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Math.PI / 4 === Math.atan(1) // expected output: true
Math.PI / 2 === 2 * Math.atan(1 / Math.sqrt(2)) + Math.atan(1 / Math.sqrt(8)) // expected output: true
(4 * (4 * arccot(5) - arccot(239))).toPrecision(precision)
{
function* arccot(x) {
let i = 1,
x_squared = x * x,
dividend = 1 / x,
divisor = 1,
series = dividend;
for (let term; ; ) {
dividend = -dividend / x_squared;
divisor += 2;
if (
dividend === 0 ||
String(series) === String(series + (term = dividend / divisor))
) {
break;
}
let reset = yield {
iterations: i++,
term: term,
result: (series += term)
};
if (reset) {
(i = 1), (dividend = 1 / x), (divisor = 1), (series = dividend);
}
}
return i;
}
await visibility();
for (
let generator = pi(arccot, precision), series;
!(series && series.done);
series = generator.next()
) {
if (series && series.value) yield Promises.delay(duration, series.value);
}
}
function arccot(x) {
let x_squared = x * x,
dividend = 1 / x,
divisor = 1,
series = dividend;
for (let term; ; ) {
dividend = -dividend / x_squared;
divisor += 2;
if (
dividend === 0 ||
String(series) === String(series + (term = dividend / divisor))
) {
break;
}
series += term;
}
return series;
}
{
if (!Number.MAX_SAFE_INTEGER) {
Number.MAX_SAFE_INTEGER = Math.pow(2, 53) - 1;
}
await visibility();
GREGORY_LEIBNIZ_SERIES: for (
let series = 0, dividend = 1, divisor = 1;
divisor < Number.MAX_SAFE_INTEGER && (series += dividend / divisor);
dividend *= -1, divisor += 2
) {
yield Promises.delay(100, (4 * series).toPrecision(precision));
}
}
(4 * (4 * arccotEuler(5) - arccotEuler(239))).toPrecision(precision)
{
function* arccot(x) {
let i = 1,
coefficient = 0,
x_squared_plus_1 = x * x + 1,
series = x / x_squared_plus_1;
for (let term = series; ; ) {
term *= (coefficient += 2) / ((coefficient + 1) * x_squared_plus_1);
if (term === 0 || String(series) === String(series + term)) {
break;
}
let reset = yield {
iterations: i++,
term: term,
result: (series += term)
};
if (reset) {
(i = 1), (coefficient = 0), (term = series = x / x_squared_plus_1);
}
}
return i;
}
await visibility();
for (
let generator = pi(arccot, precision), series;
!(series && series.done);
series = generator.next()
) {
if (series && series.value) yield Promises.delay(duration, series.value);
}
}
function arccotEuler(x) {
let coefficient = 0,
x_squared_plus_1 = x * x + 1,
series = x / x_squared_plus_1;
for (let term = series; ; ) {
term *= (coefficient += 2) / ((coefficient + 1) * x_squared_plus_1);
if (term === 0 || String(series) === String(series + term)) {
break;
}
series += term;
}
return series;
}
/*!
* In 1706 John Machin came up with the first really fast method of
* calculating π and used it to calculate π to 100 decimal places:
*
* π/4 = 4 * arctan(1/5) - arctan(1/239)
*
* Quite an achievement considering he did that entirely with pencil
* and paper.
*/
function* pi(arccot, precision = 20) {
let n = 1,
a = arccot(5),
b = arccot(239),
expansionOf = {};
for (let series; ; ) {
series = { a: a.next(), b: b.next() };
if (!series.a.done) expansionOf.a = series.a.value;
if (!series.b.done) expansionOf.b = series.b.value;
if (series.a.done && series.b.done) {
break;
}
let reset = yield {
n: n++,
"arccot(5)": expansionOf.a,
"arccot(239)": expansionOf.b,
pi: (4 * (4 * expansionOf.a.result - expansionOf.b.result)).toPrecision(
precision
)
};
if (reset) {
(n = 1), (a = arccot(5)), (b = arccot(239)), (expansionOf = {});
}
}
return n;
}
precision = 20
Decimal = require("decimal.js-light@2.5.1/decimal.js")
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