# 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 '

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Wasi von Deutschland on 26 May 2017
Edited: Stephen23 on 25 Aug 2018
function integerize(A)
int8(A<2^7-1);
int16(A<2^15-1);
int32(A< 2^31-1);
int64(A<2^63-1);
end
##### 3 CommentsShow 1 older commentHide 1 older comment
Wasi von Deutschland on 26 May 2017
if A is zero then what would be the class name?
Stephen23 on 26 May 2017
For a change, zero is not really a special case. It could have the same class as one.

Stephen23 on 26 May 2017
Edited: Stephen23 on 29 May 2018
EDIT: see Guillermo Varela Carbajal's answer below for a really neat solution.
Try something like this:
function typ = integerize(A)
if A >= intmin('int8') & A <= intmax('int8')
typ = 'int8';
elseif A >= intmin('int16') & A <= intmax('int16')
typ = 'int16';
elseif A >= intmin('int32') & A <= intmax('int32')
typ = 'int32';
elseif A >= intmin('int64') & A <= intmax('int64')
typ = 'int64';
else
typ = 'NONE';
end
end
and tested:
>> integerize([128,127;-127,0])
ans = int16
Just for the sake of discussion, here is a function where the list of accepted classes are specified as an input argument (as long as the order from smallest to largest is kept):
function typ = integerize(A,C)
for k = 1:numel(C)
typ = C{k};
if A >= intmin(typ) & A <= intmax(typ)
return
end
end
typ = 'NONE';
end
and tested:
>> integerize(A,{'int8','int16','int32','int64'})
ans = int16
>> integerize(A,{'int8','int32','int64'})
ans = int32
>> integerize(A,{'int8','int64'})
ans = int64
>> integerize(A,{'int8'})
ans = NONE

function out = integerize (A)
if A==int8(A)
out='int8';
elseif A==int16(A)
out='int16';
elseif A==int32(A)
out='int32';
elseif A==int64(A)
out='int64';
else
out='NONE';
end
Stephen23 on 7 Jun 2017
Edited: Stephen23 on 29 May 2018
+1 nice and tidy. I really like that!
Yes, it works.

Jan on 26 May 2017
Edited: Jan on 26 May 2017
Get the largest elemt at first:
maxA = max(A(:));
Then use the logarithm to the base of 2 to determine the number of bits, which are required.
Finally some IF command let you create the output string 'int8', 'int16', 'int32' or 'int64'.
Walter Roberson on 26 May 2017
-128 fits in int8 but +128 is int16
[-1 0 23 -129 122] needs int16 because -129 does not fit in int8
Jan on 26 May 2017
Edited: Jan on 26 May 2017
@Wasi: Do you see the problem? You check for < 127, but -129 is smaller than 127 also. Add this:
minA = min(A(:));
if maxA <= 127 && minA >= -128
Another hint to simplify the code:
if maxA<=2^7-1;
x='int8';
elseif maxA <= 2^15-1 % This is not needed: && maxA>2^7-1
The case maxA <= 127 has been excluded before, then you do not have to check for > 127 anymore.

Jorge Briceño on 9 Feb 2018
Hi,
Another answer would be like this:
function [ smallA ] = integerize( A )
minimum = min(A(:));
maximum = max(A(:));
if minimum >= -2^7 && maximum<=2^7-1
smallA='int8';
elseif minimum >=-2^15 && maximum<=2^15-1
smallA='int16';
elseif minimum >=-2^31 && maximum<=2^31-1
smallA='int32';
elseif minimum >=-2^63 && maximum<=2^63-1
smallA='int64';
else
smallA='NONE';
end

Erfan Pakdamanian on 28 May 2018
Edited: Erfan Pakdamanian on 28 May 2018
My algorithm may seem to have a little bit more lines than Stephen but it does pretty much the same thing with basic functions
function s=integerize(A)
[ii,jj]=size(A);
y1=0;y2=0;y3=0; y4=0;
for ii=1:ii
for jj=1:jj
if A(ii,jj)>= -128 && A(ii,jj)<= 127
end y1=y1+1;
elseif (A(ii,jj) <= -129 && A(ii,jj)>127) || (A(ii,jj)>= -32768 && A(ii,jj)<=32767)
y2=y2+1;
elseif (A(ii,jj) <-3276 && A(ii,jj)>32767) || (A(ii,jj)>= -(2)^31 && A(ii,jj)< 2^31)
y3=y3+1;
elseif (A(ii,jj) < -(2)^31 && A(ii,jj)>= 2^31) || (A(ii,jj)>= -(2)^63 && A(ii,jj)<= 2^63)
y4=y4+1;
else
s='NONE';
return;
end
end
end
if y4>0
s='int64';
elseif y4==0 && y3>0
s='int32';
elseif y4==0 && y3==0 && y2>0
s='int16';
else
s='int8';
end
end
Walter Roberson on 28 May 2018
Edited: Walter Roberson on 28 May 2018
That "end" is out of place on the line after the first "if" statement.
The constant -3276 in the second "elseif" appears to be a typing mistake.

Gurleen Singh on 25 Aug 2018
This is a bit simpler(but longer) code.
function c = integerize(A)
m = max(A(:));
n = min(A(:));
if n>=-128 && m<= 127
m = int8(m);
n = int8(n);
c = class(m);
c = class(n);
elseif n>=-2^15 && m<=2^15-1
m = int16(m);
n = int16(n);
c = class(m);
c = class(n);
elseif n>=-2^31 && m<=2^31-1
m = int32(m);
n = int32(n);
c = class(m);
c = class(n);
elseif n>=-2^63 && m<=2^63-1
m = int64(m);
n = int64(n);
c = class(m);
c = class(n);
else
c = 'NONE';
end
Walter Roberson on 25 Aug 2018
Why are you writing to c twice for each case?
Why are you bothering to convert m and n to an explicit data type and then take class() of that data? Why not just assign 'int8' or whatever directly?
Stephen23 on 25 Aug 2018
Edited: Stephen23 on 25 Aug 2018
Why call class twice within each if / elseif block, and yet throw away the answer for the first call?
If you already know the class (which you do, because you have explicitly written uint8, int16, etc.), then why call those four lines within each block? E.g. rather than this:
m = int8(m); % <- look, you already use INT8!
n = int8(n);
c = class(m);
c = class(n);
you just need
c = 'int8'; % so why not just write 'INT8' ?