wrong value for pi?

wrong value for pi?

[Julius Plenz]

Hi!

Playing around, I noticed that Z-Shell wrongly evaluates the
expression "4.0*atan(1)" (which is equal to pi):

    zsh> zmodload zsh/mathfunc
    zsh> typeset -F 48 pi='4.0*atan(1)'
    zsh> echo $pi
    3.141592653589793115997963468544185161590576171875
                     ^- here the first error occurs

Is this indended, a bug or just owing to some sort of optimization or some C
library's shortcomings?

Julius

Re: wrong value for pi?

[Peter Stephenson]

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Julius Plenz wrote:
> Hi!
> 
> Playing around, I noticed that Z-Shell wrongly evaluates the
> expression "4.0*atan(1)" (which is equal to pi):
> 
>     zsh> zmodload zsh/mathfunc
>     zsh> typeset -F 48 pi='4.0*atan(1)'
>     zsh> echo $pi
>     3.141592653589793115997963468544185161590576171875
>                      ^- here the first error occurs
> 
> Is this indended, a bug or just owing to some sort of optimization or some C
> library's shortcomings?

It's simply a question of what double precision actually gives on your
system, as it says in the manual (" Floating point arithmetic always
uses the ‘double’ type with whatever corresponding precision is
provided by the compiler and the library.").  Beyond that the digits
will certainly be gobbledygook.

-- 
Peter Stephenson <pws@csr.com>                  Software Engineer
CSR PLC, Churchill House, Cambridge Business Park, Cowley Road
Cambridge, CB4 0WZ, UK                          Tel: +44 (0)1223 692070

Re: wrong value for pi?

[Vincent Lefevre]

On 2008-07-30 14:13:21 +0100, Peter Stephenson wrote:
> It's simply a question of what double precision actually gives on your
> system, as it says in the manual (" Floating point arithmetic always
> uses the ???double??? type with whatever corresponding precision is
> provided by the compiler and the library.").  Beyond that the digits
> will certainly be gobbledygook.

In fact, the digits should be correct for the double precision number
(i.e. after rounding).

BTW, zsh could optionally use MPFR. :)

-- 
Vincent Lefèvre <vincent@vinc17.org> - Web: <http://www.vinc17.org/>
100% accessible validated (X)HTML - Blog: <http://www.vinc17.org/blog/>
Work: CR INRIA - computer arithmetic / Arenaire project (LIP, ENS-Lyon)