Scaling 32 bit data to 16 bits

[Ponnu Prasad]

Hi, I am trying to model a DSP system in C++ using fixed point arithmetic. At one point I've come across the need to scale down a 32 bit data to 16 bits. Does anybody have an algorithm/C++ code to do this.

Any info in this regard will be of great help. Thanks in anticpation.

[johny10151981]

can you explain what do you mean by scale down?
if you want to store a 32 bit data in two 16 data field it is very much possible....

but if you want to loose data more than 16 bit it also possible.

but if you think to fit 32 bit data in 16 bit field. So far this is impossible(as far i know)

[Ponnu Prasad]

Well yes, what I am asking is if we can fit 32 bit data into a 16 bit field. The actual requirement is to compare two values; one 16 bit (say 'a') and the other 32 bit (say 'b').

It doesn't make sense to assign 'b' (32 bit) directly to a 16 bit value as the fixed point library I am using will saturate the value to 2^16 and will still be the greater of 'a' and 'b'.

So is there any way/algorithm to represent a 32 bit data in an equivalent 16 bit form without losing information.

I know this sounds crazy, but there could be some way out.

[donbock]

You refer to a fixed point library. What precisely are the types (and encodings) of the two variables?

"So is there any way/algorithm to represent a 32 bit data in an equivalent 16 bit form without losing information."
If such technique existed it could be used to reduce 32 bit data into 16 bits, then used again to reduce the 16 bit data into 8 bits, and used over and over again until only one bit is left.
There are certain degenerate cases where you can accomplish a semblance of this -- consider a 32-bit integer whose high-order 16 bits are all zero. In this case you have 16-bit data in a 32-bit variable, so there is no problem copying the data into a 16-bit variable.

[Ponnu Prasad]

Thanks donbock;


Yes, the library uses variables of 'fxpt' (fixed point) type whose structures and functions are defined in a .h and .cpp file respectively. The fxpt data are basically floating point numbers converted to fixed point representation using the normal fp to fxpt conversion technique. (i.e (floating pt num)*(2^N); where N is the desired number of bits representing the fractional part of floating pt num in its fxpt representation).

The degenerate case as mentioned by you is not an option in my case as the data seldom has 16 '0' higher order bits.

[hype261]

Maybe I am missing something, but if your requirement is to compare at 32 bit field and a 16 bit field why can't you convert the 16 bit field into a 32 bit? That way you don't have to worry about any loss of data.

[donbock]

You haven't provided a precise description of the fixed point types so I can't give you a precise answer.

In general, more bits means more significant digits. Generic oversimplification follows... You convert from narrower to wider type by appending zeros to the right of the decimal point; you convert from wider to narrower type by truncating some of the right-most decimal digits.

These fixed-point types are not part of the C Standard so you can't merely cast from one to the other. Presumably your library provides interconversion functions or macros. (Unless this is one of the ways in which C++ differs from C.)

[Rabbit]

In essence, what you are asking is, can I represent the number 327 using only 2 digits? The answer is no. But if you are asking, can I represent the number 027 using only 2 digits? Then yes.