Error calculating pi using the Chudnovsky algorithm - Java
algorithm, apfloat, java
Solution
The denominator for the Chudnovsky algorithm involves 640320^(3k + 3/2) - you only use 640320^(3k).
Problem
I have been trying to write a simple program to calculate pi using the Chudnovsky algorithm however I keep getting the wrong value output. The latest code i have written is below and outputs: 9.642715619298075837448823278218780086541162343253084414940204168864066834806498471622628399332216456e11 Can anyone tell me where I went wrong. As Peter de Rivaz pointed out I was discarding the value of b with that fixed the output is now: -1.767799793836391576547649814416358906088808474079217493588416202147617900180583600120191582474909093e-2 ``` Apfloat sum = new Apfloat(0); for(int k = 0; k < n; k++) { int thrk= 3*k; Apfloat a = ApintMath.factorial(6*k); //(6k)! * (-1)^k a = a.multiply(ApintMath.pow(new Apint(-1),k)); Apfloat b = new Apfloat(545140134); b = b.multiply(new Apfloat(k)); b = b.add(new Apfloat(13591409)); // 13591409 + 545140134k Apfloat c = ApintMath.factorial(thrk); // (3k!) Apfloat d = ApintMath.factorial(k); d = ApfloatMath.pow(d, 3); // (k!)^3 Apfloat e = new Apfloat(640320); e = ApfloatMath.pow(e,(thrk)); // (640320)^(3k) a = a.multiply(b); // a is know the numerator c = c.multiply(d).multiply(e); // c in know the denominator Apfloat div = a.divide(c.precision(digits)); sum = sum.add(div); } Apfloat f = new Apfloat(10005, digits);// Works out the constant sqrt part f = ApfloatMath.sqrt(f); f = f.divide(new Apfloat(42709344*100)); Apfloat pi = ApfloatMath.pow(sum.multiply(f), -1); System.out.println(pi); ```