<HTML>
<HEAD>
<META NAME="keywords" CONTENT="Pi, machin, javascipt, numerical methods, multiple precision, series">
<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("<BR>")
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><FONT SIZE=' + fontsize + ' FACE="' + fontname + '">')
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("</FONT>")
document.write("<BR><BR><B>" + (4 * nCells) + " digits calculated in ")
document.write((Math.floor(elapsed)/1000.0) + " seconds.</B>")
document.write("</UL>")
}PiSetup()// -->
</SCRIPT>
</HEAD><BOD>
<br><CENTER>
<B><FONT SIZE=+1>Machin's Arctangent Series for Pi in JavaScript</FONT></B>
</CENTER>
<hr><SCRIPT LANGUAGE="JavaScript">
<!--
Crunch("Courier New", 4)
// -->
</SCRIPT></BODY>
</HTML>
<HEAD>
<META NAME="keywords" CONTENT="Pi, machin, javascipt, numerical methods, multiple precision, series">
<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("<BR>")
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><FONT SIZE=' + fontsize + ' FACE="' + fontname + '">')
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("</FONT>")
document.write("<BR><BR><B>" + (4 * nCells) + " digits calculated in ")
document.write((Math.floor(elapsed)/1000.0) + " seconds.</B>")
document.write("</UL>")
}PiSetup()// -->
</SCRIPT>
</HEAD><BOD>
<br><CENTER>
<B><FONT SIZE=+1>Machin's Arctangent Series for Pi in JavaScript</FONT></B>
</CENTER>
<hr><SCRIPT LANGUAGE="JavaScript">
<!--
Crunch("Courier New", 4)
// -->
</SCRIPT></BODY>
</HTML>
js浮点很弱的,能计算出来都不准确
--------------------------------------------------------------------------------
Pi = 3.1415926535897932384626433832795028841971
693993751058209749445923078164062862089986280348
253421170679821480865132823066470938446095505822
317253594081284811174502841027019385211055596446
22948954930381964428208 digits calculated in 0.188 seconds.
好像是这么回事。