22 » Mon, Nov 26, 2018, 8:44 PM UTC

Re: Float Exposed

#2

Post by tedyoung » Tue, Nov 27, 2018, 1:02 AM UTC

This is really nice! It'll come in very handy for my next training class -- students are always asking why they shouldn't use floating point for money and I always explain it, but having a tool where they can play around with it is much better.

Re: Float Exposed

#3

Post by StefanKarpinski » Tue, Nov 27, 2018, 4:06 AM UTC

Very cool tool! A couple of comments/suggestions:

It doesn't handle very large or small floating-point numbers. I'm not sure where the cutoff is, but it's around 1e40 and 1e-46. It would be cool to be able to explore the whole range of 64-bit floats, including subnormals like 5.0e-324.

It would be interesting to leave the input as-is and show two related decimal representations:

1. The precise decimal representation (what is printed now). 2. The shortest decimal representation as determined by algorithms like Grisu [1] and Ryu [2].

It would also be cool to allow jumping to the next/previous representable floating-point number. Showing eps(x) would also be handy—i.e. the difference between the current value and the next closest representable floating-point value.

[1] https://www.cs.tufts.edu/~nr/cs257/archive/florian-loitsch/p...

[2] https://dl.acm.org/citation.cfm?id=3192369

Re: Float Exposed

#4

Post by simonbyrne » Tue, Nov 27, 2018, 4:28 AM UTC

StefanKarpinski wrote: post #3

Very cool tool! A couple of comments/suggestions: It doesn't handle very large or small floating-point numbers. I'm not sure where the cutoff is, but it's around 1e40 and 1e-46. It would be cool to be able to explore the whole range of 64-bit floats, including subnormals like 5.0e-324. It would be interesting to leave the input as-is and show two related decimal representations: 1. The precise decimal representation…

They're 32-bit IEEE floats (i.e. a typical "C float"), so the subnormal range is below 2e-38. Also, it isn't printing exact values, since for any non-integer value, the last digit should always be 5, though I agree it would be nice to have.

Re: Float Exposed

#5

Post by johnhenry » Tue, Nov 27, 2018, 6:41 AM UTC

This is really cool!

I believe this uses IEEE https://en.wikipedia.org/wiki/IEEE_754? An additional cool feature would be the ability to toggle between this, and other standards such as DEC64 and UNUM.

Re: Float Exposed

#6

Post by StefanKarpinski » Tue, Nov 27, 2018, 7:21 AM UTC

simonbyrne wrote: post #4

StefanKarpinski wrote: post #3

Very cool tool! A couple of comments/suggestions: It doesn't handle very large or small floating-point numbers. I'm not sure where the cutoff is, but it's around 1e40 and 1e-46. It would be cool to be able to explore the whole range of 64-bit floats, including subnormals like 5.0e-324. It would be interesting to leave the input as-is and show two related decimal representations: 1. The precise decimal representation…

They're 32-bit IEEE floats (i.e. a typical "C float"), so the subnormal range is below 2e-38. Also, it isn't printing exact values, since for any non-integer value, the last digit should always be 5, though I agree it would be nice to have.

Hah, I should have realized that there weren't enough bits for Float64. I also realized that the little `+` and `-` signs on the integer representations have the effect of next/previous float values. Showing eps(x) would still be handy.

Re: Float Exposed

#7

Post by tfeldmann » Tue, Nov 27, 2018, 11:01 AM UTC

Very cool to quickly estimate the errors in certain number regions.