Why do operations on single or int32 data types take longer time than on double data types on a 64 bit machine?

On a 64 bit machine the following code takes more time to run when "a" and "b" are int32 or single(32 bits) than when they are double(64 bits):

a = 4096;

b = 128;

start = cputime;

for i=1:1048576

c = a/b;

end

t = cputime-start;

disp(t);

a = single(4096);

b = single(128);

start = cputime;

for i=1:1048576

c = a/b;

end

t = cputime-start;

disp(t);

Answer 1

[MathWorks Support Team]

It is possible for the 32-bit operations to run at the same speed or a bit slower than the 64-bit operations while working on a 64-bit machine. This is because of the architecture of the processors. One explanation could be that the registers in 64-bit machines are 64-bit wide and are faster in processing 64 bit operations than 32-bit operations.

On the other hand, if the machine is 32-bit the operations on single data types are faster than those on double data types.