What is the "net slope"

In matlab doc, there is only "handling net slope computation".

I want to know meaning of "net slope", not method of dealing with net slope like above I said.

So, let me know the "net slope" itself.

[John D'Errico]

Where? In which MATLAB doc, since there are thousands of pages of MATLAB docs?

I can start looking now, but I expect it to be weeks before I have read EVERY page of EVERY MATLAB doc.

[MIN HOON]

@John D'Errico

When I type "net slope" at Matlab doc search blank to find out information about net slope, there is no knoweledge about net slope itself. There are just usages of it.

Answer 1

[Andy Bartlett]

Net slope is used in fixed-point operations to achieve agreement of scaling. The slopes of all the variables involved in an operation are combined into one multiplicative term called the net slope.

For example, multiply two variables with 10 bits to the right of the binary point and assign the product to a type with 12 bits to the right of the binary point.

The real world operation is

Vout = V1 * V2

The fixed-point scalings for these variables showing the slopes and stored integers are

Vout = (2^-12) * Qout

V1 = (2^-10) * Q1

V1 = (2^-10) * Q2

Via substitution we get

(2^-12) * Qout = (2^-10) * Q1 * (2^-10) * Q2

solving for the output stored integer and conslidating terms, we will see the Net Slope

Qout = (2^(-10-10+12)) * Q1 * Q2

NetSlope = 2^(-10-10+12) = 2^-8

In this case, the NetSlope can be perfectly represented in fixed-point. In fact, a simple shift right of 8 bits will efficiently achieve agreement of all the scalings.

The NetSlope gets more challenging when it is not an exact power of two.

Suppose the two inputs and the output had slopes of 6, 4, and 9 respectively. In that case, we have

NetSlope = (6*4)/9 = 8/3

To avoid costly division, this will get approximated with a fixed-point variable such as

format long g
fi(8/3,0,16)

ans = 
          2.66668701171875

          DataTypeMode: Fixed-point: binary point scaling
            Signedness: Unsigned
            WordLength: 16
        FractionLength: 14

The documentation of Rules of Arithmetic Operations gives more examples of computing net slopes

[MIN HOON]

Thank you so much!

Um... I have a little difficulty in comprehancing meaning of "net"

May I ask you to explain it?

[Andy Bartlett]

One meaning of "net" is "final."

You may be familiar with a business term like "net profit" which is the "final" profit after all the calculations with revenue and expenses are complete.

"net slope" is similar in spirit. Loosely speaking all the individual slope terms have been mathematically combined into one "final" value.

In the multiplication examples above, the three individual slope terms were combined into one "net slope."

[MIN HOON]

@Andy Bartlett

Oh.. my ... god!!!

Thank you so~~~ much!!!! Andy!

Certainly, expert is different from ordinary people...

I'm not a guy in english culture, so it's hard to understand hidden meaning of any word.

They, just like you, always give me clearly and perfectly resolve my problem!

Thank you~!

[MIN HOON]

@Andy Bartlett

Hello, Andy

I have one question in your example.

Why do we consider Qout instead of Vout?

Isn't Vout What we want to get finally?