# Pi Day MMXVIII

Today it is the fourteenth of March 2018. Today’s date — when written in the M/D/Y format –, 3/14/18, looks close enough to Archimedes’ constant’s decimal representation for it to be the constant’s celebratory day.
As always on Pi Day, I have implemented an algorithm to generate $\pi$, albeit this year’s accuracy is not the greatest (Try it online).

                        typedef double d;typedef long l;l f(l n
){l f=1;while(n>1)f*=n--;return f;}d ne(d v,
l p){d r=1;for(l k=0;k<p;k++)r*=v;return r;}d
ps(d(*c)(l),l i,d x){d s=0;for(l k=0;k<i;k++)s
+=c(k)*       ne(x,        k);return
s;}           d exc         (     l
n){            return       1./f (n)
; } d         exp(d x
)   {         return
ps(exc        ,20,x);}
d G( d         x){return
exp(-x        *x);}d I
(d a,d         b,d g,d
(* f)(d         )){d cs=
0;for( d         x=a;x<=
b;x +=g)         cs+=f(x)
*g;return          cs ;  }          int
main( ) { d          pi_root         =I(
-2.5, 2.5 ,           1e-4,G);      d pi
= pi_root *            pi_root+(0xf&0xf0
) ; printf(             "%c%c%c%c%c%f%c"
,'p','i',                ' ','=',' ',pi
,'\n'                     ) ; }                           

I use various methods of generating $\pi$ throughout the Pi Days; this time I chose to use an improper integral paired with a power series. $\pi$ is calculated using a famous identity involving infinite continuous sums, roots, $e$, statistics and — of course — $\pi$.

$\int\limits_{-\infty}^\infty e^{-x^2}\mathrm{d}x = \sqrt{\pi}$

Furthermore, to compute $e$, the following identity is used.

$\exp{x} = \sum\limits_{n=0}^\infty\frac{x^n}{n!}$

Both formulae are combined, the approximated value of $\sqrt{\pi}$ is squared and $\pi$ is printed to stdout.

You can download this program’s prettified (some call it obfuscated, see above) source code pi.c and also the (nearly, as #include  is not missing so that the compiler does not need to guess my dependencies) equivalent code in a more traditional source layout tpi.c.

Happy Pi Day!

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