]>
Hi David,
as far as I understood Kahan says that the complex arithmetic in
FORTRAN and many C++ libraries is wrong. I tested:
sqrt( (0.0 , -1.0)**2 ) vs. sqrt( (0.0 , 1.0)**2 )
on a DEC Alpha with FORTRAN and C++ (source and output below).
They both give the correct result. A naive approach abviously gives
the same result (0.0, 1.0) for both expressions. Can you tell us how you
implemented the correct behaviour in OCaml (or Nml)?
BTW what about sqrt( (-1.0 , -1.0)**2 ) and sqrt( (-1.0 , 1.0)**2 ), which
result in (1.0, 1.0) and (1.0, -1.0) on the DEC Alpha. What should the
results be in this case?
Rolf
// c++ on DEC Alpha
#include <complex>
#include <iostream>
main()
{
complex<double> a,b,c,d,e,f;
a = complex<double>(0.0,-1.0);
b = complex<double>(0.0, 1.0);
c = a*a;
d = b*b;
e = sqrt(c);
f = sqrt(d);
cout << a << " , " << b << endl;
cout << c << " , " << d << endl;
cout << e << " , " << f << endl;
}
Output:
(0,-1) , (0,1)
(-1,-0) , (-1,0)
(6.12323e-17,-1) , (6.12323e-17,1)
//f77 on DEC Alpha
complex*16 a,b,c,d,e,f
a = (0.0,-1.0)
b = (0.0, 1.0)
c = a**2
d = b**2
e = sqrt(c)
f = sqrt(d)
write(6,*) a,b
write(6,*) c,d
write(6,*) e,f
stop
end
Output:
(0.000000000000000E+000,-1.00000000000000)
(0.000000000000000E+000,1.00000000000000)
(-1.00000000000000,0.000000000000000E+000)
(-1.00000000000000,0.000000000000000E+000)
(0.000000000000000E+000,-1.00000000000000)
(0.000000000000000E+000,1.00000000000000)
-------------------------------------
Rolf Wester
wester@ilt.fhg.de
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