Colour Decision List

Phil Rhodes · April 1, 2009

Next time someone's speaking to a member of the ASC committee that defined the CDL algorithms, could you please say:

"fractional exponentiation of negative reals"

...and report back to the forum what the reaction is?

Ahem.

-P

Satsuki Murashige · April 1, 2009

Next time someone's speaking to a member of the ASC committee that defined the CDL algorithms, could you please say:

"fractional exponentiation of negative reals"

What exactly does that mean Phil? I don't wanna get punched in the face or anything...

Phil Rhodes · April 1, 2009

What exactly does that mean Phil? I don't wanna get punched in the face or anything...

OK, it was four in the morning, I was wrestling with mathematics and - sob - things just got completely out of hand...

The algorithm for CDLs is as follows:

output = (input * slope + offset)^power

Since offset is unbounded (thus can be negative), the entire bracketed expression can be negative. Power can be any positive number, including (and in fact typically) non-integers.

So, what's the value of, say, minus 80 raised to the power 1.02?

P

John Sprung · April 1, 2009

So, what's the value of, say, minus 80 raised to the power 1.02?

It's undefined or "not a number", sometimes abbreviated as NAN. The only fractional power of a negative we ever use is the "imaginary" square root of negative one: i = (-1)^0.5, which is kinda useful, as it give us the complex number system as a way of dealing with stuff on a two dimensional plane.

The CDL lets you do undefined stuff, just as your car could be driven fast into a brick wall. In both cases, we just have to be smart enough not to..... ;-)

-- J.S.

Phil Rhodes · April 1, 2009

...yes, I know, it's a complex number. Until the Java Math.pow() is capable of returning a complex set, this will remain NaN <_<

Does the CDL spec mention this?

P

Will Earl · April 1, 2009

I managed to get the same answer out of google and python... :)

-80 to the power of 1.02 = -87.3276527

Edited April 1, 2009 by Will Earl

Phil Rhodes · April 1, 2009

I managed to get the same answer out of google and python... :)

-80 to the power of 1.02 = -87.3276527

I think the operative point is that any meaningful value of it is less than zero, so it really doesn't matter much as regards CDL

P

John Sprung · April 2, 2009

I managed to get the same answer out of google and python... :)

-80 to the power of 1.02 = -87.3276527

They both got it wrong. They've given you -(80^1.02), which is a real number. What Phil's asking about is (-80)^1.02, which is NaN. It isn't even an imaginary or complex number. Check out Wolfram's Mathematica 7 for this kind of thing:

http://www.wolfram.com/

-- J.S.

Phil Rhodes · April 2, 2009

Um. How is it not a complex number?

P

Will Earl · April 2, 2009

Oh well, I'm sure the ASC tech committee knows what they're doing.

>>>(-80)**1.02
ValueError: negative number cannot be raised to a fractional power

>>> -(80)**1.02
-87.327652683387186

John Sprung · April 3, 2009

Um. How is it not a complex number?

P

Complex numbers consist of a real number plus a real number times "i", the Imaginary square root of -1: x + iy

Taking a negative to any (edit to insert: non-integer) power other than 0.5, which is the same as square root, can't be expressed in terms of reals and i. It's just undefined.

Complex numbers can be visualized on a two dimensional plane, where you can do stuff like multiplying them:

(x + i y)(a + ib) = xa - yb + i(xb + ya)

IIRC, there's some stuff in physics where complex numbers are useful.

-- J.S.