I have a π approximation program that I've been working on. It uses the Rananujen-Chudnovsky series(https://stackoverflow.com/a/531/2058221) to approximate π. I test the number generated by having 2 variants of π statically loaded in memory from different sources which I test against. The empirical version that I compute consistently fails to get the number correct past 29 digits for some reason. I've used the MathContext on just about everything I possibly can use it on. NOTE: broadcastSystemMessage() is essentially a System.out.println() but makes the formatting "nice", essentially think of the first argument as the title + : and the second as the body.
Algorithm Implementation:
/**
* The much faster Ramanujan-Chudnovsky algorithm.
*/
RAMANUJAN_CHUDNOVSKY {
private final long k1 = 545140134, k2 = 13591409, k3 = 640320,
k4 = 100100025, k5 = 327843840, k6 = 53360;
@Override
public String getAlgorithmName() {
return "Ramanujan-Chudnovsky";
}
@Override
public String getAlgorithmFormula() {
return "S=Σ from 0 to ∞(-1^n *(6n)! * (k2 + n * k1) / ((n!) ^ 3 * (3n)! * 8 * k4 * k5) ^ n)"
+ "π = k6 * sqrt(k3) / S";
}
@Override
public BigDecimal initCalculation(long iterations, long significantDigits) {
//God, if you're real, please forgive me for this; Java didn't give me a choice.
MathContext context = new MathContext((int) significantDigits);
BigDecimal s = new BigDecimal(0, context);
for (int n = 0; n < iterations; n++) {
s = s.add(new BigDecimal(Math.pow(-1, n), context).multiply(new BigDecimal(factorial(6 * n), context), context)
.multiply(new BigDecimal(BigInteger.valueOf(k2).add(BigInteger.valueOf(n).multiply(BigInteger.valueOf(k1))),
context), context).divide(new BigDecimal(factorial(n).pow(3), context).multiply(
new BigDecimal(factorial(new BigDecimal(3 * n, context).toBigInteger()), context), context)
.multiply(new BigDecimal(BigInteger.valueOf(8).multiply(BigInteger.valueOf(k4))
.multiply(BigInteger.valueOf(k5)), context), context).pow(n, context), context), context);
}
Main.brodcastSystemMessage("Check", k6 + " || + " + k3 + " || " + sqrt(new BigDecimal(k3, context), context));
return new BigDecimal(k6, context).multiply(sqrt(new BigDecimal(k3, context), context),
context).divide(s, context);
//Square Root of k3 approximation: 800.19997500624804755833750301086
}
}
π:
public static final BigDecimal π = new BigDecimal("3.14159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706798214808651328230664709384460955058223172535940812848111745028410270193852110555964462294895493038196442881097566593344612847564823378678316527120190914564856692346034861045432664821339360726024914127372458700660631558817488152092096282925409171536436789259036001133053054882046652138414695194151160943305727036575959195309218611738193261179310511854807446237996274956735188575272489122793818301194912983367336244065664308602139494639522473719070217986094370277053921717629317675238467481846766940513200056812714526356082778577134275778960917363717872146844090122495343014654958537105079227968925892354201995611212902196086403441815981362977477130996051870721134999999837297804995105973173281609631859502445945534690830264252230825334468503526193118817101000313783875288658753320838142061717766914730359825349042875546873115956286388235378759375195778185778053217122680661300192787661119590921642019893809525720106548586327886593615338182796823030195203530185296899577362259941389124972177528347913151557485724245415069595082953311686172785588907509838175463746493931925506040092770167113900984882401285836160356370766010471018194295559619894676783744944825537977472684710404753464620804668425906949129331367702898915210475216205696602405803815019351125338243003558764024749647326391419927260426992279678235478163600934172164121992458631503028618297455570674983850549458858692699569092721079750930295532116534498720275596023648066549911988183479775356636980742654252786255181841757467289097777279380008164706001614524919217321721477235014144197356854816136115735255213347574184946843852332390739414333454776241686251898356948556209921922218427255025425688767179049460165346680498862723279178608578438382796797668145410095388378636095068006422512520511739298489608412848862694560424196528502221066118630674427862203919494504712371378696095636437191728746776465757396241389086583264599581339");
Calling Method:
BigDecimal π = PIAlgorithms.RAMANUJAN_CHUDNOVSKY.initCalculation(10,
1000);
brodcastSystemMessage("π Calculation Result", π + "");
brodcastSystemMessage("", StringUtils.getCommonPrefix(π.toPlainString(), PIAlgorithms.π.toPlainString()).length() + "");
Misc. Functions Used in Algorithm:
/**
* Custom factorial function.
*
* @param integer The integer to use
* @return The factorial of the number
*/
private static BigInteger factorial(int integer) {
return factorial(BigInteger.valueOf(integer));
}
/**
* Custom factorial function.
*
* @param integer The integer to use
* @return The factorial of the number
*/
private static BigInteger factorial(@NotNull BigInteger integer) {
if (integer.equals(BigInteger.ZERO)) {
return BigInteger.ONE;
} else if (integer.compareTo(BigInteger.ZERO) < 0) {
throw new IllegalArgumentException("Can't take the factorial of a number less than zero");
}
BigInteger i = integer.equals(BigInteger.ONE) ? integer : integer.multiply(factorial(integer.subtract(BigInteger.ONE)));
System.out.println(integer + "! --> " + i);
return i;
}
private static BigDecimal sqrt(BigDecimal number, MathContext context) {
BigDecimal first = new BigDecimal("0", context);
BigDecimal second = new BigDecimal(Math.sqrt(number.doubleValue()), context);
while (!first.equals(second)) {
first = second;
second = number.divide(first, context);
second = second.add(first, context);
second = second.divide(new BigDecimal("2"), context);
}
return second;
}
Edit: First 5 Terms: 3.141592653589793238462643383587297242678 First 10 Terms: 3.141592653589793238462643383587297242678 First 15 Terms: 3.141592653589793238462643383587297242678 Comparison<π>: 3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628
