What's special about the number $1.000000015047466$E+$30$?

Question

I'm a programmer by trade by I've run into a weirdly special number and need some help deciphering its significance.

I was writing some machine learning code that compiles into GPU kernel code and the compiler output the number 1.000000015047466E+30 as part of its generated code. It doesn't seem to be a common number of interest from the field of CS (e.g. it's not a power of $2$).

Google searching for this constant just yields a handful of results that seem to suggest it may be a physical constant of some kind:

This MATLAB forum link suggests it may be a default value for some physical phenomena.
This Github repo on whole cell electrophysiology seems to use it as a max limit of some kind.
This Opensea NFT link shows that the number is somehow used as a parameter for some kind of fractal art?

I'm absolutely baffled I have absolutely no clue why this number is appearing in my ML code and why it's also being used in hard science research and fractal art. It lends me to believe this number has some special properties, but I'm not sure what. Any leads would be greatly appreciated.

Well, it's neither prime nor irrational anyway. Floating point can produce some odd results, this might just be one of them. — badjohn, Mar 31 '22 at 21:38
Google "What every programmer needs to know about floating-point numbers". — Andreas Rejbrand, Apr 01 '22 at 08:09

score 19 · Accepted Answer · answered Mar 31 '22 at 21:39

19

Could be the single precision floating point number closest to 10^30, so the number you’d get in say C if you write float x = 1e30. You’d need a floating point number with a 70 bit mantissa to represent 10^30 exactly.

answered Mar 31 '22 at 21:39

gnasher729

10,611
20
38

2

I've tried it (try e.g. printf("%.6f", (float)1e30);): it turns out to be $1.000000015047466\color{red}{21987668885504}e+30$. The question now is why $\pm10^{30}$ is used, as an extremum or otherwise. – J.G. Mar 31 '22 at 21:43
3

To get the same precision as OP is seeing you can write also printf("%.15e\n", 1e30f);. The value $10^{30}$ is not mysterious at all, you can try the same with $10^{20}$ and you will find out that value 1.000000020040877e+20 is used on many places as welll, probably most other powers of $10$ will be used somewhere... – Sil Mar 31 '22 at 21:50
2

@Sil Thanks for the improved C. I don't use it much. – J.G. Mar 31 '22 at 21:51
1

You can see it in the IEEE-754 simulator here https://www.h-schmidt.net/FloatConverter/IEEE754.html . Paste your number into "decimal representation". You'll see the binary rep of the mantissa ends ....10. If you flip those last two to ...01 you get 9.9999993949e+29 – Dan Apr 01 '22 at 08:22

What's special about the number $1.000000015047466$E+$30$?

1 Answers1