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From: Niklas Holsti <niklas.holsti@tidorum.invalid>
Newsgroups: comp.lang.ada
Subject: Re: small example, using complex variables in Ada
Date: Wed, 09 Jun 2010 15:43:56 +0300
Organization: Tidorum Ltd
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Date: 2010-06-09T15:43:56+03:00
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Nasser M. Abbasi wrote [much snipped]:
> I wrote a simple program, to find the DFT of 
> an array of 3 elements {1,2,3} (DFT=discrete Fourier transform).
> I also wrote a FORTRAN equivalent of the small Ada function.  Here is 
> below the Ada code, and the FORTRAN code.
> 
> ====== START ADA ============
>             X(k) := X(k) + data(m) * exp(- J*(2.0*Pi)/float(N) * 
> float(m*k) );

> ======= FORTRAN code ===========
>       X(k) = X(k) + data(m) * EXP(-1.0*J*2.0*Pi/N *(m-1)*(k-1) )

There is an obscure difference in these computations, which can cause 
trouble when the data vector is much longer than the N = 3 in the 
example. The Ada version may then fail because the product m*k may 
overflow the Integer range. It would be safer to write float(m)*float(k).

In the Fortran version, as far as I understand the Fortran rules, the 
compiler may choose to multiply the integer subexpressions (m-1) and 
(k-1) as integers, and then convert the product to REAL (as is done in 
Nasser's Ada version), or the compiler may choose to convert separately 
(m-1) to REAL and (k-1) to REAL and use REAL multiplication, as I 
suggest above for the Ada code. IIUC it would be safer in Fortran, too, 
to prevent integer overflow by explicit conversions of (m-1) and (k-1) 
to REAL before multiplication.

-- 
Niklas Holsti
Tidorum Ltd
niklas holsti tidorum fi
       .      @       .