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計算圓周率_日期時間特效

計算圓周率,您可以先修改部分代碼再運行.

<HTML>
<HEAD>
<META NAME="keywords" CONTENT="Pi, machin, javascipt, numerical methods, multiple precision, series">
<TITLE>PI in JavaScript－模板無憂www.ghpqjb.com</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) {
 this.length = n;
 for (var i = 1; i <= n; i++) {
 this[i] = 0;
 }
 return this;
}
function PiSetup() {
 term5 = new MakeArray(vectorsize);
 term239 = new MakeArray(vectorsize);
 sum = new MakeArray(vectorsize);
 series = new MakeArray(vectorsize);

term5[1] = 5;
   term239[1] = 239;
}
function DivideTerms() {
    var total5 = term5[1];
    var total239 = term239[1];

// Divide the terms by 25 or 57121
 for (var i = Currdigit; i <= nCells + 2; i++) {
 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];
 }
}
function SubtractTerms() {
 var carry = 0;
 var total = 0;

for (var i = nCells + 1; i > Currdigit; i--) {
        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 );
    }
}
function DivideSum() {
    var total = sum[1];
    var reciprocal = 1.0 / TwoNplus1;

for( var i = Currdigit; i <= nCells + 2; i++) {
 sum[i] = Math.floor( total * reciprocal + REPAIR );
 total = BASE * total - Basex2n_1 * sum[i] + sum[i+1];
 }
}
function AddShowDigits(nchars,lwidth) {
 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--) {
        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 );
    }

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

return (4 * ccount);
}

function Crunch(fontname,fontsize) { 
    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>')
 document.write(IntroString)

while (Currdigit < nCells) {
 DivideTerms()
 SubtractTerms()
 DivideSum()
 linelength = AddShowDigits(linelength, linewidth)

// Set up the next value of n 
        TwoNplus1 += 2.0;  
        Basex2n_1 = BASE * TwoNplus1;
        sgn = 0 - sgn;
    }

var time1 = new Date();
 var elapsed = time1.getTime() - time0.getTime();
 document.write("")
 document.write(" " + (4 * nCells) + " digits calculated in ")
 document.write((Math.floor(elapsed)/1000.0) + " seconds.")
 document.write("</UL>")
}

PiSetup()

// -->
</SCRIPT>
</HEAD>

<CENTER>
Machin's Arctangent Series for Pi in JavaScript
 <A HREF="test/test.html">
<IMG SRC="http://p1.mb5u.com/texiao/17/20100523005042124.gif" BORDER="0" HSPACE=14 HEIGHT=40 WIDTH=110 ALIGN=ABSCENTER></A>
</CENTER>
<hr>

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

<PRE> PI = 16 arctan(1/5) - 4 arctan(1/239)</PRE>
 
and used it to calculate the first one hundred digits of Pi. He combined
his formula with the Taylor series expansion for the inverse tangent of 
x. (Brook Taylor was Machin's contemporary in Cambridge.) 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.   As 
late as 1973, Guilloud and Bouyer used a variation of it to compute one 
million digits of Pi on a CDC 7600.

This program uses arrays of multiple precision digits for the two series 
terms, for their sum, and for the series. Each 'digit' is a modulo 10000 
integer. The number base is 10,000.

In the end, John Machin was never cured.

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

所屬頻道：日期時間特效/更新時間：2012-05-08

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