I have encountered a difference in the result of gsl_eigen_nonsymm as a 32- vs. 64-bit executable.  The program is attached.  What am I doing wrong?

GSL Version: 2.4
Hardware: AMD FX-8350 CPU, AUSTek Sabertooth 990FX R2.0
OS: Windows 10 Pro (64-bit)
Description:

For the 4x4 integer-valued double-precision matrix in the source file, the 32-bit executable displays results different from the 64-bit executable.  I think that the 64-bit results are correct, but they are both very close.

In particular, the results differ in the both real and imaginary parts of the resulting Eigenvalues.  For example, the 32-bit version returns the real parts of the four Eigenvalues as

0.9999999999999996
0.9999999999999996
1.0000000000000009
1.0000000000000009

whereas the 64-bit version returns the real parts as all exactly 1.  The differences between the 32- and 64-bit results for both real and imaginary parts are all in the low-order three bits of the hexadecimal form of the double-precision result.

See the comments in the attached source file for the hexadecimal displays of the real and imaginary parts.