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

[Christopher Barker]

Robert Kern wrote:
> Christopher Barker wrote:
>> I wonder if there are any C math libs that do a better job than you'd 
>> expect from standard FP? (short of unlimited precision ones)
> 
> With respect to π and the zeros of sin() and cos()? Not really. If
> numpy.sin(numpy.pi) were to give you 0.0, it would be *wrong*. numpy.sin() is
> supposed to give you the most accurate result representable in double-precision
> for the input you gave it.

But does it?

> numpy.pi is not π.

More precisely, it's the best IEEE754 64 bit FP approximation of pi.

Right. I think that was the trick that HP used -- they somehow stored 
and worked with pi with more digits. The things you can do if you're 
making dedicated hardware.

I do wonder if there would be some way to use the extended precision 
built in to Intel FP hardware -- i.e. have a pi that you can pass in 
that has the full 80 bits that can be used internally. I don't know if 
the trig functions can be done with extended precision though.

-Chris


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