Re: [Haskell-cafe] Sinus in Haskell

9 Nov 2007


      On Fri, 2007-11-09 at 14:30 -0500, Brent Yorgey wrote:
...
On Nov 9, 2007 2:08 PM, Hans van Thiel  wrote:
        Hello All,
        Can anybody explain the results for 1.0, 2.0 and 3.0 times pi
        below?
        GHCi yields the same results. I did search the Haskell report
        and my
        text books, but to no avail. Thanks in advance,
        Hans van Thiel
Hugs> sin (0.0 * pi)
        0.0
        Hugs> sin (0.5 * pi)
        1.0
        Hugs> sin (1.0 * pi)
        1.22460635382238e-16
        Hugs> sin (1.5 * pi)
        -1.0
        Hugs> sin (2.0 * pi)
        -2.44921270764475e-16
        Hugs> sin ( 2.5 * pi)
        1.0
        Hugs> sin (3.0 * pi)
        3.67381906146713e-16
        Hugs>
More generally, this is due to the fact that floating-point numbers
can only have finite precision, so a little bit of rounding error is
inevitable when dealing with irrational numbers like pi.   This
problem is in no way specific to Haskell.
-Brent
All right, I'd have guessed that myself, if it hadn't been for the exact
computation results for 0, 0.5, 1.5 and 2.5 times pi. So the rounding
errors are only manifest for 1.0, 2.0 and 3.0 times pi. But look at the
difference between sin (1.0 * pi) and sin (3.0 * pi). That's not a
rounding error, but a factor 3 difference.. and sin (as well as cos) are
modulo (2 * pi), right? 

Regards,
Hans