Program to Find N-digits of PiDate: 9/11/96 at 11:4:15 From: Anonymous Subject: Program to Find N-digits of Pi Do you know where I can find C code for doing N-digit decimal arithmetic in C? I want to encode Euler's iterative formula for approximating pi, n=1 sum(1/n^2) -> (pi^2)/6 as n -> inf But if I use unsigned longs, the max n is 65536 because 65536^2 == 2^32. 65536 terms gives you a pretty fair approximation (6 digits worth, or so), but it gets that in about a decisecond on my pentium- 120; I want an iterative algorithm I can run for DAYS. So obviously I'll need to store my numbers in strings, limited only by my RAM. I've written N-digit arithmetic, (just finished division last night, that was tough!) but it only uses whole numbers (division will generate a real, but currently can't use reals for the divisor or dividend (yet). I tried it, but since I'm storing the numbers from LSB to MSB in the string, I ended up just making a big mess. If there's code out there that already does this, I'd love to get my hands on it. Gack Date: 9/12/96 at 0:39:3 From: Doctor Pete Subject: Re: Program to Find N-digits of Pi I know this isn't quite what you're asking for, but there are series expressions that converge to pi *much* faster than the one you gave. Similar to yours, the formula Sum[1/n^4,{n,1,Infinity}] = Pi^4/90 is also true, and is slightly faster. Incidentally, there is an infinite family of such series; i.e., Sum[1/n^(2k),{n,1,Infinity}] = Pi^(2k)*P/Q, for positive integers P, Q, which derives from the properties of the Riemann zeta function. Even faster are series based on arctangent formulae, such as 4*Sum[(-1)^n/((2n+1)*5^(2n+1)),{n,0,Infinity}] -Sum[(-1)^n/((2n+1)*239^(2n+1)),{n,0,Infinity}] = Pi/4. Incredibly fast are some series by Ramanujan; i.e., (Sqrt[8]/9801)*Sum[(4n)!*(1103+26390n)/((n!)^4*396^(4n)), {n,0,Infinity}] = 1/Pi . Regarding your question, there do exist arbitrary precision libraries, I believe, on the net. Try a web search. If you want to know more about the series expressions I mentioned here, as well as additional formulae, visit the following site: http://pauillac.inria.fr/algo/bsolve/constant/pi/pi.html -Doctor Pete, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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