[Haskell-cafe] Re: Sinus in Haskell

Hans van Thiel writes:

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>

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?

but sin theta ~ theta for small theta, and the angle you're getting the (approximate) sine of is the difference between 2*pi and 2π. So I'm not too surprised that we have -2*sin pi = sin (2*pi) -- Jón Fairbairn Jon.Fairbairn@cl.cam.ac.uk