Solving Pi

[ken at boring.UUCP]

I decided to rewrite the posted program in "bc". (If you think having
only 286 distinct names in BASIC is bad, try using "bc"!) To get more
decimal places I had to use scaling, see program for details.
Fortunately, we know 1 < pi < 10 :-).

It took 2 hours to compute pi to a 1000 places on a 780 but it is
limited only by the amount of memory "dc" can get. And at last I have
something to soak up all those spare CPU cycles.

Anybody know a faster converging series for pi?

	Enjoy, Ken

#! /bin/sh
# This is a shell archive, meaning:
# 1. Remove everything above the #! /bin/sh line.
# 2. Save the resulting text in a file.
# 3. Execute the file with /bin/sh (not csh) to create the files:
#	pi.b
#	pi.sh
# This archive created: Fri Jul 26 15:37:57 1985
# By:	Ken Yap ()
export PATH; PATH=/bin:$PATH
if test -f 'pi.b'
then
	echo shar: will not over-write existing file "'pi.b'"
else
cat << \SHAR_EOF > 'pi.b'
/*
** NAME
**	pi -- a program to calculate the value of pi
**
** SYNOPSIS
**	bc pi.b
**
** DESCRIPTION
**	Pi calculates the value of pi to the number of digits
**	specified.
**
**	This is an adaptation in BC of the BASIC program "Apple Pi"
**	by Robert J. Bishop, published in Micro Apple (c) 1981
**	Micro Ink, Inc. That program, when run on an Apple II,
**	took 40 hours to solve pi to 1000 places. The
**	program solves pi using the series expansion:
**
**	      infinity                    infinity
**	      ____  16*(-1e(k+1))         ____  4*(-1e(k+1))
**	      \                           \
**	pi =   >    -------------    -     >    ------------
**	      /                           /
**	      ----  (2k-1)*5e(2k-1)       ----  (2k-1)*239e(2k-1)
**	      k = 1                       k = 1
**
** AUTHORS
**	Bryan Costales ( ...!dual!ptsfa!ski!eeg!bcx )
**	pi.c (c) 1985 Bryan Costales
**
**	Modified for bc by Ken Yap (..!seismo!{rochester,mcvax}!ken)
**	pi.b
**
** BUGS
**	
*/
 
scale = 99;
d/*en*/ = 1;

define i(p/*laces*/) {
	auto x;

	for (x = 0; x < p/*laces*/; x++) d/*en*/ *= 10;
	"Result will be pi times 10 to the power of ";
	return (p/*laces*/);
}

define p/*i*/(k) {
 
	k *= 2;
	s/*ign*/ = 1;
	x = 0;
	y = 0;
	m = 5;
	n = 239;
	for(e/*xp*/ = 1; e/*xp*/ < k; e/*xp*/ += 2) {
		f = d/*en*/ / (e/*xp*/ * m);
		g = d/*en*/ / (e/*xp*/ * n);
		if ( s/*ign*/ > 0 ) {
			x += f;
			y += g;
		}
		if ( s/*ign*/ < 0 ) {
			x -= f;
			y -= g;
		}
		m *= 25;
		n *= 57121;
		s/*ign*/ *= -1;
	}
	return(x * 16 - y * 4);
}
SHAR_EOF
if test 1529 -ne "`wc -c < 'pi.b'`"
then
	echo shar: error transmitting "'pi.b'" '(should have been 1529 characters)'
fi
fi # end of overwriting check
if test -f 'pi.sh'
then
	echo shar: will not over-write existing file "'pi.sh'"
else
cat << \SHAR_EOF > 'pi.sh'
#! /bin/sh
bc -c pi.b > pi.d << PROG
i(1000)
p(1000)
PROG
nice dc < pi.d > pi.1000 &
SHAR_EOF
if test 85 -ne "`wc -c < 'pi.sh'`"
then
	echo shar: error transmitting "'pi.sh'" '(should have been 85 characters)'
fi
chmod +x 'pi.sh'
fi # end of overwriting check
#	End of shell archive
exit 0
-- 
UUCP: ..!{seismo,okstate,garfield,decvax,philabs}!mcvax!ken Voice: Ken!
Mail: Centrum voor Wiskunde en Informatica, Kruislaan 413, 1098 SJ, Amsterdam.