[Numpy-discussion] what goes wrong with cos(), sin()

Anne Archibald peridot.faceted@gmail....
Wed Feb 21 12:27:16 CST 2007

On 21/02/07, WolfgangZillig <wollez@gmx.net> wrote:
> Hi,
> I'm quite new to numpy/scipy so please excuse if my problem is too obvious.
> example code:
> import numpy as n
> print n.sin(n.pi)
> print n.cos(n.pi/2.0)
> results in:
> 1.22460635382e-016
> 6.12303176911e-017
> I've expected something around 0. Can anybody explain what I am doing
> wrong here?

Well, nothing. It is around zero. Try (without numpy)
>>> (1.+1e-16)-1.
That is, for floating-point numbers, 1e-16 is about the fractional
error you can expect from any calculation, and since pi is of order
unity, you should expect its representation to have about that big an
error on it; feed that through sin and you get an error of about the
same size.

Or, to see more clearly, try taking (on a pocket calculator, say)
sin(3.14) (or even sin(pi)). Roundoff error is a basic fact of life in
numerical computations.


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