On: Lies my calculator and computer told me (1987) [pd...

[jepler]

a neat calculator is spigot. It has no trouble getting exactly 0 for this calculation:

    $ spigot '(2/3)*3-2'
    0

furthermore, when you specify a precision number, this sets the precision of the final result, NOT the precision of intermediaries (which is what bc & dc, and many other arbitrary precision calculators do); every printed digit is correctly rounded. [edited to add: truncated towards zero by default; other rounding modes available as commandline flag]

    $ spigot -d72 'sin(1)-cos(1)'
    0.301168678939756789251565714187322395890252640180448838002654454610810009

There are still conditions where spigot can't give an answer, such as

    $ spigot 'sin(asin(0.12345))'

.. spigot can never determine the next correctly rounded digit after "0.1234" with certainty, for reasons elucidated in the documentation.

spigot is in debian and here's the author's page with links to a lot more background: https://www.chiark.greenend.org.uk/~sgtatham/spigot/

[zozbot234 → jepler]

> spigot can never determine the next correctly rounded digit after "0.1234" with certainty, for reasons elucidated in the documentation.

Because spigot rounds towards zero in that mode, and it can only bound the result as arbitrarily close to 0.12345 - i.e., it can never decide between 0.12344999..99something and 0.12345000..00something because the "something" part that might break the tie never appears. This is a general issue with exact real computation; in more complicated cases, it can even be undecidable whether some expression is exactly zero.