Re: [Maxima-discuss] significant difference?

[Barton W. <wi...@un...>]

Pretty good guess--the value from the book is correctly rounded to all shown decimal places.  Using purely binary64 numbers, Maxima's value is wrong in the last few digits.  Evidence:


(%i1851)    q(k):= (%e)^(-%pi * elliptic_kc(1-k^2)/elliptic_kc(k^2))$

(%i1852)    X : q(sin(%pi * 86/180))$

(%i1855)    float(block([fpprec :  15], bfloat(X)));
(%o1855)    0.2954883855586909

(%i1856)    float(block([fpprec :  45], bfloat(X)));
(%o1856)    0.2954883855586914

(%i1857)    float(block([fpprec :  85], bfloat(X)));
(%o1857)    0.2954883855586914


As the author of some numerical code, I know how difficult it is to balance speed and accuracy--in general it's fairly changeling to get the last few digits correct and to do the calculation in purely using hardware floats.


--Barton
________________________________
From: Peter van Summeren <pet...@gm...>
Sent: Monday, June 10, 2019 8:54:41 AM
To: max...@li...
Subject: [Maxima-discuss] significant difference?

Hello,
I am checking a book from Miroslav Lutovac for the nomen q(k)=e^(-pi * K'/K) of the elliptic functions.
He gives for k=sin(86degrees) a q of 0.2954883855586914 on page 512.
I did:
q(k):= (%e)^(-%pi * elliptic_kc(1-k^2)/elliptic_kc(k^2));
q(sin(%pi * 86/180)),numer;
And got: 0.2954883855586907
It is a very small difference - only in the last two digits, but is it significant for something wrong?
Can anyone check this result?
with friendly greetings,
Peter