MATLAB: Write a function called integerize that takes as its input a matrix A of integers of type double, and returns the name of the “smallest” signed integer class to which A can be converted without loss of information. If no such class exists, the text

homeworkintegerize

%for every input the function gives int8 as an output
function x=integerize(A)
[m,n]=size(A);
for ii=1:m
    for jj=1:n
 if isa(A(ii,jj),'double')
     b=min(A); 
   if -128 <= b <= ((2^7)-1)
           x='int8';
       elseif (-2^15)<= b <= ((2^15)-1)
           x='int16';
       elseif (-2^31)<=b<= ((-2^31)-1)
           x='int32';
       elseif (-2^63)<=b<=((2^63)-1)
           x='int64';
       else
           x='NONE';
   end
   else
       x='NONE';
   end
      end
  end

Best Answer

You can't write multiple if conditions this way in MATLAB:
   if -128 <= b <= ((2^7)-1)
You have to break it up into individual conditions. E.g.,
   if -128 <= b & b <= ((2^7)-1)
Why are you doing the following:
     b=min(A);
Hint: The following will turn A into a column vector of all the elements:
    b = A(:);
Instead of using for loops, you can then write logic to test all of the elements of b at once to get your result.
Caution: You are going to have a problem with this part of your test for int64:
       elseif (-2^63)<=b & b<=((2^63)-1)
The reason is that an int64 actually has more precision than a double, so you can get into trouble comparing numbers near the limits. E.g.,
>> intmax('int64')
ans =
  int64
   9223372036854775807
>> b = 2^63;
>> num2strexact(b)
ans =
    '9.223372036854775808e18'
Just looking at these numbers you can see that b is too large to fit in an int64 class variable. But look what happens with the test that you have:
>> b <= ((2^63)-1)
ans =
  logical
   1
It returned true! Obviously this is an incorrect result for what you are trying to test. What is the problem? It is the fact that a double precision variable does not have enough precision to do the (2^63)-1 calculation exactly. E.g.,
>> eps(2^63)
ans =
        2048
The spacing between numbers near 2^63 in IEEE double is 2048, much larger than the 1 you are trying to do arithmetic with. E.g., look at these results:
>> num2strexact((2^63))
ans =
    '9.223372036854775808e18'
>> num2strexact((2^63)-1)
ans =
    '9.223372036854775808e18'
>> num2strexact((2^63)-10)
ans =
    '9.223372036854775808e18'
>> num2strexact((2^63)-100)
ans =
    '9.223372036854775808e18'
You get the same number in each case. Subtracting 1, 10, or 100 had no effect on the answer because they are too far below eps(2^63). So, you will need to rewrite this test. Hint: What would happen if you tried to do this test in int64 arithmetic instead of double arithmetic? Try it out ...
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