Re^4: Anyone with XS experience willing to create a high performance data type for Perl?

[jdporter]

10 and 99 (1E1 and 9.9E1) are the same order of magnitude, but 99 and 100 (9.9E1 and 1E2) are different orders of magnitude

No. That's the problem with taking such a definition literally. The "order of magnitude" of a number is its base-10 logarithm, usually rounded to the nearest whole number.

Try this: round( log₁₀(X) - log₁₀(Y) )

In terms of "order of magnitude", 99 and 100 are the same number.

[talexb]

:) OK, then, I guess I need to move my scale around. I could have said that 31 and 32 are different orders of magnitude (log of 31 is 1.49, log of 32 is 1.51).

Using this (corrected) scale, 33 and 2 are actually two orders of magnitude apart (log of 33 is 1.51, log of 2 is of course .30). Two orders does count as 'several' orders, but a 16x difference, while large, is not gigantic. A recent improvement at work sped a database operation up from 5-6 minutes to about 15-20 seconds -- about a 20x improvement. I was happy with that.

[jdporter]

I could have said that 31 and 32 are different orders of magnitude (log of 31 is 1.49, log of 32 is 1.51)

That would mean you still weren't getting it. You have to round after doing the difference, not before.

You could also think of it like this, which is mathematically equivalent: round( log₁₀( X / Y ) ).

[talexb]

OK -- thank you, I get it now. I was looking at absolute orders of magnitude, when I should have been looking at relative orders of magnitude.

[LanX]

FWIW the WP article only talks about truncating (int) not rounding the logarithm.

But they also claim that Saturn with factor 95 has 2 magnitudes more mass than earth. 🤷🏻‍♂️