20070308 圆周率 pi
http://www.yippeesoft.com

由搜狗广告文想到的 作一个好玩的网页，每来一个人点击一下就多计算一位，可是觉得会被服务提供商痛扁的，呵呵
主要是可能CPU占用会比较高，比较这玩意是拿来测试CPU速率的，
资料：
四行代码计算圆周率800位的怪异程序

求PI精确值的怪异程序
pi1.c(487bytes)/pi2.c(552bytes)

前者就是被称为「外星人程序」的求PI小程序..
四行求PI到小数点后八百位..真的不是人写得出来的..
后者写法也是相当奇怪..

—————————

/*某年Obfuscated C Contest佳作选录:*/

long a=10000,b,c=2800,d,e,f[2801],g;
main()&leftsign;for(;b-c;)f[b++]=a/5;
for(;d=0,g=c*2;c-=14,printf("%.4d",e+d/a),e=d%a)
for(b=c;d+=f*a,f=d%–g,d/=g–,–b;d*=b);&rightsign;

<SCRIPT>
var ct=100000,rs=0;
for(var i=1;i<=ct*2;i+=4)rs+=1/i-1/(i+2);
document.write(4*rs);
</SCRIPT>

<HTML>
<HEAD>
<META NAME="keywords" CONTENT="Pi, machin, javascipt, numerical methods, multiple precision, series">
<TITLE>PI in JavaScript</TITLE>
<SCRIPT LANGUAGE="JavaScript">
<!–
//
//  arctangent series for Pi a la mode by Bohr
//
var vectorsize = 53;          // number of elements in each of four arrays
var nCells = 52;              // number of array elements displayed

// constant
var BASE = 10000.0;           // The number base
var TENTHOUSANDTH = 0.0001;   // avoids floating point division
var SQ_239E4 = 571210000.0;   // = BASE x 239 squared
var SQ_5E4 = 250000.0;        // = BASE x 5 squared
var REPAIR = 0.000005;        // roundoff correction
var RECIPR_25 = 0.04;         // the reciprocal of 25 is 0.04
var RECIPR_239= 1.0 / 57121;  // reciprocal of 239 squared

// arrays
var term5 = null;             // = (1/5)^(2n+1), integer array
var term239 = null;           // = (1/239)^(2n+1), integer array
var sum = null;               // = 16term5-4term239, integer array
var series = null;            // = PI

// floating or integer
var TwoNplus1 = 1.0;          // 2n+1 = 1,3,5,7,…
var Basex2n_1 = BASE;         // = 10000*(2n+1)  
var Currdigit = 1;            // index of the series[] element being printed
var sgn = 1;                  // = (-1)^n; takes the values -1 and 1

// strings
var IntroString = " Pi = 3.";

function MakeArray(n) &leftsign;
  this.length = n;
  for (var i = 1; i <= n; i++) &leftsign;
      this[i] = 0;
  &rightsign;
  return this;
&rightsign;
function PiSetup() &leftsign;
  term5   = new MakeArray(vectorsize);
  term239 = new MakeArray(vectorsize);
  sum     = new MakeArray(vectorsize);
  series  = new MakeArray(vectorsize);

  term5[1] = 5;
  term239[1] = 239;
&rightsign;
function DivideTerms() &leftsign;
   var total5 = term5[1];
   var total239 = term239[1];

   // Divide the terms by 25 or 57121
   for (var i = Currdigit; i <= nCells + 2; i++) &leftsign;
       term5[i] = Math.floor( RECIPR_25 * total5 + REPAIR );
       total5 = BASE * total5 – SQ_5E4 * term5[i] + term5[i+1];
       term239[i] = Math.floor( total239 * RECIPR_239 + REPAIR );
       total239 = BASE * total239 – SQ_239E4 * term239[i] + term239[i+1];
   &rightsign;
&rightsign;
function SubtractTerms() &leftsign;
   var carry = 0;
   var total = 0;

   for (var i = nCells + 1; i > Currdigit; i–) &leftsign;
       total = 16.0 * term5[i] – 4.0 * term239[i] + carry + 60000.0;
       carry = Math.floor( total * TENTHOUSANDTH + REPAIR ) – 6.0;
       sum[i] = Math.floor( total – BASE * carry – 60000.0 );
   &rightsign;
&rightsign;
function DivideSum() &leftsign;
   var total = sum[1];
   var reciprocal = 1.0 / TwoNplus1;

   for( var i = Currdigit; i <= nCells + 2; i++) &leftsign;
       sum[i] = Math.floor( total * reciprocal + REPAIR );
       total = BASE * total – Basex2n_1 * sum[i] + sum[i+1];
   &rightsign;
&rightsign;
function AddShowDigits(nchars,lwidth) &leftsign;
   var i = 0;
   var total = 0;
   var carry = 0;
   var ccount = nchars / 4;
   var strg = "x";
   var old1 = series[Currdigit+1];
   var old2 = series[Currdigit+2];

   // Add the sum to the series
   for (i = nCells + 1; i >= Currdigit; i–) &leftsign;
       total = series[i] + sgn * sum[i] + carry + 30000.0;
       carry = Math.floor( total * TENTHOUSANDTH + REPAIR ) – 3.0;
       series[i] = Math.floor( total – BASE * carry – 30000.0 );
   &rightsign;

   // if stable, display digits
   if((old1==series[Currdigit+1]) && (old2==series[Currdigit+2])) &leftsign;
       Currdigit++;
       ccount++;
       if (ccount > lwidth / 4) &leftsign;
           document.write("<BR>")
           ccount = 1;
       &rightsign;
       strg = (BASE + series[Currdigit]) + " ";
       document.write(strg.substring(1,5))
   &rightsign;

   return (4 * ccount);
&rightsign;

function Crunch(fontname,fontsize) &leftsign;
   var linelength = IntroString.length;
   var time0 = new Date();
   var linewidth = 4 * Math.floor(50.0 / fontsize)

   window.status = ".. calculating "+(4 * nCells)+" digits, please wait .."
   document.write(\’<UL><FONT SIZE=\’ + fontsize + \’ FACE="\’ + fontname + \’">\’)
   document.write(IntroString)

   while (Currdigit < nCells) &leftsign;
       DivideTerms()
       SubtractTerms()
       DivideSum()
       linelength = AddShowDigits(linelength, linewidth)

       // Set up the next value of n
       TwoNplus1 += 2.0;  
       Basex2n_1 = BASE * TwoNplus1;
       sgn = 0 – sgn;
   &rightsign;

   var time1 = new Date();
   var elapsed = time1.getTime() – time0.getTime();
   document.write("</FONT>")
   document.write("<BR><BR><B>" + (4 * nCells) + " digits calculated in ")
   document.write((Math.floor(elapsed)/1000.0) + " seconds.</B>")
   document.write("</UL>")
&rightsign;

PiSetup()

// –>
</SCRIPT>
</HEAD>

<BODY TEXT="#000000" LINK="#0000EE" VLINK="#551A8B" ALINK="#FF0000" BACKGROUND="litepie3.jpg">
<br>

<CENTER>
<B><FONT SIZE=+1>Machin\’s Arctangent Series for Pi in JavaScript</FONT></B>
&nbsp;<A HREF="../mathindex.html">
<IMG SRC="p_btn3.jpg" BORDER="0" HSPACE=14 HEIGHT=40 WIDTH=110 ALIGN=ABSCENTER></A>
</CENTER>
<hr>

<SCRIPT LANGUAGE="JavaScript">
<!–
   Crunch("Courier New", 4)
// –>
</SCRIPT>

<hr>
<CENTER>Click "View: Page Source" to see the Javascript source code</CENTER>
<P><B>In 1706 John Machin</B> discovered the trigonometric identity</P>

<PRE>      PI = 16 arctan(1/5) – 4 arctan(1/239)</PRE>
       
and used it to calculate the first one hundred digits of Pi. &nbsp;&nbsp;He combined
his formula with the Taylor series expansion for the inverse tangent of
x. &nbsp;(Brook Taylor was Machin\’s contemporary in Cambridge.) &nbsp;&nbsp;The arctangent
series is

<PRE>                      3      5      7             n 2n+1
    arctan(x) = x – x /3 + x /5 – x /7 +…+ (-1) x    /(2n+1) +..</PRE>

Machin\’s formula remained the primary tool of Pi-hunters for centuries. &nbsp;&nbsp;As
late as 1973, Guilloud and Bouyer used a variation of it to compute one
million digits of Pi on a CDC 7600.

<P>This program uses arrays of multiple precision digits for the two series
terms, for their sum, and for the series. &nbsp;&nbsp;Each \’digit\’ is a modulo 10000
integer. &nbsp;&nbsp;The number base is 10,000.
</P>

<P>In the end, John Machin was never cured.
</P>

<HR SIZE=3 WIDTH="100%">
<B><FONT SIZE=-1>AUTHOR:</FONT></B>&nbsp;<TT> John Bohr  </TT>
<A HREF="mailto:jnbohr@netscape.net">email me</A>
<BR><TT>Last updated:  1 October 1998</TT>
<BR>
</BODY>
</HTML>

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八月 10, 2007 at 10:24 下午 by yippee 1,003 次
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