'Re: [Scilab-users] On computational speed'

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List:       scilab-users
Subject:    Re: [Scilab-users] On computational speed
From:       Federico Miyara <fmiyara () fceia ! unr ! edu ! ar>
Date:       2023-11-30 15:51:48
Message-ID: 12d98323-c8ee-d6e3-1ec6-a5df23a5530d () fceia ! unr ! edu ! ar
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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 <fmiyara@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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