More on using i and j as variables in Matlab: speed

Question

The Matlab documentation says that

For speed and improved robustness, you can replace complex i and j by 1i. For example, instead of using

a = i;

use

a = 1i;

The robustness part is clear, as there might be variables called i or j. However, as for speed, I have made a simple test in Matlab 2010b and I obtain results which seem to contradict the claim:

>>clear all

>> a=0; tic, for n=1:1e8, a=i; end, toc
Elapsed time is 3.056741 seconds.

>> a=0; tic, for n=1:1e8, a=1i; end, toc
Elapsed time is 3.205472 seconds.

Any ideas? Could it be a version-related issue?

After comments by @TryHard and @horchler, I have tried assigning other values to the variable a, with these results:

Increasing order of elapsed time:

"i" < "1i" < "1*i" (trend "A")

"2i" < "2*1i" < "2*i" (trend "B")

"1+1i" < "1+i" < "1+1*i" (trend "A")

"2+2i" < "2+2*1i" < "2+2*i" (trend "B")

Answer 1

I think you are looking at a pathological example. Try something more complex (results shown for R2012b on OSX):

(repeated addition)

>> clear all
>> a=0; tic, for n=1:1e8, a = a + i; end, toc
Elapsed time is 2.217482 seconds. % <-- slower
>> clear all
>> a=0; tic, for n=1:1e8, a = a + 1i; end, toc
Elapsed time is 1.962985 seconds. % <-- faster

(repeated multiplication)

>> clear all
>> a=0; tic, for n=1:1e8, a = a * i; end, toc
Elapsed time is 2.239134 seconds. % <-- slower
>> clear all
>> a=0; tic, for n=1:1e8, a = a * 1i; end, toc
Elapsed time is 1.998718 seconds. % <-- faster