[Numpy-discussion] Re: numpy.sin

[Robert K. <rob...@gm...>]

Alan G Isaac wrote:
> On Thu, 25 May 2006, Robert Kern apparently wrote: 
> 
>>The method you showed of using % (2*pi) is only accurate 
>>when the values are created by multiplying the same pi by 
>>another value. Otherwise, it just introduces another 
>>source of error, I think.
> 
> Just to be clear, I meant not (!) to presumptuosly propose 
> a method for improving thigs, but just to illustrate the 
> issue: both the loss of accuracy, and the obvious conceptual 
> point that there is (in an abstract sense, at least) no need 
> for sin(x) and sin(x+ 2*pi) to differ.

But numpy doesn't deal with abstract senses. It deals with concrete floating
point arithmetic. The best value you can *use* for pi in that expression is not
the real irrational π. And the best floating-point algorithm you can use for
sin() won't (and shouldn't!) assume that sin(x) will equal sin(x + 2*pi).

That your demonstration results in the desired exact 0.0 for multiples of 2*pi
is an accident. The results for values other than integer multiples of pi will
be as wrong or more wrong. It does not demonstrate that floating-point sin(x)
and sin(x + 2*pi) need not differ.

-- 
Robert Kern

"I have come to believe that the whole world is an enigma, a harmless enigma
 that is made terrible by our own mad attempt to interpret it as though it had
 an underlying truth."
  -- Umberto Eco