# Re: [Scilab-users] On computational speed

```
Heinz,```
```
Thank you for your timings, which confirm that, even if about an order
of magnitude faster (I use a rather old i7 laptop), the simple squaring
operation takes much longer than it should.

Regards,

Federico Miyara

On 30/11/2023 02:14, Heinz Nabielek wrote:
```
```Thanks. In the 1960s FORTRAN, we would always write A2=A*A rather than A2=A**2.

Below the Federico examples on my M1 Apple silicon iMac:
Heinz

--> tic, u = rand(1,1e7); toc
ans  =   0.111413

--> tic, v = sqrt(u); toc
ans  =   0.0384130

-->  tic, v = u.*u; toc
ans  =   0.023148

--> tic, v = u.*%pi; toc
ans  =   0.017872

--> tic, v = u.^2; toc
ans  =   0.156129

--> tic, v = u.^%pi; toc
ans  =   0.1537830

--> tic, v = log(u); toc
ans  =   0.093586

--> tic, v = exp(u); toc
ans  =   0.0821170

--> tic, v = exp(2*log(u)); toc
ans  =   0.139802

```
```Am 30.11.2023 um 00:46 schrieb Federico Miyara <fmiy...@fceia.unr.edu.ar>:

Dear All,

I was trying to make some simple experiments regarding computational speed of
several functions and operations and some results puzzled me. To perform the
tests I used massive data to minimize the effect of idle time due to priority
handling by the operating system or whatever.

--> tic, u = rand(1,1e7); toc
ans  =
0.4948326

This creates ten million random numbers in half a second. Very decent
performance. Then

--> tic, v = sqrt(u); toc
ans  =
0.282802

The algorithm for square root seems quite fast. Multiplication

--> tic, v = u.*u; toc
ans  =
0.1218028

--> tic, v = u.*%pi; toc
ans  =
0.119245

is really fast. But when it comes to power or exponentiation:

--> tic, v = u.^2; toc
ans  =
1.9633435

--> tic, v = u.^%pi; toc
ans  =
1.958321

it is quite slow. Logarithm is much faster:

--> tic, v = log(u); toc
ans  =
0.5166959

Even the exponential function with base e is much faster:

--> tic, v = exp(u); toc
ans  =
0.5451482

I wonder why special cases such as small integer powers are not dealt with by
simple multiplication. Particularly the square is very frequently used on large
vectors representing discrete signals (for instance to get energy measures) and
no warning is issued in the documentation.

I also notice that computing the square using this formula (a cannon to kill a
mosquito!)

--> tic, v = exp(2*log(u)); toc
ans  =
1.2789763

is faster than using the power operator ^.

This seems to be an inconsistent approach, since many special functions are
painstakingly tailored to be very efficient, yet one of the simplest of all
operations, raising to power 2, is sluggishly slow...

Regards,

Federico Miyara

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