How to convert /map uint16 to int16 maintaining the dynamic range so that [0] and [2^16-1] in uint16 beomes [-2^15] and [2^15-1] without going through double

I would like to convert my uint16 values to int16 values amd maintain the dynamic range. All my attempts with typecast and cast still map value 0 (uint16) to 0 (int16). I would like it to map 0 (uint16) directly to -2^15 (int16). I need to convert a rather large dataset so I would like to circumvent doing to double or single if I can.

The data comes from fread and if I can do the mapping there directly then that would be even better. This is what I use now to read the data:

Data        = fread(fid,[m n],'uint16=>uint16')';

Ive tried asking for 'uint16=>int16', but that also cuts the data

[Micke Malmström]

% Example uint16 data
uint16Data = uint16([0, 2^16-1]);

% Map uint16 to int16 
int16Data = int16(uint16Data - 2^15); % here is where the problem lies and I cant figure out how to circumvent going through double or single...

% Display the results
disp(['Original uint16 data: ', num2str(uint16Data)]);

Original uint16 data: 0  65535

disp(['Mapped int16 data: ', num2str(int16Data)]); % my desired result here is Mapped int16 data: -32768  32767

Mapped int16 data: 0  32767

Answer 1

[Stephen23]

inp = uint16([-Inf,pi,Inf])

inp = 1×3

0 3 65535

Method one: use INT32 for the intermediate values:

off = int32(intmin('int16'));
out = int16(int32(inp)+off)

out = 1×3

-32768 -32765 32767

Method two: convert from two's complement to offset binary, which you can then simply TYPECAST into INT16:

out = typecast(bitset(inp,16,1-bitget(inp,16)),'int16')

out = 1×3

-32768 -32765 32767

https://www.mathworks.com/help/matlab/matlab_prog/bit-wise-operations.html

https://en.wikipedia.org/wiki/Two%27s_complement

https://en.wikipedia.org/wiki/Offset_binary

Answer 2

[Bruno Luong]

If you have C compiler this simple mex file will do the job:

/**************************************************************************
 * Matlab Mex file castint16.C
 Convert uint16 to int16 by adding 2^15 in 2-complement binary coding
 Example:
    a = uint16([0 2^16-1])
    b = castint16(a)

    will return

  1×2 int16 row vector

   -32768    32767

Compile:
   mex -R2018a castint16.c
 *************************************************************************/

#include "mex.h"
#include "matrix.h"

#define A prhs[0]
#define B plhs[0]
        
void mexFunction(int nlhs, mxArray *plhs[],
                 int nrhs, const mxArray *prhs[]) {
    
    size_t i, n;
    mxUint16 *a, *b;

    if (nrhs!=1)
        mexErrMsgTxt("castint16 missing input argument");    
    
    /* n = numel(A) */
    n = mxGetNumberOfElements(A);
    if (mxGetClassID(A) == mxUINT16_CLASS) {
        a = mxGetUint16s (A);
        B = mxCreateNumericMatrix(mxGetM(A), mxGetN(A), mxINT16_CLASS, mxREAL);
        b = mxGetInt16s(B);
        for (i = 0; i < n; i++)
            b[i] = a[i] + 0x8000;
    } else
        mexErrMsgTxt("castint16 suports only UINT16 input");
}