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 Post subject: Helping with VMK's
PostPosted: Sun Feb 11, 2007 9:15 pm 
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Joined: Sun Feb 11, 2007 8:59 am
Posts: 1105
Location: Ontario Canada
The ability to map one set of numbers to another set of numbers is very useful in many applications. This VMK shows you how to set up a linear relationship between the input and the output values.

 Post subject: Don't be mad about MADD
PostPosted: Mon Feb 09, 2009 12:41 pm 

Joined: Wed Aug 06, 2008 7:53 pm
Posts: 182
Location: Russia
It would be interesting to note that in some cases general formulae mentioned in this VMK, namely (in short form)
Y = M * X + B                   (*)

might be more efficient even when it is used for two particular cases (when output is in the range [0, 1] and [1, 0]) than the formula for those cases, i.e.:
Y = (X - Ax) / (Bx - Ax)        (**)

The point is that modern hardware can have a dedicated instruction MADD, stands for Multiply then ADD. It has three arguments: MADD(a, b, c) and equivalent to a * b + c.
The multiplication-add (MADD) is merely a multiplication followed by a summation. Some processors, such as AltiVec, do not support a stand-alone multiplication, some support only the multiplication-add, and some support both. But it is much more efficient to call a MADD-type instruction when appropriate, instead of separately.

So, to use MADD for (*) one can write
Y = MADD(X, M, B).

But to extract MADDs' arguments from the formula (**), although that formula seems more compact then full version of (*), one has to convert it back to (**) anyway, i.e.:
Y = (X - Ax) / (Bx - Ax)  =>

// preliminaries
M = 1 / ( Bx - Ax )
B = - Ax * M

// maybe in cycle
Y = MADD(X, M, B).

Quite importantly, MADD is available on most modern GPU and accessible via shader's assembly languages (for shader programming mostly). For instance, OpenGL HLSL syntax for MADD is:
mad dst, src0, src1, src2

OK, this is just a side thought. I like this VMK.

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