[Haskell-cafe] Sinus in Haskell
Hans van Thiel
hthiel.char at zonnet.nl
Fri Nov 9 15:02:05 EST 2007
On Fri, 2007-11-09 at 14:30 -0500, Brent Yorgey wrote:
>
> On Nov 9, 2007 2:08 PM, Hans van Thiel <hthiel.char at zonnet.nl> 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
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