Thanks for the response. I read through the Inferno and there's a lot of
useful stuff in there. However I think you may have missed something.

Having some experience with other languages, I know that floating point
numbers aren't represented exactly, the issue is that R is off by much more
than would be expected. On my computer, cell 9,2 of (mat * 100) %% 1 is
larger than .99 and the correct result is 0. That difference seems too large
to be a problem with representing floating point numbers.

Likewise, identical( (4.1 * 100 ) %/% 1 , 409 ) returns TRUE on my computer,
so the result is off by exactly 1, too larger to be explained by floating
point error.

I think there's a problem with how the %% and %/% operators are getting
their results.
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