[Numpy-discussion] what goes wrong with cos(), sin()
Wed Feb 21 14:40:58 CST 2007
I grew up a TI guy - my recollection is that they stated in the user
manual that though the display could show "only" 10 decimal digits,
memory saved and computations used 16; perhaps nowadays it is even more,
but unless you're doing millions of sequential calculations (how often
do you do that on a handheld scientific calculator?) you shouldn't be
seeing cumulative error problems, right?
Christopher Barker wrote:
> 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.
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