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Kenneth_Smith
Joined: 18 May 2012 Posts: 176 Location: Glasgow, Scotland.

Posted: Fri Feb 17, 2017 11:53 am Post subject: Complex variables 


In ClearWin+ we have support for real numbers i.e. %rf
It would be really advantageous, and simplify coding if there was a similar control that supported complex variables i.e. A + jB (or A + iB to keep the mathematicians happy!), as it gets a bit messy working separately with real and imaginary parts  especially if they require updating when the code is running.
I've tied myself in knots a few times over this and never came up with a slick solution. Perhaps somebody can point the way for me?
Ken 

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LitusSaxonicum
Joined: 23 Aug 2005 Posts: 1797 Location: Yateley, Hants, UK

Posted: Fri Feb 17, 2017 1:31 pm Post subject: 


My understanding is that COMPLEX variables are stored as 2 consecutive REALs, so surely this is a case for EQUIVALENCE? Say EQUIVALENCE complex C to real D(2), and if you want A & B, equivalence A to D(1) and B to D(2)?
I would be happy to be corrected, because COMPLEX numbers are a closed book to me, but I'm always ready to learn.
Eddie 

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mecej4
Joined: 31 Oct 2006 Posts: 924

Posted: Fri Feb 17, 2017 2:15 pm Post subject: 


There are two issues here. The first one is support for I/O of complex variables in ClearWin+. I have nothing to say about that.
The other is the equivalencing of REAL and COMPLEX variables. Here, care is necessary, because such equivalencing can introduce a bug that can remain dormant for a long time. The Fortran standard states (I am taking the following quote from Fortran 2008, but I think that the rule applies to Fortran 95 as well):
Quote:  16.6.6 Events that cause variables to become undefined
7 1 Variables become undefined by the following events.
8 (1) With the exceptions noted immediately below, when a variable of a given type becomes defined, all
9 associated variables of different type become undefined.
10 (a) When a default real variable is partially associated with a default complex variable, the complex
11 variable does not become undefined when the real variable becomes defined and the real variable
12 does not become undefined when the complex variable becomes defined. 
According to this rule, the output of the following program is "undefined".
Code:  program tst
implicit none
real r(2)
double precision d(1)
equivalence (r,d)
!
r(1)=1.0; r(2)=2.0
print *,d
end program



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LitusSaxonicum
Joined: 23 Aug 2005 Posts: 1797 Location: Yateley, Hants, UK

Posted: Fri Feb 17, 2017 2:47 pm Post subject: 


Mecej4,
Isn't that what the first 4 lines of your extract say  which is very believable, and useful to point out.
But don't the last 3 lines say something else, i.e. that you CAN deal with a COMPLEX as 2 REALs without that particular issue?
Even I can see that if you equivalence a double precision to two single precisions and mess around with one of the latter, you will generate absolute nonsense, but if a complex genuinely is two consecutive reals then each can surely be manipulated independently.
As in:
Code:  program tst
real r(2)
complex d(1)
equivalence (r,d)
r(1)=1.0
r(2)=2.0
print *,d
r(1)=3.0
print *,d
r(2)=1.0
print *,d
end 
Standard conforming or not, it works.
Eddie 

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Kenneth_Smith
Joined: 18 May 2012 Posts: 176 Location: Glasgow, Scotland.

Posted: Fri Feb 17, 2017 4:52 pm Post subject: 


Thanks for the suggestions. I've noted the word of caution about equivalence but as the following shows it does appear to work. (Actually I've never used equivalence before in 30 years dabbling in Fortran).
Just need to fix the sign of j when the imaginary part is negative +j0.5 looks a bit clumsy (and is misleading).
Code:  module test
implicit none
complex(kind = 2) a_c, b_c, c_c
real(kind = 2) a(2), b(2), c(2)
equivalence (a_c, a)
equivalence (b_c, b)
equivalence (c_c, c)
contains
integer function init()
complex(kind = 2) j
j = cmplx(0.d0,1.d0)
a_c = 0.5d0  j*0.5d0
b_c = 0.5d0  j*0.5d0
c_c = a_c*b_c
init = 1
end function init
integer function c_m()
include<windows.ins>
c_c = a_c * b_c
c_m = 1
end function c_m
integer function window()
include <windows.ins>
integer i
i = winio@('%cn%ws&','Multiply two complex numbers')
i = winio@('%2nl&')
i = winio@('%cn%8.1ob&')
i = winio@('%bg&',rgb@(250,250,250))
i = winio@('%^rf&',a(1),c_m)
i = winio@('%cb&')
i = winio@('%ws&','+j')
i = winio@('%^rf&',a(2),c_m)
i = winio@('%cb&')
i = winio@('%ws&','x')
i = winio@('%cb&')
i = winio@('%^rf&',b(1),c_m)
i = winio@('%cb&')
i = winio@('%ws&','+j')
i = winio@('%^rf&',b(2),c_m)
i = winio@('%cb&')
i = winio@('%ws&','=')
i = winio@('%cb&')
i = winio@('%`rf&',c(1))
i = winio@('%cb&')
i = winio@('%ws&','+j')
i = winio@('%`rf&',c(2))
i = winio@('%cb')
window = 1
end function window
end module test
program main
use test
implicit none
integer i
i = init()
i = window()
end program main



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mecej4
Joined: 31 Oct 2006 Posts: 924

Posted: Fri Feb 17, 2017 5:40 pm Post subject: Re: 


LitusSaxonicum wrote: 
But don't the last 3 lines say something else, i.e. that you CAN deal with a COMPLEX as 2 REALs without that particular issue?

Only in the exceptional case where the association is partial. In my example, the association is complete.
This property (of the inactive member of an EQUIVALENCE pair becoming undefined as a side effect of the active member being given a new value) is something that was a big surprise for me when I first saw it a few years ago. The context was a program that worked correctly with the NAG compiler without checking options, but gave an "undefined variable" with C=undefined. I complained, and the NAG people straightened me out by quoting references to the Fortran standard. 

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LitusSaxonicum
Joined: 23 Aug 2005 Posts: 1797 Location: Yateley, Hants, UK

Posted: Fri Feb 17, 2017 5:57 pm Post subject: 


I have a feeling that the COMPLEX case ought to always work because a COMPLEX variable is axiomatically made up of two REALs. A DOUBLE PRECISION is never made up of two REALs. An Integer might be made up of a signed integer and an unsigned one (both of smaller length), but it would matter if you were bigendian or littleendian which was which.
The standards extract probably means it will work with COMPLEX, may work with INTEGER and definitely won't work with REAL!
Of course, what matters is whether it works with FTN95 and any other compiler that exploits Clearwin+, because when you add 40,000 lines* to a 400 line Fortran program you cease to care whether it will work with a compiler that doesn't 'do' CW!
Eddie
*Not to forget the 300 or more icons you drew ... 

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PaulLaidler Site Admin
Joined: 21 Feb 2005 Posts: 5416 Location: Salford, UK

Posted: Tue Feb 21, 2017 1:13 pm Post subject: 


There are various ways to avoid EQUIVALENCE in this program.
Here is one that defines a user operator for complex multiplication.
(A simple function call is a less frightening alternative to a user operator.)
For complex addition and subtraction one can just use the default + and  on the whole arrays.
Code:  module test
implicit none
real(kind = 2) a(2), b(2), c(2)
interface operator (.x.)
module procedure cmult
end interface
contains
function cmult(a,b)
real(kind = 2),intent(in)::a(2),b(2)
real cmult(2)
cmult(1) = a(1)*b(1)  a(2)*b(2)
cmult(2) = a(2)*b(1) + a(1)*b(2)
end function cmult
integer function init()
a = (/0.5d0,0.5d0/)
b = (/0.5d0,0.5d0/)
c = a.x.b
init = 1
end function init
integer function c_m()
c = a.x.b
c_m = 1
end function c_m
integer function window() 


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