Am Freitag, 9. November 2007 21:02 schrieb Hans van Thiel: > On Fri, 2007-11-09 at 14:30 -0500, Brent Yorgey wrote: > > On Nov 9, 2007 2:08 PM, Hans van Thiel <[EMAIL PROTECTED]> 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 > The exact results for 0, 0.5*pi and 2.5*pi aren't surprising. Leaving out the more than obvious case 0, we have two cases with sin x == 1. Now what's the smallest positive Double epsilon such that show (1+epsilon) /= show 1.0? I think, on my box it's 2^^(-52), which is roughly 2.22e-16, but the result calculated is closer to 1 than that, so the result is actually represented as 1.0, which by a lucky coincidence is the exact value. Regarding sin (1.0*pi) and sin (3.0*pi), I don't know how the sine is implemented,that they return nonzero values is expected, that actually sin (3.0*pi) == 3.0*sin pi does surprise me, too. Can anybody knowing more about the implementation of sine enlighten me?
Cheers, Daniel _______________________________________________ Haskell-Cafe mailing list [email protected] http://www.haskell.org/mailman/listinfo/haskell-cafe
