mathjs
Version:
Math.js is an extensive math library for JavaScript and Node.js. It features a flexible expression parser and offers an integrated solution to work with numbers, big numbers, complex numbers, units, and matrices.
64 lines (48 loc) • 1.91 kB
HTML
<html>
<head>
<title>Pi Machin</title>
<script src="../node_modules/decimal.js/decimal.js"></script>
</head>
<body>
<script language="javascript">
Decimal.config({precision: 100});
// arctan(x) = x - x^3/3 + x^5/5 - x^7/7 + x^9/9 - ...
// = x - x^2*x^1/3 + x^2*x^3/5 - x^2*x^5/7 + x^2*x^7/9 - ...
function arctan(x) {
var y = x;
var yPrev = NaN;
var x2 = x.times(x);
var num = x;
var sign = -1;
for (var k = 3; !y.equals(yPrev); k += 2) {
num = num.times(x2);
yPrev = y;
y = (sign > 0) ? y.plus(num.div(k)) : y.minus(num.div(k));
sign = -sign;
}
return y;
}
function pi() {
// Machin: Pi / 4 = 4 * arctan(1 / 5) - arctan(1/239)
// http://milan.milanovic.org/math/english/pi/machin.html
// we calculate pi with a few decimal places extra to prevent round off issues
var DecimalPlus = Decimal.constructor({precision: Decimal.precision + 4});
var pi4th = new DecimalPlus(4).times(arctan(new DecimalPlus(1).div(5)))
.minus(arctan(new DecimalPlus(1).div(239)));
// the final pi has the requested number of decimals
return new Decimal(4).times(pi4th);
}
console.time('calculation');
var calculatedPi = pi();
console.timeEnd('calculation');
var mathematicaPi = '3.14159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706798214808651328230664...';
document.write('<code>Calculated: ' + calculatedPi + '</code><br>');
document.write('<code>Mathematica: ' + mathematicaPi + '</code>');
/*
var mathematicaPi = '3.14159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706798214808651328230664...';
document.write('<code>Calculated: ' + pi + '</code><br>');
document.write('<code>Mathematica: ' + mathematicaPi + '</code>');
*/
</script>
</body>
</html>