Very interesting test! I could not understand at first why multiplying with an
even integer factor would introduce rounding errors. So it seemed, but when I went one step back and ignored the multiplication I saw: the value itself is not expressible as a fixedpoint binary number.
So there are two ways to look at it (numerically and as a string):
$ perl -wE '$x=35784.45; printf "%.15f\n%s", $x, $x;'
35784.449999999997090
35784.45
Since now I always assumed the string representation were made from the numerical representation thus giving the same output. That was obviously wrong.
Update:
A second counter test
$ perl -wE '$x=35784.449999999997090; printf "%.15f\n%s", $x, $x;'
35784.449999999997090
35784.45
reveals: the string representation always uses some rounding.
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