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From: "Nasser M. Abbasi" <nma@12000.org>
Newsgroups: comp.lang.ada
Subject: Re: small example, using complex variables in Ada
Date: Thu, 10 Jun 2010 02:34:27 -0700
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Date: 2010-06-10T02:34:27-07:00
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On 6/10/2010 12:23 AM, Stephen Leake wrote:

>
>> -- gnatmake dft.adb
>> --
>> -- ./dft.exe
>> -- ( 6.00000E+00, 0.00000E+00)
>> -- (-1.50000E+00, 8.66026E-01)
>> -- (-1.50000E+00,-8.66025E-01)
>> -- $
>>
>> ======= FORTRAN code ===========
>> ! dtf.f90, compiled with GCC 4.3.4
>> ! under CYGWIN 1.7.5
>> ! gfortran -Wall dft.f90
>> ! ./a.exe
>> ! (  6.0000000    ,  0.0000000    )
>> ! ( -1.4999999    , 0.86602557    )
>> ! ( -1.5000005    ,-0.86602497    )
>> !
>

> It would be good to explain the small differences here; something about
> how the floating point options are set, I suspect.
>

Yes, I noticed that too. Need to look more into. It could be just a 
formating thing. I just used Print*, in Fortran becuase at the time was 
too lazy to lookin up the other formating functions in Fortran. In Ada, 
I used the predefined Put on Complex of float types.

> It would be good to state the theoretically correct answer; I hope it's
> 1.5, not 1.499... :).
>

Well, the extact answer is -1.5 for the real part of those terms.

Can be seen also by using a CAS such as Mathematica which allows one to 
set an arbitrary precision. Here is one with 50 precision:

SetPrecision[Fourier[{1., 2., 3.}, FourierParameters ->{1, -1}],50]


{6.0000000000000000000000000000000000000000000000000+0.*10^-50 I,

-1.5000000000000000000000000000000000000000000000000 +
0.8660254037844385965340919530941476978114224039018 I,

-1.5000000000000000000000000000000000000000000000000
-0.8660254037844385965340919530941476978114224039018 I}

So, it is 1.5 not 1.499999... (can also be seen by expanding the sum 
itself. and using Euler relation to convert exp() to trig functions and 
looking at the resulting cosine and sin terms, one can see this term 
comes out to be an exact -3/2).

well look into why Fortan prints -1.499999 and correct my code if it is 
because I am not doing something right.


--Nasser