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floating-pointroundingquantization

Floating point quantization from double to 8bit

How can I round a double precision floating point to the value that can be stored in a 8bit floating point? I'm trying to do it mathematically but I have no idea how to do.

I have an x double number and I should find the nearest y that I can express with n*2^b with n and b integer and n in [-128,127]. But how can I find the best n and b?

Solution

  • I've solved with this algorithm:

    function y = DoubleTo8bit( x )
s=sign(x);
x=abs(x);

if x==0
    y=0;
    return; 
end
b=floor(log2(x)+1)-8+(s>0);
m=s*round(x/2^b);

y=m*2^b;
end